L2_7, coset d^1 f^0 (r=2), p=7: 179 subgroups
  |X|=7    7-group      centralized by some beta in c: False |O_p(N_S(X))|=7    |N_S(X)/F*|=3   beta in c normalizing X: 21, acting trivially on N/F*: 21
  |X|=3    3-group      centralized by some beta in c: True  |O_p(N_S(X))|=1    |N_S(X)/F*|=2   beta in c normalizing X: 6, acting trivially on N/F*: 6
  |X|=2    2-group      centralized by some beta in c: True  |O_p(N_S(X))|=1    |N_S(X)/F*|=1   beta in c normalizing X: 8, acting trivially on N/F*: 8
  |X|=4    2-group      centralized by some beta in c: True  |O_p(N_S(X))|=1    |N_S(X)/F*|=1   beta in c normalizing X: 8, acting trivially on N/F*: 8
  |X|=8    2-group      centralized by some beta in c: False |O_p(N_S(X))|=1    |N_S(X)/F*|=1   beta in c normalizing X: 8, acting trivially on N/F*: 8
  |X|=6    not p-group  centralized by some beta in c: True  |O_p(N_S(X))|=1    |N_S(X)/F*|=2   beta in c normalizing X: 6, acting trivially on N/F*: 6
  |X|=21   not p-group  centralized by some beta in c: False |O_p(N_S(X))|=7    |N_S(X)/F*|=3   beta in c normalizing X: 21, acting trivially on N/F*: 21
L2_9, coset d^1 f^0 (r=2), p=3: 501 subgroups
  |X|=5    5-group      centralized by some beta in c: True  |O_p(N_S(X))|=1    |N_S(X)/F*|=2   beta in c normalizing X: 10, acting trivially on N/F*: 10
  |X|=2    2-group      centralized by some beta in c: True  |O_p(N_S(X))|=1    |N_S(X)/F*|=1   beta in c normalizing X: 8, acting trivially on N/F*: 8
  |X|=4    2-group      centralized by some beta in c: True  |O_p(N_S(X))|=1    |N_S(X)/F*|=1   beta in c normalizing X: 8, acting trivially on N/F*: 8
  |X|=8    2-group      centralized by some beta in c: False |O_p(N_S(X))|=1    |N_S(X)/F*|=1   beta in c normalizing X: 8, acting trivially on N/F*: 8
  |X|=9    3-group      centralized by some beta in c: False |O_p(N_S(X))|=9    |N_S(X)/F*|=4   beta in c normalizing X: 36, acting trivially on N/F*: 36
  |X|=18   not p-group  centralized by some beta in c: False |O_p(N_S(X))|=9    |N_S(X)/F*|=4   beta in c normalizing X: 36, acting trivially on N/F*: 36
  |X|=36   not p-group  centralized by some beta in c: False |O_p(N_S(X))|=9    |N_S(X)/F*|=4   beta in c normalizing X: 36, acting trivially on N/F*: 36
  |X|=10   not p-group  centralized by some beta in c: True  |O_p(N_S(X))|=1    |N_S(X)/F*|=2   beta in c normalizing X: 10, acting trivially on N/F*: 10
L2_17, coset d^1 f^0 (r=2), p=17: 2420 subgroups
  |X|=2    2-group      centralized by some beta in c: True  |O_p(N_S(X))|=1    |N_S(X)/F*|=1   beta in c normalizing X: 16, acting trivially on N/F*: 16
  |X|=3    3-group      centralized by some beta in c: True  |O_p(N_S(X))|=1    |N_S(X)/F*|=2   beta in c normalizing X: 18, acting trivially on N/F*: 18
  |X|=17   17-group     centralized by some beta in c: False |O_p(N_S(X))|=17   |N_S(X)/F*|=8   beta in c normalizing X: 136, acting trivially on N/F*: 136
  |X|=34   not p-group  centralized by some beta in c: False |O_p(N_S(X))|=17   |N_S(X)/F*|=8   beta in c normalizing X: 136, acting trivially on N/F*: 136
  |X|=68   not p-group  centralized by some beta in c: False |O_p(N_S(X))|=17   |N_S(X)/F*|=8   beta in c normalizing X: 136, acting trivially on N/F*: 136
  |X|=136  not p-group  centralized by some beta in c: False |O_p(N_S(X))|=17   |N_S(X)/F*|=8   beta in c normalizing X: 136, acting trivially on N/F*: 136
  |X|=6    not p-group  centralized by some beta in c: True  |O_p(N_S(X))|=1    |N_S(X)/F*|=2   beta in c normalizing X: 6, acting trivially on N/F*: 6
  |X|=9    3-group      centralized by some beta in c: True  |O_p(N_S(X))|=1    |N_S(X)/F*|=2   beta in c normalizing X: 18, acting trivially on N/F*: 18
  |X|=18   not p-group  centralized by some beta in c: True  |O_p(N_S(X))|=1    |N_S(X)/F*|=2   beta in c normalizing X: 18, acting trivially on N/F*: 18
  |X|=4    2-group      centralized by some beta in c: True  |O_p(N_S(X))|=1    |N_S(X)/F*|=1   beta in c normalizing X: 16, acting trivially on N/F*: 16
  |X|=8    2-group      centralized by some beta in c: True  |O_p(N_S(X))|=1    |N_S(X)/F*|=1   beta in c normalizing X: 16, acting trivially on N/F*: 16
  |X|=16   2-group      centralized by some beta in c: False |O_p(N_S(X))|=1    |N_S(X)/F*|=1   beta in c normalizing X: 16, acting trivially on N/F*: 16
L2_25, coset d^1 f^0 (r=2), p=5: 9559 subgroups
  |X|=13   13-group     centralized by some beta in c: True  |O_p(N_S(X))|=1    |N_S(X)/F*|=2   beta in c normalizing X: 26, acting trivially on N/F*: 26
  |X|=2    2-group      centralized by some beta in c: True  |O_p(N_S(X))|=1    |N_S(X)/F*|=2   beta in c normalizing X: 24, acting trivially on N/F*: 24
  |X|=3    3-group      centralized by some beta in c: True  |O_p(N_S(X))|=1    |N_S(X)/F*|=2   beta in c normalizing X: 24, acting trivially on N/F*: 24
  |X|=25   5-group      centralized by some beta in c: False |O_p(N_S(X))|=25   |N_S(X)/F*|=12  beta in c normalizing X: 300, acting trivially on N/F*: 300
  |X|=75   not p-group  centralized by some beta in c: False |O_p(N_S(X))|=25   |N_S(X)/F*|=12  beta in c normalizing X: 300, acting trivially on N/F*: 300
  |X|=50   not p-group  centralized by some beta in c: False |O_p(N_S(X))|=25   |N_S(X)/F*|=12  beta in c normalizing X: 300, acting trivially on N/F*: 300
  |X|=100  not p-group  centralized by some beta in c: False |O_p(N_S(X))|=25   |N_S(X)/F*|=12  beta in c normalizing X: 300, acting trivially on N/F*: 300
  |X|=150  not p-group  centralized by some beta in c: False |O_p(N_S(X))|=25   |N_S(X)/F*|=12  beta in c normalizing X: 300, acting trivially on N/F*: 300
  |X|=300  not p-group  centralized by some beta in c: False |O_p(N_S(X))|=25   |N_S(X)/F*|=12  beta in c normalizing X: 300, acting trivially on N/F*: 300
  |X|=6    not p-group  centralized by some beta in c: True  |O_p(N_S(X))|=1    |N_S(X)/F*|=2   beta in c normalizing X: 24, acting trivially on N/F*: 24
  |X|=24   not p-group  centralized by some beta in c: False |O_p(N_S(X))|=1    |N_S(X)/F*|=2   beta in c normalizing X: 24, acting trivially on N/F*: 24
  |X|=12   not p-group  centralized by some beta in c: True  |O_p(N_S(X))|=1    |N_S(X)/F*|=2   beta in c normalizing X: 24, acting trivially on N/F*: 24
  |X|=4    2-group      centralized by some beta in c: True  |O_p(N_S(X))|=1    |N_S(X)/F*|=2   beta in c normalizing X: 24, acting trivially on N/F*: 24
  |X|=8    2-group      centralized by some beta in c: False |O_p(N_S(X))|=1    |N_S(X)/F*|=1   beta in c normalizing X: 8, acting trivially on N/F*: 8
  |X|=26   not p-group  centralized by some beta in c: True  |O_p(N_S(X))|=1    |N_S(X)/F*|=2   beta in c normalizing X: 26, acting trivially on N/F*: 26
