PSL(3,4): |P|=20160 |Q|=960 k=21 |T|=60 |phi(Q)|=60; Q-orbits on T minus 1: 4; |Q_t| = [48, 64, 80, 80]; M = 80; |P|/M = 252
  Q_t of order 80: 68 subgroups R with |R| > M/k = 3.81
  Q_t of order 80: 68 subgroups R with |R| > M/k = 3.81
  Q_t of order 64: 225 subgroups R with |R| > M/k = 3.81
  Q_t of order 48: 72 subgroups R with |R| > M/k = 3.81
  total distinct R: 280  (time 0.4s)
  R #8 |R|=32: 4 subgroups S of order > M with S cap Q = R, max order 160
  R #11 |R|=32: 4 subgroups S of order > M with S cap Q = R, max order 160
  R #15 |R|=32: 4 subgroups S of order > M with S cap Q = R, max order 160
  ... 50/280 R done, best so far 160, t=3s
  ... 100/280 R done, best so far 160, t=4s
  R #107 |R|=8: 4 subgroups S of order > M with S cap Q = R, max order 160
  R #108 |R|=8: 4 subgroups S of order > M with S cap Q = R, max order 160
  R #109 |R|=8: 4 subgroups S of order > M with S cap Q = R, max order 160
  R #110 |R|=8: 4 subgroups S of order > M with S cap Q = R, max order 160
  R #115 |R|=8: 4 subgroups S of order > M with S cap Q = R, max order 160
  R #116 |R|=8: 4 subgroups S of order > M with S cap Q = R, max order 160
  R #131 |R|=8: 4 subgroups S of order > M with S cap Q = R, max order 160
  R #134 |R|=8: 4 subgroups S of order > M with S cap Q = R, max order 160
  R #135 |R|=8: 4 subgroups S of order > M with S cap Q = R, max order 160
  R #146 |R|=8: 4 subgroups S of order > M with S cap Q = R, max order 160
  ... 150/280 R done, best so far 160, t=5s
  R #150 |R|=8: 4 subgroups S of order > M with S cap Q = R, max order 160
  R #151 |R|=8: 4 subgroups S of order > M with S cap Q = R, max order 160
  ... 200/280 R done, best so far 160, t=7s
  ... 250/280 R done, best so far 160, t=9s
RESULT PSL(3,4): M = 80, M_G = 160, |P|/M = 252, |P|/M_G = 126, strict = True  (time 10.0s)
  witness: |S| = 160, |S cap Q| = 32, orbit of base point = [0, 2, 9, 13, 17]
  generators: [(0, 1, 17, 20, 18, 19, 6, 7, 8, 13, 15, 16, 14, 9, 12, 10, 11, 2, 4, 5, 3), (0, 3, 2, 1, 5, 4, 10, 15, 20, 9, 6, 19, 16, 13, 18, 7, 12, 17, 14, 11, 8), (0, 4, 2, 5, 1, 3, 18, 11, 16, 9, 14, 7, 20, 13, 10, 19, 8, 17, 6, 15, 12), (2, 1, 0, 7, 8, 6, 5, 3, 4, 17, 19, 20, 18, 13, 14, 15, 16, 9, 12, 10, 11)]
