q = 7: |PGL(2,q)| = 336, c_q (brute force) = 16 (formula 16), M = 4704  [0s]
subgroup classes of PGL(2,7): 23  [0s]
  |Hbar| =   336 |H cap Z| =   2 |X| =     32928: affine point: |stab| 672, |induced| 336, good False; point (1, 0) of m (orbit 8): |stab| 4116, |induced| 42, good False; line m: |stab| 32928, |induced| 336, good False; affine line, direction (1, 0): |stab| 588, |induced| 42, good False
  |Hbar| =   336 |H cap Z| =   6 |X| =     98784: affine point: |stab| 2016, |induced| 336, good False; point (1, 0) of m (orbit 8): |stab| 12348, |induced| 42, good False; line m: |stab| 98784, |induced| 336, good False; affine line, direction (1, 0): |stab| 1764, |induced| 42, good False
  |Hbar| =   168 |H cap Z| =   2 |X| =     16464: affine point: |stab| 336, |induced| 168, good False; point (1, 0) of m (orbit 8): |stab| 2058, |induced| 42, good False; line m: |stab| 16464, |induced| 168, good False; affine line, direction (1, 0): |stab| 294, |induced| 42, good False
  |Hbar| =   168 |H cap Z| =   6 |X| =     49392: affine point: |stab| 1008, |induced| 168, good False; point (1, 0) of m (orbit 8): |stab| 6174, |induced| 42, good False; line m: |stab| 49392, |induced| 168, good False; affine line, direction (1, 0): |stab| 882, |induced| 42, good False
  |Hbar| =    42 |H cap Z| =   3 |X| =      6174: affine point: |stab| 126, |induced| 42, good False; point (1, 0) of m (orbit 1): |stab| 6174, |induced| 42, good False; point (1, 1) of m (orbit 7): |stab| 882, |induced| 21, good False; line m: |stab| 6174, |induced| 42, good False; affine line, direction (1, 0): |stab| 882, |induced| 21, good False; affine line, direction (1, 1): |stab| 126, |induced| 42, good False
  |Hbar| =    42 |H cap Z| =   3 |X| =      6174: affine point: |stab| 126, |induced| 42, good False; point (1, 0) of m (orbit 1): |stab| 6174, |induced| 21, good False; point (1, 1) of m (orbit 7): |stab| 882, |induced| 42, good False; line m: |stab| 6174, |induced| 42, good False; affine line, direction (1, 0): |stab| 882, |induced| 42, good False; affine line, direction (1, 1): |stab| 126, |induced| 21, good False
  |Hbar| =    42 |H cap Z| =   6 |X| =     12348: affine point: |stab| 252, |induced| 42, good False; point (1, 0) of m (orbit 1): |stab| 12348, |induced| 42, good False; point (1, 1) of m (orbit 7): |stab| 1764, |induced| 42, good False; line m: |stab| 12348, |induced| 42, good False; affine line, direction (1, 0): |stab| 1764, |induced| 42, good False; affine line, direction (1, 1): |stab| 252, |induced| 42, good False
  |Hbar| =    24 |H cap Z| =   6 |X| =      7056: affine point: |stab| 144, |induced| 24, good False; point (1, 0) of m (orbit 8): |stab| 882, |induced| 42, good False; line m: |stab| 7056, |induced| 24, good False; affine line, direction (1, 0): |stab| 126, |induced| 42, good False
  |Hbar| =    21 |H cap Z| =   6 |X| =      6174: affine point: |stab| 126, |induced| 21, good False; point (1, 0) of m (orbit 1): |stab| 6174, |induced| 42, good False; point (1, 1) of m (orbit 7): |stab| 882, |induced| 42, good False; line m: |stab| 6174, |induced| 21, good False; affine line, direction (1, 0): |stab| 882, |induced| 42, good False; affine line, direction (1, 1): |stab| 126, |induced| 42, good False
RESULT q = 7: 9 subgroups H (|X| = q^2|H| > M = 4704) tested; good ones: none  [2s]
