q = 8: n = 73 points, |P_y| = |P_l| = 225792, |phi(Q)| = 504, |T| = 504, M = 4032  [105s]
point stabiliser P_y: Levi GL(2,8) of order 3528: 33 classes of subgroups (1042 subgroups); classes H with |H| |E| > M = 4032: 5  [109s]
   |H| =  3528  |S| = |E||H| = 225792  invariant N with |N||H| > M: [64] (only E)  good = False  orbits (length, |S_d|, |image|, fixes t != 1): [(1, 225792, 504, False), (72, 3136, 56, False)]
   |H| =   504  |S| = |E||H| =  32256  invariant N with |N||H| > M: [64] (only E)  good = False  orbits (length, |S_d|, |image|, fixes t != 1): [(1, 32256, 504, False), (72, 448, 56, False)]
   |H| =   392  |S| = |E||H| =  25088  invariant N with |N||H| > M: [64] (only E)  good = False  orbits (length, |S_d|, |image|, fixes t != 1): [(1, 25088, 56, False), (8, 3136, 56, False), (64, 392, 56, False)]
   |H| =   126  |S| = |E||H| =   8064  invariant N with |N||H| > M: [64] (only E)  good = False  orbits (length, |S_d|, |image|, fixes t != 1): [(1, 8064, 18, False), (72, 112, 56, False)]
   |H| =    98  |S| = |E||H| =   6272  invariant N with |N||H| > M: [64] (only E)  good = False  orbits (length, |S_d|, |image|, fixes t != 1): [(1, 6272, 14, False), (16, 392, 56, False), (56, 112, 56, False)]
line stabiliser P_l: Levi GL(2,8) of order 3528: 33 classes of subgroups (1042 subgroups); classes H with |H| |E| > M = 4032: 5  [310s]
   |H| =  3528  |S| = |E||H| = 225792  invariant N with |N||H| > M: [64] (only E)  good = False  orbits (length, |S_d|, |image|, fixes t != 1): [(9, 25088, 56, False), (64, 3528, 504, False)]
   |H| =   504  |S| = |E||H| =  32256  invariant N with |N||H| > M: [64] (only E)  good = False  orbits (length, |S_d|, |image|, fixes t != 1): [(9, 3584, 56, False), (64, 504, 504, False)]
   |H| =   392  |S| = |E||H| =  25088  invariant N with |N||H| > M: [64] (only E)  good = False  orbits (length, |S_d|, |image|, fixes t != 1): [(1, 25088, 56, False), (8, 3136, 56, False), (64, 392, 56, False)]
   |H| =   126  |S| = |E||H| =   8064  invariant N with |N||H| > M: [64] (only E)  good = False  orbits (length, |S_d|, |image|, fixes t != 1): [(9, 896, 56, False), (64, 126, 18, False)]
   |H| =    98  |S| = |E||H| =   6272  invariant N with |N||H| > M: [64] (only E)  good = False  orbits (length, |S_d|, |image|, fixes t != 1): [(2, 3136, 56, False), (7, 896, 56, False), (64, 98, 14, False)]
RESULT q = 8: largest order of a good subgroup among the subgroups of order > M of the two parabolic subgroups: none; M = 4032.  With (F1) and (F2): M_G = M, EQUALITY MinSubDeg(G) = k MinSubDeg(H)  [526s]
