q = 7: n = 57 points, |P_y| = |P_l| = 98784, |phi(Q)| = 336, |T| = 168, M = 4704  [10s]
point stabiliser P_y: Levi GL(2,7) of order 2016: 84 classes of subgroups (1704 subgroups); classes H with |H| |E| > M = 4704: 9  [11s]
   |H| =  2016  |S| = |E||H| =  98784  invariant N with |N||H| > M: [49] (only E)  good = False  orbits (length, |S_d|, |image|, fixes t != 1): [(1, 98784, 336, False), (56, 1764, 42, False)]
   |H| =  1008  |S| = |E||H| =  49392  invariant N with |N||H| > M: [49] (only E)  good = False  orbits (length, |S_d|, |image|, fixes t != 1): [(1, 49392, 168, False), (56, 882, 42, False)]
   |H| =   672  |S| = |E||H| =  32928  invariant N with |N||H| > M: [49] (only E)  good = False  orbits (length, |S_d|, |image|, fixes t != 1): [(1, 32928, 336, False), (56, 588, 42, False)]
   |H| =   336  |S| = |E||H| =  16464  invariant N with |N||H| > M: [49] (only E)  good = False  orbits (length, |S_d|, |image|, fixes t != 1): [(1, 16464, 168, False), (56, 294, 42, False)]
   |H| =   252  |S| = |E||H| =  12348  invariant N with |N||H| > M: [49] (only E)  good = False  orbits (length, |S_d|, |image|, fixes t != 1): [(1, 12348, 42, False), (7, 1764, 42, False), (49, 252, 42, False)]
   |H| =   144  |S| = |E||H| =   7056  invariant N with |N||H| > M: [49] (only E)  good = False  orbits (length, |S_d|, |image|, fixes t != 1): [(1, 7056, 24, False), (56, 126, 42, False)]
   |H| =   126  |S| = |E||H| =   6174  invariant N with |N||H| > M: [49] (only E)  good = False  orbits (length, |S_d|, |image|, fixes t != 1): [(1, 6174, 42, False), (7, 882, 42, False), (49, 126, 21, False)]
   |H| =   126  |S| = |E||H| =   6174  invariant N with |N||H| > M: [49] (only E)  good = False  orbits (length, |S_d|, |image|, fixes t != 1): [(1, 6174, 42, False), (7, 882, 21, False), (49, 126, 42, False)]
   |H| =   126  |S| = |E||H| =   6174  invariant N with |N||H| > M: [49] (only E)  good = False  orbits (length, |S_d|, |image|, fixes t != 1): [(1, 6174, 21, False), (7, 882, 42, False), (49, 126, 42, False)]
line stabiliser P_l: Levi GL(2,7) of order 2016: 84 classes of subgroups (1704 subgroups); classes H with |H| |E| > M = 4704: 9  [16s]
   |H| =  2016  |S| = |E||H| =  98784  invariant N with |N||H| > M: [49] (only E)  good = False  orbits (length, |S_d|, |image|, fixes t != 1): [(8, 12348, 42, False), (49, 2016, 336, False)]
   |H| =  1008  |S| = |E||H| =  49392  invariant N with |N||H| > M: [49] (only E)  good = False  orbits (length, |S_d|, |image|, fixes t != 1): [(8, 6174, 42, False), (49, 1008, 168, False)]
   |H| =   672  |S| = |E||H| =  32928  invariant N with |N||H| > M: [49] (only E)  good = False  orbits (length, |S_d|, |image|, fixes t != 1): [(8, 4116, 42, False), (49, 672, 336, False)]
   |H| =   336  |S| = |E||H| =  16464  invariant N with |N||H| > M: [49] (only E)  good = False  orbits (length, |S_d|, |image|, fixes t != 1): [(8, 2058, 42, False), (49, 336, 168, False)]
   |H| =   252  |S| = |E||H| =  12348  invariant N with |N||H| > M: [49] (only E)  good = False  orbits (length, |S_d|, |image|, fixes t != 1): [(1, 12348, 42, False), (7, 1764, 42, False), (49, 252, 42, False)]
   |H| =   144  |S| = |E||H| =   7056  invariant N with |N||H| > M: [49] (only E)  good = False  orbits (length, |S_d|, |image|, fixes t != 1): [(8, 882, 42, False), (49, 144, 24, False)]
   |H| =   126  |S| = |E||H| =   6174  invariant N with |N||H| > M: [49] (only E)  good = False  orbits (length, |S_d|, |image|, fixes t != 1): [(1, 6174, 21, False), (7, 882, 42, False), (49, 126, 42, False)]
   |H| =   126  |S| = |E||H| =   6174  invariant N with |N||H| > M: [49] (only E)  good = False  orbits (length, |S_d|, |image|, fixes t != 1): [(1, 6174, 42, False), (7, 882, 21, False), (49, 126, 42, False)]
   |H| =   126  |S| = |E||H| =   6174  invariant N with |N||H| > M: [49] (only E)  good = False  orbits (length, |S_d|, |image|, fixes t != 1): [(1, 6174, 42, False), (7, 882, 42, False), (49, 126, 21, False)]
RESULT q = 7: largest order of a good subgroup among the subgroups of order > M of the two parabolic subgroups: none; M = 4704.  With (F1) and (F2): M_G = M, EQUALITY MinSubDeg(G) = k MinSubDeg(H)  [18s]
