PGAMMAL(3,4): |P| = 120960, k = 21, |Q| = 5760, |phibar(Q)| = 120, |Q_t| by o(t): {2: [384], 3: [288], 5: [240]}, M = 384, |P|/M = 315
  [lattice] processed 1/11 classes, closures 10, 0s
  [lattice] processed 11/172 classes, closures 2775, 18s
  [lattice] processed 21/189 classes, closures 5800, 41s
  [lattice] processed 31/200 classes, closures 8008, 52s
  [lattice] processed 41/209 classes, closures 9828, 63s
  [lattice] processed 51/213 classes, closures 14327, 104s
  [lattice] processed 61/213 classes, closures 16461, 125s
  [lattice] processed 71/213 classes, closures 20471, 164s
  [lattice] processed 81/219 classes, closures 22572, 181s
  [lattice] processed 91/221 classes, closures 23702, 194s
  [lattice] processed 101/221 classes, closures 27185, 230s
  [lattice] processed 111/221 classes, closures 30889, 273s
  [lattice] processed 121/221 classes, closures 33336, 295s
  [lattice] processed 131/222 classes, closures 36778, 335s
  [lattice] processed 141/222 classes, closures 39390, 382s
  [lattice] processed 151/222 classes, closures 41226, 409s
  [lattice] processed 161/222 classes, closures 43414, 442s
  [lattice] processed 171/222 classes, closures 46418, 486s
  [lattice] processed 181/224 classes, closures 48589, 506s
  [lattice] processed 191/224 classes, closures 51031, 539s
  [lattice] processed 201/225 classes, closures 52487, 551s
  [lattice] processed 211/226 classes, closures 54257, 564s
  [lattice] processed 221/226 classes, closures 56471, 596s
  [lattice] processed 226/226 classes, closures 56952, 602s
classes of subgroups: 226; subgroups: 299632; time 602s
normal subgroups (orders): [1, 20160, 60480, 120960]
order histogram of classes: {1: 1, 2: 2, 3: 3, 4: 6, 5: 1, 6: 6, 7: 1, 8: 16, 9: 3, 10: 1, 12: 9, 14: 1, 15: 1, 16: 17, 18: 6, 20: 1, 21: 3, 24: 13, 27: 1, 30: 1, 32: 13, 36: 4, 42: 2, 48: 16, 54: 3, 60: 4, 63: 1, 64: 7, 72: 4, 80: 2, 96: 14, 108: 1, 120: 3, 126: 1, 128: 1, 144: 3, 160: 2, 168: 1, 180: 1, 192: 10, 216: 1, 240: 2, 288: 6, 320: 2, 336: 1, 360: 2, 384: 4, 432: 1, 480: 2, 576: 3, 720: 1, 960: 4, 1152: 1, 1920: 2, 2880: 2, 5760: 2, 20160: 1, 40320: 1, 60480: 1, 120960: 1}

classes with |S| >= M = 384:  (order, conjugates, [(orbit length, |S_d|, induced order on the lines through d, good at d)], good)
  120960      1  [(21, 5760, 120, False)]  not good
   60480      1  [(21, 2880, 60, False)]  not good
   40320      3  [(21, 1920, 120, False)]  not good
   20160      1  [(21, 960, 60, False)]  not good
    5760     21  [(20, 288, 24, False), (1, 5760, 120, False)]  not good
    5760     21  [(16, 360, 120, False), (5, 1152, 24, False)]  not good
    2880     21  [(20, 144, 12, False), (1, 2880, 60, False)]  not good
    2880     21  [(16, 180, 60, False), (5, 576, 12, False)]  not good
    1920     63  [(16, 120, 120, False), (5, 384, 24, False)]  not good
    1920     63  [(20, 96, 24, False), (1, 1920, 120, False)]  not good
    1152    105  [(16, 72, 24, False), (1, 1152, 24, False), (4, 288, 24, False)]  not good
     960     21  [(20, 48, 12, False), (1, 960, 60, False)]  not good
     960     21  [(5, 192, 12, False), (16, 60, 60, False)]  not good
     960    126  [(20, 48, 24, False), (1, 960, 20, False)]  not good
     960    126  [(16, 60, 20, False), (5, 192, 24, False)]  not good
     720    168  [(15, 48, 12, False), (6, 120, 120, False)]  not good
     576    105  [(4, 144, 12, False), (16, 36, 12, False), (1, 576, 12, False)]  not good
     576    210  [(12, 48, 24, False), (1, 576, 12, False), (8, 72, 24, False)]  not good
     576    210  [(3, 192, 24, False), (16, 36, 12, False), (2, 288, 24, False)]  not good
     480    126  [(16, 30, 10, False), (5, 96, 12, False)]  not good
     480    126  [(20, 24, 12, False), (1, 480, 10, False)]  not good
     432    280  [(12, 36, 12, False), (9, 48, 24, False)]  not good
     384    315  [(16, 24, 24, False), (1, 384, 24, False), (4, 96, 24, False)]  not good
     384    315  [(16, 24, 24, False), (1, 384, 24, False), (4, 96, 8, True)]  GOOD
     384    315  [(4, 96, 24, False), (16, 24, 24, False), (1, 384, 8, True)]  GOOD
     384    315  [(16, 24, 8, True), (1, 384, 24, False), (4, 96, 24, False)]  GOOD

RESULT PGAMMAL(3,4): M = 384; M_G = largest order of a good subgroup over all 226 classes = 384; classes with |S| > M: 22, of which good: 0; good classes of order M: 3; |P|/M = 315, |P|/M_G = 315; strict inequality: False
number of subgroups of order >= M that are good at the base point, by order: {384: 315}
total time 602s
