Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
1962 conjugacy classes of subgroups.
The subgroup lattice has 562 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #11743329 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11743155 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C7×#3166 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11740780 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C2×#89839 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11739407 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #11739403 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #11739354 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | #11739353 | C2 | 1 | 4 | yes | maximal, complemented |
| 10 | #11736658 | C2 | 1 | 4 | yes | maximal, complemented |
| 11 | #11736646 | C2 | 1 | 4 | yes | maximal, complemented |
| 12 | #11735975 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #11735961 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | C7×#533 | C22 | 1 | 1 | yes | characteristic |
| 15 | C2×C7×#125 | C22 | 1 | 1 | yes | characteristic |
| 16 | C2×#6471 | C22 | 1 | 4 | yes | — |
| 17 | C2×#6470 | C22 | 1 | 2 | yes | — |
| 18 | #90416 | C22 | 1 | 4 | yes | — |
| 19 | #90389 | C22 | 1 | 4 | yes | — |
| 20 | #90389 | C22 | 1 | 2 | yes | complemented |
| 21 | #90388 | C22 | 1 | 2 | yes | complemented |
| 22 | #90386 | — | 2 | 2 | no | — |
| 23 | #90385 | — | 2 | 2 | no | — |
| 24 | #90382 | C22 | 1 | 4 | yes | complemented |
| 25 | #90321 | — | 2 | 4 | no | — |
| 26 | #90276 | — | 2 | 2 | no | — |
| 27 | #90268 | — | 2 | 2 | no | — |
| 28 | #90216 | C22 | 1 | 2 | yes | — |
| 29 | #90212 | C22 | 1 | 2 | yes | — |
| 30 | #90205 | — | 2 | 4 | no | — |
| 31 | #90201 | C22 | 1 | 2 | yes | — |
| 32 | #90195 | C22 | 1 | 2 | yes | — |
| 33 | #90168 | C22 | 1 | 1 | yes | characteristic |
| 34 | C2×#6437 | C22 | 1 | 1 | yes | characteristic |
| 35 | C4×#1157 | C22 | 1 | 1 | yes | characteristic |
| 36 | C7×#501 | C22 | 1 | 4 | yes | complemented |
| 37 | C7×#499 | C22 | 1 | 4 | yes | complemented |
| 38 | C7×#428 | C22 | 1 | 4 | yes | — |
| 39 | C4×C7×M16 | C22 | 1 | 1 | yes | characteristic |
| 40 | #89894 | C22 | 1 | 2 | yes | — |
| 41 | #89861 | C22 | 1 | 2 | yes | complemented |
| 42 | #89861 | C22 | 1 | 2 | yes | complemented |
| 43 | #89841 | C22 | 1 | 2 | yes | complemented |
| 44 | #89839 | C22 | 1 | 2 | yes | — |
| 45 | #89839 | C22 | 1 | 2 | yes | — |
| 46 | #89839 | C22 | 1 | 4 | yes | — |
| 47 | #89839 | C22 | 1 | 2 | yes | complemented |
| 48 | #89774 | C22 | 1 | 4 | yes | — |
| 49 | C2×#6383 | C22 | 1 | 4 | yes | — |
| 50 | C2×#6377 | C22 | 1 | 1 | yes | characteristic |
| 51 | #89661 | C22 | 1 | 8 | yes | complemented |
| 52 | #89658 | C22 | 1 | 8 | yes | complemented |
| 53 | #89655 | C22 | 1 | 8 | yes | complemented |
| 54 | #89644 | C22 | 1 | 8 | yes | complemented |
| 55 | #89641 | C22 | 1 | 8 | yes | complemented |
| 56 | #89637 | C22 | 1 | 8 | yes | complemented |
| 57 | #89636 | C22 | 1 | 8 | yes | complemented |
| 58 | #89624 | C22 | 1 | 8 | yes | complemented |
| 59 | #89484 | C22 | 1 | 4 | yes | — |
| 60 | #89479 | C22 | 1 | 2 | yes | complemented |
| 61 | D7×#97 | C22 | 1 | 2 | yes | complemented |
| 62 | #89467 | C22 | 1 | 2 | yes | — |
| 63 | #89465 | C22 | 1 | 2 | yes | — |
| 64 | #89461 | C22 | 1 | 4 | yes | complemented |
| 65 | #60725 | — | 7 | 1 | no | maximal, Sylow |
| 66 | C2×#1161 | — | 2 | 4 | no | — |
| 67 | C2×#1157 | C23 | 1 | 1 | yes | characteristic |
| 68 | C2×#1157 | C23 | 1 | 2 | yes | — |
| 69 | C22×D28 | — | 2 | 2 | no | — |
| 70 | C22×D28 | C23 | 1 | 2 | yes | — |
| 71 | C2×C7×M16 | C23 | 1 | 2 | yes | — |
| 72 | C7×C4⋊Q8 | C23 | 1 | 2 | yes | — |
| 73 | C7×#125 | — | 2 | 2 | no | — |
| 74 | C7×#125 | C23 | 1 | 2 | yes | — |
| 75 | C7×#125 | C23 | 1 | 2 | yes | — |
| 76 | C7×#125 | C23 | 1 | 2 | yes | — |
| 77 | C7×C22⋊Q8 | — | 2 | 2 | no | — |
| 78 | C4×C7×Q8 | — | 2 | 2 | no | — |
| 79 | C7×#117 | C23 | 1 | 2 | yes | — |
| 80 | C2×C7×C4⋊C4 | — | 2 | 2 | no | — |
| 81 | C2×C7×C4⋊C4 | C23 | 1 | 2 | yes | — |
| 82 | C2×C42×C7 | C23 | 1 | 1 | yes | characteristic |
| 83 | #6510 | — | 2 | 4 | no | — |
| 84 | #6493 | — | 2 | 2 | no | — |
| 85 | #6493 | — | 2 | 4 | no | — |
| 86 | C4×C22⋊D7 | — | 2 | 4 | no | — |
| 87 | C4×C22⋊D7 | D4 | 1 | 4 | yes | — |
| 88 | #6489 | C23 | 1 | 1 | yes | characteristic |
| 89 | C22×C7⋊C8 | C23 | 1 | 2 | yes | — |
| 90 | #6471 | — | 2 | 16 | no | — |
| 91 | #6470 | — | 2 | 8 | no | — |
| 92 | C2×D56 | C23 | 1 | 8 | yes | — |
| 93 | C2×#1132 | C23 | 1 | 8 | yes | — |
| 94 | C2×#1131 | C23 | 1 | 4 | yes | — |
| 95 | C2×C8×D7 | C23 | 1 | 4 | yes | — |
| 96 | #6461 | — | 2 | 4 | no | — |
| 97 | #6461 | — | 2 | 4 | no | — |
| 98 | #6460 | — | 2 | 2 | no | — |
| 99 | #6460 | C23 | 1 | 4 | yes | — |
| 100 | #6458 | — | 2 | 2 | no | — |
| 101 | #6458 | — | 2 | 4 | no | — |
| 102 | #6458 | — | 2 | 4 | no | — |
| 103 | #6458 | — | 2 | 8 | no | — |
| 104 | #6458 | C23 | 1 | 4 | yes | — |
| 105 | #6458 | C23 | 1 | 8 | yes | — |
| 106 | #6457 | — | 2 | 4 | no | — |
| 107 | #6457 | — | 2 | 4 | no | — |
| 108 | #6457 | — | 2 | 8 | no | — |
| 109 | #6456 | — | 2 | 4 | no | — |
| 110 | #6456 | — | 2 | 4 | no | — |
| 111 | #6456 | C23 | 1 | 4 | yes | — |
| 112 | #6456 | C23 | 1 | 8 | yes | — |
| 113 | #6455 | — | 2 | 2 | no | — |
| 114 | #6455 | — | 2 | 4 | no | — |
| 115 | D7×C4⋊C4 | — | 2 | 2 | no | — |
| 116 | #6453 | — | 2 | 4 | no | — |
| 117 | #6450 | C23 | 1 | 4 | yes | — |
| 118 | #6445 | — | 2 | 4 | no | — |
| 119 | D7×C22⋊C4 | — | 2 | 4 | no | — |
| 120 | #6438 | — | 2 | 2 | no | — |
| 121 | #6438 | C23 | 1 | 2 | yes | — |
| 122 | #6437 | — | 2 | 2 | no | — |
| 123 | #6437 | — | 2 | 2 | no | — |
| 124 | #6437 | C23 | 1 | 2 | yes | — |
| 125 | #6437 | C23 | 1 | 1 | yes | characteristic |
| 126 | #6437 | C23 | 1 | 2 | yes | — |
| 127 | C4×D28 | — | 2 | 2 | no | — |
| 128 | C4×D28 | — | 2 | 4 | no | — |
| 129 | C4×D28 | D4 | 1 | 2 | yes | — |
| 130 | #6435 | C23 | 1 | 2 | yes | — |
| 131 | C42×D7 | C23 | 1 | 2 | yes | — |
| 132 | #6432 | C23 | 1 | 1 | yes | characteristic |
| 133 | C4×Dic14 | D4 | 1 | 2 | yes | — |
| 134 | C7×#107 | C23 | 1 | 8 | yes | — |
| 135 | C7×#106 | C23 | 1 | 8 | yes | — |
| 136 | C7×#97 | C23 | 1 | 2 | yes | — |
| 137 | C4×C7×C8 | C23 | 1 | 2 | yes | — |
| 138 | #6389 | C23 | 1 | 4 | yes | — |
| 139 | C8×Dic7 | C23 | 1 | 4 | yes | — |
| 140 | #6384 | C23 | 1 | 4 | yes | — |
| 141 | #6384 | C23 | 1 | 4 | yes | — |
| 142 | #6383 | C23 | 1 | 4 | yes | — |
| 143 | #6383 | C23 | 1 | 4 | yes | — |
| 144 | #6383 | C23 | 1 | 8 | yes | — |
| 145 | #6383 | C23 | 1 | 8 | yes | — |
| 146 | #6377 | C23 | 1 | 1 | yes | characteristic |
| 147 | #6377 | C23 | 1 | 1 | yes | characteristic |
| 148 | #6377 | C23 | 1 | 2 | yes | — |
| 149 | #3512 | — | 7 | 1 | no | — |
| 150 | #3508 | — | 7 | 1 | no | — |
| 151 | #3180 | — | 7 | 4 | no | — |
| 152 | #3176 | — | 7 | 4 | no | — |
| 153 | #3174 | — | 7 | 4 | no | — |
| 154 | #3171 | — | 7 | 4 | no | — |
| 155 | #3166 | D7 | 1 | 1 | yes | characteristic, complemented |
| 156 | #3151 | — | 7 | 1 | no | — |
| 157 | #3135 | — | 7 | 1 | no | — |
| 158 | C2×#490 | — | 7 | 1 | no | — |
| 159 | #3062 | — | 7 | 4 | no | — |
| 160 | #2946 | — | 7 | 4 | no | — |
| 161 | #2875 | — | 7 | 1 | no | — |
| 162 | C23×D7 | — | 2 | 2 | no | — |
| 163 | C2×C7×Q8 | — | 2 | 2 | no | — |
| 164 | C22×C4×C7 | — | 2 | 2 | no | — |
| 165 | C22×C4×C7 | C2×D4 | 1 | 2 | yes | — |
| 166 | C22×C4×C7 | C24 | 1 | 1 | yes | characteristic |
| 167 | C2×C22⋊D7 | — | 2 | 2 | no | — |
| 168 | C2×C22⋊D7 | C2×D4 | 1 | 2 | yes | — |
| 169 | #1161 | — | 8 | 8 | no | — |
| 170 | #1157 | — | 2 | 4 | no | — |
| 171 | #1157 | — | 2 | 8 | no | — |
| 172 | C2×D28 | — | 2 | 8 | no | — |
| 173 | C2×D28 | — | 2 | 2 | no | — |
| 174 | C2×D28 | — | 2 | 4 | no | — |
| 175 | C2×D28 | — | 2 | 8 | no | — |
| 176 | C2×D28 | — | 2 | 4 | no | — |
| 177 | C2×D28 | — | 2 | 2 | no | — |
| 178 | C2×D28 | — | 2 | 4 | no | — |
| 179 | C2×D28 | — | 8 | 4 | no | — |
| 180 | C2×D28 | C2×D4 | 1 | 1 | yes | characteristic |
| 181 | C2×D28 | C24 | 1 | 4 | yes | — |
| 182 | C2×D28 | C24 | 1 | 2 | yes | — |
| 183 | C2×C4×D7 | — | 2 | 2 | no | — |
| 184 | C2×C4×D7 | — | 2 | 8 | no | — |
| 185 | C2×C4×D7 | — | 2 | 4 | no | — |
| 186 | C2×C4×D7 | C2×D4 | 1 | 4 | yes | — |
| 187 | C2×C4×D7 | C24 | 1 | 2 | yes | — |
| 188 | C2×Dic14 | C2×D4 | 1 | 1 | yes | characteristic |
| 189 | C2×Dic14 | C24 | 1 | 2 | yes | — |
| 190 | C7×M16 | #41 | 1 | 8 | yes | complemented |
| 191 | C2×C7×C8 | C24 | 1 | 4 | yes | — |
| 192 | C7×C4⋊C4 | — | 2 | 4 | no | — |
| 193 | C7×C4⋊C4 | — | 2 | 2 | no | — |
| 194 | C7×C4⋊C4 | — | 2 | 4 | no | — |
| 195 | C7×C4⋊C4 | — | 2 | 2 | no | — |
| 196 | C7×C4⋊C4 | — | 2 | 4 | no | — |
| 197 | C7×C4⋊C4 | C24 | 1 | 4 | yes | — |
| 198 | C7×C4⋊C4 | C24 | 1 | 4 | yes | — |
| 199 | C7×C22⋊C4 | — | 2 | 2 | no | — |
| 200 | C42×C7 | — | 2 | 2 | no | — |
| 201 | C42×C7 | C2×D4 | 1 | 2 | yes | — |
| 202 | C42×C7 | C24 | 1 | 1 | yes | characteristic |
| 203 | C42×C7 | C24 | 1 | 1 | yes | characteristic |
| 204 | C22⋊Dic7 | C2×D4 | 1 | 2 | yes | — |
| 205 | (C2×D7)⋊C4 | — | 2 | 4 | no | — |
| 206 | (C2×D7)⋊C4 | — | 2 | 2 | no | — |
| 207 | (C2×D7)⋊C4 | — | 2 | 2 | no | — |
| 208 | (C2×D7)⋊C4 | — | 2 | 8 | no | — |
| 209 | (C2×D7)⋊C4 | — | 2 | 8 | no | — |
| 210 | (C2×D7)⋊C4 | — | 2 | 4 | no | — |
| 211 | (C2×D7)⋊C4 | — | 2 | 4 | no | — |
| 212 | (C2×D7)⋊C4 | C2×D4 | 1 | 4 | yes | — |
| 213 | C4⋊Dic7 | — | 2 | 2 | no | — |
| 214 | C4⋊Dic7 | — | 2 | 4 | no | — |
| 215 | C4⋊Dic7 | C2×D4 | 1 | 2 | yes | — |
| 216 | Dic7⋊C4 | — | 2 | 4 | no | — |
| 217 | Dic7⋊C4 | C2×D4 | 1 | 4 | yes | — |
| 218 | C4×Dic7 | — | 2 | 4 | no | — |
| 219 | C4×Dic7 | C2×D4 | 1 | 4 | yes | — |
| 220 | C4×Dic7 | C24 | 1 | 2 | yes | — |
| 221 | C2×C7⋊C8 | — | 2 | 4 | no | — |
| 222 | C2×C7⋊C8 | C24 | 1 | 2 | yes | — |
| 223 | C2×C7⋊C8 | C24 | 1 | 2 | yes | — |
| 224 | D56 | — | 2 | 16 | no | — |
| 225 | #1132 | — | 2 | 16 | no | — |
| 226 | #1131 | — | 2 | 8 | no | — |
| 227 | C8×D7 | — | 2 | 8 | no | — |
| 228 | C2×AGL(1,ℤ/8) | — | 7 | 4 | no | — |
| 229 | C2×#131 | — | 7 | 2 | no | — |
| 230 | #559 | — | 14 | 2 | no | — |
| 231 | #553 | — | 14 | 4 | no | — |
| 232 | #553 | — | 14 | 2 | no | — |
| 233 | #552 | — | 14 | 2 | no | — |
| 234 | #550 | — | 14 | 2 | no | — |
| 235 | #546 | — | 14 | 4 | no | — |
| 236 | #541 | — | 7 | 2 | no | — |
| 237 | #540 | — | 7 | 4 | no | — |
| 238 | #540 | — | 7 | 2 | no | — |
| 239 | #537 | — | 7 | 2 | no | — |
| 240 | #535 | — | 7 | 2 | no | — |
| 241 | #533 | C2×D7 | 1 | 1 | yes | characteristic |
| 242 | #532 | — | 7 | 4 | no | — |
| 243 | #532 | — | 7 | 1 | no | — |
| 244 | C2×#127 | — | 7 | 1 | no | — |
| 245 | #529 | — | 7 | 4 | no | — |
| 246 | C2×#125 | C2×D7 | 1 | 1 | yes | characteristic |
| 247 | #520 | — | 7 | 2 | no | — |
| 248 | #518 | — | 7 | 2 | no | — |
| 249 | C4×#41 | — | 7 | 1 | no | — |
| 250 | #501 | C2×D7 | 1 | 4 | yes | complemented |
| 251 | #499 | C2×D7 | 1 | 4 | yes | complemented |
| 252 | #496 | — | 7 | 4 | no | — |
| 253 | #493 | — | 7 | 2 | no | — |
| 254 | #492 | — | 7 | 2 | no | — |
| 255 | #491 | — | 7 | 2 | no | — |
| 256 | #490 | — | 7 | 2 | no | — |
| 257 | #490 | — | 7 | 4 | no | — |
| 258 | #490 | — | 7 | 2 | no | — |
| 259 | #490 | — | 7 | 2 | no | — |
| 260 | #489 | — | 7 | 2 | no | — |
| 261 | #489 | — | 7 | 2 | no | — |
| 262 | #469 | — | 7 | 8 | no | — |
| 263 | #468 | — | 7 | 8 | no | — |
| 264 | #466 | — | 7 | 8 | no | — |
| 265 | #465 | — | 7 | 8 | no | — |
| 266 | #442 | — | 7 | 8 | no | — |
| 267 | #440 | — | 7 | 8 | no | — |
| 268 | C4×SD16 | — | 7 | 8 | no | — |
| 269 | C4×D8 | — | 7 | 8 | no | — |
| 270 | #428 | C2×D7 | 1 | 4 | yes | — |
| 271 | #416 | — | 7 | 4 | no | — |
| 272 | C2×#102 | — | 7 | 4 | no | — |
| 273 | #405 | — | 7 | 2 | no | — |
| 274 | #405 | — | 7 | 4 | no | — |
| 275 | C4×M16 | — | 7 | 2 | no | — |
| 276 | C4×M16 | C2×D7 | 1 | 1 | yes | characteristic |
| 277 | C2×#97 | — | 7 | 1 | no | — |
| 278 | C2×#97 | — | 7 | 2 | no | — |
| 279 | C23×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 280 | C22×D7 | — | 2 | 2 | no | — |
| 281 | C22×D7 | — | 2 | 4 | no | — |
| 282 | C22×D7 | — | 4 | 4 | no | — |
| 283 | C22×D7 | — | 8 | 4 | no | — |
| 284 | C22×D7 | C22×D4 | 1 | 2 | yes | — |
| 285 | C7×Q8 | — | 4 | 4 | no | — |
| 286 | C2×C4×C7 | — | 2 | 4 | no | — |
| 287 | C2×C4×C7 | — | 2 | 4 | no | — |
| 288 | C2×C4×C7 | — | 4 | 2 | no | — |
| 289 | C2×C4×C7 | — | 8 | 2 | no | — |
| 290 | C2×C4×C7 | C22×D4 | 1 | 2 | yes | — |
| 291 | C2×C4×C7 | C22×D4 | 1 | 2 | yes | — |
| 292 | C2×C4×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 293 | C2×C4×C7 | C2×#41 | 1 | 4 | yes | — |
| 294 | C2×C4×C7 | C25 | 1 | 1 | yes | characteristic |
| 295 | C22⋊D7 | — | 2 | 4 | no | — |
| 296 | C22⋊D7 | — | 4 | 4 | no | — |
| 297 | C2×Dic7 | — | 2 | 2 | no | — |
| 298 | C2×Dic7 | C22×D4 | 1 | 4 | yes | — |
| 299 | C2×Dic7 | C22×D4 | 1 | 2 | yes | — |
| 300 | D28 | — | 2 | 2 | no | — |
| 301 | D28 | — | 2 | 8 | no | — |
| 302 | D28 | — | 2 | 4 | no | — |
| 303 | D28 | — | 4 | 8 | no | — |
| 304 | D28 | — | 4 | 4 | no | — |
| 305 | D28 | — | 8 | 2 | no | — |
| 306 | D28 | — | 8 | 4 | no | — |
| 307 | D28 | — | 8 | 4 | no | — |
| 308 | D28 | — | 8 | 8 | no | — |
| 309 | C4×D7 | — | 2 | 4 | no | — |
| 310 | C4×D7 | — | 4 | 4 | no | — |
| 311 | C4×D7 | — | 4 | 4 | no | — |
| 312 | C4×D7 | — | 8 | 4 | no | — |
| 313 | C4×D7 | — | 8 | 8 | no | — |
| 314 | Dic14 | — | 2 | 2 | no | — |
| 315 | Dic14 | — | 2 | 4 | no | — |
| 316 | C7×C8 | C2×#41 | 1 | 8 | yes | — |
| 317 | C7⋊C8 | — | 2 | 2 | no | — |
| 318 | C7⋊C8 | — | 2 | 2 | no | — |
| 319 | C2×#41 | — | 7 | 1 | no | — |
| 320 | C2×#41 | — | 7 | 2 | no | — |
| 321 | C2×#41 | — | 14 | 4 | no | — |
| 322 | C22×D4 | — | 7 | 2 | no | — |
| 323 | C22×D4 | — | 14 | 2 | no | — |
| 324 | AGL(1,ℤ/8) | — | 14 | 16 | no | — |
| 325 | C2×SD16 | — | 7 | 8 | no | — |
| 326 | C2×D8 | — | 7 | 8 | no | — |
| 327 | #131 | — | 14 | 8 | no | — |
| 328 | C2×M16 | — | 7 | 4 | no | — |
| 329 | C2×M16 | C22×D7 | 1 | 2 | yes | — |
| 330 | C22×C8 | — | 7 | 2 | no | — |
| 331 | C22×C8 | — | 7 | 4 | no | — |
| 332 | C4⋊Q8 | — | 7 | 1 | no | — |
| 333 | C4⋊Q8 | C22×D7 | 1 | 2 | yes | — |
| 334 | #127 | — | 7 | 2 | no | — |
| 335 | #127 | — | 7 | 2 | no | — |
| 336 | #127 | — | 7 | 1 | no | — |
| 337 | #127 | — | 14 | 2 | no | — |
| 338 | #127 | — | 14 | 2 | no | — |
| 339 | #126 | — | 14 | 4 | no | — |
| 340 | #126 | — | 14 | 4 | no | — |
| 341 | #125 | — | 2 | 2 | no | — |
| 342 | #125 | — | 14 | 4 | no | — |
| 343 | #125 | C22×D7 | 1 | 2 | yes | — |
| 344 | #125 | C22×D7 | 1 | 2 | yes | — |
| 345 | #125 | C22×D7 | 1 | 2 | yes | — |
| 346 | #124 | — | 7 | 2 | no | — |
| 347 | #124 | — | 14 | 2 | no | — |
| 348 | #124 | — | 14 | 4 | no | — |
| 349 | #123 | — | 14 | 8 | no | — |
| 350 | #123 | — | 14 | 4 | no | — |
| 351 | #123 | — | 14 | 4 | no | — |
| 352 | C22⋊Q8 | — | 2 | 2 | no | — |
| 353 | C22⋊Q8 | — | 7 | 4 | no | — |
| 354 | C22⋊Q8 | — | 14 | 2 | no | — |
| 355 | #121 | — | 7 | 4 | no | — |
| 356 | #121 | — | 7 | 8 | no | — |
| 357 | #121 | — | 14 | 8 | no | — |
| 358 | #121 | — | 14 | 4 | no | — |
| 359 | #121 | — | 14 | 4 | no | — |
| 360 | #121 | — | 14 | 2 | no | — |
| 361 | #121 | — | 14 | 4 | no | — |
| 362 | #121 | — | 14 | 2 | no | — |
| 363 | #120 | — | 14 | 4 | no | — |
| 364 | C4×Q8 | — | 2 | 2 | no | — |
| 365 | C4×Q8 | — | 7 | 2 | no | — |
| 366 | C4×Q8 | — | 7 | 4 | no | — |
| 367 | C4×D4 | — | 7 | 4 | no | — |
| 368 | C4×D4 | — | 7 | 8 | no | — |
| 369 | C4×D4 | — | 7 | 4 | no | — |
| 370 | C4×D4 | — | 7 | 2 | no | — |
| 371 | C4×D4 | — | 14 | 4 | no | — |
| 372 | C4×D4 | — | 14 | 4 | no | — |
| 373 | C4×D4 | — | 14 | 4 | no | — |
| 374 | C4×D4 | — | 14 | 4 | no | — |
| 375 | C4×D4 | — | 14 | 2 | no | — |
| 376 | #117 | — | 7 | 1 | no | — |
| 377 | #117 | — | 7 | 2 | no | — |
| 378 | #117 | — | 14 | 4 | no | — |
| 379 | #117 | — | 14 | 2 | no | — |
| 380 | #117 | C22×D7 | 1 | 2 | yes | — |
| 381 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 382 | C2×C4⋊C4 | — | 14 | 2 | no | — |
| 383 | C2×C4⋊C4 | C22×D7 | 1 | 2 | yes | — |
| 384 | C2×C22⋊C4 | — | 14 | 4 | no | — |
| 385 | C2×C42 | — | 7 | 2 | no | — |
| 386 | C2×C42 | C22×D7 | 1 | 1 | yes | characteristic |
| 387 | #107 | C22×D7 | 1 | 8 | yes | — |
| 388 | #106 | C22×D7 | 1 | 8 | yes | — |
| 389 | #103 | — | 7 | 4 | no | — |
| 390 | #103 | — | 7 | 4 | no | — |
| 391 | #102 | — | 7 | 8 | no | — |
| 392 | #102 | — | 7 | 8 | no | — |
| 393 | #102 | — | 7 | 4 | no | — |
| 394 | #102 | — | 7 | 4 | no | — |
| 395 | #97 | — | 7 | 4 | no | — |
| 396 | #97 | — | 7 | 1 | no | — |
| 397 | #97 | — | 7 | 1 | no | — |
| 398 | #97 | — | 7 | 2 | no | — |
| 399 | #97 | C22×D7 | 1 | 2 | yes | — |
| 400 | C4×C8 | — | 7 | 4 | no | — |
| 401 | C4×C8 | C22×D7 | 1 | 2 | yes | — |
| 402 | C22×C7 | — | 2 | 2 | no | — |
| 403 | C22×C7 | #532 | 1 | 2 | yes | — |
| 404 | C22×C7 | C23×D4 | 1 | 1 | yes | characteristic |
| 405 | C2×D7 | — | 2 | 4 | no | — |
| 406 | C2×D7 | — | 2 | 2 | no | — |
| 407 | C2×D7 | — | 4 | 2 | no | — |
| 408 | C2×D7 | — | 4 | 8 | no | — |
| 409 | C2×D7 | — | 4 | 2 | no | — |
| 410 | C2×D7 | — | 4 | 2 | no | — |
| 411 | C2×D7 | — | 4 | 4 | no | — |
| 412 | C2×D7 | — | 16 | 4 | no | — |
| 413 | C4×C7 | — | 2 | 2 | no | — |
| 414 | C4×C7 | — | 2 | 2 | no | — |
| 415 | C4×C7 | — | 4 | 4 | no | — |
| 416 | C4×C7 | — | 4 | 4 | no | — |
| 417 | C4×C7 | #532 | 1 | 2 | yes | — |
| 418 | C4×C7 | C22×#41 | 1 | 2 | yes | — |
| 419 | Dic7 | — | 2 | 4 | no | — |
| 420 | Dic7 | — | 2 | 2 | no | — |
| 421 | Dic7 | — | 4 | 2 | no | — |
| 422 | C24 | — | 14 | 2 | no | — |
| 423 | #41 | — | 14 | 4 | no | — |
| 424 | #41 | — | 14 | 8 | no | — |
| 425 | #41 | — | 56 | 8 | no | — |
| 426 | C2×Q8 | — | 2 | 2 | no | — |
| 427 | C2×Q8 | — | 7 | 1 | no | — |
| 428 | C2×Q8 | — | 7 | 2 | no | — |
| 429 | C2×D4 | — | 7 | 2 | no | — |
| 430 | C2×D4 | — | 7 | 1 | no | — |
| 431 | C2×D4 | — | 7 | 2 | no | — |
| 432 | C2×D4 | — | 7 | 4 | no | — |
| 433 | C2×D4 | — | 14 | 4 | no | — |
| 434 | C2×D4 | — | 14 | 8 | no | — |
| 435 | C2×D4 | — | 14 | 2 | no | — |
| 436 | C2×D4 | — | 14 | 2 | no | — |
| 437 | C2×D4 | — | 14 | 4 | no | — |
| 438 | C2×D4 | — | 14 | 2 | no | — |
| 439 | C2×D4 | — | 14 | 4 | no | — |
| 440 | C2×D4 | — | 14 | 8 | no | — |
| 441 | C2×D4 | — | 56 | 4 | no | — |
| 442 | C22×C4 | — | 2 | 2 | no | — |
| 443 | C22×C4 | — | 7 | 2 | no | — |
| 444 | C22×C4 | — | 7 | 4 | no | — |
| 445 | C22×C4 | — | 14 | 8 | no | — |
| 446 | C22×C4 | — | 14 | 4 | no | — |
| 447 | C22×C4 | — | 14 | 2 | no | — |
| 448 | C22×C4 | D4×D7 | 1 | 2 | yes | — |
| 449 | C22×C4 | C23×D7 | 1 | 1 | yes | characteristic |
| 450 | SD16 | — | 14 | 16 | no | — |
| 451 | D8 | — | 14 | 16 | no | — |
| 452 | M16 | — | 14 | 8 | no | — |
| 453 | M16 | #1161 | 1 | 8 | yes | complemented |
| 454 | C2×C8 | — | 7 | 2 | no | — |
| 455 | C2×C8 | — | 7 | 2 | no | — |
| 456 | C2×C8 | — | 14 | 4 | no | — |
| 457 | C2×C8 | — | 14 | 8 | no | — |
| 458 | C2×C8 | C23×D7 | 1 | 4 | yes | — |
| 459 | C4⋊C4 | — | 2 | 4 | no | — |
| 460 | C4⋊C4 | — | 2 | 4 | no | — |
| 461 | C4⋊C4 | — | 2 | 2 | no | — |
| 462 | C4⋊C4 | — | 2 | 2 | no | — |
| 463 | C4⋊C4 | — | 2 | 4 | no | — |
| 464 | C4⋊C4 | — | 7 | 4 | no | — |
| 465 | C4⋊C4 | — | 7 | 2 | no | — |
| 466 | C4⋊C4 | — | 14 | 4 | no | — |
| 467 | C4⋊C4 | — | 14 | 4 | no | — |
| 468 | C4⋊C4 | — | 14 | 2 | no | — |
| 469 | C4⋊C4 | C23×D7 | 1 | 4 | yes | — |
| 470 | C4⋊C4 | C23×D7 | 1 | 4 | yes | — |
| 471 | C22⋊C4 | — | 2 | 2 | no | — |
| 472 | C22⋊C4 | — | 7 | 2 | no | — |
| 473 | C22⋊C4 | — | 7 | 4 | no | — |
| 474 | C22⋊C4 | — | 14 | 8 | no | — |
| 475 | C22⋊C4 | — | 14 | 4 | no | — |
| 476 | C22⋊C4 | — | 14 | 4 | no | — |
| 477 | C22⋊C4 | — | 14 | 8 | no | — |
| 478 | C22⋊C4 | — | 14 | 4 | no | — |
| 479 | C22⋊C4 | — | 14 | 2 | no | — |
| 480 | C22⋊C4 | — | 14 | 2 | no | — |
| 481 | C42 | — | 2 | 2 | no | — |
| 482 | C42 | — | 7 | 4 | no | — |
| 483 | C42 | — | 7 | 2 | no | — |
| 484 | C42 | — | 14 | 4 | no | — |
| 485 | C42 | D4×D7 | 1 | 2 | yes | — |
| 486 | C42 | C23×D7 | 1 | 1 | yes | characteristic |
| 487 | C42 | C23×D7 | 1 | 1 | yes | characteristic |
| 488 | C2×C7 | — | 2 | 2 | no | — |
| 489 | C2×C7 | C2×#532 | 1 | 1 | yes | characteristic |
| 490 | C2×C7 | #3585 | 1 | 2 | yes | — |
| 491 | D7 | — | 4 | 2 | no | — |
| 492 | D7 | — | 8 | 2 | no | — |
| 493 | D7 | — | 8 | 4 | no | — |
| 494 | C23 | — | 7 | 2 | no | — |
| 495 | C23 | — | 14 | 2 | no | — |
| 496 | C23 | — | 14 | 4 | no | — |
| 497 | C23 | — | 28 | 4 | no | — |
| 498 | C23 | — | 56 | 4 | no | — |
| 499 | C23 | C2×D4×D7 | 1 | 1 | yes | characteristic |
| 500 | Q8 | — | 4 | 4 | no | — |
| 501 | Q8 | — | 14 | 2 | no | — |
| 502 | Q8 | — | 14 | 4 | no | — |
| 503 | D4 | — | 14 | 4 | no | — |
| 504 | D4 | — | 14 | 2 | no | — |
| 505 | D4 | — | 14 | 4 | no | — |
| 506 | D4 | — | 14 | 8 | no | — |
| 507 | D4 | — | 28 | 8 | no | — |
| 508 | D4 | — | 28 | 4 | no | — |
| 509 | D4 | — | 28 | 4 | no | — |
| 510 | D4 | — | 56 | 2 | no | — |
| 511 | D4 | — | 56 | 4 | no | — |
| 512 | D4 | — | 56 | 4 | no | — |
| 513 | D4 | — | 56 | 8 | no | — |
| 514 | C2×C4 | — | 2 | 4 | no | — |
| 515 | C2×C4 | — | 2 | 4 | no | — |
| 516 | C2×C4 | — | 4 | 2 | no | — |
| 517 | C2×C4 | — | 7 | 4 | no | — |
| 518 | C2×C4 | — | 7 | 2 | no | — |
| 519 | C2×C4 | — | 8 | 2 | no | — |
| 520 | C2×C4 | — | 14 | 4 | no | — |
| 521 | C2×C4 | — | 14 | 2 | no | — |
| 522 | C2×C4 | — | 28 | 4 | no | — |
| 523 | C2×C4 | — | 28 | 4 | no | — |
| 524 | C2×C4 | — | 56 | 4 | no | — |
| 525 | C2×C4 | — | 56 | 8 | no | — |
| 526 | C2×C4 | C2×D4×D7 | 1 | 2 | yes | — |
| 527 | C2×C4 | C2×D4×D7 | 1 | 2 | yes | — |
| 528 | C2×C4 | C2×D4×D7 | 1 | 1 | yes | characteristic |
| 529 | C2×C4 | C2×#1161 | 1 | 4 | yes | — |
| 530 | C2×C4 | C24×D7 | 1 | 1 | yes | characteristic |
| 531 | C8 | — | 14 | 2 | no | — |
| 532 | C8 | — | 14 | 2 | no | — |
| 533 | C8 | C2×#1161 | 1 | 8 | yes | — |
| 534 | C7 | #60725 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 535 | C22 | — | 2 | 2 | no | — |
| 536 | C22 | — | 14 | 4 | no | — |
| 537 | C22 | — | 14 | 2 | no | — |
| 538 | C22 | — | 28 | 2 | no | — |
| 539 | C22 | — | 28 | 8 | no | — |
| 540 | C22 | — | 28 | 2 | no | — |
| 541 | C22 | — | 28 | 2 | no | — |
| 542 | C22 | — | 28 | 4 | no | — |
| 543 | C22 | — | 112 | 4 | no | — |
| 544 | C22 | #90416 | 1 | 2 | yes | — |
| 545 | C22 | C22×D4×D7 | 1 | 1 | yes | characteristic |
| 546 | C4 | — | 2 | 2 | no | — |
| 547 | C4 | — | 2 | 2 | no | — |
| 548 | C4 | — | 4 | 4 | no | — |
| 549 | C4 | — | 4 | 4 | no | — |
| 550 | C4 | — | 14 | 4 | no | — |
| 551 | C4 | — | 14 | 2 | no | — |
| 552 | C4 | — | 28 | 2 | no | — |
| 553 | C4 | #90416 | 1 | 2 | yes | — |
| 554 | C4 | C22×#1161 | 1 | 2 | yes | — |
| 555 | C2 | — | 2 | 2 | no | — |
| 556 | C2 | — | 28 | 2 | no | — |
| 557 | C2 | — | 56 | 4 | no | — |
| 558 | C2 | — | 56 | 2 | no | — |
| 559 | C2 | C2×#90416 | 1 | 1 | yes | characteristic |
| 560 | C2 | #11744268 | 1 | 2 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11743329 | C2 | semidirect |
| 2. #11743155 | C2 | semidirect |
| 3. C7×#3166 | C2 | semidirect |
| 4. #11740780 | C2 | semidirect |
| 5. C2×#89839 | C2 | semidirect |
| 6. #11739407 | C2 | semidirect |
| 7. #11739403 | C2 | semidirect |
| 8. #11739354 | C2 | semidirect |
| 9. #11739353 | C2 | semidirect |
| 10. #11736658 | C2 | semidirect |
| 11. #11736646 | C2 | semidirect |
| 12. #11735975 | C2 | semidirect |
| 13. #11735961 | C2 | semidirect |
| 20. #90389 | C22 | semidirect |
| 21. #90388 | C22 | semidirect |
| 24. #90382 | C22 | semidirect |
| 36. C7×#501 | C22 | semidirect |
| 37. C7×#499 | C22 | semidirect |
| 41. #89861 | C22 | semidirect |
| 42. #89861 | C22 | semidirect |
| 43. #89841 | C22 | semidirect |
| 47. #89839 | C22 | semidirect |
| 51. #89661 | C22 | semidirect |
| 52. #89658 | C22 | semidirect |
| 53. #89655 | C22 | semidirect |
| 54. #89644 | C22 | semidirect |
| 55. #89641 | C22 | semidirect |
| 56. #89637 | C22 | semidirect |
| 57. #89636 | C22 | semidirect |
| 58. #89624 | C22 | semidirect |
| 60. #89479 | C22 | semidirect |
| 61. D7×#97 | C22 | semidirect |
| 64. #89461 | C22 | semidirect |
| 155. #3166 | D7 | semidirect |
| 190. C7×M16 | #41 | semidirect |
| 250. #501 | C2×D7 | semidirect |
| 251. #499 | C2×D7 | semidirect |
| 453. M16 | #1161 | semidirect |
| 534. C7 | #60725 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11743329 | 2 |
| #11743155 | 2 |
| C7×#3166 | 2 |
| #11740780 | 2 |
| C2×#89839 | 2 |
| #11739407 | 2 |
| #11739403 | 2 |
| #11739354 | 2 |
| #11739353 | 2 |
| #11736658 | 2 |
| #11736646 | 2 |
| #11735975 | 2 |
| #11735961 | 2 |
| #60725 | 7 |