← #32889379
Subgroups — #32889379
Order 18176.
1746 conjugacy classes of subgroups.
The subgroup lattice has 474 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #22602740 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #22601360 | C2 | 1 | 4 | yes | maximal, complemented |
| 3 | #22601317 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #22601117 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #22600985 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #22599401 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #22599265 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #22598631 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | #22598400 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #22597442 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | C71×#3509 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #17986747 | — | 2 | 2 | no | — |
| 13 | #17986709 | C22 | 1 | 4 | yes | — |
| 14 | #17986671 | C22 | 1 | 4 | yes | — |
| 15 | #17986652 | — | 2 | 2 | no | — |
| 16 | #17986604 | C22 | 1 | 4 | yes | — |
| 17 | #17986579 | — | 2 | 4 | no | — |
| 18 | #17986549 | C22 | 1 | 2 | yes | — |
| 19 | #17986389 | C22 | 1 | 4 | yes | — |
| 20 | #17986373 | C22 | 1 | 4 | yes | — |
| 21 | #17986373 | C22 | 1 | 4 | yes | — |
| 22 | #17986367 | C22 | 1 | 4 | yes | — |
| 23 | #17986353 | C22 | 1 | 4 | yes | — |
| 24 | #17986349 | C22 | 1 | 4 | yes | — |
| 25 | #17986323 | C22 | 1 | 4 | yes | — |
| 26 | #17986306 | C22 | 1 | 8 | yes | — |
| 27 | #17986294 | C22 | 1 | 2 | yes | — |
| 28 | #17986289 | C22 | 1 | 2 | yes | — |
| 29 | #17986211 | C22 | 1 | 8 | yes | — |
| 30 | #17986201 | C22 | 1 | 4 | yes | — |
| 31 | #17986201 | C22 | 1 | 4 | yes | — |
| 32 | #17986201 | C22 | 1 | 8 | yes | — |
| 33 | #17986199 | C22 | 1 | 2 | yes | — |
| 34 | #17986199 | C22 | 1 | 8 | yes | — |
| 35 | #17986194 | C22 | 1 | 2 | yes | — |
| 36 | #17986144 | C22 | 1 | 4 | yes | — |
| 37 | #17986138 | C22 | 1 | 8 | yes | — |
| 38 | #17986130 | C22 | 1 | 4 | yes | — |
| 39 | Q8×C71⋊C8 | C22 | 1 | 4 | yes | — |
| 40 | #17986097 | C22 | 1 | 8 | yes | — |
| 41 | C4×#11765852 | C22 | 1 | 4 | yes | — |
| 42 | C4×#11765852 | C22 | 1 | 8 | yes | — |
| 43 | C4×#11765850 | C22 | 1 | 4 | yes | — |
| 44 | #17986060 | C22 | 1 | 4 | yes | — |
| 45 | #17986052 | C22 | 1 | 2 | yes | — |
| 46 | #557×C71 | C22 | 1 | 4 | yes | — |
| 47 | #556×C71 | C22 | 1 | 4 | yes | — |
| 48 | #552×C71 | — | 2 | 4 | no | — |
| 49 | #541×C71 | — | 2 | 2 | no | — |
| 50 | #536×C71 | C22 | 1 | 2 | yes | — |
| 51 | #533×C71 | — | 2 | 2 | no | — |
| 52 | #533×C71 | C22 | 1 | 1 | yes | characteristic |
| 53 | C2×C4⋊Q8×C71 | C22 | 1 | 1 | yes | characteristic |
| 54 | #519×C71 | C22 | 1 | 2 | yes | — |
| 55 | C4×#41×C71 | C22 | 1 | 1 | yes | characteristic |
| 56 | C2×#11765866 | — | 2 | 4 | no | — |
| 57 | C2×#11765865 | — | 2 | 2 | no | — |
| 58 | C2×#11765852 | C23 | 1 | 8 | yes | — |
| 59 | C2×#11765852 | C23 | 1 | 4 | yes | — |
| 60 | C2×#11765852 | C23 | 1 | 8 | yes | — |
| 61 | C2×#11765850 | C23 | 1 | 4 | yes | — |
| 62 | #14556128 | C23 | 1 | 2 | yes | — |
| 63 | #14556125 | C23 | 1 | 4 | yes | — |
| 64 | #14556125 | C23 | 1 | 2 | yes | — |
| 65 | #14556120 | C23 | 1 | 4 | yes | — |
| 66 | #14556116 | — | 2 | 2 | no | — |
| 67 | #14556113 | — | 2 | 8 | no | — |
| 68 | #14556106 | — | 2 | 8 | no | — |
| 69 | #14556104 | — | 2 | 4 | no | — |
| 70 | #14556103 | — | 2 | 4 | no | — |
| 71 | #14556103 | — | 2 | 8 | no | — |
| 72 | #14556102 | — | 2 | 2 | no | — |
| 73 | #14556102 | C23 | 1 | 4 | yes | — |
| 74 | #14556101 | — | 2 | 8 | no | — |
| 75 | C4×D284 | — | 2 | 2 | no | — |
| 76 | C4×D284 | C23 | 1 | 4 | yes | — |
| 77 | C4×D284 | C23 | 1 | 8 | yes | — |
| 78 | C4⋊C4×D71 | — | 2 | 4 | no | — |
| 79 | #14556061 | C23 | 1 | 4 | yes | — |
| 80 | #14556059 | C23 | 1 | 4 | yes | — |
| 81 | C4⋊(C71⋊C8) | C23 | 1 | 8 | yes | — |
| 82 | C4⋊(C71⋊C8) | C23 | 1 | 2 | yes | — |
| 83 | C4⋊(C71⋊C8) | C23 | 1 | 2 | yes | — |
| 84 | #14556052 | C23 | 1 | 8 | yes | — |
| 85 | #14556052 | C23 | 1 | 8 | yes | — |
| 86 | #14556052 | C23 | 1 | 4 | yes | — |
| 87 | #14556049 | C23 | 1 | 4 | yes | — |
| 88 | #14556048 | C23 | 1 | 4 | yes | — |
| 89 | #14556048 | C23 | 1 | 4 | yes | — |
| 90 | C22⋊(C71⋊C8) | C23 | 1 | 4 | yes | — |
| 91 | #14556039 | C23 | 1 | 4 | yes | — |
| 92 | C4×C71⋊C8 | C23 | 1 | 4 | yes | — |
| 93 | C4×C71⋊C8 | C23 | 1 | 4 | yes | — |
| 94 | C2×#41×C71 | C23 | 1 | 1 | yes | characteristic |
| 95 | C22×Q8×C71 | C23 | 1 | 2 | yes | — |
| 96 | C4⋊Q8×C71 | — | 2 | 1 | no | — |
| 97 | C4⋊Q8×C71 | — | 2 | 1 | no | — |
| 98 | C4⋊Q8×C71 | D4 | 1 | 2 | yes | — |
| 99 | C4⋊Q8×C71 | C23 | 1 | 4 | yes | — |
| 100 | C4⋊Q8×C71 | C23 | 1 | 4 | yes | — |
| 101 | #126×C71 | — | 2 | 8 | no | — |
| 102 | #125×C71 | — | 2 | 4 | no | — |
| 103 | #125×C71 | — | 2 | 8 | no | — |
| 104 | #125×C71 | D4 | 1 | 2 | yes | — |
| 105 | #124×C71 | C23 | 1 | 4 | yes | — |
| 106 | #123×C71 | — | 2 | 4 | no | — |
| 107 | C22⋊Q8×C71 | — | 2 | 4 | no | — |
| 108 | C22⋊Q8×C71 | — | 2 | 4 | no | — |
| 109 | C22⋊Q8×C71 | D4 | 1 | 4 | yes | — |
| 110 | C4×Q8×C71 | — | 2 | 4 | no | — |
| 111 | C4×Q8×C71 | — | 2 | 4 | no | — |
| 112 | C4×Q8×C71 | C23 | 1 | 8 | yes | — |
| 113 | C4×Q8×C71 | C23 | 1 | 2 | yes | — |
| 114 | C4×Q8×C71 | C23 | 1 | 4 | yes | — |
| 115 | C4×D4×C71 | — | 2 | 2 | no | — |
| 116 | C4×D4×C71 | C23 | 1 | 2 | yes | — |
| 117 | #117×C71 | — | 2 | 4 | no | — |
| 118 | #117×C71 | — | 2 | 4 | no | — |
| 119 | #117×C71 | — | 2 | 1 | no | — |
| 120 | #117×C71 | C23 | 1 | 1 | yes | characteristic |
| 121 | #117×C71 | C23 | 1 | 2 | yes | — |
| 122 | C2×C4⋊C4×C71 | — | 2 | 2 | no | — |
| 123 | C2×C42×C71 | — | 2 | 1 | no | — |
| 124 | C2×C42×C71 | C23 | 1 | 1 | yes | characteristic |
| 125 | #11765866 | — | 8 | 8 | no | — |
| 126 | #11765865 | — | 8 | 4 | no | — |
| 127 | C2×Dic142 | — | 2 | 2 | no | — |
| 128 | C2×D284 | — | 2 | 2 | no | — |
| 129 | C2×D284 | — | 2 | 2 | no | — |
| 130 | C2×D284 | — | 2 | 8 | no | — |
| 131 | C2×D284 | C24 | 1 | 4 | yes | — |
| 132 | C2×C22⋊D71 | — | 2 | 4 | no | — |
| 133 | C2×C4×D71 | — | 2 | 4 | no | — |
| 134 | C2×C4×D71 | — | 2 | 8 | no | — |
| 135 | #11765852 | — | 4 | 8 | no | — |
| 136 | #11765852 | — | 4 | 8 | no | — |
| 137 | #11765852 | — | 4 | 4 | no | — |
| 138 | #11765850 | — | 4 | 4 | no | — |
| 139 | C2×C71⋊C8 | C24 | 1 | 4 | yes | — |
| 140 | C2×C71⋊C8 | C24 | 1 | 4 | yes | — |
| 141 | C4⋊Dic71 | — | 2 | 2 | no | — |
| 142 | C4⋊Dic71 | C24 | 1 | 4 | yes | — |
| 143 | Dic71⋊C4 | — | 2 | 8 | no | — |
| 144 | (C2×D71)⋊C4 | — | 2 | 4 | no | — |
| 145 | (C2×D71)⋊C4 | — | 2 | 8 | no | — |
| 146 | (C2×D71)⋊C4 | — | 2 | 4 | no | — |
| 147 | #41×C71 | — | 4 | 2 | no | — |
| 148 | C2×Q8×C71 | — | 2 | 2 | no | — |
| 149 | C2×Q8×C71 | — | 4 | 4 | no | — |
| 150 | C2×Q8×C71 | C2×D4 | 1 | 4 | yes | — |
| 151 | C2×Q8×C71 | C24 | 1 | 4 | yes | — |
| 152 | C2×Q8×C71 | C24 | 1 | 1 | yes | characteristic |
| 153 | C2×D4×C71 | — | 2 | 1 | no | — |
| 154 | C2×D4×C71 | C24 | 1 | 1 | yes | characteristic |
| 155 | C22×C4×C71 | — | 2 | 2 | no | — |
| 156 | C22×C4×C71 | — | 2 | 2 | no | — |
| 157 | C22×C4×C71 | — | 2 | 1 | no | — |
| 158 | C22×C4×C71 | C2×D4 | 1 | 2 | yes | — |
| 159 | C22×C4×C71 | C24 | 1 | 1 | yes | characteristic |
| 160 | C4⋊C4×C71 | — | 2 | 4 | no | — |
| 161 | C4⋊C4×C71 | — | 2 | 4 | no | — |
| 162 | C4⋊C4×C71 | — | 2 | 2 | no | — |
| 163 | C4⋊C4×C71 | — | 2 | 8 | no | — |
| 164 | C4⋊C4×C71 | — | 2 | 8 | no | — |
| 165 | C4⋊C4×C71 | C2×D4 | 1 | 4 | yes | — |
| 166 | C4⋊C4×C71 | C2×D4 | 1 | 4 | yes | — |
| 167 | C4⋊C4×C71 | C2×D4 | 1 | 8 | yes | — |
| 168 | C4⋊C4×C71 | C24 | 1 | 2 | yes | — |
| 169 | C22⋊C4×C71 | — | 2 | 1 | no | — |
| 170 | C22⋊C4×C71 | — | 2 | 2 | no | — |
| 171 | C22⋊C4×C71 | — | 2 | 8 | no | — |
| 172 | C22⋊C4×C71 | C2×D4 | 1 | 4 | yes | — |
| 173 | C42×C71 | — | 2 | 1 | no | — |
| 174 | C42×C71 | — | 2 | 2 | no | — |
| 175 | C42×C71 | — | 2 | 8 | no | — |
| 176 | C42×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 177 | C42×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 178 | C42×C71 | C24 | 1 | 2 | yes | — |
| 179 | C42×C71 | C24 | 1 | 4 | yes | — |
| 180 | C23×C71 | — | 2 | 1 | no | — |
| 181 | C23×C71 | C22×D4 | 1 | 1 | yes | characteristic |
| 182 | C22×D71 | — | 2 | 4 | no | — |
| 183 | Q8×C71 | — | 2 | 8 | no | — |
| 184 | Q8×C71 | — | 2 | 8 | no | — |
| 185 | Q8×C71 | — | 2 | 2 | no | — |
| 186 | Q8×C71 | — | 4 | 4 | no | — |
| 187 | D4×C71 | — | 2 | 2 | no | — |
| 188 | D4×C71 | — | 4 | 2 | no | — |
| 189 | C2×C4×C71 | — | 2 | 4 | no | — |
| 190 | C2×C4×C71 | — | 2 | 2 | no | — |
| 191 | C2×C4×C71 | — | 2 | 2 | no | — |
| 192 | C2×C4×C71 | — | 2 | 4 | no | — |
| 193 | C2×C4×C71 | — | 2 | 1 | no | — |
| 194 | C2×C4×C71 | — | 4 | 2 | no | — |
| 195 | C2×C4×C71 | — | 4 | 4 | no | — |
| 196 | C2×C4×C71 | — | 4 | 4 | no | — |
| 197 | C2×C4×C71 | C22×D4 | 1 | 1 | yes | characteristic |
| 198 | C2×C4×C71 | C22×D4 | 1 | 8 | yes | — |
| 199 | C2×C4×C71 | C22×D4 | 1 | 2 | yes | — |
| 200 | C2×C4×C71 | C22×D4 | 1 | 2 | yes | — |
| 201 | C2×C4×C71 | C25 | 1 | 1 | yes | characteristic |
| 202 | C22⋊D71 | — | 8 | 4 | no | — |
| 203 | C2×Dic71 | — | 2 | 4 | no | — |
| 204 | D284 | — | 2 | 4 | no | — |
| 205 | D284 | — | 2 | 4 | no | — |
| 206 | D284 | — | 4 | 4 | no | — |
| 207 | D284 | — | 8 | 2 | no | — |
| 208 | D284 | — | 8 | 8 | no | — |
| 209 | C4×D71 | — | 4 | 8 | no | — |
| 210 | C4×D71 | — | 8 | 8 | no | — |
| 211 | Dic142 | — | 8 | 2 | no | — |
| 212 | C71⋊C8 | — | 2 | 4 | no | — |
| 213 | C71⋊C8 | — | 2 | 4 | no | — |
| 214 | C22×C71 | — | 2 | 1 | no | — |
| 215 | C22×C71 | — | 2 | 2 | no | — |
| 216 | C22×C71 | — | 4 | 1 | no | — |
| 217 | C22×C71 | — | 4 | 2 | no | — |
| 218 | C22×C71 | C23×D4 | 1 | 1 | yes | characteristic |
| 219 | C2×D71 | — | 4 | 4 | no | — |
| 220 | C2×D71 | — | 4 | 4 | no | — |
| 221 | C2×D71 | — | 4 | 4 | no | — |
| 222 | C4×C71 | — | 2 | 1 | no | — |
| 223 | C4×C71 | — | 2 | 2 | no | — |
| 224 | C4×C71 | — | 2 | 8 | no | — |
| 225 | C4×C71 | — | 4 | 1 | no | — |
| 226 | C4×C71 | — | 4 | 4 | no | — |
| 227 | C4×C71 | — | 4 | 2 | no | — |
| 228 | C4×C71 | #577 | 1 | 4 | yes | — |
| 229 | C4×C71 | #585 | 1 | 2 | yes | — |
| 230 | Dic71 | — | 4 | 4 | no | — |
| 231 | #61935 | — | 71 | 1 | no | maximal, Sylow |
| 232 | C2×C71 | — | 4 | 1 | no | — |
| 233 | C2×C71 | — | 8 | 1 | no | — |
| 234 | C2×C71 | #3487 | 1 | 1 | yes | characteristic |
| 235 | C2×C71 | C2×#577 | 1 | 2 | yes | — |
| 236 | D71 | — | 8 | 4 | no | — |
| 237 | #3548 | — | 71 | 1 | no | — |
| 238 | #3509 | D71 | 1 | 1 | yes | characteristic, complemented |
| 239 | #3397 | — | 71 | 4 | no | — |
| 240 | #3392 | — | 71 | 4 | no | — |
| 241 | #3372 | — | 71 | 4 | no | — |
| 242 | #3360 | — | 71 | 4 | no | — |
| 243 | #3221 | — | 71 | 4 | no | — |
| 244 | #3206 | — | 71 | 2 | no | — |
| 245 | #3126 | — | 71 | 4 | no | — |
| 246 | #3106 | — | 71 | 2 | no | — |
| 247 | #2986 | — | 71 | 1 | no | — |
| 248 | C71 | #61935 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 249 | #562 | — | 142 | 2 | no | — |
| 250 | #557 | C2×D71 | 1 | 4 | yes | — |
| 251 | #556 | C2×D71 | 1 | 4 | yes | — |
| 252 | #554 | — | 71 | 4 | no | — |
| 253 | #552 | — | 2 | 4 | no | — |
| 254 | #550 | — | 71 | 4 | no | — |
| 255 | #547 | — | 142 | 2 | no | — |
| 256 | #541 | — | 2 | 2 | no | — |
| 257 | #540 | — | 71 | 4 | no | — |
| 258 | #537 | — | 142 | 4 | no | — |
| 259 | #536 | C2×D71 | 1 | 2 | yes | — |
| 260 | #533 | — | 2 | 2 | no | — |
| 261 | #533 | C2×D71 | 1 | 1 | yes | characteristic |
| 262 | #532 | — | 71 | 2 | no | — |
| 263 | C2×C4⋊Q8 | C2×D71 | 1 | 1 | yes | characteristic |
| 264 | #519 | C2×D71 | 1 | 2 | yes | — |
| 265 | C4×#41 | C2×D71 | 1 | 1 | yes | characteristic |
| 266 | #496 | — | 71 | 4 | no | — |
| 267 | #492 | — | 71 | 4 | no | — |
| 268 | #492 | — | 71 | 4 | no | — |
| 269 | #491 | — | 71 | 4 | no | — |
| 270 | #488 | — | 71 | 4 | no | — |
| 271 | #487 | — | 71 | 4 | no | — |
| 272 | #482 | — | 71 | 4 | no | — |
| 273 | #479 | — | 71 | 8 | no | — |
| 274 | #477 | — | 71 | 2 | no | — |
| 275 | #476 | — | 71 | 2 | no | — |
| 276 | #463 | — | 71 | 8 | no | — |
| 277 | #461 | — | 71 | 4 | no | — |
| 278 | #461 | — | 71 | 8 | no | — |
| 279 | #461 | — | 71 | 4 | no | — |
| 280 | #460 | — | 71 | 2 | no | — |
| 281 | #460 | — | 71 | 8 | no | — |
| 282 | #459 | — | 71 | 2 | no | — |
| 283 | #449 | — | 71 | 4 | no | — |
| 284 | #448 | — | 71 | 8 | no | — |
| 285 | #446 | — | 71 | 4 | no | — |
| 286 | C8×Q8 | — | 71 | 4 | no | — |
| 287 | #440 | — | 71 | 8 | no | — |
| 288 | C4×SD16 | — | 71 | 8 | no | — |
| 289 | C4×SD16 | — | 71 | 4 | no | — |
| 290 | C4×D8 | — | 71 | 4 | no | — |
| 291 | #433 | — | 71 | 4 | no | — |
| 292 | #431 | — | 71 | 2 | no | — |
| 293 | C2×#41 | — | 142 | 4 | no | — |
| 294 | C2×#41 | — | 142 | 2 | no | — |
| 295 | C2×#41 | C22×D71 | 1 | 1 | yes | characteristic |
| 296 | C22×Q8 | C22×D71 | 1 | 2 | yes | — |
| 297 | C2×SD16 | — | 71 | 8 | no | — |
| 298 | C2×SD16 | — | 71 | 4 | no | — |
| 299 | C2×SD16 | — | 71 | 8 | no | — |
| 300 | C2×D8 | — | 71 | 4 | no | — |
| 301 | C4⋊Q8 | — | 2 | 1 | no | — |
| 302 | C4⋊Q8 | — | 2 | 1 | no | — |
| 303 | C4⋊Q8 | — | 71 | 2 | no | — |
| 304 | C4⋊Q8 | C22⋊D71 | 1 | 2 | yes | — |
| 305 | C4⋊Q8 | C22×D71 | 1 | 4 | yes | — |
| 306 | C4⋊Q8 | C22×D71 | 1 | 4 | yes | — |
| 307 | #127 | — | 71 | 2 | no | — |
| 308 | #127 | — | 71 | 4 | no | — |
| 309 | #126 | — | 2 | 8 | no | — |
| 310 | #125 | — | 2 | 4 | no | — |
| 311 | #125 | — | 2 | 8 | no | — |
| 312 | #125 | — | 71 | 4 | no | — |
| 313 | #125 | C22⋊D71 | 1 | 2 | yes | — |
| 314 | #124 | — | 142 | 2 | no | — |
| 315 | #124 | C22×D71 | 1 | 4 | yes | — |
| 316 | #123 | — | 2 | 4 | no | — |
| 317 | #123 | — | 142 | 8 | no | — |
| 318 | C22⋊Q8 | — | 2 | 4 | no | — |
| 319 | C22⋊Q8 | — | 2 | 4 | no | — |
| 320 | C22⋊Q8 | — | 142 | 4 | no | — |
| 321 | C22⋊Q8 | — | 142 | 8 | no | — |
| 322 | C22⋊Q8 | C22⋊D71 | 1 | 4 | yes | — |
| 323 | #121 | — | 71 | 4 | no | — |
| 324 | #121 | — | 142 | 2 | no | — |
| 325 | #121 | — | 142 | 4 | no | — |
| 326 | #121 | — | 142 | 8 | no | — |
| 327 | #121 | — | 142 | 8 | no | — |
| 328 | C4×Q8 | — | 2 | 4 | no | — |
| 329 | C4×Q8 | — | 2 | 4 | no | — |
| 330 | C4×Q8 | C22×D71 | 1 | 2 | yes | — |
| 331 | C4×Q8 | C22×D71 | 1 | 8 | yes | — |
| 332 | C4×Q8 | C22×D71 | 1 | 4 | yes | — |
| 333 | C4×D4 | — | 2 | 2 | no | — |
| 334 | C4×D4 | — | 71 | 4 | no | — |
| 335 | C4×D4 | — | 71 | 8 | no | — |
| 336 | C4×D4 | — | 142 | 2 | no | — |
| 337 | C4×D4 | C22×D71 | 1 | 2 | yes | — |
| 338 | #117 | — | 2 | 4 | no | — |
| 339 | #117 | — | 2 | 4 | no | — |
| 340 | #117 | — | 2 | 1 | no | — |
| 341 | #117 | C22×D71 | 1 | 1 | yes | characteristic |
| 342 | #117 | C22×D71 | 1 | 2 | yes | — |
| 343 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 344 | C2×C4⋊C4 | — | 142 | 4 | no | — |
| 345 | C2×C42 | — | 2 | 1 | no | — |
| 346 | C2×C42 | C22×D71 | 1 | 1 | yes | characteristic |
| 347 | #107 | — | 71 | 4 | no | — |
| 348 | #106 | — | 71 | 4 | no | — |
| 349 | C4⋊C8 | — | 71 | 2 | no | — |
| 350 | C4⋊C8 | — | 71 | 2 | no | — |
| 351 | C4⋊C8 | — | 71 | 8 | no | — |
| 352 | #103 | — | 71 | 8 | no | — |
| 353 | #103 | — | 71 | 4 | no | — |
| 354 | #103 | — | 71 | 8 | no | — |
| 355 | #102 | — | 71 | 4 | no | — |
| 356 | #102 | — | 71 | 4 | no | — |
| 357 | #102 | — | 71 | 4 | no | — |
| 358 | C22⋊C8 | — | 71 | 4 | no | — |
| 359 | #97 | — | 71 | 4 | no | — |
| 360 | C4×C8 | — | 71 | 4 | no | — |
| 361 | C4×C8 | — | 71 | 4 | no | — |
| 362 | #41 | — | 4 | 2 | no | — |
| 363 | #41 | — | 568 | 4 | no | — |
| 364 | #41 | — | 568 | 8 | no | — |
| 365 | C2×Q8 | — | 2 | 2 | no | — |
| 366 | C2×Q8 | — | 4 | 4 | no | — |
| 367 | C2×Q8 | — | 142 | 2 | no | — |
| 368 | C2×Q8 | C2×C22⋊D71 | 1 | 4 | yes | — |
| 369 | C2×Q8 | C23×D71 | 1 | 4 | yes | — |
| 370 | C2×Q8 | C23×D71 | 1 | 1 | yes | characteristic |
| 371 | C2×D4 | — | 2 | 1 | no | — |
| 372 | C2×D4 | — | 71 | 4 | no | — |
| 373 | C2×D4 | — | 142 | 4 | no | — |
| 374 | C2×D4 | — | 142 | 2 | no | — |
| 375 | C2×D4 | — | 142 | 8 | no | — |
| 376 | C2×D4 | — | 142 | 2 | no | — |
| 377 | C2×D4 | C23×D71 | 1 | 1 | yes | characteristic |
| 378 | C22×C4 | — | 2 | 2 | no | — |
| 379 | C22×C4 | — | 2 | 2 | no | — |
| 380 | C22×C4 | — | 2 | 1 | no | — |
| 381 | C22×C4 | — | 142 | 4 | no | — |
| 382 | C22×C4 | — | 142 | 8 | no | — |
| 383 | C22×C4 | C2×C22⋊D71 | 1 | 2 | yes | — |
| 384 | C22×C4 | C23×D71 | 1 | 1 | yes | characteristic |
| 385 | SD16 | — | 284 | 8 | no | — |
| 386 | SD16 | — | 284 | 8 | no | — |
| 387 | SD16 | — | 284 | 4 | no | — |
| 388 | D8 | — | 284 | 4 | no | — |
| 389 | C2×C8 | — | 71 | 4 | no | — |
| 390 | C2×C8 | — | 71 | 4 | no | — |
| 391 | C4⋊C4 | — | 2 | 4 | no | — |
| 392 | C4⋊C4 | — | 2 | 4 | no | — |
| 393 | C4⋊C4 | — | 2 | 2 | no | — |
| 394 | C4⋊C4 | — | 2 | 8 | no | — |
| 395 | C4⋊C4 | — | 2 | 8 | no | — |
| 396 | C4⋊C4 | — | 71 | 4 | no | — |
| 397 | C4⋊C4 | — | 142 | 8 | no | — |
| 398 | C4⋊C4 | — | 142 | 2 | no | — |
| 399 | C4⋊C4 | C2×C22⋊D71 | 1 | 4 | yes | — |
| 400 | C4⋊C4 | C2×C22⋊D71 | 1 | 4 | yes | — |
| 401 | C4⋊C4 | C2×C22⋊D71 | 1 | 8 | yes | — |
| 402 | C4⋊C4 | C23×D71 | 1 | 2 | yes | — |
| 403 | C22⋊C4 | — | 2 | 1 | no | — |
| 404 | C22⋊C4 | — | 2 | 2 | no | — |
| 405 | C22⋊C4 | — | 2 | 8 | no | — |
| 406 | C22⋊C4 | — | 142 | 8 | no | — |
| 407 | C22⋊C4 | — | 142 | 4 | no | — |
| 408 | C22⋊C4 | — | 142 | 4 | no | — |
| 409 | C22⋊C4 | C2×C22⋊D71 | 1 | 4 | yes | — |
| 410 | C42 | — | 2 | 1 | no | — |
| 411 | C42 | — | 2 | 2 | no | — |
| 412 | C42 | — | 2 | 8 | no | — |
| 413 | C42 | C2×C22⋊D71 | 1 | 1 | yes | characteristic |
| 414 | C42 | C2×C22⋊D71 | 1 | 1 | yes | characteristic |
| 415 | C42 | C23×D71 | 1 | 2 | yes | — |
| 416 | C42 | C23×D71 | 1 | 4 | yes | — |
| 417 | C23 | — | 2 | 1 | no | — |
| 418 | C23 | — | 142 | 4 | no | — |
| 419 | C23 | C22×C22⋊D71 | 1 | 1 | yes | characteristic |
| 420 | Q8 | — | 2 | 8 | no | — |
| 421 | Q8 | — | 2 | 8 | no | — |
| 422 | Q8 | — | 2 | 2 | no | — |
| 423 | Q8 | — | 4 | 4 | no | — |
| 424 | Q8 | — | 568 | 2 | no | — |
| 425 | D4 | — | 2 | 2 | no | — |
| 426 | D4 | — | 4 | 2 | no | — |
| 427 | D4 | — | 284 | 4 | no | — |
| 428 | D4 | — | 568 | 2 | no | — |
| 429 | D4 | — | 568 | 8 | no | — |
| 430 | D4 | — | 568 | 4 | no | — |
| 431 | D4 | — | 142 | 4 | no | — |
| 432 | D4 | — | 142 | 4 | no | — |
| 433 | C2×C4 | — | 2 | 2 | no | — |
| 434 | C2×C4 | — | 2 | 4 | no | — |
| 435 | C2×C4 | — | 2 | 2 | no | — |
| 436 | C2×C4 | — | 2 | 4 | no | — |
| 437 | C2×C4 | — | 2 | 1 | no | — |
| 438 | C2×C4 | — | 4 | 2 | no | — |
| 439 | C2×C4 | — | 4 | 4 | no | — |
| 440 | C2×C4 | — | 4 | 4 | no | — |
| 441 | C2×C4 | — | 284 | 8 | no | — |
| 442 | C2×C4 | — | 568 | 8 | no | — |
| 443 | C2×C4 | — | 142 | 4 | no | — |
| 444 | C2×C4 | C22×C22⋊D71 | 1 | 1 | yes | characteristic |
| 445 | C2×C4 | C22×C22⋊D71 | 1 | 8 | yes | — |
| 446 | C2×C4 | C22×C22⋊D71 | 1 | 2 | yes | — |
| 447 | C2×C4 | C22×C22⋊D71 | 1 | 2 | yes | — |
| 448 | C2×C4 | C24×D71 | 1 | 1 | yes | characteristic |
| 449 | C8 | — | 142 | 4 | no | — |
| 450 | C8 | — | 142 | 4 | no | — |
| 451 | C22 | — | 2 | 1 | no | — |
| 452 | C22 | — | 2 | 2 | no | — |
| 453 | C22 | — | 4 | 1 | no | — |
| 454 | C22 | — | 4 | 2 | no | — |
| 455 | C22 | — | 284 | 4 | no | — |
| 456 | C22 | — | 284 | 4 | no | — |
| 457 | C22 | — | 284 | 4 | no | — |
| 458 | C22 | C23×C22⋊D71 | 1 | 1 | yes | characteristic |
| 459 | C4 | — | 2 | 1 | no | — |
| 460 | C4 | — | 2 | 2 | no | — |
| 461 | C4 | — | 2 | 8 | no | — |
| 462 | C4 | — | 4 | 1 | no | — |
| 463 | C4 | — | 4 | 4 | no | — |
| 464 | C4 | — | 4 | 2 | no | — |
| 465 | C4 | — | 284 | 4 | no | — |
| 466 | C4 | #17986807 | 1 | 4 | yes | — |
| 467 | C4 | #17986835 | 1 | 2 | yes | — |
| 468 | C2 | — | 4 | 1 | no | — |
| 469 | C2 | — | 8 | 1 | no | — |
| 470 | C2 | — | 568 | 4 | no | — |
| 471 | C2 | #22601998 | 1 | 1 | yes | characteristic |
| 472 | C2 | C2×#17986807 | 1 | 2 | yes | — |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta