← #32887706
Subgroups — #32887706
Order 18176.
1668 conjugacy classes of subgroups.
The subgroup lattice has 812 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×#17986727 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #22601303 | C2 | 1 | 4 | yes | maximal, complemented |
| 3 | #22601261 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #22601227 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #22601176 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #22601139 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #22601021 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #22599567 | C2 | 1 | 1 | yes | maximal, characteristic |
| 9 | #22599542 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #22599504 | C2 | 1 | 2 | yes | maximal |
| 11 | #22599488 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #22598507 | C2 | 1 | 2 | yes | maximal |
| 13 | #22598466 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #22598416 | C2 | 1 | 1 | yes | maximal, characteristic |
| 15 | #22598375 | C2 | 1 | 2 | yes | maximal, complemented |
| 16 | #22597429 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 17 | C71×#3523 | C2 | 1 | 1 | yes | maximal, characteristic |
| 18 | #17986727 | — | 2 | 1 | no | — |
| 19 | #17986727 | — | 2 | 2 | no | — |
| 20 | #17986727 | — | 2 | 1 | no | — |
| 21 | #17986727 | C22 | 1 | 2 | yes | — |
| 22 | #17986727 | C22 | 1 | 2 | yes | — |
| 23 | #17986727 | C22 | 1 | 4 | yes | — |
| 24 | C2×#14556128 | C22 | 1 | 1 | yes | characteristic |
| 25 | C2×#14556126 | — | 2 | 1 | no | — |
| 26 | C2×#14556120 | C22 | 1 | 2 | yes | — |
| 27 | C2×#14556118 | — | 2 | 2 | no | — |
| 28 | C2×C4×Dic142 | C22 | 1 | 1 | yes | characteristic |
| 29 | C2×C4×Dic142 | C22 | 1 | 2 | yes | — |
| 30 | C2×#14556093 | — | 2 | 1 | no | — |
| 31 | #17986409 | C22 | 1 | 2 | yes | — |
| 32 | #17986405 | C22 | 1 | 4 | yes | — |
| 33 | #17986402 | C22 | 1 | 2 | yes | — |
| 34 | #17986398 | C22 | 1 | 4 | yes | — |
| 35 | #17986367 | C22 | 1 | 4 | yes | — |
| 36 | #17986358 | C22 | 1 | 2 | yes | — |
| 37 | #17986353 | C22 | 1 | 4 | yes | — |
| 38 | #17986349 | C22 | 1 | 2 | yes | — |
| 39 | #17986332 | C22 | 1 | 2 | yes | — |
| 40 | #17986332 | C22 | 1 | 2 | yes | — |
| 41 | #17986332 | C22 | 1 | 2 | yes | — |
| 42 | #17986327 | C22 | 1 | 1 | yes | characteristic |
| 43 | #17986327 | C22 | 1 | 2 | yes | — |
| 44 | #17986315 | C22 | 1 | 2 | yes | — |
| 45 | #17986310 | C22 | 1 | 1 | yes | characteristic |
| 46 | #17986306 | C22 | 1 | 4 | yes | — |
| 47 | #17986306 | C22 | 1 | 4 | yes | — |
| 48 | #17986306 | C22 | 1 | 4 | yes | — |
| 49 | #17986303 | C22 | 1 | 4 | yes | — |
| 50 | #17986303 | C22 | 1 | 2 | yes | — |
| 51 | #17986299 | C22 | 1 | 4 | yes | — |
| 52 | #17986294 | C22 | 1 | 4 | yes | — |
| 53 | #17986291 | C22 | 1 | 4 | yes | — |
| 54 | #17986284 | C22 | 1 | 2 | yes | — |
| 55 | #17986281 | C22 | 1 | 2 | yes | — |
| 56 | #17986279 | C22 | 1 | 2 | yes | — |
| 57 | #17986218 | C22 | 1 | 2 | yes | — |
| 58 | #17986218 | C22 | 1 | 4 | yes | — |
| 59 | #17986206 | C22 | 1 | 2 | yes | — |
| 60 | #17986206 | C22 | 1 | 4 | yes | — |
| 61 | #17986154 | C22 | 1 | 1 | yes | characteristic |
| 62 | #17986154 | C22 | 1 | 2 | yes | — |
| 63 | #17986137 | C22 | 1 | 1 | yes | characteristic |
| 64 | #17986130 | C22 | 1 | 2 | yes | — |
| 65 | #17986130 | C22 | 1 | 4 | yes | — |
| 66 | Q8×C71⋊C8 | C22 | 1 | 2 | yes | — |
| 67 | #17986104 | C22 | 1 | 4 | yes | — |
| 68 | #17986104 | C22 | 1 | 4 | yes | — |
| 69 | #17986099 | C22 | 1 | 4 | yes | — |
| 70 | C4×#11765855 | C22 | 1 | 2 | yes | — |
| 71 | C4×#11765855 | C22 | 1 | 4 | yes | — |
| 72 | C4×#11765855 | C22 | 1 | 4 | yes | — |
| 73 | C4×#11765853 | C22 | 1 | 2 | yes | — |
| 74 | #17986056 | C22 | 1 | 1 | yes | characteristic |
| 75 | #17986056 | C22 | 1 | 2 | yes | — |
| 76 | #17986052 | C22 | 1 | 1 | yes | characteristic |
| 77 | #17986052 | C22 | 1 | 2 | yes | — |
| 78 | #557×C71 | C22 | 1 | 1 | yes | characteristic |
| 79 | #557×C71 | C22 | 1 | 1 | yes | characteristic |
| 80 | #557×C71 | C22 | 1 | 2 | yes | — |
| 81 | #556×C71 | C22 | 1 | 1 | yes | characteristic |
| 82 | #556×C71 | C22 | 1 | 2 | yes | — |
| 83 | #552×C71 | — | 2 | 1 | no | — |
| 84 | #552×C71 | — | 2 | 2 | no | — |
| 85 | D4×Q8×C71 | — | 2 | 1 | no | — |
| 86 | D4×Q8×C71 | C22 | 1 | 1 | yes | characteristic |
| 87 | #541×C71 | — | 2 | 2 | no | — |
| 88 | #541×C71 | — | 2 | 1 | no | — |
| 89 | #533×C71 | C22 | 1 | 1 | yes | characteristic |
| 90 | #533×C71 | C22 | 1 | 2 | yes | — |
| 91 | #529×C71 | C22 | 1 | 1 | yes | characteristic |
| 92 | #529×C71 | C22 | 1 | 2 | yes | — |
| 93 | #519×C71 | — | 2 | 1 | no | — |
| 94 | C2×C4×Q8×C71 | C22 | 1 | 1 | yes | characteristic |
| 95 | C22×Dic142 | — | 2 | 1 | no | — |
| 96 | C22×Dic142 | C23 | 1 | 1 | yes | characteristic |
| 97 | C2×#11765855 | C23 | 1 | 2 | yes | — |
| 98 | C2×#11765855 | C23 | 1 | 4 | yes | — |
| 99 | C2×#11765853 | C23 | 1 | 2 | yes | — |
| 100 | #14556128 | — | 2 | 1 | no | — |
| 101 | #14556128 | — | 2 | 1 | no | — |
| 102 | #14556128 | C23 | 1 | 2 | yes | — |
| 103 | #14556128 | C23 | 1 | 2 | yes | — |
| 104 | #14556126 | — | 2 | 2 | no | — |
| 105 | #14556126 | — | 2 | 2 | no | — |
| 106 | #14556126 | — | 2 | 4 | no | — |
| 107 | #14556120 | — | 2 | 2 | no | — |
| 108 | #14556120 | — | 2 | 2 | no | — |
| 109 | #14556120 | C23 | 1 | 4 | yes | — |
| 110 | #14556120 | C23 | 1 | 4 | yes | — |
| 111 | #14556118 | — | 2 | 4 | no | — |
| 112 | #14556118 | — | 2 | 4 | no | — |
| 113 | #14556118 | — | 2 | 4 | no | — |
| 114 | #14556118 | — | 2 | 4 | no | — |
| 115 | C4×Dic142 | — | 2 | 2 | no | — |
| 116 | C4×Dic142 | — | 2 | 1 | no | — |
| 117 | C4×Dic142 | — | 2 | 2 | no | — |
| 118 | C4×Dic142 | — | 2 | 1 | no | — |
| 119 | C4×Dic142 | C23 | 1 | 2 | yes | — |
| 120 | C4×Dic142 | C23 | 1 | 4 | yes | — |
| 121 | C4×Dic142 | C23 | 1 | 4 | yes | — |
| 122 | C4×Dic142 | C23 | 1 | 2 | yes | — |
| 123 | #14556093 | — | 2 | 2 | no | — |
| 124 | #14556093 | — | 2 | 2 | no | — |
| 125 | #14556093 | — | 2 | 4 | no | — |
| 126 | C2×C4⋊Dic71 | — | 2 | 1 | no | — |
| 127 | C2×C4⋊Dic71 | C23 | 1 | 1 | yes | characteristic |
| 128 | C2×C4⋊Dic71 | C23 | 1 | 2 | yes | — |
| 129 | C2×Dic71⋊C4 | — | 2 | 2 | no | — |
| 130 | C2×Dic71⋊C4 | — | 2 | 1 | no | — |
| 131 | C2×Dic71⋊C4 | — | 2 | 2 | no | — |
| 132 | C2×Dic71⋊C4 | — | 2 | 2 | no | — |
| 133 | C2×C4×Dic71 | — | 2 | 2 | no | — |
| 134 | C2×C4×Dic71 | — | 2 | 1 | no | — |
| 135 | #14556061 | C23 | 1 | 2 | yes | — |
| 136 | #14556061 | C23 | 1 | 4 | yes | — |
| 137 | #14556061 | C23 | 1 | 4 | yes | — |
| 138 | #14556061 | C23 | 1 | 4 | yes | — |
| 139 | #14556059 | C23 | 1 | 2 | yes | — |
| 140 | #14556059 | C23 | 1 | 4 | yes | — |
| 141 | #14556059 | C23 | 1 | 4 | yes | — |
| 142 | C4⋊(C71⋊C8) | C23 | 1 | 4 | yes | — |
| 143 | C4⋊(C71⋊C8) | C23 | 1 | 4 | yes | — |
| 144 | C4⋊(C71⋊C8) | C23 | 1 | 2 | yes | — |
| 145 | C4⋊(C71⋊C8) | C23 | 1 | 2 | yes | — |
| 146 | #14556052 | C23 | 1 | 2 | yes | — |
| 147 | #14556052 | C23 | 1 | 4 | yes | — |
| 148 | #14556052 | C23 | 1 | 4 | yes | — |
| 149 | #14556052 | C23 | 1 | 4 | yes | — |
| 150 | #14556052 | C23 | 1 | 4 | yes | — |
| 151 | #14556051 | C23 | 1 | 2 | yes | — |
| 152 | #14556051 | C23 | 1 | 4 | yes | — |
| 153 | #14556051 | C23 | 1 | 2 | yes | — |
| 154 | #14556049 | C23 | 1 | 2 | yes | — |
| 155 | #14556049 | C23 | 1 | 4 | yes | — |
| 156 | C22⋊(C71⋊C8) | C23 | 1 | 1 | yes | characteristic |
| 157 | C22⋊(C71⋊C8) | C23 | 1 | 2 | yes | — |
| 158 | C22⋊(C71⋊C8) | C23 | 1 | 1 | yes | characteristic |
| 159 | #14556039 | C23 | 1 | 4 | yes | — |
| 160 | #14556039 | C23 | 1 | 2 | yes | — |
| 161 | C4×C71⋊C8 | C23 | 1 | 2 | yes | — |
| 162 | C4×C71⋊C8 | C23 | 1 | 4 | yes | — |
| 163 | C22×Q8×C71 | — | 2 | 1 | no | — |
| 164 | C22×Q8×C71 | D4 | 1 | 1 | yes | characteristic |
| 165 | C4⋊Q8×C71 | — | 2 | 1 | no | — |
| 166 | C4⋊Q8×C71 | — | 2 | 2 | no | — |
| 167 | C4⋊Q8×C71 | C23 | 1 | 1 | yes | characteristic |
| 168 | C4⋊Q8×C71 | C23 | 1 | 2 | yes | — |
| 169 | C4⋊Q8×C71 | C23 | 1 | 1 | yes | characteristic |
| 170 | C4⋊Q8×C71 | C23 | 1 | 2 | yes | — |
| 171 | #126×C71 | — | 2 | 2 | no | — |
| 172 | #126×C71 | — | 2 | 2 | no | — |
| 173 | #126×C71 | — | 2 | 2 | no | — |
| 174 | #126×C71 | — | 2 | 2 | no | — |
| 175 | #126×C71 | — | 2 | 1 | no | — |
| 176 | #125×C71 | — | 2 | 2 | no | — |
| 177 | #125×C71 | — | 2 | 2 | no | — |
| 178 | #125×C71 | — | 2 | 2 | no | — |
| 179 | #125×C71 | — | 2 | 1 | no | — |
| 180 | #125×C71 | — | 2 | 2 | no | — |
| 181 | #125×C71 | — | 2 | 2 | no | — |
| 182 | #125×C71 | — | 2 | 1 | no | — |
| 183 | #125×C71 | C23 | 1 | 2 | yes | — |
| 184 | #125×C71 | C23 | 1 | 1 | yes | characteristic |
| 185 | #124×C71 | C23 | 1 | 2 | yes | — |
| 186 | #124×C71 | C23 | 1 | 1 | yes | characteristic |
| 187 | #123×C71 | — | 2 | 2 | no | — |
| 188 | #123×C71 | — | 2 | 1 | no | — |
| 189 | C22⋊Q8×C71 | — | 2 | 1 | no | — |
| 190 | C22⋊Q8×C71 | — | 2 | 2 | no | — |
| 191 | C22⋊Q8×C71 | — | 2 | 1 | no | — |
| 192 | C22⋊Q8×C71 | — | 2 | 2 | no | — |
| 193 | C22⋊Q8×C71 | — | 2 | 1 | no | — |
| 194 | C22⋊Q8×C71 | — | 2 | 2 | no | — |
| 195 | C22⋊Q8×C71 | C23 | 1 | 1 | yes | characteristic |
| 196 | C22⋊Q8×C71 | C23 | 1 | 2 | yes | — |
| 197 | #121×C71 | C23 | 1 | 1 | yes | characteristic |
| 198 | C4×Q8×C71 | — | 2 | 1 | no | — |
| 199 | C4×Q8×C71 | — | 2 | 1 | no | — |
| 200 | C4×Q8×C71 | — | 2 | 2 | no | — |
| 201 | C4×Q8×C71 | — | 2 | 2 | no | — |
| 202 | C4×Q8×C71 | — | 2 | 1 | no | — |
| 203 | C4×Q8×C71 | D4 | 1 | 1 | yes | characteristic |
| 204 | C4×Q8×C71 | D4 | 1 | 2 | yes | — |
| 205 | C4×Q8×C71 | D4 | 1 | 1 | yes | characteristic |
| 206 | C4×Q8×C71 | C23 | 1 | 2 | yes | — |
| 207 | C4×Q8×C71 | C23 | 1 | 2 | yes | — |
| 208 | C4×Q8×C71 | C23 | 1 | 2 | yes | — |
| 209 | C4×Q8×C71 | C23 | 1 | 1 | yes | characteristic |
| 210 | C4×Q8×C71 | C23 | 1 | 2 | yes | — |
| 211 | C4×Q8×C71 | C23 | 1 | 1 | yes | characteristic |
| 212 | C4×Q8×C71 | C23 | 1 | 1 | yes | characteristic |
| 213 | C4×Q8×C71 | C23 | 1 | 2 | yes | — |
| 214 | C4×D4×C71 | — | 2 | 1 | no | — |
| 215 | C4×D4×C71 | — | 2 | 2 | no | — |
| 216 | C4×D4×C71 | C23 | 1 | 1 | yes | characteristic |
| 217 | C4×D4×C71 | C23 | 1 | 2 | yes | — |
| 218 | #117×C71 | — | 2 | 2 | no | — |
| 219 | #117×C71 | — | 2 | 1 | no | — |
| 220 | #117×C71 | — | 2 | 1 | no | — |
| 221 | #117×C71 | — | 2 | 2 | no | — |
| 222 | #117×C71 | — | 2 | 2 | no | — |
| 223 | #117×C71 | — | 2 | 1 | no | — |
| 224 | C2×C4⋊C4×C71 | D4 | 1 | 1 | yes | characteristic |
| 225 | C2×C4⋊C4×C71 | D4 | 1 | 2 | yes | — |
| 226 | C2×C42×C71 | C23 | 1 | 2 | yes | — |
| 227 | C2×C42×C71 | C23 | 1 | 1 | yes | characteristic |
| 228 | C2×Dic142 | — | 2 | 1 | no | — |
| 229 | C2×Dic142 | — | 2 | 4 | no | — |
| 230 | C2×Dic142 | — | 2 | 2 | no | — |
| 231 | C2×Dic142 | — | 2 | 2 | no | — |
| 232 | C2×Dic142 | — | 4 | 4 | no | — |
| 233 | C2×Dic142 | C24 | 1 | 2 | yes | — |
| 234 | C22×Dic71 | — | 2 | 1 | no | — |
| 235 | C22×Dic71 | — | 2 | 2 | no | — |
| 236 | C22×Dic71 | — | 2 | 1 | no | — |
| 237 | #11765855 | — | 2 | 4 | no | — |
| 238 | #11765855 | — | 2 | 8 | no | — |
| 239 | #11765853 | — | 2 | 4 | no | — |
| 240 | C2×C71⋊C8 | C24 | 1 | 2 | yes | — |
| 241 | C2×C71⋊C8 | C24 | 1 | 4 | yes | — |
| 242 | C2×C71⋊C8 | C24 | 1 | 2 | yes | — |
| 243 | C4⋊Dic71 | — | 2 | 2 | no | — |
| 244 | C4⋊Dic71 | — | 2 | 2 | no | — |
| 245 | C4⋊Dic71 | — | 2 | 1 | no | — |
| 246 | C4⋊Dic71 | — | 2 | 2 | no | — |
| 247 | C4⋊Dic71 | C24 | 1 | 2 | yes | — |
| 248 | C4⋊Dic71 | C24 | 1 | 4 | yes | — |
| 249 | Dic71⋊C4 | — | 2 | 4 | no | — |
| 250 | Dic71⋊C4 | — | 2 | 4 | no | — |
| 251 | Dic71⋊C4 | — | 2 | 2 | no | — |
| 252 | Dic71⋊C4 | — | 2 | 2 | no | — |
| 253 | Dic71⋊C4 | — | 2 | 4 | no | — |
| 254 | Dic71⋊C4 | — | 2 | 4 | no | — |
| 255 | Dic71⋊C4 | — | 2 | 4 | no | — |
| 256 | Dic71⋊C4 | — | 2 | 4 | no | — |
| 257 | C4×Dic71 | — | 2 | 4 | no | — |
| 258 | C4×Dic71 | — | 2 | 4 | no | — |
| 259 | C4×Dic71 | — | 2 | 2 | no | — |
| 260 | C4×Dic71 | — | 2 | 2 | no | — |
| 261 | C2×Q8×C71 | — | 2 | 2 | no | — |
| 262 | C2×Q8×C71 | — | 2 | 1 | no | — |
| 263 | C2×Q8×C71 | — | 4 | 2 | no | — |
| 264 | C2×Q8×C71 | — | 4 | 4 | no | — |
| 265 | C2×Q8×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 266 | C2×Q8×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 267 | C2×Q8×C71 | C2×D4 | 1 | 2 | yes | — |
| 268 | C2×Q8×C71 | C24 | 1 | 1 | yes | characteristic |
| 269 | C2×Q8×C71 | C24 | 1 | 2 | yes | — |
| 270 | C2×D4×C71 | — | 2 | 1 | no | — |
| 271 | C2×D4×C71 | C24 | 1 | 1 | yes | characteristic |
| 272 | C22×C4×C71 | — | 2 | 2 | no | — |
| 273 | C22×C4×C71 | — | 2 | 1 | no | — |
| 274 | C22×C4×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 275 | C22×C4×C71 | C2×D4 | 1 | 2 | yes | — |
| 276 | C22×C4×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 277 | C22×C4×C71 | C2×D4 | 1 | 2 | yes | — |
| 278 | C22×C4×C71 | C24 | 1 | 1 | yes | characteristic |
| 279 | C4⋊C4×C71 | — | 2 | 2 | no | — |
| 280 | C4⋊C4×C71 | — | 2 | 1 | no | — |
| 281 | C4⋊C4×C71 | — | 2 | 2 | no | — |
| 282 | C4⋊C4×C71 | — | 2 | 1 | no | — |
| 283 | C4⋊C4×C71 | — | 2 | 2 | no | — |
| 284 | C4⋊C4×C71 | — | 2 | 1 | no | — |
| 285 | C4⋊C4×C71 | — | 2 | 2 | no | — |
| 286 | C4⋊C4×C71 | — | 2 | 1 | no | — |
| 287 | C4⋊C4×C71 | — | 2 | 2 | no | — |
| 288 | C4⋊C4×C71 | — | 2 | 1 | no | — |
| 289 | C4⋊C4×C71 | — | 2 | 1 | no | — |
| 290 | C4⋊C4×C71 | — | 2 | 2 | no | — |
| 291 | C4⋊C4×C71 | — | 2 | 2 | no | — |
| 292 | C4⋊C4×C71 | — | 2 | 2 | no | — |
| 293 | C4⋊C4×C71 | — | 2 | 2 | no | — |
| 294 | C4⋊C4×C71 | — | 2 | 2 | no | — |
| 295 | C4⋊C4×C71 | — | 2 | 1 | no | — |
| 296 | C4⋊C4×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 297 | C4⋊C4×C71 | C2×D4 | 1 | 2 | yes | — |
| 298 | C4⋊C4×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 299 | C4⋊C4×C71 | C2×D4 | 1 | 2 | yes | — |
| 300 | C4⋊C4×C71 | C2×D4 | 1 | 2 | yes | — |
| 301 | C4⋊C4×C71 | C2×D4 | 1 | 2 | yes | — |
| 302 | C4⋊C4×C71 | C2×D4 | 1 | 2 | yes | — |
| 303 | C4⋊C4×C71 | C24 | 1 | 1 | yes | characteristic |
| 304 | C4⋊C4×C71 | C24 | 1 | 2 | yes | — |
| 305 | C4⋊C4×C71 | C24 | 1 | 1 | yes | characteristic |
| 306 | C22⋊C4×C71 | — | 2 | 1 | no | — |
| 307 | C22⋊C4×C71 | — | 2 | 2 | no | — |
| 308 | C22⋊C4×C71 | — | 2 | 1 | no | — |
| 309 | C22⋊C4×C71 | — | 2 | 2 | no | — |
| 310 | C22⋊C4×C71 | — | 2 | 1 | no | — |
| 311 | C22⋊C4×C71 | — | 2 | 1 | no | — |
| 312 | C22⋊C4×C71 | — | 2 | 2 | no | — |
| 313 | C22⋊C4×C71 | — | 2 | 2 | no | — |
| 314 | C22⋊C4×C71 | — | 2 | 1 | no | — |
| 315 | C42×C71 | — | 2 | 2 | no | — |
| 316 | C42×C71 | — | 2 | 2 | no | — |
| 317 | C42×C71 | — | 2 | 2 | no | — |
| 318 | C42×C71 | — | 2 | 2 | no | — |
| 319 | C42×C71 | — | 2 | 1 | no | — |
| 320 | C42×C71 | C2×D4 | 1 | 2 | yes | — |
| 321 | C42×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 322 | C42×C71 | C2×D4 | 1 | 2 | yes | — |
| 323 | C42×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 324 | C42×C71 | C24 | 1 | 1 | yes | characteristic |
| 325 | C42×C71 | C24 | 1 | 2 | yes | — |
| 326 | C42×C71 | C24 | 1 | 2 | yes | — |
| 327 | C42×C71 | C24 | 1 | 1 | yes | characteristic |
| 328 | C23×C71 | — | 2 | 1 | no | — |
| 329 | C23×C71 | C22×D4 | 1 | 1 | yes | characteristic |
| 330 | Q8×C71 | — | 2 | 2 | no | — |
| 331 | Q8×C71 | — | 2 | 2 | no | — |
| 332 | Q8×C71 | — | 2 | 2 | no | — |
| 333 | Q8×C71 | — | 2 | 4 | no | — |
| 334 | Q8×C71 | — | 4 | 2 | no | — |
| 335 | Q8×C71 | — | 4 | 4 | no | — |
| 336 | Q8×C71 | — | 4 | 2 | no | — |
| 337 | D4×C71 | — | 2 | 2 | no | — |
| 338 | D4×C71 | — | 4 | 2 | no | — |
| 339 | C2×C4×C71 | — | 2 | 4 | no | — |
| 340 | C2×C4×C71 | — | 2 | 2 | no | — |
| 341 | C2×C4×C71 | — | 2 | 2 | no | — |
| 342 | C2×C4×C71 | — | 2 | 2 | no | — |
| 343 | C2×C4×C71 | — | 2 | 1 | no | — |
| 344 | C2×C4×C71 | — | 2 | 2 | no | — |
| 345 | C2×C4×C71 | — | 2 | 1 | no | — |
| 346 | C2×C4×C71 | — | 2 | 2 | no | — |
| 347 | C2×C4×C71 | — | 2 | 1 | no | — |
| 348 | C2×C4×C71 | — | 4 | 2 | no | — |
| 349 | C2×C4×C71 | — | 4 | 4 | no | — |
| 350 | C2×C4×C71 | — | 4 | 2 | no | — |
| 351 | C2×C4×C71 | C22×D4 | 1 | 2 | yes | — |
| 352 | C2×C4×C71 | C22×D4 | 1 | 1 | yes | characteristic |
| 353 | C2×C4×C71 | C22×D4 | 1 | 2 | yes | — |
| 354 | C2×C4×C71 | C22×D4 | 1 | 1 | yes | characteristic |
| 355 | C2×C4×C71 | C22×D4 | 1 | 2 | yes | — |
| 356 | C2×C4×C71 | C22×D4 | 1 | 1 | yes | characteristic |
| 357 | C2×C4×C71 | C22×D4 | 1 | 1 | yes | characteristic |
| 358 | C2×C4×C71 | C22×D4 | 1 | 2 | yes | — |
| 359 | C2×C4×C71 | C22×D4 | 1 | 1 | yes | characteristic |
| 360 | C2×C4×C71 | C25 | 1 | 1 | yes | characteristic |
| 361 | C2×Dic71 | — | 2 | 4 | no | — |
| 362 | C2×Dic71 | — | 2 | 2 | no | — |
| 363 | C2×Dic71 | — | 2 | 2 | no | — |
| 364 | C2×Dic71 | — | 2 | 4 | no | — |
| 365 | C2×Dic71 | — | 4 | 4 | no | — |
| 366 | C2×Dic71 | — | 4 | 2 | no | — |
| 367 | Dic142 | — | 2 | 4 | no | — |
| 368 | Dic142 | — | 2 | 2 | no | — |
| 369 | Dic142 | — | 4 | 4 | no | — |
| 370 | Dic142 | — | 4 | 4 | no | — |
| 371 | Dic142 | 2−1+4 | 1 | 4 | yes | — |
| 372 | C71⋊C8 | — | 2 | 2 | no | — |
| 373 | C71⋊C8 | — | 2 | 2 | no | — |
| 374 | C71⋊C8 | — | 2 | 4 | no | — |
| 375 | C22×C71 | — | 2 | 1 | no | — |
| 376 | C22×C71 | — | 2 | 1 | no | — |
| 377 | C22×C71 | — | 4 | 1 | no | — |
| 378 | C22×C71 | — | 4 | 1 | no | — |
| 379 | C22×C71 | — | 4 | 1 | no | — |
| 380 | C22×C71 | #578 | 1 | 2 | yes | — |
| 381 | C22×C71 | C23×D4 | 1 | 1 | yes | characteristic |
| 382 | C4×C71 | — | 2 | 1 | no | — |
| 383 | C4×C71 | — | 2 | 1 | no | — |
| 384 | C4×C71 | — | 2 | 2 | no | — |
| 385 | C4×C71 | — | 2 | 2 | no | — |
| 386 | C4×C71 | — | 2 | 2 | no | — |
| 387 | C4×C71 | — | 2 | 1 | no | — |
| 388 | C4×C71 | — | 2 | 2 | no | — |
| 389 | C4×C71 | — | 2 | 1 | no | — |
| 390 | C4×C71 | — | 4 | 1 | no | — |
| 391 | C4×C71 | — | 4 | 2 | no | — |
| 392 | C4×C71 | — | 4 | 2 | no | — |
| 393 | C4×C71 | — | 4 | 1 | no | — |
| 394 | C4×C71 | — | 4 | 1 | no | — |
| 395 | C4×C71 | #575 | 1 | 2 | yes | — |
| 396 | C4×C71 | C2×2−1+4 | 1 | 2 | yes | — |
| 397 | Dic71 | — | 2 | 4 | no | — |
| 398 | Dic71 | — | 4 | 4 | no | — |
| 399 | Dic71 | — | 4 | 2 | no | — |
| 400 | #61842 | — | 71 | 1 | no | maximal, Sylow |
| 401 | C2×C71 | — | 2 | 2 | no | — |
| 402 | C2×C71 | — | 8 | 1 | no | — |
| 403 | C2×C71 | #3486 | 1 | 1 | yes | characteristic |
| 404 | C2×C71 | C2×#575 | 1 | 1 | yes | characteristic |
| 405 | C2×C71 | C2×#578 | 1 | 1 | yes | characteristic |
| 406 | #3523 | D71 | 1 | 1 | yes | characteristic |
| 407 | C2×#557 | — | 71 | 1 | no | — |
| 408 | #3390 | — | 71 | 4 | no | — |
| 409 | #3386 | — | 71 | 2 | no | — |
| 410 | #3383 | — | 71 | 2 | no | — |
| 411 | #3377 | — | 71 | 4 | no | — |
| 412 | #3374 | — | 71 | 2 | no | — |
| 413 | #3364 | — | 71 | 2 | no | — |
| 414 | #3239 | — | 71 | 1 | no | — |
| 415 | #3236 | — | 71 | 2 | no | — |
| 416 | #3232 | — | 71 | 2 | no | — |
| 417 | #3230 | — | 71 | 1 | no | — |
| 418 | #3117 | — | 71 | 2 | no | — |
| 419 | #3113 | — | 71 | 1 | no | — |
| 420 | #3108 | — | 71 | 1 | no | — |
| 421 | #3104 | — | 71 | 2 | no | — |
| 422 | #2984 | — | 71 | 1 | no | — |
| 423 | C71 | #61842 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 424 | #557 | — | 71 | 2 | no | — |
| 425 | #557 | — | 71 | 2 | no | — |
| 426 | #557 | — | 71 | 4 | no | — |
| 427 | #557 | — | 142 | 1 | no | — |
| 428 | #557 | — | 142 | 1 | no | — |
| 429 | #557 | — | 142 | 2 | no | — |
| 430 | #557 | C2×D71 | 1 | 1 | yes | characteristic |
| 431 | #557 | C2×D71 | 1 | 1 | yes | characteristic |
| 432 | #557 | C2×D71 | 1 | 2 | yes | — |
| 433 | #556 | C2×D71 | 1 | 1 | yes | characteristic |
| 434 | #556 | C2×D71 | 1 | 2 | yes | — |
| 435 | #552 | — | 2 | 1 | no | — |
| 436 | #552 | — | 2 | 2 | no | — |
| 437 | D4×Q8 | — | 2 | 1 | no | — |
| 438 | D4×Q8 | C2×D71 | 1 | 1 | yes | characteristic |
| 439 | #541 | — | 2 | 2 | no | — |
| 440 | #541 | — | 2 | 1 | no | — |
| 441 | #533 | C2×D71 | 1 | 2 | yes | — |
| 442 | #533 | C2×D71 | 1 | 1 | yes | characteristic |
| 443 | C2×C4⋊Q8 | — | 71 | 1 | no | — |
| 444 | C2×C4⋊Q8 | — | 142 | 1 | no | — |
| 445 | #529 | C2×D71 | 1 | 1 | yes | characteristic |
| 446 | #529 | C2×D71 | 1 | 2 | yes | — |
| 447 | C2×#125 | — | 71 | 2 | no | — |
| 448 | C2×#125 | — | 142 | 2 | no | — |
| 449 | #519 | — | 2 | 1 | no | — |
| 450 | C2×C4×Q8 | — | 71 | 2 | no | — |
| 451 | C2×C4×Q8 | — | 71 | 1 | no | — |
| 452 | C2×C4×Q8 | — | 142 | 1 | no | — |
| 453 | C2×C4×Q8 | C2×D71 | 1 | 1 | yes | characteristic |
| 454 | #501 | — | 71 | 4 | no | — |
| 455 | #501 | — | 71 | 2 | no | — |
| 456 | #500 | — | 71 | 2 | no | — |
| 457 | #499 | — | 71 | 4 | no | — |
| 458 | #491 | — | 71 | 4 | no | — |
| 459 | #489 | — | 71 | 2 | no | — |
| 460 | #488 | — | 71 | 4 | no | — |
| 461 | #487 | — | 71 | 2 | no | — |
| 462 | #484 | — | 71 | 2 | no | — |
| 463 | #484 | — | 71 | 2 | no | — |
| 464 | #484 | — | 71 | 2 | no | — |
| 465 | #483 | — | 71 | 1 | no | — |
| 466 | #483 | — | 71 | 2 | no | — |
| 467 | #481 | — | 71 | 2 | no | — |
| 468 | #480 | — | 71 | 1 | no | — |
| 469 | #479 | — | 71 | 2 | no | — |
| 470 | #479 | — | 71 | 4 | no | — |
| 471 | #479 | — | 71 | 4 | no | — |
| 472 | #479 | — | 71 | 4 | no | — |
| 473 | #479 | — | 71 | 4 | no | — |
| 474 | #478 | — | 71 | 4 | no | — |
| 475 | #477 | — | 71 | 4 | no | — |
| 476 | #477 | — | 71 | 4 | no | — |
| 477 | #475 | — | 71 | 2 | no | — |
| 478 | #475 | — | 71 | 2 | no | — |
| 479 | #474 | — | 71 | 2 | no | — |
| 480 | #464 | — | 71 | 2 | no | — |
| 481 | #464 | — | 71 | 4 | no | — |
| 482 | #462 | — | 71 | 4 | no | — |
| 483 | #462 | — | 71 | 2 | no | — |
| 484 | #451 | — | 71 | 1 | no | — |
| 485 | #451 | — | 71 | 2 | no | — |
| 486 | #448 | — | 71 | 1 | no | — |
| 487 | #446 | — | 71 | 2 | no | — |
| 488 | #446 | — | 71 | 4 | no | — |
| 489 | C8×Q8 | — | 71 | 2 | no | — |
| 490 | #441 | — | 71 | 4 | no | — |
| 491 | #441 | — | 71 | 4 | no | — |
| 492 | #440 | — | 71 | 4 | no | — |
| 493 | C4×Q16 | — | 71 | 4 | no | — |
| 494 | C4×Q16 | — | 71 | 4 | no | — |
| 495 | C4×Q16 | — | 71 | 2 | no | — |
| 496 | C4×SD16 | — | 71 | 2 | no | — |
| 497 | #432 | — | 71 | 1 | no | — |
| 498 | #432 | — | 71 | 2 | no | — |
| 499 | #431 | — | 71 | 2 | no | — |
| 500 | #431 | — | 71 | 1 | no | — |
| 501 | C22×Q8 | — | 2 | 1 | no | — |
| 502 | C22×Q8 | — | 71 | 1 | no | — |
| 503 | C22×Q8 | — | 142 | 1 | no | — |
| 504 | C22×Q8 | C22⋊D71 | 1 | 1 | yes | characteristic |
| 505 | C2×Q16 | — | 71 | 2 | no | — |
| 506 | C2×Q16 | — | 71 | 4 | no | — |
| 507 | C2×SD16 | — | 71 | 2 | no | — |
| 508 | C4⋊Q8 | — | 2 | 1 | no | — |
| 509 | C4⋊Q8 | — | 2 | 2 | no | — |
| 510 | C4⋊Q8 | — | 71 | 2 | no | — |
| 511 | C4⋊Q8 | — | 71 | 2 | no | — |
| 512 | C4⋊Q8 | — | 142 | 2 | no | — |
| 513 | C4⋊Q8 | — | 142 | 2 | no | — |
| 514 | C4⋊Q8 | — | 142 | 4 | no | — |
| 515 | C4⋊Q8 | — | 142 | 1 | no | — |
| 516 | C4⋊Q8 | — | 142 | 1 | no | — |
| 517 | C4⋊Q8 | C22×D71 | 1 | 1 | yes | characteristic |
| 518 | C4⋊Q8 | C22×D71 | 1 | 2 | yes | — |
| 519 | C4⋊Q8 | C22×D71 | 1 | 1 | yes | characteristic |
| 520 | C4⋊Q8 | C22×D71 | 1 | 2 | yes | — |
| 521 | #126 | — | 2 | 2 | no | — |
| 522 | #126 | — | 2 | 2 | no | — |
| 523 | #126 | — | 2 | 2 | no | — |
| 524 | #126 | — | 2 | 2 | no | — |
| 525 | #126 | — | 2 | 1 | no | — |
| 526 | #125 | — | 2 | 2 | no | — |
| 527 | #125 | — | 2 | 2 | no | — |
| 528 | #125 | — | 2 | 2 | no | — |
| 529 | #125 | — | 2 | 1 | no | — |
| 530 | #125 | — | 2 | 2 | no | — |
| 531 | #125 | — | 2 | 2 | no | — |
| 532 | #125 | — | 2 | 1 | no | — |
| 533 | #125 | — | 71 | 4 | no | — |
| 534 | #125 | — | 71 | 4 | no | — |
| 535 | #125 | — | 142 | 4 | no | — |
| 536 | #125 | — | 142 | 4 | no | — |
| 537 | #125 | — | 142 | 4 | no | — |
| 538 | #125 | — | 142 | 4 | no | — |
| 539 | #125 | — | 142 | 2 | no | — |
| 540 | #125 | — | 142 | 2 | no | — |
| 541 | #125 | C22×D71 | 1 | 2 | yes | — |
| 542 | #125 | C22×D71 | 1 | 1 | yes | characteristic |
| 543 | #124 | C22×D71 | 1 | 2 | yes | — |
| 544 | #124 | C22×D71 | 1 | 1 | yes | characteristic |
| 545 | #123 | — | 2 | 2 | no | — |
| 546 | #123 | — | 2 | 1 | no | — |
| 547 | C22⋊Q8 | — | 2 | 1 | no | — |
| 548 | C22⋊Q8 | — | 2 | 2 | no | — |
| 549 | C22⋊Q8 | — | 2 | 1 | no | — |
| 550 | C22⋊Q8 | — | 2 | 2 | no | — |
| 551 | C22⋊Q8 | — | 2 | 1 | no | — |
| 552 | C22⋊Q8 | — | 2 | 2 | no | — |
| 553 | C22⋊Q8 | C22×D71 | 1 | 1 | yes | characteristic |
| 554 | C22⋊Q8 | C22×D71 | 1 | 2 | yes | — |
| 555 | #121 | C22×D71 | 1 | 1 | yes | characteristic |
| 556 | C4×Q8 | — | 2 | 1 | no | — |
| 557 | C4×Q8 | — | 2 | 1 | no | — |
| 558 | C4×Q8 | — | 2 | 2 | no | — |
| 559 | C4×Q8 | — | 2 | 2 | no | — |
| 560 | C4×Q8 | — | 2 | 1 | no | — |
| 561 | C4×Q8 | — | 71 | 2 | no | — |
| 562 | C4×Q8 | — | 71 | 4 | no | — |
| 563 | C4×Q8 | — | 71 | 4 | no | — |
| 564 | C4×Q8 | — | 71 | 2 | no | — |
| 565 | C4×Q8 | — | 142 | 2 | no | — |
| 566 | C4×Q8 | — | 142 | 2 | no | — |
| 567 | C4×Q8 | — | 142 | 4 | no | — |
| 568 | C4×Q8 | — | 142 | 2 | no | — |
| 569 | C4×Q8 | — | 142 | 2 | no | — |
| 570 | C4×Q8 | — | 142 | 1 | no | — |
| 571 | C4×Q8 | — | 142 | 1 | no | — |
| 572 | C4×Q8 | C22⋊D71 | 1 | 1 | yes | characteristic |
| 573 | C4×Q8 | C22⋊D71 | 1 | 2 | yes | — |
| 574 | C4×Q8 | C22⋊D71 | 1 | 1 | yes | characteristic |
| 575 | C4×Q8 | C22×D71 | 1 | 1 | yes | characteristic |
| 576 | C4×Q8 | C22×D71 | 1 | 2 | yes | — |
| 577 | C4×Q8 | C22×D71 | 1 | 2 | yes | — |
| 578 | C4×Q8 | C22×D71 | 1 | 2 | yes | — |
| 579 | C4×Q8 | C22×D71 | 1 | 2 | yes | — |
| 580 | C4×Q8 | C22×D71 | 1 | 1 | yes | characteristic |
| 581 | C4×Q8 | C22×D71 | 1 | 1 | yes | characteristic |
| 582 | C4×Q8 | C22×D71 | 1 | 2 | yes | — |
| 583 | C4×D4 | — | 2 | 1 | no | — |
| 584 | C4×D4 | — | 2 | 2 | no | — |
| 585 | C4×D4 | C22×D71 | 1 | 1 | yes | characteristic |
| 586 | C4×D4 | C22×D71 | 1 | 2 | yes | — |
| 587 | #117 | — | 2 | 2 | no | — |
| 588 | #117 | — | 2 | 1 | no | — |
| 589 | #117 | — | 2 | 1 | no | — |
| 590 | #117 | — | 2 | 2 | no | — |
| 591 | #117 | — | 2 | 2 | no | — |
| 592 | #117 | — | 2 | 1 | no | — |
| 593 | C2×C4⋊C4 | — | 71 | 1 | no | — |
| 594 | C2×C4⋊C4 | — | 71 | 2 | no | — |
| 595 | C2×C4⋊C4 | — | 142 | 1 | no | — |
| 596 | C2×C4⋊C4 | — | 142 | 2 | no | — |
| 597 | C2×C4⋊C4 | — | 142 | 2 | no | — |
| 598 | C2×C4⋊C4 | — | 142 | 2 | no | — |
| 599 | C2×C4⋊C4 | — | 142 | 1 | no | — |
| 600 | C2×C4⋊C4 | C22⋊D71 | 1 | 1 | yes | characteristic |
| 601 | C2×C4⋊C4 | C22⋊D71 | 1 | 2 | yes | — |
| 602 | C2×C42 | — | 142 | 2 | no | — |
| 603 | C2×C42 | — | 142 | 1 | no | — |
| 604 | C2×C42 | C22×D71 | 1 | 2 | yes | — |
| 605 | C2×C42 | C22×D71 | 1 | 1 | yes | characteristic |
| 606 | #107 | — | 71 | 4 | no | — |
| 607 | #107 | — | 71 | 4 | no | — |
| 608 | #107 | — | 71 | 2 | no | — |
| 609 | #107 | — | 71 | 4 | no | — |
| 610 | #106 | — | 71 | 2 | no | — |
| 611 | #106 | — | 71 | 4 | no | — |
| 612 | #106 | — | 71 | 4 | no | — |
| 613 | C4⋊C8 | — | 71 | 4 | no | — |
| 614 | C4⋊C8 | — | 71 | 2 | no | — |
| 615 | C4⋊C8 | — | 71 | 2 | no | — |
| 616 | C4⋊C8 | — | 71 | 4 | no | — |
| 617 | #103 | — | 71 | 4 | no | — |
| 618 | #103 | — | 71 | 4 | no | — |
| 619 | #103 | — | 71 | 2 | no | — |
| 620 | #103 | — | 71 | 4 | no | — |
| 621 | #103 | — | 71 | 4 | no | — |
| 622 | #103 | — | 71 | 2 | no | — |
| 623 | #103 | — | 71 | 4 | no | — |
| 624 | #103 | — | 71 | 2 | no | — |
| 625 | #102 | — | 71 | 2 | no | — |
| 626 | #102 | — | 71 | 4 | no | — |
| 627 | C22⋊C8 | — | 71 | 1 | no | — |
| 628 | C22⋊C8 | — | 71 | 1 | no | — |
| 629 | C22⋊C8 | — | 71 | 2 | no | — |
| 630 | #97 | — | 71 | 4 | no | — |
| 631 | #97 | — | 71 | 2 | no | — |
| 632 | C4×C8 | — | 71 | 2 | no | — |
| 633 | C4×C8 | — | 71 | 4 | no | — |
| 634 | C2×Q8 | — | 2 | 2 | no | — |
| 635 | C2×Q8 | — | 2 | 1 | no | — |
| 636 | C2×Q8 | — | 4 | 2 | no | — |
| 637 | C2×Q8 | — | 4 | 4 | no | — |
| 638 | C2×Q8 | — | 284 | 4 | no | — |
| 639 | C2×Q8 | — | 71 | 2 | no | — |
| 640 | C2×Q8 | — | 142 | 4 | no | — |
| 641 | C2×Q8 | — | 142 | 2 | no | — |
| 642 | C2×Q8 | — | 142 | 2 | no | — |
| 643 | C2×Q8 | — | 142 | 1 | no | — |
| 644 | C2×Q8 | C2×C22⋊D71 | 1 | 1 | yes | characteristic |
| 645 | C2×Q8 | C2×C22⋊D71 | 1 | 1 | yes | characteristic |
| 646 | C2×Q8 | C2×C22⋊D71 | 1 | 2 | yes | — |
| 647 | C2×Q8 | C23×D71 | 1 | 1 | yes | characteristic |
| 648 | C2×Q8 | C23×D71 | 1 | 2 | yes | — |
| 649 | C2×D4 | — | 2 | 1 | no | — |
| 650 | C2×D4 | C23×D71 | 1 | 1 | yes | characteristic |
| 651 | C22×C4 | — | 2 | 2 | no | — |
| 652 | C22×C4 | — | 2 | 1 | no | — |
| 653 | C22×C4 | — | 142 | 1 | no | — |
| 654 | C22×C4 | — | 142 | 2 | no | — |
| 655 | C22×C4 | — | 142 | 1 | no | — |
| 656 | C22×C4 | C2×C22⋊D71 | 1 | 2 | yes | — |
| 657 | C22×C4 | C2×C22⋊D71 | 1 | 1 | yes | characteristic |
| 658 | C22×C4 | C2×C22⋊D71 | 1 | 1 | yes | characteristic |
| 659 | C22×C4 | C2×C22⋊D71 | 1 | 2 | yes | — |
| 660 | C22×C4 | C23×D71 | 1 | 1 | yes | characteristic |
| 661 | Q16 | — | 142 | 4 | no | — |
| 662 | Q16 | — | 142 | 8 | no | — |
| 663 | SD16 | — | 142 | 4 | no | — |
| 664 | C2×C8 | — | 71 | 2 | no | — |
| 665 | C2×C8 | — | 71 | 4 | no | — |
| 666 | C2×C8 | — | 71 | 2 | no | — |
| 667 | C4⋊C4 | — | 2 | 2 | no | — |
| 668 | C4⋊C4 | — | 2 | 1 | no | — |
| 669 | C4⋊C4 | — | 2 | 2 | no | — |
| 670 | C4⋊C4 | — | 2 | 1 | no | — |
| 671 | C4⋊C4 | — | 2 | 2 | no | — |
| 672 | C4⋊C4 | — | 2 | 1 | no | — |
| 673 | C4⋊C4 | — | 2 | 2 | no | — |
| 674 | C4⋊C4 | — | 2 | 1 | no | — |
| 675 | C4⋊C4 | — | 2 | 2 | no | — |
| 676 | C4⋊C4 | — | 2 | 1 | no | — |
| 677 | C4⋊C4 | — | 2 | 1 | no | — |
| 678 | C4⋊C4 | — | 2 | 2 | no | — |
| 679 | C4⋊C4 | — | 2 | 2 | no | — |
| 680 | C4⋊C4 | — | 2 | 2 | no | — |
| 681 | C4⋊C4 | — | 2 | 2 | no | — |
| 682 | C4⋊C4 | — | 2 | 2 | no | — |
| 683 | C4⋊C4 | — | 2 | 1 | no | — |
| 684 | C4⋊C4 | — | 71 | 2 | no | — |
| 685 | C4⋊C4 | — | 71 | 4 | no | — |
| 686 | C4⋊C4 | — | 142 | 2 | no | — |
| 687 | C4⋊C4 | — | 142 | 2 | no | — |
| 688 | C4⋊C4 | — | 142 | 4 | no | — |
| 689 | C4⋊C4 | — | 142 | 4 | no | — |
| 690 | C4⋊C4 | — | 142 | 4 | no | — |
| 691 | C4⋊C4 | — | 142 | 4 | no | — |
| 692 | C4⋊C4 | — | 142 | 4 | no | — |
| 693 | C4⋊C4 | — | 142 | 4 | no | — |
| 694 | C4⋊C4 | — | 142 | 1 | no | — |
| 695 | C4⋊C4 | — | 142 | 2 | no | — |
| 696 | C4⋊C4 | — | 142 | 2 | no | — |
| 697 | C4⋊C4 | — | 142 | 2 | no | — |
| 698 | C4⋊C4 | C2×C22⋊D71 | 1 | 1 | yes | characteristic |
| 699 | C4⋊C4 | C2×C22⋊D71 | 1 | 2 | yes | — |
| 700 | C4⋊C4 | C2×C22⋊D71 | 1 | 1 | yes | characteristic |
| 701 | C4⋊C4 | C2×C22⋊D71 | 1 | 2 | yes | — |
| 702 | C4⋊C4 | C2×C22⋊D71 | 1 | 2 | yes | — |
| 703 | C4⋊C4 | C2×C22⋊D71 | 1 | 2 | yes | — |
| 704 | C4⋊C4 | C2×C22⋊D71 | 1 | 2 | yes | — |
| 705 | C4⋊C4 | C23×D71 | 1 | 1 | yes | characteristic |
| 706 | C4⋊C4 | C23×D71 | 1 | 1 | yes | characteristic |
| 707 | C4⋊C4 | C23×D71 | 1 | 2 | yes | — |
| 708 | C22⋊C4 | — | 2 | 1 | no | — |
| 709 | C22⋊C4 | — | 2 | 2 | no | — |
| 710 | C22⋊C4 | — | 2 | 1 | no | — |
| 711 | C22⋊C4 | — | 2 | 2 | no | — |
| 712 | C22⋊C4 | — | 2 | 1 | no | — |
| 713 | C22⋊C4 | — | 2 | 1 | no | — |
| 714 | C22⋊C4 | — | 2 | 2 | no | — |
| 715 | C22⋊C4 | — | 2 | 2 | no | — |
| 716 | C22⋊C4 | — | 2 | 1 | no | — |
| 717 | C42 | — | 2 | 2 | no | — |
| 718 | C42 | — | 2 | 2 | no | — |
| 719 | C42 | — | 2 | 2 | no | — |
| 720 | C42 | — | 2 | 2 | no | — |
| 721 | C42 | — | 2 | 1 | no | — |
| 722 | C42 | — | 142 | 4 | no | — |
| 723 | C42 | — | 142 | 4 | no | — |
| 724 | C42 | — | 142 | 2 | no | — |
| 725 | C42 | — | 142 | 2 | no | — |
| 726 | C42 | C2×C22⋊D71 | 1 | 2 | yes | — |
| 727 | C42 | C2×C22⋊D71 | 1 | 1 | yes | characteristic |
| 728 | C42 | C2×C22⋊D71 | 1 | 2 | yes | — |
| 729 | C42 | C2×C22⋊D71 | 1 | 1 | yes | characteristic |
| 730 | C42 | C23×D71 | 1 | 1 | yes | characteristic |
| 731 | C42 | C23×D71 | 1 | 2 | yes | — |
| 732 | C42 | C23×D71 | 1 | 2 | yes | — |
| 733 | C42 | C23×D71 | 1 | 1 | yes | characteristic |
| 734 | C23 | — | 2 | 1 | no | — |
| 735 | C23 | C22×C22⋊D71 | 1 | 1 | yes | characteristic |
| 736 | Q8 | — | 2 | 2 | no | — |
| 737 | Q8 | — | 2 | 2 | no | — |
| 738 | Q8 | — | 2 | 2 | no | — |
| 739 | Q8 | — | 2 | 4 | no | — |
| 740 | Q8 | — | 4 | 2 | no | — |
| 741 | Q8 | — | 4 | 4 | no | — |
| 742 | Q8 | — | 4 | 2 | no | — |
| 743 | Q8 | — | 284 | 4 | no | — |
| 744 | Q8 | — | 284 | 4 | no | — |
| 745 | Q8 | — | 71 | 4 | no | — |
| 746 | Q8 | — | 142 | 4 | no | — |
| 747 | Q8 | — | 142 | 2 | no | — |
| 748 | D4 | — | 2 | 2 | no | — |
| 749 | D4 | — | 4 | 2 | no | — |
| 750 | C2×C4 | — | 2 | 4 | no | — |
| 751 | C2×C4 | — | 2 | 2 | no | — |
| 752 | C2×C4 | — | 2 | 2 | no | — |
| 753 | C2×C4 | — | 2 | 2 | no | — |
| 754 | C2×C4 | — | 2 | 1 | no | — |
| 755 | C2×C4 | — | 2 | 2 | no | — |
| 756 | C2×C4 | — | 2 | 1 | no | — |
| 757 | C2×C4 | — | 2 | 2 | no | — |
| 758 | C2×C4 | — | 2 | 1 | no | — |
| 759 | C2×C4 | — | 4 | 2 | no | — |
| 760 | C2×C4 | — | 4 | 4 | no | — |
| 761 | C2×C4 | — | 4 | 2 | no | — |
| 762 | C2×C4 | — | 284 | 4 | no | — |
| 763 | C2×C4 | — | 284 | 2 | no | — |
| 764 | C2×C4 | — | 142 | 2 | no | — |
| 765 | C2×C4 | — | 142 | 4 | no | — |
| 766 | C2×C4 | — | 142 | 4 | no | — |
| 767 | C2×C4 | — | 142 | 2 | no | — |
| 768 | C2×C4 | C22×C22⋊D71 | 1 | 2 | yes | — |
| 769 | C2×C4 | C22×C22⋊D71 | 1 | 1 | yes | characteristic |
| 770 | C2×C4 | C22×C22⋊D71 | 1 | 2 | yes | — |
| 771 | C2×C4 | C22×C22⋊D71 | 1 | 2 | yes | — |
| 772 | C2×C4 | C22×C22⋊D71 | 1 | 1 | yes | characteristic |
| 773 | C2×C4 | C22×C22⋊D71 | 1 | 1 | yes | characteristic |
| 774 | C2×C4 | C22×C22⋊D71 | 1 | 1 | yes | characteristic |
| 775 | C2×C4 | C22×C22⋊D71 | 1 | 2 | yes | — |
| 776 | C2×C4 | C22×C22⋊D71 | 1 | 1 | yes | characteristic |
| 777 | C2×C4 | C24×D71 | 1 | 1 | yes | characteristic |
| 778 | C8 | — | 142 | 2 | no | — |
| 779 | C8 | — | 142 | 2 | no | — |
| 780 | C8 | — | 142 | 4 | no | — |
| 781 | C22 | — | 2 | 1 | no | — |
| 782 | C22 | — | 2 | 1 | no | — |
| 783 | C22 | — | 4 | 1 | no | — |
| 784 | C22 | — | 4 | 1 | no | — |
| 785 | C22 | — | 4 | 1 | no | — |
| 786 | C22 | #17986814 | 1 | 2 | yes | — |
| 787 | C22 | C23×C22⋊D71 | 1 | 1 | yes | characteristic |
| 788 | C4 | — | 2 | 1 | no | — |
| 789 | C4 | — | 2 | 1 | no | — |
| 790 | C4 | — | 2 | 2 | no | — |
| 791 | C4 | — | 2 | 2 | no | — |
| 792 | C4 | — | 2 | 2 | no | — |
| 793 | C4 | — | 2 | 1 | no | — |
| 794 | C4 | — | 2 | 2 | no | — |
| 795 | C4 | — | 2 | 1 | no | — |
| 796 | C4 | — | 4 | 1 | no | — |
| 797 | C4 | — | 4 | 2 | no | — |
| 798 | C4 | — | 4 | 2 | no | — |
| 799 | C4 | — | 4 | 1 | no | — |
| 800 | C4 | — | 4 | 1 | no | — |
| 801 | C4 | — | 284 | 4 | no | — |
| 802 | C4 | — | 284 | 2 | no | — |
| 803 | C4 | — | 142 | 4 | no | — |
| 804 | C4 | #17986797 | 1 | 2 | yes | — |
| 805 | C4 | 2−1+4×D71 | 1 | 2 | yes | — |
| 806 | C2 | — | 2 | 2 | no | — |
| 807 | C2 | — | 8 | 1 | no | — |
| 808 | C2 | #22601988 | 1 | 1 | yes | characteristic |
| 809 | C2 | C2×#17986797 | 1 | 1 | yes | characteristic |
| 810 | C2 | C2×#17986814 | 1 | 1 | yes | characteristic |
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