← #32155397
Subgroups — #32155397
Order 18176.
450 conjugacy classes of subgroups.
The subgroup lattice has 424 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #22601228 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | Q16×Dic142 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #22590627 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #22590624 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | #22590621 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | #22590502 | C2 | 1 | 1 | yes | maximal, characteristic |
| 7 | #22590491 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | #22590483 | C2 | 1 | 1 | yes | maximal, characteristic |
| 9 | #22590481 | C2 | 1 | 1 | yes | maximal, characteristic |
| 10 | #22590480 | C2 | 1 | 1 | yes | maximal, characteristic |
| 11 | #22590247 | C2 | 1 | 1 | yes | maximal, characteristic |
| 12 | #22590209 | C2 | 1 | 1 | yes | maximal, characteristic |
| 13 | #22590208 | C2 | 1 | 1 | yes | maximal, characteristic |
| 14 | #22590196 | C2 | 1 | 1 | yes | maximal, characteristic |
| 15 | C71×#2229 | C2 | 1 | 1 | yes | maximal, characteristic |
| 16 | Q8×Dic142 | — | 2 | 1 | no | — |
| 17 | #17986726 | — | 2 | 1 | no | — |
| 18 | C2×#14556074 | C22 | 1 | 1 | yes | characteristic |
| 19 | #17986404 | C22 | 1 | 1 | yes | characteristic |
| 20 | #17986403 | C22 | 1 | 1 | yes | characteristic |
| 21 | #17986403 | C22 | 1 | 1 | yes | characteristic |
| 22 | #17986403 | C22 | 1 | 1 | yes | characteristic |
| 23 | #17986400 | C22 | 1 | 1 | yes | characteristic |
| 24 | #17986309 | — | 2 | 1 | no | — |
| 25 | #17986303 | — | 2 | 1 | no | — |
| 26 | #17986294 | — | 2 | 1 | no | — |
| 27 | #17986292 | — | 2 | 1 | no | — |
| 28 | #17986292 | — | 2 | 1 | no | — |
| 29 | #17986283 | — | 2 | 1 | no | — |
| 30 | C8×Dic142 | C22 | 1 | 1 | yes | characteristic |
| 31 | C4×Dic284 | C22 | 1 | 1 | yes | characteristic |
| 32 | Q16×Dic71 | C22 | 1 | 1 | yes | characteristic |
| 33 | Q16×Dic71 | C22 | 1 | 1 | yes | characteristic |
| 34 | #17986093 | C22 | 1 | 1 | yes | characteristic |
| 35 | #17986093 | C22 | 1 | 1 | yes | characteristic |
| 36 | #17985827 | C22 | 1 | 1 | yes | characteristic |
| 37 | #17985827 | C22 | 1 | 1 | yes | characteristic |
| 38 | #17985826 | C22 | 1 | 1 | yes | characteristic |
| 39 | #17985826 | C22 | 1 | 1 | yes | characteristic |
| 40 | #17985826 | C22 | 1 | 1 | yes | characteristic |
| 41 | #17985824 | C22 | 1 | 1 | yes | characteristic |
| 42 | #17985824 | C22 | 1 | 1 | yes | characteristic |
| 43 | Dic71⋊C16 | C22 | 1 | 1 | yes | characteristic |
| 44 | Dic71⋊C16 | C22 | 1 | 1 | yes | characteristic |
| 45 | #17985804 | C22 | 1 | 1 | yes | characteristic |
| 46 | #17985804 | C22 | 1 | 1 | yes | characteristic |
| 47 | #17985803 | C22 | 1 | 1 | yes | characteristic |
| 48 | #17985802 | C22 | 1 | 1 | yes | characteristic |
| 49 | #17985775 | C22 | 1 | 1 | yes | characteristic |
| 50 | #17985774 | C22 | 1 | 1 | yes | characteristic |
| 51 | C16×Dic71 | C22 | 1 | 1 | yes | characteristic |
| 52 | #499×C71 | C22 | 1 | 1 | yes | characteristic |
| 53 | C4×Q16×C71 | C22 | 1 | 1 | yes | characteristic |
| 54 | #367×C71 | C22 | 1 | 1 | yes | characteristic |
| 55 | #366×C71 | C22 | 1 | 1 | yes | characteristic |
| 56 | C4⋊C16×C71 | C22 | 1 | 1 | yes | characteristic |
| 57 | #358×C71 | C22 | 1 | 1 | yes | characteristic |
| 58 | #358×C71 | C22 | 1 | 1 | yes | characteristic |
| 59 | C2×Dic284 | C23 | 1 | 1 | yes | characteristic |
| 60 | #14556128 | — | 2 | 1 | no | — |
| 61 | #14556128 | — | 4 | 1 | no | — |
| 62 | #14556127 | — | 2 | 1 | no | — |
| 63 | #14556127 | — | 2 | 1 | no | — |
| 64 | #14556127 | — | 2 | 1 | no | — |
| 65 | #14556127 | — | 4 | 1 | no | — |
| 66 | #14556127 | — | 4 | 1 | no | — |
| 67 | #14556127 | — | 4 | 1 | no | — |
| 68 | #14556119 | — | 2 | 1 | no | — |
| 69 | #14556118 | — | 4 | 1 | no | — |
| 70 | #14556118 | — | 4 | 1 | no | — |
| 71 | Q8×Dic71 | — | 2 | 1 | no | — |
| 72 | Q8×Dic71 | — | 2 | 1 | no | — |
| 73 | C4×Dic142 | — | 2 | 1 | no | — |
| 74 | C4×Dic142 | — | 4 | 1 | no | — |
| 75 | C4×Dic142 | D4 | 1 | 1 | yes | characteristic |
| 76 | #14556093 | — | 2 | 1 | no | — |
| 77 | #14556093 | — | 2 | 1 | no | — |
| 78 | #14556093 | — | 4 | 1 | no | — |
| 79 | #14556074 | Q8 | 1 | 4 | yes | complemented |
| 80 | C2×C71⋊C16 | C23 | 1 | 1 | yes | characteristic |
| 81 | C2×C71⋊C16 | C23 | 1 | 1 | yes | characteristic |
| 82 | #14556062 | — | 2 | 1 | no | — |
| 83 | #14556062 | C23 | 1 | 1 | yes | characteristic |
| 84 | #14556062 | C23 | 1 | 1 | yes | characteristic |
| 85 | #14556062 | C23 | 1 | 1 | yes | characteristic |
| 86 | #14556061 | — | 2 | 1 | no | — |
| 87 | #14556061 | — | 2 | 1 | no | — |
| 88 | #14556061 | — | 2 | 1 | no | — |
| 89 | #14556059 | — | 2 | 1 | no | — |
| 90 | C4⋊(C71⋊C8) | D4 | 1 | 1 | yes | characteristic |
| 91 | Dic71⋊C8 | D4 | 1 | 1 | yes | characteristic |
| 92 | Dic71⋊C8 | D4 | 1 | 1 | yes | characteristic |
| 93 | #14556053 | — | 2 | 1 | no | — |
| 94 | #14556052 | — | 2 | 1 | no | — |
| 95 | #14556052 | — | 2 | 1 | no | — |
| 96 | #14556051 | — | 2 | 1 | no | — |
| 97 | #14556051 | — | 2 | 1 | no | — |
| 98 | C8×Dic71 | C23 | 1 | 1 | yes | characteristic |
| 99 | C8×Dic71 | C23 | 1 | 1 | yes | characteristic |
| 100 | C2×Q16×C71 | C23 | 1 | 1 | yes | characteristic |
| 101 | #125×C71 | — | 2 | 1 | no | — |
| 102 | C4×Q8×C71 | — | 2 | 1 | no | — |
| 103 | C2×C16×C71 | C23 | 1 | 1 | yes | characteristic |
| 104 | C2×C16×C71 | C23 | 1 | 1 | yes | characteristic |
| 105 | #107×C71 | C23 | 1 | 1 | yes | characteristic |
| 106 | #107×C71 | C23 | 1 | 1 | yes | characteristic |
| 107 | #107×C71 | C23 | 1 | 1 | yes | characteristic |
| 108 | #106×C71 | — | 2 | 1 | no | — |
| 109 | #103×C71 | — | 2 | 1 | no | — |
| 110 | C4×C8×C71 | C23 | 1 | 1 | yes | characteristic |
| 111 | C2×Dic142 | — | 2 | 1 | no | — |
| 112 | C2×Dic142 | — | 4 | 1 | no | — |
| 113 | C2×Dic142 | — | 4 | 1 | no | — |
| 114 | C2×Dic142 | — | 4 | 1 | no | — |
| 115 | C2×Dic142 | — | 4 | 1 | no | — |
| 116 | C2×Dic142 | D8 | 1 | 1 | yes | characteristic |
| 117 | Dic284 | — | 2 | 1 | no | — |
| 118 | Dic284 | C2×Q8 | 1 | 2 | yes | — |
| 119 | C2×C71⋊C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 120 | C2×C71⋊C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 121 | C4⋊Dic71 | — | 2 | 1 | no | — |
| 122 | C4⋊Dic71 | — | 2 | 1 | no | — |
| 123 | C4⋊Dic71 | — | 2 | 1 | no | — |
| 124 | C4⋊Dic71 | — | 4 | 1 | no | — |
| 125 | C4⋊Dic71 | — | 4 | 1 | no | — |
| 126 | C4⋊Dic71 | — | 4 | 1 | no | — |
| 127 | C4⋊Dic71 | — | 4 | 1 | no | — |
| 128 | C4⋊Dic71 | D8 | 1 | 1 | yes | characteristic |
| 129 | Dic71⋊C4 | — | 4 | 1 | no | — |
| 130 | Dic71⋊C4 | — | 4 | 1 | no | — |
| 131 | Dic71⋊C4 | — | 4 | 1 | no | — |
| 132 | Dic71⋊C4 | — | 4 | 1 | no | — |
| 133 | Dic71⋊C4 | — | 4 | 1 | no | — |
| 134 | Dic71⋊C4 | — | 4 | 1 | no | — |
| 135 | Dic71⋊C4 | — | 4 | 1 | no | — |
| 136 | Dic71⋊C4 | D8 | 1 | 1 | yes | characteristic |
| 137 | Dic71⋊C4 | D8 | 1 | 1 | yes | characteristic |
| 138 | C4×Dic71 | — | 4 | 1 | no | — |
| 139 | C4×Dic71 | — | 4 | 1 | no | — |
| 140 | C4×Dic71 | — | 4 | 1 | no | — |
| 141 | C4×Dic71 | — | 4 | 1 | no | — |
| 142 | C4×Dic71 | — | 4 | 1 | no | — |
| 143 | C4×Dic71 | C2×D4 | 1 | 1 | yes | characteristic |
| 144 | C4×Dic71 | C2×D4 | 1 | 1 | yes | characteristic |
| 145 | C71⋊C16 | — | 2 | 1 | no | — |
| 146 | C71⋊C16 | C2×Q8 | 1 | 2 | yes | — |
| 147 | C2×Q8×C71 | — | 2 | 1 | no | — |
| 148 | Q16×C71 | — | 2 | 1 | no | — |
| 149 | Q16×C71 | C2×Q8 | 1 | 2 | yes | — |
| 150 | C2×C8×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 151 | C2×C8×C71 | C24 | 1 | 1 | yes | characteristic |
| 152 | C4⋊C4×C71 | — | 2 | 1 | no | — |
| 153 | C4⋊C4×C71 | — | 2 | 1 | no | — |
| 154 | C4⋊C4×C71 | — | 2 | 1 | no | — |
| 155 | C4⋊C4×C71 | — | 4 | 1 | no | — |
| 156 | C4⋊C4×C71 | — | 4 | 1 | no | — |
| 157 | C4⋊C4×C71 | — | 4 | 1 | no | — |
| 158 | C42×C71 | — | 4 | 1 | no | — |
| 159 | C42×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 160 | C16×C71 | — | 2 | 1 | no | — |
| 161 | C16×C71 | — | 2 | 1 | no | — |
| 162 | Q8×C71 | — | 2 | 2 | no | — |
| 163 | Q8×C71 | — | 4 | 1 | no | — |
| 164 | C2×C4×C71 | — | 4 | 1 | no | — |
| 165 | C2×C4×C71 | — | 4 | 1 | no | — |
| 166 | C2×C4×C71 | — | 4 | 1 | no | — |
| 167 | C2×C4×C71 | — | 4 | 1 | no | — |
| 168 | C2×C4×C71 | C2×D8 | 1 | 1 | yes | characteristic |
| 169 | C2×C4×C71 | C2×D8 | 1 | 1 | yes | characteristic |
| 170 | C2×C4×C71 | C22×D4 | 1 | 1 | yes | characteristic |
| 171 | C2×Dic71 | — | 4 | 1 | no | — |
| 172 | C2×Dic71 | — | 4 | 1 | no | — |
| 173 | C2×Dic71 | — | 4 | 1 | no | — |
| 174 | C2×Dic71 | — | 4 | 1 | no | — |
| 175 | C2×Dic71 | C2×D8 | 1 | 1 | yes | characteristic |
| 176 | C2×Dic71 | C2×D8 | 1 | 1 | yes | characteristic |
| 177 | C2×Dic71 | C2×D8 | 1 | 1 | yes | characteristic |
| 178 | C2×Dic71 | C2×D8 | 1 | 1 | yes | characteristic |
| 179 | Dic142 | — | 2 | 2 | no | — |
| 180 | Dic142 | — | 2 | 2 | no | — |
| 181 | Dic142 | — | 4 | 1 | no | — |
| 182 | Dic142 | — | 8 | 2 | no | — |
| 183 | Dic142 | — | 16 | 1 | no | — |
| 184 | Dic142 | — | 16 | 1 | no | — |
| 185 | Dic142 | — | 16 | 1 | no | — |
| 186 | C8×C71 | — | 2 | 1 | no | — |
| 187 | C8×C71 | C22×Q8 | 1 | 1 | yes | characteristic |
| 188 | C8×C71 | 2−1+4 | 1 | 1 | yes | characteristic |
| 189 | C71⋊C8 | — | 2 | 1 | no | — |
| 190 | C71⋊C8 | — | 2 | 1 | no | — |
| 191 | C22×C71 | C22×D8 | 1 | 1 | yes | characteristic |
| 192 | C4×C71 | — | 2 | 1 | no | — |
| 193 | C4×C71 | — | 2 | 1 | no | — |
| 194 | C4×C71 | — | 4 | 2 | no | — |
| 195 | C4×C71 | — | 8 | 1 | no | — |
| 196 | C4×C71 | — | 8 | 1 | no | — |
| 197 | C4×C71 | — | 8 | 1 | no | — |
| 198 | C4×C71 | D4×Q8 | 1 | 1 | yes | characteristic |
| 199 | C4×C71 | #578 | 1 | 1 | yes | characteristic |
| 200 | Dic71 | — | 2 | 1 | no | — |
| 201 | Dic71 | — | 2 | 1 | no | — |
| 202 | Dic71 | — | 2 | 1 | no | — |
| 203 | Dic71 | — | 4 | 2 | no | — |
| 204 | Dic71 | — | 8 | 1 | no | — |
| 205 | Dic71 | — | 8 | 1 | no | — |
| 206 | Dic71 | — | 8 | 1 | no | — |
| 207 | Dic71 | #510 | 1 | 2 | yes | — |
| 208 | #33954 | — | 71 | 1 | no | maximal, Sylow |
| 209 | C2×C71 | Q8×D8 | 1 | 1 | yes | characteristic |
| 210 | C2×C71 | C2×#510 | 1 | 1 | yes | characteristic |
| 211 | C2×C71 | #3416 | 1 | 1 | yes | characteristic |
| 212 | #3383 | — | 71 | 1 | no | — |
| 213 | Q8×Q16 | — | 71 | 1 | no | — |
| 214 | #2255 | — | 71 | 1 | no | — |
| 215 | #2255 | — | 71 | 1 | no | — |
| 216 | #2254 | — | 71 | 1 | no | — |
| 217 | #2229 | — | 71 | 1 | no | — |
| 218 | #2229 | D71 | 1 | 1 | yes | characteristic |
| 219 | #2227 | — | 71 | 1 | no | — |
| 220 | #2225 | — | 71 | 1 | no | — |
| 221 | #2225 | — | 71 | 1 | no | — |
| 222 | #2225 | — | 71 | 1 | no | — |
| 223 | #2183 | — | 71 | 1 | no | — |
| 224 | #2176 | — | 71 | 1 | no | — |
| 225 | #2176 | — | 71 | 1 | no | — |
| 226 | C4×Q32 | — | 71 | 1 | no | — |
| 227 | C71 | #33954 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 228 | Q82 | — | 142 | 1 | no | — |
| 229 | #557 | — | 142 | 1 | no | — |
| 230 | C2×Q32 | — | 71 | 1 | no | — |
| 231 | #500 | — | 71 | 1 | no | — |
| 232 | #500 | — | 71 | 1 | no | — |
| 233 | #500 | — | 71 | 1 | no | — |
| 234 | #500 | — | 71 | 1 | no | — |
| 235 | #499 | — | 71 | 1 | no | — |
| 236 | #499 | C2×D71 | 1 | 1 | yes | characteristic |
| 237 | #479 | — | 142 | 1 | no | — |
| 238 | #479 | — | 142 | 1 | no | — |
| 239 | #477 | — | 142 | 1 | no | — |
| 240 | #477 | — | 142 | 1 | no | — |
| 241 | #477 | — | 142 | 1 | no | — |
| 242 | #475 | — | 142 | 1 | no | — |
| 243 | C8×Q8 | — | 71 | 1 | no | — |
| 244 | C4×Q16 | — | 71 | 1 | no | — |
| 245 | C4×Q16 | — | 71 | 1 | no | — |
| 246 | C4×Q16 | — | 71 | 1 | no | — |
| 247 | C4×Q16 | — | 71 | 1 | no | — |
| 248 | C4×Q16 | — | 71 | 1 | no | — |
| 249 | C4×Q16 | C2×D71 | 1 | 1 | yes | characteristic |
| 250 | #367 | — | 71 | 1 | no | — |
| 251 | #367 | — | 71 | 1 | no | — |
| 252 | #367 | — | 71 | 1 | no | — |
| 253 | #367 | — | 71 | 1 | no | — |
| 254 | #367 | — | 71 | 1 | no | — |
| 255 | #367 | C2×D71 | 1 | 1 | yes | characteristic |
| 256 | #366 | — | 71 | 1 | no | — |
| 257 | #366 | — | 71 | 1 | no | — |
| 258 | #366 | C2×D71 | 1 | 1 | yes | characteristic |
| 259 | C4⋊C16 | — | 71 | 1 | no | — |
| 260 | C4⋊C16 | — | 71 | 1 | no | — |
| 261 | C4⋊C16 | C2×D71 | 1 | 1 | yes | characteristic |
| 262 | #358 | — | 71 | 1 | no | — |
| 263 | #358 | — | 71 | 1 | no | — |
| 264 | #358 | — | 71 | 1 | no | — |
| 265 | #358 | — | 71 | 1 | no | — |
| 266 | #358 | C2×D71 | 1 | 1 | yes | characteristic |
| 267 | #358 | C2×D71 | 1 | 1 | yes | characteristic |
| 268 | #346 | — | 71 | 1 | no | — |
| 269 | #346 | — | 71 | 1 | no | — |
| 270 | C4×C16 | — | 71 | 1 | no | — |
| 271 | C2×Q16 | — | 71 | 1 | no | — |
| 272 | C2×Q16 | C22×D71 | 1 | 1 | yes | characteristic |
| 273 | C4⋊Q8 | — | 284 | 1 | no | — |
| 274 | C4⋊Q8 | — | 284 | 1 | no | — |
| 275 | C4⋊Q8 | — | 284 | 1 | no | — |
| 276 | C4⋊Q8 | — | 284 | 1 | no | — |
| 277 | C4⋊Q8 | — | 142 | 1 | no | — |
| 278 | C4⋊Q8 | — | 142 | 1 | no | — |
| 279 | C4⋊Q8 | — | 142 | 1 | no | — |
| 280 | C4⋊Q8 | — | 142 | 1 | no | — |
| 281 | #125 | — | 2 | 1 | no | — |
| 282 | #125 | — | 284 | 1 | no | — |
| 283 | #125 | — | 284 | 1 | no | — |
| 284 | #125 | — | 142 | 1 | no | — |
| 285 | C4×Q8 | — | 2 | 1 | no | — |
| 286 | C4×Q8 | — | 284 | 1 | no | — |
| 287 | C4×Q8 | — | 284 | 1 | no | — |
| 288 | C4×Q8 | — | 71 | 1 | no | — |
| 289 | C4×Q8 | — | 142 | 1 | no | — |
| 290 | C4×Q8 | — | 142 | 1 | no | — |
| 291 | C4×Q8 | — | 142 | 1 | no | — |
| 292 | C4×Q8 | — | 142 | 1 | no | — |
| 293 | C4×Q8 | — | 142 | 1 | no | — |
| 294 | Q32 | — | 71 | 4 | no | — |
| 295 | C2×C16 | — | 71 | 1 | no | — |
| 296 | C2×C16 | — | 71 | 1 | no | — |
| 297 | C2×C16 | C22×D71 | 1 | 1 | yes | characteristic |
| 298 | C2×C16 | C22×D71 | 1 | 1 | yes | characteristic |
| 299 | #107 | — | 71 | 1 | no | — |
| 300 | #107 | — | 71 | 1 | no | — |
| 301 | #107 | — | 71 | 1 | no | — |
| 302 | #107 | — | 142 | 1 | no | — |
| 303 | #107 | — | 142 | 1 | no | — |
| 304 | #107 | — | 142 | 1 | no | — |
| 305 | #107 | — | 142 | 1 | no | — |
| 306 | #107 | C22×D71 | 1 | 1 | yes | characteristic |
| 307 | #107 | C22×D71 | 1 | 1 | yes | characteristic |
| 308 | #107 | C22×D71 | 1 | 1 | yes | characteristic |
| 309 | #106 | — | 2 | 1 | no | — |
| 310 | #106 | — | 142 | 1 | no | — |
| 311 | C4⋊C8 | — | 71 | 1 | no | — |
| 312 | C4⋊C8 | — | 71 | 1 | no | — |
| 313 | C4⋊C8 | — | 71 | 1 | no | — |
| 314 | #103 | — | 2 | 1 | no | — |
| 315 | #103 | — | 142 | 1 | no | — |
| 316 | #103 | — | 142 | 1 | no | — |
| 317 | #103 | — | 142 | 1 | no | — |
| 318 | #103 | — | 142 | 1 | no | — |
| 319 | #103 | — | 142 | 1 | no | — |
| 320 | C4×C8 | — | 71 | 1 | no | — |
| 321 | C4×C8 | — | 71 | 1 | no | — |
| 322 | C4×C8 | C22×D71 | 1 | 1 | yes | characteristic |
| 323 | C2×Q8 | — | 2 | 1 | no | — |
| 324 | C2×Q8 | — | 284 | 1 | no | — |
| 325 | C2×Q8 | — | 284 | 1 | no | — |
| 326 | C2×Q8 | — | 284 | 1 | no | — |
| 327 | C2×Q8 | — | 284 | 1 | no | — |
| 328 | C2×Q8 | — | 71 | 1 | no | — |
| 329 | C2×Q8 | — | 142 | 1 | no | — |
| 330 | Q16 | — | 2 | 1 | no | — |
| 331 | Q16 | — | 71 | 2 | no | — |
| 332 | Q16 | — | 142 | 1 | no | — |
| 333 | Q16 | Q8×D71 | 1 | 2 | yes | — |
| 334 | C2×C8 | — | 71 | 1 | no | — |
| 335 | C2×C8 | — | 71 | 1 | no | — |
| 336 | C2×C8 | D4×D71 | 1 | 1 | yes | characteristic |
| 337 | C2×C8 | C23×D71 | 1 | 1 | yes | characteristic |
| 338 | C4⋊C4 | — | 2 | 1 | no | — |
| 339 | C4⋊C4 | — | 2 | 1 | no | — |
| 340 | C4⋊C4 | — | 2 | 1 | no | — |
| 341 | C4⋊C4 | — | 4 | 1 | no | — |
| 342 | C4⋊C4 | — | 4 | 1 | no | — |
| 343 | C4⋊C4 | — | 4 | 1 | no | — |
| 344 | C4⋊C4 | — | 284 | 1 | no | — |
| 345 | C4⋊C4 | — | 284 | 1 | no | — |
| 346 | C4⋊C4 | — | 284 | 1 | no | — |
| 347 | C4⋊C4 | — | 284 | 1 | no | — |
| 348 | C4⋊C4 | — | 284 | 1 | no | — |
| 349 | C4⋊C4 | — | 284 | 1 | no | — |
| 350 | C4⋊C4 | — | 284 | 1 | no | — |
| 351 | C4⋊C4 | — | 284 | 1 | no | — |
| 352 | C4⋊C4 | — | 284 | 1 | no | — |
| 353 | C4⋊C4 | — | 284 | 1 | no | — |
| 354 | C4⋊C4 | — | 284 | 1 | no | — |
| 355 | C4⋊C4 | — | 71 | 1 | no | — |
| 356 | C4⋊C4 | — | 71 | 1 | no | — |
| 357 | C4⋊C4 | — | 71 | 1 | no | — |
| 358 | C4⋊C4 | — | 142 | 1 | no | — |
| 359 | C4⋊C4 | — | 142 | 1 | no | — |
| 360 | C4⋊C4 | — | 142 | 1 | no | — |
| 361 | C42 | — | 4 | 1 | no | — |
| 362 | C42 | — | 284 | 1 | no | — |
| 363 | C42 | — | 284 | 1 | no | — |
| 364 | C42 | — | 284 | 1 | no | — |
| 365 | C42 | — | 284 | 1 | no | — |
| 366 | C42 | — | 284 | 1 | no | — |
| 367 | C42 | — | 71 | 1 | no | — |
| 368 | C42 | — | 71 | 1 | no | — |
| 369 | C42 | D4×D71 | 1 | 1 | yes | characteristic |
| 370 | C16 | — | 2 | 1 | no | — |
| 371 | C16 | — | 2 | 1 | no | — |
| 372 | C16 | — | 71 | 2 | no | — |
| 373 | C16 | — | 142 | 1 | no | — |
| 374 | Q8 | — | 2 | 2 | no | — |
| 375 | Q8 | — | 4 | 1 | no | — |
| 376 | Q8 | — | 284 | 1 | no | — |
| 377 | Q8 | — | 568 | 2 | no | — |
| 378 | Q8 | — | 1136 | 1 | no | — |
| 379 | Q8 | — | 1136 | 1 | no | — |
| 380 | Q8 | — | 1136 | 1 | no | — |
| 381 | Q8 | — | 142 | 2 | no | — |
| 382 | Q8 | — | 142 | 2 | no | — |
| 383 | C2×C4 | — | 4 | 1 | no | — |
| 384 | C2×C4 | — | 4 | 1 | no | — |
| 385 | C2×C4 | — | 4 | 1 | no | — |
| 386 | C2×C4 | — | 4 | 1 | no | — |
| 387 | C2×C4 | — | 284 | 1 | no | — |
| 388 | C2×C4 | — | 284 | 1 | no | — |
| 389 | C2×C4 | — | 284 | 1 | no | — |
| 390 | C2×C4 | — | 284 | 1 | no | — |
| 391 | C2×C4 | — | 71 | 1 | no | — |
| 392 | C2×C4 | — | 71 | 1 | no | — |
| 393 | C2×C4 | — | 71 | 1 | no | — |
| 394 | C2×C4 | — | 71 | 1 | no | — |
| 395 | C2×C4 | D8×D71 | 1 | 1 | yes | characteristic |
| 396 | C2×C4 | D8×D71 | 1 | 1 | yes | characteristic |
| 397 | C2×C4 | C2×D4×D71 | 1 | 1 | yes | characteristic |
| 398 | C8 | — | 2 | 1 | no | — |
| 399 | C8 | — | 142 | 1 | no | — |
| 400 | C8 | — | 142 | 1 | no | — |
| 401 | C8 | C2×Q8×D71 | 1 | 1 | yes | characteristic |
| 402 | C8 | #14556175 | 1 | 1 | yes | characteristic |
| 403 | C22 | C2×D8×D71 | 1 | 1 | yes | characteristic |
| 404 | C4 | — | 2 | 1 | no | — |
| 405 | C4 | — | 2 | 1 | no | — |
| 406 | C4 | — | 4 | 2 | no | — |
| 407 | C4 | — | 8 | 1 | no | — |
| 408 | C4 | — | 8 | 1 | no | — |
| 409 | C4 | — | 8 | 1 | no | — |
| 410 | C4 | — | 284 | 2 | no | — |
| 411 | C4 | — | 568 | 1 | no | — |
| 412 | C4 | — | 568 | 1 | no | — |
| 413 | C4 | — | 568 | 1 | no | — |
| 414 | C4 | — | 71 | 2 | no | — |
| 415 | C4 | — | 142 | 1 | no | — |
| 416 | C4 | — | 142 | 1 | no | — |
| 417 | C4 | — | 142 | 1 | no | — |
| 418 | C4 | #17986662 | 1 | 1 | yes | characteristic |
| 419 | C4 | #17986815 | 1 | 1 | yes | characteristic |
| 420 | C2 | #22601190 | 1 | 1 | yes | characteristic |
| 421 | C2 | #510×D71 | 1 | 1 | yes | characteristic |
| 422 | C2 | #22601483 | 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