← #31981300
Subgroups — #31981300
Order 18176.
602 conjugacy classes of subgroups.
The subgroup lattice has 442 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #22598922 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #22598145 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | C2×Q8×C71⋊C8 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #22587800 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #22587796 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #22587742 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #22587708 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #22587098 | C2 | 1 | 1 | yes | maximal, characteristic |
| 9 | #22587031 | C2 | 1 | 1 | yes | maximal, characteristic |
| 10 | #22587030 | C2 | 1 | 1 | yes | maximal, characteristic |
| 11 | C71×#3078 | C2 | 1 | 1 | yes | maximal, characteristic |
| 12 | #17986556 | C22 | 1 | 1 | yes | characteristic |
| 13 | #17986402 | C22 | 1 | 1 | yes | characteristic |
| 14 | #17986378 | C22 | 1 | 1 | yes | characteristic |
| 15 | #17986351 | C22 | 1 | 1 | yes | characteristic |
| 16 | #17986349 | C22 | 1 | 1 | yes | characteristic |
| 17 | #17986306 | — | 2 | 2 | no | — |
| 18 | #17986294 | C22 | 1 | 2 | yes | — |
| 19 | #17986284 | C22 | 1 | 2 | yes | — |
| 20 | #17986238 | — | 2 | 1 | no | — |
| 21 | #17986238 | — | 2 | 1 | no | — |
| 22 | Q8×C71⋊C8 | — | 2 | 1 | no | — |
| 23 | Q8×C71⋊C8 | — | 2 | 1 | no | — |
| 24 | Q8×C71⋊C8 | C22 | 1 | 2 | yes | — |
| 25 | Q8×C71⋊C8 | C22 | 1 | 2 | yes | — |
| 26 | C4×#11765855 | — | 2 | 1 | no | — |
| 27 | C4×#11765855 | — | 2 | 1 | no | — |
| 28 | #17986039 | — | 2 | 1 | no | — |
| 29 | #17986023 | C22 | 1 | 1 | yes | characteristic |
| 30 | C2×C4⋊(C71⋊C8) | — | 2 | 1 | no | — |
| 31 | C2×C4⋊(C71⋊C8) | C22 | 1 | 1 | yes | characteristic |
| 32 | #17986008 | — | 2 | 1 | no | — |
| 33 | C2×C4×C71⋊C8 | — | 2 | 1 | no | — |
| 34 | C2×C4×C71⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 35 | #17985751 | C22 | 1 | 2 | yes | — |
| 36 | #17985751 | C22 | 1 | 2 | yes | — |
| 37 | #17985748 | C22 | 1 | 2 | yes | — |
| 38 | #17985747 | C22 | 1 | 2 | yes | — |
| 39 | #17985745 | C22 | 1 | 2 | yes | — |
| 40 | #17985744 | C22 | 1 | 2 | yes | — |
| 41 | #533×C71 | C22 | 1 | 1 | yes | characteristic |
| 42 | C2×C4×Q8×C71 | C22 | 1 | 1 | yes | characteristic |
| 43 | #479×C71 | — | 2 | 2 | no | — |
| 44 | #477×C71 | C22 | 1 | 2 | yes | — |
| 45 | #475×C71 | C22 | 1 | 2 | yes | — |
| 46 | #428×C71 | — | 2 | 1 | no | — |
| 47 | #423×C71 | C22 | 1 | 1 | yes | characteristic |
| 48 | #419×C71 | — | 2 | 1 | no | — |
| 49 | C2×#11765855 | — | 2 | 1 | no | — |
| 50 | C2×#11765855 | — | 2 | 1 | no | — |
| 51 | C2×#11765849 | — | 2 | 1 | no | — |
| 52 | C22×C71⋊C8 | — | 2 | 1 | no | — |
| 53 | C22×C71⋊C8 | D4 | 1 | 1 | yes | characteristic |
| 54 | C22×C71⋊C8 | D4 | 1 | 1 | yes | characteristic |
| 55 | #14556128 | C23 | 1 | 1 | yes | characteristic |
| 56 | #14556128 | C23 | 1 | 1 | yes | characteristic |
| 57 | #14556120 | — | 2 | 1 | no | — |
| 58 | #14556107 | — | 2 | 1 | no | — |
| 59 | #14556107 | — | 2 | 1 | no | — |
| 60 | C4×Dic142 | — | 2 | 1 | no | — |
| 61 | C4×Dic142 | — | 2 | 1 | no | — |
| 62 | #14556087 | — | 2 | 1 | no | — |
| 63 | #14556061 | — | 2 | 1 | no | — |
| 64 | #14556061 | — | 2 | 1 | no | — |
| 65 | #14556061 | — | 2 | 2 | no | — |
| 66 | #14556059 | — | 2 | 2 | no | — |
| 67 | C4⋊(C71⋊C8) | — | 2 | 2 | no | — |
| 68 | C4⋊(C71⋊C8) | — | 2 | 2 | no | — |
| 69 | C4⋊(C71⋊C8) | — | 2 | 1 | no | — |
| 70 | C4⋊(C71⋊C8) | — | 2 | 1 | no | — |
| 71 | C4⋊(C71⋊C8) | C23 | 1 | 2 | yes | — |
| 72 | C4⋊(C71⋊C8) | C23 | 1 | 2 | yes | — |
| 73 | #14556052 | — | 2 | 1 | no | — |
| 74 | #14556052 | — | 2 | 1 | no | — |
| 75 | #14556052 | — | 2 | 2 | no | — |
| 76 | #14556052 | — | 2 | 2 | no | — |
| 77 | #14556051 | — | 2 | 1 | no | — |
| 78 | #14556051 | — | 2 | 1 | no | — |
| 79 | C4×C71⋊C8 | — | 2 | 2 | no | — |
| 80 | C4×C71⋊C8 | — | 2 | 2 | no | — |
| 81 | C4×C71⋊C8 | D4 | 1 | 1 | yes | characteristic |
| 82 | C4×C71⋊C8 | D4 | 1 | 1 | yes | characteristic |
| 83 | C4×C71⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 84 | C4×C71⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 85 | C22×Q8×C71 | D4 | 1 | 1 | yes | characteristic |
| 86 | C2×M16×C71 | — | 2 | 1 | no | — |
| 87 | C4⋊Q8×C71 | C23 | 1 | 1 | yes | characteristic |
| 88 | C4⋊Q8×C71 | C23 | 1 | 1 | yes | characteristic |
| 89 | #125×C71 | — | 2 | 1 | no | — |
| 90 | C22⋊Q8×C71 | — | 2 | 1 | no | — |
| 91 | C22⋊Q8×C71 | — | 2 | 1 | no | — |
| 92 | C4×Q8×C71 | — | 2 | 1 | no | — |
| 93 | C4×Q8×C71 | — | 2 | 1 | no | — |
| 94 | C4×Q8×C71 | — | 2 | 1 | no | — |
| 95 | C4×Q8×C71 | — | 2 | 1 | no | — |
| 96 | C4×Q8×C71 | D4 | 1 | 2 | yes | — |
| 97 | C4×Q8×C71 | C23 | 1 | 2 | yes | — |
| 98 | #117×C71 | — | 2 | 1 | no | — |
| 99 | C2×C4⋊C4×C71 | — | 2 | 1 | no | — |
| 100 | C2×C4⋊C4×C71 | D4 | 1 | 1 | yes | characteristic |
| 101 | C2×C42×C71 | — | 2 | 1 | no | — |
| 102 | C2×C42×C71 | C23 | 1 | 1 | yes | characteristic |
| 103 | #107×C71 | — | 2 | 2 | no | — |
| 104 | #106×C71 | — | 2 | 2 | no | — |
| 105 | C4⋊C8×C71 | — | 2 | 1 | no | — |
| 106 | C4⋊C8×C71 | C23 | 1 | 2 | yes | — |
| 107 | #103×C71 | — | 2 | 2 | no | — |
| 108 | #103×C71 | — | 2 | 2 | no | — |
| 109 | C2×Dic142 | — | 2 | 1 | no | — |
| 110 | C2×Dic142 | — | 2 | 1 | no | — |
| 111 | #11765855 | — | 4 | 2 | no | — |
| 112 | #11765855 | — | 4 | 2 | no | — |
| 113 | #11765849 | — | 4 | 2 | no | — |
| 114 | C2×C71⋊C8 | — | 2 | 2 | no | — |
| 115 | C2×C71⋊C8 | — | 2 | 2 | no | — |
| 116 | C2×C71⋊C8 | — | 2 | 2 | no | — |
| 117 | C2×C71⋊C8 | — | 4 | 1 | no | — |
| 118 | C2×C71⋊C8 | — | 4 | 2 | no | — |
| 119 | C2×C71⋊C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 120 | C2×C71⋊C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 121 | C2×C71⋊C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 122 | C2×C71⋊C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 123 | C4⋊Dic71 | — | 2 | 1 | no | — |
| 124 | C4⋊Dic71 | — | 2 | 1 | no | — |
| 125 | C4⋊Dic71 | — | 2 | 1 | no | — |
| 126 | C4⋊Dic71 | — | 2 | 1 | no | — |
| 127 | Dic71⋊C4 | — | 4 | 1 | no | — |
| 128 | Dic71⋊C4 | — | 4 | 1 | no | — |
| 129 | C22⋊Dic71 | — | 4 | 1 | no | — |
| 130 | C4×Dic71 | — | 4 | 1 | no | — |
| 131 | C2×Q8×C71 | — | 2 | 1 | no | — |
| 132 | C2×Q8×C71 | — | 2 | 2 | no | — |
| 133 | C2×Q8×C71 | — | 2 | 1 | no | — |
| 134 | C2×Q8×C71 | — | 2 | 1 | no | — |
| 135 | C2×Q8×C71 | Q16 | 1 | 4 | yes | complemented |
| 136 | C2×Q8×C71 | C2×D4 | 1 | 2 | yes | — |
| 137 | C22×C4×C71 | — | 2 | 1 | no | — |
| 138 | C22×C4×C71 | — | 2 | 1 | no | — |
| 139 | C22×C4×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 140 | C22×C4×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 141 | C22×C4×C71 | #41 | 1 | 1 | yes | characteristic |
| 142 | M16×C71 | — | 4 | 2 | no | — |
| 143 | C2×C8×C71 | — | 2 | 2 | no | — |
| 144 | C4⋊C4×C71 | — | 2 | 2 | no | — |
| 145 | C4⋊C4×C71 | — | 2 | 1 | no | — |
| 146 | C4⋊C4×C71 | — | 2 | 2 | no | — |
| 147 | C4⋊C4×C71 | — | 2 | 1 | no | — |
| 148 | C4⋊C4×C71 | — | 2 | 1 | no | — |
| 149 | C4⋊C4×C71 | — | 2 | 1 | no | — |
| 150 | C4⋊C4×C71 | — | 2 | 1 | no | — |
| 151 | C4⋊C4×C71 | — | 4 | 1 | no | — |
| 152 | C4⋊C4×C71 | — | 4 | 1 | no | — |
| 153 | C4⋊C4×C71 | C2×D4 | 1 | 2 | yes | — |
| 154 | C22⋊C4×C71 | — | 4 | 1 | no | — |
| 155 | C42×C71 | — | 2 | 2 | no | — |
| 156 | C42×C71 | — | 2 | 2 | no | — |
| 157 | C42×C71 | — | 4 | 1 | no | — |
| 158 | C42×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 159 | C42×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 160 | C42×C71 | #41 | 1 | 1 | yes | characteristic |
| 161 | C42×C71 | C24 | 1 | 1 | yes | characteristic |
| 162 | C23×C71 | #121 | 1 | 1 | yes | characteristic |
| 163 | Q8×C71 | — | 2 | 2 | no | — |
| 164 | Q8×C71 | — | 2 | 4 | no | — |
| 165 | Q8×C71 | — | 4 | 1 | no | — |
| 166 | Q8×C71 | — | 4 | 1 | no | — |
| 167 | Q8×C71 | — | 8 | 1 | no | — |
| 168 | Q8×C71 | C2×Q16 | 1 | 4 | yes | — |
| 169 | C2×C4×C71 | — | 2 | 2 | no | — |
| 170 | C2×C4×C71 | — | 2 | 4 | no | — |
| 171 | C2×C4×C71 | — | 2 | 1 | no | — |
| 172 | C2×C4×C71 | — | 2 | 1 | no | — |
| 173 | C2×C4×C71 | — | 2 | 2 | no | — |
| 174 | C2×C4×C71 | — | 4 | 1 | no | — |
| 175 | C2×C4×C71 | — | 4 | 2 | no | — |
| 176 | C2×C4×C71 | — | 4 | 1 | no | — |
| 177 | C2×C4×C71 | — | 4 | 1 | no | — |
| 178 | C2×C4×C71 | #121 | 1 | 1 | yes | characteristic |
| 179 | C2×C4×C71 | #121 | 1 | 1 | yes | characteristic |
| 180 | C2×C4×C71 | #121 | 1 | 1 | yes | characteristic |
| 181 | C2×C4×C71 | C2×Q16 | 1 | 2 | yes | — |
| 182 | C2×C4×C71 | #135 | 1 | 2 | yes | — |
| 183 | C2×C4×C71 | C22×D4 | 1 | 1 | yes | characteristic |
| 184 | C2×C4×C71 | C22×D4 | 1 | 1 | yes | characteristic |
| 185 | C2×C4×C71 | C2×#41 | 1 | 1 | yes | characteristic |
| 186 | C2×Dic71 | — | 4 | 1 | no | — |
| 187 | C2×Dic71 | — | 4 | 1 | no | — |
| 188 | Dic142 | — | 4 | 1 | no | — |
| 189 | Dic142 | — | 4 | 1 | no | — |
| 190 | Dic142 | — | 8 | 1 | no | — |
| 191 | C8×C71 | — | 4 | 2 | no | — |
| 192 | C71⋊C8 | — | 2 | 1 | no | — |
| 193 | C71⋊C8 | — | 2 | 1 | no | — |
| 194 | C71⋊C8 | — | 2 | 1 | no | — |
| 195 | C71⋊C8 | — | 4 | 2 | no | — |
| 196 | C71⋊C8 | — | 4 | 2 | no | — |
| 197 | C71⋊C8 | #137 | 1 | 2 | yes | — |
| 198 | C22×C71 | — | 2 | 1 | no | — |
| 199 | C22×C71 | — | 2 | 1 | no | — |
| 200 | C22×C71 | #467 | 1 | 2 | yes | — |
| 201 | C22×C71 | C2×#121 | 1 | 1 | yes | characteristic |
| 202 | C4×C71 | — | 2 | 1 | no | — |
| 203 | C4×C71 | — | 2 | 4 | no | — |
| 204 | C4×C71 | — | 2 | 1 | no | — |
| 205 | C4×C71 | — | 2 | 1 | no | — |
| 206 | C4×C71 | — | 4 | 2 | no | — |
| 207 | C4×C71 | — | 8 | 1 | no | — |
| 208 | C4×C71 | — | 8 | 1 | no | — |
| 209 | C4×C71 | #467 | 1 | 2 | yes | — |
| 210 | C4×C71 | C22×Q16 | 1 | 1 | yes | characteristic |
| 211 | C4×C71 | C2×#135 | 1 | 1 | yes | characteristic |
| 212 | C4×C71 | C2×#137 | 1 | 1 | yes | characteristic |
| 213 | C4×C71 | #575 | 1 | 1 | yes | characteristic |
| 214 | Dic71 | — | 8 | 1 | no | — |
| 215 | Dic71 | — | 8 | 1 | no | — |
| 216 | #19262 | — | 71 | 1 | no | maximal, Sylow |
| 217 | C2×C71 | — | 2 | 2 | no | — |
| 218 | C2×C71 | #3037 | 1 | 1 | yes | characteristic |
| 219 | C2×C71 | C2×#467 | 1 | 1 | yes | characteristic |
| 220 | C2×C71 | #3067 | 1 | 1 | yes | characteristic |
| 221 | #3170 | — | 71 | 1 | no | — |
| 222 | #3078 | — | 71 | 1 | no | — |
| 223 | #3078 | D71 | 1 | 1 | yes | characteristic |
| 224 | C2×C8×Q8 | — | 71 | 1 | no | — |
| 225 | #1684 | — | 71 | 2 | no | — |
| 226 | #1684 | — | 71 | 2 | no | — |
| 227 | #1676 | — | 71 | 2 | no | — |
| 228 | #1670 | — | 71 | 2 | no | — |
| 229 | #1567 | — | 71 | 1 | no | — |
| 230 | #1550 | — | 71 | 1 | no | — |
| 231 | #1550 | — | 71 | 1 | no | — |
| 232 | C71 | #19262 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 233 | #533 | — | 71 | 1 | no | — |
| 234 | #533 | C2×D71 | 1 | 1 | yes | characteristic |
| 235 | C2×C4×Q8 | C2×D71 | 1 | 1 | yes | characteristic |
| 236 | #500 | — | 71 | 1 | no | — |
| 237 | #494 | — | 71 | 1 | no | — |
| 238 | #487 | — | 71 | 1 | no | — |
| 239 | #487 | — | 71 | 1 | no | — |
| 240 | #479 | — | 2 | 2 | no | — |
| 241 | #479 | — | 142 | 2 | no | — |
| 242 | #477 | — | 71 | 2 | no | — |
| 243 | #477 | C2×D71 | 1 | 2 | yes | — |
| 244 | #475 | — | 71 | 2 | no | — |
| 245 | #475 | C2×D71 | 1 | 2 | yes | — |
| 246 | #467 | — | 142 | 1 | no | — |
| 247 | #467 | — | 142 | 1 | no | — |
| 248 | C8×Q8 | — | 71 | 2 | no | — |
| 249 | C8×Q8 | — | 71 | 2 | no | — |
| 250 | C8×Q8 | — | 142 | 1 | no | — |
| 251 | C8×Q8 | — | 142 | 1 | no | — |
| 252 | C4×Q16 | — | 142 | 1 | no | — |
| 253 | C4×Q16 | — | 142 | 1 | no | — |
| 254 | #428 | — | 2 | 1 | no | — |
| 255 | #428 | — | 142 | 1 | no | — |
| 256 | #423 | — | 71 | 1 | no | — |
| 257 | #423 | C2×D71 | 1 | 1 | yes | characteristic |
| 258 | C2×C4⋊C8 | — | 71 | 1 | no | — |
| 259 | C2×C4⋊C8 | — | 142 | 1 | no | — |
| 260 | #419 | — | 2 | 1 | no | — |
| 261 | #419 | — | 142 | 1 | no | — |
| 262 | C2×C4×C8 | — | 71 | 1 | no | — |
| 263 | C2×C4×C8 | — | 142 | 1 | no | — |
| 264 | #335 | — | 71 | 2 | no | — |
| 265 | #335 | — | 71 | 2 | no | — |
| 266 | #333 | — | 71 | 2 | no | — |
| 267 | #333 | — | 71 | 2 | no | — |
| 268 | #332 | — | 71 | 2 | no | — |
| 269 | #332 | — | 71 | 2 | no | — |
| 270 | C22×Q8 | C22⋊D71 | 1 | 1 | yes | characteristic |
| 271 | C2×Q16 | — | 142 | 1 | no | — |
| 272 | C2×Q16 | — | 142 | 1 | no | — |
| 273 | C2×M16 | — | 2 | 1 | no | — |
| 274 | C2×M16 | — | 142 | 1 | no | — |
| 275 | C22×C8 | — | 71 | 1 | no | — |
| 276 | C22×C8 | — | 71 | 1 | no | — |
| 277 | C22×C8 | — | 142 | 1 | no | — |
| 278 | C4⋊Q8 | — | 71 | 1 | no | — |
| 279 | C4⋊Q8 | — | 71 | 1 | no | — |
| 280 | C4⋊Q8 | C22×D71 | 1 | 1 | yes | characteristic |
| 281 | C4⋊Q8 | C22×D71 | 1 | 1 | yes | characteristic |
| 282 | #125 | — | 2 | 1 | no | — |
| 283 | #125 | — | 142 | 1 | no | — |
| 284 | C22⋊Q8 | — | 2 | 1 | no | — |
| 285 | C22⋊Q8 | — | 2 | 1 | no | — |
| 286 | C22⋊Q8 | — | 142 | 1 | no | — |
| 287 | C22⋊Q8 | — | 142 | 1 | no | — |
| 288 | C4×Q8 | — | 2 | 1 | no | — |
| 289 | C4×Q8 | — | 2 | 1 | no | — |
| 290 | C4×Q8 | — | 2 | 1 | no | — |
| 291 | C4×Q8 | — | 2 | 1 | no | — |
| 292 | C4×Q8 | — | 142 | 1 | no | — |
| 293 | C4×Q8 | — | 142 | 1 | no | — |
| 294 | C4×Q8 | C22⋊D71 | 1 | 2 | yes | — |
| 295 | C4×Q8 | C22×D71 | 1 | 2 | yes | — |
| 296 | #117 | — | 2 | 1 | no | — |
| 297 | #117 | — | 142 | 1 | no | — |
| 298 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 299 | C2×C4⋊C4 | C22⋊D71 | 1 | 1 | yes | characteristic |
| 300 | C2×C42 | — | 2 | 1 | no | — |
| 301 | C2×C42 | C22×D71 | 1 | 1 | yes | characteristic |
| 302 | #107 | — | 2 | 2 | no | — |
| 303 | #107 | — | 142 | 1 | no | — |
| 304 | #107 | — | 142 | 1 | no | — |
| 305 | #107 | — | 142 | 2 | no | — |
| 306 | #106 | — | 2 | 2 | no | — |
| 307 | #106 | — | 142 | 2 | no | — |
| 308 | C4⋊C8 | — | 2 | 1 | no | — |
| 309 | C4⋊C8 | — | 71 | 2 | no | — |
| 310 | C4⋊C8 | — | 71 | 2 | no | — |
| 311 | C4⋊C8 | — | 142 | 2 | no | — |
| 312 | C4⋊C8 | — | 142 | 2 | no | — |
| 313 | C4⋊C8 | — | 142 | 1 | no | — |
| 314 | C4⋊C8 | — | 142 | 1 | no | — |
| 315 | C4⋊C8 | C22×D71 | 1 | 2 | yes | — |
| 316 | #103 | — | 2 | 2 | no | — |
| 317 | #103 | — | 2 | 2 | no | — |
| 318 | #103 | — | 142 | 1 | no | — |
| 319 | #103 | — | 142 | 1 | no | — |
| 320 | #103 | — | 142 | 1 | no | — |
| 321 | #103 | — | 142 | 1 | no | — |
| 322 | #103 | — | 142 | 2 | no | — |
| 323 | #103 | — | 142 | 2 | no | — |
| 324 | C4×C8 | — | 71 | 1 | no | — |
| 325 | C4×C8 | — | 71 | 1 | no | — |
| 326 | C4×C8 | — | 71 | 1 | no | — |
| 327 | C4×C8 | — | 71 | 1 | no | — |
| 328 | C4×C8 | — | 142 | 2 | no | — |
| 329 | C4×C8 | — | 142 | 2 | no | — |
| 330 | C2×Q8 | — | 2 | 1 | no | — |
| 331 | C2×Q8 | — | 2 | 2 | no | — |
| 332 | C2×Q8 | — | 2 | 1 | no | — |
| 333 | C2×Q8 | — | 2 | 1 | no | — |
| 334 | C2×Q8 | — | 142 | 1 | no | — |
| 335 | C2×Q8 | — | 142 | 1 | no | — |
| 336 | C2×Q8 | #11765855 | 1 | 4 | yes | complemented |
| 337 | C2×Q8 | C2×C22⋊D71 | 1 | 2 | yes | — |
| 338 | C22×C4 | — | 2 | 1 | no | — |
| 339 | C22×C4 | — | 2 | 1 | no | — |
| 340 | C22×C4 | D4×D71 | 1 | 1 | yes | characteristic |
| 341 | C22×C4 | C2×C22⋊D71 | 1 | 1 | yes | characteristic |
| 342 | C22×C4 | #11765864 | 1 | 1 | yes | characteristic |
| 343 | Q16 | — | 284 | 2 | no | — |
| 344 | Q16 | — | 284 | 2 | no | — |
| 345 | M16 | — | 4 | 2 | no | — |
| 346 | M16 | — | 284 | 2 | no | — |
| 347 | C2×C8 | — | 2 | 2 | no | — |
| 348 | C2×C8 | — | 284 | 2 | no | — |
| 349 | C2×C8 | — | 284 | 1 | no | — |
| 350 | C2×C8 | — | 71 | 1 | no | — |
| 351 | C2×C8 | — | 71 | 1 | no | — |
| 352 | C2×C8 | — | 71 | 1 | no | — |
| 353 | C2×C8 | — | 71 | 1 | no | — |
| 354 | C2×C8 | — | 142 | 2 | no | — |
| 355 | C2×C8 | — | 142 | 2 | no | — |
| 356 | C2×C8 | — | 142 | 2 | no | — |
| 357 | C4⋊C4 | — | 2 | 2 | no | — |
| 358 | C4⋊C4 | — | 2 | 2 | no | — |
| 359 | C4⋊C4 | — | 2 | 1 | no | — |
| 360 | C4⋊C4 | — | 2 | 1 | no | — |
| 361 | C4⋊C4 | — | 2 | 1 | no | — |
| 362 | C4⋊C4 | — | 2 | 1 | no | — |
| 363 | C4⋊C4 | — | 2 | 1 | no | — |
| 364 | C4⋊C4 | — | 4 | 1 | no | — |
| 365 | C4⋊C4 | — | 4 | 1 | no | — |
| 366 | C4⋊C4 | — | 284 | 1 | no | — |
| 367 | C4⋊C4 | — | 284 | 1 | no | — |
| 368 | C4⋊C4 | — | 142 | 1 | no | — |
| 369 | C4⋊C4 | — | 142 | 1 | no | — |
| 370 | C4⋊C4 | — | 142 | 1 | no | — |
| 371 | C4⋊C4 | — | 142 | 1 | no | — |
| 372 | C4⋊C4 | C2×C22⋊D71 | 1 | 2 | yes | — |
| 373 | C22⋊C4 | — | 4 | 1 | no | — |
| 374 | C22⋊C4 | — | 284 | 1 | no | — |
| 375 | C42 | — | 2 | 2 | no | — |
| 376 | C42 | — | 2 | 2 | no | — |
| 377 | C42 | — | 4 | 1 | no | — |
| 378 | C42 | — | 284 | 1 | no | — |
| 379 | C42 | D4×D71 | 1 | 1 | yes | characteristic |
| 380 | C42 | C2×C22⋊D71 | 1 | 1 | yes | characteristic |
| 381 | C42 | #11765864 | 1 | 1 | yes | characteristic |
| 382 | C42 | C23×D71 | 1 | 1 | yes | characteristic |
| 383 | C23 | #14556100 | 1 | 1 | yes | characteristic |
| 384 | Q8 | — | 2 | 4 | no | — |
| 385 | Q8 | — | 2 | 2 | no | — |
| 386 | Q8 | — | 4 | 1 | no | — |
| 387 | Q8 | — | 4 | 1 | no | — |
| 388 | Q8 | — | 8 | 1 | no | — |
| 389 | Q8 | — | 284 | 1 | no | — |
| 390 | Q8 | — | 284 | 1 | no | — |
| 391 | Q8 | — | 568 | 1 | no | — |
| 392 | Q8 | C2×#11765855 | 1 | 4 | yes | — |
| 393 | C2×C4 | — | 2 | 2 | no | — |
| 394 | C2×C4 | — | 2 | 4 | no | — |
| 395 | C2×C4 | — | 2 | 1 | no | — |
| 396 | C2×C4 | — | 2 | 1 | no | — |
| 397 | C2×C4 | — | 2 | 2 | no | — |
| 398 | C2×C4 | — | 4 | 1 | no | — |
| 399 | C2×C4 | — | 4 | 2 | no | — |
| 400 | C2×C4 | — | 4 | 1 | no | — |
| 401 | C2×C4 | — | 4 | 1 | no | — |
| 402 | C2×C4 | — | 284 | 1 | no | — |
| 403 | C2×C4 | — | 284 | 1 | no | — |
| 404 | C2×C4 | #14556100 | 1 | 1 | yes | characteristic |
| 405 | C2×C4 | #14556100 | 1 | 1 | yes | characteristic |
| 406 | C2×C4 | #14556100 | 1 | 1 | yes | characteristic |
| 407 | C2×C4 | C2×#11765855 | 1 | 2 | yes | — |
| 408 | C2×C4 | #14556148 | 1 | 2 | yes | — |
| 409 | C2×C4 | C2×D4×D71 | 1 | 1 | yes | characteristic |
| 410 | C2×C4 | C22×C22⋊D71 | 1 | 1 | yes | characteristic |
| 411 | C2×C4 | C2×#11765864 | 1 | 1 | yes | characteristic |
| 412 | C8 | — | 4 | 2 | no | — |
| 413 | C8 | — | 284 | 2 | no | — |
| 414 | C8 | — | 284 | 2 | no | — |
| 415 | C8 | — | 71 | 2 | no | — |
| 416 | C8 | — | 142 | 1 | no | — |
| 417 | C8 | — | 142 | 1 | no | — |
| 418 | C8 | — | 142 | 1 | no | — |
| 419 | C22 | — | 2 | 1 | no | — |
| 420 | C22 | — | 2 | 1 | no | — |
| 421 | C22 | #17986238 | 1 | 2 | yes | — |
| 422 | C22 | C2×#14556100 | 1 | 1 | yes | characteristic |
| 423 | C4 | — | 2 | 4 | no | — |
| 424 | C4 | — | 2 | 1 | no | — |
| 425 | C4 | — | 2 | 1 | no | — |
| 426 | C4 | — | 2 | 1 | no | — |
| 427 | C4 | — | 4 | 2 | no | — |
| 428 | C4 | — | 8 | 1 | no | — |
| 429 | C4 | — | 8 | 1 | no | — |
| 430 | C4 | — | 568 | 1 | no | — |
| 431 | C4 | — | 568 | 1 | no | — |
| 432 | C4 | #17986238 | 1 | 2 | yes | — |
| 433 | C4 | C22×#11765855 | 1 | 1 | yes | characteristic |
| 434 | C4 | C2×#14556148 | 1 | 1 | yes | characteristic |
| 435 | C4 | #137×D71 | 1 | 1 | yes | characteristic |
| 436 | C4 | #17986798 | 1 | 1 | yes | characteristic |
| 437 | C2 | — | 2 | 2 | no | — |
| 438 | C2 | #22597809 | 1 | 1 | yes | characteristic |
| 439 | C2 | C2×#17986238 | 1 | 1 | yes | characteristic |
| 440 | C2 | #22598057 | 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