← #32889496
Subgroups — #32889496
Order 18176.
1762 conjugacy classes of subgroups.
The subgroup lattice has 624 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 | #22601378 | C2 | 1 | 4 | yes | maximal, complemented |
| 3 | #22601360 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #22601161 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #22601087 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #22599401 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #22599390 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #22599327 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #22598631 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #22598583 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #22598491 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | #22597446 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | C71×#3510 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #17986747 | — | 2 | 2 | no | — |
| 15 | #17986709 | C22 | 1 | 4 | yes | complemented |
| 16 | #17986671 | C22 | 1 | 4 | yes | complemented |
| 17 | #17986652 | — | 2 | 2 | no | — |
| 18 | #17986604 | C22 | 1 | 2 | yes | — |
| 19 | #17986604 | C22 | 1 | 2 | yes | — |
| 20 | #17986579 | — | 2 | 4 | no | — |
| 21 | #17986549 | C22 | 1 | 2 | yes | — |
| 22 | #17986389 | C22 | 1 | 2 | yes | — |
| 23 | #17986389 | C22 | 1 | 4 | yes | — |
| 24 | #17986389 | C22 | 1 | 2 | yes | complemented |
| 25 | #17986375 | C22 | 1 | 2 | yes | — |
| 26 | #17986373 | C22 | 1 | 2 | yes | complemented |
| 27 | #17986367 | C22 | 1 | 2 | yes | complemented |
| 28 | #17986363 | C22 | 1 | 2 | yes | — |
| 29 | #17986358 | C22 | 1 | 4 | yes | — |
| 30 | #17986353 | C22 | 1 | 2 | yes | — |
| 31 | #17986353 | C22 | 1 | 2 | yes | complemented |
| 32 | #17986323 | C22 | 1 | 4 | yes | — |
| 33 | #17986306 | C22 | 1 | 4 | yes | complemented |
| 34 | #17986299 | C22 | 1 | 4 | yes | — |
| 35 | #17986284 | C22 | 1 | 2 | yes | complemented |
| 36 | #17986279 | C22 | 1 | 2 | yes | complemented |
| 37 | #17986211 | C22 | 1 | 4 | yes | — |
| 38 | #17986211 | C22 | 1 | 4 | yes | — |
| 39 | #17986211 | C22 | 1 | 4 | yes | — |
| 40 | #17986211 | C22 | 1 | 4 | yes | complemented |
| 41 | #17986201 | C22 | 1 | 4 | yes | complemented |
| 42 | #17986199 | C22 | 1 | 2 | yes | complemented |
| 43 | #17986199 | C22 | 1 | 4 | yes | complemented |
| 44 | #17986194 | C22 | 1 | 4 | yes | — |
| 45 | #17986194 | C22 | 1 | 2 | yes | complemented |
| 46 | #17986191 | C22 | 1 | 4 | yes | — |
| 47 | #17986144 | C22 | 1 | 4 | yes | — |
| 48 | #17986138 | C22 | 1 | 4 | yes | — |
| 49 | #17986133 | C22 | 1 | 4 | yes | — |
| 50 | #17986130 | C22 | 1 | 4 | yes | complemented |
| 51 | #17986130 | C22 | 1 | 4 | yes | complemented |
| 52 | #17986109 | C22 | 1 | 4 | yes | — |
| 53 | #17986109 | C22 | 1 | 4 | yes | complemented |
| 54 | #17986097 | C22 | 1 | 4 | yes | complemented |
| 55 | #17986097 | C22 | 1 | 4 | yes | complemented |
| 56 | C4×#11765852 | C22 | 1 | 4 | yes | complemented |
| 57 | C4×#11765850 | C22 | 1 | 4 | yes | — |
| 58 | #17986060 | C22 | 1 | 2 | yes | — |
| 59 | #17986060 | C22 | 1 | 2 | yes | — |
| 60 | #17986056 | C22 | 1 | 2 | yes | — |
| 61 | #559×C71 | C22 | 1 | 4 | yes | — |
| 62 | #556×C71 | C22 | 1 | 4 | yes | — |
| 63 | #551×C71 | — | 2 | 4 | no | — |
| 64 | #542×C71 | — | 2 | 2 | no | — |
| 65 | #536×C71 | C22 | 1 | 1 | yes | characteristic |
| 66 | #535×C71 | C22 | 1 | 1 | yes | characteristic |
| 67 | #533×C71 | C22 | 1 | 1 | yes | characteristic |
| 68 | #529×C71 | — | 2 | 2 | no | — |
| 69 | C2×#124×C71 | C22 | 1 | 1 | yes | characteristic |
| 70 | #519×C71 | C22 | 1 | 1 | yes | characteristic |
| 71 | #518×C71 | C22 | 1 | 1 | yes | characteristic |
| 72 | C4×#41×C71 | C22 | 1 | 1 | yes | characteristic |
| 73 | C2×#11765866 | — | 2 | 4 | no | — |
| 74 | C2×#11765865 | — | 2 | 2 | no | — |
| 75 | C2×#11765852 | C23 | 1 | 4 | yes | — |
| 76 | C2×#11765852 | C23 | 1 | 4 | yes | — |
| 77 | C2×#11765852 | C23 | 1 | 4 | yes | — |
| 78 | C2×#11765850 | C23 | 1 | 4 | yes | — |
| 79 | C2×#11765850 | C23 | 1 | 4 | yes | — |
| 80 | C2×#11765850 | C23 | 1 | 4 | yes | — |
| 81 | #14556128 | C23 | 1 | 2 | yes | — |
| 82 | #14556125 | C23 | 1 | 2 | yes | — |
| 83 | #14556125 | C23 | 1 | 2 | yes | — |
| 84 | #14556125 | C23 | 1 | 2 | yes | — |
| 85 | #14556120 | C23 | 1 | 2 | yes | — |
| 86 | #14556120 | C23 | 1 | 2 | yes | — |
| 87 | #14556116 | — | 2 | 2 | no | — |
| 88 | #14556113 | — | 2 | 4 | no | — |
| 89 | #14556113 | — | 2 | 4 | no | — |
| 90 | #14556106 | — | 2 | 4 | no | — |
| 91 | #14556106 | — | 2 | 4 | no | — |
| 92 | #14556104 | — | 2 | 4 | no | — |
| 93 | #14556103 | — | 2 | 4 | no | — |
| 94 | #14556103 | — | 2 | 4 | no | — |
| 95 | #14556103 | — | 2 | 4 | no | — |
| 96 | #14556102 | — | 2 | 2 | no | — |
| 97 | #14556102 | C23 | 1 | 4 | yes | — |
| 98 | #14556101 | — | 2 | 4 | no | — |
| 99 | #14556101 | — | 2 | 4 | no | — |
| 100 | C4×D284 | — | 2 | 2 | no | — |
| 101 | C4×D284 | C23 | 1 | 4 | yes | — |
| 102 | C4×D284 | C23 | 1 | 4 | yes | — |
| 103 | C4×D284 | C23 | 1 | 4 | yes | — |
| 104 | C4⋊C4×D71 | — | 2 | 4 | no | — |
| 105 | #14556061 | C23 | 1 | 4 | yes | — |
| 106 | #14556059 | C23 | 1 | 4 | yes | — |
| 107 | C4⋊(C71⋊C8) | C23 | 1 | 4 | yes | — |
| 108 | C4⋊(C71⋊C8) | C23 | 1 | 2 | yes | — |
| 109 | C4⋊(C71⋊C8) | C23 | 1 | 2 | yes | — |
| 110 | C4⋊(C71⋊C8) | C23 | 1 | 4 | yes | — |
| 111 | #14556052 | C23 | 1 | 4 | yes | — |
| 112 | #14556052 | C23 | 1 | 4 | yes | — |
| 113 | #14556052 | C23 | 1 | 4 | yes | — |
| 114 | #14556049 | C23 | 1 | 4 | yes | — |
| 115 | #14556049 | C23 | 1 | 4 | yes | — |
| 116 | #14556049 | C23 | 1 | 4 | yes | — |
| 117 | #14556048 | C23 | 1 | 4 | yes | — |
| 118 | #14556048 | C23 | 1 | 4 | yes | — |
| 119 | C22⋊(C71⋊C8) | C23 | 1 | 4 | yes | — |
| 120 | #14556039 | C23 | 1 | 4 | yes | — |
| 121 | #14556039 | C23 | 1 | 2 | yes | — |
| 122 | #14556039 | C23 | 1 | 2 | yes | — |
| 123 | C4×C71⋊C8 | C23 | 1 | 2 | yes | — |
| 124 | C4×C71⋊C8 | C23 | 1 | 2 | yes | — |
| 125 | C2×#41×C71 | C23 | 1 | 1 | yes | characteristic |
| 126 | C22×Q8×C71 | C23 | 1 | 1 | yes | characteristic |
| 127 | C22×D4×C71 | C23 | 1 | 1 | yes | characteristic |
| 128 | C4⋊Q8×C71 | D4 | 1 | 2 | yes | — |
| 129 | C4⋊Q8×C71 | C23 | 1 | 2 | yes | — |
| 130 | #127×C71 | C23 | 1 | 2 | yes | — |
| 131 | #126×C71 | — | 2 | 4 | no | — |
| 132 | #126×C71 | — | 2 | 4 | no | — |
| 133 | #125×C71 | D4 | 1 | 2 | yes | — |
| 134 | #124×C71 | — | 2 | 4 | no | — |
| 135 | #124×C71 | — | 2 | 1 | no | — |
| 136 | #124×C71 | — | 2 | 1 | no | — |
| 137 | #124×C71 | C23 | 1 | 2 | yes | — |
| 138 | #124×C71 | C23 | 1 | 2 | yes | — |
| 139 | #124×C71 | C23 | 1 | 4 | yes | — |
| 140 | #123×C71 | — | 2 | 4 | no | — |
| 141 | #123×C71 | — | 2 | 4 | no | — |
| 142 | #123×C71 | — | 2 | 2 | no | — |
| 143 | C22⋊Q8×C71 | — | 2 | 4 | no | — |
| 144 | C22⋊Q8×C71 | — | 2 | 2 | no | — |
| 145 | C22⋊Q8×C71 | D4 | 1 | 4 | yes | — |
| 146 | #121×C71 | — | 2 | 2 | no | — |
| 147 | #120×C71 | — | 2 | 2 | no | — |
| 148 | C4×Q8×C71 | — | 2 | 2 | no | — |
| 149 | C4×Q8×C71 | C23 | 1 | 4 | yes | — |
| 150 | C4×Q8×C71 | C23 | 1 | 2 | yes | — |
| 151 | C4×Q8×C71 | C23 | 1 | 4 | yes | — |
| 152 | C4×D4×C71 | — | 2 | 2 | no | — |
| 153 | C4×D4×C71 | — | 2 | 2 | no | — |
| 154 | C4×D4×C71 | — | 2 | 4 | no | — |
| 155 | C4×D4×C71 | C23 | 1 | 4 | yes | — |
| 156 | C4×D4×C71 | C23 | 1 | 2 | yes | — |
| 157 | #117×C71 | — | 2 | 4 | no | — |
| 158 | #117×C71 | — | 2 | 2 | no | — |
| 159 | #117×C71 | — | 2 | 1 | no | — |
| 160 | #117×C71 | C23 | 1 | 1 | yes | characteristic |
| 161 | #117×C71 | C23 | 1 | 1 | yes | characteristic |
| 162 | #117×C71 | C23 | 1 | 1 | yes | characteristic |
| 163 | C2×C22⋊C4×C71 | — | 2 | 2 | no | — |
| 164 | C2×C22⋊C4×C71 | — | 2 | 2 | no | — |
| 165 | C2×C42×C71 | — | 2 | 1 | no | — |
| 166 | C2×C42×C71 | C23 | 1 | 1 | yes | characteristic |
| 167 | #11765866 | — | 8 | 8 | no | — |
| 168 | #11765865 | — | 8 | 4 | no | — |
| 169 | C2×Dic142 | — | 2 | 2 | no | — |
| 170 | C2×D284 | — | 2 | 2 | no | — |
| 171 | C2×D284 | — | 2 | 2 | no | — |
| 172 | C2×D284 | — | 2 | 4 | no | — |
| 173 | C2×D284 | — | 2 | 4 | no | — |
| 174 | C2×D284 | C24 | 1 | 4 | yes | — |
| 175 | C2×C22⋊D71 | — | 2 | 4 | no | — |
| 176 | C2×C4×D71 | — | 2 | 4 | no | — |
| 177 | C2×C4×D71 | — | 2 | 4 | no | — |
| 178 | C2×C4×D71 | — | 2 | 4 | no | — |
| 179 | #11765852 | — | 4 | 4 | no | — |
| 180 | #11765852 | — | 4 | 4 | no | — |
| 181 | #11765852 | — | 4 | 4 | no | — |
| 182 | #11765850 | — | 4 | 4 | no | — |
| 183 | #11765850 | — | 4 | 4 | no | — |
| 184 | #11765850 | — | 4 | 4 | no | — |
| 185 | C2×C71⋊C8 | C24 | 1 | 4 | yes | — |
| 186 | C2×C71⋊C8 | C24 | 1 | 4 | yes | — |
| 187 | C4⋊Dic71 | — | 2 | 2 | no | — |
| 188 | C4⋊Dic71 | C24 | 1 | 4 | yes | — |
| 189 | Dic71⋊C4 | — | 2 | 4 | no | — |
| 190 | Dic71⋊C4 | — | 2 | 4 | no | — |
| 191 | (C2×D71)⋊C4 | — | 2 | 4 | no | — |
| 192 | (C2×D71)⋊C4 | — | 2 | 4 | no | — |
| 193 | (C2×D71)⋊C4 | — | 2 | 4 | no | — |
| 194 | (C2×D71)⋊C4 | — | 2 | 4 | no | — |
| 195 | C24×C71 | — | 2 | 1 | no | — |
| 196 | #41×C71 | — | 4 | 2 | no | — |
| 197 | C2×Q8×C71 | — | 2 | 1 | no | — |
| 198 | C2×Q8×C71 | — | 4 | 2 | no | — |
| 199 | C2×Q8×C71 | C2×D4 | 1 | 4 | yes | — |
| 200 | C2×Q8×C71 | C24 | 1 | 2 | yes | — |
| 201 | C2×Q8×C71 | C24 | 1 | 1 | yes | characteristic |
| 202 | C2×D4×C71 | — | 2 | 1 | no | — |
| 203 | C2×D4×C71 | — | 2 | 1 | no | — |
| 204 | C2×D4×C71 | — | 2 | 4 | no | — |
| 205 | C2×D4×C71 | — | 4 | 2 | no | — |
| 206 | C2×D4×C71 | C24 | 1 | 2 | yes | — |
| 207 | C2×D4×C71 | C24 | 1 | 1 | yes | characteristic |
| 208 | C22×C4×C71 | — | 2 | 1 | no | — |
| 209 | C22×C4×C71 | — | 2 | 1 | no | — |
| 210 | C22×C4×C71 | — | 2 | 2 | no | — |
| 211 | C22×C4×C71 | — | 2 | 4 | no | — |
| 212 | C22×C4×C71 | C2×D4 | 1 | 2 | yes | — |
| 213 | C22×C4×C71 | C24 | 1 | 1 | yes | characteristic |
| 214 | C4⋊C4×C71 | — | 2 | 2 | no | — |
| 215 | C4⋊C4×C71 | — | 2 | 4 | no | — |
| 216 | C4⋊C4×C71 | — | 2 | 4 | no | — |
| 217 | C4⋊C4×C71 | C2×D4 | 1 | 4 | yes | — |
| 218 | C4⋊C4×C71 | C2×D4 | 1 | 2 | yes | — |
| 219 | C4⋊C4×C71 | C2×D4 | 1 | 2 | yes | — |
| 220 | C4⋊C4×C71 | C2×D4 | 1 | 4 | yes | — |
| 221 | C4⋊C4×C71 | C2×D4 | 1 | 4 | yes | — |
| 222 | C4⋊C4×C71 | C24 | 1 | 2 | yes | — |
| 223 | C22⋊C4×C71 | — | 2 | 1 | no | — |
| 224 | C22⋊C4×C71 | — | 2 | 4 | no | — |
| 225 | C22⋊C4×C71 | — | 2 | 4 | no | — |
| 226 | C22⋊C4×C71 | — | 2 | 4 | no | — |
| 227 | C22⋊C4×C71 | — | 2 | 2 | no | — |
| 228 | C22⋊C4×C71 | — | 2 | 4 | no | — |
| 229 | C22⋊C4×C71 | — | 2 | 4 | no | — |
| 230 | C22⋊C4×C71 | C2×D4 | 1 | 2 | yes | — |
| 231 | C22⋊C4×C71 | C2×D4 | 1 | 2 | yes | — |
| 232 | C42×C71 | — | 2 | 2 | no | — |
| 233 | C42×C71 | — | 2 | 1 | no | — |
| 234 | C42×C71 | — | 2 | 4 | no | — |
| 235 | C42×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 236 | C42×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 237 | C42×C71 | C24 | 1 | 2 | yes | — |
| 238 | C42×C71 | C24 | 1 | 2 | yes | — |
| 239 | C42×C71 | C24 | 1 | 2 | yes | — |
| 240 | C23×C71 | — | 2 | 2 | no | — |
| 241 | C23×C71 | — | 2 | 1 | no | — |
| 242 | C23×C71 | — | 4 | 2 | no | — |
| 243 | C23×C71 | — | 8 | 2 | no | — |
| 244 | C23×C71 | C22×D4 | 1 | 1 | yes | characteristic |
| 245 | C22×D71 | — | 2 | 4 | no | — |
| 246 | Q8×C71 | — | 2 | 4 | no | — |
| 247 | Q8×C71 | — | 2 | 2 | no | — |
| 248 | Q8×C71 | — | 4 | 4 | no | — |
| 249 | Q8×C71 | — | 4 | 2 | no | — |
| 250 | D4×C71 | — | 2 | 4 | no | — |
| 251 | D4×C71 | — | 2 | 2 | no | — |
| 252 | D4×C71 | — | 4 | 2 | no | — |
| 253 | D4×C71 | — | 4 | 2 | no | — |
| 254 | D4×C71 | — | 8 | 4 | no | — |
| 255 | C2×C4×C71 | — | 2 | 2 | no | — |
| 256 | C2×C4×C71 | — | 2 | 2 | no | — |
| 257 | C2×C4×C71 | — | 2 | 2 | no | — |
| 258 | C2×C4×C71 | — | 2 | 1 | no | — |
| 259 | C2×C4×C71 | — | 4 | 2 | no | — |
| 260 | C2×C4×C71 | — | 4 | 2 | no | — |
| 261 | C2×C4×C71 | — | 4 | 2 | no | — |
| 262 | C2×C4×C71 | — | 8 | 2 | no | — |
| 263 | C2×C4×C71 | — | 8 | 4 | no | — |
| 264 | C2×C4×C71 | C22×D4 | 1 | 1 | yes | characteristic |
| 265 | C2×C4×C71 | C22×D4 | 1 | 2 | yes | — |
| 266 | C2×C4×C71 | C22×D4 | 1 | 4 | yes | — |
| 267 | C2×C4×C71 | C22×D4 | 1 | 2 | yes | — |
| 268 | C2×C4×C71 | C22×D4 | 1 | 4 | yes | — |
| 269 | C2×C4×C71 | C25 | 1 | 1 | yes | characteristic |
| 270 | C22⋊D71 | — | 8 | 4 | no | — |
| 271 | C2×Dic71 | — | 2 | 4 | no | — |
| 272 | D284 | — | 2 | 4 | no | — |
| 273 | D284 | — | 2 | 4 | no | — |
| 274 | D284 | — | 4 | 4 | no | — |
| 275 | D284 | — | 8 | 2 | no | — |
| 276 | D284 | — | 8 | 4 | no | — |
| 277 | D284 | — | 8 | 4 | no | — |
| 278 | C4×D71 | — | 4 | 8 | no | — |
| 279 | C4×D71 | — | 8 | 4 | no | — |
| 280 | C4×D71 | — | 8 | 4 | no | — |
| 281 | Dic142 | — | 8 | 2 | no | — |
| 282 | C71⋊C8 | — | 2 | 4 | no | — |
| 283 | C71⋊C8 | — | 2 | 4 | no | — |
| 284 | C22×C71 | — | 2 | 2 | no | — |
| 285 | C22×C71 | — | 2 | 1 | no | — |
| 286 | C22×C71 | — | 4 | 2 | no | — |
| 287 | C22×C71 | — | 4 | 4 | no | — |
| 288 | C22×C71 | — | 4 | 1 | no | — |
| 289 | C22×C71 | — | 4 | 2 | no | — |
| 290 | C22×C71 | — | 16 | 2 | no | — |
| 291 | C22×C71 | C23×D4 | 1 | 1 | yes | characteristic |
| 292 | C2×D71 | — | 4 | 4 | no | — |
| 293 | C2×D71 | — | 4 | 4 | no | — |
| 294 | C2×D71 | — | 4 | 4 | no | — |
| 295 | C4×C71 | — | 2 | 2 | no | — |
| 296 | C4×C71 | — | 2 | 2 | no | — |
| 297 | C4×C71 | — | 2 | 4 | no | — |
| 298 | C4×C71 | — | 2 | 4 | no | — |
| 299 | C4×C71 | — | 2 | 1 | no | — |
| 300 | C4×C71 | — | 4 | 2 | no | — |
| 301 | C4×C71 | — | 4 | 1 | no | — |
| 302 | C4×C71 | — | 4 | 2 | no | — |
| 303 | C4×C71 | #585 | 1 | 2 | yes | — |
| 304 | Dic71 | — | 4 | 4 | no | — |
| 305 | #61942 | — | 71 | 1 | no | maximal, Sylow |
| 306 | C2×C71 | — | 4 | 1 | no | — |
| 307 | C2×C71 | — | 8 | 1 | no | — |
| 308 | C2×C71 | — | 8 | 2 | no | — |
| 309 | C2×C71 | #3487 | 1 | 1 | yes | characteristic |
| 310 | C2×C71 | #3585 | 1 | 2 | yes | — |
| 311 | D71 | — | 8 | 4 | no | — |
| 312 | #3548 | — | 71 | 1 | no | — |
| 313 | #3510 | D71 | 1 | 1 | yes | characteristic, complemented |
| 314 | #3399 | — | 71 | 4 | no | — |
| 315 | #3397 | — | 71 | 4 | no | — |
| 316 | #3376 | — | 71 | 4 | no | — |
| 317 | #3370 | — | 71 | 4 | no | — |
| 318 | #3221 | — | 71 | 2 | no | — |
| 319 | #3220 | — | 71 | 2 | no | — |
| 320 | #3213 | — | 71 | 2 | no | — |
| 321 | #3126 | — | 71 | 2 | no | — |
| 322 | #3122 | — | 71 | 2 | no | — |
| 323 | #3115 | — | 71 | 2 | no | — |
| 324 | #2987 | — | 71 | 1 | no | — |
| 325 | C71 | #61942 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 326 | #562 | — | 142 | 2 | no | — |
| 327 | #559 | C2×D71 | 1 | 4 | yes | — |
| 328 | #556 | C2×D71 | 1 | 4 | yes | — |
| 329 | #554 | — | 71 | 4 | no | — |
| 330 | #551 | — | 2 | 4 | no | — |
| 331 | #550 | — | 71 | 4 | no | — |
| 332 | #547 | — | 142 | 2 | no | — |
| 333 | #542 | — | 2 | 2 | no | — |
| 334 | #540 | — | 71 | 2 | no | — |
| 335 | #540 | — | 71 | 2 | no | — |
| 336 | #537 | — | 142 | 4 | no | — |
| 337 | #536 | C2×D71 | 1 | 1 | yes | characteristic |
| 338 | #535 | C2×D71 | 1 | 1 | yes | characteristic |
| 339 | #533 | C2×D71 | 1 | 1 | yes | characteristic |
| 340 | #532 | — | 71 | 2 | no | — |
| 341 | #529 | — | 2 | 2 | no | — |
| 342 | C2×#124 | C2×D71 | 1 | 1 | yes | characteristic |
| 343 | #519 | C2×D71 | 1 | 1 | yes | characteristic |
| 344 | #518 | C2×D71 | 1 | 1 | yes | characteristic |
| 345 | C4×#41 | C2×D71 | 1 | 1 | yes | characteristic |
| 346 | #496 | — | 71 | 2 | no | — |
| 347 | #496 | — | 71 | 4 | no | — |
| 348 | #496 | — | 71 | 2 | no | — |
| 349 | #493 | — | 71 | 2 | no | — |
| 350 | #492 | — | 71 | 2 | no | — |
| 351 | #491 | — | 71 | 2 | no | — |
| 352 | #490 | — | 71 | 2 | no | — |
| 353 | #489 | — | 71 | 4 | no | — |
| 354 | #488 | — | 71 | 2 | no | — |
| 355 | #488 | — | 71 | 2 | no | — |
| 356 | #482 | — | 71 | 4 | no | — |
| 357 | #479 | — | 71 | 4 | no | — |
| 358 | #478 | — | 71 | 4 | no | — |
| 359 | #475 | — | 71 | 2 | no | — |
| 360 | #474 | — | 71 | 2 | no | — |
| 361 | #463 | — | 71 | 4 | no | — |
| 362 | #463 | — | 71 | 4 | no | — |
| 363 | #463 | — | 71 | 4 | no | — |
| 364 | #463 | — | 71 | 4 | no | — |
| 365 | #461 | — | 71 | 4 | no | — |
| 366 | #460 | — | 71 | 2 | no | — |
| 367 | #460 | — | 71 | 4 | no | — |
| 368 | #459 | — | 71 | 4 | no | — |
| 369 | #459 | — | 71 | 2 | no | — |
| 370 | #459 | — | 71 | 4 | no | — |
| 371 | #449 | — | 71 | 4 | no | — |
| 372 | #448 | — | 71 | 4 | no | — |
| 373 | #447 | — | 71 | 4 | no | — |
| 374 | #446 | — | 71 | 4 | no | — |
| 375 | #446 | — | 71 | 4 | no | — |
| 376 | #442 | — | 71 | 4 | no | — |
| 377 | #442 | — | 71 | 4 | no | — |
| 378 | #440 | — | 71 | 4 | no | — |
| 379 | #440 | — | 71 | 4 | no | — |
| 380 | C4×SD16 | — | 71 | 4 | no | — |
| 381 | C4×D8 | — | 71 | 4 | no | — |
| 382 | #433 | — | 71 | 2 | no | — |
| 383 | #433 | — | 71 | 2 | no | — |
| 384 | #432 | — | 71 | 2 | no | — |
| 385 | C2×#41 | — | 142 | 4 | no | — |
| 386 | C2×#41 | — | 142 | 2 | no | — |
| 387 | C2×#41 | C22×D71 | 1 | 1 | yes | characteristic |
| 388 | C22×Q8 | C22×D71 | 1 | 1 | yes | characteristic |
| 389 | C22×D4 | C22×D71 | 1 | 1 | yes | characteristic |
| 390 | C2×SD16 | — | 71 | 4 | no | — |
| 391 | C2×SD16 | — | 71 | 4 | no | — |
| 392 | C2×SD16 | — | 71 | 4 | no | — |
| 393 | C2×D8 | — | 71 | 4 | no | — |
| 394 | C2×D8 | — | 71 | 4 | no | — |
| 395 | C2×D8 | — | 71 | 4 | no | — |
| 396 | C4⋊Q8 | — | 71 | 2 | no | — |
| 397 | C4⋊Q8 | C22⋊D71 | 1 | 2 | yes | — |
| 398 | C4⋊Q8 | C22×D71 | 1 | 2 | yes | — |
| 399 | #127 | — | 71 | 2 | no | — |
| 400 | #127 | — | 71 | 2 | no | — |
| 401 | #127 | — | 71 | 2 | no | — |
| 402 | #127 | C22×D71 | 1 | 2 | yes | — |
| 403 | #126 | — | 2 | 4 | no | — |
| 404 | #126 | — | 2 | 4 | no | — |
| 405 | #125 | — | 71 | 2 | no | — |
| 406 | #125 | — | 71 | 2 | no | — |
| 407 | #125 | C22⋊D71 | 1 | 2 | yes | — |
| 408 | #124 | — | 2 | 4 | no | — |
| 409 | #124 | — | 2 | 1 | no | — |
| 410 | #124 | — | 2 | 1 | no | — |
| 411 | #124 | — | 142 | 2 | no | — |
| 412 | #124 | C22×D71 | 1 | 4 | yes | — |
| 413 | #124 | C22×D71 | 1 | 2 | yes | — |
| 414 | #124 | C22×D71 | 1 | 2 | yes | — |
| 415 | #123 | — | 2 | 4 | no | — |
| 416 | #123 | — | 2 | 4 | no | — |
| 417 | #123 | — | 2 | 2 | no | — |
| 418 | #123 | — | 142 | 4 | no | — |
| 419 | #123 | — | 142 | 4 | no | — |
| 420 | C22⋊Q8 | — | 2 | 4 | no | — |
| 421 | C22⋊Q8 | — | 2 | 2 | no | — |
| 422 | C22⋊Q8 | — | 142 | 4 | no | — |
| 423 | C22⋊Q8 | — | 142 | 4 | no | — |
| 424 | C22⋊Q8 | — | 142 | 4 | no | — |
| 425 | C22⋊Q8 | C22⋊D71 | 1 | 4 | yes | — |
| 426 | #121 | — | 2 | 2 | no | — |
| 427 | #121 | — | 71 | 4 | no | — |
| 428 | #121 | — | 142 | 2 | no | — |
| 429 | #121 | — | 142 | 4 | no | — |
| 430 | #121 | — | 142 | 4 | no | — |
| 431 | #121 | — | 142 | 4 | no | — |
| 432 | #121 | — | 142 | 4 | no | — |
| 433 | #121 | — | 142 | 4 | no | — |
| 434 | #120 | — | 2 | 2 | no | — |
| 435 | C4×Q8 | — | 2 | 2 | no | — |
| 436 | C4×Q8 | C22×D71 | 1 | 2 | yes | — |
| 437 | C4×Q8 | C22×D71 | 1 | 4 | yes | — |
| 438 | C4×Q8 | C22×D71 | 1 | 4 | yes | — |
| 439 | C4×D4 | — | 2 | 2 | no | — |
| 440 | C4×D4 | — | 2 | 2 | no | — |
| 441 | C4×D4 | — | 2 | 4 | no | — |
| 442 | C4×D4 | — | 71 | 4 | no | — |
| 443 | C4×D4 | — | 71 | 4 | no | — |
| 444 | C4×D4 | — | 71 | 4 | no | — |
| 445 | C4×D4 | — | 142 | 2 | no | — |
| 446 | C4×D4 | C22×D71 | 1 | 2 | yes | — |
| 447 | C4×D4 | C22×D71 | 1 | 4 | yes | — |
| 448 | #117 | — | 2 | 4 | no | — |
| 449 | #117 | — | 2 | 2 | no | — |
| 450 | #117 | — | 2 | 1 | no | — |
| 451 | #117 | C22×D71 | 1 | 1 | yes | characteristic |
| 452 | #117 | C22×D71 | 1 | 1 | yes | characteristic |
| 453 | #117 | C22×D71 | 1 | 1 | yes | characteristic |
| 454 | C2×C4⋊C4 | — | 142 | 4 | no | — |
| 455 | C2×C22⋊C4 | — | 2 | 2 | no | — |
| 456 | C2×C22⋊C4 | — | 2 | 2 | no | — |
| 457 | C2×C42 | — | 2 | 1 | no | — |
| 458 | C2×C42 | C22×D71 | 1 | 1 | yes | characteristic |
| 459 | #107 | — | 71 | 4 | no | — |
| 460 | #106 | — | 71 | 4 | no | — |
| 461 | C4⋊C8 | — | 71 | 2 | no | — |
| 462 | C4⋊C8 | — | 71 | 2 | no | — |
| 463 | C4⋊C8 | — | 71 | 4 | no | — |
| 464 | C4⋊C8 | — | 71 | 4 | no | — |
| 465 | #103 | — | 71 | 4 | no | — |
| 466 | #103 | — | 71 | 4 | no | — |
| 467 | #103 | — | 71 | 4 | no | — |
| 468 | #102 | — | 71 | 4 | no | — |
| 469 | #102 | — | 71 | 4 | no | — |
| 470 | #102 | — | 71 | 4 | no | — |
| 471 | #102 | — | 71 | 4 | no | — |
| 472 | #102 | — | 71 | 4 | no | — |
| 473 | C22⋊C8 | — | 71 | 4 | no | — |
| 474 | #97 | — | 71 | 4 | no | — |
| 475 | #97 | — | 71 | 2 | no | — |
| 476 | #97 | — | 71 | 2 | no | — |
| 477 | C4×C8 | — | 71 | 2 | no | — |
| 478 | C4×C8 | — | 71 | 2 | no | — |
| 479 | C24 | — | 2 | 1 | no | — |
| 480 | #41 | — | 4 | 2 | no | — |
| 481 | #41 | — | 568 | 4 | no | — |
| 482 | #41 | — | 568 | 8 | no | — |
| 483 | C2×Q8 | — | 2 | 1 | no | — |
| 484 | C2×Q8 | — | 4 | 2 | no | — |
| 485 | C2×Q8 | — | 142 | 2 | no | — |
| 486 | C2×Q8 | C2×C22⋊D71 | 1 | 4 | yes | — |
| 487 | C2×Q8 | C23×D71 | 1 | 2 | yes | — |
| 488 | C2×Q8 | C23×D71 | 1 | 1 | yes | characteristic |
| 489 | C2×D4 | — | 2 | 1 | no | — |
| 490 | C2×D4 | — | 2 | 1 | no | — |
| 491 | C2×D4 | — | 2 | 4 | no | — |
| 492 | C2×D4 | — | 4 | 2 | no | — |
| 493 | C2×D4 | — | 71 | 4 | no | — |
| 494 | C2×D4 | — | 142 | 4 | no | — |
| 495 | C2×D4 | — | 142 | 2 | no | — |
| 496 | C2×D4 | — | 142 | 4 | no | — |
| 497 | C2×D4 | — | 142 | 4 | no | — |
| 498 | C2×D4 | — | 142 | 2 | no | — |
| 499 | C2×D4 | C23×D71 | 1 | 2 | yes | — |
| 500 | C2×D4 | C23×D71 | 1 | 1 | yes | characteristic |
| 501 | C22×C4 | — | 2 | 1 | no | — |
| 502 | C22×C4 | — | 2 | 1 | no | — |
| 503 | C22×C4 | — | 2 | 2 | no | — |
| 504 | C22×C4 | — | 2 | 4 | no | — |
| 505 | C22×C4 | — | 142 | 4 | no | — |
| 506 | C22×C4 | — | 142 | 4 | no | — |
| 507 | C22×C4 | — | 142 | 4 | no | — |
| 508 | C22×C4 | C2×C22⋊D71 | 1 | 2 | yes | — |
| 509 | C22×C4 | C23×D71 | 1 | 1 | yes | characteristic |
| 510 | SD16 | — | 284 | 4 | no | — |
| 511 | SD16 | — | 284 | 4 | no | — |
| 512 | SD16 | — | 284 | 4 | no | — |
| 513 | D8 | — | 284 | 4 | no | — |
| 514 | D8 | — | 284 | 4 | no | — |
| 515 | D8 | — | 284 | 4 | no | — |
| 516 | C2×C8 | — | 71 | 4 | no | — |
| 517 | C2×C8 | — | 71 | 4 | no | — |
| 518 | C4⋊C4 | — | 2 | 2 | no | — |
| 519 | C4⋊C4 | — | 2 | 4 | no | — |
| 520 | C4⋊C4 | — | 2 | 4 | no | — |
| 521 | C4⋊C4 | — | 71 | 4 | no | — |
| 522 | C4⋊C4 | — | 142 | 4 | no | — |
| 523 | C4⋊C4 | — | 142 | 4 | no | — |
| 524 | C4⋊C4 | — | 142 | 2 | no | — |
| 525 | C4⋊C4 | C2×C22⋊D71 | 1 | 4 | yes | — |
| 526 | C4⋊C4 | C2×C22⋊D71 | 1 | 4 | yes | — |
| 527 | C4⋊C4 | C2×C22⋊D71 | 1 | 2 | yes | — |
| 528 | C4⋊C4 | C2×C22⋊D71 | 1 | 2 | yes | — |
| 529 | C4⋊C4 | C2×C22⋊D71 | 1 | 4 | yes | — |
| 530 | C4⋊C4 | C23×D71 | 1 | 2 | yes | — |
| 531 | C22⋊C4 | — | 2 | 1 | no | — |
| 532 | C22⋊C4 | — | 2 | 4 | no | — |
| 533 | C22⋊C4 | — | 2 | 4 | no | — |
| 534 | C22⋊C4 | — | 2 | 4 | no | — |
| 535 | C22⋊C4 | — | 2 | 2 | no | — |
| 536 | C22⋊C4 | — | 2 | 4 | no | — |
| 537 | C22⋊C4 | — | 2 | 4 | no | — |
| 538 | C22⋊C4 | — | 142 | 4 | no | — |
| 539 | C22⋊C4 | — | 142 | 4 | no | — |
| 540 | C22⋊C4 | — | 142 | 4 | no | — |
| 541 | C22⋊C4 | — | 142 | 4 | no | — |
| 542 | C22⋊C4 | C2×C22⋊D71 | 1 | 2 | yes | — |
| 543 | C22⋊C4 | C2×C22⋊D71 | 1 | 2 | yes | — |
| 544 | C42 | — | 2 | 2 | no | — |
| 545 | C42 | — | 2 | 1 | no | — |
| 546 | C42 | — | 2 | 4 | no | — |
| 547 | C42 | C2×C22⋊D71 | 1 | 1 | yes | characteristic |
| 548 | C42 | C2×C22⋊D71 | 1 | 1 | yes | characteristic |
| 549 | C42 | C23×D71 | 1 | 2 | yes | — |
| 550 | C42 | C23×D71 | 1 | 2 | yes | — |
| 551 | C42 | C23×D71 | 1 | 2 | yes | — |
| 552 | C23 | — | 2 | 2 | no | — |
| 553 | C23 | — | 2 | 1 | no | — |
| 554 | C23 | — | 4 | 2 | no | — |
| 555 | C23 | — | 8 | 2 | no | — |
| 556 | C23 | — | 142 | 4 | no | — |
| 557 | C23 | C22×C22⋊D71 | 1 | 1 | yes | characteristic |
| 558 | Q8 | — | 2 | 4 | no | — |
| 559 | Q8 | — | 2 | 2 | no | — |
| 560 | Q8 | — | 4 | 4 | no | — |
| 561 | Q8 | — | 4 | 2 | no | — |
| 562 | Q8 | — | 568 | 2 | no | — |
| 563 | D4 | — | 2 | 4 | no | — |
| 564 | D4 | — | 2 | 2 | no | — |
| 565 | D4 | — | 4 | 2 | no | — |
| 566 | D4 | — | 4 | 2 | no | — |
| 567 | D4 | — | 8 | 4 | no | — |
| 568 | D4 | — | 284 | 4 | no | — |
| 569 | D4 | — | 568 | 2 | no | — |
| 570 | D4 | — | 568 | 4 | no | — |
| 571 | D4 | — | 568 | 4 | no | — |
| 572 | D4 | — | 568 | 4 | no | — |
| 573 | D4 | — | 142 | 4 | no | — |
| 574 | D4 | — | 142 | 4 | no | — |
| 575 | C2×C4 | — | 2 | 2 | no | — |
| 576 | C2×C4 | — | 2 | 2 | no | — |
| 577 | C2×C4 | — | 2 | 2 | no | — |
| 578 | C2×C4 | — | 2 | 1 | no | — |
| 579 | C2×C4 | — | 4 | 2 | no | — |
| 580 | C2×C4 | — | 4 | 2 | no | — |
| 581 | C2×C4 | — | 4 | 2 | no | — |
| 582 | C2×C4 | — | 8 | 2 | no | — |
| 583 | C2×C4 | — | 8 | 4 | no | — |
| 584 | C2×C4 | — | 284 | 8 | no | — |
| 585 | C2×C4 | — | 568 | 4 | no | — |
| 586 | C2×C4 | — | 568 | 4 | no | — |
| 587 | C2×C4 | — | 142 | 4 | no | — |
| 588 | C2×C4 | C22×C22⋊D71 | 1 | 1 | yes | characteristic |
| 589 | C2×C4 | C22×C22⋊D71 | 1 | 2 | yes | — |
| 590 | C2×C4 | C22×C22⋊D71 | 1 | 4 | yes | — |
| 591 | C2×C4 | C22×C22⋊D71 | 1 | 2 | yes | — |
| 592 | C2×C4 | C22×C22⋊D71 | 1 | 4 | yes | — |
| 593 | C2×C4 | C24×D71 | 1 | 1 | yes | characteristic |
| 594 | C8 | — | 142 | 4 | no | — |
| 595 | C8 | — | 142 | 4 | no | — |
| 596 | C22 | — | 2 | 1 | no | — |
| 597 | C22 | — | 2 | 2 | no | — |
| 598 | C22 | — | 4 | 1 | no | — |
| 599 | C22 | — | 4 | 2 | no | — |
| 600 | C22 | — | 4 | 2 | no | — |
| 601 | C22 | — | 4 | 4 | no | — |
| 602 | C22 | — | 16 | 2 | no | — |
| 603 | C22 | — | 284 | 4 | no | — |
| 604 | C22 | — | 284 | 4 | no | — |
| 605 | C22 | — | 284 | 4 | no | — |
| 606 | C22 | C23×C22⋊D71 | 1 | 1 | yes | characteristic |
| 607 | C4 | — | 2 | 1 | no | — |
| 608 | C4 | — | 2 | 2 | no | — |
| 609 | C4 | — | 2 | 2 | no | — |
| 610 | C4 | — | 2 | 4 | no | — |
| 611 | C4 | — | 2 | 4 | no | — |
| 612 | C4 | — | 4 | 1 | no | — |
| 613 | C4 | — | 4 | 2 | no | — |
| 614 | C4 | — | 4 | 2 | no | — |
| 615 | C4 | — | 284 | 4 | no | — |
| 616 | C4 | #17986835 | 1 | 2 | yes | — |
| 617 | C2 | — | 4 | 1 | no | — |
| 618 | C2 | — | 8 | 2 | no | — |
| 619 | C2 | — | 8 | 1 | no | — |
| 620 | C2 | — | 568 | 4 | no | — |
| 621 | C2 | #22601998 | 1 | 1 | yes | characteristic |
| 622 | C2 | #22603119 | 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