← #32870353
Subgroups — #32870353
Order 18176.
1910 conjugacy classes of subgroups.
The subgroup lattice has 594 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #22601637 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #22599742 | C2 | 1 | 4 | yes | maximal, complemented |
| 3 | #22599723 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #22599721 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #22599711 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #22599705 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #22598123 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #22597951 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | #22597798 | C2 | 1 | 4 | yes | maximal, complemented |
| 10 | #423×D71 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | C71×#3255 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C2×#14556151 | C22 | 1 | 4 | yes | — |
| 13 | C2×M16×D71 | C22 | 1 | 2 | yes | — |
| 14 | #17986554 | C22 | 1 | 2 | yes | — |
| 15 | #17986554 | C22 | 1 | 2 | yes | — |
| 16 | #17986550 | C22 | 1 | 2 | yes | — |
| 17 | #17986550 | C22 | 1 | 2 | yes | — |
| 18 | #17986549 | C22 | 1 | 2 | yes | — |
| 19 | #17986536 | — | 2 | 2 | no | — |
| 20 | #17986536 | C22 | 1 | 4 | yes | — |
| 21 | #17986535 | — | 2 | 2 | no | — |
| 22 | #17986535 | C22 | 1 | 4 | yes | — |
| 23 | #17986534 | — | 2 | 2 | no | — |
| 24 | #17986534 | — | 2 | 2 | no | — |
| 25 | #17986512 | — | 2 | 2 | no | — |
| 26 | #17986512 | C22 | 1 | 4 | yes | — |
| 27 | #17986511 | — | 2 | 2 | no | — |
| 28 | C4×#11765866 | — | 2 | 2 | no | — |
| 29 | C4×#11765866 | C22 | 1 | 4 | yes | — |
| 30 | #17986467 | — | 2 | 2 | no | — |
| 31 | C2×C42×D71 | C22 | 1 | 1 | yes | characteristic |
| 32 | #17986304 | C22 | 1 | 8 | yes | complemented |
| 33 | #17986298 | C22 | 1 | 8 | yes | complemented |
| 34 | #17986294 | C22 | 1 | 4 | yes | complemented |
| 35 | #17986290 | C22 | 1 | 4 | yes | complemented |
| 36 | #17986276 | C22 | 1 | 4 | yes | complemented |
| 37 | #17986254 | C22 | 1 | 4 | yes | — |
| 38 | #17986253 | C22 | 1 | 4 | yes | — |
| 39 | #17986252 | C22 | 1 | 4 | yes | — |
| 40 | #17986248 | C22 | 1 | 8 | yes | — |
| 41 | #17986247 | C22 | 1 | 8 | yes | — |
| 42 | #17986223 | C22 | 1 | 8 | yes | complemented |
| 43 | #17986217 | C22 | 1 | 8 | yes | complemented |
| 44 | #17986201 | C22 | 1 | 4 | yes | complemented |
| 45 | #17986199 | C22 | 1 | 4 | yes | complemented |
| 46 | #17986195 | C22 | 1 | 4 | yes | complemented |
| 47 | #17986034 | C22 | 1 | 4 | yes | — |
| 48 | #17986023 | C22 | 1 | 1 | yes | characteristic |
| 49 | #17986022 | C22 | 1 | 2 | yes | — |
| 50 | #17986021 | C22 | 1 | 4 | yes | — |
| 51 | C4⋊C8×D71 | C22 | 1 | 4 | yes | — |
| 52 | #17985994 | C22 | 1 | 8 | yes | — |
| 53 | #533×C71 | C22 | 1 | 2 | yes | — |
| 54 | #475×C71 | C22 | 1 | 4 | yes | complemented |
| 55 | #470×C71 | C22 | 1 | 4 | yes | — |
| 56 | #462×C71 | C22 | 1 | 4 | yes | complemented |
| 57 | #423×C71 | C22 | 1 | 1 | yes | characteristic |
| 58 | C2×#11765866 | — | 2 | 2 | no | — |
| 59 | C2×#11765866 | C23 | 1 | 4 | yes | — |
| 60 | C2×#11765865 | — | 2 | 2 | no | — |
| 61 | C22×C4×D71 | D4 | 1 | 2 | yes | — |
| 62 | C22×C4×D71 | C23 | 1 | 1 | yes | characteristic |
| 63 | #14556151 | — | 4 | 8 | no | — |
| 64 | C2×#11765852 | C23 | 1 | 8 | yes | — |
| 65 | C2×D568 | C23 | 1 | 4 | yes | — |
| 66 | C2×#11765849 | C23 | 1 | 2 | yes | — |
| 67 | C2×#11765848 | C23 | 1 | 4 | yes | — |
| 68 | M16×D71 | — | 4 | 4 | no | — |
| 69 | C2×C8×D71 | C23 | 1 | 4 | yes | — |
| 70 | #14556128 | C23 | 1 | 2 | yes | — |
| 71 | #14556125 | C23 | 1 | 2 | yes | — |
| 72 | #14556123 | — | 2 | 4 | no | — |
| 73 | #14556123 | — | 2 | 4 | no | — |
| 74 | #14556119 | — | 2 | 2 | no | — |
| 75 | #14556119 | C23 | 1 | 4 | yes | — |
| 76 | #14556117 | — | 2 | 2 | no | — |
| 77 | #14556117 | C23 | 1 | 4 | yes | — |
| 78 | #14556116 | — | 2 | 2 | no | — |
| 79 | #14556113 | — | 2 | 4 | no | — |
| 80 | #14556113 | — | 2 | 4 | no | — |
| 81 | #14556112 | — | 2 | 4 | no | — |
| 82 | #14556108 | — | 2 | 2 | no | — |
| 83 | #14556108 | — | 2 | 2 | no | — |
| 84 | #14556104 | — | 2 | 2 | no | — |
| 85 | #14556104 | C23 | 1 | 4 | yes | — |
| 86 | #14556103 | — | 2 | 2 | no | — |
| 87 | #14556103 | — | 2 | 2 | no | — |
| 88 | #14556103 | — | 2 | 2 | no | — |
| 89 | #14556103 | C23 | 1 | 4 | yes | — |
| 90 | #14556102 | — | 2 | 2 | no | — |
| 91 | #14556102 | C23 | 1 | 4 | yes | — |
| 92 | #14556098 | — | 2 | 4 | no | — |
| 93 | Q8×Dic71 | — | 2 | 2 | no | — |
| 94 | Q8×Dic71 | C23 | 1 | 4 | yes | — |
| 95 | #14556093 | — | 2 | 2 | no | — |
| 96 | #14556093 | — | 2 | 2 | no | — |
| 97 | C4×D284 | — | 2 | 4 | no | — |
| 98 | C4×D284 | — | 2 | 4 | no | — |
| 99 | C4×D284 | — | 2 | 2 | no | — |
| 100 | C4×D284 | C23 | 1 | 4 | yes | — |
| 101 | #14556090 | — | 2 | 4 | no | — |
| 102 | #14556090 | — | 2 | 4 | no | — |
| 103 | #14556090 | — | 2 | 2 | no | — |
| 104 | #14556090 | — | 2 | 2 | no | — |
| 105 | #14556090 | — | 2 | 2 | no | — |
| 106 | #14556090 | C23 | 1 | 4 | yes | — |
| 107 | (C22⋊D71)⋊C4 | — | 2 | 4 | no | — |
| 108 | (C22⋊D71)⋊C4 | — | 2 | 4 | no | — |
| 109 | #14556086 | — | 2 | 2 | no | — |
| 110 | #14556086 | — | 2 | 4 | no | — |
| 111 | #14556086 | — | 2 | 4 | no | — |
| 112 | #14556086 | C23 | 1 | 4 | yes | — |
| 113 | #14556085 | — | 2 | 4 | no | — |
| 114 | C2×C4×Dic71 | D4 | 1 | 2 | yes | — |
| 115 | C2×C4×Dic71 | C23 | 1 | 1 | yes | characteristic |
| 116 | C42×D71 | — | 2 | 4 | no | — |
| 117 | C42×D71 | D4 | 1 | 1 | yes | characteristic |
| 118 | C42×D71 | D4 | 1 | 1 | yes | characteristic |
| 119 | C42×D71 | D4 | 1 | 1 | yes | characteristic |
| 120 | C42×D71 | D4 | 1 | 1 | yes | characteristic |
| 121 | C42×D71 | C23 | 1 | 2 | yes | — |
| 122 | C42×D71 | C23 | 1 | 2 | yes | — |
| 123 | #14556061 | C23 | 1 | 8 | yes | — |
| 124 | #14556060 | C23 | 1 | 4 | yes | — |
| 125 | C4⋊(C71⋊C8) | C23 | 1 | 4 | yes | — |
| 126 | Dic71⋊C8 | C23 | 1 | 8 | yes | — |
| 127 | #14556052 | C23 | 1 | 8 | yes | — |
| 128 | #14556050 | C23 | 1 | 8 | yes | — |
| 129 | #14556048 | C23 | 1 | 8 | yes | — |
| 130 | C2×Q16×C71 | C23 | 1 | 4 | yes | — |
| 131 | C2×M16×C71 | C23 | 1 | 2 | yes | — |
| 132 | C4⋊Q8×C71 | C23 | 1 | 2 | yes | — |
| 133 | C4⋊Q8×C71 | C23 | 1 | 2 | yes | — |
| 134 | #125×C71 | — | 2 | 2 | no | — |
| 135 | C22⋊Q8×C71 | — | 2 | 2 | no | — |
| 136 | C22⋊Q8×C71 | C23 | 1 | 4 | yes | — |
| 137 | C4×Q8×C71 | — | 2 | 2 | no | — |
| 138 | C4×Q8×C71 | C23 | 1 | 4 | yes | — |
| 139 | #117×C71 | — | 2 | 2 | no | — |
| 140 | C2×C42×C71 | C23 | 1 | 1 | yes | characteristic |
| 141 | #106×C71 | C23 | 1 | 4 | yes | — |
| 142 | C4⋊C8×C71 | C23 | 1 | 4 | yes | — |
| 143 | #103×C71 | C23 | 1 | 8 | yes | — |
| 144 | C23×D71 | C2×D4 | 1 | 1 | yes | characteristic |
| 145 | #11765866 | — | 2 | 8 | no | — |
| 146 | #11765866 | — | 2 | 8 | no | — |
| 147 | #11765866 | — | 4 | 8 | no | — |
| 148 | #11765865 | — | 4 | 8 | no | — |
| 149 | C2×Dic142 | — | 2 | 2 | no | — |
| 150 | C2×D284 | — | 2 | 4 | no | — |
| 151 | C2×D284 | — | 2 | 4 | no | — |
| 152 | C2×D284 | — | 2 | 2 | no | — |
| 153 | C2×D284 | — | 2 | 2 | no | — |
| 154 | C2×D284 | C24 | 1 | 4 | yes | — |
| 155 | C2×C22⋊D71 | — | 2 | 4 | no | — |
| 156 | C22×Dic71 | C2×D4 | 1 | 1 | yes | characteristic |
| 157 | C22×Dic71 | C2×D4 | 1 | 2 | yes | — |
| 158 | C2×C4×D71 | — | 2 | 2 | no | — |
| 159 | C2×C4×D71 | — | 2 | 2 | no | — |
| 160 | C2×C4×D71 | — | 2 | 4 | no | — |
| 161 | C2×C4×D71 | — | 2 | 4 | no | — |
| 162 | C2×C4×D71 | — | 2 | 4 | no | — |
| 163 | C2×C4×D71 | — | 4 | 4 | no | — |
| 164 | C2×C4×D71 | C2×D4 | 1 | 2 | yes | — |
| 165 | C2×C4×D71 | C2×D4 | 1 | 2 | yes | — |
| 166 | C2×C4×D71 | C2×D4 | 1 | 1 | yes | characteristic |
| 167 | C2×C4×D71 | C2×D4 | 1 | 1 | yes | characteristic |
| 168 | C2×C4×D71 | C2×D4 | 1 | 2 | yes | — |
| 169 | C2×C4×D71 | C2×D4 | 1 | 2 | yes | — |
| 170 | C2×C4×D71 | C24 | 1 | 1 | yes | characteristic |
| 171 | C2×C4×D71 | C24 | 1 | 1 | yes | characteristic |
| 172 | #11765852 | — | 4 | 8 | no | — |
| 173 | D568 | — | 4 | 4 | no | — |
| 174 | #11765849 | — | 4 | 2 | no | — |
| 175 | #11765848 | — | 4 | 4 | no | — |
| 176 | C2×C71⋊C8 | C24 | 1 | 4 | yes | — |
| 177 | C8×D71 | — | 2 | 8 | no | — |
| 178 | C4⋊Dic71 | — | 2 | 2 | no | — |
| 179 | C4⋊Dic71 | — | 2 | 4 | no | — |
| 180 | C4⋊Dic71 | — | 2 | 4 | no | — |
| 181 | C4⋊Dic71 | C24 | 1 | 4 | yes | — |
| 182 | Dic71⋊C4 | — | 2 | 4 | no | — |
| 183 | Dic71⋊C4 | — | 2 | 4 | no | — |
| 184 | (C2×D71)⋊C4 | — | 2 | 4 | no | — |
| 185 | (C2×D71)⋊C4 | — | 2 | 4 | no | — |
| 186 | (C2×D71)⋊C4 | — | 2 | 4 | no | — |
| 187 | (C2×D71)⋊C4 | — | 2 | 4 | no | — |
| 188 | (C2×D71)⋊C4 | — | 2 | 4 | no | — |
| 189 | (C2×D71)⋊C4 | — | 2 | 4 | no | — |
| 190 | (C2×D71)⋊C4 | — | 2 | 4 | no | — |
| 191 | (C2×D71)⋊C4 | — | 2 | 4 | no | — |
| 192 | C4×Dic71 | — | 2 | 4 | no | — |
| 193 | C4×Dic71 | — | 2 | 4 | no | — |
| 194 | C4×Dic71 | C2×D4 | 1 | 2 | yes | — |
| 195 | C4×Dic71 | C2×D4 | 1 | 1 | yes | characteristic |
| 196 | C4×Dic71 | C2×D4 | 1 | 1 | yes | characteristic |
| 197 | C4×Dic71 | C2×D4 | 1 | 2 | yes | — |
| 198 | C4×Dic71 | C2×D4 | 1 | 2 | yes | — |
| 199 | C4×Dic71 | C2×D4 | 1 | 2 | yes | — |
| 200 | C4×Dic71 | C24 | 1 | 2 | yes | — |
| 201 | C2×Q8×C71 | — | 2 | 2 | no | — |
| 202 | C2×Q8×C71 | C24 | 1 | 4 | yes | — |
| 203 | C22×C4×C71 | C2×D4 | 1 | 2 | yes | — |
| 204 | C22×C4×C71 | C24 | 1 | 1 | yes | characteristic |
| 205 | Q16×C71 | — | 4 | 4 | no | — |
| 206 | M16×C71 | — | 4 | 2 | no | — |
| 207 | C2×C8×C71 | C24 | 1 | 4 | yes | — |
| 208 | C4⋊C4×C71 | — | 2 | 2 | no | — |
| 209 | C4⋊C4×C71 | — | 2 | 2 | no | — |
| 210 | C4⋊C4×C71 | — | 2 | 2 | no | — |
| 211 | C4⋊C4×C71 | — | 2 | 4 | no | — |
| 212 | C4⋊C4×C71 | — | 2 | 4 | no | — |
| 213 | C4⋊C4×C71 | C24 | 1 | 4 | yes | — |
| 214 | C22⋊C4×C71 | — | 2 | 4 | no | — |
| 215 | C42×C71 | — | 2 | 4 | no | — |
| 216 | C42×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 217 | C42×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 218 | C42×C71 | C24 | 1 | 2 | yes | — |
| 219 | C23×C71 | C22×D4 | 1 | 1 | yes | characteristic |
| 220 | C22×D71 | — | 2 | 2 | no | — |
| 221 | C22×D71 | — | 2 | 4 | no | — |
| 222 | C22×D71 | — | 4 | 2 | no | — |
| 223 | C22×D71 | C22×D4 | 1 | 1 | yes | characteristic |
| 224 | C22×D71 | C22×D4 | 1 | 1 | yes | characteristic |
| 225 | Q8×C71 | — | 2 | 4 | no | — |
| 226 | Q8×C71 | — | 2 | 4 | no | — |
| 227 | Q8×C71 | — | 4 | 4 | no | — |
| 228 | C2×C4×C71 | — | 2 | 4 | no | — |
| 229 | C2×C4×C71 | — | 2 | 1 | no | — |
| 230 | C2×C4×C71 | — | 2 | 1 | no | — |
| 231 | C2×C4×C71 | — | 2 | 4 | no | — |
| 232 | C2×C4×C71 | — | 2 | 4 | no | — |
| 233 | C2×C4×C71 | C22×D4 | 1 | 1 | yes | characteristic |
| 234 | C2×C4×C71 | C22×D4 | 1 | 2 | yes | — |
| 235 | C2×C4×C71 | C22×D4 | 1 | 2 | yes | — |
| 236 | C2×C4×C71 | C25 | 1 | 1 | yes | characteristic |
| 237 | C22⋊D71 | — | 4 | 8 | no | — |
| 238 | C2×Dic71 | — | 2 | 2 | no | — |
| 239 | C2×Dic71 | — | 2 | 4 | no | — |
| 240 | C2×Dic71 | — | 4 | 2 | no | — |
| 241 | C2×Dic71 | C22×D4 | 1 | 2 | yes | — |
| 242 | C2×Dic71 | C22×D4 | 1 | 1 | yes | characteristic |
| 243 | C2×Dic71 | C22×D4 | 1 | 2 | yes | — |
| 244 | C2×Dic71 | C22×D4 | 1 | 1 | yes | characteristic |
| 245 | D284 | — | 2 | 4 | no | — |
| 246 | D284 | — | 2 | 4 | no | — |
| 247 | D284 | — | 4 | 4 | no | — |
| 248 | D284 | — | 4 | 8 | no | — |
| 249 | D284 | — | 4 | 8 | no | — |
| 250 | D284 | — | 4 | 4 | no | — |
| 251 | C4×D71 | — | 2 | 2 | no | — |
| 252 | C4×D71 | — | 2 | 4 | no | — |
| 253 | C4×D71 | — | 2 | 4 | no | — |
| 254 | C4×D71 | — | 2 | 1 | no | — |
| 255 | C4×D71 | — | 2 | 1 | no | — |
| 256 | C4×D71 | — | 2 | 2 | no | — |
| 257 | C4×D71 | — | 4 | 2 | no | — |
| 258 | C4×D71 | — | 4 | 2 | no | — |
| 259 | C4×D71 | — | 4 | 8 | no | — |
| 260 | C4×D71 | — | 4 | 8 | no | — |
| 261 | C4×D71 | — | 4 | 8 | no | — |
| 262 | C4×D71 | H(5,𝔽2) | 1 | 2 | yes | — |
| 263 | C4×D71 | 2−1+4 | 1 | 2 | yes | — |
| 264 | Dic142 | — | 4 | 4 | no | — |
| 265 | C8×C71 | — | 2 | 4 | no | — |
| 266 | C71⋊C8 | — | 2 | 4 | no | — |
| 267 | C22×C71 | — | 2 | 1 | no | — |
| 268 | C22×C71 | — | 2 | 2 | no | — |
| 269 | C22×C71 | C23×D4 | 1 | 1 | yes | characteristic |
| 270 | C2×D71 | — | 2 | 2 | no | — |
| 271 | C2×D71 | — | 2 | 1 | no | — |
| 272 | C2×D71 | — | 2 | 2 | no | — |
| 273 | C2×D71 | — | 4 | 4 | no | — |
| 274 | C2×D71 | — | 4 | 4 | no | — |
| 275 | C2×D71 | — | 4 | 4 | no | — |
| 276 | C2×D71 | — | 4 | 4 | no | — |
| 277 | C2×D71 | #537 | 1 | 2 | yes | — |
| 278 | C4×C71 | — | 2 | 1 | no | — |
| 279 | C4×C71 | — | 2 | 2 | no | — |
| 280 | C4×C71 | — | 4 | 4 | no | — |
| 281 | C4×C71 | — | 4 | 4 | no | — |
| 282 | C4×C71 | #575 | 1 | 4 | yes | — |
| 283 | C4×C71 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 284 | C4×C71 | C2×2−1+4 | 1 | 1 | yes | characteristic |
| 285 | Dic71 | — | 2 | 1 | no | — |
| 286 | Dic71 | — | 2 | 2 | no | — |
| 287 | Dic71 | — | 2 | 2 | no | — |
| 288 | Dic71 | — | 4 | 4 | no | — |
| 289 | Dic71 | #537 | 1 | 2 | yes | — |
| 290 | #60907 | — | 71 | 1 | no | maximal, Sylow |
| 291 | C2×C71 | — | 4 | 1 | no | — |
| 292 | C2×C71 | C2×#537 | 1 | 1 | yes | characteristic |
| 293 | C2×C71 | C2×#575 | 1 | 2 | yes | — |
| 294 | D71 | — | 2 | 2 | no | — |
| 295 | D71 | — | 4 | 1 | no | — |
| 296 | D71 | — | 8 | 4 | no | — |
| 297 | #3444 | — | 71 | 2 | no | — |
| 298 | #3256 | — | 71 | 4 | no | — |
| 299 | #3255 | D71 | 1 | 1 | yes | characteristic, complemented |
| 300 | #3254 | — | 71 | 2 | no | — |
| 301 | #3253 | — | 71 | 1 | no | — |
| 302 | #3252 | — | 71 | 4 | no | — |
| 303 | #3251 | — | 71 | 4 | no | — |
| 304 | #3076 | — | 71 | 4 | no | — |
| 305 | #3054 | — | 71 | 4 | no | — |
| 306 | #3035 | — | 71 | 4 | no | — |
| 307 | C2×#423 | — | 71 | 1 | no | — |
| 308 | C71 | #60907 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 309 | C2×#135 | — | 71 | 4 | no | — |
| 310 | C22×M16 | — | 71 | 2 | no | — |
| 311 | #533 | — | 71 | 2 | no | — |
| 312 | #533 | — | 71 | 2 | no | — |
| 313 | #533 | C2×D71 | 1 | 2 | yes | — |
| 314 | #532 | — | 71 | 2 | no | — |
| 315 | #532 | — | 71 | 2 | no | — |
| 316 | #532 | — | 71 | 2 | no | — |
| 317 | #529 | — | 71 | 4 | no | — |
| 318 | #529 | — | 71 | 4 | no | — |
| 319 | #529 | — | 142 | 2 | no | — |
| 320 | #529 | — | 142 | 2 | no | — |
| 321 | #529 | — | 142 | 2 | no | — |
| 322 | #529 | — | 142 | 2 | no | — |
| 323 | #525 | — | 71 | 4 | no | — |
| 324 | #525 | — | 142 | 2 | no | — |
| 325 | #525 | — | 142 | 2 | no | — |
| 326 | C4×#41 | — | 71 | 4 | no | — |
| 327 | C4×#41 | — | 142 | 2 | no | — |
| 328 | C4×#41 | — | 142 | 2 | no | — |
| 329 | C22×C42 | — | 71 | 1 | no | — |
| 330 | #479 | — | 71 | 8 | no | — |
| 331 | #478 | — | 71 | 8 | no | — |
| 332 | #477 | — | 71 | 4 | no | — |
| 333 | #476 | — | 71 | 4 | no | — |
| 334 | #475 | C2×D71 | 1 | 4 | yes | complemented |
| 335 | #474 | — | 71 | 4 | no | — |
| 336 | #470 | — | 71 | 4 | no | — |
| 337 | #470 | C2×D71 | 1 | 4 | yes | — |
| 338 | #469 | — | 71 | 4 | no | — |
| 339 | #469 | — | 71 | 4 | no | — |
| 340 | #468 | — | 71 | 8 | no | — |
| 341 | #468 | — | 71 | 8 | no | — |
| 342 | #464 | — | 71 | 8 | no | — |
| 343 | #463 | — | 71 | 8 | no | — |
| 344 | #462 | C2×D71 | 1 | 4 | yes | complemented |
| 345 | #461 | — | 71 | 4 | no | — |
| 346 | #460 | — | 71 | 4 | no | — |
| 347 | #459 | — | 71 | 4 | no | — |
| 348 | #427 | — | 71 | 4 | no | — |
| 349 | #423 | — | 71 | 2 | no | — |
| 350 | #423 | — | 71 | 1 | no | — |
| 351 | #423 | — | 71 | 4 | no | — |
| 352 | #423 | C2×D71 | 1 | 1 | yes | characteristic |
| 353 | C2×C4⋊C8 | — | 71 | 4 | no | — |
| 354 | #416 | — | 71 | 8 | no | — |
| 355 | C2×#41 | — | 71 | 4 | no | — |
| 356 | C2×#41 | — | 142 | 2 | no | — |
| 357 | C2×#41 | — | 142 | 2 | no | — |
| 358 | C23×C4 | — | 71 | 2 | no | — |
| 359 | C23×C4 | — | 71 | 1 | no | — |
| 360 | #135 | — | 284 | 8 | no | — |
| 361 | C2×Q16 | C22×D71 | 1 | 4 | yes | — |
| 362 | C2×SD16 | — | 71 | 8 | no | — |
| 363 | C2×D8 | — | 71 | 4 | no | — |
| 364 | C2×M16 | — | 284 | 4 | no | — |
| 365 | C2×M16 | — | 71 | 2 | no | — |
| 366 | C2×M16 | — | 71 | 4 | no | — |
| 367 | C2×M16 | C22×D71 | 1 | 2 | yes | — |
| 368 | C22×C8 | — | 71 | 4 | no | — |
| 369 | C4⋊Q8 | — | 71 | 2 | no | — |
| 370 | C4⋊Q8 | C22×D71 | 1 | 2 | yes | — |
| 371 | C4⋊Q8 | C22×D71 | 1 | 2 | yes | — |
| 372 | #127 | — | 71 | 2 | no | — |
| 373 | #126 | — | 142 | 4 | no | — |
| 374 | #126 | — | 142 | 4 | no | — |
| 375 | #125 | — | 2 | 2 | no | — |
| 376 | #125 | — | 71 | 4 | no | — |
| 377 | #125 | — | 142 | 2 | no | — |
| 378 | #124 | — | 71 | 4 | no | — |
| 379 | #124 | — | 142 | 2 | no | — |
| 380 | #124 | — | 142 | 2 | no | — |
| 381 | #123 | — | 142 | 4 | no | — |
| 382 | #123 | — | 142 | 4 | no | — |
| 383 | #123 | — | 142 | 4 | no | — |
| 384 | C22⋊Q8 | — | 2 | 2 | no | — |
| 385 | C22⋊Q8 | — | 71 | 4 | no | — |
| 386 | C22⋊Q8 | — | 142 | 2 | no | — |
| 387 | C22⋊Q8 | — | 142 | 2 | no | — |
| 388 | C22⋊Q8 | — | 142 | 2 | no | — |
| 389 | C22⋊Q8 | C22×D71 | 1 | 4 | yes | — |
| 390 | #121 | — | 71 | 4 | no | — |
| 391 | #121 | — | 71 | 4 | no | — |
| 392 | #121 | — | 142 | 2 | no | — |
| 393 | #121 | — | 142 | 2 | no | — |
| 394 | #121 | — | 142 | 2 | no | — |
| 395 | #121 | — | 142 | 2 | no | — |
| 396 | #120 | — | 142 | 4 | no | — |
| 397 | C4×Q8 | — | 2 | 2 | no | — |
| 398 | C4×Q8 | — | 71 | 4 | no | — |
| 399 | C4×Q8 | — | 142 | 2 | no | — |
| 400 | C4×Q8 | — | 142 | 2 | no | — |
| 401 | C4×Q8 | — | 142 | 2 | no | — |
| 402 | C4×Q8 | C22×D71 | 1 | 4 | yes | — |
| 403 | C4×D4 | — | 71 | 4 | no | — |
| 404 | C4×D4 | — | 71 | 4 | no | — |
| 405 | C4×D4 | — | 142 | 4 | no | — |
| 406 | C4×D4 | — | 142 | 4 | no | — |
| 407 | C4×D4 | — | 142 | 2 | no | — |
| 408 | C4×D4 | — | 142 | 2 | no | — |
| 409 | C4×D4 | — | 142 | 2 | no | — |
| 410 | C4×D4 | — | 142 | 4 | no | — |
| 411 | C4×D4 | — | 142 | 4 | no | — |
| 412 | C4×D4 | — | 142 | 4 | no | — |
| 413 | C4×D4 | — | 142 | 4 | no | — |
| 414 | C4×D4 | — | 142 | 2 | no | — |
| 415 | #117 | — | 2 | 2 | no | — |
| 416 | #117 | — | 71 | 4 | no | — |
| 417 | #117 | — | 142 | 4 | no | — |
| 418 | #117 | — | 142 | 4 | no | — |
| 419 | #117 | — | 142 | 4 | no | — |
| 420 | #117 | — | 142 | 2 | no | — |
| 421 | C2×C42 | — | 71 | 2 | no | — |
| 422 | C2×C42 | — | 71 | 1 | no | — |
| 423 | C2×C42 | — | 71 | 1 | no | — |
| 424 | C2×C42 | — | 71 | 1 | no | — |
| 425 | C2×C42 | — | 71 | 1 | no | — |
| 426 | C2×C42 | — | 71 | 1 | no | — |
| 427 | C2×C42 | — | 71 | 2 | no | — |
| 428 | C2×C42 | — | 71 | 2 | no | — |
| 429 | C2×C42 | — | 142 | 4 | no | — |
| 430 | C2×C42 | C22×D71 | 1 | 1 | yes | characteristic |
| 431 | #107 | — | 71 | 8 | no | — |
| 432 | #106 | — | 71 | 4 | no | — |
| 433 | #106 | C22×D71 | 1 | 4 | yes | — |
| 434 | C4⋊C8 | — | 71 | 8 | no | — |
| 435 | C4⋊C8 | — | 71 | 4 | no | — |
| 436 | C4⋊C8 | C22×D71 | 1 | 4 | yes | — |
| 437 | #103 | — | 71 | 8 | no | — |
| 438 | #103 | C22×D71 | 1 | 8 | yes | — |
| 439 | #102 | — | 71 | 8 | no | — |
| 440 | #102 | — | 71 | 8 | no | — |
| 441 | C24 | — | 71 | 1 | no | — |
| 442 | #41 | — | 284 | 8 | no | — |
| 443 | #41 | — | 284 | 8 | no | — |
| 444 | #41 | — | 142 | 8 | no | — |
| 445 | #41 | — | 142 | 8 | no | — |
| 446 | C2×Q8 | — | 2 | 2 | no | — |
| 447 | C2×Q8 | — | 142 | 2 | no | — |
| 448 | C2×Q8 | C23×D71 | 1 | 4 | yes | — |
| 449 | C2×D4 | — | 71 | 4 | no | — |
| 450 | C2×D4 | — | 142 | 4 | no | — |
| 451 | C2×D4 | — | 142 | 4 | no | — |
| 452 | C2×D4 | — | 142 | 4 | no | — |
| 453 | C2×D4 | — | 142 | 2 | no | — |
| 454 | C2×D4 | — | 142 | 2 | no | — |
| 455 | C22×C4 | — | 284 | 4 | no | — |
| 456 | C22×C4 | — | 71 | 2 | no | — |
| 457 | C22×C4 | — | 71 | 2 | no | — |
| 458 | C22×C4 | — | 71 | 2 | no | — |
| 459 | C22×C4 | — | 71 | 1 | no | — |
| 460 | C22×C4 | — | 71 | 1 | no | — |
| 461 | C22×C4 | — | 71 | 2 | no | — |
| 462 | C22×C4 | — | 71 | 1 | no | — |
| 463 | C22×C4 | — | 71 | 2 | no | — |
| 464 | C22×C4 | — | 71 | 1 | no | — |
| 465 | C22×C4 | — | 71 | 1 | no | — |
| 466 | C22×C4 | — | 142 | 4 | no | — |
| 467 | C22×C4 | — | 142 | 4 | no | — |
| 468 | C22×C4 | — | 142 | 2 | no | — |
| 469 | C22×C4 | — | 142 | 2 | no | — |
| 470 | C22×C4 | — | 142 | 4 | no | — |
| 471 | C22×C4 | D4×D71 | 1 | 2 | yes | — |
| 472 | C22×C4 | C23×D71 | 1 | 1 | yes | characteristic |
| 473 | Q16 | — | 4 | 4 | no | — |
| 474 | SD16 | — | 284 | 8 | no | — |
| 475 | D8 | — | 284 | 4 | no | — |
| 476 | M16 | — | 4 | 2 | no | — |
| 477 | M16 | — | 284 | 4 | no | — |
| 478 | M16 | — | 284 | 2 | no | — |
| 479 | C2×C8 | — | 71 | 4 | no | — |
| 480 | C2×C8 | — | 142 | 8 | no | — |
| 481 | C2×C8 | C23×D71 | 1 | 4 | yes | — |
| 482 | C4⋊C4 | — | 2 | 2 | no | — |
| 483 | C4⋊C4 | — | 2 | 2 | no | — |
| 484 | C4⋊C4 | — | 2 | 2 | no | — |
| 485 | C4⋊C4 | — | 2 | 4 | no | — |
| 486 | C4⋊C4 | — | 2 | 4 | no | — |
| 487 | C4⋊C4 | — | 71 | 4 | no | — |
| 488 | C4⋊C4 | — | 142 | 4 | no | — |
| 489 | C4⋊C4 | — | 142 | 4 | no | — |
| 490 | C4⋊C4 | — | 142 | 4 | no | — |
| 491 | C4⋊C4 | — | 142 | 4 | no | — |
| 492 | C4⋊C4 | — | 142 | 2 | no | — |
| 493 | C4⋊C4 | C23×D71 | 1 | 4 | yes | — |
| 494 | C22⋊C4 | — | 2 | 4 | no | — |
| 495 | C22⋊C4 | — | 142 | 4 | no | — |
| 496 | C22⋊C4 | — | 142 | 4 | no | — |
| 497 | C22⋊C4 | — | 142 | 4 | no | — |
| 498 | C22⋊C4 | — | 142 | 4 | no | — |
| 499 | C22⋊C4 | — | 142 | 4 | no | — |
| 500 | C22⋊C4 | — | 142 | 4 | no | — |
| 501 | C22⋊C4 | — | 142 | 4 | no | — |
| 502 | C22⋊C4 | — | 142 | 4 | no | — |
| 503 | C42 | — | 2 | 4 | no | — |
| 504 | C42 | — | 71 | 2 | no | — |
| 505 | C42 | — | 71 | 1 | no | — |
| 506 | C42 | — | 71 | 2 | no | — |
| 507 | C42 | — | 71 | 2 | no | — |
| 508 | C42 | — | 71 | 2 | no | — |
| 509 | C42 | — | 71 | 1 | no | — |
| 510 | C42 | — | 71 | 2 | no | — |
| 511 | C42 | — | 142 | 4 | no | — |
| 512 | C42 | — | 142 | 4 | no | — |
| 513 | C42 | D4×D71 | 1 | 1 | yes | characteristic |
| 514 | C42 | D4×D71 | 1 | 1 | yes | characteristic |
| 515 | C42 | C23×D71 | 1 | 2 | yes | — |
| 516 | C23 | — | 284 | 2 | no | — |
| 517 | C23 | — | 71 | 1 | no | — |
| 518 | C23 | — | 71 | 1 | no | — |
| 519 | C23 | — | 142 | 2 | no | — |
| 520 | C23 | — | 142 | 4 | no | — |
| 521 | C23 | C2×D4×D71 | 1 | 1 | yes | characteristic |
| 522 | Q8 | — | 2 | 4 | no | — |
| 523 | Q8 | — | 2 | 4 | no | — |
| 524 | Q8 | — | 4 | 4 | no | — |
| 525 | Q8 | — | 284 | 4 | no | — |
| 526 | D4 | — | 284 | 4 | no | — |
| 527 | D4 | — | 284 | 8 | no | — |
| 528 | D4 | — | 284 | 8 | no | — |
| 529 | D4 | — | 284 | 8 | no | — |
| 530 | D4 | — | 284 | 4 | no | — |
| 531 | D4 | — | 142 | 4 | no | — |
| 532 | D4 | — | 142 | 4 | no | — |
| 533 | C2×C4 | — | 2 | 1 | no | — |
| 534 | C2×C4 | — | 2 | 1 | no | — |
| 535 | C2×C4 | — | 2 | 4 | no | — |
| 536 | C2×C4 | — | 2 | 4 | no | — |
| 537 | C2×C4 | — | 2 | 4 | no | — |
| 538 | C2×C4 | — | 284 | 2 | no | — |
| 539 | C2×C4 | — | 284 | 2 | no | — |
| 540 | C2×C4 | — | 284 | 8 | no | — |
| 541 | C2×C4 | — | 284 | 8 | no | — |
| 542 | C2×C4 | — | 284 | 8 | no | — |
| 543 | C2×C4 | — | 284 | 2 | no | — |
| 544 | C2×C4 | — | 71 | 1 | no | — |
| 545 | C2×C4 | — | 71 | 2 | no | — |
| 546 | C2×C4 | — | 71 | 2 | no | — |
| 547 | C2×C4 | — | 71 | 2 | no | — |
| 548 | C2×C4 | — | 71 | 2 | no | — |
| 549 | C2×C4 | — | 71 | 1 | no | — |
| 550 | C2×C4 | — | 142 | 2 | no | — |
| 551 | C2×C4 | — | 142 | 2 | no | — |
| 552 | C2×C4 | — | 142 | 4 | no | — |
| 553 | C2×C4 | — | 142 | 2 | no | — |
| 554 | C2×C4 | — | 142 | 1 | no | — |
| 555 | C2×C4 | — | 142 | 1 | no | — |
| 556 | C2×C4 | — | 142 | 4 | no | — |
| 557 | C2×C4 | — | 142 | 4 | no | — |
| 558 | C2×C4 | C2×D4×D71 | 1 | 1 | yes | characteristic |
| 559 | C2×C4 | C2×D4×D71 | 1 | 2 | yes | — |
| 560 | C2×C4 | C2×D4×D71 | 1 | 2 | yes | — |
| 561 | C2×C4 | C24×D71 | 1 | 1 | yes | characteristic |
| 562 | C8 | — | 2 | 4 | no | — |
| 563 | C8 | — | 142 | 4 | no | — |
| 564 | C22 | — | 2 | 2 | no | — |
| 565 | C22 | — | 2 | 1 | no | — |
| 566 | C22 | — | 284 | 4 | no | — |
| 567 | C22 | — | 284 | 4 | no | — |
| 568 | C22 | — | 284 | 4 | no | — |
| 569 | C22 | — | 284 | 4 | no | — |
| 570 | C22 | — | 71 | 2 | no | — |
| 571 | C22 | — | 142 | 2 | no | — |
| 572 | C22 | — | 142 | 1 | no | — |
| 573 | C22 | — | 142 | 2 | no | — |
| 574 | C22 | C22×D4×D71 | 1 | 1 | yes | characteristic |
| 575 | C4 | — | 2 | 2 | no | — |
| 576 | C4 | — | 2 | 1 | no | — |
| 577 | C4 | — | 4 | 4 | no | — |
| 578 | C4 | — | 4 | 4 | no | — |
| 579 | C4 | — | 284 | 4 | no | — |
| 580 | C4 | — | 71 | 2 | no | — |
| 581 | C4 | — | 142 | 2 | no | — |
| 582 | C4 | — | 142 | 2 | no | — |
| 583 | C4 | — | 142 | 1 | no | — |
| 584 | C4 | #17986798 | 1 | 4 | yes | — |
| 585 | C4 | H(5,𝔽2)×D71 | 1 | 1 | yes | characteristic |
| 586 | C4 | 2−1+4×D71 | 1 | 1 | yes | characteristic |
| 587 | C2 | — | 4 | 1 | no | — |
| 588 | C2 | — | 284 | 1 | no | — |
| 589 | C2 | — | 568 | 4 | no | — |
| 590 | C2 | — | 142 | 2 | no | — |
| 591 | C2 | #537×D71 | 1 | 1 | yes | characteristic |
| 592 | C2 | C2×#17986798 | 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