← #32863287
Subgroups — #32863287
Order 18176.
1892 conjugacy classes of subgroups.
The subgroup lattice has 492 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #22601948 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #22597490 | C2 | 1 | 4 | yes | maximal, complemented |
| 3 | #22597469 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #22597398 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #22597378 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #22597347 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #22597301 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | D4×#11765848 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | #22597052 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #22597046 | C2 | 1 | 4 | yes | maximal, complemented |
| 11 | C71×#2979 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C2×#14556135 | C22 | 1 | 2 | yes | complemented |
| 13 | C22×#11765848 | C22 | 1 | 4 | yes | complemented |
| 14 | #17986735 | C4 | 1 | 1 | yes | characteristic |
| 15 | #17986710 | C4 | 1 | 2 | yes | — |
| 16 | #17986696 | C4 | 1 | 4 | yes | — |
| 17 | #17986679 | C4 | 1 | 4 | yes | — |
| 18 | #17986646 | C4 | 1 | 4 | yes | — |
| 19 | #17986634 | C4 | 1 | 1 | yes | characteristic |
| 20 | #17986531 | C22 | 1 | 4 | yes | — |
| 21 | #17986506 | C22 | 1 | 4 | yes | — |
| 22 | C4×#11765865 | C22 | 1 | 2 | yes | — |
| 23 | C4×D4×D71 | C22 | 1 | 4 | yes | — |
| 24 | #17986126 | C22 | 1 | 2 | yes | complemented |
| 25 | #17986126 | C22 | 1 | 2 | yes | complemented |
| 26 | C8×Dic142 | C22 | 1 | 4 | yes | complemented |
| 27 | #17986078 | C22 | 1 | 4 | yes | — |
| 28 | #17986077 | C22 | 1 | 4 | yes | complemented |
| 29 | #17986076 | C22 | 1 | 2 | yes | — |
| 30 | #17986076 | C22 | 1 | 2 | yes | — |
| 31 | #17986075 | C22 | 1 | 8 | yes | complemented |
| 32 | #17986074 | C22 | 1 | 8 | yes | complemented |
| 33 | #17986074 | C22 | 1 | 8 | yes | complemented |
| 34 | #17986070 | C22 | 1 | 8 | yes | complemented |
| 35 | #17986067 | C22 | 1 | 4 | yes | complemented |
| 36 | #17986067 | C22 | 1 | 4 | yes | complemented |
| 37 | #17986067 | C22 | 1 | 8 | yes | complemented |
| 38 | D4×C71⋊C8 | C22 | 1 | 4 | yes | complemented |
| 39 | #17986057 | C22 | 1 | 8 | yes | complemented |
| 40 | #17986051 | C22 | 1 | 4 | yes | complemented |
| 41 | #17986050 | C22 | 1 | 4 | yes | complemented |
| 42 | #17986025 | C22 | 1 | 4 | yes | complemented |
| 43 | #17986023 | C22 | 1 | 1 | yes | characteristic, complemented |
| 44 | #17986021 | C22 | 1 | 4 | yes | complemented |
| 45 | #17985966 | C22 | 1 | 2 | yes | complemented |
| 46 | #17985962 | C22 | 1 | 4 | yes | complemented |
| 47 | #17985961 | C22 | 1 | 8 | yes | complemented |
| 48 | #17985957 | C22 | 1 | 4 | yes | complemented |
| 49 | C4×#11765848 | C22 | 1 | 4 | yes | complemented |
| 50 | C2×C4×C71⋊C8 | C22 | 1 | 1 | yes | characteristic, complemented |
| 51 | #532×C71 | C22 | 1 | 1 | yes | characteristic |
| 52 | #436×C71 | C22 | 1 | 4 | yes | complemented |
| 53 | C8×D4×C71 | C22 | 1 | 4 | yes | complemented |
| 54 | #431×C71 | C22 | 1 | 2 | yes | complemented |
| 55 | #408×C71 | C22 | 1 | 4 | yes | complemented |
| 56 | C2×#11765865 | C2×C4 | 1 | 2 | yes | — |
| 57 | C2×D4×D71 | C2×C4 | 1 | 4 | yes | — |
| 58 | C22×C4×D71 | C23 | 1 | 4 | yes | — |
| 59 | #14556135 | — | 4 | 4 | no | — |
| 60 | C2×#11765849 | C23 | 1 | 2 | yes | — |
| 61 | C2×#11765849 | C23 | 1 | 4 | yes | — |
| 62 | C2×#11765848 | — | 4 | 8 | no | — |
| 63 | C2×#11765848 | C23 | 1 | 4 | yes | — |
| 64 | C2×#11765848 | C23 | 1 | 4 | yes | — |
| 65 | C2×#11765848 | C23 | 1 | 8 | yes | — |
| 66 | C22×C71⋊C8 | C23 | 1 | 4 | yes | — |
| 67 | C22×C71⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 68 | C22×C71⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 69 | #14556121 | C2×C4 | 1 | 8 | yes | — |
| 70 | #14556119 | C2×C4 | 1 | 4 | yes | — |
| 71 | #14556115 | C2×C4 | 1 | 4 | yes | — |
| 72 | #14556110 | C2×C4 | 1 | 8 | yes | — |
| 73 | #14556109 | C2×C4 | 1 | 4 | yes | — |
| 74 | #14556109 | C2×C4 | 1 | 4 | yes | — |
| 75 | #14556108 | C2×C4 | 1 | 4 | yes | — |
| 76 | #14556104 | C2×C4 | 1 | 8 | yes | — |
| 77 | #14556099 | C2×C4 | 1 | 4 | yes | — |
| 78 | #14556099 | C2×C4 | 1 | 8 | yes | — |
| 79 | #14556096 | C2×C4 | 1 | 4 | yes | — |
| 80 | #14556096 | C2×C4 | 1 | 4 | yes | — |
| 81 | C4×Dic142 | C2×C4 | 1 | 2 | yes | — |
| 82 | C4×Dic142 | C23 | 1 | 2 | yes | — |
| 83 | C4×D284 | C2×C4 | 1 | 2 | yes | — |
| 84 | C4×D284 | C23 | 1 | 2 | yes | — |
| 85 | D4×Dic71 | C2×C4 | 1 | 4 | yes | — |
| 86 | #14556090 | C2×C4 | 1 | 4 | yes | — |
| 87 | C4×C22⋊D71 | C2×C4 | 1 | 4 | yes | — |
| 88 | C4×C22⋊D71 | C23 | 1 | 4 | yes | — |
| 89 | C4×C22⋊D71 | C23 | 1 | 8 | yes | — |
| 90 | (C22⋊D71)⋊C4 | C2×C4 | 1 | 8 | yes | — |
| 91 | #14556087 | C2×C4 | 1 | 2 | yes | — |
| 92 | #14556087 | C23 | 1 | 4 | yes | — |
| 93 | #14556085 | C2×C4 | 1 | 4 | yes | — |
| 94 | C4⋊C4×D71 | C2×C4 | 1 | 4 | yes | — |
| 95 | C22⋊C4×D71 | C2×C4 | 1 | 8 | yes | — |
| 96 | C42×D71 | C23 | 1 | 4 | yes | — |
| 97 | C4⋊(C71⋊C8) | C23 | 1 | 4 | yes | — |
| 98 | Dic71⋊C8 | C23 | 1 | 4 | yes | — |
| 99 | Dic71⋊C8 | C23 | 1 | 4 | yes | — |
| 100 | Dic71⋊C8 | C23 | 1 | 8 | yes | — |
| 101 | C22⋊(C71⋊C8) | C23 | 1 | 8 | yes | — |
| 102 | (C2×D71)⋊C8 | C23 | 1 | 4 | yes | — |
| 103 | (C2×D71)⋊C8 | C23 | 1 | 4 | yes | — |
| 104 | (C2×D71)⋊C8 | C23 | 1 | 8 | yes | — |
| 105 | #14556038 | C23 | 1 | 4 | yes | — |
| 106 | #14556038 | C23 | 1 | 4 | yes | — |
| 107 | C4×C71⋊C8 | C23 | 1 | 2 | yes | — |
| 108 | C4×C71⋊C8 | C23 | 1 | 2 | yes | — |
| 109 | C8×Dic71 | C23 | 1 | 8 | yes | — |
| 110 | C2×#41×C71 | C23 | 1 | 2 | yes | — |
| 111 | C2×M16×C71 | C23 | 1 | 4 | yes | — |
| 112 | C22×C8×C71 | C23 | 1 | 4 | yes | — |
| 113 | C4⋊Q8×C71 | C2×C4 | 1 | 1 | yes | characteristic |
| 114 | #127×C71 | C2×C4 | 1 | 1 | yes | characteristic |
| 115 | #124×C71 | C2×C4 | 1 | 2 | yes | — |
| 116 | #121×C71 | C2×C4 | 1 | 4 | yes | — |
| 117 | C4×D4×C71 | C23 | 1 | 4 | yes | — |
| 118 | C2×C42×C71 | C23 | 1 | 1 | yes | characteristic |
| 119 | C4⋊C8×C71 | C23 | 1 | 2 | yes | — |
| 120 | C4⋊C8×C71 | C23 | 1 | 2 | yes | — |
| 121 | C22⋊C8×C71 | C23 | 1 | 4 | yes | — |
| 122 | C22⋊C8×C71 | C23 | 1 | 8 | yes | — |
| 123 | C4×C8×C71 | C23 | 1 | 4 | yes | — |
| 124 | C23×D71 | C22×C4 | 1 | 4 | yes | — |
| 125 | #11765865 | — | 4 | 4 | no | — |
| 126 | C2×Dic142 | C22×C4 | 1 | 2 | yes | — |
| 127 | C2×D284 | C22×C4 | 1 | 2 | yes | — |
| 128 | C2×C22⋊D71 | C22×C4 | 1 | 8 | yes | — |
| 129 | C2×C22⋊D71 | C22×C4 | 1 | 4 | yes | — |
| 130 | D4×D71 | — | 4 | 8 | no | — |
| 131 | C22×Dic71 | C22×C4 | 1 | 4 | yes | — |
| 132 | C2×C4×D71 | — | 4 | 4 | no | — |
| 133 | C2×C4×D71 | — | 4 | 4 | no | — |
| 134 | C2×C4×D71 | C22×C4 | 1 | 4 | yes | — |
| 135 | C2×C4×D71 | C22×C4 | 1 | 8 | yes | — |
| 136 | C2×C4×D71 | C22×C4 | 1 | 4 | yes | — |
| 137 | C2×C4×D71 | C24 | 1 | 4 | yes | — |
| 138 | #11765849 | — | 4 | 2 | no | — |
| 139 | #11765849 | — | 4 | 4 | no | — |
| 140 | #11765848 | — | 2 | 8 | no | — |
| 141 | #11765848 | — | 4 | 8 | no | — |
| 142 | #11765848 | — | 4 | 4 | no | — |
| 143 | C2×C71⋊C8 | — | 2 | 8 | no | — |
| 144 | C2×C71⋊C8 | — | 2 | 2 | no | — |
| 145 | C2×C71⋊C8 | — | 4 | 1 | no | — |
| 146 | C2×C71⋊C8 | C24 | 1 | 4 | yes | — |
| 147 | C2×C71⋊C8 | C24 | 1 | 2 | yes | — |
| 148 | C2×C71⋊C8 | C24 | 1 | 1 | yes | characteristic |
| 149 | C2×C71⋊C8 | C24 | 1 | 1 | yes | characteristic |
| 150 | C4⋊Dic71 | C22×C4 | 1 | 2 | yes | — |
| 151 | C4⋊Dic71 | C22×C4 | 1 | 2 | yes | — |
| 152 | C4⋊Dic71 | C22×C4 | 1 | 8 | yes | — |
| 153 | Dic71⋊C4 | C22×C4 | 1 | 8 | yes | — |
| 154 | Dic71⋊C4 | C22×C4 | 1 | 4 | yes | — |
| 155 | Dic71⋊C4 | C22×C4 | 1 | 4 | yes | — |
| 156 | C22⋊Dic71 | C22×C4 | 1 | 8 | yes | — |
| 157 | C22⋊Dic71 | C22×C4 | 1 | 4 | yes | — |
| 158 | C22⋊Dic71 | C22×C4 | 1 | 4 | yes | — |
| 159 | C22⋊Dic71 | C22×C4 | 1 | 4 | yes | — |
| 160 | (C2×D71)⋊C4 | C22×C4 | 1 | 4 | yes | — |
| 161 | (C2×D71)⋊C4 | C22×C4 | 1 | 8 | yes | — |
| 162 | (C2×D71)⋊C4 | C22×C4 | 1 | 4 | yes | — |
| 163 | C4×Dic71 | C22×C4 | 1 | 4 | yes | — |
| 164 | C4×Dic71 | C22×C4 | 1 | 4 | yes | — |
| 165 | C4×Dic71 | C24 | 1 | 4 | yes | — |
| 166 | #41×C71 | — | 4 | 2 | no | — |
| 167 | #41×C71 | — | 4 | 2 | no | — |
| 168 | C2×Q8×C71 | C22×C4 | 1 | 2 | yes | — |
| 169 | C2×D4×C71 | C22×C4 | 1 | 4 | yes | — |
| 170 | C2×D4×C71 | C22×C4 | 1 | 4 | yes | — |
| 171 | C2×D4×C71 | C22×C4 | 1 | 2 | yes | — |
| 172 | C22×C4×C71 | C22×C4 | 1 | 2 | yes | — |
| 173 | C22×C4×C71 | C24 | 1 | 4 | yes | — |
| 174 | C22×C4×C71 | C24 | 1 | 1 | yes | characteristic |
| 175 | M16×C71 | — | 4 | 4 | no | — |
| 176 | C2×C8×C71 | — | 4 | 4 | no | — |
| 177 | C2×C8×C71 | C24 | 1 | 4 | yes | — |
| 178 | C2×C8×C71 | C24 | 1 | 4 | yes | — |
| 179 | C4⋊C4×C71 | C22×C4 | 1 | 4 | yes | — |
| 180 | C22⋊C4×C71 | C22×C4 | 1 | 8 | yes | — |
| 181 | C42×C71 | C22×C4 | 1 | 1 | yes | characteristic |
| 182 | C42×C71 | C22×C4 | 1 | 1 | yes | characteristic |
| 183 | C42×C71 | C24 | 1 | 2 | yes | — |
| 184 | C23×C71 | C23×C4 | 1 | 4 | yes | — |
| 185 | C23×C71 | C23×C4 | 1 | 1 | yes | characteristic |
| 186 | C22×D71 | — | 4 | 4 | no | — |
| 187 | C22×D71 | — | 4 | 8 | no | — |
| 188 | C22×D71 | C23×C4 | 1 | 4 | yes | — |
| 189 | Q8×C71 | — | 4 | 2 | no | — |
| 190 | D4×C71 | — | 2 | 8 | no | — |
| 191 | D4×C71 | — | 4 | 4 | no | — |
| 192 | D4×C71 | — | 4 | 2 | no | — |
| 193 | C2×C4×C71 | — | 2 | 4 | no | — |
| 194 | C2×C4×C71 | — | 2 | 4 | no | — |
| 195 | C2×C4×C71 | — | 2 | 1 | no | — |
| 196 | C2×C4×C71 | — | 2 | 4 | no | — |
| 197 | C2×C4×C71 | — | 2 | 1 | no | — |
| 198 | C2×C4×C71 | C23×C4 | 1 | 1 | yes | characteristic |
| 199 | C2×C4×C71 | C23×C4 | 1 | 2 | yes | — |
| 200 | C2×C4×C71 | C23×C4 | 1 | 4 | yes | — |
| 201 | C2×C4×C71 | C23×C4 | 1 | 2 | yes | — |
| 202 | C2×C4×C71 | C25 | 1 | 1 | yes | characteristic |
| 203 | C22⋊D71 | — | 4 | 8 | no | — |
| 204 | C22⋊D71 | — | 4 | 4 | no | — |
| 205 | C2×Dic71 | — | 4 | 4 | no | — |
| 206 | C2×Dic71 | C23×C4 | 1 | 4 | yes | — |
| 207 | C2×Dic71 | C23×C4 | 1 | 4 | yes | — |
| 208 | C2×Dic71 | C23×C4 | 1 | 4 | yes | — |
| 209 | D284 | — | 2 | 4 | no | — |
| 210 | C4×D71 | — | 2 | 8 | no | — |
| 211 | C4×D71 | — | 2 | 4 | no | — |
| 212 | C4×D71 | — | 2 | 4 | no | — |
| 213 | C4×D71 | — | 4 | 8 | no | — |
| 214 | C4×D71 | — | 4 | 4 | no | — |
| 215 | Dic142 | — | 2 | 4 | no | — |
| 216 | C8×C71 | — | 2 | 4 | no | — |
| 217 | C8×C71 | — | 2 | 4 | no | — |
| 218 | C71⋊C8 | — | 2 | 4 | no | — |
| 219 | C71⋊C8 | — | 2 | 1 | no | — |
| 220 | C71⋊C8 | — | 2 | 2 | no | — |
| 221 | C71⋊C8 | H(5,𝔽2) | 1 | 2 | yes | — |
| 222 | C22×C71 | — | 2 | 4 | no | — |
| 223 | C22×C71 | — | 2 | 1 | no | — |
| 224 | C22×C71 | — | 2 | 2 | no | — |
| 225 | C22×C71 | — | 2 | 8 | no | — |
| 226 | C22×C71 | C24×C4 | 1 | 1 | yes | characteristic |
| 227 | C2×D71 | — | 2 | 4 | no | — |
| 228 | C2×D71 | — | 2 | 4 | no | — |
| 229 | C2×D71 | — | 2 | 4 | no | — |
| 230 | C2×D71 | — | 8 | 8 | no | — |
| 231 | C4×C71 | — | 2 | 4 | no | — |
| 232 | C4×C71 | — | 2 | 1 | no | — |
| 233 | C4×C71 | — | 2 | 2 | no | — |
| 234 | C4×C71 | #568 | 1 | 4 | yes | — |
| 235 | C4×C71 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 236 | C4×C71 | #585 | 1 | 1 | yes | characteristic |
| 237 | Dic71 | — | 2 | 4 | no | — |
| 238 | Dic71 | — | 2 | 4 | no | — |
| 239 | Dic71 | — | 2 | 4 | no | — |
| 240 | #60317 | — | 71 | 1 | no | maximal, Sylow |
| 241 | C2×C71 | — | 4 | 4 | no | — |
| 242 | C2×C71 | — | 4 | 1 | no | — |
| 243 | C2×C71 | C4×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 244 | C2×C71 | C2×#568 | 1 | 2 | yes | — |
| 245 | D71 | — | 4 | 4 | no | — |
| 246 | #3481 | — | 71 | 1 | no | — |
| 247 | #2993 | — | 71 | 4 | no | — |
| 248 | #2991 | — | 71 | 2 | no | — |
| 249 | #2979 | D71 | 1 | 1 | yes | characteristic, complemented |
| 250 | #2978 | — | 71 | 4 | no | — |
| 251 | #2975 | — | 71 | 4 | no | — |
| 252 | #2969 | — | 71 | 4 | no | — |
| 253 | #2965 | — | 71 | 2 | no | — |
| 254 | D4×M16 | — | 71 | 4 | no | — |
| 255 | #2931 | — | 71 | 1 | no | — |
| 256 | #2930 | — | 71 | 4 | no | — |
| 257 | C71 | #60317 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 258 | C2×#131 | — | 71 | 2 | no | — |
| 259 | C22×M16 | — | 71 | 4 | no | — |
| 260 | #559 | — | 71 | 1 | no | — |
| 261 | #554 | — | 71 | 2 | no | — |
| 262 | #553 | — | 71 | 4 | no | — |
| 263 | #551 | — | 71 | 4 | no | — |
| 264 | #546 | — | 71 | 4 | no | — |
| 265 | D42 | — | 71 | 1 | no | — |
| 266 | #532 | C2×D71 | 1 | 1 | yes | characteristic |
| 267 | #529 | — | 71 | 4 | no | — |
| 268 | #525 | — | 71 | 4 | no | — |
| 269 | C4×#41 | — | 71 | 2 | no | — |
| 270 | C2×C4×D4 | — | 71 | 4 | no | — |
| 271 | #446 | — | 71 | 2 | no | — |
| 272 | #446 | — | 71 | 2 | no | — |
| 273 | C8×Q8 | — | 71 | 4 | no | — |
| 274 | #436 | — | 71 | 8 | no | — |
| 275 | #436 | — | 71 | 4 | no | — |
| 276 | #436 | — | 71 | 2 | no | — |
| 277 | #436 | — | 71 | 2 | no | — |
| 278 | #436 | — | 71 | 8 | no | — |
| 279 | #436 | — | 71 | 8 | no | — |
| 280 | #436 | — | 71 | 4 | no | — |
| 281 | #436 | C2×D71 | 1 | 4 | yes | complemented |
| 282 | #435 | — | 71 | 8 | no | — |
| 283 | #435 | — | 71 | 4 | no | — |
| 284 | #435 | — | 71 | 8 | no | — |
| 285 | #435 | — | 71 | 4 | no | — |
| 286 | C8×D4 | — | 71 | 4 | no | — |
| 287 | C8×D4 | C2×D71 | 1 | 4 | yes | complemented |
| 288 | #433 | — | 71 | 8 | no | — |
| 289 | #431 | — | 71 | 4 | no | — |
| 290 | #431 | — | 71 | 4 | no | — |
| 291 | #431 | C2×D71 | 1 | 2 | yes | complemented |
| 292 | #424 | — | 71 | 4 | no | — |
| 293 | #423 | — | 71 | 1 | no | — |
| 294 | #423 | — | 71 | 4 | no | — |
| 295 | #408 | — | 71 | 2 | no | — |
| 296 | #408 | C2×D71 | 1 | 4 | yes | complemented |
| 297 | #407 | — | 71 | 4 | no | — |
| 298 | #407 | — | 71 | 8 | no | — |
| 299 | #405 | — | 71 | 4 | no | — |
| 300 | C4×M16 | — | 71 | 4 | no | — |
| 301 | C2×C4×C8 | — | 71 | 1 | no | — |
| 302 | C2×#41 | — | 71 | 2 | no | — |
| 303 | C2×#41 | C22×D71 | 1 | 2 | yes | — |
| 304 | C22×D4 | — | 71 | 4 | no | — |
| 305 | C23×C4 | — | 71 | 4 | no | — |
| 306 | #131 | — | 284 | 4 | no | — |
| 307 | C2×M16 | — | 284 | 8 | no | — |
| 308 | C2×M16 | — | 71 | 4 | no | — |
| 309 | C2×M16 | — | 71 | 2 | no | — |
| 310 | C2×M16 | — | 71 | 8 | no | — |
| 311 | C2×M16 | — | 71 | 4 | no | — |
| 312 | C2×M16 | — | 71 | 4 | no | — |
| 313 | C2×M16 | C22×D71 | 1 | 4 | yes | — |
| 314 | C22×C8 | — | 71 | 1 | no | — |
| 315 | C22×C8 | — | 71 | 4 | no | — |
| 316 | C22×C8 | — | 71 | 1 | no | — |
| 317 | C22×C8 | C22×D71 | 1 | 4 | yes | — |
| 318 | C4⋊Q8 | C4×D71 | 1 | 1 | yes | characteristic |
| 319 | #127 | C4×D71 | 1 | 1 | yes | characteristic |
| 320 | #126 | — | 71 | 8 | no | — |
| 321 | #125 | — | 71 | 4 | no | — |
| 322 | #124 | — | 71 | 4 | no | — |
| 323 | #124 | C4×D71 | 1 | 2 | yes | — |
| 324 | #123 | — | 71 | 4 | no | — |
| 325 | #123 | — | 71 | 4 | no | — |
| 326 | #123 | — | 71 | 8 | no | — |
| 327 | C22⋊Q8 | — | 71 | 8 | no | — |
| 328 | C22⋊Q8 | — | 71 | 4 | no | — |
| 329 | #121 | — | 71 | 8 | no | — |
| 330 | #121 | — | 71 | 4 | no | — |
| 331 | #121 | C4×D71 | 1 | 4 | yes | — |
| 332 | #120 | — | 71 | 4 | no | — |
| 333 | #120 | — | 71 | 4 | no | — |
| 334 | C4×Q8 | — | 71 | 2 | no | — |
| 335 | C4×Q8 | — | 71 | 2 | no | — |
| 336 | C4×D4 | — | 71 | 4 | no | — |
| 337 | C4×D4 | — | 71 | 4 | no | — |
| 338 | C4×D4 | — | 71 | 8 | no | — |
| 339 | C4×D4 | — | 71 | 4 | no | — |
| 340 | C4×D4 | — | 71 | 4 | no | — |
| 341 | C4×D4 | — | 71 | 8 | no | — |
| 342 | C4×D4 | — | 71 | 2 | no | — |
| 343 | C4×D4 | — | 71 | 2 | no | — |
| 344 | C4×D4 | C22×D71 | 1 | 4 | yes | — |
| 345 | #117 | — | 71 | 2 | no | — |
| 346 | #117 | — | 71 | 4 | no | — |
| 347 | #117 | — | 71 | 4 | no | — |
| 348 | C2×C4⋊C4 | — | 71 | 4 | no | — |
| 349 | C2×C22⋊C4 | — | 71 | 8 | no | — |
| 350 | C2×C42 | — | 71 | 4 | no | — |
| 351 | C2×C42 | C22×D71 | 1 | 1 | yes | characteristic |
| 352 | C4⋊C8 | — | 71 | 8 | no | — |
| 353 | C4⋊C8 | — | 71 | 4 | no | — |
| 354 | C4⋊C8 | — | 71 | 4 | no | — |
| 355 | C4⋊C8 | — | 71 | 4 | no | — |
| 356 | C4⋊C8 | C22×D71 | 1 | 2 | yes | — |
| 357 | C4⋊C8 | C22×D71 | 1 | 2 | yes | — |
| 358 | C22⋊C8 | — | 71 | 8 | no | — |
| 359 | C22⋊C8 | — | 71 | 4 | no | — |
| 360 | C22⋊C8 | — | 71 | 4 | no | — |
| 361 | C22⋊C8 | — | 71 | 8 | no | — |
| 362 | C22⋊C8 | C22×D71 | 1 | 8 | yes | — |
| 363 | C22⋊C8 | C22×D71 | 1 | 4 | yes | — |
| 364 | #97 | — | 71 | 4 | no | — |
| 365 | #97 | — | 71 | 4 | no | — |
| 366 | C4×C8 | — | 71 | 8 | no | — |
| 367 | C4×C8 | — | 71 | 2 | no | — |
| 368 | C4×C8 | — | 71 | 2 | no | — |
| 369 | C4×C8 | C22×D71 | 1 | 4 | yes | — |
| 370 | C24 | — | 71 | 4 | no | — |
| 371 | #41 | — | 4 | 2 | no | — |
| 372 | #41 | — | 4 | 2 | no | — |
| 373 | #41 | — | 284 | 4 | no | — |
| 374 | C2×Q8 | — | 71 | 2 | no | — |
| 375 | C2×Q8 | C2×C4×D71 | 1 | 2 | yes | — |
| 376 | C2×D4 | — | 284 | 8 | no | — |
| 377 | C2×D4 | — | 71 | 4 | no | — |
| 378 | C2×D4 | — | 71 | 8 | no | — |
| 379 | C2×D4 | — | 71 | 2 | no | — |
| 380 | C2×D4 | C2×C4×D71 | 1 | 4 | yes | — |
| 381 | C2×D4 | C2×C4×D71 | 1 | 2 | yes | — |
| 382 | C2×D4 | C2×C4×D71 | 1 | 4 | yes | — |
| 383 | C22×C4 | — | 284 | 4 | no | — |
| 384 | C22×C4 | — | 284 | 4 | no | — |
| 385 | C22×C4 | — | 71 | 4 | no | — |
| 386 | C22×C4 | — | 71 | 4 | no | — |
| 387 | C22×C4 | — | 71 | 8 | no | — |
| 388 | C22×C4 | — | 71 | 4 | no | — |
| 389 | C22×C4 | — | 71 | 4 | no | — |
| 390 | C22×C4 | C2×C4×D71 | 1 | 2 | yes | — |
| 391 | C22×C4 | C23×D71 | 1 | 4 | yes | — |
| 392 | C22×C4 | C23×D71 | 1 | 1 | yes | characteristic |
| 393 | M16 | — | 4 | 4 | no | — |
| 394 | M16 | — | 284 | 8 | no | — |
| 395 | M16 | — | 284 | 4 | no | — |
| 396 | M16 | — | 284 | 4 | no | — |
| 397 | M16 | — | 284 | 2 | no | — |
| 398 | M16 | — | 142 | 8 | no | — |
| 399 | C2×C8 | — | 4 | 4 | no | — |
| 400 | C2×C8 | — | 284 | 1 | no | — |
| 401 | C2×C8 | — | 71 | 1 | no | — |
| 402 | C2×C8 | — | 71 | 2 | no | — |
| 403 | C2×C8 | — | 71 | 4 | no | — |
| 404 | C2×C8 | — | 71 | 1 | no | — |
| 405 | C2×C8 | — | 142 | 8 | no | — |
| 406 | C2×C8 | — | 142 | 2 | no | — |
| 407 | C2×C8 | C23×D71 | 1 | 4 | yes | — |
| 408 | C2×C8 | C23×D71 | 1 | 4 | yes | — |
| 409 | C4⋊C4 | — | 71 | 8 | no | — |
| 410 | C4⋊C4 | — | 71 | 4 | no | — |
| 411 | C4⋊C4 | — | 71 | 4 | no | — |
| 412 | C4⋊C4 | — | 71 | 2 | no | — |
| 413 | C4⋊C4 | — | 71 | 2 | no | — |
| 414 | C4⋊C4 | — | 71 | 8 | no | — |
| 415 | C4⋊C4 | C2×C4×D71 | 1 | 4 | yes | — |
| 416 | C22⋊C4 | — | 71 | 8 | no | — |
| 417 | C22⋊C4 | — | 71 | 4 | no | — |
| 418 | C22⋊C4 | — | 71 | 4 | no | — |
| 419 | C22⋊C4 | — | 71 | 4 | no | — |
| 420 | C22⋊C4 | — | 71 | 4 | no | — |
| 421 | C22⋊C4 | — | 71 | 8 | no | — |
| 422 | C22⋊C4 | — | 71 | 4 | no | — |
| 423 | C22⋊C4 | C2×C4×D71 | 1 | 8 | yes | — |
| 424 | C42 | — | 71 | 4 | no | — |
| 425 | C42 | — | 71 | 4 | no | — |
| 426 | C42 | — | 71 | 4 | no | — |
| 427 | C42 | C2×C4×D71 | 1 | 1 | yes | characteristic |
| 428 | C42 | C2×C4×D71 | 1 | 1 | yes | characteristic |
| 429 | C42 | C23×D71 | 1 | 2 | yes | — |
| 430 | C23 | — | 284 | 4 | no | — |
| 431 | C23 | — | 284 | 8 | no | — |
| 432 | C23 | — | 71 | 4 | no | — |
| 433 | C23 | C22×C4×D71 | 1 | 4 | yes | — |
| 434 | C23 | C22×C4×D71 | 1 | 1 | yes | characteristic |
| 435 | Q8 | — | 4 | 2 | no | — |
| 436 | Q8 | — | 142 | 4 | no | — |
| 437 | D4 | — | 2 | 8 | no | — |
| 438 | D4 | — | 4 | 4 | no | — |
| 439 | D4 | — | 4 | 2 | no | — |
| 440 | D4 | — | 284 | 8 | no | — |
| 441 | D4 | — | 284 | 4 | no | — |
| 442 | D4 | — | 142 | 4 | no | — |
| 443 | C2×C4 | — | 2 | 4 | no | — |
| 444 | C2×C4 | — | 2 | 1 | no | — |
| 445 | C2×C4 | — | 2 | 1 | no | — |
| 446 | C2×C4 | — | 2 | 4 | no | — |
| 447 | C2×C4 | — | 2 | 4 | no | — |
| 448 | C2×C4 | — | 284 | 8 | no | — |
| 449 | C2×C4 | — | 284 | 4 | no | — |
| 450 | C2×C4 | — | 284 | 4 | no | — |
| 451 | C2×C4 | — | 71 | 4 | no | — |
| 452 | C2×C4 | — | 71 | 4 | no | — |
| 453 | C2×C4 | — | 71 | 4 | no | — |
| 454 | C2×C4 | — | 142 | 4 | no | — |
| 455 | C2×C4 | — | 142 | 4 | no | — |
| 456 | C2×C4 | — | 142 | 8 | no | — |
| 457 | C2×C4 | C22×C4×D71 | 1 | 2 | yes | — |
| 458 | C2×C4 | C22×C4×D71 | 1 | 1 | yes | characteristic |
| 459 | C2×C4 | C22×C4×D71 | 1 | 4 | yes | — |
| 460 | C2×C4 | C22×C4×D71 | 1 | 2 | yes | — |
| 461 | C2×C4 | C24×D71 | 1 | 1 | yes | characteristic |
| 462 | C8 | — | 2 | 4 | no | — |
| 463 | C8 | — | 2 | 4 | no | — |
| 464 | C8 | — | 71 | 2 | no | — |
| 465 | C8 | — | 142 | 4 | no | — |
| 466 | C8 | — | 142 | 1 | no | — |
| 467 | C8 | — | 142 | 2 | no | — |
| 468 | C22 | — | 2 | 2 | no | — |
| 469 | C22 | — | 2 | 8 | no | — |
| 470 | C22 | — | 2 | 4 | no | — |
| 471 | C22 | — | 2 | 1 | no | — |
| 472 | C22 | — | 568 | 8 | no | — |
| 473 | C22 | — | 142 | 4 | no | — |
| 474 | C22 | — | 142 | 4 | no | — |
| 475 | C22 | — | 142 | 4 | no | — |
| 476 | C22 | C23×C4×D71 | 1 | 1 | yes | characteristic |
| 477 | C4 | — | 2 | 2 | no | — |
| 478 | C4 | — | 2 | 4 | no | — |
| 479 | C4 | — | 2 | 1 | no | — |
| 480 | C4 | — | 142 | 4 | no | — |
| 481 | C4 | — | 142 | 4 | no | — |
| 482 | C4 | — | 142 | 4 | no | — |
| 483 | C4 | #17986764 | 1 | 4 | yes | — |
| 484 | C4 | H(5,𝔽2)×D71 | 1 | 1 | yes | characteristic |
| 485 | C4 | #17986834 | 1 | 1 | yes | characteristic |
| 486 | C2 | — | 4 | 4 | no | — |
| 487 | C2 | — | 4 | 1 | no | — |
| 488 | C2 | — | 284 | 4 | no | — |
| 489 | C2 | #22601544 | 1 | 1 | yes | characteristic |
| 490 | C2 | C2×#17986764 | 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