← C2×#22602224 #32905890
Subgroups — C2×#22602224 #32905890
Order 18176.
7022 conjugacy classes of subgroups.
The subgroup lattice has 456 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #22602224 | C2 | 1 | 32 | yes | maximal, direct product factor |
| 2 | C2×#17986724 | C2 | 1 | 4 | yes | maximal, complemented |
| 3 | C2×#17986723 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | C2×#17986684 | C2 | 1 | 8 | yes | maximal, complemented |
| 5 | C2×#17986610 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | C2×#17986573 | C2 | 1 | 2 | yes | maximal |
| 7 | C2×#17986556 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C2×#17986554 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | C2×#17986477 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | C2×C4×#11765865 | C2 | 1 | 1 | yes | maximal, characteristic |
| 11 | C22×C4⋊Q8×C71 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C22×#11765865 | C22 | 1 | 1 | yes | characteristic |
| 13 | #17986724 | C22 | 1 | 64 | yes | complemented |
| 14 | #17986723 | C22 | 1 | 64 | yes | complemented |
| 15 | #17986684 | C22 | 1 | 128 | yes | complemented |
| 16 | #17986610 | C22 | 1 | 64 | yes | complemented |
| 17 | #17986573 | C22 | 1 | 32 | yes | — |
| 18 | #17986556 | C22 | 1 | 16 | yes | complemented |
| 19 | #17986554 | C22 | 1 | 64 | yes | complemented |
| 20 | C2×#14556128 | C22 | 1 | 2 | yes | — |
| 21 | C2×#14556126 | C22 | 1 | 4 | yes | — |
| 22 | C2×#14556123 | C22 | 1 | 16 | yes | — |
| 23 | C2×#14556120 | C22 | 1 | 2 | yes | — |
| 24 | C2×#14556119 | C22 | 1 | 8 | yes | — |
| 25 | C2×#14556118 | C22 | 1 | 16 | yes | — |
| 26 | C2×#14556117 | C22 | 1 | 4 | yes | — |
| 27 | C2×#14556111 | C22 | 1 | 8 | yes | — |
| 28 | C2×#14556108 | C22 | 1 | 8 | yes | — |
| 29 | C2×#14556107 | C22 | 1 | 4 | yes | — |
| 30 | C2×#14556104 | C22 | 1 | 8 | yes | — |
| 31 | #17986477 | C22 | 1 | 32 | yes | complemented |
| 32 | C4×#11765865 | C22 | 1 | 16 | yes | — |
| 33 | C2×Q8×Dic71 | C22 | 1 | 8 | yes | — |
| 34 | C2×Q8×Dic71 | C22 | 1 | 8 | yes | — |
| 35 | C2×C4×Dic142 | C22 | 1 | 2 | yes | — |
| 36 | C2×C4×Dic142 | C22 | 1 | 4 | yes | — |
| 37 | C2×#14556093 | C22 | 1 | 8 | yes | — |
| 38 | C2×C4×D284 | C22 | 1 | 2 | yes | — |
| 39 | C2×C4×C22⋊D71 | C22 | 1 | 4 | yes | — |
| 40 | C2×#14556087 | C22 | 1 | 1 | yes | characteristic |
| 41 | C2×#14556087 | C22 | 1 | 8 | yes | — |
| 42 | C2×#14556087 | C22 | 1 | 2 | yes | — |
| 43 | C2×#14556086 | C22 | 1 | 8 | yes | — |
| 44 | C2×#14556085 | C22 | 1 | 2 | yes | — |
| 45 | C2×C42×D71 | C22 | 1 | 2 | yes | — |
| 46 | C23×Q8×C71 | C22 | 1 | 2 | yes | — |
| 47 | C2×C4⋊Q8×C71 | C22 | 1 | 2 | yes | — |
| 48 | C2×C4⋊Q8×C71 | C22 | 1 | 4 | yes | — |
| 49 | C2×C4⋊Q8×C71 | C22 | 1 | 2 | yes | — |
| 50 | C2×C4⋊Q8×C71 | C22 | 1 | 16 | yes | complemented |
| 51 | C22×C4⋊C4×C71 | C22 | 1 | 4 | yes | — |
| 52 | C22×C42×C71 | C22 | 1 | 1 | yes | characteristic |
| 53 | C2×#11765865 | — | 2 | 8 | no | — |
| 54 | C2×#11765865 | C23 | 1 | 8 | yes | — |
| 55 | C22×Dic142 | C23 | 1 | 1 | yes | characteristic |
| 56 | C22×Dic142 | C23 | 1 | 4 | yes | — |
| 57 | C22×D284 | C23 | 1 | 1 | yes | characteristic |
| 58 | C22×C22⋊D71 | C23 | 1 | 2 | yes | — |
| 59 | C22×C4×D71 | C23 | 1 | 2 | yes | — |
| 60 | C22×C4×D71 | C23 | 1 | 4 | yes | — |
| 61 | #14556128 | C23 | 1 | 16 | yes | — |
| 62 | #14556126 | C23 | 1 | 32 | yes | — |
| 63 | #14556123 | C23 | 1 | 128 | yes | — |
| 64 | #14556120 | C23 | 1 | 16 | yes | — |
| 65 | #14556119 | C23 | 1 | 64 | yes | — |
| 66 | #14556118 | C23 | 1 | 128 | yes | — |
| 67 | #14556117 | C23 | 1 | 32 | yes | — |
| 68 | #14556111 | C23 | 1 | 64 | yes | — |
| 69 | #14556108 | C23 | 1 | 64 | yes | — |
| 70 | #14556107 | C23 | 1 | 32 | yes | — |
| 71 | #14556104 | C23 | 1 | 64 | yes | — |
| 72 | Q8×Dic71 | C23 | 1 | 64 | yes | — |
| 73 | Q8×Dic71 | C23 | 1 | 64 | yes | — |
| 74 | C4×Dic142 | C23 | 1 | 32 | yes | — |
| 75 | C4×Dic142 | C23 | 1 | 16 | yes | — |
| 76 | #14556093 | C23 | 1 | 64 | yes | — |
| 77 | C4×D284 | C23 | 1 | 16 | yes | — |
| 78 | C4×C22⋊D71 | C23 | 1 | 32 | yes | — |
| 79 | #14556087 | C23 | 1 | 16 | yes | — |
| 80 | #14556087 | C23 | 1 | 64 | yes | — |
| 81 | #14556087 | C23 | 1 | 8 | yes | — |
| 82 | #14556086 | C23 | 1 | 64 | yes | — |
| 83 | #14556085 | C23 | 1 | 16 | yes | — |
| 84 | C2×C4⋊Dic71 | C23 | 1 | 4 | yes | — |
| 85 | C2×C4⋊Dic71 | C23 | 1 | 2 | yes | — |
| 86 | C2×C4⋊Dic71 | C23 | 1 | 4 | yes | — |
| 87 | C2×C4⋊Dic71 | C23 | 1 | 16 | yes | — |
| 88 | C2×Dic71⋊C4 | C23 | 1 | 4 | yes | — |
| 89 | C2×Dic71⋊C4 | C23 | 1 | 16 | yes | — |
| 90 | C2×Dic71⋊C4 | C23 | 1 | 8 | yes | — |
| 91 | C2×C22⋊Dic71 | C23 | 1 | 2 | yes | — |
| 92 | C2×C22⋊Dic71 | C23 | 1 | 4 | yes | — |
| 93 | C2×(C2×D71)⋊C4 | C23 | 1 | 4 | yes | — |
| 94 | C2×(C2×D71)⋊C4 | C23 | 1 | 16 | yes | — |
| 95 | C2×C4×Dic71 | C23 | 1 | 2 | yes | — |
| 96 | C2×C4×Dic71 | C23 | 1 | 4 | yes | — |
| 97 | C2×C4×Dic71 | C23 | 1 | 16 | yes | — |
| 98 | C2×C4×Dic71 | C23 | 1 | 4 | yes | — |
| 99 | C42×D71 | C23 | 1 | 16 | yes | — |
| 100 | C22×Q8×C71 | — | 2 | 16 | no | — |
| 101 | C22×Q8×C71 | C23 | 1 | 16 | yes | — |
| 102 | C22×Q8×C71 | C23 | 1 | 4 | yes | — |
| 103 | C22×Q8×C71 | C23 | 1 | 4 | yes | — |
| 104 | C23×C4×C71 | C23 | 1 | 2 | yes | — |
| 105 | C23×C4×C71 | C23 | 1 | 4 | yes | — |
| 106 | C23×C4×C71 | C23 | 1 | 1 | yes | characteristic |
| 107 | C4⋊Q8×C71 | C23 | 1 | 16 | yes | — |
| 108 | C4⋊Q8×C71 | C23 | 1 | 32 | yes | — |
| 109 | C4⋊Q8×C71 | C23 | 1 | 16 | yes | — |
| 110 | C2×C4⋊C4×C71 | C23 | 1 | 32 | yes | — |
| 111 | C2×C4⋊C4×C71 | C23 | 1 | 8 | yes | — |
| 112 | C2×C4⋊C4×C71 | C23 | 1 | 8 | yes | — |
| 113 | C2×C42×C71 | C23 | 1 | 1 | yes | characteristic |
| 114 | C2×C42×C71 | C23 | 1 | 1 | yes | characteristic |
| 115 | C2×C42×C71 | C23 | 1 | 2 | yes | — |
| 116 | C2×C42×C71 | C23 | 1 | 8 | yes | — |
| 117 | C23×D71 | C24 | 1 | 2 | yes | — |
| 118 | #11765865 | — | 2 | 32 | no | — |
| 119 | C2×Dic142 | — | 2 | 4 | no | — |
| 120 | C2×Dic142 | — | 2 | 16 | no | — |
| 121 | C2×Dic142 | C24 | 1 | 4 | yes | — |
| 122 | C2×Dic142 | C24 | 1 | 16 | yes | — |
| 123 | C2×D284 | — | 2 | 4 | no | — |
| 124 | C2×D284 | C24 | 1 | 4 | yes | — |
| 125 | C2×C22⋊D71 | — | 2 | 8 | no | — |
| 126 | C2×C22⋊D71 | C24 | 1 | 8 | yes | — |
| 127 | C22×Dic71 | C24 | 1 | 2 | yes | — |
| 128 | C22×Dic71 | C24 | 1 | 4 | yes | — |
| 129 | C22×Dic71 | C24 | 1 | 8 | yes | — |
| 130 | C2×C4×D71 | — | 2 | 8 | no | — |
| 131 | C2×C4×D71 | — | 2 | 16 | no | — |
| 132 | C2×C4×D71 | C24 | 1 | 8 | yes | — |
| 133 | C2×C4×D71 | C24 | 1 | 16 | yes | — |
| 134 | C4⋊Dic71 | C24 | 1 | 16 | yes | — |
| 135 | C4⋊Dic71 | C24 | 1 | 8 | yes | — |
| 136 | C4⋊Dic71 | C24 | 1 | 16 | yes | — |
| 137 | C4⋊Dic71 | C24 | 1 | 64 | yes | — |
| 138 | Dic71⋊C4 | C24 | 1 | 16 | yes | — |
| 139 | Dic71⋊C4 | C24 | 1 | 64 | yes | — |
| 140 | Dic71⋊C4 | C24 | 1 | 32 | yes | — |
| 141 | C22⋊Dic71 | C24 | 1 | 8 | yes | — |
| 142 | C22⋊Dic71 | C24 | 1 | 16 | yes | — |
| 143 | (C2×D71)⋊C4 | C24 | 1 | 16 | yes | — |
| 144 | (C2×D71)⋊C4 | C24 | 1 | 64 | yes | — |
| 145 | C4×Dic71 | C24 | 1 | 8 | yes | — |
| 146 | C4×Dic71 | C24 | 1 | 16 | yes | — |
| 147 | C4×Dic71 | C24 | 1 | 64 | yes | — |
| 148 | C4×Dic71 | C24 | 1 | 16 | yes | — |
| 149 | C24×C71 | C24 | 1 | 1 | yes | characteristic |
| 150 | C2×Q8×C71 | — | 2 | 16 | no | — |
| 151 | C2×Q8×C71 | — | 2 | 16 | no | — |
| 152 | C2×Q8×C71 | — | 2 | 64 | no | — |
| 153 | C2×Q8×C71 | C24 | 1 | 16 | yes | — |
| 154 | C2×Q8×C71 | C24 | 1 | 16 | yes | — |
| 155 | C22×C4×C71 | — | 2 | 16 | no | — |
| 156 | C22×C4×C71 | — | 2 | 8 | no | — |
| 157 | C22×C4×C71 | #41 | 1 | 8 | yes | — |
| 158 | C22×C4×C71 | C24 | 1 | 2 | yes | — |
| 159 | C22×C4×C71 | C24 | 1 | 8 | yes | — |
| 160 | C22×C4×C71 | C24 | 1 | 8 | yes | — |
| 161 | C22×C4×C71 | C24 | 1 | 16 | yes | — |
| 162 | C22×C4×C71 | C24 | 1 | 1 | yes | characteristic |
| 163 | C22×C4×C71 | C24 | 1 | 1 | yes | characteristic |
| 164 | C22×C4×C71 | C24 | 1 | 4 | yes | — |
| 165 | C22×C4×C71 | C24 | 1 | 2 | yes | — |
| 166 | C4⋊C4×C71 | C24 | 1 | 32 | yes | — |
| 167 | C4⋊C4×C71 | C24 | 1 | 32 | yes | — |
| 168 | C42×C71 | C24 | 1 | 4 | yes | — |
| 169 | C42×C71 | C24 | 1 | 4 | yes | — |
| 170 | C42×C71 | C24 | 1 | 8 | yes | — |
| 171 | C23×C71 | — | 2 | 4 | no | — |
| 172 | C23×C71 | C2×#41 | 1 | 4 | yes | — |
| 173 | C23×C71 | C25 | 1 | 2 | yes | — |
| 174 | C23×C71 | C25 | 1 | 1 | yes | characteristic |
| 175 | C22×D71 | — | 2 | 4 | no | — |
| 176 | C22×D71 | — | 2 | 8 | no | — |
| 177 | C22×D71 | C25 | 1 | 4 | yes | — |
| 178 | Q8×C71 | — | 2 | 32 | no | — |
| 179 | Q8×C71 | — | 2 | 32 | no | — |
| 180 | C2×C4×C71 | — | 2 | 32 | no | — |
| 181 | C2×C4×C71 | — | 2 | 16 | no | — |
| 182 | C2×C4×C71 | — | 2 | 4 | no | — |
| 183 | C2×C4×C71 | — | 2 | 16 | no | — |
| 184 | C2×C4×C71 | C2×#41 | 1 | 4 | yes | — |
| 185 | C2×C4×C71 | C2×#41 | 1 | 4 | yes | — |
| 186 | C2×C4×C71 | C2×#41 | 1 | 16 | yes | — |
| 187 | C2×C4×C71 | 2−1+4 | 1 | 8 | yes | — |
| 188 | C2×C4×C71 | C25 | 1 | 4 | yes | — |
| 189 | C2×C4×C71 | C25 | 1 | 16 | yes | — |
| 190 | C2×C4×C71 | C25 | 1 | 2 | yes | — |
| 191 | C2×C4×C71 | C25 | 1 | 2 | yes | — |
| 192 | C2×C4×C71 | C25 | 1 | 4 | yes | — |
| 193 | C22⋊D71 | — | 2 | 16 | no | — |
| 194 | C2×Dic71 | — | 2 | 4 | no | — |
| 195 | C2×Dic71 | — | 2 | 8 | no | — |
| 196 | C2×Dic71 | — | 2 | 16 | no | — |
| 197 | C2×Dic71 | C25 | 1 | 8 | yes | — |
| 198 | C2×Dic71 | C25 | 1 | 16 | yes | — |
| 199 | C2×Dic71 | C25 | 1 | 4 | yes | — |
| 200 | D284 | — | 2 | 8 | no | — |
| 201 | C4×D71 | — | 2 | 16 | no | — |
| 202 | C4×D71 | — | 2 | 32 | no | — |
| 203 | Dic142 | — | 2 | 8 | no | — |
| 204 | Dic142 | — | 2 | 32 | no | — |
| 205 | C22×C71 | — | 2 | 4 | no | — |
| 206 | C22×C71 | — | 2 | 8 | no | — |
| 207 | C22×C71 | C22×#41 | 1 | 4 | yes | — |
| 208 | C22×C71 | C22×#41 | 1 | 2 | yes | — |
| 209 | C22×C71 | C2×2−1+4 | 1 | 4 | yes | — |
| 210 | C22×C71 | C26 | 1 | 1 | yes | characteristic |
| 211 | C2×D71 | — | 2 | 4 | no | — |
| 212 | C2×D71 | — | 2 | 8 | no | — |
| 213 | C2×D71 | — | 4 | 8 | no | — |
| 214 | C4×C71 | — | 2 | 16 | no | — |
| 215 | C4×C71 | — | 2 | 4 | no | — |
| 216 | C4×C71 | C22×#41 | 1 | 4 | yes | — |
| 217 | C4×C71 | C22×#41 | 1 | 4 | yes | — |
| 218 | C4×C71 | C2×2−1+4 | 1 | 8 | yes | — |
| 219 | Dic71 | — | 2 | 4 | no | — |
| 220 | Dic71 | — | 2 | 16 | no | — |
| 221 | Dic71 | — | 2 | 8 | no | — |
| 222 | C2×#3509 | — | 71 | 1 | no | maximal, Sylow |
| 223 | C2×C71 | — | 2 | 4 | no | — |
| 224 | C2×C71 | #3509 | 1 | 4 | yes | complemented |
| 225 | C2×C71 | C23×#41 | 1 | 1 | yes | characteristic |
| 226 | C2×C71 | C22×2−1+4 | 1 | 2 | yes | — |
| 227 | D71 | — | 4 | 4 | no | — |
| 228 | #3509 | — | 71 | 32 | no | — |
| 229 | C2×#557 | — | 71 | 4 | no | — |
| 230 | C2×#556 | — | 71 | 4 | no | — |
| 231 | C2×#552 | — | 71 | 8 | no | — |
| 232 | C2×#541 | — | 71 | 4 | no | — |
| 233 | C2×#536 | — | 71 | 2 | no | — |
| 234 | C2×#533 | — | 71 | 1 | no | — |
| 235 | C2×#533 | — | 71 | 4 | no | — |
| 236 | C22×C4⋊Q8 | D71 | 1 | 1 | yes | characteristic, complemented |
| 237 | C2×#519 | — | 71 | 2 | no | — |
| 238 | C2×C4×#41 | — | 71 | 1 | no | — |
| 239 | C71 | C2×#3509 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 240 | C22×#41 | — | 71 | 1 | no | — |
| 241 | C23×Q8 | C2×D71 | 1 | 2 | yes | — |
| 242 | #557 | — | 71 | 64 | no | — |
| 243 | #556 | — | 71 | 64 | no | — |
| 244 | #552 | — | 71 | 128 | no | — |
| 245 | #541 | — | 71 | 64 | no | — |
| 246 | #536 | — | 71 | 32 | no | — |
| 247 | #533 | — | 71 | 64 | no | — |
| 248 | #533 | — | 71 | 16 | no | — |
| 249 | C2×C4⋊Q8 | — | 71 | 4 | no | — |
| 250 | C2×C4⋊Q8 | — | 71 | 2 | no | — |
| 251 | C2×C4⋊Q8 | C2×D71 | 1 | 2 | yes | — |
| 252 | C2×C4⋊Q8 | C2×D71 | 1 | 2 | yes | — |
| 253 | C2×C4⋊Q8 | C2×D71 | 1 | 4 | yes | — |
| 254 | C2×C4⋊Q8 | C2×D71 | 1 | 16 | yes | complemented |
| 255 | C2×#126 | — | 71 | 16 | no | — |
| 256 | C2×#125 | — | 71 | 8 | no | — |
| 257 | C2×#125 | — | 71 | 16 | no | — |
| 258 | C2×#125 | — | 71 | 2 | no | — |
| 259 | C2×#124 | — | 71 | 4 | no | — |
| 260 | C2×#123 | — | 71 | 8 | no | — |
| 261 | C2×C22⋊Q8 | — | 71 | 8 | no | — |
| 262 | C2×C22⋊Q8 | — | 71 | 4 | no | — |
| 263 | C2×C22⋊Q8 | — | 71 | 8 | no | — |
| 264 | #519 | — | 71 | 32 | no | — |
| 265 | C4×#41 | — | 71 | 16 | no | — |
| 266 | C2×C4×Q8 | — | 71 | 8 | no | — |
| 267 | C2×C4×Q8 | — | 71 | 8 | no | — |
| 268 | C2×C4×Q8 | — | 71 | 8 | no | — |
| 269 | C2×C4×Q8 | — | 71 | 2 | no | — |
| 270 | C2×C4×Q8 | — | 71 | 4 | no | — |
| 271 | C2×C4×D4 | — | 71 | 4 | no | — |
| 272 | C2×C4×D4 | — | 71 | 2 | no | — |
| 273 | C2×#117 | — | 71 | 1 | no | — |
| 274 | C2×#117 | — | 71 | 2 | no | — |
| 275 | C2×#117 | — | 71 | 8 | no | — |
| 276 | C2×#117 | — | 71 | 8 | no | — |
| 277 | C2×#117 | — | 71 | 2 | no | — |
| 278 | C22×C4⋊C4 | C2×D71 | 1 | 4 | yes | — |
| 279 | C22×C42 | — | 71 | 2 | no | — |
| 280 | C22×C42 | C2×D71 | 1 | 1 | yes | characteristic |
| 281 | C2×#41 | — | 71 | 8 | no | — |
| 282 | C2×#41 | — | 142 | 8 | no | — |
| 283 | C22×Q8 | — | 2 | 16 | no | — |
| 284 | C22×Q8 | — | 71 | 4 | no | — |
| 285 | C22×Q8 | — | 71 | 1 | no | — |
| 286 | C22×Q8 | C22×D71 | 1 | 4 | yes | — |
| 287 | C22×Q8 | C22×D71 | 1 | 4 | yes | — |
| 288 | C22×Q8 | C22×D71 | 1 | 16 | yes | — |
| 289 | C22×D4 | — | 71 | 2 | no | — |
| 290 | C22×D4 | — | 71 | 1 | no | — |
| 291 | C23×C4 | — | 71 | 4 | no | — |
| 292 | C23×C4 | — | 71 | 2 | no | — |
| 293 | C23×C4 | C22×D71 | 1 | 4 | yes | — |
| 294 | C23×C4 | C22×D71 | 1 | 2 | yes | — |
| 295 | C23×C4 | C22×D71 | 1 | 1 | yes | characteristic |
| 296 | C4⋊Q8 | — | 71 | 32 | no | — |
| 297 | C4⋊Q8 | — | 71 | 16 | no | — |
| 298 | C4⋊Q8 | C22×D71 | 1 | 16 | yes | — |
| 299 | C4⋊Q8 | C22×D71 | 1 | 16 | yes | — |
| 300 | C4⋊Q8 | C22×D71 | 1 | 32 | yes | — |
| 301 | #126 | — | 71 | 128 | no | — |
| 302 | #125 | — | 71 | 64 | no | — |
| 303 | #125 | — | 71 | 128 | no | — |
| 304 | #125 | — | 71 | 16 | no | — |
| 305 | #124 | — | 71 | 32 | no | — |
| 306 | #123 | — | 71 | 64 | no | — |
| 307 | C22⋊Q8 | — | 71 | 64 | no | — |
| 308 | C22⋊Q8 | — | 71 | 32 | no | — |
| 309 | C22⋊Q8 | — | 71 | 64 | no | — |
| 310 | C4×Q8 | — | 71 | 64 | no | — |
| 311 | C4×Q8 | — | 71 | 64 | no | — |
| 312 | C4×Q8 | — | 71 | 64 | no | — |
| 313 | C4×Q8 | — | 71 | 16 | no | — |
| 314 | C4×Q8 | — | 71 | 32 | no | — |
| 315 | C4×D4 | — | 71 | 32 | no | — |
| 316 | C4×D4 | — | 71 | 16 | no | — |
| 317 | #117 | — | 71 | 8 | no | — |
| 318 | #117 | — | 71 | 16 | no | — |
| 319 | #117 | — | 71 | 64 | no | — |
| 320 | #117 | — | 71 | 64 | no | — |
| 321 | #117 | — | 71 | 16 | no | — |
| 322 | C2×C4⋊C4 | — | 71 | 4 | no | — |
| 323 | C2×C4⋊C4 | — | 71 | 2 | no | — |
| 324 | C2×C4⋊C4 | — | 71 | 4 | no | — |
| 325 | C2×C4⋊C4 | — | 71 | 4 | no | — |
| 326 | C2×C4⋊C4 | — | 71 | 16 | no | — |
| 327 | C2×C4⋊C4 | — | 71 | 16 | no | — |
| 328 | C2×C4⋊C4 | — | 71 | 8 | no | — |
| 329 | C2×C4⋊C4 | C22×D71 | 1 | 8 | yes | — |
| 330 | C2×C4⋊C4 | C22×D71 | 1 | 8 | yes | — |
| 331 | C2×C4⋊C4 | C22×D71 | 1 | 32 | yes | — |
| 332 | C2×C22⋊C4 | — | 71 | 2 | no | — |
| 333 | C2×C22⋊C4 | — | 71 | 4 | no | — |
| 334 | C2×C22⋊C4 | — | 71 | 4 | no | — |
| 335 | C2×C22⋊C4 | — | 71 | 16 | no | — |
| 336 | C2×C42 | — | 71 | 2 | no | — |
| 337 | C2×C42 | — | 71 | 16 | no | — |
| 338 | C2×C42 | — | 71 | 4 | no | — |
| 339 | C2×C42 | — | 71 | 4 | no | — |
| 340 | C2×C42 | — | 71 | 16 | no | — |
| 341 | C2×C42 | C22×D71 | 1 | 1 | yes | characteristic |
| 342 | C2×C42 | C22×D71 | 1 | 2 | yes | — |
| 343 | C2×C42 | C22×D71 | 1 | 8 | yes | — |
| 344 | C2×C42 | C22×D71 | 1 | 1 | yes | characteristic |
| 345 | C24 | — | 71 | 2 | no | — |
| 346 | C24 | C23×D71 | 1 | 1 | yes | characteristic |
| 347 | #41 | — | 142 | 32 | no | — |
| 348 | C2×Q8 | — | 2 | 16 | no | — |
| 349 | C2×Q8 | — | 2 | 16 | no | — |
| 350 | C2×Q8 | — | 2 | 64 | no | — |
| 351 | C2×Q8 | — | 71 | 16 | no | — |
| 352 | C2×Q8 | — | 71 | 4 | no | — |
| 353 | C2×Q8 | — | 142 | 4 | no | — |
| 354 | C2×Q8 | — | 142 | 16 | no | — |
| 355 | C2×Q8 | C23×D71 | 1 | 16 | yes | — |
| 356 | C2×Q8 | C23×D71 | 1 | 16 | yes | — |
| 357 | C2×D4 | — | 71 | 8 | no | — |
| 358 | C2×D4 | — | 71 | 4 | no | — |
| 359 | C2×D4 | — | 142 | 8 | no | — |
| 360 | C2×D4 | — | 142 | 4 | no | — |
| 361 | C22×C4 | — | 2 | 16 | no | — |
| 362 | C22×C4 | — | 2 | 8 | no | — |
| 363 | C22×C4 | — | 71 | 4 | no | — |
| 364 | C22×C4 | — | 71 | 8 | no | — |
| 365 | C22×C4 | — | 71 | 2 | no | — |
| 366 | C22×C4 | — | 71 | 16 | no | — |
| 367 | C22×C4 | — | 71 | 8 | no | — |
| 368 | C22×C4 | — | 142 | 8 | no | — |
| 369 | C22×C4 | — | 142 | 16 | no | — |
| 370 | C22×C4 | #11765864 | 1 | 8 | yes | — |
| 371 | C22×C4 | C23×D71 | 1 | 8 | yes | — |
| 372 | C22×C4 | C23×D71 | 1 | 16 | yes | — |
| 373 | C22×C4 | C23×D71 | 1 | 8 | yes | — |
| 374 | C22×C4 | C23×D71 | 1 | 2 | yes | — |
| 375 | C22×C4 | C23×D71 | 1 | 4 | yes | — |
| 376 | C22×C4 | C23×D71 | 1 | 1 | yes | characteristic |
| 377 | C22×C4 | C23×D71 | 1 | 1 | yes | characteristic |
| 378 | C22×C4 | C23×D71 | 1 | 2 | yes | — |
| 379 | C4⋊C4 | — | 71 | 16 | no | — |
| 380 | C4⋊C4 | — | 71 | 64 | no | — |
| 381 | C4⋊C4 | — | 71 | 32 | no | — |
| 382 | C4⋊C4 | — | 71 | 16 | no | — |
| 383 | C4⋊C4 | — | 71 | 8 | no | — |
| 384 | C4⋊C4 | — | 71 | 16 | no | — |
| 385 | C4⋊C4 | — | 71 | 64 | no | — |
| 386 | C4⋊C4 | C23×D71 | 1 | 32 | yes | — |
| 387 | C4⋊C4 | C23×D71 | 1 | 32 | yes | — |
| 388 | C22⋊C4 | — | 71 | 8 | no | — |
| 389 | C22⋊C4 | — | 71 | 16 | no | — |
| 390 | C22⋊C4 | — | 71 | 16 | no | — |
| 391 | C22⋊C4 | — | 71 | 64 | no | — |
| 392 | C42 | — | 71 | 8 | no | — |
| 393 | C42 | — | 71 | 16 | no | — |
| 394 | C42 | — | 71 | 64 | no | — |
| 395 | C42 | — | 71 | 16 | no | — |
| 396 | C42 | C23×D71 | 1 | 4 | yes | — |
| 397 | C42 | C23×D71 | 1 | 4 | yes | — |
| 398 | C42 | C23×D71 | 1 | 8 | yes | — |
| 399 | C23 | — | 2 | 4 | no | — |
| 400 | C23 | — | 71 | 4 | no | — |
| 401 | C23 | — | 142 | 4 | no | — |
| 402 | C23 | — | 142 | 8 | no | — |
| 403 | C23 | C2×#11765864 | 1 | 4 | yes | — |
| 404 | C23 | C24×D71 | 1 | 2 | yes | — |
| 405 | C23 | C24×D71 | 1 | 1 | yes | characteristic |
| 406 | Q8 | — | 2 | 32 | no | — |
| 407 | Q8 | — | 2 | 32 | no | — |
| 408 | Q8 | — | 142 | 8 | no | — |
| 409 | Q8 | — | 142 | 32 | no | — |
| 410 | D4 | — | 142 | 16 | no | — |
| 411 | D4 | — | 142 | 8 | no | — |
| 412 | C2×C4 | — | 2 | 32 | no | — |
| 413 | C2×C4 | — | 2 | 16 | no | — |
| 414 | C2×C4 | — | 2 | 4 | no | — |
| 415 | C2×C4 | — | 2 | 16 | no | — |
| 416 | C2×C4 | — | 71 | 8 | no | — |
| 417 | C2×C4 | — | 71 | 16 | no | — |
| 418 | C2×C4 | — | 71 | 4 | no | — |
| 419 | C2×C4 | — | 142 | 4 | no | — |
| 420 | C2×C4 | — | 142 | 8 | no | — |
| 421 | C2×C4 | — | 142 | 16 | no | — |
| 422 | C2×C4 | — | 142 | 16 | no | — |
| 423 | C2×C4 | — | 142 | 32 | no | — |
| 424 | C2×C4 | C2×#11765864 | 1 | 4 | yes | — |
| 425 | C2×C4 | C2×#11765864 | 1 | 4 | yes | — |
| 426 | C2×C4 | C2×#11765864 | 1 | 16 | yes | — |
| 427 | C2×C4 | #14556176 | 1 | 8 | yes | — |
| 428 | C2×C4 | C24×D71 | 1 | 16 | yes | — |
| 429 | C2×C4 | C24×D71 | 1 | 4 | yes | — |
| 430 | C2×C4 | C24×D71 | 1 | 2 | yes | — |
| 431 | C2×C4 | C24×D71 | 1 | 2 | yes | — |
| 432 | C2×C4 | C24×D71 | 1 | 4 | yes | — |
| 433 | C22 | — | 2 | 4 | no | — |
| 434 | C22 | — | 2 | 8 | no | — |
| 435 | C22 | — | 284 | 8 | no | — |
| 436 | C22 | — | 142 | 4 | no | — |
| 437 | C22 | — | 142 | 8 | no | — |
| 438 | C22 | C22×#11765864 | 1 | 4 | yes | — |
| 439 | C22 | C22×#11765864 | 1 | 2 | yes | — |
| 440 | C22 | C2×#14556176 | 1 | 4 | yes | — |
| 441 | C22 | C25×D71 | 1 | 1 | yes | characteristic |
| 442 | C4 | — | 2 | 16 | no | — |
| 443 | C4 | — | 2 | 4 | no | — |
| 444 | C4 | — | 142 | 4 | no | — |
| 445 | C4 | — | 142 | 8 | no | — |
| 446 | C4 | — | 142 | 16 | no | — |
| 447 | C4 | C22×#11765864 | 1 | 4 | yes | — |
| 448 | C4 | C22×#11765864 | 1 | 4 | yes | — |
| 449 | C4 | C2×#14556176 | 1 | 8 | yes | — |
| 450 | C2 | — | 2 | 4 | no | — |
| 451 | C2 | — | 284 | 4 | no | — |
| 452 | C2 | #22602224 | 1 | 4 | yes | direct product factor |
| 453 | C2 | C23×#11765864 | 1 | 1 | yes | characteristic |
| 454 | C2 | C22×#14556176 | 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