← #32150315
Subgroups — #32150315
Order 18176.
1176 conjugacy classes of subgroups.
The subgroup lattice has 662 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #22602122 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #22596820 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #22590033 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #22590029 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #22590026 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #22590022 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | C2×#17985797 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #356×D71 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | C71×#2133 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | C2×#14556176 | C22 | 1 | 1 | yes | characteristic |
| 11 | C2×#14556175 | C4 | 1 | 1 | yes | characteristic |
| 12 | #17986765 | — | 2 | 2 | no | — |
| 13 | #17986662 | — | 2 | 2 | no | — |
| 14 | #17986651 | — | 2 | 2 | no | — |
| 15 | #17986647 | — | 2 | 2 | no | — |
| 16 | #17986647 | — | 2 | 2 | no | — |
| 17 | #17986575 | C4 | 1 | 1 | yes | characteristic |
| 18 | #17986574 | C4 | 1 | 1 | yes | characteristic |
| 19 | #17986574 | C22 | 1 | 1 | yes | characteristic |
| 20 | #17986569 | C4 | 1 | 1 | yes | characteristic |
| 21 | #17986569 | C22 | 1 | 1 | yes | characteristic |
| 22 | #17986548 | C4 | 1 | 1 | yes | characteristic |
| 23 | #17986548 | C22 | 1 | 1 | yes | characteristic |
| 24 | #17986545 | C4 | 1 | 1 | yes | characteristic |
| 25 | C2×#14556126 | C22 | 1 | 1 | yes | characteristic |
| 26 | C4⋊Q8×D71 | C4 | 1 | 1 | yes | characteristic |
| 27 | C4⋊Q8×D71 | C22 | 1 | 1 | yes | characteristic |
| 28 | #17986467 | C4 | 1 | 1 | yes | characteristic |
| 29 | #17985982 | — | 2 | 2 | no | — |
| 30 | #17985982 | C22 | 1 | 4 | yes | — |
| 31 | #17985981 | — | 2 | 2 | no | — |
| 32 | C2×#14556047 | C22 | 1 | 2 | yes | — |
| 33 | #101×D71 | — | 2 | 2 | no | — |
| 34 | #101×D71 | C22 | 1 | 4 | yes | — |
| 35 | #17985798 | C22 | 1 | 2 | yes | — |
| 36 | #17985797 | C22 | 1 | 4 | yes | — |
| 37 | #17985797 | C22 | 1 | 4 | yes | — |
| 38 | #17985796 | C22 | 1 | 2 | yes | — |
| 39 | #536×C71 | C22 | 1 | 1 | yes | characteristic |
| 40 | C2×#101×C71 | C22 | 1 | 2 | yes | — |
| 41 | #356×C71 | C22 | 1 | 2 | yes | — |
| 42 | #355×C71 | C22 | 1 | 2 | yes | — |
| 43 | #14556176 | — | 4 | 4 | no | — |
| 44 | #14556175 | — | 4 | 4 | no | — |
| 45 | C2×#11765866 | C2×C4 | 1 | 1 | yes | characteristic |
| 46 | C2×#11765866 | D4 | 1 | 2 | yes | — |
| 47 | C2×#11765866 | C23 | 1 | 1 | yes | characteristic |
| 48 | C2×#11765865 | — | 2 | 1 | no | — |
| 49 | C2×#11765865 | C2×C4 | 1 | 1 | yes | characteristic |
| 50 | C2×#11765865 | C2×C4 | 1 | 1 | yes | characteristic |
| 51 | C2×#11765865 | D4 | 1 | 2 | yes | — |
| 52 | C2×#11765865 | D4 | 1 | 2 | yes | — |
| 53 | C2×#11765864 | — | 2 | 1 | no | — |
| 54 | C2×#11765864 | — | 2 | 1 | no | — |
| 55 | C2×#11765864 | C2×C4 | 1 | 1 | yes | characteristic |
| 56 | C2×#11765864 | C2×C4 | 1 | 1 | yes | characteristic |
| 57 | C22×Dic142 | — | 2 | 1 | no | — |
| 58 | C22×Dic142 | C2×C4 | 1 | 1 | yes | characteristic |
| 59 | C2×Q8×D71 | C2×C4 | 1 | 1 | yes | characteristic |
| 60 | C2×Q8×D71 | C2×C4 | 1 | 1 | yes | characteristic |
| 61 | C2×Q8×D71 | C2×C4 | 1 | 1 | yes | characteristic |
| 62 | C2×Q8×D71 | D4 | 1 | 2 | yes | — |
| 63 | C2×Q8×D71 | C23 | 1 | 1 | yes | characteristic |
| 64 | #14556136 | — | 4 | 4 | no | — |
| 65 | #14556134 | — | 4 | 4 | no | — |
| 66 | C2×#11765849 | — | 2 | 2 | no | — |
| 67 | M16×D71 | — | 2 | 4 | no | — |
| 68 | M16×D71 | — | 2 | 4 | no | — |
| 69 | #14556128 | C2×C4 | 1 | 1 | yes | characteristic |
| 70 | #14556128 | C2×C4 | 1 | 1 | yes | characteristic |
| 71 | #14556127 | — | 2 | 2 | no | — |
| 72 | #14556127 | — | 2 | 2 | no | — |
| 73 | #14556126 | — | 2 | 2 | no | — |
| 74 | #14556126 | C2×C4 | 1 | 1 | yes | characteristic |
| 75 | #14556126 | C2×C4 | 1 | 1 | yes | characteristic |
| 76 | #14556126 | C2×C4 | 1 | 1 | yes | characteristic |
| 77 | #14556126 | C23 | 1 | 1 | yes | characteristic |
| 78 | #14556126 | C23 | 1 | 1 | yes | characteristic |
| 79 | #14556124 | C2×C4 | 1 | 1 | yes | characteristic |
| 80 | #14556117 | C2×C4 | 1 | 1 | yes | characteristic |
| 81 | #14556116 | C2×C4 | 1 | 1 | yes | characteristic |
| 82 | #14556116 | C2×C4 | 1 | 1 | yes | characteristic |
| 83 | #14556115 | C2×C4 | 1 | 1 | yes | characteristic |
| 84 | #14556113 | — | 2 | 2 | no | — |
| 85 | #14556113 | — | 2 | 2 | no | — |
| 86 | #14556112 | — | 2 | 2 | no | — |
| 87 | #14556110 | — | 2 | 2 | no | — |
| 88 | #14556110 | — | 2 | 2 | no | — |
| 89 | #14556108 | — | 2 | 2 | no | — |
| 90 | #14556106 | — | 2 | 2 | no | — |
| 91 | #14556106 | — | 2 | 2 | no | — |
| 92 | #14556105 | — | 2 | 2 | no | — |
| 93 | #14556105 | — | 2 | 2 | no | — |
| 94 | #14556101 | — | 2 | 2 | no | — |
| 95 | #14556101 | — | 2 | 2 | no | — |
| 96 | #14556100 | — | 2 | 2 | no | — |
| 97 | #14556093 | — | 2 | 1 | no | — |
| 98 | #14556090 | — | 2 | 1 | no | — |
| 99 | C4×C22⋊D71 | — | 2 | 2 | no | — |
| 100 | (C22⋊D71)⋊C4 | — | 2 | 1 | no | — |
| 101 | (C22⋊D71)⋊C4 | — | 2 | 1 | no | — |
| 102 | (C22⋊D71)⋊C4 | — | 2 | 2 | no | — |
| 103 | (C22⋊D71)⋊C4 | — | 2 | 2 | no | — |
| 104 | #14556085 | C2×C4 | 1 | 1 | yes | characteristic |
| 105 | #14556085 | C2×C4 | 1 | 1 | yes | characteristic |
| 106 | C2×Dic71⋊C4 | — | 2 | 2 | no | — |
| 107 | C4⋊C4×D71 | — | 2 | 2 | no | — |
| 108 | C4⋊C4×D71 | — | 2 | 2 | no | — |
| 109 | C2×C4×Dic71 | C2×C4 | 1 | 1 | yes | characteristic |
| 110 | C42×D71 | C2×C4 | 1 | 1 | yes | characteristic |
| 111 | C42×D71 | C2×C4 | 1 | 1 | yes | characteristic |
| 112 | #14556047 | — | 2 | 2 | no | — |
| 113 | #14556047 | C23 | 1 | 4 | yes | — |
| 114 | #14556046 | — | 2 | 4 | no | — |
| 115 | #14556044 | — | 2 | 4 | no | — |
| 116 | C2×#41×C71 | C2×C4 | 1 | 1 | yes | characteristic |
| 117 | C22×Q8×C71 | C23 | 1 | 1 | yes | characteristic |
| 118 | C2×M16×C71 | — | 2 | 2 | no | — |
| 119 | C4⋊Q8×C71 | C2×C4 | 1 | 1 | yes | characteristic |
| 120 | C4⋊Q8×C71 | C23 | 1 | 1 | yes | characteristic |
| 121 | #124×C71 | C2×C4 | 1 | 1 | yes | characteristic |
| 122 | #124×C71 | C23 | 1 | 1 | yes | characteristic |
| 123 | #123×C71 | — | 2 | 2 | no | — |
| 124 | C22⋊Q8×C71 | — | 2 | 2 | no | — |
| 125 | #117×C71 | C2×C4 | 1 | 1 | yes | characteristic |
| 126 | #101×C71 | — | 2 | 2 | no | — |
| 127 | #101×C71 | C23 | 1 | 4 | yes | — |
| 128 | #11765866 | — | 4 | 2 | no | — |
| 129 | #11765866 | — | 4 | 2 | no | — |
| 130 | #11765866 | — | 4 | 4 | no | — |
| 131 | #11765865 | — | 2 | 4 | no | — |
| 132 | #11765865 | — | 2 | 4 | no | — |
| 133 | #11765865 | — | 2 | 4 | no | — |
| 134 | #11765865 | — | 4 | 4 | no | — |
| 135 | #11765865 | — | 4 | 2 | no | — |
| 136 | #11765865 | — | 4 | 2 | no | — |
| 137 | #11765865 | — | 4 | 2 | no | — |
| 138 | #11765864 | — | 4 | 2 | no | — |
| 139 | #11765864 | — | 4 | 2 | no | — |
| 140 | #11765864 | — | 4 | 4 | no | — |
| 141 | #11765864 | — | 4 | 4 | no | — |
| 142 | C2×Dic142 | — | 2 | 1 | no | — |
| 143 | C2×Dic142 | — | 2 | 1 | no | — |
| 144 | C2×Dic142 | — | 2 | 1 | no | — |
| 145 | C2×Dic142 | — | 4 | 4 | no | — |
| 146 | C2×Dic142 | — | 4 | 2 | no | — |
| 147 | C2×Dic142 | C22⋊C4 | 1 | 2 | yes | — |
| 148 | C2×Dic142 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 149 | C2×Dic142 | C22×C4 | 1 | 1 | yes | characteristic |
| 150 | C2×Dic142 | C22×C4 | 1 | 1 | yes | characteristic |
| 151 | C2×Dic142 | C22×C4 | 1 | 1 | yes | characteristic |
| 152 | C2×Dic142 | C2×D4 | 1 | 2 | yes | — |
| 153 | Q8×D71 | — | 4 | 2 | no | — |
| 154 | Q8×D71 | — | 4 | 4 | no | — |
| 155 | Q8×D71 | — | 4 | 2 | no | — |
| 156 | Q8×D71 | — | 4 | 2 | no | — |
| 157 | Q8×D71 | — | 4 | 2 | no | — |
| 158 | C2×D284 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 159 | C2×D284 | C22⋊C4 | 1 | 2 | yes | — |
| 160 | C2×D284 | C22×C4 | 1 | 1 | yes | characteristic |
| 161 | C2×D284 | C2×D4 | 1 | 2 | yes | — |
| 162 | C2×C22⋊D71 | — | 2 | 1 | no | — |
| 163 | C2×C22⋊D71 | — | 2 | 1 | no | — |
| 164 | C2×C22⋊D71 | — | 2 | 2 | no | — |
| 165 | C2×C22⋊D71 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 166 | C2×C22⋊D71 | C22⋊C4 | 1 | 2 | yes | — |
| 167 | C2×C22⋊D71 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 168 | C22×Dic71 | — | 2 | 1 | no | — |
| 169 | C22×Dic71 | — | 2 | 1 | no | — |
| 170 | C22×Dic71 | — | 2 | 1 | no | — |
| 171 | C22×Dic71 | — | 2 | 1 | no | — |
| 172 | C2×C4×D71 | — | 2 | 1 | no | — |
| 173 | C2×C4×D71 | — | 2 | 1 | no | — |
| 174 | C2×C4×D71 | — | 2 | 1 | no | — |
| 175 | C2×C4×D71 | — | 2 | 1 | no | — |
| 176 | C2×C4×D71 | C22⋊C4 | 1 | 2 | yes | — |
| 177 | C2×C4×D71 | C22⋊C4 | 1 | 2 | yes | — |
| 178 | C2×C4×D71 | C22⋊C4 | 1 | 2 | yes | — |
| 179 | C2×C4×D71 | C22×C4 | 1 | 1 | yes | characteristic |
| 180 | C2×C4×D71 | C22×C4 | 1 | 1 | yes | characteristic |
| 181 | C2×C4×D71 | C2×D4 | 1 | 2 | yes | — |
| 182 | C2×C4×D71 | C2×D4 | 1 | 2 | yes | — |
| 183 | #11765849 | — | 2 | 4 | no | — |
| 184 | #11765849 | — | 4 | 2 | no | — |
| 185 | #11765848 | — | 4 | 4 | no | — |
| 186 | #11765848 | — | 4 | 4 | no | — |
| 187 | C2×C71⋊C8 | — | 4 | 2 | no | — |
| 188 | C8×D71 | — | 4 | 4 | no | — |
| 189 | C8×D71 | — | 4 | 4 | no | — |
| 190 | C4⋊Dic71 | — | 2 | 2 | no | — |
| 191 | C4⋊Dic71 | — | 2 | 2 | no | — |
| 192 | Dic71⋊C4 | — | 2 | 2 | no | — |
| 193 | Dic71⋊C4 | — | 2 | 2 | no | — |
| 194 | Dic71⋊C4 | — | 2 | 2 | no | — |
| 195 | Dic71⋊C4 | — | 2 | 2 | no | — |
| 196 | Dic71⋊C4 | — | 2 | 2 | no | — |
| 197 | Dic71⋊C4 | — | 2 | 1 | no | — |
| 198 | Dic71⋊C4 | — | 2 | 1 | no | — |
| 199 | C22⋊Dic71 | — | 2 | 2 | no | — |
| 200 | (C2×D71)⋊C4 | — | 2 | 1 | no | — |
| 201 | (C2×D71)⋊C4 | — | 2 | 1 | no | — |
| 202 | (C2×D71)⋊C4 | — | 2 | 2 | no | — |
| 203 | (C2×D71)⋊C4 | — | 2 | 2 | no | — |
| 204 | (C2×D71)⋊C4 | — | 2 | 2 | no | — |
| 205 | C4×Dic71 | — | 2 | 1 | no | — |
| 206 | C4×Dic71 | — | 2 | 1 | no | — |
| 207 | C4×Dic71 | — | 2 | 1 | no | — |
| 208 | C4×Dic71 | C22×C4 | 1 | 1 | yes | characteristic |
| 209 | C4×Dic71 | C22×C4 | 1 | 1 | yes | characteristic |
| 210 | #41×C71 | — | 4 | 2 | no | — |
| 211 | C2×Q8×C71 | — | 4 | 2 | no | — |
| 212 | C2×Q8×C71 | C22×C4 | 1 | 1 | yes | characteristic |
| 213 | C2×Q8×C71 | C22×C4 | 1 | 1 | yes | characteristic |
| 214 | C2×Q8×C71 | C2×D4 | 1 | 2 | yes | — |
| 215 | C2×Q8×C71 | C24 | 1 | 1 | yes | characteristic |
| 216 | C2×D4×C71 | — | 2 | 1 | no | — |
| 217 | C2×D4×C71 | C22×C4 | 1 | 1 | yes | characteristic |
| 218 | C22×C4×C71 | — | 2 | 1 | no | — |
| 219 | C22×C4×C71 | C22×C4 | 1 | 1 | yes | characteristic |
| 220 | C22×C4×C71 | C2×D4 | 1 | 2 | yes | — |
| 221 | M16×C71 | — | 2 | 4 | no | — |
| 222 | M16×C71 | — | 4 | 2 | no | — |
| 223 | C2×C8×C71 | — | 4 | 2 | no | — |
| 224 | C4⋊C4×C71 | — | 2 | 1 | no | — |
| 225 | C4⋊C4×C71 | — | 2 | 2 | no | — |
| 226 | C4⋊C4×C71 | — | 2 | 2 | no | — |
| 227 | C22⋊C4×C71 | — | 2 | 1 | no | — |
| 228 | C22⋊C4×C71 | — | 2 | 2 | no | — |
| 229 | C22⋊C4×C71 | — | 2 | 2 | no | — |
| 230 | C42×C71 | C22×C4 | 1 | 1 | yes | characteristic |
| 231 | C42×C71 | C22×C4 | 1 | 1 | yes | characteristic |
| 232 | C23×C71 | — | 2 | 1 | no | — |
| 233 | C23×C71 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 234 | C22×D71 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 235 | C22×D71 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 236 | C22×D71 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 237 | Q8×C71 | — | 4 | 1 | no | — |
| 238 | Q8×C71 | — | 4 | 2 | no | — |
| 239 | Q8×C71 | — | 4 | 1 | no | — |
| 240 | Q8×C71 | — | 4 | 1 | no | — |
| 241 | D4×C71 | — | 4 | 1 | no | — |
| 242 | D4×C71 | — | 4 | 2 | no | — |
| 243 | C2×C4×C71 | — | 2 | 2 | no | — |
| 244 | C2×C4×C71 | — | 2 | 2 | no | — |
| 245 | C2×C4×C71 | — | 2 | 2 | no | — |
| 246 | C2×C4×C71 | — | 2 | 1 | no | — |
| 247 | C2×C4×C71 | — | 2 | 1 | no | — |
| 248 | C2×C4×C71 | — | 2 | 1 | no | — |
| 249 | C2×C4×C71 | — | 4 | 2 | no | — |
| 250 | C2×C4×C71 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 251 | C2×C4×C71 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 252 | C2×C4×C71 | C23×C4 | 1 | 1 | yes | characteristic |
| 253 | C2×C4×C71 | C22×D4 | 1 | 2 | yes | — |
| 254 | C22⋊D71 | — | 2 | 2 | no | — |
| 255 | C22⋊D71 | — | 2 | 2 | no | — |
| 256 | C22⋊D71 | — | 2 | 2 | no | — |
| 257 | C22⋊D71 | — | 4 | 4 | no | — |
| 258 | C22⋊D71 | — | 4 | 2 | no | — |
| 259 | C22⋊D71 | — | 4 | 2 | no | — |
| 260 | C22⋊D71 | #99 | 1 | 4 | yes | — |
| 261 | C2×Dic71 | — | 2 | 1 | no | — |
| 262 | C2×Dic71 | — | 2 | 1 | no | — |
| 263 | C2×Dic71 | — | 2 | 1 | no | — |
| 264 | C2×Dic71 | — | 2 | 1 | no | — |
| 265 | C2×Dic71 | — | 4 | 2 | no | — |
| 266 | C2×Dic71 | — | 4 | 2 | no | — |
| 267 | C2×Dic71 | — | 4 | 2 | no | — |
| 268 | C2×Dic71 | — | 4 | 2 | no | — |
| 269 | C2×Dic71 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 270 | C2×Dic71 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 271 | C2×Dic71 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 272 | D284 | — | 2 | 2 | no | — |
| 273 | D284 | — | 2 | 4 | no | — |
| 274 | D284 | — | 4 | 1 | no | — |
| 275 | D284 | — | 4 | 2 | no | — |
| 276 | C4×D71 | — | 2 | 4 | no | — |
| 277 | C4×D71 | — | 2 | 2 | no | — |
| 278 | C4×D71 | — | 2 | 4 | no | — |
| 279 | C4×D71 | — | 2 | 2 | no | — |
| 280 | C4×D71 | — | 4 | 2 | no | — |
| 281 | C4×D71 | — | 4 | 2 | no | — |
| 282 | C4×D71 | — | 4 | 2 | no | — |
| 283 | C4×D71 | — | 4 | 2 | no | — |
| 284 | C4×D71 | — | 4 | 2 | no | — |
| 285 | C4×D71 | — | 4 | 2 | no | — |
| 286 | C4×D71 | — | 4 | 2 | no | — |
| 287 | Dic142 | — | 2 | 2 | no | — |
| 288 | Dic142 | — | 2 | 4 | no | — |
| 289 | Dic142 | — | 4 | 1 | no | — |
| 290 | Dic142 | — | 4 | 2 | no | — |
| 291 | Dic142 | — | 4 | 2 | no | — |
| 292 | Dic142 | — | 4 | 2 | no | — |
| 293 | Dic142 | — | 4 | 2 | no | — |
| 294 | Dic142 | — | 4 | 1 | no | — |
| 295 | Dic142 | — | 4 | 1 | no | — |
| 296 | C8×C71 | — | 4 | 4 | no | — |
| 297 | C71⋊C8 | — | 4 | 4 | no | — |
| 298 | C22×C71 | — | 4 | 1 | no | — |
| 299 | C22×C71 | — | 4 | 2 | no | — |
| 300 | C22×C71 | — | 4 | 1 | no | — |
| 301 | C22×C71 | C2×#99 | 1 | 2 | yes | — |
| 302 | C22×C71 | C22×C22⋊C4 | 1 | 1 | yes | characteristic |
| 303 | C2×D71 | — | 2 | 1 | no | — |
| 304 | C2×D71 | — | 2 | 2 | no | — |
| 305 | C2×D71 | — | 4 | 1 | no | — |
| 306 | C2×D71 | — | 4 | 1 | no | — |
| 307 | C2×D71 | — | 4 | 2 | no | — |
| 308 | C2×D71 | C2×#99 | 1 | 2 | yes | — |
| 309 | C4×C71 | — | 2 | 2 | no | — |
| 310 | C4×C71 | — | 2 | 1 | no | — |
| 311 | C4×C71 | — | 2 | 2 | no | — |
| 312 | C4×C71 | — | 2 | 1 | no | — |
| 313 | C4×C71 | — | 4 | 1 | no | — |
| 314 | C4×C71 | — | 4 | 1 | no | — |
| 315 | C4×C71 | — | 4 | 1 | no | — |
| 316 | Dic71 | — | 2 | 2 | no | — |
| 317 | Dic71 | — | 2 | 1 | no | — |
| 318 | Dic71 | — | 2 | 2 | no | — |
| 319 | Dic71 | — | 4 | 1 | no | — |
| 320 | Dic71 | — | 4 | 1 | no | — |
| 321 | Dic71 | — | 4 | 1 | no | — |
| 322 | Dic71 | C2×#99 | 1 | 2 | yes | — |
| 323 | #33372 | — | 71 | 1 | no | maximal, Sylow |
| 324 | C2×C71 | — | 2 | 1 | no | — |
| 325 | C2×C71 | — | 2 | 2 | no | — |
| 326 | C2×C71 | — | 8 | 1 | no | — |
| 327 | C2×C71 | C22×#99 | 1 | 1 | yes | characteristic |
| 328 | D71 | — | 2 | 2 | no | — |
| 329 | D71 | — | 4 | 1 | no | — |
| 330 | D71 | — | 4 | 2 | no | — |
| 331 | #3499 | — | 71 | 1 | no | — |
| 332 | #2889 | — | 71 | 2 | no | — |
| 333 | #2135 | — | 71 | 2 | no | — |
| 334 | #2133 | — | 71 | 2 | no | — |
| 335 | #2133 | — | 71 | 1 | no | — |
| 336 | #2133 | D71 | 1 | 1 | yes | characteristic, complemented |
| 337 | #2132 | — | 71 | 2 | no | — |
| 338 | C2×#356 | — | 71 | 2 | no | — |
| 339 | C2×#356 | — | 71 | 2 | no | — |
| 340 | C71 | #33372 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 341 | C2×2−1+4 | — | 71 | 1 | no | — |
| 342 | C2×2−1+4 | — | 71 | 1 | no | — |
| 343 | #568 | — | 142 | 2 | no | — |
| 344 | D4×Q8 | — | 142 | 2 | no | — |
| 345 | #547 | — | 142 | 2 | no | — |
| 346 | #547 | — | 142 | 2 | no | — |
| 347 | #547 | — | 142 | 2 | no | — |
| 348 | #536 | — | 71 | 1 | no | — |
| 349 | #536 | — | 71 | 1 | no | — |
| 350 | #536 | — | 71 | 1 | no | — |
| 351 | #536 | — | 71 | 1 | no | — |
| 352 | #536 | — | 71 | 1 | no | — |
| 353 | #536 | C2×D71 | 1 | 1 | yes | characteristic |
| 354 | #532 | — | 71 | 1 | no | — |
| 355 | #532 | — | 71 | 1 | no | — |
| 356 | #532 | — | 71 | 1 | no | — |
| 357 | C2×C4⋊Q8 | — | 71 | 1 | no | — |
| 358 | C2×C4⋊Q8 | — | 71 | 1 | no | — |
| 359 | C2×C4⋊Q8 | — | 71 | 1 | no | — |
| 360 | C4×#41 | — | 71 | 1 | no | — |
| 361 | #413 | — | 71 | 4 | no | — |
| 362 | #413 | — | 142 | 2 | no | — |
| 363 | #413 | — | 142 | 2 | no | — |
| 364 | C2×#101 | — | 71 | 2 | no | — |
| 365 | C2×#101 | — | 71 | 4 | no | — |
| 366 | C2×#101 | — | 142 | 2 | no | — |
| 367 | C2×#101 | C2×D71 | 1 | 2 | yes | — |
| 368 | #356 | — | 71 | 2 | no | — |
| 369 | #356 | — | 71 | 4 | no | — |
| 370 | #356 | — | 71 | 4 | no | — |
| 371 | #356 | C2×D71 | 1 | 2 | yes | — |
| 372 | #355 | — | 71 | 2 | no | — |
| 373 | #355 | C2×D71 | 1 | 2 | yes | — |
| 374 | 2−1+4 | — | 284 | 4 | no | — |
| 375 | 2−1+4 | — | 284 | 4 | no | — |
| 376 | C2×#41 | — | 71 | 1 | no | — |
| 377 | C2×#41 | — | 71 | 2 | no | — |
| 378 | C2×#41 | — | 71 | 1 | no | — |
| 379 | C2×#41 | — | 71 | 1 | no | — |
| 380 | C2×#41 | — | 71 | 1 | no | — |
| 381 | C2×#41 | — | 71 | 2 | no | — |
| 382 | C2×#41 | — | 71 | 2 | no | — |
| 383 | C2×#41 | — | 71 | 1 | no | — |
| 384 | C2×#41 | — | 71 | 1 | no | — |
| 385 | C2×#41 | — | 142 | 1 | no | — |
| 386 | C2×#41 | — | 142 | 1 | no | — |
| 387 | C2×#41 | — | 142 | 1 | no | — |
| 388 | C2×#41 | C4×D71 | 1 | 1 | yes | characteristic |
| 389 | C22×Q8 | — | 71 | 1 | no | — |
| 390 | C22×Q8 | — | 71 | 2 | no | — |
| 391 | C22×Q8 | — | 71 | 1 | no | — |
| 392 | C22×Q8 | — | 71 | 1 | no | — |
| 393 | C22×Q8 | — | 71 | 1 | no | — |
| 394 | C22×Q8 | — | 71 | 1 | no | — |
| 395 | C22×Q8 | — | 142 | 1 | no | — |
| 396 | C22×Q8 | C22×D71 | 1 | 1 | yes | characteristic |
| 397 | #131 | — | 284 | 4 | no | — |
| 398 | #131 | — | 284 | 4 | no | — |
| 399 | C2×M16 | — | 2 | 2 | no | — |
| 400 | C2×M16 | — | 142 | 4 | no | — |
| 401 | C2×M16 | — | 142 | 4 | no | — |
| 402 | C2×M16 | — | 142 | 2 | no | — |
| 403 | C4⋊Q8 | — | 71 | 1 | no | — |
| 404 | C4⋊Q8 | — | 71 | 1 | no | — |
| 405 | C4⋊Q8 | — | 71 | 1 | no | — |
| 406 | C4⋊Q8 | — | 71 | 1 | no | — |
| 407 | C4⋊Q8 | — | 71 | 1 | no | — |
| 408 | C4⋊Q8 | — | 71 | 1 | no | — |
| 409 | C4⋊Q8 | — | 71 | 1 | no | — |
| 410 | C4⋊Q8 | — | 142 | 2 | no | — |
| 411 | C4⋊Q8 | — | 142 | 2 | no | — |
| 412 | C4⋊Q8 | — | 142 | 2 | no | — |
| 413 | C4⋊Q8 | C4×D71 | 1 | 1 | yes | characteristic |
| 414 | C4⋊Q8 | C22×D71 | 1 | 1 | yes | characteristic |
| 415 | #127 | — | 71 | 1 | no | — |
| 416 | #124 | — | 71 | 1 | no | — |
| 417 | #124 | — | 71 | 1 | no | — |
| 418 | #124 | — | 71 | 1 | no | — |
| 419 | #124 | — | 71 | 1 | no | — |
| 420 | #124 | C4×D71 | 1 | 1 | yes | characteristic |
| 421 | #124 | C22×D71 | 1 | 1 | yes | characteristic |
| 422 | #123 | — | 2 | 2 | no | — |
| 423 | #123 | — | 142 | 2 | no | — |
| 424 | #123 | — | 142 | 2 | no | — |
| 425 | #123 | — | 142 | 2 | no | — |
| 426 | #123 | — | 142 | 2 | no | — |
| 427 | #123 | — | 142 | 2 | no | — |
| 428 | C22⋊Q8 | — | 2 | 2 | no | — |
| 429 | C22⋊Q8 | — | 142 | 2 | no | — |
| 430 | C22⋊Q8 | — | 142 | 2 | no | — |
| 431 | C22⋊Q8 | — | 142 | 2 | no | — |
| 432 | C22⋊Q8 | — | 142 | 2 | no | — |
| 433 | C22⋊Q8 | — | 142 | 2 | no | — |
| 434 | #121 | — | 142 | 2 | no | — |
| 435 | #121 | — | 142 | 2 | no | — |
| 436 | #121 | — | 142 | 2 | no | — |
| 437 | C4×Q8 | — | 142 | 1 | no | — |
| 438 | C4×D4 | — | 142 | 2 | no | — |
| 439 | C4×D4 | — | 142 | 2 | no | — |
| 440 | C4×D4 | — | 142 | 1 | no | — |
| 441 | C4×D4 | — | 142 | 1 | no | — |
| 442 | C4×D4 | — | 142 | 1 | no | — |
| 443 | C4×D4 | — | 142 | 2 | no | — |
| 444 | #117 | — | 71 | 1 | no | — |
| 445 | #117 | — | 71 | 1 | no | — |
| 446 | #117 | C4×D71 | 1 | 1 | yes | characteristic |
| 447 | C2×C4⋊C4 | — | 142 | 2 | no | — |
| 448 | C2×C4⋊C4 | — | 142 | 2 | no | — |
| 449 | C2×C4⋊C4 | — | 142 | 2 | no | — |
| 450 | C2×C42 | — | 71 | 1 | no | — |
| 451 | C2×C42 | — | 71 | 1 | no | — |
| 452 | C2×C42 | — | 71 | 1 | no | — |
| 453 | #101 | — | 2 | 2 | no | — |
| 454 | #101 | — | 71 | 4 | no | — |
| 455 | #101 | — | 142 | 4 | no | — |
| 456 | #101 | — | 142 | 2 | no | — |
| 457 | #101 | C22×D71 | 1 | 4 | yes | — |
| 458 | #100 | — | 142 | 4 | no | — |
| 459 | #41 | — | 4 | 2 | no | — |
| 460 | #41 | — | 284 | 2 | no | — |
| 461 | #41 | — | 284 | 2 | no | — |
| 462 | #41 | — | 284 | 2 | no | — |
| 463 | #41 | — | 284 | 4 | no | — |
| 464 | #41 | — | 284 | 4 | no | — |
| 465 | #41 | — | 284 | 4 | no | — |
| 466 | #41 | — | 284 | 2 | no | — |
| 467 | #41 | — | 284 | 4 | no | — |
| 468 | #41 | — | 284 | 2 | no | — |
| 469 | #41 | — | 284 | 2 | no | — |
| 470 | #41 | — | 284 | 2 | no | — |
| 471 | #41 | — | 142 | 4 | no | — |
| 472 | #41 | — | 142 | 4 | no | — |
| 473 | #41 | — | 142 | 4 | no | — |
| 474 | C2×Q8 | — | 4 | 2 | no | — |
| 475 | C2×Q8 | — | 284 | 2 | no | — |
| 476 | C2×Q8 | — | 284 | 4 | no | — |
| 477 | C2×Q8 | — | 284 | 2 | no | — |
| 478 | C2×Q8 | — | 284 | 4 | no | — |
| 479 | C2×Q8 | — | 284 | 2 | no | — |
| 480 | C2×Q8 | — | 284 | 2 | no | — |
| 481 | C2×Q8 | — | 284 | 2 | no | — |
| 482 | C2×Q8 | — | 71 | 1 | no | — |
| 483 | C2×Q8 | — | 71 | 2 | no | — |
| 484 | C2×Q8 | — | 71 | 1 | no | — |
| 485 | C2×Q8 | — | 71 | 2 | no | — |
| 486 | C2×Q8 | — | 71 | 1 | no | — |
| 487 | C2×Q8 | — | 71 | 1 | no | — |
| 488 | C2×Q8 | — | 142 | 1 | no | — |
| 489 | C2×Q8 | — | 142 | 1 | no | — |
| 490 | C2×Q8 | — | 142 | 1 | no | — |
| 491 | C2×Q8 | C2×C4×D71 | 1 | 1 | yes | characteristic |
| 492 | C2×Q8 | C2×C4×D71 | 1 | 1 | yes | characteristic |
| 493 | C2×Q8 | D4×D71 | 1 | 2 | yes | — |
| 494 | C2×Q8 | C23×D71 | 1 | 1 | yes | characteristic |
| 495 | C2×D4 | — | 2 | 1 | no | — |
| 496 | C2×D4 | — | 71 | 1 | no | — |
| 497 | C2×D4 | — | 71 | 1 | no | — |
| 498 | C2×D4 | — | 71 | 2 | no | — |
| 499 | C2×D4 | — | 71 | 1 | no | — |
| 500 | C2×D4 | — | 71 | 2 | no | — |
| 501 | C2×D4 | — | 71 | 1 | no | — |
| 502 | C2×D4 | — | 71 | 2 | no | — |
| 503 | C2×D4 | — | 142 | 2 | no | — |
| 504 | C2×D4 | — | 142 | 1 | no | — |
| 505 | C2×D4 | — | 142 | 1 | no | — |
| 506 | C2×D4 | C2×C4×D71 | 1 | 1 | yes | characteristic |
| 507 | C22×C4 | — | 2 | 1 | no | — |
| 508 | C22×C4 | — | 71 | 2 | no | — |
| 509 | C22×C4 | — | 71 | 2 | no | — |
| 510 | C22×C4 | — | 71 | 2 | no | — |
| 511 | C22×C4 | — | 71 | 1 | no | — |
| 512 | C22×C4 | — | 71 | 1 | no | — |
| 513 | C22×C4 | — | 71 | 2 | no | — |
| 514 | C22×C4 | — | 71 | 2 | no | — |
| 515 | C22×C4 | — | 142 | 1 | no | — |
| 516 | C22×C4 | — | 142 | 1 | no | — |
| 517 | C22×C4 | — | 142 | 1 | no | — |
| 518 | C22×C4 | — | 142 | 1 | no | — |
| 519 | C22×C4 | — | 142 | 1 | no | — |
| 520 | C22×C4 | — | 142 | 1 | no | — |
| 521 | C22×C4 | — | 142 | 1 | no | — |
| 522 | C22×C4 | — | 142 | 1 | no | — |
| 523 | C22×C4 | C2×C4×D71 | 1 | 1 | yes | characteristic |
| 524 | C22×C4 | D4×D71 | 1 | 2 | yes | — |
| 525 | M16 | — | 2 | 4 | no | — |
| 526 | M16 | — | 4 | 2 | no | — |
| 527 | M16 | — | 284 | 4 | no | — |
| 528 | M16 | — | 284 | 4 | no | — |
| 529 | M16 | — | 284 | 2 | no | — |
| 530 | M16 | — | 142 | 4 | no | — |
| 531 | C2×C8 | — | 4 | 2 | no | — |
| 532 | C2×C8 | — | 284 | 4 | no | — |
| 533 | C2×C8 | — | 284 | 4 | no | — |
| 534 | C2×C8 | — | 284 | 2 | no | — |
| 535 | C4⋊C4 | — | 2 | 2 | no | — |
| 536 | C4⋊C4 | — | 2 | 2 | no | — |
| 537 | C4⋊C4 | — | 2 | 1 | no | — |
| 538 | C4⋊C4 | — | 142 | 2 | no | — |
| 539 | C4⋊C4 | — | 142 | 1 | no | — |
| 540 | C4⋊C4 | — | 142 | 1 | no | — |
| 541 | C4⋊C4 | — | 142 | 2 | no | — |
| 542 | C4⋊C4 | — | 142 | 2 | no | — |
| 543 | C4⋊C4 | — | 142 | 2 | no | — |
| 544 | C4⋊C4 | — | 142 | 2 | no | — |
| 545 | C4⋊C4 | — | 142 | 2 | no | — |
| 546 | C4⋊C4 | — | 142 | 2 | no | — |
| 547 | C22⋊C4 | — | 2 | 1 | no | — |
| 548 | C22⋊C4 | — | 2 | 2 | no | — |
| 549 | C22⋊C4 | — | 2 | 2 | no | — |
| 550 | C22⋊C4 | — | 142 | 1 | no | — |
| 551 | C22⋊C4 | — | 142 | 1 | no | — |
| 552 | C22⋊C4 | — | 142 | 2 | no | — |
| 553 | C22⋊C4 | — | 142 | 2 | no | — |
| 554 | C22⋊C4 | — | 142 | 2 | no | — |
| 555 | C22⋊C4 | — | 142 | 2 | no | — |
| 556 | C42 | — | 71 | 1 | no | — |
| 557 | C42 | — | 71 | 1 | no | — |
| 558 | C42 | — | 142 | 1 | no | — |
| 559 | C42 | — | 142 | 1 | no | — |
| 560 | C42 | — | 142 | 1 | no | — |
| 561 | C42 | C2×C4×D71 | 1 | 1 | yes | characteristic |
| 562 | C42 | C2×C4×D71 | 1 | 1 | yes | characteristic |
| 563 | C23 | — | 2 | 1 | no | — |
| 564 | C23 | — | 71 | 1 | no | — |
| 565 | C23 | — | 71 | 2 | no | — |
| 566 | C23 | — | 71 | 1 | no | — |
| 567 | C23 | C22⋊C4×D71 | 1 | 1 | yes | characteristic |
| 568 | Q8 | — | 4 | 1 | no | — |
| 569 | Q8 | — | 4 | 2 | no | — |
| 570 | Q8 | — | 4 | 1 | no | — |
| 571 | Q8 | — | 4 | 1 | no | — |
| 572 | Q8 | — | 284 | 1 | no | — |
| 573 | Q8 | — | 284 | 1 | no | — |
| 574 | Q8 | — | 284 | 2 | no | — |
| 575 | Q8 | — | 284 | 2 | no | — |
| 576 | Q8 | — | 284 | 1 | no | — |
| 577 | Q8 | — | 284 | 2 | no | — |
| 578 | Q8 | — | 284 | 2 | no | — |
| 579 | Q8 | — | 142 | 2 | no | — |
| 580 | Q8 | — | 142 | 4 | no | — |
| 581 | D4 | — | 4 | 1 | no | — |
| 582 | D4 | — | 4 | 2 | no | — |
| 583 | D4 | — | 284 | 2 | no | — |
| 584 | D4 | — | 284 | 1 | no | — |
| 585 | D4 | — | 284 | 2 | no | — |
| 586 | D4 | — | 284 | 2 | no | — |
| 587 | D4 | — | 284 | 4 | no | — |
| 588 | D4 | — | 71 | 4 | no | — |
| 589 | D4 | — | 142 | 2 | no | — |
| 590 | D4 | — | 142 | 4 | no | — |
| 591 | D4 | — | 142 | 2 | no | — |
| 592 | D4 | — | 142 | 2 | no | — |
| 593 | D4 | — | 142 | 2 | no | — |
| 594 | C2×C4 | — | 2 | 2 | no | — |
| 595 | C2×C4 | — | 2 | 2 | no | — |
| 596 | C2×C4 | — | 2 | 2 | no | — |
| 597 | C2×C4 | — | 2 | 1 | no | — |
| 598 | C2×C4 | — | 2 | 1 | no | — |
| 599 | C2×C4 | — | 2 | 1 | no | — |
| 600 | C2×C4 | — | 4 | 2 | no | — |
| 601 | C2×C4 | — | 284 | 2 | no | — |
| 602 | C2×C4 | — | 284 | 2 | no | — |
| 603 | C2×C4 | — | 284 | 2 | no | — |
| 604 | C2×C4 | — | 284 | 2 | no | — |
| 605 | C2×C4 | — | 284 | 2 | no | — |
| 606 | C2×C4 | — | 284 | 2 | no | — |
| 607 | C2×C4 | — | 284 | 2 | no | — |
| 608 | C2×C4 | — | 284 | 2 | no | — |
| 609 | C2×C4 | — | 284 | 2 | no | — |
| 610 | C2×C4 | — | 284 | 2 | no | — |
| 611 | C2×C4 | — | 284 | 2 | no | — |
| 612 | C2×C4 | — | 71 | 1 | no | — |
| 613 | C2×C4 | — | 71 | 1 | no | — |
| 614 | C2×C4 | — | 71 | 2 | no | — |
| 615 | C2×C4 | — | 142 | 4 | no | — |
| 616 | C2×C4 | — | 142 | 2 | no | — |
| 617 | C2×C4 | — | 142 | 4 | no | — |
| 618 | C2×C4 | — | 142 | 2 | no | — |
| 619 | C2×C4 | — | 142 | 1 | no | — |
| 620 | C2×C4 | — | 142 | 1 | no | — |
| 621 | C2×C4 | — | 142 | 1 | no | — |
| 622 | C2×C4 | — | 142 | 1 | no | — |
| 623 | C2×C4 | C22⋊C4×D71 | 1 | 1 | yes | characteristic |
| 624 | C2×C4 | C22⋊C4×D71 | 1 | 2 | yes | — |
| 625 | C2×C4 | C22×C4×D71 | 1 | 1 | yes | characteristic |
| 626 | C2×C4 | C2×D4×D71 | 1 | 2 | yes | — |
| 627 | C8 | — | 4 | 4 | no | — |
| 628 | C8 | — | 284 | 4 | no | — |
| 629 | C22 | — | 4 | 1 | no | — |
| 630 | C22 | — | 4 | 2 | no | — |
| 631 | C22 | — | 4 | 1 | no | — |
| 632 | C22 | — | 284 | 1 | no | — |
| 633 | C22 | — | 284 | 2 | no | — |
| 634 | C22 | — | 284 | 1 | no | — |
| 635 | C22 | — | 71 | 2 | no | — |
| 636 | C22 | — | 142 | 1 | no | — |
| 637 | C22 | — | 142 | 2 | no | — |
| 638 | C22 | #99×D71 | 1 | 2 | yes | — |
| 639 | C22 | C2×C22⋊C4×D71 | 1 | 1 | yes | characteristic |
| 640 | C4 | — | 2 | 2 | no | — |
| 641 | C4 | — | 2 | 1 | no | — |
| 642 | C4 | — | 2 | 2 | no | — |
| 643 | C4 | — | 2 | 1 | no | — |
| 644 | C4 | — | 4 | 1 | no | — |
| 645 | C4 | — | 4 | 1 | no | — |
| 646 | C4 | — | 4 | 1 | no | — |
| 647 | C4 | — | 284 | 1 | no | — |
| 648 | C4 | — | 284 | 1 | no | — |
| 649 | C4 | — | 284 | 1 | no | — |
| 650 | C4 | — | 71 | 2 | no | — |
| 651 | C4 | — | 142 | 2 | no | — |
| 652 | C4 | — | 142 | 1 | no | — |
| 653 | C4 | — | 142 | 2 | no | — |
| 654 | C2 | — | 2 | 1 | no | — |
| 655 | C2 | — | 2 | 2 | no | — |
| 656 | C2 | — | 8 | 1 | no | — |
| 657 | C2 | — | 284 | 1 | no | — |
| 658 | C2 | — | 284 | 2 | no | — |
| 659 | C2 | — | 142 | 2 | no | — |
| 660 | C2 | C2×#99×D71 | 1 | 1 | yes | characteristic |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta