← #31892327
Subgroups — #31892327
Order 18176.
476 conjugacy classes of subgroups.
The subgroup lattice has 414 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #22596908 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #22586795 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #22586743 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #22586722 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | #22586237 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #22586174 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C71×#3076 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | C2×#14556135 | — | 2 | 1 | no | — |
| 9 | #17986052 | C22 | 1 | 1 | yes | characteristic |
| 10 | #17986026 | — | 2 | 2 | no | — |
| 11 | #17986026 | — | 2 | 1 | no | — |
| 12 | #17986023 | — | 2 | 1 | no | — |
| 13 | #17986023 | C22 | 1 | 1 | yes | characteristic |
| 14 | C2×C4⋊(C71⋊C8) | — | 2 | 1 | no | — |
| 15 | C2×C4⋊(C71⋊C8) | C22 | 1 | 1 | yes | characteristic |
| 16 | C2×C4×C71⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 17 | Q8⋊(C71⋊C8) | — | 2 | 1 | no | — |
| 18 | Q8⋊(C71⋊C8) | — | 2 | 1 | no | — |
| 19 | Q8⋊(C71⋊C8) | — | 2 | 2 | no | — |
| 20 | Q8⋊(C71⋊C8) | — | 2 | 1 | no | — |
| 21 | D4⋊(C71⋊C8) | — | 2 | 1 | no | — |
| 22 | #533×C71 | C22 | 1 | 1 | yes | characteristic |
| 23 | C4×#41×C71 | C22 | 1 | 1 | yes | characteristic |
| 24 | #479×C71 | — | 2 | 1 | no | — |
| 25 | #478×C71 | — | 2 | 1 | no | — |
| 26 | #477×C71 | C4 | 1 | 1 | yes | characteristic |
| 27 | #476×C71 | C4 | 1 | 1 | yes | characteristic |
| 28 | #475×C71 | C4 | 1 | 1 | yes | characteristic |
| 29 | #474×C71 | C4 | 1 | 1 | yes | characteristic |
| 30 | #427×C71 | — | 2 | 1 | no | — |
| 31 | C2×C4⋊C8×C71 | C22 | 1 | 1 | yes | characteristic |
| 32 | #416×C71 | — | 2 | 1 | no | — |
| 33 | #14556135 | — | 4 | 2 | no | — |
| 34 | #14556135 | — | 4 | 2 | no | — |
| 35 | C2×#11765849 | — | 2 | 2 | no | — |
| 36 | C2×#11765849 | — | 2 | 1 | no | — |
| 37 | C22×C71⋊C8 | — | 2 | 2 | no | — |
| 38 | C22×C71⋊C8 | — | 2 | 1 | no | — |
| 39 | C22×C71⋊C8 | — | 2 | 1 | no | — |
| 40 | C4⋊(C71⋊C8) | — | 2 | 2 | no | — |
| 41 | C4⋊(C71⋊C8) | — | 2 | 2 | no | — |
| 42 | C4⋊(C71⋊C8) | — | 2 | 1 | no | — |
| 43 | C4⋊(C71⋊C8) | — | 2 | 1 | no | — |
| 44 | C4⋊(C71⋊C8) | — | 2 | 1 | no | — |
| 45 | C4⋊(C71⋊C8) | D4 | 1 | 1 | yes | characteristic |
| 46 | C4⋊(C71⋊C8) | D4 | 1 | 1 | yes | characteristic |
| 47 | C4⋊(C71⋊C8) | D4 | 1 | 2 | yes | — |
| 48 | C22⋊(C71⋊C8) | — | 2 | 1 | no | — |
| 49 | C4×C71⋊C8 | — | 2 | 1 | no | — |
| 50 | C4×C71⋊C8 | — | 2 | 1 | no | — |
| 51 | C4×C71⋊C8 | — | 2 | 1 | no | — |
| 52 | C2×#41×C71 | D4 | 1 | 1 | yes | characteristic |
| 53 | C22×C8×C71 | — | 2 | 1 | no | — |
| 54 | C4⋊Q8×C71 | C2×C4 | 1 | 1 | yes | characteristic |
| 55 | C4⋊Q8×C71 | C2×C4 | 1 | 1 | yes | characteristic |
| 56 | #125×C71 | — | 2 | 1 | no | — |
| 57 | C22⋊Q8×C71 | — | 2 | 1 | no | — |
| 58 | C22⋊Q8×C71 | — | 2 | 1 | no | — |
| 59 | C4×Q8×C71 | — | 2 | 1 | no | — |
| 60 | C4×Q8×C71 | — | 2 | 1 | no | — |
| 61 | C4×Q8×C71 | C2×C4 | 1 | 1 | yes | characteristic |
| 62 | C4×Q8×C71 | D4 | 1 | 1 | yes | characteristic |
| 63 | C4×D4×C71 | — | 2 | 1 | no | — |
| 64 | C4×D4×C71 | — | 2 | 1 | no | — |
| 65 | C4×D4×C71 | C2×C4 | 1 | 1 | yes | characteristic |
| 66 | C4×D4×C71 | D4 | 1 | 1 | yes | characteristic |
| 67 | #117×C71 | — | 2 | 1 | no | — |
| 68 | #117×C71 | — | 2 | 1 | no | — |
| 69 | #117×C71 | D4 | 1 | 1 | yes | characteristic |
| 70 | C2×C42×C71 | — | 2 | 1 | no | — |
| 71 | C2×C42×C71 | C23 | 1 | 1 | yes | characteristic |
| 72 | #107×C71 | — | 2 | 1 | no | — |
| 73 | #107×C71 | — | 2 | 1 | no | — |
| 74 | #106×C71 | — | 2 | 1 | no | — |
| 75 | #106×C71 | — | 2 | 1 | no | — |
| 76 | C4⋊C8×C71 | — | 2 | 1 | no | — |
| 77 | C4⋊C8×C71 | C2×C4 | 1 | 1 | yes | characteristic |
| 78 | C4⋊C8×C71 | C2×C4 | 1 | 1 | yes | characteristic |
| 79 | #103×C71 | — | 2 | 1 | no | — |
| 80 | #103×C71 | — | 2 | 1 | no | — |
| 81 | #102×C71 | — | 2 | 1 | no | — |
| 82 | #102×C71 | — | 2 | 1 | no | — |
| 83 | #11765849 | — | 4 | 4 | no | — |
| 84 | #11765849 | — | 4 | 1 | no | — |
| 85 | #11765849 | — | 4 | 1 | no | — |
| 86 | C2×C71⋊C8 | — | 2 | 2 | no | — |
| 87 | C2×C71⋊C8 | — | 2 | 1 | no | — |
| 88 | C2×C71⋊C8 | — | 2 | 2 | no | — |
| 89 | C2×C71⋊C8 | — | 2 | 1 | no | — |
| 90 | C2×C71⋊C8 | — | 4 | 1 | no | — |
| 91 | C2×C71⋊C8 | — | 4 | 4 | no | — |
| 92 | C2×C71⋊C8 | — | 4 | 1 | no | — |
| 93 | C2×C71⋊C8 | — | 4 | 1 | no | — |
| 94 | C2×C71⋊C8 | — | 4 | 1 | no | — |
| 95 | C2×C71⋊C8 | — | 4 | 1 | no | — |
| 96 | #41×C71 | — | 2 | 1 | no | — |
| 97 | #41×C71 | — | 2 | 1 | no | — |
| 98 | #41×C71 | SD16 | 1 | 2 | yes | — |
| 99 | #41×C71 | Q16 | 1 | 2 | yes | — |
| 100 | C2×Q8×C71 | — | 2 | 1 | no | — |
| 101 | C2×Q8×C71 | — | 2 | 1 | no | — |
| 102 | C2×Q8×C71 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 103 | C2×D4×C71 | — | 2 | 1 | no | — |
| 104 | C2×D4×C71 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 105 | C22×C4×C71 | — | 2 | 1 | no | — |
| 106 | C22×C4×C71 | — | 2 | 1 | no | — |
| 107 | C22×C4×C71 | — | 2 | 1 | no | — |
| 108 | C22×C4×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 109 | C22×C4×C71 | #41 | 1 | 1 | yes | characteristic |
| 110 | C22×C4×C71 | #41 | 1 | 1 | yes | characteristic |
| 111 | C2×C8×C71 | — | 2 | 1 | no | — |
| 112 | C2×C8×C71 | — | 2 | 1 | no | — |
| 113 | C2×C8×C71 | — | 4 | 1 | no | — |
| 114 | C2×C8×C71 | — | 4 | 1 | no | — |
| 115 | C4⋊C4×C71 | — | 2 | 1 | no | — |
| 116 | C4⋊C4×C71 | — | 2 | 1 | no | — |
| 117 | C4⋊C4×C71 | — | 2 | 1 | no | — |
| 118 | C4⋊C4×C71 | — | 2 | 1 | no | — |
| 119 | C4⋊C4×C71 | — | 2 | 1 | no | — |
| 120 | C4⋊C4×C71 | — | 2 | 1 | no | — |
| 121 | C4⋊C4×C71 | — | 4 | 1 | no | — |
| 122 | C4⋊C4×C71 | — | 4 | 1 | no | — |
| 123 | C4⋊C4×C71 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 124 | C4⋊C4×C71 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 125 | C22⋊C4×C71 | — | 2 | 1 | no | — |
| 126 | C22⋊C4×C71 | — | 2 | 1 | no | — |
| 127 | C22⋊C4×C71 | — | 2 | 1 | no | — |
| 128 | C22⋊C4×C71 | — | 4 | 1 | no | — |
| 129 | C42×C71 | — | 2 | 1 | no | — |
| 130 | C42×C71 | — | 2 | 1 | no | — |
| 131 | C42×C71 | — | 2 | 1 | no | — |
| 132 | C42×C71 | — | 4 | 1 | no | — |
| 133 | C42×C71 | C22×C4 | 1 | 1 | yes | characteristic |
| 134 | C42×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 135 | C42×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 136 | C42×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 137 | C23×C71 | — | 2 | 1 | no | — |
| 138 | C23×C71 | #123 | 1 | 1 | yes | characteristic |
| 139 | Q8×C71 | — | 2 | 1 | no | — |
| 140 | Q8×C71 | — | 4 | 2 | no | — |
| 141 | Q8×C71 | — | 4 | 1 | no | — |
| 142 | Q8×C71 | — | 4 | 1 | no | — |
| 143 | Q8×C71 | #103 | 1 | 2 | yes | — |
| 144 | D4×C71 | — | 2 | 2 | no | — |
| 145 | D4×C71 | — | 2 | 2 | no | — |
| 146 | D4×C71 | — | 2 | 1 | no | — |
| 147 | D4×C71 | #103 | 1 | 2 | yes | — |
| 148 | C2×C4×C71 | — | 2 | 1 | no | — |
| 149 | C2×C4×C71 | — | 2 | 1 | no | — |
| 150 | C2×C4×C71 | — | 2 | 1 | no | — |
| 151 | C2×C4×C71 | — | 2 | 2 | no | — |
| 152 | C2×C4×C71 | — | 2 | 2 | no | — |
| 153 | C2×C4×C71 | — | 2 | 1 | no | — |
| 154 | C2×C4×C71 | — | 2 | 1 | no | — |
| 155 | C2×C4×C71 | — | 4 | 1 | no | — |
| 156 | C2×C4×C71 | — | 4 | 1 | no | — |
| 157 | C2×C4×C71 | — | 4 | 1 | no | — |
| 158 | C2×C4×C71 | — | 4 | 1 | no | — |
| 159 | C2×C4×C71 | — | 4 | 1 | no | — |
| 160 | C2×C4×C71 | — | 8 | 1 | no | — |
| 161 | C2×C4×C71 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 162 | C2×C4×C71 | C4×D4 | 1 | 1 | yes | characteristic |
| 163 | C2×C4×C71 | C4×D4 | 1 | 1 | yes | characteristic |
| 164 | C2×C4×C71 | #120 | 1 | 1 | yes | characteristic |
| 165 | C2×C4×C71 | #121 | 1 | 1 | yes | characteristic |
| 166 | C2×C4×C71 | #121 | 1 | 1 | yes | characteristic |
| 167 | C2×C4×C71 | C2×SD16 | 1 | 1 | yes | characteristic |
| 168 | C2×C4×C71 | C2×Q16 | 1 | 1 | yes | characteristic |
| 169 | C2×C4×C71 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 170 | C2×C4×C71 | #137 | 1 | 1 | yes | characteristic |
| 171 | C8×C71 | — | 4 | 1 | no | — |
| 172 | C8×C71 | — | 4 | 1 | no | — |
| 173 | C71⋊C8 | — | 4 | 2 | no | — |
| 174 | C71⋊C8 | — | 4 | 1 | no | — |
| 175 | C71⋊C8 | — | 4 | 2 | no | — |
| 176 | C71⋊C8 | — | 4 | 1 | no | — |
| 177 | C71⋊C8 | — | 8 | 1 | no | — |
| 178 | C22×C71 | — | 2 | 1 | no | — |
| 179 | C22×C71 | — | 2 | 1 | no | — |
| 180 | C22×C71 | — | 2 | 2 | no | — |
| 181 | C22×C71 | — | 4 | 1 | no | — |
| 182 | C22×C71 | — | 4 | 1 | no | — |
| 183 | C22×C71 | #386 | 1 | 1 | yes | characteristic |
| 184 | C22×C71 | #483 | 1 | 1 | yes | characteristic |
| 185 | C22×C71 | #484 | 1 | 1 | yes | characteristic |
| 186 | C4×C71 | — | 2 | 2 | no | — |
| 187 | C4×C71 | — | 2 | 1 | no | — |
| 188 | C4×C71 | — | 2 | 1 | no | — |
| 189 | C4×C71 | — | 2 | 1 | no | — |
| 190 | C4×C71 | — | 4 | 1 | no | — |
| 191 | C4×C71 | — | 4 | 1 | no | — |
| 192 | C4×C71 | — | 8 | 1 | no | — |
| 193 | C4×C71 | — | 8 | 1 | no | — |
| 194 | C4×C71 | C2×#103 | 1 | 1 | yes | characteristic |
| 195 | C4×C71 | #417 | 1 | 1 | yes | characteristic |
| 196 | C4×C71 | #443 | 1 | 1 | yes | characteristic |
| 197 | C4×C71 | #444 | 1 | 1 | yes | characteristic |
| 198 | C4×C71 | #450 | 1 | 1 | yes | characteristic |
| 199 | C4×C71 | #451 | 1 | 1 | yes | characteristic |
| 200 | #8993 | — | 71 | 1 | no | maximal, Sylow |
| 201 | C2×C71 | — | 2 | 1 | no | — |
| 202 | C2×C71 | — | 2 | 1 | no | — |
| 203 | C2×C71 | — | 4 | 2 | no | — |
| 204 | C2×C71 | #1872 | 1 | 1 | yes | characteristic |
| 205 | C2×C71 | #1876 | 1 | 1 | yes | characteristic |
| 206 | C2×C71 | #1881 | 1 | 1 | yes | characteristic |
| 207 | #3076 | D71 | 1 | 1 | yes | characteristic |
| 208 | #2906 | — | 71 | 1 | no | — |
| 209 | #1493 | — | 71 | 1 | no | — |
| 210 | #1481 | — | 71 | 1 | no | — |
| 211 | #1476 | — | 71 | 1 | no | — |
| 212 | #1301 | — | 71 | 1 | no | — |
| 213 | #1277 | — | 71 | 1 | no | — |
| 214 | C71 | #8993 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 215 | C2×#131 | — | 142 | 1 | no | — |
| 216 | #533 | C2×D71 | 1 | 1 | yes | characteristic |
| 217 | C4×#41 | C2×D71 | 1 | 1 | yes | characteristic |
| 218 | #479 | — | 2 | 1 | no | — |
| 219 | #478 | — | 2 | 1 | no | — |
| 220 | #477 | Dic71 | 1 | 1 | yes | characteristic |
| 221 | #476 | Dic71 | 1 | 1 | yes | characteristic |
| 222 | #475 | Dic71 | 1 | 1 | yes | characteristic |
| 223 | #474 | Dic71 | 1 | 1 | yes | characteristic |
| 224 | #431 | — | 71 | 1 | no | — |
| 225 | #427 | — | 2 | 1 | no | — |
| 226 | #424 | — | 142 | 2 | no | — |
| 227 | #424 | — | 142 | 1 | no | — |
| 228 | #423 | — | 71 | 1 | no | — |
| 229 | #423 | — | 142 | 1 | no | — |
| 230 | C2×C4⋊C8 | — | 71 | 1 | no | — |
| 231 | C2×C4⋊C8 | — | 142 | 1 | no | — |
| 232 | C2×C4⋊C8 | C2×D71 | 1 | 1 | yes | characteristic |
| 233 | #416 | — | 2 | 1 | no | — |
| 234 | C2×C4×C8 | — | 71 | 1 | no | — |
| 235 | Q8⋊C8 | — | 142 | 1 | no | — |
| 236 | Q8⋊C8 | — | 142 | 1 | no | — |
| 237 | Q8⋊C8 | — | 142 | 2 | no | — |
| 238 | Q8⋊C8 | — | 142 | 1 | no | — |
| 239 | D4⋊C8 | — | 142 | 1 | no | — |
| 240 | C2×#41 | C22⋊D71 | 1 | 1 | yes | characteristic |
| 241 | #131 | — | 284 | 2 | no | — |
| 242 | #131 | — | 284 | 2 | no | — |
| 243 | C2×M16 | — | 142 | 2 | no | — |
| 244 | C2×M16 | — | 142 | 1 | no | — |
| 245 | C22×C8 | — | 2 | 1 | no | — |
| 246 | C22×C8 | — | 142 | 2 | no | — |
| 247 | C22×C8 | — | 142 | 1 | no | — |
| 248 | C22×C8 | — | 142 | 1 | no | — |
| 249 | C4⋊Q8 | C2×Dic71 | 1 | 1 | yes | characteristic |
| 250 | C4⋊Q8 | C2×Dic71 | 1 | 1 | yes | characteristic |
| 251 | #125 | — | 2 | 1 | no | — |
| 252 | C22⋊Q8 | — | 2 | 1 | no | — |
| 253 | C22⋊Q8 | — | 2 | 1 | no | — |
| 254 | C4×Q8 | — | 2 | 1 | no | — |
| 255 | C4×Q8 | — | 2 | 1 | no | — |
| 256 | C4×Q8 | C2×Dic71 | 1 | 1 | yes | characteristic |
| 257 | C4×Q8 | C22⋊D71 | 1 | 1 | yes | characteristic |
| 258 | C4×D4 | — | 2 | 1 | no | — |
| 259 | C4×D4 | — | 2 | 1 | no | — |
| 260 | C4×D4 | C2×Dic71 | 1 | 1 | yes | characteristic |
| 261 | C4×D4 | C22⋊D71 | 1 | 1 | yes | characteristic |
| 262 | #117 | — | 2 | 1 | no | — |
| 263 | #117 | — | 2 | 1 | no | — |
| 264 | #117 | C22⋊D71 | 1 | 1 | yes | characteristic |
| 265 | C2×C42 | — | 2 | 1 | no | — |
| 266 | C2×C42 | C22×D71 | 1 | 1 | yes | characteristic |
| 267 | #107 | — | 2 | 1 | no | — |
| 268 | #107 | — | 2 | 1 | no | — |
| 269 | #106 | — | 2 | 1 | no | — |
| 270 | #106 | — | 2 | 1 | no | — |
| 271 | C4⋊C8 | — | 2 | 1 | no | — |
| 272 | C4⋊C8 | — | 71 | 1 | no | — |
| 273 | C4⋊C8 | — | 71 | 1 | no | — |
| 274 | C4⋊C8 | — | 71 | 2 | no | — |
| 275 | C4⋊C8 | — | 142 | 2 | no | — |
| 276 | C4⋊C8 | — | 142 | 2 | no | — |
| 277 | C4⋊C8 | — | 142 | 1 | no | — |
| 278 | C4⋊C8 | — | 142 | 1 | no | — |
| 279 | C4⋊C8 | — | 142 | 1 | no | — |
| 280 | C4⋊C8 | C2×Dic71 | 1 | 1 | yes | characteristic |
| 281 | C4⋊C8 | C2×Dic71 | 1 | 1 | yes | characteristic |
| 282 | #103 | — | 2 | 1 | no | — |
| 283 | #103 | — | 2 | 1 | no | — |
| 284 | #102 | — | 2 | 1 | no | — |
| 285 | #102 | — | 2 | 1 | no | — |
| 286 | C22⋊C8 | — | 142 | 1 | no | — |
| 287 | C4×C8 | — | 142 | 1 | no | — |
| 288 | C4×C8 | — | 142 | 1 | no | — |
| 289 | C4×C8 | — | 142 | 1 | no | — |
| 290 | #41 | — | 2 | 1 | no | — |
| 291 | #41 | — | 2 | 1 | no | — |
| 292 | #41 | #11765852 | 1 | 2 | yes | — |
| 293 | #41 | #11765855 | 1 | 2 | yes | — |
| 294 | C2×Q8 | — | 2 | 1 | no | — |
| 295 | C2×Q8 | — | 2 | 1 | no | — |
| 296 | C2×Q8 | C22⋊Dic71 | 1 | 1 | yes | characteristic |
| 297 | C2×D4 | — | 2 | 1 | no | — |
| 298 | C2×D4 | C22⋊Dic71 | 1 | 1 | yes | characteristic |
| 299 | C22×C4 | — | 2 | 1 | no | — |
| 300 | C22×C4 | — | 2 | 1 | no | — |
| 301 | C22×C4 | — | 2 | 1 | no | — |
| 302 | C22×C4 | C2×C22⋊D71 | 1 | 1 | yes | characteristic |
| 303 | C22×C4 | #11765864 | 1 | 1 | yes | characteristic |
| 304 | C22×C4 | #11765864 | 1 | 1 | yes | characteristic |
| 305 | M16 | — | 284 | 4 | no | — |
| 306 | M16 | — | 284 | 1 | no | — |
| 307 | M16 | — | 284 | 1 | no | — |
| 308 | C2×C8 | — | 2 | 1 | no | — |
| 309 | C2×C8 | — | 2 | 1 | no | — |
| 310 | C2×C8 | — | 4 | 1 | no | — |
| 311 | C2×C8 | — | 4 | 1 | no | — |
| 312 | C2×C8 | — | 284 | 1 | no | — |
| 313 | C2×C8 | — | 284 | 4 | no | — |
| 314 | C2×C8 | — | 284 | 1 | no | — |
| 315 | C2×C8 | — | 284 | 1 | no | — |
| 316 | C2×C8 | — | 284 | 1 | no | — |
| 317 | C2×C8 | — | 284 | 1 | no | — |
| 318 | C2×C8 | — | 142 | 2 | no | — |
| 319 | C2×C8 | — | 142 | 1 | no | — |
| 320 | C2×C8 | — | 142 | 1 | no | — |
| 321 | C2×C8 | — | 142 | 2 | no | — |
| 322 | C4⋊C4 | — | 2 | 1 | no | — |
| 323 | C4⋊C4 | — | 2 | 1 | no | — |
| 324 | C4⋊C4 | — | 2 | 1 | no | — |
| 325 | C4⋊C4 | — | 2 | 1 | no | — |
| 326 | C4⋊C4 | — | 2 | 1 | no | — |
| 327 | C4⋊C4 | — | 2 | 1 | no | — |
| 328 | C4⋊C4 | — | 4 | 1 | no | — |
| 329 | C4⋊C4 | — | 4 | 1 | no | — |
| 330 | C4⋊C4 | C22⋊Dic71 | 1 | 1 | yes | characteristic |
| 331 | C4⋊C4 | C22⋊Dic71 | 1 | 1 | yes | characteristic |
| 332 | C22⋊C4 | — | 2 | 1 | no | — |
| 333 | C22⋊C4 | — | 2 | 1 | no | — |
| 334 | C22⋊C4 | — | 2 | 1 | no | — |
| 335 | C22⋊C4 | — | 4 | 1 | no | — |
| 336 | C42 | — | 2 | 1 | no | — |
| 337 | C42 | — | 2 | 1 | no | — |
| 338 | C42 | — | 2 | 1 | no | — |
| 339 | C42 | — | 4 | 1 | no | — |
| 340 | C42 | C22×Dic71 | 1 | 1 | yes | characteristic |
| 341 | C42 | D4×D71 | 1 | 1 | yes | characteristic |
| 342 | C42 | D4×D71 | 1 | 1 | yes | characteristic |
| 343 | C42 | C2×C22⋊D71 | 1 | 1 | yes | characteristic |
| 344 | C23 | — | 2 | 1 | no | — |
| 345 | C23 | #14556109 | 1 | 1 | yes | characteristic |
| 346 | Q8 | — | 2 | 1 | no | — |
| 347 | Q8 | — | 4 | 2 | no | — |
| 348 | Q8 | — | 4 | 1 | no | — |
| 349 | Q8 | — | 4 | 1 | no | — |
| 350 | Q8 | #14556052 | 1 | 2 | yes | — |
| 351 | D4 | — | 2 | 2 | no | — |
| 352 | D4 | — | 2 | 2 | no | — |
| 353 | D4 | — | 2 | 1 | no | — |
| 354 | D4 | #14556052 | 1 | 2 | yes | — |
| 355 | C2×C4 | — | 2 | 1 | no | — |
| 356 | C2×C4 | — | 2 | 1 | no | — |
| 357 | C2×C4 | — | 2 | 1 | no | — |
| 358 | C2×C4 | — | 2 | 2 | no | — |
| 359 | C2×C4 | — | 2 | 2 | no | — |
| 360 | C2×C4 | — | 2 | 1 | no | — |
| 361 | C2×C4 | — | 2 | 1 | no | — |
| 362 | C2×C4 | — | 4 | 1 | no | — |
| 363 | C2×C4 | — | 4 | 1 | no | — |
| 364 | C2×C4 | — | 4 | 1 | no | — |
| 365 | C2×C4 | — | 4 | 1 | no | — |
| 366 | C2×C4 | — | 4 | 1 | no | — |
| 367 | C2×C4 | — | 8 | 1 | no | — |
| 368 | C2×C4 | C2×C22⋊Dic71 | 1 | 1 | yes | characteristic |
| 369 | C2×C4 | D4×Dic71 | 1 | 1 | yes | characteristic |
| 370 | C2×C4 | D4×Dic71 | 1 | 1 | yes | characteristic |
| 371 | C2×C4 | #14556096 | 1 | 1 | yes | characteristic |
| 372 | C2×C4 | #14556100 | 1 | 1 | yes | characteristic |
| 373 | C2×C4 | #14556100 | 1 | 1 | yes | characteristic |
| 374 | C2×C4 | C2×#11765852 | 1 | 1 | yes | characteristic |
| 375 | C2×C4 | C2×#11765855 | 1 | 1 | yes | characteristic |
| 376 | C2×C4 | #14556153 | 1 | 1 | yes | characteristic |
| 377 | C2×C4 | #14556158 | 1 | 1 | yes | characteristic |
| 378 | C8 | — | 4 | 1 | no | — |
| 379 | C8 | — | 4 | 1 | no | — |
| 380 | C8 | — | 284 | 2 | no | — |
| 381 | C8 | — | 284 | 1 | no | — |
| 382 | C8 | — | 284 | 2 | no | — |
| 383 | C8 | — | 284 | 1 | no | — |
| 384 | C8 | — | 568 | 1 | no | — |
| 385 | C22 | — | 2 | 1 | no | — |
| 386 | C22 | — | 2 | 1 | no | — |
| 387 | C22 | — | 2 | 2 | no | — |
| 388 | C22 | — | 4 | 1 | no | — |
| 389 | C22 | — | 4 | 1 | no | — |
| 390 | C22 | #17985879 | 1 | 1 | yes | characteristic |
| 391 | C22 | #17986327 | 1 | 1 | yes | characteristic |
| 392 | C22 | #17986332 | 1 | 1 | yes | characteristic |
| 393 | C4 | — | 2 | 1 | no | — |
| 394 | C4 | — | 2 | 1 | no | — |
| 395 | C4 | — | 2 | 2 | no | — |
| 396 | C4 | — | 2 | 1 | no | — |
| 397 | C4 | — | 4 | 1 | no | — |
| 398 | C4 | — | 4 | 1 | no | — |
| 399 | C4 | — | 8 | 1 | no | — |
| 400 | C4 | — | 8 | 1 | no | — |
| 401 | C4 | C2×#14556052 | 1 | 1 | yes | characteristic |
| 402 | C4 | #17986000 | 1 | 1 | yes | characteristic |
| 403 | C4 | #17986116 | 1 | 1 | yes | characteristic |
| 404 | C4 | #17986121 | 1 | 1 | yes | characteristic |
| 405 | C4 | #17986149 | 1 | 1 | yes | characteristic |
| 406 | C4 | #17986154 | 1 | 1 | yes | characteristic |
| 407 | C2 | — | 2 | 1 | no | — |
| 408 | C2 | — | 2 | 1 | no | — |
| 409 | C2 | — | 4 | 2 | no | — |
| 410 | C2 | #22588648 | 1 | 1 | yes | characteristic |
| 411 | C2 | #22588669 | 1 | 1 | yes | characteristic |
| 412 | C2 | #22588704 | 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