← #14738475
Subgroups — #14738475
Order 2816.
616 conjugacy classes of subgroups.
The subgroup lattice has 346 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #13079629 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #13079195 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #13077550 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #13068135 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #13068101 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #13068061 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #13067339 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | C11×#1568 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #10623008 | C22 | 1 | 2 | yes | — |
| 10 | #10623001 | C22 | 1 | 1 | yes | characteristic |
| 11 | C11×#432 | C22 | 1 | 2 | yes | — |
| 12 | C2×C4×C8×C11 | C22 | 1 | 1 | yes | characteristic |
| 13 | #10622728 | — | 2 | 1 | no | — |
| 14 | #10622728 | — | 2 | 1 | no | — |
| 15 | #10622715 | — | 2 | 1 | no | — |
| 16 | #10622714 | — | 2 | 1 | no | — |
| 17 | #10622537 | C22 | 1 | 1 | yes | characteristic |
| 18 | #10622462 | C22 | 1 | 4 | yes | — |
| 19 | #10622461 | C22 | 1 | 4 | yes | — |
| 20 | #10622346 | — | 2 | 4 | no | — |
| 21 | #10622328 | — | 2 | 2 | no | — |
| 22 | #10622327 | — | 2 | 2 | no | — |
| 23 | #10622308 | C22 | 1 | 1 | yes | characteristic |
| 24 | #10622307 | C22 | 1 | 2 | yes | — |
| 25 | C4×D88 | — | 2 | 1 | no | — |
| 26 | C4×D88 | — | 2 | 1 | no | — |
| 27 | #10622295 | C22 | 1 | 1 | yes | characteristic |
| 28 | #10622292 | — | 2 | 1 | no | — |
| 29 | #10622292 | C22 | 1 | 2 | yes | — |
| 30 | C8×Dic22 | — | 2 | 1 | no | — |
| 31 | C8×Dic22 | C22 | 1 | 2 | yes | — |
| 32 | C11×#335 | C22 | 1 | 2 | yes | — |
| 33 | C11×#334 | C22 | 1 | 2 | yes | — |
| 34 | #10622123 | C22 | 1 | 4 | yes | — |
| 35 | #10622120 | C22 | 1 | 4 | yes | — |
| 36 | C2×#4339 | — | 2 | 2 | no | — |
| 37 | C22×C8×C11 | D4 | 1 | 1 | yes | characteristic |
| 38 | C22×C8×C11 | D4 | 1 | 1 | yes | characteristic |
| 39 | C2×C42×C11 | C23 | 1 | 1 | yes | characteristic |
| 40 | #66983 | — | 2 | 2 | no | — |
| 41 | #66983 | — | 2 | 2 | no | — |
| 42 | #66979 | — | 2 | 1 | no | — |
| 43 | #66977 | — | 2 | 1 | no | — |
| 44 | #66977 | D4 | 1 | 2 | yes | — |
| 45 | C2×#4318 | — | 2 | 1 | no | — |
| 46 | C2×Dic44 | — | 2 | 4 | no | — |
| 47 | C2×D88 | — | 2 | 1 | no | — |
| 48 | C2×D88 | — | 2 | 1 | no | — |
| 49 | C2×#4314 | — | 2 | 4 | no | — |
| 50 | #66928 | — | 2 | 2 | no | — |
| 51 | #66927 | C23 | 1 | 2 | yes | — |
| 52 | C4×D44 | — | 2 | 2 | no | — |
| 53 | C4×D44 | — | 2 | 2 | no | — |
| 54 | #66923 | — | 2 | 1 | no | — |
| 55 | #66922 | D4 | 1 | 1 | yes | characteristic |
| 56 | #66922 | D4 | 1 | 1 | yes | characteristic |
| 57 | #66922 | C23 | 1 | 2 | yes | — |
| 58 | C4×Dic22 | — | 2 | 1 | no | — |
| 59 | C4×Dic22 | C23 | 1 | 2 | yes | — |
| 60 | C11×C4⋊C8 | C23 | 1 | 4 | yes | — |
| 61 | C11×C22⋊C8 | — | 2 | 2 | no | — |
| 62 | C11×#97 | — | 2 | 2 | no | — |
| 63 | C4×C8×C11 | D4 | 1 | 1 | yes | characteristic |
| 64 | C4×C8×C11 | D4 | 1 | 1 | yes | characteristic |
| 65 | C4×C8×C11 | C23 | 1 | 1 | yes | characteristic |
| 66 | C4×C8×C11 | C23 | 1 | 1 | yes | characteristic |
| 67 | #66885 | — | 2 | 2 | no | — |
| 68 | #66885 | — | 2 | 2 | no | — |
| 69 | #66885 | — | 2 | 4 | no | — |
| 70 | #66882 | — | 2 | 1 | no | — |
| 71 | #66882 | — | 2 | 1 | no | — |
| 72 | #66880 | — | 2 | 4 | no | — |
| 73 | #66879 | — | 2 | 2 | no | — |
| 74 | Dic11⋊C8 | — | 2 | 2 | no | — |
| 75 | Dic11⋊C8 | — | 2 | 2 | no | — |
| 76 | C8×Dic11 | — | 2 | 2 | no | — |
| 77 | C4⋊(C11⋊C8) | — | 2 | 1 | no | — |
| 78 | C4⋊(C11⋊C8) | C23 | 1 | 2 | yes | — |
| 79 | #19347 | — | 11 | 1 | no | maximal, Sylow |
| 80 | C22×C4×C11 | C2×D4 | 1 | 1 | yes | characteristic |
| 81 | C22×C4×C11 | C2×D4 | 1 | 1 | yes | characteristic |
| 82 | C22×C4×C11 | #41 | 1 | 1 | yes | characteristic |
| 83 | C2×C22⋊D11 | — | 4 | 2 | no | — |
| 84 | #4339 | — | 8 | 4 | no | — |
| 85 | C2×D44 | — | 2 | 2 | no | — |
| 86 | C2×D44 | — | 2 | 2 | no | — |
| 87 | C2×D44 | — | 2 | 2 | no | — |
| 88 | C2×C4×D11 | — | 4 | 2 | no | — |
| 89 | C2×Dic22 | — | 2 | 1 | no | — |
| 90 | C2×Dic22 | — | 2 | 2 | no | — |
| 91 | C2×Dic22 | C2×D4 | 1 | 2 | yes | — |
| 92 | C2×C8×C11 | — | 2 | 2 | no | — |
| 93 | C2×C8×C11 | — | 2 | 4 | no | — |
| 94 | C2×C8×C11 | — | 4 | 1 | no | — |
| 95 | C2×C8×C11 | C2×D4 | 1 | 1 | yes | characteristic |
| 96 | C2×C8×C11 | C2×D4 | 1 | 1 | yes | characteristic |
| 97 | C2×C8×C11 | C2×D4 | 1 | 1 | yes | characteristic |
| 98 | C2×C8×C11 | C2×D4 | 1 | 1 | yes | characteristic |
| 99 | C42×C11 | C2×D4 | 1 | 1 | yes | characteristic |
| 100 | C42×C11 | C2×D4 | 1 | 1 | yes | characteristic |
| 101 | C42×C11 | #41 | 1 | 1 | yes | characteristic |
| 102 | C42×C11 | C24 | 1 | 1 | yes | characteristic |
| 103 | C22⋊Dic11 | — | 2 | 2 | no | — |
| 104 | (C2×D11)⋊C4 | — | 4 | 2 | no | — |
| 105 | (C2×D11)⋊C4 | — | 4 | 2 | no | — |
| 106 | C4⋊Dic11 | — | 2 | 1 | no | — |
| 107 | C4⋊Dic11 | — | 2 | 1 | no | — |
| 108 | C4⋊Dic11 | — | 2 | 1 | no | — |
| 109 | C4⋊Dic11 | — | 2 | 2 | no | — |
| 110 | C4⋊Dic11 | — | 2 | 2 | no | — |
| 111 | C4⋊Dic11 | C2×D4 | 1 | 2 | yes | — |
| 112 | Dic11⋊C4 | — | 2 | 2 | no | — |
| 113 | Dic11⋊C4 | — | 2 | 2 | no | — |
| 114 | C4×Dic11 | — | 2 | 2 | no | — |
| 115 | #4318 | — | 4 | 2 | no | — |
| 116 | C2×C11⋊C8 | — | 2 | 2 | no | — |
| 117 | Dic44 | — | 8 | 4 | no | — |
| 118 | D88 | — | 4 | 2 | no | — |
| 119 | D88 | — | 4 | 2 | no | — |
| 120 | #4314 | — | 8 | 4 | no | — |
| 121 | #3216 | — | 11 | 2 | no | — |
| 122 | #3169 | — | 11 | 1 | no | — |
| 123 | #2960 | — | 11 | 1 | no | — |
| 124 | #1694 | — | 11 | 2 | no | — |
| 125 | #1688 | — | 11 | 2 | no | — |
| 126 | #1682 | — | 11 | 4 | no | — |
| 127 | #1568 | D11 | 1 | 1 | yes | characteristic, complemented |
| 128 | #1557 | — | 11 | 2 | no | — |
| 129 | C23×C11 | #121 | 1 | 1 | yes | characteristic |
| 130 | C22×D11 | — | 4 | 2 | no | — |
| 131 | C2×C4×C11 | — | 2 | 1 | no | — |
| 132 | C2×C4×C11 | — | 2 | 1 | no | — |
| 133 | C2×C4×C11 | — | 2 | 2 | no | — |
| 134 | C2×C4×C11 | — | 4 | 1 | no | — |
| 135 | C2×C4×C11 | #121 | 1 | 1 | yes | characteristic |
| 136 | C2×C4×C11 | #121 | 1 | 1 | yes | characteristic |
| 137 | C2×C4×C11 | #121 | 1 | 1 | yes | characteristic |
| 138 | C2×C4×C11 | C22×D4 | 1 | 1 | yes | characteristic |
| 139 | C2×C4×C11 | C22×D4 | 1 | 1 | yes | characteristic |
| 140 | C2×C4×C11 | C2×#41 | 1 | 1 | yes | characteristic |
| 141 | C22⋊D11 | — | 8 | 4 | no | — |
| 142 | C2×Dic11 | — | 2 | 2 | no | — |
| 143 | C2×Dic11 | — | 2 | 2 | no | — |
| 144 | C2×Dic11 | — | 4 | 2 | no | — |
| 145 | D44 | — | 4 | 2 | no | — |
| 146 | D44 | — | 4 | 2 | no | — |
| 147 | D44 | — | 4 | 4 | no | — |
| 148 | D44 | — | 8 | 2 | no | — |
| 149 | C4×D11 | — | 8 | 4 | no | — |
| 150 | Dic22 | — | 2 | 4 | no | — |
| 151 | Dic22 | — | 4 | 2 | no | — |
| 152 | Dic22 | — | 4 | 4 | no | — |
| 153 | C8×C11 | — | 2 | 1 | no | — |
| 154 | C8×C11 | — | 2 | 1 | no | — |
| 155 | C8×C11 | — | 2 | 1 | no | — |
| 156 | C8×C11 | — | 4 | 4 | no | — |
| 157 | C8×C11 | #137 | 1 | 2 | yes | — |
| 158 | C11⋊C8 | — | 4 | 2 | no | — |
| 159 | #533 | — | 11 | 1 | no | — |
| 160 | #532 | — | 11 | 2 | no | — |
| 161 | #500 | — | 11 | 1 | no | — |
| 162 | #497 | — | 22 | 2 | no | — |
| 163 | #493 | — | 11 | 1 | no | — |
| 164 | #489 | — | 22 | 2 | no | — |
| 165 | #486 | — | 11 | 2 | no | — |
| 166 | #466 | — | 22 | 1 | no | — |
| 167 | #466 | — | 22 | 1 | no | — |
| 168 | #462 | — | 11 | 4 | no | — |
| 169 | #460 | — | 11 | 4 | no | — |
| 170 | #452 | — | 22 | 4 | no | — |
| 171 | #446 | — | 11 | 2 | no | — |
| 172 | #446 | — | 22 | 1 | no | — |
| 173 | C8×Q8 | — | 11 | 2 | no | — |
| 174 | C8×Q8 | — | 22 | 1 | no | — |
| 175 | C4×D8 | — | 22 | 1 | no | — |
| 176 | C4×D8 | — | 22 | 1 | no | — |
| 177 | #432 | C2×D11 | 1 | 2 | yes | — |
| 178 | #424 | — | 22 | 1 | no | — |
| 179 | #423 | — | 11 | 1 | no | — |
| 180 | #405 | — | 22 | 1 | no | — |
| 181 | C2×C4×C8 | C2×D11 | 1 | 1 | yes | characteristic |
| 182 | #335 | C2×D11 | 1 | 2 | yes | — |
| 183 | #334 | C2×D11 | 1 | 2 | yes | — |
| 184 | #332 | — | 11 | 4 | no | — |
| 185 | #331 | — | 11 | 4 | no | — |
| 186 | C22×C11 | — | 2 | 1 | no | — |
| 187 | C22×C11 | — | 2 | 1 | no | — |
| 188 | C22×C11 | — | 2 | 1 | no | — |
| 189 | C22×C11 | C2×#121 | 1 | 1 | yes | characteristic |
| 190 | C2×D11 | — | 8 | 2 | no | — |
| 191 | C2×D11 | — | 8 | 2 | no | — |
| 192 | C2×D11 | — | 8 | 2 | no | — |
| 193 | C4×C11 | — | 2 | 1 | no | — |
| 194 | C4×C11 | — | 2 | 1 | no | — |
| 195 | C4×C11 | — | 2 | 1 | no | — |
| 196 | C4×C11 | — | 2 | 1 | no | — |
| 197 | C4×C11 | C2×#137 | 1 | 1 | yes | characteristic |
| 198 | C4×C11 | #575 | 1 | 1 | yes | characteristic |
| 199 | C4×C11 | #576 | 1 | 2 | yes | — |
| 200 | Dic11 | — | 4 | 2 | no | — |
| 201 | Dic11 | — | 4 | 2 | no | — |
| 202 | Dic11 | — | 8 | 2 | no | — |
| 203 | C2×#41 | — | 22 | 2 | no | — |
| 204 | C2×Q16 | — | 22 | 4 | no | — |
| 205 | C2×SD16 | — | 22 | 4 | no | — |
| 206 | C2×D8 | — | 22 | 1 | no | — |
| 207 | C2×D8 | — | 22 | 1 | no | — |
| 208 | C2×M16 | — | 22 | 1 | no | — |
| 209 | C22×C8 | D44 | 1 | 1 | yes | characteristic |
| 210 | C22×C8 | D44 | 1 | 1 | yes | characteristic |
| 211 | C4⋊Q8 | — | 11 | 1 | no | — |
| 212 | C4⋊Q8 | — | 11 | 1 | no | — |
| 213 | C4⋊Q8 | — | 11 | 2 | no | — |
| 214 | #127 | — | 11 | 2 | no | — |
| 215 | #125 | — | 22 | 1 | no | — |
| 216 | #124 | — | 22 | 2 | no | — |
| 217 | C22⋊Q8 | — | 11 | 2 | no | — |
| 218 | C22⋊Q8 | — | 22 | 1 | no | — |
| 219 | #121 | — | 22 | 2 | no | — |
| 220 | #121 | — | 22 | 2 | no | — |
| 221 | C4×Q8 | — | 11 | 2 | no | — |
| 222 | C4×Q8 | — | 22 | 1 | no | — |
| 223 | C4×D4 | — | 22 | 2 | no | — |
| 224 | C4×D4 | — | 22 | 2 | no | — |
| 225 | #117 | — | 22 | 1 | no | — |
| 226 | C2×C42 | C22×D11 | 1 | 1 | yes | characteristic |
| 227 | #107 | — | 22 | 1 | no | — |
| 228 | #107 | — | 22 | 1 | no | — |
| 229 | C4⋊C8 | — | 11 | 2 | no | — |
| 230 | C4⋊C8 | — | 22 | 2 | no | — |
| 231 | C4⋊C8 | — | 22 | 2 | no | — |
| 232 | C4⋊C8 | — | 22 | 1 | no | — |
| 233 | C4⋊C8 | C22×D11 | 1 | 4 | yes | — |
| 234 | #103 | — | 22 | 4 | no | — |
| 235 | #102 | — | 22 | 4 | no | — |
| 236 | #102 | — | 22 | 2 | no | — |
| 237 | #102 | — | 22 | 2 | no | — |
| 238 | C22⋊C8 | — | 2 | 2 | no | — |
| 239 | #97 | — | 2 | 2 | no | — |
| 240 | #97 | — | 22 | 2 | no | — |
| 241 | C4×C8 | — | 22 | 2 | no | — |
| 242 | C4×C8 | D44 | 1 | 1 | yes | characteristic |
| 243 | C4×C8 | D44 | 1 | 1 | yes | characteristic |
| 244 | C4×C8 | C22×D11 | 1 | 1 | yes | characteristic |
| 245 | C4×C8 | C22×D11 | 1 | 1 | yes | characteristic |
| 246 | C2×C11 | — | 4 | 1 | no | — |
| 247 | C2×C11 | #3037 | 1 | 1 | yes | characteristic |
| 248 | C2×C11 | #3058 | 1 | 1 | yes | characteristic |
| 249 | C2×C11 | #3067 | 1 | 1 | yes | characteristic |
| 250 | D11 | — | 16 | 2 | no | — |
| 251 | #41 | — | 88 | 4 | no | — |
| 252 | C2×Q8 | — | 11 | 2 | no | — |
| 253 | C2×Q8 | — | 22 | 1 | no | — |
| 254 | C2×Q8 | — | 22 | 2 | no | — |
| 255 | C2×D4 | — | 22 | 2 | no | — |
| 256 | C2×D4 | — | 22 | 2 | no | — |
| 257 | C2×D4 | — | 22 | 2 | no | — |
| 258 | C2×D4 | — | 44 | 2 | no | — |
| 259 | C22×C4 | — | 44 | 2 | no | — |
| 260 | C22×C4 | C2×D44 | 1 | 1 | yes | characteristic |
| 261 | C22×C4 | D4×D11 | 1 | 1 | yes | characteristic |
| 262 | C22×C4 | #4343 | 1 | 1 | yes | characteristic |
| 263 | Q16 | — | 88 | 4 | no | — |
| 264 | SD16 | — | 88 | 4 | no | — |
| 265 | D8 | — | 44 | 2 | no | — |
| 266 | D8 | — | 44 | 2 | no | — |
| 267 | M16 | — | 44 | 2 | no | — |
| 268 | C2×C8 | — | 2 | 2 | no | — |
| 269 | C2×C8 | — | 2 | 4 | no | — |
| 270 | C2×C8 | — | 4 | 1 | no | — |
| 271 | C2×C8 | — | 22 | 2 | no | — |
| 272 | C2×C8 | C2×D44 | 1 | 1 | yes | characteristic |
| 273 | C2×C8 | C2×D44 | 1 | 1 | yes | characteristic |
| 274 | C2×C8 | C2×D44 | 1 | 1 | yes | characteristic |
| 275 | C2×C8 | C2×D44 | 1 | 1 | yes | characteristic |
| 276 | C4⋊C4 | — | 11 | 2 | no | — |
| 277 | C4⋊C4 | — | 22 | 1 | no | — |
| 278 | C4⋊C4 | — | 22 | 1 | no | — |
| 279 | C4⋊C4 | — | 22 | 2 | no | — |
| 280 | C4⋊C4 | — | 22 | 1 | no | — |
| 281 | C4⋊C4 | — | 22 | 2 | no | — |
| 282 | C4⋊C4 | — | 22 | 2 | no | — |
| 283 | C4⋊C4 | — | 22 | 2 | no | — |
| 284 | C22⋊C4 | — | 22 | 2 | no | — |
| 285 | C22⋊C4 | — | 44 | 2 | no | — |
| 286 | C22⋊C4 | — | 44 | 2 | no | — |
| 287 | C42 | — | 22 | 2 | no | — |
| 288 | C42 | C2×D44 | 1 | 1 | yes | characteristic |
| 289 | C42 | D4×D11 | 1 | 1 | yes | characteristic |
| 290 | C42 | #4343 | 1 | 1 | yes | characteristic |
| 291 | C42 | C23×D11 | 1 | 1 | yes | characteristic |
| 292 | C11 | #19347 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 293 | C23 | — | 44 | 2 | no | — |
| 294 | C23 | #66948 | 1 | 1 | yes | characteristic |
| 295 | Q8 | — | 22 | 4 | no | — |
| 296 | Q8 | — | 44 | 2 | no | — |
| 297 | Q8 | — | 44 | 4 | no | — |
| 298 | D4 | — | 44 | 2 | no | — |
| 299 | D4 | — | 44 | 2 | no | — |
| 300 | D4 | — | 44 | 4 | no | — |
| 301 | D4 | — | 88 | 2 | no | — |
| 302 | D4 | — | 88 | 4 | no | — |
| 303 | C2×C4 | — | 2 | 1 | no | — |
| 304 | C2×C4 | — | 2 | 1 | no | — |
| 305 | C2×C4 | — | 2 | 2 | no | — |
| 306 | C2×C4 | — | 4 | 1 | no | — |
| 307 | C2×C4 | — | 22 | 2 | no | — |
| 308 | C2×C4 | — | 22 | 2 | no | — |
| 309 | C2×C4 | — | 44 | 2 | no | — |
| 310 | C2×C4 | — | 88 | 4 | no | — |
| 311 | C2×C4 | #66948 | 1 | 1 | yes | characteristic |
| 312 | C2×C4 | #66948 | 1 | 1 | yes | characteristic |
| 313 | C2×C4 | #66948 | 1 | 1 | yes | characteristic |
| 314 | C2×C4 | C22×D44 | 1 | 1 | yes | characteristic |
| 315 | C2×C4 | C2×D4×D11 | 1 | 1 | yes | characteristic |
| 316 | C2×C4 | C2×#4343 | 1 | 1 | yes | characteristic |
| 317 | C8 | — | 2 | 1 | no | — |
| 318 | C8 | — | 2 | 1 | no | — |
| 319 | C8 | — | 2 | 1 | no | — |
| 320 | C8 | — | 4 | 4 | no | — |
| 321 | C8 | — | 44 | 2 | no | — |
| 322 | C8 | #66962 | 1 | 2 | yes | — |
| 323 | C22 | — | 2 | 1 | no | — |
| 324 | C22 | — | 2 | 1 | no | — |
| 325 | C22 | — | 2 | 1 | no | — |
| 326 | C22 | — | 88 | 2 | no | — |
| 327 | C22 | — | 88 | 2 | no | — |
| 328 | C22 | — | 88 | 2 | no | — |
| 329 | C22 | C2×#66948 | 1 | 1 | yes | characteristic |
| 330 | C4 | — | 2 | 1 | no | — |
| 331 | C4 | — | 2 | 1 | no | — |
| 332 | C4 | — | 2 | 1 | no | — |
| 333 | C4 | — | 2 | 1 | no | — |
| 334 | C4 | — | 44 | 2 | no | — |
| 335 | C4 | — | 44 | 2 | no | — |
| 336 | C4 | — | 88 | 2 | no | — |
| 337 | C4 | C2×#66962 | 1 | 1 | yes | characteristic |
| 338 | C4 | #10623279 | 1 | 1 | yes | characteristic |
| 339 | C4 | #10623300 | 1 | 2 | yes | — |
| 340 | C2 | — | 4 | 1 | no | — |
| 341 | C2 | — | 176 | 2 | no | — |
| 342 | C2 | #13078090 | 1 | 1 | yes | characteristic |
| 343 | C2 | #13078265 | 1 | 1 | yes | characteristic |
| 344 | C2 | #13078337 | 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