← #14724615
Subgroups — #14724615
Order 2816.
624 conjugacy classes of subgroups.
The subgroup lattice has 286 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #13079195 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #13077694 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #13067479 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #13067444 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #13067084 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #13066908 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C11×#1568 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #10623008 | C22 | 1 | 2 | yes | — |
| 9 | C11×#432 | C22 | 1 | 2 | yes | — |
| 10 | C2×C4×C8×C11 | C22 | 1 | 1 | yes | characteristic |
| 11 | #10622728 | C4 | 1 | 2 | yes | — |
| 12 | #10622728 | C4 | 1 | 2 | yes | — |
| 13 | #10622538 | C22 | 1 | 1 | yes | characteristic |
| 14 | #10622538 | C22 | 1 | 1 | yes | characteristic |
| 15 | #10622451 | C22 | 1 | 4 | yes | — |
| 16 | #10622447 | C22 | 1 | 4 | yes | — |
| 17 | #10622340 | — | 2 | 4 | no | — |
| 18 | #10622319 | — | 2 | 4 | no | — |
| 19 | #10622308 | C4 | 1 | 1 | yes | characteristic |
| 20 | #10622307 | C4 | 1 | 2 | yes | — |
| 21 | C4×D88 | C22 | 1 | 2 | yes | — |
| 22 | C4×D88 | C22 | 1 | 2 | yes | — |
| 23 | #10622295 | C4 | 1 | 1 | yes | characteristic |
| 24 | C11×#335 | C22 | 1 | 2 | yes | — |
| 25 | C11×#334 | C22 | 1 | 2 | yes | — |
| 26 | #10622121 | C22 | 1 | 8 | yes | — |
| 27 | #10622092 | C22 | 1 | 2 | yes | — |
| 28 | #10622092 | C22 | 1 | 2 | yes | — |
| 29 | C2×#4339 | — | 2 | 2 | no | — |
| 30 | C22×C8×C11 | C2×C4 | 1 | 1 | yes | characteristic |
| 31 | C22×C8×C11 | C2×C4 | 1 | 1 | yes | characteristic |
| 32 | C2×C42×C11 | C23 | 1 | 1 | yes | characteristic |
| 33 | #66983 | — | 2 | 2 | no | — |
| 34 | #66983 | C2×C4 | 1 | 4 | yes | — |
| 35 | C2×D88 | C2×C4 | 1 | 2 | yes | — |
| 36 | C2×D88 | C2×C4 | 1 | 2 | yes | — |
| 37 | C2×#4313 | — | 2 | 4 | no | — |
| 38 | C2×C8×D11 | — | 2 | 4 | no | — |
| 39 | #66928 | — | 2 | 2 | no | — |
| 40 | #66927 | C2×C4 | 1 | 2 | yes | — |
| 41 | C4×D44 | — | 2 | 2 | no | — |
| 42 | C4×D44 | C23 | 1 | 4 | yes | — |
| 43 | #66922 | C2×C4 | 1 | 2 | yes | — |
| 44 | C11×C4⋊C8 | C23 | 1 | 4 | yes | — |
| 45 | C11×C22⋊C8 | — | 2 | 2 | no | — |
| 46 | C11×#97 | — | 2 | 2 | no | — |
| 47 | C4×C8×C11 | C2×C4 | 1 | 1 | yes | characteristic |
| 48 | C4×C8×C11 | C2×C4 | 1 | 1 | yes | characteristic |
| 49 | C4×C8×C11 | C23 | 1 | 1 | yes | characteristic |
| 50 | C4×C8×C11 | C23 | 1 | 1 | yes | characteristic |
| 51 | C22⋊(C11⋊C8) | — | 2 | 1 | no | — |
| 52 | C22⋊(C11⋊C8) | D4 | 1 | 2 | yes | — |
| 53 | #66885 | C2×C4 | 1 | 4 | yes | — |
| 54 | #66885 | C2×C4 | 1 | 4 | yes | — |
| 55 | (C2×D11)⋊C8 | — | 2 | 4 | no | — |
| 56 | (C2×D11)⋊C8 | — | 2 | 4 | no | — |
| 57 | #66882 | C2×C4 | 1 | 2 | yes | — |
| 58 | #66882 | C2×C4 | 1 | 2 | yes | — |
| 59 | C4⋊(C11⋊C8) | — | 2 | 1 | no | — |
| 60 | C4⋊(C11⋊C8) | D4 | 1 | 2 | yes | — |
| 61 | C4×C11⋊C8 | C23 | 1 | 2 | yes | — |
| 62 | C4×C11⋊C8 | C23 | 1 | 2 | yes | — |
| 63 | #17989 | — | 11 | 1 | no | maximal, Sylow |
| 64 | C22×C4×C11 | C22×C4 | 1 | 1 | yes | characteristic |
| 65 | C22×C4×C11 | C2×D4 | 1 | 1 | yes | characteristic |
| 66 | C22×C4×C11 | #41 | 1 | 1 | yes | characteristic |
| 67 | C2×C22⋊D11 | — | 2 | 4 | no | — |
| 68 | #4339 | — | 8 | 4 | no | — |
| 69 | C2×D44 | — | 2 | 2 | no | — |
| 70 | C2×D44 | — | 2 | 2 | no | — |
| 71 | C2×D44 | C22×C4 | 1 | 4 | yes | — |
| 72 | C2×C4×D11 | — | 2 | 4 | no | — |
| 73 | C2×Dic22 | — | 2 | 2 | no | — |
| 74 | C2×C8×C11 | — | 2 | 4 | no | — |
| 75 | C2×C8×C11 | — | 4 | 1 | no | — |
| 76 | C2×C8×C11 | — | 4 | 1 | no | — |
| 77 | C2×C8×C11 | C22×C4 | 1 | 1 | yes | characteristic |
| 78 | C2×C8×C11 | C22×C4 | 1 | 1 | yes | characteristic |
| 79 | C2×C8×C11 | C22×C4 | 1 | 1 | yes | characteristic |
| 80 | C2×C8×C11 | C22×C4 | 1 | 1 | yes | characteristic |
| 81 | C42×C11 | C22×C4 | 1 | 1 | yes | characteristic |
| 82 | C42×C11 | C2×D4 | 1 | 1 | yes | characteristic |
| 83 | C42×C11 | #41 | 1 | 1 | yes | characteristic |
| 84 | C42×C11 | C24 | 1 | 1 | yes | characteristic |
| 85 | (C2×D11)⋊C4 | — | 2 | 4 | no | — |
| 86 | (C2×D11)⋊C4 | — | 2 | 4 | no | — |
| 87 | C4⋊Dic11 | — | 2 | 2 | no | — |
| 88 | C4⋊Dic11 | C22×C4 | 1 | 4 | yes | — |
| 89 | C2×C11⋊C8 | — | 2 | 2 | no | — |
| 90 | C2×C11⋊C8 | C2×D4 | 1 | 4 | yes | — |
| 91 | D88 | — | 4 | 2 | no | — |
| 92 | D88 | — | 4 | 2 | no | — |
| 93 | #4313 | — | 8 | 4 | no | — |
| 94 | C8×D11 | — | 8 | 4 | no | — |
| 95 | #3169 | — | 11 | 1 | no | — |
| 96 | #2981 | — | 11 | 2 | no | — |
| 97 | #1586 | — | 11 | 4 | no | — |
| 98 | #1581 | — | 11 | 4 | no | — |
| 99 | #1568 | D11 | 1 | 1 | yes | characteristic, complemented |
| 100 | #1496 | — | 11 | 2 | no | — |
| 101 | #1452 | — | 11 | 1 | no | — |
| 102 | C23×C11 | C4×D4 | 1 | 1 | yes | characteristic |
| 103 | C22×D11 | — | 2 | 4 | no | — |
| 104 | C2×C4×C11 | — | 2 | 1 | no | — |
| 105 | C2×C4×C11 | — | 2 | 1 | no | — |
| 106 | C2×C4×C11 | — | 2 | 2 | no | — |
| 107 | C2×C4×C11 | — | 4 | 1 | no | — |
| 108 | C2×C4×C11 | C4×D4 | 1 | 1 | yes | characteristic |
| 109 | C2×C4×C11 | C4×D4 | 1 | 1 | yes | characteristic |
| 110 | C2×C4×C11 | C4×D4 | 1 | 1 | yes | characteristic |
| 111 | C2×C4×C11 | C23×C4 | 1 | 1 | yes | characteristic |
| 112 | C2×C4×C11 | C22×D4 | 1 | 1 | yes | characteristic |
| 113 | C2×C4×C11 | C2×#41 | 1 | 1 | yes | characteristic |
| 114 | C22⋊D11 | — | 8 | 4 | no | — |
| 115 | C2×Dic11 | — | 2 | 4 | no | — |
| 116 | D44 | — | 2 | 4 | no | — |
| 117 | D44 | — | 2 | 4 | no | — |
| 118 | D44 | — | 8 | 2 | no | — |
| 119 | D44 | — | 8 | 2 | no | — |
| 120 | C4×D11 | — | 4 | 4 | no | — |
| 121 | C4×D11 | — | 4 | 4 | no | — |
| 122 | Dic22 | — | 8 | 2 | no | — |
| 123 | C8×C11 | — | 2 | 1 | no | — |
| 124 | C8×C11 | — | 2 | 1 | no | — |
| 125 | C8×C11 | — | 2 | 1 | no | — |
| 126 | C8×C11 | — | 2 | 1 | no | — |
| 127 | C8×C11 | — | 4 | 4 | no | — |
| 128 | C11⋊C8 | — | 2 | 4 | no | — |
| 129 | C11⋊C8 | — | 4 | 2 | no | — |
| 130 | #532 | — | 11 | 2 | no | — |
| 131 | #500 | — | 11 | 1 | no | — |
| 132 | #493 | — | 11 | 1 | no | — |
| 133 | #486 | — | 11 | 2 | no | — |
| 134 | #466 | — | 11 | 2 | no | — |
| 135 | #466 | — | 11 | 2 | no | — |
| 136 | C4×D8 | — | 11 | 2 | no | — |
| 137 | C4×D8 | — | 11 | 2 | no | — |
| 138 | #436 | — | 11 | 4 | no | — |
| 139 | #435 | — | 22 | 4 | no | — |
| 140 | C8×D4 | — | 11 | 4 | no | — |
| 141 | #432 | C2×D11 | 1 | 2 | yes | — |
| 142 | #431 | — | 11 | 1 | no | — |
| 143 | #431 | — | 11 | 1 | no | — |
| 144 | #408 | — | 22 | 4 | no | — |
| 145 | C2×C4×C8 | C2×D11 | 1 | 1 | yes | characteristic |
| 146 | #335 | C2×D11 | 1 | 2 | yes | — |
| 147 | #334 | C2×D11 | 1 | 2 | yes | — |
| 148 | D4⋊C8 | — | 11 | 8 | no | — |
| 149 | #322 | — | 11 | 2 | no | — |
| 150 | #322 | — | 11 | 2 | no | — |
| 151 | C22×C11 | — | 2 | 1 | no | — |
| 152 | C22×C11 | — | 2 | 1 | no | — |
| 153 | C22×C11 | — | 2 | 1 | no | — |
| 154 | C22×C11 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 155 | C2×D11 | — | 4 | 4 | no | — |
| 156 | C2×D11 | — | 4 | 4 | no | — |
| 157 | C2×D11 | — | 4 | 4 | no | — |
| 158 | C4×C11 | — | 2 | 1 | no | — |
| 159 | C4×C11 | — | 2 | 1 | no | — |
| 160 | C4×C11 | — | 2 | 1 | no | — |
| 161 | C4×C11 | — | 2 | 1 | no | — |
| 162 | C4×C11 | #568 | 1 | 1 | yes | characteristic |
| 163 | C4×C11 | #568 | 1 | 1 | yes | characteristic |
| 164 | C4×C11 | #576 | 1 | 2 | yes | — |
| 165 | Dic11 | — | 4 | 4 | no | — |
| 166 | C2×#41 | — | 22 | 2 | no | — |
| 167 | C2×D8 | — | 11 | 2 | no | — |
| 168 | C2×D8 | — | 11 | 2 | no | — |
| 169 | C2×M16 | — | 22 | 4 | no | — |
| 170 | C22×C8 | — | 22 | 4 | no | — |
| 171 | C22×C8 | C4×D11 | 1 | 1 | yes | characteristic |
| 172 | C22×C8 | C4×D11 | 1 | 1 | yes | characteristic |
| 173 | C4⋊Q8 | — | 11 | 2 | no | — |
| 174 | #127 | — | 11 | 2 | no | — |
| 175 | #124 | — | 22 | 2 | no | — |
| 176 | #121 | — | 11 | 4 | no | — |
| 177 | #121 | — | 22 | 2 | no | — |
| 178 | C4×D4 | — | 11 | 4 | no | — |
| 179 | C4×D4 | — | 22 | 2 | no | — |
| 180 | C2×C42 | C22×D11 | 1 | 1 | yes | characteristic |
| 181 | #107 | — | 11 | 2 | no | — |
| 182 | #107 | — | 11 | 2 | no | — |
| 183 | C4⋊C8 | — | 11 | 2 | no | — |
| 184 | C4⋊C8 | — | 22 | 1 | no | — |
| 185 | C4⋊C8 | C22×D11 | 1 | 4 | yes | — |
| 186 | #102 | — | 11 | 4 | no | — |
| 187 | #102 | — | 11 | 4 | no | — |
| 188 | C22⋊C8 | — | 2 | 2 | no | — |
| 189 | C22⋊C8 | — | 11 | 2 | no | — |
| 190 | C22⋊C8 | — | 22 | 4 | no | — |
| 191 | C22⋊C8 | — | 22 | 4 | no | — |
| 192 | C22⋊C8 | — | 22 | 1 | no | — |
| 193 | #97 | — | 2 | 2 | no | — |
| 194 | C4×C8 | — | 11 | 2 | no | — |
| 195 | C4×C8 | — | 11 | 2 | no | — |
| 196 | C4×C8 | C4×D11 | 1 | 1 | yes | characteristic |
| 197 | C4×C8 | C4×D11 | 1 | 1 | yes | characteristic |
| 198 | C4×C8 | C22×D11 | 1 | 1 | yes | characteristic |
| 199 | C4×C8 | C22×D11 | 1 | 1 | yes | characteristic |
| 200 | C2×C11 | — | 4 | 1 | no | — |
| 201 | C2×C11 | #2932 | 1 | 1 | yes | characteristic |
| 202 | C2×C11 | #2948 | 1 | 1 | yes | characteristic |
| 203 | C2×C11 | #2957 | 1 | 1 | yes | characteristic |
| 204 | D11 | — | 8 | 4 | no | — |
| 205 | #41 | — | 88 | 4 | no | — |
| 206 | C2×Q8 | — | 22 | 2 | no | — |
| 207 | C2×D4 | — | 11 | 4 | no | — |
| 208 | C2×D4 | — | 22 | 4 | no | — |
| 209 | C2×D4 | — | 22 | 2 | no | — |
| 210 | C2×D4 | — | 22 | 2 | no | — |
| 211 | C22×C4 | — | 22 | 4 | no | — |
| 212 | C22×C4 | C2×C4×D11 | 1 | 1 | yes | characteristic |
| 213 | C22×C4 | D4×D11 | 1 | 1 | yes | characteristic |
| 214 | C22×C4 | #4343 | 1 | 1 | yes | characteristic |
| 215 | D8 | — | 44 | 2 | no | — |
| 216 | D8 | — | 44 | 2 | no | — |
| 217 | M16 | — | 88 | 4 | no | — |
| 218 | C2×C8 | — | 2 | 4 | no | — |
| 219 | C2×C8 | — | 4 | 1 | no | — |
| 220 | C2×C8 | — | 4 | 1 | no | — |
| 221 | C2×C8 | — | 11 | 4 | no | — |
| 222 | C2×C8 | — | 22 | 2 | no | — |
| 223 | C2×C8 | — | 88 | 4 | no | — |
| 224 | C2×C8 | C2×C4×D11 | 1 | 1 | yes | characteristic |
| 225 | C2×C8 | C2×C4×D11 | 1 | 1 | yes | characteristic |
| 226 | C2×C8 | C2×C4×D11 | 1 | 1 | yes | characteristic |
| 227 | C2×C8 | C2×C4×D11 | 1 | 1 | yes | characteristic |
| 228 | C4⋊C4 | — | 11 | 4 | no | — |
| 229 | C4⋊C4 | — | 22 | 2 | no | — |
| 230 | C22⋊C4 | — | 22 | 4 | no | — |
| 231 | C22⋊C4 | — | 22 | 4 | no | — |
| 232 | C42 | C2×C4×D11 | 1 | 1 | yes | characteristic |
| 233 | C42 | D4×D11 | 1 | 1 | yes | characteristic |
| 234 | C42 | #4343 | 1 | 1 | yes | characteristic |
| 235 | C42 | C23×D11 | 1 | 1 | yes | characteristic |
| 236 | C11 | #17989 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 237 | C23 | — | 22 | 4 | no | — |
| 238 | C23 | #66946 | 1 | 1 | yes | characteristic |
| 239 | Q8 | — | 88 | 2 | no | — |
| 240 | D4 | — | 22 | 4 | no | — |
| 241 | D4 | — | 22 | 4 | no | — |
| 242 | D4 | — | 88 | 2 | no | — |
| 243 | D4 | — | 88 | 2 | no | — |
| 244 | D4 | — | 88 | 4 | no | — |
| 245 | C2×C4 | — | 2 | 1 | no | — |
| 246 | C2×C4 | — | 2 | 1 | no | — |
| 247 | C2×C4 | — | 2 | 2 | no | — |
| 248 | C2×C4 | — | 4 | 1 | no | — |
| 249 | C2×C4 | — | 22 | 4 | no | — |
| 250 | C2×C4 | — | 44 | 4 | no | — |
| 251 | C2×C4 | — | 44 | 4 | no | — |
| 252 | C2×C4 | #66946 | 1 | 1 | yes | characteristic |
| 253 | C2×C4 | #66946 | 1 | 1 | yes | characteristic |
| 254 | C2×C4 | #66946 | 1 | 1 | yes | characteristic |
| 255 | C2×C4 | C22×C4×D11 | 1 | 1 | yes | characteristic |
| 256 | C2×C4 | C2×D4×D11 | 1 | 1 | yes | characteristic |
| 257 | C2×C4 | C2×#4343 | 1 | 1 | yes | characteristic |
| 258 | C8 | — | 2 | 1 | no | — |
| 259 | C8 | — | 2 | 1 | no | — |
| 260 | C8 | — | 2 | 1 | no | — |
| 261 | C8 | — | 2 | 1 | no | — |
| 262 | C8 | — | 4 | 4 | no | — |
| 263 | C8 | — | 22 | 4 | no | — |
| 264 | C8 | — | 44 | 2 | no | — |
| 265 | C22 | — | 2 | 1 | no | — |
| 266 | C22 | — | 2 | 1 | no | — |
| 267 | C22 | — | 2 | 1 | no | — |
| 268 | C22 | — | 44 | 4 | no | — |
| 269 | C22 | — | 44 | 4 | no | — |
| 270 | C22 | — | 44 | 4 | no | — |
| 271 | C22 | C2×#66946 | 1 | 1 | yes | characteristic |
| 272 | C4 | — | 2 | 1 | no | — |
| 273 | C4 | — | 2 | 1 | no | — |
| 274 | C4 | — | 2 | 1 | no | — |
| 275 | C4 | — | 2 | 1 | no | — |
| 276 | C4 | — | 44 | 4 | no | — |
| 277 | C4 | #10623276 | 1 | 1 | yes | characteristic |
| 278 | C4 | #10623276 | 1 | 1 | yes | characteristic |
| 279 | C4 | #10623300 | 1 | 2 | yes | — |
| 280 | C2 | — | 4 | 1 | no | — |
| 281 | C2 | — | 88 | 4 | no | — |
| 282 | C2 | #13077333 | 1 | 1 | yes | characteristic |
| 283 | C2 | #13077467 | 1 | 1 | yes | characteristic |
| 284 | C2 | #13077532 | 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