← #14746103
Subgroups — #14746103
Order 2816.
590 conjugacy classes of subgroups.
The subgroup lattice has 334 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #13081667 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #13081314 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #13068208 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #13068089 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #13068060 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #13067860 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #13067677 | C2 | 1 | 2 | yes | maximal |
| 8 | #13067514 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | C8×C11×Q16 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #10623116 | C22 | 1 | 2 | yes | — |
| 11 | #10623098 | C22 | 1 | 2 | yes | — |
| 12 | C8×Q8×C11 | C22 | 1 | 2 | yes | — |
| 13 | C4×C11×Q16 | C22 | 1 | 1 | yes | characteristic |
| 14 | #10622803 | — | 2 | 2 | no | — |
| 15 | #10622644 | C22 | 1 | 2 | yes | — |
| 16 | #10622640 | C22 | 1 | 2 | yes | — |
| 17 | #10622502 | — | 2 | 2 | no | — |
| 18 | #10622464 | C22 | 1 | 2 | yes | — |
| 19 | #10622461 | C22 | 1 | 2 | yes | — |
| 20 | #10622460 | — | 2 | 2 | no | — |
| 21 | #10622458 | — | 2 | 2 | no | — |
| 22 | #10622431 | — | 2 | 2 | no | — |
| 23 | #10622411 | — | 2 | 2 | no | — |
| 24 | C4×Dic44 | C22 | 1 | 1 | yes | characteristic |
| 25 | #10622310 | — | 2 | 2 | no | — |
| 26 | #10622308 | C22 | 1 | 1 | yes | characteristic |
| 27 | #10622307 | C22 | 1 | 2 | yes | — |
| 28 | #10622306 | C22 | 1 | 2 | yes | — |
| 29 | C4×#4314 | — | 2 | 2 | no | — |
| 30 | #10622295 | C22 | 1 | 1 | yes | characteristic |
| 31 | #10622292 | C22 | 1 | 2 | yes | — |
| 32 | C11×#335 | C22 | 1 | 1 | yes | characteristic |
| 33 | C11×Q8⋊C8 | C22 | 1 | 2 | yes | — |
| 34 | C82×C11 | C22 | 1 | 1 | yes | characteristic |
| 35 | #10622124 | C22 | 1 | 2 | yes | — |
| 36 | #10622123 | C22 | 1 | 2 | yes | — |
| 37 | #10622096 | C22 | 1 | 1 | yes | characteristic |
| 38 | #10622094 | C22 | 1 | 2 | yes | — |
| 39 | C2×C11×Q16 | D4 | 1 | 1 | yes | characteristic |
| 40 | C4×Q8×C11 | C23 | 1 | 2 | yes | — |
| 41 | #67000 | — | 2 | 2 | no | — |
| 42 | #66997 | — | 2 | 2 | no | — |
| 43 | C2×#4326 | — | 2 | 2 | no | — |
| 44 | C2×#4325 | — | 2 | 2 | no | — |
| 45 | C2×Dic44 | D4 | 1 | 1 | yes | characteristic |
| 46 | C2×D88 | — | 4 | 1 | no | — |
| 47 | C2×#4314 | — | 2 | 2 | no | — |
| 48 | C2×#4314 | — | 2 | 2 | no | — |
| 49 | C2×#4314 | — | 2 | 2 | no | — |
| 50 | #66947 | — | 4 | 2 | no | — |
| 51 | #66946 | — | 2 | 2 | no | — |
| 52 | #66942 | — | 4 | 2 | no | — |
| 53 | #66940 | — | 2 | 2 | no | — |
| 54 | #66928 | — | 2 | 2 | no | — |
| 55 | #66927 | C23 | 1 | 2 | yes | — |
| 56 | C4×D44 | — | 2 | 2 | no | — |
| 57 | #66923 | — | 2 | 2 | no | — |
| 58 | #66922 | C23 | 1 | 2 | yes | — |
| 59 | C4×Dic22 | — | 2 | 2 | no | — |
| 60 | C4×Dic22 | C23 | 1 | 2 | yes | — |
| 61 | C11×#107 | D4 | 1 | 1 | yes | characteristic |
| 62 | C11×C4⋊C8 | — | 2 | 2 | no | — |
| 63 | C11×C4⋊C8 | C23 | 1 | 2 | yes | — |
| 64 | C11×#103 | D4 | 1 | 2 | yes | — |
| 65 | C4×C8×C11 | — | 2 | 2 | no | — |
| 66 | C4×C8×C11 | C23 | 1 | 1 | yes | characteristic |
| 67 | C4×C8×C11 | C23 | 1 | 1 | yes | characteristic |
| 68 | C4×C8×C11 | C23 | 1 | 1 | yes | characteristic |
| 69 | #66885 | — | 2 | 2 | no | — |
| 70 | #66885 | — | 2 | 2 | no | — |
| 71 | #66885 | — | 2 | 2 | no | — |
| 72 | #66882 | — | 4 | 1 | no | — |
| 73 | #66882 | D4 | 1 | 1 | yes | characteristic |
| 74 | #66881 | — | 2 | 2 | no | — |
| 75 | #66880 | — | 2 | 2 | no | — |
| 76 | #66880 | D4 | 1 | 2 | yes | — |
| 77 | #66879 | — | 2 | 2 | no | — |
| 78 | Dic11⋊C8 | — | 2 | 2 | no | — |
| 79 | #66874 | — | 2 | 2 | no | — |
| 80 | #66873 | — | 2 | 2 | no | — |
| 81 | C4⋊(C11⋊C8) | C23 | 1 | 2 | yes | — |
| 82 | #19965 | — | 11 | 1 | no | maximal, Sylow |
| 83 | C2×Q8×C11 | C2×D4 | 1 | 2 | yes | — |
| 84 | C2×D44 | — | 2 | 2 | no | — |
| 85 | C2×D44 | — | 2 | 2 | no | — |
| 86 | C2×D44 | — | 2 | 2 | no | — |
| 87 | C2×C4×D11 | — | 4 | 2 | no | — |
| 88 | C2×Dic22 | — | 2 | 2 | no | — |
| 89 | C2×Dic22 | C2×D4 | 1 | 2 | yes | — |
| 90 | C11×Q16 | — | 2 | 2 | no | — |
| 91 | C2×C8×C11 | — | 2 | 2 | no | — |
| 92 | C2×C8×C11 | — | 2 | 1 | no | — |
| 93 | C2×C8×C11 | C2×D4 | 1 | 1 | yes | characteristic |
| 94 | C2×C8×C11 | C2×D4 | 1 | 1 | yes | characteristic |
| 95 | C2×C8×C11 | C2×D4 | 1 | 1 | yes | characteristic |
| 96 | C2×C8×C11 | C2×D4 | 1 | 1 | yes | characteristic |
| 97 | C11×C4⋊C4 | — | 2 | 2 | no | — |
| 98 | C11×C4⋊C4 | C2×D4 | 1 | 2 | yes | — |
| 99 | C42×C11 | — | 2 | 2 | no | — |
| 100 | C42×C11 | C24 | 1 | 1 | yes | characteristic |
| 101 | #4326 | — | 8 | 2 | no | — |
| 102 | #4325 | — | 8 | 2 | no | — |
| 103 | (C2×D11)⋊C4 | — | 4 | 2 | no | — |
| 104 | (C2×D11)⋊C4 | — | 4 | 2 | no | — |
| 105 | (C2×D11)⋊C4 | — | 4 | 2 | no | — |
| 106 | C4⋊Dic11 | — | 2 | 2 | no | — |
| 107 | C4⋊Dic11 | — | 2 | 2 | no | — |
| 108 | C4⋊Dic11 | C2×D4 | 1 | 2 | yes | — |
| 109 | Dic11⋊C4 | — | 2 | 2 | no | — |
| 110 | Dic11⋊C4 | — | 4 | 2 | no | — |
| 111 | Dic11⋊C4 | — | 4 | 2 | no | — |
| 112 | Dic11⋊C4 | — | 4 | 2 | no | — |
| 113 | C4×Dic11 | — | 2 | 2 | no | — |
| 114 | C4×Dic11 | — | 4 | 2 | no | — |
| 115 | C2×C11⋊C8 | — | 2 | 2 | no | — |
| 116 | Dic44 | — | 4 | 1 | no | — |
| 117 | D88 | — | 8 | 2 | no | — |
| 118 | #4314 | — | 4 | 4 | no | — |
| 119 | #4314 | — | 4 | 4 | no | — |
| 120 | #4314 | — | 8 | 2 | no | — |
| 121 | #3400 | — | 11 | 2 | no | — |
| 122 | #3365 | — | 11 | 2 | no | — |
| 123 | #1706 | — | 11 | 1 | no | — |
| 124 | #1686 | — | 11 | 2 | no | — |
| 125 | #1682 | — | 11 | 2 | no | — |
| 126 | #1648 | — | 11 | 2 | no | — |
| 127 | #1620 | — | 11 | 2 | no | — |
| 128 | #1591 | — | 11 | 1 | no | — |
| 129 | C8×Q16 | D11 | 1 | 1 | yes | characteristic, complemented |
| 130 | C22×D11 | — | 4 | 2 | no | — |
| 131 | Q8×C11 | — | 2 | 2 | no | — |
| 132 | Q8×C11 | — | 2 | 2 | no | — |
| 133 | C2×C4×C11 | — | 2 | 2 | no | — |
| 134 | C2×C4×C11 | — | 2 | 2 | no | — |
| 135 | C2×C4×C11 | C22×D4 | 1 | 1 | yes | characteristic |
| 136 | C2×C4×C11 | C22×D4 | 1 | 1 | yes | characteristic |
| 137 | C2×C4×C11 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 138 | C2×Dic11 | — | 2 | 2 | no | — |
| 139 | C2×Dic11 | — | 2 | 2 | no | — |
| 140 | C2×Dic11 | — | 4 | 2 | no | — |
| 141 | D44 | — | 4 | 2 | no | — |
| 142 | D44 | — | 4 | 2 | no | — |
| 143 | D44 | — | 4 | 2 | no | — |
| 144 | D44 | — | 4 | 2 | no | — |
| 145 | D44 | — | 8 | 2 | no | — |
| 146 | C4×D11 | — | 16 | 2 | no | — |
| 147 | Dic22 | — | 2 | 2 | no | — |
| 148 | Dic22 | — | 2 | 2 | no | — |
| 149 | Dic22 | — | 4 | 2 | no | — |
| 150 | Dic22 | — | 4 | 2 | no | — |
| 151 | C8×C11 | — | 2 | 2 | no | — |
| 152 | C8×C11 | — | 2 | 1 | no | — |
| 153 | C8×C11 | — | 2 | 1 | no | — |
| 154 | C8×C11 | — | 2 | 1 | no | — |
| 155 | C8×C11 | — | 4 | 2 | no | — |
| 156 | C8×C11 | #135 | 1 | 2 | yes | — |
| 157 | C11⋊C8 | — | 4 | 2 | no | — |
| 158 | #559 | — | 11 | 2 | no | — |
| 159 | #557 | — | 11 | 2 | no | — |
| 160 | #500 | — | 11 | 1 | no | — |
| 161 | #497 | — | 22 | 2 | no | — |
| 162 | #493 | — | 11 | 1 | no | — |
| 163 | #492 | — | 11 | 2 | no | — |
| 164 | #488 | — | 22 | 2 | no | — |
| 165 | #486 | — | 11 | 2 | no | — |
| 166 | #478 | — | 22 | 2 | no | — |
| 167 | #475 | — | 11 | 2 | no | — |
| 168 | #464 | — | 22 | 2 | no | — |
| 169 | #464 | — | 22 | 2 | no | — |
| 170 | #462 | — | 11 | 2 | no | — |
| 171 | #461 | — | 22 | 2 | no | — |
| 172 | #460 | — | 11 | 2 | no | — |
| 173 | #460 | — | 11 | 2 | no | — |
| 174 | #446 | — | 11 | 2 | no | — |
| 175 | C8×Q8 | C2×D11 | 1 | 2 | yes | — |
| 176 | #440 | — | 22 | 2 | no | — |
| 177 | C4×Q16 | — | 11 | 1 | no | — |
| 178 | C4×Q16 | C2×D11 | 1 | 1 | yes | characteristic |
| 179 | C4×SD16 | — | 22 | 2 | no | — |
| 180 | #335 | — | 11 | 1 | no | — |
| 181 | #335 | C2×D11 | 1 | 1 | yes | characteristic |
| 182 | #332 | — | 11 | 2 | no | — |
| 183 | #331 | — | 11 | 2 | no | — |
| 184 | Q8⋊C8 | — | 11 | 2 | no | — |
| 185 | Q8⋊C8 | C2×D11 | 1 | 2 | yes | — |
| 186 | C82 | C2×D11 | 1 | 1 | yes | characteristic |
| 187 | C22×C11 | D42 | 1 | 1 | yes | characteristic |
| 188 | C2×D11 | — | 8 | 2 | no | — |
| 189 | C2×D11 | — | 8 | 2 | no | — |
| 190 | C2×D11 | — | 8 | 2 | no | — |
| 191 | C4×C11 | — | 2 | 1 | no | — |
| 192 | C4×C11 | — | 4 | 2 | no | — |
| 193 | C4×C11 | — | 4 | 2 | no | — |
| 194 | C4×C11 | C2×#135 | 1 | 1 | yes | characteristic |
| 195 | C4×C11 | #575 | 1 | 1 | yes | characteristic |
| 196 | C4×C11 | #576 | 1 | 1 | yes | characteristic |
| 197 | C4×C11 | #578 | 1 | 1 | yes | characteristic |
| 198 | Dic11 | — | 4 | 2 | no | — |
| 199 | Dic11 | — | 4 | 2 | no | — |
| 200 | Dic11 | — | 8 | 2 | no | — |
| 201 | C2×Q16 | — | 11 | 1 | no | — |
| 202 | C2×Q16 | — | 22 | 2 | no | — |
| 203 | C2×Q16 | D44 | 1 | 1 | yes | characteristic |
| 204 | C2×SD16 | — | 22 | 2 | no | — |
| 205 | C2×SD16 | — | 22 | 2 | no | — |
| 206 | C2×SD16 | — | 22 | 2 | no | — |
| 207 | C2×SD16 | — | 22 | 2 | no | — |
| 208 | C2×D8 | — | 44 | 1 | no | — |
| 209 | C4⋊Q8 | — | 11 | 2 | no | — |
| 210 | C4⋊Q8 | — | 22 | 2 | no | — |
| 211 | #127 | — | 11 | 2 | no | — |
| 212 | #125 | — | 22 | 2 | no | — |
| 213 | #125 | — | 44 | 2 | no | — |
| 214 | #124 | — | 22 | 2 | no | — |
| 215 | #124 | — | 22 | 2 | no | — |
| 216 | #123 | — | 44 | 2 | no | — |
| 217 | C4×Q8 | — | 11 | 2 | no | — |
| 218 | C4×Q8 | — | 22 | 2 | no | — |
| 219 | C4×Q8 | — | 22 | 2 | no | — |
| 220 | C4×Q8 | C22×D11 | 1 | 2 | yes | — |
| 221 | C4×D4 | — | 22 | 2 | no | — |
| 222 | C4×D4 | — | 22 | 2 | no | — |
| 223 | #107 | — | 11 | 1 | no | — |
| 224 | #107 | — | 44 | 1 | no | — |
| 225 | #107 | D44 | 1 | 1 | yes | characteristic |
| 226 | #106 | — | 22 | 2 | no | — |
| 227 | C4⋊C8 | — | 2 | 2 | no | — |
| 228 | C4⋊C8 | — | 11 | 2 | no | — |
| 229 | C4⋊C8 | — | 22 | 2 | no | — |
| 230 | C4⋊C8 | C22×D11 | 1 | 2 | yes | — |
| 231 | #103 | — | 11 | 2 | no | — |
| 232 | #103 | — | 22 | 2 | no | — |
| 233 | #103 | — | 22 | 2 | no | — |
| 234 | #103 | D44 | 1 | 2 | yes | — |
| 235 | #102 | — | 22 | 2 | no | — |
| 236 | #102 | — | 22 | 2 | no | — |
| 237 | #102 | — | 22 | 2 | no | — |
| 238 | #102 | — | 22 | 2 | no | — |
| 239 | #97 | — | 22 | 2 | no | — |
| 240 | C4×C8 | — | 2 | 2 | no | — |
| 241 | C4×C8 | C22×D11 | 1 | 1 | yes | characteristic |
| 242 | C4×C8 | C22×D11 | 1 | 1 | yes | characteristic |
| 243 | C4×C8 | C22×D11 | 1 | 1 | yes | characteristic |
| 244 | C2×C11 | #3277 | 1 | 1 | yes | characteristic |
| 245 | C2×C11 | #3287 | 1 | 1 | yes | characteristic |
| 246 | C2×C11 | #3291 | 1 | 1 | yes | characteristic |
| 247 | D11 | — | 16 | 2 | no | — |
| 248 | C2×Q8 | — | 11 | 2 | no | — |
| 249 | C2×Q8 | — | 22 | 2 | no | — |
| 250 | C2×Q8 | C2×D44 | 1 | 2 | yes | — |
| 251 | C2×D4 | — | 22 | 2 | no | — |
| 252 | C2×D4 | — | 22 | 2 | no | — |
| 253 | C2×D4 | — | 22 | 2 | no | — |
| 254 | C22×C4 | — | 44 | 2 | no | — |
| 255 | Q16 | — | 2 | 2 | no | — |
| 256 | Q16 | — | 44 | 1 | no | — |
| 257 | Q16 | — | 88 | 2 | no | — |
| 258 | SD16 | — | 44 | 4 | no | — |
| 259 | SD16 | — | 44 | 4 | no | — |
| 260 | SD16 | — | 88 | 2 | no | — |
| 261 | SD16 | — | 88 | 2 | no | — |
| 262 | D8 | — | 88 | 2 | no | — |
| 263 | C2×C8 | — | 2 | 1 | no | — |
| 264 | C2×C8 | — | 2 | 2 | no | — |
| 265 | C2×C8 | — | 22 | 2 | no | — |
| 266 | C2×C8 | C2×D44 | 1 | 1 | yes | characteristic |
| 267 | C2×C8 | C2×D44 | 1 | 1 | yes | characteristic |
| 268 | C2×C8 | D4×D11 | 1 | 1 | yes | characteristic |
| 269 | C2×C8 | D4×D11 | 1 | 1 | yes | characteristic |
| 270 | C4⋊C4 | — | 2 | 2 | no | — |
| 271 | C4⋊C4 | — | 11 | 2 | no | — |
| 272 | C4⋊C4 | — | 22 | 2 | no | — |
| 273 | C4⋊C4 | — | 22 | 2 | no | — |
| 274 | C4⋊C4 | — | 22 | 2 | no | — |
| 275 | C4⋊C4 | — | 44 | 2 | no | — |
| 276 | C4⋊C4 | — | 44 | 2 | no | — |
| 277 | C4⋊C4 | — | 44 | 2 | no | — |
| 278 | C4⋊C4 | C2×D44 | 1 | 2 | yes | — |
| 279 | C22⋊C4 | — | 44 | 2 | no | — |
| 280 | C22⋊C4 | — | 44 | 2 | no | — |
| 281 | C22⋊C4 | — | 44 | 2 | no | — |
| 282 | C42 | — | 2 | 2 | no | — |
| 283 | C42 | — | 22 | 2 | no | — |
| 284 | C42 | — | 44 | 2 | no | — |
| 285 | C42 | C23×D11 | 1 | 1 | yes | characteristic |
| 286 | C11 | #19965 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 287 | C23 | — | 44 | 2 | no | — |
| 288 | Q8 | — | 2 | 2 | no | — |
| 289 | Q8 | — | 2 | 2 | no | — |
| 290 | Q8 | — | 22 | 2 | no | — |
| 291 | Q8 | — | 22 | 2 | no | — |
| 292 | Q8 | — | 44 | 2 | no | — |
| 293 | Q8 | — | 44 | 2 | no | — |
| 294 | D4 | — | 44 | 2 | no | — |
| 295 | D4 | — | 44 | 2 | no | — |
| 296 | D4 | — | 44 | 2 | no | — |
| 297 | D4 | — | 44 | 2 | no | — |
| 298 | D4 | — | 88 | 2 | no | — |
| 299 | C2×C4 | — | 2 | 2 | no | — |
| 300 | C2×C4 | — | 2 | 2 | no | — |
| 301 | C2×C4 | — | 22 | 2 | no | — |
| 302 | C2×C4 | — | 22 | 2 | no | — |
| 303 | C2×C4 | — | 44 | 2 | no | — |
| 304 | C2×C4 | — | 176 | 2 | no | — |
| 305 | C2×C4 | C22×D44 | 1 | 1 | yes | characteristic |
| 306 | C2×C4 | C2×D4×D11 | 1 | 1 | yes | characteristic |
| 307 | C2×C4 | #67042 | 1 | 1 | yes | characteristic |
| 308 | C8 | — | 2 | 2 | no | — |
| 309 | C8 | — | 2 | 1 | no | — |
| 310 | C8 | — | 2 | 1 | no | — |
| 311 | C8 | — | 2 | 1 | no | — |
| 312 | C8 | — | 4 | 2 | no | — |
| 313 | C8 | — | 44 | 2 | no | — |
| 314 | C8 | #66957 | 1 | 2 | yes | — |
| 315 | C22 | — | 88 | 2 | no | — |
| 316 | C22 | — | 88 | 2 | no | — |
| 317 | C22 | — | 88 | 2 | no | — |
| 318 | C22 | D4×D44 | 1 | 1 | yes | characteristic |
| 319 | C4 | — | 2 | 1 | no | — |
| 320 | C4 | — | 4 | 2 | no | — |
| 321 | C4 | — | 4 | 2 | no | — |
| 322 | C4 | — | 44 | 2 | no | — |
| 323 | C4 | — | 44 | 2 | no | — |
| 324 | C4 | — | 88 | 2 | no | — |
| 325 | C4 | C2×#66957 | 1 | 1 | yes | characteristic |
| 326 | C4 | #10623283 | 1 | 1 | yes | characteristic |
| 327 | C4 | #10623297 | 1 | 1 | yes | characteristic |
| 328 | C4 | #10623299 | 1 | 1 | yes | characteristic |
| 329 | C2 | — | 176 | 2 | no | — |
| 330 | C2 | #13080272 | 1 | 1 | yes | characteristic |
| 331 | C2 | #13080376 | 1 | 1 | yes | characteristic |
| 332 | C2 | #13080410 | 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