← #14911399
Subgroups — #14911399
Order 2816.
470 conjugacy classes of subgroups.
The subgroup lattice has 326 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #13081047 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #13081009 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #13070898 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #13070825 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #13070814 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #13070769 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #13070759 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #13070724 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | C4×Dic88 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #13070404 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | C11×#2169 | C2 | 1 | 1 | yes | maximal, characteristic |
| 12 | #10623074 | — | 2 | 1 | no | — |
| 13 | #10623073 | — | 2 | 1 | no | — |
| 14 | C2×C11×M32 | C22 | 1 | 2 | yes | — |
| 15 | C8×D4×C11 | C22 | 1 | 1 | yes | characteristic |
| 16 | #10622729 | C22 | 1 | 2 | yes | — |
| 17 | #10622729 | C22 | 1 | 2 | yes | — |
| 18 | #10622719 | C22 | 1 | 2 | yes | — |
| 19 | C2×#66882 | C22 | 1 | 2 | yes | — |
| 20 | C2×Dic88 | C22 | 1 | 1 | yes | characteristic |
| 21 | #10622464 | — | 2 | 1 | no | — |
| 22 | #10622463 | — | 2 | 1 | no | — |
| 23 | #10622336 | — | 2 | 2 | no | — |
| 24 | #10622335 | — | 2 | 2 | no | — |
| 25 | C4×Dic44 | C22 | 1 | 1 | yes | characteristic |
| 26 | C4×Dic44 | C22 | 1 | 1 | yes | characteristic |
| 27 | #10622295 | C22 | 1 | 1 | yes | characteristic |
| 28 | #10622295 | C22 | 1 | 1 | yes | characteristic |
| 29 | C11×C4⋊C16 | C22 | 1 | 1 | yes | characteristic |
| 30 | C11×C22⋊C16 | C22 | 1 | 2 | yes | — |
| 31 | C4×C11×C16 | C22 | 1 | 1 | yes | characteristic |
| 32 | #10622143 | C22 | 1 | 2 | yes | — |
| 33 | #10622143 | C22 | 1 | 2 | yes | — |
| 34 | #10622143 | C22 | 1 | 2 | yes | — |
| 35 | #10622142 | C22 | 1 | 1 | yes | characteristic |
| 36 | #10622142 | C22 | 1 | 2 | yes | — |
| 37 | #10622141 | C22 | 1 | 2 | yes | — |
| 38 | #10622141 | C22 | 1 | 2 | yes | — |
| 39 | #10622141 | C22 | 1 | 1 | yes | characteristic |
| 40 | #10622141 | C22 | 1 | 1 | yes | characteristic |
| 41 | C22×C8×C11 | C23 | 1 | 2 | yes | — |
| 42 | C4×D4×C11 | D4 | 1 | 1 | yes | characteristic |
| 43 | #66989 | — | 4 | 1 | no | — |
| 44 | D4×Dic11 | — | 4 | 1 | no | — |
| 45 | #66979 | — | 2 | 2 | no | — |
| 46 | C2×C4⋊Dic11 | — | 2 | 2 | no | — |
| 47 | #66977 | — | 2 | 2 | no | — |
| 48 | #66977 | — | 2 | 2 | no | — |
| 49 | C2×Dic44 | C23 | 1 | 1 | yes | characteristic |
| 50 | C2×Dic44 | C23 | 1 | 1 | yes | characteristic |
| 51 | #66943 | — | 4 | 1 | no | — |
| 52 | #66940 | — | 4 | 1 | no | — |
| 53 | #66932 | — | 4 | 2 | no | — |
| 54 | #66931 | — | 4 | 2 | no | — |
| 55 | #66922 | — | 2 | 1 | no | — |
| 56 | #66922 | — | 2 | 1 | no | — |
| 57 | C4×Dic22 | — | 2 | 1 | no | — |
| 58 | C4×Dic22 | — | 2 | 1 | no | — |
| 59 | C11×M32 | — | 2 | 4 | no | — |
| 60 | C2×C11×C16 | C23 | 1 | 2 | yes | — |
| 61 | C2×C11×C16 | C23 | 1 | 1 | yes | characteristic |
| 62 | C2×C11×C16 | C23 | 1 | 1 | yes | characteristic |
| 63 | C11×C4⋊C8 | D4 | 1 | 1 | yes | characteristic |
| 64 | C11×C22⋊C8 | D4 | 1 | 2 | yes | — |
| 65 | C4×C8×C11 | C23 | 1 | 1 | yes | characteristic |
| 66 | #66882 | — | 2 | 1 | no | — |
| 67 | #66882 | — | 2 | 1 | no | — |
| 68 | #66882 | — | 2 | 2 | no | — |
| 69 | #66882 | C23 | 1 | 2 | yes | — |
| 70 | #66882 | C23 | 1 | 2 | yes | — |
| 71 | #66882 | C23 | 1 | 1 | yes | characteristic |
| 72 | #66882 | C23 | 1 | 1 | yes | characteristic |
| 73 | #66881 | — | 2 | 2 | no | — |
| 74 | #66880 | — | 2 | 2 | no | — |
| 75 | #66880 | — | 2 | 2 | no | — |
| 76 | #66880 | — | 2 | 1 | no | — |
| 77 | #66880 | — | 2 | 1 | no | — |
| 78 | Dic88 | — | 2 | 2 | no | — |
| 79 | #33923 | — | 11 | 1 | no | maximal, Sylow |
| 80 | C2×D4×C11 | D8 | 1 | 1 | yes | characteristic |
| 81 | C22×C4×C11 | C2×D4 | 1 | 2 | yes | — |
| 82 | C22×Dic11 | — | 4 | 2 | no | — |
| 83 | C2×Dic22 | — | 2 | 1 | no | — |
| 84 | C2×Dic22 | — | 2 | 1 | no | — |
| 85 | C2×Dic22 | — | 4 | 1 | no | — |
| 86 | C2×Dic22 | — | 4 | 1 | no | — |
| 87 | C2×C8×C11 | — | 2 | 2 | no | — |
| 88 | C2×C8×C11 | — | 2 | 2 | no | — |
| 89 | C2×C8×C11 | C2×D4 | 1 | 2 | yes | — |
| 90 | C2×C8×C11 | C2×D4 | 1 | 1 | yes | characteristic |
| 91 | C2×C8×C11 | C24 | 1 | 1 | yes | characteristic |
| 92 | C11×C4⋊C4 | D8 | 1 | 1 | yes | characteristic |
| 93 | C11×C22⋊C4 | D8 | 1 | 2 | yes | — |
| 94 | C42×C11 | C2×D4 | 1 | 1 | yes | characteristic |
| 95 | C22⋊Dic11 | — | 4 | 2 | no | — |
| 96 | C22⋊Dic11 | — | 4 | 2 | no | — |
| 97 | C22⋊Dic11 | — | 4 | 2 | no | — |
| 98 | C4⋊Dic11 | — | 2 | 1 | no | — |
| 99 | C4⋊Dic11 | — | 2 | 2 | no | — |
| 100 | C4⋊Dic11 | — | 2 | 1 | no | — |
| 101 | C4⋊Dic11 | — | 2 | 2 | no | — |
| 102 | C4⋊Dic11 | — | 4 | 1 | no | — |
| 103 | C4⋊Dic11 | — | 4 | 1 | no | — |
| 104 | C4⋊Dic11 | — | 4 | 2 | no | — |
| 105 | Dic11⋊C4 | — | 4 | 1 | no | — |
| 106 | Dic11⋊C4 | — | 4 | 1 | no | — |
| 107 | Dic11⋊C4 | — | 4 | 2 | no | — |
| 108 | Dic11⋊C4 | — | 4 | 2 | no | — |
| 109 | C4×Dic11 | — | 4 | 1 | no | — |
| 110 | C4×Dic11 | — | 4 | 1 | no | — |
| 111 | C4×Dic11 | — | 4 | 2 | no | — |
| 112 | Dic44 | — | 2 | 1 | no | — |
| 113 | Dic44 | — | 2 | 1 | no | — |
| 114 | Dic44 | — | 2 | 1 | no | — |
| 115 | Dic44 | — | 2 | 1 | no | — |
| 116 | C11×C16 | — | 2 | 2 | no | — |
| 117 | C11×C16 | — | 2 | 1 | no | — |
| 118 | C11×C16 | #41 | 1 | 2 | yes | — |
| 119 | #3342 | — | 11 | 1 | no | — |
| 120 | #3338 | — | 11 | 1 | no | — |
| 121 | #2254 | — | 11 | 1 | no | — |
| 122 | #2237 | — | 11 | 2 | no | — |
| 123 | #2235 | — | 11 | 2 | no | — |
| 124 | #2227 | — | 11 | 1 | no | — |
| 125 | #2225 | — | 11 | 1 | no | — |
| 126 | #2219 | — | 11 | 2 | no | — |
| 127 | C4×Q32 | — | 11 | 1 | no | — |
| 128 | #2169 | D11 | 1 | 1 | yes | characteristic |
| 129 | #2159 | — | 11 | 2 | no | — |
| 130 | C23×C11 | C2×D8 | 1 | 2 | yes | — |
| 131 | D4×C11 | — | 2 | 2 | no | — |
| 132 | C2×C4×C11 | — | 2 | 2 | no | — |
| 133 | C2×C4×C11 | — | 2 | 2 | no | — |
| 134 | C2×C4×C11 | C2×D8 | 1 | 2 | yes | — |
| 135 | C2×C4×C11 | C2×D8 | 1 | 1 | yes | characteristic |
| 136 | C2×C4×C11 | C2×D8 | 1 | 1 | yes | characteristic |
| 137 | C2×C4×C11 | C22×D4 | 1 | 1 | yes | characteristic |
| 138 | C2×Dic11 | — | 4 | 1 | no | — |
| 139 | C2×Dic11 | — | 4 | 1 | no | — |
| 140 | C2×Dic11 | — | 4 | 1 | no | — |
| 141 | C2×Dic11 | — | 4 | 1 | no | — |
| 142 | C2×Dic11 | — | 4 | 2 | no | — |
| 143 | C2×Dic11 | — | 4 | 2 | no | — |
| 144 | C2×Dic11 | — | 16 | 2 | no | — |
| 145 | Dic22 | — | 4 | 1 | no | — |
| 146 | Dic22 | — | 4 | 1 | no | — |
| 147 | Dic22 | — | 4 | 1 | no | — |
| 148 | Dic22 | — | 4 | 1 | no | — |
| 149 | Dic22 | — | 8 | 2 | no | — |
| 150 | Dic22 | — | 16 | 1 | no | — |
| 151 | C8×C11 | — | 2 | 2 | no | — |
| 152 | C8×C11 | — | 2 | 1 | no | — |
| 153 | C8×C11 | C2×#41 | 1 | 1 | yes | characteristic |
| 154 | C8×C11 | 2−1+4 | 1 | 1 | yes | characteristic |
| 155 | #556 | — | 22 | 1 | no | — |
| 156 | #554 | — | 22 | 1 | no | — |
| 157 | C2×Q32 | — | 11 | 1 | no | — |
| 158 | C2×M32 | C2×D11 | 1 | 2 | yes | — |
| 159 | #500 | — | 11 | 1 | no | — |
| 160 | #500 | — | 11 | 1 | no | — |
| 161 | #485 | — | 22 | 2 | no | — |
| 162 | #484 | — | 22 | 2 | no | — |
| 163 | #477 | — | 22 | 1 | no | — |
| 164 | #475 | — | 22 | 1 | no | — |
| 165 | #467 | — | 11 | 2 | no | — |
| 166 | #467 | — | 11 | 2 | no | — |
| 167 | C4×Q16 | — | 11 | 1 | no | — |
| 168 | C4×Q16 | — | 11 | 1 | no | — |
| 169 | C8×D4 | C2×D11 | 1 | 1 | yes | characteristic |
| 170 | #427 | — | 11 | 2 | no | — |
| 171 | C2×#107 | — | 11 | 2 | no | — |
| 172 | #367 | — | 11 | 2 | no | — |
| 173 | #367 | — | 11 | 2 | no | — |
| 174 | #367 | — | 11 | 2 | no | — |
| 175 | #366 | — | 11 | 1 | no | — |
| 176 | #366 | — | 11 | 2 | no | — |
| 177 | C4⋊C16 | C2×D11 | 1 | 1 | yes | characteristic |
| 178 | #358 | — | 11 | 1 | no | — |
| 179 | #358 | — | 11 | 1 | no | — |
| 180 | #358 | — | 11 | 2 | no | — |
| 181 | #358 | — | 11 | 2 | no | — |
| 182 | C22⋊C16 | C2×D11 | 1 | 2 | yes | — |
| 183 | C4×C16 | C2×D11 | 1 | 1 | yes | characteristic |
| 184 | C22×C11 | — | 2 | 2 | no | — |
| 185 | C22×C11 | — | 2 | 2 | no | — |
| 186 | C22×C11 | — | 2 | 2 | no | — |
| 187 | C22×C11 | C22×D8 | 1 | 1 | yes | characteristic |
| 188 | C4×C11 | — | 2 | 2 | no | — |
| 189 | C4×C11 | — | 2 | 1 | no | — |
| 190 | C4×C11 | #510 | 1 | 2 | yes | — |
| 191 | C4×C11 | #547 | 1 | 1 | yes | characteristic |
| 192 | C4×C11 | #578 | 1 | 1 | yes | characteristic |
| 193 | Dic11 | — | 8 | 1 | no | — |
| 194 | Dic11 | — | 8 | 1 | no | — |
| 195 | Dic11 | — | 8 | 2 | no | — |
| 196 | Dic11 | — | 8 | 2 | no | — |
| 197 | Dic11 | — | 8 | 1 | no | — |
| 198 | Dic11 | — | 8 | 1 | no | — |
| 199 | C2×Q16 | — | 11 | 1 | no | — |
| 200 | C2×Q16 | — | 11 | 1 | no | — |
| 201 | C22×C8 | C22×D11 | 1 | 2 | yes | — |
| 202 | C4⋊Q8 | — | 22 | 1 | no | — |
| 203 | C4⋊Q8 | — | 22 | 1 | no | — |
| 204 | #126 | — | 44 | 2 | no | — |
| 205 | #125 | — | 44 | 1 | no | — |
| 206 | #124 | — | 44 | 1 | no | — |
| 207 | C22⋊Q8 | — | 22 | 2 | no | — |
| 208 | C22⋊Q8 | — | 22 | 2 | no | — |
| 209 | C22⋊Q8 | — | 44 | 2 | no | — |
| 210 | C4×Q8 | — | 22 | 1 | no | — |
| 211 | C4×Q8 | — | 22 | 1 | no | — |
| 212 | C4×Q8 | — | 44 | 1 | no | — |
| 213 | C4×D4 | — | 44 | 1 | no | — |
| 214 | C4×D4 | D44 | 1 | 1 | yes | characteristic |
| 215 | #117 | — | 22 | 2 | no | — |
| 216 | C2×C4⋊C4 | — | 22 | 2 | no | — |
| 217 | Q32 | — | 22 | 2 | no | — |
| 218 | M32 | — | 2 | 4 | no | — |
| 219 | C2×C16 | C22×D11 | 1 | 1 | yes | characteristic |
| 220 | C2×C16 | C22×D11 | 1 | 2 | yes | — |
| 221 | C2×C16 | C22×D11 | 1 | 1 | yes | characteristic |
| 222 | #107 | — | 11 | 1 | no | — |
| 223 | #107 | — | 11 | 1 | no | — |
| 224 | #107 | — | 11 | 2 | no | — |
| 225 | #107 | — | 11 | 2 | no | — |
| 226 | #107 | — | 22 | 2 | no | — |
| 227 | #107 | — | 22 | 1 | no | — |
| 228 | #107 | — | 22 | 1 | no | — |
| 229 | #106 | — | 22 | 2 | no | — |
| 230 | C4⋊C8 | D44 | 1 | 1 | yes | characteristic |
| 231 | #103 | — | 22 | 1 | no | — |
| 232 | #103 | — | 22 | 1 | no | — |
| 233 | #103 | — | 22 | 2 | no | — |
| 234 | #103 | — | 22 | 2 | no | — |
| 235 | C22⋊C8 | D44 | 1 | 2 | yes | — |
| 236 | C4×C8 | C22×D11 | 1 | 1 | yes | characteristic |
| 237 | C2×C11 | — | 4 | 2 | no | — |
| 238 | C2×C11 | #3334 | 1 | 1 | yes | characteristic |
| 239 | C2×C11 | C2×#510 | 1 | 1 | yes | characteristic |
| 240 | C2×C11 | #3416 | 1 | 1 | yes | characteristic |
| 241 | C2×Q8 | — | 22 | 1 | no | — |
| 242 | C2×Q8 | — | 22 | 1 | no | — |
| 243 | C2×Q8 | — | 44 | 1 | no | — |
| 244 | C2×Q8 | — | 44 | 1 | no | — |
| 245 | C2×D4 | D88 | 1 | 1 | yes | characteristic |
| 246 | C22×C4 | — | 44 | 2 | no | — |
| 247 | C22×C4 | C2×D44 | 1 | 2 | yes | — |
| 248 | Q16 | — | 22 | 1 | no | — |
| 249 | Q16 | — | 22 | 1 | no | — |
| 250 | Q16 | — | 22 | 1 | no | — |
| 251 | Q16 | — | 22 | 1 | no | — |
| 252 | C2×C8 | — | 2 | 2 | no | — |
| 253 | C2×C8 | — | 2 | 2 | no | — |
| 254 | C2×C8 | C2×D44 | 1 | 1 | yes | characteristic |
| 255 | C2×C8 | C2×D44 | 1 | 2 | yes | — |
| 256 | C2×C8 | C23×D11 | 1 | 1 | yes | characteristic |
| 257 | C4⋊C4 | — | 22 | 1 | no | — |
| 258 | C4⋊C4 | — | 22 | 2 | no | — |
| 259 | C4⋊C4 | — | 22 | 1 | no | — |
| 260 | C4⋊C4 | — | 22 | 2 | no | — |
| 261 | C4⋊C4 | — | 44 | 2 | no | — |
| 262 | C4⋊C4 | — | 44 | 1 | no | — |
| 263 | C4⋊C4 | — | 44 | 1 | no | — |
| 264 | C4⋊C4 | — | 44 | 1 | no | — |
| 265 | C4⋊C4 | — | 44 | 2 | no | — |
| 266 | C4⋊C4 | — | 44 | 2 | no | — |
| 267 | C4⋊C4 | — | 44 | 1 | no | — |
| 268 | C4⋊C4 | D88 | 1 | 1 | yes | characteristic |
| 269 | C22⋊C4 | — | 44 | 2 | no | — |
| 270 | C22⋊C4 | — | 44 | 2 | no | — |
| 271 | C22⋊C4 | — | 44 | 2 | no | — |
| 272 | C22⋊C4 | D88 | 1 | 2 | yes | — |
| 273 | C42 | — | 44 | 2 | no | — |
| 274 | C42 | — | 44 | 1 | no | — |
| 275 | C42 | — | 44 | 1 | no | — |
| 276 | C42 | C2×D44 | 1 | 1 | yes | characteristic |
| 277 | C16 | — | 2 | 2 | no | — |
| 278 | C16 | — | 2 | 1 | no | — |
| 279 | C16 | #4341 | 1 | 2 | yes | — |
| 280 | C11 | #33923 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 281 | C23 | C2×D88 | 1 | 2 | yes | — |
| 282 | Q8 | — | 44 | 1 | no | — |
| 283 | Q8 | — | 44 | 1 | no | — |
| 284 | Q8 | — | 44 | 1 | no | — |
| 285 | Q8 | — | 44 | 1 | no | — |
| 286 | Q8 | — | 88 | 2 | no | — |
| 287 | Q8 | — | 176 | 1 | no | — |
| 288 | D4 | — | 2 | 2 | no | — |
| 289 | C2×C4 | — | 2 | 2 | no | — |
| 290 | C2×C4 | — | 2 | 2 | no | — |
| 291 | C2×C4 | — | 44 | 1 | no | — |
| 292 | C2×C4 | — | 44 | 2 | no | — |
| 293 | C2×C4 | — | 44 | 1 | no | — |
| 294 | C2×C4 | — | 44 | 1 | no | — |
| 295 | C2×C4 | — | 44 | 1 | no | — |
| 296 | C2×C4 | — | 44 | 2 | no | — |
| 297 | C2×C4 | — | 176 | 2 | no | — |
| 298 | C2×C4 | C2×D88 | 1 | 2 | yes | — |
| 299 | C2×C4 | C2×D88 | 1 | 1 | yes | characteristic |
| 300 | C2×C4 | C2×D88 | 1 | 1 | yes | characteristic |
| 301 | C2×C4 | C22×D44 | 1 | 1 | yes | characteristic |
| 302 | C8 | — | 2 | 1 | no | — |
| 303 | C8 | — | 2 | 2 | no | — |
| 304 | C8 | C2×#4341 | 1 | 1 | yes | characteristic |
| 305 | C8 | #67043 | 1 | 1 | yes | characteristic |
| 306 | C22 | — | 2 | 2 | no | — |
| 307 | C22 | — | 2 | 2 | no | — |
| 308 | C22 | — | 2 | 2 | no | — |
| 309 | C22 | C22×D88 | 1 | 1 | yes | characteristic |
| 310 | C4 | — | 2 | 2 | no | — |
| 311 | C4 | — | 2 | 1 | no | — |
| 312 | C4 | — | 88 | 1 | no | — |
| 313 | C4 | — | 88 | 1 | no | — |
| 314 | C4 | — | 88 | 2 | no | — |
| 315 | C4 | — | 88 | 1 | no | — |
| 316 | C4 | — | 88 | 2 | no | — |
| 317 | C4 | — | 88 | 1 | no | — |
| 318 | C4 | #10622522 | 1 | 2 | yes | — |
| 319 | C4 | #10623086 | 1 | 1 | yes | characteristic |
| 320 | C4 | #10623284 | 1 | 1 | yes | characteristic |
| 321 | C2 | — | 4 | 2 | no | — |
| 322 | C2 | #13080964 | 1 | 1 | yes | characteristic |
| 323 | C2 | C2×#10622522 | 1 | 1 | yes | characteristic |
| 324 | C2 | #13081764 | 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