← #14909692
Subgroups — #14909692
Order 2816.
686 conjugacy classes of subgroups.
The subgroup lattice has 320 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #13079202 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #13070871 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #13070839 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #13070653 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #13070545 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #13070415 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C2×C11×#493 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | C22×C11×D8 | — | 2 | 1 | no | — |
| 9 | C22×C11×D8 | C22 | 1 | 2 | yes | — |
| 10 | C2×C11×#127 | — | 2 | 1 | no | — |
| 11 | #10623001 | — | 2 | 1 | no | — |
| 12 | C11×#493 | — | 2 | 1 | no | — |
| 13 | C11×#493 | — | 2 | 1 | no | — |
| 14 | C11×#493 | C22 | 1 | 2 | yes | — |
| 15 | C11×#493 | C22 | 1 | 2 | yes | — |
| 16 | C2×C4×C8×C11 | C22 | 1 | 1 | yes | characteristic |
| 17 | C2×#66891 | C22 | 1 | 8 | yes | complemented |
| 18 | #10622729 | — | 2 | 1 | no | — |
| 19 | #10622729 | C22 | 1 | 2 | yes | — |
| 20 | #10622312 | C22 | 1 | 1 | yes | characteristic, complemented |
| 21 | C4×Dic44 | — | 2 | 1 | no | — |
| 22 | C4×Dic44 | C22 | 1 | 2 | yes | complemented |
| 23 | #10622295 | C22 | 1 | 1 | yes | characteristic, complemented |
| 24 | #10622294 | — | 2 | 1 | no | — |
| 25 | #10622200 | C22 | 1 | 8 | yes | complemented |
| 26 | C22⋊(C11⋊C16) | C22 | 1 | 2 | yes | — |
| 27 | C4⋊(C11⋊C16) | C22 | 1 | 2 | yes | complemented |
| 28 | C4×C11⋊C16 | C22 | 1 | 2 | yes | complemented |
| 29 | C22×D4×C11 | — | 2 | 2 | no | — |
| 30 | C22×D4×C11 | — | 4 | 1 | no | — |
| 31 | C22×D4×C11 | — | 4 | 1 | no | — |
| 32 | C2×C11×D8 | — | 2 | 2 | no | — |
| 33 | C2×C11×D8 | — | 2 | 2 | no | — |
| 34 | C2×C11×D8 | — | 2 | 2 | no | — |
| 35 | C2×C11×D8 | — | 4 | 4 | no | — |
| 36 | C2×C11×D8 | — | 4 | 4 | no | — |
| 37 | C2×C11×D8 | C23 | 1 | 4 | yes | — |
| 38 | C22×C8×C11 | D4 | 1 | 1 | yes | characteristic |
| 39 | C22×C8×C11 | C23 | 1 | 1 | yes | characteristic |
| 40 | C11×#127 | — | 2 | 2 | no | — |
| 41 | C11×#127 | — | 2 | 2 | no | — |
| 42 | C11×#127 | — | 4 | 1 | no | — |
| 43 | C11×#127 | — | 4 | 1 | no | — |
| 44 | C2×C42×C11 | D4 | 1 | 1 | yes | characteristic |
| 45 | #66979 | — | 4 | 1 | no | — |
| 46 | #66977 | — | 2 | 2 | no | — |
| 47 | #66977 | — | 4 | 1 | no | — |
| 48 | C2×Dic44 | — | 2 | 1 | no | — |
| 49 | C2×Dic44 | C23 | 1 | 2 | yes | — |
| 50 | #66923 | — | 4 | 1 | no | — |
| 51 | #66922 | — | 2 | 1 | no | — |
| 52 | #66922 | — | 2 | 1 | no | — |
| 53 | C4×Dic22 | — | 2 | 2 | no | — |
| 54 | C4×Dic22 | — | 4 | 1 | no | — |
| 55 | C4×C8×C11 | D4 | 1 | 1 | yes | characteristic |
| 56 | C4×C8×C11 | D4 | 1 | 1 | yes | characteristic |
| 57 | C4×C8×C11 | C23 | 1 | 1 | yes | characteristic |
| 58 | C4×C8×C11 | C23 | 1 | 1 | yes | characteristic |
| 59 | #66891 | — | 4 | 8 | no | — |
| 60 | #66882 | — | 2 | 1 | no | — |
| 61 | #66882 | C23 | 1 | 2 | yes | — |
| 62 | #66880 | — | 2 | 2 | no | — |
| 63 | #66880 | — | 2 | 2 | no | — |
| 64 | C2×C11⋊C16 | C23 | 1 | 4 | yes | — |
| 65 | #33774 | — | 11 | 1 | no | maximal, Sylow |
| 66 | C24×C11 | — | 4 | 2 | no | — |
| 67 | C2×D4×C11 | — | 2 | 4 | no | — |
| 68 | C2×D4×C11 | — | 4 | 4 | no | — |
| 69 | C2×D4×C11 | — | 4 | 4 | no | — |
| 70 | C2×D4×C11 | — | 4 | 2 | no | — |
| 71 | C2×D4×C11 | — | 4 | 2 | no | — |
| 72 | C2×D4×C11 | — | 4 | 2 | no | — |
| 73 | C2×D4×C11 | — | 4 | 2 | no | — |
| 74 | C2×D4×C11 | — | 4 | 2 | no | — |
| 75 | C2×D4×C11 | — | 8 | 4 | no | — |
| 76 | C2×D4×C11 | — | 8 | 4 | no | — |
| 77 | C22×C4×C11 | D8 | 1 | 1 | yes | characteristic |
| 78 | C22×C4×C11 | D8 | 1 | 1 | yes | characteristic |
| 79 | C22×C4×C11 | C2×D4 | 1 | 1 | yes | characteristic |
| 80 | C2×Dic22 | — | 2 | 2 | no | — |
| 81 | C2×Dic22 | — | 4 | 1 | no | — |
| 82 | C11×D8 | — | 2 | 8 | no | — |
| 83 | C11×D8 | — | 4 | 4 | no | — |
| 84 | C11×D8 | — | 4 | 4 | no | — |
| 85 | C11×D8 | — | 4 | 4 | no | — |
| 86 | C2×C8×C11 | — | 2 | 2 | no | — |
| 87 | C2×C8×C11 | — | 2 | 2 | no | — |
| 88 | C2×C8×C11 | C2×D4 | 1 | 1 | yes | characteristic |
| 89 | C2×C8×C11 | C2×D4 | 1 | 1 | yes | characteristic |
| 90 | C2×C8×C11 | C2×D4 | 1 | 1 | yes | characteristic |
| 91 | C2×C8×C11 | C24 | 1 | 1 | yes | characteristic |
| 92 | C42×C11 | D8 | 1 | 1 | yes | characteristic |
| 93 | C42×C11 | D8 | 1 | 1 | yes | characteristic |
| 94 | C42×C11 | C2×D4 | 1 | 1 | yes | characteristic |
| 95 | C42×C11 | C2×D4 | 1 | 1 | yes | characteristic |
| 96 | C22⋊Dic11 | — | 4 | 2 | no | — |
| 97 | C4⋊Dic11 | — | 2 | 2 | no | — |
| 98 | C4⋊Dic11 | — | 4 | 1 | no | — |
| 99 | C4⋊Dic11 | — | 4 | 1 | no | — |
| 100 | C4⋊Dic11 | — | 4 | 1 | no | — |
| 101 | Dic11⋊C4 | — | 4 | 2 | no | — |
| 102 | Dic11⋊C4 | — | 4 | 2 | no | — |
| 103 | C4×Dic11 | — | 4 | 2 | no | — |
| 104 | Dic44 | — | 2 | 4 | no | — |
| 105 | Dic44 | — | 4 | 2 | no | — |
| 106 | C11⋊C16 | — | 2 | 4 | no | — |
| 107 | #3170 | — | 11 | 1 | no | — |
| 108 | C2×#493 | D11 | 1 | 1 | yes | characteristic |
| 109 | #2248 | — | 11 | 2 | no | — |
| 110 | #2240 | — | 11 | 2 | no | — |
| 111 | #2207 | — | 11 | 4 | no | — |
| 112 | #2187 | — | 11 | 4 | no | — |
| 113 | #2162 | — | 11 | 1 | no | — |
| 114 | C23×C11 | — | 4 | 4 | no | — |
| 115 | C23×C11 | — | 8 | 4 | no | — |
| 116 | C23×C11 | — | 8 | 4 | no | — |
| 117 | C23×C11 | — | 8 | 4 | no | — |
| 118 | C23×C11 | C2×D8 | 1 | 1 | yes | characteristic |
| 119 | D4×C11 | — | 4 | 4 | no | — |
| 120 | D4×C11 | — | 4 | 4 | no | — |
| 121 | D4×C11 | — | 8 | 4 | no | — |
| 122 | D4×C11 | — | 8 | 4 | no | — |
| 123 | D4×C11 | — | 8 | 4 | no | — |
| 124 | D4×C11 | — | 8 | 4 | no | — |
| 125 | D4×C11 | — | 8 | 4 | no | — |
| 126 | C2×C4×C11 | — | 2 | 1 | no | — |
| 127 | C2×C4×C11 | — | 2 | 1 | no | — |
| 128 | C2×C4×C11 | — | 2 | 2 | no | — |
| 129 | C2×C4×C11 | SD32 | 1 | 4 | yes | complemented |
| 130 | C2×C4×C11 | C2×D8 | 1 | 1 | yes | characteristic |
| 131 | C2×C4×C11 | C2×D8 | 1 | 1 | yes | characteristic |
| 132 | C2×C4×C11 | C2×D8 | 1 | 1 | yes | characteristic |
| 133 | C2×C4×C11 | C2×D8 | 1 | 1 | yes | characteristic |
| 134 | C2×C4×C11 | C2×D8 | 1 | 1 | yes | characteristic |
| 135 | C2×C4×C11 | C22×D4 | 1 | 1 | yes | characteristic |
| 136 | C2×Dic11 | — | 4 | 2 | no | — |
| 137 | C2×Dic11 | — | 4 | 2 | no | — |
| 138 | Dic22 | — | 4 | 2 | no | — |
| 139 | Dic22 | — | 4 | 2 | no | — |
| 140 | Dic22 | — | 8 | 2 | no | — |
| 141 | C8×C11 | — | 2 | 1 | no | — |
| 142 | C8×C11 | — | 2 | 1 | no | — |
| 143 | C8×C11 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 144 | C8×C11 | H(5,𝔽2) | 1 | 2 | yes | — |
| 145 | C22×D8 | — | 2 | 1 | no | — |
| 146 | C22×D8 | C2×D11 | 1 | 2 | yes | — |
| 147 | #533 | — | 22 | 1 | no | — |
| 148 | C2×#127 | — | 2 | 1 | no | — |
| 149 | C2×SD32 | — | 11 | 8 | no | — |
| 150 | #500 | — | 11 | 1 | no | — |
| 151 | #494 | — | 11 | 1 | no | — |
| 152 | #493 | — | 2 | 1 | no | — |
| 153 | #493 | — | 2 | 1 | no | — |
| 154 | #493 | C2×D11 | 1 | 2 | yes | — |
| 155 | #493 | C2×D11 | 1 | 2 | yes | — |
| 156 | #487 | — | 22 | 1 | no | — |
| 157 | #467 | — | 11 | 2 | no | — |
| 158 | #467 | — | 22 | 1 | no | — |
| 159 | C4×Q16 | — | 11 | 2 | no | — |
| 160 | C4×Q16 | — | 22 | 1 | no | — |
| 161 | C2×C4×C8 | C2×D11 | 1 | 1 | yes | characteristic |
| 162 | C4⋊C16 | — | 11 | 2 | no | — |
| 163 | #357 | — | 11 | 8 | no | — |
| 164 | C22⋊C16 | — | 11 | 2 | no | — |
| 165 | C4×C16 | — | 11 | 2 | no | — |
| 166 | C22×C11 | — | 2 | 1 | no | — |
| 167 | C22×C11 | — | 2 | 1 | no | — |
| 168 | C22×C11 | — | 8 | 4 | no | — |
| 169 | C22×C11 | — | 8 | 4 | no | — |
| 170 | C22×C11 | — | 8 | 4 | no | — |
| 171 | C22×C11 | — | 16 | 8 | no | — |
| 172 | C22×C11 | C2×SD32 | 1 | 2 | yes | — |
| 173 | C22×C11 | C22×D8 | 1 | 1 | yes | characteristic |
| 174 | C4×C11 | — | 2 | 1 | no | — |
| 175 | C4×C11 | — | 2 | 1 | no | — |
| 176 | C4×C11 | C2×SD32 | 1 | 2 | yes | — |
| 177 | C4×C11 | C2×SD32 | 1 | 2 | yes | — |
| 178 | C4×C11 | #509 | 1 | 2 | yes | — |
| 179 | C4×C11 | #535 | 1 | 1 | yes | characteristic |
| 180 | C4×C11 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 181 | Dic11 | — | 8 | 2 | no | — |
| 182 | Dic11 | — | 8 | 2 | no | — |
| 183 | C22×D4 | — | 2 | 2 | no | — |
| 184 | C22×D4 | — | 4 | 1 | no | — |
| 185 | C22×D4 | — | 4 | 1 | no | — |
| 186 | C2×Q16 | — | 11 | 2 | no | — |
| 187 | C2×Q16 | — | 22 | 1 | no | — |
| 188 | C2×D8 | — | 2 | 2 | no | — |
| 189 | C2×D8 | — | 2 | 2 | no | — |
| 190 | C2×D8 | — | 2 | 2 | no | — |
| 191 | C2×D8 | — | 4 | 4 | no | — |
| 192 | C2×D8 | — | 4 | 4 | no | — |
| 193 | C2×D8 | C22×D11 | 1 | 4 | yes | — |
| 194 | C22×C8 | C22⋊D11 | 1 | 1 | yes | characteristic |
| 195 | C22×C8 | C22×D11 | 1 | 1 | yes | characteristic |
| 196 | C4⋊Q8 | — | 22 | 1 | no | — |
| 197 | C4⋊Q8 | — | 22 | 1 | no | — |
| 198 | #127 | — | 2 | 2 | no | — |
| 199 | #127 | — | 2 | 2 | no | — |
| 200 | #127 | — | 4 | 1 | no | — |
| 201 | #127 | — | 4 | 1 | no | — |
| 202 | #125 | — | 44 | 1 | no | — |
| 203 | C22⋊Q8 | — | 22 | 2 | no | — |
| 204 | C22⋊Q8 | — | 44 | 1 | no | — |
| 205 | C4×Q8 | — | 22 | 2 | no | — |
| 206 | C4×Q8 | — | 44 | 1 | no | — |
| 207 | #117 | — | 44 | 1 | no | — |
| 208 | C2×C42 | C22⋊D11 | 1 | 1 | yes | characteristic |
| 209 | SD32 | — | 44 | 8 | no | — |
| 210 | C2×C16 | — | 11 | 4 | no | — |
| 211 | #107 | — | 11 | 2 | no | — |
| 212 | #107 | — | 22 | 1 | no | — |
| 213 | #103 | — | 22 | 2 | no | — |
| 214 | #103 | — | 22 | 2 | no | — |
| 215 | C4×C8 | C22⋊D11 | 1 | 1 | yes | characteristic |
| 216 | C4×C8 | C22⋊D11 | 1 | 1 | yes | characteristic |
| 217 | C4×C8 | C22×D11 | 1 | 1 | yes | characteristic |
| 218 | C4×C8 | C22×D11 | 1 | 1 | yes | characteristic |
| 219 | C2×C11 | — | 2 | 2 | no | — |
| 220 | C2×C11 | — | 16 | 4 | no | — |
| 221 | C2×C11 | #3205 | 1 | 1 | yes | characteristic |
| 222 | C2×C11 | C22×SD32 | 1 | 1 | yes | characteristic |
| 223 | C2×C11 | C2×#509 | 1 | 1 | yes | characteristic |
| 224 | C24 | — | 4 | 2 | no | — |
| 225 | C2×Q8 | — | 22 | 2 | no | — |
| 226 | C2×Q8 | — | 44 | 1 | no | — |
| 227 | C2×D4 | — | 2 | 4 | no | — |
| 228 | C2×D4 | — | 4 | 4 | no | — |
| 229 | C2×D4 | — | 4 | 4 | no | — |
| 230 | C2×D4 | — | 4 | 2 | no | — |
| 231 | C2×D4 | — | 4 | 2 | no | — |
| 232 | C2×D4 | — | 4 | 2 | no | — |
| 233 | C2×D4 | — | 4 | 2 | no | — |
| 234 | C2×D4 | — | 4 | 2 | no | — |
| 235 | C2×D4 | — | 8 | 4 | no | — |
| 236 | C2×D4 | — | 8 | 4 | no | — |
| 237 | C22×C4 | #4323 | 1 | 1 | yes | characteristic |
| 238 | C22×C4 | #4323 | 1 | 1 | yes | characteristic |
| 239 | C22×C4 | C2×C22⋊D11 | 1 | 1 | yes | characteristic |
| 240 | Q16 | — | 22 | 4 | no | — |
| 241 | Q16 | — | 44 | 2 | no | — |
| 242 | D8 | — | 2 | 8 | no | — |
| 243 | D8 | — | 4 | 4 | no | — |
| 244 | D8 | — | 4 | 4 | no | — |
| 245 | D8 | — | 4 | 4 | no | — |
| 246 | C2×C8 | — | 2 | 2 | no | — |
| 247 | C2×C8 | — | 2 | 2 | no | — |
| 248 | C2×C8 | C2×C22⋊D11 | 1 | 1 | yes | characteristic |
| 249 | C2×C8 | C2×C22⋊D11 | 1 | 1 | yes | characteristic |
| 250 | C2×C8 | C2×C22⋊D11 | 1 | 1 | yes | characteristic |
| 251 | C2×C8 | C23×D11 | 1 | 1 | yes | characteristic |
| 252 | C4⋊C4 | — | 22 | 2 | no | — |
| 253 | C4⋊C4 | — | 44 | 1 | no | — |
| 254 | C4⋊C4 | — | 44 | 1 | no | — |
| 255 | C4⋊C4 | — | 44 | 2 | no | — |
| 256 | C4⋊C4 | — | 44 | 2 | no | — |
| 257 | C4⋊C4 | — | 44 | 1 | no | — |
| 258 | C22⋊C4 | — | 44 | 2 | no | — |
| 259 | C42 | — | 44 | 2 | no | — |
| 260 | C42 | #4323 | 1 | 1 | yes | characteristic |
| 261 | C42 | #4323 | 1 | 1 | yes | characteristic |
| 262 | C42 | C2×C22⋊D11 | 1 | 1 | yes | characteristic |
| 263 | C42 | C2×C22⋊D11 | 1 | 1 | yes | characteristic |
| 264 | C16 | — | 22 | 4 | no | — |
| 265 | C11 | #33774 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 266 | C23 | — | 4 | 4 | no | — |
| 267 | C23 | — | 8 | 4 | no | — |
| 268 | C23 | — | 8 | 4 | no | — |
| 269 | C23 | — | 8 | 4 | no | — |
| 270 | C23 | C2×#4323 | 1 | 1 | yes | characteristic |
| 271 | Q8 | — | 44 | 2 | no | — |
| 272 | Q8 | — | 44 | 2 | no | — |
| 273 | Q8 | — | 88 | 2 | no | — |
| 274 | D4 | — | 4 | 4 | no | — |
| 275 | D4 | — | 4 | 4 | no | — |
| 276 | D4 | — | 8 | 4 | no | — |
| 277 | D4 | — | 8 | 4 | no | — |
| 278 | D4 | — | 8 | 4 | no | — |
| 279 | D4 | — | 8 | 4 | no | — |
| 280 | D4 | — | 8 | 4 | no | — |
| 281 | C2×C4 | — | 2 | 2 | no | — |
| 282 | C2×C4 | — | 2 | 1 | no | — |
| 283 | C2×C4 | — | 2 | 1 | no | — |
| 284 | C2×C4 | — | 44 | 2 | no | — |
| 285 | C2×C4 | — | 44 | 2 | no | — |
| 286 | C2×C4 | #66891 | 1 | 4 | yes | complemented |
| 287 | C2×C4 | C2×#4323 | 1 | 1 | yes | characteristic |
| 288 | C2×C4 | C2×#4323 | 1 | 1 | yes | characteristic |
| 289 | C2×C4 | C2×#4323 | 1 | 1 | yes | characteristic |
| 290 | C2×C4 | C2×#4323 | 1 | 1 | yes | characteristic |
| 291 | C2×C4 | C2×#4323 | 1 | 1 | yes | characteristic |
| 292 | C2×C4 | C22×C22⋊D11 | 1 | 1 | yes | characteristic |
| 293 | C8 | — | 2 | 1 | no | — |
| 294 | C8 | — | 2 | 1 | no | — |
| 295 | C8 | #66985 | 1 | 2 | yes | — |
| 296 | C8 | #67037 | 1 | 2 | yes | — |
| 297 | C22 | — | 2 | 1 | no | — |
| 298 | C22 | — | 2 | 1 | no | — |
| 299 | C22 | — | 8 | 4 | no | — |
| 300 | C22 | — | 8 | 4 | no | — |
| 301 | C22 | — | 8 | 4 | no | — |
| 302 | C22 | — | 16 | 8 | no | — |
| 303 | C22 | C2×#66891 | 1 | 2 | yes | — |
| 304 | C22 | C22×#4323 | 1 | 1 | yes | characteristic |
| 305 | C4 | — | 2 | 1 | no | — |
| 306 | C4 | — | 2 | 1 | no | — |
| 307 | C4 | — | 88 | 2 | no | — |
| 308 | C4 | — | 88 | 2 | no | — |
| 309 | C4 | #10622760 | 1 | 2 | yes | — |
| 310 | C4 | C2×#66891 | 1 | 2 | yes | — |
| 311 | C4 | C2×#66891 | 1 | 2 | yes | — |
| 312 | C4 | C2×#66985 | 1 | 1 | yes | characteristic |
| 313 | C4 | #10623336 | 1 | 1 | yes | characteristic |
| 314 | C2 | — | 2 | 2 | no | — |
| 315 | C2 | — | 16 | 4 | no | — |
| 316 | C2 | #13079534 | 1 | 1 | yes | characteristic |
| 317 | C2 | C22×#66891 | 1 | 1 | yes | characteristic |
| 318 | C2 | C2×#10622760 | 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