← #14722733
Subgroups — #14722733
Order 2816.
1244 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 | #13082394 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #13077748 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #13067349 | C2 | 1 | 3 | yes | maximal, complemented |
| 4 | #13067285 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | #13067283 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | #13067276 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | C11×#2991 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C2×#67042 | C4 | 1 | 2 | yes | — |
| 9 | C4×C11×#41 | C22 | 1 | 1 | yes | characteristic |
| 10 | #10623108 | — | 2 | 1 | no | — |
| 11 | #10623108 | — | 2 | 1 | no | — |
| 12 | D4×D44 | — | 2 | 3 | no | — |
| 13 | D4×D44 | — | 2 | 3 | no | — |
| 14 | #10623056 | C4 | 1 | 6 | yes | — |
| 15 | #10623008 | C22 | 1 | 3 | yes | — |
| 16 | C2×#66927 | C22 | 1 | 3 | yes | — |
| 17 | C8×Q8×C11 | — | 2 | 1 | no | — |
| 18 | C11×#436 | — | 2 | 3 | no | — |
| 19 | C11×#431 | C22 | 1 | 3 | yes | complemented |
| 20 | C11×#423 | C22 | 1 | 3 | yes | complemented |
| 21 | Q8×C11⋊C8 | — | 2 | 1 | no | — |
| 22 | #10622625 | — | 2 | 3 | no | — |
| 23 | #10622538 | C22 | 1 | 3 | yes | complemented |
| 24 | #10622537 | C22 | 1 | 3 | yes | complemented |
| 25 | #10622123 | C22 | 1 | 3 | yes | complemented |
| 26 | #10622123 | C22 | 1 | 3 | yes | complemented |
| 27 | #10622123 | C22 | 1 | 6 | yes | complemented |
| 28 | #10622119 | C22 | 1 | 1 | yes | characteristic, complemented |
| 29 | #10622119 | C22 | 1 | 3 | yes | complemented |
| 30 | C2×C11×#41 | C2×C4 | 1 | 1 | yes | characteristic |
| 31 | #67042 | — | 4 | 8 | no | — |
| 32 | C2×#4343 | — | 2 | 2 | no | — |
| 33 | C2×D4×D11 | — | 2 | 6 | no | — |
| 34 | C2×#4339 | C2×C4 | 1 | 6 | yes | — |
| 35 | C22×D44 | — | 2 | 3 | no | — |
| 36 | C22×D44 | — | 2 | 3 | no | — |
| 37 | C22×D44 | C2×C4 | 1 | 6 | yes | — |
| 38 | C2×C11×M16 | — | 2 | 3 | no | — |
| 39 | C4×Q8×C11 | D4 | 1 | 1 | yes | characteristic |
| 40 | C4×Q8×C11 | D4 | 1 | 1 | yes | characteristic |
| 41 | C4×D4×C11 | D4 | 1 | 3 | yes | — |
| 42 | C4×D4×C11 | D4 | 1 | 3 | yes | — |
| 43 | C11×#117 | C2×C4 | 1 | 3 | yes | — |
| 44 | C2×C42×C11 | C23 | 1 | 3 | yes | — |
| 45 | #66983 | — | 2 | 3 | no | — |
| 46 | #66983 | — | 2 | 3 | no | — |
| 47 | C2×#4318 | — | 2 | 3 | no | — |
| 48 | #66948 | — | 2 | 6 | no | — |
| 49 | #66948 | — | 2 | 6 | no | — |
| 50 | #66935 | — | 2 | 12 | no | — |
| 51 | #66928 | C2×C4 | 1 | 6 | yes | — |
| 52 | #66927 | — | 2 | 3 | no | — |
| 53 | #66927 | — | 2 | 3 | no | — |
| 54 | #66927 | C2×C4 | 1 | 6 | yes | — |
| 55 | #66927 | C23 | 1 | 3 | yes | — |
| 56 | C4×D44 | — | 2 | 3 | no | — |
| 57 | C4×D44 | — | 2 | 3 | no | — |
| 58 | #66922 | C23 | 1 | 1 | yes | characteristic |
| 59 | C11×C4⋊C8 | — | 2 | 3 | no | — |
| 60 | C11×C4⋊C8 | C23 | 1 | 3 | yes | — |
| 61 | C11×C4⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 62 | C11×C22⋊C8 | — | 2 | 3 | no | — |
| 63 | C4×C8×C11 | — | 2 | 3 | no | — |
| 64 | C22⋊(C11⋊C8) | — | 2 | 3 | no | — |
| 65 | C4⋊(C11⋊C8) | — | 2 | 3 | no | — |
| 66 | C4⋊(C11⋊C8) | C23 | 1 | 3 | yes | — |
| 67 | C4⋊(C11⋊C8) | C23 | 1 | 1 | yes | characteristic |
| 68 | C4×C11⋊C8 | — | 2 | 3 | no | — |
| 69 | #17782 | — | 11 | 1 | no | maximal, Sylow |
| 70 | C23×D11 | — | 2 | 6 | no | — |
| 71 | C11×#41 | — | 2 | 4 | no | — |
| 72 | C2×Q8×C11 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 73 | C2×D4×C11 | C22⋊C4 | 1 | 3 | yes | — |
| 74 | C22×C4×C11 | C22×C4 | 1 | 3 | yes | — |
| 75 | C22×C4×C11 | C2×D4 | 1 | 3 | yes | — |
| 76 | C22×C4×C11 | C2×D4 | 1 | 3 | yes | — |
| 77 | C2×C22⋊D11 | — | 2 | 6 | no | — |
| 78 | #4343 | — | 4 | 8 | no | — |
| 79 | D4×D11 | — | 4 | 24 | no | — |
| 80 | #4339 | — | 4 | 12 | no | — |
| 81 | C2×D44 | — | 2 | 6 | no | — |
| 82 | C2×D44 | — | 2 | 6 | no | — |
| 83 | C2×D44 | — | 2 | 6 | no | — |
| 84 | C2×D44 | — | 2 | 3 | no | — |
| 85 | C2×D44 | — | 2 | 3 | no | — |
| 86 | C2×D44 | — | 4 | 12 | no | — |
| 87 | C2×D44 | — | 8 | 3 | no | — |
| 88 | C2×D44 | — | 8 | 3 | no | — |
| 89 | C2×D44 | — | 8 | 3 | no | — |
| 90 | C2×D44 | — | 8 | 3 | no | — |
| 91 | C2×D44 | C22×C4 | 1 | 6 | yes | — |
| 92 | C2×C4×D11 | — | 2 | 6 | no | — |
| 93 | C2×Dic22 | C22×C4 | 1 | 2 | yes | — |
| 94 | C11×M16 | — | 8 | 3 | no | — |
| 95 | C2×C8×C11 | — | 2 | 1 | no | — |
| 96 | C2×C8×C11 | — | 2 | 3 | no | — |
| 97 | C11×C4⋊C4 | C22⋊C4 | 1 | 3 | yes | — |
| 98 | C11×C4⋊C4 | C22⋊C4 | 1 | 3 | yes | — |
| 99 | C11×C22⋊C4 | C22⋊C4 | 1 | 6 | yes | — |
| 100 | C42×C11 | C22×C4 | 1 | 3 | yes | — |
| 101 | C42×C11 | C2×D4 | 1 | 3 | yes | — |
| 102 | C42×C11 | C2×D4 | 1 | 3 | yes | — |
| 103 | C42×C11 | C24 | 1 | 1 | yes | characteristic |
| 104 | (C2×D11)⋊C4 | — | 2 | 6 | no | — |
| 105 | (C2×D11)⋊C4 | — | 2 | 6 | no | — |
| 106 | C4⋊Dic11 | — | 2 | 1 | no | — |
| 107 | C4⋊Dic11 | — | 2 | 1 | no | — |
| 108 | #4318 | — | 8 | 3 | no | — |
| 109 | C2×C11⋊C8 | — | 2 | 1 | no | — |
| 110 | C2×C11⋊C8 | — | 2 | 3 | no | — |
| 111 | #3498 | — | 11 | 1 | no | — |
| 112 | #2991 | — | 11 | 1 | no | — |
| 113 | #2991 | D11 | 1 | 1 | yes | characteristic, complemented |
| 114 | #1560 | — | 11 | 3 | no | — |
| 115 | #1545 | — | 11 | 3 | no | — |
| 116 | #1545 | — | 11 | 3 | no | — |
| 117 | #1543 | — | 11 | 3 | no | — |
| 118 | C23×C11 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 119 | C22×D11 | — | 2 | 6 | no | — |
| 120 | C22×D11 | — | 4 | 12 | no | — |
| 121 | C22×D11 | — | 8 | 6 | no | — |
| 122 | C22×D11 | — | 8 | 6 | no | — |
| 123 | Q8×C11 | #100 | 1 | 4 | yes | — |
| 124 | D4×C11 | — | 2 | 6 | no | — |
| 125 | C2×C4×C11 | — | 2 | 3 | no | — |
| 126 | C2×C4×C11 | — | 2 | 3 | no | — |
| 127 | C2×C4×C11 | — | 2 | 3 | no | — |
| 128 | C2×C4×C11 | — | 2 | 3 | no | — |
| 129 | C2×C4×C11 | — | 2 | 6 | no | — |
| 130 | C2×C4×C11 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 131 | C2×C4×C11 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 132 | C2×C4×C11 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 133 | C2×C4×C11 | C23×C4 | 1 | 1 | yes | characteristic |
| 134 | C2×C4×C11 | C22×D4 | 1 | 1 | yes | characteristic |
| 135 | C2×C4×C11 | C22×D4 | 1 | 1 | yes | characteristic |
| 136 | C22⋊D11 | — | 4 | 12 | no | — |
| 137 | C2×Dic11 | — | 2 | 2 | no | — |
| 138 | D44 | — | 4 | 6 | no | — |
| 139 | D44 | — | 4 | 3 | no | — |
| 140 | D44 | — | 4 | 3 | no | — |
| 141 | D44 | — | 4 | 3 | no | — |
| 142 | D44 | — | 4 | 3 | no | — |
| 143 | D44 | — | 4 | 12 | no | — |
| 144 | D44 | — | 8 | 6 | no | — |
| 145 | D44 | — | 8 | 6 | no | — |
| 146 | C4×D11 | — | 4 | 12 | no | — |
| 147 | Dic22 | — | 4 | 2 | no | — |
| 148 | C8×C11 | — | 4 | 3 | no | — |
| 149 | C8×C11 | — | 4 | 1 | no | — |
| 150 | C11⋊C8 | — | 4 | 3 | no | — |
| 151 | C11⋊C8 | — | 4 | 1 | no | — |
| 152 | C2×H(5,𝔽2) | — | 11 | 2 | no | — |
| 153 | #550 | — | 22 | 1 | no | — |
| 154 | #550 | — | 22 | 1 | no | — |
| 155 | D42 | — | 22 | 3 | no | — |
| 156 | D42 | — | 22 | 3 | no | — |
| 157 | #535 | — | 11 | 6 | no | — |
| 158 | #532 | — | 11 | 3 | no | — |
| 159 | C2×#127 | — | 11 | 3 | no | — |
| 160 | C4×#41 | C2×D11 | 1 | 1 | yes | characteristic |
| 161 | C8×Q8 | — | 2 | 1 | no | — |
| 162 | C8×Q8 | — | 22 | 1 | no | — |
| 163 | #436 | — | 2 | 3 | no | — |
| 164 | #436 | — | 22 | 3 | no | — |
| 165 | #431 | — | 11 | 3 | no | — |
| 166 | #431 | C2×D11 | 1 | 3 | yes | complemented |
| 167 | #423 | — | 11 | 3 | no | — |
| 168 | #423 | C2×D11 | 1 | 3 | yes | complemented |
| 169 | #333 | — | 11 | 1 | no | — |
| 170 | #333 | — | 11 | 3 | no | — |
| 171 | #331 | — | 11 | 3 | no | — |
| 172 | #331 | — | 11 | 3 | no | — |
| 173 | #331 | — | 11 | 6 | no | — |
| 174 | C22×C11 | — | 2 | 3 | no | — |
| 175 | C22×C11 | — | 2 | 3 | no | — |
| 176 | C22×C11 | — | 2 | 3 | no | — |
| 177 | C22×C11 | C22×C22⋊C4 | 1 | 1 | yes | characteristic |
| 178 | C2×D11 | — | 4 | 6 | no | — |
| 179 | C2×D11 | — | 4 | 6 | no | — |
| 180 | C2×D11 | — | 4 | 6 | no | — |
| 181 | C2×D11 | — | 16 | 12 | no | — |
| 182 | C4×C11 | — | 2 | 1 | no | — |
| 183 | C4×C11 | — | 2 | 3 | no | — |
| 184 | C4×C11 | — | 2 | 3 | no | — |
| 185 | C4×C11 | C2×#100 | 1 | 6 | yes | — |
| 186 | C4×C11 | #576 | 1 | 1 | yes | characteristic |
| 187 | C4×C11 | #576 | 1 | 1 | yes | characteristic |
| 188 | C4×C11 | #577 | 1 | 1 | yes | characteristic |
| 189 | C4×C11 | #577 | 1 | 1 | yes | characteristic |
| 190 | Dic11 | — | 4 | 2 | no | — |
| 191 | H(5,𝔽2) | — | 44 | 8 | no | — |
| 192 | C2×#41 | — | 11 | 6 | no | — |
| 193 | C2×#41 | — | 22 | 2 | no | — |
| 194 | C2×#41 | C4×D11 | 1 | 1 | yes | characteristic |
| 195 | C22×D4 | — | 11 | 6 | no | — |
| 196 | C22×D4 | — | 22 | 6 | no | — |
| 197 | C22×D4 | — | 22 | 3 | no | — |
| 198 | C22×D4 | — | 22 | 3 | no | — |
| 199 | C2×M16 | — | 2 | 3 | no | — |
| 200 | C2×M16 | — | 22 | 3 | no | — |
| 201 | C4⋊Q8 | — | 11 | 1 | no | — |
| 202 | #127 | — | 11 | 6 | no | — |
| 203 | #127 | — | 11 | 3 | no | — |
| 204 | #127 | — | 22 | 3 | no | — |
| 205 | #127 | — | 22 | 3 | no | — |
| 206 | #124 | — | 11 | 6 | no | — |
| 207 | #121 | — | 22 | 3 | no | — |
| 208 | #121 | — | 22 | 3 | no | — |
| 209 | #121 | — | 22 | 6 | no | — |
| 210 | #121 | — | 22 | 6 | no | — |
| 211 | #120 | — | 22 | 12 | no | — |
| 212 | C4×Q8 | D44 | 1 | 1 | yes | characteristic |
| 213 | C4×Q8 | C22⋊D11 | 1 | 1 | yes | characteristic |
| 214 | C4×D4 | — | 22 | 3 | no | — |
| 215 | C4×D4 | — | 22 | 3 | no | — |
| 216 | C4×D4 | D44 | 1 | 3 | yes | — |
| 217 | C4×D4 | C22⋊D11 | 1 | 3 | yes | — |
| 218 | #117 | C4×D11 | 1 | 3 | yes | — |
| 219 | C2×C42 | C22×D11 | 1 | 3 | yes | — |
| 220 | C4⋊C8 | — | 2 | 3 | no | — |
| 221 | C4⋊C8 | — | 11 | 3 | no | — |
| 222 | C4⋊C8 | — | 11 | 1 | no | — |
| 223 | C4⋊C8 | — | 22 | 3 | no | — |
| 224 | C4⋊C8 | C22×D11 | 1 | 3 | yes | — |
| 225 | C4⋊C8 | C22×D11 | 1 | 1 | yes | characteristic |
| 226 | C22⋊C8 | — | 2 | 3 | no | — |
| 227 | C22⋊C8 | — | 22 | 3 | no | — |
| 228 | C4×C8 | — | 2 | 3 | no | — |
| 229 | C4×C8 | — | 22 | 3 | no | — |
| 230 | C2×C11 | — | 4 | 3 | no | — |
| 231 | C2×C11 | C22×#100 | 1 | 1 | yes | characteristic |
| 232 | C2×C11 | #2897 | 1 | 1 | yes | characteristic |
| 233 | C2×C11 | #2897 | 1 | 1 | yes | characteristic |
| 234 | D11 | — | 8 | 6 | no | — |
| 235 | C24 | — | 22 | 6 | no | — |
| 236 | #41 | — | 2 | 4 | no | — |
| 237 | #41 | — | 44 | 12 | no | — |
| 238 | #41 | — | 44 | 8 | no | — |
| 239 | C2×Q8 | — | 11 | 2 | no | — |
| 240 | C2×Q8 | (C2×D11)⋊C4 | 1 | 1 | yes | characteristic |
| 241 | C2×D4 | — | 11 | 6 | no | — |
| 242 | C2×D4 | — | 22 | 6 | no | — |
| 243 | C2×D4 | — | 22 | 6 | no | — |
| 244 | C2×D4 | — | 22 | 6 | no | — |
| 245 | C2×D4 | — | 22 | 6 | no | — |
| 246 | C2×D4 | — | 22 | 3 | no | — |
| 247 | C2×D4 | — | 22 | 3 | no | — |
| 248 | C2×D4 | — | 44 | 12 | no | — |
| 249 | C2×D4 | — | 44 | 24 | no | — |
| 250 | C2×D4 | — | 88 | 3 | no | — |
| 251 | C2×D4 | — | 88 | 3 | no | — |
| 252 | C2×D4 | — | 88 | 3 | no | — |
| 253 | C2×D4 | — | 88 | 3 | no | — |
| 254 | C2×D4 | (C2×D11)⋊C4 | 1 | 3 | yes | — |
| 255 | C22×C4 | — | 22 | 6 | no | — |
| 256 | C22×C4 | C2×C4×D11 | 1 | 3 | yes | — |
| 257 | C22×C4 | C2×D44 | 1 | 3 | yes | — |
| 258 | C22×C4 | C2×C22⋊D11 | 1 | 3 | yes | — |
| 259 | M16 | — | 8 | 3 | no | — |
| 260 | M16 | — | 88 | 3 | no | — |
| 261 | C2×C8 | — | 2 | 1 | no | — |
| 262 | C2×C8 | — | 2 | 3 | no | — |
| 263 | C2×C8 | — | 22 | 1 | no | — |
| 264 | C2×C8 | — | 22 | 3 | no | — |
| 265 | C4⋊C4 | — | 22 | 1 | no | — |
| 266 | C4⋊C4 | — | 22 | 1 | no | — |
| 267 | C4⋊C4 | (C2×D11)⋊C4 | 1 | 3 | yes | — |
| 268 | C4⋊C4 | (C2×D11)⋊C4 | 1 | 3 | yes | — |
| 269 | C22⋊C4 | — | 22 | 6 | no | — |
| 270 | C22⋊C4 | — | 22 | 6 | no | — |
| 271 | C22⋊C4 | (C2×D11)⋊C4 | 1 | 6 | yes | — |
| 272 | C42 | C2×C4×D11 | 1 | 3 | yes | — |
| 273 | C42 | C2×D44 | 1 | 3 | yes | — |
| 274 | C42 | C2×C22⋊D11 | 1 | 3 | yes | — |
| 275 | C42 | C23×D11 | 1 | 1 | yes | characteristic |
| 276 | C11 | #17782 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 277 | C23 | — | 22 | 6 | no | — |
| 278 | C23 | — | 44 | 12 | no | — |
| 279 | C23 | — | 88 | 6 | no | — |
| 280 | C23 | — | 88 | 6 | no | — |
| 281 | C23 | C2×(C2×D11)⋊C4 | 1 | 3 | yes | — |
| 282 | Q8 | — | 44 | 2 | no | — |
| 283 | Q8 | #66887 | 1 | 4 | yes | — |
| 284 | D4 | — | 2 | 6 | no | — |
| 285 | D4 | — | 44 | 6 | no | — |
| 286 | D4 | — | 44 | 12 | no | — |
| 287 | D4 | — | 44 | 12 | no | — |
| 288 | D4 | — | 44 | 3 | no | — |
| 289 | D4 | — | 44 | 3 | no | — |
| 290 | D4 | — | 44 | 3 | no | — |
| 291 | D4 | — | 44 | 3 | no | — |
| 292 | D4 | — | 88 | 6 | no | — |
| 293 | D4 | — | 88 | 6 | no | — |
| 294 | C2×C4 | — | 2 | 6 | no | — |
| 295 | C2×C4 | — | 2 | 3 | no | — |
| 296 | C2×C4 | — | 2 | 3 | no | — |
| 297 | C2×C4 | — | 2 | 3 | no | — |
| 298 | C2×C4 | — | 2 | 3 | no | — |
| 299 | C2×C4 | — | 22 | 2 | no | — |
| 300 | C2×C4 | — | 44 | 12 | no | — |
| 301 | C2×C4 | C2×(C2×D11)⋊C4 | 1 | 3 | yes | — |
| 302 | C2×C4 | C2×(C2×D11)⋊C4 | 1 | 3 | yes | — |
| 303 | C2×C4 | C2×(C2×D11)⋊C4 | 1 | 3 | yes | — |
| 304 | C2×C4 | C22×C4×D11 | 1 | 1 | yes | characteristic |
| 305 | C2×C4 | C22×D44 | 1 | 1 | yes | characteristic |
| 306 | C2×C4 | C22×C22⋊D11 | 1 | 1 | yes | characteristic |
| 307 | C8 | — | 4 | 3 | no | — |
| 308 | C8 | — | 4 | 1 | no | — |
| 309 | C8 | — | 44 | 1 | no | — |
| 310 | C8 | — | 44 | 3 | no | — |
| 311 | C22 | — | 2 | 3 | no | — |
| 312 | C22 | — | 2 | 3 | no | — |
| 313 | C22 | — | 2 | 3 | no | — |
| 314 | C22 | — | 44 | 6 | no | — |
| 315 | C22 | — | 44 | 6 | no | — |
| 316 | C22 | — | 44 | 6 | no | — |
| 317 | C22 | — | 176 | 12 | no | — |
| 318 | C22 | C22×(C2×D11)⋊C4 | 1 | 1 | yes | characteristic |
| 319 | C4 | — | 2 | 1 | no | — |
| 320 | C4 | — | 2 | 3 | no | — |
| 321 | C4 | — | 2 | 3 | no | — |
| 322 | C4 | — | 44 | 2 | no | — |
| 323 | C4 | C2×#66887 | 1 | 6 | yes | — |
| 324 | C4 | #10623282 | 1 | 1 | yes | characteristic |
| 325 | C4 | #10623283 | 1 | 1 | yes | characteristic |
| 326 | C4 | #10623366 | 1 | 1 | yes | characteristic |
| 327 | C4 | #10623368 | 1 | 1 | yes | characteristic |
| 328 | C2 | — | 4 | 3 | no | — |
| 329 | C2 | — | 88 | 6 | no | — |
| 330 | C2 | C22×#66887 | 1 | 1 | yes | characteristic |
| 331 | C2 | #13077139 | 1 | 1 | yes | characteristic |
| 332 | C2 | #13077143 | 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