← #14909653
Subgroups — #14909653
Order 2816.
576 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 | #13078286 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #13070819 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #13070797 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #13070729 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #13070707 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #13070702 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #13070558 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #13070541 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | C11×#2113 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | C2×C11×#131 | C22 | 1 | 1 | yes | characteristic |
| 11 | #10623364 | — | 2 | 2 | no | — |
| 12 | C2×#66957 | C22 | 1 | 2 | yes | — |
| 13 | C2×C11×M32 | C22 | 1 | 1 | yes | characteristic |
| 14 | C22×C11×C16 | C22 | 1 | 1 | yes | characteristic |
| 15 | #10622747 | — | 2 | 2 | no | — |
| 16 | #10622747 | — | 2 | 2 | no | — |
| 17 | #10622746 | — | 2 | 2 | no | — |
| 18 | #10622729 | C22 | 1 | 2 | yes | — |
| 19 | #10622729 | C22 | 1 | 2 | yes | — |
| 20 | #10622728 | C22 | 1 | 2 | yes | — |
| 21 | #10622728 | C22 | 1 | 2 | yes | — |
| 22 | C2×#66882 | C22 | 1 | 2 | yes | — |
| 23 | C2×Dic88 | C22 | 1 | 1 | yes | characteristic |
| 24 | C2×#66864 | C22 | 1 | 2 | yes | — |
| 25 | C2×D176 | C22 | 1 | 1 | yes | characteristic |
| 26 | C11×C22⋊C16 | C22 | 1 | 2 | yes | — |
| 27 | C11×C22⋊C16 | C22 | 1 | 2 | yes | — |
| 28 | #10622147 | C22 | 1 | 2 | yes | — |
| 29 | #10622147 | C22 | 1 | 2 | yes | — |
| 30 | #10622142 | C22 | 1 | 1 | yes | characteristic |
| 31 | #10622142 | C22 | 1 | 1 | yes | characteristic |
| 32 | #10622142 | C22 | 1 | 2 | yes | — |
| 33 | #10622141 | C22 | 1 | 2 | yes | — |
| 34 | #10622141 | C22 | 1 | 2 | yes | — |
| 35 | C2×C11×#41 | D4 | 1 | 1 | yes | characteristic |
| 36 | C2×#4339 | — | 2 | 2 | no | — |
| 37 | C11×#131 | — | 4 | 1 | no | — |
| 38 | C11×#131 | — | 4 | 1 | no | — |
| 39 | C2×C11×M16 | D4 | 1 | 2 | yes | — |
| 40 | C2×C11×M16 | D4 | 1 | 1 | yes | characteristic |
| 41 | C22×C8×C11 | C23 | 1 | 1 | yes | characteristic |
| 42 | C22×C8×C11 | C23 | 1 | 2 | yes | — |
| 43 | #66999 | — | 4 | 2 | no | — |
| 44 | #66992 | — | 4 | 2 | no | — |
| 45 | #66992 | — | 4 | 2 | no | — |
| 46 | #66991 | — | 4 | 2 | no | — |
| 47 | #66983 | — | 2 | 2 | no | — |
| 48 | #66983 | — | 2 | 2 | no | — |
| 49 | C2×C4⋊Dic11 | — | 2 | 2 | no | — |
| 50 | #66977 | — | 2 | 2 | no | — |
| 51 | #66977 | — | 2 | 2 | no | — |
| 52 | C2×Dic44 | C23 | 1 | 2 | yes | — |
| 53 | #66957 | — | 4 | 2 | no | — |
| 54 | #66957 | — | 4 | 2 | no | — |
| 55 | C2×D88 | C23 | 1 | 2 | yes | — |
| 56 | C2×#4314 | — | 2 | 2 | no | — |
| 57 | C11×M32 | — | 4 | 1 | no | — |
| 58 | C2×C11×C16 | — | 4 | 1 | no | — |
| 59 | C2×C11×C16 | C23 | 1 | 1 | yes | characteristic |
| 60 | C2×C11×C16 | C23 | 1 | 1 | yes | characteristic |
| 61 | C2×C11×C16 | C23 | 1 | 2 | yes | — |
| 62 | #66885 | — | 2 | 2 | no | — |
| 63 | #66885 | — | 2 | 2 | no | — |
| 64 | #66882 | — | 2 | 2 | no | — |
| 65 | #66882 | C23 | 1 | 2 | yes | — |
| 66 | #66882 | C23 | 1 | 2 | yes | — |
| 67 | #66880 | — | 2 | 2 | no | — |
| 68 | #66880 | — | 2 | 2 | no | — |
| 69 | Dic88 | — | 4 | 1 | no | — |
| 70 | #66864 | — | 4 | 2 | no | — |
| 71 | D176 | — | 4 | 1 | no | — |
| 72 | #33769 | — | 11 | 1 | no | maximal, Sylow |
| 73 | C11×#41 | — | 4 | 1 | no | — |
| 74 | C11×#41 | — | 4 | 1 | no | — |
| 75 | C2×Q8×C11 | D8 | 1 | 1 | yes | characteristic |
| 76 | C2×D4×C11 | D8 | 1 | 2 | yes | — |
| 77 | C2×D4×C11 | D8 | 1 | 1 | yes | characteristic |
| 78 | C22×C4×C11 | C2×D4 | 1 | 1 | yes | characteristic |
| 79 | C22×C4×C11 | C2×D4 | 1 | 2 | yes | — |
| 80 | C2×C22⋊D11 | — | 4 | 2 | no | — |
| 81 | C2×C22⋊D11 | — | 4 | 2 | no | — |
| 82 | C2×C22⋊D11 | — | 4 | 2 | no | — |
| 83 | C22×Dic11 | — | 4 | 2 | no | — |
| 84 | #4339 | — | 4 | 4 | no | — |
| 85 | #4339 | — | 4 | 4 | no | — |
| 86 | C2×D44 | — | 2 | 2 | no | — |
| 87 | C2×C4×D11 | — | 4 | 2 | no | — |
| 88 | C2×Dic22 | — | 2 | 2 | no | — |
| 89 | C11×M16 | — | 4 | 2 | no | — |
| 90 | C11×M16 | — | 4 | 1 | no | — |
| 91 | C2×C8×C11 | — | 2 | 1 | no | — |
| 92 | C2×C8×C11 | — | 2 | 1 | no | — |
| 93 | C2×C8×C11 | — | 2 | 2 | no | — |
| 94 | C2×C8×C11 | — | 2 | 2 | no | — |
| 95 | C2×C8×C11 | C2×D4 | 1 | 1 | yes | characteristic |
| 96 | C2×C8×C11 | C2×D4 | 1 | 2 | yes | — |
| 97 | C2×C8×C11 | C24 | 1 | 1 | yes | characteristic |
| 98 | C22⋊Dic11 | — | 4 | 2 | no | — |
| 99 | C22⋊Dic11 | — | 4 | 2 | no | — |
| 100 | (C2×D11)⋊C4 | — | 4 | 2 | no | — |
| 101 | (C2×D11)⋊C4 | — | 4 | 2 | no | — |
| 102 | C4⋊Dic11 | — | 2 | 2 | no | — |
| 103 | C4⋊Dic11 | — | 2 | 2 | no | — |
| 104 | C4⋊Dic11 | — | 4 | 2 | no | — |
| 105 | Dic11⋊C4 | — | 4 | 2 | no | — |
| 106 | Dic11⋊C4 | — | 4 | 2 | no | — |
| 107 | Dic44 | — | 2 | 2 | no | — |
| 108 | Dic44 | — | 2 | 2 | no | — |
| 109 | D88 | — | 2 | 2 | no | — |
| 110 | D88 | — | 2 | 2 | no | — |
| 111 | #4314 | — | 4 | 4 | no | — |
| 112 | C11×C16 | — | 2 | 1 | no | — |
| 113 | C11×C16 | — | 2 | 2 | no | — |
| 114 | C11×C16 | — | 2 | 1 | no | — |
| 115 | #3061 | — | 11 | 2 | no | — |
| 116 | #2236 | — | 11 | 2 | no | — |
| 117 | #2232 | — | 11 | 2 | no | — |
| 118 | #2220 | — | 11 | 2 | no | — |
| 119 | #2216 | — | 11 | 1 | no | — |
| 120 | #2215 | — | 11 | 1 | no | — |
| 121 | #2189 | — | 11 | 2 | no | — |
| 122 | #2186 | — | 11 | 2 | no | — |
| 123 | #2113 | D11 | 1 | 1 | yes | characteristic, complemented |
| 124 | C23×C11 | C2×D8 | 1 | 1 | yes | characteristic |
| 125 | C23×C11 | C2×D8 | 1 | 2 | yes | — |
| 126 | C22×D11 | — | 4 | 2 | no | — |
| 127 | Q8×C11 | — | 4 | 1 | no | — |
| 128 | D4×C11 | — | 4 | 1 | no | — |
| 129 | D4×C11 | — | 4 | 2 | no | — |
| 130 | C2×C4×C11 | — | 2 | 2 | no | — |
| 131 | C2×C4×C11 | — | 2 | 1 | no | — |
| 132 | C2×C4×C11 | — | 2 | 2 | no | — |
| 133 | C2×C4×C11 | — | 2 | 1 | no | — |
| 134 | C2×C4×C11 | C2×D8 | 1 | 1 | yes | characteristic |
| 135 | C2×C4×C11 | C2×D8 | 1 | 2 | yes | — |
| 136 | C2×C4×C11 | C22×D4 | 1 | 1 | yes | characteristic |
| 137 | C22⋊D11 | — | 8 | 4 | no | — |
| 138 | C22⋊D11 | — | 16 | 2 | no | — |
| 139 | C22⋊D11 | — | 16 | 2 | no | — |
| 140 | C2×Dic11 | — | 4 | 2 | no | — |
| 141 | C2×Dic11 | — | 4 | 2 | no | — |
| 142 | C2×Dic11 | — | 4 | 2 | no | — |
| 143 | C2×Dic11 | — | 16 | 2 | no | — |
| 144 | D44 | — | 4 | 2 | no | — |
| 145 | D44 | — | 4 | 2 | no | — |
| 146 | C4×D11 | — | 8 | 4 | no | — |
| 147 | Dic22 | — | 4 | 2 | no | — |
| 148 | Dic22 | — | 4 | 2 | no | — |
| 149 | C8×C11 | — | 2 | 2 | no | — |
| 150 | C8×C11 | — | 2 | 1 | no | — |
| 151 | C8×C11 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 152 | C8×C11 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 153 | C2×#135 | — | 11 | 2 | no | — |
| 154 | C2×#131 | C2×D11 | 1 | 1 | yes | characteristic |
| 155 | #537 | — | 22 | 2 | no | — |
| 156 | C2×Q32 | — | 11 | 1 | no | — |
| 157 | C2×SD32 | — | 11 | 2 | no | — |
| 158 | C2×D16 | — | 11 | 1 | no | — |
| 159 | C2×M32 | C2×D11 | 1 | 1 | yes | characteristic |
| 160 | C22×C16 | C2×D11 | 1 | 1 | yes | characteristic |
| 161 | #468 | — | 22 | 2 | no | — |
| 162 | #468 | — | 22 | 2 | no | — |
| 163 | #467 | — | 11 | 2 | no | — |
| 164 | #467 | — | 11 | 2 | no | — |
| 165 | #466 | — | 11 | 2 | no | — |
| 166 | #466 | — | 11 | 2 | no | — |
| 167 | C2×#107 | — | 11 | 2 | no | — |
| 168 | #417 | — | 22 | 2 | no | — |
| 169 | #366 | — | 11 | 1 | no | — |
| 170 | #366 | — | 11 | 1 | no | — |
| 171 | #366 | — | 11 | 2 | no | — |
| 172 | #358 | — | 11 | 2 | no | — |
| 173 | #358 | — | 11 | 2 | no | — |
| 174 | #357 | — | 11 | 2 | no | — |
| 175 | #357 | — | 11 | 2 | no | — |
| 176 | C22⋊C16 | C2×D11 | 1 | 2 | yes | — |
| 177 | C22⋊C16 | C2×D11 | 1 | 2 | yes | — |
| 178 | C22×C11 | — | 2 | 2 | no | — |
| 179 | C22×C11 | — | 2 | 1 | no | — |
| 180 | C22×C11 | — | 2 | 1 | no | — |
| 181 | C22×C11 | — | 2 | 2 | no | — |
| 182 | C22×C11 | — | 2 | 1 | no | — |
| 183 | C22×C11 | — | 2 | 2 | no | — |
| 184 | C22×C11 | C22×D8 | 1 | 1 | yes | characteristic |
| 185 | C2×D11 | — | 8 | 2 | no | — |
| 186 | C2×D11 | — | 8 | 2 | no | — |
| 187 | C2×D11 | — | 8 | 2 | no | — |
| 188 | C4×C11 | — | 2 | 1 | no | — |
| 189 | C4×C11 | — | 2 | 2 | no | — |
| 190 | C4×C11 | #534 | 1 | 1 | yes | characteristic |
| 191 | C4×C11 | #575 | 1 | 1 | yes | characteristic |
| 192 | Dic11 | — | 8 | 2 | no | — |
| 193 | Dic11 | — | 8 | 2 | no | — |
| 194 | Dic11 | — | 8 | 2 | no | — |
| 195 | C2×#41 | — | 22 | 2 | no | — |
| 196 | C2×#41 | D44 | 1 | 1 | yes | characteristic |
| 197 | #135 | — | 44 | 2 | no | — |
| 198 | #135 | — | 44 | 2 | no | — |
| 199 | C2×Q16 | — | 11 | 2 | no | — |
| 200 | C2×SD16 | — | 22 | 2 | no | — |
| 201 | C2×D8 | — | 11 | 2 | no | — |
| 202 | #131 | — | 4 | 1 | no | — |
| 203 | #131 | — | 4 | 1 | no | — |
| 204 | C2×M16 | D44 | 1 | 2 | yes | — |
| 205 | C2×M16 | D44 | 1 | 1 | yes | characteristic |
| 206 | C22×C8 | C22×D11 | 1 | 2 | yes | — |
| 207 | C22×C8 | C22×D11 | 1 | 1 | yes | characteristic |
| 208 | C22⋊Q8 | — | 22 | 2 | no | — |
| 209 | C22⋊Q8 | — | 22 | 2 | no | — |
| 210 | C22⋊Q8 | — | 44 | 2 | no | — |
| 211 | #121 | — | 22 | 2 | no | — |
| 212 | #121 | — | 22 | 2 | no | — |
| 213 | #121 | — | 44 | 2 | no | — |
| 214 | #121 | — | 44 | 2 | no | — |
| 215 | #121 | — | 44 | 2 | no | — |
| 216 | C2×C4⋊C4 | — | 22 | 2 | no | — |
| 217 | Q32 | — | 44 | 1 | no | — |
| 218 | SD32 | — | 44 | 2 | no | — |
| 219 | D16 | — | 44 | 1 | no | — |
| 220 | M32 | — | 4 | 1 | no | — |
| 221 | C2×C16 | — | 4 | 1 | no | — |
| 222 | C2×C16 | C22×D11 | 1 | 1 | yes | characteristic |
| 223 | C2×C16 | C22×D11 | 1 | 2 | yes | — |
| 224 | C2×C16 | C22×D11 | 1 | 1 | yes | characteristic |
| 225 | #107 | — | 11 | 2 | no | — |
| 226 | #107 | — | 11 | 2 | no | — |
| 227 | #107 | — | 22 | 2 | no | — |
| 228 | #103 | — | 22 | 2 | no | — |
| 229 | #103 | — | 22 | 2 | no | — |
| 230 | #102 | — | 22 | 2 | no | — |
| 231 | #102 | — | 22 | 2 | no | — |
| 232 | C2×C11 | — | 4 | 2 | no | — |
| 233 | C2×C11 | — | 4 | 1 | no | — |
| 234 | C2×C11 | #3186 | 1 | 1 | yes | characteristic |
| 235 | C2×C11 | #3415 | 1 | 1 | yes | characteristic |
| 236 | C2×C11 | #3417 | 1 | 1 | yes | characteristic |
| 237 | D11 | — | 16 | 2 | no | — |
| 238 | #41 | — | 4 | 1 | no | — |
| 239 | #41 | — | 4 | 1 | no | — |
| 240 | #41 | — | 44 | 4 | no | — |
| 241 | #41 | — | 44 | 4 | no | — |
| 242 | C2×Q8 | — | 22 | 2 | no | — |
| 243 | C2×Q8 | D88 | 1 | 1 | yes | characteristic |
| 244 | C2×D4 | — | 22 | 2 | no | — |
| 245 | C2×D4 | — | 44 | 2 | no | — |
| 246 | C2×D4 | — | 44 | 2 | no | — |
| 247 | C2×D4 | — | 44 | 2 | no | — |
| 248 | C2×D4 | D88 | 1 | 1 | yes | characteristic |
| 249 | C2×D4 | D88 | 1 | 2 | yes | — |
| 250 | C22×C4 | — | 44 | 2 | no | — |
| 251 | C22×C4 | — | 44 | 2 | no | — |
| 252 | C22×C4 | C2×D44 | 1 | 2 | yes | — |
| 253 | C22×C4 | C2×D44 | 1 | 1 | yes | characteristic |
| 254 | Q16 | — | 22 | 2 | no | — |
| 255 | Q16 | — | 22 | 2 | no | — |
| 256 | SD16 | — | 44 | 4 | no | — |
| 257 | D8 | — | 22 | 2 | no | — |
| 258 | D8 | — | 22 | 2 | no | — |
| 259 | M16 | — | 4 | 1 | no | — |
| 260 | M16 | — | 4 | 2 | no | — |
| 261 | C2×C8 | — | 2 | 1 | no | — |
| 262 | C2×C8 | — | 2 | 1 | no | — |
| 263 | C2×C8 | — | 2 | 2 | no | — |
| 264 | C2×C8 | — | 2 | 2 | no | — |
| 265 | C2×C8 | C2×D44 | 1 | 1 | yes | characteristic |
| 266 | C2×C8 | C2×D44 | 1 | 2 | yes | — |
| 267 | C2×C8 | C23×D11 | 1 | 1 | yes | characteristic |
| 268 | C4⋊C4 | — | 22 | 2 | no | — |
| 269 | C4⋊C4 | — | 22 | 2 | no | — |
| 270 | C4⋊C4 | — | 44 | 2 | no | — |
| 271 | C4⋊C4 | — | 44 | 2 | no | — |
| 272 | C4⋊C4 | — | 44 | 2 | no | — |
| 273 | C22⋊C4 | — | 44 | 2 | no | — |
| 274 | C22⋊C4 | — | 44 | 2 | no | — |
| 275 | C22⋊C4 | — | 44 | 2 | no | — |
| 276 | C22⋊C4 | — | 44 | 2 | no | — |
| 277 | C16 | — | 2 | 1 | no | — |
| 278 | C16 | — | 2 | 1 | no | — |
| 279 | C16 | — | 2 | 2 | no | — |
| 280 | C11 | #33769 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 281 | C23 | — | 44 | 2 | no | — |
| 282 | C23 | C2×D88 | 1 | 1 | yes | characteristic |
| 283 | C23 | C2×D88 | 1 | 2 | yes | — |
| 284 | Q8 | — | 4 | 1 | no | — |
| 285 | Q8 | — | 44 | 2 | no | — |
| 286 | Q8 | — | 44 | 2 | no | — |
| 287 | D4 | — | 4 | 2 | no | — |
| 288 | D4 | — | 4 | 1 | no | — |
| 289 | D4 | — | 44 | 2 | no | — |
| 290 | D4 | — | 44 | 2 | no | — |
| 291 | D4 | — | 88 | 4 | no | — |
| 292 | D4 | — | 176 | 2 | no | — |
| 293 | D4 | — | 176 | 2 | no | — |
| 294 | C2×C4 | — | 2 | 1 | no | — |
| 295 | C2×C4 | — | 2 | 2 | no | — |
| 296 | C2×C4 | — | 2 | 1 | no | — |
| 297 | C2×C4 | — | 2 | 2 | no | — |
| 298 | C2×C4 | — | 44 | 2 | no | — |
| 299 | C2×C4 | — | 44 | 2 | no | — |
| 300 | C2×C4 | — | 44 | 2 | no | — |
| 301 | C2×C4 | — | 88 | 4 | no | — |
| 302 | C2×C4 | — | 176 | 2 | no | — |
| 303 | C2×C4 | C2×D88 | 1 | 1 | yes | characteristic |
| 304 | C2×C4 | C2×D88 | 1 | 2 | yes | — |
| 305 | C2×C4 | C22×D44 | 1 | 1 | yes | characteristic |
| 306 | C8 | — | 2 | 2 | no | — |
| 307 | C8 | — | 2 | 1 | no | — |
| 308 | C8 | #67037 | 1 | 1 | yes | characteristic |
| 309 | C8 | #67037 | 1 | 1 | yes | characteristic |
| 310 | C22 | — | 2 | 2 | no | — |
| 311 | C22 | — | 2 | 1 | no | — |
| 312 | C22 | — | 2 | 2 | no | — |
| 313 | C22 | — | 2 | 1 | no | — |
| 314 | C22 | — | 2 | 1 | no | — |
| 315 | C22 | — | 2 | 2 | no | — |
| 316 | C22 | — | 88 | 2 | no | — |
| 317 | C22 | — | 88 | 2 | no | — |
| 318 | C22 | — | 88 | 2 | no | — |
| 319 | C22 | C22×D88 | 1 | 1 | yes | characteristic |
| 320 | C4 | — | 2 | 2 | no | — |
| 321 | C4 | — | 2 | 1 | no | — |
| 322 | C4 | — | 88 | 2 | no | — |
| 323 | C4 | — | 88 | 2 | no | — |
| 324 | C4 | — | 88 | 2 | no | — |
| 325 | C4 | #10623024 | 1 | 1 | yes | characteristic |
| 326 | C4 | #10623279 | 1 | 1 | yes | characteristic |
| 327 | C2 | — | 4 | 2 | no | — |
| 328 | C2 | — | 4 | 1 | no | — |
| 329 | C2 | — | 176 | 2 | no | — |
| 330 | C2 | #13079367 | 1 | 1 | yes | characteristic |
| 331 | C2 | #13081757 | 1 | 1 | yes | characteristic |
| 332 | C2 | #13081769 | 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