← #14780341
Subgroups — #14780341
Order 2816.
688 conjugacy classes of subgroups.
The subgroup lattice has 348 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #13079075 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #13069111 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #13069109 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #13069090 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #13069088 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #13069008 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #13068998 | C2 | 1 | 2 | yes | maximal |
| 8 | #13068765 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | C11×#1841 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | C2×#66962 | C22 | 1 | 2 | yes | — |
| 11 | C2×#66962 | C22 | 1 | 2 | yes | — |
| 12 | #10623276 | C22 | 1 | 2 | yes | — |
| 13 | #10623047 | C22 | 1 | 2 | yes | — |
| 14 | #10623008 | C22 | 1 | 1 | yes | characteristic |
| 15 | C2×#66922 | C22 | 1 | 1 | yes | characteristic |
| 16 | C4×C11×M16 | C22 | 1 | 1 | yes | characteristic |
| 17 | #10622752 | C22 | 1 | 2 | yes | — |
| 18 | C2×#66888 | C22 | 1 | 2 | yes | — |
| 19 | #10622733 | C22 | 1 | 2 | yes | — |
| 20 | #10622619 | C22 | 1 | 2 | yes | — |
| 21 | #10622618 | C22 | 1 | 2 | yes | — |
| 22 | #10622617 | C22 | 1 | 2 | yes | — |
| 23 | #10622328 | C4 | 1 | 4 | yes | complemented |
| 24 | #10622312 | C4 | 1 | 2 | yes | complemented |
| 25 | #10622306 | C4 | 1 | 2 | yes | complemented |
| 26 | C11×#344 | C22 | 1 | 2 | yes | — |
| 27 | C11×#339 | C22 | 1 | 2 | yes | — |
| 28 | C11×#338 | C22 | 1 | 1 | yes | characteristic |
| 29 | C11×H(3,ℤ/4) | C22 | 1 | 1 | yes | characteristic |
| 30 | C11⋊#338 | C22 | 1 | 1 | yes | characteristic |
| 31 | #10622195 | C22 | 1 | 1 | yes | characteristic |
| 32 | #10622194 | C22 | 1 | 2 | yes | — |
| 33 | #10622161 | C22 | 1 | 2 | yes | — |
| 34 | C2×#4339 | C23 | 1 | 2 | yes | — |
| 35 | C22×Dic22 | C23 | 1 | 2 | yes | — |
| 36 | C2×C11×M16 | C23 | 1 | 2 | yes | — |
| 37 | C2×C11×M16 | C23 | 1 | 1 | yes | characteristic |
| 38 | C2×C11×M16 | C23 | 1 | 1 | yes | characteristic |
| 39 | C11×#117 | C23 | 1 | 2 | yes | — |
| 40 | C2×C42×C11 | C23 | 1 | 1 | yes | characteristic |
| 41 | #66983 | — | 4 | 1 | no | — |
| 42 | #66979 | C23 | 1 | 2 | yes | — |
| 43 | C2×C4⋊Dic11 | — | 4 | 1 | no | — |
| 44 | C2×#4318 | C23 | 1 | 2 | yes | — |
| 45 | #66962 | — | 4 | 2 | no | — |
| 46 | #66962 | — | 4 | 2 | no | — |
| 47 | #66962 | — | 4 | 2 | no | — |
| 48 | #66962 | — | 4 | 2 | no | — |
| 49 | #66960 | — | 4 | 2 | no | — |
| 50 | M16×D11 | — | 4 | 2 | no | — |
| 51 | C2×Dic44 | C2×C4 | 1 | 4 | yes | — |
| 52 | C2×Dic44 | C2×C4 | 1 | 4 | yes | — |
| 53 | C2×#4314 | C2×C4 | 1 | 4 | yes | — |
| 54 | C2×#4314 | C2×C4 | 1 | 4 | yes | — |
| 55 | #66954 | — | 4 | 2 | no | — |
| 56 | #66940 | — | 4 | 2 | no | — |
| 57 | #66930 | — | 4 | 2 | no | — |
| 58 | #66928 | C2×C4 | 1 | 2 | yes | — |
| 59 | #66927 | C2×C4 | 1 | 1 | yes | characteristic |
| 60 | C4×D44 | — | 4 | 1 | no | — |
| 61 | #66922 | — | 4 | 1 | no | — |
| 62 | #66922 | C2×C4 | 1 | 2 | yes | — |
| 63 | #66922 | C2×C4 | 1 | 2 | yes | — |
| 64 | #66922 | C2×C4 | 1 | 1 | yes | characteristic |
| 65 | C4×Dic22 | — | 4 | 2 | no | — |
| 66 | C11×#97 | C2×C4 | 1 | 2 | yes | — |
| 67 | C4×C8×C11 | C2×C4 | 1 | 2 | yes | — |
| 68 | #66889 | — | 4 | 2 | no | — |
| 69 | #66888 | — | 4 | 2 | no | — |
| 70 | #66880 | — | 4 | 2 | no | — |
| 71 | #66874 | — | 4 | 2 | no | — |
| 72 | #66870 | — | 4 | 2 | no | — |
| 73 | #66869 | — | 4 | 2 | no | — |
| 74 | #23360 | — | 11 | 1 | no | maximal, Sylow |
| 75 | C22×C4×C11 | — | 2 | 1 | no | — |
| 76 | C22×C4×C11 | C24 | 1 | 1 | yes | characteristic |
| 77 | C2×C22⋊D11 | — | 2 | 2 | no | — |
| 78 | C22×Dic11 | — | 2 | 2 | no | — |
| 79 | #4339 | — | 2 | 2 | no | — |
| 80 | #4339 | — | 2 | 2 | no | — |
| 81 | #4339 | — | 2 | 2 | no | — |
| 82 | #4339 | — | 2 | 2 | no | — |
| 83 | C2×D44 | — | 4 | 1 | no | — |
| 84 | C2×D44 | C22×C4 | 1 | 2 | yes | — |
| 85 | C2×C4×D11 | — | 2 | 2 | no | — |
| 86 | C2×Dic22 | — | 2 | 2 | no | — |
| 87 | C2×Dic22 | — | 2 | 2 | no | — |
| 88 | C2×Dic22 | — | 2 | 2 | no | — |
| 89 | C2×Dic22 | — | 2 | 2 | no | — |
| 90 | C2×Dic22 | — | 2 | 2 | no | — |
| 91 | C2×Dic22 | C22×C4 | 1 | 4 | yes | — |
| 92 | C2×Dic22 | C22×C4 | 1 | 2 | yes | — |
| 93 | C11×M16 | — | 2 | 2 | no | — |
| 94 | C11×M16 | — | 2 | 2 | no | — |
| 95 | C11×M16 | — | 2 | 2 | no | — |
| 96 | C11×M16 | — | 2 | 2 | no | — |
| 97 | C2×C8×C11 | — | 2 | 2 | no | — |
| 98 | C2×C8×C11 | C22×C4 | 1 | 2 | yes | — |
| 99 | C2×C8×C11 | C22×C4 | 1 | 2 | yes | — |
| 100 | C11×C4⋊C4 | — | 2 | 2 | no | — |
| 101 | C11×C22⋊C4 | — | 2 | 2 | no | — |
| 102 | C42×C11 | — | 2 | 1 | no | — |
| 103 | C42×C11 | — | 2 | 2 | no | — |
| 104 | C42×C11 | C22×C4 | 1 | 1 | yes | characteristic |
| 105 | C42×C11 | C22×C4 | 1 | 1 | yes | characteristic |
| 106 | C22⋊Dic11 | — | 2 | 2 | no | — |
| 107 | (C2×D11)⋊C4 | — | 4 | 2 | no | — |
| 108 | C4⋊Dic11 | — | 2 | 2 | no | — |
| 109 | C4⋊Dic11 | — | 4 | 2 | no | — |
| 110 | C4⋊Dic11 | — | 4 | 2 | no | — |
| 111 | C4⋊Dic11 | — | 4 | 1 | no | — |
| 112 | Dic11⋊C4 | — | 4 | 4 | no | — |
| 113 | C4×Dic11 | — | 2 | 2 | no | — |
| 114 | C4×Dic11 | — | 4 | 4 | no | — |
| 115 | #4318 | — | 2 | 2 | no | — |
| 116 | #4318 | — | 2 | 2 | no | — |
| 117 | C2×C11⋊C8 | — | 2 | 2 | no | — |
| 118 | Dic44 | — | 4 | 4 | no | — |
| 119 | Dic44 | — | 4 | 4 | no | — |
| 120 | #4314 | — | 4 | 4 | no | — |
| 121 | #4314 | — | 4 | 4 | no | — |
| 122 | #4313 | — | 4 | 4 | no | — |
| 123 | C8×D11 | — | 4 | 4 | no | — |
| 124 | #3152 | — | 11 | 1 | no | — |
| 125 | #1905 | — | 11 | 2 | no | — |
| 126 | #1905 | — | 11 | 2 | no | — |
| 127 | #1902 | — | 11 | 2 | no | — |
| 128 | #1902 | — | 11 | 2 | no | — |
| 129 | #1886 | — | 11 | 2 | no | — |
| 130 | #1884 | — | 11 | 2 | no | — |
| 131 | #1841 | — | 11 | 1 | no | — |
| 132 | #1841 | D11 | 1 | 1 | yes | characteristic, complemented |
| 133 | C23×C11 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 134 | C22×D11 | — | 2 | 2 | no | — |
| 135 | C2×C4×C11 | — | 2 | 1 | no | — |
| 136 | C2×C4×C11 | — | 2 | 1 | no | — |
| 137 | C2×C4×C11 | — | 4 | 2 | no | — |
| 138 | C2×C4×C11 | — | 4 | 2 | no | — |
| 139 | C2×C4×C11 | C23×C4 | 1 | 1 | yes | characteristic |
| 140 | C2×C4×C11 | H(5,𝔽2) | 1 | 2 | yes | — |
| 141 | C2×C4×C11 | H(5,𝔽2) | 1 | 2 | yes | — |
| 142 | C2×C4×C11 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 143 | C22⋊D11 | — | 4 | 2 | no | — |
| 144 | C22⋊D11 | — | 4 | 2 | no | — |
| 145 | C2×Dic11 | — | 2 | 4 | no | — |
| 146 | C2×Dic11 | — | 2 | 2 | no | — |
| 147 | C2×Dic11 | — | 4 | 2 | no | — |
| 148 | C2×Dic11 | — | 4 | 2 | no | — |
| 149 | C2×Dic11 | — | 4 | 2 | no | — |
| 150 | D44 | — | 2 | 2 | no | — |
| 151 | D44 | — | 2 | 2 | no | — |
| 152 | D44 | — | 8 | 2 | no | — |
| 153 | C4×D11 | — | 4 | 2 | no | — |
| 154 | C4×D11 | — | 4 | 2 | no | — |
| 155 | Dic22 | — | 2 | 4 | no | — |
| 156 | Dic22 | — | 2 | 4 | no | — |
| 157 | Dic22 | — | 2 | 2 | no | — |
| 158 | Dic22 | — | 2 | 2 | no | — |
| 159 | Dic22 | — | 4 | 2 | no | — |
| 160 | Dic22 | — | 4 | 2 | no | — |
| 161 | C8×C11 | — | 2 | 2 | no | — |
| 162 | C8×C11 | — | 2 | 2 | no | — |
| 163 | C8×C11 | — | 4 | 2 | no | — |
| 164 | C11⋊C8 | — | 4 | 2 | no | — |
| 165 | C2×#137 | — | 11 | 2 | no | — |
| 166 | C2×#137 | — | 11 | 2 | no | — |
| 167 | #568 | — | 11 | 2 | no | — |
| 168 | #532 | — | 11 | 1 | no | — |
| 169 | C2×C4⋊Q8 | — | 11 | 1 | no | — |
| 170 | #519 | — | 11 | 2 | no | — |
| 171 | #497 | — | 11 | 4 | no | — |
| 172 | #494 | — | 11 | 2 | no | — |
| 173 | #492 | — | 11 | 2 | no | — |
| 174 | #421 | — | 11 | 2 | no | — |
| 175 | #421 | — | 11 | 2 | no | — |
| 176 | #419 | — | 11 | 2 | no | — |
| 177 | #419 | — | 11 | 2 | no | — |
| 178 | C2×#101 | — | 11 | 2 | no | — |
| 179 | #410 | — | 11 | 2 | no | — |
| 180 | C4×M16 | C2×D11 | 1 | 1 | yes | characteristic |
| 181 | #344 | — | 11 | 2 | no | — |
| 182 | #344 | C2×D11 | 1 | 2 | yes | — |
| 183 | #339 | — | 11 | 2 | no | — |
| 184 | #339 | C2×D11 | 1 | 2 | yes | — |
| 185 | #338 | — | 11 | 1 | no | — |
| 186 | #338 | C2×D11 | 1 | 1 | yes | characteristic |
| 187 | H(3,ℤ/4) | — | 11 | 1 | no | — |
| 188 | H(3,ℤ/4) | C2×D11 | 1 | 1 | yes | characteristic |
| 189 | C22×C11 | — | 4 | 1 | no | — |
| 190 | C22×C11 | #518 | 1 | 1 | yes | characteristic |
| 191 | C22×C11 | #560 | 1 | 2 | yes | — |
| 192 | C2×D11 | — | 4 | 2 | no | — |
| 193 | C2×D11 | — | 8 | 2 | no | — |
| 194 | C4×C11 | — | 2 | 2 | no | — |
| 195 | C4×C11 | — | 4 | 1 | no | — |
| 196 | C4×C11 | — | 8 | 2 | no | — |
| 197 | C4×C11 | #518 | 1 | 1 | yes | characteristic |
| 198 | C4×C11 | #518 | 1 | 1 | yes | characteristic |
| 199 | C4×C11 | #560 | 1 | 2 | yes | — |
| 200 | Dic11 | — | 4 | 4 | no | — |
| 201 | Dic11 | — | 4 | 2 | no | — |
| 202 | Dic11 | — | 8 | 2 | no | — |
| 203 | C2×#41 | — | 11 | 2 | no | — |
| 204 | C22×Q8 | — | 11 | 2 | no | — |
| 205 | #137 | — | 44 | 2 | no | — |
| 206 | #137 | — | 44 | 2 | no | — |
| 207 | #137 | — | 44 | 2 | no | — |
| 208 | #137 | — | 44 | 2 | no | — |
| 209 | C2×Q16 | — | 11 | 4 | no | — |
| 210 | C2×Q16 | — | 11 | 4 | no | — |
| 211 | C2×SD16 | — | 11 | 4 | no | — |
| 212 | C2×SD16 | — | 11 | 4 | no | — |
| 213 | #131 | — | 44 | 2 | no | — |
| 214 | #131 | — | 44 | 2 | no | — |
| 215 | C2×M16 | — | 11 | 2 | no | — |
| 216 | C2×M16 | — | 44 | 2 | no | — |
| 217 | C2×M16 | C22×D11 | 1 | 2 | yes | — |
| 218 | C2×M16 | C22×D11 | 1 | 1 | yes | characteristic |
| 219 | C2×M16 | C22×D11 | 1 | 1 | yes | characteristic |
| 220 | C4⋊Q8 | — | 11 | 2 | no | — |
| 221 | C4⋊Q8 | — | 11 | 2 | no | — |
| 222 | C4⋊Q8 | — | 11 | 1 | no | — |
| 223 | C4⋊Q8 | — | 44 | 1 | no | — |
| 224 | #127 | — | 11 | 1 | no | — |
| 225 | #124 | — | 11 | 2 | no | — |
| 226 | #121 | — | 44 | 1 | no | — |
| 227 | C4×Q8 | — | 44 | 2 | no | — |
| 228 | C4×Q8 | — | 44 | 2 | no | — |
| 229 | C4×D4 | — | 44 | 1 | no | — |
| 230 | #117 | — | 11 | 2 | no | — |
| 231 | #117 | — | 44 | 2 | no | — |
| 232 | #117 | C22×D11 | 1 | 2 | yes | — |
| 233 | C2×C4⋊C4 | — | 44 | 1 | no | — |
| 234 | C2×C42 | C22×D11 | 1 | 1 | yes | characteristic |
| 235 | #104 | — | 44 | 2 | no | — |
| 236 | #104 | — | 44 | 2 | no | — |
| 237 | #103 | — | 44 | 2 | no | — |
| 238 | #103 | — | 44 | 2 | no | — |
| 239 | #101 | — | 44 | 2 | no | — |
| 240 | #99 | — | 44 | 2 | no | — |
| 241 | #97 | C4×D11 | 1 | 2 | yes | — |
| 242 | C4×C8 | C4×D11 | 1 | 2 | yes | — |
| 243 | C2×C11 | — | 2 | 2 | no | — |
| 244 | C2×C11 | — | 2 | 1 | no | — |
| 245 | C2×C11 | #2380 | 1 | 1 | yes | characteristic |
| 246 | D11 | — | 8 | 2 | no | — |
| 247 | #41 | — | 22 | 2 | no | — |
| 248 | #41 | — | 22 | 2 | no | — |
| 249 | #41 | — | 22 | 2 | no | — |
| 250 | #41 | — | 22 | 2 | no | — |
| 251 | C2×Q8 | — | 11 | 2 | no | — |
| 252 | C2×Q8 | — | 11 | 4 | no | — |
| 253 | C2×Q8 | — | 22 | 2 | no | — |
| 254 | C2×Q8 | — | 22 | 2 | no | — |
| 255 | C2×Q8 | — | 22 | 2 | no | — |
| 256 | C2×Q8 | — | 22 | 2 | no | — |
| 257 | C2×Q8 | — | 22 | 2 | no | — |
| 258 | C2×D4 | — | 11 | 2 | no | — |
| 259 | C2×D4 | — | 22 | 2 | no | — |
| 260 | C2×D4 | — | 44 | 1 | no | — |
| 261 | C22×C4 | — | 2 | 1 | no | — |
| 262 | C22×C4 | — | 22 | 2 | no | — |
| 263 | C22×C4 | — | 22 | 2 | no | — |
| 264 | C22×C4 | C23×D11 | 1 | 1 | yes | characteristic |
| 265 | Q16 | — | 44 | 4 | no | — |
| 266 | Q16 | — | 44 | 4 | no | — |
| 267 | SD16 | — | 44 | 4 | no | — |
| 268 | SD16 | — | 44 | 4 | no | — |
| 269 | M16 | — | 2 | 2 | no | — |
| 270 | M16 | — | 2 | 2 | no | — |
| 271 | M16 | — | 2 | 2 | no | — |
| 272 | M16 | — | 2 | 2 | no | — |
| 273 | M16 | — | 22 | 2 | no | — |
| 274 | M16 | — | 22 | 2 | no | — |
| 275 | M16 | — | 44 | 4 | no | — |
| 276 | C2×C8 | — | 2 | 2 | no | — |
| 277 | C2×C8 | — | 22 | 2 | no | — |
| 278 | C2×C8 | — | 44 | 4 | no | — |
| 279 | C2×C8 | C2×C4×D11 | 1 | 2 | yes | — |
| 280 | C2×C8 | C2×C4×D11 | 1 | 2 | yes | — |
| 281 | C4⋊C4 | — | 2 | 2 | no | — |
| 282 | C4⋊C4 | — | 22 | 2 | no | — |
| 283 | C4⋊C4 | — | 44 | 2 | no | — |
| 284 | C4⋊C4 | — | 44 | 2 | no | — |
| 285 | C4⋊C4 | — | 44 | 1 | no | — |
| 286 | C4⋊C4 | — | 44 | 4 | no | — |
| 287 | C22⋊C4 | — | 2 | 2 | no | — |
| 288 | C22⋊C4 | — | 22 | 2 | no | — |
| 289 | C22⋊C4 | — | 44 | 2 | no | — |
| 290 | C42 | — | 2 | 1 | no | — |
| 291 | C42 | — | 2 | 2 | no | — |
| 292 | C42 | — | 22 | 2 | no | — |
| 293 | C42 | — | 44 | 4 | no | — |
| 294 | C42 | C2×C4×D11 | 1 | 1 | yes | characteristic |
| 295 | C42 | C2×C4×D11 | 1 | 1 | yes | characteristic |
| 296 | C11 | #23360 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 297 | C23 | — | 22 | 2 | no | — |
| 298 | C23 | #67042 | 1 | 1 | yes | characteristic |
| 299 | Q8 | — | 22 | 4 | no | — |
| 300 | Q8 | — | 22 | 4 | no | — |
| 301 | Q8 | — | 22 | 2 | no | — |
| 302 | Q8 | — | 22 | 2 | no | — |
| 303 | Q8 | — | 44 | 2 | no | — |
| 304 | Q8 | — | 44 | 2 | no | — |
| 305 | D4 | — | 22 | 2 | no | — |
| 306 | D4 | — | 22 | 2 | no | — |
| 307 | D4 | — | 44 | 2 | no | — |
| 308 | D4 | — | 44 | 2 | no | — |
| 309 | D4 | — | 88 | 2 | no | — |
| 310 | C2×C4 | — | 2 | 1 | no | — |
| 311 | C2×C4 | — | 2 | 1 | no | — |
| 312 | C2×C4 | — | 4 | 2 | no | — |
| 313 | C2×C4 | — | 4 | 2 | no | — |
| 314 | C2×C4 | — | 22 | 2 | no | — |
| 315 | C2×C4 | — | 22 | 4 | no | — |
| 316 | C2×C4 | — | 44 | 2 | no | — |
| 317 | C2×C4 | — | 44 | 2 | no | — |
| 318 | C2×C4 | — | 44 | 2 | no | — |
| 319 | C2×C4 | — | 44 | 2 | no | — |
| 320 | C2×C4 | — | 44 | 2 | no | — |
| 321 | C2×C4 | C22×C4×D11 | 1 | 1 | yes | characteristic |
| 322 | C2×C4 | #67042 | 1 | 1 | yes | characteristic |
| 323 | C2×C4 | #67042 | 1 | 2 | yes | — |
| 324 | C2×C4 | #67042 | 1 | 2 | yes | — |
| 325 | C8 | — | 2 | 2 | no | — |
| 326 | C8 | — | 2 | 2 | no | — |
| 327 | C8 | — | 4 | 2 | no | — |
| 328 | C8 | — | 44 | 2 | no | — |
| 329 | C22 | — | 4 | 1 | no | — |
| 330 | C22 | — | 44 | 2 | no | — |
| 331 | C22 | — | 88 | 2 | no | — |
| 332 | C22 | #10623052 | 1 | 1 | yes | characteristic |
| 333 | C22 | #10623242 | 1 | 2 | yes | — |
| 334 | C4 | — | 2 | 2 | no | — |
| 335 | C4 | — | 4 | 1 | no | — |
| 336 | C4 | — | 8 | 2 | no | — |
| 337 | C4 | — | 44 | 2 | no | — |
| 338 | C4 | — | 44 | 4 | no | — |
| 339 | C4 | — | 88 | 2 | no | — |
| 340 | C4 | #10623052 | 1 | 1 | yes | characteristic |
| 341 | C4 | #10623052 | 1 | 1 | yes | characteristic |
| 342 | C4 | #10623242 | 1 | 2 | yes | — |
| 343 | C2 | — | 2 | 1 | no | — |
| 344 | C2 | — | 2 | 2 | no | — |
| 345 | C2 | — | 88 | 2 | no | — |
| 346 | C2 | #13071792 | 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