Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
906 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 906 conjugacy classes of subgroups — too many to draw. Only its 139 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #13083306 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #13079635 | C2 | 1 | 3 | yes | maximal, complemented |
| 3 | #13067918 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #13067911 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | #13067908 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | #13067246 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | C11×#1658 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C11×#564 | C22 | 1 | 1 | yes | characteristic, complemented |
| 9 | D11×#127 | C22 | 1 | 1 | yes | characteristic |
| 10 | #10623231 | C22 | 1 | 3 | yes | complemented |
| 11 | #10623229 | — | 2 | 3 | no | — |
| 12 | #10623226 | — | 2 | 3 | no | — |
| 13 | #10623224 | — | 2 | 3 | no | — |
| 14 | #10623223 | — | 2 | 3 | no | — |
| 15 | #10623222 | C22 | 1 | 3 | yes | — |
| 16 | C11×#490 | C22 | 1 | 3 | yes | — |
| 17 | #10622687 | C22 | 1 | 3 | yes | — |
| 18 | #10622680 | C22 | 1 | 3 | yes | — |
| 19 | #10622399 | — | 2 | 3 | no | — |
| 20 | #10622389 | — | 2 | 3 | no | — |
| 21 | #10622386 | — | 2 | 3 | no | — |
| 22 | #10622375 | — | 2 | 3 | no | — |
| 23 | #10622325 | C22 | 1 | 3 | yes | — |
| 24 | #10622318 | C22 | 1 | 3 | yes | — |
| 25 | C11×#330 | C22 | 1 | 3 | yes | complemented |
| 26 | #10622181 | C22 | 1 | 3 | yes | complemented |
| 27 | #10622102 | C22 | 1 | 6 | yes | complemented |
| 28 | C2×D4×D11 | — | 2 | 3 | no | — |
| 29 | C11×#127 | C23 | 1 | 1 | yes | characteristic |
| 30 | C11×#125 | — | 2 | 3 | no | — |
| 31 | C11×#125 | — | 2 | 3 | no | — |
| 32 | C11×#125 | C23 | 1 | 3 | yes | — |
| 33 | #66993 | — | 2 | 3 | no | — |
| 34 | C2×#4324 | — | 2 | 3 | no | — |
| 35 | C2×#4323 | — | 2 | 3 | no | — |
| 36 | C2×D88 | — | 2 | 3 | no | — |
| 37 | C2×#4314 | — | 2 | 3 | no | — |
| 38 | #66951 | — | 2 | 3 | no | — |
| 39 | #66951 | — | 2 | 3 | no | — |
| 40 | #66950 | D4 | 1 | 3 | yes | — |
| 41 | #66949 | — | 2 | 3 | no | — |
| 42 | #66949 | — | 2 | 3 | no | — |
| 43 | #66948 | — | 2 | 3 | no | — |
| 44 | #66948 | — | 2 | 3 | no | — |
| 45 | #66948 | — | 2 | 3 | no | — |
| 46 | #66948 | — | 2 | 3 | no | — |
| 47 | #66948 | D4 | 1 | 3 | yes | — |
| 48 | #66947 | — | 2 | 3 | no | — |
| 49 | #66947 | — | 2 | 3 | no | — |
| 50 | #66947 | — | 2 | 3 | no | — |
| 51 | #66947 | — | 2 | 3 | no | — |
| 52 | #66947 | — | 2 | 3 | no | — |
| 53 | #66946 | — | 2 | 3 | no | — |
| 54 | #66946 | — | 2 | 3 | no | — |
| 55 | #66946 | D4 | 1 | 3 | yes | — |
| 56 | #66945 | — | 2 | 3 | no | — |
| 57 | C4⋊C4×D11 | — | 2 | 3 | no | — |
| 58 | #66942 | — | 2 | 3 | no | — |
| 59 | #66940 | D4 | 1 | 3 | yes | — |
| 60 | #66929 | — | 2 | 1 | no | — |
| 61 | #66928 | C23 | 1 | 3 | yes | — |
| 62 | #66927 | — | 2 | 1 | no | — |
| 63 | #66927 | C23 | 1 | 1 | yes | characteristic |
| 64 | C4×D44 | — | 2 | 3 | no | — |
| 65 | #66925 | — | 2 | 3 | no | — |
| 66 | C42×D11 | C23 | 1 | 1 | yes | characteristic |
| 67 | C11×#102 | — | 2 | 3 | no | — |
| 68 | C11×#102 | — | 2 | 3 | no | — |
| 69 | C11×#97 | C23 | 1 | 3 | yes | — |
| 70 | (C2×D11)⋊C8 | — | 2 | 3 | no | — |
| 71 | Dic11⋊C8 | — | 2 | 3 | no | — |
| 72 | #66873 | — | 2 | 3 | no | — |
| 73 | #66873 | — | 2 | 3 | no | — |
| 74 | #66867 | C23 | 1 | 3 | yes | — |
| 75 | #19096 | — | 11 | 1 | no | maximal, Sylow |
| 76 | C23×D11 | — | 4 | 1 | no | — |
| 77 | C2×D4×C11 | — | 2 | 3 | no | — |
| 78 | C2×C22⋊D11 | — | 4 | 3 | no | — |
| 79 | D4×D11 | — | 8 | 3 | no | — |
| 80 | D4×D11 | — | 8 | 3 | no | — |
| 81 | C2×D44 | — | 2 | 3 | no | — |
| 82 | C2×D44 | — | 2 | 3 | no | — |
| 83 | C2×D44 | — | 2 | 3 | no | — |
| 84 | C2×D44 | — | 2 | 3 | no | — |
| 85 | C2×D44 | C2×D4 | 1 | 3 | yes | — |
| 86 | C2×C4×D11 | — | 2 | 3 | no | — |
| 87 | C2×C4×D11 | — | 2 | 3 | no | — |
| 88 | C2×C4×D11 | — | 2 | 3 | no | — |
| 89 | C2×C4×D11 | C2×D4 | 1 | 3 | yes | — |
| 90 | C2×Dic22 | C2×D4 | 1 | 3 | yes | — |
| 91 | C2×C8×C11 | — | 2 | 3 | no | — |
| 92 | C11×C4⋊C4 | — | 2 | 3 | no | — |
| 93 | C11×C4⋊C4 | — | 2 | 3 | no | — |
| 94 | C11×C4⋊C4 | — | 2 | 3 | no | — |
| 95 | C11×C4⋊C4 | — | 2 | 3 | no | — |
| 96 | C11×C4⋊C4 | C2×D4 | 1 | 3 | yes | — |
| 97 | C11×C4⋊C4 | C2×D4 | 1 | 3 | yes | — |
| 98 | C42×C11 | — | 2 | 1 | no | — |
| 99 | C42×C11 | — | 2 | 1 | no | — |
| 100 | C42×C11 | C24 | 1 | 1 | yes | characteristic |
| 101 | #4324 | — | 8 | 3 | no | — |
| 102 | #4323 | — | 8 | 3 | no | — |
| 103 | (C2×D11)⋊C4 | — | 2 | 3 | no | — |
| 104 | (C2×D11)⋊C4 | — | 2 | 3 | no | — |
| 105 | (C2×D11)⋊C4 | — | 2 | 3 | no | — |
| 106 | (C2×D11)⋊C4 | — | 2 | 3 | no | — |
| 107 | (C2×D11)⋊C4 | — | 2 | 3 | no | — |
| 108 | (C2×D11)⋊C4 | — | 2 | 3 | no | — |
| 109 | (C2×D11)⋊C4 | — | 2 | 3 | no | — |
| 110 | C4⋊Dic11 | — | 2 | 3 | no | — |
| 111 | Dic11⋊C4 | — | 2 | 3 | no | — |
| 112 | Dic11⋊C4 | — | 2 | 3 | no | — |
| 113 | Dic11⋊C4 | — | 2 | 3 | no | — |
| 114 | C4×Dic11 | — | 2 | 3 | no | — |
| 115 | C4×Dic11 | C2×D4 | 1 | 3 | yes | — |
| 116 | C2×C11⋊C8 | — | 2 | 3 | no | — |
| 117 | D88 | — | 8 | 3 | no | — |
| 118 | #4314 | — | 8 | 3 | no | — |
| 119 | #3567 | — | 11 | 1 | no | — |
| 120 | #3217 | — | 11 | 3 | no | — |
| 121 | #1658 | — | 11 | 1 | no | — |
| 122 | #1658 | D11 | 1 | 1 | yes | characteristic, complemented |
| 123 | #1656 | — | 11 | 3 | no | — |
| 124 | #1656 | — | 11 | 3 | no | — |
| 125 | #1535 | — | 11 | 3 | no | — |
| 126 | C23×C11 | — | 4 | 1 | no | — |
| 127 | C22×D11 | — | 2 | 3 | no | — |
| 128 | C22×D11 | — | 4 | 1 | no | — |
| 129 | C22×D11 | — | 8 | 6 | no | — |
| 130 | C22×D11 | #120 | 1 | 1 | yes | characteristic |
| 131 | D4×C11 | — | 4 | 3 | no | — |
| 132 | D4×C11 | — | 4 | 3 | no | — |
| 133 | C2×C4×C11 | — | 2 | 3 | no | — |
| 134 | C2×C4×C11 | — | 2 | 3 | no | — |
| 135 | C2×C4×C11 | C22×D4 | 1 | 3 | yes | — |
| 136 | C22⋊D11 | — | 8 | 6 | no | — |
| 137 | C2×Dic11 | — | 2 | 3 | no | — |
| 138 | C2×Dic11 | #120 | 1 | 3 | yes | — |
| 139 | D44 | — | 4 | 3 | no | — |
| 140 | D44 | — | 4 | 3 | no | — |
| 141 | D44 | — | 4 | 3 | no | — |
| 142 | D44 | — | 8 | 3 | no | — |
| 143 | D44 | — | 8 | 3 | no | — |
| 144 | D44 | — | 8 | 3 | no | — |
| 145 | C4×D11 | — | 4 | 3 | no | — |
| 146 | C4×D11 | — | 8 | 3 | no | — |
| 147 | C4×D11 | — | 8 | 3 | no | — |
| 148 | C4×D11 | — | 8 | 3 | no | — |
| 149 | Dic22 | — | 4 | 3 | no | — |
| 150 | C8×C11 | — | 4 | 3 | no | — |
| 151 | C11⋊C8 | — | 4 | 3 | no | — |
| 152 | #564 | C2×D11 | 1 | 1 | yes | characteristic, complemented |
| 153 | #562 | — | 11 | 3 | no | — |
| 154 | #553 | — | 22 | 3 | no | — |
| 155 | #552 | — | 22 | 3 | no | — |
| 156 | #540 | — | 22 | 3 | no | — |
| 157 | #539 | — | 22 | 3 | no | — |
| 158 | C2×#127 | — | 11 | 1 | no | — |
| 159 | #529 | — | 11 | 3 | no | — |
| 160 | #496 | — | 11 | 3 | no | — |
| 161 | #496 | — | 11 | 3 | no | — |
| 162 | #490 | — | 11 | 3 | no | — |
| 163 | #490 | C2×D11 | 1 | 3 | yes | — |
| 164 | #460 | — | 22 | 3 | no | — |
| 165 | #459 | — | 22 | 3 | no | — |
| 166 | #450 | — | 22 | 3 | no | — |
| 167 | #447 | — | 22 | 3 | no | — |
| 168 | #432 | — | 11 | 3 | no | — |
| 169 | #330 | — | 11 | 3 | no | — |
| 170 | #330 | C2×D11 | 1 | 3 | yes | complemented |
| 171 | #329 | — | 11 | 6 | no | — |
| 172 | C22×C11 | — | 8 | 3 | no | — |
| 173 | C22×C11 | C2×#120 | 1 | 1 | yes | characteristic |
| 174 | C2×D11 | — | 2 | 3 | no | — |
| 175 | C2×D11 | — | 4 | 3 | no | — |
| 176 | C2×D11 | — | 4 | 3 | no | — |
| 177 | C2×D11 | — | 4 | 3 | no | — |
| 178 | C2×D11 | — | 8 | 3 | no | — |
| 179 | C2×D11 | — | 16 | 4 | no | — |
| 180 | C4×C11 | — | 2 | 3 | no | — |
| 181 | C4×C11 | — | 4 | 3 | no | — |
| 182 | C4×C11 | — | 4 | 3 | no | — |
| 183 | Dic11 | — | 2 | 3 | no | — |
| 184 | Dic11 | — | 4 | 3 | no | — |
| 185 | C22×D4 | — | 22 | 3 | no | — |
| 186 | C2×SD16 | — | 22 | 3 | no | — |
| 187 | C2×SD16 | — | 22 | 3 | no | — |
| 188 | C2×D8 | — | 22 | 3 | no | — |
| 189 | C2×D8 | — | 22 | 3 | no | — |
| 190 | #127 | — | 11 | 1 | no | — |
| 191 | #127 | — | 22 | 1 | no | — |
| 192 | #127 | — | 22 | 3 | no | — |
| 193 | #127 | C22×D11 | 1 | 1 | yes | characteristic |
| 194 | #126 | — | 22 | 1 | no | — |
| 195 | #126 | — | 22 | 3 | no | — |
| 196 | #126 | — | 22 | 3 | no | — |
| 197 | #125 | — | 2 | 3 | no | — |
| 198 | #125 | — | 2 | 3 | no | — |
| 199 | #125 | — | 22 | 3 | no | — |
| 200 | #125 | C22×D11 | 1 | 3 | yes | — |
| 201 | #124 | — | 11 | 3 | no | — |
| 202 | #123 | — | 22 | 3 | no | — |
| 203 | #123 | — | 22 | 3 | no | — |
| 204 | #123 | — | 22 | 3 | no | — |
| 205 | #123 | — | 22 | 3 | no | — |
| 206 | #123 | — | 22 | 3 | no | — |
| 207 | C22⋊Q8 | — | 11 | 3 | no | — |
| 208 | C22⋊Q8 | — | 22 | 3 | no | — |
| 209 | C22⋊Q8 | — | 22 | 3 | no | — |
| 210 | #121 | — | 11 | 3 | no | — |
| 211 | #121 | — | 22 | 3 | no | — |
| 212 | #121 | — | 22 | 3 | no | — |
| 213 | #121 | — | 22 | 3 | no | — |
| 214 | #121 | — | 22 | 3 | no | — |
| 215 | C4×Q8 | — | 11 | 3 | no | — |
| 216 | C4×D4 | — | 11 | 3 | no | — |
| 217 | C4×D4 | — | 22 | 3 | no | — |
| 218 | C4×D4 | — | 22 | 3 | no | — |
| 219 | C4×D4 | — | 22 | 3 | no | — |
| 220 | #117 | — | 22 | 3 | no | — |
| 221 | #117 | — | 22 | 3 | no | — |
| 222 | C2×C4⋊C4 | — | 22 | 3 | no | — |
| 223 | C2×C42 | — | 11 | 1 | no | — |
| 224 | C4⋊C8 | — | 22 | 3 | no | — |
| 225 | #102 | — | 2 | 3 | no | — |
| 226 | #102 | — | 2 | 3 | no | — |
| 227 | #102 | — | 22 | 3 | no | — |
| 228 | #102 | — | 22 | 3 | no | — |
| 229 | C22⋊C8 | — | 22 | 3 | no | — |
| 230 | #97 | — | 11 | 3 | no | — |
| 231 | #97 | C22×D11 | 1 | 3 | yes | — |
| 232 | C2×C11 | — | 16 | 1 | no | — |
| 233 | C2×C11 | #3021 | 1 | 3 | yes | — |
| 234 | D11 | — | 4 | 1 | no | — |
| 235 | D11 | — | 8 | 3 | no | — |
| 236 | D11 | — | 16 | 1 | no | — |
| 237 | C24 | — | 44 | 1 | no | — |
| 238 | C2×Q8 | — | 11 | 3 | no | — |
| 239 | C2×D4 | — | 2 | 3 | no | — |
| 240 | C2×D4 | — | 11 | 3 | no | — |
| 241 | C2×D4 | — | 22 | 3 | no | — |
| 242 | C2×D4 | — | 22 | 3 | no | — |
| 243 | C2×D4 | — | 22 | 3 | no | — |
| 244 | C2×D4 | — | 22 | 3 | no | — |
| 245 | C2×D4 | — | 44 | 3 | no | — |
| 246 | C2×D4 | — | 88 | 3 | no | — |
| 247 | C2×D4 | — | 88 | 3 | no | — |
| 248 | C22×C4 | — | 11 | 3 | no | — |
| 249 | C22×C4 | — | 22 | 3 | no | — |
| 250 | C22×C4 | — | 22 | 3 | no | — |
| 251 | C22×C4 | — | 22 | 3 | no | — |
| 252 | SD16 | — | 88 | 3 | no | — |
| 253 | SD16 | — | 88 | 3 | no | — |
| 254 | D8 | — | 88 | 3 | no | — |
| 255 | D8 | — | 88 | 3 | no | — |
| 256 | C2×C8 | — | 2 | 3 | no | — |
| 257 | C2×C8 | — | 22 | 3 | no | — |
| 258 | C4⋊C4 | — | 2 | 3 | no | — |
| 259 | C4⋊C4 | — | 2 | 3 | no | — |
| 260 | C4⋊C4 | — | 2 | 3 | no | — |
| 261 | C4⋊C4 | — | 2 | 3 | no | — |
| 262 | C4⋊C4 | — | 22 | 3 | no | — |
| 263 | C4⋊C4 | — | 22 | 3 | no | — |
| 264 | C4⋊C4 | — | 22 | 3 | no | — |
| 265 | C4⋊C4 | — | 22 | 3 | no | — |
| 266 | C4⋊C4 | D4×D11 | 1 | 3 | yes | — |
| 267 | C4⋊C4 | D4×D11 | 1 | 3 | yes | — |
| 268 | C22⋊C4 | — | 22 | 3 | no | — |
| 269 | C22⋊C4 | — | 22 | 3 | no | — |
| 270 | C22⋊C4 | — | 22 | 3 | no | — |
| 271 | C22⋊C4 | — | 22 | 3 | no | — |
| 272 | C22⋊C4 | — | 22 | 3 | no | — |
| 273 | C22⋊C4 | — | 22 | 3 | no | — |
| 274 | C22⋊C4 | — | 22 | 3 | no | — |
| 275 | C42 | — | 2 | 1 | no | — |
| 276 | C42 | — | 2 | 1 | no | — |
| 277 | C42 | — | 11 | 3 | no | — |
| 278 | C42 | — | 22 | 3 | no | — |
| 279 | C42 | C23×D11 | 1 | 1 | yes | characteristic |
| 280 | C11 | #19096 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 281 | C23 | — | 4 | 1 | no | — |
| 282 | C23 | — | 11 | 1 | no | — |
| 283 | C23 | — | 22 | 3 | no | — |
| 284 | C23 | — | 44 | 1 | no | — |
| 285 | C23 | — | 88 | 6 | no | — |
| 286 | Q8 | — | 44 | 3 | no | — |
| 287 | D4 | — | 4 | 3 | no | — |
| 288 | D4 | — | 4 | 3 | no | — |
| 289 | D4 | — | 44 | 3 | no | — |
| 290 | D4 | — | 44 | 3 | no | — |
| 291 | D4 | — | 44 | 3 | no | — |
| 292 | D4 | — | 88 | 3 | no | — |
| 293 | D4 | — | 88 | 3 | no | — |
| 294 | D4 | — | 88 | 3 | no | — |
| 295 | D4 | — | 88 | 6 | no | — |
| 296 | C2×C4 | — | 2 | 3 | no | — |
| 297 | C2×C4 | — | 2 | 3 | no | — |
| 298 | C2×C4 | — | 11 | 3 | no | — |
| 299 | C2×C4 | — | 22 | 3 | no | — |
| 300 | C2×C4 | — | 44 | 3 | no | — |
| 301 | C2×C4 | — | 88 | 3 | no | — |
| 302 | C2×C4 | — | 88 | 3 | no | — |
| 303 | C2×C4 | — | 88 | 3 | no | — |
| 304 | C2×C4 | C2×D4×D11 | 1 | 3 | yes | — |
| 305 | C8 | — | 4 | 3 | no | — |
| 306 | C8 | — | 44 | 3 | no | — |
| 307 | C22 | — | 8 | 3 | no | — |
| 308 | C22 | — | 22 | 3 | no | — |
| 309 | C22 | — | 44 | 3 | no | — |
| 310 | C22 | — | 44 | 3 | no | — |
| 311 | C22 | — | 44 | 3 | no | — |
| 312 | C22 | — | 88 | 3 | no | — |
| 313 | C22 | — | 176 | 4 | no | — |
| 314 | C22 | D11×#120 | 1 | 1 | yes | characteristic |
| 315 | C4 | — | 2 | 3 | no | — |
| 316 | C4 | — | 4 | 3 | no | — |
| 317 | C4 | — | 4 | 3 | no | — |
| 318 | C4 | — | 22 | 3 | no | — |
| 319 | C4 | — | 44 | 3 | no | — |
| 320 | C2 | — | 16 | 1 | no | — |
| 321 | C2 | — | 44 | 1 | no | — |
| 322 | C2 | — | 88 | 3 | no | — |
| 323 | C2 | — | 176 | 1 | no | — |
| 324 | C2 | #13077986 | 1 | 3 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13083306 | C2 | semidirect |
| 2. #13079635 | C2 | semidirect |
| 3. #13067918 | C2 | semidirect |
| 4. #13067911 | C2 | semidirect |
| 5. #13067908 | C2 | semidirect |
| 6. #13067246 | C2 | semidirect |
| 7. C11×#1658 | C2 | semidirect |
| 8. C11×#564 | C22 | semidirect |
| 10. #10623231 | C22 | semidirect |
| 25. C11×#330 | C22 | semidirect |
| 26. #10622181 | C22 | semidirect |
| 27. #10622102 | C22 | semidirect |
| 122. #1658 | D11 | semidirect |
| 152. #564 | C2×D11 | semidirect |
| 170. #330 | C2×D11 | semidirect |
| 280. C11 | #19096 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13083306 | 2 |
| #13079635 | 2 |
| #13067918 | 2 |
| #13067911 | 2 |
| #13067908 | 2 |
| #13067246 | 2 |
| C11×#1658 | 2 |
| #19096 | 11 |