Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
1078 conjugacy classes of subgroups; only the 207 normal subgroups are shown.
This group has 1078 conjugacy classes of subgroups — too many to draw. Only its 207 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 | D11×#430 | C2 | 1 | 3 | yes | maximal, complemented |
| 2 | C2×D11×#100 | C2 | 1 | 3 | yes | maximal |
| 3 | #13070015 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #13070014 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | #13070013 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | D11×#338 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C11×#2069 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C22×D4×D11 | C22 | 1 | 1 | yes | characteristic |
| 9 | C2×M16×D11 | C22 | 1 | 3 | yes | — |
| 10 | C2×M16×D11 | C22 | 1 | 3 | yes | — |
| 11 | C11×#430 | C22 | 1 | 3 | yes | complemented |
| 12 | C2×C11×#100 | C22 | 1 | 3 | yes | — |
| 13 | C2×#66897 | C22 | 1 | 3 | yes | — |
| 14 | C2×#66887 | C22 | 1 | 3 | yes | — |
| 15 | C2×#66887 | C22 | 1 | 3 | yes | — |
| 16 | #10622738 | C22 | 1 | 3 | yes | complemented |
| 17 | #10622737 | C22 | 1 | 3 | yes | complemented |
| 18 | #10622737 | C22 | 1 | 3 | yes | complemented |
| 19 | #10622506 | — | 2 | 6 | no | — |
| 20 | D11×#108 | — | 2 | 6 | no | — |
| 21 | D11×#100 | — | 2 | 6 | no | — |
| 22 | D11×#100 | — | 2 | 6 | no | — |
| 23 | C11×#338 | C22 | 1 | 1 | yes | characteristic, complemented |
| 24 | C11⋊#338 | C22 | 1 | 3 | yes | complemented |
| 25 | C24×D11 | Q8 | 1 | 2 | yes | — |
| 26 | C22×D4×C11 | C23 | 1 | 1 | yes | characteristic |
| 27 | C22×C22⋊D11 | Q8 | 1 | 2 | yes | — |
| 28 | C2×D4×D11 | — | 2 | 3 | no | — |
| 29 | C2×D4×D11 | — | 2 | 3 | no | — |
| 30 | C2×D4×D11 | — | 2 | 3 | no | — |
| 31 | C2×D4×D11 | — | 2 | 3 | no | — |
| 32 | C22×D44 | C23 | 1 | 1 | yes | characteristic |
| 33 | C22×C4×D11 | C23 | 1 | 1 | yes | characteristic |
| 34 | C2×C11×M16 | C23 | 1 | 3 | yes | — |
| 35 | C2×C11×M16 | C23 | 1 | 3 | yes | — |
| 36 | C2×#4318 | C23 | 1 | 3 | yes | — |
| 37 | C2×#4318 | C23 | 1 | 3 | yes | — |
| 38 | M16×D11 | — | 2 | 3 | no | — |
| 39 | M16×D11 | — | 2 | 3 | no | — |
| 40 | M16×D11 | — | 2 | 3 | no | — |
| 41 | M16×D11 | — | 2 | 3 | no | — |
| 42 | M16×D11 | — | 2 | 3 | no | — |
| 43 | M16×D11 | — | 2 | 3 | no | — |
| 44 | M16×D11 | D4 | 1 | 6 | yes | — |
| 45 | M16×D11 | D4 | 1 | 6 | yes | — |
| 46 | C2×#4313 | — | 2 | 3 | no | — |
| 47 | C2×#4313 | — | 2 | 3 | no | — |
| 48 | C2×C8×D11 | — | 2 | 3 | no | — |
| 49 | C2×C8×D11 | — | 2 | 3 | no | — |
| 50 | C11×#108 | — | 2 | 6 | no | — |
| 51 | C11×#100 | — | 2 | 6 | no | — |
| 52 | #66897 | — | 2 | 6 | no | — |
| 53 | #66887 | — | 2 | 6 | no | — |
| 54 | #66887 | — | 2 | 6 | no | — |
| 55 | #66886 | — | 2 | 6 | no | — |
| 56 | #66886 | — | 2 | 6 | no | — |
| 57 | #66883 | — | 2 | 6 | no | — |
| 58 | C2×#2069 | — | 11 | 1 | no | maximal, Sylow |
| 59 | C24×C11 | C2×Q8 | 1 | 2 | yes | — |
| 60 | C23×D11 | — | 2 | 6 | no | — |
| 61 | C23×D11 | — | 2 | 6 | no | — |
| 62 | C23×D11 | — | 8 | 4 | no | — |
| 63 | C23×D11 | C2×Q8 | 1 | 2 | yes | — |
| 64 | C23×D11 | C2×Q8 | 1 | 1 | yes | characteristic |
| 65 | C2×D4×C11 | — | 2 | 3 | no | — |
| 66 | C2×D4×C11 | — | 2 | 3 | no | — |
| 67 | C22×C4×C11 | C24 | 1 | 1 | yes | characteristic |
| 68 | C2×C22⋊D11 | — | 2 | 6 | no | — |
| 69 | C2×C22⋊D11 | — | 2 | 6 | no | — |
| 70 | C22×Dic11 | C2×Q8 | 1 | 1 | yes | characteristic |
| 71 | D4×D11 | — | 4 | 3 | no | — |
| 72 | D4×D11 | — | 4 | 3 | no | — |
| 73 | D4×D11 | — | 4 | 3 | no | — |
| 74 | D4×D11 | — | 4 | 3 | no | — |
| 75 | D4×D11 | — | 4 | 3 | no | — |
| 76 | D4×D11 | — | 4 | 1 | no | — |
| 77 | C2×D44 | — | 2 | 3 | no | — |
| 78 | C2×D44 | — | 2 | 3 | no | — |
| 79 | C2×C4×D11 | C2×D4 | 1 | 3 | yes | — |
| 80 | C2×C4×D11 | C2×D4 | 1 | 3 | yes | — |
| 81 | C2×C4×D11 | #41 | 1 | 3 | yes | — |
| 82 | C2×C4×D11 | #41 | 1 | 3 | yes | — |
| 83 | C11×M16 | — | 2 | 3 | no | — |
| 84 | C11×M16 | — | 2 | 3 | no | — |
| 85 | C11×M16 | — | 2 | 3 | no | — |
| 86 | C11×M16 | C2×D4 | 1 | 6 | yes | — |
| 87 | C2×C8×C11 | — | 2 | 3 | no | — |
| 88 | C2×C8×C11 | — | 2 | 3 | no | — |
| 89 | #4318 | — | 2 | 3 | no | — |
| 90 | #4318 | — | 2 | 3 | no | — |
| 91 | #4318 | — | 2 | 3 | no | — |
| 92 | #4318 | C2×D4 | 1 | 6 | yes | — |
| 93 | C2×C11⋊C8 | — | 2 | 3 | no | — |
| 94 | C2×C11⋊C8 | — | 2 | 3 | no | — |
| 95 | #4313 | — | 2 | 6 | no | — |
| 96 | #4313 | — | 2 | 6 | no | — |
| 97 | #4313 | — | 4 | 3 | no | — |
| 98 | #4313 | — | 4 | 3 | no | — |
| 99 | C8×D11 | — | 2 | 6 | no | — |
| 100 | C8×D11 | — | 2 | 6 | no | — |
| 101 | C8×D11 | — | 4 | 3 | no | — |
| 102 | C8×D11 | — | 4 | 3 | no | — |
| 103 | C2×#430 | — | 11 | 3 | no | — |
| 104 | C22×#100 | — | 11 | 3 | no | — |
| 105 | #2069 | — | 11 | 3 | no | — |
| 106 | #2069 | — | 11 | 3 | no | — |
| 107 | #2069 | — | 11 | 1 | no | — |
| 108 | #2069 | D11 | 1 | 1 | yes | characteristic, direct product factor |
| 109 | C2×#338 | — | 11 | 1 | no | — |
| 110 | C23×C11 | — | 2 | 6 | no | — |
| 111 | C23×C11 | — | 8 | 2 | no | — |
| 112 | C23×C11 | C22×Q8 | 1 | 1 | yes | characteristic |
| 113 | C22×D11 | — | 2 | 6 | no | — |
| 114 | C22×D11 | — | 4 | 2 | no | — |
| 115 | C22×D11 | — | 4 | 6 | no | — |
| 116 | C22×D11 | — | 4 | 2 | no | — |
| 117 | C22×D11 | — | 8 | 12 | no | — |
| 118 | C22×D11 | — | 8 | 12 | no | — |
| 119 | C22×D11 | — | 8 | 2 | no | — |
| 120 | C22×D11 | C22⋊Q8 | 1 | 3 | yes | — |
| 121 | C22×D11 | C22⋊Q8 | 1 | 3 | yes | — |
| 122 | D4×C11 | — | 4 | 3 | no | — |
| 123 | D4×C11 | — | 4 | 1 | no | — |
| 124 | C2×C4×C11 | C22×D4 | 1 | 3 | yes | — |
| 125 | C2×C4×C11 | C2×#41 | 1 | 3 | yes | — |
| 126 | C22⋊D11 | — | 4 | 6 | no | — |
| 127 | C22⋊D11 | — | 4 | 2 | no | — |
| 128 | C2×Dic11 | C22⋊Q8 | 1 | 3 | yes | — |
| 129 | C2×Dic11 | C22⋊Q8 | 1 | 3 | yes | — |
| 130 | D44 | — | 4 | 3 | no | — |
| 131 | D44 | — | 4 | 1 | no | — |
| 132 | C4×D11 | #121 | 1 | 3 | yes | — |
| 133 | C4×D11 | #121 | 1 | 3 | yes | — |
| 134 | C4×D11 | #121 | 1 | 3 | yes | — |
| 135 | C4×D11 | #121 | 1 | 3 | yes | — |
| 136 | C4×D11 | #126 | 1 | 3 | yes | — |
| 137 | C4×D11 | #126 | 1 | 1 | yes | characteristic |
| 138 | C8×C11 | — | 2 | 6 | no | — |
| 139 | C8×C11 | — | 4 | 3 | no | — |
| 140 | C11⋊C8 | — | 2 | 6 | no | — |
| 141 | C11⋊C8 | — | 4 | 3 | no | — |
| 142 | C23×D4 | — | 11 | 1 | no | — |
| 143 | C22×M16 | — | 11 | 3 | no | — |
| 144 | C22×M16 | — | 11 | 3 | no | — |
| 145 | #430 | — | 11 | 3 | no | — |
| 146 | #430 | — | 11 | 3 | no | — |
| 147 | #430 | — | 11 | 3 | no | — |
| 148 | #430 | — | 22 | 6 | no | — |
| 149 | #430 | C2×D11 | 1 | 3 | yes | complemented |
| 150 | C2×#108 | — | 22 | 6 | no | — |
| 151 | C2×#100 | — | 11 | 3 | no | — |
| 152 | C2×#100 | — | 11 | 3 | no | — |
| 153 | C2×#100 | — | 11 | 3 | no | — |
| 154 | C2×#100 | — | 22 | 6 | no | — |
| 155 | C2×#100 | — | 22 | 6 | no | — |
| 156 | C2×#100 | C2×D11 | 1 | 3 | yes | — |
| 157 | #338 | — | 11 | 3 | no | — |
| 158 | #338 | C2×D11 | 1 | 1 | yes | characteristic, complemented |
| 159 | C22×C11 | — | 4 | 1 | no | — |
| 160 | C22×C11 | — | 4 | 2 | no | — |
| 161 | C22×C11 | — | 8 | 6 | no | — |
| 162 | C22×C11 | C2×C22⋊Q8 | 1 | 3 | yes | — |
| 163 | C2×D11 | — | 2 | 6 | no | — |
| 164 | C2×D11 | — | 4 | 3 | no | — |
| 165 | C2×D11 | — | 4 | 2 | no | — |
| 166 | C2×D11 | — | 8 | 12 | no | — |
| 167 | C2×D11 | — | 8 | 4 | no | — |
| 168 | C2×D11 | — | 8 | 6 | no | — |
| 169 | C2×D11 | #396 | 1 | 3 | yes | — |
| 170 | C2×D11 | #396 | 1 | 1 | yes | characteristic |
| 171 | C4×C11 | C2×#121 | 1 | 3 | yes | — |
| 172 | C4×C11 | C2×#126 | 1 | 1 | yes | characteristic |
| 173 | Dic11 | #396 | 1 | 3 | yes | — |
| 174 | Dic11 | #396 | 1 | 1 | yes | characteristic |
| 175 | C25 | — | 11 | 2 | no | — |
| 176 | C22×D4 | — | 11 | 2 | no | — |
| 177 | C22×D4 | — | 11 | 1 | no | — |
| 178 | C22×D4 | — | 22 | 3 | no | — |
| 179 | C22×D4 | — | 22 | 3 | no | — |
| 180 | C22×D4 | — | 22 | 3 | no | — |
| 181 | C22×D4 | — | 22 | 3 | no | — |
| 182 | C22×D4 | C22×D11 | 1 | 1 | yes | characteristic |
| 183 | C23×C4 | — | 11 | 1 | no | — |
| 184 | C2×M16 | — | 11 | 3 | no | — |
| 185 | C2×M16 | — | 11 | 6 | no | — |
| 186 | C2×M16 | — | 11 | 6 | no | — |
| 187 | C2×M16 | — | 11 | 3 | no | — |
| 188 | C2×M16 | — | 22 | 3 | no | — |
| 189 | C2×M16 | — | 22 | 3 | no | — |
| 190 | C2×M16 | — | 22 | 3 | no | — |
| 191 | C2×M16 | — | 22 | 3 | no | — |
| 192 | C2×M16 | — | 22 | 3 | no | — |
| 193 | C2×M16 | — | 22 | 3 | no | — |
| 194 | C2×M16 | — | 22 | 3 | no | — |
| 195 | C2×M16 | — | 22 | 3 | no | — |
| 196 | C2×M16 | C22×D11 | 1 | 3 | yes | — |
| 197 | C2×M16 | C22×D11 | 1 | 3 | yes | — |
| 198 | C22×C8 | — | 22 | 3 | no | — |
| 199 | C22×C8 | — | 22 | 3 | no | — |
| 200 | #108 | — | 2 | 6 | no | — |
| 201 | #108 | — | 22 | 6 | no | — |
| 202 | #108 | — | 22 | 6 | no | — |
| 203 | #108 | — | 22 | 6 | no | — |
| 204 | #100 | — | 2 | 6 | no | — |
| 205 | #100 | — | 22 | 6 | no | — |
| 206 | #100 | — | 22 | 6 | no | — |
| 207 | #100 | — | 22 | 6 | no | — |
| 208 | C2×C11 | — | 2 | 3 | no | — |
| 209 | C2×C11 | — | 8 | 2 | no | — |
| 210 | C2×C11 | C2×#396 | 1 | 1 | yes | characteristic |
| 211 | D11 | — | 2 | 3 | no | — |
| 212 | D11 | — | 8 | 2 | no | — |
| 213 | D11 | #2069 | 1 | 2 | yes | direct product factor |
| 214 | C24 | — | 11 | 1 | no | — |
| 215 | C24 | — | 11 | 2 | no | — |
| 216 | C24 | — | 22 | 6 | no | — |
| 217 | C24 | — | 22 | 6 | no | — |
| 218 | C24 | — | 88 | 4 | no | — |
| 219 | C24 | Q8×D11 | 1 | 2 | yes | — |
| 220 | C2×D4 | — | 2 | 3 | no | — |
| 221 | C2×D4 | — | 2 | 3 | no | — |
| 222 | C2×D4 | — | 22 | 6 | no | — |
| 223 | C2×D4 | — | 22 | 6 | no | — |
| 224 | C2×D4 | — | 22 | 3 | no | — |
| 225 | C2×D4 | — | 22 | 3 | no | — |
| 226 | C2×D4 | — | 44 | 1 | no | — |
| 227 | C2×D4 | — | 44 | 3 | no | — |
| 228 | C2×D4 | — | 44 | 3 | no | — |
| 229 | C2×D4 | — | 44 | 3 | no | — |
| 230 | C2×D4 | — | 44 | 3 | no | — |
| 231 | C2×D4 | — | 44 | 3 | no | — |
| 232 | C22×C4 | — | 11 | 1 | no | — |
| 233 | C22×C4 | — | 11 | 3 | no | — |
| 234 | C22×C4 | — | 11 | 3 | no | — |
| 235 | C22×C4 | — | 11 | 3 | no | — |
| 236 | C22×C4 | — | 11 | 3 | no | — |
| 237 | C22×C4 | C23×D11 | 1 | 1 | yes | characteristic |
| 238 | M16 | — | 2 | 3 | no | — |
| 239 | M16 | — | 2 | 3 | no | — |
| 240 | M16 | — | 2 | 3 | no | — |
| 241 | M16 | — | 11 | 6 | no | — |
| 242 | M16 | — | 22 | 6 | no | — |
| 243 | M16 | — | 22 | 6 | no | — |
| 244 | M16 | — | 22 | 3 | no | — |
| 245 | M16 | — | 22 | 3 | no | — |
| 246 | M16 | — | 22 | 3 | no | — |
| 247 | M16 | — | 44 | 3 | no | — |
| 248 | M16 | — | 44 | 3 | no | — |
| 249 | M16 | D4×D11 | 1 | 6 | yes | — |
| 250 | C2×C8 | — | 2 | 3 | no | — |
| 251 | C2×C8 | — | 2 | 3 | no | — |
| 252 | C2×C8 | — | 22 | 6 | no | — |
| 253 | C2×C8 | — | 22 | 6 | no | — |
| 254 | C2×C8 | — | 22 | 3 | no | — |
| 255 | C2×C8 | — | 22 | 3 | no | — |
| 256 | C2×C8 | — | 44 | 3 | no | — |
| 257 | C2×C8 | — | 44 | 3 | no | — |
| 258 | C11 | C2×#2069 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 259 | C23 | — | 2 | 6 | no | — |
| 260 | C23 | — | 8 | 2 | no | — |
| 261 | C23 | — | 11 | 3 | no | — |
| 262 | C23 | — | 11 | 3 | no | — |
| 263 | C23 | — | 22 | 6 | no | — |
| 264 | C23 | — | 44 | 2 | no | — |
| 265 | C23 | — | 44 | 6 | no | — |
| 266 | C23 | — | 44 | 2 | no | — |
| 267 | C23 | — | 88 | 2 | no | — |
| 268 | C23 | — | 88 | 12 | no | — |
| 269 | C23 | — | 88 | 12 | no | — |
| 270 | C23 | C2×Q8×D11 | 1 | 1 | yes | characteristic |
| 271 | D4 | — | 4 | 1 | no | — |
| 272 | D4 | — | 4 | 3 | no | — |
| 273 | D4 | — | 44 | 6 | no | — |
| 274 | D4 | — | 44 | 2 | no | — |
| 275 | D4 | — | 44 | 1 | no | — |
| 276 | D4 | — | 44 | 3 | no | — |
| 277 | C2×C4 | — | 11 | 3 | no | — |
| 278 | C2×C4 | — | 11 | 3 | no | — |
| 279 | C2×C4 | — | 11 | 1 | no | — |
| 280 | C2×C4 | — | 11 | 3 | no | — |
| 281 | C2×C4 | — | 11 | 3 | no | — |
| 282 | C2×C4 | — | 11 | 3 | no | — |
| 283 | C2×C4 | — | 11 | 3 | no | — |
| 284 | C2×C4 | — | 11 | 3 | no | — |
| 285 | C2×C4 | C2×D4×D11 | 1 | 3 | yes | — |
| 286 | C2×C4 | #41×D11 | 1 | 3 | yes | — |
| 287 | C8 | — | 2 | 6 | no | — |
| 288 | C8 | — | 4 | 3 | no | — |
| 289 | C8 | — | 22 | 6 | no | — |
| 290 | C8 | — | 44 | 3 | no | — |
| 291 | C22 | — | 4 | 1 | no | — |
| 292 | C22 | — | 4 | 2 | no | — |
| 293 | C22 | — | 8 | 6 | no | — |
| 294 | C22 | — | 11 | 1 | no | — |
| 295 | C22 | — | 11 | 3 | no | — |
| 296 | C22 | — | 22 | 6 | no | — |
| 297 | C22 | — | 44 | 3 | no | — |
| 298 | C22 | — | 44 | 2 | no | — |
| 299 | C22 | — | 88 | 6 | no | — |
| 300 | C22 | — | 88 | 4 | no | — |
| 301 | C22 | — | 88 | 12 | no | — |
| 302 | C22 | D11×C22⋊Q8 | 1 | 3 | yes | — |
| 303 | C4 | — | 11 | 3 | no | — |
| 304 | C4 | — | 11 | 1 | no | — |
| 305 | C4 | D11×#121 | 1 | 3 | yes | — |
| 306 | C4 | D11×#126 | 1 | 1 | yes | characteristic |
| 307 | C2 | — | 2 | 3 | no | — |
| 308 | C2 | — | 8 | 2 | no | — |
| 309 | C2 | — | 11 | 2 | no | — |
| 310 | C2 | — | 22 | 3 | no | — |
| 311 | C2 | — | 88 | 2 | no | — |
| 312 | C2 | D11×#396 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. D11×#430 | C2 | semidirect |
| 3. #13070015 | C2 | semidirect |
| 4. #13070014 | C2 | semidirect |
| 5. #13070013 | C2 | semidirect |
| 6. D11×#338 | C2 | semidirect |
| 7. C11×#2069 | C2 | semidirect |
| 11. C11×#430 | C22 | semidirect |
| 16. #10622738 | C22 | semidirect |
| 17. #10622737 | C22 | semidirect |
| 18. #10622737 | C22 | semidirect |
| 23. C11×#338 | C22 | semidirect |
| 24. C11⋊#338 | C22 | semidirect |
| 108. #2069 | D11 | direct (N × H) |
| 149. #430 | C2×D11 | semidirect |
| 158. #338 | C2×D11 | semidirect |
| 213. D11 | #2069 | direct (N × H) |
| 258. C11 | C2×#2069 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D11×#430 | 2 |
| C2×D11×#100 | 2 |
| #13070015 | 2 |
| #13070014 | 2 |
| #13070013 | 2 |
| D11×#338 | 2 |
| C11×#2069 | 2 |
| C2×#2069 | 11 |