← C22×#10622702 #15622984
Subgroups — C22×#10622702 #15622984
Order 2816.
2486 conjugacy classes of subgroups.
The subgroup lattice has 274 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C22×#66928 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C2×#10622702 | C2 | 1 | 24 | yes | maximal, direct product factor |
| 3 | C22×#66874 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | C22×#66873 | C2 | 1 | 2 | yes | maximal |
| 5 | C22×#66867 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C22×C11×C4⋊Q8 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C23×Q8×C11 | — | 2 | 1 | no | — |
| 8 | C23×D44 | C22 | 1 | 1 | yes | characteristic |
| 9 | C23×Dic22 | C22 | 1 | 1 | yes | characteristic |
| 10 | C2×C11×C4⋊Q8 | — | 2 | 6 | no | — |
| 11 | C2×C11×C4⋊Q8 | C22 | 1 | 12 | yes | complemented |
| 12 | C22×C11×C4⋊C4 | — | 2 | 1 | no | — |
| 13 | C22×C11×C4⋊C4 | C22 | 1 | 2 | yes | — |
| 14 | C22×C42×C11 | C22 | 1 | 1 | yes | characteristic |
| 15 | C22×(C2×D11)⋊C4 | — | 2 | 1 | no | — |
| 16 | C22×(C2×D11)⋊C4 | — | 2 | 1 | no | — |
| 17 | C23×C11⋊C8 | C22 | 1 | 2 | yes | — |
| 18 | C2×#66928 | — | 2 | 6 | no | — |
| 19 | C2×#66928 | C22 | 1 | 12 | yes | — |
| 20 | #10622702 | C22 | 1 | 64 | yes | direct product factor |
| 21 | C2×#66874 | C22 | 1 | 24 | yes | complemented |
| 22 | C2×#66873 | C22 | 1 | 24 | yes | — |
| 23 | C2×#66867 | C22 | 1 | 12 | yes | complemented |
| 24 | C24×D11 | — | 2 | 1 | no | — |
| 25 | C22×Q8×C11 | — | 2 | 12 | no | — |
| 26 | C22×Q8×C11 | — | 4 | 8 | no | — |
| 27 | C23×C4×C11 | — | 2 | 2 | no | — |
| 28 | C23×C4×C11 | D4 | 1 | 1 | yes | characteristic |
| 29 | C23×C4×C11 | D4 | 1 | 1 | yes | characteristic |
| 30 | C23×C4×C11 | C23 | 1 | 1 | yes | characteristic |
| 31 | C23×Dic11 | — | 2 | 1 | no | — |
| 32 | C22×D44 | — | 2 | 8 | no | — |
| 33 | C22×D44 | — | 2 | 3 | no | — |
| 34 | C22×D44 | C23 | 1 | 6 | yes | — |
| 35 | C22×Dic22 | — | 2 | 8 | no | — |
| 36 | C22×Dic22 | — | 2 | 3 | no | — |
| 37 | C22×Dic22 | C23 | 1 | 6 | yes | — |
| 38 | C11×C4⋊Q8 | — | 2 | 24 | no | — |
| 39 | C11×C4⋊Q8 | C23 | 1 | 16 | yes | complemented |
| 40 | C2×C11×C4⋊C4 | — | 2 | 12 | no | — |
| 41 | C2×C11×C4⋊C4 | — | 2 | 6 | no | — |
| 42 | C2×C11×C4⋊C4 | C23 | 1 | 12 | yes | — |
| 43 | C2×C42×C11 | D4 | 1 | 6 | yes | — |
| 44 | C2×C42×C11 | C23 | 1 | 6 | yes | — |
| 45 | C2×(C2×D11)⋊C4 | — | 2 | 12 | no | — |
| 46 | C2×(C2×D11)⋊C4 | — | 2 | 12 | no | — |
| 47 | C22×C11⋊C8 | — | 2 | 8 | no | — |
| 48 | C22×C11⋊C8 | C23 | 1 | 12 | yes | — |
| 49 | #66928 | — | 2 | 24 | no | — |
| 50 | #66928 | C23 | 1 | 16 | yes | — |
| 51 | #66874 | C23 | 1 | 32 | yes | complemented |
| 52 | #66873 | C23 | 1 | 32 | yes | — |
| 53 | #66867 | C23 | 1 | 16 | yes | complemented |
| 54 | C22×#489 | — | 11 | 1 | no | maximal, Sylow |
| 55 | C24×C11 | C2×D4 | 1 | 1 | yes | characteristic |
| 56 | C23×D11 | — | 2 | 6 | no | — |
| 57 | C23×D11 | — | 4 | 4 | no | — |
| 58 | C23×D11 | — | 4 | 4 | no | — |
| 59 | C23×D11 | — | 4 | 4 | no | — |
| 60 | C2×Q8×C11 | — | 2 | 16 | no | — |
| 61 | C2×Q8×C11 | — | 4 | 48 | no | — |
| 62 | C22×C4×C11 | — | 2 | 4 | no | — |
| 63 | C22×C4×C11 | — | 2 | 4 | no | — |
| 64 | C22×C4×C11 | — | 2 | 12 | no | — |
| 65 | C22×C4×C11 | — | 4 | 8 | no | — |
| 66 | C22×C4×C11 | C2×D4 | 1 | 6 | yes | — |
| 67 | C22×C4×C11 | C2×D4 | 1 | 6 | yes | — |
| 68 | C22×C4×C11 | C2×D4 | 1 | 3 | yes | — |
| 69 | C22×C4×C11 | #41 | 1 | 8 | yes | — |
| 70 | C22×C4×C11 | C24 | 1 | 3 | yes | — |
| 71 | C22×Dic11 | — | 2 | 6 | no | — |
| 72 | C22×Dic11 | — | 4 | 4 | no | — |
| 73 | C2×D44 | — | 2 | 6 | no | — |
| 74 | C2×D44 | — | 2 | 24 | no | — |
| 75 | C2×D44 | — | 4 | 12 | no | — |
| 76 | C2×D44 | C24 | 1 | 4 | yes | — |
| 77 | C2×Dic22 | — | 2 | 6 | no | — |
| 78 | C2×Dic22 | — | 2 | 24 | no | — |
| 79 | C2×Dic22 | — | 4 | 12 | no | — |
| 80 | C2×Dic22 | C24 | 1 | 4 | yes | — |
| 81 | C11×C4⋊C4 | — | 2 | 16 | no | — |
| 82 | C11×C4⋊C4 | — | 2 | 12 | no | — |
| 83 | C11×C4⋊C4 | C24 | 1 | 8 | yes | — |
| 84 | C42×C11 | C2×D4 | 1 | 12 | yes | — |
| 85 | C42×C11 | C24 | 1 | 4 | yes | — |
| 86 | (C2×D11)⋊C4 | — | 2 | 16 | no | — |
| 87 | (C2×D11)⋊C4 | — | 2 | 16 | no | — |
| 88 | C2×C11⋊C8 | — | 2 | 24 | no | — |
| 89 | C2×C11⋊C8 | C24 | 1 | 8 | yes | — |
| 90 | C22×C4⋊Q8 | D11 | 1 | 1 | yes | characteristic, complemented |
| 91 | C22×#124 | — | 11 | 1 | no | — |
| 92 | C2×#489 | — | 11 | 24 | no | — |
| 93 | C22×#103 | — | 11 | 2 | no | — |
| 94 | C22×#102 | — | 11 | 2 | no | — |
| 95 | C22×#97 | — | 11 | 1 | no | — |
| 96 | C23×C11 | #124 | 1 | 4 | yes | — |
| 97 | C23×C11 | AGL(1,ℤ/8) | 1 | 4 | yes | — |
| 98 | C23×C11 | #137 | 1 | 4 | yes | — |
| 99 | C23×C11 | C22×D4 | 1 | 3 | yes | — |
| 100 | C22×D11 | — | 2 | 4 | no | — |
| 101 | C22×D11 | — | 4 | 12 | no | — |
| 102 | C22×D11 | — | 4 | 12 | no | — |
| 103 | C22×D11 | — | 4 | 12 | no | — |
| 104 | C22×D11 | — | 8 | 16 | no | — |
| 105 | Q8×C11 | — | 4 | 32 | no | — |
| 106 | C2×C4×C11 | — | 2 | 12 | no | — |
| 107 | C2×C4×C11 | — | 2 | 12 | no | — |
| 108 | C2×C4×C11 | — | 2 | 8 | no | — |
| 109 | C2×C4×C11 | — | 4 | 24 | no | — |
| 110 | C2×C4×C11 | #124 | 1 | 12 | yes | — |
| 111 | C2×C4×C11 | C22×D4 | 1 | 4 | yes | — |
| 112 | C2×C4×C11 | C22×D4 | 1 | 4 | yes | — |
| 113 | C2×C4×C11 | C22×D4 | 1 | 3 | yes | — |
| 114 | C2×C4×C11 | C2×#41 | 1 | 12 | yes | — |
| 115 | C2×C4×C11 | C25 | 1 | 1 | yes | characteristic |
| 116 | C2×Dic11 | — | 2 | 4 | no | — |
| 117 | C2×Dic11 | — | 4 | 12 | no | — |
| 118 | D44 | — | 2 | 8 | no | — |
| 119 | D44 | — | 4 | 12 | no | — |
| 120 | Dic22 | — | 2 | 8 | no | — |
| 121 | Dic22 | — | 4 | 12 | no | — |
| 122 | C11⋊C8 | — | 2 | 8 | no | — |
| 123 | C23×Q8 | — | 2 | 1 | no | — |
| 124 | C23×Q8 | — | 11 | 1 | no | — |
| 125 | C23×D4 | — | 11 | 1 | no | — |
| 126 | C23×C8 | — | 11 | 2 | no | — |
| 127 | C2×C4⋊Q8 | — | 2 | 6 | no | — |
| 128 | C2×C4⋊Q8 | C2×D11 | 1 | 12 | yes | complemented |
| 129 | C2×#124 | — | 11 | 12 | no | — |
| 130 | C2×#124 | — | 22 | 6 | no | — |
| 131 | C22×C4⋊C4 | — | 2 | 1 | no | — |
| 132 | C22×C4⋊C4 | C2×D11 | 1 | 2 | yes | — |
| 133 | C22×C22⋊C4 | — | 22 | 1 | no | — |
| 134 | C22×C22⋊C4 | — | 22 | 1 | no | — |
| 135 | C22×C42 | C2×D11 | 1 | 1 | yes | characteristic |
| 136 | #489 | — | 11 | 64 | no | — |
| 137 | C2×#103 | — | 11 | 24 | no | — |
| 138 | C2×#102 | — | 11 | 24 | no | — |
| 139 | C2×#97 | — | 11 | 12 | no | — |
| 140 | C22×C11 | #489 | 1 | 16 | yes | complemented |
| 141 | C22×C11 | C2×#124 | 1 | 6 | yes | — |
| 142 | C22×C11 | C2×AGL(1,ℤ/8) | 1 | 6 | yes | — |
| 143 | C22×C11 | C2×#137 | 1 | 6 | yes | — |
| 144 | C22×C11 | C23×D4 | 1 | 1 | yes | characteristic |
| 145 | C2×D11 | — | 4 | 4 | no | — |
| 146 | C2×D11 | — | 4 | 4 | no | — |
| 147 | C2×D11 | — | 4 | 4 | no | — |
| 148 | C2×D11 | — | 8 | 24 | no | — |
| 149 | C4×C11 | — | 2 | 4 | no | — |
| 150 | C4×C11 | — | 2 | 4 | no | — |
| 151 | C4×C11 | — | 4 | 8 | no | — |
| 152 | C4×C11 | C2×#124 | 1 | 6 | yes | — |
| 153 | C4×C11 | C22×#41 | 1 | 2 | yes | — |
| 154 | Dic11 | — | 4 | 4 | no | — |
| 155 | C25 | — | 22 | 1 | no | — |
| 156 | C22×Q8 | — | 2 | 12 | no | — |
| 157 | C22×Q8 | — | 4 | 8 | no | — |
| 158 | C22×Q8 | — | 11 | 6 | no | — |
| 159 | C22×Q8 | — | 22 | 3 | no | — |
| 160 | C22×Q8 | — | 22 | 8 | no | — |
| 161 | C22×D4 | — | 11 | 6 | no | — |
| 162 | C22×D4 | — | 22 | 8 | no | — |
| 163 | C22×D4 | — | 22 | 3 | no | — |
| 164 | C23×C4 | — | 2 | 2 | no | — |
| 165 | C23×C4 | — | 22 | 1 | no | — |
| 166 | C23×C4 | C22⋊D11 | 1 | 1 | yes | characteristic |
| 167 | C23×C4 | C22⋊D11 | 1 | 1 | yes | characteristic |
| 168 | C23×C4 | C22×D11 | 1 | 1 | yes | characteristic |
| 169 | C22×C8 | — | 11 | 12 | no | — |
| 170 | C22×C8 | — | 22 | 8 | no | — |
| 171 | C4⋊Q8 | — | 2 | 24 | no | — |
| 172 | C4⋊Q8 | C22×D11 | 1 | 16 | yes | complemented |
| 173 | #124 | — | 11 | 16 | no | — |
| 174 | #124 | — | 22 | 24 | no | — |
| 175 | C2×C4⋊C4 | — | 2 | 12 | no | — |
| 176 | C2×C4⋊C4 | — | 2 | 6 | no | — |
| 177 | C2×C4⋊C4 | C22×D11 | 1 | 12 | yes | — |
| 178 | C2×C22⋊C4 | — | 22 | 12 | no | — |
| 179 | C2×C22⋊C4 | — | 22 | 12 | no | — |
| 180 | C2×C42 | C22⋊D11 | 1 | 6 | yes | — |
| 181 | C2×C42 | C22×D11 | 1 | 6 | yes | — |
| 182 | #103 | — | 11 | 32 | no | — |
| 183 | #102 | — | 11 | 32 | no | — |
| 184 | #97 | — | 11 | 16 | no | — |
| 185 | C2×C11 | C2×#489 | 1 | 12 | yes | complemented |
| 186 | C2×C11 | C22×#124 | 1 | 1 | yes | characteristic |
| 187 | C2×C11 | C22×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 188 | C2×C11 | C22×#137 | 1 | 1 | yes | characteristic |
| 189 | D11 | — | 8 | 4 | no | — |
| 190 | C24 | — | 22 | 6 | no | — |
| 191 | C24 | — | 44 | 4 | no | — |
| 192 | C24 | — | 44 | 4 | no | — |
| 193 | C24 | — | 44 | 4 | no | — |
| 194 | C24 | C2×C22⋊D11 | 1 | 1 | yes | characteristic |
| 195 | C2×Q8 | — | 2 | 16 | no | — |
| 196 | C2×Q8 | — | 4 | 48 | no | — |
| 197 | C2×Q8 | — | 11 | 4 | no | — |
| 198 | C2×Q8 | — | 22 | 6 | no | — |
| 199 | C2×Q8 | — | 22 | 24 | no | — |
| 200 | C2×Q8 | — | 44 | 12 | no | — |
| 201 | C2×D4 | — | 11 | 4 | no | — |
| 202 | C2×D4 | — | 22 | 24 | no | — |
| 203 | C2×D4 | — | 22 | 6 | no | — |
| 204 | C2×D4 | — | 44 | 12 | no | — |
| 205 | C22×C4 | — | 2 | 4 | no | — |
| 206 | C22×C4 | — | 2 | 4 | no | — |
| 207 | C22×C4 | — | 2 | 12 | no | — |
| 208 | C22×C4 | — | 4 | 8 | no | — |
| 209 | C22×C4 | — | 22 | 6 | no | — |
| 210 | C22×C4 | — | 44 | 4 | no | — |
| 211 | C22×C4 | #4343 | 1 | 8 | yes | — |
| 212 | C22×C4 | C2×C22⋊D11 | 1 | 6 | yes | — |
| 213 | C22×C4 | C2×C22⋊D11 | 1 | 6 | yes | — |
| 214 | C22×C4 | C2×C22⋊D11 | 1 | 3 | yes | — |
| 215 | C22×C4 | C23×D11 | 1 | 3 | yes | — |
| 216 | C2×C8 | — | 11 | 8 | no | — |
| 217 | C2×C8 | — | 22 | 24 | no | — |
| 218 | C4⋊C4 | — | 2 | 16 | no | — |
| 219 | C4⋊C4 | — | 2 | 12 | no | — |
| 220 | C4⋊C4 | C23×D11 | 1 | 8 | yes | — |
| 221 | C22⋊C4 | — | 22 | 16 | no | — |
| 222 | C22⋊C4 | — | 22 | 16 | no | — |
| 223 | C42 | C2×C22⋊D11 | 1 | 12 | yes | — |
| 224 | C42 | C23×D11 | 1 | 4 | yes | — |
| 225 | C11 | C22×#489 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 226 | C23 | — | 22 | 4 | no | — |
| 227 | C23 | — | 44 | 12 | no | — |
| 228 | C23 | — | 44 | 12 | no | — |
| 229 | C23 | — | 44 | 12 | no | — |
| 230 | C23 | — | 88 | 16 | no | — |
| 231 | C23 | #66985 | 1 | 4 | yes | — |
| 232 | C23 | #66995 | 1 | 4 | yes | — |
| 233 | C23 | #67000 | 1 | 4 | yes | — |
| 234 | C23 | C22×C22⋊D11 | 1 | 3 | yes | — |
| 235 | Q8 | — | 4 | 32 | no | — |
| 236 | Q8 | — | 22 | 8 | no | — |
| 237 | Q8 | — | 44 | 12 | no | — |
| 238 | D4 | — | 22 | 8 | no | — |
| 239 | D4 | — | 44 | 12 | no | — |
| 240 | C2×C4 | — | 2 | 12 | no | — |
| 241 | C2×C4 | — | 2 | 12 | no | — |
| 242 | C2×C4 | — | 2 | 8 | no | — |
| 243 | C2×C4 | — | 4 | 24 | no | — |
| 244 | C2×C4 | — | 22 | 4 | no | — |
| 245 | C2×C4 | — | 44 | 12 | no | — |
| 246 | C2×C4 | #67000 | 1 | 12 | yes | — |
| 247 | C2×C4 | C2×#4343 | 1 | 12 | yes | — |
| 248 | C2×C4 | C22×C22⋊D11 | 1 | 4 | yes | — |
| 249 | C2×C4 | C22×C22⋊D11 | 1 | 4 | yes | — |
| 250 | C2×C4 | C22×C22⋊D11 | 1 | 3 | yes | — |
| 251 | C2×C4 | C24×D11 | 1 | 1 | yes | characteristic |
| 252 | C8 | — | 22 | 8 | no | — |
| 253 | C22 | — | 44 | 4 | no | — |
| 254 | C22 | — | 44 | 4 | no | — |
| 255 | C22 | — | 44 | 4 | no | — |
| 256 | C22 | — | 88 | 24 | no | — |
| 257 | C22 | #10622702 | 1 | 16 | yes | direct product factor |
| 258 | C22 | C2×#66985 | 1 | 6 | yes | — |
| 259 | C22 | C2×#66995 | 1 | 6 | yes | — |
| 260 | C22 | C2×#67000 | 1 | 6 | yes | — |
| 261 | C22 | C23×C22⋊D11 | 1 | 1 | yes | characteristic |
| 262 | C4 | — | 2 | 4 | no | — |
| 263 | C4 | — | 2 | 4 | no | — |
| 264 | C4 | — | 4 | 8 | no | — |
| 265 | C4 | — | 44 | 4 | no | — |
| 266 | C4 | C2×#67000 | 1 | 6 | yes | — |
| 267 | C4 | C22×#4343 | 1 | 2 | yes | — |
| 268 | C2 | — | 88 | 4 | no | — |
| 269 | C2 | C2×#10622702 | 1 | 12 | yes | direct product factor |
| 270 | C2 | C22×#67000 | 1 | 1 | yes | characteristic |
| 271 | C2 | C22×#66985 | 1 | 1 | yes | characteristic |
| 272 | C2 | C22×#66995 | 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