Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1225 conjugacy classes of subgroups; only the 164 normal subgroups are shown.
This group has 1225 conjugacy classes of subgroups — too many to draw. Only its 164 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 | C3⋊D3×#127 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #10593948 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C3×#5071 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #10591480 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #10591416 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #10590322 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #10590282 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | D3×#490 | — | 3 | 2 | no | maximal |
| 9 | C2×D4×C3⋊D3 | — | 2 | 2 | no | — |
| 10 | C2×D4×C3⋊D3 | C22 | 1 | 2 | yes | — |
| 11 | C32×#127 | C22 | 1 | 1 | yes | characteristic |
| 12 | #64149 | — | 2 | 2 | no | — |
| 13 | #64149 | C22 | 1 | 2 | yes | — |
| 14 | #64083 | C22 | 1 | 1 | yes | characteristic |
| 15 | C42×C3⋊D3 | C22 | 1 | 1 | yes | characteristic |
| 16 | C3×#870 | C22 | 1 | 2 | yes | complemented |
| 17 | #63900 | C22 | 1 | 2 | yes | — |
| 18 | #63883 | — | 2 | 2 | no | — |
| 19 | #63872 | C22 | 1 | 2 | yes | complemented |
| 20 | #63870 | — | 2 | 2 | no | — |
| 21 | C2×#3710 | C22 | 1 | 2 | yes | — |
| 22 | C3×#832 | C22 | 1 | 8 | yes | complemented |
| 23 | C3×#803 | C22 | 1 | 2 | yes | complemented |
| 24 | #63564 | C22 | 1 | 8 | yes | complemented |
| 25 | #63555 | C22 | 1 | 2 | yes | complemented |
| 26 | D3×#127 | — | 3 | 2 | no | — |
| 27 | D3×#127 | — | 6 | 1 | no | — |
| 28 | D3×#125 | — | 3 | 2 | no | — |
| 29 | C3×#490 | — | 3 | 2 | no | — |
| 30 | #5071 | D3 | 1 | 2 | yes | complemented |
| 31 | #5067 | — | 3 | 2 | no | — |
| 32 | D3×#102 | — | 3 | 8 | no | — |
| 33 | #4764 | — | 3 | 8 | no | — |
| 34 | #4713 | — | 3 | 2 | no | — |
| 35 | D3×#97 | — | 3 | 2 | no | — |
| 36 | C23×C3⋊D3 | — | 2 | 2 | no | — |
| 37 | C2×C32×D4 | — | 2 | 2 | no | — |
| 38 | C2×C32×D4 | C23 | 1 | 2 | yes | — |
| 39 | C2×#638 | — | 2 | 4 | no | — |
| 40 | C2×#638 | — | 2 | 2 | no | — |
| 41 | D4×C3⋊D3 | — | 2 | 8 | no | — |
| 42 | D4×C3⋊D3 | — | 4 | 8 | no | — |
| 43 | C2×C4⋊(C3⋊D3) | — | 2 | 2 | no | — |
| 44 | C2×C4⋊(C3⋊D3) | C23 | 1 | 2 | yes | — |
| 45 | C2×C4×C3⋊D3 | D4 | 1 | 2 | yes | — |
| 46 | C2×C4×C3⋊D3 | C23 | 1 | 1 | yes | characteristic |
| 47 | C2×#624 | — | 2 | 2 | no | — |
| 48 | C32×C42 | C23 | 1 | 1 | yes | characteristic |
| 49 | C4×C3⋊Dic3 | D4 | 1 | 2 | yes | — |
| 50 | C4×C3⋊Dic3 | C23 | 1 | 1 | yes | characteristic |
| 51 | C3×C4⋊Dic3 | C23 | 1 | 4 | yes | — |
| 52 | C3×Dic3⋊C4 | — | 2 | 4 | no | — |
| 53 | C2×C3×C3⋊C8 | C23 | 1 | 4 | yes | — |
| 54 | #3724 | — | 2 | 2 | no | — |
| 55 | Dic3⋊Dic3 | — | 2 | 4 | no | — |
| 56 | #3710 | — | 2 | 4 | no | — |
| 57 | C2×#490 | — | 9 | 1 | no | Sylow |
| 58 | C2×D3×D4 | — | 3 | 4 | no | — |
| 59 | C2×D3×D4 | — | 6 | 2 | no | — |
| 60 | C2×D3×D4 | — | 6 | 4 | no | — |
| 61 | C2×D3×D4 | — | 6 | 4 | no | — |
| 62 | C3×#127 | — | 2 | 1 | no | — |
| 63 | C3×#127 | C2×D3 | 1 | 2 | yes | — |
| 64 | C3×#125 | — | 3 | 2 | no | — |
| 65 | #940 | — | 3 | 4 | no | — |
| 66 | #940 | — | 6 | 2 | no | — |
| 67 | #940 | — | 6 | 4 | no | — |
| 68 | #940 | — | 6 | 4 | no | — |
| 69 | C2×D3×C8 | — | 3 | 4 | no | — |
| 70 | D3×C4⋊C4 | — | 3 | 4 | no | — |
| 71 | D3×C4⋊C4 | — | 6 | 4 | no | — |
| 72 | #890 | — | 3 | 4 | no | — |
| 73 | #889 | — | 6 | 4 | no | — |
| 74 | #874 | — | 3 | 2 | no | — |
| 75 | #874 | — | 6 | 1 | no | — |
| 76 | C42×D3 | — | 3 | 2 | no | — |
| 77 | C42×D3 | — | 6 | 1 | no | — |
| 78 | #870 | C2×D3 | 1 | 2 | yes | complemented |
| 79 | C3×#102 | — | 3 | 8 | no | — |
| 80 | C3×#97 | — | 3 | 2 | no | — |
| 81 | #832 | C2×D3 | 1 | 8 | yes | complemented |
| 82 | #821 | — | 3 | 8 | no | — |
| 83 | #815 | — | 3 | 4 | no | — |
| 84 | #809 | — | 3 | 8 | no | — |
| 85 | #803 | C2×D3 | 1 | 2 | yes | complemented |
| 86 | C23×C32 | — | 2 | 2 | no | — |
| 87 | C22×C3⋊D3 | — | 2 | 2 | no | — |
| 88 | C22×C3⋊D3 | — | 4 | 4 | no | — |
| 89 | C22×C3⋊D3 | — | 4 | 8 | no | — |
| 90 | C22×C3⋊D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 91 | C32×D4 | — | 2 | 4 | no | — |
| 92 | C32×D4 | — | 4 | 4 | no | — |
| 93 | C2×C32×C4 | C2×D4 | 1 | 2 | yes | — |
| 94 | C2×C32×C4 | C24 | 1 | 1 | yes | characteristic |
| 95 | #638 | — | 4 | 8 | no | — |
| 96 | #638 | — | 4 | 4 | no | — |
| 97 | C2×C3⋊Dic3 | C2×D4 | 1 | 2 | yes | — |
| 98 | C2×C3⋊Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 99 | C4⋊(C3⋊D3) | — | 2 | 4 | no | — |
| 100 | C4⋊(C3⋊D3) | — | 4 | 4 | no | — |
| 101 | C4×C3⋊D3 | — | 2 | 4 | no | — |
| 102 | C4×C3⋊D3 | #41 | 1 | 4 | yes | — |
| 103 | C2×C3×Dic3 | — | 2 | 4 | no | — |
| 104 | #624 | — | 4 | 4 | no | — |
| 105 | C3×C3⋊C8 | — | 2 | 4 | no | — |
| 106 | C2×#127 | — | 9 | 1 | no | — |
| 107 | C2×#125 | — | 9 | 1 | no | — |
| 108 | #490 | — | 3 | 2 | no | — |
| 109 | #490 | — | 9 | 2 | no | — |
| 110 | #490 | — | 9 | 4 | no | — |
| 111 | C2×#102 | — | 9 | 4 | no | — |
| 112 | C2×#97 | — | 9 | 1 | no | — |
| 113 | C23×D3 | — | 6 | 4 | no | — |
| 114 | C23×D3 | — | 6 | 4 | no | — |
| 115 | C2×C3×D4 | — | 2 | 4 | no | — |
| 116 | C2×C3×D4 | — | 2 | 4 | no | — |
| 117 | C2×C3×D4 | — | 2 | 2 | no | — |
| 118 | C2×C3×D4 | C22×D3 | 1 | 4 | yes | — |
| 119 | C2×#67 | — | 6 | 8 | no | — |
| 120 | C2×#67 | — | 6 | 4 | no | — |
| 121 | C2×#67 | — | 6 | 8 | no | — |
| 122 | C2×#67 | — | 6 | 4 | no | — |
| 123 | D3×D4 | — | 6 | 16 | no | — |
| 124 | D3×D4 | — | 12 | 8 | no | — |
| 125 | D3×D4 | — | 12 | 16 | no | — |
| 126 | D3×D4 | — | 12 | 16 | no | — |
| 127 | C2×D12 | — | 3 | 4 | no | — |
| 128 | C2×D12 | — | 6 | 2 | no | — |
| 129 | C2×D12 | — | 6 | 4 | no | — |
| 130 | C2×D12 | — | 6 | 4 | no | — |
| 131 | C2×C4×D3 | — | 3 | 2 | no | — |
| 132 | C2×C4×D3 | — | 3 | 4 | no | — |
| 133 | C2×C4×D3 | — | 6 | 2 | no | — |
| 134 | C2×C4×D3 | — | 6 | 1 | no | — |
| 135 | C2×C4×D3 | — | 6 | 4 | no | — |
| 136 | C2×C3×C8 | — | 3 | 4 | no | — |
| 137 | C3×C4⋊C4 | — | 3 | 4 | no | — |
| 138 | C3×C4⋊C4 | — | 6 | 4 | no | — |
| 139 | C3×C42 | — | 2 | 1 | no | — |
| 140 | C3×C42 | C22×D3 | 1 | 2 | yes | — |
| 141 | C4⋊Dic3 | — | 6 | 4 | no | — |
| 142 | C4⋊Dic3 | C22×D3 | 1 | 4 | yes | — |
| 143 | Dic3⋊C4 | — | 2 | 4 | no | — |
| 144 | Dic3⋊C4 | — | 6 | 4 | no | — |
| 145 | Dic3⋊C4 | — | 6 | 4 | no | — |
| 146 | C4×Dic3 | — | 3 | 4 | no | — |
| 147 | C4×Dic3 | — | 3 | 2 | no | — |
| 148 | C4×Dic3 | — | 6 | 2 | no | — |
| 149 | C4×Dic3 | — | 6 | 1 | no | — |
| 150 | C2×C3⋊C8 | C22×D3 | 1 | 4 | yes | — |
| 151 | D3×C8 | — | 6 | 8 | no | — |
| 152 | C22×C32 | — | 4 | 2 | no | — |
| 153 | C22×C32 | — | 4 | 4 | no | — |
| 154 | C22×C32 | C22×D4 | 1 | 1 | yes | characteristic |
| 155 | C2×C3⋊D3 | — | 4 | 2 | no | — |
| 156 | C2×C3⋊D3 | — | 4 | 4 | no | — |
| 157 | C2×C3⋊D3 | — | 8 | 8 | no | — |
| 158 | C2×C3⋊D3 | #124 | 1 | 2 | yes | — |
| 159 | C2×C3⋊D3 | AGL(1,ℤ/8) | 1 | 4 | yes | — |
| 160 | C32×C4 | — | 2 | 2 | no | — |
| 161 | C32×C4 | C2×#41 | 1 | 2 | yes | — |
| 162 | C3⋊Dic3 | — | 2 | 2 | no | — |
| 163 | C3⋊Dic3 | #124 | 1 | 2 | yes | — |
| 164 | C3×Dic3 | — | 4 | 4 | no | — |
| 165 | C22×D4 | — | 9 | 2 | no | — |
| 166 | C22×D4 | — | 18 | 2 | no | — |
| 167 | C22×C8 | — | 9 | 2 | no | — |
| 168 | #127 | — | 9 | 2 | no | — |
| 169 | #127 | — | 9 | 1 | no | — |
| 170 | #127 | — | 18 | 2 | no | — |
| 171 | #127 | D32 | 1 | 1 | yes | characteristic |
| 172 | #125 | — | 3 | 2 | no | — |
| 173 | #125 | — | 9 | 2 | no | — |
| 174 | #125 | — | 18 | 2 | no | — |
| 175 | C2×C4⋊C4 | — | 9 | 2 | no | — |
| 176 | C2×C4⋊C4 | — | 18 | 2 | no | — |
| 177 | C2×C42 | — | 9 | 1 | no | — |
| 178 | #102 | — | 3 | 8 | no | — |
| 179 | #102 | — | 9 | 8 | no | — |
| 180 | #97 | — | 3 | 2 | no | — |
| 181 | #97 | — | 9 | 2 | no | — |
| 182 | C23×C3 | — | 2 | 4 | no | — |
| 183 | C23×C3 | — | 2 | 4 | no | — |
| 184 | C22×D3 | — | 3 | 2 | no | — |
| 185 | C22×D3 | — | 6 | 1 | no | — |
| 186 | C22×D3 | — | 6 | 4 | no | — |
| 187 | C22×D3 | — | 6 | 4 | no | — |
| 188 | C22×D3 | — | 12 | 8 | no | — |
| 189 | C22×D3 | — | 12 | 16 | no | — |
| 190 | C22×D3 | — | 12 | 8 | no | — |
| 191 | C22×D3 | — | 12 | 16 | no | — |
| 192 | C3×D4 | — | 2 | 8 | no | — |
| 193 | C3×D4 | — | 4 | 4 | no | — |
| 194 | C3×D4 | — | 4 | 8 | no | — |
| 195 | C3×D4 | — | 4 | 8 | no | — |
| 196 | C2×C3×C4 | — | 2 | 1 | no | — |
| 197 | C2×C3×C4 | — | 2 | 2 | no | — |
| 198 | C2×C3×C4 | — | 6 | 4 | no | — |
| 199 | C2×C3×C4 | D3×D4 | 1 | 4 | yes | — |
| 200 | C2×C3×C4 | C23×D3 | 1 | 2 | yes | — |
| 201 | #67 | — | 12 | 8 | no | — |
| 202 | #67 | — | 12 | 8 | no | — |
| 203 | #67 | — | 12 | 16 | no | — |
| 204 | #67 | — | 12 | 16 | no | — |
| 205 | C2×Dic3 | — | 2 | 4 | no | — |
| 206 | C2×Dic3 | — | 3 | 2 | no | — |
| 207 | C2×Dic3 | — | 3 | 4 | no | — |
| 208 | C2×Dic3 | — | 6 | 1 | no | — |
| 209 | C2×Dic3 | — | 6 | 2 | no | — |
| 210 | D12 | — | 6 | 8 | no | — |
| 211 | D12 | — | 12 | 4 | no | — |
| 212 | D12 | — | 12 | 8 | no | — |
| 213 | D12 | — | 12 | 8 | no | — |
| 214 | C4×D3 | — | 3 | 8 | no | — |
| 215 | C4×D3 | — | 6 | 4 | no | — |
| 216 | C4×D3 | — | 6 | 8 | no | — |
| 217 | C4×D3 | — | 6 | 8 | no | — |
| 218 | C4×D3 | — | 12 | 8 | no | — |
| 219 | C3×C8 | — | 6 | 4 | no | — |
| 220 | C3⋊C8 | — | 2 | 4 | no | — |
| 221 | C2×C32 | — | 8 | 2 | no | — |
| 222 | C2×C32 | C2×#124 | 1 | 1 | yes | characteristic |
| 223 | C2×C32 | C2×AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 224 | C3⋊D3 | — | 8 | 2 | no | — |
| 225 | C3⋊D3 | #490 | 1 | 4 | yes | complemented |
| 226 | C24 | — | 18 | 2 | no | — |
| 227 | C2×D4 | — | 2 | 2 | no | — |
| 228 | C2×D4 | — | 9 | 2 | no | — |
| 229 | C2×D4 | — | 18 | 8 | no | — |
| 230 | C2×D4 | — | 18 | 4 | no | — |
| 231 | C2×D4 | — | 18 | 2 | no | — |
| 232 | C2×D4 | — | 18 | 2 | no | — |
| 233 | C2×D4 | — | 36 | 8 | no | — |
| 234 | C2×D4 | C2×D32 | 1 | 2 | yes | — |
| 235 | C22×C4 | — | 9 | 1 | no | — |
| 236 | C22×C4 | — | 9 | 2 | no | — |
| 237 | C22×C4 | — | 18 | 2 | no | — |
| 238 | C2×C8 | — | 3 | 4 | no | — |
| 239 | C2×C8 | — | 18 | 4 | no | — |
| 240 | C4⋊C4 | — | 3 | 4 | no | — |
| 241 | C4⋊C4 | — | 6 | 4 | no | — |
| 242 | C4⋊C4 | — | 18 | 2 | no | — |
| 243 | C4⋊C4 | — | 18 | 4 | no | — |
| 244 | C42 | — | 9 | 1 | no | — |
| 245 | C42 | — | 9 | 2 | no | — |
| 246 | C42 | C2×D32 | 1 | 1 | yes | characteristic |
| 247 | C22×C3 | — | 2 | 1 | no | — |
| 248 | C22×C3 | — | 4 | 8 | no | — |
| 249 | C22×C3 | — | 4 | 4 | no | — |
| 250 | C22×C3 | — | 4 | 4 | no | — |
| 251 | C22×C3 | — | 4 | 8 | no | — |
| 252 | C22×C3 | C2×D3×D4 | 1 | 2 | yes | — |
| 253 | C2×D3 | — | 3 | 4 | no | — |
| 254 | C2×D3 | — | 3 | 8 | no | — |
| 255 | C2×D3 | — | 6 | 2 | no | — |
| 256 | C2×D3 | — | 6 | 4 | no | — |
| 257 | C2×D3 | — | 12 | 8 | no | — |
| 258 | C2×D3 | — | 12 | 4 | no | — |
| 259 | C2×D3 | — | 12 | 4 | no | — |
| 260 | C2×D3 | — | 12 | 8 | no | — |
| 261 | C2×D3 | — | 24 | 16 | no | — |
| 262 | C2×D3 | — | 24 | 16 | no | — |
| 263 | C3×C4 | — | 2 | 4 | no | — |
| 264 | C3×C4 | — | 2 | 4 | no | — |
| 265 | C3×C4 | — | 2 | 2 | no | — |
| 266 | C3×C4 | — | 12 | 4 | no | — |
| 267 | C3×C4 | D3×#41 | 1 | 4 | yes | — |
| 268 | Dic3 | — | 3 | 4 | no | — |
| 269 | Dic3 | — | 4 | 4 | no | — |
| 270 | Dic3 | — | 6 | 2 | no | — |
| 271 | Dic3 | — | 6 | 4 | no | — |
| 272 | Dic3 | — | 6 | 4 | no | — |
| 273 | C32 | C2×#490 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 274 | C23 | — | 2 | 2 | no | — |
| 275 | C23 | — | 9 | 1 | no | — |
| 276 | C23 | — | 18 | 2 | no | — |
| 277 | C23 | — | 36 | 4 | no | — |
| 278 | C23 | — | 36 | 8 | no | — |
| 279 | D4 | — | 2 | 4 | no | — |
| 280 | D4 | — | 4 | 4 | no | — |
| 281 | D4 | — | 18 | 4 | no | — |
| 282 | D4 | — | 36 | 4 | no | — |
| 283 | D4 | — | 36 | 4 | no | — |
| 284 | D4 | — | 36 | 8 | no | — |
| 285 | C2×C4 | — | 6 | 4 | no | — |
| 286 | C2×C4 | — | 9 | 1 | no | — |
| 287 | C2×C4 | — | 9 | 4 | no | — |
| 288 | C2×C4 | — | 9 | 2 | no | — |
| 289 | C2×C4 | — | 18 | 4 | no | — |
| 290 | C2×C4 | — | 36 | 4 | no | — |
| 291 | C2×C4 | #3811 | 1 | 2 | yes | — |
| 292 | C2×C4 | C22×D32 | 1 | 1 | yes | characteristic |
| 293 | C8 | — | 6 | 4 | no | — |
| 294 | C2×C3 | — | 2 | 2 | no | — |
| 295 | C2×C3 | — | 2 | 1 | no | — |
| 296 | C2×C3 | — | 8 | 4 | no | — |
| 297 | C2×C3 | — | 8 | 4 | no | — |
| 298 | C2×C3 | D3×#124 | 1 | 2 | yes | — |
| 299 | C2×C3 | D3×AGL(1,ℤ/8) | 1 | 4 | yes | — |
| 300 | D3 | — | 3 | 8 | no | — |
| 301 | D3 | — | 6 | 4 | no | — |
| 302 | D3 | — | 24 | 4 | no | — |
| 303 | D3 | — | 24 | 4 | no | — |
| 304 | C22 | — | 4 | 4 | no | — |
| 305 | C22 | — | 4 | 2 | no | — |
| 306 | C22 | — | 9 | 4 | no | — |
| 307 | C22 | — | 9 | 2 | no | — |
| 308 | C22 | — | 36 | 4 | no | — |
| 309 | C22 | — | 36 | 2 | no | — |
| 310 | C22 | — | 72 | 8 | no | — |
| 311 | C22 | C2×#3811 | 1 | 1 | yes | characteristic |
| 312 | C4 | — | 2 | 2 | no | — |
| 313 | C4 | — | 9 | 2 | no | — |
| 314 | C4 | — | 12 | 4 | no | — |
| 315 | C4 | — | 18 | 2 | no | — |
| 316 | C4 | #64312 | 1 | 2 | yes | — |
| 317 | C3 | — | 2 | 1 | no | — |
| 318 | C3 | D3×#490 | 1 | 2 | yes | complemented |
| 319 | C2 | — | 8 | 2 | no | — |
| 320 | C2 | — | 9 | 4 | no | — |
| 321 | C2 | — | 72 | 2 | no | — |
| 322 | C2 | #10595100 | 1 | 2 | yes | — |
| 323 | C2 | #10595170 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #10593948 | C2 | semidirect |
| 3. C3×#5071 | C2 | semidirect |
| 4. #10591480 | C2 | semidirect |
| 5. #10591416 | C2 | semidirect |
| 6. #10590322 | C2 | semidirect |
| 7. #10590282 | C2 | semidirect |
| 16. C3×#870 | C22 | semidirect |
| 19. #63872 | C22 | semidirect |
| 22. C3×#832 | C22 | semidirect |
| 23. C3×#803 | C22 | semidirect |
| 24. #63564 | C22 | semidirect |
| 25. #63555 | C22 | semidirect |
| 30. #5071 | D3 | semidirect |
| 78. #870 | C2×D3 | semidirect |
| 81. #832 | C2×D3 | semidirect |
| 85. #803 | C2×D3 | semidirect |
| 225. C3⋊D3 | #490 | semidirect |
| 273. C32 | C2×#490 | semidirect |
| 318. C3 | D3×#490 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3⋊D3×#127 | 2 |
| #10593948 | 2 |
| C3×#5071 | 2 |
| #10591480 | 2 |
| #10591416 | 2 |
| #10590322 | 2 |
| #10590282 | 2 |
| D3×#490 | 3 |