Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
842 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 842 conjugacy classes of subgroups — too many to draw. Only its 92 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 | #10596188 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C3×#5076 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #10590300 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | C3×#4544 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #10589082 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #71266 | — | 3 | 1 | no | maximal |
| 7 | #68391 | — | 3 | 1 | no | maximal |
| 8 | C2×D4×C3⋊D3 | — | 2 | 2 | no | — |
| 9 | C32×#127 | C22 | 1 | 1 | yes | characteristic |
| 10 | #64147 | — | 2 | 2 | no | — |
| 11 | #64146 | — | 2 | 2 | no | — |
| 12 | C4×C4⋊(C3⋊D3) | C22 | 1 | 2 | yes | — |
| 13 | C2×C3×#214 | — | 2 | 2 | no | — |
| 14 | C3×#869 | C22 | 1 | 1 | yes | characteristic, complemented |
| 15 | C3×C4⋊(C3⋊C8) | C22 | 1 | 2 | yes | complemented |
| 16 | C3×C4×C3⋊C8 | C22 | 1 | 1 | yes | characteristic, complemented |
| 17 | #63573 | — | 2 | 2 | no | — |
| 18 | #63564 | — | 2 | 2 | no | — |
| 19 | #5717 | — | 3 | 1 | no | — |
| 20 | #5717 | — | 3 | 1 | no | — |
| 21 | #5717 | — | 6 | 1 | no | — |
| 22 | C3×#492 | — | 3 | 1 | no | — |
| 23 | #5084 | — | 3 | 2 | no | — |
| 24 | #5076 | D3 | 1 | 1 | yes | characteristic, complemented |
| 25 | #4842 | — | 3 | 2 | no | — |
| 26 | C3×#331 | — | 3 | 1 | no | — |
| 27 | #4544 | D3 | 1 | 1 | yes | characteristic, complemented |
| 28 | #4483 | — | 3 | 2 | no | — |
| 29 | #4459 | — | 3 | 2 | no | — |
| 30 | C23×C3⋊D3 | — | 2 | 2 | no | — |
| 31 | C2×C32×D4 | — | 2 | 2 | no | — |
| 32 | C2×C32×D4 | D4 | 1 | 2 | yes | — |
| 33 | C2×#638 | — | 2 | 4 | no | — |
| 34 | D4×C3⋊D3 | — | 4 | 4 | no | — |
| 35 | D4×C3⋊D3 | — | 4 | 4 | no | — |
| 36 | C2×C4⋊(C3⋊D3) | D4 | 1 | 2 | yes | — |
| 37 | C2×C4×C3⋊D3 | — | 2 | 2 | no | — |
| 38 | C2×C3×Dic6 | — | 2 | 1 | no | — |
| 39 | C32×C42 | C23 | 1 | 1 | yes | characteristic |
| 40 | #3757 | — | 2 | 2 | no | — |
| 41 | #3752 | — | 2 | 2 | no | — |
| 42 | C4⋊(C3⋊Dic3) | D4 | 1 | 2 | yes | — |
| 43 | C3×#214 | — | 4 | 4 | no | — |
| 44 | C3×C4⋊Dic3 | — | 2 | 2 | no | — |
| 45 | C2×C3×C3⋊C8 | — | 2 | 1 | no | — |
| 46 | C2×C3×C3⋊C8 | — | 2 | 2 | no | — |
| 47 | #1629 | — | 9 | 1 | no | Sylow |
| 48 | C2×D3×D4 | — | 6 | 2 | no | — |
| 49 | C2×D3×D4 | — | 6 | 2 | no | — |
| 50 | C2×D3×D4 | — | 6 | 4 | no | — |
| 51 | C2×C3×SD16 | — | 6 | 2 | no | — |
| 52 | C3×C4⋊Q8 | — | 3 | 1 | no | — |
| 53 | C3×#127 | — | 2 | 1 | no | — |
| 54 | C3×#127 | C2×D3 | 1 | 1 | yes | characteristic |
| 55 | C3×#127 | C2×D3 | 1 | 1 | yes | characteristic |
| 56 | #938 | — | 6 | 2 | no | — |
| 57 | #938 | — | 6 | 2 | no | — |
| 58 | #938 | — | 6 | 4 | no | — |
| 59 | #937 | — | 6 | 4 | no | — |
| 60 | #937 | — | 6 | 2 | no | — |
| 61 | #937 | — | 6 | 2 | no | — |
| 62 | C2×#214 | — | 2 | 2 | no | — |
| 63 | C4×D12 | — | 3 | 2 | no | — |
| 64 | C4×D12 | — | 3 | 2 | no | — |
| 65 | C4×D12 | — | 6 | 2 | no | — |
| 66 | #869 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 67 | C3×C4⋊C8 | — | 3 | 2 | no | — |
| 68 | C3×C4×C8 | — | 3 | 1 | no | — |
| 69 | #821 | — | 6 | 2 | no | — |
| 70 | #817 | — | 6 | 2 | no | — |
| 71 | #809 | — | 6 | 2 | no | — |
| 72 | #808 | — | 6 | 2 | no | — |
| 73 | C4⋊(C3⋊C8) | C2×D3 | 1 | 2 | yes | complemented |
| 74 | C4×C3⋊C8 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 75 | C23×C32 | — | 2 | 2 | no | — |
| 76 | C22×C3⋊D3 | — | 2 | 2 | no | — |
| 77 | C22×C3⋊D3 | — | 4 | 8 | no | — |
| 78 | C22×C3⋊D3 | — | 8 | 2 | no | — |
| 79 | C32×D4 | — | 4 | 2 | no | — |
| 80 | C32×D4 | — | 4 | 2 | no | — |
| 81 | C32×D4 | — | 4 | 2 | no | — |
| 82 | C2×C32×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 83 | C2×C32×C4 | C2×D4 | 1 | 2 | yes | — |
| 84 | #638 | — | 4 | 8 | no | — |
| 85 | C2×C3⋊Dic3 | — | 2 | 2 | no | — |
| 86 | C4⋊(C3⋊D3) | — | 2 | 2 | no | — |
| 87 | C4⋊(C3⋊D3) | SD16 | 1 | 4 | yes | complemented |
| 88 | C4×C3⋊D3 | — | 4 | 2 | no | — |
| 89 | C4×C3⋊D3 | — | 4 | 2 | no | — |
| 90 | C2×C3×Dic3 | — | 4 | 1 | no | — |
| 91 | C3×Dic6 | — | 4 | 2 | no | — |
| 92 | C3×C3⋊C8 | — | 2 | 2 | no | — |
| 93 | C3×C3⋊C8 | — | 4 | 2 | no | — |
| 94 | D42 | — | 9 | 1 | no | — |
| 95 | #492 | — | 3 | 1 | no | — |
| 96 | #476 | — | 9 | 2 | no | — |
| 97 | #331 | — | 3 | 1 | no | — |
| 98 | D4⋊C8 | — | 9 | 2 | no | — |
| 99 | C23×D3 | — | 6 | 4 | no | — |
| 100 | C23×D3 | — | 6 | 2 | no | — |
| 101 | C23×D3 | — | 6 | 2 | no | — |
| 102 | C2×C3×Q8 | — | 6 | 1 | no | — |
| 103 | C2×C3×D4 | — | 2 | 4 | no | — |
| 104 | C2×C3×D4 | — | 2 | 2 | no | — |
| 105 | C2×C3×D4 | — | 2 | 2 | no | — |
| 106 | C2×C3×D4 | — | 2 | 2 | no | — |
| 107 | C2×C3×D4 | D12 | 1 | 2 | yes | — |
| 108 | C2×C3×D4 | #67 | 1 | 2 | yes | — |
| 109 | C2×#67 | — | 6 | 8 | no | — |
| 110 | C2×#67 | — | 6 | 4 | no | — |
| 111 | C2×#67 | — | 6 | 4 | no | — |
| 112 | D3×D4 | — | 12 | 4 | no | — |
| 113 | D3×D4 | — | 12 | 4 | no | — |
| 114 | D3×D4 | — | 12 | 8 | no | — |
| 115 | D3×D4 | — | 12 | 8 | no | — |
| 116 | D3×D4 | — | 12 | 4 | no | — |
| 117 | D3×D4 | — | 12 | 4 | no | — |
| 118 | C2×D12 | — | 3 | 2 | no | — |
| 119 | C2×D12 | — | 3 | 2 | no | — |
| 120 | C2×D12 | — | 6 | 2 | no | — |
| 121 | C2×C4×D3 | — | 6 | 4 | no | — |
| 122 | C2×C4×D3 | — | 6 | 2 | no | — |
| 123 | C2×C4×D3 | — | 6 | 2 | no | — |
| 124 | C2×Dic6 | — | 2 | 1 | no | — |
| 125 | C3×SD16 | — | 12 | 4 | no | — |
| 126 | C2×C3×C8 | — | 6 | 1 | no | — |
| 127 | C2×C3×C8 | — | 6 | 2 | no | — |
| 128 | C3×C4⋊C4 | — | 6 | 2 | no | — |
| 129 | C3×C42 | — | 2 | 1 | no | — |
| 130 | C3×C42 | C22×D3 | 1 | 1 | yes | characteristic |
| 131 | C3×C42 | C22×D3 | 1 | 1 | yes | characteristic |
| 132 | #217 | — | 6 | 4 | no | — |
| 133 | #217 | — | 6 | 2 | no | — |
| 134 | #217 | — | 6 | 2 | no | — |
| 135 | #214 | — | 4 | 4 | no | — |
| 136 | (C2×D3)⋊C4 | — | 6 | 4 | no | — |
| 137 | (C2×D3)⋊C4 | — | 6 | 2 | no | — |
| 138 | (C2×D3)⋊C4 | — | 6 | 2 | no | — |
| 139 | C4⋊Dic3 | — | 2 | 2 | no | — |
| 140 | C4⋊Dic3 | — | 3 | 2 | no | — |
| 141 | C4⋊Dic3 | — | 3 | 2 | no | — |
| 142 | C4⋊Dic3 | — | 6 | 2 | no | — |
| 143 | C2×C3⋊C8 | — | 2 | 1 | no | — |
| 144 | C2×C3⋊C8 | — | 2 | 2 | no | — |
| 145 | C22×C32 | — | 4 | 4 | no | — |
| 146 | C22×C32 | — | 4 | 2 | no | — |
| 147 | C22×C32 | #120 | 1 | 1 | yes | characteristic |
| 148 | C2×C3⋊D3 | — | 2 | 4 | no | — |
| 149 | C2×C3⋊D3 | — | 4 | 2 | no | — |
| 150 | C2×C3⋊D3 | — | 4 | 2 | no | — |
| 151 | C2×C3⋊D3 | — | 8 | 8 | no | — |
| 152 | C32×C4 | — | 2 | 1 | no | — |
| 153 | C32×C4 | C2×SD16 | 1 | 2 | yes | — |
| 154 | C32×C4 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 155 | C3⋊Dic3 | — | 4 | 2 | no | — |
| 156 | C3×Dic3 | — | 8 | 1 | no | — |
| 157 | C22×D4 | — | 18 | 2 | no | — |
| 158 | C2×SD16 | — | 6 | 2 | no | — |
| 159 | C4⋊Q8 | — | 3 | 1 | no | — |
| 160 | #127 | D32 | 1 | 1 | yes | characteristic |
| 161 | #121 | — | 18 | 2 | no | — |
| 162 | #120 | — | 18 | 2 | no | — |
| 163 | C4×D4 | — | 9 | 2 | no | — |
| 164 | #106 | — | 18 | 2 | no | — |
| 165 | C4⋊C8 | — | 3 | 2 | no | — |
| 166 | #102 | — | 18 | 2 | no | — |
| 167 | C4×C8 | — | 3 | 1 | no | — |
| 168 | C23×C3 | — | 2 | 4 | no | — |
| 169 | C23×C3 | — | 2 | 2 | no | — |
| 170 | C23×C3 | — | 2 | 2 | no | — |
| 171 | C22×D3 | — | 6 | 4 | no | — |
| 172 | C22×D3 | — | 6 | 2 | no | — |
| 173 | C22×D3 | — | 6 | 2 | no | — |
| 174 | C22×D3 | — | 12 | 16 | no | — |
| 175 | C22×D3 | — | 12 | 8 | no | — |
| 176 | C22×D3 | — | 12 | 8 | no | — |
| 177 | C22×D3 | — | 24 | 4 | no | — |
| 178 | C22×D3 | — | 24 | 2 | no | — |
| 179 | C22×D3 | — | 24 | 2 | no | — |
| 180 | C3×Q8 | — | 12 | 2 | no | — |
| 181 | C3×D4 | — | 4 | 2 | no | — |
| 182 | C3×D4 | — | 4 | 2 | no | — |
| 183 | C3×D4 | — | 4 | 4 | no | — |
| 184 | C3×D4 | — | 4 | 4 | no | — |
| 185 | C3×D4 | — | 4 | 2 | no | — |
| 186 | C3×D4 | — | 4 | 2 | no | — |
| 187 | C3×D4 | — | 4 | 2 | no | — |
| 188 | C3×D4 | — | 4 | 2 | no | — |
| 189 | C3×D4 | — | 8 | 2 | no | — |
| 190 | C2×C3×C4 | — | 2 | 1 | no | — |
| 191 | C2×C3×C4 | — | 2 | 2 | no | — |
| 192 | C2×C3×C4 | — | 12 | 1 | no | — |
| 193 | C2×C3×C4 | C2×D12 | 1 | 1 | yes | characteristic |
| 194 | C2×C3×C4 | D3×D4 | 1 | 2 | yes | — |
| 195 | C2×C3×C4 | D3×D4 | 1 | 2 | yes | — |
| 196 | C2×C3×C4 | C2×#67 | 1 | 1 | yes | characteristic |
| 197 | #67 | — | 12 | 16 | no | — |
| 198 | #67 | — | 12 | 8 | no | — |
| 199 | #67 | — | 12 | 8 | no | — |
| 200 | C2×Dic3 | — | 4 | 1 | no | — |
| 201 | C2×Dic3 | — | 6 | 4 | no | — |
| 202 | C2×Dic3 | — | 6 | 2 | no | — |
| 203 | C2×Dic3 | — | 6 | 2 | no | — |
| 204 | D12 | — | 3 | 4 | no | — |
| 205 | D12 | — | 3 | 4 | no | — |
| 206 | D12 | — | 6 | 4 | no | — |
| 207 | D12 | — | 6 | 4 | no | — |
| 208 | D12 | — | 6 | 2 | no | — |
| 209 | D12 | — | 6 | 2 | no | — |
| 210 | C4×D3 | — | 12 | 4 | no | — |
| 211 | C4×D3 | — | 12 | 4 | no | — |
| 212 | C4×D3 | — | 12 | 2 | no | — |
| 213 | C4×D3 | — | 12 | 2 | no | — |
| 214 | C4×D3 | — | 12 | 2 | no | — |
| 215 | C4×D3 | — | 12 | 2 | no | — |
| 216 | Dic6 | — | 4 | 2 | no | — |
| 217 | C3×C8 | — | 6 | 2 | no | — |
| 218 | C3×C8 | — | 12 | 2 | no | — |
| 219 | C3⋊C8 | — | 2 | 2 | no | — |
| 220 | C3⋊C8 | — | 4 | 2 | no | — |
| 221 | C2×C32 | — | 8 | 2 | no | — |
| 222 | C2×C32 | #450 | 1 | 2 | yes | — |
| 223 | C2×C32 | #453 | 1 | 1 | yes | characteristic |
| 224 | C3⋊D3 | — | 4 | 4 | no | — |
| 225 | C24 | — | 18 | 2 | no | — |
| 226 | C2×Q8 | — | 6 | 1 | no | — |
| 227 | C2×D4 | — | 2 | 2 | no | — |
| 228 | C2×D4 | — | 9 | 2 | no | — |
| 229 | C2×D4 | — | 18 | 4 | no | — |
| 230 | C2×D4 | — | 36 | 4 | no | — |
| 231 | C2×D4 | — | 36 | 4 | no | — |
| 232 | C2×D4 | #626 | 1 | 2 | yes | — |
| 233 | C22×C4 | — | 18 | 2 | no | — |
| 234 | SD16 | — | 12 | 4 | no | — |
| 235 | C2×C8 | — | 6 | 1 | no | — |
| 236 | C2×C8 | — | 6 | 2 | no | — |
| 237 | C4⋊C4 | — | 6 | 2 | no | — |
| 238 | C4⋊C4 | — | 9 | 2 | no | — |
| 239 | C22⋊C4 | — | 18 | 2 | no | — |
| 240 | C22⋊C4 | — | 18 | 2 | no | — |
| 241 | C42 | C2×D32 | 1 | 1 | yes | characteristic |
| 242 | C22×C3 | — | 2 | 1 | no | — |
| 243 | C22×C3 | — | 4 | 8 | no | — |
| 244 | C22×C3 | — | 4 | 4 | no | — |
| 245 | C22×C3 | — | 4 | 4 | no | — |
| 246 | C22×C3 | — | 4 | 2 | no | — |
| 247 | C22×C3 | — | 4 | 4 | no | — |
| 248 | C22×C3 | — | 4 | 2 | no | — |
| 249 | C22×C3 | #882 | 1 | 1 | yes | characteristic |
| 250 | C22×C3 | #937 | 1 | 1 | yes | characteristic |
| 251 | C2×D3 | — | 6 | 8 | no | — |
| 252 | C2×D3 | — | 6 | 4 | no | — |
| 253 | C2×D3 | — | 6 | 4 | no | — |
| 254 | C2×D3 | — | 12 | 4 | no | — |
| 255 | C2×D3 | — | 12 | 4 | no | — |
| 256 | C2×D3 | — | 12 | 2 | no | — |
| 257 | C2×D3 | — | 12 | 2 | no | — |
| 258 | C2×D3 | — | 12 | 2 | no | — |
| 259 | C2×D3 | — | 12 | 2 | no | — |
| 260 | C2×D3 | — | 24 | 16 | no | — |
| 261 | C2×D3 | — | 24 | 8 | no | — |
| 262 | C2×D3 | — | 24 | 8 | no | — |
| 263 | C3×C4 | — | 2 | 1 | no | — |
| 264 | C3×C4 | — | 2 | 1 | no | — |
| 265 | C3×C4 | — | 2 | 2 | no | — |
| 266 | C3×C4 | — | 2 | 2 | no | — |
| 267 | C3×C4 | — | 4 | 1 | no | — |
| 268 | C3×C4 | — | 24 | 1 | no | — |
| 269 | C3×C4 | #911 | 1 | 2 | yes | — |
| 270 | C3×C4 | D3×SD16 | 1 | 2 | yes | — |
| 271 | C3×C4 | D3×SD16 | 1 | 2 | yes | — |
| 272 | C3×C4 | #914 | 1 | 2 | yes | — |
| 273 | Dic3 | — | 8 | 1 | no | — |
| 274 | Dic3 | — | 12 | 4 | no | — |
| 275 | Dic3 | — | 12 | 2 | no | — |
| 276 | Dic3 | — | 12 | 2 | no | — |
| 277 | C32 | #1629 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 278 | C23 | — | 2 | 2 | no | — |
| 279 | C23 | — | 18 | 2 | no | — |
| 280 | C23 | — | 36 | 8 | no | — |
| 281 | C23 | — | 72 | 2 | no | — |
| 282 | Q8 | — | 12 | 2 | no | — |
| 283 | D4 | — | 4 | 2 | no | — |
| 284 | D4 | — | 4 | 2 | no | — |
| 285 | D4 | — | 4 | 2 | no | — |
| 286 | D4 | — | 9 | 4 | no | — |
| 287 | D4 | — | 18 | 2 | no | — |
| 288 | D4 | — | 36 | 8 | no | — |
| 289 | C2×C4 | — | 12 | 1 | no | — |
| 290 | C2×C4 | — | 18 | 2 | no | — |
| 291 | C2×C4 | — | 36 | 2 | no | — |
| 292 | C2×C4 | — | 36 | 2 | no | — |
| 293 | C2×C4 | C2×#626 | 1 | 1 | yes | characteristic |
| 294 | C2×C4 | #3811 | 1 | 2 | yes | — |
| 295 | C8 | — | 6 | 2 | no | — |
| 296 | C8 | — | 12 | 2 | no | — |
| 297 | C2×C3 | — | 2 | 1 | no | — |
| 298 | C2×C3 | — | 2 | 2 | no | — |
| 299 | C2×C3 | — | 8 | 4 | no | — |
| 300 | C2×C3 | — | 8 | 2 | no | — |
| 301 | C2×C3 | — | 8 | 2 | no | — |
| 302 | C2×C3 | #4747 | 1 | 1 | yes | characteristic |
| 303 | C2×C3 | #4776 | 1 | 2 | yes | — |
| 304 | C2×C3 | #5077 | 1 | 1 | yes | characteristic |
| 305 | C2×C3 | #5169 | 1 | 2 | yes | — |
| 306 | D3 | — | 12 | 8 | no | — |
| 307 | D3 | — | 12 | 4 | no | — |
| 308 | D3 | — | 12 | 4 | no | — |
| 309 | C22 | — | 4 | 2 | no | — |
| 310 | C22 | — | 4 | 4 | no | — |
| 311 | C22 | — | 18 | 4 | no | — |
| 312 | C22 | — | 36 | 2 | no | — |
| 313 | C22 | — | 36 | 2 | no | — |
| 314 | C22 | — | 72 | 8 | no | — |
| 315 | C22 | #63981 | 1 | 1 | yes | characteristic |
| 316 | C4 | — | 2 | 1 | no | — |
| 317 | C4 | — | 24 | 1 | no | — |
| 318 | C4 | — | 36 | 2 | no | — |
| 319 | C4 | #63930 | 1 | 2 | yes | — |
| 320 | C4 | #63937 | 1 | 2 | yes | — |
| 321 | C3 | — | 2 | 1 | no | — |
| 322 | C3 | #68391 | 1 | 1 | yes | characteristic, complemented |
| 323 | C3 | #71266 | 1 | 1 | yes | characteristic, complemented |
| 324 | C2 | — | 8 | 2 | no | — |
| 325 | C2 | — | 36 | 4 | no | — |
| 326 | C2 | #10591467 | 1 | 2 | yes | — |
| 327 | C2 | #10591511 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3×#5076 | C2 | semidirect |
| 3. #10590300 | C2 | semidirect |
| 4. C3×#4544 | C2 | semidirect |
| 5. #10589082 | C2 | semidirect |
| 14. C3×#869 | C22 | semidirect |
| 15. C3×C4⋊(C3⋊C8) | C22 | semidirect |
| 16. C3×C4×C3⋊C8 | C22 | semidirect |
| 24. #5076 | D3 | semidirect |
| 27. #4544 | D3 | semidirect |
| 66. #869 | C2×D3 | semidirect |
| 73. C4⋊(C3⋊C8) | C2×D3 | semidirect |
| 74. C4×C3⋊C8 | C2×D3 | semidirect |
| 87. C4⋊(C3⋊D3) | SD16 | semidirect |
| 277. C32 | #1629 | semidirect |
| 322. C3 | #68391 | semidirect |
| 323. C3 | #71266 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10596188 | 2 |
| C3×#5076 | 2 |
| #10590300 | 2 |
| C3×#4544 | 2 |
| #10589082 | 2 |
| #71266 | 3 |
| #68391 | 3 |