Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
699 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 699 conjugacy classes of subgroups — too many to draw. Only its 100 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×#5717 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #10592775 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #10590268 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | C3×#4544 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #10589080 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #71907 | — | 3 | 1 | no | maximal |
| 7 | #68391 | — | 3 | 1 | no | maximal |
| 8 | C2×C3×D3×D4 | — | 2 | 2 | no | — |
| 9 | C32×#127 | C22 | 1 | 1 | yes | characteristic |
| 10 | C2×#3754 | — | 2 | 2 | no | — |
| 11 | #64078 | C22 | 1 | 1 | yes | characteristic, complemented |
| 12 | C3×#938 | — | 2 | 2 | no | — |
| 13 | C3×#937 | — | 2 | 2 | no | — |
| 14 | C3×C4×D12 | C22 | 1 | 2 | yes | — |
| 15 | C4×C3⋊(C3⋊C8) | C22 | 1 | 1 | yes | characteristic, complemented |
| 16 | C3×C4⋊(C3⋊C8) | C22 | 1 | 2 | yes | complemented |
| 17 | #63573 | — | 2 | 2 | no | — |
| 18 | #63563 | — | 2 | 2 | no | — |
| 19 | C3×D42 | — | 3 | 1 | no | — |
| 20 | #5717 | D3 | 1 | 1 | yes | characteristic |
| 21 | #5076 | — | 3 | 1 | no | — |
| 22 | #5076 | — | 3 | 1 | no | — |
| 23 | #5076 | — | 6 | 1 | no | — |
| 24 | #5008 | — | 3 | 2 | no | — |
| 25 | #4842 | — | 3 | 2 | no | — |
| 26 | C3×#331 | — | 3 | 1 | no | — |
| 27 | #4544 | D3 | 1 | 1 | yes | characteristic, complemented |
| 28 | D4⋊(C3⋊C8) | — | 3 | 2 | no | — |
| 29 | #4483 | — | 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×#634 | — | 2 | 1 | no | — |
| 34 | C2×C3×#67 | — | 2 | 4 | no | — |
| 35 | C3×D3×D4 | — | 4 | 4 | no | — |
| 36 | C3×D3×D4 | — | 4 | 4 | no | — |
| 37 | C2×C3×D12 | D4 | 1 | 2 | yes | — |
| 38 | C2×C3×C4×D3 | — | 2 | 2 | no | — |
| 39 | C32×C42 | C23 | 1 | 1 | yes | characteristic |
| 40 | #3754 | — | 4 | 4 | no | — |
| 41 | C4⋊(C3⋊Dic3) | — | 2 | 2 | no | — |
| 42 | C2×C3⋊(C3⋊C8) | — | 2 | 1 | no | — |
| 43 | C3×#217 | — | 2 | 2 | no | — |
| 44 | C3×(C2×D3)⋊C4 | — | 2 | 2 | no | — |
| 45 | C3×C4⋊Dic3 | D4 | 1 | 2 | yes | — |
| 46 | C2×C3×C3⋊C8 | — | 2 | 2 | no | — |
| 47 | #1629 | — | 9 | 1 | no | Sylow |
| 48 | C22×C3×D4 | — | 6 | 2 | no | — |
| 49 | C2×D3×D4 | — | 2 | 2 | no | — |
| 50 | C3×#127 | — | 2 | 1 | no | — |
| 51 | C3×#127 | C2×D3 | 1 | 1 | yes | characteristic |
| 52 | C3×#127 | C2×D3 | 1 | 1 | yes | characteristic |
| 53 | C3×#121 | — | 6 | 2 | no | — |
| 54 | C3×#120 | — | 6 | 2 | no | — |
| 55 | C3×C4×D4 | — | 3 | 2 | no | — |
| 56 | #938 | — | 2 | 2 | no | — |
| 57 | #937 | — | 2 | 2 | no | — |
| 58 | C2×#214 | — | 6 | 4 | no | — |
| 59 | C2×#214 | — | 6 | 2 | no | — |
| 60 | C2×#214 | — | 6 | 2 | no | — |
| 61 | C4×D12 | C2×D3 | 1 | 2 | yes | — |
| 62 | #869 | — | 3 | 1 | no | — |
| 63 | #869 | — | 3 | 1 | no | — |
| 64 | #869 | — | 6 | 1 | no | — |
| 65 | C3×C4⋊C8 | — | 3 | 2 | no | — |
| 66 | #832 | — | 6 | 2 | no | — |
| 67 | #821 | — | 6 | 2 | no | — |
| 68 | #817 | — | 6 | 2 | no | — |
| 69 | #808 | — | 6 | 2 | no | — |
| 70 | C4⋊(C3⋊C8) | C2×D3 | 1 | 2 | yes | complemented |
| 71 | C4×C3⋊C8 | — | 3 | 1 | no | — |
| 72 | C4×C3⋊C8 | — | 3 | 1 | no | — |
| 73 | C4×C3⋊C8 | — | 6 | 1 | no | — |
| 74 | C23×C32 | — | 2 | 2 | no | — |
| 75 | C22×C3×D3 | — | 2 | 2 | no | — |
| 76 | C22×C3×D3 | — | 4 | 8 | no | — |
| 77 | C22×C3×D3 | — | 8 | 2 | no | — |
| 78 | C32×D4 | — | 4 | 2 | no | — |
| 79 | C32×D4 | — | 4 | 2 | no | — |
| 80 | C32×D4 | — | 4 | 2 | no | — |
| 81 | C2×C32×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 82 | C2×C32×C4 | C2×D4 | 1 | 2 | yes | — |
| 83 | C2×C3⋊Dic3 | — | 4 | 1 | no | — |
| 84 | #634 | — | 4 | 2 | no | — |
| 85 | C3×#67 | — | 4 | 8 | no | — |
| 86 | C2×C3×Dic3 | — | 2 | 2 | no | — |
| 87 | C3×D12 | — | 2 | 2 | no | — |
| 88 | C3×D12 | SD16 | 1 | 4 | yes | complemented |
| 89 | C3×C4×D3 | — | 4 | 2 | no | — |
| 90 | C3×C4×D3 | — | 4 | 2 | no | — |
| 91 | C3⋊(C3⋊C8) | — | 2 | 2 | no | — |
| 92 | C3×C3⋊C8 | — | 4 | 2 | no | — |
| 93 | D42 | — | 3 | 1 | no | — |
| 94 | #492 | — | 9 | 1 | no | — |
| 95 | #476 | — | 9 | 2 | no | — |
| 96 | #331 | — | 3 | 1 | no | — |
| 97 | D4⋊C8 | — | 9 | 2 | no | — |
| 98 | C24×C3 | — | 6 | 2 | no | — |
| 99 | C23×D3 | — | 2 | 2 | no | — |
| 100 | C2×C3×D4 | — | 2 | 2 | no | — |
| 101 | C2×C3×D4 | — | 2 | 2 | no | — |
| 102 | C2×C3×D4 | — | 2 | 2 | no | — |
| 103 | C2×C3×D4 | — | 3 | 2 | no | — |
| 104 | C2×C3×D4 | — | 4 | 2 | no | — |
| 105 | C2×C3×D4 | — | 6 | 4 | no | — |
| 106 | C2×C3×D4 | — | 12 | 4 | no | — |
| 107 | C2×C3×D4 | — | 12 | 4 | no | — |
| 108 | C2×C3×D4 | D12 | 1 | 2 | yes | — |
| 109 | C2×C3×D4 | #67 | 1 | 2 | yes | — |
| 110 | C22×C3×C4 | — | 6 | 2 | no | — |
| 111 | C2×#67 | — | 2 | 4 | no | — |
| 112 | D3×D4 | — | 4 | 4 | no | — |
| 113 | D3×D4 | — | 4 | 4 | no | — |
| 114 | C2×D12 | #67 | 1 | 2 | yes | — |
| 115 | C2×C4×D3 | — | 2 | 2 | no | — |
| 116 | C2×Dic6 | — | 6 | 2 | no | — |
| 117 | C2×Dic6 | — | 6 | 1 | no | — |
| 118 | C2×Dic6 | — | 6 | 1 | no | — |
| 119 | C2×C3×C8 | — | 6 | 2 | no | — |
| 120 | C3×C4⋊C4 | — | 3 | 2 | no | — |
| 121 | C3×C22⋊C4 | — | 6 | 2 | no | — |
| 122 | C3×C22⋊C4 | — | 6 | 2 | no | — |
| 123 | C3×C42 | — | 2 | 1 | no | — |
| 124 | C3×C42 | C22×D3 | 1 | 1 | yes | characteristic |
| 125 | C3×C42 | C22×D3 | 1 | 1 | yes | characteristic |
| 126 | #217 | — | 2 | 2 | no | — |
| 127 | #214 | — | 12 | 4 | no | — |
| 128 | #214 | — | 12 | 4 | no | — |
| 129 | #214 | — | 12 | 8 | no | — |
| 130 | (C2×D3)⋊C4 | — | 2 | 2 | no | — |
| 131 | C4⋊Dic3 | — | 6 | 2 | no | — |
| 132 | C4⋊Dic3 | — | 6 | 2 | no | — |
| 133 | C4⋊Dic3 | — | 12 | 2 | no | — |
| 134 | C4⋊Dic3 | #67 | 1 | 2 | yes | — |
| 135 | C2×C3⋊C8 | — | 2 | 2 | no | — |
| 136 | C2×C3⋊C8 | — | 6 | 2 | no | — |
| 137 | C2×C3⋊C8 | — | 6 | 1 | no | — |
| 138 | C2×C3⋊C8 | — | 6 | 1 | no | — |
| 139 | C22×C32 | — | 4 | 4 | no | — |
| 140 | C22×C32 | — | 4 | 2 | no | — |
| 141 | C22×C32 | #120 | 1 | 1 | yes | characteristic |
| 142 | C2×C3×D3 | — | 2 | 4 | no | — |
| 143 | C2×C3×D3 | — | 4 | 2 | no | — |
| 144 | C2×C3×D3 | — | 4 | 2 | no | — |
| 145 | C2×C3×D3 | — | 8 | 8 | no | — |
| 146 | C32×C4 | — | 2 | 1 | no | — |
| 147 | C32×C4 | C2×SD16 | 1 | 2 | yes | — |
| 148 | C32×C4 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 149 | C3⋊Dic3 | — | 8 | 1 | no | — |
| 150 | C3×Dic3 | — | 4 | 2 | no | — |
| 151 | C22×D4 | — | 6 | 2 | no | — |
| 152 | C2×SD16 | — | 18 | 2 | no | — |
| 153 | C4⋊Q8 | — | 9 | 1 | no | — |
| 154 | #127 | D32 | 1 | 1 | yes | characteristic |
| 155 | #121 | — | 6 | 2 | no | — |
| 156 | #120 | — | 6 | 2 | no | — |
| 157 | C4×D4 | — | 3 | 2 | no | — |
| 158 | #106 | — | 18 | 2 | no | — |
| 159 | C4⋊C8 | — | 3 | 2 | no | — |
| 160 | #102 | — | 18 | 2 | no | — |
| 161 | C4×C8 | — | 9 | 1 | no | — |
| 162 | C23×C3 | — | 2 | 2 | no | — |
| 163 | C23×C3 | — | 2 | 2 | no | — |
| 164 | C23×C3 | — | 4 | 2 | no | — |
| 165 | C23×C3 | — | 6 | 2 | no | — |
| 166 | C23×C3 | — | 12 | 8 | no | — |
| 167 | C23×C3 | — | 24 | 2 | no | — |
| 168 | C22×D3 | — | 2 | 2 | no | — |
| 169 | C22×D3 | — | 4 | 8 | no | — |
| 170 | C22×D3 | — | 8 | 2 | no | — |
| 171 | C3×D4 | — | 3 | 4 | no | — |
| 172 | C3×D4 | — | 4 | 2 | no | — |
| 173 | C3×D4 | — | 4 | 2 | no | — |
| 174 | C3×D4 | — | 4 | 4 | no | — |
| 175 | C3×D4 | — | 4 | 2 | no | — |
| 176 | C3×D4 | — | 4 | 2 | no | — |
| 177 | C3×D4 | — | 4 | 2 | no | — |
| 178 | C3×D4 | — | 4 | 2 | no | — |
| 179 | C3×D4 | — | 6 | 2 | no | — |
| 180 | C3×D4 | — | 8 | 2 | no | — |
| 181 | C3×D4 | — | 8 | 2 | no | — |
| 182 | C3×D4 | — | 12 | 8 | no | — |
| 183 | C2×C3×C4 | — | 2 | 1 | no | — |
| 184 | C2×C3×C4 | — | 2 | 2 | no | — |
| 185 | C2×C3×C4 | — | 6 | 2 | no | — |
| 186 | C2×C3×C4 | — | 12 | 2 | no | — |
| 187 | C2×C3×C4 | — | 12 | 2 | no | — |
| 188 | C2×C3×C4 | C2×D12 | 1 | 1 | yes | characteristic |
| 189 | C2×C3×C4 | D3×D4 | 1 | 2 | yes | — |
| 190 | C2×C3×C4 | C2×#67 | 1 | 1 | yes | characteristic |
| 191 | C2×C3×C4 | C2×#67 | 1 | 2 | yes | — |
| 192 | #67 | — | 4 | 8 | no | — |
| 193 | C2×Dic3 | — | 2 | 2 | no | — |
| 194 | C2×Dic3 | — | 12 | 2 | no | — |
| 195 | C2×Dic3 | — | 12 | 1 | no | — |
| 196 | C2×Dic3 | — | 12 | 1 | no | — |
| 197 | D12 | — | 2 | 2 | no | — |
| 198 | D12 | #214 | 1 | 4 | yes | complemented |
| 199 | C4×D3 | — | 4 | 2 | no | — |
| 200 | C4×D3 | — | 4 | 2 | no | — |
| 201 | Dic6 | — | 12 | 4 | no | — |
| 202 | Dic6 | — | 12 | 2 | no | — |
| 203 | Dic6 | — | 12 | 2 | no | — |
| 204 | C3×C8 | — | 12 | 2 | no | — |
| 205 | C3⋊C8 | — | 4 | 2 | no | — |
| 206 | C3⋊C8 | — | 6 | 4 | no | — |
| 207 | C3⋊C8 | — | 6 | 2 | no | — |
| 208 | C3⋊C8 | — | 6 | 2 | no | — |
| 209 | C2×C32 | — | 8 | 2 | no | — |
| 210 | C2×C32 | #450 | 1 | 2 | yes | — |
| 211 | C2×C32 | #453 | 1 | 1 | yes | characteristic |
| 212 | C3×D3 | — | 4 | 4 | no | — |
| 213 | C24 | — | 6 | 2 | no | — |
| 214 | C2×Q8 | — | 18 | 1 | no | — |
| 215 | C2×D4 | — | 2 | 2 | no | — |
| 216 | C2×D4 | — | 3 | 2 | no | — |
| 217 | C2×D4 | — | 6 | 4 | no | — |
| 218 | C2×D4 | — | 12 | 4 | no | — |
| 219 | C2×D4 | — | 12 | 4 | no | — |
| 220 | C2×D4 | #626 | 1 | 2 | yes | — |
| 221 | C22×C4 | — | 6 | 2 | no | — |
| 222 | SD16 | — | 36 | 4 | no | — |
| 223 | C2×C8 | — | 6 | 2 | no | — |
| 224 | C2×C8 | — | 18 | 1 | no | — |
| 225 | C4⋊C4 | — | 3 | 2 | no | — |
| 226 | C4⋊C4 | — | 18 | 2 | no | — |
| 227 | C22⋊C4 | — | 6 | 2 | no | — |
| 228 | C22⋊C4 | — | 6 | 2 | no | — |
| 229 | C42 | C2×D32 | 1 | 1 | yes | characteristic |
| 230 | C22×C3 | — | 2 | 1 | no | — |
| 231 | C22×C3 | — | 4 | 4 | no | — |
| 232 | C22×C3 | — | 4 | 2 | no | — |
| 233 | C22×C3 | — | 4 | 2 | no | — |
| 234 | C22×C3 | — | 4 | 4 | no | — |
| 235 | C22×C3 | — | 6 | 4 | no | — |
| 236 | C22×C3 | — | 8 | 2 | no | — |
| 237 | C22×C3 | — | 8 | 4 | no | — |
| 238 | C22×C3 | — | 12 | 2 | no | — |
| 239 | C22×C3 | — | 12 | 2 | no | — |
| 240 | C22×C3 | — | 24 | 8 | no | — |
| 241 | C22×C3 | #882 | 1 | 1 | yes | characteristic |
| 242 | C22×C3 | #953 | 1 | 1 | yes | characteristic |
| 243 | C2×D3 | — | 2 | 4 | no | — |
| 244 | C2×D3 | — | 4 | 2 | no | — |
| 245 | C2×D3 | — | 4 | 2 | no | — |
| 246 | C2×D3 | — | 8 | 8 | no | — |
| 247 | C3×C4 | — | 2 | 2 | no | — |
| 248 | C3×C4 | — | 2 | 1 | no | — |
| 249 | C3×C4 | — | 2 | 1 | no | — |
| 250 | C3×C4 | — | 2 | 2 | no | — |
| 251 | C3×C4 | — | 2 | 2 | no | — |
| 252 | C3×C4 | — | 12 | 2 | no | — |
| 253 | C3×C4 | #911 | 1 | 2 | yes | — |
| 254 | C3×C4 | D3×SD16 | 1 | 2 | yes | — |
| 255 | C3×C4 | #932 | 1 | 2 | yes | — |
| 256 | C3×C4 | C2×#214 | 1 | 2 | yes | — |
| 257 | Dic3 | — | 4 | 2 | no | — |
| 258 | Dic3 | — | 24 | 2 | no | — |
| 259 | Dic3 | — | 24 | 1 | no | — |
| 260 | Dic3 | — | 24 | 1 | no | — |
| 261 | C32 | #1629 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 262 | C23 | — | 2 | 2 | no | — |
| 263 | C23 | — | 6 | 2 | no | — |
| 264 | C23 | — | 12 | 8 | no | — |
| 265 | C23 | — | 24 | 2 | no | — |
| 266 | Q8 | — | 36 | 2 | no | — |
| 267 | D4 | — | 3 | 4 | no | — |
| 268 | D4 | — | 4 | 2 | no | — |
| 269 | D4 | — | 4 | 2 | no | — |
| 270 | D4 | — | 4 | 2 | no | — |
| 271 | D4 | — | 6 | 2 | no | — |
| 272 | D4 | — | 12 | 8 | no | — |
| 273 | C2×C4 | — | 6 | 2 | no | — |
| 274 | C2×C4 | — | 12 | 2 | no | — |
| 275 | C2×C4 | — | 12 | 2 | no | — |
| 276 | C2×C4 | — | 36 | 1 | no | — |
| 277 | C2×C4 | C2×#626 | 1 | 1 | yes | characteristic |
| 278 | C2×C4 | D3×#67 | 1 | 2 | yes | — |
| 279 | C8 | — | 12 | 2 | no | — |
| 280 | C8 | — | 18 | 2 | no | — |
| 281 | C2×C3 | — | 2 | 1 | no | — |
| 282 | C2×C3 | — | 2 | 2 | no | — |
| 283 | C2×C3 | — | 8 | 2 | no | — |
| 284 | C2×C3 | — | 8 | 2 | no | — |
| 285 | C2×C3 | — | 12 | 4 | no | — |
| 286 | C2×C3 | — | 16 | 2 | no | — |
| 287 | C2×C3 | #4747 | 1 | 1 | yes | characteristic |
| 288 | C2×C3 | #4776 | 1 | 2 | yes | — |
| 289 | C2×C3 | #5218 | 1 | 2 | yes | — |
| 290 | C2×C3 | #5241 | 1 | 1 | yes | characteristic |
| 291 | D3 | — | 4 | 4 | no | — |
| 292 | C22 | — | 4 | 2 | no | — |
| 293 | C22 | — | 4 | 4 | no | — |
| 294 | C22 | — | 6 | 4 | no | — |
| 295 | C22 | — | 12 | 2 | no | — |
| 296 | C22 | — | 12 | 2 | no | — |
| 297 | C22 | — | 24 | 8 | no | — |
| 298 | C22 | #63977 | 1 | 1 | yes | characteristic |
| 299 | C4 | — | 2 | 1 | no | — |
| 300 | C4 | — | 12 | 2 | no | — |
| 301 | C4 | — | 72 | 1 | no | — |
| 302 | C4 | D3×#214 | 1 | 2 | yes | — |
| 303 | C4 | #63932 | 1 | 2 | yes | — |
| 304 | C3 | — | 2 | 1 | no | — |
| 305 | C3 | #68391 | 1 | 1 | yes | characteristic, complemented |
| 306 | C3 | #71907 | 1 | 1 | yes | characteristic, complemented |
| 307 | C2 | — | 8 | 2 | no | — |
| 308 | C2 | — | 12 | 4 | no | — |
| 309 | C2 | #10591459 | 1 | 2 | yes | — |
| 310 | C2 | #10591510 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #10592775 | C2 | semidirect |
| 3. #10590268 | C2 | semidirect |
| 4. C3×#4544 | C2 | semidirect |
| 5. #10589080 | C2 | semidirect |
| 11. #64078 | C22 | semidirect |
| 15. C4×C3⋊(C3⋊C8) | C22 | semidirect |
| 16. C3×C4⋊(C3⋊C8) | C22 | semidirect |
| 27. #4544 | D3 | semidirect |
| 70. C4⋊(C3⋊C8) | C2×D3 | semidirect |
| 88. C3×D12 | SD16 | semidirect |
| 198. D12 | #214 | semidirect |
| 261. C32 | #1629 | semidirect |
| 305. C3 | #68391 | semidirect |
| 306. C3 | #71907 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5717 | 2 |
| #10592775 | 2 |
| #10590268 | 2 |
| C3×#4544 | 2 |
| #10589080 | 2 |
| #71907 | 3 |
| #68391 | 3 |