Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
824 conjugacy classes of subgroups; only the 196 normal subgroups are shown.
This group has 824 conjugacy classes of subgroups — too many to draw. Only its 196 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 | #10596224 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C3×#5753 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C3×#5140 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #10590642 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | C2×#63551 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | #10590638 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | #10590632 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | #84017 | — | 3 | 1 | no | maximal |
| 9 | #82015 | — | 3 | 1 | no | maximal |
| 10 | #64367 | — | 2 | 1 | no | — |
| 11 | C3×#1010 | — | 2 | 1 | no | — |
| 12 | C32×#131 | C22 | 1 | 1 | yes | characteristic |
| 13 | #64118 | — | 2 | 3 | no | — |
| 14 | C2×#3746 | C22 | 1 | 3 | yes | — |
| 15 | #64113 | C22 | 1 | 3 | yes | — |
| 16 | C3×#909 | — | 2 | 3 | no | — |
| 17 | C2×C3×Dic12 | C22 | 1 | 3 | yes | — |
| 18 | C3×#904 | C22 | 1 | 3 | yes | — |
| 19 | C3×#812 | C22 | 1 | 3 | yes | — |
| 20 | C2×C3×C3⋊C16 | C22 | 1 | 3 | yes | — |
| 21 | #63551 | C22 | 1 | 3 | yes | — |
| 22 | #63551 | C22 | 1 | 6 | yes | — |
| 23 | #63549 | C22 | 1 | 3 | yes | — |
| 24 | #63548 | C22 | 1 | 3 | yes | — |
| 25 | #63546 | C22 | 1 | 1 | yes | characteristic |
| 26 | C3×#578 | — | 3 | 1 | no | — |
| 27 | #5753 | — | 3 | 1 | no | — |
| 28 | #5753 | — | 3 | 1 | no | — |
| 29 | #5753 | — | 6 | 1 | no | — |
| 30 | #5753 | D3 | 1 | 1 | yes | characteristic, complemented |
| 31 | C3×#504 | — | 3 | 1 | no | — |
| 32 | #5195 | — | 3 | 3 | no | — |
| 33 | #5194 | — | 3 | 3 | no | — |
| 34 | C2×#829 | — | 3 | 3 | no | — |
| 35 | #5179 | — | 3 | 3 | no | — |
| 36 | #5140 | D3 | 1 | 1 | yes | characteristic, complemented |
| 37 | #4909 | — | 3 | 3 | no | — |
| 38 | #4909 | — | 3 | 3 | no | — |
| 39 | C2×Dic24 | — | 3 | 3 | no | — |
| 40 | #4904 | — | 3 | 3 | no | — |
| 41 | C32×#41 | D4 | 1 | 1 | yes | characteristic |
| 42 | Q8×C3⋊D3 | — | 4 | 1 | no | — |
| 43 | #3830 | — | 4 | 3 | no | — |
| 44 | #3828 | — | 2 | 3 | no | — |
| 45 | C2×#634 | — | 2 | 3 | no | — |
| 46 | C3×D3×Q8 | — | 4 | 1 | no | — |
| 47 | C3×#237 | — | 4 | 3 | no | — |
| 48 | C3×#235 | — | 2 | 3 | no | — |
| 49 | C2×C3×Dic6 | — | 2 | 3 | no | — |
| 50 | C32×M16 | D4 | 1 | 3 | yes | — |
| 51 | C2×C32×C8 | C23 | 1 | 3 | yes | — |
| 52 | #3746 | — | 2 | 3 | no | — |
| 53 | #3746 | C23 | 1 | 3 | yes | — |
| 54 | #3745 | C23 | 1 | 1 | yes | characteristic |
| 55 | #3744 | — | 2 | 3 | no | — |
| 56 | C3×Dic12 | — | 2 | 3 | no | — |
| 57 | C3×Dic12 | C23 | 1 | 3 | yes | — |
| 58 | C3×D24 | C23 | 1 | 1 | yes | characteristic |
| 59 | C3×#204 | — | 2 | 3 | no | — |
| 60 | C3×C3⋊C16 | C23 | 1 | 1 | yes | characteristic |
| 61 | C3×C3⋊C16 | C23 | 1 | 3 | yes | — |
| 62 | #3417 | — | 9 | 1 | no | Sylow |
| 63 | C3×2−1+4 | — | 6 | 1 | no | — |
| 64 | #1010 | — | 2 | 1 | no | — |
| 65 | #1010 | — | 6 | 2 | no | — |
| 66 | #1010 | — | 6 | 1 | no | — |
| 67 | #1010 | — | 6 | 1 | no | — |
| 68 | C3×#137 | — | 6 | 3 | no | — |
| 69 | C3×#135 | — | 3 | 3 | no | — |
| 70 | C2×C3×Q16 | — | 3 | 3 | no | — |
| 71 | C3×#131 | — | 2 | 1 | no | — |
| 72 | C3×#131 | C2×D3 | 1 | 1 | yes | characteristic |
| 73 | C3×#131 | C2×D3 | 1 | 1 | yes | characteristic |
| 74 | #909 | — | 2 | 3 | no | — |
| 75 | #909 | — | 6 | 6 | no | — |
| 76 | #909 | — | 6 | 3 | no | — |
| 77 | #909 | — | 6 | 3 | no | — |
| 78 | C2×Dic12 | — | 3 | 3 | no | — |
| 79 | C2×Dic12 | — | 3 | 3 | no | — |
| 80 | C2×Dic12 | — | 6 | 3 | no | — |
| 81 | C2×Dic12 | C2×D3 | 1 | 3 | yes | — |
| 82 | #904 | — | 3 | 3 | no | — |
| 83 | #904 | — | 3 | 3 | no | — |
| 84 | #904 | — | 6 | 3 | no | — |
| 85 | #904 | C2×D3 | 1 | 3 | yes | — |
| 86 | C3×M32 | — | 3 | 3 | no | — |
| 87 | C2×C3×C16 | — | 3 | 3 | no | — |
| 88 | #829 | — | 3 | 6 | no | — |
| 89 | #829 | — | 3 | 3 | no | — |
| 90 | #828 | — | 3 | 3 | no | — |
| 91 | #827 | — | 3 | 3 | no | — |
| 92 | #826 | — | 3 | 1 | no | — |
| 93 | #812 | C2×D3 | 1 | 3 | yes | — |
| 94 | C2×C3⋊C16 | C2×D3 | 1 | 3 | yes | — |
| 95 | Dic24 | — | 3 | 3 | no | — |
| 96 | Dic24 | — | 3 | 6 | no | — |
| 97 | #800 | — | 3 | 3 | no | — |
| 98 | #800 | — | 3 | 3 | no | — |
| 99 | D48 | — | 3 | 1 | no | — |
| 100 | C32×Q8 | D8 | 1 | 1 | yes | characteristic |
| 101 | C32×D4 | D8 | 1 | 3 | yes | — |
| 102 | C2×C32×C4 | C2×D4 | 1 | 3 | yes | — |
| 103 | #638 | — | 4 | 3 | no | — |
| 104 | C2×C3⋊Dic3 | — | 4 | 3 | no | — |
| 105 | C4⋊(C3⋊D3) | — | 2 | 1 | no | — |
| 106 | C4×C3⋊D3 | — | 4 | 3 | no | — |
| 107 | #634 | — | 2 | 3 | no | — |
| 108 | #634 | — | 4 | 3 | no | — |
| 109 | C3×#67 | — | 4 | 3 | no | — |
| 110 | C2×C3×Dic3 | — | 4 | 3 | no | — |
| 111 | C3×D12 | — | 2 | 1 | no | — |
| 112 | C3×C4×D3 | — | 4 | 3 | no | — |
| 113 | C3×Dic6 | — | 2 | 3 | no | — |
| 114 | C3×Dic6 | — | 4 | 3 | no | — |
| 115 | C32×C8 | C2×D4 | 1 | 3 | yes | — |
| 116 | C32×C8 | C24 | 1 | 1 | yes | characteristic |
| 117 | #578 | — | 3 | 1 | no | — |
| 118 | #578 | — | 9 | 1 | no | — |
| 119 | #510 | — | 9 | 3 | no | — |
| 120 | #510 | — | 9 | 3 | no | — |
| 121 | #508 | — | 9 | 3 | no | — |
| 122 | C2×Q32 | — | 9 | 3 | no | — |
| 123 | #504 | — | 3 | 1 | no | — |
| 124 | C3×#41 | — | 2 | 1 | no | — |
| 125 | C3×#41 | — | 6 | 3 | no | — |
| 126 | C3×#41 | — | 12 | 3 | no | — |
| 127 | C3×#41 | D12 | 1 | 1 | yes | characteristic |
| 128 | C3×#41 | #67 | 1 | 1 | yes | characteristic |
| 129 | C2×C3×Q8 | — | 6 | 3 | no | — |
| 130 | C2×C3×Q8 | — | 12 | 1 | no | — |
| 131 | D3×Q8 | — | 4 | 1 | no | — |
| 132 | D3×Q8 | — | 12 | 2 | no | — |
| 133 | D3×Q8 | — | 12 | 1 | no | — |
| 134 | D3×Q8 | — | 12 | 1 | no | — |
| 135 | #237 | — | 4 | 3 | no | — |
| 136 | #237 | — | 12 | 6 | no | — |
| 137 | #237 | — | 12 | 3 | no | — |
| 138 | #237 | — | 12 | 3 | no | — |
| 139 | #235 | — | 2 | 3 | no | — |
| 140 | #235 | — | 6 | 6 | no | — |
| 141 | #235 | — | 6 | 3 | no | — |
| 142 | #235 | — | 6 | 3 | no | — |
| 143 | C2×Dic6 | — | 2 | 3 | no | — |
| 144 | C2×Dic6 | — | 6 | 6 | no | — |
| 145 | C2×Dic6 | — | 6 | 3 | no | — |
| 146 | C2×Dic6 | — | 6 | 3 | no | — |
| 147 | C3×Q16 | — | 3 | 3 | no | — |
| 148 | C3×Q16 | — | 6 | 3 | no | — |
| 149 | C3×SD16 | — | 6 | 3 | no | — |
| 150 | C3×D8 | — | 3 | 1 | no | — |
| 151 | C3×M16 | — | 2 | 3 | no | — |
| 152 | C3×M16 | D12 | 1 | 3 | yes | — |
| 153 | C3×M16 | #67 | 1 | 3 | yes | — |
| 154 | C2×C3×C8 | — | 2 | 3 | no | — |
| 155 | C2×C3×C8 | C22×D3 | 1 | 3 | yes | — |
| 156 | C2×C3×C8 | C22×D3 | 1 | 3 | yes | — |
| 157 | Dic12 | — | 2 | 3 | no | — |
| 158 | Dic12 | — | 3 | 3 | no | — |
| 159 | Dic12 | — | 3 | 3 | no | — |
| 160 | Dic12 | — | 6 | 3 | no | — |
| 161 | Dic12 | — | 6 | 6 | no | — |
| 162 | Dic12 | — | 6 | 3 | no | — |
| 163 | Dic12 | — | 6 | 3 | no | — |
| 164 | Dic12 | C22×D3 | 1 | 3 | yes | — |
| 165 | D24 | — | 3 | 1 | no | — |
| 166 | D24 | — | 3 | 1 | no | — |
| 167 | D24 | — | 6 | 1 | no | — |
| 168 | D24 | C22×D3 | 1 | 1 | yes | characteristic |
| 169 | #204 | — | 2 | 3 | no | — |
| 170 | #204 | — | 6 | 6 | no | — |
| 171 | #204 | — | 6 | 3 | no | — |
| 172 | #204 | — | 6 | 3 | no | — |
| 173 | C3×C16 | — | 3 | 1 | no | — |
| 174 | C3×C16 | — | 3 | 3 | no | — |
| 175 | C3⋊C16 | C22×D3 | 1 | 1 | yes | characteristic |
| 176 | C3⋊C16 | C22×D3 | 1 | 3 | yes | — |
| 177 | C22×C32 | C2×D8 | 1 | 3 | yes | — |
| 178 | C2×C3⋊D3 | — | 4 | 1 | no | — |
| 179 | C2×C3×D3 | — | 4 | 1 | no | — |
| 180 | C32×C4 | C2×D8 | 1 | 3 | yes | — |
| 181 | C32×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 182 | C3⋊Dic3 | — | 4 | 3 | no | — |
| 183 | C3×Dic3 | — | 4 | 3 | no | — |
| 184 | 2−1+4 | — | 6 | 1 | no | — |
| 185 | 2−1+4 | — | 18 | 1 | no | — |
| 186 | #137 | — | 6 | 3 | no | — |
| 187 | #137 | — | 18 | 3 | no | — |
| 188 | #135 | — | 3 | 3 | no | — |
| 189 | #135 | — | 9 | 3 | no | — |
| 190 | C2×Q16 | — | 3 | 3 | no | — |
| 191 | C2×Q16 | — | 9 | 3 | no | — |
| 192 | #131 | D32 | 1 | 1 | yes | characteristic |
| 193 | Q32 | — | 9 | 3 | no | — |
| 194 | Q32 | — | 9 | 6 | no | — |
| 195 | SD32 | — | 9 | 3 | no | — |
| 196 | SD32 | — | 9 | 3 | no | — |
| 197 | D16 | — | 9 | 1 | no | — |
| 198 | M32 | — | 3 | 3 | no | — |
| 199 | C2×C16 | — | 3 | 3 | no | — |
| 200 | C3×Q8 | — | 2 | 1 | no | — |
| 201 | C3×Q8 | — | 6 | 3 | no | — |
| 202 | C3×Q8 | — | 12 | 3 | no | — |
| 203 | C3×Q8 | D24 | 1 | 1 | yes | characteristic |
| 204 | C3×Q8 | #213 | 1 | 1 | yes | characteristic |
| 205 | C3×D4 | — | 2 | 3 | no | — |
| 206 | C3×D4 | — | 6 | 1 | no | — |
| 207 | C3×D4 | — | 12 | 3 | no | — |
| 208 | C3×D4 | D24 | 1 | 3 | yes | — |
| 209 | C3×D4 | #213 | 1 | 3 | yes | — |
| 210 | C2×C3×C4 | — | 2 | 3 | no | — |
| 211 | C2×C3×C4 | — | 12 | 3 | no | — |
| 212 | C2×C3×C4 | — | 12 | 3 | no | — |
| 213 | C2×C3×C4 | C2×D12 | 1 | 3 | yes | — |
| 214 | C2×C3×C4 | C2×#67 | 1 | 3 | yes | — |
| 215 | #67 | — | 4 | 3 | no | — |
| 216 | #67 | — | 12 | 6 | no | — |
| 217 | #67 | — | 12 | 3 | no | — |
| 218 | #67 | — | 12 | 3 | no | — |
| 219 | C2×Dic3 | — | 4 | 3 | no | — |
| 220 | C2×Dic3 | — | 12 | 6 | no | — |
| 221 | C2×Dic3 | — | 12 | 3 | no | — |
| 222 | C2×Dic3 | — | 12 | 3 | no | — |
| 223 | D12 | — | 2 | 1 | no | — |
| 224 | D12 | — | 6 | 2 | no | — |
| 225 | D12 | — | 6 | 1 | no | — |
| 226 | D12 | — | 6 | 1 | no | — |
| 227 | C4×D3 | — | 4 | 3 | no | — |
| 228 | C4×D3 | — | 12 | 6 | no | — |
| 229 | C4×D3 | — | 12 | 3 | no | — |
| 230 | C4×D3 | — | 12 | 3 | no | — |
| 231 | Dic6 | — | 2 | 3 | no | — |
| 232 | Dic6 | — | 4 | 3 | no | — |
| 233 | Dic6 | — | 6 | 6 | no | — |
| 234 | Dic6 | — | 6 | 3 | no | — |
| 235 | Dic6 | — | 6 | 3 | no | — |
| 236 | Dic6 | — | 12 | 6 | no | — |
| 237 | Dic6 | — | 12 | 3 | no | — |
| 238 | Dic6 | — | 12 | 3 | no | — |
| 239 | C3×C8 | — | 2 | 1 | no | — |
| 240 | C3×C8 | — | 2 | 3 | no | — |
| 241 | C3×C8 | C2×D12 | 1 | 3 | yes | — |
| 242 | C3×C8 | C2×#67 | 1 | 3 | yes | — |
| 243 | C3×C8 | C23×D3 | 1 | 1 | yes | characteristic |
| 244 | C3×C8 | C23×D3 | 1 | 1 | yes | characteristic |
| 245 | C2×C32 | — | 2 | 3 | no | — |
| 246 | C2×C32 | C22×D8 | 1 | 1 | yes | characteristic |
| 247 | C3⋊D3 | — | 8 | 1 | no | — |
| 248 | C3×D3 | — | 8 | 1 | no | — |
| 249 | #41 | — | 6 | 3 | no | — |
| 250 | #41 | — | 12 | 3 | no | — |
| 251 | #41 | — | 18 | 3 | no | — |
| 252 | #41 | — | 36 | 3 | no | — |
| 253 | #41 | #626 | 1 | 1 | yes | characteristic |
| 254 | C2×Q8 | — | 6 | 3 | no | — |
| 255 | C2×Q8 | — | 12 | 1 | no | — |
| 256 | C2×Q8 | — | 18 | 3 | no | — |
| 257 | C2×Q8 | — | 36 | 1 | no | — |
| 258 | Q16 | — | 3 | 3 | no | — |
| 259 | Q16 | — | 6 | 3 | no | — |
| 260 | Q16 | — | 9 | 3 | no | — |
| 261 | Q16 | — | 18 | 3 | no | — |
| 262 | SD16 | — | 6 | 3 | no | — |
| 263 | SD16 | — | 18 | 3 | no | — |
| 264 | D8 | — | 3 | 1 | no | — |
| 265 | D8 | — | 9 | 1 | no | — |
| 266 | M16 | #626 | 1 | 3 | yes | — |
| 267 | C2×C8 | C2×D32 | 1 | 3 | yes | — |
| 268 | C16 | — | 3 | 1 | no | — |
| 269 | C16 | — | 3 | 3 | no | — |
| 270 | C22×C3 | — | 2 | 3 | no | — |
| 271 | C22×C3 | — | 12 | 1 | no | — |
| 272 | C22×C3 | C2×D24 | 1 | 3 | yes | — |
| 273 | C22×C3 | C2×#213 | 1 | 3 | yes | — |
| 274 | C2×D3 | — | 4 | 1 | no | — |
| 275 | C2×D3 | — | 12 | 2 | no | — |
| 276 | C2×D3 | — | 12 | 1 | no | — |
| 277 | C2×D3 | — | 12 | 1 | no | — |
| 278 | C3×C4 | — | 2 | 1 | no | — |
| 279 | C3×C4 | — | 2 | 3 | no | — |
| 280 | C3×C4 | — | 12 | 3 | no | — |
| 281 | C3×C4 | C2×D24 | 1 | 3 | yes | — |
| 282 | C3×C4 | C2×#213 | 1 | 3 | yes | — |
| 283 | C3×C4 | C22×D12 | 1 | 1 | yes | characteristic |
| 284 | C3×C4 | C22×#67 | 1 | 1 | yes | characteristic |
| 285 | Dic3 | — | 4 | 3 | no | — |
| 286 | Dic3 | — | 12 | 6 | no | — |
| 287 | Dic3 | — | 12 | 3 | no | — |
| 288 | Dic3 | — | 12 | 3 | no | — |
| 289 | C32 | #3417 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 290 | Q8 | — | 6 | 3 | no | — |
| 291 | Q8 | — | 12 | 3 | no | — |
| 292 | Q8 | — | 18 | 3 | no | — |
| 293 | Q8 | — | 36 | 3 | no | — |
| 294 | Q8 | #3714 | 1 | 1 | yes | characteristic |
| 295 | D4 | — | 6 | 1 | no | — |
| 296 | D4 | — | 12 | 3 | no | — |
| 297 | D4 | — | 18 | 1 | no | — |
| 298 | D4 | — | 36 | 3 | no | — |
| 299 | D4 | #3714 | 1 | 3 | yes | — |
| 300 | C2×C4 | — | 12 | 3 | no | — |
| 301 | C2×C4 | — | 12 | 3 | no | — |
| 302 | C2×C4 | — | 36 | 3 | no | — |
| 303 | C2×C4 | — | 36 | 3 | no | — |
| 304 | C2×C4 | C2×#626 | 1 | 3 | yes | — |
| 305 | C8 | C2×#626 | 1 | 3 | yes | — |
| 306 | C8 | C22×D32 | 1 | 1 | yes | characteristic |
| 307 | C2×C3 | — | 2 | 3 | no | — |
| 308 | C2×C3 | — | 2 | 3 | no | — |
| 309 | C2×C3 | — | 2 | 1 | no | — |
| 310 | C2×C3 | — | 4 | 3 | no | — |
| 311 | C2×C3 | — | 24 | 1 | no | — |
| 312 | C2×C3 | C22×D24 | 1 | 1 | yes | characteristic |
| 313 | C2×C3 | C22×#213 | 1 | 1 | yes | characteristic |
| 314 | D3 | — | 8 | 1 | no | — |
| 315 | D3 | — | 24 | 2 | no | — |
| 316 | D3 | — | 24 | 1 | no | — |
| 317 | D3 | — | 24 | 1 | no | — |
| 318 | C22 | — | 12 | 1 | no | — |
| 319 | C22 | — | 36 | 1 | no | — |
| 320 | C22 | C2×#3714 | 1 | 3 | yes | — |
| 321 | C4 | — | 12 | 3 | no | — |
| 322 | C4 | — | 36 | 3 | no | — |
| 323 | C4 | C2×#3714 | 1 | 3 | yes | — |
| 324 | C4 | C22×#626 | 1 | 1 | yes | characteristic |
| 325 | C3 | — | 2 | 1 | no | — |
| 326 | C3 | #82015 | 1 | 1 | yes | characteristic, complemented |
| 327 | C3 | #84017 | 1 | 1 | yes | characteristic, complemented |
| 328 | C2 | — | 2 | 3 | no | — |
| 329 | C2 | — | 24 | 1 | no | — |
| 330 | C2 | — | 72 | 1 | no | — |
| 331 | C2 | C22×#3714 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10596224 | C2 | semidirect |
| 2. C3×#5753 | C2 | semidirect |
| 3. C3×#5140 | C2 | semidirect |
| 4. #10590642 | C2 | semidirect |
| 5. C2×#63551 | C2 | semidirect |
| 6. #10590638 | C2 | semidirect |
| 7. #10590632 | C2 | semidirect |
| 30. #5753 | D3 | semidirect |
| 36. #5140 | D3 | semidirect |
| 289. C32 | #3417 | semidirect |
| 326. C3 | #82015 | semidirect |
| 327. C3 | #84017 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10596224 | 2 |
| C3×#5753 | 2 |
| C3×#5140 | 2 |
| #10590642 | 2 |
| C2×#63551 | 2 |
| #10590638 | 2 |
| #10590632 | 2 |
| #84017 | 3 |
| #82015 | 3 |