Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
573 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 573 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 | C2×#64128 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #10590913 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #10590625 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C3×#4565 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #10589128 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #69266 | — | 3 | 2 | no | maximal |
| 7 | C2×#3832 | — | 2 | 1 | no | — |
| 8 | C2×C32×Q16 | C22 | 1 | 1 | yes | characteristic |
| 9 | C2×#3755 | — | 2 | 1 | no | — |
| 10 | #64128 | — | 2 | 1 | no | — |
| 11 | #64128 | — | 2 | 1 | no | — |
| 12 | #64128 | C4 | 1 | 2 | yes | — |
| 13 | #64128 | C4 | 1 | 2 | yes | — |
| 14 | C2×#3745 | C22 | 1 | 1 | yes | characteristic |
| 15 | C2×C8×C3⋊D3 | C22 | 1 | 1 | yes | characteristic |
| 16 | #63818 | — | 2 | 1 | no | — |
| 17 | C3×#819 | C22 | 1 | 2 | yes | — |
| 18 | C3×#812 | C22 | 1 | 2 | yes | — |
| 19 | #63578 | — | 2 | 1 | no | — |
| 20 | #63544 | — | 2 | 1 | no | — |
| 21 | #63542 | — | 2 | 1 | no | — |
| 22 | C2×#919 | — | 3 | 2 | no | — |
| 23 | C2×#919 | — | 6 | 1 | no | — |
| 24 | D3×M32 | — | 3 | 2 | no | — |
| 25 | D3×#108 | — | 3 | 2 | no | — |
| 26 | C3×#362 | — | 3 | 2 | no | — |
| 27 | #4565 | D3 | 1 | 2 | yes | complemented |
| 28 | #4516 | — | 3 | 2 | no | — |
| 29 | #4495 | — | 3 | 2 | no | — |
| 30 | C2×C32×Q8 | — | 2 | 1 | no | — |
| 31 | #3832 | — | 2 | 2 | no | — |
| 32 | #3832 | — | 2 | 2 | no | — |
| 33 | #3832 | — | 4 | 1 | no | — |
| 34 | #3832 | — | 4 | 1 | no | — |
| 35 | C2×C4⋊(C3⋊D3) | — | 2 | 1 | no | — |
| 36 | C2×C4⋊(C3⋊D3) | — | 4 | 1 | no | — |
| 37 | C2×C4×C3⋊D3 | — | 4 | 1 | no | — |
| 38 | C2×C4×C3⋊D3 | D4 | 1 | 1 | yes | characteristic |
| 39 | C32×Q16 | — | 2 | 1 | no | — |
| 40 | C32×Q16 | C2×C4 | 1 | 2 | yes | — |
| 41 | C2×C32×C8 | C23 | 1 | 1 | yes | characteristic |
| 42 | #3755 | — | 2 | 2 | no | — |
| 43 | #3755 | — | 2 | 2 | no | — |
| 44 | C2×C3⋊(C3⋊C8) | D4 | 1 | 1 | yes | characteristic |
| 45 | #3745 | — | 2 | 1 | no | — |
| 46 | #3745 | C2×C4 | 1 | 2 | yes | — |
| 47 | C8×C3⋊D3 | C2×C4 | 1 | 1 | yes | characteristic |
| 48 | C8×C3⋊D3 | C2×C4 | 1 | 1 | yes | characteristic |
| 49 | C8×C3⋊D3 | D4 | 1 | 1 | yes | characteristic |
| 50 | C8×C3⋊D3 | D4 | 1 | 1 | yes | characteristic |
| 51 | C3×#208 | — | 2 | 2 | no | — |
| 52 | #3712 | — | 4 | 1 | no | — |
| 53 | #3710 | — | 4 | 1 | no | — |
| 54 | C3×C3⋊C16 | — | 2 | 2 | no | — |
| 55 | #2148 | — | 9 | 1 | no | Sylow |
| 56 | C2×#239 | — | 6 | 2 | no | — |
| 57 | C2×#239 | — | 6 | 2 | no | — |
| 58 | C2×C3×Q16 | — | 2 | 1 | no | — |
| 59 | C2×C3×Q16 | C2×D3 | 1 | 2 | yes | — |
| 60 | C2×#215 | — | 6 | 2 | no | — |
| 61 | C2×#215 | — | 6 | 2 | no | — |
| 62 | #919 | — | 3 | 4 | no | — |
| 63 | #919 | — | 3 | 4 | no | — |
| 64 | #919 | — | 6 | 2 | no | — |
| 65 | #919 | — | 6 | 2 | no | — |
| 66 | #919 | — | 6 | 2 | no | — |
| 67 | #919 | — | 6 | 2 | no | — |
| 68 | #919 | — | 6 | 2 | no | — |
| 69 | #919 | — | 6 | 2 | no | — |
| 70 | D3×M16 | — | 6 | 2 | no | — |
| 71 | C2×D24 | — | 3 | 2 | no | — |
| 72 | C2×D24 | — | 6 | 1 | no | — |
| 73 | C2×D3×C8 | — | 3 | 2 | no | — |
| 74 | C2×D3×C8 | — | 6 | 1 | no | — |
| 75 | C3×M32 | — | 3 | 2 | no | — |
| 76 | C3×#108 | — | 3 | 2 | no | — |
| 77 | #822 | — | 6 | 2 | no | — |
| 78 | #819 | C2×D3 | 1 | 2 | yes | — |
| 79 | #812 | C2×D3 | 1 | 2 | yes | — |
| 80 | #798 | — | 6 | 2 | no | — |
| 81 | D3×C16 | — | 6 | 2 | no | — |
| 82 | C22×C3⋊D3 | — | 4 | 1 | no | — |
| 83 | C22×C3⋊D3 | SD16 | 1 | 1 | yes | characteristic |
| 84 | C32×Q8 | — | 2 | 2 | no | — |
| 85 | C32×Q8 | — | 4 | 1 | no | — |
| 86 | C2×C32×C4 | — | 4 | 1 | no | — |
| 87 | C2×C32×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 88 | C2×C3⋊Dic3 | SD16 | 1 | 1 | yes | characteristic |
| 89 | C4⋊(C3⋊D3) | — | 2 | 2 | no | — |
| 90 | C4⋊(C3⋊D3) | — | 4 | 2 | no | — |
| 91 | C4⋊(C3⋊D3) | — | 4 | 2 | no | — |
| 92 | C4⋊(C3⋊D3) | — | 4 | 1 | no | — |
| 93 | C4×C3⋊D3 | — | 4 | 2 | no | — |
| 94 | C4×C3⋊D3 | — | 4 | 2 | no | — |
| 95 | C4×C3⋊D3 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 96 | C4×C3⋊D3 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 97 | C4×C3⋊D3 | D8 | 1 | 1 | yes | characteristic |
| 98 | C4×C3⋊D3 | D8 | 1 | 1 | yes | characteristic |
| 99 | C32×C8 | C22×C4 | 1 | 1 | yes | characteristic |
| 100 | C32×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 101 | C3⋊(C3⋊C8) | C22⋊C4 | 1 | 1 | yes | characteristic |
| 102 | C3⋊(C3⋊C8) | C22⋊C4 | 1 | 1 | yes | characteristic |
| 103 | C3×C3⋊C8 | — | 4 | 2 | no | — |
| 104 | C2×#135 | — | 9 | 1 | no | — |
| 105 | C2×M32 | — | 9 | 1 | no | — |
| 106 | C2×#108 | — | 9 | 1 | no | — |
| 107 | #362 | — | 3 | 2 | no | — |
| 108 | #361 | — | 9 | 2 | no | — |
| 109 | C2×C3×Q8 | — | 2 | 2 | no | — |
| 110 | C2×C3×Q8 | — | 2 | 2 | no | — |
| 111 | #239 | — | 6 | 4 | no | — |
| 112 | #239 | — | 6 | 4 | no | — |
| 113 | #239 | — | 6 | 4 | no | — |
| 114 | #239 | — | 6 | 4 | no | — |
| 115 | #239 | — | 12 | 2 | no | — |
| 116 | #239 | — | 12 | 2 | no | — |
| 117 | #239 | — | 12 | 2 | no | — |
| 118 | #239 | — | 12 | 2 | no | — |
| 119 | C2×D12 | — | 6 | 2 | no | — |
| 120 | C2×D12 | — | 6 | 2 | no | — |
| 121 | C2×D12 | — | 12 | 2 | no | — |
| 122 | C2×D12 | — | 12 | 2 | no | — |
| 123 | C2×C4×D3 | — | 3 | 2 | no | — |
| 124 | C2×C4×D3 | — | 6 | 1 | no | — |
| 125 | C2×C4×D3 | — | 12 | 2 | no | — |
| 126 | C2×C4×D3 | — | 12 | 2 | no | — |
| 127 | C3×Q16 | — | 2 | 2 | no | — |
| 128 | C3×Q16 | — | 2 | 2 | no | — |
| 129 | C3×Q16 | — | 2 | 2 | no | — |
| 130 | C3×Q16 | C4×D3 | 1 | 4 | yes | — |
| 131 | C3×M16 | — | 6 | 2 | no | — |
| 132 | C2×C3×C8 | — | 2 | 1 | no | — |
| 133 | C2×C3×C8 | C22×D3 | 1 | 2 | yes | — |
| 134 | #215 | — | 6 | 4 | no | — |
| 135 | #215 | — | 6 | 4 | no | — |
| 136 | #215 | — | 6 | 4 | no | — |
| 137 | #215 | — | 6 | 4 | no | — |
| 138 | #208 | — | 2 | 2 | no | — |
| 139 | C2×C3⋊C8 | — | 3 | 2 | no | — |
| 140 | C2×C3⋊C8 | — | 6 | 1 | no | — |
| 141 | D24 | — | 3 | 4 | no | — |
| 142 | D24 | — | 6 | 2 | no | — |
| 143 | D24 | — | 6 | 2 | no | — |
| 144 | D24 | — | 6 | 2 | no | — |
| 145 | ΓL(1,𝔽25) | — | 12 | 2 | no | — |
| 146 | D3×C8 | — | 3 | 2 | no | — |
| 147 | D3×C8 | — | 3 | 2 | no | — |
| 148 | D3×C8 | — | 3 | 2 | no | — |
| 149 | D3×C8 | — | 3 | 2 | no | — |
| 150 | D3×C8 | — | 6 | 1 | no | — |
| 151 | D3×C8 | — | 6 | 1 | no | — |
| 152 | D3×C8 | — | 6 | 1 | no | — |
| 153 | D3×C8 | — | 6 | 1 | no | — |
| 154 | D3×C8 | — | 12 | 2 | no | — |
| 155 | C3×C16 | — | 6 | 2 | no | — |
| 156 | C3⋊C16 | — | 2 | 2 | no | — |
| 157 | C22×C32 | C2×SD16 | 1 | 1 | yes | characteristic |
| 158 | C2×C3⋊D3 | — | 4 | 1 | no | — |
| 159 | C2×C3⋊D3 | — | 4 | 2 | no | — |
| 160 | C2×C3⋊D3 | — | 8 | 2 | no | — |
| 161 | C2×C3⋊D3 | #102 | 1 | 1 | yes | characteristic |
| 162 | C2×C3⋊D3 | #102 | 1 | 1 | yes | characteristic |
| 163 | C32×C4 | — | 4 | 2 | no | — |
| 164 | C32×C4 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 165 | C32×C4 | C2×D8 | 1 | 1 | yes | characteristic |
| 166 | C3⋊Dic3 | #102 | 1 | 1 | yes | characteristic |
| 167 | C3⋊Dic3 | #102 | 1 | 1 | yes | characteristic |
| 168 | C2×#41 | — | 18 | 1 | no | — |
| 169 | #135 | — | 9 | 2 | no | — |
| 170 | #135 | — | 9 | 2 | no | — |
| 171 | #135 | — | 18 | 1 | no | — |
| 172 | #135 | — | 18 | 1 | no | — |
| 173 | C2×Q16 | D32 | 1 | 1 | yes | characteristic |
| 174 | C2×SD16 | — | 18 | 1 | no | — |
| 175 | C2×D8 | — | 9 | 1 | no | — |
| 176 | C2×M16 | — | 18 | 1 | no | — |
| 177 | C22×C8 | — | 9 | 1 | no | — |
| 178 | M32 | — | 3 | 2 | no | — |
| 179 | M32 | — | 18 | 1 | no | — |
| 180 | C2×C16 | — | 18 | 1 | no | — |
| 181 | #108 | — | 3 | 2 | no | — |
| 182 | #108 | — | 18 | 1 | no | — |
| 183 | C22×D3 | — | 3 | 2 | no | — |
| 184 | C22×D3 | — | 6 | 1 | no | — |
| 185 | C22×D3 | — | 12 | 2 | no | — |
| 186 | C22×D3 | — | 12 | 2 | no | — |
| 187 | C3×Q8 | — | 2 | 4 | no | — |
| 188 | C3×Q8 | — | 2 | 4 | no | — |
| 189 | C3×Q8 | — | 4 | 2 | no | — |
| 190 | C3×Q8 | — | 4 | 2 | no | — |
| 191 | C2×C3×C4 | — | 2 | 1 | no | — |
| 192 | C2×C3×C4 | — | 4 | 2 | no | — |
| 193 | C2×C3×C4 | — | 4 | 2 | no | — |
| 194 | C2×C3×C4 | D3×D4 | 1 | 2 | yes | — |
| 195 | C2×Dic3 | — | 3 | 2 | no | — |
| 196 | C2×Dic3 | — | 6 | 1 | no | — |
| 197 | D12 | — | 6 | 4 | no | — |
| 198 | D12 | — | 6 | 4 | no | — |
| 199 | D12 | — | 12 | 2 | no | — |
| 200 | D12 | — | 12 | 4 | no | — |
| 201 | D12 | — | 12 | 4 | no | — |
| 202 | D12 | — | 12 | 4 | no | — |
| 203 | D12 | — | 12 | 4 | no | — |
| 204 | D12 | — | 12 | 2 | no | — |
| 205 | C4×D3 | — | 3 | 2 | no | — |
| 206 | C4×D3 | — | 3 | 2 | no | — |
| 207 | C4×D3 | — | 3 | 2 | no | — |
| 208 | C4×D3 | — | 3 | 2 | no | — |
| 209 | C4×D3 | — | 6 | 1 | no | — |
| 210 | C4×D3 | — | 6 | 1 | no | — |
| 211 | C4×D3 | — | 6 | 1 | no | — |
| 212 | C4×D3 | — | 6 | 1 | no | — |
| 213 | C4×D3 | — | 12 | 4 | no | — |
| 214 | C4×D3 | — | 12 | 4 | no | — |
| 215 | C4×D3 | — | 12 | 4 | no | — |
| 216 | C4×D3 | — | 12 | 4 | no | — |
| 217 | C3×C8 | — | 2 | 1 | no | — |
| 218 | C3×C8 | — | 2 | 1 | no | — |
| 219 | C3×C8 | — | 12 | 2 | no | — |
| 220 | C3×C8 | C2×C4×D3 | 1 | 2 | yes | — |
| 221 | C3×C8 | D3×D4 | 1 | 2 | yes | — |
| 222 | C3⋊C8 | — | 3 | 2 | no | — |
| 223 | C3⋊C8 | — | 3 | 2 | no | — |
| 224 | C3⋊C8 | — | 4 | 2 | no | — |
| 225 | C3⋊C8 | — | 6 | 1 | no | — |
| 226 | C3⋊C8 | — | 6 | 1 | no | — |
| 227 | C2×C32 | — | 2 | 1 | no | — |
| 228 | C2×C32 | C2×#102 | 1 | 1 | yes | characteristic |
| 229 | C3⋊D3 | — | 2 | 1 | no | — |
| 230 | C3⋊D3 | — | 2 | 1 | no | — |
| 231 | C3⋊D3 | — | 8 | 2 | no | — |
| 232 | #41 | — | 18 | 2 | no | — |
| 233 | #41 | — | 18 | 2 | no | — |
| 234 | #41 | — | 36 | 1 | no | — |
| 235 | #41 | — | 36 | 1 | no | — |
| 236 | C2×Q8 | — | 2 | 1 | no | — |
| 237 | C2×D4 | — | 18 | 1 | no | — |
| 238 | C2×D4 | — | 36 | 1 | no | — |
| 239 | C22×C4 | — | 9 | 1 | no | — |
| 240 | C22×C4 | — | 36 | 1 | no | — |
| 241 | Q16 | — | 2 | 1 | no | — |
| 242 | Q16 | #624 | 1 | 2 | yes | — |
| 243 | SD16 | — | 18 | 2 | no | — |
| 244 | SD16 | — | 18 | 2 | no | — |
| 245 | D8 | — | 9 | 2 | no | — |
| 246 | D8 | — | 18 | 1 | no | — |
| 247 | M16 | — | 6 | 2 | no | — |
| 248 | M16 | — | 36 | 1 | no | — |
| 249 | C2×C8 | — | 9 | 1 | no | — |
| 250 | C2×C8 | — | 9 | 1 | no | — |
| 251 | C2×C8 | — | 9 | 1 | no | — |
| 252 | C2×C8 | — | 9 | 1 | no | — |
| 253 | C2×C8 | — | 9 | 1 | no | — |
| 254 | C2×C8 | — | 36 | 1 | no | — |
| 255 | C2×C8 | C2×D32 | 1 | 1 | yes | characteristic |
| 256 | C16 | — | 6 | 2 | no | — |
| 257 | C22×C3 | — | 2 | 1 | no | — |
| 258 | C22×C3 | D3×SD16 | 1 | 2 | yes | — |
| 259 | C2×D3 | — | 3 | 2 | no | — |
| 260 | C2×D3 | — | 3 | 2 | no | — |
| 261 | C2×D3 | — | 6 | 1 | no | — |
| 262 | C2×D3 | — | 6 | 1 | no | — |
| 263 | C2×D3 | — | 12 | 2 | no | — |
| 264 | C2×D3 | — | 12 | 2 | no | — |
| 265 | C2×D3 | — | 12 | 4 | no | — |
| 266 | C2×D3 | — | 12 | 4 | no | — |
| 267 | C2×D3 | — | 24 | 4 | no | — |
| 268 | C2×D3 | — | 24 | 4 | no | — |
| 269 | C3×C4 | — | 2 | 1 | no | — |
| 270 | C3×C4 | — | 2 | 1 | no | — |
| 271 | C3×C4 | — | 4 | 4 | no | — |
| 272 | C3×C4 | — | 4 | 4 | no | — |
| 273 | C3×C4 | D3×C22⋊C4 | 1 | 2 | yes | — |
| 274 | C3×C4 | D3×D8 | 1 | 2 | yes | — |
| 275 | Dic3 | — | 3 | 2 | no | — |
| 276 | Dic3 | — | 3 | 2 | no | — |
| 277 | Dic3 | — | 6 | 1 | no | — |
| 278 | Dic3 | — | 6 | 1 | no | — |
| 279 | C32 | #2148 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 280 | C23 | — | 9 | 1 | no | — |
| 281 | C23 | — | 36 | 1 | no | — |
| 282 | Q8 | — | 2 | 2 | no | — |
| 283 | Q8 | — | 4 | 1 | no | — |
| 284 | D4 | — | 18 | 2 | no | — |
| 285 | D4 | — | 36 | 2 | no | — |
| 286 | D4 | — | 36 | 2 | no | — |
| 287 | D4 | — | 36 | 1 | no | — |
| 288 | C2×C4 | — | 4 | 1 | no | — |
| 289 | C2×C4 | — | 9 | 1 | no | — |
| 290 | C2×C4 | — | 9 | 1 | no | — |
| 291 | C2×C4 | — | 9 | 1 | no | — |
| 292 | C2×C4 | — | 9 | 1 | no | — |
| 293 | C2×C4 | — | 9 | 1 | no | — |
| 294 | C2×C4 | — | 36 | 2 | no | — |
| 295 | C2×C4 | — | 36 | 2 | no | — |
| 296 | C2×C4 | #3811 | 1 | 1 | yes | characteristic |
| 297 | C8 | — | 9 | 1 | no | — |
| 298 | C8 | — | 9 | 1 | no | — |
| 299 | C8 | — | 12 | 2 | no | — |
| 300 | C8 | C2×#624 | 1 | 1 | yes | characteristic |
| 301 | C8 | #3811 | 1 | 1 | yes | characteristic |
| 302 | C2×C3 | — | 2 | 2 | no | — |
| 303 | C2×C3 | — | 2 | 2 | no | — |
| 304 | C2×C3 | — | 2 | 1 | no | — |
| 305 | C2×C3 | D3×#102 | 1 | 2 | yes | — |
| 306 | D3 | — | 6 | 2 | no | — |
| 307 | D3 | — | 6 | 2 | no | — |
| 308 | D3 | — | 12 | 1 | no | — |
| 309 | D3 | — | 12 | 1 | no | — |
| 310 | D3 | — | 24 | 4 | no | — |
| 311 | D3 | — | 24 | 4 | no | — |
| 312 | C22 | — | 9 | 1 | no | — |
| 313 | C22 | — | 9 | 1 | no | — |
| 314 | C22 | — | 36 | 1 | no | — |
| 315 | C22 | — | 36 | 2 | no | — |
| 316 | C22 | — | 72 | 2 | no | — |
| 317 | C22 | #63930 | 1 | 1 | yes | characteristic |
| 318 | C4 | — | 4 | 2 | no | — |
| 319 | C4 | — | 9 | 1 | no | — |
| 320 | C4 | — | 9 | 1 | no | — |
| 321 | C4 | #63926 | 1 | 1 | yes | characteristic |
| 322 | C4 | #63974 | 1 | 1 | yes | characteristic |
| 323 | C3 | — | 2 | 1 | no | — |
| 324 | C3 | #69266 | 1 | 2 | yes | complemented |
| 325 | C2 | — | 2 | 1 | no | — |
| 326 | C2 | — | 18 | 1 | no | — |
| 327 | C2 | — | 18 | 1 | no | — |
| 328 | C2 | — | 72 | 2 | no | — |
| 329 | C2 | #10591416 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #10590913 | C2 | semidirect |
| 3. #10590625 | C2 | semidirect |
| 4. C3×#4565 | C2 | semidirect |
| 5. #10589128 | C2 | semidirect |
| 27. #4565 | D3 | semidirect |
| 279. C32 | #2148 | semidirect |
| 324. C3 | #69266 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64128 | 2 |
| #10590913 | 2 |
| #10590625 | 2 |
| C3×#4565 | 2 |
| #10589128 | 2 |
| #69266 | 3 |