Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
470 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 61 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×#63797 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #10593771 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #10590625 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #10590020 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | C2×#3802 | — | 2 | 1 | no | — |
| 6 | #64283 | — | 2 | 1 | no | — |
| 7 | C2×C8×C3⋊D3 | C22 | 1 | 1 | yes | characteristic |
| 8 | C2×C3×D24 | — | 2 | 1 | no | — |
| 9 | C2×#3713 | C4 | 1 | 2 | yes | — |
| 10 | #63797 | — | 2 | 1 | no | — |
| 11 | #63797 | — | 2 | 1 | no | — |
| 12 | #63797 | C4 | 1 | 2 | yes | — |
| 13 | #63797 | C22 | 1 | 2 | yes | — |
| 14 | #63771 | C22 | 1 | 2 | yes | complemented |
| 15 | #63770 | — | 2 | 1 | no | — |
| 16 | C3×#812 | — | 2 | 1 | no | — |
| 17 | #63544 | C22 | 1 | 2 | yes | complemented |
| 18 | #63542 | — | 2 | 1 | no | — |
| 19 | C2×D3×D8 | — | 6 | 1 | no | — |
| 20 | D3×M32 | — | 6 | 1 | no | — |
| 21 | C22×D32 | — | 4 | 1 | no | — |
| 22 | C2×C4×C3⋊D3 | D4 | 1 | 1 | yes | characteristic |
| 23 | C2×C3×D12 | — | 2 | 2 | no | — |
| 24 | C2×#625 | — | 4 | 1 | no | — |
| 25 | #3802 | — | 2 | 2 | no | — |
| 26 | #3802 | — | 2 | 2 | no | — |
| 27 | #3802 | — | 4 | 1 | no | — |
| 28 | #3802 | — | 4 | 1 | no | — |
| 29 | #3792 | — | 4 | 1 | no | — |
| 30 | #3788 | — | 2 | 2 | no | — |
| 31 | #3787 | — | 4 | 1 | no | — |
| 32 | C2×C32×C8 | D4 | 1 | 1 | yes | characteristic |
| 33 | C2×C3⋊(C3⋊C8) | C2×C4 | 1 | 1 | yes | characteristic |
| 34 | C8×C3⋊D3 | C2×C4 | 1 | 1 | yes | characteristic |
| 35 | C8×C3⋊D3 | D4 | 1 | 1 | yes | characteristic |
| 36 | C8×C3⋊D3 | D4 | 1 | 1 | yes | characteristic |
| 37 | C8×C3⋊D3 | C23 | 1 | 1 | yes | characteristic |
| 38 | C3×D24 | — | 2 | 2 | no | — |
| 39 | C3×D24 | — | 2 | 2 | no | — |
| 40 | #3713 | — | 2 | 2 | no | — |
| 41 | #3713 | C2×C4 | 1 | 4 | yes | — |
| 42 | C3×C3⋊C16 | — | 2 | 2 | no | — |
| 43 | C2×#361 | — | 9 | 1 | no | maximal, Sylow |
| 44 | C2×D3×D4 | — | 6 | 2 | no | — |
| 45 | C2×C3×D8 | — | 6 | 1 | no | — |
| 46 | C2×#213 | — | 6 | 2 | no | — |
| 47 | D3×D8 | — | 6 | 2 | no | — |
| 48 | D3×D8 | — | 6 | 2 | no | — |
| 49 | D3×D8 | — | 6 | 2 | no | — |
| 50 | D3×D8 | — | 6 | 2 | no | — |
| 51 | C2×D24 | — | 2 | 1 | no | — |
| 52 | C2×D3×C8 | — | 6 | 1 | no | — |
| 53 | C2×D3×C8 | — | 6 | 1 | no | — |
| 54 | C3×M32 | — | 6 | 1 | no | — |
| 55 | #812 | — | 2 | 1 | no | — |
| 56 | #798 | — | 6 | 2 | no | — |
| 57 | D3×C16 | — | 6 | 2 | no | — |
| 58 | C22×C3⋊D3 | SD16 | 1 | 1 | yes | characteristic |
| 59 | C22×C3×D3 | — | 4 | 2 | no | — |
| 60 | C2×D32 | — | 4 | 2 | no | — |
| 61 | C2×D32 | — | 4 | 2 | no | — |
| 62 | C2×D32 | — | 8 | 4 | no | — |
| 63 | C2×C32×C4 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 64 | C2×C3⋊Dic3 | D8 | 1 | 1 | yes | characteristic |
| 65 | C4×C3⋊D3 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 66 | C4×C3⋊D3 | D8 | 1 | 1 | yes | characteristic |
| 67 | C4×C3⋊D3 | SD16 | 1 | 1 | yes | characteristic |
| 68 | C4×C3⋊D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 69 | C3×D12 | — | 2 | 4 | no | — |
| 70 | C3×D12 | — | 4 | 2 | no | — |
| 71 | #625 | — | 4 | 2 | no | — |
| 72 | #625 | — | 4 | 2 | no | — |
| 73 | #622 | — | 4 | 2 | no | — |
| 74 | C32×C8 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 75 | C32×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 76 | C3⋊(C3⋊C8) | C22⋊C4 | 1 | 1 | yes | characteristic |
| 77 | C3⋊(C3⋊C8) | C22×C4 | 1 | 1 | yes | characteristic |
| 78 | C22×D8 | — | 9 | 1 | no | — |
| 79 | C2×M32 | — | 9 | 1 | no | — |
| 80 | C2×#108 | — | 9 | 1 | no | — |
| 81 | #361 | — | 9 | 4 | no | — |
| 82 | C23×D3 | — | 12 | 2 | no | — |
| 83 | C2×C3×D4 | — | 6 | 2 | no | — |
| 84 | C2×#67 | — | 12 | 2 | no | — |
| 85 | D3×D4 | — | 6 | 4 | no | — |
| 86 | D3×D4 | — | 6 | 4 | no | — |
| 87 | D3×D4 | — | 12 | 2 | no | — |
| 88 | D3×D4 | — | 12 | 2 | no | — |
| 89 | C2×D12 | — | 2 | 2 | no | — |
| 90 | C2×C4×D3 | — | 6 | 1 | no | — |
| 91 | C2×C4×D3 | — | 6 | 1 | no | — |
| 92 | C3×D8 | — | 6 | 2 | no | — |
| 93 | C3×D8 | — | 6 | 2 | no | — |
| 94 | C2×C3×C8 | — | 2 | 1 | no | — |
| 95 | C2×C3×C8 | — | 2 | 1 | no | — |
| 96 | #213 | — | 6 | 4 | no | — |
| 97 | #213 | — | 6 | 4 | no | — |
| 98 | C2×C3⋊C8 | — | 6 | 1 | no | — |
| 99 | C2×C3⋊C8 | — | 6 | 1 | no | — |
| 100 | D24 | — | 2 | 2 | no | — |
| 101 | D24 | — | 2 | 2 | no | — |
| 102 | D3×C8 | — | 6 | 1 | no | — |
| 103 | D3×C8 | — | 6 | 1 | no | — |
| 104 | D3×C8 | — | 6 | 1 | no | — |
| 105 | D3×C8 | — | 6 | 1 | no | — |
| 106 | D3×C8 | — | 6 | 1 | no | — |
| 107 | D3×C8 | — | 6 | 1 | no | — |
| 108 | D3×C8 | — | 6 | 1 | no | — |
| 109 | D3×C8 | — | 6 | 1 | no | — |
| 110 | C3×C16 | — | 6 | 2 | no | — |
| 111 | C3⋊C16 | — | 2 | 2 | no | — |
| 112 | C22×C32 | #102 | 1 | 1 | yes | characteristic |
| 113 | C2×C3⋊D3 | — | 2 | 2 | no | — |
| 114 | C2×C3⋊D3 | #102 | 1 | 1 | yes | characteristic |
| 115 | C2×C3⋊D3 | C2×SD16 | 1 | 1 | yes | characteristic |
| 116 | C2×C3×D3 | — | 4 | 4 | no | — |
| 117 | C2×C3×D3 | — | 8 | 4 | no | — |
| 118 | D32 | — | 8 | 4 | no | — |
| 119 | D32 | — | 8 | 4 | no | — |
| 120 | C32×C4 | #102 | 1 | 1 | yes | characteristic |
| 121 | C32×C4 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 122 | C3⋊Dic3 | #102 | 1 | 1 | yes | characteristic |
| 123 | C3⋊Dic3 | C2×D8 | 1 | 1 | yes | characteristic |
| 124 | C22×D4 | — | 18 | 1 | no | — |
| 125 | C2×D8 | — | 6 | 1 | no | — |
| 126 | C2×D8 | — | 9 | 2 | no | — |
| 127 | C2×D8 | — | 9 | 2 | no | — |
| 128 | C2×D8 | — | 9 | 2 | no | — |
| 129 | C2×D8 | — | 18 | 1 | no | — |
| 130 | C2×D8 | — | 18 | 1 | no | — |
| 131 | C2×M16 | — | 18 | 1 | no | — |
| 132 | C22×C8 | — | 9 | 1 | no | — |
| 133 | M32 | — | 6 | 1 | no | — |
| 134 | M32 | — | 9 | 2 | no | — |
| 135 | C2×C16 | — | 18 | 1 | no | — |
| 136 | #108 | — | 9 | 2 | no | — |
| 137 | #108 | — | 18 | 1 | no | — |
| 138 | C23×C3 | — | 12 | 2 | no | — |
| 139 | C22×D3 | — | 4 | 2 | no | — |
| 140 | C22×D3 | — | 6 | 1 | no | — |
| 141 | C22×D3 | — | 6 | 1 | no | — |
| 142 | C22×D3 | — | 12 | 4 | no | — |
| 143 | C22×D3 | — | 12 | 4 | no | — |
| 144 | C22×D3 | — | 24 | 8 | no | — |
| 145 | C3×D4 | — | 6 | 4 | no | — |
| 146 | C3×D4 | — | 12 | 2 | no | — |
| 147 | C2×C3×C4 | — | 2 | 1 | no | — |
| 148 | C2×C3×C4 | — | 2 | 1 | no | — |
| 149 | #67 | — | 12 | 4 | no | — |
| 150 | #67 | — | 12 | 4 | no | — |
| 151 | C2×Dic3 | — | 6 | 1 | no | — |
| 152 | C2×Dic3 | — | 6 | 1 | no | — |
| 153 | D12 | — | 2 | 4 | no | — |
| 154 | D12 | — | 4 | 2 | no | — |
| 155 | C4×D3 | — | 6 | 1 | no | — |
| 156 | C4×D3 | — | 6 | 1 | no | — |
| 157 | C4×D3 | — | 6 | 1 | no | — |
| 158 | C4×D3 | — | 6 | 1 | no | — |
| 159 | C4×D3 | — | 6 | 1 | no | — |
| 160 | C4×D3 | — | 6 | 1 | no | — |
| 161 | C4×D3 | — | 6 | 1 | no | — |
| 162 | C4×D3 | — | 6 | 1 | no | — |
| 163 | C3×C8 | — | 2 | 1 | no | — |
| 164 | C3×C8 | — | 2 | 1 | no | — |
| 165 | C3×C8 | — | 2 | 1 | no | — |
| 166 | C3×C8 | — | 2 | 1 | no | — |
| 167 | C3⋊C8 | — | 6 | 1 | no | — |
| 168 | C3⋊C8 | — | 6 | 1 | no | — |
| 169 | C3⋊C8 | — | 6 | 1 | no | — |
| 170 | C3⋊C8 | — | 6 | 1 | no | — |
| 171 | C2×C32 | — | 2 | 1 | no | — |
| 172 | C2×C32 | C2×#102 | 1 | 1 | yes | characteristic |
| 173 | C3⋊D3 | — | 2 | 1 | no | — |
| 174 | C3⋊D3 | #361 | 1 | 2 | yes | complemented |
| 175 | C3×D3 | — | 8 | 4 | no | — |
| 176 | C24 | — | 36 | 1 | no | — |
| 177 | C2×D4 | — | 6 | 2 | no | — |
| 178 | C2×D4 | — | 18 | 2 | no | — |
| 179 | C2×D4 | — | 18 | 2 | no | — |
| 180 | C2×D4 | — | 36 | 1 | no | — |
| 181 | C2×D4 | — | 36 | 1 | no | — |
| 182 | C2×D4 | — | 36 | 1 | no | — |
| 183 | C22×C4 | — | 9 | 1 | no | — |
| 184 | D8 | — | 6 | 2 | no | — |
| 185 | D8 | — | 6 | 2 | no | — |
| 186 | D8 | — | 9 | 4 | no | — |
| 187 | D8 | — | 18 | 2 | no | — |
| 188 | M16 | — | 18 | 2 | no | — |
| 189 | M16 | — | 36 | 1 | no | — |
| 190 | C2×C8 | — | 9 | 1 | no | — |
| 191 | C2×C8 | — | 9 | 1 | no | — |
| 192 | C2×C8 | — | 9 | 1 | no | — |
| 193 | C2×C8 | — | 9 | 1 | no | — |
| 194 | C2×C8 | — | 9 | 1 | no | — |
| 195 | C2×C8 | — | 36 | 1 | no | — |
| 196 | C2×C8 | GO+(4,𝔽2) | 1 | 1 | yes | characteristic |
| 197 | C16 | — | 6 | 2 | no | — |
| 198 | C22×C3 | — | 2 | 1 | no | — |
| 199 | C22×C3 | — | 2 | 1 | no | — |
| 200 | C22×C3 | — | 12 | 4 | no | — |
| 201 | C22×C3 | — | 24 | 4 | no | — |
| 202 | C2×D3 | — | 4 | 4 | no | — |
| 203 | C2×D3 | — | 6 | 1 | no | — |
| 204 | C2×D3 | — | 6 | 1 | no | — |
| 205 | C2×D3 | — | 6 | 1 | no | — |
| 206 | C2×D3 | — | 6 | 1 | no | — |
| 207 | C2×D3 | — | 6 | 4 | no | — |
| 208 | C2×D3 | — | 8 | 4 | no | — |
| 209 | C2×D3 | — | 12 | 2 | no | — |
| 210 | C2×D3 | — | 24 | 8 | no | — |
| 211 | C2×D3 | — | 24 | 8 | no | — |
| 212 | C3×C4 | — | 2 | 1 | no | — |
| 213 | C3×C4 | — | 2 | 1 | no | — |
| 214 | C3×C4 | — | 2 | 1 | no | — |
| 215 | C3×C4 | — | 2 | 1 | no | — |
| 216 | Dic3 | — | 6 | 1 | no | — |
| 217 | Dic3 | — | 6 | 1 | no | — |
| 218 | Dic3 | — | 6 | 1 | no | — |
| 219 | Dic3 | — | 6 | 1 | no | — |
| 220 | C32 | C2×#361 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 221 | C23 | — | 9 | 1 | no | — |
| 222 | C23 | — | 12 | 2 | no | — |
| 223 | C23 | — | 36 | 2 | no | — |
| 224 | C23 | — | 36 | 2 | no | — |
| 225 | C23 | — | 72 | 4 | no | — |
| 226 | D4 | — | 6 | 4 | no | — |
| 227 | D4 | — | 12 | 2 | no | — |
| 228 | D4 | — | 36 | 2 | no | — |
| 229 | D4 | — | 36 | 2 | no | — |
| 230 | C2×C4 | — | 9 | 1 | no | — |
| 231 | C2×C4 | — | 9 | 1 | no | — |
| 232 | C2×C4 | — | 9 | 1 | no | — |
| 233 | C2×C4 | — | 9 | 1 | no | — |
| 234 | C2×C4 | — | 9 | 1 | no | — |
| 235 | C2×C4 | D32⋊C4 | 1 | 1 | yes | characteristic |
| 236 | C8 | — | 9 | 1 | no | — |
| 237 | C8 | — | 9 | 1 | no | — |
| 238 | C8 | — | 36 | 2 | no | — |
| 239 | C8 | D32⋊C4 | 1 | 1 | yes | characteristic |
| 240 | C8 | C2×GO+(4,𝔽2) | 1 | 1 | yes | characteristic |
| 241 | C2×C3 | — | 2 | 2 | no | — |
| 242 | C2×C3 | — | 2 | 1 | no | — |
| 243 | C2×C3 | — | 2 | 1 | no | — |
| 244 | C2×C3 | — | 4 | 1 | no | — |
| 245 | C2×C3 | — | 24 | 4 | no | — |
| 246 | D3 | — | 6 | 2 | no | — |
| 247 | D3 | — | 6 | 2 | no | — |
| 248 | D3 | — | 6 | 2 | no | — |
| 249 | D3 | — | 8 | 4 | no | — |
| 250 | D3 | — | 12 | 1 | no | — |
| 251 | C22 | — | 9 | 1 | no | — |
| 252 | C22 | — | 9 | 1 | no | — |
| 253 | C22 | — | 12 | 4 | no | — |
| 254 | C22 | — | 18 | 2 | no | — |
| 255 | C22 | — | 24 | 4 | no | — |
| 256 | C22 | — | 72 | 4 | no | — |
| 257 | C22 | — | 72 | 4 | no | — |
| 258 | C22 | #63729 | 1 | 1 | yes | characteristic |
| 259 | C4 | — | 9 | 1 | no | — |
| 260 | C4 | — | 9 | 1 | no | — |
| 261 | C4 | #63729 | 1 | 1 | yes | characteristic |
| 262 | C4 | C2×D32⋊C4 | 1 | 1 | yes | characteristic |
| 263 | C3 | — | 2 | 1 | no | — |
| 264 | C3 | — | 2 | 1 | no | — |
| 265 | C2 | — | 2 | 1 | no | — |
| 266 | C2 | — | 9 | 2 | no | — |
| 267 | C2 | — | 18 | 1 | no | — |
| 268 | C2 | — | 24 | 4 | no | — |
| 269 | C2 | C2×#63729 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #10593771 | C2 | semidirect |
| 3. #10590625 | C2 | semidirect |
| 4. #10590020 | C2 | semidirect |
| 14. #63771 | C22 | semidirect |
| 17. #63544 | C22 | semidirect |
| 174. C3⋊D3 | #361 | semidirect |
| 220. C32 | C2×#361 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63797 | 2 |
| #10593771 | 2 |
| #10590625 | 2 |
| #10590020 | 2 |
| C2×#361 | 9 |