Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
262 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 39 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×A4×D8 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | A4×D24 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | A4×C3⋊C16 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C22×#826 | C3 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | A4×D16 | — | 3 | 1 | no | maximal |
| 6 | C3×D4×A4 | — | 2 | 1 | no | — |
| 7 | A4×D12 | — | 2 | 1 | no | — |
| 8 | C3×C8×A4 | C22 | 1 | 1 | yes | characteristic |
| 9 | C3×#826 | — | 4 | 1 | no | maximal |
| 10 | C22×C3×D8 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 11 | C22×D24 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 12 | A4×D8 | — | 2 | 1 | no | — |
| 13 | A4×D8 | — | 3 | 1 | no | — |
| 14 | A4×D8 | D3 | 1 | 1 | yes | characteristic, complemented |
| 15 | C2×#826 | — | 3 | 1 | no | — |
| 16 | C2×#826 | — | 3 | 1 | no | — |
| 17 | C2×#826 | — | 3 | 1 | no | — |
| 18 | C2×#826 | — | 3 | 1 | no | — |
| 19 | C22×C3⋊C16 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 20 | A4×C16 | — | 3 | 1 | no | — |
| 21 | C22×C3×A4 | — | 4 | 1 | no | — |
| 22 | C2×D3×A4 | — | 4 | 1 | no | — |
| 23 | C3×C4×A4 | D4 | 1 | 1 | yes | characteristic |
| 24 | C32×D8 | — | 4 | 1 | no | — |
| 25 | C3×D24 | — | 4 | 1 | no | — |
| 26 | C3×C3⋊C16 | — | 4 | 1 | no | — |
| 27 | C22×D16 | — | 3 | 1 | no | Sylow |
| 28 | C22×C3×D4 | — | 2 | 1 | no | — |
| 29 | C22×D12 | — | 2 | 1 | no | — |
| 30 | D4×A4 | — | 2 | 2 | no | — |
| 31 | D4×A4 | — | 2 | 1 | no | — |
| 32 | D4×A4 | — | 6 | 1 | no | — |
| 33 | C2×C3×D8 | — | 3 | 1 | no | — |
| 34 | C2×C3×D8 | — | 3 | 1 | no | — |
| 35 | C2×C3×D8 | — | 6 | 1 | no | — |
| 36 | C22×C3×C8 | C22×C3 | 1 | 1 | yes | characteristic |
| 37 | C2×D24 | — | 3 | 1 | no | — |
| 38 | C2×D24 | — | 3 | 1 | no | — |
| 39 | C2×D24 | — | 6 | 1 | no | — |
| 40 | C8×A4 | — | 2 | 1 | no | — |
| 41 | C8×A4 | C2×D3 | 1 | 1 | yes | characteristic |
| 42 | C3×D16 | — | 12 | 1 | no | — |
| 43 | #826 | — | 3 | 2 | no | — |
| 44 | #826 | — | 3 | 1 | no | — |
| 45 | #826 | — | 3 | 1 | no | — |
| 46 | #826 | — | 3 | 1 | no | — |
| 47 | #826 | A4 | 1 | 1 | yes | characteristic, direct product factor |
| 48 | C2×C3⋊C16 | — | 3 | 1 | no | — |
| 49 | C2×C3⋊C16 | — | 3 | 1 | no | — |
| 50 | C2×C3×A4 | — | 8 | 1 | no | — |
| 51 | C2×C3×A4 | D8 | 1 | 1 | yes | characteristic |
| 52 | D3×A4 | — | 8 | 1 | no | — |
| 53 | C32×D4 | — | 8 | 1 | no | — |
| 54 | C3×D12 | — | 8 | 1 | no | — |
| 55 | C32×C8 | — | 4 | 1 | no | — |
| 56 | C22×D8 | — | 3 | 1 | no | — |
| 57 | C22×D8 | C3×D3 | 1 | 1 | yes | characteristic, complemented |
| 58 | C2×D16 | — | 9 | 1 | no | — |
| 59 | C2×D16 | — | 9 | 1 | no | — |
| 60 | C2×D16 | — | 9 | 1 | no | — |
| 61 | C2×D16 | — | 9 | 1 | no | — |
| 62 | C22×C16 | — | 3 | 1 | no | — |
| 63 | C24×C3 | — | 4 | 1 | no | — |
| 64 | C23×D3 | — | 4 | 1 | no | — |
| 65 | C22×A4 | — | 4 | 2 | no | — |
| 66 | C22×A4 | — | 4 | 1 | no | — |
| 67 | C22×A4 | — | 12 | 1 | no | — |
| 68 | C2×C3×D4 | — | 6 | 1 | no | — |
| 69 | C2×C3×D4 | — | 6 | 1 | no | — |
| 70 | C2×C3×D4 | — | 12 | 1 | no | — |
| 71 | C22×C3×C4 | C3×D4 | 1 | 1 | yes | characteristic |
| 72 | C2×D12 | — | 6 | 1 | no | — |
| 73 | C2×D12 | — | 6 | 1 | no | — |
| 74 | C2×D12 | — | 12 | 1 | no | — |
| 75 | C4×A4 | — | 2 | 1 | no | — |
| 76 | C4×A4 | #67 | 1 | 1 | yes | characteristic |
| 77 | C3×D8 | — | 3 | 1 | no | — |
| 78 | C3×D8 | — | 4 | 1 | no | — |
| 79 | C3×D8 | — | 6 | 1 | no | — |
| 80 | C3×D8 | — | 6 | 1 | no | — |
| 81 | C3×D8 | — | 8 | 1 | no | — |
| 82 | C3×D8 | — | 12 | 1 | no | — |
| 83 | C3×D8 | C2×A4 | 1 | 1 | yes | characteristic, complemented |
| 84 | C2×C3×C8 | — | 3 | 1 | no | — |
| 85 | C2×C3×C8 | — | 3 | 1 | no | — |
| 86 | D24 | — | 3 | 1 | no | — |
| 87 | D24 | — | 6 | 1 | no | — |
| 88 | D24 | — | 6 | 1 | no | — |
| 89 | D24 | C2×A4 | 1 | 1 | yes | characteristic, complemented |
| 90 | C3×C16 | — | 12 | 1 | no | — |
| 91 | C3⋊C16 | — | 3 | 1 | no | — |
| 92 | C3⋊C16 | C2×A4 | 1 | 1 | yes | characteristic, complemented |
| 93 | C22×C32 | — | 16 | 1 | no | — |
| 94 | C2×C3×D3 | — | 16 | 1 | no | — |
| 95 | C3×A4 | D16 | 1 | 1 | yes | characteristic, complemented |
| 96 | C32×C4 | — | 4 | 1 | no | — |
| 97 | C22×D4 | — | 2 | 1 | no | — |
| 98 | C22×D4 | — | 6 | 1 | no | — |
| 99 | C2×D8 | — | 3 | 1 | no | — |
| 100 | C2×D8 | — | 3 | 1 | no | — |
| 101 | C2×D8 | — | 6 | 1 | no | — |
| 102 | C2×D8 | — | 9 | 1 | no | — |
| 103 | C2×D8 | — | 9 | 1 | no | — |
| 104 | C2×D8 | — | 18 | 1 | no | — |
| 105 | C22×C8 | C2×C3×D3 | 1 | 1 | yes | characteristic |
| 106 | D16 | — | 3 | 1 | no | — |
| 107 | D16 | — | 9 | 1 | no | — |
| 108 | D16 | — | 9 | 1 | no | — |
| 109 | D16 | — | 9 | 2 | no | — |
| 110 | D16 | — | 9 | 1 | no | — |
| 111 | C2×C16 | — | 9 | 1 | no | — |
| 112 | C2×C16 | — | 9 | 1 | no | — |
| 113 | C23×C3 | — | 8 | 1 | no | — |
| 114 | C23×C3 | — | 12 | 1 | no | — |
| 115 | C23×C3 | — | 12 | 1 | no | — |
| 116 | C23×C3 | — | 24 | 1 | no | — |
| 117 | C23×C3 | C3×D8 | 1 | 1 | yes | characteristic |
| 118 | C22×D3 | — | 8 | 1 | no | — |
| 119 | C22×D3 | — | 12 | 1 | no | — |
| 120 | C22×D3 | — | 12 | 1 | no | — |
| 121 | C22×D3 | — | 24 | 1 | no | — |
| 122 | C2×A4 | — | 2 | 1 | no | — |
| 123 | C2×A4 | — | 8 | 2 | no | — |
| 124 | C2×A4 | — | 8 | 1 | no | — |
| 125 | C2×A4 | — | 24 | 1 | no | — |
| 126 | C2×A4 | #213 | 1 | 1 | yes | characteristic |
| 127 | C3×D4 | — | 2 | 1 | no | — |
| 128 | C3×D4 | — | 6 | 1 | no | — |
| 129 | C3×D4 | — | 8 | 1 | no | — |
| 130 | C3×D4 | — | 8 | 2 | no | — |
| 131 | C3×D4 | — | 12 | 1 | no | — |
| 132 | C3×D4 | — | 12 | 1 | no | — |
| 133 | C3×D4 | — | 24 | 1 | no | — |
| 134 | C2×C3×C4 | — | 3 | 1 | no | — |
| 135 | C2×C3×C4 | — | 3 | 1 | no | — |
| 136 | D12 | — | 2 | 1 | no | — |
| 137 | D12 | — | 6 | 1 | no | — |
| 138 | D12 | — | 12 | 1 | no | — |
| 139 | D12 | — | 12 | 1 | no | — |
| 140 | C3×C8 | — | 3 | 1 | no | — |
| 141 | C3×C8 | — | 4 | 1 | no | — |
| 142 | C3×C8 | — | 8 | 1 | no | — |
| 143 | C3×C8 | C22×A4 | 1 | 1 | yes | characteristic |
| 144 | C2×C32 | — | 4 | 1 | no | — |
| 145 | C2×C32 | — | 32 | 1 | no | — |
| 146 | C3×D3 | — | 32 | 1 | no | — |
| 147 | C24 | — | 4 | 1 | no | — |
| 148 | C24 | — | 12 | 1 | no | — |
| 149 | C2×D4 | — | 6 | 1 | no | — |
| 150 | C2×D4 | — | 6 | 1 | no | — |
| 151 | C2×D4 | — | 12 | 1 | no | — |
| 152 | C2×D4 | — | 18 | 1 | no | — |
| 153 | C2×D4 | — | 18 | 1 | no | — |
| 154 | C2×D4 | — | 36 | 1 | no | — |
| 155 | C22×C4 | C3×#67 | 1 | 1 | yes | characteristic |
| 156 | D8 | — | 3 | 1 | no | — |
| 157 | D8 | — | 3 | 1 | no | — |
| 158 | D8 | — | 6 | 1 | no | — |
| 159 | D8 | — | 6 | 1 | no | — |
| 160 | D8 | — | 9 | 1 | no | — |
| 161 | D8 | — | 18 | 1 | no | — |
| 162 | D8 | — | 18 | 1 | no | — |
| 163 | D8 | D3×A4 | 1 | 1 | yes | characteristic, complemented |
| 164 | C2×C8 | — | 3 | 1 | no | — |
| 165 | C2×C8 | — | 3 | 1 | no | — |
| 166 | C16 | — | 3 | 1 | no | — |
| 167 | C16 | — | 9 | 1 | no | — |
| 168 | C22×C3 | — | 3 | 1 | no | — |
| 169 | C22×C3 | — | 3 | 1 | no | — |
| 170 | C22×C3 | — | 4 | 1 | no | — |
| 171 | C22×C3 | — | 12 | 1 | no | — |
| 172 | C22×C3 | — | 16 | 1 | no | — |
| 173 | C22×C3 | — | 16 | 2 | no | — |
| 174 | C22×C3 | — | 24 | 1 | no | — |
| 175 | C22×C3 | — | 24 | 1 | no | — |
| 176 | C22×C3 | — | 24 | 1 | no | — |
| 177 | C22×C3 | — | 24 | 1 | no | — |
| 178 | C22×C3 | — | 48 | 1 | no | — |
| 179 | C22×C3 | C3×D16 | 1 | 1 | yes | characteristic, complemented |
| 180 | C2×D3 | — | 4 | 1 | no | — |
| 181 | C2×D3 | — | 12 | 1 | no | — |
| 182 | C2×D3 | — | 24 | 1 | no | — |
| 183 | C2×D3 | — | 24 | 1 | no | — |
| 184 | C2×D3 | — | 24 | 1 | no | — |
| 185 | C2×D3 | — | 24 | 1 | no | — |
| 186 | A4 | — | 2 | 1 | no | — |
| 187 | A4 | #826 | 1 | 1 | yes | characteristic, direct product factor |
| 188 | C3×C4 | — | 3 | 1 | no | — |
| 189 | C3×C4 | — | 4 | 1 | no | — |
| 190 | C3×C4 | — | 8 | 1 | no | — |
| 191 | C3×C4 | D4×A4 | 1 | 1 | yes | characteristic |
| 192 | C32 | — | 4 | 1 | no | Sylow |
| 193 | C23 | — | 8 | 1 | no | — |
| 194 | C23 | — | 12 | 1 | no | — |
| 195 | C23 | — | 12 | 1 | no | — |
| 196 | C23 | — | 24 | 1 | no | — |
| 197 | C23 | — | 24 | 1 | no | — |
| 198 | C23 | — | 36 | 1 | no | — |
| 199 | C23 | — | 36 | 1 | no | — |
| 200 | C23 | — | 72 | 1 | no | — |
| 201 | C23 | C3×#213 | 1 | 1 | yes | characteristic |
| 202 | D4 | — | 2 | 1 | no | — |
| 203 | D4 | — | 6 | 1 | no | — |
| 204 | D4 | — | 6 | 1 | no | — |
| 205 | D4 | — | 12 | 1 | no | — |
| 206 | D4 | — | 12 | 1 | no | — |
| 207 | D4 | — | 18 | 1 | no | — |
| 208 | D4 | — | 36 | 1 | no | — |
| 209 | D4 | — | 36 | 1 | no | — |
| 210 | C2×C4 | — | 3 | 1 | no | — |
| 211 | C2×C4 | — | 3 | 1 | no | — |
| 212 | C8 | — | 3 | 1 | no | — |
| 213 | C8 | C2×D3×A4 | 1 | 1 | yes | characteristic |
| 214 | C2×C3 | — | 3 | 1 | no | — |
| 215 | C2×C3 | — | 3 | 1 | no | — |
| 216 | C2×C3 | — | 4 | 1 | no | — |
| 217 | C2×C3 | — | 8 | 1 | no | — |
| 218 | C2×C3 | — | 8 | 1 | no | — |
| 219 | C2×C3 | — | 24 | 1 | no | — |
| 220 | C2×C3 | — | 32 | 1 | no | — |
| 221 | C2×C3 | — | 32 | 2 | no | — |
| 222 | C2×C3 | — | 96 | 1 | no | — |
| 223 | C2×C3 | A4×D8 | 1 | 1 | yes | characteristic |
| 224 | D3 | — | 8 | 1 | no | — |
| 225 | D3 | — | 24 | 1 | no | — |
| 226 | C22 | — | 3 | 1 | no | — |
| 227 | C22 | — | 3 | 1 | no | — |
| 228 | C22 | — | 4 | 1 | no | — |
| 229 | C22 | — | 12 | 1 | no | — |
| 230 | C22 | — | 12 | 1 | no | — |
| 231 | C22 | — | 24 | 1 | no | — |
| 232 | C22 | — | 24 | 1 | no | — |
| 233 | C22 | — | 24 | 1 | no | — |
| 234 | C22 | — | 24 | 1 | no | — |
| 235 | C22 | — | 36 | 1 | no | — |
| 236 | C22 | — | 72 | 1 | no | — |
| 237 | C22 | — | 72 | 1 | no | — |
| 238 | C22 | — | 72 | 1 | no | — |
| 239 | C22 | — | 72 | 1 | no | — |
| 240 | C22 | C3×#826 | 1 | 1 | yes | characteristic, complemented |
| 241 | C4 | — | 3 | 1 | no | — |
| 242 | C4 | A4×#67 | 1 | 1 | yes | characteristic |
| 243 | C3 | — | 4 | 1 | no | — |
| 244 | C3 | — | 8 | 1 | no | — |
| 245 | C3 | A4×D16 | 1 | 1 | yes | characteristic, complemented |
| 246 | C2 | — | 3 | 1 | no | — |
| 247 | C2 | — | 3 | 1 | no | — |
| 248 | C2 | — | 8 | 1 | no | — |
| 249 | C2 | — | 24 | 1 | no | — |
| 250 | C2 | — | 24 | 1 | no | — |
| 251 | C2 | — | 72 | 1 | no | — |
| 252 | C2 | A4×#213 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×A4×D8 | C2 | semidirect |
| 2. A4×D24 | C2 | semidirect |
| 3. A4×C3⋊C16 | C2 | semidirect |
| 4. C22×#826 | C3 | semidirect |
| 10. C22×C3×D8 | C2×C3 | semidirect |
| 11. C22×D24 | C2×C3 | semidirect |
| 14. A4×D8 | D3 | semidirect |
| 19. C22×C3⋊C16 | C2×C3 | semidirect |
| 47. #826 | A4 | direct (N × H) |
| 57. C22×D8 | C3×D3 | semidirect |
| 83. C3×D8 | C2×A4 | semidirect |
| 89. D24 | C2×A4 | semidirect |
| 92. C3⋊C16 | C2×A4 | semidirect |
| 95. C3×A4 | D16 | semidirect |
| 163. D8 | D3×A4 | semidirect |
| 179. C22×C3 | C3×D16 | semidirect |
| 187. A4 | #826 | direct (N × H) |
| 240. C22 | C3×#826 | semidirect |
| 245. C3 | A4×D16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×A4×D8 | 2 |
| A4×D24 | 2 |
| A4×C3⋊C16 | 2 |
| C22×#826 | 3 |
| A4×D16 | 3 |
| C3×#826 | 4 |