Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
702 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 702 conjugacy classes of subgroups — too many to draw. Only its 111 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×#63822 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C22×#3713 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×#63773 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C2×#63735 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #10593334 | C2 | 1 | 8 | yes | maximal, direct product factor |
| 6 | C2×#63734 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | C2×C3×#235 | — | 2 | 1 | no | — |
| 8 | C22×C3×D12 | — | 2 | 1 | no | — |
| 9 | C22×C3⋊(C3⋊C8) | C22 | 1 | 1 | yes | characteristic |
| 10 | C2×#3718 | C22 | 1 | 1 | yes | characteristic, complemented |
| 11 | C2×#3715 | — | 2 | 1 | no | — |
| 12 | #63822 | — | 2 | 2 | no | — |
| 13 | #63822 | C22 | 1 | 4 | yes | complemented |
| 14 | C2×#3713 | — | 2 | 2 | no | — |
| 15 | C2×#3713 | — | 2 | 1 | no | — |
| 16 | C2×#3713 | C22 | 1 | 2 | yes | — |
| 17 | C2×#3713 | C22 | 1 | 4 | yes | complemented |
| 18 | C2×#3713 | C22 | 1 | 1 | yes | characteristic, complemented |
| 19 | #63773 | C22 | 1 | 4 | yes | complemented |
| 20 | C2×#3708 | C22 | 1 | 2 | yes | complemented |
| 21 | #63735 | C22 | 1 | 8 | yes | complemented |
| 22 | #63734 | C22 | 1 | 8 | yes | complemented |
| 23 | C2×#950 | — | 6 | 1 | no | — |
| 24 | C22×#213 | — | 6 | 1 | no | — |
| 25 | C23×C3×D3 | — | 4 | 1 | no | — |
| 26 | C22×C32×C4 | D4 | 1 | 1 | yes | characteristic |
| 27 | C2×C3×#67 | — | 4 | 1 | no | — |
| 28 | C3×#235 | — | 2 | 4 | no | — |
| 29 | C3×#235 | — | 4 | 2 | no | — |
| 30 | C2×C3×D12 | — | 2 | 2 | no | — |
| 31 | C2×C3×D12 | — | 2 | 4 | no | — |
| 32 | C2×C3×D12 | — | 2 | 1 | no | — |
| 33 | C2×C3×D12 | — | 4 | 1 | no | — |
| 34 | C2×C3×D12 | — | 4 | 2 | no | — |
| 35 | C2×C3×C4×D3 | — | 4 | 1 | no | — |
| 36 | C2×C3×Dic6 | — | 2 | 1 | no | — |
| 37 | C2×C3⋊(C3⋊C8) | D4 | 1 | 2 | yes | — |
| 38 | C2×C3⋊(C3⋊C8) | D4 | 1 | 1 | yes | characteristic |
| 39 | C2×C3⋊(C3⋊C8) | C23 | 1 | 1 | yes | characteristic |
| 40 | C2×C3⋊(C3⋊C8) | C23 | 1 | 2 | yes | — |
| 41 | #3718 | — | 2 | 1 | no | — |
| 42 | #3718 | C23 | 1 | 2 | yes | complemented |
| 43 | #3715 | — | 2 | 4 | no | — |
| 44 | #3713 | — | 2 | 2 | no | — |
| 45 | #3713 | — | 2 | 4 | no | — |
| 46 | #3713 | — | 2 | 1 | no | — |
| 47 | #3713 | C23 | 1 | 4 | yes | — |
| 48 | #3713 | C23 | 1 | 2 | yes | complemented |
| 49 | #3708 | C23 | 1 | 4 | yes | complemented |
| 50 | C2×#509 | — | 9 | 1 | no | maximal, Sylow |
| 51 | C2×C3×#41 | — | 6 | 1 | no | — |
| 52 | C22×C3×D4 | — | 6 | 1 | no | — |
| 53 | C2×#235 | — | 2 | 1 | no | — |
| 54 | C22×D12 | — | 2 | 1 | no | — |
| 55 | #950 | — | 6 | 4 | no | — |
| 56 | #950 | — | 6 | 4 | no | — |
| 57 | C2×#216 | — | 6 | 1 | no | — |
| 58 | C2×#215 | — | 6 | 1 | no | — |
| 59 | C2×#214 | — | 6 | 1 | no | — |
| 60 | C2×#213 | — | 6 | 2 | no | — |
| 61 | C2×#213 | — | 6 | 4 | no | — |
| 62 | C2×#213 | — | 6 | 1 | no | — |
| 63 | C2×#213 | — | 6 | 2 | no | — |
| 64 | C2×#213 | — | 6 | 4 | no | — |
| 65 | C22×C3⋊C8 | — | 6 | 1 | no | — |
| 66 | C22×C3⋊C8 | — | 6 | 1 | no | — |
| 67 | C23×C32 | D8 | 1 | 1 | yes | characteristic |
| 68 | C22×C3×D3 | — | 4 | 4 | no | — |
| 69 | C22×C3×D3 | — | 4 | 2 | no | — |
| 70 | C22×C3×D3 | — | 4 | 1 | no | — |
| 71 | C22×C3×D3 | — | 8 | 4 | no | — |
| 72 | C2×C32×C4 | D8 | 1 | 1 | yes | characteristic |
| 73 | C2×C32×C4 | D8 | 1 | 2 | yes | — |
| 74 | C2×C32×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 75 | C2×C32×C4 | C2×D4 | 1 | 2 | yes | — |
| 76 | C3×#67 | — | 4 | 4 | no | — |
| 77 | C2×C3×Dic3 | — | 4 | 1 | no | — |
| 78 | C3×D12 | — | 2 | 4 | no | — |
| 79 | C3×D12 | — | 2 | 2 | no | — |
| 80 | C3×D12 | — | 4 | 2 | no | — |
| 81 | C3×D12 | — | 4 | 4 | no | — |
| 82 | C3×D12 | — | 4 | 1 | no | — |
| 83 | C3×C4×D3 | — | 4 | 4 | no | — |
| 84 | C3×Dic6 | — | 2 | 2 | no | — |
| 85 | C3×Dic6 | — | 4 | 1 | no | — |
| 86 | C3⋊(C3⋊C8) | C2×D4 | 1 | 1 | yes | characteristic |
| 87 | C3⋊(C3⋊C8) | C2×D4 | 1 | 2 | yes | — |
| 88 | C3⋊(C3⋊C8) | C24 | 1 | 1 | yes | characteristic |
| 89 | C2×#135 | — | 9 | 1 | no | — |
| 90 | C22×D8 | — | 9 | 1 | no | — |
| 91 | #509 | — | 9 | 8 | no | — |
| 92 | C2×SD32 | — | 9 | 2 | no | — |
| 93 | C2×D16 | — | 9 | 2 | no | — |
| 94 | C2×M32 | — | 9 | 1 | no | — |
| 95 | C24×C3 | — | 12 | 1 | no | — |
| 96 | C23×D3 | — | 4 | 1 | no | — |
| 97 | C3×#41 | — | 6 | 4 | no | — |
| 98 | C3×#41 | — | 12 | 2 | no | — |
| 99 | C2×C3×Q8 | — | 6 | 1 | no | — |
| 100 | C2×C3×D4 | — | 6 | 2 | no | — |
| 101 | C2×C3×D4 | — | 6 | 4 | no | — |
| 102 | C2×C3×D4 | — | 6 | 1 | no | — |
| 103 | C2×C3×D4 | — | 12 | 2 | no | — |
| 104 | C2×C3×D4 | — | 12 | 1 | no | — |
| 105 | C2×C3×D4 | — | 12 | 1 | no | — |
| 106 | C22×C3×C4 | — | 2 | 1 | no | — |
| 107 | C22×C3×C4 | — | 2 | 1 | no | — |
| 108 | C22×C3×C4 | — | 12 | 1 | no | — |
| 109 | C2×#67 | — | 4 | 1 | no | — |
| 110 | #235 | — | 2 | 4 | no | — |
| 111 | #235 | — | 4 | 2 | no | — |
| 112 | C2×D12 | — | 2 | 2 | no | — |
| 113 | C2×D12 | — | 2 | 4 | no | — |
| 114 | C2×D12 | — | 2 | 1 | no | — |
| 115 | C2×D12 | — | 4 | 2 | no | — |
| 116 | C2×D12 | — | 4 | 1 | no | — |
| 117 | C2×C4×D3 | — | 4 | 1 | no | — |
| 118 | C2×Dic6 | — | 2 | 1 | no | — |
| 119 | #216 | — | 6 | 2 | no | — |
| 120 | #216 | — | 6 | 2 | no | — |
| 121 | #215 | — | 6 | 4 | no | — |
| 122 | #214 | — | 6 | 4 | no | — |
| 123 | #213 | — | 6 | 4 | no | — |
| 124 | #213 | — | 6 | 2 | no | — |
| 125 | #213 | — | 6 | 4 | no | — |
| 126 | #213 | — | 6 | 8 | no | — |
| 127 | #213 | — | 6 | 2 | no | — |
| 128 | C2×C3⋊C8 | — | 6 | 1 | no | — |
| 129 | C2×C3⋊C8 | — | 6 | 2 | no | — |
| 130 | C2×C3⋊C8 | — | 6 | 1 | no | — |
| 131 | C2×C3⋊C8 | — | 6 | 2 | no | — |
| 132 | C2×C3⋊C8 | — | 6 | 1 | no | — |
| 133 | C2×C3⋊C8 | — | 6 | 1 | no | — |
| 134 | C2×C3⋊C8 | — | 6 | 2 | no | — |
| 135 | C2×C3⋊C8 | — | 6 | 2 | no | — |
| 136 | C22×C32 | — | 2 | 2 | no | — |
| 137 | C22×C32 | C2×D8 | 1 | 2 | yes | — |
| 138 | C22×C32 | C2×D8 | 1 | 1 | yes | characteristic |
| 139 | C2×C3×D3 | — | 4 | 2 | no | — |
| 140 | C2×C3×D3 | — | 4 | 4 | no | — |
| 141 | C2×C3×D3 | — | 8 | 8 | no | — |
| 142 | C2×C3×D3 | — | 8 | 2 | no | — |
| 143 | C2×C3×D3 | — | 8 | 4 | no | — |
| 144 | C32×C4 | C2×D8 | 1 | 1 | yes | characteristic |
| 145 | C32×C4 | C2×D8 | 1 | 2 | yes | — |
| 146 | C32×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 147 | C3×Dic3 | — | 4 | 2 | no | — |
| 148 | C2×#41 | — | 6 | 1 | no | — |
| 149 | C22×D4 | — | 6 | 1 | no | — |
| 150 | #135 | — | 9 | 4 | no | — |
| 151 | #135 | — | 18 | 2 | no | — |
| 152 | C2×Q16 | — | 9 | 1 | no | — |
| 153 | C2×SD16 | — | 18 | 1 | no | — |
| 154 | C2×D8 | — | 9 | 2 | no | — |
| 155 | C2×D8 | — | 9 | 4 | no | — |
| 156 | C2×D8 | — | 9 | 1 | no | — |
| 157 | C2×D8 | — | 18 | 1 | no | — |
| 158 | C2×D8 | — | 18 | 2 | no | — |
| 159 | C22×C8 | — | 9 | 1 | no | — |
| 160 | SD32 | — | 9 | 8 | no | — |
| 161 | D16 | — | 9 | 8 | no | — |
| 162 | M32 | — | 9 | 4 | no | — |
| 163 | C2×C16 | — | 9 | 2 | no | — |
| 164 | C23×C3 | — | 2 | 1 | no | — |
| 165 | C23×C3 | — | 2 | 1 | no | — |
| 166 | C23×C3 | — | 12 | 1 | no | — |
| 167 | C23×C3 | — | 12 | 4 | no | — |
| 168 | C23×C3 | — | 12 | 2 | no | — |
| 169 | C23×C3 | — | 24 | 4 | no | — |
| 170 | C22×D3 | — | 4 | 1 | no | — |
| 171 | C22×D3 | — | 4 | 4 | no | — |
| 172 | C22×D3 | — | 4 | 2 | no | — |
| 173 | C22×D3 | — | 8 | 4 | no | — |
| 174 | C3×Q8 | — | 6 | 2 | no | — |
| 175 | C3×Q8 | — | 12 | 1 | no | — |
| 176 | C3×D4 | — | 6 | 4 | no | — |
| 177 | C3×D4 | — | 6 | 2 | no | — |
| 178 | C3×D4 | — | 12 | 4 | no | — |
| 179 | C3×D4 | — | 12 | 2 | no | — |
| 180 | C3×D4 | — | 12 | 1 | no | — |
| 181 | C3×D4 | — | 12 | 4 | no | — |
| 182 | C2×C3×C4 | — | 2 | 1 | no | — |
| 183 | C2×C3×C4 | — | 2 | 2 | no | — |
| 184 | C2×C3×C4 | — | 2 | 1 | no | — |
| 185 | C2×C3×C4 | — | 2 | 2 | no | — |
| 186 | C2×C3×C4 | — | 2 | 1 | no | — |
| 187 | C2×C3×C4 | — | 2 | 2 | no | — |
| 188 | C2×C3×C4 | — | 2 | 1 | no | — |
| 189 | C2×C3×C4 | — | 2 | 2 | no | — |
| 190 | C2×C3×C4 | — | 12 | 4 | no | — |
| 191 | C2×C3×C4 | — | 12 | 1 | no | — |
| 192 | #67 | — | 4 | 4 | no | — |
| 193 | C2×Dic3 | — | 4 | 1 | no | — |
| 194 | D12 | — | 2 | 4 | no | — |
| 195 | D12 | — | 2 | 2 | no | — |
| 196 | D12 | — | 4 | 4 | no | — |
| 197 | D12 | — | 4 | 2 | no | — |
| 198 | D12 | — | 4 | 1 | no | — |
| 199 | C4×D3 | — | 4 | 4 | no | — |
| 200 | Dic6 | — | 2 | 2 | no | — |
| 201 | Dic6 | — | 4 | 1 | no | — |
| 202 | C3⋊C8 | — | 6 | 1 | no | — |
| 203 | C3⋊C8 | — | 6 | 2 | no | — |
| 204 | C3⋊C8 | — | 6 | 1 | no | — |
| 205 | C3⋊C8 | — | 6 | 2 | no | — |
| 206 | C3⋊C8 | — | 6 | 1 | no | — |
| 207 | C3⋊C8 | — | 6 | 1 | no | — |
| 208 | C2×C32 | — | 2 | 2 | no | — |
| 209 | C2×C32 | #509 | 1 | 2 | yes | complemented |
| 210 | C2×C32 | C22×D8 | 1 | 1 | yes | characteristic |
| 211 | C3×D3 | — | 8 | 2 | no | — |
| 212 | C3×D3 | — | 8 | 4 | no | — |
| 213 | C24 | — | 12 | 1 | no | — |
| 214 | #41 | — | 6 | 4 | no | — |
| 215 | #41 | — | 12 | 2 | no | — |
| 216 | C2×Q8 | — | 6 | 1 | no | — |
| 217 | C2×D4 | — | 6 | 4 | no | — |
| 218 | C2×D4 | — | 6 | 2 | no | — |
| 219 | C2×D4 | — | 6 | 1 | no | — |
| 220 | C2×D4 | — | 12 | 1 | no | — |
| 221 | C2×D4 | — | 12 | 2 | no | — |
| 222 | C2×D4 | — | 12 | 1 | no | — |
| 223 | C22×C4 | — | 12 | 1 | no | — |
| 224 | C22×C4 | GO+(4,𝔽2) | 1 | 1 | yes | characteristic |
| 225 | Q16 | — | 9 | 2 | no | — |
| 226 | Q16 | — | 18 | 1 | no | — |
| 227 | SD16 | — | 18 | 4 | no | — |
| 228 | D8 | — | 9 | 2 | no | — |
| 229 | D8 | — | 9 | 4 | no | — |
| 230 | D8 | — | 18 | 2 | no | — |
| 231 | D8 | — | 18 | 4 | no | — |
| 232 | D8 | — | 18 | 1 | no | — |
| 233 | C2×C8 | — | 9 | 1 | no | — |
| 234 | C2×C8 | — | 9 | 2 | no | — |
| 235 | C2×C8 | — | 9 | 1 | no | — |
| 236 | C2×C8 | — | 9 | 2 | no | — |
| 237 | C16 | — | 9 | 4 | no | — |
| 238 | C22×C3 | — | 2 | 4 | no | — |
| 239 | C22×C3 | — | 2 | 2 | no | — |
| 240 | C22×C3 | — | 2 | 2 | no | — |
| 241 | C22×C3 | — | 2 | 1 | no | — |
| 242 | C22×C3 | — | 2 | 1 | no | — |
| 243 | C22×C3 | — | 4 | 2 | no | — |
| 244 | C22×C3 | — | 12 | 2 | no | — |
| 245 | C22×C3 | — | 12 | 4 | no | — |
| 246 | C22×C3 | — | 24 | 8 | no | — |
| 247 | C22×C3 | — | 24 | 4 | no | — |
| 248 | C22×C3 | — | 24 | 2 | no | — |
| 249 | C2×D3 | — | 4 | 2 | no | — |
| 250 | C2×D3 | — | 4 | 4 | no | — |
| 251 | C2×D3 | — | 8 | 8 | no | — |
| 252 | C2×D3 | — | 8 | 4 | no | — |
| 253 | C2×D3 | — | 8 | 2 | no | — |
| 254 | C3×C4 | — | 2 | 1 | no | — |
| 255 | C3×C4 | — | 2 | 1 | no | — |
| 256 | C3×C4 | — | 2 | 1 | no | — |
| 257 | C3×C4 | — | 2 | 2 | no | — |
| 258 | C3×C4 | — | 2 | 2 | no | — |
| 259 | C3×C4 | — | 2 | 1 | no | — |
| 260 | C3×C4 | — | 12 | 2 | no | — |
| 261 | Dic3 | — | 4 | 2 | no | — |
| 262 | C32 | C2×#509 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 263 | C23 | — | 12 | 4 | no | — |
| 264 | C23 | — | 12 | 1 | no | — |
| 265 | C23 | — | 12 | 2 | no | — |
| 266 | C23 | — | 24 | 4 | no | — |
| 267 | C23 | #3774 | 1 | 1 | yes | characteristic |
| 268 | Q8 | — | 6 | 2 | no | — |
| 269 | Q8 | — | 12 | 1 | no | — |
| 270 | D4 | — | 6 | 4 | no | — |
| 271 | D4 | — | 6 | 2 | no | — |
| 272 | D4 | — | 12 | 4 | no | — |
| 273 | D4 | — | 12 | 4 | no | — |
| 274 | D4 | — | 12 | 2 | no | — |
| 275 | D4 | — | 12 | 1 | no | — |
| 276 | C2×C4 | — | 12 | 1 | no | — |
| 277 | C2×C4 | — | 12 | 4 | no | — |
| 278 | C2×C4 | #3774 | 1 | 2 | yes | — |
| 279 | C2×C4 | #3774 | 1 | 1 | yes | characteristic |
| 280 | C2×C4 | C2×GO+(4,𝔽2) | 1 | 2 | yes | — |
| 281 | C2×C4 | C2×GO+(4,𝔽2) | 1 | 1 | yes | characteristic |
| 282 | C8 | — | 9 | 1 | no | — |
| 283 | C8 | — | 9 | 1 | no | — |
| 284 | C8 | — | 9 | 2 | no | — |
| 285 | C2×C3 | — | 2 | 4 | no | — |
| 286 | C2×C3 | — | 2 | 2 | no | — |
| 287 | C2×C3 | — | 2 | 2 | no | — |
| 288 | C2×C3 | — | 2 | 1 | no | — |
| 289 | C2×C3 | — | 2 | 1 | no | — |
| 290 | C2×C3 | — | 4 | 2 | no | — |
| 291 | C2×C3 | — | 24 | 4 | no | — |
| 292 | C2×C3 | — | 24 | 2 | no | — |
| 293 | D3 | — | 8 | 4 | no | — |
| 294 | D3 | — | 8 | 2 | no | — |
| 295 | C22 | — | 2 | 2 | no | — |
| 296 | C22 | — | 12 | 2 | no | — |
| 297 | C22 | — | 12 | 4 | no | — |
| 298 | C22 | — | 24 | 8 | no | — |
| 299 | C22 | — | 24 | 4 | no | — |
| 300 | C22 | — | 24 | 2 | no | — |
| 301 | C22 | C2×#3774 | 1 | 2 | yes | — |
| 302 | C22 | C2×#3774 | 1 | 1 | yes | characteristic |
| 303 | C4 | — | 12 | 2 | no | — |
| 304 | C4 | C2×#3774 | 1 | 2 | yes | — |
| 305 | C4 | C2×#3774 | 1 | 1 | yes | characteristic |
| 306 | C4 | C22×GO+(4,𝔽2) | 1 | 1 | yes | characteristic |
| 307 | C3 | — | 2 | 1 | no | — |
| 308 | C3 | — | 2 | 1 | no | — |
| 309 | C2 | — | 2 | 2 | no | — |
| 310 | C2 | — | 24 | 4 | no | — |
| 311 | C2 | — | 24 | 2 | no | — |
| 312 | C2 | #10593334 | 1 | 2 | yes | direct product factor |
| 313 | C2 | C22×#3774 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#63822 | C2 | semidirect |
| 2. C22×#3713 | C2 | semidirect |
| 3. C2×#63773 | C2 | semidirect |
| 4. C2×#63735 | C2 | semidirect |
| 5. #10593334 | C2 | direct (N × H) |
| 6. C2×#63734 | C2 | semidirect |
| 10. C2×#3718 | C22 | semidirect |
| 13. #63822 | C22 | semidirect |
| 17. C2×#3713 | C22 | semidirect |
| 18. C2×#3713 | C22 | semidirect |
| 19. #63773 | C22 | semidirect |
| 20. C2×#3708 | C22 | semidirect |
| 21. #63735 | C22 | semidirect |
| 22. #63734 | C22 | semidirect |
| 42. #3718 | C23 | semidirect |
| 48. #3713 | C23 | semidirect |
| 49. #3708 | C23 | semidirect |
| 209. C2×C32 | #509 | semidirect |
| 262. C32 | C2×#509 | semidirect |
| 312. C2 | #10593334 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63822 | 2 |
| C22×#3713 | 2 |
| C2×#63773 | 2 |
| C2×#63735 | 2 |
| #10593334 | 2 |
| C2×#63734 | 2 |
| C2×#509 | 9 |