Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1089 conjugacy classes of subgroups; only the 164 normal subgroups are shown.
This group has 1089 conjugacy classes of subgroups — too many to draw. Only its 164 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⋊D3×#125 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #10594008 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | C3×#5067 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #10590593 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #10590554 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #10590322 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #10590275 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | D3×#490 | — | 3 | 2 | no | maximal |
| 9 | C2×#3802 | — | 2 | 2 | no | — |
| 10 | C2×#3802 | C22 | 1 | 2 | yes | — |
| 11 | C32×#125 | C22 | 1 | 1 | yes | characteristic, complemented |
| 12 | C4⋊C4×C3⋊D3 | — | 2 | 2 | no | — |
| 13 | C4⋊C4×C3⋊D3 | C22 | 1 | 2 | yes | — |
| 14 | #64099 | C22 | 1 | 2 | yes | complemented |
| 15 | #64098 | — | 2 | 2 | no | — |
| 16 | C42×C3⋊D3 | C22 | 1 | 1 | yes | characteristic |
| 17 | #64079 | C22 | 1 | 1 | yes | characteristic, complemented |
| 18 | C3×#874 | C22 | 1 | 2 | yes | — |
| 19 | #63914 | — | 2 | 2 | no | — |
| 20 | #63914 | C22 | 1 | 2 | yes | — |
| 21 | C2×#3710 | C22 | 1 | 2 | yes | — |
| 22 | C3×#809 | C22 | 1 | 8 | yes | complemented |
| 23 | C3×#803 | C22 | 1 | 2 | yes | complemented |
| 24 | #63563 | C22 | 1 | 8 | yes | complemented |
| 25 | #63555 | C22 | 1 | 2 | yes | complemented |
| 26 | D3×#127 | — | 3 | 2 | no | — |
| 27 | D3×#125 | — | 3 | 2 | no | — |
| 28 | D3×#125 | — | 6 | 1 | no | — |
| 29 | C3×#490 | — | 3 | 2 | no | — |
| 30 | #5071 | — | 3 | 2 | no | — |
| 31 | #5067 | D3 | 1 | 2 | yes | complemented |
| 32 | D3×#102 | — | 3 | 8 | no | — |
| 33 | #4764 | — | 3 | 8 | no | — |
| 34 | #4713 | — | 3 | 2 | no | — |
| 35 | D3×#97 | — | 3 | 2 | no | — |
| 36 | C22×D32 | — | 2 | 2 | no | — |
| 37 | C2×C4×C3⋊D3 | — | 2 | 2 | no | — |
| 38 | C2×C4×C3⋊D3 | D4 | 1 | 2 | yes | — |
| 39 | C2×C4×C3⋊D3 | C23 | 1 | 1 | yes | characteristic |
| 40 | C2×C3×D12 | — | 2 | 4 | no | — |
| 41 | C2×C3×D12 | C23 | 1 | 4 | yes | — |
| 42 | C2×#625 | — | 2 | 4 | no | — |
| 43 | C2×#625 | — | 2 | 2 | no | — |
| 44 | #3802 | — | 2 | 8 | no | — |
| 45 | #3802 | — | 4 | 8 | no | — |
| 46 | C32×C4⋊C4 | — | 2 | 2 | no | — |
| 47 | C32×C4⋊C4 | C23 | 1 | 2 | yes | — |
| 48 | C32×C42 | C23 | 1 | 1 | yes | characteristic |
| 49 | C4⋊(C3⋊Dic3) | — | 2 | 2 | no | — |
| 50 | C4⋊(C3⋊Dic3) | C23 | 1 | 2 | yes | — |
| 51 | #3750 | — | 2 | 2 | no | — |
| 52 | #3750 | — | 2 | 2 | no | — |
| 53 | #3750 | — | 2 | 2 | no | — |
| 54 | C4×C3⋊Dic3 | D4 | 1 | 2 | yes | — |
| 55 | C4×C3⋊Dic3 | C23 | 1 | 1 | yes | characteristic |
| 56 | C2×C3×C3⋊C8 | C23 | 1 | 4 | yes | — |
| 57 | #3710 | — | 2 | 4 | no | — |
| 58 | C2×#490 | — | 9 | 1 | no | Sylow |
| 59 | C2×D3×D4 | — | 3 | 4 | no | — |
| 60 | C2×D3×D4 | — | 6 | 4 | no | — |
| 61 | C3×#127 | — | 3 | 2 | no | — |
| 62 | C3×#125 | — | 2 | 1 | no | — |
| 63 | C3×#125 | C2×D3 | 1 | 2 | yes | complemented |
| 64 | #940 | — | 3 | 4 | no | — |
| 65 | #940 | — | 6 | 4 | no | — |
| 66 | C2×D3×C8 | — | 3 | 4 | no | — |
| 67 | D3×C4⋊C4 | — | 3 | 4 | no | — |
| 68 | D3×C4⋊C4 | — | 6 | 2 | no | — |
| 69 | D3×C4⋊C4 | — | 6 | 4 | no | — |
| 70 | D3×C4⋊C4 | — | 6 | 4 | no | — |
| 71 | #890 | — | 3 | 4 | no | — |
| 72 | #890 | — | 6 | 2 | no | — |
| 73 | #889 | — | 6 | 4 | no | — |
| 74 | #889 | — | 6 | 4 | no | — |
| 75 | #874 | C2×D3 | 1 | 2 | yes | — |
| 76 | C42×D3 | — | 3 | 2 | no | — |
| 77 | C42×D3 | — | 6 | 1 | no | — |
| 78 | #870 | — | 3 | 2 | no | — |
| 79 | #870 | — | 6 | 1 | no | — |
| 80 | C3×#102 | — | 3 | 8 | no | — |
| 81 | C3×#97 | — | 3 | 2 | no | — |
| 82 | #832 | — | 3 | 8 | no | — |
| 83 | #821 | — | 3 | 8 | no | — |
| 84 | #815 | — | 3 | 4 | no | — |
| 85 | #809 | C2×D3 | 1 | 8 | yes | complemented |
| 86 | #803 | C2×D3 | 1 | 2 | yes | complemented |
| 87 | C22×C3⋊D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 88 | C22×C3×D3 | — | 2 | 4 | no | — |
| 89 | C2×D32 | — | 4 | 4 | no | — |
| 90 | C2×D32 | — | 4 | 8 | no | — |
| 91 | C2×C32×C4 | — | 2 | 2 | no | — |
| 92 | C2×C32×C4 | C2×D4 | 1 | 2 | yes | — |
| 93 | C2×C32×C4 | C24 | 1 | 1 | yes | characteristic |
| 94 | C2×C3⋊Dic3 | — | 2 | 2 | no | — |
| 95 | C2×C3⋊Dic3 | C2×D4 | 1 | 2 | yes | — |
| 96 | C2×C3⋊Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 97 | C4×C3⋊D3 | — | 2 | 4 | no | — |
| 98 | C4×C3⋊D3 | — | 4 | 4 | no | — |
| 99 | C4×C3⋊D3 | #41 | 1 | 4 | yes | — |
| 100 | C3×D12 | — | 2 | 8 | no | — |
| 101 | C3×D12 | — | 4 | 8 | no | — |
| 102 | #625 | — | 4 | 8 | no | — |
| 103 | #625 | — | 4 | 4 | no | — |
| 104 | C3×C3⋊C8 | — | 2 | 4 | no | — |
| 105 | C2×#127 | — | 9 | 1 | no | — |
| 106 | C2×#125 | — | 9 | 1 | no | — |
| 107 | #490 | — | 3 | 2 | no | — |
| 108 | #490 | — | 9 | 2 | no | — |
| 109 | #490 | — | 9 | 4 | no | — |
| 110 | C2×#102 | — | 9 | 4 | no | — |
| 111 | C2×#97 | — | 9 | 1 | no | — |
| 112 | C23×D3 | — | 6 | 4 | no | — |
| 113 | C2×C3×D4 | — | 3 | 4 | no | — |
| 114 | C2×C3×D4 | — | 6 | 4 | no | — |
| 115 | C2×#67 | — | 6 | 8 | no | — |
| 116 | C2×#67 | — | 6 | 4 | no | — |
| 117 | D3×D4 | — | 6 | 16 | no | — |
| 118 | D3×D4 | — | 12 | 16 | no | — |
| 119 | C2×D12 | — | 2 | 4 | no | — |
| 120 | C2×D12 | C22×D3 | 1 | 4 | yes | — |
| 121 | C2×C4×D3 | — | 3 | 2 | no | — |
| 122 | C2×C4×D3 | — | 3 | 4 | no | — |
| 123 | C2×C4×D3 | — | 6 | 1 | no | — |
| 124 | C2×C4×D3 | — | 6 | 2 | no | — |
| 125 | C2×C4×D3 | — | 6 | 4 | no | — |
| 126 | C2×C4×D3 | — | 6 | 4 | no | — |
| 127 | C2×C3×C8 | — | 3 | 4 | no | — |
| 128 | C3×C4⋊C4 | — | 2 | 4 | no | — |
| 129 | C3×C4⋊C4 | — | 2 | 4 | no | — |
| 130 | C3×C4⋊C4 | — | 2 | 2 | no | — |
| 131 | C3×C4⋊C4 | C22×D3 | 1 | 4 | yes | — |
| 132 | C3×C42 | — | 2 | 1 | no | — |
| 133 | C3×C42 | C22×D3 | 1 | 2 | yes | — |
| 134 | C4⋊Dic3 | — | 3 | 4 | no | — |
| 135 | C4⋊Dic3 | — | 6 | 2 | no | — |
| 136 | C4⋊Dic3 | — | 6 | 4 | no | — |
| 137 | C4⋊Dic3 | — | 6 | 4 | no | — |
| 138 | Dic3⋊C4 | — | 6 | 4 | no | — |
| 139 | Dic3⋊C4 | — | 6 | 4 | no | — |
| 140 | Dic3⋊C4 | — | 6 | 4 | no | — |
| 141 | Dic3⋊C4 | — | 6 | 4 | no | — |
| 142 | Dic3⋊C4 | — | 6 | 4 | no | — |
| 143 | Dic3⋊C4 | — | 6 | 4 | no | — |
| 144 | C4×Dic3 | — | 3 | 4 | no | — |
| 145 | C4×Dic3 | — | 3 | 2 | no | — |
| 146 | C4×Dic3 | — | 6 | 2 | no | — |
| 147 | C4×Dic3 | — | 6 | 1 | no | — |
| 148 | C2×C3⋊C8 | C22×D3 | 1 | 4 | yes | — |
| 149 | D3×C8 | — | 6 | 8 | no | — |
| 150 | C22×C32 | C22×D4 | 1 | 1 | yes | characteristic |
| 151 | C2×C3⋊D3 | #124 | 1 | 2 | yes | — |
| 152 | C2×C3⋊D3 | AGL(1,ℤ/8) | 1 | 4 | yes | — |
| 153 | C2×C3×D3 | — | 4 | 4 | no | — |
| 154 | C2×C3×D3 | — | 4 | 8 | no | — |
| 155 | D32 | — | 8 | 8 | no | — |
| 156 | C32×C4 | — | 2 | 2 | no | — |
| 157 | C32×C4 | — | 4 | 2 | no | — |
| 158 | C32×C4 | C2×#41 | 1 | 2 | yes | — |
| 159 | C3⋊Dic3 | — | 2 | 2 | no | — |
| 160 | C3⋊Dic3 | — | 4 | 2 | no | — |
| 161 | C3⋊Dic3 | #124 | 1 | 2 | yes | — |
| 162 | C22×D4 | — | 9 | 2 | no | — |
| 163 | C22×D4 | — | 18 | 2 | no | — |
| 164 | C22×C8 | — | 9 | 2 | no | — |
| 165 | #127 | — | 3 | 2 | no | — |
| 166 | #127 | — | 9 | 2 | no | — |
| 167 | #127 | — | 18 | 2 | no | — |
| 168 | #125 | — | 9 | 2 | no | — |
| 169 | #125 | — | 9 | 1 | no | — |
| 170 | #125 | — | 18 | 2 | no | — |
| 171 | #125 | D32 | 1 | 1 | yes | characteristic, complemented |
| 172 | C2×C4⋊C4 | — | 9 | 2 | no | — |
| 173 | C2×C4⋊C4 | — | 18 | 2 | no | — |
| 174 | C2×C42 | — | 9 | 1 | no | — |
| 175 | #102 | — | 3 | 8 | no | — |
| 176 | #102 | — | 9 | 8 | no | — |
| 177 | #97 | — | 3 | 2 | no | — |
| 178 | #97 | — | 9 | 2 | no | — |
| 179 | C23×C3 | — | 6 | 4 | no | — |
| 180 | C22×D3 | — | 2 | 4 | no | — |
| 181 | C22×D3 | — | 3 | 2 | no | — |
| 182 | C22×D3 | — | 6 | 1 | no | — |
| 183 | C22×D3 | — | 12 | 8 | no | — |
| 184 | C22×D3 | — | 12 | 16 | no | — |
| 185 | C3×D4 | — | 6 | 8 | no | — |
| 186 | C3×D4 | — | 12 | 8 | no | — |
| 187 | C2×C3×C4 | — | 2 | 4 | no | — |
| 188 | C2×C3×C4 | — | 2 | 4 | no | — |
| 189 | C2×C3×C4 | — | 2 | 1 | no | — |
| 190 | C2×C3×C4 | — | 2 | 2 | no | — |
| 191 | C2×C3×C4 | D3×D4 | 1 | 4 | yes | — |
| 192 | C2×C3×C4 | C23×D3 | 1 | 2 | yes | — |
| 193 | #67 | — | 12 | 8 | no | — |
| 194 | #67 | — | 12 | 16 | no | — |
| 195 | C2×Dic3 | — | 3 | 2 | no | — |
| 196 | C2×Dic3 | — | 3 | 4 | no | — |
| 197 | C2×Dic3 | — | 6 | 1 | no | — |
| 198 | C2×Dic3 | — | 6 | 2 | no | — |
| 199 | C2×Dic3 | — | 6 | 4 | no | — |
| 200 | C2×Dic3 | — | 6 | 4 | no | — |
| 201 | D12 | — | 2 | 8 | no | — |
| 202 | D12 | — | 4 | 8 | no | — |
| 203 | C4×D3 | — | 3 | 8 | no | — |
| 204 | C4×D3 | — | 6 | 4 | no | — |
| 205 | C4×D3 | — | 6 | 8 | no | — |
| 206 | C4×D3 | — | 12 | 4 | no | — |
| 207 | C4×D3 | — | 12 | 8 | no | — |
| 208 | C4×D3 | — | 12 | 8 | no | — |
| 209 | C3×C8 | — | 6 | 4 | no | — |
| 210 | C3⋊C8 | — | 2 | 4 | no | — |
| 211 | C2×C32 | C2×#124 | 1 | 1 | yes | characteristic |
| 212 | C2×C32 | C2×AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 213 | C3⋊D3 | #490 | 1 | 4 | yes | complemented |
| 214 | C3×D3 | — | 8 | 4 | no | — |
| 215 | C24 | — | 18 | 2 | no | — |
| 216 | C2×D4 | — | 3 | 4 | no | — |
| 217 | C2×D4 | — | 6 | 4 | no | — |
| 218 | C2×D4 | — | 18 | 8 | no | — |
| 219 | C2×D4 | — | 18 | 4 | no | — |
| 220 | C2×D4 | — | 18 | 2 | no | — |
| 221 | C2×D4 | — | 36 | 8 | no | — |
| 222 | C22×C4 | — | 9 | 1 | no | — |
| 223 | C22×C4 | — | 9 | 2 | no | — |
| 224 | C22×C4 | — | 18 | 2 | no | — |
| 225 | C2×C8 | — | 3 | 4 | no | — |
| 226 | C2×C8 | — | 18 | 4 | no | — |
| 227 | C4⋊C4 | — | 2 | 2 | no | — |
| 228 | C4⋊C4 | — | 9 | 2 | no | — |
| 229 | C4⋊C4 | — | 18 | 2 | no | — |
| 230 | C4⋊C4 | — | 18 | 2 | no | — |
| 231 | C4⋊C4 | — | 18 | 2 | no | — |
| 232 | C4⋊C4 | — | 18 | 2 | no | — |
| 233 | C4⋊C4 | C2×D32 | 1 | 2 | yes | — |
| 234 | C42 | — | 9 | 1 | no | — |
| 235 | C42 | — | 9 | 2 | no | — |
| 236 | C42 | C2×D32 | 1 | 1 | yes | characteristic |
| 237 | C22×C3 | — | 2 | 1 | no | — |
| 238 | C22×C3 | — | 12 | 4 | no | — |
| 239 | C22×C3 | — | 12 | 8 | no | — |
| 240 | C22×C3 | C2×D3×D4 | 1 | 2 | yes | — |
| 241 | C2×D3 | — | 3 | 4 | no | — |
| 242 | C2×D3 | — | 3 | 8 | no | — |
| 243 | C2×D3 | — | 4 | 4 | no | — |
| 244 | C2×D3 | — | 4 | 8 | no | — |
| 245 | C2×D3 | — | 6 | 2 | no | — |
| 246 | C2×D3 | — | 6 | 4 | no | — |
| 247 | C2×D3 | — | 24 | 16 | no | — |
| 248 | C3×C4 | — | 2 | 4 | no | — |
| 249 | C3×C4 | — | 2 | 2 | no | — |
| 250 | C3×C4 | — | 4 | 2 | no | — |
| 251 | C3×C4 | — | 4 | 4 | no | — |
| 252 | C3×C4 | — | 4 | 4 | no | — |
| 253 | C3×C4 | D3×#41 | 1 | 4 | yes | — |
| 254 | Dic3 | — | 3 | 4 | no | — |
| 255 | Dic3 | — | 6 | 2 | no | — |
| 256 | Dic3 | — | 6 | 4 | no | — |
| 257 | Dic3 | — | 12 | 2 | no | — |
| 258 | Dic3 | — | 12 | 4 | no | — |
| 259 | Dic3 | — | 12 | 4 | no | — |
| 260 | C32 | C2×#490 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 261 | C23 | — | 6 | 4 | no | — |
| 262 | C23 | — | 9 | 1 | no | — |
| 263 | C23 | — | 36 | 4 | no | — |
| 264 | C23 | — | 36 | 8 | no | — |
| 265 | D4 | — | 6 | 8 | no | — |
| 266 | D4 | — | 12 | 8 | no | — |
| 267 | D4 | — | 36 | 4 | no | — |
| 268 | D4 | — | 36 | 8 | no | — |
| 269 | C2×C4 | — | 2 | 2 | no | — |
| 270 | C2×C4 | — | 9 | 1 | no | — |
| 271 | C2×C4 | — | 9 | 4 | no | — |
| 272 | C2×C4 | — | 9 | 2 | no | — |
| 273 | C2×C4 | — | 18 | 4 | no | — |
| 274 | C2×C4 | — | 18 | 2 | no | — |
| 275 | C2×C4 | — | 36 | 4 | no | — |
| 276 | C2×C4 | #3811 | 1 | 2 | yes | — |
| 277 | C2×C4 | C22×D32 | 1 | 1 | yes | characteristic |
| 278 | C8 | — | 6 | 4 | no | — |
| 279 | C2×C3 | — | 2 | 1 | no | — |
| 280 | C2×C3 | — | 2 | 2 | no | — |
| 281 | C2×C3 | — | 24 | 4 | no | — |
| 282 | C2×C3 | D3×#124 | 1 | 2 | yes | — |
| 283 | C2×C3 | D3×AGL(1,ℤ/8) | 1 | 4 | yes | — |
| 284 | D3 | — | 3 | 8 | no | — |
| 285 | D3 | — | 6 | 4 | no | — |
| 286 | D3 | — | 8 | 4 | no | — |
| 287 | C22 | — | 9 | 2 | no | — |
| 288 | C22 | — | 9 | 4 | no | — |
| 289 | C22 | — | 12 | 4 | no | — |
| 290 | C22 | — | 12 | 8 | no | — |
| 291 | C22 | — | 72 | 8 | no | — |
| 292 | C22 | C2×#3811 | 1 | 1 | yes | characteristic |
| 293 | C4 | — | 2 | 2 | no | — |
| 294 | C4 | — | 4 | 2 | no | — |
| 295 | C4 | — | 9 | 2 | no | — |
| 296 | C4 | — | 18 | 2 | no | — |
| 297 | C4 | — | 36 | 2 | no | — |
| 298 | C4 | #64319 | 1 | 2 | yes | — |
| 299 | C3 | — | 2 | 1 | no | — |
| 300 | C3 | D3×#490 | 1 | 2 | yes | complemented |
| 301 | C2 | — | 9 | 4 | no | — |
| 302 | C2 | — | 24 | 4 | no | — |
| 303 | C2 | #10595432 | 1 | 1 | yes | characteristic |
| 304 | C2 | #10595458 | 1 | 2 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3⋊D3×#125 | C2 | semidirect |
| 3. C3×#5067 | C2 | semidirect |
| 4. #10590593 | C2 | semidirect |
| 5. #10590554 | C2 | semidirect |
| 6. #10590322 | C2 | semidirect |
| 7. #10590275 | C2 | semidirect |
| 11. C32×#125 | C22 | semidirect |
| 14. #64099 | C22 | semidirect |
| 17. #64079 | C22 | semidirect |
| 22. C3×#809 | C22 | semidirect |
| 23. C3×#803 | C22 | semidirect |
| 24. #63563 | C22 | semidirect |
| 25. #63555 | C22 | semidirect |
| 31. #5067 | D3 | semidirect |
| 63. C3×#125 | C2×D3 | semidirect |
| 85. #809 | C2×D3 | semidirect |
| 86. #803 | C2×D3 | semidirect |
| 171. #125 | D32 | semidirect |
| 213. C3⋊D3 | #490 | semidirect |
| 260. C32 | C2×#490 | semidirect |
| 300. C3 | D3×#490 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3⋊D3×#125 | 2 |
| #10594008 | 2 |
| C3×#5067 | 2 |
| #10590593 | 2 |
| #10590554 | 2 |
| #10590322 | 2 |
| #10590275 | 2 |
| D3×#490 | 3 |