Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
763 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 763 conjugacy classes of subgroups — too many to draw. Only its 120 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 | C22×#3718 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×#63833 | C2 | 1 | 2 | yes | maximal |
| 3 | #10592828 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | C2×C3×#824 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #10589165 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #70125 | — | 3 | 2 | no | maximal |
| 7 | C2×#3828 | C22 | 1 | 1 | yes | characteristic |
| 8 | C22×C3×Dic6 | C22 | 1 | 2 | yes | — |
| 9 | C2×C32×M16 | C22 | 1 | 1 | yes | characteristic |
| 10 | C22×C3⋊(C3⋊C8) | C22 | 1 | 1 | yes | characteristic |
| 11 | C2×C3×#208 | C22 | 1 | 2 | yes | — |
| 12 | C2×#3719 | — | 2 | 2 | no | — |
| 13 | C2×#3718 | — | 2 | 4 | no | — |
| 14 | C2×#3718 | — | 2 | 2 | no | — |
| 15 | #63833 | — | 2 | 4 | no | — |
| 16 | #63833 | — | 2 | 4 | no | — |
| 17 | C2×#3717 | — | 2 | 2 | no | — |
| 18 | #63647 | — | 2 | 2 | no | — |
| 19 | C3×#824 | — | 2 | 4 | no | — |
| 20 | C22×#216 | — | 3 | 2 | no | — |
| 21 | C2×#942 | — | 3 | 2 | no | — |
| 22 | C2×#909 | — | 3 | 2 | no | — |
| 23 | C2×C3×#101 | — | 3 | 2 | no | — |
| 24 | C2×#824 | D3 | 1 | 2 | yes | complemented |
| 25 | #5129 | — | 3 | 2 | no | — |
| 26 | #5129 | — | 6 | 1 | no | — |
| 27 | #4558 | — | 3 | 2 | no | — |
| 28 | C22×C32×C4 | C23 | 1 | 1 | yes | characteristic |
| 29 | C2×#638 | — | 2 | 1 | no | — |
| 30 | #3828 | — | 2 | 2 | no | — |
| 31 | #3828 | — | 2 | 2 | no | — |
| 32 | C2×C4⋊(C3⋊D3) | D4 | 1 | 1 | yes | characteristic |
| 33 | C2×C4×C3⋊D3 | — | 2 | 1 | no | — |
| 34 | C2×#634 | D4 | 1 | 1 | yes | characteristic |
| 35 | C22×C3×Dic3 | — | 2 | 2 | no | — |
| 36 | C2×C3×Dic6 | — | 2 | 2 | no | — |
| 37 | C2×C3×Dic6 | — | 2 | 2 | no | — |
| 38 | C2×C3×Dic6 | — | 2 | 2 | no | — |
| 39 | C2×C3×Dic6 | — | 2 | 2 | no | — |
| 40 | C2×C3×Dic6 | — | 2 | 2 | no | — |
| 41 | C2×C3×Dic6 | D4 | 1 | 4 | yes | — |
| 42 | C32×M16 | — | 2 | 2 | no | — |
| 43 | C2×C32×C8 | — | 2 | 1 | no | — |
| 44 | C2×C3⋊(C3⋊C8) | — | 2 | 2 | no | — |
| 45 | C2×C3⋊(C3⋊C8) | D4 | 1 | 2 | yes | — |
| 46 | C3×#208 | — | 2 | 2 | no | — |
| 47 | C3×#208 | D4 | 1 | 4 | yes | — |
| 48 | C2×C3×C3⋊C8 | — | 2 | 2 | no | — |
| 49 | #3719 | — | 2 | 8 | no | — |
| 50 | #3718 | — | 2 | 8 | no | — |
| 51 | #3717 | — | 2 | 8 | no | — |
| 52 | #2020 | — | 9 | 1 | no | Sylow |
| 53 | C22×C3×Q8 | — | 3 | 2 | no | — |
| 54 | C2×#235 | — | 3 | 2 | no | — |
| 55 | C2×#235 | — | 6 | 1 | no | — |
| 56 | C22×Dic6 | C2×D3 | 1 | 2 | yes | — |
| 57 | C2×C3×M16 | — | 2 | 1 | no | — |
| 58 | C2×C3×M16 | — | 3 | 2 | no | — |
| 59 | C2×C3×M16 | C2×D3 | 1 | 2 | yes | — |
| 60 | C2×#216 | — | 6 | 2 | no | — |
| 61 | C2×#216 | — | 6 | 4 | no | — |
| 62 | C2×#216 | — | 6 | 4 | no | — |
| 63 | C2×#216 | — | 6 | 4 | no | — |
| 64 | #942 | — | 6 | 4 | no | — |
| 65 | #942 | — | 6 | 4 | no | — |
| 66 | C2×#215 | — | 6 | 2 | no | — |
| 67 | C2×#208 | C2×D3 | 1 | 2 | yes | — |
| 68 | C22×C3⋊C8 | — | 3 | 2 | no | — |
| 69 | C22×C3⋊C8 | — | 6 | 1 | no | — |
| 70 | #909 | — | 6 | 4 | no | — |
| 71 | #909 | — | 6 | 4 | no | — |
| 72 | C2×Dic12 | — | 6 | 2 | no | — |
| 73 | C2×#204 | — | 6 | 2 | no | — |
| 74 | C3×#101 | — | 6 | 4 | no | — |
| 75 | #824 | — | 2 | 4 | no | — |
| 76 | (C2×D3)⋊C8 | — | 6 | 4 | no | — |
| 77 | (C2×D3)⋊C8 | — | 6 | 4 | no | — |
| 78 | C23×C32 | #41 | 1 | 1 | yes | characteristic |
| 79 | C22×C3⋊D3 | — | 2 | 1 | no | — |
| 80 | C2×C32×C4 | C2×D4 | 1 | 2 | yes | — |
| 81 | C2×C32×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 82 | C2×C32×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 83 | C2×C32×C4 | C2×D4 | 1 | 2 | yes | — |
| 84 | #638 | — | 4 | 2 | no | — |
| 85 | C2×C3⋊Dic3 | — | 2 | 1 | no | — |
| 86 | C4⋊(C3⋊D3) | — | 2 | 2 | no | — |
| 87 | C4×C3⋊D3 | — | 4 | 1 | no | — |
| 88 | C4×C3⋊D3 | — | 4 | 1 | no | — |
| 89 | #634 | — | 2 | 2 | no | — |
| 90 | C2×C3×Dic3 | — | 2 | 4 | no | — |
| 91 | C2×C3×Dic3 | — | 4 | 2 | no | — |
| 92 | C2×C3×Dic3 | — | 4 | 2 | no | — |
| 93 | C3×Dic6 | — | 2 | 4 | no | — |
| 94 | C3×Dic6 | — | 2 | 4 | no | — |
| 95 | C3×Dic6 | — | 4 | 2 | no | — |
| 96 | C3×Dic6 | — | 4 | 2 | no | — |
| 97 | C32×C8 | — | 4 | 1 | no | — |
| 98 | C3⋊(C3⋊C8) | — | 2 | 2 | no | — |
| 99 | C3×C3⋊C8 | — | 2 | 4 | no | — |
| 100 | C2×#137 | — | 9 | 2 | no | — |
| 101 | C22×Q16 | — | 9 | 1 | no | — |
| 102 | C2×#101 | — | 3 | 2 | no | — |
| 103 | #408 | — | 9 | 1 | no | — |
| 104 | #341 | — | 9 | 1 | no | — |
| 105 | C2×C3×Q8 | — | 3 | 4 | no | — |
| 106 | C2×C3×Q8 | — | 6 | 2 | no | — |
| 107 | C2×C3×Q8 | — | 6 | 2 | no | — |
| 108 | C2×C3×Q8 | — | 6 | 2 | no | — |
| 109 | C2×C3×Q8 | — | 6 | 2 | no | — |
| 110 | C2×C3×Q8 | — | 6 | 2 | no | — |
| 111 | C22×C3×C4 | — | 2 | 1 | no | — |
| 112 | C22×C3×C4 | — | 6 | 2 | no | — |
| 113 | C22×C3×C4 | C22×D3 | 1 | 2 | yes | — |
| 114 | C2×#67 | — | 6 | 2 | no | — |
| 115 | C2×#67 | — | 6 | 2 | no | — |
| 116 | C22×Dic3 | — | 2 | 2 | no | — |
| 117 | #235 | — | 6 | 2 | no | — |
| 118 | #235 | — | 6 | 2 | no | — |
| 119 | #235 | — | 6 | 2 | no | — |
| 120 | #235 | — | 6 | 2 | no | — |
| 121 | #235 | — | 12 | 2 | no | — |
| 122 | #235 | — | 12 | 2 | no | — |
| 123 | C2×D12 | — | 3 | 2 | no | — |
| 124 | C2×D12 | — | 6 | 1 | no | — |
| 125 | C2×C4×D3 | — | 6 | 2 | no | — |
| 126 | C2×C4×D3 | — | 6 | 2 | no | — |
| 127 | C2×Dic6 | — | 2 | 2 | no | — |
| 128 | C2×Dic6 | — | 2 | 2 | no | — |
| 129 | C2×Dic6 | — | 2 | 2 | no | — |
| 130 | C2×Dic6 | — | 2 | 2 | no | — |
| 131 | C2×Dic6 | — | 2 | 2 | no | — |
| 132 | C2×Dic6 | — | 3 | 2 | no | — |
| 133 | C2×Dic6 | — | 6 | 1 | no | — |
| 134 | C2×Dic6 | D12 | 1 | 4 | yes | — |
| 135 | C3×M16 | — | 2 | 2 | no | — |
| 136 | C3×M16 | — | 2 | 2 | no | — |
| 137 | C3×M16 | — | 3 | 4 | no | — |
| 138 | C3×M16 | — | 4 | 2 | no | — |
| 139 | C3×M16 | — | 6 | 2 | no | — |
| 140 | C2×C3×C8 | — | 2 | 2 | no | — |
| 141 | C2×C3×C8 | — | 2 | 2 | no | — |
| 142 | C2×C3×C8 | — | 6 | 2 | no | — |
| 143 | #216 | — | 6 | 8 | no | — |
| 144 | #216 | — | 6 | 16 | no | — |
| 145 | #215 | — | 6 | 8 | no | — |
| 146 | #208 | — | 2 | 2 | no | — |
| 147 | #208 | #67 | 1 | 4 | yes | — |
| 148 | C2×C3⋊C8 | — | 2 | 2 | no | — |
| 149 | C2×C3⋊C8 | — | 3 | 4 | no | — |
| 150 | C2×C3⋊C8 | — | 6 | 2 | no | — |
| 151 | C2×C3⋊C8 | — | 6 | 2 | no | — |
| 152 | C2×C3⋊C8 | — | 6 | 2 | no | — |
| 153 | C2×C3⋊C8 | — | 12 | 2 | no | — |
| 154 | Dic12 | — | 6 | 8 | no | — |
| 155 | #204 | — | 6 | 8 | no | — |
| 156 | C22×C32 | — | 2 | 2 | no | — |
| 157 | C22×C32 | #121 | 1 | 1 | yes | characteristic |
| 158 | C22×C32 | #121 | 1 | 2 | yes | — |
| 159 | C2×C3⋊D3 | — | 4 | 1 | no | — |
| 160 | C2×C3⋊D3 | — | 4 | 2 | no | — |
| 161 | C32×C4 | #120 | 1 | 1 | yes | characteristic |
| 162 | C32×C4 | #120 | 1 | 2 | yes | — |
| 163 | C32×C4 | #127 | 1 | 1 | yes | characteristic |
| 164 | C3⋊Dic3 | — | 4 | 1 | no | — |
| 165 | C3×Dic3 | — | 4 | 4 | no | — |
| 166 | C2×#41 | — | 9 | 1 | no | — |
| 167 | C22×Q8 | — | 3 | 2 | no | — |
| 168 | #137 | — | 18 | 4 | no | — |
| 169 | #137 | — | 18 | 4 | no | — |
| 170 | C2×Q16 | — | 18 | 2 | no | — |
| 171 | C2×Q16 | — | 18 | 2 | no | — |
| 172 | C2×Q16 | — | 18 | 4 | no | — |
| 173 | C2×SD16 | — | 18 | 2 | no | — |
| 174 | C2×M16 | — | 3 | 2 | no | — |
| 175 | C2×M16 | D32 | 1 | 1 | yes | characteristic |
| 176 | C22×C8 | — | 9 | 1 | no | — |
| 177 | #101 | — | 6 | 4 | no | — |
| 178 | C22⋊C8 | — | 18 | 2 | no | — |
| 179 | C23×C3 | — | 2 | 1 | no | — |
| 180 | C23×C3 | #235 | 1 | 2 | yes | — |
| 181 | C22×D3 | — | 6 | 2 | no | — |
| 182 | C22×D3 | — | 6 | 2 | no | — |
| 183 | C3×Q8 | — | 6 | 4 | no | — |
| 184 | C3×Q8 | — | 6 | 4 | no | — |
| 185 | C3×Q8 | — | 12 | 2 | no | — |
| 186 | C3×Q8 | — | 12 | 2 | 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 | — | 2 | 1 | no | — |
| 191 | C2×C3×C4 | — | 6 | 4 | no | — |
| 192 | C2×C3×C4 | — | 12 | 2 | no | — |
| 193 | C2×C3×C4 | — | 12 | 2 | no | — |
| 194 | C2×C3×C4 | C2×D12 | 1 | 2 | yes | — |
| 195 | C2×C3×C4 | D3×D4 | 1 | 2 | yes | — |
| 196 | C2×C3×C4 | D3×D4 | 1 | 2 | yes | — |
| 197 | C2×C3×C4 | D3×D4 | 1 | 2 | yes | — |
| 198 | C2×C3×C4 | D3×D4 | 1 | 2 | yes | — |
| 199 | C2×C3×C4 | C2×#67 | 1 | 2 | yes | — |
| 200 | #67 | — | 12 | 4 | no | — |
| 201 | #67 | — | 12 | 2 | no | — |
| 202 | #67 | — | 12 | 2 | no | — |
| 203 | C2×Dic3 | — | 2 | 4 | no | — |
| 204 | C2×Dic3 | — | 4 | 2 | no | — |
| 205 | C2×Dic3 | — | 4 | 2 | no | — |
| 206 | C2×Dic3 | — | 6 | 2 | no | — |
| 207 | C2×Dic3 | — | 6 | 2 | no | — |
| 208 | D12 | — | 6 | 2 | no | — |
| 209 | D12 | — | 6 | 2 | no | — |
| 210 | D12 | — | 12 | 2 | no | — |
| 211 | C4×D3 | — | 12 | 2 | no | — |
| 212 | C4×D3 | — | 12 | 2 | no | — |
| 213 | C4×D3 | — | 12 | 2 | no | — |
| 214 | C4×D3 | — | 12 | 2 | no | — |
| 215 | Dic6 | — | 2 | 4 | no | — |
| 216 | Dic6 | — | 2 | 4 | no | — |
| 217 | Dic6 | — | 4 | 2 | no | — |
| 218 | Dic6 | — | 4 | 2 | no | — |
| 219 | Dic6 | — | 6 | 2 | no | — |
| 220 | Dic6 | — | 6 | 2 | no | — |
| 221 | Dic6 | — | 12 | 2 | no | — |
| 222 | C3×C8 | — | 4 | 2 | no | — |
| 223 | C3×C8 | — | 4 | 2 | no | — |
| 224 | C3×C8 | — | 6 | 4 | no | — |
| 225 | C3⋊C8 | — | 2 | 4 | no | — |
| 226 | C3⋊C8 | — | 6 | 4 | no | — |
| 227 | C3⋊C8 | — | 12 | 2 | no | — |
| 228 | C2×C32 | — | 2 | 2 | no | — |
| 229 | C2×C32 | #392 | 1 | 1 | yes | characteristic |
| 230 | C2×C32 | #473 | 1 | 2 | yes | — |
| 231 | C3⋊D3 | — | 8 | 1 | no | — |
| 232 | #41 | — | 18 | 2 | no | — |
| 233 | #41 | — | 18 | 2 | no | — |
| 234 | C2×Q8 | — | 3 | 4 | no | — |
| 235 | C2×Q8 | — | 6 | 2 | no | — |
| 236 | C2×Q8 | — | 6 | 2 | no | — |
| 237 | C2×Q8 | — | 6 | 2 | no | — |
| 238 | C2×Q8 | — | 6 | 2 | no | — |
| 239 | C2×Q8 | — | 6 | 2 | no | — |
| 240 | C2×Q8 | — | 9 | 1 | no | — |
| 241 | C2×D4 | — | 9 | 1 | no | — |
| 242 | C2×D4 | — | 18 | 1 | no | — |
| 243 | C22×C4 | — | 6 | 2 | no | — |
| 244 | C22×C4 | — | 18 | 1 | no | — |
| 245 | C22×C4 | C2×D32 | 1 | 1 | yes | characteristic |
| 246 | Q16 | — | 18 | 8 | no | — |
| 247 | Q16 | — | 18 | 8 | no | — |
| 248 | SD16 | — | 18 | 8 | no | — |
| 249 | M16 | — | 2 | 2 | no | — |
| 250 | M16 | — | 3 | 4 | no | — |
| 251 | M16 | — | 6 | 2 | no | — |
| 252 | C2×C8 | — | 2 | 1 | no | — |
| 253 | C2×C8 | — | 6 | 2 | no | — |
| 254 | C2×C8 | — | 9 | 2 | no | — |
| 255 | C2×C8 | — | 18 | 2 | no | — |
| 256 | C22×C3 | — | 2 | 4 | no | — |
| 257 | C22×C3 | — | 2 | 2 | no | — |
| 258 | C22×C3 | — | 2 | 1 | no | — |
| 259 | C22×C3 | — | 4 | 2 | no | — |
| 260 | C22×C3 | #884 | 1 | 2 | yes | — |
| 261 | C22×C3 | #884 | 1 | 2 | yes | — |
| 262 | C22×C3 | #930 | 1 | 2 | yes | — |
| 263 | C2×D3 | — | 12 | 2 | no | — |
| 264 | C2×D3 | — | 12 | 4 | no | — |
| 265 | C2×D3 | — | 12 | 2 | no | — |
| 266 | C2×D3 | — | 12 | 4 | no | — |
| 267 | C3×C4 | — | 2 | 2 | no | — |
| 268 | C3×C4 | — | 2 | 1 | no | — |
| 269 | C3×C4 | — | 2 | 1 | no | — |
| 270 | C3×C4 | — | 12 | 4 | no | — |
| 271 | C3×C4 | #882 | 1 | 2 | yes | — |
| 272 | C3×C4 | #882 | 1 | 2 | yes | — |
| 273 | C3×C4 | #937 | 1 | 2 | yes | — |
| 274 | C3×C4 | #940 | 1 | 2 | yes | — |
| 275 | Dic3 | — | 4 | 4 | no | — |
| 276 | Dic3 | — | 12 | 2 | no | — |
| 277 | Dic3 | — | 12 | 2 | no | — |
| 278 | C32 | #2020 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 279 | C23 | — | 18 | 1 | no | — |
| 280 | C23 | #3798 | 1 | 1 | yes | characteristic |
| 281 | Q8 | — | 6 | 4 | no | — |
| 282 | Q8 | — | 6 | 4 | no | — |
| 283 | Q8 | — | 12 | 2 | no | — |
| 284 | Q8 | — | 12 | 2 | no | — |
| 285 | Q8 | — | 18 | 2 | no | — |
| 286 | D4 | — | 18 | 2 | no | — |
| 287 | D4 | — | 36 | 2 | no | — |
| 288 | C2×C4 | — | 6 | 4 | no | — |
| 289 | C2×C4 | — | 12 | 2 | no | — |
| 290 | C2×C4 | — | 12 | 2 | no | — |
| 291 | C2×C4 | — | 18 | 1 | no | — |
| 292 | C2×C4 | — | 36 | 1 | no | — |
| 293 | C2×C4 | — | 36 | 1 | no | — |
| 294 | C2×C4 | D3×D12 | 1 | 2 | yes | — |
| 295 | C2×C4 | #3802 | 1 | 1 | yes | characteristic |
| 296 | C2×C4 | D3×#67 | 1 | 2 | yes | — |
| 297 | C2×C4 | #3811 | 1 | 1 | yes | characteristic |
| 298 | C8 | — | 4 | 1 | no | — |
| 299 | C8 | — | 6 | 4 | no | — |
| 300 | C8 | — | 18 | 2 | no | — |
| 301 | C2×C3 | — | 2 | 2 | no | — |
| 302 | C2×C3 | — | 2 | 2 | no | — |
| 303 | C2×C3 | — | 2 | 2 | no | — |
| 304 | C2×C3 | — | 2 | 1 | no | — |
| 305 | C2×C3 | — | 4 | 2 | no | — |
| 306 | C2×C3 | #4755 | 1 | 4 | yes | — |
| 307 | C2×C3 | #4960 | 1 | 2 | yes | — |
| 308 | D3 | — | 24 | 2 | no | — |
| 309 | D3 | — | 24 | 2 | no | — |
| 310 | C22 | — | 2 | 2 | no | — |
| 311 | C22 | — | 36 | 2 | no | — |
| 312 | C22 | — | 36 | 1 | no | — |
| 313 | C22 | #63906 | 1 | 2 | yes | — |
| 314 | C22 | #63912 | 1 | 1 | yes | characteristic |
| 315 | C4 | — | 12 | 4 | no | — |
| 316 | C4 | — | 36 | 1 | no | — |
| 317 | C4 | #63922 | 1 | 2 | yes | — |
| 318 | C4 | #63923 | 1 | 1 | yes | characteristic |
| 319 | C4 | #63979 | 1 | 1 | yes | characteristic |
| 320 | C3 | — | 2 | 1 | no | — |
| 321 | C3 | #70125 | 1 | 2 | yes | complemented |
| 322 | C2 | — | 2 | 2 | no | — |
| 323 | C2 | — | 72 | 1 | no | — |
| 324 | C2 | #10590993 | 1 | 2 | yes | — |
| 325 | C2 | #10591393 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#3718 | C2 | semidirect |
| 4. C2×C3×#824 | C2 | semidirect |
| 5. #10589165 | C2 | semidirect |
| 24. C2×#824 | D3 | semidirect |
| 278. C32 | #2020 | semidirect |
| 321. C3 | #70125 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#3718 | 2 |
| C2×#63833 | 2 |
| #10592828 | 2 |
| C2×C3×#824 | 2 |
| #10589165 | 2 |
| #70125 | 3 |