← #11870709
Subgroups — #11870709
Order 1152.
642 conjugacy classes of subgroups.
The subgroup lattice has 336 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×C4×Q8×C9 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #10589579 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #10588908 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #10588710 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | C4×#3675 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #10588702 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #10588651 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #10588605 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #82442 | — | 3 | 1 | no | maximal |
| 10 | C22×Q8×C9 | C22 | 1 | 1 | yes | characteristic |
| 11 | C2×#3697 | — | 2 | 1 | no | — |
| 12 | C4×Q8×C9 | — | 2 | 1 | no | — |
| 13 | C4×Q8×C9 | — | 2 | 1 | no | — |
| 14 | C4×Q8×C9 | C22 | 1 | 2 | yes | — |
| 15 | C4×Q8×C9 | C22 | 1 | 2 | yes | — |
| 16 | C2×C9×C4⋊C4 | — | 2 | 1 | no | — |
| 17 | C2×C9×C4⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×C42×C9 | — | 2 | 1 | no | — |
| 19 | C2×C42×C9 | C22 | 1 | 1 | yes | characteristic |
| 20 | C2×#3675 | C22 | 1 | 4 | yes | — |
| 21 | #63492 | — | 2 | 1 | no | — |
| 22 | #63492 | C22 | 1 | 2 | yes | — |
| 23 | #63437 | — | 2 | 1 | no | — |
| 24 | #63436 | C22 | 1 | 1 | yes | characteristic |
| 25 | C4×D36 | — | 2 | 1 | no | — |
| 26 | C4×D36 | C22 | 1 | 2 | yes | — |
| 27 | #63431 | C22 | 1 | 1 | yes | characteristic |
| 28 | #63395 | C22 | 1 | 4 | yes | — |
| 29 | #63389 | C22 | 1 | 2 | yes | — |
| 30 | #63369 | C22 | 1 | 4 | yes | — |
| 31 | #63367 | C22 | 1 | 4 | yes | — |
| 32 | C4⋊(C9⋊C8) | C22 | 1 | 2 | yes | — |
| 33 | C4×C9⋊C8 | C22 | 1 | 2 | yes | — |
| 34 | C2×C3×C4×Q8 | D3 | 1 | 1 | yes | characteristic |
| 35 | #5477 | — | 3 | 1 | no | — |
| 36 | #5227 | — | 3 | 2 | no | — |
| 37 | #5027 | — | 3 | 2 | no | — |
| 38 | C4×#215 | — | 3 | 4 | no | — |
| 39 | #5020 | — | 3 | 2 | no | — |
| 40 | #4968 | — | 3 | 2 | no | — |
| 41 | #4925 | — | 3 | 1 | no | — |
| 42 | C2×Q8×C9 | — | 2 | 4 | no | — |
| 43 | C2×Q8×C9 | — | 2 | 1 | no | — |
| 44 | C2×Q8×C9 | C23 | 1 | 2 | yes | — |
| 45 | C22×C4×C9 | — | 2 | 1 | no | — |
| 46 | C22×C4×C9 | — | 2 | 1 | no | — |
| 47 | C22×C4×C9 | D4 | 1 | 1 | yes | characteristic |
| 48 | C22×C4×C9 | D4 | 1 | 1 | yes | characteristic |
| 49 | C22×C4×C9 | C23 | 1 | 1 | yes | characteristic |
| 50 | C2×#611 | — | 2 | 2 | no | — |
| 51 | #3697 | — | 4 | 4 | no | — |
| 52 | C2×D36 | — | 2 | 1 | no | — |
| 53 | C2×D36 | — | 2 | 1 | no | — |
| 54 | C2×D36 | C23 | 1 | 2 | yes | — |
| 55 | C2×C4×D9 | — | 2 | 2 | no | — |
| 56 | C2×Dic18 | — | 2 | 1 | no | — |
| 57 | C9×C4⋊C4 | — | 2 | 2 | no | — |
| 58 | C9×C4⋊C4 | — | 2 | 2 | no | — |
| 59 | C9×C4⋊C4 | — | 2 | 1 | no | — |
| 60 | C9×C4⋊C4 | C23 | 1 | 2 | yes | — |
| 61 | C42×C9 | — | 2 | 2 | no | — |
| 62 | C42×C9 | — | 2 | 2 | no | — |
| 63 | C42×C9 | D4 | 1 | 1 | yes | characteristic |
| 64 | C42×C9 | D4 | 1 | 1 | yes | characteristic |
| 65 | C42×C9 | C23 | 1 | 1 | yes | characteristic |
| 66 | C42×C9 | C23 | 1 | 1 | yes | characteristic |
| 67 | #3675 | — | 2 | 8 | no | — |
| 68 | (C2×D9)⋊C4 | — | 2 | 2 | no | — |
| 69 | (C2×D9)⋊C4 | — | 2 | 2 | no | — |
| 70 | C4⋊Dic9 | — | 2 | 1 | no | — |
| 71 | C4⋊Dic9 | C23 | 1 | 2 | yes | — |
| 72 | C2×C9⋊C8 | C23 | 1 | 4 | yes | — |
| 73 | #3103 | — | 9 | 1 | no | Sylow |
| 74 | C22×C3×Q8 | C2×D3 | 1 | 1 | yes | characteristic |
| 75 | C2×#235 | — | 6 | 1 | no | — |
| 76 | C3×C4×Q8 | — | 2 | 1 | no | — |
| 77 | C3×C4×Q8 | — | 2 | 1 | no | — |
| 78 | C3×C4×Q8 | C2×D3 | 1 | 2 | yes | — |
| 79 | C3×C4×Q8 | C2×D3 | 1 | 2 | yes | — |
| 80 | C2×C3×C4⋊C4 | — | 2 | 1 | no | — |
| 81 | C2×C3×C4⋊C4 | C2×D3 | 1 | 1 | yes | characteristic |
| 82 | C2×C3×C42 | — | 2 | 1 | no | — |
| 83 | C2×C3×C42 | C2×D3 | 1 | 1 | yes | characteristic |
| 84 | C2×#215 | — | 3 | 4 | no | — |
| 85 | #930 | — | 3 | 2 | no | — |
| 86 | #930 | — | 6 | 1 | no | — |
| 87 | #875 | — | 6 | 1 | no | — |
| 88 | #874 | — | 3 | 1 | no | — |
| 89 | C4×D12 | — | 3 | 2 | no | — |
| 90 | C4×D12 | — | 6 | 1 | no | — |
| 91 | #869 | — | 3 | 1 | no | — |
| 92 | #835 | — | 3 | 4 | no | — |
| 93 | #830 | — | 3 | 2 | no | — |
| 94 | #809 | — | 3 | 4 | no | — |
| 95 | #808 | — | 3 | 4 | no | — |
| 96 | C4⋊(C3⋊C8) | — | 3 | 2 | no | — |
| 97 | C4×C3⋊C8 | — | 3 | 2 | no | — |
| 98 | C23×C9 | C2×D4 | 1 | 1 | yes | characteristic |
| 99 | C22×D9 | — | 2 | 2 | no | — |
| 100 | Q8×C9 | — | 2 | 4 | no | — |
| 101 | Q8×C9 | — | 2 | 2 | no | — |
| 102 | Q8×C9 | #41 | 1 | 4 | yes | complemented |
| 103 | C2×C4×C9 | — | 2 | 4 | no | — |
| 104 | C2×C4×C9 | — | 2 | 2 | no | — |
| 105 | C2×C4×C9 | — | 2 | 2 | no | — |
| 106 | C2×C4×C9 | — | 2 | 2 | no | — |
| 107 | C2×C4×C9 | — | 4 | 1 | no | — |
| 108 | C2×C4×C9 | — | 4 | 2 | no | — |
| 109 | C2×C4×C9 | SD16 | 1 | 4 | yes | complemented |
| 110 | C2×C4×C9 | C2×D4 | 1 | 1 | yes | characteristic |
| 111 | C2×C4×C9 | C2×D4 | 1 | 1 | yes | characteristic |
| 112 | C2×C4×C9 | C2×D4 | 1 | 1 | yes | characteristic |
| 113 | C2×C4×C9 | C2×D4 | 1 | 1 | yes | characteristic |
| 114 | C2×C4×C9 | C2×D4 | 1 | 1 | yes | characteristic |
| 115 | C2×C4×C9 | C24 | 1 | 1 | yes | characteristic |
| 116 | #611 | — | 4 | 4 | no | — |
| 117 | C2×Dic9 | — | 2 | 2 | no | — |
| 118 | D36 | — | 2 | 4 | no | — |
| 119 | D36 | — | 4 | 2 | no | — |
| 120 | D36 | — | 4 | 2 | no | — |
| 121 | C4×D9 | — | 4 | 4 | no | — |
| 122 | Dic18 | — | 4 | 2 | no | — |
| 123 | C9⋊C8 | — | 2 | 4 | no | — |
| 124 | #532 | — | 9 | 1 | no | — |
| 125 | C2×C4×Q8 | D9 | 1 | 1 | yes | characteristic, complemented |
| 126 | #481 | — | 9 | 2 | no | — |
| 127 | #475 | — | 9 | 2 | no | — |
| 128 | #460 | — | 9 | 2 | no | — |
| 129 | #448 | — | 9 | 2 | no | — |
| 130 | C4×SD16 | — | 9 | 4 | no | — |
| 131 | #431 | — | 9 | 1 | no | — |
| 132 | C2×C3×Q8 | — | 2 | 4 | no | — |
| 133 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 134 | C2×C3×Q8 | C22×D3 | 1 | 2 | yes | — |
| 135 | C22×C3×C4 | — | 2 | 1 | no | — |
| 136 | C22×C3×C4 | — | 2 | 1 | no | — |
| 137 | C22×C3×C4 | #67 | 1 | 1 | yes | characteristic |
| 138 | C22×C3×C4 | #67 | 1 | 1 | yes | characteristic |
| 139 | C22×C3×C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 140 | C2×#67 | — | 6 | 2 | no | — |
| 141 | #235 | — | 12 | 4 | no | — |
| 142 | C2×D12 | — | 3 | 2 | no | — |
| 143 | C2×D12 | — | 6 | 1 | no | — |
| 144 | C2×D12 | — | 6 | 1 | no | — |
| 145 | C2×C4×D3 | — | 6 | 2 | no | — |
| 146 | C2×Dic6 | — | 6 | 1 | no | — |
| 147 | C3×C4⋊C4 | — | 2 | 2 | no | — |
| 148 | C3×C4⋊C4 | — | 2 | 2 | no | — |
| 149 | C3×C4⋊C4 | — | 2 | 1 | no | — |
| 150 | C3×C4⋊C4 | C22×D3 | 1 | 2 | yes | — |
| 151 | C3×C42 | — | 2 | 2 | no | — |
| 152 | C3×C42 | — | 2 | 2 | no | — |
| 153 | C3×C42 | #67 | 1 | 1 | yes | characteristic |
| 154 | C3×C42 | #67 | 1 | 1 | yes | characteristic |
| 155 | C3×C42 | C22×D3 | 1 | 1 | yes | characteristic |
| 156 | C3×C42 | C22×D3 | 1 | 1 | yes | characteristic |
| 157 | #215 | — | 6 | 8 | no | — |
| 158 | (C2×D3)⋊C4 | — | 6 | 2 | no | — |
| 159 | (C2×D3)⋊C4 | — | 6 | 2 | no | — |
| 160 | C4⋊Dic3 | — | 3 | 2 | no | — |
| 161 | C4⋊Dic3 | — | 6 | 1 | no | — |
| 162 | C2×C3⋊C8 | — | 3 | 4 | no | — |
| 163 | C22×C9 | — | 2 | 1 | no | — |
| 164 | C22×C9 | — | 2 | 1 | no | — |
| 165 | C22×C9 | C2×SD16 | 1 | 2 | yes | — |
| 166 | C22×C9 | C22×D4 | 1 | 1 | yes | characteristic |
| 167 | C2×D9 | — | 4 | 2 | no | — |
| 168 | C2×D9 | — | 4 | 2 | no | — |
| 169 | C2×D9 | — | 4 | 2 | no | — |
| 170 | C4×C9 | — | 2 | 4 | no | — |
| 171 | C4×C9 | — | 2 | 1 | no | — |
| 172 | C4×C9 | — | 2 | 1 | no | — |
| 173 | C4×C9 | — | 2 | 1 | no | — |
| 174 | C4×C9 | — | 4 | 2 | no | — |
| 175 | C4×C9 | C2×SD16 | 1 | 2 | yes | — |
| 176 | C4×C9 | C2×SD16 | 1 | 2 | yes | — |
| 177 | C4×C9 | C2×#41 | 1 | 2 | yes | — |
| 178 | Dic9 | — | 4 | 2 | no | — |
| 179 | C2×#41 | — | 18 | 1 | no | — |
| 180 | C22×Q8 | C2×D9 | 1 | 1 | yes | characteristic |
| 181 | C2×SD16 | — | 9 | 4 | no | — |
| 182 | C4⋊Q8 | — | 9 | 1 | no | — |
| 183 | #127 | — | 9 | 1 | no | — |
| 184 | #124 | — | 18 | 1 | no | — |
| 185 | #121 | — | 9 | 2 | no | — |
| 186 | #121 | — | 18 | 1 | no | — |
| 187 | C4×Q8 | — | 2 | 1 | no | — |
| 188 | C4×Q8 | — | 2 | 1 | no | — |
| 189 | C4×Q8 | C2×D9 | 1 | 2 | yes | — |
| 190 | C4×Q8 | C2×D9 | 1 | 2 | yes | — |
| 191 | C4×D4 | — | 9 | 2 | no | — |
| 192 | C4×D4 | — | 18 | 1 | no | — |
| 193 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 194 | C2×C4⋊C4 | C2×D9 | 1 | 1 | yes | characteristic |
| 195 | C2×C42 | — | 2 | 1 | no | — |
| 196 | C2×C42 | C2×D9 | 1 | 1 | yes | characteristic |
| 197 | #106 | — | 9 | 4 | no | — |
| 198 | C4⋊C8 | — | 9 | 2 | no | — |
| 199 | #103 | — | 9 | 4 | no | — |
| 200 | #102 | — | 9 | 4 | no | — |
| 201 | C22⋊C8 | — | 9 | 2 | no | — |
| 202 | C4×C8 | — | 9 | 2 | no | — |
| 203 | C23×C3 | C2×#67 | 1 | 1 | yes | characteristic |
| 204 | C22×D3 | — | 6 | 2 | no | — |
| 205 | C3×Q8 | — | 2 | 4 | no | — |
| 206 | C3×Q8 | — | 2 | 2 | no | — |
| 207 | C3×Q8 | #235 | 1 | 4 | yes | — |
| 208 | C2×C3×C4 | — | 2 | 4 | no | — |
| 209 | C2×C3×C4 | — | 2 | 2 | no | — |
| 210 | C2×C3×C4 | — | 2 | 2 | no | — |
| 211 | C2×C3×C4 | — | 2 | 2 | no | — |
| 212 | C2×C3×C4 | — | 4 | 1 | no | — |
| 213 | C2×C3×C4 | — | 4 | 2 | no | — |
| 214 | C2×C3×C4 | #215 | 1 | 4 | yes | — |
| 215 | C2×C3×C4 | C2×#67 | 1 | 1 | yes | characteristic |
| 216 | C2×C3×C4 | C2×#67 | 1 | 1 | yes | characteristic |
| 217 | C2×C3×C4 | C2×#67 | 1 | 1 | yes | characteristic |
| 218 | C2×C3×C4 | C2×#67 | 1 | 1 | yes | characteristic |
| 219 | C2×C3×C4 | C2×#67 | 1 | 1 | yes | characteristic |
| 220 | C2×C3×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 221 | #67 | — | 12 | 4 | no | — |
| 222 | C2×Dic3 | — | 6 | 2 | no | — |
| 223 | D12 | — | 6 | 4 | no | — |
| 224 | D12 | — | 12 | 2 | no | — |
| 225 | D12 | — | 12 | 2 | no | — |
| 226 | C4×D3 | — | 12 | 4 | no | — |
| 227 | Dic6 | — | 12 | 2 | no | — |
| 228 | C3⋊C8 | — | 6 | 4 | no | — |
| 229 | C2×C9 | — | 2 | 2 | no | — |
| 230 | C2×C9 | #525 | 1 | 1 | yes | characteristic |
| 231 | C2×C9 | C22×SD16 | 1 | 1 | yes | characteristic |
| 232 | C2×C9 | #575 | 1 | 1 | yes | characteristic |
| 233 | D9 | — | 8 | 2 | no | — |
| 234 | #41 | — | 36 | 4 | no | — |
| 235 | C2×Q8 | — | 2 | 4 | no | — |
| 236 | C2×Q8 | — | 2 | 1 | no | — |
| 237 | C2×Q8 | — | 18 | 1 | no | — |
| 238 | C2×Q8 | C22×D9 | 1 | 2 | yes | — |
| 239 | C2×D4 | — | 9 | 2 | no | — |
| 240 | C2×D4 | — | 18 | 2 | no | — |
| 241 | C2×D4 | — | 18 | 1 | no | — |
| 242 | C2×D4 | — | 18 | 1 | no | — |
| 243 | C22×C4 | — | 2 | 1 | no | — |
| 244 | C22×C4 | — | 2 | 1 | no | — |
| 245 | C22×C4 | — | 18 | 2 | no | — |
| 246 | C22×C4 | #611 | 1 | 1 | yes | characteristic |
| 247 | C22×C4 | #611 | 1 | 1 | yes | characteristic |
| 248 | C22×C4 | C22×D9 | 1 | 1 | yes | characteristic |
| 249 | SD16 | — | 18 | 8 | no | — |
| 250 | C2×C8 | — | 9 | 4 | no | — |
| 251 | C4⋊C4 | — | 2 | 2 | no | — |
| 252 | C4⋊C4 | — | 2 | 2 | no | — |
| 253 | C4⋊C4 | — | 2 | 1 | no | — |
| 254 | C4⋊C4 | — | 9 | 2 | no | — |
| 255 | C4⋊C4 | — | 18 | 1 | no | — |
| 256 | C4⋊C4 | C22×D9 | 1 | 2 | yes | — |
| 257 | C22⋊C4 | — | 18 | 2 | no | — |
| 258 | C22⋊C4 | — | 18 | 2 | no | — |
| 259 | C42 | — | 2 | 2 | no | — |
| 260 | C42 | — | 2 | 2 | no | — |
| 261 | C42 | #611 | 1 | 1 | yes | characteristic |
| 262 | C42 | #611 | 1 | 1 | yes | characteristic |
| 263 | C42 | C22×D9 | 1 | 1 | yes | characteristic |
| 264 | C42 | C22×D9 | 1 | 1 | yes | characteristic |
| 265 | C22×C3 | — | 2 | 1 | no | — |
| 266 | C22×C3 | — | 2 | 1 | no | — |
| 267 | C22×C3 | C2×#215 | 1 | 2 | yes | — |
| 268 | C22×C3 | C22×#67 | 1 | 1 | yes | characteristic |
| 269 | C2×D3 | — | 12 | 2 | no | — |
| 270 | C2×D3 | — | 12 | 2 | no | — |
| 271 | C2×D3 | — | 12 | 2 | no | — |
| 272 | C3×C4 | — | 2 | 4 | no | — |
| 273 | C3×C4 | — | 2 | 1 | no | — |
| 274 | C3×C4 | — | 2 | 1 | no | — |
| 275 | C3×C4 | — | 2 | 1 | no | — |
| 276 | C3×C4 | — | 4 | 2 | no | — |
| 277 | C3×C4 | C2×#215 | 1 | 2 | yes | — |
| 278 | C3×C4 | C2×#215 | 1 | 2 | yes | — |
| 279 | C3×C4 | C2×#235 | 1 | 2 | yes | — |
| 280 | Dic3 | — | 12 | 2 | no | — |
| 281 | C9 | #3103 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 282 | C23 | — | 18 | 2 | no | — |
| 283 | C23 | C2×#611 | 1 | 1 | yes | characteristic |
| 284 | Q8 | — | 2 | 4 | no | — |
| 285 | Q8 | — | 2 | 2 | no | — |
| 286 | Q8 | — | 36 | 2 | no | — |
| 287 | Q8 | #3697 | 1 | 4 | yes | complemented |
| 288 | D4 | — | 18 | 4 | no | — |
| 289 | D4 | — | 36 | 2 | no | — |
| 290 | D4 | — | 36 | 4 | no | — |
| 291 | D4 | — | 36 | 2 | no | — |
| 292 | C2×C4 | — | 2 | 4 | no | — |
| 293 | C2×C4 | — | 2 | 2 | no | — |
| 294 | C2×C4 | — | 2 | 2 | no | — |
| 295 | C2×C4 | — | 2 | 2 | no | — |
| 296 | C2×C4 | — | 4 | 1 | no | — |
| 297 | C2×C4 | — | 4 | 2 | no | — |
| 298 | C2×C4 | — | 18 | 2 | no | — |
| 299 | C2×C4 | — | 36 | 4 | no | — |
| 300 | C2×C4 | #3675 | 1 | 4 | yes | complemented |
| 301 | C2×C4 | C2×#611 | 1 | 1 | yes | characteristic |
| 302 | C2×C4 | C2×#611 | 1 | 1 | yes | characteristic |
| 303 | C2×C4 | C2×#611 | 1 | 1 | yes | characteristic |
| 304 | C2×C4 | C2×#611 | 1 | 1 | yes | characteristic |
| 305 | C2×C4 | C2×#611 | 1 | 1 | yes | characteristic |
| 306 | C2×C4 | C23×D9 | 1 | 1 | yes | characteristic |
| 307 | C8 | — | 18 | 4 | no | — |
| 308 | C2×C3 | — | 2 | 2 | no | — |
| 309 | C2×C3 | #5791 | 1 | 1 | yes | characteristic |
| 310 | C2×C3 | C22×#215 | 1 | 1 | yes | characteristic |
| 311 | C2×C3 | #5822 | 1 | 1 | yes | characteristic |
| 312 | D3 | — | 24 | 2 | no | — |
| 313 | C22 | — | 2 | 1 | no | — |
| 314 | C22 | — | 2 | 1 | no | — |
| 315 | C22 | — | 36 | 2 | no | — |
| 316 | C22 | — | 36 | 2 | no | — |
| 317 | C22 | — | 36 | 2 | no | — |
| 318 | C22 | C2×#3675 | 1 | 2 | yes | — |
| 319 | C22 | C22×#611 | 1 | 1 | yes | characteristic |
| 320 | C4 | — | 2 | 4 | no | — |
| 321 | C4 | — | 2 | 1 | no | — |
| 322 | C4 | — | 2 | 1 | no | — |
| 323 | C4 | — | 2 | 1 | no | — |
| 324 | C4 | — | 4 | 2 | no | — |
| 325 | C4 | — | 36 | 2 | no | — |
| 326 | C4 | C2×#3675 | 1 | 2 | yes | — |
| 327 | C4 | C2×#3675 | 1 | 2 | yes | — |
| 328 | C4 | C2×#3697 | 1 | 2 | yes | — |
| 329 | C3 | #82442 | 1 | 1 | yes | characteristic |
| 330 | C2 | — | 2 | 2 | no | — |
| 331 | C2 | — | 72 | 2 | no | — |
| 332 | C2 | #10589893 | 1 | 1 | yes | characteristic |
| 333 | C2 | C22×#3675 | 1 | 1 | yes | characteristic |
| 334 | C2 | #10589925 | 1 | 1 | yes | characteristic |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta