← #11788370
Subgroups — #11788370
Order 1152.
912 conjugacy classes of subgroups.
The subgroup lattice has 324 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C32×#568 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C2×#64160 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #10592935 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | C2×#63651 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #10592819 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #10589426 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #10589425 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #72022 | — | 3 | 4 | no | maximal |
| 9 | C2×C32×#41 | C22 | 1 | 1 | yes | characteristic |
| 10 | C22×#634 | C22 | 1 | 1 | yes | characteristic |
| 11 | C32×#131 | — | 2 | 2 | no | — |
| 12 | C32×#131 | — | 2 | 2 | no | — |
| 13 | C2×C32×M16 | — | 2 | 2 | no | — |
| 14 | C2×C32×M16 | C22 | 1 | 1 | yes | characteristic |
| 15 | C2×C32×M16 | C22 | 1 | 1 | yes | characteristic |
| 16 | #64160 | — | 2 | 2 | no | — |
| 17 | #64160 | — | 2 | 2 | no | — |
| 18 | C2×#3756 | C4 | 1 | 2 | yes | complemented |
| 19 | C2×#3754 | C4 | 1 | 2 | yes | complemented |
| 20 | #64135 | C22 | 1 | 1 | yes | characteristic |
| 21 | C2×#3748 | C22 | 1 | 1 | yes | characteristic |
| 22 | C2×#3748 | C22 | 1 | 1 | yes | characteristic |
| 23 | #63664 | — | 2 | 2 | no | — |
| 24 | #63651 | — | 2 | 2 | no | — |
| 25 | #63643 | — | 2 | 2 | no | — |
| 26 | C3×#568 | D3 | 1 | 4 | yes | — |
| 27 | C2×#951 | — | 3 | 4 | no | — |
| 28 | #5236 | — | 3 | 4 | no | — |
| 29 | C2×#824 | — | 3 | 4 | no | — |
| 30 | #5120 | — | 3 | 4 | no | — |
| 31 | C3⋊#338 | — | 3 | 4 | no | — |
| 32 | #4559 | — | 3 | 4 | no | — |
| 33 | C32×#41 | — | 2 | 1 | no | — |
| 34 | C32×#41 | — | 2 | 1 | no | — |
| 35 | C32×#41 | D4 | 1 | 2 | yes | — |
| 36 | C32×#41 | D4 | 1 | 2 | yes | — |
| 37 | C2×C32×Q8 | C2×C4 | 1 | 1 | yes | characteristic |
| 38 | C2×C32×D4 | — | 2 | 1 | no | — |
| 39 | C2×C32×D4 | C2×C4 | 1 | 1 | yes | characteristic |
| 40 | C22×C32×C4 | — | 2 | 1 | no | — |
| 41 | C22×C32×C4 | C23 | 1 | 1 | yes | characteristic |
| 42 | C22×C3⋊Dic3 | — | 2 | 1 | no | — |
| 43 | C2×#634 | — | 2 | 1 | no | — |
| 44 | C2×#634 | — | 2 | 1 | no | — |
| 45 | C2×#634 | — | 2 | 1 | no | — |
| 46 | C2×#634 | — | 2 | 1 | no | — |
| 47 | C2×#634 | — | 2 | 1 | no | — |
| 48 | C2×#634 | C2×C4 | 1 | 2 | yes | — |
| 49 | C32×M16 | — | 2 | 4 | no | — |
| 50 | C32×M16 | — | 2 | 1 | no | — |
| 51 | C32×M16 | — | 2 | 1 | no | — |
| 52 | C32×M16 | — | 2 | 1 | no | — |
| 53 | C32×M16 | D4 | 1 | 2 | yes | — |
| 54 | C2×C32×C8 | — | 2 | 4 | no | — |
| 55 | C2×C32×C8 | — | 2 | 1 | no | — |
| 56 | C2×C32×C8 | D4 | 1 | 2 | yes | — |
| 57 | #3757 | — | 2 | 1 | no | — |
| 58 | #3756 | — | 2 | 4 | no | — |
| 59 | #3754 | — | 2 | 4 | no | — |
| 60 | C4⋊(C3⋊Dic3) | — | 2 | 1 | no | — |
| 61 | C4×C3⋊Dic3 | — | 2 | 1 | no | — |
| 62 | #3748 | — | 2 | 1 | no | — |
| 63 | #3748 | — | 2 | 1 | no | — |
| 64 | #3748 | — | 2 | 1 | no | — |
| 65 | #3748 | — | 2 | 1 | no | — |
| 66 | C2×C3⋊(C3⋊C8) | — | 2 | 1 | no | — |
| 67 | C2×C3⋊(C3⋊C8) | C2×C4 | 1 | 2 | yes | — |
| 68 | #1902 | — | 9 | 1 | no | Sylow |
| 69 | C2×C3×#41 | C2×D3 | 1 | 4 | yes | — |
| 70 | C22×Dic6 | — | 3 | 4 | no | — |
| 71 | C3×#131 | — | 2 | 8 | no | — |
| 72 | C3×#131 | — | 2 | 8 | no | — |
| 73 | C2×C3×M16 | — | 2 | 8 | no | — |
| 74 | C2×C3×M16 | C2×D3 | 1 | 4 | yes | — |
| 75 | C2×C3×M16 | C2×D3 | 1 | 4 | yes | — |
| 76 | #951 | — | 6 | 8 | no | — |
| 77 | #951 | — | 6 | 8 | no | — |
| 78 | C2×#216 | — | 3 | 8 | no | — |
| 79 | C2×#214 | — | 3 | 8 | no | — |
| 80 | #926 | — | 3 | 4 | no | — |
| 81 | C2×#208 | — | 3 | 4 | no | — |
| 82 | C2×#208 | — | 3 | 4 | no | — |
| 83 | #837 | — | 6 | 8 | no | — |
| 84 | #824 | — | 6 | 8 | no | — |
| 85 | #816 | — | 6 | 8 | no | — |
| 86 | C23×C32 | — | 2 | 1 | no | — |
| 87 | C23×C32 | #41 | 1 | 1 | yes | characteristic |
| 88 | C32×Q8 | — | 2 | 1 | no | — |
| 89 | C32×Q8 | C22⋊C4 | 1 | 2 | yes | — |
| 90 | C32×D4 | — | 2 | 2 | no | — |
| 91 | C32×D4 | — | 2 | 2 | no | — |
| 92 | C32×D4 | — | 2 | 1 | no | — |
| 93 | C32×D4 | C22⋊C4 | 1 | 2 | yes | — |
| 94 | C2×C32×C4 | — | 2 | 1 | no | — |
| 95 | C2×C32×C4 | — | 2 | 2 | no | — |
| 96 | C2×C32×C4 | — | 2 | 2 | no | — |
| 97 | C2×C32×C4 | C22×C4 | 1 | 1 | yes | characteristic |
| 98 | C2×C32×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 99 | C2×C32×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 100 | C2×C32×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 101 | C2×C32×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 102 | C2×C32×C4 | #41 | 1 | 1 | yes | characteristic |
| 103 | C2×C3⋊Dic3 | — | 2 | 2 | no | — |
| 104 | C2×C3⋊Dic3 | — | 4 | 1 | no | — |
| 105 | C2×C3⋊Dic3 | — | 4 | 1 | no | — |
| 106 | C2×C3⋊Dic3 | — | 4 | 1 | no | — |
| 107 | #634 | — | 2 | 2 | no | — |
| 108 | #634 | — | 2 | 2 | no | — |
| 109 | #634 | — | 4 | 1 | no | — |
| 110 | #634 | — | 4 | 1 | no | — |
| 111 | C32×C8 | — | 2 | 2 | no | — |
| 112 | C32×C8 | — | 2 | 2 | no | — |
| 113 | C3⋊(C3⋊C8) | — | 2 | 2 | no | — |
| 114 | C3⋊(C3⋊C8) | — | 4 | 1 | no | — |
| 115 | C2×#137 | — | 9 | 1 | no | — |
| 116 | #568 | C3⋊D3 | 1 | 1 | yes | characteristic |
| 117 | #421 | — | 9 | 1 | no | — |
| 118 | #419 | — | 9 | 1 | no | — |
| 119 | C2×#101 | — | 9 | 1 | no | — |
| 120 | #344 | — | 9 | 1 | no | — |
| 121 | #338 | — | 9 | 1 | no | — |
| 122 | C3×#41 | — | 2 | 4 | no | — |
| 123 | C3×#41 | — | 2 | 4 | no | — |
| 124 | C3×#41 | D12 | 1 | 8 | yes | — |
| 125 | C3×#41 | #67 | 1 | 8 | yes | — |
| 126 | C2×C3×Q8 | C4×D3 | 1 | 4 | yes | — |
| 127 | C2×C3×D4 | — | 2 | 4 | no | — |
| 128 | C2×C3×D4 | C4×D3 | 1 | 4 | yes | — |
| 129 | C22×C3×C4 | — | 2 | 4 | no | — |
| 130 | C22×C3×C4 | C22×D3 | 1 | 4 | yes | — |
| 131 | C22×Dic3 | — | 6 | 4 | no | — |
| 132 | C2×Dic6 | — | 3 | 8 | no | — |
| 133 | C2×Dic6 | — | 6 | 4 | no | — |
| 134 | C2×Dic6 | — | 6 | 4 | no | — |
| 135 | C2×Dic6 | — | 6 | 4 | no | — |
| 136 | C2×Dic6 | — | 6 | 4 | no | — |
| 137 | C2×Dic6 | — | 6 | 4 | no | — |
| 138 | C3×M16 | — | 2 | 16 | no | — |
| 139 | C3×M16 | — | 2 | 4 | no | — |
| 140 | C3×M16 | — | 2 | 4 | no | — |
| 141 | C3×M16 | — | 2 | 4 | no | — |
| 142 | C3×M16 | #67 | 1 | 8 | yes | — |
| 143 | C2×C3×C8 | — | 2 | 16 | no | — |
| 144 | C2×C3×C8 | — | 2 | 4 | no | — |
| 145 | C2×C3×C8 | #67 | 1 | 8 | yes | — |
| 146 | #217 | — | 6 | 4 | no | — |
| 147 | #216 | — | 6 | 16 | no | — |
| 148 | #214 | — | 6 | 16 | no | — |
| 149 | C4⋊Dic3 | — | 6 | 4 | no | — |
| 150 | C4×Dic3 | — | 6 | 4 | no | — |
| 151 | #208 | — | 6 | 4 | no | — |
| 152 | #208 | — | 6 | 4 | no | — |
| 153 | #208 | — | 6 | 4 | no | — |
| 154 | #208 | — | 6 | 4 | no | — |
| 155 | C2×C3⋊C8 | — | 3 | 8 | no | — |
| 156 | C2×C3⋊C8 | — | 6 | 4 | no | — |
| 157 | C22×C32 | — | 2 | 2 | no | — |
| 158 | C22×C32 | — | 4 | 1 | no | — |
| 159 | C22×C32 | — | 8 | 1 | no | — |
| 160 | C22×C32 | C4×D4 | 1 | 1 | yes | characteristic |
| 161 | C22×C32 | #121 | 1 | 1 | yes | characteristic |
| 162 | C22×C32 | #123 | 1 | 1 | yes | characteristic |
| 163 | C32×C4 | — | 2 | 2 | no | — |
| 164 | C32×C4 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 165 | C32×C4 | C4×D4 | 1 | 1 | yes | characteristic |
| 166 | C32×C4 | #120 | 1 | 1 | yes | characteristic |
| 167 | C32×C4 | #121 | 1 | 1 | yes | characteristic |
| 168 | C3⋊Dic3 | — | 4 | 2 | no | — |
| 169 | C3⋊Dic3 | — | 8 | 1 | no | — |
| 170 | C2×#41 | C2×C3⋊D3 | 1 | 1 | yes | characteristic |
| 171 | C22×Q8 | — | 9 | 1 | no | — |
| 172 | #137 | — | 18 | 2 | no | — |
| 173 | #137 | — | 18 | 2 | no | — |
| 174 | C2×Q16 | — | 9 | 2 | no | — |
| 175 | C2×SD16 | — | 9 | 2 | no | — |
| 176 | #131 | — | 2 | 2 | no | — |
| 177 | #131 | — | 2 | 2 | no | — |
| 178 | C2×M16 | — | 2 | 2 | no | — |
| 179 | C2×M16 | — | 9 | 1 | no | — |
| 180 | C2×M16 | — | 9 | 1 | no | — |
| 181 | C2×M16 | C2×C3⋊D3 | 1 | 1 | yes | characteristic |
| 182 | C2×M16 | C2×C3⋊D3 | 1 | 1 | yes | characteristic |
| 183 | #117 | — | 9 | 1 | no | — |
| 184 | #104 | — | 18 | 2 | no | — |
| 185 | #103 | — | 18 | 2 | no | — |
| 186 | #101 | — | 18 | 2 | no | — |
| 187 | C23×C3 | — | 2 | 4 | no | — |
| 188 | C23×C3 | #235 | 1 | 4 | yes | — |
| 189 | C3×Q8 | — | 2 | 4 | no | — |
| 190 | C3×Q8 | (C2×D3)⋊C4 | 1 | 8 | yes | — |
| 191 | C3×D4 | — | 2 | 8 | no | — |
| 192 | C3×D4 | — | 2 | 8 | no | — |
| 193 | C3×D4 | — | 2 | 4 | no | — |
| 194 | C3×D4 | (C2×D3)⋊C4 | 1 | 8 | yes | — |
| 195 | C2×C3×C4 | — | 2 | 4 | no | — |
| 196 | C2×C3×C4 | — | 2 | 8 | no | — |
| 197 | C2×C3×C4 | — | 2 | 8 | no | — |
| 198 | C2×C3×C4 | C2×C4×D3 | 1 | 4 | yes | — |
| 199 | C2×C3×C4 | C2×D12 | 1 | 4 | yes | — |
| 200 | C2×C3×C4 | #235 | 1 | 4 | yes | — |
| 201 | C2×C3×C4 | C2×#67 | 1 | 4 | yes | — |
| 202 | C2×C3×C4 | C2×#67 | 1 | 4 | yes | — |
| 203 | C2×C3×C4 | C2×#67 | 1 | 4 | yes | — |
| 204 | C2×Dic3 | — | 6 | 8 | no | — |
| 205 | C2×Dic3 | — | 12 | 4 | no | — |
| 206 | C2×Dic3 | — | 12 | 4 | no | — |
| 207 | C2×Dic3 | — | 12 | 4 | no | — |
| 208 | Dic6 | — | 6 | 8 | no | — |
| 209 | Dic6 | — | 6 | 8 | no | — |
| 210 | Dic6 | — | 12 | 4 | no | — |
| 211 | Dic6 | — | 12 | 4 | no | — |
| 212 | C3×C8 | — | 2 | 8 | no | — |
| 213 | C3×C8 | — | 2 | 8 | no | — |
| 214 | C3⋊C8 | — | 6 | 8 | no | — |
| 215 | C3⋊C8 | — | 12 | 4 | no | — |
| 216 | C2×C32 | — | 2 | 1 | no | — |
| 217 | C2×C32 | — | 2 | 1 | no | — |
| 218 | C2×C32 | — | 2 | 1 | no | — |
| 219 | C2×C32 | — | 4 | 2 | no | — |
| 220 | C2×C32 | #386 | 1 | 1 | yes | characteristic |
| 221 | #41 | — | 2 | 1 | no | — |
| 222 | #41 | — | 2 | 1 | no | — |
| 223 | #41 | C4⋊(C3⋊D3) | 1 | 2 | yes | — |
| 224 | #41 | #638 | 1 | 2 | yes | — |
| 225 | C2×Q8 | — | 9 | 2 | no | — |
| 226 | C2×Q8 | — | 18 | 1 | no | — |
| 227 | C2×Q8 | — | 18 | 1 | no | — |
| 228 | C2×Q8 | — | 18 | 1 | no | — |
| 229 | C2×Q8 | — | 18 | 1 | no | — |
| 230 | C2×Q8 | — | 18 | 1 | no | — |
| 231 | C2×Q8 | C4×C3⋊D3 | 1 | 1 | yes | characteristic |
| 232 | C2×D4 | — | 2 | 1 | no | — |
| 233 | C2×D4 | C4×C3⋊D3 | 1 | 1 | yes | characteristic |
| 234 | C22×C4 | — | 2 | 1 | no | — |
| 235 | C22×C4 | — | 18 | 1 | no | — |
| 236 | C22×C4 | C22×C3⋊D3 | 1 | 1 | yes | characteristic |
| 237 | Q16 | — | 18 | 4 | no | — |
| 238 | SD16 | — | 18 | 4 | no | — |
| 239 | M16 | — | 2 | 4 | no | — |
| 240 | M16 | — | 2 | 1 | no | — |
| 241 | M16 | — | 2 | 1 | no | — |
| 242 | M16 | — | 2 | 1 | no | — |
| 243 | M16 | — | 18 | 1 | no | — |
| 244 | M16 | — | 18 | 1 | no | — |
| 245 | M16 | — | 18 | 1 | no | — |
| 246 | M16 | — | 18 | 1 | no | — |
| 247 | M16 | #638 | 1 | 2 | yes | — |
| 248 | C2×C8 | — | 2 | 4 | no | — |
| 249 | C2×C8 | — | 2 | 1 | no | — |
| 250 | C2×C8 | — | 9 | 2 | no | — |
| 251 | C2×C8 | — | 18 | 1 | no | — |
| 252 | C2×C8 | #638 | 1 | 2 | yes | — |
| 253 | C4⋊C4 | — | 18 | 1 | no | — |
| 254 | C22⋊C4 | — | 18 | 1 | no | — |
| 255 | C42 | — | 18 | 1 | no | — |
| 256 | C22×C3 | — | 2 | 8 | no | — |
| 257 | C22×C3 | — | 4 | 4 | no | — |
| 258 | C22×C3 | — | 8 | 4 | no | — |
| 259 | C22×C3 | C4×#67 | 1 | 4 | yes | — |
| 260 | C22×C3 | #929 | 1 | 4 | yes | — |
| 261 | C22×C3 | #930 | 1 | 4 | yes | — |
| 262 | C3×C4 | — | 2 | 8 | no | — |
| 263 | C3×C4 | C2×(C2×D3)⋊C4 | 1 | 4 | yes | — |
| 264 | C3×C4 | C4×#67 | 1 | 4 | yes | — |
| 265 | C3×C4 | #930 | 1 | 4 | yes | — |
| 266 | C3×C4 | #953 | 1 | 4 | yes | — |
| 267 | Dic3 | — | 12 | 8 | no | — |
| 268 | Dic3 | — | 24 | 4 | no | — |
| 269 | C32 | #1902 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 270 | C23 | — | 2 | 1 | no | — |
| 271 | C23 | #3828 | 1 | 1 | yes | characteristic |
| 272 | Q8 | — | 2 | 1 | no | — |
| 273 | Q8 | — | 18 | 2 | no | — |
| 274 | Q8 | — | 18 | 2 | no | — |
| 275 | Q8 | — | 36 | 1 | no | — |
| 276 | Q8 | — | 36 | 1 | no | — |
| 277 | Q8 | #3752 | 1 | 2 | yes | — |
| 278 | D4 | — | 2 | 2 | no | — |
| 279 | D4 | — | 2 | 2 | no | — |
| 280 | D4 | — | 2 | 1 | no | — |
| 281 | D4 | #3752 | 1 | 2 | yes | — |
| 282 | C2×C4 | — | 2 | 1 | no | — |
| 283 | C2×C4 | — | 2 | 2 | no | — |
| 284 | C2×C4 | — | 2 | 2 | no | — |
| 285 | C2×C4 | — | 18 | 2 | no | — |
| 286 | C2×C4 | — | 36 | 1 | no | — |
| 287 | C2×C4 | — | 36 | 1 | no | — |
| 288 | C2×C4 | — | 36 | 1 | no | — |
| 289 | C2×C4 | C2×C4×C3⋊D3 | 1 | 1 | yes | characteristic |
| 290 | C2×C4 | C2×C4⋊(C3⋊D3) | 1 | 1 | yes | characteristic |
| 291 | C2×C4 | #3828 | 1 | 1 | yes | characteristic |
| 292 | C2×C4 | C2×#638 | 1 | 1 | yes | characteristic |
| 293 | C2×C4 | C2×#638 | 1 | 1 | yes | characteristic |
| 294 | C2×C4 | C2×#638 | 1 | 1 | yes | characteristic |
| 295 | C8 | — | 2 | 2 | no | — |
| 296 | C8 | — | 2 | 2 | no | — |
| 297 | C8 | — | 18 | 2 | no | — |
| 298 | C8 | — | 36 | 1 | no | — |
| 299 | C2×C3 | — | 2 | 4 | no | — |
| 300 | C2×C3 | — | 2 | 4 | no | — |
| 301 | C2×C3 | — | 2 | 4 | no | — |
| 302 | C2×C3 | — | 4 | 8 | no | — |
| 303 | C2×C3 | #5213 | 1 | 4 | yes | — |
| 304 | C22 | — | 2 | 2 | no | — |
| 305 | C22 | — | 4 | 1 | no | — |
| 306 | C22 | — | 8 | 1 | no | — |
| 307 | C22 | C4×#638 | 1 | 1 | yes | characteristic |
| 308 | C22 | #64138 | 1 | 1 | yes | characteristic |
| 309 | C22 | #64139 | 1 | 1 | yes | characteristic |
| 310 | C4 | — | 2 | 2 | no | — |
| 311 | C4 | — | 36 | 2 | no | — |
| 312 | C4 | — | 72 | 1 | no | — |
| 313 | C4 | C2×#3752 | 1 | 1 | yes | characteristic |
| 314 | C4 | C4×#638 | 1 | 1 | yes | characteristic |
| 315 | C4 | #64139 | 1 | 1 | yes | characteristic |
| 316 | C4 | #64162 | 1 | 1 | yes | characteristic |
| 317 | C3 | #72022 | 1 | 4 | yes | complemented |
| 318 | C2 | — | 2 | 1 | no | — |
| 319 | C2 | — | 2 | 1 | no | — |
| 320 | C2 | — | 2 | 1 | no | — |
| 321 | C2 | — | 4 | 2 | no | — |
| 322 | C2 | #10592912 | 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