← #11785605
Subgroups — #11785605
Order 1152.
792 conjugacy classes of subgroups.
The subgroup lattice has 264 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×#64110 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C2×C32×#108 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #10592832 | C2 | 1 | 2 | yes | maximal |
| 4 | C2×#63645 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #10589420 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #70721 | — | 3 | 4 | no | maximal |
| 7 | C2×#3828 | C22 | 1 | 1 | yes | characteristic |
| 8 | C2×C32×M16 | C22 | 1 | 2 | yes | — |
| 9 | C22×C32×C8 | C22 | 1 | 1 | yes | characteristic |
| 10 | C2×C4⋊(C3⋊Dic3) | C22 | 1 | 2 | yes | — |
| 11 | C2×#3748 | C22 | 1 | 1 | yes | characteristic |
| 12 | #64110 | — | 2 | 2 | no | — |
| 13 | #64110 | C4 | 1 | 4 | yes | complemented |
| 14 | C2×#3743 | — | 2 | 1 | no | — |
| 15 | C2×C8×C3⋊D3 | — | 2 | 1 | no | — |
| 16 | C32×#108 | — | 2 | 2 | no | — |
| 17 | #63648 | — | 2 | 2 | no | — |
| 18 | #63645 | — | 2 | 1 | no | — |
| 19 | #63645 | — | 2 | 1 | no | — |
| 20 | #63643 | — | 2 | 2 | no | — |
| 21 | C2×#901 | — | 3 | 4 | no | — |
| 22 | C2×C3×#108 | D3 | 1 | 4 | yes | complemented |
| 23 | #5133 | — | 3 | 8 | no | — |
| 24 | C2×#818 | — | 3 | 4 | no | — |
| 25 | #4554 | — | 3 | 8 | no | — |
| 26 | C22×C32×C4 | C23 | 1 | 1 | yes | characteristic |
| 27 | C2×#638 | — | 2 | 1 | no | — |
| 28 | C22×C3⋊Dic3 | — | 2 | 2 | no | — |
| 29 | #3828 | — | 2 | 1 | no | — |
| 30 | #3828 | — | 2 | 1 | no | — |
| 31 | #3828 | C2×C4 | 1 | 2 | yes | — |
| 32 | #3828 | Q8 | 1 | 2 | yes | — |
| 33 | C2×C4⋊(C3⋊D3) | D4 | 1 | 1 | yes | characteristic |
| 34 | C2×C4×C3⋊D3 | — | 2 | 1 | no | — |
| 35 | C2×#634 | D4 | 1 | 1 | yes | characteristic |
| 36 | C32×M16 | — | 2 | 2 | no | — |
| 37 | C32×M16 | — | 2 | 2 | no | — |
| 38 | C2×C32×C8 | — | 2 | 2 | no | — |
| 39 | C2×C32×C8 | C2×C4 | 1 | 2 | yes | — |
| 40 | C2×C32×C8 | D4 | 1 | 1 | yes | characteristic |
| 41 | C2×C32×C8 | D4 | 1 | 1 | yes | characteristic |
| 42 | C2×C32×C8 | D4 | 1 | 2 | yes | — |
| 43 | C4⋊(C3⋊Dic3) | — | 2 | 2 | no | — |
| 44 | C4⋊(C3⋊Dic3) | — | 2 | 2 | no | — |
| 45 | #3748 | — | 2 | 1 | no | — |
| 46 | #3748 | C2×C4 | 1 | 2 | yes | — |
| 47 | C2×C3⋊(C3⋊C8) | — | 2 | 1 | no | — |
| 48 | #3743 | — | 2 | 4 | no | — |
| 49 | C8×C3⋊D3 | — | 2 | 4 | no | — |
| 50 | #1816 | — | 9 | 1 | no | Sylow |
| 51 | C2×#235 | — | 3 | 4 | no | — |
| 52 | C2×C3×M16 | C2×D3 | 1 | 8 | yes | — |
| 53 | C22×C3×C8 | C2×D3 | 1 | 4 | yes | — |
| 54 | C2×C4⋊Dic3 | — | 3 | 8 | no | — |
| 55 | C2×#208 | — | 3 | 4 | no | — |
| 56 | #901 | — | 3 | 16 | no | — |
| 57 | #901 | — | 6 | 8 | no | — |
| 58 | C2×ΓL(1,𝔽25) | — | 6 | 4 | no | — |
| 59 | C2×D3×C8 | — | 6 | 4 | no | — |
| 60 | C3×#108 | — | 2 | 8 | no | — |
| 61 | #821 | — | 6 | 8 | no | — |
| 62 | #818 | — | 6 | 4 | no | — |
| 63 | #818 | — | 6 | 4 | no | — |
| 64 | #816 | — | 6 | 8 | no | — |
| 65 | C23×C32 | #41 | 1 | 1 | yes | characteristic |
| 66 | C22×C3⋊D3 | — | 2 | 1 | no | — |
| 67 | C2×C32×C4 | C22×C4 | 1 | 1 | yes | characteristic |
| 68 | C2×C32×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 69 | C2×C32×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 70 | C2×C32×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 71 | C2×C32×C4 | C2×Q8 | 1 | 1 | yes | characteristic |
| 72 | C2×C32×C4 | #41 | 1 | 1 | yes | characteristic |
| 73 | #638 | — | 2 | 2 | no | — |
| 74 | #638 | — | 2 | 2 | no | — |
| 75 | C2×C3⋊Dic3 | — | 2 | 1 | no | — |
| 76 | C2×C3⋊Dic3 | — | 4 | 2 | no | — |
| 77 | C2×C3⋊Dic3 | — | 8 | 2 | no | — |
| 78 | C4⋊(C3⋊D3) | — | 2 | 1 | no | — |
| 79 | C4⋊(C3⋊D3) | C4⋊C4 | 1 | 2 | yes | — |
| 80 | C4×C3⋊D3 | — | 2 | 2 | no | — |
| 81 | C4×C3⋊D3 | — | 2 | 2 | no | — |
| 82 | #634 | — | 2 | 1 | no | — |
| 83 | #634 | C4⋊C4 | 1 | 2 | yes | — |
| 84 | C32×C8 | — | 4 | 2 | no | — |
| 85 | C32×C8 | C22⋊C4 | 1 | 2 | yes | — |
| 86 | C32×C8 | C22⋊C4 | 1 | 2 | yes | — |
| 87 | C3⋊(C3⋊C8) | — | 2 | 2 | no | — |
| 88 | C2×#131 | — | 9 | 1 | no | — |
| 89 | C2×#108 | C3⋊D3 | 1 | 1 | yes | characteristic, complemented |
| 90 | C2×#107 | — | 9 | 1 | no | — |
| 91 | #417 | — | 9 | 2 | no | — |
| 92 | #343 | — | 9 | 2 | no | — |
| 93 | C22×C3×C4 | C22×D3 | 1 | 4 | yes | — |
| 94 | C2×#67 | — | 6 | 4 | no | — |
| 95 | C22×Dic3 | — | 6 | 8 | no | — |
| 96 | #235 | — | 3 | 8 | no | — |
| 97 | #235 | — | 3 | 8 | no | — |
| 98 | #235 | — | 6 | 4 | no | — |
| 99 | #235 | — | 6 | 4 | no | — |
| 100 | C2×D12 | — | 3 | 4 | no | — |
| 101 | C2×C4×D3 | — | 6 | 4 | no | — |
| 102 | C2×Dic6 | — | 3 | 4 | no | — |
| 103 | C3×M16 | — | 2 | 8 | no | — |
| 104 | C3×M16 | — | 2 | 8 | no | — |
| 105 | C2×C3×C8 | — | 2 | 8 | no | — |
| 106 | C2×C3×C8 | C4×D3 | 1 | 8 | yes | — |
| 107 | C2×C3×C8 | D12 | 1 | 4 | yes | — |
| 108 | C2×C3×C8 | D12 | 1 | 4 | yes | — |
| 109 | C2×C3×C8 | #67 | 1 | 8 | yes | — |
| 110 | C4⋊Dic3 | — | 6 | 8 | no | — |
| 111 | C4⋊Dic3 | — | 6 | 8 | no | — |
| 112 | #208 | — | 3 | 8 | no | — |
| 113 | #208 | — | 6 | 4 | no | — |
| 114 | C2×C3⋊C8 | — | 6 | 4 | no | — |
| 115 | ΓL(1,𝔽25) | — | 6 | 16 | no | — |
| 116 | D3×C8 | — | 6 | 16 | no | — |
| 117 | C22×C32 | — | 2 | 1 | no | — |
| 118 | C22×C32 | — | 2 | 1 | no | — |
| 119 | C22×C32 | #117 | 1 | 1 | yes | characteristic |
| 120 | C22×C32 | #121 | 1 | 1 | yes | characteristic |
| 121 | C22×C32 | C22⋊Q8 | 1 | 1 | yes | characteristic |
| 122 | C2×C3⋊D3 | — | 2 | 2 | no | — |
| 123 | C2×C3⋊D3 | — | 4 | 1 | no | — |
| 124 | C2×C3⋊D3 | — | 4 | 1 | no | — |
| 125 | C32×C4 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 126 | C32×C4 | C2×C4⋊C4 | 1 | 1 | yes | characteristic |
| 127 | C32×C4 | #121 | 1 | 1 | yes | characteristic |
| 128 | C32×C4 | C22⋊Q8 | 1 | 1 | yes | characteristic |
| 129 | C3⋊Dic3 | — | 2 | 2 | no | — |
| 130 | C3⋊Dic3 | — | 8 | 2 | no | — |
| 131 | C2×#41 | — | 9 | 1 | no | — |
| 132 | #131 | — | 9 | 4 | no | — |
| 133 | #131 | — | 18 | 2 | no | — |
| 134 | C2×M16 | — | 9 | 1 | no | — |
| 135 | C2×M16 | — | 18 | 1 | no | — |
| 136 | C2×M16 | C2×C3⋊D3 | 1 | 2 | yes | — |
| 137 | C22×C8 | — | 18 | 1 | no | — |
| 138 | C22×C8 | C2×C3⋊D3 | 1 | 1 | yes | characteristic |
| 139 | C2×C4⋊C4 | — | 9 | 2 | no | — |
| 140 | #108 | — | 2 | 2 | no | — |
| 141 | #107 | — | 18 | 1 | no | — |
| 142 | #107 | — | 18 | 1 | no | — |
| 143 | #103 | — | 18 | 2 | no | — |
| 144 | #102 | — | 18 | 2 | no | — |
| 145 | C23×C3 | #239 | 1 | 4 | yes | — |
| 146 | C22×D3 | — | 6 | 4 | no | — |
| 147 | C2×C3×C4 | C2×C4×D3 | 1 | 4 | yes | — |
| 148 | C2×C3×C4 | C2×D12 | 1 | 4 | yes | — |
| 149 | C2×C3×C4 | D3×D4 | 1 | 4 | yes | — |
| 150 | C2×C3×C4 | #237 | 1 | 4 | yes | — |
| 151 | C2×C3×C4 | D3×Q8 | 1 | 4 | yes | — |
| 152 | C2×C3×C4 | C2×#67 | 1 | 4 | yes | — |
| 153 | #67 | — | 6 | 8 | no | — |
| 154 | #67 | — | 6 | 8 | no | — |
| 155 | C2×Dic3 | — | 6 | 4 | no | — |
| 156 | C2×Dic3 | — | 12 | 8 | no | — |
| 157 | C2×Dic3 | — | 24 | 8 | no | — |
| 158 | D12 | — | 3 | 8 | no | — |
| 159 | D12 | — | 6 | 4 | no | — |
| 160 | C4×D3 | — | 6 | 8 | no | — |
| 161 | C4×D3 | — | 6 | 8 | no | — |
| 162 | Dic6 | — | 3 | 8 | no | — |
| 163 | Dic6 | — | 6 | 4 | no | — |
| 164 | C3×C8 | — | 4 | 8 | no | — |
| 165 | C3×C8 | (C2×D3)⋊C4 | 1 | 8 | yes | — |
| 166 | C3×C8 | (C2×D3)⋊C4 | 1 | 8 | yes | — |
| 167 | C3⋊C8 | — | 6 | 8 | no | — |
| 168 | C2×C32 | — | 2 | 1 | no | — |
| 169 | C2×C32 | — | 2 | 1 | no | — |
| 170 | C2×C32 | #380 | 1 | 1 | yes | characteristic |
| 171 | C2×C32 | #472 | 1 | 1 | yes | characteristic |
| 172 | C2×C32 | #473 | 1 | 1 | yes | characteristic |
| 173 | C3⋊D3 | — | 4 | 2 | no | — |
| 174 | #41 | — | 9 | 2 | no | — |
| 175 | #41 | — | 9 | 2 | no | — |
| 176 | #41 | — | 18 | 1 | no | — |
| 177 | #41 | — | 18 | 1 | no | — |
| 178 | C2×Q8 | — | 9 | 1 | no | — |
| 179 | C2×D4 | — | 9 | 1 | no | — |
| 180 | C2×D4 | — | 18 | 1 | no | — |
| 181 | C22×C4 | — | 18 | 1 | no | — |
| 182 | C22×C4 | — | 18 | 2 | no | — |
| 183 | C22×C4 | C22×C3⋊D3 | 1 | 1 | yes | characteristic |
| 184 | M16 | — | 2 | 2 | no | — |
| 185 | M16 | — | 2 | 2 | no | — |
| 186 | M16 | — | 9 | 2 | no | — |
| 187 | M16 | — | 18 | 1 | no | — |
| 188 | M16 | — | 18 | 4 | no | — |
| 189 | C2×C8 | — | 2 | 2 | no | — |
| 190 | C2×C8 | — | 18 | 1 | no | — |
| 191 | C2×C8 | — | 18 | 4 | no | — |
| 192 | C2×C8 | C4×C3⋊D3 | 1 | 2 | yes | — |
| 193 | C2×C8 | C4⋊(C3⋊D3) | 1 | 1 | yes | characteristic |
| 194 | C2×C8 | C4⋊(C3⋊D3) | 1 | 1 | yes | characteristic |
| 195 | C2×C8 | #638 | 1 | 2 | yes | — |
| 196 | C4⋊C4 | — | 18 | 2 | no | — |
| 197 | C4⋊C4 | — | 18 | 2 | no | — |
| 198 | C22×C3 | — | 2 | 4 | no | — |
| 199 | C22×C3 | — | 2 | 4 | no | — |
| 200 | C22×C3 | #892 | 1 | 4 | yes | — |
| 201 | C22×C3 | #895 | 1 | 4 | yes | — |
| 202 | C22×C3 | #946 | 1 | 4 | yes | — |
| 203 | C2×D3 | — | 6 | 8 | no | — |
| 204 | C2×D3 | — | 12 | 4 | no | — |
| 205 | C2×D3 | — | 12 | 4 | no | — |
| 206 | C3×C4 | D3×C4⋊C4 | 1 | 4 | yes | — |
| 207 | C3×C4 | #897 | 1 | 4 | yes | — |
| 208 | C3×C4 | C2×(C2×D3)⋊C4 | 1 | 4 | yes | — |
| 209 | C3×C4 | #938 | 1 | 4 | yes | — |
| 210 | Dic3 | — | 6 | 8 | no | — |
| 211 | Dic3 | — | 24 | 8 | no | — |
| 212 | C32 | #1816 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 213 | C23 | — | 18 | 1 | no | — |
| 214 | C23 | #3832 | 1 | 1 | yes | characteristic |
| 215 | Q8 | — | 9 | 2 | no | — |
| 216 | Q8 | — | 18 | 1 | no | — |
| 217 | D4 | — | 9 | 2 | no | — |
| 218 | D4 | — | 18 | 2 | no | — |
| 219 | D4 | — | 18 | 2 | no | — |
| 220 | D4 | — | 18 | 1 | no | — |
| 221 | C2×C4 | — | 18 | 1 | no | — |
| 222 | C2×C4 | — | 18 | 2 | no | — |
| 223 | C2×C4 | — | 18 | 2 | no | — |
| 224 | C2×C4 | — | 36 | 2 | no | — |
| 225 | C2×C4 | — | 72 | 2 | no | — |
| 226 | C2×C4 | C2×C4×C3⋊D3 | 1 | 1 | yes | characteristic |
| 227 | C2×C4 | C2×C4⋊(C3⋊D3) | 1 | 1 | yes | characteristic |
| 228 | C2×C4 | D4×C3⋊D3 | 1 | 1 | yes | characteristic |
| 229 | C2×C4 | #3830 | 1 | 1 | yes | characteristic |
| 230 | C2×C4 | Q8×C3⋊D3 | 1 | 1 | yes | characteristic |
| 231 | C2×C4 | C2×#638 | 1 | 1 | yes | characteristic |
| 232 | C8 | — | 4 | 2 | no | — |
| 233 | C8 | — | 18 | 2 | no | — |
| 234 | C8 | #3752 | 1 | 2 | yes | — |
| 235 | C8 | #3752 | 1 | 2 | yes | — |
| 236 | C2×C3 | — | 2 | 4 | no | — |
| 237 | C2×C3 | — | 2 | 4 | no | — |
| 238 | C2×C3 | #4896 | 1 | 4 | yes | — |
| 239 | C2×C3 | #4897 | 1 | 4 | yes | — |
| 240 | C2×C3 | #4987 | 1 | 4 | yes | — |
| 241 | D3 | — | 12 | 8 | no | — |
| 242 | C22 | — | 2 | 1 | no | — |
| 243 | C22 | — | 2 | 1 | no | — |
| 244 | C22 | — | 18 | 2 | no | — |
| 245 | C22 | — | 36 | 1 | no | — |
| 246 | C22 | — | 36 | 1 | no | — |
| 247 | C22 | #64101 | 1 | 1 | yes | characteristic |
| 248 | C22 | #64104 | 1 | 1 | yes | characteristic |
| 249 | C22 | #64155 | 1 | 1 | yes | characteristic |
| 250 | C4 | — | 18 | 2 | no | — |
| 251 | C4 | — | 72 | 2 | no | — |
| 252 | C4 | C4⋊C4×C3⋊D3 | 1 | 1 | yes | characteristic |
| 253 | C4 | #64106 | 1 | 1 | yes | characteristic |
| 254 | C4 | C2×#3752 | 1 | 1 | yes | characteristic |
| 255 | C4 | #64147 | 1 | 1 | yes | characteristic |
| 256 | C3 | #70721 | 1 | 4 | yes | complemented |
| 257 | C2 | — | 2 | 1 | no | — |
| 258 | C2 | — | 2 | 1 | no | — |
| 259 | C2 | — | 36 | 2 | no | — |
| 260 | C2 | #10592595 | 1 | 1 | yes | characteristic |
| 261 | C2 | #10592596 | 1 | 1 | yes | characteristic |
| 262 | C2 | #10592686 | 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