← #11860676
Subgroups — #11860676
Order 1152.
792 conjugacy classes of subgroups.
The subgroup lattice has 234 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C22×D72 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #10589623 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | C9×#405 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #10588813 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #10588787 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #10588392 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | C4×D72 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #78561 | — | 3 | 1 | no | maximal |
| 9 | C22×D36 | C22 | 1 | 2 | yes | — |
| 10 | C2×C9×M16 | C22 | 1 | 1 | yes | characteristic |
| 11 | C22×C8×C9 | C22 | 1 | 1 | yes | characteristic |
| 12 | C9×#117 | C22 | 1 | 1 | yes | characteristic |
| 13 | #63488 | C22 | 1 | 2 | yes | — |
| 14 | C2×D72 | C4 | 1 | 8 | yes | complemented |
| 15 | C2×D72 | C22 | 1 | 2 | yes | — |
| 16 | C2×D72 | C22 | 1 | 2 | yes | — |
| 17 | #63455 | — | 2 | 4 | no | — |
| 18 | C22⋊C4×D9 | — | 2 | 4 | no | — |
| 19 | C4×D36 | C22 | 1 | 8 | yes | complemented |
| 20 | C9×#97 | C22 | 1 | 2 | yes | complemented |
| 21 | C4×C8×C9 | C22 | 1 | 2 | yes | complemented |
| 22 | #63380 | C22 | 1 | 8 | yes | complemented |
| 23 | #63378 | C22 | 1 | 2 | yes | complemented |
| 24 | #63377 | C22 | 1 | 2 | yes | complemented |
| 25 | C22×D24 | — | 3 | 1 | no | — |
| 26 | #5521 | — | 3 | 2 | no | — |
| 27 | C3×#405 | D3 | 1 | 1 | yes | characteristic |
| 28 | #5131 | — | 3 | 2 | no | — |
| 29 | #5106 | — | 3 | 1 | no | — |
| 30 | #4711 | — | 3 | 4 | no | — |
| 31 | C4×D24 | — | 3 | 4 | no | — |
| 32 | C23×D9 | — | 2 | 2 | no | — |
| 33 | C22×C4×C9 | C23 | 1 | 1 | yes | characteristic |
| 34 | C2×D36 | — | 2 | 2 | no | — |
| 35 | C2×D36 | — | 2 | 4 | no | — |
| 36 | C2×D36 | C2×C4 | 1 | 8 | yes | complemented |
| 37 | C2×D36 | C23 | 1 | 4 | yes | — |
| 38 | C2×C4×D9 | — | 2 | 8 | no | — |
| 39 | C9×M16 | — | 2 | 2 | no | — |
| 40 | C2×C8×C9 | C2×C4 | 1 | 4 | yes | complemented |
| 41 | C2×C8×C9 | C23 | 1 | 2 | yes | — |
| 42 | C2×C8×C9 | C23 | 1 | 1 | yes | characteristic |
| 43 | C2×C8×C9 | C23 | 1 | 1 | yes | characteristic |
| 44 | C9×C4⋊C4 | D4 | 1 | 2 | yes | — |
| 45 | C9×C22⋊C4 | D4 | 1 | 2 | yes | — |
| 46 | C42×C9 | C23 | 1 | 2 | yes | — |
| 47 | #3676 | — | 2 | 2 | no | — |
| 48 | (C2×D9)⋊C4 | — | 2 | 8 | no | — |
| 49 | C4⋊Dic9 | C23 | 1 | 4 | yes | — |
| 50 | C4×Dic9 | — | 2 | 2 | no | — |
| 51 | D72 | C2×C4 | 1 | 8 | yes | complemented |
| 52 | D72 | C2×C4 | 1 | 8 | yes | complemented |
| 53 | #2948 | — | 9 | 1 | no | Sylow |
| 54 | C22×D12 | — | 3 | 2 | no | — |
| 55 | C2×C3×M16 | C2×D3 | 1 | 1 | yes | characteristic |
| 56 | C22×C3×C8 | C2×D3 | 1 | 1 | yes | characteristic |
| 57 | C3×#117 | C2×D3 | 1 | 1 | yes | characteristic |
| 58 | #926 | — | 3 | 2 | no | — |
| 59 | C2×D24 | — | 3 | 8 | no | — |
| 60 | C2×D24 | — | 3 | 2 | no | — |
| 61 | C2×D24 | — | 3 | 2 | no | — |
| 62 | #893 | — | 6 | 4 | no | — |
| 63 | D3×C22⋊C4 | — | 6 | 4 | no | — |
| 64 | C4×D12 | — | 3 | 8 | no | — |
| 65 | C3×#97 | C2×D3 | 1 | 2 | yes | — |
| 66 | C3×C4×C8 | C2×D3 | 1 | 2 | yes | — |
| 67 | #821 | — | 3 | 8 | no | — |
| 68 | #818 | — | 3 | 2 | no | — |
| 69 | #817 | — | 3 | 2 | no | — |
| 70 | C23×C9 | C2×D4 | 1 | 1 | yes | characteristic |
| 71 | C22×D9 | — | 2 | 4 | no | — |
| 72 | C22×D9 | — | 2 | 8 | no | — |
| 73 | C22×D9 | — | 8 | 4 | no | — |
| 74 | C2×C4×C9 | C22×C4 | 1 | 2 | yes | — |
| 75 | C2×C4×C9 | C2×D4 | 1 | 4 | yes | — |
| 76 | C2×C4×C9 | C2×D4 | 1 | 1 | yes | characteristic |
| 77 | C2×C4×C9 | #41 | 1 | 2 | yes | — |
| 78 | C2×C4×C9 | C24 | 1 | 1 | yes | characteristic |
| 79 | C2×Dic9 | — | 2 | 4 | no | — |
| 80 | D36 | — | 2 | 8 | no | — |
| 81 | D36 | — | 2 | 4 | no | — |
| 82 | D36 | C22×C4 | 1 | 8 | yes | — |
| 83 | C4×D9 | — | 8 | 8 | no | — |
| 84 | C8×C9 | — | 2 | 2 | no | — |
| 85 | C8×C9 | C22×C4 | 1 | 2 | yes | — |
| 86 | C8×C9 | C22×C4 | 1 | 2 | yes | — |
| 87 | C22×D8 | — | 9 | 1 | no | — |
| 88 | #518 | — | 9 | 2 | no | — |
| 89 | #442 | — | 9 | 4 | no | — |
| 90 | C4×D8 | — | 9 | 4 | no | — |
| 91 | #427 | — | 9 | 1 | no | — |
| 92 | #418 | — | 9 | 2 | no | — |
| 93 | #405 | D9 | 1 | 1 | yes | characteristic, complemented |
| 94 | C23×D3 | — | 6 | 2 | no | — |
| 95 | C22×C3×C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 96 | C2×D12 | — | 3 | 8 | no | — |
| 97 | C2×D12 | — | 3 | 4 | no | — |
| 98 | C2×D12 | — | 6 | 2 | no | — |
| 99 | C2×D12 | — | 6 | 4 | no | — |
| 100 | C2×C4×D3 | — | 6 | 8 | no | — |
| 101 | C3×M16 | — | 2 | 2 | no | — |
| 102 | C2×C3×C8 | C4×D3 | 1 | 4 | yes | — |
| 103 | C2×C3×C8 | C22×D3 | 1 | 2 | yes | — |
| 104 | C2×C3×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 105 | C2×C3×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 106 | C3×C4⋊C4 | D12 | 1 | 2 | yes | — |
| 107 | C3×C22⋊C4 | D12 | 1 | 2 | yes | — |
| 108 | C3×C42 | C22×D3 | 1 | 2 | yes | — |
| 109 | #217 | — | 6 | 2 | no | — |
| 110 | (C2×D3)⋊C4 | — | 6 | 8 | no | — |
| 111 | C4⋊Dic3 | — | 3 | 4 | no | — |
| 112 | C4×Dic3 | — | 6 | 2 | no | — |
| 113 | D24 | — | 3 | 8 | no | — |
| 114 | D24 | — | 3 | 8 | no | — |
| 115 | C22×C9 | — | 2 | 2 | no | — |
| 116 | C22×C9 | C4×D4 | 1 | 2 | yes | — |
| 117 | C22×C9 | C22×D4 | 1 | 1 | yes | characteristic |
| 118 | C2×D9 | — | 2 | 8 | no | — |
| 119 | C2×D9 | — | 4 | 8 | no | — |
| 120 | C2×D9 | — | 8 | 8 | no | — |
| 121 | C4×C9 | — | 2 | 4 | no | — |
| 122 | C4×C9 | C4×D4 | 1 | 2 | yes | — |
| 123 | C4×C9 | C23×C4 | 1 | 1 | yes | characteristic |
| 124 | C4×C9 | C2×#41 | 1 | 1 | yes | characteristic |
| 125 | Dic9 | — | 4 | 4 | no | — |
| 126 | C22×D4 | — | 9 | 2 | no | — |
| 127 | C2×D8 | — | 9 | 8 | no | — |
| 128 | C2×D8 | — | 9 | 2 | no | — |
| 129 | C2×D8 | — | 9 | 2 | no | — |
| 130 | C2×M16 | C2×D9 | 1 | 1 | yes | characteristic |
| 131 | C22×C8 | C2×D9 | 1 | 1 | yes | characteristic |
| 132 | C4×D4 | — | 9 | 8 | no | — |
| 133 | C4×D4 | — | 18 | 4 | no | — |
| 134 | #117 | — | 9 | 2 | no | — |
| 135 | #117 | C2×D9 | 1 | 1 | yes | characteristic |
| 136 | C2×C22⋊C4 | — | 18 | 4 | no | — |
| 137 | #107 | — | 9 | 2 | no | — |
| 138 | #106 | — | 9 | 2 | no | — |
| 139 | #102 | — | 9 | 8 | no | — |
| 140 | #97 | C2×D9 | 1 | 2 | yes | complemented |
| 141 | C4×C8 | C2×D9 | 1 | 2 | yes | complemented |
| 142 | C23×C3 | C2×D12 | 1 | 1 | yes | characteristic |
| 143 | C22×D3 | — | 6 | 4 | no | — |
| 144 | C22×D3 | — | 6 | 8 | no | — |
| 145 | C22×D3 | — | 24 | 4 | no | — |
| 146 | C2×C3×C4 | C2×C4×D3 | 1 | 2 | yes | — |
| 147 | C2×C3×C4 | C2×D12 | 1 | 4 | yes | — |
| 148 | C2×C3×C4 | C2×D12 | 1 | 1 | yes | characteristic |
| 149 | C2×C3×C4 | #235 | 1 | 2 | yes | — |
| 150 | C2×C3×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 151 | C2×Dic3 | — | 6 | 4 | no | — |
| 152 | D12 | — | 3 | 8 | no | — |
| 153 | D12 | — | 6 | 8 | no | — |
| 154 | D12 | — | 6 | 4 | no | — |
| 155 | C4×D3 | — | 24 | 8 | no | — |
| 156 | C3×C8 | — | 2 | 2 | no | — |
| 157 | C3×C8 | C2×C4×D3 | 1 | 2 | yes | — |
| 158 | C3×C8 | C2×C4×D3 | 1 | 2 | yes | — |
| 159 | C2×C9 | — | 2 | 2 | no | — |
| 160 | C2×C9 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 161 | C2×C9 | #576 | 1 | 2 | yes | — |
| 162 | D9 | — | 4 | 8 | no | — |
| 163 | C24 | — | 18 | 2 | no | — |
| 164 | C2×D4 | — | 9 | 8 | no | — |
| 165 | C2×D4 | — | 9 | 4 | no | — |
| 166 | C2×D4 | — | 18 | 2 | no | — |
| 167 | C2×D4 | — | 18 | 4 | no | — |
| 168 | C22×C4 | — | 18 | 8 | no | — |
| 169 | C22×C4 | C22×D9 | 1 | 1 | yes | characteristic |
| 170 | D8 | — | 9 | 8 | no | — |
| 171 | D8 | — | 9 | 8 | no | — |
| 172 | M16 | — | 2 | 2 | no | — |
| 173 | C2×C8 | C4×D9 | 1 | 4 | yes | complemented |
| 174 | C2×C8 | C22×D9 | 1 | 2 | yes | — |
| 175 | C2×C8 | C22×D9 | 1 | 1 | yes | characteristic |
| 176 | C2×C8 | C22×D9 | 1 | 1 | yes | characteristic |
| 177 | C4⋊C4 | — | 9 | 4 | no | — |
| 178 | C4⋊C4 | D36 | 1 | 2 | yes | — |
| 179 | C22⋊C4 | — | 18 | 2 | no | — |
| 180 | C22⋊C4 | — | 18 | 8 | no | — |
| 181 | C22⋊C4 | D36 | 1 | 2 | yes | — |
| 182 | C42 | — | 18 | 2 | no | — |
| 183 | C42 | C22×D9 | 1 | 2 | yes | — |
| 184 | C22×C3 | — | 2 | 2 | no | — |
| 185 | C22×C3 | C4×D12 | 1 | 2 | yes | — |
| 186 | C22×C3 | C22×D12 | 1 | 1 | yes | characteristic |
| 187 | C2×D3 | — | 6 | 8 | no | — |
| 188 | C2×D3 | — | 12 | 8 | no | — |
| 189 | C2×D3 | — | 24 | 8 | no | — |
| 190 | C3×C4 | — | 2 | 4 | no | — |
| 191 | C3×C4 | C4×D12 | 1 | 2 | yes | — |
| 192 | C3×C4 | C22×C4×D3 | 1 | 1 | yes | characteristic |
| 193 | C3×C4 | C2×#235 | 1 | 1 | yes | characteristic |
| 194 | Dic3 | — | 12 | 4 | no | — |
| 195 | C9 | #2948 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 196 | C23 | — | 18 | 4 | no | — |
| 197 | C23 | — | 18 | 8 | no | — |
| 198 | C23 | — | 72 | 4 | no | — |
| 199 | C23 | C2×D36 | 1 | 1 | yes | characteristic |
| 200 | D4 | — | 9 | 8 | no | — |
| 201 | D4 | — | 18 | 8 | no | — |
| 202 | D4 | — | 18 | 4 | no | — |
| 203 | C2×C4 | — | 18 | 4 | no | — |
| 204 | C2×C4 | — | 72 | 8 | no | — |
| 205 | C2×C4 | C2×C4×D9 | 1 | 2 | yes | — |
| 206 | C2×C4 | C2×D36 | 1 | 4 | yes | — |
| 207 | C2×C4 | C2×D36 | 1 | 1 | yes | characteristic |
| 208 | C2×C4 | #3697 | 1 | 2 | yes | — |
| 209 | C2×C4 | C23×D9 | 1 | 1 | yes | characteristic |
| 210 | C8 | — | 2 | 2 | no | — |
| 211 | C8 | C2×C4×D9 | 1 | 2 | yes | — |
| 212 | C8 | C2×C4×D9 | 1 | 2 | yes | — |
| 213 | C2×C3 | — | 2 | 2 | no | — |
| 214 | C2×C3 | C2×C4×D12 | 1 | 1 | yes | characteristic |
| 215 | C2×C3 | #5752 | 1 | 2 | yes | — |
| 216 | D3 | — | 12 | 8 | no | — |
| 217 | C22 | — | 2 | 2 | no | — |
| 218 | C22 | — | 18 | 8 | no | — |
| 219 | C22 | — | 36 | 8 | no | — |
| 220 | C22 | — | 72 | 8 | no | — |
| 221 | C22 | C4×D36 | 1 | 2 | yes | — |
| 222 | C22 | C22×D36 | 1 | 1 | yes | characteristic |
| 223 | C4 | — | 2 | 4 | no | — |
| 224 | C4 | — | 36 | 4 | no | — |
| 225 | C4 | C4×D36 | 1 | 2 | yes | — |
| 226 | C4 | C22×C4×D9 | 1 | 1 | yes | characteristic |
| 227 | C4 | C2×#3697 | 1 | 1 | yes | characteristic |
| 228 | C3 | #78561 | 1 | 1 | yes | characteristic |
| 229 | C2 | — | 2 | 2 | no | — |
| 230 | C2 | — | 36 | 8 | no | — |
| 231 | C2 | C2×C4×D36 | 1 | 1 | yes | characteristic |
| 232 | C2 | #10589854 | 1 | 2 | yes | — |
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