← #11919035
Subgroups — #11919035
Order 1152.
2196 conjugacy classes of subgroups.
The subgroup lattice has 345 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #10593139 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×#63715 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C9×#568 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #10589854 | C2 | 1 | 8 | yes | maximal, complemented |
| 5 | #10589853 | C2 | 1 | 8 | yes | maximal, complemented |
| 6 | #10589850 | C2 | 1 | 6 | yes | maximal, complemented |
| 7 | C2×#63470 | C2 | 1 | 6 | yes | maximal, complemented |
| 8 | #87167 | — | 3 | 1 | no | maximal |
| 9 | C2×C9×#41 | C22 | 1 | 1 | yes | characteristic |
| 10 | #63716 | C22 | 1 | 4 | yes | complemented |
| 11 | #63715 | — | 2 | 4 | no | — |
| 12 | #63715 | C22 | 1 | 8 | yes | complemented |
| 13 | #63715 | C22 | 1 | 4 | yes | complemented |
| 14 | #41×D9 | — | 2 | 4 | no | — |
| 15 | #63713 | — | 2 | 1 | no | — |
| 16 | C2×#3701 | — | 2 | 1 | no | — |
| 17 | #63710 | — | 2 | 3 | no | — |
| 18 | C2×D4×D9 | — | 2 | 3 | no | — |
| 19 | C2×#3697 | C22 | 1 | 3 | yes | complemented |
| 20 | C2×#3697 | C22 | 1 | 6 | yes | complemented |
| 21 | C22×D36 | C22 | 1 | 3 | yes | complemented |
| 22 | C9×#131 | C22 | 1 | 8 | yes | complemented |
| 23 | C2×C9×M16 | C22 | 1 | 6 | yes | complemented |
| 24 | #63471 | C22 | 1 | 4 | yes | complemented |
| 25 | #63471 | C22 | 1 | 12 | yes | complemented |
| 26 | #63470 | C22 | 1 | 12 | yes | complemented |
| 27 | #63470 | C22 | 1 | 24 | yes | complemented |
| 28 | #63470 | C22 | 1 | 12 | yes | complemented |
| 29 | #63467 | C22 | 1 | 24 | yes | complemented |
| 30 | C2×D72 | C22 | 1 | 12 | yes | complemented |
| 31 | C2×#3664 | C22 | 1 | 12 | yes | complemented |
| 32 | #5964 | — | 3 | 1 | no | — |
| 33 | C2×#1009 | — | 3 | 1 | no | — |
| 34 | C3×#568 | D3 | 1 | 1 | yes | characteristic |
| 35 | #5752 | — | 3 | 8 | no | — |
| 36 | #5751 | — | 3 | 8 | no | — |
| 37 | #5748 | — | 3 | 6 | no | — |
| 38 | C2×#908 | — | 3 | 6 | no | — |
| 39 | C23×D9 | — | 2 | 3 | no | — |
| 40 | C9×#41 | D4 | 1 | 4 | yes | — |
| 41 | C9×#41 | C23 | 1 | 4 | yes | — |
| 42 | C2×Q8×C9 | D4 | 1 | 1 | yes | characteristic |
| 43 | C2×D4×C9 | D4 | 1 | 3 | yes | — |
| 44 | C22×C4×C9 | C23 | 1 | 3 | yes | — |
| 45 | C2×#611 | — | 2 | 3 | no | — |
| 46 | C2×#611 | — | 2 | 6 | no | — |
| 47 | #3701 | — | 2 | 8 | no | — |
| 48 | #3701 | — | 2 | 4 | no | — |
| 49 | Q8×D9 | — | 2 | 4 | no | — |
| 50 | #3699 | — | 2 | 12 | no | — |
| 51 | D4×D9 | — | 2 | 24 | no | — |
| 52 | D4×D9 | — | 2 | 12 | no | — |
| 53 | #3697 | — | 2 | 6 | no | — |
| 54 | #3697 | — | 2 | 6 | no | — |
| 55 | #3697 | — | 2 | 6 | no | — |
| 56 | #3697 | C23 | 1 | 4 | yes | — |
| 57 | #3697 | C23 | 1 | 12 | yes | — |
| 58 | #3697 | C23 | 1 | 12 | yes | complemented |
| 59 | C2×D36 | — | 2 | 3 | no | — |
| 60 | C2×D36 | — | 2 | 6 | no | — |
| 61 | C2×D36 | C23 | 1 | 3 | yes | — |
| 62 | C2×D36 | C23 | 1 | 12 | yes | — |
| 63 | C2×D36 | C23 | 1 | 6 | yes | complemented |
| 64 | C2×C4×D9 | — | 2 | 3 | no | — |
| 65 | C2×C4×D9 | — | 2 | 6 | no | — |
| 66 | C2×Dic18 | C23 | 1 | 1 | yes | characteristic |
| 67 | C2×Dic18 | C23 | 1 | 6 | yes | complemented |
| 68 | C9×M16 | C23 | 1 | 4 | yes | — |
| 69 | C9×M16 | C23 | 1 | 12 | yes | complemented |
| 70 | C2×C8×C9 | C23 | 1 | 12 | yes | complemented |
| 71 | D72 | C23 | 1 | 24 | yes | complemented |
| 72 | #3664 | C23 | 1 | 24 | yes | complemented |
| 73 | #3664 | C23 | 1 | 8 | yes | complemented |
| 74 | Dic36 | C23 | 1 | 8 | yes | complemented |
| 75 | #3585 | — | 9 | 1 | no | Sylow |
| 76 | C2×C3×#41 | C2×D3 | 1 | 1 | yes | characteristic |
| 77 | #1010 | — | 3 | 4 | no | — |
| 78 | #1009 | — | 3 | 8 | no | — |
| 79 | #1009 | — | 3 | 4 | no | — |
| 80 | #1009 | — | 6 | 4 | no | — |
| 81 | D3×#41 | — | 6 | 4 | no | — |
| 82 | #1007 | — | 6 | 1 | no | — |
| 83 | C2×#239 | — | 6 | 1 | no | — |
| 84 | #1004 | — | 6 | 3 | no | — |
| 85 | C2×D3×D4 | — | 6 | 3 | no | — |
| 86 | C2×#235 | — | 3 | 3 | no | — |
| 87 | C2×#235 | — | 3 | 6 | no | — |
| 88 | C22×D12 | — | 3 | 3 | no | — |
| 89 | C3×#131 | C2×D3 | 1 | 8 | yes | — |
| 90 | C2×C3×M16 | C2×D3 | 1 | 6 | yes | — |
| 91 | #909 | — | 3 | 4 | no | — |
| 92 | #909 | — | 3 | 12 | no | — |
| 93 | #908 | — | 3 | 12 | no | — |
| 94 | #908 | — | 3 | 24 | no | — |
| 95 | #908 | — | 3 | 12 | no | — |
| 96 | #904 | — | 3 | 24 | no | — |
| 97 | C2×D24 | — | 3 | 12 | no | — |
| 98 | C2×#204 | — | 3 | 12 | no | — |
| 99 | C23×C9 | C2×D4 | 1 | 3 | yes | — |
| 100 | C22×D9 | — | 2 | 3 | no | — |
| 101 | C22×D9 | — | 2 | 6 | no | — |
| 102 | C22×D9 | — | 2 | 12 | no | — |
| 103 | C22×D9 | — | 8 | 6 | no | — |
| 104 | Q8×C9 | C2×D4 | 1 | 4 | yes | — |
| 105 | D4×C9 | C2×D4 | 1 | 12 | yes | — |
| 106 | C2×C4×C9 | C2×D4 | 1 | 3 | yes | — |
| 107 | C2×C4×C9 | C2×D4 | 1 | 6 | yes | — |
| 108 | C2×C4×C9 | C24 | 1 | 6 | yes | — |
| 109 | C2×C4×C9 | C24 | 1 | 1 | yes | characteristic |
| 110 | #611 | — | 2 | 4 | no | — |
| 111 | #611 | — | 2 | 12 | no | — |
| 112 | #611 | — | 2 | 12 | no | — |
| 113 | C2×Dic9 | — | 2 | 1 | no | — |
| 114 | C2×Dic9 | — | 2 | 6 | no | — |
| 115 | D36 | — | 2 | 3 | no | — |
| 116 | D36 | — | 2 | 12 | no | — |
| 117 | D36 | — | 2 | 6 | no | — |
| 118 | D36 | C24 | 1 | 6 | yes | — |
| 119 | D36 | C24 | 1 | 4 | yes | — |
| 120 | C4×D9 | — | 2 | 4 | no | — |
| 121 | C4×D9 | — | 2 | 12 | no | — |
| 122 | C4×D9 | — | 2 | 12 | no | — |
| 123 | Dic18 | — | 2 | 1 | no | — |
| 124 | Dic18 | — | 2 | 6 | no | — |
| 125 | Dic18 | C24 | 1 | 2 | yes | — |
| 126 | Dic18 | C24 | 1 | 4 | yes | — |
| 127 | C8×C9 | C24 | 1 | 8 | yes | — |
| 128 | #585 | — | 9 | 1 | no | — |
| 129 | C2×H(5,𝔽2) | — | 9 | 1 | no | — |
| 130 | #577 | — | 9 | 8 | no | — |
| 131 | #576 | — | 9 | 8 | no | — |
| 132 | #575 | — | 9 | 6 | no | — |
| 133 | C2×AGL(1,ℤ/8) | — | 9 | 6 | no | — |
| 134 | #568 | D9 | 1 | 1 | yes | characteristic, complemented |
| 135 | C23×D3 | — | 6 | 3 | no | — |
| 136 | C3×#41 | D12 | 1 | 4 | yes | — |
| 137 | C3×#41 | C22×D3 | 1 | 4 | yes | — |
| 138 | C2×C3×Q8 | D12 | 1 | 1 | yes | characteristic |
| 139 | C2×C3×D4 | D12 | 1 | 3 | yes | — |
| 140 | C22×C3×C4 | C22×D3 | 1 | 3 | yes | — |
| 141 | C2×#67 | — | 6 | 3 | no | — |
| 142 | C2×#67 | — | 6 | 6 | no | — |
| 143 | #239 | — | 6 | 8 | no | — |
| 144 | #239 | — | 6 | 4 | no | — |
| 145 | D3×Q8 | — | 6 | 4 | no | — |
| 146 | #237 | — | 6 | 12 | no | — |
| 147 | D3×D4 | — | 6 | 24 | no | — |
| 148 | D3×D4 | — | 6 | 12 | no | — |
| 149 | #235 | — | 3 | 12 | no | — |
| 150 | #235 | — | 3 | 4 | no | — |
| 151 | #235 | — | 3 | 12 | no | — |
| 152 | #235 | — | 6 | 6 | no | — |
| 153 | #235 | — | 6 | 6 | no | — |
| 154 | #235 | — | 6 | 6 | no | — |
| 155 | C2×D12 | — | 3 | 12 | no | — |
| 156 | C2×D12 | — | 3 | 3 | no | — |
| 157 | C2×D12 | — | 3 | 6 | no | — |
| 158 | C2×D12 | — | 6 | 3 | no | — |
| 159 | C2×D12 | — | 6 | 6 | no | — |
| 160 | C2×C4×D3 | — | 6 | 3 | no | — |
| 161 | C2×C4×D3 | — | 6 | 6 | no | — |
| 162 | C2×Dic6 | — | 3 | 1 | no | — |
| 163 | C2×Dic6 | — | 3 | 6 | no | — |
| 164 | C3×M16 | C22×D3 | 1 | 4 | yes | — |
| 165 | C3×M16 | C22×D3 | 1 | 12 | yes | — |
| 166 | C2×C3×C8 | C22×D3 | 1 | 12 | yes | — |
| 167 | Dic12 | — | 3 | 8 | no | — |
| 168 | D24 | — | 3 | 24 | no | — |
| 169 | #204 | — | 3 | 24 | no | — |
| 170 | #204 | — | 3 | 8 | no | — |
| 171 | C22×C9 | — | 4 | 3 | no | — |
| 172 | C22×C9 | C22×D4 | 1 | 1 | yes | characteristic |
| 173 | C22×C9 | C22×D4 | 1 | 6 | yes | — |
| 174 | C2×D9 | — | 2 | 4 | no | — |
| 175 | C2×D9 | — | 2 | 6 | no | — |
| 176 | C2×D9 | — | 4 | 6 | no | — |
| 177 | C2×D9 | — | 8 | 6 | no | — |
| 178 | C2×D9 | — | 8 | 12 | no | — |
| 179 | C4×C9 | C22×D4 | 1 | 1 | yes | characteristic |
| 180 | C4×C9 | C22×D4 | 1 | 6 | yes | — |
| 181 | C4×C9 | C25 | 1 | 1 | yes | characteristic |
| 182 | Dic9 | — | 2 | 4 | no | — |
| 183 | Dic9 | — | 2 | 2 | no | — |
| 184 | 2−1+4 | — | 9 | 4 | no | — |
| 185 | 2−1+4 | — | 18 | 1 | no | — |
| 186 | H(5,𝔽2) | — | 9 | 4 | no | — |
| 187 | H(5,𝔽2) | — | 9 | 8 | no | — |
| 188 | H(5,𝔽2) | — | 18 | 4 | no | — |
| 189 | H(5,𝔽2) | — | 18 | 3 | no | — |
| 190 | C2×#41 | — | 9 | 6 | no | — |
| 191 | C2×#41 | — | 9 | 3 | no | — |
| 192 | C2×#41 | — | 18 | 4 | no | — |
| 193 | C2×#41 | — | 18 | 1 | no | — |
| 194 | C2×#41 | C2×D9 | 1 | 1 | yes | characteristic |
| 195 | C22×D4 | — | 9 | 3 | no | — |
| 196 | C22×D4 | — | 18 | 3 | no | — |
| 197 | #137 | — | 9 | 4 | no | — |
| 198 | #137 | — | 9 | 12 | no | — |
| 199 | AGL(1,ℤ/8) | — | 9 | 12 | no | — |
| 200 | AGL(1,ℤ/8) | — | 9 | 24 | no | — |
| 201 | AGL(1,ℤ/8) | — | 9 | 12 | no | — |
| 202 | #135 | — | 9 | 24 | no | — |
| 203 | C2×SD16 | — | 9 | 12 | no | — |
| 204 | C2×D8 | — | 9 | 12 | no | — |
| 205 | #131 | C2×D9 | 1 | 8 | yes | complemented |
| 206 | C2×M16 | C2×D9 | 1 | 6 | yes | complemented |
| 207 | C23×C3 | C2×D12 | 1 | 3 | yes | — |
| 208 | C22×D3 | — | 6 | 3 | no | — |
| 209 | C22×D3 | — | 6 | 6 | no | — |
| 210 | C22×D3 | — | 6 | 12 | no | — |
| 211 | C22×D3 | — | 24 | 6 | no | — |
| 212 | C3×Q8 | C2×D12 | 1 | 4 | yes | — |
| 213 | C3×D4 | C2×D12 | 1 | 12 | yes | — |
| 214 | C2×C3×C4 | C2×D12 | 1 | 3 | yes | — |
| 215 | C2×C3×C4 | C2×D12 | 1 | 6 | yes | — |
| 216 | C2×C3×C4 | C23×D3 | 1 | 6 | yes | — |
| 217 | C2×C3×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 218 | #67 | — | 6 | 4 | no | — |
| 219 | #67 | — | 6 | 12 | no | — |
| 220 | #67 | — | 6 | 12 | no | — |
| 221 | C2×Dic3 | — | 6 | 1 | no | — |
| 222 | C2×Dic3 | — | 6 | 6 | no | — |
| 223 | D12 | — | 3 | 6 | no | — |
| 224 | D12 | — | 3 | 4 | no | — |
| 225 | D12 | — | 6 | 3 | no | — |
| 226 | D12 | — | 6 | 12 | no | — |
| 227 | D12 | — | 6 | 6 | no | — |
| 228 | C4×D3 | — | 6 | 4 | no | — |
| 229 | C4×D3 | — | 6 | 12 | no | — |
| 230 | C4×D3 | — | 6 | 12 | no | — |
| 231 | Dic6 | — | 3 | 4 | no | — |
| 232 | Dic6 | — | 3 | 2 | no | — |
| 233 | Dic6 | — | 6 | 1 | no | — |
| 234 | Dic6 | — | 6 | 6 | no | — |
| 235 | C3×C8 | C23×D3 | 1 | 8 | yes | — |
| 236 | C2×C9 | — | 2 | 1 | no | — |
| 237 | C2×C9 | — | 2 | 6 | no | — |
| 238 | C2×C9 | C23×D4 | 1 | 1 | yes | characteristic |
| 239 | D9 | — | 4 | 6 | no | — |
| 240 | D9 | — | 4 | 4 | no | — |
| 241 | C24 | — | 18 | 3 | no | — |
| 242 | #41 | — | 9 | 12 | no | — |
| 243 | #41 | — | 9 | 12 | no | — |
| 244 | #41 | — | 9 | 4 | no | — |
| 245 | #41 | — | 18 | 8 | no | — |
| 246 | #41 | — | 18 | 4 | no | — |
| 247 | #41 | — | 18 | 12 | no | — |
| 248 | #41 | — | 18 | 6 | no | — |
| 249 | #41 | — | 18 | 6 | no | — |
| 250 | #41 | — | 18 | 6 | no | — |
| 251 | #41 | D36 | 1 | 4 | yes | — |
| 252 | #41 | C22×D9 | 1 | 4 | yes | — |
| 253 | C2×Q8 | — | 9 | 6 | no | — |
| 254 | C2×Q8 | — | 9 | 1 | no | — |
| 255 | C2×Q8 | — | 18 | 4 | no | — |
| 256 | C2×Q8 | D36 | 1 | 1 | yes | characteristic |
| 257 | C2×D4 | — | 9 | 6 | no | — |
| 258 | C2×D4 | — | 9 | 12 | no | — |
| 259 | C2×D4 | — | 9 | 3 | no | — |
| 260 | C2×D4 | — | 18 | 3 | no | — |
| 261 | C2×D4 | — | 18 | 6 | no | — |
| 262 | C2×D4 | — | 18 | 24 | no | — |
| 263 | C2×D4 | — | 18 | 12 | no | — |
| 264 | C2×D4 | — | 18 | 3 | no | — |
| 265 | C2×D4 | — | 18 | 6 | no | — |
| 266 | C2×D4 | D36 | 1 | 3 | yes | — |
| 267 | C22×C4 | — | 18 | 3 | no | — |
| 268 | C22×C4 | — | 18 | 6 | no | — |
| 269 | C22×C4 | C22×D9 | 1 | 3 | yes | — |
| 270 | Q16 | — | 9 | 8 | no | — |
| 271 | SD16 | — | 9 | 24 | no | — |
| 272 | SD16 | — | 9 | 8 | no | — |
| 273 | D8 | — | 9 | 24 | no | — |
| 274 | M16 | C22×D9 | 1 | 4 | yes | — |
| 275 | M16 | C22×D9 | 1 | 12 | yes | complemented |
| 276 | C2×C8 | C22×D9 | 1 | 12 | yes | complemented |
| 277 | C22×C3 | — | 4 | 3 | no | — |
| 278 | C22×C3 | C22×D12 | 1 | 1 | yes | characteristic |
| 279 | C22×C3 | C22×D12 | 1 | 6 | yes | — |
| 280 | C2×D3 | — | 6 | 4 | no | — |
| 281 | C2×D3 | — | 6 | 6 | no | — |
| 282 | C2×D3 | — | 12 | 6 | no | — |
| 283 | C2×D3 | — | 24 | 12 | no | — |
| 284 | C2×D3 | — | 24 | 6 | no | — |
| 285 | C3×C4 | C22×D12 | 1 | 1 | yes | characteristic |
| 286 | C3×C4 | C22×D12 | 1 | 6 | yes | — |
| 287 | C3×C4 | C24×D3 | 1 | 1 | yes | characteristic |
| 288 | Dic3 | — | 6 | 4 | no | — |
| 289 | Dic3 | — | 6 | 2 | no | — |
| 290 | C9 | #3585 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 291 | C23 | — | 18 | 3 | no | — |
| 292 | C23 | — | 18 | 6 | no | — |
| 293 | C23 | — | 18 | 12 | no | — |
| 294 | C23 | — | 72 | 6 | no | — |
| 295 | C23 | C2×D36 | 1 | 3 | yes | — |
| 296 | Q8 | — | 9 | 4 | no | — |
| 297 | Q8 | — | 9 | 2 | no | — |
| 298 | Q8 | — | 18 | 6 | no | — |
| 299 | Q8 | — | 18 | 1 | no | — |
| 300 | Q8 | C2×D36 | 1 | 4 | yes | — |
| 301 | D4 | — | 9 | 4 | no | — |
| 302 | D4 | — | 9 | 6 | no | — |
| 303 | D4 | — | 18 | 12 | no | — |
| 304 | D4 | — | 18 | 4 | no | — |
| 305 | D4 | — | 18 | 12 | no | — |
| 306 | D4 | — | 18 | 3 | no | — |
| 307 | D4 | — | 18 | 12 | no | — |
| 308 | D4 | — | 18 | 6 | no | — |
| 309 | D4 | C2×D36 | 1 | 12 | yes | — |
| 310 | C2×C4 | — | 18 | 1 | no | — |
| 311 | C2×C4 | — | 18 | 6 | no | — |
| 312 | C2×C4 | — | 18 | 4 | no | — |
| 313 | C2×C4 | — | 18 | 12 | no | — |
| 314 | C2×C4 | — | 18 | 12 | no | — |
| 315 | C2×C4 | C2×D36 | 1 | 3 | yes | — |
| 316 | C2×C4 | C2×D36 | 1 | 6 | yes | — |
| 317 | C2×C4 | C23×D9 | 1 | 6 | yes | — |
| 318 | C2×C4 | C23×D9 | 1 | 1 | yes | characteristic |
| 319 | C8 | C23×D9 | 1 | 8 | yes | — |
| 320 | C2×C3 | — | 2 | 1 | no | — |
| 321 | C2×C3 | — | 2 | 6 | no | — |
| 322 | C2×C3 | C23×D12 | 1 | 1 | yes | characteristic |
| 323 | D3 | — | 12 | 6 | no | — |
| 324 | D3 | — | 12 | 4 | no | — |
| 325 | C22 | — | 4 | 3 | no | — |
| 326 | C22 | — | 18 | 4 | no | — |
| 327 | C22 | — | 18 | 6 | no | — |
| 328 | C22 | — | 36 | 6 | no | — |
| 329 | C22 | — | 72 | 12 | no | — |
| 330 | C22 | — | 72 | 6 | no | — |
| 331 | C22 | C22×D36 | 1 | 1 | yes | characteristic |
| 332 | C22 | C22×D36 | 1 | 6 | yes | — |
| 333 | C4 | — | 18 | 2 | no | — |
| 334 | C4 | — | 18 | 4 | no | — |
| 335 | C4 | C22×D36 | 1 | 1 | yes | characteristic |
| 336 | C4 | C22×D36 | 1 | 6 | yes | — |
| 337 | C4 | C24×D9 | 1 | 1 | yes | characteristic |
| 338 | C3 | #87167 | 1 | 1 | yes | characteristic |
| 339 | C2 | — | 2 | 1 | no | — |
| 340 | C2 | — | 2 | 6 | no | — |
| 341 | C2 | — | 36 | 6 | no | — |
| 342 | C2 | — | 36 | 4 | no | — |
| 343 | C2 | C23×D36 | 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