← #11919013
Subgroups — #11919013
Order 1152.
2981 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 | C3×#5964 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | C2×#64157 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #10595446 | C2 | 1 | 8 | yes | maximal, complemented |
| 4 | #10595445 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #10595444 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #10594786 | C2 | 1 | 6 | yes | maximal, complemented |
| 7 | C2×#63822 | C2 | 1 | 6 | yes | maximal, complemented |
| 8 | #87297 | — | 3 | 2 | no | maximal |
| 9 | C2×C32×#41 | C22 | 1 | 1 | yes | characteristic |
| 10 | C3×#1010 | C22 | 1 | 8 | yes | complemented |
| 11 | C3×#1009 | C22 | 1 | 8 | yes | complemented |
| 12 | C3×D3×#41 | — | 2 | 8 | no | — |
| 13 | C3×#1007 | — | 2 | 2 | no | — |
| 14 | C3×#1004 | — | 2 | 6 | no | — |
| 15 | C2×C3×#235 | C22 | 1 | 12 | yes | complemented |
| 16 | #64157 | C22 | 1 | 4 | yes | complemented |
| 17 | #64157 | C22 | 1 | 4 | yes | complemented |
| 18 | C2×#3748 | C22 | 1 | 3 | yes | complemented |
| 19 | C22×C3⋊(C3⋊C8) | C22 | 1 | 3 | yes | complemented |
| 20 | C2×#3718 | C22 | 1 | 6 | yes | complemented |
| 21 | #63827 | C22 | 1 | 24 | yes | complemented |
| 22 | C2×#3715 | C22 | 1 | 12 | yes | complemented |
| 23 | #63823 | C22 | 1 | 24 | yes | complemented |
| 24 | #63822 | C22 | 1 | 12 | yes | complemented |
| 25 | #63822 | C22 | 1 | 12 | yes | complemented |
| 26 | #63822 | C22 | 1 | 4 | yes | complemented |
| 27 | #63822 | C22 | 1 | 12 | yes | complemented |
| 28 | C2×#3713 | C22 | 1 | 6 | yes | complemented |
| 29 | C3×#585 | — | 3 | 2 | no | — |
| 30 | #5964 | D3 | 1 | 2 | yes | complemented |
| 31 | #5838 | — | 3 | 8 | no | — |
| 32 | #5837 | — | 3 | 8 | no | — |
| 33 | #5836 | — | 3 | 8 | no | — |
| 34 | #5835 | — | 3 | 8 | no | — |
| 35 | #5822 | — | 3 | 12 | no | — |
| 36 | C2×#950 | — | 3 | 12 | no | — |
| 37 | C2×#948 | — | 3 | 2 | no | — |
| 38 | C2×#948 | — | 6 | 1 | no | — |
| 39 | C32×#41 | D4 | 1 | 4 | yes | — |
| 40 | C32×#41 | C23 | 1 | 4 | yes | — |
| 41 | C2×C32×Q8 | D4 | 1 | 1 | yes | characteristic |
| 42 | C2×C32×D4 | D4 | 1 | 3 | yes | — |
| 43 | C22×C32×C4 | C23 | 1 | 3 | yes | — |
| 44 | C2×C3×#67 | — | 2 | 12 | no | — |
| 45 | C3×#239 | — | 2 | 8 | no | — |
| 46 | C3×D3×Q8 | — | 2 | 8 | no | — |
| 47 | C3×#237 | — | 2 | 24 | no | — |
| 48 | C3×D3×D4 | — | 2 | 24 | no | — |
| 49 | C3×#235 | — | 2 | 12 | no | — |
| 50 | C3×#235 | — | 2 | 12 | no | — |
| 51 | C3×#235 | C23 | 1 | 8 | yes | — |
| 52 | C3×#235 | C23 | 1 | 24 | yes | — |
| 53 | C2×C3×D12 | C23 | 1 | 12 | yes | — |
| 54 | C2×C3×C4×D3 | — | 2 | 12 | no | — |
| 55 | C2×C3×Dic6 | C23 | 1 | 12 | yes | — |
| 56 | #3748 | C23 | 1 | 12 | yes | — |
| 57 | C2×C3⋊(C3⋊C8) | C23 | 1 | 6 | yes | — |
| 58 | C2×C3⋊(C3⋊C8) | C23 | 1 | 1 | yes | characteristic |
| 59 | C2×C3⋊(C3⋊C8) | C23 | 1 | 3 | yes | — |
| 60 | C2×C3⋊(C3⋊C8) | C23 | 1 | 6 | yes | — |
| 61 | #3718 | C23 | 1 | 4 | yes | — |
| 62 | #3718 | C23 | 1 | 12 | yes | — |
| 63 | #3715 | C23 | 1 | 8 | yes | — |
| 64 | #3715 | C23 | 1 | 24 | yes | — |
| 65 | #3713 | C23 | 1 | 4 | yes | — |
| 66 | #3713 | C23 | 1 | 12 | yes | — |
| 67 | #3584 | — | 9 | 1 | no | Sylow |
| 68 | C3×2−1+4 | — | 3 | 8 | no | — |
| 69 | C3×2−1+4 | — | 6 | 2 | no | — |
| 70 | C3×H(5,𝔽2) | — | 3 | 8 | no | — |
| 71 | C3×H(5,𝔽2) | — | 6 | 6 | no | — |
| 72 | C2×C3×#41 | — | 2 | 1 | no | — |
| 73 | C2×C3×#41 | — | 3 | 12 | no | — |
| 74 | C2×C3×#41 | — | 6 | 8 | no | — |
| 75 | C2×C3×#41 | C2×D3 | 1 | 2 | yes | — |
| 76 | #1010 | C2×D3 | 1 | 8 | yes | complemented |
| 77 | #1009 | C2×D3 | 1 | 8 | yes | complemented |
| 78 | D3×#41 | — | 2 | 8 | no | — |
| 79 | #1007 | — | 2 | 2 | no | — |
| 80 | #1004 | — | 2 | 6 | no | — |
| 81 | C2×#235 | C2×D3 | 1 | 12 | yes | complemented |
| 82 | #951 | — | 3 | 24 | no | — |
| 83 | #950 | — | 3 | 8 | no | — |
| 84 | #950 | — | 3 | 24 | no | — |
| 85 | #950 | — | 3 | 24 | no | — |
| 86 | #950 | — | 3 | 24 | no | — |
| 87 | #949 | — | 3 | 24 | no | — |
| 88 | #948 | — | 3 | 8 | no | — |
| 89 | #948 | — | 3 | 8 | no | — |
| 90 | #948 | — | 6 | 4 | no | — |
| 91 | #948 | — | 6 | 4 | no | — |
| 92 | C2×#216 | — | 3 | 12 | no | — |
| 93 | #942 | — | 3 | 24 | no | — |
| 94 | C2×#215 | — | 3 | 12 | no | — |
| 95 | C2×#214 | — | 3 | 12 | no | — |
| 96 | #932 | — | 3 | 24 | no | — |
| 97 | C2×#213 | — | 3 | 12 | no | — |
| 98 | C2×#208 | — | 3 | 6 | no | — |
| 99 | C2×#208 | — | 6 | 3 | no | — |
| 100 | C22×C3⋊C8 | — | 3 | 6 | no | — |
| 101 | C22×C3⋊C8 | — | 6 | 3 | no | — |
| 102 | C23×C32 | C2×D4 | 1 | 3 | yes | — |
| 103 | C22×C3×D3 | — | 2 | 12 | no | — |
| 104 | C32×Q8 | C2×D4 | 1 | 4 | yes | — |
| 105 | C32×D4 | C2×D4 | 1 | 12 | yes | — |
| 106 | C2×C32×C4 | C2×D4 | 1 | 6 | yes | — |
| 107 | C2×C32×C4 | C2×D4 | 1 | 3 | yes | — |
| 108 | C2×C32×C4 | C24 | 1 | 1 | yes | characteristic |
| 109 | C2×C32×C4 | C24 | 1 | 6 | yes | — |
| 110 | C3×#67 | — | 2 | 8 | no | — |
| 111 | C3×#67 | — | 2 | 24 | no | — |
| 112 | C2×C3×Dic3 | — | 2 | 12 | no | — |
| 113 | C3×D12 | — | 2 | 12 | no | — |
| 114 | C3×D12 | C24 | 1 | 8 | yes | — |
| 115 | C3×C4×D3 | — | 2 | 8 | no | — |
| 116 | C3×C4×D3 | — | 2 | 24 | no | — |
| 117 | C3×Dic6 | — | 2 | 12 | no | — |
| 118 | C3×Dic6 | C24 | 1 | 8 | yes | — |
| 119 | C3⋊(C3⋊C8) | C24 | 1 | 1 | yes | characteristic |
| 120 | C3⋊(C3⋊C8) | C24 | 1 | 6 | yes | — |
| 121 | C3⋊(C3⋊C8) | C24 | 1 | 1 | yes | characteristic |
| 122 | #585 | — | 3 | 2 | no | — |
| 123 | #578 | — | 9 | 4 | no | — |
| 124 | #577 | — | 9 | 8 | no | — |
| 125 | #576 | — | 9 | 4 | no | — |
| 126 | #575 | — | 9 | 6 | no | — |
| 127 | C2×#135 | — | 9 | 6 | no | — |
| 128 | C2×#131 | — | 9 | 1 | no | — |
| 129 | C3×#41 | — | 2 | 4 | no | — |
| 130 | C3×#41 | — | 2 | 4 | no | — |
| 131 | C3×#41 | — | 3 | 24 | no | — |
| 132 | C3×#41 | — | 3 | 8 | no | — |
| 133 | C3×#41 | — | 6 | 8 | no | — |
| 134 | C3×#41 | — | 6 | 24 | no | — |
| 135 | C3×#41 | — | 6 | 12 | no | — |
| 136 | C3×#41 | — | 6 | 12 | no | — |
| 137 | C3×#41 | #67 | 1 | 8 | yes | — |
| 138 | C3×#41 | C22×D3 | 1 | 8 | yes | — |
| 139 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 140 | C2×C3×Q8 | — | 3 | 12 | no | — |
| 141 | C2×C3×Q8 | — | 6 | 8 | no | — |
| 142 | C2×C3×Q8 | #67 | 1 | 2 | yes | — |
| 143 | C2×C3×D4 | — | 2 | 3 | no | — |
| 144 | C2×C3×D4 | — | 3 | 12 | no | — |
| 145 | C2×C3×D4 | — | 6 | 12 | no | — |
| 146 | C2×C3×D4 | — | 6 | 24 | no | — |
| 147 | C2×C3×D4 | #67 | 1 | 6 | yes | — |
| 148 | C22×C3×C4 | — | 2 | 3 | no | — |
| 149 | C22×C3×C4 | — | 6 | 12 | no | — |
| 150 | C22×C3×C4 | C22×D3 | 1 | 6 | yes | — |
| 151 | C2×#67 | — | 2 | 12 | no | — |
| 152 | #239 | — | 2 | 8 | no | — |
| 153 | D3×Q8 | — | 2 | 8 | no | — |
| 154 | #237 | — | 2 | 24 | no | — |
| 155 | D3×D4 | — | 2 | 24 | no | — |
| 156 | #235 | — | 2 | 12 | no | — |
| 157 | #235 | — | 2 | 12 | no | — |
| 158 | #235 | C22×D3 | 1 | 24 | yes | — |
| 159 | #235 | C22×D3 | 1 | 8 | yes | — |
| 160 | C2×D12 | C22×D3 | 1 | 12 | yes | — |
| 161 | C2×C4×D3 | — | 2 | 12 | no | — |
| 162 | C2×Dic6 | C22×D3 | 1 | 12 | yes | — |
| 163 | #216 | — | 3 | 24 | no | — |
| 164 | #216 | — | 3 | 8 | no | — |
| 165 | #215 | — | 3 | 8 | no | — |
| 166 | #215 | — | 3 | 24 | no | — |
| 167 | #214 | — | 3 | 24 | no | — |
| 168 | #214 | — | 3 | 8 | no | — |
| 169 | #213 | — | 3 | 8 | no | — |
| 170 | #213 | — | 3 | 24 | no | — |
| 171 | #208 | — | 3 | 24 | no | — |
| 172 | #208 | — | 6 | 12 | no | — |
| 173 | C2×C3⋊C8 | — | 3 | 2 | no | — |
| 174 | C2×C3⋊C8 | — | 3 | 6 | no | — |
| 175 | C2×C3⋊C8 | — | 3 | 12 | no | — |
| 176 | C2×C3⋊C8 | — | 3 | 12 | no | — |
| 177 | C2×C3⋊C8 | — | 6 | 1 | no | — |
| 178 | C2×C3⋊C8 | — | 6 | 3 | no | — |
| 179 | C2×C3⋊C8 | — | 6 | 6 | no | — |
| 180 | C2×C3⋊C8 | — | 6 | 6 | no | — |
| 181 | C22×C32 | — | 4 | 3 | no | — |
| 182 | C22×C32 | C22×D4 | 1 | 6 | yes | — |
| 183 | C22×C32 | C22×D4 | 1 | 1 | yes | characteristic |
| 184 | C2×C3×D3 | — | 2 | 8 | no | — |
| 185 | C2×C3×D3 | — | 8 | 12 | no | — |
| 186 | C32×C4 | C22×D4 | 1 | 6 | yes | — |
| 187 | C32×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 188 | C32×C4 | C25 | 1 | 1 | yes | characteristic |
| 189 | C3×Dic3 | — | 2 | 8 | no | — |
| 190 | 2−1+4 | — | 3 | 8 | no | — |
| 191 | 2−1+4 | — | 6 | 2 | no | — |
| 192 | H(5,𝔽2) | — | 3 | 8 | no | — |
| 193 | H(5,𝔽2) | — | 6 | 6 | no | — |
| 194 | C2×#41 | — | 3 | 12 | no | — |
| 195 | C2×#41 | — | 6 | 8 | no | — |
| 196 | C2×#41 | D32 | 1 | 1 | yes | characteristic |
| 197 | #137 | — | 9 | 24 | no | — |
| 198 | AGL(1,ℤ/8) | — | 9 | 24 | no | — |
| 199 | #135 | — | 9 | 4 | no | — |
| 200 | #135 | — | 9 | 12 | no | — |
| 201 | #135 | — | 9 | 12 | no | — |
| 202 | #135 | — | 9 | 12 | no | — |
| 203 | C2×Q16 | — | 9 | 6 | no | — |
| 204 | C2×SD16 | — | 9 | 12 | no | — |
| 205 | C2×D8 | — | 9 | 6 | no | — |
| 206 | #131 | — | 9 | 4 | no | — |
| 207 | #131 | — | 9 | 4 | no | — |
| 208 | C2×M16 | — | 9 | 3 | no | — |
| 209 | C22×C8 | — | 9 | 3 | no | — |
| 210 | C23×C3 | — | 2 | 3 | no | — |
| 211 | C23×C3 | — | 6 | 12 | no | — |
| 212 | C23×C3 | C2×#67 | 1 | 6 | yes | — |
| 213 | C22×D3 | — | 2 | 12 | no | — |
| 214 | C3×Q8 | — | 2 | 4 | no | — |
| 215 | C3×Q8 | — | 3 | 8 | no | — |
| 216 | C3×Q8 | — | 6 | 12 | no | — |
| 217 | C3×Q8 | C2×#67 | 1 | 8 | yes | — |
| 218 | C3×D4 | — | 2 | 12 | no | — |
| 219 | C3×D4 | — | 3 | 8 | no | — |
| 220 | C3×D4 | — | 6 | 24 | no | — |
| 221 | C3×D4 | — | 6 | 8 | no | — |
| 222 | C3×D4 | — | 6 | 12 | no | — |
| 223 | C3×D4 | C2×#67 | 1 | 24 | yes | — |
| 224 | C2×C3×C4 | — | 2 | 1 | no | — |
| 225 | C2×C3×C4 | — | 2 | 6 | no | — |
| 226 | C2×C3×C4 | — | 2 | 3 | no | — |
| 227 | C2×C3×C4 | — | 2 | 6 | no | — |
| 228 | C2×C3×C4 | — | 6 | 12 | no | — |
| 229 | C2×C3×C4 | — | 6 | 8 | no | — |
| 230 | C2×C3×C4 | — | 6 | 24 | no | — |
| 231 | C2×C3×C4 | C2×#67 | 1 | 12 | yes | — |
| 232 | C2×C3×C4 | C2×#67 | 1 | 6 | yes | — |
| 233 | C2×C3×C4 | C23×D3 | 1 | 2 | yes | — |
| 234 | C2×C3×C4 | C23×D3 | 1 | 12 | yes | — |
| 235 | #67 | — | 2 | 8 | no | — |
| 236 | #67 | — | 2 | 24 | no | — |
| 237 | C2×Dic3 | — | 2 | 12 | no | — |
| 238 | D12 | — | 2 | 12 | no | — |
| 239 | D12 | C23×D3 | 1 | 8 | yes | — |
| 240 | C4×D3 | — | 2 | 8 | no | — |
| 241 | C4×D3 | — | 2 | 24 | no | — |
| 242 | Dic6 | — | 2 | 12 | no | — |
| 243 | Dic6 | C23×D3 | 1 | 8 | yes | — |
| 244 | C3⋊C8 | — | 3 | 2 | no | — |
| 245 | C3⋊C8 | — | 3 | 2 | no | — |
| 246 | C3⋊C8 | — | 3 | 12 | no | — |
| 247 | C3⋊C8 | — | 6 | 1 | no | — |
| 248 | C3⋊C8 | — | 6 | 1 | no | — |
| 249 | C3⋊C8 | — | 6 | 6 | no | — |
| 250 | C2×C32 | — | 2 | 1 | no | — |
| 251 | C2×C32 | — | 2 | 6 | no | — |
| 252 | C2×C32 | C23×D4 | 1 | 1 | yes | characteristic |
| 253 | C3×D3 | — | 4 | 8 | no | — |
| 254 | #41 | — | 3 | 8 | no | — |
| 255 | #41 | — | 3 | 24 | no | — |
| 256 | #41 | — | 6 | 8 | no | — |
| 257 | #41 | — | 6 | 24 | no | — |
| 258 | #41 | — | 6 | 12 | no | — |
| 259 | #41 | — | 6 | 12 | no | — |
| 260 | #41 | #625 | 1 | 4 | yes | — |
| 261 | #41 | C2×D32 | 1 | 4 | yes | — |
| 262 | C2×Q8 | — | 3 | 12 | no | — |
| 263 | C2×Q8 | — | 6 | 8 | no | — |
| 264 | C2×Q8 | #625 | 1 | 1 | yes | characteristic |
| 265 | C2×D4 | — | 3 | 12 | no | — |
| 266 | C2×D4 | — | 6 | 12 | no | — |
| 267 | C2×D4 | — | 6 | 24 | no | — |
| 268 | C2×D4 | #625 | 1 | 3 | yes | — |
| 269 | C22×C4 | — | 6 | 12 | no | — |
| 270 | C22×C4 | C2×D32 | 1 | 3 | yes | — |
| 271 | Q16 | — | 9 | 4 | no | — |
| 272 | Q16 | — | 9 | 12 | no | — |
| 273 | SD16 | — | 9 | 8 | no | — |
| 274 | SD16 | — | 9 | 24 | no | — |
| 275 | D8 | — | 9 | 4 | no | — |
| 276 | D8 | — | 9 | 12 | no | — |
| 277 | M16 | — | 9 | 12 | no | — |
| 278 | C2×C8 | — | 9 | 1 | no | — |
| 279 | C2×C8 | — | 9 | 3 | no | — |
| 280 | C2×C8 | — | 9 | 6 | no | — |
| 281 | C2×C8 | — | 9 | 6 | no | — |
| 282 | C22×C3 | — | 2 | 1 | no | — |
| 283 | C22×C3 | — | 2 | 6 | no | — |
| 284 | C22×C3 | — | 4 | 6 | no | — |
| 285 | C22×C3 | — | 4 | 6 | no | — |
| 286 | C22×C3 | — | 6 | 8 | no | — |
| 287 | C22×C3 | — | 24 | 12 | no | — |
| 288 | C22×C3 | C22×#67 | 1 | 12 | yes | — |
| 289 | C22×C3 | C22×#67 | 1 | 2 | yes | — |
| 290 | C2×D3 | — | 2 | 8 | no | — |
| 291 | C2×D3 | — | 8 | 12 | no | — |
| 292 | C3×C4 | — | 2 | 6 | no | — |
| 293 | C3×C4 | — | 2 | 1 | no | — |
| 294 | C3×C4 | — | 2 | 1 | no | — |
| 295 | C3×C4 | — | 6 | 8 | no | — |
| 296 | C3×C4 | C22×#67 | 1 | 12 | yes | — |
| 297 | C3×C4 | C22×#67 | 1 | 2 | yes | — |
| 298 | C3×C4 | C24×D3 | 1 | 2 | yes | — |
| 299 | Dic3 | — | 2 | 8 | no | — |
| 300 | C32 | #3584 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 301 | C23 | — | 6 | 12 | no | — |
| 302 | C23 | C2×#625 | 1 | 3 | yes | — |
| 303 | Q8 | — | 3 | 8 | no | — |
| 304 | Q8 | — | 6 | 12 | no | — |
| 305 | Q8 | C2×#625 | 1 | 4 | yes | — |
| 306 | D4 | — | 3 | 8 | no | — |
| 307 | D4 | — | 6 | 24 | no | — |
| 308 | D4 | — | 6 | 8 | no | — |
| 309 | D4 | — | 6 | 12 | no | — |
| 310 | D4 | C2×#625 | 1 | 12 | yes | — |
| 311 | C2×C4 | — | 6 | 12 | no | — |
| 312 | C2×C4 | — | 6 | 24 | no | — |
| 313 | C2×C4 | — | 6 | 8 | no | — |
| 314 | C2×C4 | C2×#625 | 1 | 3 | yes | — |
| 315 | C2×C4 | C2×#625 | 1 | 6 | yes | — |
| 316 | C2×C4 | C22×D32 | 1 | 6 | yes | — |
| 317 | C2×C4 | C22×D32 | 1 | 1 | yes | characteristic |
| 318 | C8 | — | 9 | 1 | no | — |
| 319 | C8 | — | 9 | 1 | no | — |
| 320 | C8 | — | 9 | 6 | no | — |
| 321 | C2×C3 | — | 2 | 2 | no | — |
| 322 | C2×C3 | — | 2 | 12 | no | — |
| 323 | C2×C3 | — | 2 | 2 | no | — |
| 324 | C2×C3 | — | 2 | 1 | no | — |
| 325 | C2×C3 | — | 4 | 6 | no | — |
| 326 | C2×C3 | — | 12 | 8 | no | — |
| 327 | C2×C3 | C23×#67 | 1 | 2 | yes | — |
| 328 | D3 | — | 4 | 8 | no | — |
| 329 | C22 | — | 4 | 3 | no | — |
| 330 | C22 | — | 6 | 8 | no | — |
| 331 | C22 | — | 24 | 12 | no | — |
| 332 | C22 | C22×#625 | 1 | 6 | yes | — |
| 333 | C22 | C22×#625 | 1 | 1 | yes | characteristic |
| 334 | C4 | — | 6 | 8 | no | — |
| 335 | C4 | C22×#625 | 1 | 6 | yes | — |
| 336 | C4 | C22×#625 | 1 | 1 | yes | characteristic |
| 337 | C4 | C23×D32 | 1 | 1 | yes | characteristic |
| 338 | C3 | — | 2 | 1 | no | — |
| 339 | C3 | #87297 | 1 | 2 | yes | complemented |
| 340 | C2 | — | 2 | 1 | no | — |
| 341 | C2 | — | 2 | 6 | no | — |
| 342 | C2 | — | 12 | 8 | no | — |
| 343 | C2 | C23×#625 | 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