Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
12141 conjugacy classes of subgroups.
The subgroup lattice has 456 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C3⋊D3×2−1+4 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C3×D3×2−1+4 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #10596694 | C2 | 1 | 10 | yes | maximal, complemented |
| 4 | D3×#1010 | C2 | 1 | 20 | yes | maximal, complemented |
| 5 | D32×#41 | C2 | 1 | 10 | yes | maximal, complemented |
| 6 | #10596687 | C2 | 1 | 5 | yes | maximal, complemented |
| 7 | D3×#1007 | C2 | 1 | 10 | yes | maximal, complemented |
| 8 | C2×D32×Q8 | C2 | 1 | 5 | yes | maximal, complemented |
| 9 | C2×D3×2−1+4 | — | 3 | 2 | no | maximal |
| 10 | C32×2−1+4 | C22 | 1 | 1 | yes | characteristic, complemented |
| 11 | #64367 | C22 | 1 | 10 | yes | complemented |
| 12 | #41×C3⋊D3 | C22 | 1 | 10 | yes | complemented |
| 13 | #64364 | C22 | 1 | 5 | yes | complemented |
| 14 | C2×Q8×C3⋊D3 | C22 | 1 | 5 | yes | complemented |
| 15 | C3×#1010 | C22 | 1 | 20 | yes | complemented |
| 16 | C3×D3×#41 | C22 | 1 | 20 | yes | complemented |
| 17 | C3×#1007 | C22 | 1 | 10 | yes | complemented |
| 18 | C2×C3×D3×Q8 | C22 | 1 | 10 | yes | complemented |
| 19 | #64319 | C22 | 1 | 10 | yes | complemented |
| 20 | D3×#239 | C22 | 1 | 20 | yes | complemented |
| 21 | D32×Q8 | C22 | 1 | 10 | yes | — |
| 22 | D32×Q8 | C22 | 1 | 40 | yes | complemented |
| 23 | D32×Q8 | C22 | 1 | 20 | yes | complemented |
| 24 | #64316 | C22 | 1 | 20 | yes | complemented |
| 25 | #64315 | C22 | 1 | 40 | yes | complemented |
| 26 | #64312 | C22 | 1 | 30 | yes | complemented |
| 27 | D3×#237 | C22 | 1 | 60 | yes | complemented |
| 28 | D32×D4 | C22 | 1 | 10 | yes | — |
| 29 | #64309 | C22 | 1 | 60 | yes | complemented |
| 30 | #64306 | C22 | 1 | 30 | yes | complemented |
| 31 | D3×#235 | C22 | 1 | 60 | yes | complemented |
| 32 | C2×C4×D32 | C22 | 1 | 15 | yes | — |
| 33 | C2×#3797 | C22 | 1 | 15 | yes | complemented |
| 34 | #64298 | C22 | 1 | 30 | yes | complemented |
| 35 | #64297 | C22 | 1 | 60 | yes | complemented |
| 36 | C2×D3×Dic6 | C22 | 1 | 30 | yes | complemented |
| 37 | C2×C3×2−1+4 | — | 3 | 2 | no | — |
| 38 | D3×2−1+4 | — | 3 | 2 | no | — |
| 39 | D3×2−1+4 | — | 3 | 20 | no | — |
| 40 | D3×2−1+4 | — | 3 | 20 | no | — |
| 41 | D3×2−1+4 | — | 3 | 10 | no | — |
| 42 | D3×2−1+4 | — | 3 | 10 | no | — |
| 43 | D3×2−1+4 | — | 6 | 1 | no | — |
| 44 | D3×2−1+4 | D3 | 1 | 2 | yes | direct product factor |
| 45 | C2×#1010 | — | 3 | 20 | no | — |
| 46 | C2×D3×#41 | — | 3 | 20 | no | — |
| 47 | C2×#1007 | — | 3 | 10 | no | — |
| 48 | C22×D3×Q8 | — | 3 | 10 | no | — |
| 49 | C22×D32 | C23 | 1 | 5 | yes | — |
| 50 | C32×#41 | C23 | 1 | 10 | yes | complemented |
| 51 | C2×C32×Q8 | C23 | 1 | 5 | yes | complemented |
| 52 | #3832 | C23 | 1 | 10 | yes | complemented |
| 53 | Q8×C3⋊D3 | C23 | 1 | 10 | yes | — |
| 54 | Q8×C3⋊D3 | C23 | 1 | 20 | yes | complemented |
| 55 | #3830 | C23 | 1 | 30 | yes | complemented |
| 56 | D4×C3⋊D3 | C23 | 1 | 10 | yes | — |
| 57 | #3828 | C23 | 1 | 30 | yes | complemented |
| 58 | C2×C4×C3⋊D3 | C23 | 1 | 15 | yes | — |
| 59 | C2×#634 | C23 | 1 | 15 | yes | complemented |
| 60 | C3×#239 | C23 | 1 | 20 | yes | complemented |
| 61 | C3×D3×Q8 | C23 | 1 | 20 | yes | — |
| 62 | C3×D3×Q8 | C23 | 1 | 40 | yes | complemented |
| 63 | C3×#237 | C23 | 1 | 60 | yes | complemented |
| 64 | C3×D3×D4 | C23 | 1 | 20 | yes | — |
| 65 | C3×#235 | C23 | 1 | 60 | yes | complemented |
| 66 | C2×C3×C4×D3 | C23 | 1 | 30 | yes | — |
| 67 | C2×C3×Dic6 | C23 | 1 | 30 | yes | complemented |
| 68 | #3811 | C23 | 1 | 20 | yes | — |
| 69 | D3×#67 | C23 | 1 | 40 | yes | — |
| 70 | C2×#627 | C23 | 1 | 30 | yes | complemented |
| 71 | C2×#624 | C23 | 1 | 15 | yes | — |
| 72 | #3805 | C23 | 1 | 60 | yes | complemented |
| 73 | #3804 | C23 | 1 | 120 | yes | complemented |
| 74 | C2×D3×Dic3 | C23 | 1 | 30 | yes | — |
| 75 | #3802 | C23 | 1 | 10 | yes | — |
| 76 | D3×D12 | C23 | 1 | 20 | yes | — |
| 77 | C4×D32 | C23 | 1 | 10 | yes | — |
| 78 | C4×D32 | C23 | 1 | 60 | yes | — |
| 79 | C4×D32 | C23 | 1 | 30 | yes | — |
| 80 | #3799 | C23 | 1 | 60 | yes | complemented |
| 81 | #3798 | C23 | 1 | 60 | yes | complemented |
| 82 | #3797 | C23 | 1 | 30 | yes | — |
| 83 | #3797 | C23 | 1 | 60 | yes | complemented |
| 84 | #3796 | C23 | 1 | 60 | yes | complemented |
| 85 | #3795 | C23 | 1 | 60 | yes | complemented |
| 86 | D3×Dic6 | C23 | 1 | 60 | yes | — |
| 87 | D3×Dic6 | C23 | 1 | 120 | yes | complemented |
| 88 | C22×2−1+4 | — | 9 | 1 | no | Sylow |
| 89 | C3×2−1+4 | — | 2 | 1 | no | — |
| 90 | C3×2−1+4 | — | 3 | 20 | no | — |
| 91 | C3×2−1+4 | — | 3 | 10 | no | — |
| 92 | C3×2−1+4 | C2×D3 | 1 | 2 | yes | complemented |
| 93 | C2×C3×#41 | — | 3 | 20 | no | — |
| 94 | C22×C3×Q8 | — | 3 | 10 | no | — |
| 95 | #1010 | — | 3 | 20 | no | — |
| 96 | #1010 | — | 3 | 40 | no | — |
| 97 | #1010 | — | 3 | 120 | no | — |
| 98 | #1010 | — | 3 | 60 | no | — |
| 99 | #1010 | — | 3 | 60 | no | — |
| 100 | #1010 | — | 6 | 10 | no | — |
| 101 | #1010 | C2×D3 | 1 | 20 | yes | complemented |
| 102 | D3×#41 | — | 3 | 20 | no | — |
| 103 | D3×#41 | — | 3 | 20 | no | — |
| 104 | D3×#41 | — | 3 | 20 | no | — |
| 105 | D3×#41 | — | 3 | 60 | no | — |
| 106 | D3×#41 | — | 3 | 60 | no | — |
| 107 | D3×#41 | — | 3 | 60 | no | — |
| 108 | D3×#41 | — | 3 | 60 | no | — |
| 109 | D3×#41 | — | 6 | 10 | no | — |
| 110 | D3×#41 | C2×D3 | 1 | 20 | yes | complemented |
| 111 | #1007 | — | 3 | 10 | no | — |
| 112 | #1007 | — | 3 | 40 | no | — |
| 113 | #1007 | — | 3 | 40 | no | — |
| 114 | #1007 | — | 3 | 60 | no | — |
| 115 | #1007 | — | 6 | 5 | no | — |
| 116 | #1007 | C2×D3 | 1 | 10 | yes | complemented |
| 117 | C2×#239 | — | 3 | 20 | no | — |
| 118 | C2×D3×Q8 | — | 3 | 10 | no | — |
| 119 | C2×D3×Q8 | — | 3 | 20 | no | — |
| 120 | C2×D3×Q8 | — | 3 | 40 | no | — |
| 121 | C2×D3×Q8 | — | 3 | 40 | no | — |
| 122 | C2×D3×Q8 | — | 3 | 40 | no | — |
| 123 | C2×D3×Q8 | — | 3 | 30 | no | — |
| 124 | C2×D3×Q8 | — | 3 | 30 | no | — |
| 125 | C2×D3×Q8 | — | 6 | 5 | no | — |
| 126 | C2×D3×Q8 | C2×D3 | 1 | 10 | yes | complemented |
| 127 | C2×#237 | — | 3 | 60 | no | — |
| 128 | C2×D3×D4 | — | 3 | 20 | no | — |
| 129 | C2×#235 | — | 3 | 60 | no | — |
| 130 | C22×C4×D3 | — | 3 | 30 | no | — |
| 131 | C22×Dic6 | — | 3 | 30 | no | — |
| 132 | C22×C3⋊D3 | C24 | 1 | 5 | yes | — |
| 133 | C22×C3×D3 | C24 | 1 | 10 | yes | — |
| 134 | C2×D32 | — | 2 | 20 | no | — |
| 135 | C2×D32 | C24 | 1 | 10 | yes | — |
| 136 | C2×D32 | C24 | 1 | 5 | yes | — |
| 137 | C2×D32 | C24 | 1 | 1 | yes | characteristic |
| 138 | C32×Q8 | C24 | 1 | 10 | yes | — |
| 139 | C32×D4 | C24 | 1 | 10 | yes | — |
| 140 | C2×C32×C4 | C24 | 1 | 15 | yes | — |
| 141 | #638 | C24 | 1 | 20 | yes | — |
| 142 | C2×C3⋊Dic3 | C24 | 1 | 15 | yes | — |
| 143 | C4⋊(C3⋊D3) | C24 | 1 | 10 | yes | — |
| 144 | C4×C3⋊D3 | C24 | 1 | 30 | yes | — |
| 145 | C4×C3⋊D3 | C24 | 1 | 10 | yes | — |
| 146 | #634 | C24 | 1 | 30 | yes | — |
| 147 | C3×#67 | C24 | 1 | 40 | yes | — |
| 148 | C2×C3×Dic3 | C24 | 1 | 30 | yes | — |
| 149 | C3×D12 | C24 | 1 | 20 | yes | — |
| 150 | C3×C4×D3 | C24 | 1 | 20 | yes | — |
| 151 | C3×C4×D3 | C24 | 1 | 60 | yes | — |
| 152 | C3×Dic6 | C24 | 1 | 60 | yes | — |
| 153 | #627 | C24 | 1 | 60 | yes | — |
| 154 | #626 | C24 | 1 | 40 | yes | — |
| 155 | #625 | C24 | 1 | 20 | yes | — |
| 156 | #624 | C24 | 1 | 10 | yes | — |
| 157 | #624 | C24 | 1 | 30 | yes | — |
| 158 | D3×Dic3 | C24 | 1 | 20 | yes | — |
| 159 | D3×Dic3 | C24 | 1 | 60 | yes | — |
| 160 | C2×2−1+4 | — | 3 | 2 | no | — |
| 161 | C2×2−1+4 | — | 9 | 10 | no | — |
| 162 | C2×2−1+4 | — | 9 | 20 | no | — |
| 163 | C2×2−1+4 | — | 9 | 10 | no | — |
| 164 | C2×2−1+4 | — | 9 | 5 | no | — |
| 165 | C2×2−1+4 | — | 9 | 1 | no | — |
| 166 | C22×#41 | — | 9 | 10 | no | — |
| 167 | C23×Q8 | — | 9 | 5 | no | — |
| 168 | C23×D3 | — | 3 | 10 | no | — |
| 169 | C3×#41 | — | 2 | 10 | no | — |
| 170 | C3×#41 | — | 3 | 20 | no | — |
| 171 | C3×#41 | — | 3 | 60 | no | — |
| 172 | C3×#41 | — | 3 | 60 | no | — |
| 173 | C3×#41 | C22×D3 | 1 | 20 | yes | complemented |
| 174 | C2×C3×Q8 | — | 2 | 5 | no | — |
| 175 | C2×C3×Q8 | — | 3 | 20 | no | — |
| 176 | C2×C3×Q8 | — | 3 | 40 | no | — |
| 177 | C2×C3×Q8 | — | 3 | 30 | no | — |
| 178 | C2×C3×Q8 | C22×D3 | 1 | 10 | yes | complemented |
| 179 | C2×C3×D4 | — | 3 | 20 | no | — |
| 180 | C22×C3×C4 | — | 3 | 30 | no | — |
| 181 | C2×#67 | — | 3 | 40 | no | — |
| 182 | C22×Dic3 | — | 3 | 30 | no | — |
| 183 | #239 | — | 3 | 20 | no | — |
| 184 | #239 | — | 3 | 60 | no | — |
| 185 | #239 | — | 3 | 60 | no | — |
| 186 | #239 | — | 6 | 10 | no | — |
| 187 | #239 | C22×D3 | 1 | 20 | yes | complemented |
| 188 | D3×Q8 | — | 3 | 20 | no | — |
| 189 | D3×Q8 | — | 3 | 40 | no | — |
| 190 | D3×Q8 | — | 3 | 60 | no | — |
| 191 | D3×Q8 | — | 3 | 120 | no | — |
| 192 | D3×Q8 | — | 3 | 60 | no | — |
| 193 | D3×Q8 | — | 3 | 120 | no | — |
| 194 | D3×Q8 | — | 6 | 10 | no | — |
| 195 | D3×Q8 | — | 6 | 20 | no | — |
| 196 | D3×Q8 | C22×D3 | 1 | 20 | yes | — |
| 197 | D3×Q8 | C22×D3 | 1 | 40 | yes | complemented |
| 198 | #237 | — | 3 | 60 | no | — |
| 199 | #237 | — | 3 | 120 | no | — |
| 200 | #237 | — | 3 | 120 | no | — |
| 201 | #237 | — | 3 | 60 | no | — |
| 202 | #237 | — | 3 | 60 | no | — |
| 203 | #237 | — | 6 | 30 | no | — |
| 204 | #237 | C22×D3 | 1 | 60 | yes | complemented |
| 205 | D3×D4 | — | 3 | 40 | no | — |
| 206 | D3×D4 | — | 3 | 20 | no | — |
| 207 | D3×D4 | — | 3 | 40 | no | — |
| 208 | D3×D4 | — | 3 | 20 | no | — |
| 209 | D3×D4 | — | 3 | 20 | no | — |
| 210 | D3×D4 | — | 6 | 10 | no | — |
| 211 | D3×D4 | C22×D3 | 1 | 20 | yes | — |
| 212 | #235 | — | 3 | 60 | no | — |
| 213 | #235 | — | 3 | 120 | no | — |
| 214 | #235 | — | 3 | 60 | no | — |
| 215 | #235 | — | 3 | 120 | no | — |
| 216 | #235 | — | 3 | 60 | no | — |
| 217 | #235 | — | 6 | 30 | no | — |
| 218 | #235 | C22×D3 | 1 | 60 | yes | complemented |
| 219 | C2×D12 | — | 3 | 20 | no | — |
| 220 | C2×C4×D3 | — | 3 | 30 | no | — |
| 221 | C2×C4×D3 | — | 3 | 30 | no | — |
| 222 | C2×C4×D3 | — | 3 | 30 | no | — |
| 223 | C2×C4×D3 | — | 3 | 20 | no | — |
| 224 | C2×C4×D3 | — | 3 | 60 | no | — |
| 225 | C2×C4×D3 | — | 3 | 60 | no | — |
| 226 | C2×C4×D3 | — | 3 | 60 | no | — |
| 227 | C2×C4×D3 | — | 6 | 15 | no | — |
| 228 | C2×C4×D3 | C22×D3 | 1 | 30 | yes | — |
| 229 | C2×Dic6 | — | 3 | 30 | no | — |
| 230 | C2×Dic6 | — | 3 | 60 | no | — |
| 231 | C2×Dic6 | — | 3 | 60 | no | — |
| 232 | C2×Dic6 | — | 3 | 120 | no | — |
| 233 | C2×Dic6 | — | 6 | 15 | no | — |
| 234 | C2×Dic6 | C22×D3 | 1 | 30 | yes | complemented |
| 235 | C22×C32 | C25 | 1 | 5 | yes | — |
| 236 | C2×C3⋊D3 | — | 2 | 10 | no | — |
| 237 | C2×C3⋊D3 | C25 | 1 | 5 | yes | — |
| 238 | C2×C3⋊D3 | C25 | 1 | 1 | yes | characteristic |
| 239 | C2×C3×D3 | — | 2 | 20 | no | — |
| 240 | C2×C3×D3 | C25 | 1 | 10 | yes | — |
| 241 | C2×C3×D3 | C25 | 1 | 2 | yes | — |
| 242 | D32 | — | 2 | 10 | no | — |
| 243 | D32 | — | 2 | 20 | no | — |
| 244 | D32 | 2−1+4 | 1 | 4 | yes | direct product factor |
| 245 | C32×C4 | C25 | 1 | 10 | yes | — |
| 246 | C3⋊Dic3 | C25 | 1 | 10 | yes | — |
| 247 | C3×Dic3 | C25 | 1 | 20 | yes | — |
| 248 | 2−1+4 | — | 3 | 20 | no | — |
| 249 | 2−1+4 | — | 3 | 10 | no | — |
| 250 | 2−1+4 | — | 9 | 20 | no | — |
| 251 | 2−1+4 | — | 9 | 40 | no | — |
| 252 | 2−1+4 | — | 9 | 60 | no | — |
| 253 | 2−1+4 | — | 9 | 60 | no | — |
| 254 | 2−1+4 | — | 9 | 30 | no | — |
| 255 | 2−1+4 | — | 9 | 10 | no | — |
| 256 | 2−1+4 | — | 9 | 5 | no | — |
| 257 | 2−1+4 | D32 | 1 | 1 | yes | characteristic, direct product factor |
| 258 | C2×#41 | — | 3 | 20 | no | — |
| 259 | C2×#41 | — | 9 | 60 | no | — |
| 260 | C2×#41 | — | 9 | 60 | no | — |
| 261 | C2×#41 | — | 9 | 20 | no | — |
| 262 | C2×#41 | — | 9 | 10 | no | — |
| 263 | C2×#41 | — | 9 | 30 | no | — |
| 264 | C2×#41 | — | 9 | 30 | no | — |
| 265 | C2×#41 | — | 9 | 10 | no | — |
| 266 | C22×Q8 | — | 3 | 10 | no | — |
| 267 | C22×Q8 | — | 9 | 30 | no | — |
| 268 | C22×Q8 | — | 9 | 10 | no | — |
| 269 | C22×Q8 | — | 9 | 40 | no | — |
| 270 | C22×Q8 | — | 9 | 20 | no | — |
| 271 | C22×Q8 | — | 9 | 15 | no | — |
| 272 | C22×Q8 | — | 9 | 5 | no | — |
| 273 | C22×D4 | — | 9 | 10 | no | — |
| 274 | C23×C4 | — | 9 | 15 | no | — |
| 275 | C23×C3 | — | 3 | 10 | no | — |
| 276 | C22×D3 | — | 3 | 2 | no | — |
| 277 | C22×D3 | — | 3 | 10 | no | — |
| 278 | C22×D3 | — | 3 | 10 | no | — |
| 279 | C22×D3 | — | 3 | 10 | no | — |
| 280 | C22×D3 | — | 3 | 10 | no | — |
| 281 | C22×D3 | — | 6 | 5 | no | — |
| 282 | C22×D3 | — | 6 | 40 | no | — |
| 283 | C22×D3 | C23×D3 | 1 | 10 | yes | — |
| 284 | C3×Q8 | — | 2 | 10 | no | — |
| 285 | C3×Q8 | — | 3 | 60 | no | — |
| 286 | C3×Q8 | C23×D3 | 1 | 20 | yes | — |
| 287 | C3×D4 | — | 2 | 10 | no | — |
| 288 | C3×D4 | — | 3 | 40 | no | — |
| 289 | C3×D4 | — | 3 | 20 | no | — |
| 290 | C3×D4 | C23×D3 | 1 | 20 | yes | — |
| 291 | C2×C3×C4 | — | 2 | 15 | no | — |
| 292 | C2×C3×C4 | — | 3 | 30 | no | — |
| 293 | C2×C3×C4 | — | 3 | 20 | no | — |
| 294 | C2×C3×C4 | — | 3 | 60 | no | — |
| 295 | C2×C3×C4 | C23×D3 | 1 | 30 | yes | — |
| 296 | #67 | — | 3 | 40 | no | — |
| 297 | #67 | — | 3 | 40 | no | — |
| 298 | #67 | — | 3 | 40 | no | — |
| 299 | #67 | — | 6 | 20 | no | — |
| 300 | #67 | C23×D3 | 1 | 40 | yes | — |
| 301 | C2×Dic3 | — | 3 | 30 | no | — |
| 302 | C2×Dic3 | — | 3 | 20 | no | — |
| 303 | C2×Dic3 | — | 3 | 60 | no | — |
| 304 | C2×Dic3 | — | 6 | 15 | no | — |
| 305 | C2×Dic3 | C23×D3 | 1 | 30 | yes | — |
| 306 | D12 | — | 3 | 40 | no | — |
| 307 | D12 | — | 3 | 20 | no | — |
| 308 | D12 | — | 6 | 10 | no | — |
| 309 | D12 | C23×D3 | 1 | 20 | yes | — |
| 310 | C4×D3 | — | 3 | 20 | no | — |
| 311 | C4×D3 | — | 3 | 60 | no | — |
| 312 | C4×D3 | — | 3 | 20 | no | — |
| 313 | C4×D3 | — | 3 | 60 | no | — |
| 314 | C4×D3 | — | 3 | 20 | no | — |
| 315 | C4×D3 | — | 3 | 60 | no | — |
| 316 | C4×D3 | — | 6 | 10 | no | — |
| 317 | C4×D3 | — | 6 | 30 | no | — |
| 318 | C4×D3 | C23×D3 | 1 | 20 | yes | — |
| 319 | C4×D3 | C23×D3 | 1 | 60 | yes | — |
| 320 | Dic6 | — | 3 | 60 | no | — |
| 321 | Dic6 | — | 3 | 120 | no | — |
| 322 | Dic6 | — | 6 | 30 | no | — |
| 323 | Dic6 | C23×D3 | 1 | 60 | yes | — |
| 324 | C2×C32 | — | 2 | 5 | no | — |
| 325 | C2×C32 | C26 | 1 | 1 | yes | characteristic |
| 326 | C3⋊D3 | — | 2 | 5 | no | — |
| 327 | C3⋊D3 | C2×2−1+4 | 1 | 2 | yes | complemented |
| 328 | C3×D3 | — | 2 | 10 | no | — |
| 329 | C3×D3 | C2×2−1+4 | 1 | 4 | yes | complemented |
| 330 | C24 | — | 9 | 5 | no | — |
| 331 | #41 | — | 3 | 20 | no | — |
| 332 | #41 | — | 3 | 60 | no | — |
| 333 | #41 | — | 3 | 60 | no | — |
| 334 | #41 | — | 9 | 60 | no | — |
| 335 | #41 | — | 9 | 120 | no | — |
| 336 | #41 | — | 9 | 60 | no | — |
| 337 | #41 | — | 9 | 60 | no | — |
| 338 | #41 | — | 9 | 60 | no | — |
| 339 | #41 | — | 9 | 60 | no | — |
| 340 | #41 | — | 9 | 10 | no | — |
| 341 | #41 | — | 9 | 30 | no | — |
| 342 | #41 | — | 9 | 30 | no | — |
| 343 | #41 | C2×D32 | 1 | 10 | yes | complemented |
| 344 | C2×Q8 | — | 3 | 20 | no | — |
| 345 | C2×Q8 | — | 3 | 40 | no | — |
| 346 | C2×Q8 | — | 3 | 30 | no | — |
| 347 | C2×Q8 | — | 9 | 30 | no | — |
| 348 | C2×Q8 | — | 9 | 60 | no | — |
| 349 | C2×Q8 | — | 9 | 120 | no | — |
| 350 | C2×Q8 | — | 9 | 30 | no | — |
| 351 | C2×Q8 | — | 9 | 60 | no | — |
| 352 | C2×Q8 | — | 9 | 10 | no | — |
| 353 | C2×Q8 | — | 9 | 20 | no | — |
| 354 | C2×Q8 | — | 9 | 15 | no | — |
| 355 | C2×Q8 | C2×D32 | 1 | 5 | yes | complemented |
| 356 | C2×D4 | — | 3 | 20 | no | — |
| 357 | C2×D4 | — | 9 | 20 | no | — |
| 358 | C2×D4 | — | 9 | 20 | no | — |
| 359 | C2×D4 | — | 9 | 10 | no | — |
| 360 | C2×D4 | — | 9 | 40 | no | — |
| 361 | C2×D4 | — | 9 | 10 | no | — |
| 362 | C22×C4 | — | 3 | 30 | no | — |
| 363 | C22×C4 | — | 9 | 10 | no | — |
| 364 | C22×C4 | — | 9 | 15 | no | — |
| 365 | C22×C4 | — | 9 | 60 | no | — |
| 366 | C22×C4 | — | 9 | 30 | no | — |
| 367 | C22×C4 | — | 9 | 30 | no | — |
| 368 | C22×C4 | — | 9 | 15 | no | — |
| 369 | C22×C3 | — | 2 | 5 | no | — |
| 370 | C22×C3 | — | 3 | 2 | no | — |
| 371 | C22×C3 | — | 3 | 10 | no | — |
| 372 | C22×C3 | — | 6 | 20 | no | — |
| 373 | C22×C3 | C24×D3 | 1 | 10 | yes | — |
| 374 | C2×D3 | — | 2 | 20 | no | — |
| 375 | C2×D3 | — | 3 | 2 | no | — |
| 376 | C2×D3 | — | 3 | 8 | no | — |
| 377 | C2×D3 | — | 3 | 10 | no | — |
| 378 | C2×D3 | — | 6 | 1 | no | — |
| 379 | C2×D3 | — | 6 | 5 | no | — |
| 380 | C2×D3 | — | 6 | 20 | no | — |
| 381 | C2×D3 | — | 6 | 20 | no | — |
| 382 | C2×D3 | — | 6 | 20 | no | — |
| 383 | C2×D3 | — | 6 | 20 | no | — |
| 384 | C2×D3 | — | 12 | 10 | no | — |
| 385 | C2×D3 | C24×D3 | 1 | 10 | yes | — |
| 386 | C2×D3 | C24×D3 | 1 | 2 | yes | — |
| 387 | C3×C4 | — | 2 | 10 | no | — |
| 388 | C3×C4 | — | 3 | 20 | no | — |
| 389 | C3×C4 | C24×D3 | 1 | 20 | yes | — |
| 390 | Dic3 | — | 3 | 20 | no | — |
| 391 | Dic3 | — | 6 | 10 | no | — |
| 392 | Dic3 | C24×D3 | 1 | 20 | yes | — |
| 393 | C32 | C22×2−1+4 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 394 | C23 | — | 3 | 10 | no | — |
| 395 | C23 | — | 9 | 1 | no | — |
| 396 | C23 | — | 9 | 10 | no | — |
| 397 | C23 | — | 9 | 5 | no | — |
| 398 | C23 | — | 9 | 5 | no | — |
| 399 | C23 | — | 18 | 20 | no | — |
| 400 | Q8 | — | 3 | 60 | no | — |
| 401 | Q8 | — | 9 | 60 | no | — |
| 402 | Q8 | — | 9 | 30 | no | — |
| 403 | Q8 | C22×D32 | 1 | 10 | yes | — |
| 404 | D4 | — | 3 | 40 | no | — |
| 405 | D4 | — | 3 | 20 | no | — |
| 406 | D4 | — | 9 | 40 | no | — |
| 407 | D4 | — | 9 | 20 | no | — |
| 408 | D4 | — | 9 | 20 | no | — |
| 409 | D4 | — | 9 | 10 | no | — |
| 410 | D4 | C22×D32 | 1 | 10 | yes | — |
| 411 | C2×C4 | — | 3 | 30 | no | — |
| 412 | C2×C4 | — | 3 | 20 | no | — |
| 413 | C2×C4 | — | 3 | 60 | no | — |
| 414 | C2×C4 | — | 9 | 10 | no | — |
| 415 | C2×C4 | — | 9 | 30 | no | — |
| 416 | C2×C4 | — | 9 | 20 | no | — |
| 417 | C2×C4 | — | 9 | 60 | no | — |
| 418 | C2×C4 | — | 9 | 15 | no | — |
| 419 | C2×C4 | — | 9 | 10 | no | — |
| 420 | C2×C4 | — | 9 | 30 | no | — |
| 421 | C2×C4 | C22×D32 | 1 | 15 | yes | — |
| 422 | C2×C3 | — | 2 | 10 | no | — |
| 423 | C2×C3 | — | 2 | 1 | no | — |
| 424 | C2×C3 | — | 3 | 4 | no | — |
| 425 | C2×C3 | — | 4 | 5 | no | — |
| 426 | C2×C3 | — | 6 | 10 | no | — |
| 427 | C2×C3 | C25×D3 | 1 | 2 | yes | — |
| 428 | D3 | — | 2 | 10 | no | — |
| 429 | D3 | — | 3 | 4 | no | — |
| 430 | D3 | — | 6 | 2 | no | — |
| 431 | D3 | — | 6 | 10 | no | — |
| 432 | D3 | — | 12 | 5 | no | — |
| 433 | D3 | D3×2−1+4 | 1 | 4 | yes | direct product factor |
| 434 | C22 | — | 3 | 2 | no | — |
| 435 | C22 | — | 3 | 10 | no | — |
| 436 | C22 | — | 6 | 20 | no | — |
| 437 | C22 | — | 9 | 4 | no | — |
| 438 | C22 | — | 9 | 1 | no | — |
| 439 | C22 | — | 9 | 5 | no | — |
| 440 | C22 | — | 18 | 10 | no | — |
| 441 | C22 | — | 18 | 20 | no | — |
| 442 | C22 | — | 18 | 10 | no | — |
| 443 | C22 | C23×D32 | 1 | 5 | yes | — |
| 444 | C4 | — | 3 | 20 | no | — |
| 445 | C4 | — | 9 | 10 | no | — |
| 446 | C4 | C23×D32 | 1 | 10 | yes | — |
| 447 | C3 | — | 2 | 1 | no | — |
| 448 | C3 | C2×D3×2−1+4 | 1 | 2 | yes | complemented |
| 449 | C2 | — | 2 | 5 | no | — |
| 450 | C2 | — | 3 | 4 | no | — |
| 451 | C2 | — | 6 | 10 | no | — |
| 452 | C2 | — | 9 | 2 | no | — |
| 453 | C2 | — | 18 | 5 | no | — |
| 454 | C2 | C24×D32 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C24×D32 |
| commutator, socle, cosocle | C2×C32 | C26 |
| Fitting | C32×2−1+4 | C22 |
| hypercenter | 2−1+4 | D32 |
| hypocenter | C32 | C22×2−1+4 |
| LCS | G ▷ C2×C32 ▷ C32 | |
| UCS | C1 ◁ C2 ◁ 2−1+4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3⋊D3×2−1+4 | C2 | semidirect |
| 2. C3×D3×2−1+4 | C2 | semidirect |
| 3. #10596694 | C2 | semidirect |
| 4. D3×#1010 | C2 | semidirect |
| 5. D32×#41 | C2 | semidirect |
| 6. #10596687 | C2 | semidirect |
| 7. D3×#1007 | C2 | semidirect |
| 8. C2×D32×Q8 | C2 | semidirect |
| 10. C32×2−1+4 | C22 | semidirect |
| 11. #64367 | C22 | semidirect |
| 12. #41×C3⋊D3 | C22 | semidirect |
| 13. #64364 | C22 | semidirect |
| 14. C2×Q8×C3⋊D3 | C22 | semidirect |
| 15. C3×#1010 | C22 | semidirect |
| 16. C3×D3×#41 | C22 | semidirect |
| 17. C3×#1007 | C22 | semidirect |
| 18. C2×C3×D3×Q8 | C22 | semidirect |
| 19. #64319 | C22 | semidirect |
| 20. D3×#239 | C22 | semidirect |
| 22. D32×Q8 | C22 | semidirect |
| 23. D32×Q8 | C22 | semidirect |
| 24. #64316 | C22 | semidirect |
| 25. #64315 | C22 | semidirect |
| 26. #64312 | C22 | semidirect |
| 27. D3×#237 | C22 | semidirect |
| 29. #64309 | C22 | semidirect |
| 30. #64306 | C22 | semidirect |
| 31. D3×#235 | C22 | semidirect |
| 33. C2×#3797 | C22 | semidirect |
| 34. #64298 | C22 | semidirect |
| 35. #64297 | C22 | semidirect |
| 36. C2×D3×Dic6 | C22 | semidirect |
| 44. D3×2−1+4 | D3 | direct (N × H) |
| 50. C32×#41 | C23 | semidirect |
| 51. C2×C32×Q8 | C23 | semidirect |
| 52. #3832 | C23 | semidirect |
| 54. Q8×C3⋊D3 | C23 | semidirect |
| 55. #3830 | C23 | semidirect |
| 57. #3828 | C23 | semidirect |
| 59. C2×#634 | C23 | semidirect |
| 60. C3×#239 | C23 | semidirect |
| 62. C3×D3×Q8 | C23 | semidirect |
| 63. C3×#237 | C23 | semidirect |
| 65. C3×#235 | C23 | semidirect |
| 67. C2×C3×Dic6 | C23 | semidirect |
| 70. C2×#627 | C23 | semidirect |
| 72. #3805 | C23 | semidirect |
| 73. #3804 | C23 | semidirect |
| 80. #3799 | C23 | semidirect |
| 81. #3798 | C23 | semidirect |
| 83. #3797 | C23 | semidirect |
| 84. #3796 | C23 | semidirect |
| 85. #3795 | C23 | semidirect |
| 87. D3×Dic6 | C23 | semidirect |
| 92. C3×2−1+4 | C2×D3 | semidirect |
| 101. #1010 | C2×D3 | semidirect |
| 110. D3×#41 | C2×D3 | semidirect |
| 116. #1007 | C2×D3 | semidirect |
| 126. C2×D3×Q8 | C2×D3 | semidirect |
| 173. C3×#41 | C22×D3 | semidirect |
| 178. C2×C3×Q8 | C22×D3 | semidirect |
| 187. #239 | C22×D3 | semidirect |
| 197. D3×Q8 | C22×D3 | semidirect |
| 204. #237 | C22×D3 | semidirect |
| 218. #235 | C22×D3 | semidirect |
| 234. C2×Dic6 | C22×D3 | semidirect |
| 244. D32 | 2−1+4 | direct (N × H) |
| 257. 2−1+4 | D32 | direct (N × H) |
| 327. C3⋊D3 | C2×2−1+4 | semidirect |
| 329. C3×D3 | C2×2−1+4 | semidirect |
| 343. #41 | C2×D32 | semidirect |
| 355. C2×Q8 | C2×D32 | semidirect |
| 393. C32 | C22×2−1+4 | semidirect |
| 433. D3 | D3×2−1+4 | direct (N × H) |
| 448. C3 | C2×D3×2−1+4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3⋊D3×2−1+4 | 2 |
| C3×D3×2−1+4 | 2 |
| #10596694 | 2 |
| D3×#1010 | 2 |
| D32×#41 | 2 |
| #10596687 | 2 |
| D3×#1007 | 2 |
| C2×D32×Q8 | 2 |
| C2×D3×2−1+4 | 3 |