Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
4476 conjugacy classes of subgroups.
The subgroup lattice has 627 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×#64367 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×#64364 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C32×#548 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #10596305 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | Q8×#638 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #10596148 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | #10596139 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | #10596103 | C2 | 1 | 3 | yes | maximal, complemented |
| 9 | #10596100 | C2 | 1 | 3 | yes | maximal, complemented |
| 10 | #10596079 | C2 | 1 | 3 | yes | maximal, complemented |
| 11 | #10596070 | C2 | 1 | 3 | yes | maximal, complemented |
| 12 | #10596047 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | C4×Q8×C3⋊D3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #10596023 | C2 | 1 | 3 | yes | maximal, complemented |
| 15 | #10596019 | C2 | 1 | 3 | yes | maximal, complemented |
| 16 | #86737 | — | 3 | 4 | no | maximal |
| 17 | C2×C32×#41 | C22 | 1 | 1 | yes | characteristic |
| 18 | C22×C32×Q8 | C22 | 1 | 1 | yes | characteristic |
| 19 | #64367 | — | 2 | 8 | no | — |
| 20 | #64364 | — | 2 | 8 | no | — |
| 21 | C2×#3832 | C22 | 1 | 3 | yes | — |
| 22 | C2×#3832 | C22 | 1 | 1 | yes | characteristic |
| 23 | C2×Q8×C3⋊D3 | C22 | 1 | 3 | yes | — |
| 24 | C2×Q8×C3⋊D3 | C22 | 1 | 1 | yes | characteristic |
| 25 | C2×Q8×C3⋊D3 | C22 | 1 | 1 | yes | characteristic |
| 26 | C2×#3830 | C22 | 1 | 3 | yes | — |
| 27 | C2×#3830 | C22 | 1 | 3 | yes | — |
| 28 | C2×#3828 | C22 | 1 | 3 | yes | — |
| 29 | C2×#3828 | C22 | 1 | 3 | yes | — |
| 30 | C2×#3828 | C22 | 1 | 3 | yes | — |
| 31 | C22×#634 | C22 | 1 | 3 | yes | — |
| 32 | C32×#124 | C22 | 1 | 3 | yes | — |
| 33 | C32×C22⋊Q8 | C22 | 1 | 3 | yes | — |
| 34 | C32×#121 | C22 | 1 | 3 | yes | — |
| 35 | C32×C4×Q8 | C22 | 1 | 1 | yes | characteristic |
| 36 | C32×C4×D4 | C22 | 1 | 3 | yes | — |
| 37 | #64155 | C22 | 1 | 3 | yes | — |
| 38 | Q8×C3⋊Dic3 | C22 | 1 | 1 | yes | characteristic |
| 39 | #64153 | C22 | 1 | 3 | yes | — |
| 40 | #64149 | C22 | 1 | 3 | yes | — |
| 41 | #64149 | C22 | 1 | 3 | yes | — |
| 42 | #64148 | C22 | 1 | 6 | yes | — |
| 43 | #64147 | C22 | 1 | 3 | yes | — |
| 44 | #64147 | C22 | 1 | 3 | yes | — |
| 45 | #64139 | C22 | 1 | 3 | yes | — |
| 46 | C4×#638 | C22 | 1 | 3 | yes | — |
| 47 | C4×#638 | C22 | 1 | 3 | yes | — |
| 48 | #64133 | C22 | 1 | 3 | yes | — |
| 49 | #64106 | C22 | 1 | 3 | yes | — |
| 50 | #64105 | C22 | 1 | 6 | yes | — |
| 51 | #64104 | C22 | 1 | 3 | yes | — |
| 52 | #64104 | C22 | 1 | 3 | yes | — |
| 53 | C4⋊C4×C3⋊D3 | C22 | 1 | 3 | yes | — |
| 54 | #64097 | C22 | 1 | 3 | yes | — |
| 55 | #64096 | C22 | 1 | 3 | yes | — |
| 56 | #64094 | C22 | 1 | 3 | yes | — |
| 57 | #64094 | C22 | 1 | 3 | yes | — |
| 58 | #64093 | C22 | 1 | 6 | yes | — |
| 59 | #64093 | C22 | 1 | 6 | yes | — |
| 60 | #64093 | C22 | 1 | 3 | yes | — |
| 61 | #64093 | C22 | 1 | 1 | yes | characteristic |
| 62 | #64090 | C22 | 1 | 6 | yes | — |
| 63 | #64090 | C22 | 1 | 6 | yes | — |
| 64 | #64087 | C22 | 1 | 6 | yes | — |
| 65 | #64084 | C22 | 1 | 3 | yes | — |
| 66 | C4×C4⋊(C3⋊D3) | C22 | 1 | 3 | yes | — |
| 67 | C42×C3⋊D3 | C22 | 1 | 3 | yes | — |
| 68 | C4×#634 | C22 | 1 | 3 | yes | — |
| 69 | C2×#1010 | — | 3 | 4 | no | — |
| 70 | C2×#1007 | — | 3 | 4 | no | — |
| 71 | C3×#548 | D3 | 1 | 4 | yes | complemented |
| 72 | #5834 | — | 3 | 4 | no | — |
| 73 | Q8×#67 | — | 3 | 4 | no | — |
| 74 | #5677 | — | 3 | 12 | no | — |
| 75 | #5668 | — | 3 | 12 | no | — |
| 76 | #5632 | — | 3 | 12 | no | — |
| 77 | #5629 | — | 3 | 12 | no | — |
| 78 | #5608 | — | 3 | 12 | no | — |
| 79 | #5599 | — | 3 | 12 | no | — |
| 80 | #5576 | — | 3 | 4 | no | — |
| 81 | C4×D3×Q8 | — | 3 | 4 | no | — |
| 82 | #5552 | — | 3 | 12 | no | — |
| 83 | #5548 | — | 3 | 12 | no | — |
| 84 | C32×#41 | — | 2 | 4 | no | — |
| 85 | C2×C32×Q8 | — | 2 | 4 | no | — |
| 86 | C2×C32×Q8 | C23 | 1 | 3 | yes | — |
| 87 | C2×C32×Q8 | C23 | 1 | 1 | yes | characteristic |
| 88 | C2×C32×D4 | C23 | 1 | 3 | yes | — |
| 89 | C2×C32×D4 | C23 | 1 | 3 | yes | — |
| 90 | C22×C32×C4 | C23 | 1 | 3 | yes | — |
| 91 | C22×C32×C4 | C23 | 1 | 3 | yes | — |
| 92 | C2×#638 | C23 | 1 | 3 | yes | — |
| 93 | C2×#638 | C23 | 1 | 3 | yes | — |
| 94 | C2×#638 | C23 | 1 | 3 | yes | — |
| 95 | C2×#638 | C23 | 1 | 1 | yes | characteristic |
| 96 | C2×#638 | C23 | 1 | 1 | yes | characteristic |
| 97 | C2×#638 | C23 | 1 | 3 | yes | — |
| 98 | C2×#638 | C23 | 1 | 6 | yes | — |
| 99 | C22×C3⋊Dic3 | C23 | 1 | 6 | yes | — |
| 100 | #3832 | — | 2 | 4 | no | — |
| 101 | #3832 | — | 2 | 12 | no | — |
| 102 | Q8×C3⋊D3 | — | 2 | 4 | no | — |
| 103 | Q8×C3⋊D3 | — | 2 | 12 | no | — |
| 104 | Q8×C3⋊D3 | D4 | 1 | 8 | yes | complemented |
| 105 | #3830 | — | 2 | 12 | no | — |
| 106 | #3830 | — | 2 | 12 | no | — |
| 107 | #3828 | — | 2 | 12 | no | — |
| 108 | #3828 | — | 2 | 12 | no | — |
| 109 | #3828 | — | 2 | 12 | no | — |
| 110 | C2×C4⋊(C3⋊D3) | C23 | 1 | 3 | yes | — |
| 111 | C2×C4⋊(C3⋊D3) | C23 | 1 | 3 | yes | — |
| 112 | C2×C4⋊(C3⋊D3) | C23 | 1 | 1 | yes | characteristic |
| 113 | C2×C4⋊(C3⋊D3) | C23 | 1 | 3 | yes | — |
| 114 | C2×C4×C3⋊D3 | C23 | 1 | 1 | yes | characteristic |
| 115 | C2×C4×C3⋊D3 | C23 | 1 | 3 | yes | — |
| 116 | C2×C4×C3⋊D3 | C23 | 1 | 3 | yes | — |
| 117 | C2×C4×C3⋊D3 | C23 | 1 | 6 | yes | — |
| 118 | C2×C4×C3⋊D3 | C23 | 1 | 3 | yes | — |
| 119 | C2×C4×C3⋊D3 | C23 | 1 | 3 | yes | — |
| 120 | C2×#634 | — | 2 | 12 | no | — |
| 121 | C2×#634 | C23 | 1 | 3 | yes | — |
| 122 | C2×#634 | C23 | 1 | 3 | yes | — |
| 123 | C2×#634 | C23 | 1 | 3 | yes | — |
| 124 | C2×#634 | C23 | 1 | 3 | yes | — |
| 125 | C32×C4⋊C4 | C23 | 1 | 3 | yes | — |
| 126 | C32×C4⋊C4 | C23 | 1 | 3 | yes | — |
| 127 | C32×C22⋊C4 | C23 | 1 | 6 | yes | — |
| 128 | C32×C22⋊C4 | C23 | 1 | 3 | yes | — |
| 129 | C32×C22⋊C4 | C23 | 1 | 1 | yes | characteristic |
| 130 | C32×C42 | C23 | 1 | 3 | yes | — |
| 131 | #3757 | C23 | 1 | 3 | yes | — |
| 132 | #3757 | C23 | 1 | 3 | yes | — |
| 133 | #3752 | C23 | 1 | 1 | yes | characteristic |
| 134 | #3752 | C23 | 1 | 3 | yes | — |
| 135 | #3752 | C23 | 1 | 6 | yes | — |
| 136 | #3752 | C23 | 1 | 3 | yes | — |
| 137 | #3752 | C23 | 1 | 3 | yes | — |
| 138 | C4⋊(C3⋊Dic3) | C23 | 1 | 3 | yes | — |
| 139 | C4⋊(C3⋊Dic3) | C23 | 1 | 3 | yes | — |
| 140 | #3750 | C23 | 1 | 6 | yes | — |
| 141 | #3750 | C23 | 1 | 6 | yes | — |
| 142 | #3750 | C23 | 1 | 3 | yes | — |
| 143 | #3750 | C23 | 1 | 1 | yes | characteristic |
| 144 | C4×C3⋊Dic3 | C23 | 1 | 3 | yes | — |
| 145 | C4×C3⋊Dic3 | C23 | 1 | 3 | yes | — |
| 146 | C4×C3⋊Dic3 | C23 | 1 | 3 | yes | — |
| 147 | #3497 | — | 9 | 1 | no | Sylow |
| 148 | C2×C3×#41 | C2×D3 | 1 | 4 | yes | — |
| 149 | C22×C3×Q8 | C2×D3 | 1 | 4 | yes | — |
| 150 | #1010 | — | 6 | 32 | no | — |
| 151 | #1007 | — | 6 | 32 | no | — |
| 152 | C2×#239 | — | 3 | 12 | no | — |
| 153 | C2×#239 | — | 3 | 4 | no | — |
| 154 | C2×D3×Q8 | — | 3 | 4 | no | — |
| 155 | C2×D3×Q8 | — | 3 | 12 | no | — |
| 156 | C2×D3×Q8 | — | 3 | 4 | no | — |
| 157 | C2×#237 | — | 3 | 12 | no | — |
| 158 | C2×#237 | — | 3 | 12 | no | — |
| 159 | C2×#235 | — | 3 | 12 | no | — |
| 160 | C2×#235 | — | 3 | 12 | no | — |
| 161 | C2×#235 | — | 3 | 12 | no | — |
| 162 | C22×Dic6 | — | 3 | 12 | no | — |
| 163 | C3×#124 | C2×D3 | 1 | 12 | yes | — |
| 164 | C3×C22⋊Q8 | C2×D3 | 1 | 12 | yes | — |
| 165 | C3×#121 | C2×D3 | 1 | 12 | yes | — |
| 166 | C3×C4×Q8 | C2×D3 | 1 | 4 | yes | — |
| 167 | C3×C4×D4 | C2×D3 | 1 | 12 | yes | — |
| 168 | #946 | — | 3 | 12 | no | — |
| 169 | Q8×Dic3 | — | 3 | 4 | no | — |
| 170 | #944 | — | 3 | 12 | no | — |
| 171 | #940 | — | 3 | 12 | no | — |
| 172 | #940 | — | 3 | 12 | no | — |
| 173 | #939 | — | 3 | 24 | no | — |
| 174 | #938 | — | 3 | 12 | no | — |
| 175 | #938 | — | 3 | 12 | no | — |
| 176 | #930 | — | 3 | 12 | no | — |
| 177 | C4×#67 | — | 3 | 12 | no | — |
| 178 | C4×#67 | — | 3 | 12 | no | — |
| 179 | #924 | — | 3 | 12 | no | — |
| 180 | #897 | — | 3 | 12 | no | — |
| 181 | #896 | — | 3 | 24 | no | — |
| 182 | #895 | — | 3 | 12 | no | — |
| 183 | #895 | — | 3 | 12 | no | — |
| 184 | D3×C4⋊C4 | — | 3 | 12 | no | — |
| 185 | #888 | — | 3 | 12 | no | — |
| 186 | #887 | — | 3 | 12 | no | — |
| 187 | #885 | — | 3 | 12 | no | — |
| 188 | #885 | — | 3 | 12 | no | — |
| 189 | #884 | — | 3 | 12 | no | — |
| 190 | #884 | — | 3 | 24 | no | — |
| 191 | #884 | — | 3 | 24 | no | — |
| 192 | #884 | — | 3 | 4 | no | — |
| 193 | #67⋊C4 | — | 3 | 24 | no | — |
| 194 | #67⋊C4 | — | 3 | 24 | no | — |
| 195 | #878 | — | 3 | 24 | no | — |
| 196 | #875 | — | 3 | 12 | no | — |
| 197 | C4×D12 | — | 3 | 12 | no | — |
| 198 | C42×D3 | — | 3 | 12 | no | — |
| 199 | C4×Dic6 | — | 3 | 12 | no | — |
| 200 | C23×C32 | C24 | 1 | 1 | yes | characteristic |
| 201 | C23×C32 | C24 | 1 | 3 | yes | — |
| 202 | C22×C3⋊D3 | C24 | 1 | 3 | yes | — |
| 203 | C22×C3⋊D3 | C24 | 1 | 1 | yes | characteristic |
| 204 | C22×C3⋊D3 | C24 | 1 | 1 | yes | characteristic |
| 205 | C32×Q8 | — | 2 | 6 | no | — |
| 206 | C32×Q8 | C2×D4 | 1 | 4 | yes | — |
| 207 | C32×D4 | — | 2 | 6 | no | — |
| 208 | C32×D4 | — | 4 | 3 | no | — |
| 209 | C2×C32×C4 | — | 2 | 6 | no | — |
| 210 | C2×C32×C4 | — | 2 | 6 | no | — |
| 211 | C2×C32×C4 | C24 | 1 | 1 | yes | characteristic |
| 212 | C2×C32×C4 | C24 | 1 | 3 | yes | — |
| 213 | C2×C32×C4 | C24 | 1 | 3 | yes | — |
| 214 | C2×C32×C4 | C24 | 1 | 1 | yes | characteristic |
| 215 | C2×C32×C4 | C24 | 1 | 3 | yes | — |
| 216 | #638 | — | 2 | 2 | no | — |
| 217 | #638 | — | 2 | 6 | no | — |
| 218 | #638 | — | 2 | 6 | no | — |
| 219 | #638 | — | 2 | 6 | no | — |
| 220 | #638 | — | 2 | 6 | no | — |
| 221 | #638 | — | 2 | 2 | no | — |
| 222 | #638 | — | 4 | 6 | no | — |
| 223 | C2×C3⋊Dic3 | — | 2 | 12 | no | — |
| 224 | C2×C3⋊Dic3 | C24 | 1 | 3 | yes | — |
| 225 | C2×C3⋊Dic3 | C24 | 1 | 3 | yes | — |
| 226 | C2×C3⋊Dic3 | C24 | 1 | 1 | yes | characteristic |
| 227 | C2×C3⋊Dic3 | C24 | 1 | 3 | yes | — |
| 228 | C2×C3⋊Dic3 | C24 | 1 | 1 | yes | characteristic |
| 229 | C4⋊(C3⋊D3) | — | 2 | 2 | no | — |
| 230 | C4⋊(C3⋊D3) | — | 2 | 6 | no | — |
| 231 | C4⋊(C3⋊D3) | — | 2 | 6 | no | — |
| 232 | C4⋊(C3⋊D3) | — | 4 | 3 | no | — |
| 233 | C4×C3⋊D3 | — | 2 | 6 | no | — |
| 234 | C4×C3⋊D3 | — | 2 | 6 | no | — |
| 235 | C4×C3⋊D3 | — | 2 | 12 | no | — |
| 236 | C4×C3⋊D3 | — | 2 | 2 | no | — |
| 237 | C4×C3⋊D3 | — | 4 | 3 | no | — |
| 238 | C4×C3⋊D3 | C2×D4 | 1 | 12 | yes | — |
| 239 | #634 | — | 2 | 6 | no | — |
| 240 | #634 | — | 2 | 6 | no | — |
| 241 | #634 | — | 2 | 6 | no | — |
| 242 | #634 | C2×D4 | 1 | 12 | yes | — |
| 243 | C2×2−1+4 | — | 9 | 1 | no | — |
| 244 | C2×2−1+4 | — | 9 | 1 | no | — |
| 245 | #550 | — | 9 | 1 | no | — |
| 246 | #550 | — | 9 | 3 | no | — |
| 247 | D4×Q8 | — | 9 | 1 | no | — |
| 248 | D4×Q8 | — | 9 | 3 | no | — |
| 249 | #548 | — | 9 | 3 | no | — |
| 250 | #548 | — | 9 | 1 | no | — |
| 251 | #548 | — | 9 | 3 | no | — |
| 252 | #548 | C3⋊D3 | 1 | 1 | yes | characteristic, complemented |
| 253 | #537 | — | 9 | 3 | no | — |
| 254 | #537 | — | 9 | 3 | no | — |
| 255 | #532 | — | 9 | 3 | no | — |
| 256 | #532 | — | 9 | 3 | no | — |
| 257 | C2×C4×Q8 | — | 9 | 1 | no | — |
| 258 | C3×#41 | — | 2 | 16 | no | — |
| 259 | C2×C3×Q8 | — | 2 | 16 | no | — |
| 260 | C2×C3×Q8 | C22×D3 | 1 | 12 | yes | — |
| 261 | C2×C3×Q8 | C22×D3 | 1 | 4 | yes | — |
| 262 | C2×C3×D4 | C22×D3 | 1 | 12 | yes | — |
| 263 | C2×C3×D4 | C22×D3 | 1 | 12 | yes | — |
| 264 | C22×C3×C4 | C22×D3 | 1 | 12 | yes | — |
| 265 | C22×C3×C4 | C22×D3 | 1 | 12 | yes | — |
| 266 | C2×#67 | — | 3 | 12 | no | — |
| 267 | C2×#67 | — | 3 | 12 | no | — |
| 268 | C2×#67 | — | 3 | 12 | no | — |
| 269 | C2×#67 | — | 3 | 4 | no | — |
| 270 | C2×#67 | — | 3 | 4 | no | — |
| 271 | C2×#67 | — | 3 | 12 | no | — |
| 272 | C2×#67 | — | 3 | 24 | no | — |
| 273 | C22×Dic3 | — | 3 | 24 | no | — |
| 274 | #239 | — | 6 | 48 | no | — |
| 275 | #239 | — | 6 | 16 | no | — |
| 276 | D3×Q8 | — | 3 | 32 | no | — |
| 277 | D3×Q8 | — | 6 | 48 | no | — |
| 278 | D3×Q8 | — | 6 | 16 | no | — |
| 279 | #237 | — | 6 | 48 | no | — |
| 280 | #237 | — | 6 | 48 | no | — |
| 281 | #235 | — | 6 | 48 | no | — |
| 282 | #235 | — | 6 | 48 | no | — |
| 283 | #235 | — | 6 | 48 | no | — |
| 284 | C2×D12 | — | 3 | 12 | no | — |
| 285 | C2×D12 | — | 3 | 12 | no | — |
| 286 | C2×D12 | — | 3 | 4 | no | — |
| 287 | C2×D12 | — | 3 | 12 | no | — |
| 288 | C2×C4×D3 | — | 3 | 12 | no | — |
| 289 | C2×C4×D3 | — | 3 | 4 | no | — |
| 290 | C2×C4×D3 | — | 3 | 12 | no | — |
| 291 | C2×C4×D3 | — | 3 | 12 | no | — |
| 292 | C2×C4×D3 | — | 3 | 24 | no | — |
| 293 | C2×C4×D3 | — | 3 | 12 | no | — |
| 294 | C2×Dic6 | — | 3 | 12 | no | — |
| 295 | C2×Dic6 | — | 3 | 12 | no | — |
| 296 | C2×Dic6 | — | 3 | 12 | no | — |
| 297 | C2×Dic6 | — | 3 | 12 | no | — |
| 298 | C2×Dic6 | — | 6 | 48 | no | — |
| 299 | C3×C4⋊C4 | C22×D3 | 1 | 12 | yes | — |
| 300 | C3×C4⋊C4 | C22×D3 | 1 | 12 | yes | — |
| 301 | C3×C22⋊C4 | C22×D3 | 1 | 24 | yes | — |
| 302 | C3×C22⋊C4 | C22×D3 | 1 | 12 | yes | — |
| 303 | C3×C22⋊C4 | C22×D3 | 1 | 4 | yes | — |
| 304 | C3×C42 | C22×D3 | 1 | 12 | yes | — |
| 305 | #217 | — | 3 | 12 | no | — |
| 306 | #217 | — | 3 | 12 | no | — |
| 307 | (C2×D3)⋊C4 | — | 3 | 4 | no | — |
| 308 | (C2×D3)⋊C4 | — | 3 | 12 | no | — |
| 309 | (C2×D3)⋊C4 | — | 3 | 24 | no | — |
| 310 | (C2×D3)⋊C4 | — | 3 | 12 | no | — |
| 311 | (C2×D3)⋊C4 | — | 3 | 12 | no | — |
| 312 | C4⋊Dic3 | — | 3 | 12 | no | — |
| 313 | C4⋊Dic3 | — | 3 | 12 | no | — |
| 314 | Dic3⋊C4 | — | 3 | 24 | no | — |
| 315 | Dic3⋊C4 | — | 3 | 24 | no | — |
| 316 | Dic3⋊C4 | — | 3 | 12 | no | — |
| 317 | Dic3⋊C4 | — | 3 | 4 | no | — |
| 318 | C4×Dic3 | — | 3 | 12 | no | — |
| 319 | C4×Dic3 | — | 3 | 12 | no | — |
| 320 | C4×Dic3 | — | 3 | 12 | no | — |
| 321 | C22×C32 | — | 2 | 3 | no | — |
| 322 | C22×C32 | — | 2 | 1 | no | — |
| 323 | C22×C32 | — | 2 | 1 | no | — |
| 324 | C22×C32 | — | 2 | 3 | no | — |
| 325 | C22×C32 | — | 2 | 3 | no | — |
| 326 | C22×C32 | — | 2 | 1 | no | — |
| 327 | C22×C32 | C25 | 1 | 1 | yes | characteristic |
| 328 | C2×C3⋊D3 | — | 2 | 1 | no | — |
| 329 | C2×C3⋊D3 | — | 2 | 1 | no | — |
| 330 | C2×C3⋊D3 | — | 2 | 3 | no | — |
| 331 | C2×C3⋊D3 | — | 2 | 1 | no | — |
| 332 | C2×C3⋊D3 | — | 2 | 3 | no | — |
| 333 | C2×C3⋊D3 | — | 2 | 1 | no | — |
| 334 | C2×C3⋊D3 | — | 2 | 1 | no | — |
| 335 | C2×C3⋊D3 | — | 2 | 3 | no | — |
| 336 | C2×C3⋊D3 | C22×D4 | 1 | 2 | yes | — |
| 337 | C32×C4 | — | 2 | 1 | no | — |
| 338 | C32×C4 | — | 2 | 3 | no | — |
| 339 | C32×C4 | — | 2 | 1 | no | — |
| 340 | C32×C4 | — | 2 | 3 | no | — |
| 341 | C32×C4 | C22×D4 | 1 | 6 | yes | — |
| 342 | C3⋊Dic3 | — | 2 | 1 | no | — |
| 343 | C3⋊Dic3 | — | 2 | 3 | no | — |
| 344 | C3⋊Dic3 | — | 2 | 3 | no | — |
| 345 | C3⋊Dic3 | C22×D4 | 1 | 6 | yes | — |
| 346 | C3⋊Dic3 | 2−1+4 | 1 | 2 | yes | complemented |
| 347 | 2−1+4 | — | 18 | 8 | no | — |
| 348 | 2−1+4 | — | 18 | 8 | no | — |
| 349 | C2×#41 | — | 9 | 3 | no | — |
| 350 | C2×#41 | — | 9 | 1 | no | — |
| 351 | C2×#41 | — | 9 | 3 | no | — |
| 352 | C2×#41 | — | 9 | 3 | no | — |
| 353 | C2×#41 | — | 9 | 3 | no | — |
| 354 | C2×#41 | — | 9 | 3 | no | — |
| 355 | C2×#41 | — | 9 | 3 | no | — |
| 356 | C2×#41 | C2×C3⋊D3 | 1 | 1 | yes | characteristic |
| 357 | C22×Q8 | — | 9 | 1 | no | — |
| 358 | C22×Q8 | — | 9 | 3 | no | — |
| 359 | C22×Q8 | — | 9 | 1 | no | — |
| 360 | C22×Q8 | — | 9 | 3 | no | — |
| 361 | C22×Q8 | C2×C3⋊D3 | 1 | 1 | yes | characteristic |
| 362 | C4⋊Q8 | — | 9 | 3 | no | — |
| 363 | C4⋊Q8 | — | 9 | 3 | no | — |
| 364 | #127 | — | 9 | 3 | no | — |
| 365 | #127 | — | 9 | 3 | no | — |
| 366 | #124 | — | 9 | 3 | no | — |
| 367 | #124 | — | 9 | 3 | no | — |
| 368 | #124 | — | 9 | 3 | no | — |
| 369 | #124 | C2×C3⋊D3 | 1 | 3 | yes | — |
| 370 | C22⋊Q8 | — | 9 | 3 | no | — |
| 371 | C22⋊Q8 | — | 9 | 3 | no | — |
| 372 | C22⋊Q8 | — | 9 | 6 | no | — |
| 373 | C22⋊Q8 | — | 9 | 3 | no | — |
| 374 | C22⋊Q8 | — | 9 | 6 | no | — |
| 375 | C22⋊Q8 | C2×C3⋊D3 | 1 | 3 | yes | — |
| 376 | #121 | — | 9 | 3 | no | — |
| 377 | #121 | — | 9 | 3 | no | — |
| 378 | #121 | — | 9 | 6 | no | — |
| 379 | #121 | — | 9 | 3 | no | — |
| 380 | #121 | — | 9 | 3 | no | — |
| 381 | #121 | — | 9 | 3 | no | — |
| 382 | #121 | — | 9 | 3 | no | — |
| 383 | #121 | — | 9 | 1 | no | — |
| 384 | #121 | — | 9 | 6 | no | — |
| 385 | #121 | — | 9 | 6 | no | — |
| 386 | #121 | C2×C3⋊D3 | 1 | 3 | yes | — |
| 387 | C4×Q8 | — | 9 | 1 | no | — |
| 388 | C4×Q8 | — | 9 | 3 | no | — |
| 389 | C4×Q8 | — | 9 | 3 | no | — |
| 390 | C4×Q8 | C2×C3⋊D3 | 1 | 1 | yes | characteristic |
| 391 | C4×D4 | — | 9 | 3 | no | — |
| 392 | C4×D4 | — | 9 | 3 | no | — |
| 393 | C4×D4 | — | 9 | 6 | no | — |
| 394 | C4×D4 | — | 9 | 6 | no | — |
| 395 | C4×D4 | — | 9 | 3 | no | — |
| 396 | C4×D4 | C2×C3⋊D3 | 1 | 3 | yes | — |
| 397 | C2×C4⋊C4 | — | 9 | 3 | no | — |
| 398 | C2×C42 | — | 9 | 3 | no | — |
| 399 | C23×C3 | C23×D3 | 1 | 4 | yes | — |
| 400 | C23×C3 | C23×D3 | 1 | 12 | yes | — |
| 401 | C22×D3 | — | 3 | 4 | no | — |
| 402 | C22×D3 | — | 3 | 12 | no | — |
| 403 | C22×D3 | — | 3 | 4 | no | — |
| 404 | C3×Q8 | — | 2 | 24 | no | — |
| 405 | C3×Q8 | D3×D4 | 1 | 16 | yes | — |
| 406 | C3×D4 | — | 2 | 24 | no | — |
| 407 | C3×D4 | — | 4 | 12 | no | — |
| 408 | C2×C3×C4 | — | 2 | 24 | no | — |
| 409 | C2×C3×C4 | — | 2 | 24 | no | — |
| 410 | C2×C3×C4 | C23×D3 | 1 | 4 | yes | — |
| 411 | C2×C3×C4 | C23×D3 | 1 | 12 | yes | — |
| 412 | C2×C3×C4 | C23×D3 | 1 | 12 | yes | — |
| 413 | C2×C3×C4 | C23×D3 | 1 | 4 | yes | — |
| 414 | C2×C3×C4 | C23×D3 | 1 | 12 | yes | — |
| 415 | #67 | — | 6 | 24 | no | — |
| 416 | #67 | — | 6 | 24 | no | — |
| 417 | #67 | — | 6 | 24 | no | — |
| 418 | #67 | — | 6 | 8 | no | — |
| 419 | #67 | — | 6 | 8 | no | — |
| 420 | #67 | — | 6 | 24 | no | — |
| 421 | #67 | — | 12 | 24 | no | — |
| 422 | C2×Dic3 | — | 3 | 4 | no | — |
| 423 | C2×Dic3 | — | 3 | 12 | no | — |
| 424 | C2×Dic3 | — | 3 | 12 | no | — |
| 425 | C2×Dic3 | — | 3 | 12 | no | — |
| 426 | C2×Dic3 | — | 3 | 4 | no | — |
| 427 | C2×Dic3 | — | 6 | 48 | no | — |
| 428 | D12 | — | 6 | 8 | no | — |
| 429 | D12 | — | 6 | 24 | no | — |
| 430 | D12 | — | 6 | 24 | no | — |
| 431 | D12 | — | 12 | 12 | no | — |
| 432 | C4×D3 | — | 3 | 48 | no | — |
| 433 | C4×D3 | — | 6 | 8 | no | — |
| 434 | C4×D3 | — | 6 | 48 | no | — |
| 435 | C4×D3 | — | 6 | 24 | no | — |
| 436 | C4×D3 | — | 6 | 24 | no | — |
| 437 | C4×D3 | — | 12 | 12 | no | — |
| 438 | Dic6 | — | 3 | 48 | no | — |
| 439 | Dic6 | — | 6 | 24 | no | — |
| 440 | Dic6 | — | 6 | 24 | no | — |
| 441 | Dic6 | — | 6 | 24 | no | — |
| 442 | C2×C32 | — | 4 | 3 | no | — |
| 443 | C2×C32 | — | 4 | 1 | no | — |
| 444 | C2×C32 | C23×D4 | 1 | 1 | yes | characteristic |
| 445 | C2×C32 | C2×2−1+4 | 1 | 1 | yes | characteristic |
| 446 | C2×C32 | #585 | 1 | 1 | yes | characteristic |
| 447 | C3⋊D3 | — | 2 | 2 | no | — |
| 448 | C3⋊D3 | — | 4 | 3 | no | — |
| 449 | C3⋊D3 | — | 4 | 1 | no | — |
| 450 | #41 | — | 2 | 4 | no | — |
| 451 | #41 | — | 18 | 12 | no | — |
| 452 | #41 | — | 18 | 12 | no | — |
| 453 | #41 | — | 18 | 12 | no | — |
| 454 | #41 | — | 18 | 12 | no | — |
| 455 | #41 | — | 18 | 12 | no | — |
| 456 | #41 | — | 18 | 12 | no | — |
| 457 | #41 | — | 18 | 4 | no | — |
| 458 | C2×Q8 | — | 2 | 4 | no | — |
| 459 | C2×Q8 | — | 9 | 8 | no | — |
| 460 | C2×Q8 | — | 9 | 3 | no | — |
| 461 | C2×Q8 | — | 9 | 3 | no | — |
| 462 | C2×Q8 | — | 9 | 3 | no | — |
| 463 | C2×Q8 | — | 9 | 3 | no | — |
| 464 | C2×Q8 | — | 18 | 12 | no | — |
| 465 | C2×Q8 | — | 18 | 12 | no | — |
| 466 | C2×Q8 | — | 18 | 4 | no | — |
| 467 | C2×Q8 | C22×C3⋊D3 | 1 | 3 | yes | — |
| 468 | C2×Q8 | C22×C3⋊D3 | 1 | 1 | yes | characteristic |
| 469 | C2×D4 | — | 9 | 1 | no | — |
| 470 | C2×D4 | — | 9 | 3 | no | — |
| 471 | C2×D4 | — | 9 | 1 | no | — |
| 472 | C2×D4 | — | 9 | 3 | no | — |
| 473 | C2×D4 | — | 9 | 3 | no | — |
| 474 | C2×D4 | — | 9 | 3 | no | — |
| 475 | C2×D4 | — | 9 | 6 | no | — |
| 476 | C2×D4 | — | 9 | 1 | no | — |
| 477 | C2×D4 | — | 9 | 3 | no | — |
| 478 | C2×D4 | — | 9 | 3 | no | — |
| 479 | C2×D4 | — | 9 | 3 | no | — |
| 480 | C2×D4 | C22×C3⋊D3 | 1 | 3 | yes | — |
| 481 | C2×D4 | C22×C3⋊D3 | 1 | 3 | yes | — |
| 482 | C22×C4 | — | 9 | 3 | no | — |
| 483 | C22×C4 | — | 9 | 6 | no | — |
| 484 | C22×C4 | — | 9 | 1 | no | — |
| 485 | C22×C4 | — | 9 | 6 | no | — |
| 486 | C22×C4 | — | 9 | 3 | no | — |
| 487 | C22×C4 | — | 9 | 3 | no | — |
| 488 | C22×C4 | — | 9 | 3 | no | — |
| 489 | C22×C4 | C22×C3⋊D3 | 1 | 3 | yes | — |
| 490 | C22×C4 | C22×C3⋊D3 | 1 | 3 | yes | — |
| 491 | C4⋊C4 | — | 9 | 6 | no | — |
| 492 | C4⋊C4 | — | 9 | 3 | no | — |
| 493 | C4⋊C4 | — | 9 | 1 | no | — |
| 494 | C4⋊C4 | — | 9 | 3 | no | — |
| 495 | C4⋊C4 | — | 9 | 6 | no | — |
| 496 | C4⋊C4 | — | 9 | 3 | no | — |
| 497 | C4⋊C4 | C22×C3⋊D3 | 1 | 3 | yes | — |
| 498 | C4⋊C4 | C22×C3⋊D3 | 1 | 3 | yes | — |
| 499 | C22⋊C4 | — | 9 | 3 | no | — |
| 500 | C22⋊C4 | — | 9 | 3 | no | — |
| 501 | C22⋊C4 | — | 9 | 3 | no | — |
| 502 | C22⋊C4 | — | 9 | 1 | no | — |
| 503 | C22⋊C4 | — | 9 | 3 | no | — |
| 504 | C22⋊C4 | — | 9 | 3 | no | — |
| 505 | C22⋊C4 | — | 9 | 6 | no | — |
| 506 | C22⋊C4 | C22×C3⋊D3 | 1 | 3 | yes | — |
| 507 | C22⋊C4 | C22×C3⋊D3 | 1 | 6 | yes | — |
| 508 | C22⋊C4 | C22×C3⋊D3 | 1 | 1 | yes | characteristic |
| 509 | C42 | — | 9 | 3 | no | — |
| 510 | C42 | — | 9 | 3 | no | — |
| 511 | C42 | — | 9 | 3 | no | — |
| 512 | C42 | C22×C3⋊D3 | 1 | 3 | yes | — |
| 513 | C22×C3 | — | 2 | 12 | no | — |
| 514 | C22×C3 | — | 2 | 4 | no | — |
| 515 | C22×C3 | — | 2 | 12 | no | — |
| 516 | C22×C3 | — | 2 | 4 | no | — |
| 517 | C22×C3 | — | 2 | 4 | no | — |
| 518 | C22×C3 | — | 2 | 12 | no | — |
| 519 | C22×C3 | C24×D3 | 1 | 4 | yes | — |
| 520 | C2×D3 | — | 3 | 8 | no | — |
| 521 | C2×D3 | — | 6 | 4 | no | — |
| 522 | C2×D3 | — | 6 | 4 | no | — |
| 523 | C2×D3 | — | 6 | 12 | no | — |
| 524 | C2×D3 | — | 6 | 4 | no | — |
| 525 | C2×D3 | — | 6 | 4 | no | — |
| 526 | C2×D3 | — | 6 | 12 | no | — |
| 527 | C2×D3 | — | 6 | 12 | no | — |
| 528 | C2×D3 | — | 6 | 4 | no | — |
| 529 | C3×C4 | — | 2 | 4 | no | — |
| 530 | C3×C4 | — | 2 | 12 | no | — |
| 531 | C3×C4 | — | 2 | 12 | no | — |
| 532 | C3×C4 | — | 2 | 4 | no | — |
| 533 | C3×C4 | C2×D3×D4 | 1 | 24 | yes | — |
| 534 | Dic3 | — | 3 | 24 | no | — |
| 535 | Dic3 | — | 3 | 8 | no | — |
| 536 | Dic3 | — | 6 | 4 | no | — |
| 537 | Dic3 | — | 6 | 12 | no | — |
| 538 | Dic3 | — | 6 | 12 | no | — |
| 539 | C32 | #3497 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 540 | C23 | — | 9 | 1 | no | — |
| 541 | C23 | — | 9 | 1 | no | — |
| 542 | C23 | — | 9 | 3 | no | — |
| 543 | C23 | C23×C3⋊D3 | 1 | 1 | yes | characteristic |
| 544 | C23 | C23×C3⋊D3 | 1 | 3 | yes | — |
| 545 | Q8 | — | 2 | 6 | no | — |
| 546 | Q8 | — | 9 | 12 | no | — |
| 547 | Q8 | — | 18 | 6 | no | — |
| 548 | Q8 | — | 18 | 6 | no | — |
| 549 | Q8 | — | 18 | 6 | no | — |
| 550 | Q8 | D4×C3⋊D3 | 1 | 4 | yes | — |
| 551 | D4 | — | 2 | 6 | no | — |
| 552 | D4 | — | 4 | 3 | no | — |
| 553 | D4 | — | 18 | 2 | no | — |
| 554 | D4 | — | 18 | 6 | no | — |
| 555 | D4 | — | 18 | 6 | no | — |
| 556 | D4 | — | 18 | 6 | no | — |
| 557 | D4 | — | 18 | 2 | no | — |
| 558 | D4 | — | 18 | 6 | no | — |
| 559 | D4 | — | 18 | 2 | no | — |
| 560 | D4 | — | 18 | 6 | no | — |
| 561 | D4 | — | 18 | 6 | no | — |
| 562 | D4 | — | 36 | 3 | no | — |
| 563 | D4 | — | 36 | 6 | no | — |
| 564 | C2×C4 | — | 2 | 6 | no | — |
| 565 | C2×C4 | — | 2 | 6 | no | — |
| 566 | C2×C4 | — | 9 | 1 | no | — |
| 567 | C2×C4 | — | 9 | 3 | no | — |
| 568 | C2×C4 | — | 9 | 12 | no | — |
| 569 | C2×C4 | — | 9 | 3 | no | — |
| 570 | C2×C4 | — | 9 | 1 | no | — |
| 571 | C2×C4 | — | 9 | 3 | no | — |
| 572 | C2×C4 | — | 18 | 12 | no | — |
| 573 | C2×C4 | — | 18 | 2 | no | — |
| 574 | C2×C4 | — | 18 | 12 | no | — |
| 575 | C2×C4 | — | 18 | 6 | no | — |
| 576 | C2×C4 | — | 18 | 6 | no | — |
| 577 | C2×C4 | — | 36 | 3 | no | — |
| 578 | C2×C4 | C23×C3⋊D3 | 1 | 1 | yes | characteristic |
| 579 | C2×C4 | C23×C3⋊D3 | 1 | 3 | yes | — |
| 580 | C2×C4 | C23×C3⋊D3 | 1 | 1 | yes | characteristic |
| 581 | C2×C4 | C23×C3⋊D3 | 1 | 3 | yes | — |
| 582 | C2×C4 | C23×C3⋊D3 | 1 | 3 | yes | — |
| 583 | C2×C3 | — | 4 | 12 | no | — |
| 584 | C2×C3 | — | 4 | 4 | no | — |
| 585 | C2×C3 | C22×D3×D4 | 1 | 4 | yes | — |
| 586 | C2×C3 | #5964 | 1 | 4 | yes | — |
| 587 | C2×C3 | D3×2−1+4 | 1 | 4 | yes | — |
| 588 | D3 | — | 6 | 8 | no | — |
| 589 | D3 | — | 12 | 12 | no | — |
| 590 | D3 | — | 12 | 4 | no | — |
| 591 | C22 | — | 2 | 1 | no | — |
| 592 | C22 | — | 2 | 3 | no | — |
| 593 | C22 | — | 2 | 1 | no | — |
| 594 | C22 | — | 2 | 3 | no | — |
| 595 | C22 | — | 2 | 1 | no | — |
| 596 | C22 | — | 2 | 3 | no | — |
| 597 | C22 | — | 9 | 2 | no | — |
| 598 | C22 | — | 18 | 1 | no | — |
| 599 | C22 | — | 18 | 1 | no | — |
| 600 | C22 | — | 18 | 3 | no | — |
| 601 | C22 | — | 18 | 1 | no | — |
| 602 | C22 | — | 18 | 1 | no | — |
| 603 | C22 | — | 18 | 3 | no | — |
| 604 | C22 | — | 18 | 1 | no | — |
| 605 | C22 | — | 18 | 3 | no | — |
| 606 | C22 | C24×C3⋊D3 | 1 | 1 | yes | characteristic |
| 607 | C4 | — | 2 | 1 | no | — |
| 608 | C4 | — | 2 | 3 | no | — |
| 609 | C4 | — | 2 | 3 | no | — |
| 610 | C4 | — | 2 | 1 | no | — |
| 611 | C4 | — | 9 | 6 | no | — |
| 612 | C4 | — | 9 | 2 | no | — |
| 613 | C4 | — | 18 | 3 | no | — |
| 614 | C4 | — | 18 | 1 | no | — |
| 615 | C4 | — | 18 | 3 | no | — |
| 616 | C4 | C2×D4×C3⋊D3 | 1 | 6 | yes | — |
| 617 | C3 | #86737 | 1 | 4 | yes | complemented |
| 618 | C2 | — | 4 | 1 | no | — |
| 619 | C2 | — | 4 | 3 | no | — |
| 620 | C2 | — | 18 | 2 | no | — |
| 621 | C2 | — | 36 | 3 | no | — |
| 622 | C2 | — | 36 | 1 | no | — |
| 623 | C2 | C22×D4×C3⋊D3 | 1 | 1 | yes | characteristic |
| 624 | C2 | #10596756 | 1 | 1 | yes | characteristic |
| 625 | C2 | C3⋊D3×2−1+4 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×C3⋊D3 |
| commutator, socle, cosocle | C22×C32 | C25 |
| Fitting | C32×#548 | C2 |
| hypercenter | #548 | C3⋊D3 |
| hypocenter | C32 | #3497 |
| LCS | G ▷ C22×C32 ▷ C32 | |
| UCS | C1 ◁ C22 ◁ #548 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#64367 | C2 | semidirect |
| 2. C2×#64364 | C2 | semidirect |
| 3. C32×#548 | C2 | semidirect |
| 4. #10596305 | C2 | semidirect |
| 5. Q8×#638 | C2 | semidirect |
| 6. #10596148 | C2 | semidirect |
| 7. #10596139 | C2 | semidirect |
| 8. #10596103 | C2 | semidirect |
| 9. #10596100 | C2 | semidirect |
| 10. #10596079 | C2 | semidirect |
| 11. #10596070 | C2 | semidirect |
| 12. #10596047 | C2 | semidirect |
| 13. C4×Q8×C3⋊D3 | C2 | semidirect |
| 14. #10596023 | C2 | semidirect |
| 15. #10596019 | C2 | semidirect |
| 71. C3×#548 | D3 | semidirect |
| 104. Q8×C3⋊D3 | D4 | semidirect |
| 252. #548 | C3⋊D3 | semidirect |
| 346. C3⋊Dic3 | 2−1+4 | semidirect |
| 539. C32 | #3497 | semidirect |
| 617. C3 | #86737 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64367 | 2 |
| C2×#64364 | 2 |
| C32×#548 | 2 |
| #10596305 | 2 |
| Q8×#638 | 2 |
| #10596148 | 2 |
| #10596139 | 2 |
| #10596103 | 2 |
| #10596100 | 2 |
| #10596079 | 2 |
| #10596070 | 2 |
| #10596047 | 2 |
| C4×Q8×C3⋊D3 | 2 |
| #10596023 | 2 |
| #10596019 | 2 |
| #86737 | 3 |