Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
3734 conjugacy classes of subgroups.
The subgroup lattice has 470 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C3×#64364 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | C2×C3×#3832 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11724627 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #11724626 | C2 | 1 | 8 | yes | maximal, complemented |
| 5 | #11724624 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #11724619 | C2 | 1 | 6 | yes | maximal, complemented |
| 7 | #11724618 | C2 | 1 | 6 | yes | maximal, complemented |
| 8 | #10596689 | — | 3 | 1 | no | maximal |
| 9 | #10596688 | — | 3 | 2 | no | maximal |
| 10 | C2×C33×Q8 | C22 | 1 | 1 | yes | characteristic, complemented |
| 11 | C3×#3832 | C22 | 1 | 4 | yes | complemented |
| 12 | C3×#3832 | C22 | 1 | 4 | yes | complemented |
| 13 | C3×#3832 | C22 | 1 | 8 | yes | complemented |
| 14 | C3×Q8×C3⋊D3 | C22 | 1 | 8 | yes | complemented |
| 15 | C3×#3828 | C22 | 1 | 12 | yes | complemented |
| 16 | C2×C3×C4⋊(C3⋊D3) | C22 | 1 | 3 | yes | complemented |
| 17 | C2×C3×C4×C3⋊D3 | C22 | 1 | 3 | yes | complemented |
| 18 | #89049 | C22 | 1 | 12 | yes | complemented |
| 19 | #89046 | C22 | 1 | 4 | yes | complemented |
| 20 | C4⋊#1113 | C22 | 1 | 6 | yes | complemented |
| 21 | C4⋊#1113 | C22 | 1 | 24 | yes | complemented |
| 22 | C4×#1113 | C22 | 1 | 12 | yes | complemented |
| 23 | #89042 | C22 | 1 | 12 | yes | complemented |
| 24 | #89041 | C22 | 1 | 12 | yes | complemented |
| 25 | #89041 | C22 | 1 | 24 | yes | complemented |
| 26 | #89040 | C22 | 1 | 6 | yes | complemented |
| 27 | #64364 | D3 | 1 | 2 | yes | complemented |
| 28 | C2×#3832 | D3 | 1 | 1 | yes | characteristic, complemented |
| 29 | C3×#1007 | — | 3 | 2 | no | — |
| 30 | C3×#1007 | — | 3 | 2 | no | — |
| 31 | C3×#1007 | — | 6 | 2 | no | — |
| 32 | C2×C3×#239 | — | 3 | 2 | no | — |
| 33 | C2×C3×#239 | — | 6 | 1 | no | — |
| 34 | #64320 | — | 3 | 8 | no | — |
| 35 | #64320 | — | 3 | 4 | no | — |
| 36 | #64319 | — | 3 | 8 | no | — |
| 37 | D3×#239 | — | 3 | 8 | no | — |
| 38 | D3×#239 | — | 3 | 8 | no | — |
| 39 | #64316 | — | 3 | 4 | no | — |
| 40 | #64315 | — | 3 | 8 | no | — |
| 41 | #64308 | — | 3 | 6 | no | — |
| 42 | #64307 | — | 3 | 12 | no | — |
| 43 | #64306 | — | 3 | 6 | no | — |
| 44 | D3×#235 | — | 3 | 12 | no | — |
| 45 | C22×C3×C3⋊D3 | C23 | 1 | 3 | yes | — |
| 46 | C2×#1113 | C23 | 1 | 12 | yes | — |
| 47 | C33×Q8 | C23 | 1 | 4 | yes | — |
| 48 | C2×C33×C4 | C23 | 1 | 3 | yes | — |
| 49 | C3×#638 | C23 | 1 | 8 | yes | — |
| 50 | C2×C3×C3⋊Dic3 | C23 | 1 | 1 | yes | characteristic |
| 51 | C3×C4⋊(C3⋊D3) | C23 | 1 | 12 | yes | — |
| 52 | C3×C4⋊(C3⋊D3) | C23 | 1 | 12 | yes | — |
| 53 | C3×C4×C3⋊D3 | C23 | 1 | 6 | yes | — |
| 54 | C3×C4×C3⋊D3 | C23 | 1 | 6 | yes | — |
| 55 | C3×C4×C3⋊D3 | C23 | 1 | 24 | yes | — |
| 56 | C3×#634 | C23 | 1 | 12 | yes | — |
| 57 | #6296 | C23 | 1 | 4 | yes | — |
| 58 | #6295 | C23 | 1 | 24 | yes | — |
| 59 | #6295 | C23 | 1 | 4 | yes | — |
| 60 | #6294 | C23 | 1 | 12 | yes | — |
| 61 | #6294 | C23 | 1 | 8 | yes | — |
| 62 | #5968 | — | 9 | 2 | no | — |
| 63 | #5964 | — | 9 | 1 | no | — |
| 64 | C2×C32×Q8 | — | 2 | 1 | no | — |
| 65 | C2×C32×Q8 | — | 2 | 2 | no | — |
| 66 | C2×C32×Q8 | — | 4 | 1 | no | — |
| 67 | C2×C32×Q8 | C2×D3 | 1 | 2 | yes | complemented |
| 68 | C2×C32×Q8 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 69 | #3832 | C2×D3 | 1 | 4 | yes | complemented |
| 70 | #3832 | C2×D3 | 1 | 4 | yes | complemented |
| 71 | #3832 | C2×D3 | 1 | 8 | yes | complemented |
| 72 | Q8×C3⋊D3 | C2×D3 | 1 | 8 | yes | complemented |
| 73 | #3828 | C2×D3 | 1 | 12 | yes | complemented |
| 74 | C2×C4⋊(C3⋊D3) | C2×D3 | 1 | 3 | yes | complemented |
| 75 | C2×C4×C3⋊D3 | C2×D3 | 1 | 3 | yes | complemented |
| 76 | C3×#239 | — | 3 | 8 | no | — |
| 77 | C3×#239 | — | 3 | 8 | no | — |
| 78 | C3×#239 | — | 3 | 8 | no | — |
| 79 | C3×#239 | — | 3 | 8 | no | — |
| 80 | C3×#239 | — | 6 | 4 | no | — |
| 81 | C3×#239 | — | 6 | 4 | no | — |
| 82 | C3×#239 | — | 6 | 8 | no | — |
| 83 | C3×D3×Q8 | — | 3 | 8 | no | — |
| 84 | C3×D3×Q8 | — | 3 | 8 | no | — |
| 85 | C3×D3×Q8 | — | 6 | 8 | no | — |
| 86 | C3×#235 | — | 3 | 12 | no | — |
| 87 | C3×#235 | — | 3 | 12 | no | — |
| 88 | C3×#235 | — | 6 | 12 | no | — |
| 89 | C2×C3×D12 | — | 3 | 6 | no | — |
| 90 | C2×C3×D12 | — | 6 | 3 | no | — |
| 91 | C2×C3×C4×D3 | — | 3 | 6 | no | — |
| 92 | C2×C3×C4×D3 | — | 6 | 3 | no | — |
| 93 | #3811 | — | 3 | 12 | no | — |
| 94 | D3×#67 | — | 3 | 24 | no | — |
| 95 | #3805 | — | 3 | 4 | no | — |
| 96 | #3804 | — | 3 | 8 | no | — |
| 97 | #3802 | — | 3 | 6 | no | — |
| 98 | #3802 | — | 3 | 24 | no | — |
| 99 | D3×D12 | — | 3 | 12 | no | — |
| 100 | D3×D12 | — | 3 | 24 | no | — |
| 101 | D3×D12 | — | 3 | 24 | no | — |
| 102 | C4×D32 | — | 3 | 24 | no | — |
| 103 | C4×D32 | — | 3 | 12 | no | — |
| 104 | #3799 | — | 3 | 12 | no | — |
| 105 | #3799 | — | 3 | 24 | no | — |
| 106 | #3798 | — | 3 | 24 | no | — |
| 107 | #3798 | — | 3 | 12 | no | — |
| 108 | #3797 | — | 3 | 6 | no | — |
| 109 | #3796 | — | 3 | 12 | no | — |
| 110 | #3796 | — | 3 | 24 | no | — |
| 111 | #3795 | — | 3 | 12 | no | — |
| 112 | #3795 | — | 3 | 24 | no | — |
| 113 | D3×Dic6 | — | 3 | 12 | no | — |
| 114 | C22×C33 | C24 | 1 | 1 | yes | characteristic |
| 115 | C2×C3×C3⋊D3 | — | 4 | 3 | no | — |
| 116 | C2×C3×C3⋊D3 | C24 | 1 | 6 | yes | — |
| 117 | C2×C3×C3⋊D3 | C24 | 1 | 8 | yes | — |
| 118 | #1113 | — | 4 | 12 | no | — |
| 119 | C33×C4 | C24 | 1 | 6 | yes | — |
| 120 | C3×C3⋊Dic3 | C24 | 1 | 1 | yes | characteristic |
| 121 | C3×C3⋊Dic3 | C24 | 1 | 8 | yes | — |
| 122 | C3×C3⋊Dic3 | C24 | 1 | 1 | yes | characteristic |
| 123 | C3×2−1+4 | — | 9 | 2 | no | — |
| 124 | C2×C3×#41 | — | 9 | 1 | no | — |
| 125 | #1010 | — | 9 | 4 | no | — |
| 126 | #1009 | — | 9 | 12 | no | — |
| 127 | #1009 | — | 9 | 4 | no | — |
| 128 | #1009 | — | 9 | 8 | no | — |
| 129 | D3×#41 | — | 9 | 12 | no | — |
| 130 | D3×#41 | — | 9 | 8 | no | — |
| 131 | D3×#41 | — | 9 | 8 | no | — |
| 132 | #1007 | — | 3 | 2 | no | — |
| 133 | #1007 | — | 3 | 2 | no | — |
| 134 | #1007 | — | 6 | 2 | no | — |
| 135 | #1007 | — | 9 | 8 | no | — |
| 136 | C2×#239 | — | 3 | 2 | no | — |
| 137 | C2×#239 | — | 6 | 1 | no | — |
| 138 | C2×#239 | — | 9 | 8 | no | — |
| 139 | #1004 | — | 9 | 6 | no | — |
| 140 | C2×#235 | — | 9 | 6 | no | — |
| 141 | C22×C3⋊D3 | C22×D3 | 1 | 3 | yes | — |
| 142 | C22×C3×D3 | — | 3 | 6 | no | — |
| 143 | C22×C3×D3 | — | 6 | 3 | no | — |
| 144 | C2×D32 | — | 3 | 12 | no | — |
| 145 | C2×D32 | — | 3 | 24 | no | — |
| 146 | C32×Q8 | — | 2 | 8 | no | — |
| 147 | C32×Q8 | — | 2 | 4 | no | — |
| 148 | C32×Q8 | — | 4 | 4 | no | — |
| 149 | C32×Q8 | C22×D3 | 1 | 4 | yes | — |
| 150 | C32×Q8 | C22×D3 | 1 | 8 | yes | — |
| 151 | C2×C32×C4 | — | 2 | 3 | no | — |
| 152 | C2×C32×C4 | — | 2 | 6 | no | — |
| 153 | C2×C32×C4 | — | 4 | 3 | no | — |
| 154 | C2×C32×C4 | C22×D3 | 1 | 6 | yes | — |
| 155 | C2×C32×C4 | C22×D3 | 1 | 3 | yes | — |
| 156 | #638 | C22×D3 | 1 | 8 | yes | — |
| 157 | C2×C3⋊Dic3 | C22×D3 | 1 | 1 | yes | characteristic |
| 158 | C4⋊(C3⋊D3) | C22×D3 | 1 | 12 | yes | — |
| 159 | C4⋊(C3⋊D3) | C22×D3 | 1 | 12 | yes | — |
| 160 | C4×C3⋊D3 | C22×D3 | 1 | 6 | yes | — |
| 161 | C4×C3⋊D3 | C22×D3 | 1 | 24 | yes | — |
| 162 | C4×C3⋊D3 | C22×D3 | 1 | 6 | yes | — |
| 163 | #634 | C22×D3 | 1 | 12 | yes | — |
| 164 | C3×#67 | — | 3 | 8 | no | — |
| 165 | C3×#67 | — | 3 | 8 | no | — |
| 166 | C3×#67 | — | 6 | 8 | no | — |
| 167 | C2×C3×Dic3 | — | 3 | 2 | no | — |
| 168 | C2×C3×Dic3 | — | 6 | 1 | no | — |
| 169 | C3×D12 | — | 3 | 24 | no | — |
| 170 | C3×D12 | — | 3 | 12 | no | — |
| 171 | C3×D12 | — | 3 | 12 | no | — |
| 172 | C3×D12 | — | 6 | 12 | no | — |
| 173 | C3×D12 | — | 6 | 12 | no | — |
| 174 | C3×C4×D3 | — | 3 | 12 | no | — |
| 175 | C3×C4×D3 | — | 3 | 24 | no | — |
| 176 | C3×C4×D3 | — | 3 | 12 | no | — |
| 177 | C3×C4×D3 | — | 3 | 24 | no | — |
| 178 | C3×C4×D3 | — | 6 | 6 | no | — |
| 179 | C3×C4×D3 | — | 6 | 6 | no | — |
| 180 | C3×C4×D3 | — | 6 | 24 | no | — |
| 181 | C3×Dic6 | — | 3 | 12 | no | — |
| 182 | C3×Dic6 | — | 3 | 12 | no | — |
| 183 | C3×Dic6 | — | 6 | 12 | no | — |
| 184 | #627 | — | 3 | 8 | no | — |
| 185 | #627 | — | 3 | 4 | no | — |
| 186 | #626 | — | 3 | 24 | no | — |
| 187 | #626 | — | 3 | 24 | no | — |
| 188 | #626 | — | 3 | 8 | no | — |
| 189 | #625 | — | 3 | 24 | no | — |
| 190 | #625 | — | 3 | 4 | no | — |
| 191 | #624 | — | 3 | 12 | no | — |
| 192 | #624 | — | 3 | 8 | no | — |
| 193 | D3×Dic3 | — | 3 | 24 | no | — |
| 194 | D3×Dic3 | — | 3 | 8 | no | — |
| 195 | D3×Dic3 | — | 3 | 8 | no | — |
| 196 | #585 | — | 27 | 1 | no | Sylow |
| 197 | C2×C33 | — | 2 | 1 | no | — |
| 198 | C2×C33 | C25 | 1 | 1 | yes | characteristic |
| 199 | C3×C3⋊D3 | — | 2 | 8 | no | — |
| 200 | C3×C3⋊D3 | — | 2 | 6 | no | — |
| 201 | C3×#41 | — | 9 | 4 | no | — |
| 202 | C3×#41 | — | 9 | 8 | no | — |
| 203 | C3×#41 | — | 9 | 4 | no | — |
| 204 | C3×#41 | — | 9 | 12 | no | — |
| 205 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 206 | C2×C3×Q8 | — | 2 | 2 | no | — |
| 207 | C2×C3×Q8 | — | 4 | 1 | no | — |
| 208 | C2×C3×Q8 | — | 9 | 8 | no | — |
| 209 | C2×C3×Q8 | D32 | 1 | 2 | yes | complemented |
| 210 | C2×C3×Q8 | D32 | 1 | 1 | yes | characteristic, complemented |
| 211 | C2×C3×D4 | — | 9 | 3 | no | — |
| 212 | C22×C3×C4 | — | 9 | 3 | no | — |
| 213 | C2×#67 | — | 9 | 12 | no | — |
| 214 | #239 | — | 3 | 8 | no | — |
| 215 | #239 | — | 3 | 8 | no | — |
| 216 | #239 | — | 3 | 8 | no | — |
| 217 | #239 | — | 3 | 8 | no | — |
| 218 | #239 | — | 6 | 4 | no | — |
| 219 | #239 | — | 6 | 4 | no | — |
| 220 | #239 | — | 6 | 8 | no | — |
| 221 | #239 | — | 9 | 12 | no | — |
| 222 | #239 | — | 9 | 24 | no | — |
| 223 | D3×Q8 | — | 3 | 8 | no | — |
| 224 | D3×Q8 | — | 3 | 8 | no | — |
| 225 | D3×Q8 | — | 6 | 8 | no | — |
| 226 | D3×Q8 | — | 9 | 12 | no | — |
| 227 | #237 | — | 9 | 24 | no | — |
| 228 | #237 | — | 9 | 12 | no | — |
| 229 | #237 | — | 9 | 8 | no | — |
| 230 | D3×D4 | — | 9 | 24 | no | — |
| 231 | D3×D4 | — | 9 | 12 | no | — |
| 232 | D3×D4 | — | 9 | 24 | no | — |
| 233 | D3×D4 | — | 9 | 24 | no | — |
| 234 | #235 | — | 3 | 12 | no | — |
| 235 | #235 | — | 3 | 12 | no | — |
| 236 | #235 | — | 6 | 12 | no | — |
| 237 | #235 | — | 9 | 12 | no | — |
| 238 | #235 | — | 9 | 24 | no | — |
| 239 | #235 | — | 9 | 12 | no | — |
| 240 | #235 | — | 9 | 24 | no | — |
| 241 | #235 | — | 9 | 4 | no | — |
| 242 | C2×D12 | — | 3 | 6 | no | — |
| 243 | C2×D12 | — | 6 | 3 | no | — |
| 244 | C2×D12 | — | 9 | 6 | no | — |
| 245 | C2×D12 | — | 9 | 24 | no | — |
| 246 | C2×C4×D3 | — | 3 | 6 | no | — |
| 247 | C2×C4×D3 | — | 6 | 3 | no | — |
| 248 | C2×C4×D3 | — | 9 | 12 | no | — |
| 249 | C2×C4×D3 | — | 9 | 24 | no | — |
| 250 | C2×Dic6 | — | 9 | 6 | no | — |
| 251 | C22×C32 | — | 2 | 1 | no | — |
| 252 | C22×C32 | — | 2 | 2 | no | — |
| 253 | C22×C32 | — | 4 | 1 | no | — |
| 254 | C22×C32 | C23×D3 | 1 | 2 | yes | — |
| 255 | C22×C32 | C23×D3 | 1 | 1 | yes | characteristic |
| 256 | C2×C3⋊D3 | — | 4 | 3 | no | — |
| 257 | C2×C3⋊D3 | C23×D3 | 1 | 6 | yes | — |
| 258 | C2×C3⋊D3 | C23×D3 | 1 | 8 | yes | — |
| 259 | C2×C3×D3 | — | 3 | 12 | no | — |
| 260 | C2×C3×D3 | — | 3 | 8 | no | — |
| 261 | C2×C3×D3 | — | 3 | 8 | no | — |
| 262 | C2×C3×D3 | — | 6 | 8 | no | — |
| 263 | C2×C3×D3 | — | 6 | 6 | no | — |
| 264 | C2×C3×D3 | — | 12 | 6 | no | — |
| 265 | C2×C3×D3 | — | 12 | 6 | no | — |
| 266 | D32 | — | 12 | 12 | no | — |
| 267 | D32 | — | 12 | 24 | no | — |
| 268 | C32×C4 | — | 2 | 12 | no | — |
| 269 | C32×C4 | — | 2 | 6 | no | — |
| 270 | C32×C4 | — | 4 | 6 | no | — |
| 271 | C32×C4 | C23×D3 | 1 | 6 | yes | — |
| 272 | C32×C4 | C23×D3 | 1 | 12 | yes | — |
| 273 | C3⋊Dic3 | C23×D3 | 1 | 1 | yes | characteristic |
| 274 | C3⋊Dic3 | C23×D3 | 1 | 8 | yes | — |
| 275 | C3⋊Dic3 | C23×D3 | 1 | 1 | yes | characteristic |
| 276 | C3×Dic3 | — | 3 | 2 | no | — |
| 277 | C3×Dic3 | — | 3 | 8 | no | — |
| 278 | C3×Dic3 | — | 3 | 8 | no | — |
| 279 | C3×Dic3 | — | 3 | 2 | no | — |
| 280 | C3×Dic3 | — | 6 | 8 | no | — |
| 281 | C3×Dic3 | — | 6 | 1 | no | — |
| 282 | C3×Dic3 | — | 6 | 1 | no | — |
| 283 | 2−1+4 | — | 9 | 2 | no | — |
| 284 | 2−1+4 | — | 27 | 4 | no | — |
| 285 | H(5,𝔽2) | — | 27 | 6 | no | — |
| 286 | H(5,𝔽2) | — | 27 | 4 | no | — |
| 287 | C2×#41 | — | 9 | 1 | no | — |
| 288 | C2×#41 | — | 27 | 6 | no | — |
| 289 | C2×#41 | — | 27 | 8 | no | — |
| 290 | C33 | #585 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 291 | C23×C3 | — | 9 | 3 | no | — |
| 292 | C22×D3 | — | 3 | 6 | no | — |
| 293 | C22×D3 | — | 6 | 3 | no | — |
| 294 | C22×D3 | — | 9 | 24 | no | — |
| 295 | C22×D3 | — | 9 | 12 | no | — |
| 296 | C3×Q8 | — | 2 | 8 | no | — |
| 297 | C3×Q8 | — | 2 | 4 | no | — |
| 298 | C3×Q8 | — | 4 | 4 | no | — |
| 299 | C3×Q8 | — | 9 | 12 | no | — |
| 300 | C3×Q8 | C2×D32 | 1 | 4 | yes | — |
| 301 | C3×Q8 | C2×D32 | 1 | 8 | yes | — |
| 302 | C3×D4 | — | 9 | 8 | no | — |
| 303 | C3×D4 | — | 9 | 12 | no | — |
| 304 | C3×D4 | — | 9 | 12 | no | — |
| 305 | C2×C3×C4 | — | 2 | 3 | no | — |
| 306 | C2×C3×C4 | — | 2 | 6 | no | — |
| 307 | C2×C3×C4 | — | 4 | 3 | no | — |
| 308 | C2×C3×C4 | — | 9 | 1 | no | — |
| 309 | C2×C3×C4 | — | 9 | 6 | no | — |
| 310 | C2×C3×C4 | — | 9 | 6 | no | — |
| 311 | C2×C3×C4 | — | 9 | 24 | no | — |
| 312 | C2×C3×C4 | C2×D32 | 1 | 6 | yes | — |
| 313 | C2×C3×C4 | C2×D32 | 1 | 3 | yes | — |
| 314 | #67 | — | 3 | 8 | no | — |
| 315 | #67 | — | 3 | 8 | no | — |
| 316 | #67 | — | 6 | 8 | no | — |
| 317 | #67 | — | 9 | 24 | no | — |
| 318 | #67 | — | 9 | 8 | no | — |
| 319 | #67 | — | 9 | 24 | no | — |
| 320 | C2×Dic3 | — | 3 | 2 | no | — |
| 321 | C2×Dic3 | — | 6 | 1 | no | — |
| 322 | C2×Dic3 | — | 9 | 12 | no | — |
| 323 | C2×Dic3 | — | 9 | 8 | no | — |
| 324 | D12 | — | 3 | 24 | no | — |
| 325 | D12 | — | 3 | 12 | no | — |
| 326 | D12 | — | 3 | 12 | no | — |
| 327 | D12 | — | 6 | 12 | no | — |
| 328 | D12 | — | 6 | 12 | no | — |
| 329 | D12 | — | 9 | 4 | no | — |
| 330 | D12 | — | 9 | 24 | no | — |
| 331 | C4×D3 | — | 3 | 12 | no | — |
| 332 | C4×D3 | — | 3 | 12 | no | — |
| 333 | C4×D3 | — | 3 | 24 | no | — |
| 334 | C4×D3 | — | 3 | 24 | no | — |
| 335 | C4×D3 | — | 6 | 6 | no | — |
| 336 | C4×D3 | — | 6 | 6 | no | — |
| 337 | C4×D3 | — | 6 | 24 | no | — |
| 338 | C4×D3 | — | 9 | 8 | no | — |
| 339 | C4×D3 | — | 9 | 8 | no | — |
| 340 | C4×D3 | — | 9 | 24 | no | — |
| 341 | Dic6 | — | 3 | 12 | no | — |
| 342 | Dic6 | — | 3 | 12 | no | — |
| 343 | Dic6 | — | 6 | 12 | no | — |
| 344 | Dic6 | — | 9 | 4 | no | — |
| 345 | Dic6 | — | 9 | 8 | no | — |
| 346 | C2×C32 | — | 2 | 1 | no | — |
| 347 | C2×C32 | — | 2 | 2 | no | — |
| 348 | C2×C32 | — | 2 | 2 | no | — |
| 349 | C2×C32 | — | 2 | 2 | no | — |
| 350 | C2×C32 | — | 2 | 1 | no | — |
| 351 | C2×C32 | — | 4 | 1 | no | — |
| 352 | C2×C32 | — | 4 | 2 | no | — |
| 353 | C2×C32 | — | 4 | 2 | no | — |
| 354 | C2×C32 | C24×D3 | 1 | 1 | yes | characteristic |
| 355 | C2×C32 | C24×D3 | 1 | 2 | yes | — |
| 356 | C3⋊D3 | — | 2 | 6 | no | — |
| 357 | C3⋊D3 | — | 2 | 8 | no | — |
| 358 | C3×D3 | — | 6 | 8 | no | — |
| 359 | C3×D3 | — | 6 | 8 | no | — |
| 360 | C3×D3 | — | 6 | 12 | no | — |
| 361 | C3×D3 | — | 12 | 8 | no | — |
| 362 | C3×D3 | — | 12 | 6 | no | — |
| 363 | #41 | — | 9 | 4 | no | — |
| 364 | #41 | — | 9 | 4 | no | — |
| 365 | #41 | — | 9 | 8 | no | — |
| 366 | #41 | — | 9 | 12 | no | — |
| 367 | #41 | — | 27 | 12 | no | — |
| 368 | #41 | — | 27 | 4 | no | — |
| 369 | #41 | — | 27 | 12 | no | — |
| 370 | #41 | — | 27 | 24 | no | — |
| 371 | C2×Q8 | — | 9 | 8 | no | — |
| 372 | C2×Q8 | — | 27 | 6 | no | — |
| 373 | C2×Q8 | #1113 | 1 | 1 | yes | characteristic, complemented |
| 374 | C2×D4 | — | 9 | 3 | no | — |
| 375 | C2×D4 | — | 27 | 6 | no | — |
| 376 | C2×D4 | — | 27 | 24 | no | — |
| 377 | C2×D4 | — | 27 | 12 | no | — |
| 378 | C22×C4 | — | 9 | 3 | no | — |
| 379 | C22×C4 | — | 27 | 12 | no | — |
| 380 | C22×C3 | — | 2 | 1 | no | — |
| 381 | C22×C3 | — | 2 | 2 | no | — |
| 382 | C22×C3 | — | 4 | 1 | no | — |
| 383 | C22×C3 | — | 9 | 6 | no | — |
| 384 | C22×C3 | — | 9 | 8 | no | — |
| 385 | C22×C3 | — | 36 | 3 | no | — |
| 386 | C22×C3 | C22×D32 | 1 | 2 | yes | — |
| 387 | C22×C3 | C22×D32 | 1 | 1 | yes | characteristic |
| 388 | C2×D3 | — | 3 | 8 | no | — |
| 389 | C2×D3 | — | 3 | 8 | no | — |
| 390 | C2×D3 | — | 3 | 12 | no | — |
| 391 | C2×D3 | — | 6 | 8 | no | — |
| 392 | C2×D3 | — | 6 | 6 | no | — |
| 393 | C2×D3 | — | 12 | 6 | no | — |
| 394 | C2×D3 | — | 12 | 6 | no | — |
| 395 | C2×D3 | — | 36 | 24 | no | — |
| 396 | C2×D3 | — | 36 | 12 | no | — |
| 397 | C3×C4 | — | 2 | 12 | no | — |
| 398 | C3×C4 | — | 2 | 6 | no | — |
| 399 | C3×C4 | — | 4 | 6 | no | — |
| 400 | C3×C4 | — | 9 | 1 | no | — |
| 401 | C3×C4 | — | 9 | 8 | no | — |
| 402 | C3×C4 | — | 9 | 1 | no | — |
| 403 | C3×C4 | C22×D32 | 1 | 6 | yes | — |
| 404 | C3×C4 | C22×D32 | 1 | 12 | yes | — |
| 405 | Dic3 | — | 3 | 8 | no | — |
| 406 | Dic3 | — | 3 | 8 | no | — |
| 407 | Dic3 | — | 3 | 2 | no | — |
| 408 | Dic3 | — | 3 | 2 | no | — |
| 409 | Dic3 | — | 6 | 8 | no | — |
| 410 | Dic3 | — | 6 | 1 | no | — |
| 411 | Dic3 | — | 6 | 1 | no | — |
| 412 | C32 | — | 2 | 2 | no | — |
| 413 | C32 | — | 2 | 1 | no | — |
| 414 | C32 | — | 4 | 1 | no | — |
| 415 | C32 | #5964 | 1 | 1 | yes | characteristic, complemented |
| 416 | C32 | #5968 | 1 | 2 | yes | complemented |
| 417 | C23 | — | 9 | 3 | no | — |
| 418 | C23 | — | 27 | 12 | no | — |
| 419 | Q8 | — | 9 | 12 | no | — |
| 420 | Q8 | — | 27 | 4 | no | — |
| 421 | Q8 | C2×#1113 | 1 | 4 | yes | — |
| 422 | D4 | — | 9 | 8 | no | — |
| 423 | D4 | — | 9 | 12 | no | — |
| 424 | D4 | — | 9 | 12 | no | — |
| 425 | D4 | — | 27 | 4 | no | — |
| 426 | D4 | — | 27 | 24 | no | — |
| 427 | C2×C4 | — | 9 | 1 | no | — |
| 428 | C2×C4 | — | 9 | 6 | no | — |
| 429 | C2×C4 | — | 9 | 6 | no | — |
| 430 | C2×C4 | — | 9 | 24 | no | — |
| 431 | C2×C4 | — | 27 | 8 | no | — |
| 432 | C2×C4 | — | 27 | 12 | no | — |
| 433 | C2×C4 | C2×#1113 | 1 | 3 | yes | — |
| 434 | C2×C3 | — | 2 | 2 | no | — |
| 435 | C2×C3 | — | 2 | 2 | no | — |
| 436 | C2×C3 | — | 2 | 1 | no | — |
| 437 | C2×C3 | — | 2 | 2 | no | — |
| 438 | C2×C3 | — | 2 | 1 | no | — |
| 439 | C2×C3 | — | 4 | 2 | no | — |
| 440 | C2×C3 | — | 4 | 2 | no | — |
| 441 | C2×C3 | — | 4 | 1 | no | — |
| 442 | C2×C3 | — | 18 | 8 | no | — |
| 443 | C2×C3 | — | 18 | 6 | no | — |
| 444 | C2×C3 | C23×D32 | 1 | 2 | yes | — |
| 445 | C2×C3 | C23×D32 | 1 | 1 | yes | characteristic |
| 446 | D3 | — | 6 | 12 | no | — |
| 447 | D3 | — | 6 | 8 | no | — |
| 448 | D3 | — | 6 | 8 | no | — |
| 449 | D3 | — | 12 | 6 | no | — |
| 450 | D3 | — | 12 | 8 | no | — |
| 451 | C22 | — | 9 | 8 | no | — |
| 452 | C22 | — | 9 | 6 | no | — |
| 453 | C22 | — | 36 | 3 | no | — |
| 454 | C22 | — | 108 | 12 | no | — |
| 455 | C22 | C22×#1113 | 1 | 1 | yes | characteristic |
| 456 | C4 | — | 9 | 1 | no | — |
| 457 | C4 | — | 9 | 1 | no | — |
| 458 | C4 | — | 9 | 8 | no | — |
| 459 | C4 | C22×#1113 | 1 | 6 | yes | — |
| 460 | C3 | — | 2 | 1 | no | — |
| 461 | C3 | — | 2 | 2 | no | — |
| 462 | C3 | — | 4 | 1 | no | — |
| 463 | C3 | #10596688 | 1 | 2 | yes | complemented |
| 464 | C3 | #10596689 | 1 | 1 | yes | characteristic, complemented |
| 465 | C2 | — | 2 | 1 | no | — |
| 466 | C2 | — | 18 | 6 | no | — |
| 467 | C2 | — | 18 | 8 | no | — |
| 468 | C2 | C23×#1113 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×#1113 |
| commutator, socle, cosocle | C2×C33 | C25 |
| Fitting | C2×C33×Q8 | C22 |
| hypercenter | C2×Q8 | #1113 |
| hypocenter | C33 | #585 |
| LCS | G ▷ C2×C33 ▷ C33 | |
| UCS | C1 ◁ C2 ◁ C2×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×#64364 | C2 | semidirect |
| 2. C2×C3×#3832 | C2 | semidirect |
| 3. #11724627 | C2 | semidirect |
| 4. #11724626 | C2 | semidirect |
| 5. #11724624 | C2 | semidirect |
| 6. #11724619 | C2 | semidirect |
| 7. #11724618 | C2 | semidirect |
| 10. C2×C33×Q8 | C22 | semidirect |
| 11. C3×#3832 | C22 | semidirect |
| 12. C3×#3832 | C22 | semidirect |
| 13. C3×#3832 | C22 | semidirect |
| 14. C3×Q8×C3⋊D3 | C22 | semidirect |
| 15. C3×#3828 | C22 | semidirect |
| 16. C2×C3×C4⋊(C3⋊D3) | C22 | semidirect |
| 17. C2×C3×C4×C3⋊D3 | C22 | semidirect |
| 18. #89049 | C22 | semidirect |
| 19. #89046 | C22 | semidirect |
| 20. C4⋊#1113 | C22 | semidirect |
| 21. C4⋊#1113 | C22 | semidirect |
| 22. C4×#1113 | C22 | semidirect |
| 23. #89042 | C22 | semidirect |
| 24. #89041 | C22 | semidirect |
| 25. #89041 | C22 | semidirect |
| 26. #89040 | C22 | semidirect |
| 27. #64364 | D3 | semidirect |
| 28. C2×#3832 | D3 | semidirect |
| 67. C2×C32×Q8 | C2×D3 | semidirect |
| 68. C2×C32×Q8 | C2×D3 | semidirect |
| 69. #3832 | C2×D3 | semidirect |
| 70. #3832 | C2×D3 | semidirect |
| 71. #3832 | C2×D3 | semidirect |
| 72. Q8×C3⋊D3 | C2×D3 | semidirect |
| 73. #3828 | C2×D3 | semidirect |
| 74. C2×C4⋊(C3⋊D3) | C2×D3 | semidirect |
| 75. C2×C4×C3⋊D3 | C2×D3 | semidirect |
| 209. C2×C3×Q8 | D32 | semidirect |
| 210. C2×C3×Q8 | D32 | semidirect |
| 290. C33 | #585 | semidirect |
| 373. C2×Q8 | #1113 | semidirect |
| 415. C32 | #5964 | semidirect |
| 416. C32 | #5968 | semidirect |
| 463. C3 | #10596688 | semidirect |
| 464. C3 | #10596689 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#64364 | 2 |
| C2×C3×#3832 | 2 |
| #11724627 | 2 |
| #11724626 | 2 |
| #11724624 | 2 |
| #11724619 | 2 |
| #11724618 | 2 |
| #10596689 | 3 |
| #10596688 | 3 |