Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
2999 conjugacy classes of subgroups.
The subgroup lattice has 545 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×#88744 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #64361⋊C3 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #11722545 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | C2×#88672 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #11722506 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #11722504 | C2 | 1 | 8 | yes | maximal, complemented |
| 7 | #11722502 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #11722491 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #11722483 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #10596678 | — | 3 | 2 | no | maximal |
| 11 | C2×D4×H(3,𝔽3) | C22 | 1 | 1 | yes | characteristic, complemented |
| 12 | C2×#6235 | C22 | 1 | 2 | yes | complemented |
| 13 | C22×#1084 | C22 | 1 | 2 | yes | complemented |
| 14 | #88744 | C22 | 1 | 4 | yes | complemented |
| 15 | #88744 | C22 | 1 | 4 | yes | complemented |
| 16 | C2×C4×#272 | C22 | 1 | 1 | yes | characteristic, complemented |
| 17 | C2×#6229 | C22 | 1 | 1 | yes | characteristic, complemented |
| 18 | C2×#638⋊C3 | C22 | 1 | 8 | yes | complemented |
| 19 | #3830⋊C3 | C22 | 1 | 8 | yes | complemented |
| 20 | D4×(C3⋊D3)⋊C3 | C22 | 1 | 8 | yes | complemented |
| 21 | #3828⋊C3 | C22 | 1 | 4 | yes | complemented |
| 22 | #88677 | C22 | 1 | 4 | yes | complemented |
| 23 | #88676 | C22 | 1 | 16 | yes | complemented |
| 24 | C2×#6198 | C22 | 1 | 4 | yes | complemented |
| 25 | #88672 | C22 | 1 | 8 | yes | complemented |
| 26 | #88672 | C22 | 1 | 8 | yes | complemented |
| 27 | #88672 | C22 | 1 | 4 | yes | complemented |
| 28 | #88672 | C22 | 1 | 8 | yes | complemented |
| 29 | #88671 | C22 | 1 | 16 | yes | complemented |
| 30 | C2×((C3⋊D3)⋊C3)⋊C4 | C22 | 1 | 8 | yes | complemented |
| 31 | C2×#6196 | C22 | 1 | 4 | yes | complemented |
| 32 | #88655 | C22 | 1 | 2 | yes | complemented |
| 33 | C4×((C3⋊D3)⋊C3)⋊C2 | C22 | 1 | 4 | yes | complemented |
| 34 | #88651 | C22 | 1 | 2 | yes | complemented |
| 35 | #88650 | C22 | 1 | 4 | yes | complemented |
| 36 | #88649 | C22 | 1 | 4 | yes | complemented |
| 37 | #88648 | C22 | 1 | 8 | yes | complemented |
| 38 | ((C3⋊D3)⋊C3)⋊Q8 | C22 | 1 | 8 | yes | complemented |
| 39 | #64361 | D3 | 1 | 2 | yes | complemented |
| 40 | C3×#1004 | — | 3 | 2 | no | — |
| 41 | C2×C3×#237 | — | 3 | 2 | no | — |
| 42 | C2×C3×#237 | — | 6 | 1 | no | — |
| 43 | #64330 | — | 3 | 8 | no | — |
| 44 | C2×#3804 | — | 3 | 8 | no | — |
| 45 | #64314 | — | 3 | 8 | no | — |
| 46 | #64312 | — | 3 | 8 | no | — |
| 47 | D3×#237 | — | 3 | 8 | no | — |
| 48 | #64309 | — | 3 | 8 | no | — |
| 49 | D3×#235 | — | 3 | 4 | no | — |
| 50 | #64297 | — | 3 | 4 | no | — |
| 51 | C23×H(3,𝔽3) | C23 | 1 | 2 | yes | — |
| 52 | C22×#272 | C23 | 1 | 1 | yes | characteristic |
| 53 | C22×(C3⋊D3)⋊C3 | C23 | 1 | 8 | yes | — |
| 54 | C2×((C3⋊D3)⋊C3)⋊C2 | C23 | 1 | 4 | yes | — |
| 55 | D4×H(3,𝔽3) | C23 | 1 | 4 | yes | — |
| 56 | C2×C4×H(3,𝔽3) | C23 | 1 | 1 | yes | characteristic |
| 57 | #6235 | C23 | 1 | 8 | yes | — |
| 58 | C2×#1084 | C23 | 1 | 4 | yes | — |
| 59 | C2×#1084 | C23 | 1 | 4 | yes | — |
| 60 | C2×#1084 | C23 | 1 | 2 | yes | — |
| 61 | C2×#1084 | C23 | 1 | 1 | yes | characteristic |
| 62 | C4×#272 | C23 | 1 | 2 | yes | — |
| 63 | C4×#272 | C23 | 1 | 2 | yes | — |
| 64 | #6229 | C23 | 1 | 4 | yes | — |
| 65 | #638⋊C3 | C23 | 1 | 16 | yes | — |
| 66 | #638⋊C3 | C23 | 1 | 8 | yes | — |
| 67 | C2×(C3⋊Dic3)⋊C3 | C23 | 1 | 8 | yes | — |
| 68 | C4⋊((C3⋊D3)⋊C3) | C23 | 1 | 4 | yes | — |
| 69 | C4×(C3⋊D3)⋊C3 | C23 | 1 | 8 | yes | — |
| 70 | #634⋊C3 | C23 | 1 | 4 | yes | — |
| 71 | #6200 | C23 | 1 | 8 | yes | — |
| 72 | #6199 | C23 | 1 | 4 | yes | — |
| 73 | #6198 | C23 | 1 | 8 | yes | — |
| 74 | #6198 | C23 | 1 | 4 | yes | — |
| 75 | ((C3⋊D3)⋊C3)⋊C4 | C23 | 1 | 16 | yes | — |
| 76 | ((C3⋊D3)⋊C3)⋊C4 | C23 | 1 | 8 | yes | — |
| 77 | #6196 | C23 | 1 | 8 | yes | — |
| 78 | #6196 | C23 | 1 | 4 | yes | — |
| 79 | #5966 | — | 9 | 2 | no | — |
| 80 | #5964 | — | 9 | 1 | no | — |
| 81 | C2×C32×D4 | — | 2 | 1 | no | — |
| 82 | C2×C32×D4 | C2×D3 | 1 | 2 | yes | complemented |
| 83 | C2×#638 | C2×D3 | 1 | 8 | yes | complemented |
| 84 | #3830 | C2×D3 | 1 | 8 | yes | complemented |
| 85 | D4×C3⋊D3 | C2×D3 | 1 | 8 | yes | complemented |
| 86 | #3828 | C2×D3 | 1 | 4 | yes | complemented |
| 87 | C2×C3×#67 | — | 3 | 8 | no | — |
| 88 | C2×C3×#67 | — | 3 | 4 | no | — |
| 89 | C2×C3×#67 | — | 6 | 2 | no | — |
| 90 | C22×C3×Dic3 | — | 3 | 4 | no | — |
| 91 | C22×C3×Dic3 | — | 6 | 2 | no | — |
| 92 | C3×#237 | — | 3 | 8 | no | — |
| 93 | C3×#237 | — | 3 | 8 | no | — |
| 94 | C3×#237 | — | 3 | 8 | no | — |
| 95 | C3×#237 | — | 6 | 4 | no | — |
| 96 | C3×#237 | — | 6 | 4 | no | — |
| 97 | C3×D3×D4 | — | 3 | 8 | no | — |
| 98 | C3×#235 | — | 3 | 4 | no | — |
| 99 | C2×C3×C4×D3 | — | 3 | 2 | no | — |
| 100 | C2×C3×C4×D3 | — | 6 | 1 | no | — |
| 101 | C2×C3×Dic6 | — | 3 | 2 | no | — |
| 102 | C2×C3×Dic6 | — | 6 | 1 | no | — |
| 103 | #3811 | — | 3 | 16 | no | — |
| 104 | D3×#67 | — | 3 | 8 | no | — |
| 105 | D3×#67 | — | 3 | 16 | no | — |
| 106 | C2×#627 | — | 3 | 8 | no | — |
| 107 | C2×#626 | — | 3 | 8 | no | — |
| 108 | C2×#624 | — | 3 | 8 | no | — |
| 109 | #3805 | — | 3 | 16 | no | — |
| 110 | #3804 | — | 3 | 16 | no | — |
| 111 | #3804 | — | 3 | 8 | no | — |
| 112 | #3804 | — | 3 | 16 | no | — |
| 113 | #3804 | — | 3 | 16 | no | — |
| 114 | #3804 | — | 3 | 16 | no | — |
| 115 | C2×D3×Dic3 | — | 3 | 8 | no | — |
| 116 | D3×D12 | — | 3 | 4 | no | — |
| 117 | C4×D32 | — | 3 | 8 | no | — |
| 118 | #3799 | — | 3 | 8 | no | — |
| 119 | #3799 | — | 3 | 4 | no | — |
| 120 | #3798 | — | 3 | 8 | no | — |
| 121 | #3797 | — | 3 | 8 | no | — |
| 122 | #3796 | — | 3 | 8 | no | — |
| 123 | #3795 | — | 3 | 4 | no | — |
| 124 | D3×Dic6 | — | 3 | 8 | no | — |
| 125 | D3×Dic6 | — | 3 | 4 | no | — |
| 126 | C22×H(3,𝔽3) | — | 4 | 2 | no | — |
| 127 | C22×H(3,𝔽3) | C24 | 1 | 4 | yes | — |
| 128 | C22×H(3,𝔽3) | C24 | 1 | 1 | yes | characteristic |
| 129 | C2×#272 | — | 4 | 1 | no | — |
| 130 | C2×#272 | C24 | 1 | 2 | yes | — |
| 131 | C2×(C3⋊D3)⋊C3 | — | 4 | 8 | no | — |
| 132 | C2×(C3⋊D3)⋊C3 | C24 | 1 | 8 | yes | — |
| 133 | ((C3⋊D3)⋊C3)⋊C2 | — | 4 | 4 | no | — |
| 134 | C4×H(3,𝔽3) | C24 | 1 | 2 | yes | — |
| 135 | #1084 | C24 | 1 | 1 | yes | characteristic |
| 136 | #1084 | C24 | 1 | 4 | yes | — |
| 137 | #1084 | C24 | 1 | 1 | yes | characteristic |
| 138 | (C3⋊Dic3)⋊C3 | C24 | 1 | 8 | yes | — |
| 139 | C3×H(5,𝔽2) | — | 9 | 2 | no | — |
| 140 | C2×C3×#41 | — | 9 | 1 | no | — |
| 141 | #1010 | — | 9 | 4 | no | — |
| 142 | #1010 | — | 9 | 4 | no | — |
| 143 | #1010 | — | 9 | 8 | no | — |
| 144 | #1009 | — | 9 | 4 | no | — |
| 145 | D3×#41 | — | 9 | 4 | no | — |
| 146 | D3×#41 | — | 9 | 8 | no | — |
| 147 | D3×#41 | — | 9 | 8 | no | — |
| 148 | #1007 | — | 9 | 2 | no | — |
| 149 | #1004 | — | 3 | 2 | no | — |
| 150 | #1004 | — | 9 | 2 | no | — |
| 151 | #1004 | — | 9 | 8 | no | — |
| 152 | #1004 | — | 9 | 4 | no | — |
| 153 | #1004 | — | 9 | 8 | no | — |
| 154 | C2×#237 | — | 3 | 2 | no | — |
| 155 | C2×#237 | — | 6 | 1 | no | — |
| 156 | C2×#237 | — | 9 | 8 | no | — |
| 157 | C2×#237 | — | 9 | 8 | no | — |
| 158 | C2×#235 | — | 9 | 2 | no | — |
| 159 | C2×#235 | — | 9 | 4 | no | — |
| 160 | C23×C32 | — | 2 | 2 | no | — |
| 161 | C23×C32 | C22×D3 | 1 | 4 | yes | — |
| 162 | C22×C3⋊D3 | C22×D3 | 1 | 8 | yes | — |
| 163 | C22×C3×D3 | — | 3 | 8 | no | — |
| 164 | C22×C3×D3 | — | 3 | 2 | no | — |
| 165 | C22×C3×D3 | — | 6 | 1 | no | — |
| 166 | C2×D32 | — | 3 | 8 | no | — |
| 167 | C32×D4 | — | 2 | 4 | no | — |
| 168 | C32×D4 | C22×D3 | 1 | 8 | yes | — |
| 169 | C2×C32×C4 | — | 2 | 1 | no | — |
| 170 | C2×C32×C4 | C22×D3 | 1 | 2 | yes | — |
| 171 | #638 | C22×D3 | 1 | 8 | yes | — |
| 172 | #638 | C22×D3 | 1 | 16 | yes | — |
| 173 | C2×C3⋊Dic3 | C22×D3 | 1 | 8 | yes | — |
| 174 | C4⋊(C3⋊D3) | C22×D3 | 1 | 4 | yes | — |
| 175 | C4×C3⋊D3 | C22×D3 | 1 | 8 | yes | — |
| 176 | #634 | C22×D3 | 1 | 4 | yes | — |
| 177 | C3×#67 | — | 3 | 8 | no | — |
| 178 | C3×#67 | — | 3 | 16 | no | — |
| 179 | C3×#67 | — | 3 | 16 | no | — |
| 180 | C3×#67 | — | 6 | 8 | no | — |
| 181 | C2×C3×Dic3 | — | 3 | 8 | no | — |
| 182 | C2×C3×Dic3 | — | 3 | 8 | no | — |
| 183 | C2×C3×Dic3 | — | 3 | 4 | no | — |
| 184 | C2×C3×Dic3 | — | 3 | 2 | no | — |
| 185 | C2×C3×Dic3 | — | 3 | 8 | no | — |
| 186 | C2×C3×Dic3 | — | 6 | 2 | no | — |
| 187 | C2×C3×Dic3 | — | 6 | 1 | no | — |
| 188 | C2×C3×Dic3 | — | 6 | 4 | no | — |
| 189 | C2×C3×Dic3 | — | 6 | 4 | no | — |
| 190 | C3×D12 | — | 3 | 4 | no | — |
| 191 | C3×C4×D3 | — | 3 | 8 | no | — |
| 192 | C3×C4×D3 | — | 3 | 4 | no | — |
| 193 | C3×C4×D3 | — | 3 | 4 | no | — |
| 194 | C3×C4×D3 | — | 6 | 2 | no | — |
| 195 | C3×C4×D3 | — | 6 | 2 | no | — |
| 196 | C3×Dic6 | — | 3 | 4 | no | — |
| 197 | C3×Dic6 | — | 3 | 8 | no | — |
| 198 | C3×Dic6 | — | 6 | 4 | no | — |
| 199 | #627 | — | 3 | 16 | no | — |
| 200 | #627 | — | 3 | 8 | no | — |
| 201 | #626 | — | 3 | 16 | no | — |
| 202 | #626 | — | 3 | 8 | no | — |
| 203 | #626 | — | 3 | 8 | no | — |
| 204 | #625 | — | 3 | 8 | no | — |
| 205 | #624 | — | 3 | 16 | no | — |
| 206 | #624 | — | 3 | 8 | no | — |
| 207 | D3×Dic3 | — | 3 | 16 | no | — |
| 208 | D3×Dic3 | — | 3 | 8 | no | — |
| 209 | D3×Dic3 | — | 3 | 8 | no | — |
| 210 | #585 | — | 27 | 1 | no | Sylow |
| 211 | C2×H(3,𝔽3) | — | 2 | 1 | no | — |
| 212 | C2×H(3,𝔽3) | — | 2 | 4 | no | — |
| 213 | C2×H(3,𝔽3) | C25 | 1 | 1 | yes | characteristic |
| 214 | #272 | — | 2 | 2 | no | — |
| 215 | (C3⋊D3)⋊C3 | — | 2 | 8 | no | — |
| 216 | C3×#41 | — | 9 | 4 | no | — |
| 217 | C3×#41 | — | 9 | 8 | no | — |
| 218 | C3×#41 | — | 9 | 4 | no | — |
| 219 | C3×#41 | — | 9 | 4 | no | — |
| 220 | C2×C3×Q8 | — | 9 | 1 | no | — |
| 221 | C2×C3×D4 | — | 3 | 2 | no | — |
| 222 | C2×C3×D4 | — | 6 | 1 | no | — |
| 223 | C2×C3×D4 | — | 9 | 8 | no | — |
| 224 | C2×C3×D4 | — | 9 | 8 | no | — |
| 225 | C2×C3×D4 | — | 9 | 2 | no | — |
| 226 | C2×C3×D4 | D32 | 1 | 1 | yes | characteristic |
| 227 | C22×C3×C4 | — | 9 | 2 | no | — |
| 228 | C22×C3×C4 | — | 9 | 1 | no | — |
| 229 | C2×#67 | — | 3 | 4 | no | — |
| 230 | C2×#67 | — | 3 | 8 | no | — |
| 231 | C2×#67 | — | 6 | 2 | no | — |
| 232 | C2×#67 | — | 9 | 8 | no | — |
| 233 | C2×#67 | — | 9 | 8 | no | — |
| 234 | C2×#67 | — | 9 | 4 | no | — |
| 235 | C2×#67 | — | 9 | 16 | no | — |
| 236 | C22×Dic3 | — | 3 | 4 | no | — |
| 237 | C22×Dic3 | — | 6 | 2 | no | — |
| 238 | C22×Dic3 | — | 9 | 8 | no | — |
| 239 | #239 | — | 9 | 8 | no | — |
| 240 | #239 | — | 9 | 4 | no | — |
| 241 | D3×Q8 | — | 9 | 8 | no | — |
| 242 | D3×Q8 | — | 9 | 8 | no | — |
| 243 | D3×Q8 | — | 9 | 4 | no | — |
| 244 | #237 | — | 3 | 8 | no | — |
| 245 | #237 | — | 3 | 8 | no | — |
| 246 | #237 | — | 3 | 8 | no | — |
| 247 | #237 | — | 6 | 4 | no | — |
| 248 | #237 | — | 6 | 4 | no | — |
| 249 | #237 | — | 9 | 8 | no | — |
| 250 | #237 | — | 9 | 8 | no | — |
| 251 | #237 | — | 9 | 4 | no | — |
| 252 | #237 | — | 9 | 16 | no | — |
| 253 | #237 | — | 9 | 8 | no | — |
| 254 | #237 | — | 9 | 16 | no | — |
| 255 | #237 | — | 9 | 16 | no | — |
| 256 | #237 | — | 9 | 16 | no | — |
| 257 | #237 | — | 9 | 16 | no | — |
| 258 | D3×D4 | — | 3 | 8 | no | — |
| 259 | D3×D4 | — | 9 | 8 | no | — |
| 260 | D3×D4 | — | 9 | 4 | no | — |
| 261 | D3×D4 | — | 9 | 16 | no | — |
| 262 | D3×D4 | — | 9 | 16 | no | — |
| 263 | D3×D4 | — | 9 | 8 | no | — |
| 264 | #235 | — | 3 | 4 | no | — |
| 265 | #235 | — | 9 | 4 | no | — |
| 266 | #235 | — | 9 | 4 | no | — |
| 267 | #235 | — | 9 | 8 | no | — |
| 268 | #235 | — | 9 | 4 | no | — |
| 269 | #235 | — | 9 | 8 | no | — |
| 270 | #235 | — | 9 | 4 | no | — |
| 271 | #235 | — | 9 | 8 | no | — |
| 272 | #235 | — | 9 | 8 | no | — |
| 273 | #235 | — | 9 | 8 | no | — |
| 274 | #235 | — | 9 | 16 | no | — |
| 275 | C2×D12 | — | 9 | 2 | no | — |
| 276 | C2×D12 | — | 9 | 4 | no | — |
| 277 | C2×C4×D3 | — | 3 | 2 | no | — |
| 278 | C2×C4×D3 | — | 6 | 1 | no | — |
| 279 | C2×C4×D3 | — | 9 | 4 | no | — |
| 280 | C2×C4×D3 | — | 9 | 8 | no | — |
| 281 | C2×C4×D3 | — | 9 | 8 | no | — |
| 282 | C2×C4×D3 | — | 9 | 8 | no | — |
| 283 | C2×Dic6 | — | 3 | 2 | no | — |
| 284 | C2×Dic6 | — | 6 | 1 | no | — |
| 285 | C2×Dic6 | — | 9 | 2 | no | — |
| 286 | C2×Dic6 | — | 9 | 8 | no | — |
| 287 | C2×Dic6 | — | 9 | 4 | no | — |
| 288 | C2×Dic6 | — | 9 | 8 | no | — |
| 289 | C22×C32 | — | 2 | 1 | no | — |
| 290 | C22×C32 | — | 2 | 4 | no | — |
| 291 | C22×C32 | — | 4 | 4 | no | — |
| 292 | C22×C32 | — | 4 | 4 | no | — |
| 293 | C22×C32 | C23×D3 | 1 | 8 | yes | — |
| 294 | C22×C32 | C23×D3 | 1 | 2 | yes | — |
| 295 | C2×C3⋊D3 | — | 4 | 8 | no | — |
| 296 | C2×C3⋊D3 | C23×D3 | 1 | 8 | yes | — |
| 297 | C2×C3×D3 | — | 3 | 8 | no | — |
| 298 | C2×C3×D3 | — | 3 | 4 | no | — |
| 299 | C2×C3×D3 | — | 6 | 2 | no | — |
| 300 | C2×C3×D3 | — | 12 | 8 | no | — |
| 301 | C2×C3×D3 | — | 12 | 2 | no | — |
| 302 | C2×C3×D3 | — | 12 | 2 | no | — |
| 303 | D32 | — | 12 | 8 | no | — |
| 304 | C32×C4 | — | 2 | 2 | no | — |
| 305 | C32×C4 | C23×D3 | 1 | 4 | yes | — |
| 306 | C3⋊Dic3 | C23×D3 | 1 | 8 | yes | — |
| 307 | C3×Dic3 | — | 3 | 8 | no | — |
| 308 | C3×Dic3 | — | 3 | 2 | no | — |
| 309 | C3×Dic3 | — | 3 | 8 | no | — |
| 310 | C3×Dic3 | — | 3 | 2 | no | — |
| 311 | C3×Dic3 | — | 6 | 4 | no | — |
| 312 | C3×Dic3 | — | 6 | 1 | no | — |
| 313 | C3×Dic3 | — | 6 | 1 | no | — |
| 314 | 2−1+4 | — | 27 | 2 | no | — |
| 315 | 2−1+4 | — | 27 | 4 | no | — |
| 316 | H(5,𝔽2) | — | 9 | 2 | no | — |
| 317 | H(5,𝔽2) | — | 27 | 4 | no | — |
| 318 | H(5,𝔽2) | — | 27 | 4 | no | — |
| 319 | C2×#41 | — | 9 | 1 | no | — |
| 320 | C2×#41 | — | 27 | 4 | no | — |
| 321 | C2×#41 | — | 27 | 2 | no | — |
| 322 | C2×#41 | — | 27 | 8 | no | — |
| 323 | H(3,𝔽3) | #585 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 324 | C23×C3 | — | 3 | 4 | no | — |
| 325 | C23×C3 | — | 6 | 2 | no | — |
| 326 | C23×C3 | — | 9 | 8 | no | — |
| 327 | C23×C3 | — | 9 | 1 | no | — |
| 328 | C23×C3 | C2×D32 | 1 | 2 | yes | — |
| 329 | C22×D3 | — | 3 | 2 | no | — |
| 330 | C22×D3 | — | 3 | 8 | no | — |
| 331 | C22×D3 | — | 6 | 1 | no | — |
| 332 | C22×D3 | — | 9 | 8 | no | — |
| 333 | C22×D3 | — | 9 | 4 | no | — |
| 334 | C22×D3 | — | 9 | 8 | no | — |
| 335 | C3×Q8 | — | 9 | 4 | no | — |
| 336 | C3×Q8 | — | 9 | 4 | no | — |
| 337 | C3×D4 | — | 3 | 8 | no | — |
| 338 | C3×D4 | — | 6 | 4 | no | — |
| 339 | C3×D4 | — | 9 | 4 | no | — |
| 340 | C3×D4 | — | 9 | 8 | no | — |
| 341 | C3×D4 | — | 9 | 16 | no | — |
| 342 | C3×D4 | — | 9 | 8 | no | — |
| 343 | C3×D4 | C2×D32 | 1 | 4 | yes | — |
| 344 | C2×C3×C4 | — | 3 | 2 | no | — |
| 345 | C2×C3×C4 | — | 6 | 1 | no | — |
| 346 | C2×C3×C4 | — | 9 | 8 | no | — |
| 347 | C2×C3×C4 | — | 9 | 8 | no | — |
| 348 | C2×C3×C4 | — | 9 | 4 | no | — |
| 349 | C2×C3×C4 | — | 9 | 4 | no | — |
| 350 | C2×C3×C4 | — | 9 | 1 | no | — |
| 351 | C2×C3×C4 | — | 9 | 2 | no | — |
| 352 | C2×C3×C4 | — | 9 | 2 | no | — |
| 353 | C2×C3×C4 | — | 9 | 2 | no | — |
| 354 | C2×C3×C4 | C2×D32 | 1 | 1 | yes | characteristic |
| 355 | #67 | — | 3 | 16 | no | — |
| 356 | #67 | — | 3 | 8 | no | — |
| 357 | #67 | — | 3 | 16 | no | — |
| 358 | #67 | — | 6 | 8 | no | — |
| 359 | #67 | — | 9 | 8 | no | — |
| 360 | #67 | — | 9 | 16 | no | — |
| 361 | #67 | — | 9 | 8 | no | — |
| 362 | #67 | — | 9 | 16 | no | — |
| 363 | #67 | — | 9 | 8 | no | — |
| 364 | #67 | — | 9 | 8 | no | — |
| 365 | C2×Dic3 | — | 3 | 4 | no | — |
| 366 | C2×Dic3 | — | 3 | 8 | no | — |
| 367 | C2×Dic3 | — | 3 | 2 | no | — |
| 368 | C2×Dic3 | — | 3 | 8 | no | — |
| 369 | C2×Dic3 | — | 3 | 8 | no | — |
| 370 | C2×Dic3 | — | 6 | 2 | no | — |
| 371 | C2×Dic3 | — | 6 | 1 | no | — |
| 372 | C2×Dic3 | — | 6 | 4 | no | — |
| 373 | C2×Dic3 | — | 6 | 4 | no | — |
| 374 | C2×Dic3 | — | 9 | 8 | no | — |
| 375 | C2×Dic3 | — | 9 | 4 | no | — |
| 376 | C2×Dic3 | — | 9 | 16 | no | — |
| 377 | C2×Dic3 | — | 9 | 8 | no | — |
| 378 | D12 | — | 3 | 4 | no | — |
| 379 | D12 | — | 9 | 4 | no | — |
| 380 | D12 | — | 9 | 4 | no | — |
| 381 | D12 | — | 9 | 8 | no | — |
| 382 | D12 | — | 9 | 8 | no | — |
| 383 | C4×D3 | — | 3 | 4 | no | — |
| 384 | C4×D3 | — | 3 | 4 | no | — |
| 385 | C4×D3 | — | 3 | 8 | no | — |
| 386 | C4×D3 | — | 6 | 2 | no | — |
| 387 | C4×D3 | — | 6 | 2 | no | — |
| 388 | C4×D3 | — | 9 | 8 | no | — |
| 389 | C4×D3 | — | 9 | 8 | no | — |
| 390 | C4×D3 | — | 9 | 16 | no | — |
| 391 | C4×D3 | — | 9 | 8 | no | — |
| 392 | C4×D3 | — | 9 | 16 | no | — |
| 393 | C4×D3 | — | 9 | 8 | no | — |
| 394 | Dic6 | — | 3 | 8 | no | — |
| 395 | Dic6 | — | 3 | 4 | no | — |
| 396 | Dic6 | — | 6 | 4 | no | — |
| 397 | Dic6 | — | 9 | 4 | no | — |
| 398 | Dic6 | — | 9 | 4 | no | — |
| 399 | Dic6 | — | 9 | 8 | no | — |
| 400 | Dic6 | — | 9 | 16 | no | — |
| 401 | Dic6 | — | 9 | 8 | no | — |
| 402 | C2×C32 | — | 2 | 2 | no | — |
| 403 | C2×C32 | — | 2 | 8 | no | — |
| 404 | C2×C32 | — | 2 | 2 | no | — |
| 405 | C2×C32 | — | 2 | 1 | no | — |
| 406 | C2×C32 | — | 4 | 4 | no | — |
| 407 | C2×C32 | C24×D3 | 1 | 2 | yes | — |
| 408 | C3⋊D3 | — | 2 | 8 | no | — |
| 409 | C3×D3 | — | 6 | 8 | no | — |
| 410 | C3×D3 | — | 6 | 4 | no | — |
| 411 | C3×D3 | — | 12 | 2 | no | — |
| 412 | #41 | — | 9 | 4 | no | — |
| 413 | #41 | — | 9 | 4 | no | — |
| 414 | #41 | — | 9 | 8 | no | — |
| 415 | #41 | — | 9 | 4 | no | — |
| 416 | #41 | — | 27 | 4 | no | — |
| 417 | #41 | — | 27 | 4 | no | — |
| 418 | #41 | — | 27 | 8 | no | — |
| 419 | #41 | — | 27 | 8 | no | — |
| 420 | #41 | — | 27 | 8 | no | — |
| 421 | #41 | — | 27 | 16 | no | — |
| 422 | #41 | — | 27 | 4 | no | — |
| 423 | #41 | — | 27 | 8 | no | — |
| 424 | C2×Q8 | — | 9 | 1 | no | — |
| 425 | C2×Q8 | — | 27 | 4 | no | — |
| 426 | C2×Q8 | — | 27 | 2 | no | — |
| 427 | C2×Q8 | — | 27 | 8 | no | — |
| 428 | C2×D4 | — | 9 | 2 | no | — |
| 429 | C2×D4 | — | 9 | 8 | no | — |
| 430 | C2×D4 | — | 9 | 8 | no | — |
| 431 | C2×D4 | — | 27 | 2 | no | — |
| 432 | C2×D4 | — | 27 | 4 | no | — |
| 433 | C2×D4 | — | 27 | 4 | no | — |
| 434 | C2×D4 | — | 27 | 16 | no | — |
| 435 | C2×D4 | ((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic, complemented |
| 436 | C22×C4 | — | 9 | 2 | no | — |
| 437 | C22×C4 | — | 9 | 1 | no | — |
| 438 | C22×C4 | — | 27 | 4 | no | — |
| 439 | C22×C4 | — | 27 | 8 | no | — |
| 440 | C22×C3 | — | 3 | 2 | no | — |
| 441 | C22×C3 | — | 3 | 8 | no | — |
| 442 | C22×C3 | — | 4 | 2 | no | — |
| 443 | C22×C3 | — | 6 | 1 | no | — |
| 444 | C22×C3 | — | 6 | 4 | no | — |
| 445 | C22×C3 | — | 9 | 8 | no | — |
| 446 | C22×C3 | — | 9 | 2 | no | — |
| 447 | C22×C3 | — | 12 | 4 | no | — |
| 448 | C22×C3 | — | 12 | 4 | no | — |
| 449 | C22×C3 | — | 36 | 1 | no | — |
| 450 | C22×C3 | — | 36 | 8 | no | — |
| 451 | C22×C3 | C22×D32 | 1 | 4 | yes | — |
| 452 | C22×C3 | C22×D32 | 1 | 1 | yes | characteristic |
| 453 | C2×D3 | — | 3 | 4 | no | — |
| 454 | C2×D3 | — | 3 | 8 | no | — |
| 455 | C2×D3 | — | 6 | 2 | no | — |
| 456 | C2×D3 | — | 9 | 8 | no | — |
| 457 | C2×D3 | — | 12 | 8 | no | — |
| 458 | C2×D3 | — | 12 | 2 | no | — |
| 459 | C2×D3 | — | 12 | 2 | no | — |
| 460 | C2×D3 | — | 36 | 8 | no | — |
| 461 | C2×D3 | — | 36 | 4 | no | — |
| 462 | C2×D3 | — | 36 | 8 | no | — |
| 463 | C3×C4 | — | 3 | 4 | no | — |
| 464 | C3×C4 | — | 6 | 2 | no | — |
| 465 | C3×C4 | — | 9 | 8 | no | — |
| 466 | C3×C4 | — | 9 | 1 | no | — |
| 467 | C3×C4 | — | 9 | 4 | no | — |
| 468 | C3×C4 | — | 9 | 1 | no | — |
| 469 | C3×C4 | C22×D32 | 1 | 2 | yes | — |
| 470 | Dic3 | — | 3 | 8 | no | — |
| 471 | Dic3 | — | 3 | 2 | no | — |
| 472 | Dic3 | — | 3 | 2 | no | — |
| 473 | Dic3 | — | 3 | 8 | no | — |
| 474 | Dic3 | — | 6 | 4 | no | — |
| 475 | Dic3 | — | 6 | 1 | no | — |
| 476 | Dic3 | — | 6 | 1 | no | — |
| 477 | Dic3 | — | 9 | 8 | no | — |
| 478 | C32 | — | 2 | 1 | no | — |
| 479 | C32 | #5966 | 1 | 2 | yes | complemented |
| 480 | C23 | — | 9 | 1 | no | — |
| 481 | C23 | — | 9 | 8 | no | — |
| 482 | C23 | — | 27 | 4 | no | — |
| 483 | C23 | C2×((C3⋊D3)⋊C3)⋊C2 | 1 | 2 | yes | — |
| 484 | Q8 | — | 9 | 4 | no | — |
| 485 | Q8 | — | 9 | 4 | no | — |
| 486 | Q8 | — | 27 | 4 | no | — |
| 487 | Q8 | — | 27 | 8 | no | — |
| 488 | D4 | — | 9 | 16 | no | — |
| 489 | D4 | — | 9 | 8 | no | — |
| 490 | D4 | — | 9 | 8 | no | — |
| 491 | D4 | — | 9 | 4 | no | — |
| 492 | D4 | — | 27 | 4 | no | — |
| 493 | D4 | — | 27 | 8 | no | — |
| 494 | D4 | — | 27 | 8 | no | — |
| 495 | D4 | C2×((C3⋊D3)⋊C3)⋊C2 | 1 | 4 | yes | — |
| 496 | C2×C4 | — | 9 | 1 | no | — |
| 497 | C2×C4 | — | 9 | 4 | no | — |
| 498 | C2×C4 | — | 9 | 2 | no | — |
| 499 | C2×C4 | — | 9 | 4 | no | — |
| 500 | C2×C4 | — | 9 | 8 | no | — |
| 501 | C2×C4 | — | 9 | 2 | no | — |
| 502 | C2×C4 | — | 9 | 2 | no | — |
| 503 | C2×C4 | — | 9 | 8 | no | — |
| 504 | C2×C4 | — | 27 | 8 | no | — |
| 505 | C2×C4 | — | 27 | 4 | no | — |
| 506 | C2×C4 | — | 27 | 16 | no | — |
| 507 | C2×C4 | C2×((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
| 508 | C2×C3 | — | 2 | 4 | no | — |
| 509 | C2×C3 | — | 2 | 1 | no | — |
| 510 | C2×C3 | — | 3 | 2 | no | — |
| 511 | C2×C3 | — | 6 | 2 | no | — |
| 512 | C2×C3 | — | 6 | 8 | no | — |
| 513 | C2×C3 | — | 6 | 2 | no | — |
| 514 | C2×C3 | — | 6 | 1 | no | — |
| 515 | C2×C3 | — | 12 | 4 | no | — |
| 516 | C2×C3 | — | 18 | 8 | no | — |
| 517 | C2×C3 | — | 18 | 2 | no | — |
| 518 | C2×C3 | C23×D32 | 1 | 1 | yes | characteristic |
| 519 | D3 | — | 6 | 4 | no | — |
| 520 | D3 | — | 6 | 8 | no | — |
| 521 | D3 | — | 12 | 2 | no | — |
| 522 | D3 | — | 18 | 8 | no | — |
| 523 | C22 | — | 4 | 2 | no | — |
| 524 | C22 | — | 9 | 2 | no | — |
| 525 | C22 | — | 9 | 8 | no | — |
| 526 | C22 | — | 36 | 1 | no | — |
| 527 | C22 | — | 36 | 8 | no | — |
| 528 | C22 | — | 108 | 4 | no | — |
| 529 | C22 | C22×((C3⋊D3)⋊C3)⋊C2 | 1 | 4 | yes | — |
| 530 | C22 | C22×((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
| 531 | C4 | — | 9 | 1 | no | — |
| 532 | C4 | — | 9 | 1 | no | — |
| 533 | C4 | — | 9 | 8 | no | — |
| 534 | C4 | — | 9 | 4 | no | — |
| 535 | C4 | C22×((C3⋊D3)⋊C3)⋊C2 | 1 | 2 | yes | — |
| 536 | C3 | — | 3 | 2 | no | — |
| 537 | C3 | — | 6 | 1 | no | — |
| 538 | C3 | #10596679 | 1 | 1 | yes | characteristic |
| 539 | C2 | — | 2 | 1 | no | — |
| 540 | C2 | — | 2 | 4 | no | — |
| 541 | C2 | — | 18 | 8 | no | — |
| 542 | C2 | — | 18 | 2 | no | — |
| 543 | C2 | C23×((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#88744 | C2 | semidirect |
| 2. #64361⋊C3 | C2 | semidirect |
| 3. #11722545 | C2 | semidirect |
| 4. C2×#88672 | C2 | semidirect |
| 5. #11722506 | C2 | semidirect |
| 6. #11722504 | C2 | semidirect |
| 7. #11722502 | C2 | semidirect |
| 8. #11722491 | C2 | semidirect |
| 9. #11722483 | C2 | semidirect |
| 11. C2×D4×H(3,𝔽3) | C22 | semidirect |
| 12. C2×#6235 | C22 | semidirect |
| 13. C22×#1084 | C22 | semidirect |
| 14. #88744 | C22 | semidirect |
| 15. #88744 | C22 | semidirect |
| 16. C2×C4×#272 | C22 | semidirect |
| 17. C2×#6229 | C22 | semidirect |
| 18. C2×#638⋊C3 | C22 | semidirect |
| 19. #3830⋊C3 | C22 | semidirect |
| 20. D4×(C3⋊D3)⋊C3 | C22 | semidirect |
| 21. #3828⋊C3 | C22 | semidirect |
| 22. #88677 | C22 | semidirect |
| 23. #88676 | C22 | semidirect |
| 24. C2×#6198 | C22 | semidirect |
| 25. #88672 | C22 | semidirect |
| 26. #88672 | C22 | semidirect |
| 27. #88672 | C22 | semidirect |
| 28. #88672 | C22 | semidirect |
| 29. #88671 | C22 | semidirect |
| 30. C2×((C3⋊D3)⋊C3)⋊C4 | C22 | semidirect |
| 31. C2×#6196 | C22 | semidirect |
| 32. #88655 | C22 | semidirect |
| 33. C4×((C3⋊D3)⋊C3)⋊C2 | C22 | semidirect |
| 34. #88651 | C22 | semidirect |
| 35. #88650 | C22 | semidirect |
| 36. #88649 | C22 | semidirect |
| 37. #88648 | C22 | semidirect |
| 38. ((C3⋊D3)⋊C3)⋊Q8 | C22 | semidirect |
| 39. #64361 | D3 | semidirect |
| 82. C2×C32×D4 | C2×D3 | semidirect |
| 83. C2×#638 | C2×D3 | semidirect |
| 84. #3830 | C2×D3 | semidirect |
| 85. D4×C3⋊D3 | C2×D3 | semidirect |
| 86. #3828 | C2×D3 | semidirect |
| 323. H(3,𝔽3) | #585 | semidirect |
| 435. C2×D4 | ((C3⋊D3)⋊C3)⋊C2 | semidirect |
| 479. C32 | #5966 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88744 | 2 |
| #64361⋊C3 | 2 |
| #11722545 | 2 |
| C2×#88672 | 2 |
| #11722506 | 2 |
| #11722504 | 2 |
| #11722502 | 2 |
| #11722491 | 2 |
| #11722483 | 2 |
| #10596678 | 3 |