Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
2999 conjugacy classes of subgroups.
The subgroup lattice has 657 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #41×#272 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #41×(C3⋊D3)⋊C3 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #11722521 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11722517 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11722516 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #11722507 | C2 | 1 | 6 | yes | maximal, complemented |
| 7 | #11722506 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | #11722502 | C2 | 1 | 3 | yes | maximal, complemented |
| 9 | #11722491 | C2 | 1 | 3 | yes | maximal, complemented |
| 10 | #11722490 | C2 | 1 | 6 | yes | maximal, complemented |
| 11 | C2×#88650 | C2 | 1 | 3 | yes | maximal, complemented |
| 12 | #10596695 | — | 3 | 2 | no | maximal |
| 13 | #41×H(3,𝔽3) | C22 | 1 | 1 | yes | characteristic, complemented |
| 14 | #88748 | C22 | 1 | 1 | yes | characteristic, complemented |
| 15 | Q8×#272 | C22 | 1 | 1 | yes | characteristic, complemented |
| 16 | #88744 | C22 | 1 | 3 | yes | complemented |
| 17 | D4×#272 | C22 | 1 | 3 | yes | complemented |
| 18 | #88740 | C22 | 1 | 3 | yes | complemented |
| 19 | C2×C4×#272 | C22 | 1 | 3 | yes | complemented |
| 20 | #88722 | C22 | 1 | 2 | yes | complemented |
| 21 | Q8×(C3⋊D3)⋊C3 | C22 | 1 | 2 | yes | complemented |
| 22 | #3830⋊C3 | C22 | 1 | 6 | yes | complemented |
| 23 | D4×(C3⋊D3)⋊C3 | C22 | 1 | 6 | yes | complemented |
| 24 | #3828⋊C3 | C22 | 1 | 6 | yes | complemented |
| 25 | C2×C4×(C3⋊D3)⋊C3 | C22 | 1 | 6 | yes | complemented |
| 26 | #88677 | C22 | 1 | 6 | yes | complemented |
| 27 | #88676 | C22 | 1 | 12 | yes | complemented |
| 28 | C2×#6200 | C22 | 1 | 6 | yes | complemented |
| 29 | C2×#6198 | C22 | 1 | 3 | yes | complemented |
| 30 | #88672 | C22 | 1 | 6 | yes | complemented |
| 31 | #88671 | C22 | 1 | 12 | yes | complemented |
| 32 | C2×#6196 | C22 | 1 | 3 | yes | complemented |
| 33 | #88655 | C22 | 1 | 3 | yes | complemented |
| 34 | #88654 | C22 | 1 | 6 | yes | complemented |
| 35 | C4×((C3⋊D3)⋊C3)⋊C2 | C22 | 1 | 6 | yes | complemented |
| 36 | #88652 | C22 | 1 | 6 | yes | complemented |
| 37 | #88651 | C22 | 1 | 3 | yes | complemented |
| 38 | #88650 | C22 | 1 | 3 | yes | complemented |
| 39 | #88650 | C22 | 1 | 3 | yes | complemented |
| 40 | #88650 | C22 | 1 | 6 | yes | complemented |
| 41 | #88650 | C22 | 1 | 1 | yes | characteristic, complemented |
| 42 | #88650 | C22 | 1 | 6 | yes | complemented |
| 43 | #88650 | C22 | 1 | 3 | yes | complemented |
| 44 | #88649 | C22 | 1 | 6 | yes | complemented |
| 45 | #88648 | C22 | 1 | 6 | yes | complemented |
| 46 | ((C3⋊D3)⋊C3)⋊Q8 | C22 | 1 | 6 | yes | complemented |
| 47 | #41×C3⋊D3 | D3 | 1 | 2 | yes | complemented |
| 48 | C3×D3×#41 | — | 3 | 2 | no | — |
| 49 | C3×D3×#41 | — | 3 | 2 | no | — |
| 50 | C3×D3×#41 | — | 6 | 1 | no | — |
| 51 | #64320 | — | 3 | 2 | no | — |
| 52 | #64316 | — | 3 | 2 | no | — |
| 53 | #64315 | — | 3 | 2 | no | — |
| 54 | #64315 | — | 3 | 2 | no | — |
| 55 | #64314 | — | 3 | 6 | no | — |
| 56 | #64314 | — | 3 | 6 | no | — |
| 57 | #64313 | — | 3 | 6 | no | — |
| 58 | #64309 | — | 3 | 6 | no | — |
| 59 | #64306 | — | 3 | 6 | no | — |
| 60 | D3×#235 | — | 3 | 6 | no | — |
| 61 | D3×#235 | — | 3 | 6 | no | — |
| 62 | C2×#3798 | — | 3 | 6 | no | — |
| 63 | C22×#272 | C23 | 1 | 3 | yes | — |
| 64 | C22×(C3⋊D3)⋊C3 | C23 | 1 | 6 | yes | — |
| 65 | C2×((C3⋊D3)⋊C3)⋊C2 | C23 | 1 | 6 | yes | — |
| 66 | Q8×H(3,𝔽3) | C23 | 1 | 1 | yes | characteristic |
| 67 | D4×H(3,𝔽3) | C23 | 1 | 3 | yes | — |
| 68 | C2×C4×H(3,𝔽3) | C23 | 1 | 3 | yes | — |
| 69 | #6235 | C23 | 1 | 6 | yes | — |
| 70 | C2×#1084 | C23 | 1 | 3 | yes | — |
| 71 | C4⋊#272 | C23 | 1 | 3 | yes | — |
| 72 | C4×#272 | C23 | 1 | 3 | yes | — |
| 73 | C4×#272 | C23 | 1 | 1 | yes | characteristic |
| 74 | C4×#272 | C23 | 1 | 3 | yes | — |
| 75 | C4×#272 | C23 | 1 | 3 | yes | — |
| 76 | #6229 | C23 | 1 | 3 | yes | — |
| 77 | #638⋊C3 | C23 | 1 | 12 | yes | — |
| 78 | C2×(C3⋊Dic3)⋊C3 | C23 | 1 | 6 | yes | — |
| 79 | C4⋊((C3⋊D3)⋊C3) | C23 | 1 | 6 | yes | — |
| 80 | C4×(C3⋊D3)⋊C3 | C23 | 1 | 6 | yes | — |
| 81 | C4×(C3⋊D3)⋊C3 | C23 | 1 | 6 | yes | — |
| 82 | C4×(C3⋊D3)⋊C3 | C23 | 1 | 2 | yes | — |
| 83 | C4×(C3⋊D3)⋊C3 | C23 | 1 | 6 | yes | — |
| 84 | #634⋊C3 | C23 | 1 | 6 | yes | — |
| 85 | #6200 | C23 | 1 | 6 | yes | — |
| 86 | #6200 | C23 | 1 | 2 | yes | — |
| 87 | #6200 | C23 | 1 | 6 | yes | — |
| 88 | #6200 | C23 | 1 | 6 | yes | — |
| 89 | #6199 | C23 | 1 | 6 | yes | — |
| 90 | #6198 | C23 | 1 | 6 | yes | — |
| 91 | #6198 | C23 | 1 | 1 | yes | characteristic |
| 92 | #6198 | C23 | 1 | 3 | yes | — |
| 93 | ((C3⋊D3)⋊C3)⋊C4 | C23 | 1 | 12 | yes | — |
| 94 | #6196 | C23 | 1 | 6 | yes | — |
| 95 | #6196 | C23 | 1 | 1 | yes | characteristic |
| 96 | #6196 | C23 | 1 | 3 | yes | — |
| 97 | #5964 | — | 9 | 1 | no | — |
| 98 | #5964 | — | 9 | 2 | no | — |
| 99 | C32×#41 | — | 2 | 1 | no | — |
| 100 | C32×#41 | C2×D3 | 1 | 2 | yes | complemented |
| 101 | #3832 | C2×D3 | 1 | 2 | yes | complemented |
| 102 | Q8×C3⋊D3 | C2×D3 | 1 | 2 | yes | complemented |
| 103 | #3830 | C2×D3 | 1 | 6 | yes | complemented |
| 104 | D4×C3⋊D3 | C2×D3 | 1 | 6 | yes | complemented |
| 105 | #3828 | C2×D3 | 1 | 6 | yes | complemented |
| 106 | C2×C4×C3⋊D3 | C2×D3 | 1 | 6 | yes | complemented |
| 107 | C3×#239 | — | 3 | 2 | no | — |
| 108 | C3×#239 | — | 3 | 2 | no | — |
| 109 | C3×#239 | — | 6 | 1 | no | — |
| 110 | C3×D3×Q8 | — | 3 | 2 | no | — |
| 111 | C3×D3×Q8 | — | 3 | 2 | no | — |
| 112 | C3×D3×Q8 | — | 6 | 1 | no | — |
| 113 | C3×#237 | — | 3 | 6 | no | — |
| 114 | C3×#237 | — | 3 | 6 | no | — |
| 115 | C3×#237 | — | 6 | 3 | no | — |
| 116 | C3×D3×D4 | — | 3 | 6 | no | — |
| 117 | C3×D3×D4 | — | 3 | 6 | no | — |
| 118 | C3×D3×D4 | — | 6 | 3 | no | — |
| 119 | C3×#235 | — | 3 | 6 | no | — |
| 120 | C3×#235 | — | 3 | 6 | no | — |
| 121 | C3×#235 | — | 6 | 3 | no | — |
| 122 | C2×C3×C4×D3 | — | 3 | 6 | no | — |
| 123 | C2×C3×C4×D3 | — | 3 | 6 | no | — |
| 124 | C2×C3×C4×D3 | — | 6 | 3 | no | — |
| 125 | #3811 | — | 3 | 12 | no | — |
| 126 | D3×#67 | — | 3 | 12 | no | — |
| 127 | D3×#67 | — | 3 | 12 | no | — |
| 128 | C2×#627 | — | 3 | 6 | no | — |
| 129 | C2×#626 | — | 3 | 6 | no | — |
| 130 | C2×#626 | — | 3 | 6 | no | — |
| 131 | C2×#625 | — | 3 | 6 | no | — |
| 132 | #3805 | — | 3 | 12 | no | — |
| 133 | #3804 | — | 3 | 12 | no | — |
| 134 | #3804 | — | 3 | 12 | no | — |
| 135 | #3802 | — | 3 | 6 | no | — |
| 136 | D3×D12 | — | 3 | 6 | no | — |
| 137 | D3×D12 | — | 3 | 6 | no | — |
| 138 | C4×D32 | — | 3 | 12 | no | — |
| 139 | #3799 | — | 3 | 6 | no | — |
| 140 | #3799 | — | 3 | 6 | no | — |
| 141 | #3798 | — | 3 | 2 | no | — |
| 142 | #3798 | — | 3 | 6 | no | — |
| 143 | #3798 | — | 3 | 6 | no | — |
| 144 | #3798 | — | 3 | 6 | no | — |
| 145 | #3798 | — | 3 | 6 | no | — |
| 146 | #3798 | — | 3 | 6 | no | — |
| 147 | #3798 | — | 3 | 6 | no | — |
| 148 | #3798 | — | 3 | 6 | no | — |
| 149 | #3797 | — | 3 | 6 | no | — |
| 150 | #3796 | — | 3 | 6 | no | — |
| 151 | #3796 | — | 3 | 6 | no | — |
| 152 | #3795 | — | 3 | 6 | no | — |
| 153 | #3795 | — | 3 | 6 | no | — |
| 154 | D3×Dic6 | — | 3 | 6 | no | — |
| 155 | D3×Dic6 | — | 3 | 6 | no | — |
| 156 | C22×H(3,𝔽3) | C24 | 1 | 3 | yes | — |
| 157 | C2×#272 | — | 4 | 3 | no | — |
| 158 | C2×#272 | C24 | 1 | 3 | yes | — |
| 159 | C2×#272 | C24 | 1 | 1 | yes | characteristic |
| 160 | C2×(C3⋊D3)⋊C3 | — | 4 | 6 | no | — |
| 161 | C2×(C3⋊D3)⋊C3 | C24 | 1 | 6 | yes | — |
| 162 | C2×(C3⋊D3)⋊C3 | C24 | 1 | 2 | yes | — |
| 163 | ((C3⋊D3)⋊C3)⋊C2 | — | 4 | 6 | no | — |
| 164 | C4×H(3,𝔽3) | C24 | 1 | 3 | yes | — |
| 165 | C4×H(3,𝔽3) | C24 | 1 | 1 | yes | characteristic |
| 166 | #1084 | C24 | 1 | 1 | yes | characteristic |
| 167 | #1084 | C24 | 1 | 3 | yes | — |
| 168 | (C3⋊Dic3)⋊C3 | C24 | 1 | 2 | yes | — |
| 169 | (C3⋊Dic3)⋊C3 | C24 | 1 | 6 | yes | — |
| 170 | C2×C3×#41 | — | 9 | 2 | no | — |
| 171 | C2×C3×#41 | — | 9 | 1 | no | — |
| 172 | #1010 | — | 9 | 3 | no | — |
| 173 | #1010 | — | 9 | 6 | no | — |
| 174 | #1010 | — | 9 | 1 | no | — |
| 175 | #1010 | — | 9 | 2 | no | — |
| 176 | #1009 | — | 9 | 3 | no | — |
| 177 | #1009 | — | 9 | 6 | no | — |
| 178 | #1009 | — | 9 | 1 | no | — |
| 179 | #1009 | — | 9 | 2 | no | — |
| 180 | D3×#41 | — | 3 | 2 | no | — |
| 181 | D3×#41 | — | 3 | 2 | no | — |
| 182 | D3×#41 | — | 6 | 1 | no | — |
| 183 | D3×#41 | — | 9 | 2 | no | — |
| 184 | D3×#41 | — | 9 | 6 | no | — |
| 185 | D3×#41 | — | 9 | 6 | no | — |
| 186 | D3×#41 | — | 9 | 6 | no | — |
| 187 | #1007 | — | 9 | 2 | no | — |
| 188 | #1007 | — | 9 | 2 | no | — |
| 189 | #1007 | — | 9 | 2 | no | — |
| 190 | #1004 | — | 9 | 6 | no | — |
| 191 | #1004 | — | 9 | 6 | no | — |
| 192 | #1004 | — | 9 | 6 | no | — |
| 193 | C2×#235 | — | 9 | 3 | no | — |
| 194 | C2×#235 | — | 9 | 6 | no | — |
| 195 | C2×#235 | — | 9 | 3 | no | — |
| 196 | C2×#235 | — | 9 | 6 | no | — |
| 197 | C22×C3⋊D3 | C22×D3 | 1 | 6 | yes | — |
| 198 | C22×C3×D3 | — | 3 | 6 | no | — |
| 199 | C22×C3×D3 | — | 3 | 6 | no | — |
| 200 | C22×C3×D3 | — | 6 | 3 | no | — |
| 201 | C2×D32 | — | 3 | 12 | no | — |
| 202 | C32×Q8 | — | 2 | 1 | no | — |
| 203 | C32×Q8 | C22×D3 | 1 | 2 | yes | — |
| 204 | C32×D4 | — | 2 | 3 | no | — |
| 205 | C32×D4 | C22×D3 | 1 | 6 | yes | — |
| 206 | C2×C32×C4 | — | 2 | 3 | no | — |
| 207 | C2×C32×C4 | C22×D3 | 1 | 6 | yes | — |
| 208 | #638 | C22×D3 | 1 | 12 | yes | — |
| 209 | C2×C3⋊Dic3 | C22×D3 | 1 | 6 | yes | — |
| 210 | C4⋊(C3⋊D3) | C22×D3 | 1 | 6 | yes | — |
| 211 | C4×C3⋊D3 | C22×D3 | 1 | 6 | yes | — |
| 212 | C4×C3⋊D3 | C22×D3 | 1 | 6 | yes | — |
| 213 | C4×C3⋊D3 | C22×D3 | 1 | 2 | yes | — |
| 214 | C4×C3⋊D3 | C22×D3 | 1 | 6 | yes | — |
| 215 | #634 | C22×D3 | 1 | 6 | yes | — |
| 216 | C3×#67 | — | 3 | 12 | no | — |
| 217 | C3×#67 | — | 3 | 12 | no | — |
| 218 | C3×#67 | — | 6 | 6 | no | — |
| 219 | C2×C3×Dic3 | — | 3 | 6 | no | — |
| 220 | C2×C3×Dic3 | — | 3 | 6 | no | — |
| 221 | C2×C3×Dic3 | — | 6 | 3 | no | — |
| 222 | C3×D12 | — | 3 | 6 | no | — |
| 223 | C3×D12 | — | 3 | 6 | no | — |
| 224 | C3×D12 | — | 6 | 3 | no | — |
| 225 | C3×C4×D3 | — | 3 | 6 | no | — |
| 226 | C3×C4×D3 | — | 3 | 6 | no | — |
| 227 | C3×C4×D3 | — | 3 | 2 | no | — |
| 228 | C3×C4×D3 | — | 3 | 6 | no | — |
| 229 | C3×C4×D3 | — | 3 | 6 | no | — |
| 230 | C3×C4×D3 | — | 3 | 6 | no | — |
| 231 | C3×C4×D3 | — | 3 | 2 | no | — |
| 232 | C3×C4×D3 | — | 3 | 6 | no | — |
| 233 | C3×C4×D3 | — | 6 | 1 | no | — |
| 234 | C3×C4×D3 | — | 6 | 3 | no | — |
| 235 | C3×C4×D3 | — | 6 | 3 | no | — |
| 236 | C3×C4×D3 | — | 6 | 3 | no | — |
| 237 | C3×Dic6 | — | 3 | 6 | no | — |
| 238 | C3×Dic6 | — | 3 | 6 | no | — |
| 239 | C3×Dic6 | — | 6 | 3 | no | — |
| 240 | #627 | — | 3 | 6 | no | — |
| 241 | #627 | — | 3 | 6 | no | — |
| 242 | #627 | — | 3 | 6 | no | — |
| 243 | #627 | — | 3 | 2 | no | — |
| 244 | #626 | — | 3 | 6 | no | — |
| 245 | #626 | — | 3 | 2 | no | — |
| 246 | #626 | — | 3 | 6 | no | — |
| 247 | #626 | — | 3 | 6 | no | — |
| 248 | #626 | — | 3 | 6 | no | — |
| 249 | #626 | — | 3 | 2 | no | — |
| 250 | #626 | — | 3 | 6 | no | — |
| 251 | #626 | — | 3 | 6 | no | — |
| 252 | #625 | — | 3 | 6 | no | — |
| 253 | #625 | — | 3 | 6 | no | — |
| 254 | #625 | — | 3 | 2 | no | — |
| 255 | #625 | — | 3 | 6 | no | — |
| 256 | #624 | — | 3 | 12 | no | — |
| 257 | D3×Dic3 | — | 3 | 12 | no | — |
| 258 | D3×Dic3 | — | 3 | 12 | no | — |
| 259 | #585 | — | 27 | 1 | no | Sylow |
| 260 | C2×H(3,𝔽3) | — | 2 | 3 | no | — |
| 261 | C2×H(3,𝔽3) | C25 | 1 | 1 | yes | characteristic |
| 262 | #272 | — | 2 | 1 | no | — |
| 263 | #272 | — | 2 | 3 | no | — |
| 264 | (C3⋊D3)⋊C3 | — | 2 | 6 | no | — |
| 265 | (C3⋊D3)⋊C3 | — | 2 | 2 | no | — |
| 266 | C3×#41 | — | 3 | 2 | no | — |
| 267 | C3×#41 | — | 6 | 1 | no | — |
| 268 | C3×#41 | — | 9 | 6 | no | — |
| 269 | C3×#41 | — | 9 | 6 | no | — |
| 270 | C3×#41 | — | 9 | 2 | no | — |
| 271 | C3×#41 | — | 9 | 1 | no | — |
| 272 | C3×#41 | — | 9 | 3 | no | — |
| 273 | C3×#41 | — | 9 | 3 | no | — |
| 274 | C3×#41 | D32 | 1 | 1 | yes | characteristic |
| 275 | C2×C3×Q8 | — | 9 | 2 | no | — |
| 276 | C2×C3×Q8 | — | 9 | 1 | no | — |
| 277 | C2×C3×D4 | — | 9 | 6 | no | — |
| 278 | C2×C3×D4 | — | 9 | 3 | no | — |
| 279 | C22×C3×C4 | — | 9 | 6 | no | — |
| 280 | C22×C3×C4 | — | 9 | 3 | no | — |
| 281 | C2×#67 | — | 9 | 6 | no | — |
| 282 | C2×#67 | — | 9 | 6 | no | — |
| 283 | C2×#67 | — | 9 | 6 | no | — |
| 284 | C2×#67 | — | 9 | 12 | no | — |
| 285 | C2×#67 | — | 9 | 6 | no | — |
| 286 | #239 | — | 3 | 2 | no | — |
| 287 | #239 | — | 3 | 2 | no | — |
| 288 | #239 | — | 6 | 1 | no | — |
| 289 | #239 | — | 9 | 2 | no | — |
| 290 | #239 | — | 9 | 6 | no | — |
| 291 | #239 | — | 9 | 6 | no | — |
| 292 | #239 | — | 9 | 6 | no | — |
| 293 | D3×Q8 | — | 3 | 2 | no | — |
| 294 | D3×Q8 | — | 3 | 2 | no | — |
| 295 | D3×Q8 | — | 6 | 1 | no | — |
| 296 | D3×Q8 | — | 9 | 2 | no | — |
| 297 | D3×Q8 | — | 9 | 6 | no | — |
| 298 | D3×Q8 | — | 9 | 6 | no | — |
| 299 | D3×Q8 | — | 9 | 6 | no | — |
| 300 | #237 | — | 3 | 6 | no | — |
| 301 | #237 | — | 3 | 6 | no | — |
| 302 | #237 | — | 6 | 3 | no | — |
| 303 | #237 | — | 9 | 6 | no | — |
| 304 | #237 | — | 9 | 6 | no | — |
| 305 | #237 | — | 9 | 6 | no | — |
| 306 | #237 | — | 9 | 6 | no | — |
| 307 | #237 | — | 9 | 12 | no | — |
| 308 | #237 | — | 9 | 12 | no | — |
| 309 | #237 | — | 9 | 12 | no | — |
| 310 | D3×D4 | — | 3 | 6 | no | — |
| 311 | D3×D4 | — | 3 | 6 | no | — |
| 312 | D3×D4 | — | 6 | 3 | no | — |
| 313 | D3×D4 | — | 9 | 6 | no | — |
| 314 | D3×D4 | — | 9 | 6 | no | — |
| 315 | D3×D4 | — | 9 | 6 | no | — |
| 316 | D3×D4 | — | 9 | 6 | no | — |
| 317 | D3×D4 | — | 9 | 12 | no | — |
| 318 | D3×D4 | — | 9 | 12 | no | — |
| 319 | D3×D4 | — | 9 | 12 | no | — |
| 320 | #235 | — | 3 | 6 | no | — |
| 321 | #235 | — | 3 | 6 | no | — |
| 322 | #235 | — | 6 | 3 | no | — |
| 323 | #235 | — | 9 | 6 | no | — |
| 324 | #235 | — | 9 | 6 | no | — |
| 325 | #235 | — | 9 | 6 | no | — |
| 326 | #235 | — | 9 | 1 | no | — |
| 327 | #235 | — | 9 | 3 | no | — |
| 328 | #235 | — | 9 | 6 | no | — |
| 329 | #235 | — | 9 | 6 | no | — |
| 330 | #235 | — | 9 | 3 | no | — |
| 331 | #235 | — | 9 | 3 | no | — |
| 332 | #235 | — | 9 | 2 | no | — |
| 333 | #235 | — | 9 | 6 | no | — |
| 334 | #235 | — | 9 | 6 | no | — |
| 335 | #235 | — | 9 | 6 | no | — |
| 336 | #235 | — | 9 | 6 | no | — |
| 337 | #235 | — | 9 | 6 | no | — |
| 338 | #235 | — | 9 | 6 | no | — |
| 339 | #235 | — | 9 | 6 | no | — |
| 340 | #235 | — | 9 | 6 | no | — |
| 341 | #235 | — | 9 | 6 | no | — |
| 342 | #235 | — | 9 | 12 | no | — |
| 343 | C2×D12 | — | 9 | 3 | no | — |
| 344 | C2×D12 | — | 9 | 6 | no | — |
| 345 | C2×D12 | — | 9 | 3 | no | — |
| 346 | C2×D12 | — | 9 | 6 | no | — |
| 347 | C2×C4×D3 | — | 3 | 6 | no | — |
| 348 | C2×C4×D3 | — | 3 | 6 | no | — |
| 349 | C2×C4×D3 | — | 6 | 3 | no | — |
| 350 | C2×C4×D3 | — | 9 | 6 | no | — |
| 351 | C2×C4×D3 | — | 9 | 6 | no | — |
| 352 | C2×C4×D3 | — | 9 | 12 | no | — |
| 353 | C2×Dic6 | — | 9 | 3 | no | — |
| 354 | C2×Dic6 | — | 9 | 6 | no | — |
| 355 | C2×Dic6 | — | 9 | 3 | no | — |
| 356 | C2×Dic6 | — | 9 | 6 | no | — |
| 357 | C22×C32 | — | 2 | 3 | no | — |
| 358 | C22×C32 | C23×D3 | 1 | 6 | yes | — |
| 359 | C2×C3⋊D3 | — | 4 | 6 | no | — |
| 360 | C2×C3⋊D3 | C23×D3 | 1 | 6 | yes | — |
| 361 | C2×C3⋊D3 | C23×D3 | 1 | 2 | yes | — |
| 362 | C2×C3×D3 | — | 3 | 6 | no | — |
| 363 | C2×C3×D3 | — | 3 | 2 | no | — |
| 364 | C2×C3×D3 | — | 3 | 6 | no | — |
| 365 | C2×C3×D3 | — | 3 | 2 | no | — |
| 366 | C2×C3×D3 | — | 6 | 1 | no | — |
| 367 | C2×C3×D3 | — | 6 | 3 | no | — |
| 368 | C2×C3×D3 | — | 12 | 6 | no | — |
| 369 | C2×C3×D3 | — | 12 | 6 | no | — |
| 370 | C2×C3×D3 | — | 12 | 6 | no | — |
| 371 | D32 | — | 12 | 12 | no | — |
| 372 | C32×C4 | — | 2 | 3 | no | — |
| 373 | C32×C4 | — | 2 | 1 | no | — |
| 374 | C32×C4 | C23×D3 | 1 | 6 | yes | — |
| 375 | C32×C4 | C23×D3 | 1 | 2 | yes | — |
| 376 | C3⋊Dic3 | C23×D3 | 1 | 6 | yes | — |
| 377 | C3⋊Dic3 | C23×D3 | 1 | 2 | yes | — |
| 378 | C3×Dic3 | — | 3 | 6 | no | — |
| 379 | C3×Dic3 | — | 3 | 2 | no | — |
| 380 | C3×Dic3 | — | 3 | 6 | no | — |
| 381 | C3×Dic3 | — | 3 | 2 | no | — |
| 382 | C3×Dic3 | — | 6 | 3 | no | — |
| 383 | C3×Dic3 | — | 6 | 1 | no | — |
| 384 | 2−1+4 | — | 27 | 2 | no | — |
| 385 | 2−1+4 | — | 27 | 1 | no | — |
| 386 | 2−1+4 | — | 27 | 3 | no | — |
| 387 | H(5,𝔽2) | — | 27 | 6 | no | — |
| 388 | H(5,𝔽2) | — | 27 | 3 | no | — |
| 389 | H(5,𝔽2) | — | 27 | 1 | no | — |
| 390 | C2×#41 | — | 9 | 1 | no | — |
| 391 | C2×#41 | — | 9 | 2 | no | — |
| 392 | C2×#41 | — | 27 | 3 | no | — |
| 393 | C2×#41 | — | 27 | 3 | no | — |
| 394 | C2×#41 | — | 27 | 6 | no | — |
| 395 | H(3,𝔽3) | #585 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 396 | C23×C3 | — | 9 | 6 | no | — |
| 397 | C23×C3 | — | 9 | 3 | no | — |
| 398 | C22×D3 | — | 3 | 6 | no | — |
| 399 | C22×D3 | — | 3 | 6 | no | — |
| 400 | C22×D3 | — | 6 | 3 | no | — |
| 401 | C22×D3 | — | 9 | 6 | no | — |
| 402 | C22×D3 | — | 9 | 6 | no | — |
| 403 | C22×D3 | — | 9 | 12 | no | — |
| 404 | C3×Q8 | — | 3 | 2 | no | — |
| 405 | C3×Q8 | — | 6 | 1 | no | — |
| 406 | C3×Q8 | — | 9 | 6 | no | — |
| 407 | C3×Q8 | — | 9 | 3 | no | — |
| 408 | C3×Q8 | C2×D32 | 1 | 1 | yes | characteristic |
| 409 | C3×D4 | — | 3 | 6 | no | — |
| 410 | C3×D4 | — | 6 | 3 | no | — |
| 411 | C3×D4 | — | 9 | 6 | no | — |
| 412 | C3×D4 | — | 9 | 12 | no | — |
| 413 | C3×D4 | — | 9 | 6 | no | — |
| 414 | C3×D4 | — | 9 | 3 | no | — |
| 415 | C3×D4 | C2×D32 | 1 | 3 | yes | — |
| 416 | C2×C3×C4 | — | 3 | 6 | no | — |
| 417 | C2×C3×C4 | — | 6 | 3 | no | — |
| 418 | C2×C3×C4 | — | 9 | 6 | no | — |
| 419 | C2×C3×C4 | — | 9 | 6 | no | — |
| 420 | C2×C3×C4 | — | 9 | 2 | no | — |
| 421 | C2×C3×C4 | — | 9 | 6 | no | — |
| 422 | C2×C3×C4 | — | 9 | 6 | no | — |
| 423 | C2×C3×C4 | — | 9 | 3 | no | — |
| 424 | C2×C3×C4 | — | 9 | 3 | no | — |
| 425 | C2×C3×C4 | — | 9 | 3 | no | — |
| 426 | C2×C3×C4 | — | 9 | 1 | no | — |
| 427 | C2×C3×C4 | — | 9 | 3 | no | — |
| 428 | C2×C3×C4 | C2×D32 | 1 | 3 | yes | — |
| 429 | #67 | — | 3 | 12 | no | — |
| 430 | #67 | — | 3 | 12 | no | — |
| 431 | #67 | — | 6 | 6 | no | — |
| 432 | #67 | — | 9 | 12 | no | — |
| 433 | #67 | — | 9 | 6 | no | — |
| 434 | #67 | — | 9 | 2 | no | — |
| 435 | #67 | — | 9 | 6 | no | — |
| 436 | #67 | — | 9 | 6 | no | — |
| 437 | #67 | — | 9 | 6 | no | — |
| 438 | #67 | — | 9 | 2 | no | — |
| 439 | #67 | — | 9 | 6 | no | — |
| 440 | #67 | — | 9 | 6 | no | — |
| 441 | #67 | — | 9 | 2 | no | — |
| 442 | #67 | — | 9 | 6 | no | — |
| 443 | #67 | — | 9 | 6 | no | — |
| 444 | #67 | — | 9 | 6 | no | — |
| 445 | C2×Dic3 | — | 3 | 6 | no | — |
| 446 | C2×Dic3 | — | 3 | 6 | no | — |
| 447 | C2×Dic3 | — | 6 | 3 | no | — |
| 448 | C2×Dic3 | — | 9 | 6 | no | — |
| 449 | C2×Dic3 | — | 9 | 6 | no | — |
| 450 | C2×Dic3 | — | 9 | 12 | no | — |
| 451 | D12 | — | 3 | 6 | no | — |
| 452 | D12 | — | 3 | 6 | no | — |
| 453 | D12 | — | 6 | 3 | no | — |
| 454 | D12 | — | 9 | 6 | no | — |
| 455 | D12 | — | 9 | 1 | no | — |
| 456 | D12 | — | 9 | 3 | no | — |
| 457 | D12 | — | 9 | 6 | no | — |
| 458 | D12 | — | 9 | 2 | no | — |
| 459 | D12 | — | 9 | 6 | no | — |
| 460 | D12 | — | 9 | 6 | no | — |
| 461 | D12 | — | 9 | 6 | no | — |
| 462 | C4×D3 | — | 3 | 2 | no | — |
| 463 | C4×D3 | — | 3 | 6 | no | — |
| 464 | C4×D3 | — | 3 | 6 | no | — |
| 465 | C4×D3 | — | 3 | 6 | no | — |
| 466 | C4×D3 | — | 3 | 2 | no | — |
| 467 | C4×D3 | — | 3 | 6 | no | — |
| 468 | C4×D3 | — | 3 | 6 | no | — |
| 469 | C4×D3 | — | 3 | 6 | no | — |
| 470 | C4×D3 | — | 6 | 1 | no | — |
| 471 | C4×D3 | — | 6 | 3 | no | — |
| 472 | C4×D3 | — | 6 | 3 | no | — |
| 473 | C4×D3 | — | 6 | 3 | no | — |
| 474 | C4×D3 | — | 9 | 2 | no | — |
| 475 | C4×D3 | — | 9 | 6 | no | — |
| 476 | C4×D3 | — | 9 | 6 | no | — |
| 477 | C4×D3 | — | 9 | 6 | no | — |
| 478 | C4×D3 | — | 9 | 12 | no | — |
| 479 | C4×D3 | — | 9 | 12 | no | — |
| 480 | C4×D3 | — | 9 | 12 | no | — |
| 481 | Dic6 | — | 3 | 6 | no | — |
| 482 | Dic6 | — | 3 | 6 | no | — |
| 483 | Dic6 | — | 6 | 3 | no | — |
| 484 | Dic6 | — | 9 | 6 | no | — |
| 485 | Dic6 | — | 9 | 3 | no | — |
| 486 | Dic6 | — | 9 | 1 | no | — |
| 487 | Dic6 | — | 9 | 6 | no | — |
| 488 | Dic6 | — | 9 | 6 | no | — |
| 489 | Dic6 | — | 9 | 2 | no | — |
| 490 | Dic6 | — | 9 | 6 | no | — |
| 491 | Dic6 | — | 9 | 6 | no | — |
| 492 | C2×C32 | — | 2 | 6 | no | — |
| 493 | C2×C32 | — | 2 | 1 | no | — |
| 494 | C2×C32 | — | 4 | 3 | no | — |
| 495 | C2×C32 | C24×D3 | 1 | 2 | yes | — |
| 496 | C3⋊D3 | — | 2 | 6 | no | — |
| 497 | C3⋊D3 | — | 2 | 2 | no | — |
| 498 | C3×D3 | — | 6 | 2 | no | — |
| 499 | C3×D3 | — | 6 | 6 | no | — |
| 500 | C3×D3 | — | 6 | 2 | no | — |
| 501 | C3×D3 | — | 6 | 6 | no | — |
| 502 | C3×D3 | — | 6 | 2 | no | — |
| 503 | C3×D3 | — | 12 | 3 | no | — |
| 504 | #41 | — | 9 | 1 | no | — |
| 505 | #41 | — | 9 | 2 | no | — |
| 506 | #41 | — | 9 | 3 | no | — |
| 507 | #41 | — | 9 | 6 | no | — |
| 508 | #41 | — | 9 | 3 | no | — |
| 509 | #41 | — | 9 | 6 | no | — |
| 510 | #41 | — | 27 | 1 | no | — |
| 511 | #41 | — | 27 | 3 | no | — |
| 512 | #41 | — | 27 | 6 | no | — |
| 513 | #41 | — | 27 | 6 | no | — |
| 514 | #41 | — | 27 | 3 | no | — |
| 515 | #41 | — | 27 | 3 | no | — |
| 516 | #41 | — | 27 | 6 | no | — |
| 517 | #41 | — | 27 | 12 | no | — |
| 518 | #41 | — | 27 | 6 | no | — |
| 519 | #41 | — | 27 | 6 | no | — |
| 520 | #41 | — | 27 | 6 | no | — |
| 521 | #41 | ((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic, complemented |
| 522 | C2×Q8 | — | 9 | 1 | no | — |
| 523 | C2×Q8 | — | 9 | 2 | no | — |
| 524 | C2×Q8 | — | 27 | 3 | no | — |
| 525 | C2×Q8 | — | 27 | 3 | no | — |
| 526 | C2×Q8 | — | 27 | 6 | no | — |
| 527 | C2×D4 | — | 9 | 3 | no | — |
| 528 | C2×D4 | — | 9 | 6 | no | — |
| 529 | C2×D4 | — | 27 | 3 | no | — |
| 530 | C2×D4 | — | 27 | 6 | no | — |
| 531 | C2×D4 | — | 27 | 3 | no | — |
| 532 | C2×D4 | — | 27 | 6 | no | — |
| 533 | C2×D4 | — | 27 | 12 | no | — |
| 534 | C2×D4 | — | 27 | 6 | no | — |
| 535 | C22×C4 | — | 9 | 3 | no | — |
| 536 | C22×C4 | — | 9 | 6 | no | — |
| 537 | C22×C4 | — | 27 | 6 | no | — |
| 538 | C22×C3 | — | 3 | 6 | no | — |
| 539 | C22×C3 | — | 6 | 3 | no | — |
| 540 | C22×C3 | — | 9 | 6 | no | — |
| 541 | C22×C3 | — | 9 | 2 | no | — |
| 542 | C22×C3 | — | 9 | 3 | no | — |
| 543 | C22×C3 | — | 9 | 1 | no | — |
| 544 | C22×C3 | — | 36 | 3 | no | — |
| 545 | C22×C3 | — | 36 | 6 | no | — |
| 546 | C22×C3 | C22×D32 | 1 | 3 | yes | — |
| 547 | C2×D3 | — | 3 | 2 | no | — |
| 548 | C2×D3 | — | 3 | 6 | no | — |
| 549 | C2×D3 | — | 3 | 2 | no | — |
| 550 | C2×D3 | — | 3 | 6 | no | — |
| 551 | C2×D3 | — | 6 | 1 | no | — |
| 552 | C2×D3 | — | 6 | 3 | no | — |
| 553 | C2×D3 | — | 9 | 2 | no | — |
| 554 | C2×D3 | — | 9 | 6 | no | — |
| 555 | C2×D3 | — | 12 | 6 | no | — |
| 556 | C2×D3 | — | 12 | 6 | no | — |
| 557 | C2×D3 | — | 12 | 6 | no | — |
| 558 | C2×D3 | — | 36 | 6 | no | — |
| 559 | C2×D3 | — | 36 | 6 | no | — |
| 560 | C2×D3 | — | 36 | 12 | no | — |
| 561 | C3×C4 | — | 3 | 6 | no | — |
| 562 | C3×C4 | — | 3 | 2 | no | — |
| 563 | C3×C4 | — | 6 | 3 | no | — |
| 564 | C3×C4 | — | 6 | 1 | no | — |
| 565 | C3×C4 | — | 9 | 2 | no | — |
| 566 | C3×C4 | — | 9 | 6 | no | — |
| 567 | C3×C4 | — | 9 | 1 | no | — |
| 568 | C3×C4 | — | 9 | 3 | no | — |
| 569 | C3×C4 | C22×D32 | 1 | 3 | yes | — |
| 570 | C3×C4 | C22×D32 | 1 | 1 | yes | characteristic |
| 571 | Dic3 | — | 3 | 6 | no | — |
| 572 | Dic3 | — | 3 | 2 | no | — |
| 573 | Dic3 | — | 3 | 6 | no | — |
| 574 | Dic3 | — | 3 | 2 | no | — |
| 575 | Dic3 | — | 6 | 3 | no | — |
| 576 | Dic3 | — | 6 | 1 | no | — |
| 577 | Dic3 | — | 9 | 2 | no | — |
| 578 | Dic3 | — | 9 | 6 | no | — |
| 579 | C32 | — | 2 | 1 | no | — |
| 580 | C32 | #5964 | 1 | 2 | yes | complemented |
| 581 | C23 | — | 9 | 3 | no | — |
| 582 | C23 | — | 9 | 6 | no | — |
| 583 | C23 | — | 27 | 6 | no | — |
| 584 | Q8 | — | 9 | 3 | no | — |
| 585 | Q8 | — | 9 | 6 | no | — |
| 586 | Q8 | — | 27 | 1 | no | — |
| 587 | Q8 | — | 27 | 3 | no | — |
| 588 | Q8 | — | 27 | 6 | no | — |
| 589 | Q8 | C2×((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
| 590 | D4 | — | 9 | 6 | no | — |
| 591 | D4 | — | 9 | 12 | no | — |
| 592 | D4 | — | 9 | 3 | no | — |
| 593 | D4 | — | 9 | 6 | no | — |
| 594 | D4 | — | 27 | 1 | no | — |
| 595 | D4 | — | 27 | 3 | no | — |
| 596 | D4 | — | 27 | 2 | no | — |
| 597 | D4 | — | 27 | 6 | no | — |
| 598 | D4 | — | 27 | 6 | no | — |
| 599 | D4 | — | 27 | 6 | no | — |
| 600 | D4 | — | 27 | 6 | no | — |
| 601 | D4 | C2×((C3⋊D3)⋊C3)⋊C2 | 1 | 3 | yes | — |
| 602 | C2×C4 | — | 9 | 3 | no | — |
| 603 | C2×C4 | — | 9 | 6 | no | — |
| 604 | C2×C4 | — | 9 | 3 | no | — |
| 605 | C2×C4 | — | 9 | 6 | no | — |
| 606 | C2×C4 | — | 9 | 3 | no | — |
| 607 | C2×C4 | — | 9 | 6 | no | — |
| 608 | C2×C4 | — | 9 | 1 | no | — |
| 609 | C2×C4 | — | 9 | 2 | no | — |
| 610 | C2×C4 | — | 9 | 3 | no | — |
| 611 | C2×C4 | — | 9 | 6 | no | — |
| 612 | C2×C4 | — | 27 | 12 | no | — |
| 613 | C2×C4 | — | 27 | 6 | no | — |
| 614 | C2×C4 | C2×((C3⋊D3)⋊C3)⋊C2 | 1 | 3 | yes | — |
| 615 | C2×C3 | — | 2 | 3 | no | — |
| 616 | C2×C3 | — | 3 | 2 | no | — |
| 617 | C2×C3 | — | 6 | 6 | no | — |
| 618 | C2×C3 | — | 6 | 1 | no | — |
| 619 | C2×C3 | — | 12 | 3 | no | — |
| 620 | C2×C3 | — | 18 | 6 | no | — |
| 621 | C2×C3 | — | 18 | 2 | no | — |
| 622 | C2×C3 | — | 18 | 3 | no | — |
| 623 | C2×C3 | — | 18 | 1 | no | — |
| 624 | C2×C3 | C23×D32 | 1 | 1 | yes | characteristic |
| 625 | D3 | — | 6 | 2 | no | — |
| 626 | D3 | — | 6 | 6 | no | — |
| 627 | D3 | — | 6 | 2 | no | — |
| 628 | D3 | — | 6 | 2 | no | — |
| 629 | D3 | — | 6 | 6 | no | — |
| 630 | D3 | — | 12 | 3 | no | — |
| 631 | D3 | — | 18 | 2 | no | — |
| 632 | D3 | — | 18 | 6 | no | — |
| 633 | C22 | — | 9 | 1 | no | — |
| 634 | C22 | — | 9 | 2 | no | — |
| 635 | C22 | — | 9 | 3 | no | — |
| 636 | C22 | — | 9 | 6 | no | — |
| 637 | C22 | — | 36 | 3 | no | — |
| 638 | C22 | — | 36 | 6 | no | — |
| 639 | C22 | — | 108 | 6 | no | — |
| 640 | C22 | C22×((C3⋊D3)⋊C3)⋊C2 | 1 | 3 | yes | — |
| 641 | C4 | — | 9 | 1 | no | — |
| 642 | C4 | — | 9 | 2 | no | — |
| 643 | C4 | — | 9 | 3 | no | — |
| 644 | C4 | — | 9 | 6 | no | — |
| 645 | C4 | C22×((C3⋊D3)⋊C3)⋊C2 | 1 | 3 | yes | — |
| 646 | C4 | C22×((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
| 647 | C3 | — | 3 | 2 | no | — |
| 648 | C3 | — | 6 | 1 | no | — |
| 649 | C3 | #10596695 | 1 | 1 | yes | characteristic |
| 650 | C2 | — | 2 | 3 | no | — |
| 651 | C2 | — | 18 | 1 | no | — |
| 652 | C2 | — | 18 | 2 | no | — |
| 653 | C2 | — | 18 | 3 | no | — |
| 654 | C2 | — | 18 | 6 | no | — |
| 655 | 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. #41×#272 | C2 | semidirect |
| 2. #41×(C3⋊D3)⋊C3 | C2 | semidirect |
| 3. #11722521 | C2 | semidirect |
| 4. #11722517 | C2 | semidirect |
| 5. #11722516 | C2 | semidirect |
| 6. #11722507 | C2 | semidirect |
| 7. #11722506 | C2 | semidirect |
| 8. #11722502 | C2 | semidirect |
| 9. #11722491 | C2 | semidirect |
| 10. #11722490 | C2 | semidirect |
| 11. C2×#88650 | C2 | semidirect |
| 13. #41×H(3,𝔽3) | C22 | semidirect |
| 14. #88748 | C22 | semidirect |
| 15. Q8×#272 | C22 | semidirect |
| 16. #88744 | C22 | semidirect |
| 17. D4×#272 | C22 | semidirect |
| 18. #88740 | C22 | semidirect |
| 19. C2×C4×#272 | C22 | semidirect |
| 20. #88722 | C22 | semidirect |
| 21. Q8×(C3⋊D3)⋊C3 | C22 | semidirect |
| 22. #3830⋊C3 | C22 | semidirect |
| 23. D4×(C3⋊D3)⋊C3 | C22 | semidirect |
| 24. #3828⋊C3 | C22 | semidirect |
| 25. C2×C4×(C3⋊D3)⋊C3 | C22 | semidirect |
| 26. #88677 | C22 | semidirect |
| 27. #88676 | C22 | semidirect |
| 28. C2×#6200 | C22 | semidirect |
| 29. C2×#6198 | C22 | semidirect |
| 30. #88672 | C22 | semidirect |
| 31. #88671 | C22 | semidirect |
| 32. C2×#6196 | C22 | semidirect |
| 33. #88655 | C22 | semidirect |
| 34. #88654 | C22 | semidirect |
| 35. C4×((C3⋊D3)⋊C3)⋊C2 | C22 | semidirect |
| 36. #88652 | C22 | semidirect |
| 37. #88651 | C22 | semidirect |
| 38. #88650 | C22 | semidirect |
| 39. #88650 | C22 | semidirect |
| 40. #88650 | C22 | semidirect |
| 41. #88650 | C22 | semidirect |
| 42. #88650 | C22 | semidirect |
| 43. #88650 | C22 | semidirect |
| 44. #88649 | C22 | semidirect |
| 45. #88648 | C22 | semidirect |
| 46. ((C3⋊D3)⋊C3)⋊Q8 | C22 | semidirect |
| 47. #41×C3⋊D3 | D3 | semidirect |
| 100. C32×#41 | C2×D3 | semidirect |
| 101. #3832 | C2×D3 | semidirect |
| 102. Q8×C3⋊D3 | C2×D3 | semidirect |
| 103. #3830 | C2×D3 | semidirect |
| 104. D4×C3⋊D3 | C2×D3 | semidirect |
| 105. #3828 | C2×D3 | semidirect |
| 106. C2×C4×C3⋊D3 | C2×D3 | semidirect |
| 395. H(3,𝔽3) | #585 | semidirect |
| 521. #41 | ((C3⋊D3)⋊C3)⋊C2 | semidirect |
| 580. C32 | #5964 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×#272 | 2 |
| #41×(C3⋊D3)⋊C3 | 2 |
| #11722521 | 2 |
| #11722517 | 2 |
| #11722516 | 2 |
| #11722507 | 2 |
| #11722506 | 2 |
| #11722502 | 2 |
| #11722491 | 2 |
| #11722490 | 2 |
| C2×#88650 | 2 |
| #10596695 | 3 |