Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
2981 conjugacy classes of subgroups.
The subgroup lattice has 549 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #11722670 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11722627 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×#88722 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11722521 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #11722520 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #11722519 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #11722516 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #11722492 | C2 | 1 | 6 | yes | maximal, complemented |
| 9 | #11722490 | C2 | 1 | 6 | yes | maximal, complemented |
| 10 | #10596689 | — | 3 | 1 | no | maximal |
| 11 | #10596688 | — | 3 | 1 | no | maximal |
| 12 | C2×Q8×H(3,𝔽3) | C22 | 1 | 1 | yes | characteristic, complemented |
| 13 | #88748 | C22 | 1 | 4 | yes | complemented |
| 14 | Q8×#272 | C22 | 1 | 4 | yes | complemented |
| 15 | #88740 | C22 | 1 | 6 | yes | complemented |
| 16 | #88722 | C22 | 1 | 4 | yes | complemented |
| 17 | #88722 | C22 | 1 | 4 | yes | complemented |
| 18 | #88722 | C22 | 1 | 4 | yes | complemented |
| 19 | Q8×(C3⋊D3)⋊C3 | C22 | 1 | 4 | yes | complemented |
| 20 | #3828⋊C3 | C22 | 1 | 6 | yes | complemented |
| 21 | C2×C4⋊((C3⋊D3)⋊C3) | C22 | 1 | 3 | yes | complemented |
| 22 | C2×C4×(C3⋊D3)⋊C3 | C22 | 1 | 3 | yes | complemented |
| 23 | #88676 | C22 | 1 | 12 | yes | complemented |
| 24 | #88671 | C22 | 1 | 4 | yes | complemented |
| 25 | #88655 | C22 | 1 | 12 | yes | complemented |
| 26 | #88654 | C22 | 1 | 12 | yes | complemented |
| 27 | #88654 | C22 | 1 | 6 | yes | complemented |
| 28 | C4×((C3⋊D3)⋊C3)⋊C2 | C22 | 1 | 12 | yes | complemented |
| 29 | #88652 | C22 | 1 | 6 | yes | complemented |
| 30 | #88650 | C22 | 1 | 12 | yes | complemented |
| 31 | #88649 | C22 | 1 | 12 | yes | complemented |
| 32 | #88648 | C22 | 1 | 12 | yes | complemented |
| 33 | #88648 | C22 | 1 | 6 | yes | complemented |
| 34 | ((C3⋊D3)⋊C3)⋊Q8 | C22 | 1 | 6 | yes | complemented |
| 35 | #64364 | D3 | 1 | 1 | yes | characteristic, complemented |
| 36 | C2×#3832 | D3 | 1 | 1 | yes | characteristic, complemented |
| 37 | C3×#1007 | — | 3 | 1 | no | — |
| 38 | C3×#1007 | — | 3 | 1 | no | — |
| 39 | C3×#1007 | — | 3 | 1 | no | — |
| 40 | C3×#1007 | — | 6 | 1 | no | — |
| 41 | C2×C3×#239 | — | 3 | 1 | no | — |
| 42 | #64320 | — | 3 | 4 | no | — |
| 43 | #64320 | — | 3 | 4 | no | — |
| 44 | #64319 | — | 3 | 4 | no | — |
| 45 | D3×#239 | — | 3 | 4 | no | — |
| 46 | D3×#239 | — | 3 | 4 | no | — |
| 47 | D3×#239 | — | 3 | 4 | no | — |
| 48 | #64316 | — | 3 | 4 | no | — |
| 49 | #64315 | — | 3 | 4 | no | — |
| 50 | #64308 | — | 3 | 6 | no | — |
| 51 | #64307 | — | 3 | 6 | no | — |
| 52 | #64306 | — | 3 | 6 | no | — |
| 53 | D3×#235 | — | 3 | 6 | no | — |
| 54 | C22×(C3⋊D3)⋊C3 | C23 | 1 | 3 | yes | — |
| 55 | C2×((C3⋊D3)⋊C3)⋊C2 | C23 | 1 | 12 | yes | — |
| 56 | Q8×H(3,𝔽3) | C23 | 1 | 4 | yes | — |
| 57 | C2×C4×H(3,𝔽3) | C23 | 1 | 3 | yes | — |
| 58 | #6235 | C23 | 1 | 4 | yes | — |
| 59 | C4⋊#272 | C23 | 1 | 6 | yes | — |
| 60 | C4×#272 | C23 | 1 | 12 | yes | — |
| 61 | #6229 | C23 | 1 | 6 | yes | — |
| 62 | #638⋊C3 | C23 | 1 | 4 | yes | — |
| 63 | C2×(C3⋊Dic3)⋊C3 | C23 | 1 | 1 | yes | characteristic |
| 64 | C4⋊((C3⋊D3)⋊C3) | C23 | 1 | 12 | yes | — |
| 65 | C4⋊((C3⋊D3)⋊C3) | C23 | 1 | 6 | yes | — |
| 66 | C4×(C3⋊D3)⋊C3 | C23 | 1 | 6 | yes | — |
| 67 | C4×(C3⋊D3)⋊C3 | C23 | 1 | 12 | yes | — |
| 68 | C4×(C3⋊D3)⋊C3 | C23 | 1 | 6 | yes | — |
| 69 | #634⋊C3 | C23 | 1 | 6 | yes | — |
| 70 | #6200 | C23 | 1 | 12 | yes | — |
| 71 | #6200 | C23 | 1 | 4 | yes | — |
| 72 | #6199 | C23 | 1 | 4 | yes | — |
| 73 | #6198 | C23 | 1 | 12 | yes | — |
| 74 | ((C3⋊D3)⋊C3)⋊C4 | C23 | 1 | 12 | yes | — |
| 75 | ((C3⋊D3)⋊C3)⋊C4 | C23 | 1 | 4 | yes | — |
| 76 | #6196 | C23 | 1 | 4 | yes | — |
| 77 | #5968 | — | 9 | 1 | no | — |
| 78 | #5968 | — | 9 | 1 | no | — |
| 79 | #5964 | — | 9 | 1 | no | — |
| 80 | C2×C32×Q8 | — | 2 | 1 | no | — |
| 81 | C2×C32×Q8 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 82 | C2×C32×Q8 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 83 | #3832 | C2×D3 | 1 | 4 | yes | complemented |
| 84 | #3832 | C2×D3 | 1 | 4 | yes | complemented |
| 85 | #3832 | C2×D3 | 1 | 4 | yes | complemented |
| 86 | Q8×C3⋊D3 | C2×D3 | 1 | 4 | yes | complemented |
| 87 | #3828 | C2×D3 | 1 | 6 | yes | complemented |
| 88 | C2×C4⋊(C3⋊D3) | C2×D3 | 1 | 3 | yes | complemented |
| 89 | C2×C4×C3⋊D3 | C2×D3 | 1 | 3 | yes | complemented |
| 90 | C3×#239 | — | 3 | 4 | no | — |
| 91 | C3×#239 | — | 3 | 4 | no | — |
| 92 | C3×#239 | — | 3 | 4 | no | — |
| 93 | C3×#239 | — | 3 | 4 | no | — |
| 94 | C3×#239 | — | 3 | 4 | no | — |
| 95 | C3×#239 | — | 6 | 4 | no | — |
| 96 | C3×D3×Q8 | — | 3 | 4 | no | — |
| 97 | C3×D3×Q8 | — | 3 | 4 | no | — |
| 98 | C3×D3×Q8 | — | 3 | 4 | no | — |
| 99 | C3×D3×Q8 | — | 6 | 4 | no | — |
| 100 | C3×#235 | — | 3 | 6 | no | — |
| 101 | C3×#235 | — | 3 | 6 | no | — |
| 102 | C3×#235 | — | 3 | 6 | no | — |
| 103 | C3×#235 | — | 6 | 6 | no | — |
| 104 | C2×C3×D12 | — | 3 | 3 | no | — |
| 105 | C2×C3×C4×D3 | — | 3 | 3 | no | — |
| 106 | #3811 | — | 3 | 12 | no | — |
| 107 | D3×#67 | — | 3 | 12 | no | — |
| 108 | #3805 | — | 3 | 4 | no | — |
| 109 | #3804 | — | 3 | 4 | no | — |
| 110 | #3802 | — | 3 | 6 | no | — |
| 111 | #3802 | — | 3 | 12 | no | — |
| 112 | D3×D12 | — | 3 | 6 | no | — |
| 113 | D3×D12 | — | 3 | 12 | no | — |
| 114 | D3×D12 | — | 3 | 12 | no | — |
| 115 | D3×D12 | — | 3 | 12 | no | — |
| 116 | C4×D32 | — | 3 | 12 | no | — |
| 117 | C4×D32 | — | 3 | 12 | no | — |
| 118 | #3799 | — | 3 | 6 | no | — |
| 119 | #3799 | — | 3 | 12 | no | — |
| 120 | #3799 | — | 3 | 12 | no | — |
| 121 | #3798 | — | 3 | 12 | no | — |
| 122 | #3798 | — | 3 | 12 | no | — |
| 123 | #3797 | — | 3 | 6 | no | — |
| 124 | #3796 | — | 3 | 6 | no | — |
| 125 | #3796 | — | 3 | 6 | no | — |
| 126 | #3796 | — | 3 | 12 | no | — |
| 127 | #3795 | — | 3 | 6 | no | — |
| 128 | #3795 | — | 3 | 12 | no | — |
| 129 | D3×Dic6 | — | 3 | 6 | no | — |
| 130 | C22×H(3,𝔽3) | C24 | 1 | 1 | yes | characteristic |
| 131 | C2×#272 | C24 | 1 | 4 | yes | — |
| 132 | C2×(C3⋊D3)⋊C3 | — | 4 | 3 | no | — |
| 133 | C2×(C3⋊D3)⋊C3 | C24 | 1 | 6 | yes | — |
| 134 | C2×(C3⋊D3)⋊C3 | C24 | 1 | 4 | yes | — |
| 135 | ((C3⋊D3)⋊C3)⋊C2 | — | 4 | 12 | no | — |
| 136 | C4×H(3,𝔽3) | C24 | 1 | 6 | yes | — |
| 137 | #1084 | C24 | 1 | 4 | yes | — |
| 138 | (C3⋊Dic3)⋊C3 | C24 | 1 | 1 | yes | characteristic |
| 139 | (C3⋊Dic3)⋊C3 | C24 | 1 | 4 | yes | — |
| 140 | (C3⋊Dic3)⋊C3 | C24 | 1 | 1 | yes | characteristic |
| 141 | C3×2−1+4 | — | 9 | 1 | no | — |
| 142 | C3×2−1+4 | — | 9 | 1 | no | — |
| 143 | C2×C3×#41 | — | 9 | 1 | no | — |
| 144 | #1010 | — | 9 | 4 | no | — |
| 145 | #1009 | — | 9 | 6 | no | — |
| 146 | #1009 | — | 9 | 6 | no | — |
| 147 | #1009 | — | 9 | 4 | no | — |
| 148 | #1009 | — | 9 | 4 | no | — |
| 149 | #1009 | — | 9 | 4 | no | — |
| 150 | D3×#41 | — | 9 | 6 | no | — |
| 151 | D3×#41 | — | 9 | 6 | no | — |
| 152 | D3×#41 | — | 9 | 4 | no | — |
| 153 | D3×#41 | — | 9 | 4 | no | — |
| 154 | D3×#41 | — | 9 | 4 | no | — |
| 155 | D3×#41 | — | 9 | 4 | no | — |
| 156 | #1007 | — | 3 | 1 | no | — |
| 157 | #1007 | — | 3 | 1 | no | — |
| 158 | #1007 | — | 3 | 1 | no | — |
| 159 | #1007 | — | 6 | 1 | no | — |
| 160 | #1007 | — | 9 | 1 | no | — |
| 161 | #1007 | — | 9 | 4 | no | — |
| 162 | #1007 | — | 9 | 4 | no | — |
| 163 | C2×#239 | — | 3 | 1 | no | — |
| 164 | C2×#239 | — | 9 | 1 | no | — |
| 165 | C2×#239 | — | 9 | 4 | no | — |
| 166 | C2×#239 | — | 9 | 4 | no | — |
| 167 | #1004 | — | 9 | 6 | no | — |
| 168 | C2×#235 | — | 9 | 6 | no | — |
| 169 | C22×C3⋊D3 | C22×D3 | 1 | 3 | yes | — |
| 170 | C22×C3×D3 | — | 3 | 3 | no | — |
| 171 | C2×D32 | — | 3 | 12 | no | — |
| 172 | C2×D32 | — | 3 | 12 | no | — |
| 173 | C32×Q8 | — | 2 | 4 | no | — |
| 174 | C32×Q8 | C22×D3 | 1 | 4 | yes | — |
| 175 | C32×Q8 | C22×D3 | 1 | 4 | yes | — |
| 176 | C2×C32×C4 | — | 2 | 3 | no | — |
| 177 | C2×C32×C4 | C22×D3 | 1 | 3 | yes | — |
| 178 | C2×C32×C4 | C22×D3 | 1 | 3 | yes | — |
| 179 | #638 | C22×D3 | 1 | 4 | yes | — |
| 180 | C2×C3⋊Dic3 | C22×D3 | 1 | 1 | yes | characteristic |
| 181 | C4⋊(C3⋊D3) | C22×D3 | 1 | 12 | yes | — |
| 182 | C4⋊(C3⋊D3) | C22×D3 | 1 | 6 | yes | — |
| 183 | C4×C3⋊D3 | C22×D3 | 1 | 6 | yes | — |
| 184 | C4×C3⋊D3 | C22×D3 | 1 | 12 | yes | — |
| 185 | C4×C3⋊D3 | C22×D3 | 1 | 6 | yes | — |
| 186 | #634 | C22×D3 | 1 | 6 | yes | — |
| 187 | C3×#67 | — | 3 | 4 | no | — |
| 188 | C3×#67 | — | 3 | 4 | no | — |
| 189 | C3×#67 | — | 3 | 4 | no | — |
| 190 | C3×#67 | — | 6 | 4 | no | — |
| 191 | C2×C3×Dic3 | — | 3 | 1 | no | — |
| 192 | C3×D12 | — | 3 | 12 | no | — |
| 193 | C3×D12 | — | 3 | 6 | no | — |
| 194 | C3×D12 | — | 3 | 6 | no | — |
| 195 | C3×D12 | — | 3 | 6 | no | — |
| 196 | C3×D12 | — | 6 | 6 | no | — |
| 197 | C3×C4×D3 | — | 3 | 6 | no | — |
| 198 | C3×C4×D3 | — | 3 | 6 | no | — |
| 199 | C3×C4×D3 | — | 3 | 12 | no | — |
| 200 | C3×C4×D3 | — | 3 | 12 | no | — |
| 201 | C3×C4×D3 | — | 3 | 12 | no | — |
| 202 | C3×C4×D3 | — | 6 | 12 | no | — |
| 203 | C3×Dic6 | — | 3 | 6 | no | — |
| 204 | C3×Dic6 | — | 3 | 6 | no | — |
| 205 | C3×Dic6 | — | 3 | 6 | no | — |
| 206 | C3×Dic6 | — | 6 | 6 | no | — |
| 207 | #627 | — | 3 | 4 | no | — |
| 208 | #627 | — | 3 | 4 | no | — |
| 209 | #626 | — | 3 | 12 | no | — |
| 210 | #626 | — | 3 | 12 | no | — |
| 211 | #626 | — | 3 | 12 | no | — |
| 212 | #626 | — | 3 | 4 | no | — |
| 213 | #625 | — | 3 | 12 | no | — |
| 214 | #625 | — | 3 | 4 | no | — |
| 215 | #624 | — | 3 | 12 | no | — |
| 216 | #624 | — | 3 | 4 | no | — |
| 217 | D3×Dic3 | — | 3 | 12 | no | — |
| 218 | D3×Dic3 | — | 3 | 4 | no | — |
| 219 | D3×Dic3 | — | 3 | 4 | no | — |
| 220 | D3×Dic3 | — | 3 | 4 | no | — |
| 221 | #585 | — | 27 | 1 | no | Sylow |
| 222 | C2×H(3,𝔽3) | — | 2 | 1 | no | — |
| 223 | C2×H(3,𝔽3) | C25 | 1 | 1 | yes | characteristic |
| 224 | #272 | — | 2 | 4 | no | — |
| 225 | (C3⋊D3)⋊C3 | — | 2 | 4 | no | — |
| 226 | (C3⋊D3)⋊C3 | — | 2 | 6 | no | — |
| 227 | C3×#41 | — | 9 | 6 | no | — |
| 228 | C3×#41 | — | 9 | 4 | no | — |
| 229 | C3×#41 | — | 9 | 4 | no | — |
| 230 | C3×#41 | — | 9 | 4 | no | — |
| 231 | C3×#41 | — | 9 | 4 | no | — |
| 232 | C3×#41 | — | 9 | 6 | no | — |
| 233 | C2×C3×Q8 | — | 3 | 1 | no | — |
| 234 | C2×C3×Q8 | — | 3 | 1 | no | — |
| 235 | C2×C3×Q8 | — | 6 | 1 | no | — |
| 236 | C2×C3×Q8 | — | 9 | 4 | no | — |
| 237 | C2×C3×Q8 | — | 9 | 4 | no | — |
| 238 | C2×C3×Q8 | D32 | 1 | 1 | yes | characteristic |
| 239 | C2×C3×D4 | — | 9 | 3 | no | — |
| 240 | C22×C3×C4 | — | 9 | 3 | no | — |
| 241 | C2×#67 | — | 9 | 12 | no | — |
| 242 | #239 | — | 3 | 4 | no | — |
| 243 | #239 | — | 3 | 4 | no | — |
| 244 | #239 | — | 3 | 4 | no | — |
| 245 | #239 | — | 3 | 4 | no | — |
| 246 | #239 | — | 3 | 4 | no | — |
| 247 | #239 | — | 6 | 4 | no | — |
| 248 | #239 | — | 9 | 4 | no | — |
| 249 | #239 | — | 9 | 4 | no | — |
| 250 | #239 | — | 9 | 4 | no | — |
| 251 | #239 | — | 9 | 6 | no | — |
| 252 | #239 | — | 9 | 12 | no | — |
| 253 | #239 | — | 9 | 12 | no | — |
| 254 | #239 | — | 9 | 6 | no | — |
| 255 | D3×Q8 | — | 3 | 4 | no | — |
| 256 | D3×Q8 | — | 3 | 4 | no | — |
| 257 | D3×Q8 | — | 3 | 4 | no | — |
| 258 | D3×Q8 | — | 6 | 4 | no | — |
| 259 | D3×Q8 | — | 9 | 4 | no | — |
| 260 | D3×Q8 | — | 9 | 6 | no | — |
| 261 | D3×Q8 | — | 9 | 6 | no | — |
| 262 | #237 | — | 9 | 6 | no | — |
| 263 | #237 | — | 9 | 12 | no | — |
| 264 | #237 | — | 9 | 6 | no | — |
| 265 | #237 | — | 9 | 12 | no | — |
| 266 | #237 | — | 9 | 4 | no | — |
| 267 | #237 | — | 9 | 4 | no | — |
| 268 | D3×D4 | — | 9 | 6 | no | — |
| 269 | D3×D4 | — | 9 | 12 | no | — |
| 270 | D3×D4 | — | 9 | 12 | no | — |
| 271 | D3×D4 | — | 9 | 12 | no | — |
| 272 | D3×D4 | — | 9 | 12 | no | — |
| 273 | D3×D4 | — | 9 | 6 | no | — |
| 274 | D3×D4 | — | 9 | 12 | no | — |
| 275 | D3×D4 | — | 9 | 12 | no | — |
| 276 | #235 | — | 3 | 6 | no | — |
| 277 | #235 | — | 3 | 6 | no | — |
| 278 | #235 | — | 3 | 6 | no | — |
| 279 | #235 | — | 6 | 6 | no | — |
| 280 | #235 | — | 9 | 6 | no | — |
| 281 | #235 | — | 9 | 12 | no | — |
| 282 | #235 | — | 9 | 6 | no | — |
| 283 | #235 | — | 9 | 12 | no | — |
| 284 | #235 | — | 9 | 12 | no | — |
| 285 | #235 | — | 9 | 12 | no | — |
| 286 | #235 | — | 9 | 12 | no | — |
| 287 | #235 | — | 9 | 6 | no | — |
| 288 | #235 | — | 9 | 4 | no | — |
| 289 | C2×D12 | — | 3 | 3 | no | — |
| 290 | C2×D12 | — | 9 | 3 | no | — |
| 291 | C2×D12 | — | 9 | 12 | no | — |
| 292 | C2×D12 | — | 9 | 6 | no | — |
| 293 | C2×D12 | — | 9 | 12 | no | — |
| 294 | C2×C4×D3 | — | 3 | 3 | no | — |
| 295 | C2×C4×D3 | — | 9 | 3 | no | — |
| 296 | C2×C4×D3 | — | 9 | 12 | no | — |
| 297 | C2×C4×D3 | — | 9 | 12 | no | — |
| 298 | C2×C4×D3 | — | 9 | 12 | no | — |
| 299 | C2×Dic6 | — | 9 | 6 | no | — |
| 300 | C22×C32 | — | 2 | 1 | no | — |
| 301 | C22×C32 | C23×D3 | 1 | 1 | yes | characteristic |
| 302 | C22×C32 | C23×D3 | 1 | 1 | yes | characteristic |
| 303 | C2×C3⋊D3 | — | 4 | 3 | no | — |
| 304 | C2×C3⋊D3 | C23×D3 | 1 | 6 | yes | — |
| 305 | C2×C3⋊D3 | C23×D3 | 1 | 4 | yes | — |
| 306 | C2×C3×D3 | — | 3 | 6 | no | — |
| 307 | C2×C3×D3 | — | 3 | 4 | no | — |
| 308 | C2×C3×D3 | — | 3 | 4 | no | — |
| 309 | C2×C3×D3 | — | 3 | 4 | no | — |
| 310 | C2×C3×D3 | — | 6 | 4 | no | — |
| 311 | C2×C3×D3 | — | 12 | 3 | no | — |
| 312 | D32 | — | 12 | 12 | no | — |
| 313 | D32 | — | 12 | 12 | no | — |
| 314 | C32×C4 | — | 2 | 6 | no | — |
| 315 | C32×C4 | C23×D3 | 1 | 6 | yes | — |
| 316 | C32×C4 | C23×D3 | 1 | 6 | yes | — |
| 317 | C3⋊Dic3 | C23×D3 | 1 | 1 | yes | characteristic |
| 318 | C3⋊Dic3 | C23×D3 | 1 | 4 | yes | — |
| 319 | C3⋊Dic3 | C23×D3 | 1 | 1 | yes | characteristic |
| 320 | C3×Dic3 | — | 3 | 1 | no | — |
| 321 | C3×Dic3 | — | 3 | 4 | no | — |
| 322 | C3×Dic3 | — | 3 | 1 | no | — |
| 323 | C3×Dic3 | — | 3 | 4 | no | — |
| 324 | C3×Dic3 | — | 3 | 4 | no | — |
| 325 | C3×Dic3 | — | 6 | 4 | no | — |
| 326 | 2−1+4 | — | 9 | 1 | no | — |
| 327 | 2−1+4 | — | 9 | 1 | no | — |
| 328 | 2−1+4 | — | 27 | 4 | no | — |
| 329 | H(5,𝔽2) | — | 27 | 6 | no | — |
| 330 | H(5,𝔽2) | — | 27 | 4 | no | — |
| 331 | C2×#41 | — | 9 | 1 | no | — |
| 332 | C2×#41 | — | 27 | 6 | no | — |
| 333 | C2×#41 | — | 27 | 4 | no | — |
| 334 | C2×#41 | — | 27 | 4 | no | — |
| 335 | H(3,𝔽3) | #585 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 336 | C23×C3 | — | 9 | 3 | no | — |
| 337 | C22×D3 | — | 3 | 3 | no | — |
| 338 | C22×D3 | — | 9 | 3 | no | — |
| 339 | C22×D3 | — | 9 | 12 | no | — |
| 340 | C22×D3 | — | 9 | 12 | no | — |
| 341 | C22×D3 | — | 9 | 12 | no | — |
| 342 | C3×Q8 | — | 3 | 4 | no | — |
| 343 | C3×Q8 | — | 3 | 4 | no | — |
| 344 | C3×Q8 | — | 6 | 4 | no | — |
| 345 | C3×Q8 | — | 9 | 6 | no | — |
| 346 | C3×Q8 | — | 9 | 6 | no | — |
| 347 | C3×Q8 | C2×D32 | 1 | 4 | yes | — |
| 348 | C3×D4 | — | 9 | 6 | no | — |
| 349 | C3×D4 | — | 9 | 12 | no | — |
| 350 | C3×D4 | — | 9 | 4 | no | — |
| 351 | C3×D4 | — | 9 | 4 | no | — |
| 352 | C3×D4 | — | 9 | 6 | no | — |
| 353 | C2×C3×C4 | — | 3 | 3 | no | — |
| 354 | C2×C3×C4 | — | 3 | 3 | no | — |
| 355 | C2×C3×C4 | — | 6 | 3 | no | — |
| 356 | C2×C3×C4 | — | 9 | 6 | no | — |
| 357 | C2×C3×C4 | — | 9 | 6 | no | — |
| 358 | C2×C3×C4 | — | 9 | 12 | no | — |
| 359 | C2×C3×C4 | — | 9 | 1 | no | — |
| 360 | C2×C3×C4 | — | 9 | 12 | no | — |
| 361 | C2×C3×C4 | C2×D32 | 1 | 3 | yes | — |
| 362 | #67 | — | 3 | 4 | no | — |
| 363 | #67 | — | 3 | 4 | no | — |
| 364 | #67 | — | 3 | 4 | no | — |
| 365 | #67 | — | 6 | 4 | no | — |
| 366 | #67 | — | 9 | 4 | no | — |
| 367 | #67 | — | 9 | 12 | no | — |
| 368 | #67 | — | 9 | 4 | no | — |
| 369 | #67 | — | 9 | 12 | no | — |
| 370 | #67 | — | 9 | 12 | no | — |
| 371 | #67 | — | 9 | 4 | no | — |
| 372 | #67 | — | 9 | 12 | no | — |
| 373 | C2×Dic3 | — | 3 | 1 | no | — |
| 374 | C2×Dic3 | — | 9 | 1 | no | — |
| 375 | C2×Dic3 | — | 9 | 4 | no | — |
| 376 | C2×Dic3 | — | 9 | 12 | no | — |
| 377 | C2×Dic3 | — | 9 | 4 | no | — |
| 378 | D12 | — | 3 | 6 | no | — |
| 379 | D12 | — | 3 | 6 | no | — |
| 380 | D12 | — | 3 | 12 | no | — |
| 381 | D12 | — | 3 | 6 | no | — |
| 382 | D12 | — | 6 | 6 | no | — |
| 383 | D12 | — | 9 | 12 | no | — |
| 384 | D12 | — | 9 | 6 | no | — |
| 385 | D12 | — | 9 | 12 | no | — |
| 386 | D12 | — | 9 | 4 | no | — |
| 387 | D12 | — | 9 | 12 | no | — |
| 388 | C4×D3 | — | 3 | 12 | no | — |
| 389 | C4×D3 | — | 3 | 12 | no | — |
| 390 | C4×D3 | — | 3 | 6 | no | — |
| 391 | C4×D3 | — | 3 | 6 | no | — |
| 392 | C4×D3 | — | 3 | 12 | no | — |
| 393 | C4×D3 | — | 6 | 12 | no | — |
| 394 | C4×D3 | — | 9 | 6 | no | — |
| 395 | C4×D3 | — | 9 | 12 | no | — |
| 396 | C4×D3 | — | 9 | 6 | no | — |
| 397 | C4×D3 | — | 9 | 4 | no | — |
| 398 | C4×D3 | — | 9 | 12 | no | — |
| 399 | C4×D3 | — | 9 | 4 | no | — |
| 400 | C4×D3 | — | 9 | 12 | no | — |
| 401 | C4×D3 | — | 9 | 4 | no | — |
| 402 | C4×D3 | — | 9 | 4 | no | — |
| 403 | Dic6 | — | 3 | 6 | no | — |
| 404 | Dic6 | — | 3 | 6 | no | — |
| 405 | Dic6 | — | 3 | 6 | no | — |
| 406 | Dic6 | — | 6 | 6 | no | — |
| 407 | Dic6 | — | 9 | 6 | no | — |
| 408 | Dic6 | — | 9 | 4 | no | — |
| 409 | Dic6 | — | 9 | 4 | no | — |
| 410 | Dic6 | — | 9 | 4 | no | — |
| 411 | C2×C32 | — | 2 | 1 | no | — |
| 412 | C2×C32 | — | 2 | 1 | no | — |
| 413 | C2×C32 | — | 2 | 1 | no | — |
| 414 | C2×C32 | — | 4 | 1 | no | — |
| 415 | C2×C32 | C24×D3 | 1 | 1 | yes | characteristic |
| 416 | C2×C32 | C24×D3 | 1 | 1 | yes | characteristic |
| 417 | C3⋊D3 | — | 2 | 6 | no | — |
| 418 | C3⋊D3 | — | 2 | 4 | no | — |
| 419 | C3×D3 | — | 6 | 4 | no | — |
| 420 | C3×D3 | — | 6 | 4 | no | — |
| 421 | C3×D3 | — | 6 | 6 | no | — |
| 422 | C3×D3 | — | 6 | 4 | no | — |
| 423 | C3×D3 | — | 12 | 4 | no | — |
| 424 | #41 | — | 9 | 4 | no | — |
| 425 | #41 | — | 9 | 4 | no | — |
| 426 | #41 | — | 9 | 4 | no | — |
| 427 | #41 | — | 9 | 4 | no | — |
| 428 | #41 | — | 9 | 6 | no | — |
| 429 | #41 | — | 9 | 6 | no | — |
| 430 | #41 | — | 27 | 12 | no | — |
| 431 | #41 | — | 27 | 4 | no | — |
| 432 | #41 | — | 27 | 6 | no | — |
| 433 | #41 | — | 27 | 6 | no | — |
| 434 | #41 | — | 27 | 12 | no | — |
| 435 | #41 | — | 27 | 12 | no | — |
| 436 | C2×Q8 | — | 9 | 4 | no | — |
| 437 | C2×Q8 | — | 9 | 4 | no | — |
| 438 | C2×Q8 | — | 27 | 6 | no | — |
| 439 | C2×Q8 | ((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic, complemented |
| 440 | C2×D4 | — | 9 | 3 | no | — |
| 441 | C2×D4 | — | 27 | 6 | no | — |
| 442 | C2×D4 | — | 27 | 12 | no | — |
| 443 | C2×D4 | — | 27 | 12 | no | — |
| 444 | C2×D4 | — | 27 | 12 | no | — |
| 445 | C22×C4 | — | 9 | 3 | no | — |
| 446 | C22×C4 | — | 27 | 12 | no | — |
| 447 | C22×C3 | — | 3 | 1 | no | — |
| 448 | C22×C3 | — | 3 | 1 | no | — |
| 449 | C22×C3 | — | 6 | 1 | no | — |
| 450 | C22×C3 | — | 9 | 6 | no | — |
| 451 | C22×C3 | — | 9 | 4 | no | — |
| 452 | C22×C3 | — | 9 | 4 | no | — |
| 453 | C22×C3 | — | 36 | 3 | no | — |
| 454 | C22×C3 | C22×D32 | 1 | 1 | yes | characteristic |
| 455 | C2×D3 | — | 3 | 4 | no | — |
| 456 | C2×D3 | — | 3 | 4 | no | — |
| 457 | C2×D3 | — | 3 | 4 | no | — |
| 458 | C2×D3 | — | 3 | 6 | no | — |
| 459 | C2×D3 | — | 6 | 4 | no | — |
| 460 | C2×D3 | — | 9 | 6 | no | — |
| 461 | C2×D3 | — | 9 | 4 | no | — |
| 462 | C2×D3 | — | 12 | 3 | no | — |
| 463 | C2×D3 | — | 36 | 3 | no | — |
| 464 | C2×D3 | — | 36 | 12 | no | — |
| 465 | C2×D3 | — | 36 | 12 | no | — |
| 466 | C2×D3 | — | 36 | 12 | no | — |
| 467 | C3×C4 | — | 3 | 6 | no | — |
| 468 | C3×C4 | — | 3 | 6 | no | — |
| 469 | C3×C4 | — | 6 | 6 | no | — |
| 470 | C3×C4 | — | 9 | 1 | no | — |
| 471 | C3×C4 | — | 9 | 4 | no | — |
| 472 | C3×C4 | — | 9 | 1 | no | — |
| 473 | C3×C4 | — | 9 | 4 | no | — |
| 474 | C3×C4 | C22×D32 | 1 | 6 | yes | — |
| 475 | Dic3 | — | 3 | 4 | no | — |
| 476 | Dic3 | — | 3 | 4 | no | — |
| 477 | Dic3 | — | 3 | 4 | no | — |
| 478 | Dic3 | — | 3 | 1 | no | — |
| 479 | Dic3 | — | 3 | 1 | no | — |
| 480 | Dic3 | — | 6 | 4 | no | — |
| 481 | Dic3 | — | 9 | 1 | no | — |
| 482 | Dic3 | — | 9 | 4 | no | — |
| 483 | Dic3 | — | 9 | 1 | no | — |
| 484 | C32 | — | 2 | 1 | no | — |
| 485 | C32 | #5964 | 1 | 1 | yes | characteristic, complemented |
| 486 | C32 | #5968 | 1 | 1 | yes | characteristic, complemented |
| 487 | C23 | — | 9 | 3 | no | — |
| 488 | C23 | — | 27 | 12 | no | — |
| 489 | Q8 | — | 9 | 6 | no | — |
| 490 | Q8 | — | 9 | 6 | no | — |
| 491 | Q8 | — | 27 | 4 | no | — |
| 492 | Q8 | C2×((C3⋊D3)⋊C3)⋊C2 | 1 | 4 | yes | — |
| 493 | D4 | — | 9 | 4 | no | — |
| 494 | D4 | — | 9 | 4 | no | — |
| 495 | D4 | — | 9 | 12 | no | — |
| 496 | D4 | — | 9 | 6 | no | — |
| 497 | D4 | — | 9 | 6 | no | — |
| 498 | D4 | — | 27 | 4 | no | — |
| 499 | D4 | — | 27 | 12 | no | — |
| 500 | D4 | — | 27 | 12 | no | — |
| 501 | C2×C4 | — | 9 | 1 | no | — |
| 502 | C2×C4 | — | 9 | 6 | no | — |
| 503 | C2×C4 | — | 9 | 6 | no | — |
| 504 | C2×C4 | — | 9 | 12 | no | — |
| 505 | C2×C4 | — | 9 | 12 | no | — |
| 506 | C2×C4 | — | 27 | 4 | no | — |
| 507 | C2×C4 | — | 27 | 4 | no | — |
| 508 | C2×C4 | — | 27 | 12 | no | — |
| 509 | C2×C4 | C2×((C3⋊D3)⋊C3)⋊C2 | 1 | 3 | yes | — |
| 510 | C2×C3 | — | 2 | 1 | no | — |
| 511 | C2×C3 | — | 3 | 1 | no | — |
| 512 | C2×C3 | — | 3 | 1 | no | — |
| 513 | C2×C3 | — | 6 | 1 | no | — |
| 514 | C2×C3 | — | 6 | 1 | no | — |
| 515 | C2×C3 | — | 6 | 1 | no | — |
| 516 | C2×C3 | — | 12 | 1 | no | — |
| 517 | C2×C3 | — | 18 | 4 | no | — |
| 518 | C2×C3 | — | 18 | 6 | no | — |
| 519 | C2×C3 | — | 18 | 4 | no | — |
| 520 | C2×C3 | C23×D32 | 1 | 1 | yes | characteristic |
| 521 | D3 | — | 6 | 4 | no | — |
| 522 | D3 | — | 6 | 4 | no | — |
| 523 | D3 | — | 6 | 6 | no | — |
| 524 | D3 | — | 6 | 4 | no | — |
| 525 | D3 | — | 12 | 4 | no | — |
| 526 | D3 | — | 18 | 6 | no | — |
| 527 | D3 | — | 18 | 4 | no | — |
| 528 | C22 | — | 9 | 4 | no | — |
| 529 | C22 | — | 9 | 4 | no | — |
| 530 | C22 | — | 9 | 6 | no | — |
| 531 | C22 | — | 36 | 3 | no | — |
| 532 | C22 | — | 108 | 12 | no | — |
| 533 | C22 | C22×((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
| 534 | C4 | — | 9 | 1 | no | — |
| 535 | C4 | — | 9 | 1 | no | — |
| 536 | C4 | — | 9 | 4 | no | — |
| 537 | C4 | — | 9 | 4 | no | — |
| 538 | C4 | C22×((C3⋊D3)⋊C3)⋊C2 | 1 | 6 | yes | — |
| 539 | C3 | — | 3 | 1 | no | — |
| 540 | C3 | — | 3 | 1 | no | — |
| 541 | C3 | — | 6 | 1 | no | — |
| 542 | C3 | #10596688 | 1 | 1 | yes | characteristic |
| 543 | C2 | — | 2 | 1 | no | — |
| 544 | C2 | — | 18 | 6 | no | — |
| 545 | C2 | — | 18 | 4 | no | — |
| 546 | C2 | — | 18 | 4 | no | — |
| 547 | 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. #11722670 | C2 | semidirect |
| 2. #11722627 | C2 | semidirect |
| 3. C2×#88722 | C2 | semidirect |
| 4. #11722521 | C2 | semidirect |
| 5. #11722520 | C2 | semidirect |
| 6. #11722519 | C2 | semidirect |
| 7. #11722516 | C2 | semidirect |
| 8. #11722492 | C2 | semidirect |
| 9. #11722490 | C2 | semidirect |
| 12. C2×Q8×H(3,𝔽3) | C22 | semidirect |
| 13. #88748 | C22 | semidirect |
| 14. Q8×#272 | C22 | semidirect |
| 15. #88740 | C22 | semidirect |
| 16. #88722 | C22 | semidirect |
| 17. #88722 | C22 | semidirect |
| 18. #88722 | C22 | semidirect |
| 19. Q8×(C3⋊D3)⋊C3 | C22 | semidirect |
| 20. #3828⋊C3 | C22 | semidirect |
| 21. C2×C4⋊((C3⋊D3)⋊C3) | C22 | semidirect |
| 22. C2×C4×(C3⋊D3)⋊C3 | C22 | semidirect |
| 23. #88676 | C22 | semidirect |
| 24. #88671 | C22 | semidirect |
| 25. #88655 | C22 | semidirect |
| 26. #88654 | C22 | semidirect |
| 27. #88654 | C22 | semidirect |
| 28. C4×((C3⋊D3)⋊C3)⋊C2 | C22 | semidirect |
| 29. #88652 | C22 | semidirect |
| 30. #88650 | C22 | semidirect |
| 31. #88649 | C22 | semidirect |
| 32. #88648 | C22 | semidirect |
| 33. #88648 | C22 | semidirect |
| 34. ((C3⋊D3)⋊C3)⋊Q8 | C22 | semidirect |
| 35. #64364 | D3 | semidirect |
| 36. C2×#3832 | D3 | semidirect |
| 81. C2×C32×Q8 | C2×D3 | semidirect |
| 82. C2×C32×Q8 | C2×D3 | semidirect |
| 83. #3832 | C2×D3 | semidirect |
| 84. #3832 | C2×D3 | semidirect |
| 85. #3832 | C2×D3 | semidirect |
| 86. Q8×C3⋊D3 | C2×D3 | semidirect |
| 87. #3828 | C2×D3 | semidirect |
| 88. C2×C4⋊(C3⋊D3) | C2×D3 | semidirect |
| 89. C2×C4×C3⋊D3 | C2×D3 | semidirect |
| 335. H(3,𝔽3) | #585 | semidirect |
| 439. C2×Q8 | ((C3⋊D3)⋊C3)⋊C2 | semidirect |
| 485. C32 | #5964 | semidirect |
| 486. C32 | #5968 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11722670 | 2 |
| #11722627 | 2 |
| C2×#88722 | 2 |
| #11722521 | 2 |
| #11722520 | 2 |
| #11722519 | 2 |
| #11722516 | 2 |
| #11722492 | 2 |
| #11722490 | 2 |
| #10596689 | 3 |
| #10596688 | 3 |