Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1736 conjugacy classes of subgroups.
The subgroup lattice has 590 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C3×#64367 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11724566 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11723991 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C32×#951 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11723586 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | C3⋊D3×#216 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #11723561 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #11723552 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #11723387 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | C2×#88798 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #11723354 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #10596250 | — | 3 | 1 | no | maximal |
| 13 | #10595465 | — | 3 | 4 | no | maximal |
| 14 | C33×#41 | C22 | 1 | 1 | yes | characteristic |
| 15 | #89076 | C22 | 1 | 1 | yes | characteristic |
| 16 | C3×Q8×C3⋊D3 | C22 | 1 | 2 | yes | — |
| 17 | C3×#3830 | — | 2 | 2 | no | — |
| 18 | C3×#3830 | C22 | 1 | 2 | yes | — |
| 19 | C3×#3828 | — | 2 | 1 | no | — |
| 20 | C3×#3828 | C22 | 1 | 1 | yes | characteristic |
| 21 | C2×C3×#634 | — | 2 | 1 | no | — |
| 22 | C2×C3×#634 | C22 | 1 | 1 | yes | characteristic |
| 23 | C2×C32×Dic6 | C22 | 1 | 1 | yes | characteristic |
| 24 | #89031 | — | 2 | 2 | no | — |
| 25 | #89019 | — | 2 | 1 | no | — |
| 26 | #89018 | C22 | 1 | 2 | yes | — |
| 27 | #89017 | — | 2 | 1 | no | — |
| 28 | C3⋊D3×Dic6 | C22 | 1 | 2 | yes | — |
| 29 | #88863 | C22 | 1 | 1 | yes | characteristic |
| 30 | #88862 | C22 | 1 | 1 | yes | characteristic |
| 31 | #88861 | C22 | 1 | 1 | yes | characteristic |
| 32 | #88860 | C22 | 1 | 1 | yes | characteristic |
| 33 | C2×C3⋊(C3⋊(C3⋊C8)) | C22 | 1 | 1 | yes | characteristic |
| 34 | C32×#216 | C22 | 1 | 2 | yes | — |
| 35 | C32×#214 | C22 | 1 | 2 | yes | — |
| 36 | C32×#208 | C22 | 1 | 1 | yes | characteristic |
| 37 | #88800 | C22 | 1 | 2 | yes | — |
| 38 | #88798 | C22 | 1 | 2 | yes | — |
| 39 | #88798 | C22 | 1 | 2 | yes | — |
| 40 | #88797 | C22 | 1 | 2 | yes | — |
| 41 | #88787 | C22 | 1 | 2 | yes | — |
| 42 | C3⋊D3×C3⋊C8 | C22 | 1 | 2 | yes | — |
| 43 | #64367 | D3 | 1 | 1 | yes | characteristic, complemented |
| 44 | #64364 | — | 3 | 1 | no | — |
| 45 | C3×#1010 | — | 3 | 4 | no | — |
| 46 | #64297 | — | 3 | 4 | no | — |
| 47 | C32×#137 | — | 3 | 1 | no | — |
| 48 | #64159 | — | 3 | 1 | no | — |
| 49 | #64159 | — | 3 | 4 | no | — |
| 50 | #64159 | — | 6 | 4 | no | — |
| 51 | C2×#3756 | — | 3 | 1 | no | — |
| 52 | #64127 | — | 3 | 2 | no | — |
| 53 | Q16×C3⋊D3 | — | 3 | 2 | no | — |
| 54 | #64125 | — | 3 | 2 | no | — |
| 55 | #64124 | — | 3 | 2 | no | — |
| 56 | #64118 | — | 3 | 1 | no | — |
| 57 | #64116 | — | 3 | 1 | no | — |
| 58 | C3×#951 | D3 | 1 | 4 | yes | complemented |
| 59 | #63948 | — | 3 | 8 | no | — |
| 60 | D3×#216 | — | 3 | 8 | no | — |
| 61 | #63935 | — | 3 | 8 | no | — |
| 62 | #63929 | — | 3 | 8 | no | — |
| 63 | C2×#3718 | — | 3 | 4 | no | — |
| 64 | #63833 | — | 3 | 4 | no | — |
| 65 | #63815 | — | 3 | 4 | no | — |
| 66 | C33×Q8 | C23 | 1 | 1 | yes | characteristic |
| 67 | C33×D4 | — | 2 | 1 | no | — |
| 68 | C33×D4 | C23 | 1 | 1 | yes | characteristic |
| 69 | C2×C33×C4 | — | 2 | 1 | no | — |
| 70 | C2×C33×C4 | C23 | 1 | 1 | yes | characteristic |
| 71 | #6312 | — | 2 | 1 | no | — |
| 72 | C4⋊(C3⋊(C3⋊D3)) | C23 | 1 | 1 | yes | characteristic |
| 73 | C4×C3⋊(C3⋊D3) | — | 2 | 1 | no | — |
| 74 | #6308 | C23 | 1 | 1 | yes | characteristic |
| 75 | C3×#638 | — | 2 | 2 | no | — |
| 76 | C3×#638 | D4 | 1 | 2 | yes | — |
| 77 | C2×C3×C3⋊Dic3 | — | 2 | 1 | no | — |
| 78 | C2×C3×C3⋊Dic3 | — | 2 | 2 | no | — |
| 79 | C3×C4⋊(C3⋊D3) | D4 | 1 | 1 | yes | characteristic |
| 80 | C3×C4×C3⋊D3 | — | 2 | 2 | no | — |
| 81 | C3×C4×C3⋊D3 | C23 | 1 | 2 | yes | — |
| 82 | C3×#634 | — | 2 | 1 | no | — |
| 83 | C3×#634 | — | 2 | 2 | no | — |
| 84 | C3×#634 | D4 | 1 | 1 | yes | characteristic |
| 85 | C3×#634 | C23 | 1 | 2 | yes | — |
| 86 | C2×C32×Dic3 | — | 2 | 1 | no | — |
| 87 | C32×Dic6 | — | 2 | 1 | no | — |
| 88 | C32×Dic6 | C23 | 1 | 2 | yes | — |
| 89 | #6293 | — | 2 | 2 | no | — |
| 90 | #6292 | — | 2 | 2 | no | — |
| 91 | #6289 | — | 2 | 2 | no | — |
| 92 | Dic3×C3⋊D3 | — | 2 | 2 | no | — |
| 93 | C3⋊(C3⋊(C3⋊C8)) | C23 | 1 | 1 | yes | characteristic |
| 94 | C3⋊(C3⋊(C3⋊C8)) | C23 | 1 | 1 | yes | characteristic |
| 95 | C32×C3⋊C8 | C23 | 1 | 2 | yes | — |
| 96 | #5838 | — | 9 | 1 | no | — |
| 97 | #5779 | — | 9 | 4 | no | — |
| 98 | C32×#41 | — | 2 | 4 | no | — |
| 99 | C32×#41 | C2×D3 | 1 | 4 | yes | — |
| 100 | C32×#41 | C2×D3 | 1 | 1 | yes | characteristic |
| 101 | C2×C32×Q8 | — | 3 | 1 | no | — |
| 102 | #3832 | — | 3 | 2 | no | — |
| 103 | #3832 | — | 6 | 1 | no | — |
| 104 | Q8×C3⋊D3 | — | 3 | 2 | no | — |
| 105 | Q8×C3⋊D3 | — | 6 | 1 | no | — |
| 106 | Q8×C3⋊D3 | C2×D3 | 1 | 2 | yes | — |
| 107 | #3830 | — | 2 | 2 | no | — |
| 108 | #3830 | C2×D3 | 1 | 2 | yes | — |
| 109 | #3828 | — | 2 | 1 | no | — |
| 110 | #3828 | — | 3 | 1 | no | — |
| 111 | #3828 | — | 3 | 4 | no | — |
| 112 | #3828 | — | 6 | 2 | no | — |
| 113 | #3828 | — | 6 | 4 | no | — |
| 114 | #3828 | C2×D3 | 1 | 1 | yes | characteristic |
| 115 | C2×#634 | — | 2 | 1 | no | — |
| 116 | C2×#634 | C2×D3 | 1 | 1 | yes | characteristic |
| 117 | C3×D3×Q8 | — | 3 | 8 | no | — |
| 118 | C3×#237 | — | 3 | 8 | no | — |
| 119 | C3×#237 | — | 6 | 8 | no | — |
| 120 | C3×#235 | — | 3 | 4 | no | — |
| 121 | C3×#235 | — | 6 | 4 | no | — |
| 122 | C2×C3×Dic6 | — | 3 | 4 | no | — |
| 123 | C2×C3×Dic6 | — | 6 | 4 | no | — |
| 124 | C2×C3×Dic6 | C2×D3 | 1 | 4 | yes | — |
| 125 | #3804 | — | 6 | 8 | no | — |
| 126 | #3799 | — | 3 | 8 | no | — |
| 127 | #3797 | — | 6 | 4 | no | — |
| 128 | #3796 | — | 6 | 4 | no | — |
| 129 | D3×Dic6 | — | 3 | 8 | no | — |
| 130 | C32×Q16 | — | 3 | 2 | no | — |
| 131 | C32×SD16 | — | 3 | 2 | no | — |
| 132 | C32×M16 | — | 3 | 1 | no | — |
| 133 | #3756 | — | 3 | 1 | no | — |
| 134 | #3756 | — | 3 | 4 | no | — |
| 135 | #3756 | — | 3 | 2 | no | — |
| 136 | #3756 | — | 3 | 2 | no | — |
| 137 | #3756 | — | 6 | 4 | no | — |
| 138 | #3755 | — | 3 | 1 | no | — |
| 139 | #3755 | — | 3 | 4 | no | — |
| 140 | #3755 | — | 6 | 4 | no | — |
| 141 | #3754 | — | 3 | 1 | no | — |
| 142 | #3754 | — | 3 | 4 | no | — |
| 143 | #3754 | — | 6 | 4 | no | — |
| 144 | #3753 | — | 3 | 1 | no | — |
| 145 | #3753 | — | 3 | 4 | no | — |
| 146 | #3753 | — | 6 | 4 | no | — |
| 147 | C2×C3⋊(C3⋊C8) | — | 3 | 1 | no | — |
| 148 | C2×C3⋊(C3⋊C8) | — | 3 | 4 | no | — |
| 149 | C2×C3⋊(C3⋊C8) | — | 6 | 4 | no | — |
| 150 | #3746 | — | 3 | 2 | no | — |
| 151 | #3744 | — | 3 | 2 | no | — |
| 152 | #3743 | — | 3 | 2 | no | — |
| 153 | C8×C3⋊D3 | — | 3 | 2 | no | — |
| 154 | C3×#216 | C2×D3 | 1 | 8 | yes | — |
| 155 | C3×#214 | C2×D3 | 1 | 8 | yes | — |
| 156 | C3×#208 | C2×D3 | 1 | 4 | yes | — |
| 157 | #3719 | — | 3 | 8 | no | — |
| 158 | #3718 | — | 3 | 8 | no | — |
| 159 | #3718 | — | 3 | 8 | no | — |
| 160 | #3717 | — | 3 | 8 | no | — |
| 161 | #3711 | — | 3 | 8 | no | — |
| 162 | D3×C3⋊C8 | — | 3 | 8 | no | — |
| 163 | C22×C33 | — | 2 | 1 | no | — |
| 164 | C22×C33 | C2×D4 | 1 | 1 | yes | characteristic |
| 165 | C2×C3⋊(C3⋊D3) | — | 2 | 1 | no | — |
| 166 | C2×C3×C3⋊D3 | C2×D4 | 1 | 2 | yes | — |
| 167 | C33×C4 | — | 2 | 1 | no | — |
| 168 | C33×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 169 | C33×C4 | C24 | 1 | 1 | yes | characteristic |
| 170 | C3⋊(C3⋊Dic3) | — | 2 | 1 | no | — |
| 171 | C3×C3⋊Dic3 | — | 2 | 2 | no | — |
| 172 | C3×C3⋊Dic3 | C2×D4 | 1 | 2 | yes | — |
| 173 | C32×Dic3 | — | 2 | 2 | no | — |
| 174 | C3×2−1+4 | — | 9 | 1 | no | — |
| 175 | #1010 | — | 3 | 4 | no | — |
| 176 | #1010 | — | 9 | 1 | no | — |
| 177 | #1007 | — | 9 | 4 | no | — |
| 178 | C3×#137 | — | 3 | 4 | no | — |
| 179 | #951 | — | 9 | 2 | no | — |
| 180 | #951 | C3⋊D3 | 1 | 1 | yes | characteristic, complemented |
| 181 | #950 | — | 9 | 4 | no | — |
| 182 | #950 | — | 9 | 1 | no | — |
| 183 | #950 | — | 9 | 2 | no | — |
| 184 | #950 | — | 18 | 4 | no | — |
| 185 | #948 | — | 9 | 1 | no | — |
| 186 | C2×#216 | — | 9 | 4 | no | — |
| 187 | C2×#216 | — | 9 | 1 | no | — |
| 188 | C2×#216 | — | 9 | 2 | no | — |
| 189 | #942 | — | 9 | 2 | no | — |
| 190 | #942 | — | 9 | 1 | no | — |
| 191 | #918 | — | 9 | 8 | no | — |
| 192 | D3×Q16 | — | 9 | 8 | no | — |
| 193 | #916 | — | 9 | 8 | no | — |
| 194 | #915 | — | 9 | 8 | no | — |
| 195 | #909 | — | 9 | 4 | no | — |
| 196 | #907 | — | 9 | 4 | no | — |
| 197 | C32×Q8 | — | 2 | 4 | no | — |
| 198 | C32×Q8 | — | 3 | 2 | no | — |
| 199 | C32×Q8 | — | 6 | 1 | no | — |
| 200 | C32×Q8 | C22×D3 | 1 | 4 | yes | — |
| 201 | C32×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 202 | C32×D4 | — | 2 | 1 | no | — |
| 203 | C32×D4 | — | 2 | 4 | no | — |
| 204 | C32×D4 | — | 2 | 4 | no | — |
| 205 | C32×D4 | — | 4 | 4 | no | — |
| 206 | C32×D4 | C22×D3 | 1 | 4 | yes | — |
| 207 | C32×D4 | C22×D3 | 1 | 1 | yes | characteristic |
| 208 | C2×C32×C4 | — | 2 | 1 | no | — |
| 209 | C2×C32×C4 | — | 2 | 4 | no | — |
| 210 | C2×C32×C4 | — | 2 | 4 | no | — |
| 211 | C2×C32×C4 | — | 4 | 4 | no | — |
| 212 | C2×C32×C4 | — | 6 | 1 | no | — |
| 213 | C2×C32×C4 | C22×D3 | 1 | 4 | yes | — |
| 214 | C2×C32×C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 215 | #638 | — | 2 | 2 | no | — |
| 216 | #638 | — | 6 | 1 | no | — |
| 217 | #638 | — | 6 | 4 | no | — |
| 218 | #638 | — | 12 | 4 | no | — |
| 219 | #638 | #67 | 1 | 2 | yes | — |
| 220 | C2×C3⋊Dic3 | — | 2 | 1 | no | — |
| 221 | C2×C3⋊Dic3 | — | 2 | 2 | no | — |
| 222 | C4⋊(C3⋊D3) | — | 3 | 1 | no | — |
| 223 | C4⋊(C3⋊D3) | — | 3 | 4 | no | — |
| 224 | C4⋊(C3⋊D3) | — | 6 | 4 | no | — |
| 225 | C4⋊(C3⋊D3) | — | 6 | 2 | no | — |
| 226 | C4⋊(C3⋊D3) | #67 | 1 | 1 | yes | characteristic |
| 227 | C4×C3⋊D3 | — | 2 | 2 | no | — |
| 228 | C4×C3⋊D3 | — | 6 | 2 | no | — |
| 229 | C4×C3⋊D3 | — | 6 | 1 | no | — |
| 230 | C4×C3⋊D3 | — | 6 | 2 | no | — |
| 231 | C4×C3⋊D3 | — | 6 | 4 | no | — |
| 232 | C4×C3⋊D3 | — | 12 | 4 | no | — |
| 233 | C4×C3⋊D3 | C22×D3 | 1 | 2 | yes | — |
| 234 | #634 | — | 2 | 1 | no | — |
| 235 | #634 | — | 2 | 2 | no | — |
| 236 | #634 | — | 3 | 1 | no | — |
| 237 | #634 | — | 3 | 4 | no | — |
| 238 | #634 | — | 6 | 4 | no | — |
| 239 | #634 | — | 6 | 2 | no | — |
| 240 | #634 | #67 | 1 | 1 | yes | characteristic |
| 241 | #634 | C22×D3 | 1 | 2 | yes | — |
| 242 | C3×#67 | — | 3 | 8 | no | — |
| 243 | C3×#67 | — | 6 | 8 | no | — |
| 244 | C2×C3×Dic3 | — | 2 | 4 | no | — |
| 245 | C2×C3×Dic3 | — | 6 | 8 | no | — |
| 246 | C2×C3×Dic3 | — | 6 | 4 | no | — |
| 247 | C3×D12 | — | 3 | 4 | no | — |
| 248 | C3×C4×D3 | — | 3 | 8 | no | — |
| 249 | C3×C4×D3 | — | 6 | 8 | no | — |
| 250 | C3×Dic6 | — | 2 | 4 | no | — |
| 251 | C3×Dic6 | — | 3 | 4 | no | — |
| 252 | C3×Dic6 | — | 3 | 8 | no | — |
| 253 | C3×Dic6 | — | 6 | 8 | no | — |
| 254 | C3×Dic6 | — | 6 | 4 | no | — |
| 255 | C3×Dic6 | C22×D3 | 1 | 8 | yes | — |
| 256 | #627 | — | 6 | 8 | no | — |
| 257 | #626 | — | 6 | 8 | no | — |
| 258 | #624 | — | 6 | 8 | no | — |
| 259 | D3×Dic3 | — | 6 | 8 | no | — |
| 260 | C32×C8 | — | 3 | 2 | no | — |
| 261 | C3⋊(C3⋊C8) | — | 3 | 1 | no | — |
| 262 | C3⋊(C3⋊C8) | — | 3 | 1 | no | — |
| 263 | C3⋊(C3⋊C8) | — | 3 | 4 | no | — |
| 264 | C3⋊(C3⋊C8) | — | 3 | 4 | no | — |
| 265 | C3⋊(C3⋊C8) | — | 6 | 4 | no | — |
| 266 | C3⋊(C3⋊C8) | — | 6 | 4 | no | — |
| 267 | C3×C3⋊C8 | C22×D3 | 1 | 8 | yes | — |
| 268 | #578 | — | 27 | 1 | no | Sylow |
| 269 | C2×C33 | — | 2 | 1 | no | — |
| 270 | C2×C33 | — | 4 | 1 | no | — |
| 271 | C2×C33 | C22×D4 | 1 | 1 | yes | characteristic |
| 272 | C3⋊(C3⋊D3) | — | 4 | 1 | no | — |
| 273 | C3×C3⋊D3 | — | 2 | 2 | no | — |
| 274 | C3×#41 | — | 2 | 4 | no | — |
| 275 | C3×#41 | — | 9 | 1 | no | — |
| 276 | C3×#41 | — | 9 | 2 | no | — |
| 277 | C3×#41 | — | 18 | 1 | no | — |
| 278 | C3×#41 | — | 18 | 2 | no | — |
| 279 | C3×#41 | D32 | 1 | 4 | yes | — |
| 280 | C3×#41 | C2×C3⋊D3 | 1 | 1 | yes | characteristic |
| 281 | C2×C3×Q8 | — | 3 | 4 | no | — |
| 282 | C2×C3×Q8 | — | 9 | 2 | no | — |
| 283 | C2×C3×Q8 | — | 9 | 1 | no | — |
| 284 | C2×C3×Q8 | — | 18 | 1 | no | — |
| 285 | #239 | — | 9 | 8 | no | — |
| 286 | #239 | — | 18 | 4 | no | — |
| 287 | D3×Q8 | — | 3 | 8 | no | — |
| 288 | D3×Q8 | — | 9 | 8 | no | — |
| 289 | D3×Q8 | — | 18 | 1 | no | — |
| 290 | D3×Q8 | — | 18 | 4 | no | — |
| 291 | #237 | — | 3 | 8 | no | — |
| 292 | #237 | — | 6 | 8 | no | — |
| 293 | #237 | — | 18 | 1 | no | — |
| 294 | #237 | — | 18 | 2 | no | — |
| 295 | #235 | — | 3 | 4 | no | — |
| 296 | #235 | — | 6 | 4 | no | — |
| 297 | #235 | — | 9 | 4 | no | — |
| 298 | #235 | — | 9 | 1 | no | — |
| 299 | #235 | — | 9 | 2 | no | — |
| 300 | #235 | — | 18 | 4 | no | — |
| 301 | #235 | — | 18 | 8 | no | — |
| 302 | C2×Dic6 | — | 3 | 4 | no | — |
| 303 | C2×Dic6 | — | 6 | 4 | no | — |
| 304 | C2×Dic6 | — | 9 | 2 | no | — |
| 305 | C2×Dic6 | C2×C3⋊D3 | 1 | 1 | yes | characteristic |
| 306 | C3×Q16 | — | 3 | 8 | no | — |
| 307 | C3×SD16 | — | 3 | 8 | no | — |
| 308 | C3×M16 | — | 3 | 4 | no | — |
| 309 | #216 | — | 9 | 8 | no | — |
| 310 | #216 | — | 9 | 8 | no | — |
| 311 | #216 | — | 9 | 4 | no | — |
| 312 | #216 | — | 9 | 1 | no | — |
| 313 | #216 | — | 9 | 2 | no | — |
| 314 | #216 | — | 9 | 2 | no | — |
| 315 | #216 | — | 9 | 2 | no | — |
| 316 | #216 | — | 18 | 4 | no | — |
| 317 | #216 | C2×C3⋊D3 | 1 | 2 | yes | — |
| 318 | #215 | — | 9 | 4 | no | — |
| 319 | #215 | — | 9 | 1 | no | — |
| 320 | #215 | — | 9 | 2 | no | — |
| 321 | #215 | — | 18 | 4 | no | — |
| 322 | #214 | — | 9 | 4 | no | — |
| 323 | #214 | — | 9 | 1 | no | — |
| 324 | #214 | — | 18 | 4 | no | — |
| 325 | #214 | C2×C3⋊D3 | 1 | 2 | yes | — |
| 326 | #213 | — | 9 | 4 | no | — |
| 327 | #213 | — | 9 | 1 | no | — |
| 328 | #213 | — | 18 | 4 | no | — |
| 329 | #208 | — | 9 | 2 | no | — |
| 330 | #208 | C2×C3⋊D3 | 1 | 1 | yes | characteristic |
| 331 | C2×C3⋊C8 | — | 9 | 4 | no | — |
| 332 | C2×C3⋊C8 | — | 9 | 1 | no | — |
| 333 | C2×C3⋊C8 | — | 9 | 2 | no | — |
| 334 | C2×C3⋊C8 | — | 18 | 4 | no | — |
| 335 | Dic12 | — | 9 | 8 | no | — |
| 336 | #204 | — | 9 | 8 | no | — |
| 337 | ΓL(1,𝔽25) | — | 9 | 8 | no | — |
| 338 | D3×C8 | — | 9 | 8 | no | — |
| 339 | C22×C32 | — | 2 | 1 | no | — |
| 340 | C22×C32 | — | 2 | 4 | no | — |
| 341 | C22×C32 | — | 2 | 4 | no | — |
| 342 | C22×C32 | — | 4 | 4 | no | — |
| 343 | C22×C32 | D3×D4 | 1 | 4 | yes | — |
| 344 | C22×C32 | C2×#67 | 1 | 1 | yes | characteristic |
| 345 | C2×C3⋊D3 | — | 6 | 1 | no | — |
| 346 | C2×C3⋊D3 | — | 6 | 4 | no | — |
| 347 | C2×C3⋊D3 | — | 12 | 4 | no | — |
| 348 | C2×C3⋊D3 | C2×#67 | 1 | 2 | yes | — |
| 349 | C2×C3×D3 | — | 3 | 8 | no | — |
| 350 | C32×C4 | — | 2 | 1 | no | — |
| 351 | C32×C4 | — | 2 | 4 | no | — |
| 352 | C32×C4 | — | 2 | 4 | no | — |
| 353 | C32×C4 | — | 2 | 4 | no | — |
| 354 | C32×C4 | — | 4 | 4 | no | — |
| 355 | C32×C4 | — | 6 | 2 | no | — |
| 356 | C32×C4 | D3×D4 | 1 | 4 | yes | — |
| 357 | C32×C4 | C2×#67 | 1 | 1 | yes | characteristic |
| 358 | C32×C4 | C23×D3 | 1 | 4 | yes | — |
| 359 | C32×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 360 | C3⋊Dic3 | — | 2 | 2 | no | — |
| 361 | C3⋊Dic3 | — | 6 | 1 | no | — |
| 362 | C3⋊Dic3 | — | 6 | 4 | no | — |
| 363 | C3⋊Dic3 | — | 12 | 4 | no | — |
| 364 | C3⋊Dic3 | C2×#67 | 1 | 2 | yes | — |
| 365 | C3×Dic3 | — | 2 | 8 | no | — |
| 366 | C3×Dic3 | — | 3 | 8 | no | — |
| 367 | C3×Dic3 | — | 6 | 8 | no | — |
| 368 | 2−1+4 | — | 9 | 1 | no | — |
| 369 | 2−1+4 | — | 27 | 1 | no | — |
| 370 | #137 | — | 3 | 1 | no | — |
| 371 | #137 | — | 27 | 1 | no | — |
| 372 | #137 | — | 27 | 2 | no | — |
| 373 | #137 | — | 27 | 2 | no | — |
| 374 | #135 | — | 27 | 2 | no | — |
| 375 | #135 | — | 27 | 1 | no | — |
| 376 | C2×Q16 | — | 27 | 2 | no | — |
| 377 | C2×Q16 | — | 27 | 1 | no | — |
| 378 | #131 | — | 27 | 1 | no | — |
| 379 | C33 | #578 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 380 | C3×Q8 | — | 2 | 4 | no | — |
| 381 | C3×Q8 | — | 3 | 8 | no | — |
| 382 | C3×Q8 | — | 6 | 4 | no | — |
| 383 | C3×Q8 | — | 9 | 1 | no | — |
| 384 | C3×Q8 | — | 9 | 2 | no | — |
| 385 | C3×Q8 | — | 18 | 2 | no | — |
| 386 | C3×Q8 | — | 18 | 1 | no | — |
| 387 | C3×Q8 | C2×D32 | 1 | 4 | yes | — |
| 388 | C3×Q8 | C22×C3⋊D3 | 1 | 1 | yes | characteristic |
| 389 | C3×D4 | — | 2 | 4 | no | — |
| 390 | C3×D4 | — | 2 | 1 | no | — |
| 391 | C3×D4 | — | 2 | 4 | no | — |
| 392 | C3×D4 | — | 4 | 4 | no | — |
| 393 | C3×D4 | — | 9 | 2 | no | — |
| 394 | C3×D4 | — | 9 | 1 | no | — |
| 395 | C3×D4 | — | 18 | 2 | no | — |
| 396 | C3×D4 | C2×D32 | 1 | 4 | yes | — |
| 397 | C3×D4 | C22×C3⋊D3 | 1 | 1 | yes | characteristic |
| 398 | C2×C3×C4 | — | 2 | 4 | no | — |
| 399 | C2×C3×C4 | — | 2 | 1 | no | — |
| 400 | C2×C3×C4 | — | 2 | 4 | no | — |
| 401 | C2×C3×C4 | — | 4 | 4 | no | — |
| 402 | C2×C3×C4 | — | 6 | 4 | no | — |
| 403 | C2×C3×C4 | — | 9 | 2 | no | — |
| 404 | C2×C3×C4 | — | 18 | 2 | no | — |
| 405 | C2×C3×C4 | — | 18 | 2 | no | — |
| 406 | C2×C3×C4 | — | 18 | 1 | no | — |
| 407 | C2×C3×C4 | C2×D32 | 1 | 4 | yes | — |
| 408 | C2×C3×C4 | C22×C3⋊D3 | 1 | 1 | yes | characteristic |
| 409 | #67 | — | 3 | 8 | no | — |
| 410 | #67 | — | 6 | 8 | no | — |
| 411 | #67 | — | 18 | 2 | no | — |
| 412 | #67 | — | 18 | 4 | no | — |
| 413 | #67 | — | 18 | 1 | no | — |
| 414 | #67 | — | 36 | 4 | no | — |
| 415 | C2×Dic3 | — | 2 | 1 | no | — |
| 416 | C2×Dic3 | — | 6 | 8 | no | — |
| 417 | C2×Dic3 | — | 6 | 4 | no | — |
| 418 | C2×Dic3 | — | 18 | 2 | no | — |
| 419 | D12 | — | 3 | 4 | no | — |
| 420 | D12 | — | 9 | 4 | no | — |
| 421 | D12 | — | 9 | 1 | no | — |
| 422 | D12 | — | 18 | 4 | no | — |
| 423 | D12 | — | 18 | 8 | no | — |
| 424 | C4×D3 | — | 3 | 8 | no | — |
| 425 | C4×D3 | — | 6 | 8 | no | — |
| 426 | C4×D3 | — | 18 | 2 | no | — |
| 427 | C4×D3 | — | 18 | 8 | no | — |
| 428 | C4×D3 | — | 18 | 8 | no | — |
| 429 | C4×D3 | — | 18 | 4 | no | — |
| 430 | C4×D3 | — | 18 | 1 | no | — |
| 431 | C4×D3 | — | 36 | 4 | no | — |
| 432 | Dic6 | — | 2 | 1 | no | — |
| 433 | Dic6 | — | 3 | 4 | no | — |
| 434 | Dic6 | — | 3 | 8 | no | — |
| 435 | Dic6 | — | 6 | 8 | no | — |
| 436 | Dic6 | — | 6 | 4 | no | — |
| 437 | Dic6 | — | 9 | 4 | no | — |
| 438 | Dic6 | — | 9 | 1 | no | — |
| 439 | Dic6 | — | 18 | 4 | no | — |
| 440 | Dic6 | — | 18 | 2 | no | — |
| 441 | Dic6 | — | 18 | 8 | no | — |
| 442 | Dic6 | C22×C3⋊D3 | 1 | 2 | yes | — |
| 443 | C3×C8 | — | 3 | 8 | no | — |
| 444 | C3⋊C8 | — | 9 | 4 | no | — |
| 445 | C3⋊C8 | — | 9 | 4 | no | — |
| 446 | C3⋊C8 | — | 9 | 1 | no | — |
| 447 | C3⋊C8 | — | 9 | 1 | no | — |
| 448 | C3⋊C8 | — | 18 | 4 | no | — |
| 449 | C3⋊C8 | — | 18 | 4 | no | — |
| 450 | C3⋊C8 | C22×C3⋊D3 | 1 | 2 | yes | — |
| 451 | C2×C32 | — | 2 | 1 | no | — |
| 452 | C2×C32 | — | 2 | 4 | no | — |
| 453 | C2×C32 | — | 2 | 4 | no | — |
| 454 | C2×C32 | — | 4 | 4 | no | — |
| 455 | C2×C32 | — | 4 | 1 | no | — |
| 456 | C2×C32 | — | 4 | 4 | no | — |
| 457 | C2×C32 | — | 8 | 4 | no | — |
| 458 | C2×C32 | C2×D3×D4 | 1 | 4 | yes | — |
| 459 | C2×C32 | C22×#67 | 1 | 1 | yes | characteristic |
| 460 | C3⋊D3 | — | 2 | 2 | no | — |
| 461 | C3⋊D3 | — | 12 | 1 | no | — |
| 462 | C3⋊D3 | — | 12 | 4 | no | — |
| 463 | C3⋊D3 | — | 24 | 4 | no | — |
| 464 | C3×D3 | — | 6 | 8 | no | — |
| 465 | #41 | — | 9 | 1 | no | — |
| 466 | #41 | — | 9 | 2 | no | — |
| 467 | #41 | — | 18 | 1 | no | — |
| 468 | #41 | — | 18 | 2 | no | — |
| 469 | #41 | — | 27 | 2 | no | — |
| 470 | #41 | — | 27 | 1 | no | — |
| 471 | #41 | — | 54 | 2 | no | — |
| 472 | #41 | — | 54 | 1 | no | — |
| 473 | #41 | D3×C3⋊D3 | 1 | 1 | yes | characteristic |
| 474 | C2×Q8 | — | 3 | 1 | no | — |
| 475 | C2×Q8 | — | 9 | 2 | no | — |
| 476 | C2×Q8 | — | 9 | 1 | no | — |
| 477 | C2×Q8 | — | 18 | 1 | no | — |
| 478 | C2×Q8 | — | 27 | 2 | no | — |
| 479 | C2×Q8 | — | 54 | 1 | no | — |
| 480 | Q16 | — | 3 | 2 | no | — |
| 481 | Q16 | — | 27 | 2 | no | — |
| 482 | Q16 | — | 27 | 2 | no | — |
| 483 | Q16 | — | 27 | 2 | no | — |
| 484 | Q16 | — | 27 | 1 | no | — |
| 485 | SD16 | — | 3 | 2 | no | — |
| 486 | SD16 | — | 27 | 2 | no | — |
| 487 | SD16 | — | 27 | 1 | no | — |
| 488 | SD16 | — | 27 | 1 | no | — |
| 489 | D8 | — | 27 | 1 | no | — |
| 490 | M16 | — | 3 | 1 | no | — |
| 491 | M16 | — | 27 | 2 | no | — |
| 492 | C2×C8 | — | 27 | 2 | no | — |
| 493 | C2×C8 | — | 27 | 1 | no | — |
| 494 | C22×C3 | — | 2 | 4 | no | — |
| 495 | C22×C3 | — | 2 | 1 | no | — |
| 496 | C22×C3 | — | 2 | 4 | no | — |
| 497 | C22×C3 | — | 4 | 4 | no | — |
| 498 | C22×C3 | — | 9 | 2 | no | — |
| 499 | C22×C3 | D3×#67 | 1 | 4 | yes | — |
| 500 | C22×C3 | D4×C3⋊D3 | 1 | 1 | yes | characteristic |
| 501 | C2×D3 | — | 3 | 8 | no | — |
| 502 | C2×D3 | — | 18 | 4 | no | — |
| 503 | C2×D3 | — | 18 | 1 | no | — |
| 504 | C2×D3 | — | 36 | 4 | no | — |
| 505 | C3×C4 | — | 2 | 4 | no | — |
| 506 | C3×C4 | — | 2 | 1 | no | — |
| 507 | C3×C4 | — | 2 | 4 | no | — |
| 508 | C3×C4 | — | 2 | 4 | no | — |
| 509 | C3×C4 | — | 4 | 4 | no | — |
| 510 | C3×C4 | — | 6 | 8 | no | — |
| 511 | C3×C4 | — | 9 | 2 | no | — |
| 512 | C3×C4 | — | 18 | 2 | no | — |
| 513 | C3×C4 | D3×#67 | 1 | 4 | yes | — |
| 514 | C3×C4 | D4×C3⋊D3 | 1 | 1 | yes | characteristic |
| 515 | C3×C4 | C22×D32 | 1 | 4 | yes | — |
| 516 | C3×C4 | C23×C3⋊D3 | 1 | 1 | yes | characteristic |
| 517 | Dic3 | — | 2 | 2 | no | — |
| 518 | Dic3 | — | 3 | 8 | no | — |
| 519 | Dic3 | — | 6 | 8 | no | — |
| 520 | Dic3 | — | 18 | 4 | no | — |
| 521 | Dic3 | — | 18 | 1 | no | — |
| 522 | Dic3 | — | 36 | 4 | no | — |
| 523 | C32 | — | 2 | 4 | no | — |
| 524 | C32 | #5779 | 1 | 4 | yes | complemented |
| 525 | C32 | #5838 | 1 | 1 | yes | characteristic, complemented |
| 526 | Q8 | — | 3 | 2 | no | — |
| 527 | Q8 | — | 6 | 1 | no | — |
| 528 | Q8 | — | 9 | 1 | no | — |
| 529 | Q8 | — | 9 | 2 | no | — |
| 530 | Q8 | — | 18 | 2 | no | — |
| 531 | Q8 | — | 18 | 1 | no | — |
| 532 | Q8 | — | 27 | 1 | no | — |
| 533 | Q8 | — | 54 | 2 | no | — |
| 534 | Q8 | C2×D3×C3⋊D3 | 1 | 1 | yes | characteristic |
| 535 | D4 | — | 2 | 1 | no | — |
| 536 | D4 | — | 9 | 2 | no | — |
| 537 | D4 | — | 9 | 1 | no | — |
| 538 | D4 | — | 18 | 2 | no | — |
| 539 | D4 | — | 27 | 1 | no | — |
| 540 | D4 | — | 54 | 2 | no | — |
| 541 | D4 | — | 54 | 1 | no | — |
| 542 | D4 | C2×D3×C3⋊D3 | 1 | 1 | yes | characteristic |
| 543 | C2×C4 | — | 2 | 1 | no | — |
| 544 | C2×C4 | — | 6 | 1 | no | — |
| 545 | C2×C4 | — | 9 | 2 | no | — |
| 546 | C2×C4 | — | 18 | 2 | no | — |
| 547 | C2×C4 | — | 18 | 2 | no | — |
| 548 | C2×C4 | — | 18 | 1 | no | — |
| 549 | C2×C4 | — | 54 | 2 | no | — |
| 550 | C2×C4 | — | 54 | 2 | no | — |
| 551 | C2×C4 | — | 54 | 1 | no | — |
| 552 | C2×C4 | C2×D3×C3⋊D3 | 1 | 1 | yes | characteristic |
| 553 | C8 | — | 3 | 2 | no | — |
| 554 | C8 | — | 27 | 1 | no | — |
| 555 | C8 | — | 27 | 1 | no | — |
| 556 | C2×C3 | — | 2 | 4 | no | — |
| 557 | C2×C3 | — | 2 | 1 | no | — |
| 558 | C2×C3 | — | 2 | 4 | no | — |
| 559 | C2×C3 | — | 4 | 4 | no | — |
| 560 | C2×C3 | — | 4 | 4 | no | — |
| 561 | C2×C3 | — | 4 | 1 | no | — |
| 562 | C2×C3 | — | 8 | 4 | no | — |
| 563 | C2×C3 | — | 18 | 2 | no | — |
| 564 | C2×C3 | C2×D3×#67 | 1 | 4 | yes | — |
| 565 | C2×C3 | C2×D4×C3⋊D3 | 1 | 1 | yes | characteristic |
| 566 | D3 | — | 6 | 8 | no | — |
| 567 | D3 | — | 36 | 4 | no | — |
| 568 | D3 | — | 36 | 1 | no | — |
| 569 | D3 | — | 72 | 4 | no | — |
| 570 | C22 | — | 2 | 1 | no | — |
| 571 | C22 | — | 9 | 2 | no | — |
| 572 | C22 | — | 54 | 1 | no | — |
| 573 | C22 | C3⋊D3×#67 | 1 | 1 | yes | characteristic |
| 574 | C4 | — | 2 | 1 | no | — |
| 575 | C4 | — | 6 | 2 | no | — |
| 576 | C4 | — | 9 | 2 | no | — |
| 577 | C4 | — | 18 | 2 | no | — |
| 578 | C4 | — | 54 | 1 | no | — |
| 579 | C4 | C3⋊D3×#67 | 1 | 1 | yes | characteristic |
| 580 | C4 | C22×D3×C3⋊D3 | 1 | 1 | yes | characteristic |
| 581 | C3 | — | 2 | 4 | no | — |
| 582 | C3 | #10595465 | 1 | 4 | yes | complemented |
| 583 | C3 | #10596250 | 1 | 1 | yes | characteristic, complemented |
| 584 | C2 | — | 2 | 1 | no | — |
| 585 | C2 | — | 4 | 1 | no | — |
| 586 | C2 | — | 18 | 2 | no | — |
| 587 | C2 | — | 108 | 1 | no | — |
| 588 | C2 | C2×C3⋊D3×#67 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×#64367 | C2 | semidirect |
| 2. #11724566 | C2 | semidirect |
| 3. #11723991 | C2 | semidirect |
| 4. C32×#951 | C2 | semidirect |
| 5. #11723586 | C2 | semidirect |
| 6. C3⋊D3×#216 | C2 | semidirect |
| 7. #11723561 | C2 | semidirect |
| 8. #11723552 | C2 | semidirect |
| 9. #11723387 | C2 | semidirect |
| 10. C2×#88798 | C2 | semidirect |
| 11. #11723354 | C2 | semidirect |
| 43. #64367 | D3 | semidirect |
| 58. C3×#951 | D3 | semidirect |
| 180. #951 | C3⋊D3 | semidirect |
| 379. C33 | #578 | semidirect |
| 524. C32 | #5779 | semidirect |
| 525. C32 | #5838 | semidirect |
| 582. C3 | #10595465 | semidirect |
| 583. C3 | #10596250 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#64367 | 2 |
| #11724566 | 2 |
| #11723991 | 2 |
| C32×#951 | 2 |
| #11723586 | 2 |
| C3⋊D3×#216 | 2 |
| #11723561 | 2 |
| #11723552 | 2 |
| #11723387 | 2 |
| C2×#88798 | 2 |
| #11723354 | 2 |
| #10596250 | 3 |
| #10595465 | 3 |