Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1736 conjugacy classes of subgroups.
The subgroup lattice has 542 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #11724582 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #11723953 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C3×#64121 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C32×#912 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11723554 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #11723552 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #11723550 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #11723331 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #11723330 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | C3⋊D3×Dic12 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | D3×#3746 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #10596242 | — | 3 | 1 | no | maximal |
| 13 | #10594737 | — | 3 | 4 | no | maximal |
| 14 | #89078 | C22 | 1 | 2 | yes | — |
| 15 | C3×#3830 | C22 | 1 | 2 | yes | — |
| 16 | C32×#237 | C22 | 1 | 2 | yes | — |
| 17 | C2×#6293 | — | 2 | 2 | no | — |
| 18 | #89031 | — | 2 | 2 | no | — |
| 19 | #89029 | — | 2 | 2 | no | — |
| 20 | #89028 | — | 2 | 2 | no | — |
| 21 | #89020 | C22 | 1 | 1 | yes | characteristic |
| 22 | #89019 | C22 | 1 | 2 | yes | — |
| 23 | C3⋊D3×Dic6 | C22 | 1 | 2 | yes | — |
| 24 | D3×#634 | C22 | 1 | 2 | yes | — |
| 25 | C33×D8 | C22 | 1 | 1 | yes | characteristic |
| 26 | #88861 | C22 | 1 | 2 | yes | — |
| 27 | #88853 | C22 | 1 | 1 | yes | characteristic |
| 28 | C8×C3⋊(C3⋊D3) | C22 | 1 | 1 | yes | characteristic |
| 29 | C3×#3754 | C22 | 1 | 2 | yes | — |
| 30 | C3×#3746 | C22 | 1 | 1 | yes | characteristic |
| 31 | C3×C8×C3⋊D3 | C22 | 1 | 1 | yes | characteristic |
| 32 | C32×#214 | C22 | 1 | 2 | yes | — |
| 33 | C32×Dic12 | C22 | 1 | 1 | yes | characteristic |
| 34 | C32×D3×C8 | C22 | 1 | 1 | yes | characteristic |
| 35 | #88800 | C22 | 1 | 2 | yes | — |
| 36 | #88799 | C22 | 1 | 2 | yes | — |
| 37 | #88798 | C22 | 1 | 2 | yes | — |
| 38 | #88788 | C22 | 1 | 1 | yes | characteristic |
| 39 | #88787 | C22 | 1 | 1 | yes | characteristic |
| 40 | #88786 | C22 | 1 | 1 | yes | characteristic |
| 41 | #64367 | — | 3 | 2 | no | — |
| 42 | #64309 | — | 3 | 8 | no | — |
| 43 | C32×#135 | — | 3 | 1 | no | — |
| 44 | #64160 | — | 3 | 2 | no | — |
| 45 | Q16×C3⋊D3 | — | 3 | 1 | no | — |
| 46 | Q16×C3⋊D3 | — | 3 | 1 | no | — |
| 47 | #64124 | — | 3 | 2 | no | — |
| 48 | #64124 | — | 3 | 2 | no | — |
| 49 | #64121 | — | 3 | 1 | no | — |
| 50 | #64121 | — | 3 | 4 | no | — |
| 51 | #64121 | — | 6 | 4 | no | — |
| 52 | #64121 | D3 | 1 | 1 | yes | characteristic, complemented |
| 53 | C2×#3746 | — | 3 | 1 | no | — |
| 54 | #64110 | — | 3 | 1 | no | — |
| 55 | C3×#912 | — | 3 | 4 | no | — |
| 56 | C3×#912 | D3 | 1 | 4 | yes | complemented |
| 57 | #63931 | — | 3 | 8 | no | — |
| 58 | #63929 | — | 3 | 8 | no | — |
| 59 | #63929 | — | 3 | 8 | no | — |
| 60 | #63803 | — | 3 | 4 | no | — |
| 61 | #63802 | — | 3 | 4 | no | — |
| 62 | D3×Dic12 | — | 3 | 4 | no | — |
| 63 | D3×Dic12 | — | 3 | 4 | no | — |
| 64 | C33×D4 | C23 | 1 | 2 | yes | — |
| 65 | #6312 | — | 2 | 2 | no | — |
| 66 | C2×C3⋊(C3⋊Dic3) | — | 2 | 2 | no | — |
| 67 | C4×C3⋊(C3⋊D3) | C23 | 1 | 1 | yes | characteristic |
| 68 | #6308 | C23 | 1 | 2 | yes | — |
| 69 | C3×#638 | — | 2 | 2 | no | — |
| 70 | C2×C3×C3⋊Dic3 | — | 2 | 2 | no | — |
| 71 | C3×C4×C3⋊D3 | C23 | 1 | 1 | yes | characteristic |
| 72 | C3×#634 | C23 | 1 | 2 | yes | — |
| 73 | C32×#67 | — | 2 | 2 | no | — |
| 74 | C2×C32×Dic3 | — | 2 | 2 | no | — |
| 75 | C32×C4×D3 | C23 | 1 | 1 | yes | characteristic |
| 76 | C32×Dic6 | C23 | 1 | 2 | yes | — |
| 77 | #6293 | — | 2 | 2 | no | — |
| 78 | #6293 | — | 2 | 2 | no | — |
| 79 | #6293 | — | 2 | 2 | no | — |
| 80 | #6293 | D4 | 1 | 1 | yes | characteristic |
| 81 | #6292 | D4 | 1 | 1 | yes | characteristic |
| 82 | #6291 | D4 | 1 | 1 | yes | characteristic |
| 83 | #6290 | D4 | 1 | 1 | yes | characteristic |
| 84 | #6289 | — | 2 | 2 | no | — |
| 85 | Dic3×C3⋊D3 | — | 2 | 2 | no | — |
| 86 | D3×C3⋊Dic3 | — | 2 | 2 | no | — |
| 87 | C33×C8 | C23 | 1 | 1 | yes | characteristic |
| 88 | C3⋊(C3⋊(C3⋊C8)) | C23 | 1 | 1 | yes | characteristic |
| 89 | C3×C3⋊(C3⋊C8) | C23 | 1 | 1 | yes | characteristic |
| 90 | C32×C3⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 91 | #5771 | — | 9 | 4 | no | — |
| 92 | #5771 | — | 9 | 1 | no | — |
| 93 | C32×#41 | — | 3 | 2 | no | — |
| 94 | Q8×C3⋊D3 | — | 3 | 2 | no | — |
| 95 | Q8×C3⋊D3 | — | 3 | 2 | no | — |
| 96 | #3830 | — | 3 | 2 | no | — |
| 97 | #3830 | — | 3 | 8 | no | — |
| 98 | #3830 | — | 6 | 2 | no | — |
| 99 | #3830 | — | 6 | 2 | no | — |
| 100 | #3830 | — | 6 | 8 | no | — |
| 101 | #3830 | C2×D3 | 1 | 2 | yes | — |
| 102 | #3828 | — | 3 | 1 | no | — |
| 103 | #3828 | — | 6 | 2 | no | — |
| 104 | C2×#634 | — | 3 | 2 | no | — |
| 105 | C2×#634 | — | 6 | 2 | no | — |
| 106 | C3×#237 | — | 3 | 8 | no | — |
| 107 | C3×#237 | C2×D3 | 1 | 8 | yes | — |
| 108 | C2×#627 | — | 6 | 8 | no | — |
| 109 | #3805 | — | 6 | 8 | no | — |
| 110 | #3804 | — | 6 | 8 | no | — |
| 111 | #3804 | — | 6 | 8 | no | — |
| 112 | #3798 | — | 3 | 4 | no | — |
| 113 | #3797 | — | 3 | 8 | no | — |
| 114 | D3×Dic6 | — | 3 | 8 | no | — |
| 115 | D3×Dic6 | — | 3 | 8 | no | — |
| 116 | C32×Q16 | — | 3 | 1 | no | — |
| 117 | C32×SD16 | — | 3 | 2 | no | — |
| 118 | C32×D8 | — | 2 | 4 | no | — |
| 119 | C32×D8 | C2×D3 | 1 | 4 | yes | — |
| 120 | C32×D8 | C2×D3 | 1 | 1 | yes | characteristic |
| 121 | C2×C32×C8 | — | 3 | 1 | no | — |
| 122 | #3756 | — | 3 | 2 | no | — |
| 123 | #3756 | — | 3 | 2 | no | — |
| 124 | #3754 | — | 3 | 2 | no | — |
| 125 | #3754 | — | 3 | 8 | no | — |
| 126 | #3754 | — | 6 | 8 | no | — |
| 127 | #3754 | C2×D3 | 1 | 2 | yes | — |
| 128 | #3748 | — | 3 | 1 | no | — |
| 129 | #3746 | — | 3 | 2 | no | — |
| 130 | #3746 | — | 3 | 1 | no | — |
| 131 | #3746 | — | 3 | 4 | no | — |
| 132 | #3746 | — | 6 | 4 | no | — |
| 133 | #3746 | C2×D3 | 1 | 1 | yes | characteristic |
| 134 | #3743 | — | 3 | 1 | no | — |
| 135 | #3743 | — | 3 | 1 | no | — |
| 136 | C8×C3⋊D3 | — | 3 | 1 | no | — |
| 137 | C8×C3⋊D3 | — | 3 | 4 | no | — |
| 138 | C8×C3⋊D3 | — | 6 | 4 | no | — |
| 139 | C8×C3⋊D3 | C2×D3 | 1 | 1 | yes | characteristic |
| 140 | C3×#214 | — | 3 | 8 | no | — |
| 141 | C3×#214 | C2×D3 | 1 | 8 | yes | — |
| 142 | C3×Dic12 | — | 3 | 4 | no | — |
| 143 | C3×Dic12 | C2×D3 | 1 | 4 | yes | — |
| 144 | C3×D3×C8 | — | 3 | 4 | no | — |
| 145 | C3×D3×C8 | C2×D3 | 1 | 4 | yes | — |
| 146 | #3719 | — | 3 | 8 | no | — |
| 147 | #3719 | — | 3 | 8 | no | — |
| 148 | #3718 | — | 3 | 8 | no | — |
| 149 | #3712 | — | 3 | 4 | no | — |
| 150 | #3711 | — | 3 | 4 | no | — |
| 151 | #3711 | — | 3 | 4 | no | — |
| 152 | C22×C33 | — | 2 | 2 | no | — |
| 153 | C2×C3⋊(C3⋊D3) | C2×D4 | 1 | 1 | yes | characteristic |
| 154 | C2×C3×C3⋊D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 155 | C2×C32×D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 156 | C33×C4 | C24 | 1 | 1 | yes | characteristic |
| 157 | C3⋊(C3⋊Dic3) | — | 2 | 2 | no | — |
| 158 | C3⋊(C3⋊Dic3) | C2×D4 | 1 | 1 | yes | characteristic |
| 159 | C3×C3⋊Dic3 | — | 2 | 2 | no | — |
| 160 | C3×C3⋊Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 161 | C32×Dic3 | — | 2 | 2 | no | — |
| 162 | C32×Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 163 | #1010 | — | 9 | 8 | no | — |
| 164 | #1010 | — | 9 | 2 | no | — |
| 165 | C3×#135 | — | 3 | 4 | no | — |
| 166 | C3×#135 | — | 9 | 1 | no | — |
| 167 | #951 | — | 9 | 8 | no | — |
| 168 | #951 | — | 9 | 2 | no | — |
| 169 | D3×Q16 | — | 9 | 4 | no | — |
| 170 | D3×Q16 | — | 9 | 4 | no | — |
| 171 | D3×Q16 | — | 9 | 1 | no | — |
| 172 | D3×Q16 | — | 9 | 1 | no | — |
| 173 | #915 | — | 9 | 8 | no | — |
| 174 | #915 | — | 9 | 8 | no | — |
| 175 | #915 | — | 9 | 2 | no | — |
| 176 | #915 | — | 9 | 2 | no | — |
| 177 | #912 | — | 3 | 4 | no | — |
| 178 | #912 | — | 9 | 4 | no | — |
| 179 | #912 | — | 9 | 1 | no | — |
| 180 | #912 | — | 18 | 4 | no | — |
| 181 | #912 | C3⋊D3 | 1 | 1 | yes | characteristic, complemented |
| 182 | C2×Dic12 | — | 9 | 4 | no | — |
| 183 | C2×Dic12 | — | 9 | 1 | no | — |
| 184 | #901 | — | 9 | 4 | no | — |
| 185 | #901 | — | 9 | 1 | no | — |
| 186 | C32×Q8 | — | 3 | 2 | no | — |
| 187 | C32×D4 | — | 2 | 8 | no | — |
| 188 | C32×D4 | — | 6 | 2 | no | — |
| 189 | C32×D4 | C22×D3 | 1 | 8 | yes | — |
| 190 | C32×D4 | C22×D3 | 1 | 2 | yes | — |
| 191 | C2×C32×C4 | — | 3 | 1 | no | — |
| 192 | C2×C32×C4 | — | 6 | 2 | no | — |
| 193 | #638 | — | 2 | 2 | no | — |
| 194 | #638 | — | 3 | 1 | no | — |
| 195 | #638 | — | 3 | 1 | no | — |
| 196 | #638 | — | 6 | 2 | no | — |
| 197 | #638 | — | 6 | 8 | no | — |
| 198 | #638 | — | 12 | 8 | no | — |
| 199 | C2×C3⋊Dic3 | — | 2 | 2 | no | — |
| 200 | C2×C3⋊Dic3 | — | 6 | 2 | no | — |
| 201 | C2×C3⋊Dic3 | — | 6 | 2 | no | — |
| 202 | C2×C3⋊Dic3 | — | 6 | 8 | no | — |
| 203 | C2×C3⋊Dic3 | — | 12 | 8 | no | — |
| 204 | C4⋊(C3⋊D3) | — | 3 | 1 | no | — |
| 205 | C4×C3⋊D3 | — | 3 | 1 | no | — |
| 206 | C4×C3⋊D3 | — | 3 | 4 | no | — |
| 207 | C4×C3⋊D3 | — | 6 | 4 | no | — |
| 208 | C4×C3⋊D3 | — | 6 | 2 | no | — |
| 209 | C4×C3⋊D3 | — | 6 | 2 | no | — |
| 210 | C4×C3⋊D3 | C22×D3 | 1 | 1 | yes | characteristic |
| 211 | #634 | — | 3 | 1 | no | — |
| 212 | #634 | — | 3 | 2 | no | — |
| 213 | #634 | — | 3 | 8 | no | — |
| 214 | #634 | — | 6 | 8 | no | — |
| 215 | #634 | — | 6 | 2 | no | — |
| 216 | #634 | — | 6 | 2 | no | — |
| 217 | #634 | — | 6 | 2 | no | — |
| 218 | #634 | C22×D3 | 1 | 2 | yes | — |
| 219 | C3×#67 | — | 2 | 8 | no | — |
| 220 | C3×#67 | — | 6 | 8 | no | — |
| 221 | C2×C3×Dic3 | — | 2 | 8 | no | — |
| 222 | C2×C3×Dic3 | — | 6 | 8 | no | — |
| 223 | C3×C4×D3 | — | 3 | 4 | no | — |
| 224 | C3×C4×D3 | C22×D3 | 1 | 4 | yes | — |
| 225 | C3×Dic6 | — | 3 | 8 | no | — |
| 226 | C3×Dic6 | C22×D3 | 1 | 8 | yes | — |
| 227 | #627 | — | 3 | 4 | no | — |
| 228 | #627 | — | 6 | 8 | no | — |
| 229 | #627 | — | 6 | 8 | no | — |
| 230 | #627 | — | 6 | 8 | no | — |
| 231 | #626 | — | 3 | 4 | no | — |
| 232 | #626 | — | 3 | 4 | no | — |
| 233 | #625 | — | 3 | 4 | no | — |
| 234 | #624 | — | 6 | 8 | no | — |
| 235 | D3×Dic3 | — | 6 | 8 | no | — |
| 236 | D3×Dic3 | — | 6 | 8 | no | — |
| 237 | C32×C8 | — | 2 | 4 | no | — |
| 238 | C32×C8 | — | 3 | 1 | no | — |
| 239 | C32×C8 | C22×D3 | 1 | 4 | yes | — |
| 240 | C32×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 241 | C3⋊(C3⋊C8) | — | 3 | 1 | no | — |
| 242 | C3⋊(C3⋊C8) | — | 3 | 4 | no | — |
| 243 | C3⋊(C3⋊C8) | — | 6 | 4 | no | — |
| 244 | C3⋊(C3⋊C8) | C22×D3 | 1 | 1 | yes | characteristic |
| 245 | C3×C3⋊C8 | — | 3 | 4 | no | — |
| 246 | C3×C3⋊C8 | C22×D3 | 1 | 4 | yes | — |
| 247 | #578 | — | 27 | 1 | no | Sylow |
| 248 | C2×C33 | — | 4 | 2 | no | — |
| 249 | C2×C33 | C22×D4 | 1 | 1 | yes | characteristic |
| 250 | C3⋊(C3⋊D3) | — | 2 | 1 | no | — |
| 251 | C3×C3⋊D3 | — | 2 | 1 | no | — |
| 252 | C32×D3 | — | 2 | 1 | no | — |
| 253 | C3×#41 | — | 3 | 8 | no | — |
| 254 | C3×#41 | — | 9 | 2 | no | — |
| 255 | D3×Q8 | — | 9 | 8 | no | — |
| 256 | D3×Q8 | — | 9 | 8 | no | — |
| 257 | D3×Q8 | — | 9 | 2 | no | — |
| 258 | D3×Q8 | — | 9 | 2 | no | — |
| 259 | #237 | — | 3 | 8 | no | — |
| 260 | #237 | — | 9 | 8 | no | — |
| 261 | #237 | — | 9 | 2 | no | — |
| 262 | #237 | — | 18 | 8 | no | — |
| 263 | #237 | — | 18 | 2 | no | — |
| 264 | #237 | — | 18 | 8 | no | — |
| 265 | #237 | — | 18 | 2 | no | — |
| 266 | #237 | — | 18 | 8 | no | — |
| 267 | #237 | C2×C3⋊D3 | 1 | 2 | yes | — |
| 268 | #235 | — | 9 | 4 | no | — |
| 269 | #235 | — | 9 | 1 | no | — |
| 270 | #235 | — | 18 | 2 | no | — |
| 271 | #235 | — | 18 | 8 | no | — |
| 272 | C2×Dic6 | — | 9 | 8 | no | — |
| 273 | C2×Dic6 | — | 9 | 2 | no | — |
| 274 | C2×Dic6 | — | 18 | 2 | no | — |
| 275 | C2×Dic6 | — | 18 | 8 | no | — |
| 276 | C3×Q16 | — | 3 | 4 | no | — |
| 277 | C3×Q16 | — | 9 | 1 | no | — |
| 278 | C3×SD16 | — | 3 | 8 | no | — |
| 279 | C3×SD16 | — | 9 | 2 | no | — |
| 280 | C3×D8 | — | 2 | 4 | no | — |
| 281 | C3×D8 | D32 | 1 | 4 | yes | — |
| 282 | C3×D8 | C2×C3⋊D3 | 1 | 1 | yes | characteristic |
| 283 | C2×C3×C8 | — | 3 | 4 | no | — |
| 284 | C2×C3×C8 | — | 9 | 1 | no | — |
| 285 | #216 | — | 9 | 8 | no | — |
| 286 | #216 | — | 9 | 8 | no | — |
| 287 | #216 | — | 9 | 2 | no | — |
| 288 | #216 | — | 9 | 2 | no | — |
| 289 | #214 | — | 3 | 8 | no | — |
| 290 | #214 | — | 9 | 8 | no | — |
| 291 | #214 | — | 9 | 2 | no | — |
| 292 | #214 | — | 18 | 8 | no | — |
| 293 | #214 | C2×C3⋊D3 | 1 | 2 | yes | — |
| 294 | #208 | — | 9 | 4 | no | — |
| 295 | #208 | — | 9 | 1 | no | — |
| 296 | Dic12 | — | 3 | 4 | no | — |
| 297 | Dic12 | — | 9 | 8 | no | — |
| 298 | Dic12 | — | 9 | 2 | no | — |
| 299 | Dic12 | — | 9 | 4 | no | — |
| 300 | Dic12 | — | 9 | 1 | no | — |
| 301 | Dic12 | — | 18 | 4 | no | — |
| 302 | Dic12 | C2×C3⋊D3 | 1 | 1 | yes | characteristic |
| 303 | ΓL(1,𝔽25) | — | 9 | 4 | no | — |
| 304 | ΓL(1,𝔽25) | — | 9 | 4 | no | — |
| 305 | ΓL(1,𝔽25) | — | 9 | 1 | no | — |
| 306 | ΓL(1,𝔽25) | — | 9 | 1 | no | — |
| 307 | D3×C8 | — | 3 | 4 | no | — |
| 308 | D3×C8 | — | 9 | 4 | no | — |
| 309 | D3×C8 | — | 9 | 1 | no | — |
| 310 | D3×C8 | — | 18 | 4 | no | — |
| 311 | D3×C8 | C2×C3⋊D3 | 1 | 1 | yes | characteristic |
| 312 | C22×C32 | — | 2 | 2 | no | — |
| 313 | C22×C32 | — | 2 | 8 | no | — |
| 314 | C22×C32 | — | 3 | 1 | no | — |
| 315 | C22×C32 | — | 4 | 8 | no | — |
| 316 | C2×C3⋊D3 | — | 3 | 1 | no | — |
| 317 | C2×C3⋊D3 | — | 3 | 4 | no | — |
| 318 | C2×C3⋊D3 | — | 6 | 4 | no | — |
| 319 | C2×C3⋊D3 | D3×D4 | 1 | 1 | yes | characteristic |
| 320 | C2×C3×D3 | — | 3 | 4 | no | — |
| 321 | C2×C3×D3 | D3×D4 | 1 | 4 | yes | — |
| 322 | C32×C4 | — | 2 | 4 | no | — |
| 323 | C32×C4 | — | 3 | 1 | no | — |
| 324 | C32×C4 | — | 6 | 2 | no | — |
| 325 | C32×C4 | C23×D3 | 1 | 4 | yes | — |
| 326 | C32×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 327 | C3⋊Dic3 | — | 2 | 2 | no | — |
| 328 | C3⋊Dic3 | — | 3 | 1 | no | — |
| 329 | C3⋊Dic3 | — | 3 | 4 | no | — |
| 330 | C3⋊Dic3 | — | 6 | 4 | no | — |
| 331 | C3⋊Dic3 | — | 6 | 2 | no | — |
| 332 | C3⋊Dic3 | — | 6 | 8 | no | — |
| 333 | C3⋊Dic3 | — | 12 | 8 | no | — |
| 334 | C3⋊Dic3 | D3×D4 | 1 | 1 | yes | characteristic |
| 335 | C3×Dic3 | — | 2 | 8 | no | — |
| 336 | C3×Dic3 | — | 3 | 4 | no | — |
| 337 | C3×Dic3 | — | 6 | 8 | no | — |
| 338 | C3×Dic3 | D3×D4 | 1 | 4 | yes | — |
| 339 | 2−1+4 | — | 27 | 2 | no | — |
| 340 | #137 | — | 27 | 2 | no | — |
| 341 | #137 | — | 27 | 2 | no | — |
| 342 | #137 | — | 27 | 2 | no | — |
| 343 | #135 | — | 3 | 1 | no | — |
| 344 | #135 | — | 9 | 1 | no | — |
| 345 | #135 | — | 27 | 1 | no | — |
| 346 | C2×Q16 | — | 27 | 1 | no | — |
| 347 | C2×Q16 | — | 27 | 1 | no | — |
| 348 | C2×Q16 | — | 27 | 1 | no | — |
| 349 | #131 | — | 27 | 1 | no | — |
| 350 | C33 | #578 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 351 | C3×Q8 | — | 3 | 8 | no | — |
| 352 | C3×Q8 | — | 9 | 2 | no | — |
| 353 | C3×D4 | — | 2 | 8 | no | — |
| 354 | C3×D4 | — | 6 | 8 | no | — |
| 355 | C3×D4 | — | 18 | 2 | no | — |
| 356 | C3×D4 | C2×D32 | 1 | 8 | yes | — |
| 357 | C3×D4 | C22×C3⋊D3 | 1 | 2 | yes | — |
| 358 | C2×C3×C4 | — | 3 | 4 | no | — |
| 359 | C2×C3×C4 | — | 6 | 8 | no | — |
| 360 | C2×C3×C4 | — | 9 | 1 | no | — |
| 361 | C2×C3×C4 | — | 18 | 2 | no | — |
| 362 | #67 | — | 2 | 2 | no | — |
| 363 | #67 | — | 6 | 8 | no | — |
| 364 | #67 | — | 9 | 4 | no | — |
| 365 | #67 | — | 9 | 4 | no | — |
| 366 | #67 | — | 9 | 1 | no | — |
| 367 | #67 | — | 9 | 1 | no | — |
| 368 | #67 | — | 18 | 2 | no | — |
| 369 | #67 | — | 18 | 8 | no | — |
| 370 | #67 | — | 36 | 8 | no | — |
| 371 | C2×Dic3 | — | 2 | 2 | no | — |
| 372 | C2×Dic3 | — | 6 | 8 | no | — |
| 373 | C2×Dic3 | — | 18 | 2 | no | — |
| 374 | C2×Dic3 | — | 18 | 8 | no | — |
| 375 | C2×Dic3 | — | 18 | 2 | no | — |
| 376 | C2×Dic3 | — | 18 | 8 | no | — |
| 377 | C2×Dic3 | — | 36 | 8 | no | — |
| 378 | D12 | — | 9 | 4 | no | — |
| 379 | D12 | — | 9 | 1 | no | — |
| 380 | C4×D3 | — | 3 | 4 | no | — |
| 381 | C4×D3 | — | 9 | 4 | no | — |
| 382 | C4×D3 | — | 9 | 1 | no | — |
| 383 | C4×D3 | — | 18 | 4 | no | — |
| 384 | C4×D3 | — | 18 | 2 | no | — |
| 385 | C4×D3 | — | 18 | 8 | no | — |
| 386 | C4×D3 | — | 18 | 8 | no | — |
| 387 | C4×D3 | — | 18 | 2 | no | — |
| 388 | C4×D3 | C22×C3⋊D3 | 1 | 1 | yes | characteristic |
| 389 | Dic6 | — | 3 | 8 | no | — |
| 390 | Dic6 | — | 9 | 4 | no | — |
| 391 | Dic6 | — | 9 | 1 | no | — |
| 392 | Dic6 | — | 9 | 8 | no | — |
| 393 | Dic6 | — | 9 | 2 | no | — |
| 394 | Dic6 | — | 18 | 8 | no | — |
| 395 | Dic6 | — | 18 | 2 | no | — |
| 396 | Dic6 | — | 18 | 2 | no | — |
| 397 | Dic6 | — | 18 | 8 | no | — |
| 398 | Dic6 | — | 18 | 8 | no | — |
| 399 | Dic6 | — | 18 | 8 | no | — |
| 400 | Dic6 | — | 18 | 2 | no | — |
| 401 | Dic6 | C22×C3⋊D3 | 1 | 2 | yes | — |
| 402 | C3×C8 | — | 2 | 4 | no | — |
| 403 | C3×C8 | — | 3 | 4 | no | — |
| 404 | C3×C8 | — | 9 | 1 | no | — |
| 405 | C3×C8 | C2×D32 | 1 | 4 | yes | — |
| 406 | C3×C8 | C22×C3⋊D3 | 1 | 1 | yes | characteristic |
| 407 | C3⋊C8 | — | 3 | 4 | no | — |
| 408 | C3⋊C8 | — | 9 | 4 | no | — |
| 409 | C3⋊C8 | — | 9 | 1 | no | — |
| 410 | C3⋊C8 | — | 18 | 4 | no | — |
| 411 | C3⋊C8 | C22×C3⋊D3 | 1 | 1 | yes | characteristic |
| 412 | C2×C32 | — | 2 | 4 | no | — |
| 413 | C2×C32 | — | 4 | 2 | no | — |
| 414 | C2×C32 | — | 4 | 8 | no | — |
| 415 | C2×C32 | — | 6 | 1 | no | — |
| 416 | C2×C32 | — | 8 | 8 | no | — |
| 417 | C2×C32 | C2×D3×D4 | 1 | 4 | yes | — |
| 418 | C2×C32 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 419 | C3⋊D3 | — | 2 | 1 | no | — |
| 420 | C3⋊D3 | — | 6 | 1 | no | — |
| 421 | C3⋊D3 | — | 6 | 4 | no | — |
| 422 | C3⋊D3 | — | 12 | 4 | no | — |
| 423 | C3×D3 | — | 2 | 4 | no | — |
| 424 | C3×D3 | — | 6 | 4 | no | — |
| 425 | #41 | — | 3 | 2 | no | — |
| 426 | #41 | — | 9 | 2 | no | — |
| 427 | #41 | — | 27 | 1 | no | — |
| 428 | #41 | — | 27 | 2 | no | — |
| 429 | #41 | — | 54 | 2 | no | — |
| 430 | #41 | — | 54 | 2 | no | — |
| 431 | #41 | — | 54 | 2 | no | — |
| 432 | C2×Q8 | — | 27 | 2 | no | — |
| 433 | C2×Q8 | — | 27 | 2 | no | — |
| 434 | C2×Q8 | — | 27 | 2 | no | — |
| 435 | C2×Q8 | — | 54 | 2 | no | — |
| 436 | Q16 | — | 3 | 1 | no | — |
| 437 | Q16 | — | 9 | 1 | no | — |
| 438 | Q16 | — | 27 | 2 | no | — |
| 439 | Q16 | — | 27 | 2 | no | — |
| 440 | Q16 | — | 27 | 2 | no | — |
| 441 | Q16 | — | 27 | 1 | no | — |
| 442 | SD16 | — | 3 | 2 | no | — |
| 443 | SD16 | — | 9 | 2 | no | — |
| 444 | SD16 | — | 27 | 2 | no | — |
| 445 | D8 | D3×C3⋊D3 | 1 | 1 | yes | characteristic |
| 446 | M16 | — | 27 | 1 | no | — |
| 447 | M16 | — | 27 | 1 | no | — |
| 448 | M16 | — | 27 | 1 | no | — |
| 449 | C2×C8 | — | 3 | 1 | no | — |
| 450 | C2×C8 | — | 9 | 1 | no | — |
| 451 | C2×C8 | — | 27 | 1 | no | — |
| 452 | C22×C3 | — | 2 | 8 | no | — |
| 453 | C22×C3 | — | 2 | 2 | no | — |
| 454 | C22×C3 | — | 3 | 4 | no | — |
| 455 | C22×C3 | — | 4 | 8 | no | — |
| 456 | C22×C3 | — | 9 | 1 | no | — |
| 457 | C2×D3 | — | 3 | 4 | no | — |
| 458 | C2×D3 | — | 9 | 4 | no | — |
| 459 | C2×D3 | — | 9 | 1 | no | — |
| 460 | C2×D3 | — | 18 | 4 | no | — |
| 461 | C2×D3 | D4×C3⋊D3 | 1 | 1 | yes | characteristic |
| 462 | C3×C4 | — | 2 | 4 | no | — |
| 463 | C3×C4 | — | 3 | 4 | no | — |
| 464 | C3×C4 | — | 6 | 8 | no | — |
| 465 | C3×C4 | — | 9 | 1 | no | — |
| 466 | C3×C4 | — | 18 | 2 | no | — |
| 467 | C3×C4 | C22×D32 | 1 | 4 | yes | — |
| 468 | C3×C4 | C23×C3⋊D3 | 1 | 1 | yes | characteristic |
| 469 | Dic3 | — | 2 | 2 | no | — |
| 470 | Dic3 | — | 3 | 4 | no | — |
| 471 | Dic3 | — | 6 | 8 | no | — |
| 472 | Dic3 | — | 9 | 4 | no | — |
| 473 | Dic3 | — | 9 | 1 | no | — |
| 474 | Dic3 | — | 18 | 4 | no | — |
| 475 | Dic3 | — | 18 | 8 | no | — |
| 476 | Dic3 | — | 18 | 2 | no | — |
| 477 | Dic3 | — | 36 | 8 | no | — |
| 478 | Dic3 | D4×C3⋊D3 | 1 | 1 | yes | characteristic |
| 479 | C32 | — | 2 | 4 | no | — |
| 480 | C32 | #5771 | 1 | 4 | yes | complemented |
| 481 | C32 | #5771 | 1 | 1 | yes | characteristic, complemented |
| 482 | Q8 | — | 3 | 2 | no | — |
| 483 | Q8 | — | 9 | 2 | no | — |
| 484 | Q8 | — | 27 | 1 | no | — |
| 485 | Q8 | — | 27 | 2 | no | — |
| 486 | Q8 | — | 54 | 2 | no | — |
| 487 | Q8 | — | 54 | 2 | no | — |
| 488 | Q8 | — | 54 | 2 | no | — |
| 489 | D4 | — | 6 | 2 | no | — |
| 490 | D4 | — | 18 | 2 | no | — |
| 491 | D4 | — | 27 | 1 | no | — |
| 492 | D4 | — | 27 | 1 | no | — |
| 493 | D4 | — | 27 | 1 | no | — |
| 494 | D4 | — | 54 | 2 | no | — |
| 495 | D4 | C2×D3×C3⋊D3 | 1 | 2 | yes | — |
| 496 | C2×C4 | — | 3 | 1 | no | — |
| 497 | C2×C4 | — | 6 | 2 | no | — |
| 498 | C2×C4 | — | 9 | 1 | no | — |
| 499 | C2×C4 | — | 18 | 2 | no | — |
| 500 | C2×C4 | — | 27 | 1 | no | — |
| 501 | C2×C4 | — | 54 | 2 | no | — |
| 502 | C2×C4 | — | 54 | 2 | no | — |
| 503 | C2×C4 | — | 54 | 2 | no | — |
| 504 | C2×C4 | — | 54 | 2 | no | — |
| 505 | C8 | — | 3 | 1 | no | — |
| 506 | C8 | — | 9 | 1 | no | — |
| 507 | C8 | — | 27 | 1 | no | — |
| 508 | C8 | C2×D3×C3⋊D3 | 1 | 1 | yes | characteristic |
| 509 | C2×C3 | — | 2 | 4 | no | — |
| 510 | C2×C3 | — | 4 | 2 | no | — |
| 511 | C2×C3 | — | 4 | 8 | no | — |
| 512 | C2×C3 | — | 6 | 4 | no | — |
| 513 | C2×C3 | — | 8 | 8 | no | — |
| 514 | C2×C3 | — | 18 | 1 | no | — |
| 515 | C2×C3 | D32×D4 | 1 | 4 | yes | — |
| 516 | C2×C3 | C2×D4×C3⋊D3 | 1 | 1 | yes | characteristic |
| 517 | D3 | — | 2 | 1 | no | — |
| 518 | D3 | — | 6 | 4 | no | — |
| 519 | D3 | — | 18 | 1 | no | — |
| 520 | D3 | — | 18 | 4 | no | — |
| 521 | D3 | — | 36 | 4 | no | — |
| 522 | C22 | — | 2 | 2 | no | — |
| 523 | C22 | — | 3 | 1 | no | — |
| 524 | C22 | — | 9 | 1 | no | — |
| 525 | C22 | — | 27 | 1 | no | — |
| 526 | C4 | — | 3 | 1 | no | — |
| 527 | C4 | — | 6 | 2 | no | — |
| 528 | C4 | — | 9 | 1 | no | — |
| 529 | C4 | — | 18 | 2 | no | — |
| 530 | C4 | — | 27 | 1 | no | — |
| 531 | C4 | — | 54 | 2 | no | — |
| 532 | C4 | C22×D3×C3⋊D3 | 1 | 1 | yes | characteristic |
| 533 | C3 | — | 2 | 4 | no | — |
| 534 | C3 | #10594737 | 1 | 4 | yes | complemented |
| 535 | C3 | #10596242 | 1 | 1 | yes | characteristic, complemented |
| 536 | C2 | — | 4 | 2 | no | — |
| 537 | C2 | — | 6 | 1 | no | — |
| 538 | C2 | — | 18 | 1 | no | — |
| 539 | C2 | — | 54 | 1 | no | — |
| 540 | C2 | D3×D4×C3⋊D3 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D3×D4×C3⋊D3 |
| commutator, cosocle | C33×C4 | C24 |
| Frattini | C4 | C22×D3×C3⋊D3 |
| Fitting | C33×D8 | C22 |
| socle | C2×C33 | C22×D4 |
| hypercenter | D8 | D3×C3⋊D3 |
| hypocenter | C33 | #578 |
| LCS | G ▷ C33×C4 ▷ C2×C33 ▷ C33 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ D8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11724582 | C2 | semidirect |
| 2. #11723953 | C2 | semidirect |
| 3. C3×#64121 | C2 | semidirect |
| 4. C32×#912 | C2 | semidirect |
| 5. #11723554 | C2 | semidirect |
| 6. #11723552 | C2 | semidirect |
| 7. #11723550 | C2 | semidirect |
| 8. #11723331 | C2 | semidirect |
| 9. #11723330 | C2 | semidirect |
| 10. C3⋊D3×Dic12 | C2 | semidirect |
| 11. D3×#3746 | C2 | semidirect |
| 52. #64121 | D3 | semidirect |
| 56. C3×#912 | D3 | semidirect |
| 181. #912 | C3⋊D3 | semidirect |
| 350. C33 | #578 | semidirect |
| 480. C32 | #5771 | semidirect |
| 481. C32 | #5771 | semidirect |
| 534. C3 | #10594737 | semidirect |
| 535. C3 | #10596242 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11724582 | 2 |
| #11723953 | 2 |
| C3×#64121 | 2 |
| C32×#912 | 2 |
| #11723554 | 2 |
| #11723552 | 2 |
| #11723550 | 2 |
| #11723331 | 2 |
| #11723330 | 2 |
| C3⋊D3×Dic12 | 2 |
| D3×#3746 | 2 |
| #10596242 | 3 |
| #10594737 | 3 |