Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1190 conjugacy classes of subgroups.
The subgroup lattice has 656 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #11724624 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | C3×#64127 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | C3×Q16×C3⋊D3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11723713 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #11723712 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #11723710 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #11723653 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #11723652 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #11723650 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #10594769 | — | 3 | 1 | no | maximal |
| 11 | #10594766 | — | 3 | 2 | no | maximal |
| 12 | C3×#3832 | C22 | 1 | 2 | yes | — |
| 13 | C3×Q8×C3⋊D3 | C22 | 1 | 2 | yes | — |
| 14 | C3×Q8×C3⋊D3 | C22 | 1 | 2 | yes | — |
| 15 | #89042 | — | 2 | 2 | no | — |
| 16 | #89042 | C22 | 1 | 1 | yes | characteristic |
| 17 | #89041 | — | 2 | 2 | no | — |
| 18 | #89041 | — | 2 | 2 | no | — |
| 19 | #89041 | C22 | 1 | 2 | yes | — |
| 20 | #89041 | C22 | 1 | 2 | yes | — |
| 21 | #89040 | — | 2 | 2 | no | — |
| 22 | #89040 | C22 | 1 | 2 | yes | — |
| 23 | C33×Q16 | C22 | 1 | 1 | yes | characteristic |
| 24 | C3×#3756 | C22 | 1 | 2 | yes | — |
| 25 | C3×#3756 | C22 | 1 | 2 | yes | — |
| 26 | C3×#3755 | C22 | 1 | 2 | yes | — |
| 27 | C3×#3746 | C22 | 1 | 1 | yes | characteristic |
| 28 | C3×#3744 | C22 | 1 | 2 | yes | — |
| 29 | C3×#3743 | C22 | 1 | 2 | yes | — |
| 30 | C3×C8×C3⋊D3 | C22 | 1 | 1 | yes | characteristic |
| 31 | #88812 | C22 | 1 | 2 | yes | — |
| 32 | #88812 | C22 | 1 | 1 | yes | characteristic |
| 33 | #88811 | C22 | 1 | 2 | yes | — |
| 34 | #88810 | C22 | 1 | 1 | yes | characteristic |
| 35 | #88809 | C22 | 1 | 1 | yes | characteristic |
| 36 | #88808 | C22 | 1 | 2 | yes | — |
| 37 | #64316 | — | 3 | 2 | no | — |
| 38 | #64315 | — | 3 | 2 | no | — |
| 39 | #64315 | — | 3 | 2 | no | — |
| 40 | #64127 | D3 | 1 | 2 | yes | complemented |
| 41 | Q16×C3⋊D3 | D3 | 1 | 1 | yes | characteristic, complemented |
| 42 | C3×#918 | — | 3 | 2 | no | — |
| 43 | C3×#918 | — | 3 | 2 | no | — |
| 44 | C3×#918 | — | 6 | 2 | no | — |
| 45 | C3×D3×Q16 | — | 3 | 2 | no | — |
| 46 | C3×D3×Q16 | — | 6 | 1 | no | — |
| 47 | #63951 | — | 3 | 2 | no | — |
| 48 | #63950 | — | 3 | 2 | no | — |
| 49 | #63949 | — | 3 | 2 | no | — |
| 50 | #63948 | — | 3 | 2 | no | — |
| 51 | #63947 | — | 3 | 2 | no | — |
| 52 | #63946 | — | 3 | 2 | no | — |
| 53 | #63944 | — | 3 | 2 | no | — |
| 54 | D3×#216 | — | 3 | 2 | no | — |
| 55 | D3×#216 | — | 3 | 2 | no | — |
| 56 | #63811 | — | 3 | 2 | no | — |
| 57 | #63809 | — | 3 | 1 | no | — |
| 58 | #63806 | — | 3 | 2 | no | — |
| 59 | #63805 | — | 3 | 1 | no | — |
| 60 | #63804 | — | 3 | 2 | no | — |
| 61 | #63801 | — | 3 | 2 | no | — |
| 62 | #63800 | — | 3 | 2 | no | — |
| 63 | C33×Q8 | C23 | 1 | 2 | yes | — |
| 64 | C3×C4⋊(C3⋊D3) | — | 2 | 2 | no | — |
| 65 | C3×C4⋊(C3⋊D3) | C23 | 1 | 2 | yes | — |
| 66 | C3×C4×C3⋊D3 | — | 2 | 2 | no | — |
| 67 | C3×C4×C3⋊D3 | — | 2 | 2 | no | — |
| 68 | C3×C4×C3⋊D3 | — | 2 | 2 | no | — |
| 69 | C3×C4×C3⋊D3 | C23 | 1 | 1 | yes | characteristic |
| 70 | C3×C4×C3⋊D3 | C23 | 1 | 2 | yes | — |
| 71 | C3×#634 | — | 2 | 2 | no | — |
| 72 | C3×#634 | — | 2 | 2 | no | — |
| 73 | C3×#634 | C23 | 1 | 2 | yes | — |
| 74 | C3×#634 | C23 | 1 | 2 | yes | — |
| 75 | #6296 | — | 2 | 2 | no | — |
| 76 | #6296 | D4 | 1 | 1 | yes | characteristic |
| 77 | #6295 | — | 2 | 2 | no | — |
| 78 | #6295 | — | 2 | 2 | no | — |
| 79 | #6295 | D4 | 1 | 1 | yes | characteristic |
| 80 | #6295 | D4 | 1 | 2 | yes | — |
| 81 | #6294 | — | 2 | 2 | no | — |
| 82 | #6294 | — | 2 | 2 | no | — |
| 83 | #6294 | — | 2 | 2 | no | — |
| 84 | C33×C8 | C23 | 1 | 1 | yes | characteristic |
| 85 | C3×C3⋊(C3⋊C8) | C23 | 1 | 1 | yes | characteristic |
| 86 | C3×C3⋊(C3⋊C8) | C23 | 1 | 2 | yes | — |
| 87 | #5779 | — | 9 | 2 | no | — |
| 88 | #5766 | — | 9 | 1 | no | — |
| 89 | #3832 | C2×D3 | 1 | 2 | yes | — |
| 90 | Q8×C3⋊D3 | C2×D3 | 1 | 2 | yes | — |
| 91 | Q8×C3⋊D3 | C2×D3 | 1 | 2 | yes | — |
| 92 | C3×#239 | — | 3 | 2 | no | — |
| 93 | C3×#239 | — | 3 | 2 | no | — |
| 94 | C3×#239 | — | 6 | 2 | no | — |
| 95 | C3×D3×Q8 | — | 3 | 2 | no | — |
| 96 | C3×D3×Q8 | — | 3 | 2 | no | — |
| 97 | C3×D3×Q8 | — | 3 | 2 | no | — |
| 98 | C3×D3×Q8 | — | 3 | 2 | no | — |
| 99 | C3×D3×Q8 | — | 6 | 2 | no | — |
| 100 | C3×D3×Q8 | — | 6 | 2 | no | — |
| 101 | #3799 | — | 3 | 2 | no | — |
| 102 | #3799 | — | 3 | 2 | no | — |
| 103 | #3799 | — | 6 | 2 | no | — |
| 104 | #3799 | — | 6 | 2 | no | — |
| 105 | #3798 | — | 3 | 1 | no | — |
| 106 | #3798 | — | 3 | 2 | no | — |
| 107 | #3798 | — | 6 | 2 | no | — |
| 108 | #3798 | — | 6 | 2 | no | — |
| 109 | #3798 | — | 6 | 2 | no | — |
| 110 | #3797 | — | 3 | 2 | no | — |
| 111 | #3797 | — | 6 | 2 | no | — |
| 112 | #3796 | — | 3 | 2 | no | — |
| 113 | #3796 | — | 3 | 2 | no | — |
| 114 | #3796 | — | 6 | 2 | no | — |
| 115 | #3796 | — | 6 | 2 | no | — |
| 116 | #3795 | — | 3 | 2 | no | — |
| 117 | #3795 | — | 3 | 2 | no | — |
| 118 | #3795 | — | 6 | 2 | no | — |
| 119 | #3795 | — | 6 | 2 | no | — |
| 120 | D3×Dic6 | — | 3 | 2 | no | — |
| 121 | D3×Dic6 | — | 3 | 2 | no | — |
| 122 | D3×Dic6 | — | 6 | 2 | no | — |
| 123 | D3×Dic6 | — | 6 | 2 | no | — |
| 124 | C32×Q16 | — | 2 | 1 | no | — |
| 125 | C32×Q16 | — | 2 | 2 | no | — |
| 126 | C32×Q16 | — | 4 | 1 | no | — |
| 127 | C32×Q16 | C2×D3 | 1 | 2 | yes | — |
| 128 | C32×Q16 | C2×D3 | 1 | 1 | yes | characteristic |
| 129 | #3756 | C2×D3 | 1 | 2 | yes | — |
| 130 | #3756 | C2×D3 | 1 | 2 | yes | — |
| 131 | #3755 | C2×D3 | 1 | 2 | yes | — |
| 132 | #3746 | C2×D3 | 1 | 1 | yes | characteristic |
| 133 | #3744 | C2×D3 | 1 | 2 | yes | — |
| 134 | #3743 | C2×D3 | 1 | 2 | yes | — |
| 135 | C8×C3⋊D3 | C2×D3 | 1 | 1 | yes | characteristic |
| 136 | C3×#216 | — | 3 | 2 | no | — |
| 137 | C3×#216 | — | 3 | 2 | no | — |
| 138 | C3×#216 | — | 3 | 2 | no | — |
| 139 | C3×#216 | — | 3 | 2 | no | — |
| 140 | C3×#216 | — | 6 | 2 | no | — |
| 141 | C3×#216 | — | 6 | 2 | no | — |
| 142 | C3×#215 | — | 3 | 2 | no | — |
| 143 | C3×#215 | — | 3 | 2 | no | — |
| 144 | C3×#215 | — | 6 | 2 | no | — |
| 145 | C3×Dic12 | — | 3 | 2 | no | — |
| 146 | C3×Dic12 | — | 6 | 1 | no | — |
| 147 | C3×#204 | — | 3 | 2 | no | — |
| 148 | C3×#204 | — | 3 | 2 | no | — |
| 149 | C3×#204 | — | 6 | 2 | no | — |
| 150 | C3×ΓL(1,𝔽25) | — | 3 | 2 | no | — |
| 151 | C3×ΓL(1,𝔽25) | — | 3 | 2 | no | — |
| 152 | C3×ΓL(1,𝔽25) | — | 6 | 2 | no | — |
| 153 | C3×D3×C8 | — | 3 | 2 | no | — |
| 154 | C3×D3×C8 | — | 6 | 1 | no | — |
| 155 | #3719 | — | 3 | 2 | no | — |
| 156 | #3719 | — | 3 | 2 | no | — |
| 157 | #3719 | — | 3 | 2 | no | — |
| 158 | #3718 | — | 3 | 1 | no | — |
| 159 | #3718 | — | 3 | 2 | no | — |
| 160 | #3717 | — | 3 | 2 | no | — |
| 161 | #3716 | — | 3 | 2 | no | — |
| 162 | #3715 | — | 3 | 2 | no | — |
| 163 | #3714 | — | 3 | 2 | no | — |
| 164 | #3713 | — | 3 | 1 | no | — |
| 165 | #3712 | — | 3 | 1 | no | — |
| 166 | #3711 | — | 3 | 2 | no | — |
| 167 | #3710 | — | 3 | 2 | no | — |
| 168 | D3×C3⋊C8 | — | 3 | 2 | no | — |
| 169 | D3×C3⋊C8 | — | 3 | 2 | no | — |
| 170 | C2×C3×C3⋊D3 | — | 2 | 2 | no | — |
| 171 | C2×C3×C3⋊D3 | C2×D4 | 1 | 2 | yes | — |
| 172 | C2×C3×C3⋊D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 173 | C33×C4 | — | 2 | 2 | no | — |
| 174 | C33×C4 | C24 | 1 | 1 | yes | characteristic |
| 175 | C3×C3⋊Dic3 | — | 2 | 2 | no | — |
| 176 | C3×C3⋊Dic3 | — | 2 | 2 | no | — |
| 177 | C3×C3⋊Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 178 | C3×C3⋊Dic3 | C2×D4 | 1 | 2 | yes | — |
| 179 | #1010 | — | 9 | 2 | no | — |
| 180 | #1007 | — | 9 | 2 | no | — |
| 181 | #1007 | — | 9 | 2 | no | — |
| 182 | C3×#137 | — | 9 | 2 | no | — |
| 183 | C2×C3×Q16 | — | 9 | 1 | no | — |
| 184 | #950 | — | 9 | 2 | no | — |
| 185 | C2×#216 | — | 9 | 2 | no | — |
| 186 | #942 | — | 9 | 2 | no | — |
| 187 | #919 | — | 9 | 2 | no | — |
| 188 | #918 | — | 3 | 2 | no | — |
| 189 | #918 | — | 3 | 2 | no | — |
| 190 | #918 | — | 6 | 2 | no | — |
| 191 | #918 | — | 9 | 2 | no | — |
| 192 | #918 | — | 9 | 2 | no | — |
| 193 | D3×Q16 | — | 3 | 2 | no | — |
| 194 | D3×Q16 | — | 6 | 1 | no | — |
| 195 | D3×Q16 | — | 9 | 2 | no | — |
| 196 | D3×Q16 | — | 9 | 2 | no | — |
| 197 | #916 | — | 9 | 2 | no | — |
| 198 | #916 | — | 9 | 2 | no | — |
| 199 | #915 | — | 9 | 2 | no | — |
| 200 | #915 | — | 9 | 2 | no | — |
| 201 | #909 | — | 9 | 2 | no | — |
| 202 | #907 | — | 9 | 2 | no | — |
| 203 | #904 | — | 9 | 1 | no | — |
| 204 | #901 | — | 9 | 1 | no | — |
| 205 | C32×Q8 | — | 2 | 2 | no | — |
| 206 | C32×Q8 | — | 2 | 2 | no | — |
| 207 | C32×Q8 | — | 2 | 2 | no | — |
| 208 | C32×Q8 | — | 4 | 2 | no | — |
| 209 | C32×Q8 | C22×D3 | 1 | 2 | yes | — |
| 210 | C32×Q8 | C22×D3 | 1 | 2 | yes | — |
| 211 | C32×Q8 | C22×D3 | 1 | 2 | yes | — |
| 212 | C4⋊(C3⋊D3) | — | 2 | 2 | no | — |
| 213 | C4⋊(C3⋊D3) | C22×D3 | 1 | 2 | yes | — |
| 214 | C4×C3⋊D3 | — | 2 | 2 | no | — |
| 215 | C4×C3⋊D3 | — | 2 | 2 | no | — |
| 216 | C4×C3⋊D3 | — | 2 | 2 | no | — |
| 217 | C4×C3⋊D3 | C22×D3 | 1 | 2 | yes | — |
| 218 | C4×C3⋊D3 | C22×D3 | 1 | 1 | yes | characteristic |
| 219 | #634 | — | 2 | 2 | no | — |
| 220 | #634 | — | 2 | 2 | no | — |
| 221 | #634 | C22×D3 | 1 | 2 | yes | — |
| 222 | #634 | C22×D3 | 1 | 2 | yes | — |
| 223 | C3×D12 | — | 3 | 2 | no | — |
| 224 | C3×D12 | — | 3 | 2 | no | — |
| 225 | C3×D12 | — | 6 | 2 | no | — |
| 226 | C3×D12 | — | 6 | 2 | no | — |
| 227 | C3×D12 | — | 6 | 2 | no | — |
| 228 | C3×D12 | — | 12 | 2 | no | — |
| 229 | C3×C4×D3 | — | 3 | 2 | no | — |
| 230 | C3×C4×D3 | — | 3 | 2 | no | — |
| 231 | C3×C4×D3 | — | 3 | 2 | no | — |
| 232 | C3×C4×D3 | — | 6 | 1 | no | — |
| 233 | C3×C4×D3 | — | 6 | 2 | no | — |
| 234 | C3×C4×D3 | — | 6 | 2 | no | — |
| 235 | C3×C4×D3 | — | 6 | 2 | no | — |
| 236 | C3×C4×D3 | — | 6 | 2 | no | — |
| 237 | C3×C4×D3 | — | 6 | 2 | no | — |
| 238 | C3×C4×D3 | — | 6 | 2 | no | — |
| 239 | C3×C4×D3 | — | 6 | 2 | no | — |
| 240 | C3×C4×D3 | — | 12 | 2 | no | — |
| 241 | C3×C4×D3 | — | 12 | 2 | no | — |
| 242 | C3×C4×D3 | — | 12 | 2 | no | — |
| 243 | C3×Dic6 | — | 3 | 2 | no | — |
| 244 | C3×Dic6 | — | 3 | 2 | no | — |
| 245 | C3×Dic6 | — | 3 | 2 | no | — |
| 246 | C3×Dic6 | — | 3 | 2 | no | — |
| 247 | C3×Dic6 | — | 6 | 2 | no | — |
| 248 | C3×Dic6 | — | 6 | 2 | no | — |
| 249 | C3×Dic6 | — | 6 | 2 | no | — |
| 250 | C3×Dic6 | — | 6 | 2 | no | — |
| 251 | C3×Dic6 | — | 6 | 2 | no | — |
| 252 | C3×Dic6 | — | 6 | 2 | no | — |
| 253 | C3×Dic6 | — | 12 | 2 | no | — |
| 254 | C3×Dic6 | — | 12 | 2 | no | — |
| 255 | #627 | — | 3 | 1 | no | — |
| 256 | #627 | — | 3 | 2 | no | — |
| 257 | #627 | — | 6 | 2 | no | — |
| 258 | #627 | — | 6 | 2 | no | — |
| 259 | #627 | — | 6 | 2 | no | — |
| 260 | #626 | — | 3 | 2 | no | — |
| 261 | #626 | — | 3 | 2 | no | — |
| 262 | #626 | — | 3 | 2 | no | — |
| 263 | #626 | — | 6 | 2 | no | — |
| 264 | #626 | — | 6 | 2 | no | — |
| 265 | #626 | — | 6 | 2 | no | — |
| 266 | #626 | — | 6 | 2 | no | — |
| 267 | #625 | — | 3 | 1 | no | — |
| 268 | #625 | — | 3 | 2 | no | — |
| 269 | #625 | — | 6 | 2 | no | — |
| 270 | #625 | — | 6 | 2 | no | — |
| 271 | #624 | — | 6 | 2 | no | — |
| 272 | #624 | — | 6 | 2 | no | — |
| 273 | #624 | — | 6 | 2 | no | — |
| 274 | D3×Dic3 | — | 6 | 2 | no | — |
| 275 | D3×Dic3 | — | 6 | 2 | no | — |
| 276 | D3×Dic3 | — | 6 | 2 | no | — |
| 277 | D3×Dic3 | — | 6 | 2 | no | — |
| 278 | D3×Dic3 | — | 6 | 2 | no | — |
| 279 | D3×Dic3 | — | 6 | 2 | no | — |
| 280 | C32×C8 | — | 2 | 1 | no | — |
| 281 | C32×C8 | — | 2 | 2 | no | — |
| 282 | C32×C8 | — | 4 | 1 | no | — |
| 283 | C32×C8 | C22×D3 | 1 | 2 | yes | — |
| 284 | C32×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 285 | C3⋊(C3⋊C8) | C22×D3 | 1 | 1 | yes | characteristic |
| 286 | C3⋊(C3⋊C8) | C22×D3 | 1 | 2 | yes | — |
| 287 | C3×C3⋊C8 | — | 3 | 2 | no | — |
| 288 | C3×C3⋊C8 | — | 3 | 2 | no | — |
| 289 | C3×C3⋊C8 | — | 3 | 2 | no | — |
| 290 | C3×C3⋊C8 | — | 6 | 1 | no | — |
| 291 | C3×C3⋊C8 | — | 6 | 2 | no | — |
| 292 | #578 | — | 27 | 1 | no | Sylow |
| 293 | C2×C33 | C22×D4 | 1 | 1 | yes | characteristic |
| 294 | C3×C3⋊D3 | — | 2 | 1 | no | — |
| 295 | C3×C3⋊D3 | — | 2 | 2 | no | — |
| 296 | C3×C3⋊D3 | — | 4 | 2 | no | — |
| 297 | C3×#41 | — | 9 | 2 | no | — |
| 298 | C2×C3×Q8 | — | 9 | 2 | no | — |
| 299 | C2×C3×Q8 | — | 9 | 2 | no | — |
| 300 | #239 | — | 3 | 2 | no | — |
| 301 | #239 | — | 3 | 2 | no | — |
| 302 | #239 | — | 6 | 2 | no | — |
| 303 | #239 | — | 9 | 2 | no | — |
| 304 | #239 | — | 9 | 2 | no | — |
| 305 | #239 | — | 18 | 2 | no | — |
| 306 | #239 | — | 18 | 2 | no | — |
| 307 | D3×Q8 | — | 3 | 2 | no | — |
| 308 | D3×Q8 | — | 3 | 2 | no | — |
| 309 | D3×Q8 | — | 3 | 2 | no | — |
| 310 | D3×Q8 | — | 3 | 2 | no | — |
| 311 | D3×Q8 | — | 6 | 2 | no | — |
| 312 | D3×Q8 | — | 6 | 2 | no | — |
| 313 | D3×Q8 | — | 9 | 2 | no | — |
| 314 | D3×Q8 | — | 9 | 2 | no | — |
| 315 | D3×Q8 | — | 18 | 2 | no | — |
| 316 | D3×Q8 | — | 18 | 2 | no | — |
| 317 | #237 | — | 9 | 2 | no | — |
| 318 | #237 | — | 9 | 2 | no | — |
| 319 | #237 | — | 18 | 2 | no | — |
| 320 | #237 | — | 18 | 2 | no | — |
| 321 | #235 | — | 9 | 2 | no | — |
| 322 | #235 | — | 9 | 2 | no | — |
| 323 | #235 | — | 9 | 1 | no | — |
| 324 | #235 | — | 9 | 2 | no | — |
| 325 | #235 | — | 18 | 2 | no | — |
| 326 | #235 | — | 18 | 2 | no | — |
| 327 | #235 | — | 18 | 2 | no | — |
| 328 | #235 | — | 18 | 2 | no | — |
| 329 | #235 | — | 18 | 2 | no | — |
| 330 | C2×Dic6 | — | 9 | 2 | no | — |
| 331 | C2×Dic6 | — | 18 | 2 | no | — |
| 332 | C3×Q16 | — | 2 | 1 | no | — |
| 333 | C3×Q16 | — | 2 | 2 | no | — |
| 334 | C3×Q16 | — | 4 | 1 | no | — |
| 335 | C3×Q16 | — | 9 | 2 | no | — |
| 336 | C3×Q16 | — | 9 | 2 | no | — |
| 337 | C3×Q16 | — | 9 | 1 | no | — |
| 338 | C3×Q16 | D32 | 1 | 2 | yes | — |
| 339 | C3×Q16 | D32 | 1 | 1 | yes | characteristic |
| 340 | C3×SD16 | — | 9 | 2 | no | — |
| 341 | C3×SD16 | — | 9 | 2 | no | — |
| 342 | C3×M16 | — | 9 | 2 | no | — |
| 343 | C2×C3×C8 | — | 9 | 1 | no | — |
| 344 | #216 | — | 3 | 2 | no | — |
| 345 | #216 | — | 3 | 2 | no | — |
| 346 | #216 | — | 3 | 2 | no | — |
| 347 | #216 | — | 3 | 2 | no | — |
| 348 | #216 | — | 6 | 2 | no | — |
| 349 | #216 | — | 6 | 2 | no | — |
| 350 | #216 | — | 9 | 2 | no | — |
| 351 | #216 | — | 9 | 2 | no | — |
| 352 | #216 | — | 9 | 2 | no | — |
| 353 | #215 | — | 3 | 2 | no | — |
| 354 | #215 | — | 3 | 2 | no | — |
| 355 | #215 | — | 6 | 2 | no | — |
| 356 | #215 | — | 9 | 2 | no | — |
| 357 | #214 | — | 9 | 2 | no | — |
| 358 | #213 | — | 9 | 2 | no | — |
| 359 | #208 | — | 9 | 1 | no | — |
| 360 | C2×C3⋊C8 | — | 9 | 2 | no | — |
| 361 | Dic12 | — | 3 | 2 | no | — |
| 362 | Dic12 | — | 6 | 1 | no | — |
| 363 | Dic12 | — | 9 | 1 | no | — |
| 364 | Dic12 | — | 9 | 2 | no | — |
| 365 | D24 | — | 9 | 1 | no | — |
| 366 | #204 | — | 3 | 2 | no | — |
| 367 | #204 | — | 3 | 2 | no | — |
| 368 | #204 | — | 6 | 2 | no | — |
| 369 | #204 | — | 9 | 2 | no | — |
| 370 | ΓL(1,𝔽25) | — | 3 | 2 | no | — |
| 371 | ΓL(1,𝔽25) | — | 3 | 2 | no | — |
| 372 | ΓL(1,𝔽25) | — | 6 | 2 | no | — |
| 373 | ΓL(1,𝔽25) | — | 9 | 2 | no | — |
| 374 | D3×C8 | — | 3 | 2 | no | — |
| 375 | D3×C8 | — | 6 | 1 | no | — |
| 376 | D3×C8 | — | 9 | 2 | no | — |
| 377 | D3×C8 | — | 9 | 2 | no | — |
| 378 | C2×C3⋊D3 | — | 2 | 2 | no | — |
| 379 | C2×C3⋊D3 | D3×D4 | 1 | 2 | yes | — |
| 380 | C2×C3⋊D3 | D3×D4 | 1 | 1 | yes | characteristic |
| 381 | C2×C3×D3 | — | 3 | 2 | no | — |
| 382 | C2×C3×D3 | — | 3 | 2 | no | — |
| 383 | C2×C3×D3 | — | 3 | 2 | no | — |
| 384 | C2×C3×D3 | — | 6 | 1 | no | — |
| 385 | C2×C3×D3 | — | 6 | 2 | no | — |
| 386 | C2×C3×D3 | — | 6 | 2 | no | — |
| 387 | C2×C3×D3 | — | 6 | 2 | no | — |
| 388 | C2×C3×D3 | — | 12 | 2 | no | — |
| 389 | C32×C4 | — | 2 | 2 | no | — |
| 390 | C32×C4 | — | 2 | 2 | no | — |
| 391 | C32×C4 | — | 2 | 2 | no | — |
| 392 | C32×C4 | — | 2 | 1 | no | — |
| 393 | C32×C4 | — | 2 | 2 | no | — |
| 394 | C32×C4 | — | 4 | 1 | no | — |
| 395 | C32×C4 | — | 4 | 2 | no | — |
| 396 | C32×C4 | — | 4 | 2 | no | — |
| 397 | C32×C4 | — | 4 | 2 | no | — |
| 398 | C32×C4 | — | 8 | 2 | no | — |
| 399 | C32×C4 | C23×D3 | 1 | 2 | yes | — |
| 400 | C32×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 401 | C3⋊Dic3 | — | 2 | 2 | no | — |
| 402 | C3⋊Dic3 | — | 2 | 2 | no | — |
| 403 | C3⋊Dic3 | D3×D4 | 1 | 1 | yes | characteristic |
| 404 | C3⋊Dic3 | D3×D4 | 1 | 2 | yes | — |
| 405 | C3×Dic3 | — | 3 | 2 | no | — |
| 406 | C3×Dic3 | — | 3 | 2 | no | — |
| 407 | C3×Dic3 | — | 3 | 2 | no | — |
| 408 | C3×Dic3 | — | 6 | 1 | no | — |
| 409 | C3×Dic3 | — | 6 | 2 | no | — |
| 410 | C3×Dic3 | — | 6 | 2 | no | — |
| 411 | C3×Dic3 | — | 6 | 2 | no | — |
| 412 | C3×Dic3 | — | 6 | 2 | no | — |
| 413 | C3×Dic3 | — | 6 | 2 | no | — |
| 414 | C3×Dic3 | — | 12 | 2 | no | — |
| 415 | C3×Dic3 | — | 12 | 2 | no | — |
| 416 | 2−1+4 | — | 27 | 2 | no | — |
| 417 | #137 | — | 9 | 2 | no | — |
| 418 | #137 | — | 27 | 2 | no | — |
| 419 | #137 | — | 27 | 2 | no | — |
| 420 | #135 | — | 27 | 1 | no | — |
| 421 | #135 | — | 27 | 2 | no | — |
| 422 | C2×Q16 | — | 9 | 1 | no | — |
| 423 | C2×Q16 | — | 27 | 2 | no | — |
| 424 | #131 | — | 27 | 1 | no | — |
| 425 | C33 | #578 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 426 | C3×Q8 | — | 2 | 2 | no | — |
| 427 | C3×Q8 | — | 2 | 2 | no | — |
| 428 | C3×Q8 | — | 2 | 2 | no | — |
| 429 | C3×Q8 | — | 4 | 2 | no | — |
| 430 | C3×Q8 | — | 9 | 2 | no | — |
| 431 | C3×Q8 | — | 9 | 2 | no | — |
| 432 | C3×Q8 | — | 18 | 2 | no | — |
| 433 | C3×Q8 | — | 18 | 2 | no | — |
| 434 | C3×Q8 | C2×D32 | 1 | 2 | yes | — |
| 435 | C3×Q8 | C2×D32 | 1 | 2 | yes | — |
| 436 | C3×Q8 | C2×D32 | 1 | 2 | yes | — |
| 437 | C3×D4 | — | 9 | 2 | no | — |
| 438 | C3×D4 | — | 18 | 2 | no | — |
| 439 | C2×C3×C4 | — | 9 | 2 | no | — |
| 440 | C2×C3×C4 | — | 9 | 1 | no | — |
| 441 | C2×C3×C4 | — | 18 | 2 | no | — |
| 442 | C2×C3×C4 | — | 18 | 2 | no | — |
| 443 | C2×C3×C4 | — | 18 | 2 | no | — |
| 444 | #67 | — | 9 | 2 | no | — |
| 445 | #67 | — | 9 | 2 | no | — |
| 446 | #67 | — | 9 | 2 | no | — |
| 447 | #67 | — | 18 | 2 | no | — |
| 448 | #67 | — | 18 | 2 | no | — |
| 449 | #67 | — | 18 | 2 | no | — |
| 450 | #67 | — | 18 | 2 | no | — |
| 451 | C2×Dic3 | — | 18 | 2 | no | — |
| 452 | C2×Dic3 | — | 18 | 2 | no | — |
| 453 | C2×Dic3 | — | 18 | 2 | no | — |
| 454 | D12 | — | 3 | 2 | no | — |
| 455 | D12 | — | 3 | 2 | no | — |
| 456 | D12 | — | 6 | 2 | no | — |
| 457 | D12 | — | 6 | 2 | no | — |
| 458 | D12 | — | 6 | 2 | no | — |
| 459 | D12 | — | 9 | 2 | no | — |
| 460 | D12 | — | 9 | 1 | no | — |
| 461 | D12 | — | 12 | 2 | no | — |
| 462 | D12 | — | 18 | 2 | no | — |
| 463 | D12 | — | 18 | 2 | no | — |
| 464 | C4×D3 | — | 3 | 2 | no | — |
| 465 | C4×D3 | — | 3 | 2 | no | — |
| 466 | C4×D3 | — | 3 | 2 | no | — |
| 467 | C4×D3 | — | 6 | 1 | no | — |
| 468 | C4×D3 | — | 6 | 2 | no | — |
| 469 | C4×D3 | — | 6 | 2 | no | — |
| 470 | C4×D3 | — | 6 | 2 | no | — |
| 471 | C4×D3 | — | 6 | 2 | no | — |
| 472 | C4×D3 | — | 6 | 2 | no | — |
| 473 | C4×D3 | — | 6 | 2 | no | — |
| 474 | C4×D3 | — | 6 | 2 | no | — |
| 475 | C4×D3 | — | 12 | 2 | no | — |
| 476 | C4×D3 | — | 12 | 2 | no | — |
| 477 | C4×D3 | — | 12 | 2 | no | — |
| 478 | C4×D3 | — | 18 | 2 | no | — |
| 479 | C4×D3 | — | 18 | 2 | no | — |
| 480 | C4×D3 | — | 18 | 2 | no | — |
| 481 | C4×D3 | — | 18 | 2 | no | — |
| 482 | C4×D3 | — | 18 | 2 | no | — |
| 483 | C4×D3 | — | 18 | 2 | no | — |
| 484 | Dic6 | — | 3 | 2 | no | — |
| 485 | Dic6 | — | 3 | 2 | no | — |
| 486 | Dic6 | — | 3 | 2 | no | — |
| 487 | Dic6 | — | 3 | 2 | no | — |
| 488 | Dic6 | — | 6 | 2 | no | — |
| 489 | Dic6 | — | 6 | 2 | no | — |
| 490 | Dic6 | — | 6 | 2 | no | — |
| 491 | Dic6 | — | 6 | 2 | no | — |
| 492 | Dic6 | — | 6 | 2 | no | — |
| 493 | Dic6 | — | 6 | 2 | no | — |
| 494 | Dic6 | — | 9 | 2 | no | — |
| 495 | Dic6 | — | 9 | 1 | no | — |
| 496 | Dic6 | — | 12 | 2 | no | — |
| 497 | Dic6 | — | 12 | 2 | no | — |
| 498 | Dic6 | — | 18 | 2 | no | — |
| 499 | Dic6 | — | 18 | 2 | no | — |
| 500 | Dic6 | — | 18 | 2 | no | — |
| 501 | C3×C8 | — | 2 | 1 | no | — |
| 502 | C3×C8 | — | 2 | 2 | no | — |
| 503 | C3×C8 | — | 4 | 1 | no | — |
| 504 | C3×C8 | — | 9 | 1 | no | — |
| 505 | C3×C8 | — | 9 | 2 | no | — |
| 506 | C3×C8 | C2×D32 | 1 | 2 | yes | — |
| 507 | C3×C8 | C2×D32 | 1 | 1 | yes | characteristic |
| 508 | C3⋊C8 | — | 3 | 2 | no | — |
| 509 | C3⋊C8 | — | 3 | 2 | no | — |
| 510 | C3⋊C8 | — | 3 | 2 | no | — |
| 511 | C3⋊C8 | — | 6 | 1 | no | — |
| 512 | C3⋊C8 | — | 6 | 2 | no | — |
| 513 | C2×C32 | — | 2 | 1 | no | — |
| 514 | C2×C32 | — | 2 | 2 | no | — |
| 515 | C2×C32 | — | 4 | 1 | no | — |
| 516 | C2×C32 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 517 | C2×C32 | C2×D3×D4 | 1 | 2 | yes | — |
| 518 | C3⋊D3 | — | 2 | 1 | no | — |
| 519 | C3⋊D3 | — | 2 | 2 | no | — |
| 520 | C3⋊D3 | — | 4 | 2 | no | — |
| 521 | C3×D3 | — | 6 | 2 | no | — |
| 522 | C3×D3 | — | 6 | 2 | no | — |
| 523 | C3×D3 | — | 6 | 2 | no | — |
| 524 | C3×D3 | — | 6 | 2 | no | — |
| 525 | C3×D3 | — | 12 | 2 | no | — |
| 526 | C3×D3 | — | 12 | 2 | no | — |
| 527 | C3×D3 | — | 12 | 2 | no | — |
| 528 | C3×D3 | — | 24 | 2 | no | — |
| 529 | #41 | — | 9 | 2 | no | — |
| 530 | #41 | — | 27 | 1 | no | — |
| 531 | #41 | — | 27 | 2 | no | — |
| 532 | #41 | — | 27 | 2 | no | — |
| 533 | #41 | — | 54 | 2 | no | — |
| 534 | #41 | — | 54 | 2 | no | — |
| 535 | #41 | — | 54 | 2 | no | — |
| 536 | C2×Q8 | — | 9 | 2 | no | — |
| 537 | C2×Q8 | — | 9 | 2 | no | — |
| 538 | C2×Q8 | — | 27 | 2 | no | — |
| 539 | C2×Q8 | — | 54 | 2 | no | — |
| 540 | Q16 | — | 9 | 2 | no | — |
| 541 | Q16 | — | 9 | 2 | no | — |
| 542 | Q16 | — | 9 | 1 | no | — |
| 543 | Q16 | — | 27 | 1 | no | — |
| 544 | Q16 | — | 27 | 2 | no | — |
| 545 | Q16 | #1113 | 1 | 1 | yes | characteristic |
| 546 | SD16 | — | 9 | 2 | no | — |
| 547 | SD16 | — | 9 | 2 | no | — |
| 548 | SD16 | — | 27 | 2 | no | — |
| 549 | D8 | — | 27 | 1 | no | — |
| 550 | M16 | — | 9 | 2 | no | — |
| 551 | M16 | — | 27 | 1 | no | — |
| 552 | C2×C8 | — | 9 | 1 | no | — |
| 553 | C2×C8 | — | 27 | 2 | no | — |
| 554 | C22×C3 | — | 9 | 2 | no | — |
| 555 | C22×C3 | — | 9 | 1 | no | — |
| 556 | C22×C3 | — | 18 | 2 | no | — |
| 557 | C2×D3 | — | 3 | 2 | no | — |
| 558 | C2×D3 | — | 3 | 2 | no | — |
| 559 | C2×D3 | — | 3 | 2 | no | — |
| 560 | C2×D3 | — | 6 | 1 | no | — |
| 561 | C2×D3 | — | 6 | 2 | no | — |
| 562 | C2×D3 | — | 6 | 2 | no | — |
| 563 | C2×D3 | — | 6 | 2 | no | — |
| 564 | C2×D3 | — | 12 | 2 | no | — |
| 565 | C3×C4 | — | 2 | 2 | no | — |
| 566 | C3×C4 | — | 2 | 2 | no | — |
| 567 | C3×C4 | — | 2 | 2 | no | — |
| 568 | C3×C4 | — | 2 | 1 | no | — |
| 569 | C3×C4 | — | 2 | 2 | no | — |
| 570 | C3×C4 | — | 4 | 2 | no | — |
| 571 | C3×C4 | — | 4 | 2 | no | — |
| 572 | C3×C4 | — | 4 | 2 | no | — |
| 573 | C3×C4 | — | 4 | 1 | no | — |
| 574 | C3×C4 | — | 8 | 2 | no | — |
| 575 | C3×C4 | — | 9 | 2 | no | — |
| 576 | C3×C4 | — | 9 | 1 | no | — |
| 577 | C3×C4 | — | 18 | 2 | no | — |
| 578 | C3×C4 | — | 18 | 2 | no | — |
| 579 | C3×C4 | C22×D32 | 1 | 2 | yes | — |
| 580 | C3×C4 | C22×D32 | 1 | 1 | yes | characteristic |
| 581 | Dic3 | — | 3 | 2 | no | — |
| 582 | Dic3 | — | 3 | 2 | no | — |
| 583 | Dic3 | — | 3 | 2 | no | — |
| 584 | Dic3 | — | 6 | 1 | no | — |
| 585 | Dic3 | — | 6 | 2 | no | — |
| 586 | Dic3 | — | 6 | 2 | no | — |
| 587 | Dic3 | — | 6 | 2 | no | — |
| 588 | Dic3 | — | 6 | 2 | no | — |
| 589 | Dic3 | — | 6 | 2 | no | — |
| 590 | Dic3 | — | 12 | 2 | no | — |
| 591 | Dic3 | — | 12 | 2 | no | — |
| 592 | C32 | — | 2 | 2 | no | — |
| 593 | C32 | — | 2 | 1 | no | — |
| 594 | C32 | — | 4 | 1 | no | — |
| 595 | C32 | #5766 | 1 | 1 | yes | characteristic, complemented |
| 596 | C32 | #5779 | 1 | 2 | yes | complemented |
| 597 | Q8 | — | 9 | 2 | no | — |
| 598 | Q8 | — | 9 | 2 | no | — |
| 599 | Q8 | — | 18 | 2 | no | — |
| 600 | Q8 | — | 18 | 2 | no | — |
| 601 | Q8 | — | 27 | 1 | no | — |
| 602 | Q8 | — | 54 | 2 | no | — |
| 603 | Q8 | C2×#1113 | 1 | 2 | yes | — |
| 604 | D4 | — | 9 | 2 | no | — |
| 605 | D4 | — | 18 | 2 | no | — |
| 606 | D4 | — | 27 | 2 | no | — |
| 607 | D4 | — | 27 | 1 | no | — |
| 608 | D4 | — | 54 | 2 | no | — |
| 609 | D4 | — | 54 | 2 | no | — |
| 610 | C2×C4 | — | 9 | 1 | no | — |
| 611 | C2×C4 | — | 9 | 2 | no | — |
| 612 | C2×C4 | — | 18 | 2 | no | — |
| 613 | C2×C4 | — | 18 | 2 | no | — |
| 614 | C2×C4 | — | 18 | 2 | no | — |
| 615 | C2×C4 | — | 54 | 2 | no | — |
| 616 | C2×C4 | — | 54 | 2 | no | — |
| 617 | C2×C4 | — | 54 | 2 | no | — |
| 618 | C8 | — | 9 | 1 | no | — |
| 619 | C8 | — | 9 | 2 | no | — |
| 620 | C8 | C2×#1113 | 1 | 1 | yes | characteristic |
| 621 | C2×C3 | — | 2 | 1 | no | — |
| 622 | C2×C3 | — | 2 | 2 | no | — |
| 623 | C2×C3 | — | 4 | 1 | no | — |
| 624 | C2×C3 | — | 18 | 2 | no | — |
| 625 | C2×C3 | — | 18 | 1 | no | — |
| 626 | C2×C3 | — | 36 | 2 | no | — |
| 627 | C2×C3 | D32×D4 | 1 | 2 | yes | — |
| 628 | C2×C3 | D32×D4 | 1 | 1 | yes | characteristic |
| 629 | D3 | — | 6 | 2 | no | — |
| 630 | D3 | — | 6 | 2 | no | — |
| 631 | D3 | — | 6 | 2 | no | — |
| 632 | D3 | — | 6 | 2 | no | — |
| 633 | D3 | — | 12 | 2 | no | — |
| 634 | D3 | — | 12 | 2 | no | — |
| 635 | D3 | — | 12 | 2 | no | — |
| 636 | D3 | — | 24 | 2 | no | — |
| 637 | C22 | — | 9 | 1 | no | — |
| 638 | C22 | — | 9 | 2 | no | — |
| 639 | C22 | — | 18 | 2 | no | — |
| 640 | C4 | — | 2 | 2 | no | — |
| 641 | C4 | — | 9 | 2 | no | — |
| 642 | C4 | — | 9 | 1 | no | — |
| 643 | C4 | — | 18 | 2 | no | — |
| 644 | C4 | — | 18 | 2 | no | — |
| 645 | C4 | C22×#1113 | 1 | 1 | yes | characteristic |
| 646 | C3 | — | 2 | 1 | no | — |
| 647 | C3 | — | 2 | 2 | no | — |
| 648 | C3 | — | 4 | 1 | no | — |
| 649 | C3 | #10594766 | 1 | 2 | yes | complemented |
| 650 | C3 | #10594769 | 1 | 1 | yes | characteristic, complemented |
| 651 | C2 | — | 18 | 1 | no | — |
| 652 | C2 | — | 18 | 2 | no | — |
| 653 | C2 | — | 36 | 2 | no | — |
| 654 | C2 | D4×#1113 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D4×#1113 |
| commutator, cosocle | C33×C4 | C24 |
| Frattini | C4 | C22×#1113 |
| Fitting | C33×Q16 | C22 |
| socle | C2×C33 | C22×D4 |
| hypercenter | Q16 | #1113 |
| hypocenter | C33 | #578 |
| LCS | G ▷ C33×C4 ▷ C2×C33 ▷ C33 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ Q16 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11724624 | C2 | semidirect |
| 2. C3×#64127 | C2 | semidirect |
| 3. C3×Q16×C3⋊D3 | C2 | semidirect |
| 4. #11723713 | C2 | semidirect |
| 5. #11723712 | C2 | semidirect |
| 6. #11723710 | C2 | semidirect |
| 7. #11723653 | C2 | semidirect |
| 8. #11723652 | C2 | semidirect |
| 9. #11723650 | C2 | semidirect |
| 40. #64127 | D3 | semidirect |
| 41. Q16×C3⋊D3 | D3 | semidirect |
| 425. C33 | #578 | semidirect |
| 595. C32 | #5766 | semidirect |
| 596. C32 | #5779 | semidirect |
| 649. C3 | #10594766 | semidirect |
| 650. C3 | #10594769 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11724624 | 2 |
| C3×#64127 | 2 |
| C3×Q16×C3⋊D3 | 2 |
| #11723713 | 2 |
| #11723712 | 2 |
| #11723710 | 2 |
| #11723653 | 2 |
| #11723652 | 2 |
| #11723650 | 2 |
| #10594769 | 3 |
| #10594766 | 3 |