Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1814 conjugacy classes of subgroups.
The subgroup lattice has 660 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×#89028 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C22×C3×#625 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11723715 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11723630 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | C3×#63976 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #11723031 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #11723004 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #11722964 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #11722953 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #10595513 | — | 3 | 2 | no | maximal |
| 11 | #10595239 | — | 3 | 1 | no | maximal |
| 12 | C23×C32×D3 | C22 | 1 | 2 | yes | — |
| 13 | C2×#6312 | C22 | 1 | 1 | yes | characteristic |
| 14 | C22×C3×C3⋊Dic3 | C22 | 1 | 1 | yes | characteristic |
| 15 | C2×C32×#67 | C22 | 1 | 1 | yes | characteristic |
| 16 | C2×#6293 | C22 | 1 | 1 | yes | characteristic, complemented |
| 17 | C2×#6291 | C22 | 1 | 1 | yes | characteristic, complemented |
| 18 | C2×#6291 | C22 | 1 | 4 | yes | complemented |
| 19 | C2×#6289 | C22 | 1 | 1 | yes | characteristic, complemented |
| 20 | #89028 | — | 2 | 4 | no | — |
| 21 | C2×D3×C3⋊Dic3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 22 | C2×C3×#625 | — | 2 | 4 | no | — |
| 23 | C2×C3×#625 | C22 | 1 | 2 | yes | — |
| 24 | C2×C3×#625 | C22 | 1 | 2 | yes | — |
| 25 | C2×C3×#625 | C22 | 1 | 4 | yes | complemented |
| 26 | C3×#3757 | C22 | 1 | 2 | yes | — |
| 27 | #88815 | C22 | 1 | 2 | yes | complemented |
| 28 | #88813 | C22 | 1 | 2 | yes | complemented |
| 29 | (C2×D3)⋊(C3⋊Dic3) | C22 | 1 | 4 | yes | complemented |
| 30 | C3×(C2×D3)⋊Dic3 | C22 | 1 | 4 | yes | complemented |
| 31 | C2×#3830 | — | 3 | 1 | no | — |
| 32 | C22×C3×#67 | — | 3 | 2 | no | — |
| 33 | C22×#625 | D3 | 1 | 1 | yes | characteristic, complemented |
| 34 | C2×#3804 | — | 3 | 2 | no | — |
| 35 | C2×#3804 | — | 6 | 1 | no | — |
| 36 | #64162 | — | 3 | 2 | no | — |
| 37 | C3×#953 | — | 3 | 2 | no | — |
| 38 | C3×#937 | — | 3 | 2 | no | — |
| 39 | #63980 | — | 3 | 2 | no | — |
| 40 | #63979 | — | 3 | 2 | no | — |
| 41 | #63979 | — | 3 | 4 | no | — |
| 42 | #63977 | — | 3 | 2 | no | — |
| 43 | #63977 | — | 3 | 2 | no | — |
| 44 | #63977 | — | 6 | 2 | no | — |
| 45 | #63976 | D3 | 1 | 2 | yes | complemented |
| 46 | #63970 | — | 3 | 4 | no | — |
| 47 | #63959 | — | 3 | 4 | no | — |
| 48 | #63958 | — | 3 | 4 | no | — |
| 49 | #63957 | — | 3 | 1 | no | — |
| 50 | #63955 | — | 3 | 2 | no | — |
| 51 | #63913 | — | 3 | 2 | no | — |
| 52 | #63912 | — | 3 | 2 | no | — |
| 53 | C23×C33 | C23 | 1 | 1 | yes | characteristic |
| 54 | C22×C3⋊(C3⋊D3) | C23 | 1 | 1 | yes | characteristic |
| 55 | C22×C32×D3 | — | 2 | 4 | no | — |
| 56 | C22×C32×D3 | — | 4 | 4 | no | — |
| 57 | C22×C32×D3 | C23 | 1 | 4 | yes | — |
| 58 | C22×C32×D3 | C23 | 1 | 1 | yes | characteristic |
| 59 | #6312 | — | 2 | 2 | no | — |
| 60 | C2×C3⋊(C3⋊Dic3) | C23 | 1 | 1 | yes | characteristic |
| 61 | C2×C3×C3⋊Dic3 | D4 | 1 | 4 | yes | complemented |
| 62 | C2×C3×C3⋊Dic3 | C23 | 1 | 4 | yes | — |
| 63 | C2×C3×C3⋊Dic3 | C23 | 1 | 1 | yes | characteristic |
| 64 | C2×C3×C3⋊Dic3 | C23 | 1 | 1 | yes | characteristic |
| 65 | C32×#67 | — | 2 | 2 | no | — |
| 66 | C2×C32×Dic3 | C23 | 1 | 1 | yes | characteristic |
| 67 | #6293 | — | 2 | 2 | no | — |
| 68 | #6291 | — | 2 | 2 | no | — |
| 69 | #6291 | — | 4 | 4 | no | — |
| 70 | #6289 | — | 2 | 2 | no | — |
| 71 | D3×C3⋊Dic3 | — | 2 | 2 | no | — |
| 72 | C3×#625 | — | 2 | 4 | no | — |
| 73 | C3×#625 | — | 2 | 4 | no | — |
| 74 | C3×#625 | — | 4 | 4 | no | — |
| 75 | #5805 | — | 9 | 1 | no | — |
| 76 | #5592 | — | 9 | 2 | no | — |
| 77 | C24×C32 | — | 3 | 2 | no | — |
| 78 | C23×C3×D3 | — | 2 | 2 | no | — |
| 79 | C23×C3×D3 | C2×D3 | 1 | 2 | yes | — |
| 80 | C23×C3×D3 | C2×D3 | 1 | 2 | yes | — |
| 81 | C2×C32×D4 | — | 3 | 1 | no | — |
| 82 | C2×#638 | — | 3 | 2 | no | — |
| 83 | C2×#638 | — | 3 | 1 | no | — |
| 84 | C2×#638 | — | 3 | 1 | no | — |
| 85 | C2×#638 | — | 3 | 4 | no | — |
| 86 | C2×#638 | — | 6 | 1 | no | — |
| 87 | C2×#638 | — | 6 | 2 | no | — |
| 88 | C2×#638 | — | 12 | 1 | no | — |
| 89 | C22×C3⋊Dic3 | — | 3 | 1 | no | — |
| 90 | C22×C3⋊Dic3 | C2×D3 | 1 | 1 | yes | characteristic |
| 91 | #3830 | — | 6 | 4 | no | — |
| 92 | C2×C4×C3⋊D3 | — | 3 | 1 | no | — |
| 93 | C2×#634 | — | 3 | 1 | no | — |
| 94 | C2×C3×#67 | — | 2 | 1 | no | — |
| 95 | C2×C3×#67 | — | 3 | 4 | no | — |
| 96 | C2×C3×#67 | — | 3 | 4 | no | — |
| 97 | C2×C3×#67 | — | 3 | 4 | no | — |
| 98 | C2×C3×#67 | — | 3 | 4 | no | — |
| 99 | C2×C3×#67 | — | 6 | 8 | no | — |
| 100 | C2×C3×#67 | C2×D3 | 1 | 2 | yes | — |
| 101 | C22×C3×Dic3 | — | 3 | 2 | no | — |
| 102 | C22×C3×Dic3 | — | 6 | 1 | no | — |
| 103 | C2×#627 | — | 3 | 2 | no | — |
| 104 | C2×#627 | — | 6 | 1 | no | — |
| 105 | C2×#626 | — | 3 | 2 | no | — |
| 106 | C2×#626 | — | 3 | 4 | no | — |
| 107 | C2×#626 | — | 3 | 4 | no | — |
| 108 | C2×#626 | — | 6 | 1 | no | — |
| 109 | C2×#626 | — | 6 | 4 | no | — |
| 110 | C2×#625 | — | 2 | 4 | no | — |
| 111 | C2×#625 | C2×D3 | 1 | 2 | yes | — |
| 112 | C2×#625 | C2×D3 | 1 | 2 | yes | — |
| 113 | C2×#625 | C2×D3 | 1 | 4 | yes | complemented |
| 114 | C2×#624 | — | 3 | 2 | no | — |
| 115 | C2×#624 | — | 6 | 1 | no | — |
| 116 | #3804 | — | 6 | 8 | no | — |
| 117 | #3804 | — | 6 | 8 | no | — |
| 118 | C2×D3×Dic3 | — | 3 | 2 | no | — |
| 119 | C2×D3×Dic3 | — | 6 | 1 | no | — |
| 120 | #3757 | — | 3 | 4 | no | — |
| 121 | #3757 | C2×D3 | 1 | 2 | yes | — |
| 122 | C3×#217 | — | 3 | 2 | no | — |
| 123 | C3×#217 | — | 3 | 2 | no | — |
| 124 | C3×#217 | — | 3 | 4 | no | — |
| 125 | C3×#217 | — | 6 | 2 | no | — |
| 126 | C3×(C2×D3)⋊C4 | — | 3 | 4 | no | — |
| 127 | #3724 | — | 3 | 2 | no | — |
| 128 | Dic3⋊Dic3 | — | 3 | 4 | no | — |
| 129 | (C2×D3)⋊Dic3 | — | 3 | 4 | no | — |
| 130 | (C2×D3)⋊Dic3 | — | 3 | 4 | no | — |
| 131 | (C2×D3)⋊Dic3 | — | 6 | 4 | no | — |
| 132 | (C2×D3)⋊Dic3 | C2×D3 | 1 | 4 | yes | complemented |
| 133 | Dic32 | — | 3 | 2 | no | — |
| 134 | Dic32 | — | 3 | 4 | no | — |
| 135 | C22×C33 | — | 2 | 2 | no | — |
| 136 | C22×C33 | C2×D4 | 1 | 2 | yes | — |
| 137 | C22×C33 | C24 | 1 | 1 | yes | characteristic |
| 138 | C2×C3⋊(C3⋊D3) | — | 2 | 1 | no | — |
| 139 | C2×C3⋊(C3⋊D3) | — | 2 | 2 | no | — |
| 140 | C2×C32×D3 | — | 2 | 1 | no | — |
| 141 | C2×C32×D3 | — | 2 | 4 | no | — |
| 142 | C2×C32×D3 | — | 2 | 4 | no | — |
| 143 | C2×C32×D3 | — | 2 | 2 | no | — |
| 144 | C2×C32×D3 | — | 2 | 4 | no | — |
| 145 | C2×C32×D3 | — | 4 | 8 | no | — |
| 146 | C3⋊(C3⋊Dic3) | — | 2 | 1 | no | — |
| 147 | C3×C3⋊Dic3 | — | 2 | 4 | no | — |
| 148 | C3×C3⋊Dic3 | C2×D4 | 1 | 2 | yes | — |
| 149 | C3×C3⋊Dic3 | C2×D4 | 1 | 2 | yes | — |
| 150 | C32×Dic3 | — | 2 | 1 | no | — |
| 151 | C22×C3×D4 | — | 9 | 1 | no | — |
| 152 | C22×#67 | — | 3 | 2 | no | — |
| 153 | C2×#237 | — | 9 | 2 | no | — |
| 154 | C2×#237 | — | 18 | 1 | no | — |
| 155 | C2×#235 | — | 9 | 1 | no | — |
| 156 | C3×#120 | — | 9 | 2 | no | — |
| 157 | #953 | — | 3 | 2 | no | — |
| 158 | #953 | — | 9 | 2 | no | — |
| 159 | #953 | — | 9 | 2 | no | — |
| 160 | #953 | — | 18 | 2 | no | — |
| 161 | #940 | — | 9 | 2 | no | — |
| 162 | #940 | — | 9 | 4 | no | — |
| 163 | #939 | — | 9 | 4 | no | — |
| 164 | #938 | — | 9 | 2 | no | — |
| 165 | #938 | — | 9 | 2 | no | — |
| 166 | #937 | — | 3 | 2 | no | — |
| 167 | #936 | — | 9 | 2 | no | — |
| 168 | #926 | — | 9 | 1 | no | — |
| 169 | #885 | — | 9 | 4 | no | — |
| 170 | #884 | — | 9 | 4 | no | — |
| 171 | #882 | — | 9 | 2 | no | — |
| 172 | #877 | — | 9 | 2 | no | — |
| 173 | C23×C32 | — | 2 | 2 | no | — |
| 174 | C23×C32 | — | 2 | 1 | no | — |
| 175 | C23×C32 | — | 3 | 4 | no | — |
| 176 | C23×C32 | — | 3 | 1 | no | — |
| 177 | C23×C32 | — | 4 | 1 | no | — |
| 178 | C23×C32 | — | 6 | 4 | no | — |
| 179 | C23×C32 | — | 12 | 4 | no | — |
| 180 | C23×C32 | C22×D3 | 1 | 2 | yes | — |
| 181 | C23×C32 | C22×D3 | 1 | 1 | yes | characteristic |
| 182 | C22×C3⋊D3 | — | 3 | 2 | no | — |
| 183 | C22×C3⋊D3 | — | 3 | 1 | no | — |
| 184 | C22×C3⋊D3 | — | 6 | 1 | no | — |
| 185 | C22×C3⋊D3 | — | 6 | 2 | no | — |
| 186 | C22×C3⋊D3 | — | 12 | 1 | no | — |
| 187 | C22×C3×D3 | — | 2 | 4 | no | — |
| 188 | C22×C3×D3 | — | 2 | 4 | no | — |
| 189 | C22×C3×D3 | — | 2 | 4 | no | — |
| 190 | C22×C3×D3 | — | 2 | 1 | no | — |
| 191 | C22×C3×D3 | — | 4 | 4 | no | — |
| 192 | C22×C3×D3 | — | 4 | 4 | no | — |
| 193 | C22×C3×D3 | — | 4 | 4 | no | — |
| 194 | C22×C3×D3 | — | 4 | 8 | no | — |
| 195 | C22×C3×D3 | C22×D3 | 1 | 4 | yes | — |
| 196 | C22×C3×D3 | C22×D3 | 1 | 4 | yes | — |
| 197 | C22×C3×D3 | C22×D3 | 1 | 2 | yes | — |
| 198 | C32×D4 | — | 6 | 2 | no | — |
| 199 | C2×C32×C4 | — | 3 | 1 | no | — |
| 200 | #638 | — | 6 | 2 | no | — |
| 201 | #638 | — | 6 | 2 | no | — |
| 202 | #638 | — | 6 | 4 | no | — |
| 203 | #638 | — | 6 | 4 | no | — |
| 204 | #638 | — | 12 | 4 | no | — |
| 205 | #638 | — | 12 | 4 | no | — |
| 206 | #638 | — | 12 | 4 | no | — |
| 207 | C2×C3⋊Dic3 | — | 3 | 1 | no | — |
| 208 | C2×C3⋊Dic3 | — | 3 | 2 | no | — |
| 209 | C2×C3⋊Dic3 | — | 6 | 1 | no | — |
| 210 | C2×C3⋊Dic3 | — | 6 | 2 | no | — |
| 211 | C2×C3⋊Dic3 | — | 6 | 2 | no | — |
| 212 | C2×C3⋊Dic3 | — | 12 | 1 | no | — |
| 213 | C2×C3⋊Dic3 | #67 | 1 | 4 | yes | complemented |
| 214 | C2×C3⋊Dic3 | C22×D3 | 1 | 4 | yes | — |
| 215 | C2×C3⋊Dic3 | C22×D3 | 1 | 1 | yes | characteristic |
| 216 | C2×C3⋊Dic3 | C22×D3 | 1 | 1 | yes | characteristic |
| 217 | C4×C3⋊D3 | — | 6 | 2 | no | — |
| 218 | #634 | — | 6 | 2 | no | — |
| 219 | C3×#67 | — | 2 | 4 | no | — |
| 220 | C3×#67 | — | 2 | 4 | no | — |
| 221 | C3×#67 | — | 6 | 8 | no | — |
| 222 | C3×#67 | — | 6 | 8 | no | — |
| 223 | C3×#67 | — | 12 | 4 | no | — |
| 224 | C3×#67 | — | 12 | 4 | no | — |
| 225 | C2×C3×Dic3 | — | 2 | 1 | no | — |
| 226 | C2×C3×Dic3 | — | 3 | 8 | no | — |
| 227 | C2×C3×Dic3 | — | 3 | 2 | no | — |
| 228 | C2×C3×Dic3 | — | 3 | 2 | no | — |
| 229 | C2×C3×Dic3 | — | 3 | 4 | no | — |
| 230 | C2×C3×Dic3 | — | 3 | 4 | no | — |
| 231 | C2×C3×Dic3 | — | 6 | 4 | no | — |
| 232 | C2×C3×Dic3 | — | 6 | 1 | no | — |
| 233 | C2×C3×Dic3 | — | 6 | 1 | no | — |
| 234 | C2×C3×Dic3 | — | 6 | 4 | no | — |
| 235 | C2×C3×Dic3 | C22×D3 | 1 | 2 | yes | — |
| 236 | #627 | — | 6 | 4 | no | — |
| 237 | #627 | — | 6 | 4 | no | — |
| 238 | #626 | — | 6 | 4 | no | — |
| 239 | #626 | — | 6 | 4 | no | — |
| 240 | #626 | — | 12 | 4 | no | — |
| 241 | #626 | — | 12 | 4 | no | — |
| 242 | #626 | — | 12 | 8 | no | — |
| 243 | #625 | — | 2 | 4 | no | — |
| 244 | #625 | — | 2 | 4 | no | — |
| 245 | #625 | — | 4 | 4 | no | — |
| 246 | #624 | — | 6 | 4 | no | — |
| 247 | #624 | — | 6 | 4 | no | — |
| 248 | D3×Dic3 | — | 6 | 4 | no | — |
| 249 | D3×Dic3 | — | 6 | 4 | no | — |
| 250 | #535 | — | 27 | 1 | no | Sylow |
| 251 | C2×C33 | — | 2 | 2 | no | — |
| 252 | C2×C33 | C22×D4 | 1 | 1 | yes | characteristic |
| 253 | C2×C33 | H(5,𝔽2) | 1 | 2 | yes | — |
| 254 | C3⋊(C3⋊D3) | — | 4 | 1 | no | — |
| 255 | C32×D3 | — | 4 | 1 | no | — |
| 256 | C32×D3 | — | 4 | 4 | no | — |
| 257 | C24×C3 | — | 3 | 2 | no | — |
| 258 | C24×C3 | — | 3 | 2 | no | — |
| 259 | C24×C3 | — | 6 | 2 | no | — |
| 260 | C23×D3 | D32 | 1 | 2 | yes | — |
| 261 | C2×C3×D4 | — | 3 | 2 | no | — |
| 262 | C2×C3×D4 | — | 6 | 1 | no | — |
| 263 | C2×C3×D4 | — | 9 | 2 | no | — |
| 264 | C2×C3×D4 | — | 9 | 2 | no | — |
| 265 | C2×C3×D4 | — | 9 | 4 | no | — |
| 266 | C2×C3×D4 | — | 18 | 4 | no | — |
| 267 | C22×C3×C4 | — | 9 | 1 | no | — |
| 268 | C2×#67 | — | 3 | 4 | no | — |
| 269 | C2×#67 | — | 3 | 4 | no | — |
| 270 | C2×#67 | — | 3 | 4 | no | — |
| 271 | C2×#67 | — | 3 | 4 | no | — |
| 272 | C2×#67 | — | 6 | 8 | no | — |
| 273 | C2×#67 | — | 9 | 2 | no | — |
| 274 | C2×#67 | — | 9 | 4 | no | — |
| 275 | C2×#67 | — | 9 | 4 | no | — |
| 276 | C2×#67 | — | 9 | 2 | no | — |
| 277 | C2×#67 | — | 9 | 1 | no | — |
| 278 | C2×#67 | — | 18 | 1 | no | — |
| 279 | C2×#67 | — | 18 | 4 | no | — |
| 280 | C2×#67 | — | 18 | 1 | no | — |
| 281 | C2×#67 | — | 18 | 2 | no | — |
| 282 | C2×#67 | — | 36 | 1 | no | — |
| 283 | C2×#67 | D32 | 1 | 1 | yes | characteristic |
| 284 | C22×Dic3 | — | 3 | 2 | no | — |
| 285 | C22×Dic3 | — | 6 | 1 | no | — |
| 286 | C22×Dic3 | — | 9 | 2 | no | — |
| 287 | C22×Dic3 | — | 18 | 1 | no | — |
| 288 | #237 | — | 18 | 8 | no | — |
| 289 | #237 | — | 18 | 8 | no | — |
| 290 | #235 | — | 18 | 4 | no | — |
| 291 | C2×D12 | — | 9 | 1 | no | — |
| 292 | C2×D12 | — | 9 | 4 | no | — |
| 293 | C2×C4×D3 | — | 9 | 2 | no | — |
| 294 | C2×C4×D3 | — | 9 | 1 | no | — |
| 295 | C2×C4×D3 | — | 9 | 1 | no | — |
| 296 | C2×C4×D3 | — | 18 | 1 | no | — |
| 297 | C2×Dic6 | — | 9 | 2 | no | — |
| 298 | C2×Dic6 | — | 9 | 1 | no | — |
| 299 | C2×Dic6 | — | 18 | 1 | no | — |
| 300 | C3×C22⋊C4 | — | 9 | 4 | no | — |
| 301 | C3×C22⋊C4 | — | 9 | 2 | no | — |
| 302 | #217 | — | 3 | 2 | no | — |
| 303 | #217 | — | 3 | 2 | no | — |
| 304 | #217 | — | 3 | 4 | no | — |
| 305 | #217 | — | 6 | 2 | no | — |
| 306 | #217 | — | 9 | 4 | no | — |
| 307 | #217 | — | 9 | 4 | no | — |
| 308 | #217 | — | 18 | 4 | no | — |
| 309 | (C2×D3)⋊C4 | — | 3 | 4 | no | — |
| 310 | (C2×D3)⋊C4 | — | 9 | 4 | no | — |
| 311 | C4⋊Dic3 | — | 9 | 2 | no | — |
| 312 | Dic3⋊C4 | — | 9 | 4 | no | — |
| 313 | C4×Dic3 | — | 9 | 4 | no | — |
| 314 | C4×Dic3 | — | 9 | 2 | no | — |
| 315 | C22×C32 | — | 2 | 2 | no | — |
| 316 | C22×C32 | — | 2 | 4 | no | — |
| 317 | C22×C32 | — | 2 | 1 | no | — |
| 318 | C22×C32 | — | 2 | 2 | no | — |
| 319 | C22×C32 | — | 2 | 4 | no | — |
| 320 | C22×C32 | — | 2 | 2 | no | — |
| 321 | C22×C32 | — | 4 | 1 | no | — |
| 322 | C22×C32 | — | 4 | 2 | no | — |
| 323 | C22×C32 | — | 4 | 4 | no | — |
| 324 | C22×C32 | — | 4 | 2 | no | — |
| 325 | C22×C32 | — | 6 | 4 | no | — |
| 326 | C22×C32 | — | 6 | 1 | no | — |
| 327 | C22×C32 | — | 6 | 4 | no | — |
| 328 | C22×C32 | — | 6 | 2 | no | — |
| 329 | C22×C32 | — | 6 | 4 | no | — |
| 330 | C22×C32 | — | 8 | 2 | no | — |
| 331 | C22×C32 | — | 12 | 8 | no | — |
| 332 | C22×C32 | D3×D4 | 1 | 4 | yes | — |
| 333 | C22×C32 | C2×#67 | 1 | 2 | yes | — |
| 334 | C22×C32 | C23×D3 | 1 | 2 | yes | — |
| 335 | C22×C32 | C23×D3 | 1 | 1 | yes | characteristic |
| 336 | C2×C3⋊D3 | — | 6 | 1 | no | — |
| 337 | C2×C3⋊D3 | — | 6 | 2 | no | — |
| 338 | C2×C3⋊D3 | — | 6 | 2 | no | — |
| 339 | C2×C3⋊D3 | — | 6 | 2 | no | — |
| 340 | C2×C3⋊D3 | — | 6 | 4 | no | — |
| 341 | C2×C3⋊D3 | — | 12 | 2 | no | — |
| 342 | C2×C3⋊D3 | — | 12 | 2 | no | — |
| 343 | C2×C3⋊D3 | — | 12 | 2 | no | — |
| 344 | C2×C3⋊D3 | — | 12 | 4 | no | — |
| 345 | C2×C3⋊D3 | — | 24 | 2 | no | — |
| 346 | C2×C3×D3 | — | 2 | 2 | no | — |
| 347 | C2×C3×D3 | — | 2 | 8 | no | — |
| 348 | C2×C3×D3 | — | 2 | 2 | no | — |
| 349 | C2×C3×D3 | — | 2 | 4 | no | — |
| 350 | C2×C3×D3 | — | 2 | 4 | no | — |
| 351 | C2×C3×D3 | — | 2 | 4 | no | — |
| 352 | C2×C3×D3 | — | 2 | 4 | no | — |
| 353 | C2×C3×D3 | — | 2 | 4 | no | — |
| 354 | C2×C3×D3 | — | 2 | 4 | no | — |
| 355 | C2×C3×D3 | — | 2 | 4 | no | — |
| 356 | C2×C3×D3 | — | 4 | 2 | no | — |
| 357 | C2×C3×D3 | — | 4 | 4 | no | — |
| 358 | C2×C3×D3 | — | 4 | 4 | no | — |
| 359 | C2×C3×D3 | — | 4 | 8 | no | — |
| 360 | C2×C3×D3 | — | 4 | 8 | no | — |
| 361 | C2×C3×D3 | — | 4 | 16 | no | — |
| 362 | C32×C4 | — | 6 | 1 | no | — |
| 363 | C3⋊Dic3 | — | 2 | 4 | no | — |
| 364 | C3⋊Dic3 | — | 6 | 1 | no | — |
| 365 | C3⋊Dic3 | — | 6 | 2 | no | — |
| 366 | C3⋊Dic3 | — | 6 | 2 | no | — |
| 367 | C3⋊Dic3 | — | 12 | 2 | no | — |
| 368 | C3⋊Dic3 | — | 12 | 2 | no | — |
| 369 | C3⋊Dic3 | C2×#67 | 1 | 2 | yes | — |
| 370 | C3⋊Dic3 | C2×#67 | 1 | 2 | yes | — |
| 371 | C3×Dic3 | — | 2 | 2 | no | — |
| 372 | C3×Dic3 | — | 2 | 2 | no | — |
| 373 | C3×Dic3 | — | 3 | 4 | no | — |
| 374 | C3×Dic3 | — | 3 | 4 | no | — |
| 375 | C3×Dic3 | — | 6 | 2 | no | — |
| 376 | C3×Dic3 | — | 6 | 2 | no | — |
| 377 | C3×Dic3 | — | 6 | 4 | no | — |
| 378 | C3×Dic3 | — | 6 | 4 | no | — |
| 379 | C3×Dic3 | — | 12 | 4 | no | — |
| 380 | C2×#41 | — | 27 | 1 | no | — |
| 381 | C22×D4 | — | 9 | 1 | no | — |
| 382 | #127 | — | 27 | 2 | no | — |
| 383 | #124 | — | 27 | 2 | no | — |
| 384 | #121 | — | 27 | 2 | no | — |
| 385 | #121 | — | 27 | 2 | no | — |
| 386 | #120 | — | 9 | 2 | no | — |
| 387 | #120 | — | 27 | 2 | no | — |
| 388 | #117 | — | 27 | 1 | no | — |
| 389 | C33 | #535 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 390 | C23×C3 | — | 2 | 2 | no | — |
| 391 | C23×C3 | — | 2 | 1 | no | — |
| 392 | C23×C3 | — | 3 | 4 | no | — |
| 393 | C23×C3 | — | 3 | 4 | no | — |
| 394 | C23×C3 | — | 3 | 2 | no | — |
| 395 | C23×C3 | — | 4 | 1 | no | — |
| 396 | C23×C3 | — | 6 | 4 | no | — |
| 397 | C23×C3 | — | 6 | 1 | no | — |
| 398 | C23×C3 | — | 6 | 4 | no | — |
| 399 | C23×C3 | — | 6 | 4 | no | — |
| 400 | C23×C3 | — | 12 | 4 | no | — |
| 401 | C23×C3 | — | 12 | 4 | no | — |
| 402 | C23×C3 | — | 12 | 4 | no | — |
| 403 | C23×C3 | — | 12 | 8 | no | — |
| 404 | C23×C3 | C2×D32 | 1 | 2 | yes | — |
| 405 | C23×C3 | C2×D32 | 1 | 1 | yes | characteristic |
| 406 | C22×D3 | — | 2 | 4 | no | — |
| 407 | C22×D3 | — | 4 | 4 | no | — |
| 408 | C22×D3 | — | 9 | 2 | no | — |
| 409 | C22×D3 | — | 9 | 1 | no | — |
| 410 | C22×D3 | — | 18 | 1 | no | — |
| 411 | C22×D3 | — | 18 | 2 | no | — |
| 412 | C22×D3 | — | 36 | 1 | no | — |
| 413 | C22×D3 | C2×D32 | 1 | 4 | yes | — |
| 414 | C22×D3 | C2×D32 | 1 | 1 | yes | characteristic |
| 415 | C3×D4 | — | 6 | 4 | no | — |
| 416 | C3×D4 | — | 6 | 4 | no | — |
| 417 | C3×D4 | — | 18 | 4 | no | — |
| 418 | C3×D4 | — | 18 | 4 | no | — |
| 419 | C3×D4 | — | 36 | 4 | no | — |
| 420 | C2×C3×C4 | — | 3 | 2 | no | — |
| 421 | C2×C3×C4 | — | 6 | 1 | no | — |
| 422 | C2×C3×C4 | — | 9 | 1 | no | — |
| 423 | C2×C3×C4 | — | 9 | 1 | no | — |
| 424 | C2×C3×C4 | — | 9 | 4 | no | — |
| 425 | C2×C3×C4 | — | 9 | 4 | no | — |
| 426 | #67 | — | 2 | 2 | no | — |
| 427 | #67 | — | 6 | 8 | no | — |
| 428 | #67 | — | 6 | 8 | no | — |
| 429 | #67 | — | 12 | 4 | no | — |
| 430 | #67 | — | 12 | 4 | no | — |
| 431 | #67 | — | 18 | 4 | no | — |
| 432 | #67 | — | 18 | 4 | no | — |
| 433 | #67 | — | 18 | 4 | no | — |
| 434 | #67 | — | 18 | 4 | no | — |
| 435 | #67 | — | 18 | 2 | no | — |
| 436 | #67 | — | 36 | 4 | no | — |
| 437 | #67 | — | 36 | 4 | no | — |
| 438 | #67 | — | 36 | 4 | no | — |
| 439 | #67 | — | 36 | 4 | no | — |
| 440 | #67 | — | 36 | 8 | no | — |
| 441 | C2×Dic3 | — | 3 | 2 | no | — |
| 442 | C2×Dic3 | — | 3 | 2 | no | — |
| 443 | C2×Dic3 | — | 3 | 8 | no | — |
| 444 | C2×Dic3 | — | 3 | 4 | no | — |
| 445 | C2×Dic3 | — | 3 | 4 | no | — |
| 446 | C2×Dic3 | — | 6 | 4 | no | — |
| 447 | C2×Dic3 | — | 6 | 1 | no | — |
| 448 | C2×Dic3 | — | 6 | 1 | no | — |
| 449 | C2×Dic3 | — | 6 | 4 | no | — |
| 450 | C2×Dic3 | — | 9 | 2 | no | — |
| 451 | C2×Dic3 | — | 9 | 1 | no | — |
| 452 | C2×Dic3 | — | 18 | 1 | no | — |
| 453 | C2×Dic3 | — | 18 | 2 | no | — |
| 454 | C2×Dic3 | — | 18 | 4 | no | — |
| 455 | C2×Dic3 | — | 18 | 4 | no | — |
| 456 | C2×Dic3 | — | 36 | 1 | no | — |
| 457 | C2×Dic3 | C2×D32 | 1 | 1 | yes | characteristic |
| 458 | D12 | — | 18 | 2 | no | — |
| 459 | D12 | — | 36 | 4 | no | — |
| 460 | C4×D3 | — | 18 | 2 | no | — |
| 461 | C4×D3 | — | 18 | 4 | no | — |
| 462 | C4×D3 | — | 18 | 4 | no | — |
| 463 | C4×D3 | — | 18 | 2 | no | — |
| 464 | Dic6 | — | 18 | 2 | no | — |
| 465 | Dic6 | — | 18 | 4 | no | — |
| 466 | Dic6 | — | 18 | 4 | no | — |
| 467 | C2×C32 | — | 2 | 2 | no | — |
| 468 | C2×C32 | — | 2 | 4 | no | — |
| 469 | C2×C32 | — | 2 | 2 | no | — |
| 470 | C2×C32 | — | 2 | 2 | no | — |
| 471 | C2×C32 | — | 2 | 1 | no | — |
| 472 | C2×C32 | — | 2 | 4 | no | — |
| 473 | C2×C32 | — | 4 | 1 | no | — |
| 474 | C2×C32 | — | 4 | 2 | no | — |
| 475 | C2×C32 | — | 4 | 4 | no | — |
| 476 | C2×C32 | — | 4 | 2 | no | — |
| 477 | C2×C32 | — | 8 | 2 | no | — |
| 478 | C2×C32 | — | 12 | 1 | no | — |
| 479 | C2×C32 | — | 12 | 4 | no | — |
| 480 | C2×C32 | C2×D3×D4 | 1 | 2 | yes | — |
| 481 | C2×C32 | #1004 | 1 | 4 | yes | — |
| 482 | C2×C32 | #1004 | 1 | 2 | yes | — |
| 483 | C2×C32 | C22×#67 | 1 | 1 | yes | characteristic |
| 484 | C3⋊D3 | — | 12 | 1 | no | — |
| 485 | C3⋊D3 | — | 12 | 2 | no | — |
| 486 | C3⋊D3 | — | 12 | 2 | no | — |
| 487 | C3⋊D3 | — | 24 | 2 | no | — |
| 488 | C3⋊D3 | — | 24 | 2 | no | — |
| 489 | C3×D3 | — | 4 | 2 | no | — |
| 490 | C3×D3 | — | 4 | 8 | no | — |
| 491 | C3×D3 | — | 4 | 4 | no | — |
| 492 | C3×D3 | — | 4 | 2 | no | — |
| 493 | C3×D3 | — | 4 | 4 | no | — |
| 494 | C24 | — | 3 | 2 | no | — |
| 495 | #41 | — | 54 | 4 | no | — |
| 496 | C2×Q8 | — | 27 | 1 | no | — |
| 497 | C2×D4 | — | 3 | 1 | no | — |
| 498 | C2×D4 | — | 9 | 2 | no | — |
| 499 | C2×D4 | — | 9 | 2 | no | — |
| 500 | C2×D4 | — | 9 | 4 | no | — |
| 501 | C2×D4 | — | 18 | 4 | no | — |
| 502 | C2×D4 | — | 27 | 1 | no | — |
| 503 | C2×D4 | — | 27 | 4 | no | — |
| 504 | C2×D4 | — | 27 | 1 | no | — |
| 505 | C22×C4 | — | 9 | 1 | no | — |
| 506 | C22×C4 | — | 27 | 1 | no | — |
| 507 | C22×C4 | — | 27 | 1 | no | — |
| 508 | C4⋊C4 | — | 27 | 2 | no | — |
| 509 | C22⋊C4 | — | 9 | 4 | no | — |
| 510 | C22⋊C4 | — | 9 | 2 | no | — |
| 511 | C22⋊C4 | — | 27 | 4 | no | — |
| 512 | C42 | — | 27 | 2 | no | — |
| 513 | C22×C3 | — | 2 | 2 | no | — |
| 514 | C22×C3 | — | 2 | 4 | no | — |
| 515 | C22×C3 | — | 2 | 1 | no | — |
| 516 | C22×C3 | — | 2 | 2 | no | — |
| 517 | C22×C3 | — | 2 | 2 | no | — |
| 518 | C22×C3 | — | 2 | 4 | no | — |
| 519 | C22×C3 | — | 4 | 4 | no | — |
| 520 | C22×C3 | — | 4 | 2 | no | — |
| 521 | C22×C3 | — | 4 | 1 | no | — |
| 522 | C22×C3 | — | 4 | 2 | no | — |
| 523 | C22×C3 | — | 6 | 2 | no | — |
| 524 | C22×C3 | — | 6 | 8 | no | — |
| 525 | C22×C3 | — | 6 | 4 | no | — |
| 526 | C22×C3 | — | 6 | 4 | no | — |
| 527 | C22×C3 | — | 6 | 2 | no | — |
| 528 | C22×C3 | — | 6 | 4 | no | — |
| 529 | C22×C3 | — | 6 | 4 | no | — |
| 530 | C22×C3 | — | 6 | 4 | no | — |
| 531 | C22×C3 | — | 6 | 4 | no | — |
| 532 | C22×C3 | — | 6 | 4 | no | — |
| 533 | C22×C3 | — | 8 | 2 | no | — |
| 534 | C22×C3 | — | 12 | 4 | no | — |
| 535 | C22×C3 | — | 12 | 4 | no | — |
| 536 | C22×C3 | — | 12 | 2 | no | — |
| 537 | C22×C3 | — | 12 | 8 | no | — |
| 538 | C22×C3 | — | 12 | 8 | no | — |
| 539 | C22×C3 | — | 12 | 16 | no | — |
| 540 | C22×C3 | D3×#67 | 1 | 4 | yes | — |
| 541 | C22×C3 | #3811 | 1 | 2 | yes | — |
| 542 | C22×C3 | C22×D32 | 1 | 1 | yes | characteristic |
| 543 | C22×C3 | C22×D32 | 1 | 2 | yes | — |
| 544 | C2×D3 | — | 2 | 2 | no | — |
| 545 | C2×D3 | — | 2 | 4 | no | — |
| 546 | C2×D3 | — | 2 | 1 | no | — |
| 547 | C2×D3 | — | 2 | 4 | no | — |
| 548 | C2×D3 | — | 2 | 4 | no | — |
| 549 | C2×D3 | — | 4 | 8 | no | — |
| 550 | C2×D3 | — | 18 | 2 | no | — |
| 551 | C2×D3 | — | 18 | 2 | no | — |
| 552 | C2×D3 | — | 18 | 2 | no | — |
| 553 | C2×D3 | — | 18 | 1 | no | — |
| 554 | C2×D3 | — | 18 | 4 | no | — |
| 555 | C2×D3 | — | 36 | 2 | no | — |
| 556 | C2×D3 | — | 36 | 2 | no | — |
| 557 | C2×D3 | — | 36 | 4 | no | — |
| 558 | C2×D3 | — | 36 | 2 | no | — |
| 559 | C2×D3 | — | 72 | 2 | no | — |
| 560 | C3×C4 | — | 6 | 2 | no | — |
| 561 | C3×C4 | — | 6 | 2 | no | — |
| 562 | C3×C4 | — | 9 | 2 | no | — |
| 563 | C3×C4 | — | 9 | 2 | no | — |
| 564 | C3×C4 | — | 18 | 4 | no | — |
| 565 | Dic3 | — | 2 | 1 | no | — |
| 566 | Dic3 | — | 3 | 4 | no | — |
| 567 | Dic3 | — | 3 | 4 | no | — |
| 568 | Dic3 | — | 6 | 2 | no | — |
| 569 | Dic3 | — | 6 | 2 | no | — |
| 570 | Dic3 | — | 6 | 4 | no | — |
| 571 | Dic3 | — | 6 | 4 | no | — |
| 572 | Dic3 | — | 12 | 4 | no | — |
| 573 | Dic3 | — | 18 | 2 | no | — |
| 574 | Dic3 | — | 18 | 2 | no | — |
| 575 | Dic3 | — | 18 | 1 | no | — |
| 576 | Dic3 | — | 36 | 2 | no | — |
| 577 | Dic3 | — | 36 | 2 | no | — |
| 578 | C32 | — | 2 | 1 | no | — |
| 579 | C32 | — | 2 | 2 | no | — |
| 580 | C32 | — | 4 | 1 | no | — |
| 581 | C32 | #5592 | 1 | 2 | yes | complemented |
| 582 | C32 | #5805 | 1 | 1 | yes | characteristic, complemented |
| 583 | C23 | — | 3 | 4 | no | — |
| 584 | C23 | — | 3 | 1 | no | — |
| 585 | C23 | — | 6 | 4 | no | — |
| 586 | C23 | — | 12 | 4 | no | — |
| 587 | C23 | — | 27 | 1 | no | — |
| 588 | C23 | D33 | 1 | 1 | yes | characteristic |
| 589 | Q8 | — | 54 | 2 | no | — |
| 590 | D4 | — | 6 | 2 | no | — |
| 591 | D4 | — | 18 | 4 | no | — |
| 592 | D4 | — | 18 | 4 | no | — |
| 593 | D4 | — | 36 | 4 | no | — |
| 594 | D4 | — | 54 | 2 | no | — |
| 595 | D4 | — | 54 | 2 | no | — |
| 596 | D4 | — | 108 | 4 | no | — |
| 597 | C2×C4 | — | 3 | 1 | no | — |
| 598 | C2×C4 | — | 9 | 1 | no | — |
| 599 | C2×C4 | — | 9 | 1 | no | — |
| 600 | C2×C4 | — | 9 | 4 | no | — |
| 601 | C2×C4 | — | 9 | 4 | no | — |
| 602 | C2×C4 | — | 27 | 1 | no | — |
| 603 | C2×C4 | — | 54 | 2 | no | — |
| 604 | C2×C4 | — | 54 | 2 | no | — |
| 605 | C2×C3 | — | 2 | 2 | no | — |
| 606 | C2×C3 | — | 2 | 4 | no | — |
| 607 | C2×C3 | — | 2 | 4 | no | — |
| 608 | C2×C3 | — | 2 | 2 | no | — |
| 609 | C2×C3 | — | 2 | 1 | no | — |
| 610 | C2×C3 | — | 2 | 2 | no | — |
| 611 | C2×C3 | — | 4 | 4 | no | — |
| 612 | C2×C3 | — | 4 | 2 | no | — |
| 613 | C2×C3 | — | 4 | 2 | no | — |
| 614 | C2×C3 | — | 4 | 1 | no | — |
| 615 | C2×C3 | — | 8 | 2 | no | — |
| 616 | C2×C3 | — | 12 | 8 | no | — |
| 617 | C2×C3 | — | 12 | 2 | no | — |
| 618 | C2×C3 | — | 12 | 4 | no | — |
| 619 | C2×C3 | — | 12 | 4 | no | — |
| 620 | C2×C3 | — | 12 | 2 | no | — |
| 621 | C2×C3 | #64313 | 1 | 2 | yes | — |
| 622 | C2×C3 | C2×D3×#67 | 1 | 2 | yes | — |
| 623 | C2×C3 | C2×#3811 | 1 | 1 | yes | characteristic |
| 624 | C2×C3 | #64330 | 1 | 4 | yes | — |
| 625 | D3 | — | 4 | 1 | no | — |
| 626 | D3 | — | 4 | 4 | no | — |
| 627 | D3 | — | 36 | 2 | no | — |
| 628 | D3 | — | 36 | 1 | no | — |
| 629 | D3 | — | 36 | 2 | no | — |
| 630 | D3 | — | 72 | 2 | no | — |
| 631 | D3 | — | 72 | 2 | no | — |
| 632 | C22 | — | 2 | 2 | no | — |
| 633 | C22 | — | 6 | 2 | no | — |
| 634 | C22 | — | 6 | 4 | no | — |
| 635 | C22 | — | 6 | 4 | no | — |
| 636 | C22 | — | 6 | 1 | no | — |
| 637 | C22 | — | 6 | 4 | no | — |
| 638 | C22 | — | 12 | 8 | no | — |
| 639 | C22 | — | 54 | 2 | no | — |
| 640 | C22 | — | 54 | 1 | no | — |
| 641 | C22 | #88952 | 1 | 2 | yes | — |
| 642 | C22 | C2×D33 | 1 | 1 | yes | characteristic |
| 643 | C4 | — | 6 | 1 | no | — |
| 644 | C4 | — | 9 | 2 | no | — |
| 645 | C4 | — | 9 | 2 | no | — |
| 646 | C4 | — | 18 | 4 | no | — |
| 647 | C4 | — | 54 | 1 | no | — |
| 648 | C3 | — | 2 | 1 | no | — |
| 649 | C3 | — | 2 | 2 | no | — |
| 650 | C3 | — | 4 | 1 | no | — |
| 651 | C3 | #10595239 | 1 | 1 | yes | characteristic, complemented |
| 652 | C3 | #10595513 | 1 | 2 | yes | complemented |
| 653 | C2 | — | 2 | 2 | no | — |
| 654 | C2 | — | 12 | 4 | no | — |
| 655 | C2 | — | 12 | 1 | no | — |
| 656 | C2 | — | 108 | 1 | no | — |
| 657 | C2 | #11724414 | 1 | 2 | yes | — |
| 658 | C2 | C2×#88952 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C2×D33 |
| commutator, socle, cosocle | C22×C33 | C24 |
| Fitting | C23×C33 | C23 |
| hypercenter | C23 | D33 |
| hypocenter | C33 | #535 |
| LCS | G ▷ C22×C33 ▷ C33 | |
| UCS | C1 ◁ C22 ◁ C23 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#89028 | C2 | semidirect |
| 2. C22×C3×#625 | C2 | semidirect |
| 3. #11723715 | C2 | semidirect |
| 4. #11723630 | C2 | semidirect |
| 5. C3×#63976 | C2 | semidirect |
| 6. #11723031 | C2 | semidirect |
| 7. #11723004 | C2 | semidirect |
| 8. #11722964 | C2 | semidirect |
| 9. #11722953 | C2 | semidirect |
| 16. C2×#6293 | C22 | semidirect |
| 17. C2×#6291 | C22 | semidirect |
| 18. C2×#6291 | C22 | semidirect |
| 19. C2×#6289 | C22 | semidirect |
| 21. C2×D3×C3⋊Dic3 | C22 | semidirect |
| 25. C2×C3×#625 | C22 | semidirect |
| 27. #88815 | C22 | semidirect |
| 28. #88813 | C22 | semidirect |
| 29. (C2×D3)⋊(C3⋊Dic3) | C22 | semidirect |
| 30. C3×(C2×D3)⋊Dic3 | C22 | semidirect |
| 33. C22×#625 | D3 | semidirect |
| 45. #63976 | D3 | semidirect |
| 61. C2×C3×C3⋊Dic3 | D4 | semidirect |
| 113. C2×#625 | C2×D3 | semidirect |
| 132. (C2×D3)⋊Dic3 | C2×D3 | semidirect |
| 213. C2×C3⋊Dic3 | #67 | semidirect |
| 389. C33 | #535 | semidirect |
| 581. C32 | #5592 | semidirect |
| 582. C32 | #5805 | semidirect |
| 651. C3 | #10595239 | semidirect |
| 652. C3 | #10595513 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89028 | 2 |
| C22×C3×#625 | 2 |
| #11723715 | 2 |
| #11723630 | 2 |
| C3×#63976 | 2 |
| #11723031 | 2 |
| #11723004 | 2 |
| #11722964 | 2 |
| #11722953 | 2 |
| #10595513 | 3 |
| #10595239 | 3 |