Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
6624 conjugacy classes of subgroups.
The subgroup lattice has 416 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C3×#3549 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #87088 | C2 | 1 | 8 | yes | maximal, complemented |
| 3 | #86963 | C2 | 1 | 12 | yes | maximal, complemented |
| 4 | #86610 | C2 | 1 | 12 | yes | maximal, complemented |
| 5 | #86322 | C2 | 1 | 12 | yes | maximal, complemented |
| 6 | #86320 | C2 | 1 | 12 | yes | maximal, complemented |
| 7 | #86231 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | #86219 | C2 | 1 | 3 | yes | maximal, complemented |
| 9 | #62841 | — | 3 | 1 | no | maximal, Sylow |
| 10 | C3×H(3,𝔽4) | C22 | 1 | 4 | yes | complemented |
| 11 | C3×#555 | C22 | 1 | 6 | yes | complemented |
| 12 | C3×D42 | C22 | 1 | 6 | yes | complemented |
| 13 | C3×#535 | C22 | 1 | 12 | yes | — |
| 14 | C3×#532 | C22 | 1 | 3 | yes | — |
| 15 | #5828 | C22 | 1 | 6 | yes | complemented |
| 16 | Dic3×#41 | C22 | 1 | 6 | yes | complemented |
| 17 | #5825 | C22 | 1 | 12 | yes | complemented |
| 18 | #5806 | C22 | 1 | 24 | yes | complemented |
| 19 | #5798 | C22 | 1 | 12 | yes | complemented |
| 20 | C2×#936 | C22 | 1 | 12 | yes | complemented |
| 21 | #5728 | C22 | 1 | 6 | yes | complemented |
| 22 | #5722 | C22 | 1 | 6 | yes | complemented |
| 23 | #5720 | C22 | 1 | 8 | yes | complemented |
| 24 | #5716 | C22 | 1 | 6 | yes | — |
| 25 | #5713 | C22 | 1 | 24 | yes | complemented |
| 26 | #5713 | C22 | 1 | 6 | yes | complemented |
| 27 | #5680 | C22 | 1 | 12 | yes | complemented |
| 28 | #5672 | C22 | 1 | 12 | yes | complemented |
| 29 | #5671 | C22 | 1 | 48 | yes | complemented |
| 30 | #5669 | C22 | 1 | 48 | yes | complemented |
| 31 | #5616 | C22 | 1 | 24 | yes | complemented |
| 32 | #5606 | C22 | 1 | 12 | yes | complemented |
| 33 | #5603 | C22 | 1 | 24 | yes | complemented |
| 34 | #5603 | C22 | 1 | 24 | yes | complemented |
| 35 | #5600 | C22 | 1 | 12 | yes | complemented |
| 36 | #5600 | C22 | 1 | 24 | yes | complemented |
| 37 | #5598 | C22 | 1 | 24 | yes | complemented |
| 38 | #5594 | C22 | 1 | 8 | yes | complemented |
| 39 | #5593 | C22 | 1 | 48 | yes | complemented |
| 40 | #5587 | C22 | 1 | 24 | yes | complemented |
| 41 | #5587 | C22 | 1 | 48 | yes | complemented |
| 42 | #5557 | C22 | 1 | 12 | yes | complemented |
| 43 | #5542 | C22 | 1 | 12 | yes | complemented |
| 44 | D4×Dic6 | C22 | 1 | 12 | yes | complemented |
| 45 | C4×#237 | C22 | 1 | 12 | yes | complemented |
| 46 | #5533 | C22 | 1 | 24 | yes | complemented |
| 47 | #5517 | C22 | 1 | 12 | yes | complemented |
| 48 | #5516 | C22 | 1 | 12 | yes | complemented |
| 49 | C2×C42×D3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 50 | #5470 | C22 | 1 | 3 | yes | complemented |
| 51 | #3568 | — | 3 | 8 | no | — |
| 52 | #3550 | — | 3 | 3 | no | — |
| 53 | #3549 | D3 | 1 | 1 | yes | characteristic, complemented |
| 54 | #3540 | — | 3 | 12 | no | — |
| 55 | #3518 | — | 3 | 12 | no | — |
| 56 | #3514 | — | 3 | 12 | no | — |
| 57 | #3510 | — | 3 | 12 | no | — |
| 58 | #3444 | — | 3 | 3 | no | — |
| 59 | C2×C3×#41 | C23 | 1 | 6 | yes | — |
| 60 | C22×C3×D4 | C23 | 1 | 12 | yes | — |
| 61 | C2×#237 | C23 | 1 | 12 | yes | — |
| 62 | C22×C4×D3 | C23 | 1 | 3 | yes | — |
| 63 | C22×Dic6 | C23 | 1 | 12 | yes | — |
| 64 | C3×C4⋊Q8 | C23 | 1 | 3 | yes | — |
| 65 | C3×#127 | C23 | 1 | 8 | yes | — |
| 66 | C3×#127 | C23 | 1 | 3 | yes | — |
| 67 | C3×#124 | C23 | 1 | 6 | yes | — |
| 68 | C3×#124 | C23 | 1 | 24 | yes | — |
| 69 | C3×#121 | C23 | 1 | 24 | yes | — |
| 70 | C3×#121 | C23 | 1 | 12 | yes | — |
| 71 | C3×#120 | C23 | 1 | 24 | yes | — |
| 72 | C3×#120 | C23 | 1 | 8 | yes | — |
| 73 | C3×C4×D4 | C23 | 1 | 12 | yes | — |
| 74 | C3×#117 | C23 | 1 | 12 | yes | — |
| 75 | C2×C3×C42 | C23 | 1 | 1 | yes | characteristic |
| 76 | #953 | C23 | 1 | 16 | yes | — |
| 77 | C2×#217 | C23 | 1 | 48 | yes | — |
| 78 | #946 | C23 | 1 | 12 | yes | — |
| 79 | Q8×Dic3 | C23 | 1 | 12 | yes | — |
| 80 | #944 | C23 | 1 | 24 | yes | — |
| 81 | #939 | C23 | 1 | 48 | yes | — |
| 82 | #938 | C23 | 1 | 12 | yes | — |
| 83 | #938 | C23 | 1 | 12 | yes | — |
| 84 | #937 | C23 | 1 | 12 | yes | — |
| 85 | #936 | C23 | 1 | 48 | yes | — |
| 86 | #936 | C23 | 1 | 24 | yes | — |
| 87 | #936 | C23 | 1 | 24 | yes | — |
| 88 | #936 | C23 | 1 | 12 | yes | — |
| 89 | #935 | C23 | 1 | 48 | yes | — |
| 90 | #935 | C23 | 1 | 24 | yes | — |
| 91 | #935 | C23 | 1 | 12 | yes | — |
| 92 | #935 | C23 | 1 | 24 | yes | — |
| 93 | D4×Dic3 | C23 | 1 | 48 | yes | — |
| 94 | D4×Dic3 | C23 | 1 | 12 | yes | — |
| 95 | D4×Dic3 | C23 | 1 | 24 | yes | — |
| 96 | D4×Dic3 | C23 | 1 | 24 | yes | — |
| 97 | D4×Dic3 | C23 | 1 | 12 | yes | — |
| 98 | C4×#67 | C23 | 1 | 24 | yes | — |
| 99 | #926 | C23 | 1 | 6 | yes | — |
| 100 | #926 | C23 | 1 | 12 | yes | — |
| 101 | #926 | C23 | 1 | 12 | yes | — |
| 102 | #924 | C23 | 1 | 12 | yes | — |
| 103 | #924 | C23 | 1 | 24 | yes | — |
| 104 | C2×C4×Dic3 | C23 | 1 | 3 | yes | — |
| 105 | C2×C4×Dic3 | C23 | 1 | 12 | yes | — |
| 106 | #897 | C23 | 1 | 12 | yes | — |
| 107 | #892 | C23 | 1 | 12 | yes | — |
| 108 | #890 | C23 | 1 | 12 | yes | — |
| 109 | #888 | C23 | 1 | 24 | yes | — |
| 110 | #887 | C23 | 1 | 24 | yes | — |
| 111 | #887 | C23 | 1 | 12 | yes | — |
| 112 | #885 | C23 | 1 | 48 | yes | — |
| 113 | #883 | C23 | 1 | 24 | yes | — |
| 114 | #67⋊C4 | C23 | 1 | 24 | yes | — |
| 115 | #879 | C23 | 1 | 48 | yes | — |
| 116 | #879 | C23 | 1 | 24 | yes | — |
| 117 | #879 | C23 | 1 | 48 | yes | — |
| 118 | #878 | C23 | 1 | 48 | yes | — |
| 119 | #878 | C23 | 1 | 48 | yes | — |
| 120 | #877 | C23 | 1 | 48 | yes | — |
| 121 | #877 | C23 | 1 | 24 | yes | — |
| 122 | #876 | C23 | 1 | 16 | yes | — |
| 123 | C42×D3 | C23 | 1 | 2 | yes | — |
| 124 | C42×D3 | C23 | 1 | 6 | yes | — |
| 125 | #870 | C23 | 1 | 6 | yes | — |
| 126 | #869 | C23 | 1 | 6 | yes | — |
| 127 | C4×Dic6 | C23 | 1 | 48 | yes | — |
| 128 | C4×Dic6 | C23 | 1 | 12 | yes | — |
| 129 | #563 | — | 3 | 12 | no | — |
| 130 | H(3,𝔽4) | — | 3 | 8 | no | — |
| 131 | H(3,𝔽4) | C2×D3 | 1 | 4 | yes | complemented |
| 132 | #560 | — | 3 | 8 | no | — |
| 133 | #559 | — | 3 | 24 | no | — |
| 134 | #559 | — | 3 | 6 | no | — |
| 135 | Q82 | — | 3 | 6 | no | — |
| 136 | #556 | — | 3 | 48 | no | — |
| 137 | #556 | — | 3 | 12 | no | — |
| 138 | #556 | — | 3 | 24 | no | — |
| 139 | #555 | — | 3 | 24 | no | — |
| 140 | #555 | C2×D3 | 1 | 6 | yes | complemented |
| 141 | #551 | — | 3 | 24 | no | — |
| 142 | #551 | — | 3 | 48 | no | — |
| 143 | D4×Q8 | — | 3 | 12 | no | — |
| 144 | #548 | — | 3 | 24 | no | — |
| 145 | #546 | — | 3 | 24 | no | — |
| 146 | D42 | C2×D3 | 1 | 6 | yes | complemented |
| 147 | #542 | — | 3 | 48 | no | — |
| 148 | #542 | — | 3 | 24 | no | — |
| 149 | #542 | — | 3 | 24 | no | — |
| 150 | #538 | — | 3 | 48 | no | — |
| 151 | #536 | — | 3 | 12 | no | — |
| 152 | #535 | C2×D3 | 1 | 12 | yes | — |
| 153 | #533 | — | 3 | 6 | no | — |
| 154 | #533 | — | 3 | 12 | no | — |
| 155 | #533 | — | 3 | 3 | no | — |
| 156 | #532 | — | 3 | 6 | no | — |
| 157 | #532 | C2×D3 | 1 | 3 | yes | — |
| 158 | #529 | — | 3 | 12 | no | — |
| 159 | #529 | — | 3 | 12 | no | — |
| 160 | #529 | — | 3 | 24 | no | — |
| 161 | #529 | — | 3 | 12 | no | — |
| 162 | C2×#124 | — | 3 | 12 | no | — |
| 163 | #525 | — | 3 | 6 | no | — |
| 164 | #525 | — | 3 | 12 | no | — |
| 165 | #519 | — | 3 | 12 | no | — |
| 166 | #518 | — | 3 | 12 | no | — |
| 167 | C4×#41 | — | 3 | 6 | no | — |
| 168 | C4×#41 | — | 3 | 12 | no | — |
| 169 | C22×C42 | — | 3 | 1 | no | — |
| 170 | C24×C3 | C24 | 1 | 8 | yes | — |
| 171 | C23×D3 | C24 | 1 | 1 | yes | characteristic |
| 172 | C3×#41 | — | 4 | 12 | no | — |
| 173 | C2×C3×Q8 | C24 | 1 | 6 | yes | — |
| 174 | C2×C3×D4 | — | 4 | 24 | no | — |
| 175 | C2×C3×D4 | C24 | 1 | 12 | yes | — |
| 176 | C2×C3×D4 | C24 | 1 | 6 | yes | — |
| 177 | C2×C3×D4 | C24 | 1 | 12 | yes | — |
| 178 | C2×C3×D4 | C24 | 1 | 24 | yes | — |
| 179 | C22×C3×C4 | C24 | 1 | 3 | yes | — |
| 180 | C22×C3×C4 | C24 | 1 | 12 | yes | — |
| 181 | C2×#67 | C24 | 1 | 24 | yes | — |
| 182 | C22×Dic3 | C24 | 1 | 24 | yes | — |
| 183 | C22×Dic3 | C24 | 1 | 24 | yes | — |
| 184 | C22×Dic3 | C24 | 1 | 3 | yes | — |
| 185 | #237 | — | 4 | 24 | no | — |
| 186 | C2×C4×D3 | — | 4 | 6 | no | — |
| 187 | C2×C4×D3 | C24 | 1 | 6 | yes | — |
| 188 | C2×C4×D3 | C24 | 1 | 6 | yes | — |
| 189 | C2×Dic6 | — | 4 | 24 | no | — |
| 190 | C2×Dic6 | C24 | 1 | 12 | yes | — |
| 191 | C2×Dic6 | C24 | 1 | 24 | yes | — |
| 192 | C3×C4⋊C4 | C24 | 1 | 12 | yes | — |
| 193 | C3×C22⋊C4 | C24 | 1 | 24 | yes | — |
| 194 | C3×C22⋊C4 | C24 | 1 | 24 | yes | — |
| 195 | C3×C42 | C24 | 1 | 8 | yes | — |
| 196 | C3×C42 | C24 | 1 | 3 | yes | — |
| 197 | C3×C42 | C24 | 1 | 1 | yes | characteristic |
| 198 | #217 | C24 | 1 | 24 | yes | — |
| 199 | #217 | C24 | 1 | 24 | yes | — |
| 200 | #217 | C24 | 1 | 24 | yes | — |
| 201 | #217 | C24 | 1 | 48 | yes | — |
| 202 | #217 | C24 | 1 | 12 | yes | — |
| 203 | (C2×D3)⋊C4 | C24 | 1 | 24 | yes | — |
| 204 | C4⋊Dic3 | C24 | 1 | 24 | yes | — |
| 205 | C4⋊Dic3 | C24 | 1 | 12 | yes | — |
| 206 | C4⋊Dic3 | C24 | 1 | 12 | yes | — |
| 207 | Dic3⋊C4 | C24 | 1 | 24 | yes | — |
| 208 | Dic3⋊C4 | C24 | 1 | 24 | yes | — |
| 209 | Dic3⋊C4 | C24 | 1 | 48 | yes | — |
| 210 | C4×Dic3 | C24 | 1 | 24 | yes | — |
| 211 | C4×Dic3 | C24 | 1 | 24 | yes | — |
| 212 | C4×Dic3 | C24 | 1 | 12 | yes | — |
| 213 | C4×Dic3 | C24 | 1 | 6 | yes | — |
| 214 | C4×Dic3 | C24 | 1 | 3 | yes | — |
| 215 | C4×Dic3 | C24 | 1 | 3 | yes | — |
| 216 | C2×#41 | — | 3 | 12 | no | — |
| 217 | C2×#41 | C22×D3 | 1 | 6 | yes | — |
| 218 | C22×Q8 | — | 3 | 12 | no | — |
| 219 | C22×D4 | C22×D3 | 1 | 12 | yes | — |
| 220 | C23×C4 | — | 3 | 3 | no | — |
| 221 | C4⋊Q8 | — | 3 | 24 | no | — |
| 222 | C4⋊Q8 | — | 3 | 24 | no | — |
| 223 | C4⋊Q8 | — | 3 | 6 | no | — |
| 224 | C4⋊Q8 | C22×D3 | 1 | 3 | yes | — |
| 225 | #127 | C22×D3 | 1 | 3 | yes | — |
| 226 | #127 | C22×D3 | 1 | 8 | yes | — |
| 227 | #126 | — | 3 | 24 | no | — |
| 228 | #126 | — | 3 | 48 | no | — |
| 229 | #126 | — | 3 | 48 | no | — |
| 230 | #126 | — | 3 | 16 | no | — |
| 231 | #125 | — | 3 | 12 | no | — |
| 232 | #125 | — | 3 | 6 | no | — |
| 233 | #124 | — | 3 | 12 | no | — |
| 234 | #124 | — | 3 | 48 | no | — |
| 235 | #124 | — | 3 | 24 | no | — |
| 236 | #124 | — | 3 | 24 | no | — |
| 237 | #124 | — | 3 | 48 | no | — |
| 238 | #124 | C22×D3 | 1 | 6 | yes | — |
| 239 | #124 | C22×D3 | 1 | 24 | yes | — |
| 240 | #123 | — | 3 | 12 | no | — |
| 241 | #123 | — | 3 | 48 | no | — |
| 242 | #123 | — | 3 | 24 | no | — |
| 243 | #123 | — | 3 | 24 | no | — |
| 244 | #123 | — | 3 | 24 | no | — |
| 245 | C22⋊Q8 | — | 3 | 12 | no | — |
| 246 | C22⋊Q8 | — | 3 | 12 | no | — |
| 247 | C22⋊Q8 | — | 3 | 24 | no | — |
| 248 | C22⋊Q8 | — | 3 | 12 | no | — |
| 249 | C22⋊Q8 | — | 3 | 48 | no | — |
| 250 | C22⋊Q8 | — | 3 | 48 | no | — |
| 251 | #121 | — | 3 | 12 | no | — |
| 252 | #121 | — | 3 | 12 | no | — |
| 253 | #121 | — | 3 | 48 | no | — |
| 254 | #121 | C22×D3 | 1 | 12 | yes | — |
| 255 | #121 | C22×D3 | 1 | 24 | yes | — |
| 256 | #120 | — | 3 | 16 | no | — |
| 257 | #120 | — | 3 | 12 | no | — |
| 258 | #120 | C22×D3 | 1 | 8 | yes | — |
| 259 | #120 | C22×D3 | 1 | 24 | yes | — |
| 260 | C4×Q8 | — | 3 | 12 | no | — |
| 261 | C4×Q8 | — | 3 | 12 | no | — |
| 262 | C4×Q8 | — | 3 | 24 | no | — |
| 263 | C4×Q8 | — | 3 | 12 | no | — |
| 264 | C4×Q8 | — | 3 | 48 | no | — |
| 265 | C4×D4 | — | 3 | 12 | no | — |
| 266 | C4×D4 | — | 3 | 24 | no | — |
| 267 | C4×D4 | — | 3 | 12 | no | — |
| 268 | C4×D4 | — | 3 | 48 | no | — |
| 269 | C4×D4 | — | 3 | 24 | no | — |
| 270 | C4×D4 | — | 3 | 24 | no | — |
| 271 | C4×D4 | — | 3 | 24 | no | — |
| 272 | C4×D4 | C22×D3 | 1 | 12 | yes | — |
| 273 | #117 | — | 3 | 12 | no | — |
| 274 | #117 | — | 3 | 6 | no | — |
| 275 | #117 | — | 3 | 12 | no | — |
| 276 | #117 | — | 3 | 12 | no | — |
| 277 | #117 | — | 3 | 24 | no | — |
| 278 | #117 | — | 3 | 48 | no | — |
| 279 | #117 | C22×D3 | 1 | 12 | yes | — |
| 280 | C2×C22⋊C4 | — | 3 | 48 | no | — |
| 281 | C2×C42 | — | 3 | 12 | no | — |
| 282 | C2×C42 | — | 3 | 3 | no | — |
| 283 | C2×C42 | — | 3 | 6 | no | — |
| 284 | C2×C42 | — | 3 | 2 | no | — |
| 285 | C2×C42 | C22×D3 | 1 | 1 | yes | characteristic |
| 286 | C23×C3 | — | 4 | 24 | no | — |
| 287 | C23×C3 | C25 | 1 | 1 | yes | characteristic |
| 288 | C23×C3 | C25 | 1 | 12 | yes | — |
| 289 | C22×D3 | — | 4 | 3 | no | — |
| 290 | C22×D3 | C25 | 1 | 2 | yes | — |
| 291 | C3×Q8 | — | 4 | 6 | no | — |
| 292 | C3×D4 | — | 2 | 24 | no | — |
| 293 | C3×D4 | — | 4 | 24 | no | — |
| 294 | C3×D4 | — | 4 | 12 | no | — |
| 295 | C3×D4 | — | 4 | 6 | no | — |
| 296 | C2×C3×C4 | — | 2 | 24 | no | — |
| 297 | C2×C3×C4 | — | 2 | 6 | no | — |
| 298 | C2×C3×C4 | C25 | 1 | 12 | yes | — |
| 299 | C2×C3×C4 | C25 | 1 | 3 | yes | — |
| 300 | C2×C3×C4 | C25 | 1 | 3 | yes | — |
| 301 | #67 | — | 4 | 24 | no | — |
| 302 | C2×Dic3 | — | 4 | 24 | no | — |
| 303 | C2×Dic3 | — | 4 | 3 | no | — |
| 304 | C2×Dic3 | — | 4 | 24 | no | — |
| 305 | C2×Dic3 | C25 | 1 | 6 | yes | — |
| 306 | C2×Dic3 | C25 | 1 | 24 | yes | — |
| 307 | C4×D3 | — | 2 | 12 | no | — |
| 308 | C4×D3 | — | 4 | 6 | no | — |
| 309 | Dic6 | — | 2 | 24 | no | — |
| 310 | Dic6 | — | 4 | 24 | no | — |
| 311 | C24 | — | 3 | 1 | no | — |
| 312 | C24 | C23×D3 | 1 | 8 | yes | — |
| 313 | #41 | — | 4 | 12 | no | — |
| 314 | #41 | — | 12 | 24 | no | — |
| 315 | C2×Q8 | — | 3 | 12 | no | — |
| 316 | C2×Q8 | — | 3 | 24 | no | — |
| 317 | C2×Q8 | — | 12 | 24 | no | — |
| 318 | C2×Q8 | C23×D3 | 1 | 6 | yes | — |
| 319 | C2×D4 | — | 3 | 24 | no | — |
| 320 | C2×D4 | — | 4 | 24 | no | — |
| 321 | C2×D4 | C23×D3 | 1 | 12 | yes | — |
| 322 | C2×D4 | C23×D3 | 1 | 12 | yes | — |
| 323 | C2×D4 | C23×D3 | 1 | 6 | yes | — |
| 324 | C2×D4 | C23×D3 | 1 | 24 | yes | — |
| 325 | C22×C4 | — | 3 | 3 | no | — |
| 326 | C22×C4 | — | 3 | 24 | no | — |
| 327 | C22×C4 | — | 3 | 24 | no | — |
| 328 | C22×C4 | — | 3 | 6 | no | — |
| 329 | C22×C4 | — | 3 | 6 | no | — |
| 330 | C22×C4 | — | 12 | 6 | no | — |
| 331 | C22×C4 | C23×D3 | 1 | 3 | yes | — |
| 332 | C22×C4 | C23×D3 | 1 | 12 | yes | — |
| 333 | C4⋊C4 | — | 3 | 12 | no | — |
| 334 | C4⋊C4 | — | 3 | 24 | no | — |
| 335 | C4⋊C4 | — | 3 | 24 | no | — |
| 336 | C4⋊C4 | — | 3 | 12 | no | — |
| 337 | C4⋊C4 | — | 3 | 24 | no | — |
| 338 | C4⋊C4 | — | 3 | 48 | no | — |
| 339 | C4⋊C4 | C23×D3 | 1 | 12 | yes | — |
| 340 | C22⋊C4 | — | 3 | 24 | no | — |
| 341 | C22⋊C4 | — | 3 | 24 | no | — |
| 342 | C22⋊C4 | — | 3 | 24 | no | — |
| 343 | C22⋊C4 | — | 3 | 48 | no | — |
| 344 | C22⋊C4 | — | 3 | 12 | no | — |
| 345 | C22⋊C4 | — | 3 | 24 | no | — |
| 346 | C22⋊C4 | C23×D3 | 1 | 24 | yes | — |
| 347 | C22⋊C4 | C23×D3 | 1 | 24 | yes | — |
| 348 | C42 | — | 3 | 3 | no | — |
| 349 | C42 | — | 3 | 3 | no | — |
| 350 | C42 | — | 3 | 6 | no | — |
| 351 | C42 | — | 3 | 24 | no | — |
| 352 | C42 | — | 3 | 12 | no | — |
| 353 | C42 | — | 3 | 24 | no | — |
| 354 | C42 | C23×D3 | 1 | 3 | yes | — |
| 355 | C42 | C23×D3 | 1 | 1 | yes | characteristic |
| 356 | C42 | C23×D3 | 1 | 8 | yes | — |
| 357 | C22×C3 | — | 2 | 12 | no | — |
| 358 | C22×C3 | — | 2 | 24 | no | — |
| 359 | C22×C3 | — | 2 | 3 | no | — |
| 360 | C22×C3 | — | 16 | 8 | no | — |
| 361 | C22×C3 | C26 | 1 | 1 | yes | characteristic |
| 362 | C2×D3 | — | 2 | 6 | no | — |
| 363 | C2×D3 | — | 4 | 4 | no | — |
| 364 | C3×C4 | — | 2 | 12 | no | — |
| 365 | C3×C4 | — | 2 | 3 | no | — |
| 366 | C3×C4 | #585 | 1 | 6 | yes | — |
| 367 | Dic3 | — | 2 | 24 | no | — |
| 368 | Dic3 | — | 2 | 6 | no | — |
| 369 | C23 | — | 3 | 2 | no | — |
| 370 | C23 | — | 4 | 24 | no | — |
| 371 | C23 | — | 12 | 3 | no | — |
| 372 | C23 | C24×D3 | 1 | 1 | yes | characteristic |
| 373 | C23 | C24×D3 | 1 | 12 | yes | — |
| 374 | Q8 | — | 4 | 6 | no | — |
| 375 | Q8 | — | 6 | 24 | no | — |
| 376 | Q8 | — | 12 | 24 | no | — |
| 377 | D4 | — | 2 | 24 | no | — |
| 378 | D4 | — | 4 | 24 | no | — |
| 379 | D4 | — | 4 | 6 | no | — |
| 380 | D4 | — | 4 | 12 | no | — |
| 381 | D4 | — | 12 | 24 | no | — |
| 382 | C2×C4 | — | 2 | 6 | no | — |
| 383 | C2×C4 | — | 2 | 24 | no | — |
| 384 | C2×C4 | — | 3 | 6 | no | — |
| 385 | C2×C4 | — | 3 | 24 | no | — |
| 386 | C2×C4 | — | 6 | 12 | no | — |
| 387 | C2×C4 | — | 12 | 6 | no | — |
| 388 | C2×C4 | — | 12 | 3 | no | — |
| 389 | C2×C4 | — | 12 | 24 | no | — |
| 390 | C2×C4 | — | 12 | 24 | no | — |
| 391 | C2×C4 | C24×D3 | 1 | 12 | yes | — |
| 392 | C2×C4 | C24×D3 | 1 | 3 | yes | — |
| 393 | C2×C4 | C24×D3 | 1 | 3 | yes | — |
| 394 | C2×C3 | — | 4 | 1 | no | — |
| 395 | C2×C3 | — | 4 | 12 | no | — |
| 396 | C2×C3 | C2×#585 | 1 | 3 | yes | — |
| 397 | D3 | — | 4 | 2 | no | — |
| 398 | C22 | — | 2 | 12 | no | — |
| 399 | C22 | — | 2 | 3 | no | — |
| 400 | C22 | — | 2 | 24 | no | — |
| 401 | C22 | — | 6 | 6 | no | — |
| 402 | C22 | — | 12 | 4 | no | — |
| 403 | C22 | — | 16 | 8 | no | — |
| 404 | C22 | C25×D3 | 1 | 1 | yes | characteristic |
| 405 | C4 | — | 2 | 3 | no | — |
| 406 | C4 | — | 2 | 12 | no | — |
| 407 | C4 | — | 6 | 6 | no | — |
| 408 | C4 | — | 6 | 24 | no | — |
| 409 | C4 | #5966 | 1 | 6 | yes | — |
| 410 | C3 | #62841 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 411 | C2 | — | 4 | 1 | no | — |
| 412 | C2 | — | 4 | 12 | no | — |
| 413 | C2 | — | 12 | 2 | no | — |
| 414 | C2 | C2×#5966 | 1 | 3 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C25×D3 |
| commutator, socle, cosocle | C22×C3 | C26 |
| Fitting | C3×#3549 | C2 |
| hypercenter | #3549 | D3 |
| hypocenter | C3 | #62841 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C22 ◁ #3549 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×#3549 | C2 | semidirect |
| 2. #87088 | C2 | semidirect |
| 3. #86963 | C2 | semidirect |
| 4. #86610 | C2 | semidirect |
| 5. #86322 | C2 | semidirect |
| 6. #86320 | C2 | semidirect |
| 7. #86231 | C2 | semidirect |
| 8. #86219 | C2 | semidirect |
| 10. C3×H(3,𝔽4) | C22 | semidirect |
| 11. C3×#555 | C22 | semidirect |
| 12. C3×D42 | C22 | semidirect |
| 15. #5828 | C22 | semidirect |
| 16. Dic3×#41 | C22 | semidirect |
| 17. #5825 | C22 | semidirect |
| 18. #5806 | C22 | semidirect |
| 19. #5798 | C22 | semidirect |
| 20. C2×#936 | C22 | semidirect |
| 21. #5728 | C22 | semidirect |
| 22. #5722 | C22 | semidirect |
| 23. #5720 | C22 | semidirect |
| 25. #5713 | C22 | semidirect |
| 26. #5713 | C22 | semidirect |
| 27. #5680 | C22 | semidirect |
| 28. #5672 | C22 | semidirect |
| 29. #5671 | C22 | semidirect |
| 30. #5669 | C22 | semidirect |
| 31. #5616 | C22 | semidirect |
| 32. #5606 | C22 | semidirect |
| 33. #5603 | C22 | semidirect |
| 34. #5603 | C22 | semidirect |
| 35. #5600 | C22 | semidirect |
| 36. #5600 | C22 | semidirect |
| 37. #5598 | C22 | semidirect |
| 38. #5594 | C22 | semidirect |
| 39. #5593 | C22 | semidirect |
| 40. #5587 | C22 | semidirect |
| 41. #5587 | C22 | semidirect |
| 42. #5557 | C22 | semidirect |
| 43. #5542 | C22 | semidirect |
| 44. D4×Dic6 | C22 | semidirect |
| 45. C4×#237 | C22 | semidirect |
| 46. #5533 | C22 | semidirect |
| 47. #5517 | C22 | semidirect |
| 48. #5516 | C22 | semidirect |
| 49. C2×C42×D3 | C22 | semidirect |
| 50. #5470 | C22 | semidirect |
| 53. #3549 | D3 | semidirect |
| 131. H(3,𝔽4) | C2×D3 | semidirect |
| 140. #555 | C2×D3 | semidirect |
| 146. D42 | C2×D3 | semidirect |
| 410. C3 | #62841 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3549 | 2 |
| #87088 | 2 |
| #86963 | 2 |
| #86610 | 2 |
| #86322 | 2 |
| #86320 | 2 |
| #86231 | 2 |
| #86219 | 2 |
| #62841 | 3 |