Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
6608 conjugacy classes of subgroups.
The subgroup lattice has 944 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C3×#3548 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #87106 | C2 | 1 | 8 | yes | maximal, complemented |
| 3 | #86931 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #86930 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #86774 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #86773 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #86684 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #86683 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | #86472 | C2 | 1 | 4 | yes | maximal, complemented |
| 10 | #86469 | C2 | 1 | 4 | yes | maximal, complemented |
| 11 | #86371 | C2 | 1 | 8 | yes | maximal, complemented |
| 12 | #86369 | C2 | 1 | 8 | yes | maximal, complemented |
| 13 | #86270 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #86257 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | #86251 | C2 | 1 | 2 | yes | maximal, complemented |
| 16 | #86219 | C2 | 1 | 2 | yes | maximal, complemented |
| 17 | #62840 | — | 3 | 1 | no | maximal, Sylow |
| 18 | C3×#562 | C22 | 1 | 4 | yes | complemented |
| 19 | C3×#554 | C22 | 1 | 4 | yes | complemented |
| 20 | C3×#550 | C22 | 1 | 4 | yes | complemented |
| 21 | C3×#547 | C22 | 1 | 4 | yes | complemented |
| 22 | C3×#540 | C22 | 1 | 4 | yes | — |
| 23 | C3×#537 | C22 | 1 | 8 | yes | — |
| 24 | C3×#533 | C22 | 1 | 1 | yes | characteristic |
| 25 | C3×#532 | C22 | 1 | 2 | yes | — |
| 26 | #5834 | C22 | 1 | 8 | yes | — |
| 27 | #5833 | C22 | 1 | 8 | yes | — |
| 28 | #5832 | C22 | 1 | 8 | yes | complemented |
| 29 | #5828 | C22 | 1 | 4 | yes | — |
| 30 | #5827 | C22 | 1 | 8 | yes | complemented |
| 31 | Dic3×#41 | C22 | 1 | 4 | yes | — |
| 32 | #5824 | C22 | 1 | 8 | yes | — |
| 33 | #5730 | C22 | 1 | 4 | yes | complemented |
| 34 | #5728 | C22 | 1 | 2 | yes | — |
| 35 | #5728 | C22 | 1 | 2 | yes | — |
| 36 | #5728 | C22 | 1 | 2 | yes | — |
| 37 | #5725 | C22 | 1 | 2 | yes | — |
| 38 | #5721 | C22 | 1 | 4 | yes | complemented |
| 39 | #5719 | C22 | 1 | 4 | yes | complemented |
| 40 | #5718 | C22 | 1 | 8 | yes | — |
| 41 | #5718 | C22 | 1 | 4 | yes | complemented |
| 42 | #5716 | C22 | 1 | 2 | yes | — |
| 43 | #5716 | C22 | 1 | 2 | yes | — |
| 44 | #5716 | C22 | 1 | 4 | yes | complemented |
| 45 | #5698 | C22 | 1 | 4 | yes | complemented |
| 46 | #5694 | C22 | 1 | 8 | yes | — |
| 47 | #5691 | C22 | 1 | 4 | yes | — |
| 48 | D3×#125 | C22 | 1 | 4 | yes | complemented |
| 49 | C3⋊#564 | C22 | 1 | 4 | yes | complemented |
| 50 | #5684 | C22 | 1 | 8 | yes | complemented |
| 51 | #5680 | C22 | 1 | 4 | yes | — |
| 52 | #5680 | C22 | 1 | 4 | yes | — |
| 53 | #5665 | C22 | 1 | 16 | yes | — |
| 54 | #5663 | C22 | 1 | 16 | yes | — |
| 55 | #5661 | C22 | 1 | 16 | yes | complemented |
| 56 | #5650 | C22 | 1 | 16 | yes | complemented |
| 57 | #5645 | C22 | 1 | 16 | yes | — |
| 58 | #5642 | C22 | 1 | 8 | yes | — |
| 59 | #5642 | C22 | 1 | 16 | yes | complemented |
| 60 | #5639 | C22 | 1 | 16 | yes | complemented |
| 61 | #5638 | C22 | 1 | 16 | yes | — |
| 62 | #5631 | C22 | 1 | 8 | yes | — |
| 63 | #5627 | C22 | 1 | 4 | yes | — |
| 64 | #5625 | C22 | 1 | 8 | yes | — |
| 65 | #5625 | C22 | 1 | 8 | yes | complemented |
| 66 | #5624 | C22 | 1 | 4 | yes | — |
| 67 | #5624 | C22 | 1 | 8 | yes | complemented |
| 68 | #5620 | C22 | 1 | 16 | yes | — |
| 69 | #5619 | C22 | 1 | 16 | yes | — |
| 70 | #5619 | C22 | 1 | 8 | yes | — |
| 71 | #5619 | C22 | 1 | 8 | yes | complemented |
| 72 | #5618 | C22 | 1 | 16 | yes | — |
| 73 | #5618 | C22 | 1 | 8 | yes | — |
| 74 | #5618 | C22 | 1 | 16 | yes | complemented |
| 75 | #5615 | C22 | 1 | 16 | yes | — |
| 76 | #5614 | C22 | 1 | 16 | yes | — |
| 77 | #5608 | C22 | 1 | 8 | yes | — |
| 78 | #5606 | C22 | 1 | 4 | yes | — |
| 79 | #5606 | C22 | 1 | 4 | yes | — |
| 80 | #5601 | C22 | 1 | 16 | yes | — |
| 81 | #5601 | C22 | 1 | 16 | yes | complemented |
| 82 | #5600 | C22 | 1 | 4 | yes | — |
| 83 | #5600 | C22 | 1 | 4 | yes | — |
| 84 | #5600 | C22 | 1 | 8 | yes | complemented |
| 85 | #5599 | C22 | 1 | 8 | yes | — |
| 86 | #5580 | C22 | 1 | 4 | yes | — |
| 87 | C4×#239 | C22 | 1 | 4 | yes | — |
| 88 | #5570 | C22 | 1 | 4 | yes | complemented |
| 89 | #5567 | C22 | 1 | 4 | yes | complemented |
| 90 | #5558 | C22 | 1 | 8 | yes | — |
| 91 | #5557 | C22 | 1 | 4 | yes | — |
| 92 | #5557 | C22 | 1 | 4 | yes | — |
| 93 | #5557 | C22 | 1 | 8 | yes | complemented |
| 94 | #5555 | C22 | 1 | 8 | yes | — |
| 95 | #5555 | C22 | 1 | 4 | yes | complemented |
| 96 | #5553 | C22 | 1 | 4 | yes | complemented |
| 97 | #5551 | C22 | 1 | 4 | yes | complemented |
| 98 | #5546 | C22 | 1 | 8 | yes | complemented |
| 99 | #5543 | C22 | 1 | 4 | yes | complemented |
| 100 | C4×#237 | C22 | 1 | 4 | yes | — |
| 101 | C4×#237 | C22 | 1 | 4 | yes | — |
| 102 | #5524 | C22 | 1 | 2 | yes | — |
| 103 | #5522 | C22 | 1 | 2 | yes | — |
| 104 | #5518 | C22 | 1 | 4 | yes | — |
| 105 | #5514 | C22 | 1 | 8 | yes | — |
| 106 | #5513 | C22 | 1 | 8 | yes | — |
| 107 | #5504 | C22 | 1 | 8 | yes | complemented |
| 108 | C2×#890 | C22 | 1 | 8 | yes | complemented |
| 109 | #5477 | C22 | 1 | 1 | yes | characteristic |
| 110 | C2×C42×D3 | C22 | 1 | 1 | yes | characteristic |
| 111 | #5470 | C22 | 1 | 2 | yes | — |
| 112 | #3567 | — | 3 | 8 | no | — |
| 113 | #3556 | — | 3 | 1 | no | — |
| 114 | #3548 | — | 3 | 2 | no | — |
| 115 | #3548 | D3 | 1 | 1 | yes | characteristic, complemented |
| 116 | #3539 | — | 3 | 4 | no | — |
| 117 | #3539 | — | 3 | 8 | no | — |
| 118 | #3517 | — | 3 | 4 | no | — |
| 119 | #3517 | — | 3 | 4 | no | — |
| 120 | #3517 | — | 3 | 4 | no | — |
| 121 | #3515 | — | 3 | 4 | no | — |
| 122 | #3515 | — | 3 | 4 | no | — |
| 123 | #3515 | — | 3 | 4 | no | — |
| 124 | #3512 | — | 3 | 4 | no | — |
| 125 | #3512 | — | 3 | 8 | no | — |
| 126 | #3444 | — | 3 | 1 | no | — |
| 127 | #3444 | — | 3 | 2 | no | — |
| 128 | C2×C3×#41 | C23 | 1 | 8 | yes | — |
| 129 | C2×C3×#41 | C23 | 1 | 4 | yes | — |
| 130 | C2×#239 | C23 | 1 | 4 | yes | — |
| 131 | C2×#237 | C23 | 1 | 4 | yes | — |
| 132 | C2×#237 | C23 | 1 | 4 | yes | — |
| 133 | C2×#237 | C23 | 1 | 8 | yes | — |
| 134 | C2×#235 | C23 | 1 | 2 | yes | — |
| 135 | C2×#235 | C23 | 1 | 8 | yes | — |
| 136 | C22×C4×D3 | C23 | 1 | 1 | yes | characteristic |
| 137 | C22×C4×D3 | C23 | 1 | 2 | yes | — |
| 138 | C3×C4⋊Q8 | C23 | 1 | 2 | yes | — |
| 139 | C3×C4⋊Q8 | C23 | 1 | 2 | yes | — |
| 140 | C3×#127 | C23 | 1 | 2 | yes | — |
| 141 | C3×#127 | C23 | 1 | 4 | yes | — |
| 142 | C3×#125 | C23 | 1 | 2 | yes | — |
| 143 | C3×#125 | C23 | 1 | 4 | yes | — |
| 144 | C3×#124 | C23 | 1 | 4 | yes | — |
| 145 | C3×#123 | C23 | 1 | 16 | yes | — |
| 146 | C3×C22⋊Q8 | C23 | 1 | 16 | yes | — |
| 147 | C3×C22⋊Q8 | C23 | 1 | 8 | yes | — |
| 148 | C3×C22⋊Q8 | C23 | 1 | 4 | yes | — |
| 149 | C3×#121 | C23 | 1 | 16 | yes | — |
| 150 | C3×#121 | C23 | 1 | 8 | yes | — |
| 151 | C3×#121 | C23 | 1 | 4 | yes | — |
| 152 | C3×#121 | C23 | 1 | 4 | yes | — |
| 153 | C3×#121 | C23 | 1 | 16 | yes | — |
| 154 | C3×C4×Q8 | C23 | 1 | 4 | yes | — |
| 155 | C3×C4×D4 | C23 | 1 | 4 | yes | — |
| 156 | C3×C4×D4 | C23 | 1 | 4 | yes | — |
| 157 | C3×C4×D4 | C23 | 1 | 8 | yes | — |
| 158 | C3×#117 | C23 | 1 | 2 | yes | — |
| 159 | C2×C3×C4⋊C4 | C23 | 1 | 8 | yes | — |
| 160 | C2×C3×C42 | C23 | 1 | 1 | yes | characteristic |
| 161 | #947 | C23 | 1 | 4 | yes | — |
| 162 | #946 | C23 | 1 | 4 | yes | — |
| 163 | #946 | C23 | 1 | 16 | yes | — |
| 164 | #946 | C23 | 1 | 4 | yes | — |
| 165 | #946 | C23 | 1 | 4 | yes | — |
| 166 | Q8×Dic3 | C23 | 1 | 4 | yes | — |
| 167 | Q8×Dic3 | C23 | 1 | 8 | yes | — |
| 168 | Q8×Dic3 | C23 | 1 | 4 | yes | — |
| 169 | Q8×Dic3 | C23 | 1 | 4 | yes | — |
| 170 | #944 | C23 | 1 | 8 | yes | — |
| 171 | #940 | C23 | 1 | 16 | yes | — |
| 172 | #940 | C23 | 1 | 8 | yes | — |
| 173 | #939 | C23 | 1 | 16 | yes | — |
| 174 | #939 | C23 | 1 | 16 | yes | — |
| 175 | #939 | C23 | 1 | 16 | yes | — |
| 176 | #939 | C23 | 1 | 16 | yes | — |
| 177 | #939 | C23 | 1 | 16 | yes | — |
| 178 | #938 | C23 | 1 | 16 | yes | — |
| 179 | #938 | C23 | 1 | 4 | yes | — |
| 180 | #938 | C23 | 1 | 4 | yes | — |
| 181 | #938 | C23 | 1 | 4 | yes | — |
| 182 | #938 | C23 | 1 | 4 | yes | — |
| 183 | #938 | C23 | 1 | 8 | yes | — |
| 184 | #938 | C23 | 1 | 16 | yes | — |
| 185 | #937 | C23 | 1 | 8 | yes | — |
| 186 | #936 | C23 | 1 | 4 | yes | — |
| 187 | #936 | C23 | 1 | 4 | yes | — |
| 188 | #935 | C23 | 1 | 16 | yes | — |
| 189 | #935 | C23 | 1 | 8 | yes | — |
| 190 | D4×Dic3 | C23 | 1 | 16 | yes | — |
| 191 | D4×Dic3 | C23 | 1 | 16 | yes | — |
| 192 | D4×Dic3 | C23 | 1 | 4 | yes | — |
| 193 | D4×Dic3 | C23 | 1 | 4 | yes | — |
| 194 | D4×Dic3 | C23 | 1 | 4 | yes | — |
| 195 | D4×Dic3 | C23 | 1 | 4 | yes | — |
| 196 | D4×Dic3 | C23 | 1 | 8 | yes | — |
| 197 | D4×Dic3 | C23 | 1 | 8 | yes | — |
| 198 | D4×Dic3 | C23 | 1 | 8 | yes | — |
| 199 | #930 | C23 | 1 | 16 | yes | — |
| 200 | #930 | C23 | 1 | 4 | yes | — |
| 201 | #930 | C23 | 1 | 8 | yes | — |
| 202 | #929 | C23 | 1 | 16 | yes | — |
| 203 | C4×#67 | C23 | 1 | 16 | yes | — |
| 204 | C4×#67 | C23 | 1 | 16 | yes | — |
| 205 | C4×#67 | C23 | 1 | 8 | yes | — |
| 206 | C4×#67 | C23 | 1 | 16 | yes | — |
| 207 | C4×#67 | C23 | 1 | 8 | yes | — |
| 208 | #926 | C23 | 1 | 16 | yes | — |
| 209 | #926 | C23 | 1 | 4 | yes | — |
| 210 | #926 | C23 | 1 | 8 | yes | — |
| 211 | C2×C4⋊Dic3 | C23 | 1 | 8 | yes | — |
| 212 | C2×C4⋊Dic3 | C23 | 1 | 16 | yes | — |
| 213 | #924 | C23 | 1 | 4 | yes | — |
| 214 | #924 | C23 | 1 | 4 | yes | — |
| 215 | #924 | C23 | 1 | 8 | yes | — |
| 216 | C2×Dic3⋊C4 | C23 | 1 | 16 | yes | — |
| 217 | C2×C4×Dic3 | C23 | 1 | 1 | yes | characteristic |
| 218 | C2×C4×Dic3 | C23 | 1 | 2 | yes | — |
| 219 | C2×C4×Dic3 | C23 | 1 | 8 | yes | — |
| 220 | #898 | C23 | 1 | 16 | yes | — |
| 221 | #898 | C23 | 1 | 8 | yes | — |
| 222 | #898 | C23 | 1 | 16 | yes | — |
| 223 | #897 | C23 | 1 | 4 | yes | — |
| 224 | #897 | C23 | 1 | 4 | yes | — |
| 225 | #897 | C23 | 1 | 8 | yes | — |
| 226 | #897 | C23 | 1 | 4 | yes | — |
| 227 | #895 | C23 | 1 | 4 | yes | — |
| 228 | #895 | C23 | 1 | 4 | yes | — |
| 229 | #894 | C23 | 1 | 16 | yes | — |
| 230 | #894 | C23 | 1 | 8 | yes | — |
| 231 | #893 | C23 | 1 | 8 | yes | — |
| 232 | #893 | C23 | 1 | 4 | yes | — |
| 233 | #893 | C23 | 1 | 4 | yes | — |
| 234 | #893 | C23 | 1 | 8 | yes | — |
| 235 | #892 | C23 | 1 | 8 | yes | — |
| 236 | #892 | C23 | 1 | 16 | yes | — |
| 237 | #892 | C23 | 1 | 4 | yes | — |
| 238 | #892 | C23 | 1 | 4 | yes | — |
| 239 | #892 | C23 | 1 | 4 | yes | — |
| 240 | D3×C4⋊C4 | C23 | 1 | 16 | yes | — |
| 241 | D3×C4⋊C4 | C23 | 1 | 8 | yes | — |
| 242 | #890 | C23 | 1 | 16 | yes | — |
| 243 | #890 | C23 | 1 | 16 | yes | — |
| 244 | #890 | C23 | 1 | 8 | yes | — |
| 245 | #890 | C23 | 1 | 16 | yes | — |
| 246 | #890 | C23 | 1 | 4 | yes | — |
| 247 | #890 | C23 | 1 | 8 | yes | — |
| 248 | #890 | C23 | 1 | 4 | yes | — |
| 249 | #890 | C23 | 1 | 4 | yes | — |
| 250 | #889 | C23 | 1 | 16 | yes | — |
| 251 | #889 | C23 | 1 | 16 | yes | — |
| 252 | #889 | C23 | 1 | 16 | yes | — |
| 253 | #887 | C23 | 1 | 4 | yes | — |
| 254 | #887 | C23 | 1 | 4 | yes | — |
| 255 | #887 | C23 | 1 | 8 | yes | — |
| 256 | #887 | C23 | 1 | 4 | yes | — |
| 257 | #886 | C23 | 1 | 16 | yes | — |
| 258 | #886 | C23 | 1 | 16 | yes | — |
| 259 | #886 | C23 | 1 | 16 | yes | — |
| 260 | #886 | C23 | 1 | 4 | yes | — |
| 261 | #884 | C23 | 1 | 16 | yes | — |
| 262 | #884 | C23 | 1 | 16 | yes | — |
| 263 | #883 | C23 | 1 | 8 | yes | — |
| 264 | #883 | C23 | 1 | 16 | yes | — |
| 265 | #883 | C23 | 1 | 16 | yes | — |
| 266 | #883 | C23 | 1 | 8 | yes | — |
| 267 | #882 | C23 | 1 | 4 | yes | — |
| 268 | #67⋊C4 | C23 | 1 | 8 | yes | — |
| 269 | #67⋊C4 | C23 | 1 | 16 | yes | — |
| 270 | #67⋊C4 | C23 | 1 | 8 | yes | — |
| 271 | #67⋊C4 | C23 | 1 | 8 | yes | — |
| 272 | #879 | C23 | 1 | 16 | yes | — |
| 273 | #879 | C23 | 1 | 8 | yes | — |
| 274 | #879 | C23 | 1 | 16 | yes | — |
| 275 | #879 | C23 | 1 | 8 | yes | — |
| 276 | #879 | C23 | 1 | 16 | yes | — |
| 277 | #878 | C23 | 1 | 16 | yes | — |
| 278 | #877 | C23 | 1 | 16 | yes | — |
| 279 | #877 | C23 | 1 | 8 | yes | — |
| 280 | #877 | C23 | 1 | 8 | yes | — |
| 281 | #875 | C23 | 1 | 2 | yes | — |
| 282 | #874 | C23 | 1 | 1 | yes | characteristic |
| 283 | C4×D12 | C23 | 1 | 8 | yes | — |
| 284 | C4×D12 | C23 | 1 | 4 | yes | — |
| 285 | #872 | C23 | 1 | 4 | yes | — |
| 286 | C42×D3 | C23 | 1 | 2 | yes | — |
| 287 | C42×D3 | C23 | 1 | 4 | yes | — |
| 288 | C42×D3 | C23 | 1 | 2 | yes | — |
| 289 | C42×D3 | C23 | 1 | 2 | yes | — |
| 290 | C42×D3 | C23 | 1 | 2 | yes | — |
| 291 | #870 | C23 | 1 | 4 | yes | — |
| 292 | #870 | C23 | 1 | 4 | yes | — |
| 293 | #869 | C23 | 1 | 4 | yes | — |
| 294 | #869 | C23 | 1 | 2 | yes | — |
| 295 | #869 | C23 | 1 | 2 | yes | — |
| 296 | #869 | C23 | 1 | 1 | yes | characteristic |
| 297 | C4×Dic6 | C23 | 1 | 8 | yes | — |
| 298 | C4×Dic6 | C23 | 1 | 4 | yes | — |
| 299 | C4×Dic6 | C23 | 1 | 4 | yes | — |
| 300 | #564 | — | 3 | 4 | no | — |
| 301 | #562 | — | 3 | 8 | no | — |
| 302 | #562 | C2×D3 | 1 | 4 | yes | complemented |
| 303 | #560 | — | 3 | 16 | no | — |
| 304 | #557 | — | 3 | 4 | no | — |
| 305 | #557 | — | 3 | 4 | no | — |
| 306 | #557 | — | 3 | 4 | no | — |
| 307 | #554 | — | 3 | 4 | no | — |
| 308 | #554 | — | 3 | 4 | no | — |
| 309 | #554 | C2×D3 | 1 | 4 | yes | complemented |
| 310 | #553 | — | 3 | 16 | no | — |
| 311 | #553 | — | 3 | 16 | no | — |
| 312 | #553 | — | 3 | 16 | no | — |
| 313 | #553 | — | 3 | 16 | no | — |
| 314 | #553 | — | 3 | 16 | no | — |
| 315 | #553 | — | 3 | 16 | no | — |
| 316 | #553 | — | 3 | 8 | no | — |
| 317 | #553 | — | 3 | 8 | no | — |
| 318 | #553 | — | 3 | 8 | no | — |
| 319 | #552 | — | 3 | 8 | no | — |
| 320 | #552 | — | 3 | 16 | no | — |
| 321 | #552 | — | 3 | 16 | no | — |
| 322 | #552 | — | 3 | 8 | no | — |
| 323 | #552 | — | 3 | 16 | no | — |
| 324 | #552 | — | 3 | 8 | no | — |
| 325 | #550 | — | 3 | 8 | no | — |
| 326 | #550 | — | 3 | 8 | no | — |
| 327 | #550 | — | 3 | 4 | no | — |
| 328 | #550 | — | 3 | 8 | no | — |
| 329 | #550 | — | 3 | 4 | no | — |
| 330 | #550 | C2×D3 | 1 | 4 | yes | complemented |
| 331 | #547 | — | 3 | 8 | no | — |
| 332 | #547 | — | 3 | 8 | no | — |
| 333 | #547 | — | 3 | 4 | no | — |
| 334 | #547 | — | 3 | 8 | no | — |
| 335 | #547 | — | 3 | 4 | no | — |
| 336 | #547 | C2×D3 | 1 | 4 | yes | complemented |
| 337 | #541 | — | 3 | 4 | no | — |
| 338 | #541 | — | 3 | 8 | no | — |
| 339 | #541 | — | 3 | 8 | no | — |
| 340 | #541 | — | 3 | 4 | no | — |
| 341 | #540 | — | 3 | 4 | no | — |
| 342 | #540 | — | 3 | 16 | no | — |
| 343 | #540 | — | 3 | 8 | no | — |
| 344 | #540 | — | 3 | 8 | no | — |
| 345 | #540 | — | 3 | 16 | no | — |
| 346 | #540 | — | 3 | 16 | no | — |
| 347 | #540 | C2×D3 | 1 | 4 | yes | — |
| 348 | #539 | — | 3 | 16 | no | — |
| 349 | #539 | — | 3 | 16 | no | — |
| 350 | #539 | — | 3 | 16 | no | — |
| 351 | #537 | — | 3 | 8 | no | — |
| 352 | #537 | — | 3 | 8 | no | — |
| 353 | #537 | C2×D3 | 1 | 8 | yes | — |
| 354 | #533 | — | 3 | 2 | no | — |
| 355 | #533 | — | 3 | 2 | no | — |
| 356 | #533 | — | 3 | 2 | no | — |
| 357 | #533 | — | 3 | 2 | no | — |
| 358 | #533 | C2×D3 | 1 | 1 | yes | characteristic |
| 359 | #532 | — | 3 | 8 | no | — |
| 360 | #532 | — | 3 | 2 | no | — |
| 361 | #532 | — | 3 | 2 | no | — |
| 362 | #532 | — | 3 | 2 | no | — |
| 363 | #532 | — | 3 | 4 | no | — |
| 364 | #532 | — | 3 | 1 | no | — |
| 365 | #532 | C2×D3 | 1 | 2 | yes | — |
| 366 | #529 | — | 3 | 4 | no | — |
| 367 | #529 | — | 3 | 4 | no | — |
| 368 | #529 | — | 3 | 4 | no | — |
| 369 | #529 | — | 3 | 4 | no | — |
| 370 | #529 | — | 3 | 8 | no | — |
| 371 | #529 | — | 3 | 4 | no | — |
| 372 | #529 | — | 3 | 4 | no | — |
| 373 | #529 | — | 3 | 8 | no | — |
| 374 | #529 | — | 3 | 4 | no | — |
| 375 | #529 | — | 3 | 4 | no | — |
| 376 | #529 | — | 3 | 4 | no | — |
| 377 | #529 | — | 3 | 8 | no | — |
| 378 | C2×#125 | — | 3 | 4 | no | — |
| 379 | C2×#125 | — | 3 | 8 | no | — |
| 380 | #525 | — | 3 | 4 | no | — |
| 381 | #525 | — | 3 | 4 | no | — |
| 382 | #525 | — | 3 | 4 | no | — |
| 383 | #525 | — | 3 | 4 | no | — |
| 384 | #525 | — | 3 | 2 | no | — |
| 385 | #520 | — | 3 | 8 | no | — |
| 386 | #520 | — | 3 | 8 | no | — |
| 387 | #520 | — | 3 | 8 | no | — |
| 388 | C4×#41 | — | 3 | 4 | no | — |
| 389 | C4×#41 | — | 3 | 4 | no | — |
| 390 | C4×#41 | — | 3 | 4 | no | — |
| 391 | C4×#41 | — | 3 | 4 | no | — |
| 392 | C4×#41 | — | 3 | 2 | no | — |
| 393 | C22×C42 | — | 3 | 1 | no | — |
| 394 | C23×D3 | C24 | 1 | 1 | yes | characteristic |
| 395 | C3×#41 | — | 4 | 8 | no | — |
| 396 | C3×#41 | — | 4 | 16 | no | — |
| 397 | C2×C3×Q8 | C24 | 1 | 4 | yes | — |
| 398 | C2×C3×Q8 | C24 | 1 | 4 | yes | — |
| 399 | C2×C3×D4 | C24 | 1 | 4 | yes | — |
| 400 | C2×C3×D4 | C24 | 1 | 4 | yes | — |
| 401 | C2×C3×D4 | C24 | 1 | 8 | yes | — |
| 402 | C2×C3×D4 | C24 | 1 | 16 | yes | — |
| 403 | C2×C3×D4 | C24 | 1 | 4 | yes | — |
| 404 | C22×C3×C4 | C24 | 1 | 1 | yes | characteristic |
| 405 | C22×C3×C4 | C24 | 1 | 2 | yes | — |
| 406 | C22×C3×C4 | C24 | 1 | 8 | yes | — |
| 407 | C22×C3×C4 | C24 | 1 | 16 | yes | — |
| 408 | C2×#67 | C24 | 1 | 4 | yes | — |
| 409 | C2×#67 | C24 | 1 | 8 | yes | — |
| 410 | C2×#67 | C24 | 1 | 8 | yes | — |
| 411 | C2×#67 | C24 | 1 | 16 | yes | — |
| 412 | C2×#67 | C24 | 1 | 16 | yes | — |
| 413 | C22×Dic3 | C24 | 1 | 16 | yes | — |
| 414 | C22×Dic3 | C24 | 1 | 8 | yes | — |
| 415 | C22×Dic3 | C24 | 1 | 8 | yes | — |
| 416 | C22×Dic3 | C24 | 1 | 2 | yes | — |
| 417 | C22×Dic3 | C24 | 1 | 1 | yes | characteristic |
| 418 | #239 | — | 4 | 8 | no | — |
| 419 | #237 | — | 4 | 8 | no | — |
| 420 | #237 | — | 4 | 8 | no | — |
| 421 | #237 | — | 4 | 16 | no | — |
| 422 | #235 | — | 4 | 16 | no | — |
| 423 | #235 | — | 4 | 4 | no | — |
| 424 | C2×D12 | C24 | 1 | 4 | yes | — |
| 425 | C2×D12 | C24 | 1 | 8 | yes | — |
| 426 | C2×D12 | C24 | 1 | 2 | yes | — |
| 427 | C2×C4×D3 | — | 4 | 2 | no | — |
| 428 | C2×C4×D3 | — | 4 | 4 | no | — |
| 429 | C2×C4×D3 | C24 | 1 | 2 | yes | — |
| 430 | C2×C4×D3 | C24 | 1 | 2 | yes | — |
| 431 | C2×C4×D3 | C24 | 1 | 2 | yes | — |
| 432 | C2×C4×D3 | C24 | 1 | 4 | yes | — |
| 433 | C2×C4×D3 | C24 | 1 | 2 | yes | — |
| 434 | C2×C4×D3 | C24 | 1 | 2 | yes | — |
| 435 | C2×C4×D3 | C24 | 1 | 2 | yes | — |
| 436 | C2×C4×D3 | C24 | 1 | 8 | yes | — |
| 437 | C2×C4×D3 | C24 | 1 | 16 | yes | — |
| 438 | C2×Dic6 | C24 | 1 | 4 | yes | — |
| 439 | C2×Dic6 | C24 | 1 | 4 | yes | — |
| 440 | C2×Dic6 | C24 | 1 | 2 | yes | — |
| 441 | C3×C4⋊C4 | C24 | 1 | 4 | yes | — |
| 442 | C3×C4⋊C4 | C24 | 1 | 4 | yes | — |
| 443 | C3×C4⋊C4 | C24 | 1 | 4 | yes | — |
| 444 | C3×C4⋊C4 | C24 | 1 | 4 | yes | — |
| 445 | C3×C4⋊C4 | C24 | 1 | 8 | yes | — |
| 446 | C3×C4⋊C4 | C24 | 1 | 16 | yes | — |
| 447 | C3×C22⋊C4 | C24 | 1 | 8 | yes | — |
| 448 | C3×C22⋊C4 | C24 | 1 | 16 | yes | — |
| 449 | C3×C22⋊C4 | C24 | 1 | 8 | yes | — |
| 450 | C3×C22⋊C4 | C24 | 1 | 4 | yes | — |
| 451 | C3×C42 | C24 | 1 | 1 | yes | characteristic |
| 452 | C3×C42 | C24 | 1 | 2 | yes | — |
| 453 | C3×C42 | C24 | 1 | 4 | yes | — |
| 454 | C3×C42 | C24 | 1 | 1 | yes | characteristic |
| 455 | #217 | C24 | 1 | 8 | yes | — |
| 456 | #217 | C24 | 1 | 8 | yes | — |
| 457 | #217 | C24 | 1 | 16 | yes | — |
| 458 | #217 | C24 | 1 | 8 | yes | — |
| 459 | #217 | C24 | 1 | 8 | yes | — |
| 460 | #217 | C24 | 1 | 8 | yes | — |
| 461 | (C2×D3)⋊C4 | C24 | 1 | 8 | yes | — |
| 462 | (C2×D3)⋊C4 | C24 | 1 | 8 | yes | — |
| 463 | (C2×D3)⋊C4 | C24 | 1 | 8 | yes | — |
| 464 | (C2×D3)⋊C4 | C24 | 1 | 8 | yes | — |
| 465 | (C2×D3)⋊C4 | C24 | 1 | 8 | yes | — |
| 466 | (C2×D3)⋊C4 | C24 | 1 | 8 | yes | — |
| 467 | (C2×D3)⋊C4 | C24 | 1 | 16 | yes | — |
| 468 | C4⋊Dic3 | C24 | 1 | 4 | yes | — |
| 469 | C4⋊Dic3 | C24 | 1 | 4 | yes | — |
| 470 | C4⋊Dic3 | C24 | 1 | 4 | yes | — |
| 471 | C4⋊Dic3 | C24 | 1 | 4 | yes | — |
| 472 | C4⋊Dic3 | C24 | 1 | 4 | yes | — |
| 473 | C4⋊Dic3 | C24 | 1 | 16 | yes | — |
| 474 | C4⋊Dic3 | C24 | 1 | 8 | yes | — |
| 475 | C4⋊Dic3 | C24 | 1 | 16 | yes | — |
| 476 | C4⋊Dic3 | C24 | 1 | 8 | yes | — |
| 477 | C4⋊Dic3 | C24 | 1 | 8 | yes | — |
| 478 | Dic3⋊C4 | C24 | 1 | 8 | yes | — |
| 479 | Dic3⋊C4 | C24 | 1 | 8 | yes | — |
| 480 | Dic3⋊C4 | C24 | 1 | 16 | yes | — |
| 481 | Dic3⋊C4 | C24 | 1 | 16 | yes | — |
| 482 | Dic3⋊C4 | C24 | 1 | 8 | yes | — |
| 483 | Dic3⋊C4 | C24 | 1 | 16 | yes | — |
| 484 | Dic3⋊C4 | C24 | 1 | 8 | yes | — |
| 485 | Dic3⋊C4 | C24 | 1 | 8 | yes | — |
| 486 | C4×Dic3 | C24 | 1 | 8 | yes | — |
| 487 | C4×Dic3 | C24 | 1 | 16 | yes | — |
| 488 | C4×Dic3 | C24 | 1 | 1 | yes | characteristic |
| 489 | C4×Dic3 | C24 | 1 | 1 | yes | characteristic |
| 490 | C4×Dic3 | C24 | 1 | 2 | yes | — |
| 491 | C4×Dic3 | C24 | 1 | 2 | yes | — |
| 492 | C4×Dic3 | C24 | 1 | 2 | yes | — |
| 493 | C4×Dic3 | C24 | 1 | 2 | yes | — |
| 494 | C4×Dic3 | C24 | 1 | 2 | yes | — |
| 495 | C4×Dic3 | C24 | 1 | 8 | yes | — |
| 496 | C4×Dic3 | C24 | 1 | 8 | yes | — |
| 497 | C4×Dic3 | C24 | 1 | 8 | yes | — |
| 498 | C2×#41 | — | 3 | 4 | no | — |
| 499 | C2×#41 | — | 3 | 4 | no | — |
| 500 | C2×#41 | — | 3 | 4 | no | — |
| 501 | C2×#41 | — | 3 | 8 | no | — |
| 502 | C2×#41 | — | 3 | 2 | no | — |
| 503 | C2×#41 | — | 3 | 8 | no | — |
| 504 | C2×#41 | C22×D3 | 1 | 4 | yes | — |
| 505 | C2×#41 | C22×D3 | 1 | 8 | yes | — |
| 506 | C23×C4 | — | 3 | 2 | no | — |
| 507 | C23×C4 | — | 3 | 1 | no | — |
| 508 | C4⋊Q8 | — | 3 | 8 | no | — |
| 509 | C4⋊Q8 | — | 3 | 2 | no | — |
| 510 | C4⋊Q8 | — | 3 | 2 | no | — |
| 511 | C4⋊Q8 | — | 3 | 1 | no | — |
| 512 | C4⋊Q8 | — | 3 | 4 | no | — |
| 513 | C4⋊Q8 | C22×D3 | 1 | 2 | yes | — |
| 514 | C4⋊Q8 | C22×D3 | 1 | 2 | yes | — |
| 515 | #127 | — | 3 | 8 | no | — |
| 516 | #127 | — | 3 | 16 | no | — |
| 517 | #127 | — | 3 | 1 | no | — |
| 518 | #127 | C22×D3 | 1 | 2 | yes | — |
| 519 | #127 | C22×D3 | 1 | 4 | yes | — |
| 520 | #126 | — | 3 | 8 | no | — |
| 521 | #126 | — | 3 | 16 | no | — |
| 522 | #126 | — | 3 | 16 | no | — |
| 523 | #126 | — | 3 | 8 | no | — |
| 524 | #126 | — | 3 | 8 | no | — |
| 525 | #126 | — | 3 | 16 | no | — |
| 526 | #126 | — | 3 | 16 | no | — |
| 527 | #126 | — | 3 | 16 | no | — |
| 528 | #125 | — | 3 | 4 | no | — |
| 529 | #125 | — | 3 | 4 | no | — |
| 530 | #125 | — | 3 | 4 | no | — |
| 531 | #125 | — | 3 | 16 | no | — |
| 532 | #125 | — | 3 | 16 | no | — |
| 533 | #125 | — | 3 | 16 | no | — |
| 534 | #125 | — | 3 | 8 | no | — |
| 535 | #125 | — | 3 | 8 | no | — |
| 536 | #125 | — | 3 | 16 | no | — |
| 537 | #125 | — | 3 | 16 | no | — |
| 538 | #125 | — | 3 | 16 | no | — |
| 539 | #125 | — | 3 | 4 | no | — |
| 540 | #125 | — | 3 | 4 | no | — |
| 541 | #125 | C22×D3 | 1 | 4 | yes | — |
| 542 | #125 | C22×D3 | 1 | 2 | yes | — |
| 543 | #124 | — | 3 | 4 | no | — |
| 544 | #124 | — | 3 | 4 | no | — |
| 545 | #124 | — | 3 | 4 | no | — |
| 546 | #124 | — | 3 | 2 | no | — |
| 547 | #124 | C22×D3 | 1 | 4 | yes | — |
| 548 | #123 | — | 3 | 8 | no | — |
| 549 | #123 | — | 3 | 16 | no | — |
| 550 | #123 | — | 3 | 16 | no | — |
| 551 | #123 | — | 3 | 8 | no | — |
| 552 | #123 | — | 3 | 16 | no | — |
| 553 | #123 | — | 3 | 8 | no | — |
| 554 | #123 | — | 3 | 8 | no | — |
| 555 | #123 | — | 3 | 4 | no | — |
| 556 | #123 | — | 3 | 16 | no | — |
| 557 | #123 | — | 3 | 16 | no | — |
| 558 | #123 | — | 3 | 16 | no | — |
| 559 | #123 | — | 3 | 16 | no | — |
| 560 | #123 | — | 3 | 16 | no | — |
| 561 | #123 | C22×D3 | 1 | 16 | yes | — |
| 562 | C22⋊Q8 | — | 3 | 4 | no | — |
| 563 | C22⋊Q8 | — | 3 | 4 | no | — |
| 564 | C22⋊Q8 | — | 3 | 4 | no | — |
| 565 | C22⋊Q8 | — | 3 | 16 | no | — |
| 566 | C22⋊Q8 | — | 3 | 4 | no | — |
| 567 | C22⋊Q8 | — | 3 | 4 | no | — |
| 568 | C22⋊Q8 | — | 3 | 8 | no | — |
| 569 | C22⋊Q8 | — | 3 | 4 | no | — |
| 570 | C22⋊Q8 | — | 3 | 4 | no | — |
| 571 | C22⋊Q8 | — | 3 | 4 | no | — |
| 572 | C22⋊Q8 | — | 3 | 8 | no | — |
| 573 | C22⋊Q8 | — | 3 | 16 | no | — |
| 574 | C22⋊Q8 | C22×D3 | 1 | 4 | yes | — |
| 575 | C22⋊Q8 | C22×D3 | 1 | 8 | yes | — |
| 576 | C22⋊Q8 | C22×D3 | 1 | 16 | yes | — |
| 577 | #121 | — | 3 | 4 | no | — |
| 578 | #121 | — | 3 | 4 | no | — |
| 579 | #121 | — | 3 | 4 | no | — |
| 580 | #121 | — | 3 | 4 | no | — |
| 581 | #121 | — | 3 | 8 | no | — |
| 582 | #121 | — | 3 | 16 | no | — |
| 583 | #121 | — | 3 | 16 | no | — |
| 584 | #121 | — | 3 | 16 | no | — |
| 585 | #121 | — | 3 | 16 | no | — |
| 586 | #121 | — | 3 | 16 | no | — |
| 587 | #121 | — | 3 | 16 | no | — |
| 588 | #121 | — | 3 | 16 | no | — |
| 589 | #121 | — | 3 | 4 | no | — |
| 590 | #121 | — | 3 | 8 | no | — |
| 591 | #121 | — | 3 | 16 | no | — |
| 592 | #121 | — | 3 | 4 | no | — |
| 593 | #121 | — | 3 | 4 | no | — |
| 594 | #121 | — | 3 | 16 | no | — |
| 595 | #121 | — | 3 | 16 | no | — |
| 596 | #121 | C22×D3 | 1 | 4 | yes | — |
| 597 | #121 | C22×D3 | 1 | 4 | yes | — |
| 598 | #121 | C22×D3 | 1 | 8 | yes | — |
| 599 | #121 | C22×D3 | 1 | 16 | yes | — |
| 600 | #121 | C22×D3 | 1 | 16 | yes | — |
| 601 | #120 | — | 3 | 8 | no | — |
| 602 | #120 | — | 3 | 4 | no | — |
| 603 | C4×Q8 | — | 3 | 4 | no | — |
| 604 | C4×Q8 | — | 3 | 4 | no | — |
| 605 | C4×Q8 | — | 3 | 4 | no | — |
| 606 | C4×Q8 | — | 3 | 8 | no | — |
| 607 | C4×Q8 | — | 3 | 4 | no | — |
| 608 | C4×Q8 | — | 3 | 4 | no | — |
| 609 | C4×Q8 | — | 3 | 4 | no | — |
| 610 | C4×Q8 | — | 3 | 8 | no | — |
| 611 | C4×Q8 | — | 3 | 4 | no | — |
| 612 | C4×Q8 | — | 3 | 4 | no | — |
| 613 | C4×Q8 | — | 3 | 8 | no | — |
| 614 | C4×Q8 | C22×D3 | 1 | 4 | yes | — |
| 615 | C4×D4 | — | 3 | 4 | no | — |
| 616 | C4×D4 | — | 3 | 4 | no | — |
| 617 | C4×D4 | — | 3 | 8 | no | — |
| 618 | C4×D4 | — | 3 | 8 | no | — |
| 619 | C4×D4 | — | 3 | 4 | no | — |
| 620 | C4×D4 | — | 3 | 4 | no | — |
| 621 | C4×D4 | — | 3 | 16 | no | — |
| 622 | C4×D4 | — | 3 | 8 | no | — |
| 623 | C4×D4 | — | 3 | 16 | no | — |
| 624 | C4×D4 | — | 3 | 8 | no | — |
| 625 | C4×D4 | — | 3 | 8 | no | — |
| 626 | C4×D4 | — | 3 | 16 | no | — |
| 627 | C4×D4 | — | 3 | 16 | no | — |
| 628 | C4×D4 | — | 3 | 16 | no | — |
| 629 | C4×D4 | — | 3 | 4 | no | — |
| 630 | C4×D4 | — | 3 | 8 | no | — |
| 631 | C4×D4 | — | 3 | 4 | no | — |
| 632 | C4×D4 | — | 3 | 8 | no | — |
| 633 | C4×D4 | — | 3 | 8 | no | — |
| 634 | C4×D4 | — | 3 | 8 | no | — |
| 635 | C4×D4 | — | 3 | 8 | no | — |
| 636 | C4×D4 | — | 3 | 16 | no | — |
| 637 | C4×D4 | — | 3 | 8 | no | — |
| 638 | C4×D4 | — | 3 | 4 | no | — |
| 639 | C4×D4 | C22×D3 | 1 | 4 | yes | — |
| 640 | C4×D4 | C22×D3 | 1 | 4 | yes | — |
| 641 | C4×D4 | C22×D3 | 1 | 8 | yes | — |
| 642 | #117 | — | 3 | 8 | no | — |
| 643 | #117 | — | 3 | 4 | no | — |
| 644 | #117 | — | 3 | 16 | no | — |
| 645 | #117 | — | 3 | 4 | no | — |
| 646 | #117 | — | 3 | 4 | no | — |
| 647 | #117 | — | 3 | 4 | no | — |
| 648 | #117 | — | 3 | 8 | no | — |
| 649 | #117 | — | 3 | 16 | no | — |
| 650 | #117 | — | 3 | 8 | no | — |
| 651 | #117 | — | 3 | 8 | no | — |
| 652 | #117 | — | 3 | 16 | no | — |
| 653 | #117 | — | 3 | 4 | no | — |
| 654 | #117 | C22×D3 | 1 | 2 | yes | — |
| 655 | C2×C4⋊C4 | — | 3 | 8 | no | — |
| 656 | C2×C4⋊C4 | — | 3 | 16 | no | — |
| 657 | C2×C4⋊C4 | — | 3 | 16 | no | — |
| 658 | C2×C4⋊C4 | — | 3 | 8 | no | — |
| 659 | C2×C4⋊C4 | — | 3 | 16 | no | — |
| 660 | C2×C4⋊C4 | C22×D3 | 1 | 8 | yes | — |
| 661 | C2×C42 | — | 3 | 8 | no | — |
| 662 | C2×C42 | — | 3 | 2 | no | — |
| 663 | C2×C42 | — | 3 | 1 | no | — |
| 664 | C2×C42 | — | 3 | 4 | no | — |
| 665 | C2×C42 | — | 3 | 2 | no | — |
| 666 | C2×C42 | — | 3 | 2 | no | — |
| 667 | C2×C42 | — | 3 | 2 | no | — |
| 668 | C2×C42 | — | 3 | 2 | no | — |
| 669 | C2×C42 | C22×D3 | 1 | 1 | yes | characteristic |
| 670 | C23×C3 | C25 | 1 | 1 | yes | characteristic |
| 671 | C23×C3 | C25 | 1 | 8 | yes | — |
| 672 | C22×D3 | — | 4 | 2 | no | — |
| 673 | C22×D3 | — | 4 | 1 | no | — |
| 674 | C22×D3 | C25 | 1 | 2 | yes | — |
| 675 | C22×D3 | C25 | 1 | 4 | yes | — |
| 676 | C3×Q8 | — | 2 | 8 | no | — |
| 677 | C3×Q8 | — | 4 | 4 | no | — |
| 678 | C3×D4 | — | 2 | 8 | no | — |
| 679 | C3×D4 | — | 2 | 8 | no | — |
| 680 | C3×D4 | — | 4 | 8 | no | — |
| 681 | C3×D4 | — | 4 | 4 | no | — |
| 682 | C3×D4 | — | 4 | 16 | no | — |
| 683 | C2×C3×C4 | — | 2 | 2 | no | — |
| 684 | C2×C3×C4 | — | 2 | 4 | no | — |
| 685 | C2×C3×C4 | — | 2 | 16 | no | — |
| 686 | C2×C3×C4 | — | 4 | 16 | no | — |
| 687 | C2×C3×C4 | C25 | 1 | 8 | yes | — |
| 688 | C2×C3×C4 | C25 | 1 | 1 | yes | characteristic |
| 689 | C2×C3×C4 | C25 | 1 | 2 | yes | — |
| 690 | C2×C3×C4 | C25 | 1 | 8 | yes | — |
| 691 | C2×C3×C4 | C25 | 1 | 2 | yes | — |
| 692 | C2×C3×C4 | C25 | 1 | 1 | yes | characteristic |
| 693 | #67 | — | 4 | 16 | no | — |
| 694 | #67 | — | 4 | 4 | no | — |
| 695 | #67 | — | 4 | 8 | no | — |
| 696 | #67 | — | 4 | 8 | no | — |
| 697 | #67 | — | 4 | 16 | no | — |
| 698 | C2×Dic3 | — | 4 | 2 | no | — |
| 699 | C2×Dic3 | — | 4 | 1 | no | — |
| 700 | C2×Dic3 | — | 4 | 8 | no | — |
| 701 | C2×Dic3 | — | 4 | 16 | no | — |
| 702 | C2×Dic3 | — | 4 | 8 | no | — |
| 703 | C2×Dic3 | C25 | 1 | 2 | yes | — |
| 704 | C2×Dic3 | C25 | 1 | 2 | yes | — |
| 705 | C2×Dic3 | C25 | 1 | 2 | yes | — |
| 706 | C2×Dic3 | C25 | 1 | 8 | yes | — |
| 707 | C2×Dic3 | C25 | 1 | 8 | yes | — |
| 708 | C2×Dic3 | C25 | 1 | 4 | yes | — |
| 709 | D12 | — | 2 | 8 | no | — |
| 710 | D12 | — | 4 | 2 | no | — |
| 711 | D12 | — | 4 | 8 | no | — |
| 712 | C4×D3 | — | 2 | 4 | no | — |
| 713 | C4×D3 | — | 2 | 4 | no | — |
| 714 | C4×D3 | — | 2 | 4 | no | — |
| 715 | C4×D3 | — | 2 | 8 | no | — |
| 716 | C4×D3 | — | 4 | 2 | no | — |
| 717 | C4×D3 | — | 4 | 2 | no | — |
| 718 | C4×D3 | — | 4 | 2 | no | — |
| 719 | C4×D3 | — | 4 | 16 | no | — |
| 720 | C4×D3 | — | 4 | 8 | no | — |
| 721 | Dic6 | — | 2 | 8 | no | — |
| 722 | Dic6 | — | 2 | 8 | no | — |
| 723 | Dic6 | — | 4 | 2 | no | — |
| 724 | C24 | — | 3 | 1 | no | — |
| 725 | #41 | — | 4 | 8 | no | — |
| 726 | #41 | — | 4 | 16 | no | — |
| 727 | #41 | — | 12 | 4 | no | — |
| 728 | #41 | — | 12 | 16 | no | — |
| 729 | #41 | — | 12 | 8 | no | — |
| 730 | #41 | — | 12 | 8 | no | — |
| 731 | #41 | — | 12 | 16 | no | — |
| 732 | #41 | — | 12 | 8 | no | — |
| 733 | C2×Q8 | — | 3 | 4 | no | — |
| 734 | C2×Q8 | — | 3 | 4 | no | — |
| 735 | C2×Q8 | — | 3 | 2 | no | — |
| 736 | C2×Q8 | C23×D3 | 1 | 4 | yes | — |
| 737 | C2×Q8 | C23×D3 | 1 | 4 | yes | — |
| 738 | C2×D4 | — | 3 | 4 | no | — |
| 739 | C2×D4 | — | 3 | 8 | no | — |
| 740 | C2×D4 | — | 3 | 8 | no | — |
| 741 | C2×D4 | — | 3 | 16 | no | — |
| 742 | C2×D4 | — | 3 | 16 | no | — |
| 743 | C2×D4 | — | 3 | 4 | no | — |
| 744 | C2×D4 | — | 3 | 8 | no | — |
| 745 | C2×D4 | — | 3 | 2 | no | — |
| 746 | C2×D4 | C23×D3 | 1 | 4 | yes | — |
| 747 | C2×D4 | C23×D3 | 1 | 4 | yes | — |
| 748 | C2×D4 | C23×D3 | 1 | 8 | yes | — |
| 749 | C2×D4 | C23×D3 | 1 | 4 | yes | — |
| 750 | C2×D4 | C23×D3 | 1 | 16 | yes | — |
| 751 | C22×C4 | — | 3 | 1 | no | — |
| 752 | C22×C4 | — | 3 | 2 | no | — |
| 753 | C22×C4 | — | 3 | 8 | no | — |
| 754 | C22×C4 | — | 3 | 8 | no | — |
| 755 | C22×C4 | — | 3 | 16 | no | — |
| 756 | C22×C4 | — | 3 | 2 | no | — |
| 757 | C22×C4 | — | 3 | 2 | no | — |
| 758 | C22×C4 | — | 3 | 2 | no | — |
| 759 | C22×C4 | — | 3 | 4 | no | — |
| 760 | C22×C4 | — | 3 | 2 | no | — |
| 761 | C22×C4 | — | 3 | 2 | no | — |
| 762 | C22×C4 | — | 3 | 2 | no | — |
| 763 | C22×C4 | — | 3 | 8 | no | — |
| 764 | C22×C4 | — | 3 | 16 | no | — |
| 765 | C22×C4 | — | 12 | 4 | no | — |
| 766 | C22×C4 | — | 12 | 2 | no | — |
| 767 | C22×C4 | C23×D3 | 1 | 2 | yes | — |
| 768 | C22×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 769 | C22×C4 | C23×D3 | 1 | 8 | yes | — |
| 770 | C22×C4 | C23×D3 | 1 | 16 | yes | — |
| 771 | C4⋊C4 | — | 3 | 8 | no | — |
| 772 | C4⋊C4 | — | 3 | 8 | no | — |
| 773 | C4⋊C4 | — | 3 | 8 | no | — |
| 774 | C4⋊C4 | — | 3 | 4 | no | — |
| 775 | C4⋊C4 | — | 3 | 8 | no | — |
| 776 | C4⋊C4 | — | 3 | 8 | no | — |
| 777 | C4⋊C4 | — | 3 | 8 | no | — |
| 778 | C4⋊C4 | — | 3 | 4 | no | — |
| 779 | C4⋊C4 | — | 3 | 4 | no | — |
| 780 | C4⋊C4 | — | 3 | 16 | no | — |
| 781 | C4⋊C4 | — | 3 | 16 | no | — |
| 782 | C4⋊C4 | — | 3 | 16 | no | — |
| 783 | C4⋊C4 | — | 3 | 16 | no | — |
| 784 | C4⋊C4 | — | 3 | 16 | no | — |
| 785 | C4⋊C4 | — | 3 | 8 | no | — |
| 786 | C4⋊C4 | — | 3 | 8 | no | — |
| 787 | C4⋊C4 | — | 3 | 4 | no | — |
| 788 | C4⋊C4 | — | 3 | 4 | no | — |
| 789 | C4⋊C4 | C23×D3 | 1 | 4 | yes | — |
| 790 | C4⋊C4 | C23×D3 | 1 | 16 | yes | — |
| 791 | C4⋊C4 | C23×D3 | 1 | 4 | yes | — |
| 792 | C4⋊C4 | C23×D3 | 1 | 4 | yes | — |
| 793 | C4⋊C4 | C23×D3 | 1 | 8 | yes | — |
| 794 | C4⋊C4 | C23×D3 | 1 | 4 | yes | — |
| 795 | C22⋊C4 | — | 3 | 8 | no | — |
| 796 | C22⋊C4 | — | 3 | 8 | no | — |
| 797 | C22⋊C4 | — | 3 | 8 | no | — |
| 798 | C22⋊C4 | — | 3 | 8 | no | — |
| 799 | C22⋊C4 | — | 3 | 8 | no | — |
| 800 | C22⋊C4 | — | 3 | 16 | no | — |
| 801 | C22⋊C4 | — | 3 | 8 | no | — |
| 802 | C22⋊C4 | — | 3 | 8 | no | — |
| 803 | C22⋊C4 | — | 3 | 8 | no | — |
| 804 | C22⋊C4 | — | 3 | 8 | no | — |
| 805 | C22⋊C4 | — | 3 | 8 | no | — |
| 806 | C22⋊C4 | — | 3 | 16 | no | — |
| 807 | C22⋊C4 | — | 3 | 8 | no | — |
| 808 | C22⋊C4 | C23×D3 | 1 | 8 | yes | — |
| 809 | C22⋊C4 | C23×D3 | 1 | 16 | yes | — |
| 810 | C22⋊C4 | C23×D3 | 1 | 8 | yes | — |
| 811 | C22⋊C4 | C23×D3 | 1 | 4 | yes | — |
| 812 | C42 | — | 3 | 2 | no | — |
| 813 | C42 | — | 3 | 1 | no | — |
| 814 | C42 | — | 3 | 2 | no | — |
| 815 | C42 | — | 3 | 1 | no | — |
| 816 | C42 | — | 3 | 2 | no | — |
| 817 | C42 | — | 3 | 2 | no | — |
| 818 | C42 | — | 3 | 2 | no | — |
| 819 | C42 | — | 3 | 8 | no | — |
| 820 | C42 | — | 3 | 8 | no | — |
| 821 | C42 | — | 3 | 8 | no | — |
| 822 | C42 | — | 3 | 8 | no | — |
| 823 | C42 | — | 3 | 16 | no | — |
| 824 | C42 | C23×D3 | 1 | 2 | yes | — |
| 825 | C42 | C23×D3 | 1 | 1 | yes | characteristic |
| 826 | C42 | C23×D3 | 1 | 1 | yes | characteristic |
| 827 | C42 | C23×D3 | 1 | 4 | yes | — |
| 828 | C22×C3 | — | 2 | 8 | no | — |
| 829 | C22×C3 | — | 2 | 1 | no | — |
| 830 | C22×C3 | — | 2 | 8 | no | — |
| 831 | C22×C3 | — | 2 | 2 | no | — |
| 832 | C22×C3 | — | 2 | 8 | no | — |
| 833 | C22×C3 | C26 | 1 | 1 | yes | characteristic |
| 834 | C2×D3 | — | 2 | 2 | no | — |
| 835 | C2×D3 | — | 2 | 2 | no | — |
| 836 | C2×D3 | — | 2 | 2 | no | — |
| 837 | C2×D3 | — | 2 | 4 | no | — |
| 838 | C2×D3 | — | 2 | 8 | no | — |
| 839 | C2×D3 | — | 4 | 4 | no | — |
| 840 | C3×C4 | — | 2 | 1 | no | — |
| 841 | C3×C4 | — | 2 | 8 | no | — |
| 842 | C3×C4 | — | 2 | 2 | no | — |
| 843 | C3×C4 | — | 2 | 8 | no | — |
| 844 | C3×C4 | #585 | 1 | 4 | yes | — |
| 845 | C3×C4 | #585 | 1 | 2 | yes | — |
| 846 | Dic3 | — | 2 | 8 | no | — |
| 847 | Dic3 | — | 2 | 8 | no | — |
| 848 | Dic3 | — | 2 | 4 | no | — |
| 849 | Dic3 | — | 2 | 2 | no | — |
| 850 | Dic3 | — | 2 | 2 | no | — |
| 851 | Dic3 | — | 2 | 2 | no | — |
| 852 | C23 | — | 3 | 2 | no | — |
| 853 | C23 | — | 3 | 4 | no | — |
| 854 | C23 | — | 12 | 2 | no | — |
| 855 | C23 | — | 12 | 1 | no | — |
| 856 | C23 | C24×D3 | 1 | 1 | yes | characteristic |
| 857 | C23 | C24×D3 | 1 | 8 | yes | — |
| 858 | Q8 | — | 2 | 8 | no | — |
| 859 | Q8 | — | 4 | 4 | no | — |
| 860 | Q8 | — | 6 | 8 | no | — |
| 861 | Q8 | — | 6 | 8 | no | — |
| 862 | Q8 | — | 12 | 2 | no | — |
| 863 | D4 | — | 2 | 8 | no | — |
| 864 | D4 | — | 2 | 8 | no | — |
| 865 | D4 | — | 4 | 8 | no | — |
| 866 | D4 | — | 4 | 4 | no | — |
| 867 | D4 | — | 4 | 16 | no | — |
| 868 | D4 | — | 6 | 8 | no | — |
| 869 | D4 | — | 12 | 8 | no | — |
| 870 | D4 | — | 12 | 2 | no | — |
| 871 | D4 | — | 12 | 16 | no | — |
| 872 | D4 | — | 12 | 8 | no | — |
| 873 | D4 | — | 12 | 4 | no | — |
| 874 | D4 | — | 12 | 8 | no | — |
| 875 | D4 | — | 12 | 16 | no | — |
| 876 | C2×C4 | — | 2 | 4 | no | — |
| 877 | C2×C4 | — | 2 | 16 | no | — |
| 878 | C2×C4 | — | 2 | 2 | no | — |
| 879 | C2×C4 | — | 3 | 2 | no | — |
| 880 | C2×C4 | — | 3 | 2 | no | — |
| 881 | C2×C4 | — | 3 | 2 | no | — |
| 882 | C2×C4 | — | 3 | 8 | no | — |
| 883 | C2×C4 | — | 3 | 8 | no | — |
| 884 | C2×C4 | — | 3 | 4 | no | — |
| 885 | C2×C4 | — | 4 | 16 | no | — |
| 886 | C2×C4 | — | 6 | 4 | no | — |
| 887 | C2×C4 | — | 6 | 4 | no | — |
| 888 | C2×C4 | — | 6 | 4 | no | — |
| 889 | C2×C4 | — | 6 | 8 | no | — |
| 890 | C2×C4 | — | 12 | 2 | no | — |
| 891 | C2×C4 | — | 12 | 2 | no | — |
| 892 | C2×C4 | — | 12 | 2 | no | — |
| 893 | C2×C4 | — | 12 | 16 | no | — |
| 894 | C2×C4 | — | 12 | 8 | no | — |
| 895 | C2×C4 | — | 12 | 2 | no | — |
| 896 | C2×C4 | — | 12 | 1 | no | — |
| 897 | C2×C4 | — | 12 | 8 | no | — |
| 898 | C2×C4 | — | 12 | 8 | no | — |
| 899 | C2×C4 | — | 12 | 16 | no | — |
| 900 | C2×C4 | C24×D3 | 1 | 8 | yes | — |
| 901 | C2×C4 | C24×D3 | 1 | 2 | yes | — |
| 902 | C2×C4 | C24×D3 | 1 | 1 | yes | characteristic |
| 903 | C2×C4 | C24×D3 | 1 | 8 | yes | — |
| 904 | C2×C4 | C24×D3 | 1 | 2 | yes | — |
| 905 | C2×C4 | C24×D3 | 1 | 1 | yes | characteristic |
| 906 | C2×C3 | — | 4 | 1 | no | — |
| 907 | C2×C3 | — | 4 | 8 | no | — |
| 908 | C2×C3 | C2×#585 | 1 | 2 | yes | — |
| 909 | C2×C3 | C2×#585 | 1 | 1 | yes | characteristic |
| 910 | D3 | — | 4 | 4 | no | — |
| 911 | D3 | — | 4 | 2 | no | — |
| 912 | C22 | — | 2 | 2 | no | — |
| 913 | C22 | — | 2 | 8 | no | — |
| 914 | C22 | — | 2 | 8 | no | — |
| 915 | C22 | — | 2 | 1 | no | — |
| 916 | C22 | — | 2 | 8 | no | — |
| 917 | C22 | — | 6 | 2 | no | — |
| 918 | C22 | — | 6 | 2 | no | — |
| 919 | C22 | — | 6 | 8 | no | — |
| 920 | C22 | — | 6 | 2 | no | — |
| 921 | C22 | — | 6 | 4 | no | — |
| 922 | C22 | — | 12 | 4 | no | — |
| 923 | C22 | C25×D3 | 1 | 1 | yes | characteristic |
| 924 | C4 | — | 2 | 8 | no | — |
| 925 | C4 | — | 2 | 2 | no | — |
| 926 | C4 | — | 2 | 8 | no | — |
| 927 | C4 | — | 2 | 1 | no | — |
| 928 | C4 | — | 6 | 2 | no | — |
| 929 | C4 | — | 6 | 2 | no | — |
| 930 | C4 | — | 6 | 8 | no | — |
| 931 | C4 | — | 6 | 2 | no | — |
| 932 | C4 | — | 6 | 4 | no | — |
| 933 | C4 | — | 6 | 8 | no | — |
| 934 | C4 | #5966 | 1 | 4 | yes | — |
| 935 | C4 | #5968 | 1 | 2 | yes | — |
| 936 | C3 | #62840 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 937 | C2 | — | 4 | 1 | no | — |
| 938 | C2 | — | 4 | 8 | no | — |
| 939 | C2 | — | 12 | 2 | no | — |
| 940 | C2 | — | 12 | 4 | no | — |
| 941 | C2 | C2×#5966 | 1 | 2 | yes | — |
| 942 | C2 | C2×#5968 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C25×D3 |
| commutator, socle, cosocle | C22×C3 | C26 |
| Fitting | C3×#3548 | C2 |
| hypercenter | #3548 | D3 |
| hypocenter | C3 | #62840 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C22 ◁ #3548 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×#3548 | C2 | semidirect |
| 2. #87106 | C2 | semidirect |
| 3. #86931 | C2 | semidirect |
| 4. #86930 | C2 | semidirect |
| 5. #86774 | C2 | semidirect |
| 6. #86773 | C2 | semidirect |
| 7. #86684 | C2 | semidirect |
| 8. #86683 | C2 | semidirect |
| 9. #86472 | C2 | semidirect |
| 10. #86469 | C2 | semidirect |
| 11. #86371 | C2 | semidirect |
| 12. #86369 | C2 | semidirect |
| 13. #86270 | C2 | semidirect |
| 14. #86257 | C2 | semidirect |
| 15. #86251 | C2 | semidirect |
| 16. #86219 | C2 | semidirect |
| 18. C3×#562 | C22 | semidirect |
| 19. C3×#554 | C22 | semidirect |
| 20. C3×#550 | C22 | semidirect |
| 21. C3×#547 | C22 | semidirect |
| 28. #5832 | C22 | semidirect |
| 30. #5827 | C22 | semidirect |
| 33. #5730 | C22 | semidirect |
| 38. #5721 | C22 | semidirect |
| 39. #5719 | C22 | semidirect |
| 41. #5718 | C22 | semidirect |
| 44. #5716 | C22 | semidirect |
| 45. #5698 | C22 | semidirect |
| 48. D3×#125 | C22 | semidirect |
| 49. C3⋊#564 | C22 | semidirect |
| 50. #5684 | C22 | semidirect |
| 55. #5661 | C22 | semidirect |
| 56. #5650 | C22 | semidirect |
| 59. #5642 | C22 | semidirect |
| 60. #5639 | C22 | semidirect |
| 65. #5625 | C22 | semidirect |
| 67. #5624 | C22 | semidirect |
| 71. #5619 | C22 | semidirect |
| 74. #5618 | C22 | semidirect |
| 81. #5601 | C22 | semidirect |
| 84. #5600 | C22 | semidirect |
| 88. #5570 | C22 | semidirect |
| 89. #5567 | C22 | semidirect |
| 93. #5557 | C22 | semidirect |
| 95. #5555 | C22 | semidirect |
| 96. #5553 | C22 | semidirect |
| 97. #5551 | C22 | semidirect |
| 98. #5546 | C22 | semidirect |
| 99. #5543 | C22 | semidirect |
| 107. #5504 | C22 | semidirect |
| 108. C2×#890 | C22 | semidirect |
| 115. #3548 | D3 | semidirect |
| 302. #562 | C2×D3 | semidirect |
| 309. #554 | C2×D3 | semidirect |
| 330. #550 | C2×D3 | semidirect |
| 336. #547 | C2×D3 | semidirect |
| 936. C3 | #62840 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3548 | 2 |
| #87106 | 2 |
| #86931 | 2 |
| #86930 | 2 |
| #86774 | 2 |
| #86773 | 2 |
| #86684 | 2 |
| #86683 | 2 |
| #86472 | 2 |
| #86469 | 2 |
| #86371 | 2 |
| #86369 | 2 |
| #86270 | 2 |
| #86257 | 2 |
| #86251 | 2 |
| #86219 | 2 |
| #62840 | 3 |