Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
7226 conjugacy classes of subgroups.
The subgroup lattice has 974 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C3×#3459 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #86572 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #86571 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #86429 | C2 | 1 | 6 | yes | maximal, complemented |
| 5 | #86427 | C2 | 1 | 6 | yes | maximal, complemented |
| 6 | #86389 | C2 | 1 | 6 | yes | maximal, complemented |
| 7 | #86387 | C2 | 1 | 6 | yes | maximal, complemented |
| 8 | #86295 | C2 | 1 | 3 | yes | maximal, complemented |
| 9 | #86294 | C2 | 1 | 3 | yes | maximal, complemented |
| 10 | #86120 | C2 | 1 | 6 | yes | maximal, complemented |
| 11 | #86119 | C2 | 1 | 6 | yes | maximal, complemented |
| 12 | #86020 | C2 | 1 | 6 | yes | maximal, complemented |
| 13 | #86018 | C2 | 1 | 6 | yes | maximal, complemented |
| 14 | #85776 | C2 | 1 | 3 | yes | maximal, complemented |
| 15 | C2×C4×#237 | C2 | 1 | 3 | yes | maximal, complemented |
| 16 | #62686 | — | 3 | 1 | no | maximal, Sylow |
| 17 | C22×#237 | C22 | 1 | 3 | yes | — |
| 18 | C3×#543 | C22 | 1 | 1 | yes | characteristic |
| 19 | C3×#539 | C22 | 1 | 6 | yes | complemented |
| 20 | C3×#538 | C22 | 1 | 6 | yes | complemented |
| 21 | C3×#534 | C22 | 1 | 3 | yes | — |
| 22 | C3×#529 | C22 | 1 | 6 | yes | complemented |
| 23 | C3×#525 | C22 | 1 | 6 | yes | complemented |
| 24 | C2×C3×C4×D4 | C22 | 1 | 3 | yes | — |
| 25 | #5832 | C22 | 1 | 6 | yes | complemented |
| 26 | Dic3×#41 | C22 | 1 | 2 | yes | complemented |
| 27 | #5804 | C22 | 1 | 6 | yes | — |
| 28 | C2×D4×Dic3 | C22 | 1 | 3 | yes | — |
| 29 | #5791 | C22 | 1 | 6 | yes | complemented |
| 30 | C2×C4×#67 | C22 | 1 | 3 | yes | — |
| 31 | C2×C4×#67 | C22 | 1 | 3 | yes | complemented |
| 32 | C22×C4×Dic3 | C22 | 1 | 1 | yes | characteristic |
| 33 | C22×C4×Dic3 | C22 | 1 | 3 | yes | complemented |
| 34 | #5710 | C22 | 1 | 12 | yes | complemented |
| 35 | #5706 | C22 | 1 | 12 | yes | complemented |
| 36 | #5706 | C22 | 1 | 12 | yes | complemented |
| 37 | #5701 | C22 | 1 | 12 | yes | complemented |
| 38 | #5696 | C22 | 1 | 12 | yes | complemented |
| 39 | #5691 | C22 | 1 | 6 | yes | complemented |
| 40 | #5688 | C22 | 1 | 6 | yes | complemented |
| 41 | #5680 | C22 | 1 | 6 | yes | complemented |
| 42 | #5669 | C22 | 1 | 12 | yes | complemented |
| 43 | #5668 | C22 | 1 | 6 | yes | complemented |
| 44 | #5665 | C22 | 1 | 12 | yes | complemented |
| 45 | #5663 | C22 | 1 | 12 | yes | complemented |
| 46 | #5662 | C22 | 1 | 12 | yes | complemented |
| 47 | #5656 | C22 | 1 | 12 | yes | complemented |
| 48 | #5649 | C22 | 1 | 12 | yes | complemented |
| 49 | #5649 | C22 | 1 | 12 | yes | complemented |
| 50 | #5649 | C22 | 1 | 12 | yes | complemented |
| 51 | #5648 | C22 | 1 | 12 | yes | complemented |
| 52 | #5645 | C22 | 1 | 6 | yes | complemented |
| 53 | #5644 | C22 | 1 | 6 | yes | complemented |
| 54 | #5640 | C22 | 1 | 12 | yes | complemented |
| 55 | #5627 | C22 | 1 | 6 | yes | complemented |
| 56 | #5624 | C22 | 1 | 6 | yes | complemented |
| 57 | #5624 | C22 | 1 | 6 | yes | complemented |
| 58 | #5623 | C22 | 1 | 6 | yes | complemented |
| 59 | #5623 | C22 | 1 | 6 | yes | complemented |
| 60 | #5622 | C22 | 1 | 6 | yes | complemented |
| 61 | #5622 | C22 | 1 | 6 | yes | complemented |
| 62 | #5622 | C22 | 1 | 6 | yes | complemented |
| 63 | #5617 | C22 | 1 | 6 | yes | complemented |
| 64 | #5615 | C22 | 1 | 12 | yes | complemented |
| 65 | #5606 | C22 | 1 | 6 | yes | complemented |
| 66 | #5602 | C22 | 1 | 6 | yes | complemented |
| 67 | #5600 | C22 | 1 | 6 | yes | complemented |
| 68 | #5600 | C22 | 1 | 6 | yes | complemented |
| 69 | #5597 | C22 | 1 | 6 | yes | — |
| 70 | #5597 | C22 | 1 | 6 | yes | — |
| 71 | #5596 | C22 | 1 | 6 | yes | — |
| 72 | #5596 | C22 | 1 | 6 | yes | — |
| 73 | #5596 | C22 | 1 | 6 | yes | complemented |
| 74 | #5593 | C22 | 1 | 12 | yes | complemented |
| 75 | #5592 | C22 | 1 | 12 | yes | complemented |
| 76 | #5586 | C22 | 1 | 12 | yes | complemented |
| 77 | #5586 | C22 | 1 | 12 | yes | complemented |
| 78 | #5578 | C22 | 1 | 6 | yes | complemented |
| 79 | C4×#239 | C22 | 1 | 2 | yes | complemented |
| 80 | #5564 | C22 | 1 | 12 | yes | complemented |
| 81 | #5560 | C22 | 1 | 12 | yes | complemented |
| 82 | #5548 | C22 | 1 | 6 | yes | complemented |
| 83 | #5547 | C22 | 1 | 12 | yes | complemented |
| 84 | #5538 | C22 | 1 | 12 | yes | complemented |
| 85 | #5538 | C22 | 1 | 12 | yes | complemented |
| 86 | C4×#237 | C22 | 1 | 6 | yes | complemented |
| 87 | C4×#237 | C22 | 1 | 12 | yes | complemented |
| 88 | C4×#237 | C22 | 1 | 12 | yes | complemented |
| 89 | C4×#237 | C22 | 1 | 12 | yes | complemented |
| 90 | C4×#237 | C22 | 1 | 12 | yes | complemented |
| 91 | #5528 | C22 | 1 | 12 | yes | complemented |
| 92 | #5522 | C22 | 1 | 6 | yes | complemented |
| 93 | #5517 | C22 | 1 | 6 | yes | complemented |
| 94 | #5515 | C22 | 1 | 6 | yes | complemented |
| 95 | C2×#892 | C22 | 1 | 3 | yes | complemented |
| 96 | C2×#887 | C22 | 1 | 3 | yes | complemented |
| 97 | #5494 | C22 | 1 | 6 | yes | complemented |
| 98 | #5493 | C22 | 1 | 3 | yes | — |
| 99 | C2×#67⋊C4 | C22 | 1 | 3 | yes | — |
| 100 | C2×#67⋊C4 | C22 | 1 | 3 | yes | complemented |
| 101 | #5483 | C22 | 1 | 3 | yes | — |
| 102 | C2×#877 | C22 | 1 | 3 | yes | — |
| 103 | C2×#877 | C22 | 1 | 3 | yes | complemented |
| 104 | #5479 | C22 | 1 | 6 | yes | complemented |
| 105 | C2×C42×D3 | C22 | 1 | 3 | yes | complemented |
| 106 | C2×C4×Dic6 | C22 | 1 | 3 | yes | complemented |
| 107 | #3461 | — | 3 | 6 | no | — |
| 108 | #3461 | — | 3 | 6 | no | — |
| 109 | #3460 | — | 3 | 6 | no | — |
| 110 | #3460 | — | 3 | 6 | no | — |
| 111 | #3459 | — | 3 | 1 | no | — |
| 112 | #3459 | — | 3 | 3 | no | — |
| 113 | #3459 | — | 3 | 3 | no | — |
| 114 | #3459 | D3 | 1 | 1 | yes | characteristic, complemented |
| 115 | #3458 | — | 3 | 1 | no | — |
| 116 | #3455 | — | 3 | 6 | no | — |
| 117 | #3455 | — | 3 | 6 | no | — |
| 118 | #3449 | — | 3 | 3 | no | — |
| 119 | #3444 | — | 3 | 6 | no | — |
| 120 | #3444 | — | 3 | 6 | no | — |
| 121 | C2×C4×#41 | — | 3 | 3 | no | — |
| 122 | C2×C3×#41 | C23 | 1 | 2 | yes | — |
| 123 | C22×C3×D4 | C23 | 1 | 3 | yes | — |
| 124 | C23×C3×C4 | C23 | 1 | 1 | yes | characteristic |
| 125 | C23×C3×C4 | C23 | 1 | 3 | yes | — |
| 126 | C22×#67 | C23 | 1 | 3 | yes | — |
| 127 | C22×#67 | C23 | 1 | 3 | yes | — |
| 128 | C23×Dic3 | C23 | 1 | 3 | yes | — |
| 129 | C23×Dic3 | C23 | 1 | 1 | yes | characteristic |
| 130 | C23×Dic3 | C23 | 1 | 3 | yes | — |
| 131 | C23×Dic3 | C23 | 1 | 1 | yes | characteristic |
| 132 | C2×#239 | C23 | 1 | 2 | yes | — |
| 133 | C2×#237 | — | 2 | 24 | no | — |
| 134 | C2×#237 | C23 | 1 | 12 | yes | — |
| 135 | C2×#237 | C23 | 1 | 12 | yes | — |
| 136 | C2×#237 | C23 | 1 | 6 | yes | — |
| 137 | C2×#235 | C23 | 1 | 6 | yes | — |
| 138 | C22×C4×D3 | C23 | 1 | 3 | yes | — |
| 139 | C22×C4×D3 | C23 | 1 | 3 | yes | — |
| 140 | C22×C4×D3 | C23 | 1 | 3 | yes | — |
| 141 | C22×Dic6 | C23 | 1 | 3 | yes | — |
| 142 | C3×#126 | C23 | 1 | 12 | yes | — |
| 143 | C3×#125 | C23 | 1 | 6 | yes | — |
| 144 | C3×#124 | C23 | 1 | 6 | yes | — |
| 145 | C3×#123 | C23 | 1 | 12 | yes | — |
| 146 | C3×#123 | C23 | 1 | 12 | yes | — |
| 147 | C3×C22⋊Q8 | C23 | 1 | 6 | yes | — |
| 148 | C3×C22⋊Q8 | C23 | 1 | 6 | yes | — |
| 149 | C3×C22⋊Q8 | C23 | 1 | 6 | yes | — |
| 150 | C3×#121 | C23 | 1 | 6 | yes | — |
| 151 | C3×#121 | C23 | 1 | 6 | yes | — |
| 152 | C3×#121 | C23 | 1 | 6 | yes | — |
| 153 | C3×#120 | C23 | 1 | 12 | yes | — |
| 154 | C3×C4×Q8 | C23 | 1 | 2 | yes | — |
| 155 | C3×C4×D4 | C23 | 1 | 12 | yes | — |
| 156 | C3×C4×D4 | C23 | 1 | 12 | yes | — |
| 157 | C3×C4×D4 | C23 | 1 | 6 | yes | — |
| 158 | C3×#117 | C23 | 1 | 6 | yes | — |
| 159 | C2×C3×C4⋊C4 | C23 | 1 | 3 | yes | — |
| 160 | C2×C3×C22⋊C4 | C23 | 1 | 3 | yes | — |
| 161 | C2×C3×C22⋊C4 | C23 | 1 | 3 | yes | — |
| 162 | C2×C3×C42 | C23 | 1 | 3 | yes | — |
| 163 | #953 | C23 | 1 | 12 | yes | — |
| 164 | C2×#217 | C23 | 1 | 3 | yes | — |
| 165 | C2×#217 | C23 | 1 | 3 | yes | — |
| 166 | #947 | C23 | 1 | 6 | yes | — |
| 167 | #946 | C23 | 1 | 6 | yes | — |
| 168 | Q8×Dic3 | C23 | 1 | 2 | yes | — |
| 169 | Q8×Dic3 | C23 | 1 | 2 | yes | — |
| 170 | Q8×Dic3 | C23 | 1 | 2 | yes | — |
| 171 | #944 | C23 | 1 | 6 | yes | — |
| 172 | #944 | C23 | 1 | 6 | yes | — |
| 173 | #940 | C23 | 1 | 6 | yes | — |
| 174 | #940 | C23 | 1 | 6 | yes | — |
| 175 | #939 | C23 | 1 | 12 | yes | — |
| 176 | #939 | C23 | 1 | 12 | yes | — |
| 177 | #939 | C23 | 1 | 12 | yes | — |
| 178 | #939 | C23 | 1 | 12 | yes | — |
| 179 | #939 | C23 | 1 | 12 | yes | — |
| 180 | #938 | C23 | 1 | 6 | yes | — |
| 181 | #937 | C23 | 1 | 12 | yes | — |
| 182 | #936 | C23 | 1 | 6 | yes | — |
| 183 | #935 | C23 | 1 | 12 | yes | — |
| 184 | #935 | C23 | 1 | 12 | yes | — |
| 185 | D4×Dic3 | C23 | 1 | 6 | yes | — |
| 186 | D4×Dic3 | C23 | 1 | 6 | yes | — |
| 187 | D4×Dic3 | C23 | 1 | 12 | yes | — |
| 188 | D4×Dic3 | C23 | 1 | 12 | yes | — |
| 189 | D4×Dic3 | C23 | 1 | 6 | yes | — |
| 190 | #930 | C23 | 1 | 6 | yes | — |
| 191 | #930 | C23 | 1 | 6 | yes | — |
| 192 | #930 | C23 | 1 | 6 | yes | — |
| 193 | #929 | C23 | 1 | 12 | yes | — |
| 194 | #929 | C23 | 1 | 12 | yes | — |
| 195 | C4×#67 | C23 | 1 | 12 | yes | — |
| 196 | C4×#67 | C23 | 1 | 12 | yes | — |
| 197 | C4×#67 | C23 | 1 | 12 | yes | — |
| 198 | C4×#67 | C23 | 1 | 12 | yes | — |
| 199 | C4×#67 | C23 | 1 | 12 | yes | — |
| 200 | C2×(C2×D3)⋊C4 | C23 | 1 | 3 | yes | — |
| 201 | C2×(C2×D3)⋊C4 | C23 | 1 | 3 | yes | — |
| 202 | #926 | C23 | 1 | 6 | yes | — |
| 203 | C2×C4⋊Dic3 | C23 | 1 | 3 | yes | — |
| 204 | #924 | C23 | 1 | 6 | yes | — |
| 205 | #924 | C23 | 1 | 6 | yes | — |
| 206 | #924 | C23 | 1 | 6 | yes | — |
| 207 | C2×Dic3⋊C4 | C23 | 1 | 3 | yes | — |
| 208 | C2×Dic3⋊C4 | C23 | 1 | 3 | yes | — |
| 209 | C2×Dic3⋊C4 | C23 | 1 | 3 | yes | — |
| 210 | C2×Dic3⋊C4 | C23 | 1 | 3 | yes | — |
| 211 | C2×C4×Dic3 | C23 | 1 | 3 | yes | — |
| 212 | C2×C4×Dic3 | C23 | 1 | 6 | yes | — |
| 213 | C2×C4×Dic3 | C23 | 1 | 6 | yes | — |
| 214 | C2×C4×Dic3 | C23 | 1 | 3 | yes | — |
| 215 | C2×C4×Dic3 | C23 | 1 | 3 | yes | — |
| 216 | C2×C4×Dic3 | C23 | 1 | 3 | yes | — |
| 217 | C2×C4×Dic3 | C23 | 1 | 3 | yes | — |
| 218 | C2×C4×Dic3 | C23 | 1 | 3 | yes | — |
| 219 | C2×C4×Dic3 | C23 | 1 | 3 | yes | — |
| 220 | C2×C4×Dic3 | C23 | 1 | 3 | yes | — |
| 221 | C2×C4×Dic3 | C23 | 1 | 3 | yes | — |
| 222 | C2×C4×Dic3 | C23 | 1 | 6 | yes | — |
| 223 | C2×C4×Dic3 | C23 | 1 | 6 | yes | — |
| 224 | #898 | C23 | 1 | 12 | yes | — |
| 225 | #898 | C23 | 1 | 12 | yes | — |
| 226 | #898 | C23 | 1 | 12 | yes | — |
| 227 | #897 | C23 | 1 | 6 | yes | — |
| 228 | #896 | C23 | 1 | 12 | yes | — |
| 229 | #896 | C23 | 1 | 12 | yes | — |
| 230 | #896 | C23 | 1 | 12 | yes | — |
| 231 | #895 | C23 | 1 | 6 | yes | — |
| 232 | #894 | C23 | 1 | 12 | yes | — |
| 233 | #894 | C23 | 1 | 12 | yes | — |
| 234 | #893 | C23 | 1 | 6 | yes | — |
| 235 | #893 | C23 | 1 | 6 | yes | — |
| 236 | #893 | C23 | 1 | 6 | yes | — |
| 237 | #892 | C23 | 1 | 12 | yes | — |
| 238 | #892 | C23 | 1 | 6 | yes | — |
| 239 | #892 | C23 | 1 | 6 | yes | — |
| 240 | #892 | C23 | 1 | 12 | yes | — |
| 241 | #890 | C23 | 1 | 6 | yes | — |
| 242 | #890 | C23 | 1 | 6 | yes | — |
| 243 | #889 | C23 | 1 | 12 | yes | — |
| 244 | #889 | C23 | 1 | 12 | yes | — |
| 245 | #889 | C23 | 1 | 12 | yes | — |
| 246 | #889 | C23 | 1 | 12 | yes | — |
| 247 | #888 | C23 | 1 | 6 | yes | — |
| 248 | #888 | C23 | 1 | 6 | yes | — |
| 249 | #888 | C23 | 1 | 6 | yes | — |
| 250 | #888 | C23 | 1 | 6 | yes | — |
| 251 | #887 | C23 | 1 | 12 | yes | — |
| 252 | #887 | C23 | 1 | 6 | yes | — |
| 253 | #887 | C23 | 1 | 6 | yes | — |
| 254 | #887 | C23 | 1 | 12 | yes | — |
| 255 | #887 | C23 | 1 | 6 | yes | — |
| 256 | #886 | C23 | 1 | 12 | yes | — |
| 257 | #886 | C23 | 1 | 12 | yes | — |
| 258 | #885 | C23 | 1 | 12 | yes | — |
| 259 | #885 | C23 | 1 | 12 | yes | — |
| 260 | #885 | C23 | 1 | 12 | yes | — |
| 261 | #885 | C23 | 1 | 12 | yes | — |
| 262 | #884 | C23 | 1 | 12 | yes | — |
| 263 | #884 | C23 | 1 | 12 | yes | — |
| 264 | #884 | C23 | 1 | 12 | yes | — |
| 265 | #883 | C23 | 1 | 12 | yes | — |
| 266 | #883 | C23 | 1 | 12 | yes | — |
| 267 | #882 | C23 | 1 | 12 | yes | — |
| 268 | #67⋊C4 | C23 | 1 | 12 | yes | — |
| 269 | #67⋊C4 | C23 | 1 | 12 | yes | — |
| 270 | #67⋊C4 | C23 | 1 | 12 | yes | — |
| 271 | #67⋊C4 | C23 | 1 | 12 | yes | — |
| 272 | #67⋊C4 | C23 | 1 | 12 | yes | — |
| 273 | #67⋊C4 | C23 | 1 | 12 | yes | — |
| 274 | #67⋊C4 | C23 | 1 | 12 | yes | — |
| 275 | #879 | C23 | 1 | 12 | yes | — |
| 276 | #879 | C23 | 1 | 12 | yes | — |
| 277 | #879 | C23 | 1 | 12 | yes | — |
| 278 | #878 | C23 | 1 | 12 | yes | — |
| 279 | #878 | C23 | 1 | 12 | yes | — |
| 280 | #878 | C23 | 1 | 12 | yes | — |
| 281 | #878 | C23 | 1 | 12 | yes | — |
| 282 | #878 | C23 | 1 | 12 | yes | — |
| 283 | #877 | C23 | 1 | 12 | yes | — |
| 284 | #877 | C23 | 1 | 12 | yes | — |
| 285 | #877 | C23 | 1 | 12 | yes | — |
| 286 | #877 | C23 | 1 | 12 | yes | — |
| 287 | #877 | C23 | 1 | 12 | yes | — |
| 288 | #876 | C23 | 1 | 12 | yes | — |
| 289 | #875 | C23 | 1 | 6 | yes | — |
| 290 | C4×D12 | C23 | 1 | 6 | yes | — |
| 291 | #872 | C23 | 1 | 12 | yes | — |
| 292 | C42×D3 | C23 | 1 | 6 | yes | — |
| 293 | C42×D3 | C23 | 1 | 6 | yes | — |
| 294 | C42×D3 | C23 | 1 | 6 | yes | — |
| 295 | C42×D3 | C23 | 1 | 6 | yes | — |
| 296 | #870 | C23 | 1 | 6 | yes | — |
| 297 | C4×Dic6 | C23 | 1 | 12 | yes | — |
| 298 | C4×Dic6 | C23 | 1 | 12 | yes | — |
| 299 | C4×Dic6 | C23 | 1 | 6 | yes | — |
| 300 | C22×#41 | — | 3 | 3 | no | — |
| 301 | #544 | — | 3 | 6 | no | — |
| 302 | #544 | — | 3 | 6 | no | — |
| 303 | #543 | — | 3 | 3 | no | — |
| 304 | #543 | C2×D3 | 1 | 1 | yes | characteristic |
| 305 | #542 | — | 3 | 12 | no | — |
| 306 | #542 | — | 3 | 12 | no | — |
| 307 | #542 | — | 3 | 12 | no | — |
| 308 | #542 | — | 3 | 12 | no | — |
| 309 | #541 | — | 3 | 12 | no | — |
| 310 | #541 | — | 3 | 12 | no | — |
| 311 | #540 | — | 3 | 12 | no | — |
| 312 | #540 | — | 3 | 12 | no | — |
| 313 | #539 | — | 3 | 12 | no | — |
| 314 | #539 | — | 3 | 6 | no | — |
| 315 | #539 | — | 3 | 6 | no | — |
| 316 | #539 | — | 3 | 12 | no | — |
| 317 | #539 | — | 3 | 6 | no | — |
| 318 | #539 | C2×D3 | 1 | 6 | yes | complemented |
| 319 | #538 | — | 3 | 6 | no | — |
| 320 | #538 | — | 3 | 6 | no | — |
| 321 | #538 | — | 3 | 12 | no | — |
| 322 | #538 | — | 3 | 12 | no | — |
| 323 | #538 | — | 3 | 6 | no | — |
| 324 | #538 | C2×D3 | 1 | 6 | yes | complemented |
| 325 | #537 | — | 3 | 6 | no | — |
| 326 | #537 | — | 3 | 6 | no | — |
| 327 | #536 | — | 3 | 12 | no | — |
| 328 | #535 | — | 3 | 12 | no | — |
| 329 | #534 | — | 3 | 6 | no | — |
| 330 | #534 | — | 3 | 3 | no | — |
| 331 | #534 | C2×D3 | 1 | 3 | yes | — |
| 332 | #533 | — | 3 | 6 | no | — |
| 333 | #533 | — | 3 | 6 | no | — |
| 334 | #533 | — | 3 | 6 | no | — |
| 335 | #533 | — | 3 | 6 | no | — |
| 336 | #533 | — | 3 | 6 | no | — |
| 337 | #533 | — | 3 | 6 | no | — |
| 338 | #532 | — | 3 | 6 | no | — |
| 339 | #532 | — | 3 | 6 | no | — |
| 340 | #532 | — | 3 | 6 | no | — |
| 341 | #532 | — | 3 | 6 | no | — |
| 342 | #532 | — | 3 | 6 | no | — |
| 343 | #532 | — | 3 | 6 | no | — |
| 344 | #529 | — | 3 | 12 | no | — |
| 345 | #529 | — | 3 | 12 | no | — |
| 346 | #529 | — | 3 | 6 | no | — |
| 347 | #529 | — | 3 | 6 | no | — |
| 348 | #529 | — | 3 | 12 | no | — |
| 349 | #529 | — | 3 | 12 | no | — |
| 350 | #529 | — | 3 | 12 | no | — |
| 351 | #529 | — | 3 | 6 | no | — |
| 352 | #529 | — | 3 | 6 | no | — |
| 353 | #529 | — | 3 | 6 | no | — |
| 354 | #529 | — | 3 | 6 | no | — |
| 355 | #529 | — | 3 | 12 | no | — |
| 356 | #529 | — | 3 | 12 | no | — |
| 357 | #529 | — | 3 | 12 | no | — |
| 358 | #529 | — | 3 | 6 | no | — |
| 359 | #529 | C2×D3 | 1 | 6 | yes | complemented |
| 360 | #525 | — | 3 | 6 | no | — |
| 361 | #525 | — | 3 | 12 | no | — |
| 362 | #525 | — | 3 | 6 | no | — |
| 363 | #525 | — | 3 | 6 | no | — |
| 364 | #525 | — | 3 | 12 | no | — |
| 365 | #525 | — | 3 | 12 | no | — |
| 366 | #525 | — | 3 | 12 | no | — |
| 367 | #525 | C2×D3 | 1 | 6 | yes | complemented |
| 368 | C4×#41 | — | 3 | 2 | no | — |
| 369 | C4×#41 | — | 3 | 2 | no | — |
| 370 | C4×#41 | — | 3 | 12 | no | — |
| 371 | C4×#41 | — | 3 | 12 | no | — |
| 372 | C4×#41 | — | 3 | 12 | no | — |
| 373 | C4×#41 | — | 3 | 12 | no | — |
| 374 | C4×#41 | — | 3 | 6 | no | — |
| 375 | C4×#41 | — | 3 | 6 | no | — |
| 376 | C2×C4×Q8 | — | 3 | 3 | no | — |
| 377 | C2×C4×Q8 | — | 3 | 3 | no | — |
| 378 | C2×C4×D4 | — | 3 | 3 | no | — |
| 379 | C2×C4×D4 | — | 3 | 3 | no | — |
| 380 | C2×C4×D4 | — | 3 | 3 | no | — |
| 381 | C2×C4×D4 | — | 3 | 3 | no | — |
| 382 | C2×C4×D4 | — | 3 | 3 | no | — |
| 383 | C2×C4×D4 | C2×D3 | 1 | 3 | yes | — |
| 384 | C2×#117 | — | 3 | 3 | no | — |
| 385 | C2×#117 | — | 3 | 3 | no | — |
| 386 | C2×#117 | — | 3 | 3 | no | — |
| 387 | C22×C42 | — | 3 | 1 | no | — |
| 388 | C22×C42 | — | 3 | 3 | no | — |
| 389 | C22×C42 | — | 3 | 3 | no | — |
| 390 | C24×C3 | C24 | 1 | 3 | yes | — |
| 391 | C24×C3 | C24 | 1 | 1 | yes | characteristic |
| 392 | C23×D3 | C24 | 1 | 3 | yes | — |
| 393 | C3×#41 | — | 4 | 4 | no | — |
| 394 | C2×C3×Q8 | C24 | 1 | 2 | yes | — |
| 395 | C2×C3×Q8 | C24 | 1 | 2 | yes | — |
| 396 | C2×C3×D4 | — | 2 | 12 | no | — |
| 397 | C2×C3×D4 | C24 | 1 | 12 | yes | — |
| 398 | C2×C3×D4 | C24 | 1 | 6 | yes | — |
| 399 | C2×C3×D4 | C24 | 1 | 6 | yes | — |
| 400 | C22×C3×C4 | — | 4 | 2 | no | — |
| 401 | C22×C3×C4 | — | 4 | 6 | no | — |
| 402 | C22×C3×C4 | C24 | 1 | 3 | yes | — |
| 403 | C22×C3×C4 | C24 | 1 | 6 | yes | — |
| 404 | C22×C3×C4 | C24 | 1 | 3 | yes | — |
| 405 | C22×C3×C4 | C24 | 1 | 3 | yes | — |
| 406 | C22×C3×C4 | C24 | 1 | 3 | yes | — |
| 407 | C22×C3×C4 | C24 | 1 | 6 | yes | — |
| 408 | C22×C3×C4 | C24 | 1 | 3 | yes | — |
| 409 | C2×#67 | — | 2 | 12 | no | — |
| 410 | C2×#67 | — | 2 | 12 | no | — |
| 411 | C2×#67 | C24 | 1 | 12 | yes | — |
| 412 | C2×#67 | C24 | 1 | 12 | yes | — |
| 413 | C2×#67 | C24 | 1 | 12 | yes | — |
| 414 | C2×#67 | C24 | 1 | 12 | yes | — |
| 415 | C22×Dic3 | — | 2 | 12 | no | — |
| 416 | C22×Dic3 | — | 4 | 2 | no | — |
| 417 | C22×Dic3 | — | 4 | 6 | no | — |
| 418 | C22×Dic3 | #41 | 1 | 8 | yes | complemented |
| 419 | C22×Dic3 | C24 | 1 | 6 | yes | — |
| 420 | C22×Dic3 | C24 | 1 | 6 | yes | — |
| 421 | C22×Dic3 | C24 | 1 | 6 | yes | — |
| 422 | C22×Dic3 | C24 | 1 | 3 | yes | — |
| 423 | C22×Dic3 | C24 | 1 | 3 | yes | — |
| 424 | C22×Dic3 | C24 | 1 | 3 | yes | — |
| 425 | C22×Dic3 | C24 | 1 | 3 | yes | — |
| 426 | C22×Dic3 | C24 | 1 | 6 | yes | — |
| 427 | C22×Dic3 | C24 | 1 | 3 | yes | — |
| 428 | C22×Dic3 | C24 | 1 | 3 | yes | — |
| 429 | C22×Dic3 | C24 | 1 | 3 | yes | — |
| 430 | #239 | — | 4 | 4 | no | — |
| 431 | #237 | — | 2 | 48 | no | — |
| 432 | #237 | — | 2 | 48 | no | — |
| 433 | #237 | — | 4 | 12 | no | — |
| 434 | #235 | — | 4 | 12 | no | — |
| 435 | C2×D12 | C24 | 1 | 6 | yes | — |
| 436 | C2×D12 | C24 | 1 | 6 | yes | — |
| 437 | C2×C4×D3 | — | 2 | 12 | no | — |
| 438 | C2×C4×D3 | — | 4 | 6 | no | — |
| 439 | C2×C4×D3 | — | 4 | 6 | no | — |
| 440 | C2×C4×D3 | C24 | 1 | 6 | yes | — |
| 441 | C2×C4×D3 | C24 | 1 | 6 | yes | — |
| 442 | C2×C4×D3 | C24 | 1 | 6 | yes | — |
| 443 | C2×C4×D3 | C24 | 1 | 6 | yes | — |
| 444 | C2×C4×D3 | C24 | 1 | 6 | yes | — |
| 445 | C2×C4×D3 | C24 | 1 | 6 | yes | — |
| 446 | C2×Dic6 | — | 2 | 12 | no | — |
| 447 | C2×Dic6 | C24 | 1 | 12 | yes | — |
| 448 | C2×Dic6 | C24 | 1 | 6 | yes | — |
| 449 | C2×Dic6 | C24 | 1 | 6 | yes | — |
| 450 | C3×C4⋊C4 | C24 | 1 | 12 | yes | — |
| 451 | C3×C4⋊C4 | C24 | 1 | 6 | yes | — |
| 452 | C3×C4⋊C4 | C24 | 1 | 6 | yes | — |
| 453 | C3×C4⋊C4 | C24 | 1 | 6 | yes | — |
| 454 | C3×C4⋊C4 | C24 | 1 | 6 | yes | — |
| 455 | C3×C22⋊C4 | C24 | 1 | 12 | yes | — |
| 456 | C3×C22⋊C4 | C24 | 1 | 12 | yes | — |
| 457 | C3×C22⋊C4 | C24 | 1 | 12 | yes | — |
| 458 | C3×C22⋊C4 | C24 | 1 | 12 | yes | — |
| 459 | C3×C42 | C24 | 1 | 6 | yes | — |
| 460 | C3×C42 | C24 | 1 | 6 | yes | — |
| 461 | #217 | C24 | 1 | 12 | yes | — |
| 462 | #217 | C24 | 1 | 12 | yes | — |
| 463 | #217 | C24 | 1 | 12 | yes | — |
| 464 | #217 | C24 | 1 | 12 | yes | — |
| 465 | (C2×D3)⋊C4 | C24 | 1 | 12 | yes | — |
| 466 | (C2×D3)⋊C4 | C24 | 1 | 12 | yes | — |
| 467 | (C2×D3)⋊C4 | C24 | 1 | 12 | yes | — |
| 468 | (C2×D3)⋊C4 | C24 | 1 | 12 | yes | — |
| 469 | (C2×D3)⋊C4 | C24 | 1 | 12 | yes | — |
| 470 | (C2×D3)⋊C4 | C24 | 1 | 12 | yes | — |
| 471 | C4⋊Dic3 | C24 | 1 | 12 | yes | — |
| 472 | C4⋊Dic3 | C24 | 1 | 6 | yes | — |
| 473 | C4⋊Dic3 | C24 | 1 | 6 | yes | — |
| 474 | C4⋊Dic3 | C24 | 1 | 6 | yes | — |
| 475 | C4⋊Dic3 | C24 | 1 | 6 | yes | — |
| 476 | Dic3⋊C4 | C24 | 1 | 12 | yes | — |
| 477 | Dic3⋊C4 | C24 | 1 | 12 | yes | — |
| 478 | Dic3⋊C4 | C24 | 1 | 12 | yes | — |
| 479 | Dic3⋊C4 | C24 | 1 | 12 | yes | — |
| 480 | Dic3⋊C4 | C24 | 1 | 12 | yes | — |
| 481 | Dic3⋊C4 | C24 | 1 | 12 | yes | — |
| 482 | Dic3⋊C4 | C24 | 1 | 12 | yes | — |
| 483 | Dic3⋊C4 | C24 | 1 | 12 | yes | — |
| 484 | C4×Dic3 | C24 | 1 | 3 | yes | — |
| 485 | C4×Dic3 | C24 | 1 | 6 | yes | — |
| 486 | C4×Dic3 | C24 | 1 | 6 | yes | — |
| 487 | C4×Dic3 | C24 | 1 | 6 | yes | — |
| 488 | C4×Dic3 | C24 | 1 | 1 | yes | characteristic |
| 489 | C4×Dic3 | C24 | 1 | 6 | yes | — |
| 490 | C4×Dic3 | C24 | 1 | 6 | yes | — |
| 491 | C4×Dic3 | C24 | 1 | 3 | yes | — |
| 492 | C4×Dic3 | C24 | 1 | 6 | yes | — |
| 493 | C4×Dic3 | C24 | 1 | 6 | yes | — |
| 494 | C4×Dic3 | C24 | 1 | 3 | yes | — |
| 495 | C4×Dic3 | C24 | 1 | 6 | yes | — |
| 496 | C4×Dic3 | C24 | 1 | 6 | yes | — |
| 497 | C4×Dic3 | C24 | 1 | 6 | yes | — |
| 498 | C4×Dic3 | C24 | 1 | 6 | yes | — |
| 499 | C2×#41 | — | 3 | 2 | no | — |
| 500 | C2×#41 | — | 3 | 12 | no | — |
| 501 | C2×#41 | — | 3 | 12 | no | — |
| 502 | C2×#41 | — | 3 | 6 | no | — |
| 503 | C2×#41 | — | 3 | 6 | no | — |
| 504 | C2×#41 | — | 6 | 24 | no | — |
| 505 | C2×#41 | C22×D3 | 1 | 2 | yes | — |
| 506 | C22×Q8 | — | 3 | 3 | no | — |
| 507 | C22×D4 | — | 3 | 3 | no | — |
| 508 | C22×D4 | — | 3 | 3 | no | — |
| 509 | C22×D4 | C22×D3 | 1 | 3 | yes | — |
| 510 | C23×C4 | — | 3 | 1 | no | — |
| 511 | C23×C4 | — | 3 | 3 | no | — |
| 512 | C23×C4 | — | 3 | 1 | no | — |
| 513 | C23×C4 | — | 3 | 3 | no | — |
| 514 | C23×C4 | — | 3 | 3 | no | — |
| 515 | C23×C4 | — | 3 | 3 | no | — |
| 516 | C23×C4 | — | 3 | 3 | no | — |
| 517 | C23×C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 518 | C23×C4 | C22×D3 | 1 | 3 | yes | — |
| 519 | C4⋊Q8 | — | 3 | 6 | no | — |
| 520 | C4⋊Q8 | — | 3 | 6 | no | — |
| 521 | C4⋊Q8 | — | 3 | 6 | no | — |
| 522 | C4⋊Q8 | — | 3 | 6 | no | — |
| 523 | C4⋊Q8 | — | 3 | 6 | no | — |
| 524 | C4⋊Q8 | — | 3 | 6 | no | — |
| 525 | #127 | — | 3 | 6 | no | — |
| 526 | #127 | — | 3 | 6 | no | — |
| 527 | #126 | — | 3 | 12 | no | — |
| 528 | #126 | — | 3 | 12 | no | — |
| 529 | #126 | — | 3 | 12 | no | — |
| 530 | #126 | — | 3 | 12 | no | — |
| 531 | #126 | — | 3 | 12 | no | — |
| 532 | #126 | — | 3 | 12 | no | — |
| 533 | #126 | — | 3 | 12 | no | — |
| 534 | #126 | C22×D3 | 1 | 12 | yes | — |
| 535 | #125 | — | 3 | 12 | no | — |
| 536 | #125 | — | 3 | 12 | no | — |
| 537 | #125 | — | 3 | 6 | no | — |
| 538 | #125 | — | 3 | 6 | no | — |
| 539 | #125 | — | 3 | 12 | no | — |
| 540 | #125 | — | 3 | 12 | no | — |
| 541 | #125 | — | 3 | 6 | no | — |
| 542 | #125 | C22×D3 | 1 | 6 | yes | — |
| 543 | #124 | — | 3 | 6 | no | — |
| 544 | #124 | — | 3 | 6 | no | — |
| 545 | #124 | — | 3 | 12 | no | — |
| 546 | #124 | — | 3 | 12 | no | — |
| 547 | #124 | — | 3 | 12 | no | — |
| 548 | #124 | — | 3 | 12 | no | — |
| 549 | #124 | — | 3 | 6 | no | — |
| 550 | #124 | C22×D3 | 1 | 6 | yes | — |
| 551 | #123 | — | 3 | 12 | no | — |
| 552 | #123 | — | 3 | 12 | no | — |
| 553 | #123 | — | 3 | 12 | no | — |
| 554 | #123 | — | 3 | 12 | no | — |
| 555 | #123 | — | 3 | 12 | no | — |
| 556 | #123 | — | 3 | 12 | no | — |
| 557 | #123 | — | 3 | 12 | no | — |
| 558 | #123 | — | 3 | 12 | no | — |
| 559 | #123 | — | 3 | 12 | no | — |
| 560 | #123 | — | 3 | 12 | no | — |
| 561 | #123 | C22×D3 | 1 | 12 | yes | — |
| 562 | #123 | C22×D3 | 1 | 12 | yes | — |
| 563 | C22⋊Q8 | — | 3 | 6 | no | — |
| 564 | C22⋊Q8 | — | 3 | 6 | no | — |
| 565 | C22⋊Q8 | — | 3 | 6 | no | — |
| 566 | C22⋊Q8 | — | 3 | 6 | no | — |
| 567 | C22⋊Q8 | — | 3 | 12 | no | — |
| 568 | C22⋊Q8 | — | 3 | 12 | no | — |
| 569 | C22⋊Q8 | — | 3 | 12 | no | — |
| 570 | C22⋊Q8 | — | 3 | 6 | no | — |
| 571 | C22⋊Q8 | — | 3 | 12 | no | — |
| 572 | C22⋊Q8 | — | 3 | 12 | no | — |
| 573 | C22⋊Q8 | — | 3 | 12 | no | — |
| 574 | C22⋊Q8 | — | 3 | 12 | no | — |
| 575 | C22⋊Q8 | — | 3 | 12 | no | — |
| 576 | C22⋊Q8 | C22×D3 | 1 | 6 | yes | — |
| 577 | C22⋊Q8 | C22×D3 | 1 | 6 | yes | — |
| 578 | C22⋊Q8 | C22×D3 | 1 | 6 | yes | — |
| 579 | #121 | — | 3 | 12 | no | — |
| 580 | #121 | — | 3 | 12 | no | — |
| 581 | #121 | — | 3 | 12 | no | — |
| 582 | #121 | — | 3 | 12 | no | — |
| 583 | #121 | — | 3 | 6 | no | — |
| 584 | #121 | — | 3 | 12 | no | — |
| 585 | #121 | — | 3 | 6 | no | — |
| 586 | #121 | — | 3 | 6 | no | — |
| 587 | #121 | — | 3 | 6 | no | — |
| 588 | #121 | — | 3 | 6 | no | — |
| 589 | #121 | — | 3 | 12 | no | — |
| 590 | #121 | — | 3 | 12 | no | — |
| 591 | #121 | — | 3 | 12 | no | — |
| 592 | #121 | C22×D3 | 1 | 6 | yes | — |
| 593 | #121 | C22×D3 | 1 | 6 | yes | — |
| 594 | #121 | C22×D3 | 1 | 6 | yes | — |
| 595 | #120 | — | 3 | 12 | no | — |
| 596 | #120 | — | 3 | 12 | no | — |
| 597 | #120 | — | 3 | 12 | no | — |
| 598 | #120 | C22×D3 | 1 | 12 | yes | — |
| 599 | C4×Q8 | — | 3 | 2 | no | — |
| 600 | C4×Q8 | — | 3 | 2 | no | — |
| 601 | C4×Q8 | — | 3 | 2 | no | — |
| 602 | C4×Q8 | — | 3 | 12 | no | — |
| 603 | C4×Q8 | — | 3 | 12 | no | — |
| 604 | C4×Q8 | — | 3 | 6 | no | — |
| 605 | C4×Q8 | — | 3 | 6 | no | — |
| 606 | C4×Q8 | — | 3 | 6 | no | — |
| 607 | C4×Q8 | — | 3 | 12 | no | — |
| 608 | C4×Q8 | — | 3 | 12 | no | — |
| 609 | C4×Q8 | — | 3 | 6 | no | — |
| 610 | C4×Q8 | C22×D3 | 1 | 2 | yes | — |
| 611 | C4×D4 | — | 3 | 12 | no | — |
| 612 | C4×D4 | — | 3 | 12 | no | — |
| 613 | C4×D4 | — | 3 | 6 | no | — |
| 614 | C4×D4 | — | 3 | 6 | no | — |
| 615 | C4×D4 | — | 3 | 6 | no | — |
| 616 | C4×D4 | — | 3 | 12 | no | — |
| 617 | C4×D4 | — | 3 | 12 | no | — |
| 618 | C4×D4 | — | 3 | 12 | no | — |
| 619 | C4×D4 | — | 3 | 12 | no | — |
| 620 | C4×D4 | — | 3 | 12 | no | — |
| 621 | C4×D4 | — | 3 | 6 | no | — |
| 622 | C4×D4 | — | 3 | 6 | no | — |
| 623 | C4×D4 | — | 3 | 6 | no | — |
| 624 | C4×D4 | — | 3 | 12 | no | — |
| 625 | C4×D4 | — | 3 | 12 | no | — |
| 626 | C4×D4 | — | 3 | 12 | no | — |
| 627 | C4×D4 | — | 3 | 12 | no | — |
| 628 | C4×D4 | — | 3 | 12 | no | — |
| 629 | C4×D4 | — | 3 | 12 | no | — |
| 630 | C4×D4 | — | 3 | 12 | no | — |
| 631 | C4×D4 | — | 3 | 6 | no | — |
| 632 | C4×D4 | C22×D3 | 1 | 12 | yes | — |
| 633 | C4×D4 | C22×D3 | 1 | 12 | yes | — |
| 634 | C4×D4 | C22×D3 | 1 | 6 | yes | — |
| 635 | #117 | — | 3 | 6 | no | — |
| 636 | #117 | — | 3 | 12 | no | — |
| 637 | #117 | — | 3 | 12 | no | — |
| 638 | #117 | — | 3 | 6 | no | — |
| 639 | #117 | — | 3 | 6 | no | — |
| 640 | #117 | — | 3 | 12 | no | — |
| 641 | #117 | — | 3 | 12 | no | — |
| 642 | #117 | — | 3 | 12 | no | — |
| 643 | #117 | — | 3 | 12 | no | — |
| 644 | #117 | — | 3 | 12 | no | — |
| 645 | #117 | — | 3 | 12 | no | — |
| 646 | #117 | C22×D3 | 1 | 6 | yes | — |
| 647 | C2×C4⋊C4 | — | 3 | 3 | no | — |
| 648 | C2×C4⋊C4 | — | 3 | 3 | no | — |
| 649 | C2×C4⋊C4 | — | 3 | 3 | no | — |
| 650 | C2×C4⋊C4 | — | 3 | 3 | no | — |
| 651 | C2×C4⋊C4 | — | 3 | 3 | no | — |
| 652 | C2×C4⋊C4 | C22×D3 | 1 | 3 | yes | — |
| 653 | C2×C22⋊C4 | — | 3 | 3 | no | — |
| 654 | C2×C22⋊C4 | — | 3 | 3 | no | — |
| 655 | C2×C22⋊C4 | — | 3 | 3 | no | — |
| 656 | C2×C22⋊C4 | — | 3 | 3 | no | — |
| 657 | C2×C22⋊C4 | C22×D3 | 1 | 3 | yes | — |
| 658 | C2×C22⋊C4 | C22×D3 | 1 | 3 | yes | — |
| 659 | C2×C42 | — | 3 | 3 | no | — |
| 660 | C2×C42 | — | 3 | 3 | no | — |
| 661 | C2×C42 | — | 3 | 3 | no | — |
| 662 | C2×C42 | — | 3 | 3 | no | — |
| 663 | C2×C42 | — | 3 | 3 | no | — |
| 664 | C2×C42 | — | 3 | 3 | no | — |
| 665 | C2×C42 | — | 3 | 3 | no | — |
| 666 | C2×C42 | — | 3 | 3 | no | — |
| 667 | C2×C42 | — | 3 | 6 | no | — |
| 668 | C2×C42 | — | 3 | 3 | no | — |
| 669 | C2×C42 | — | 3 | 6 | no | — |
| 670 | C2×C42 | — | 3 | 6 | no | — |
| 671 | C2×C42 | — | 3 | 6 | no | — |
| 672 | C2×C42 | — | 3 | 6 | no | — |
| 673 | C2×C42 | — | 3 | 6 | no | — |
| 674 | C2×C42 | — | 3 | 6 | no | — |
| 675 | C2×C42 | — | 3 | 6 | no | — |
| 676 | C2×C42 | C22×D3 | 1 | 3 | yes | — |
| 677 | C23×C3 | — | 2 | 6 | no | — |
| 678 | C23×C3 | — | 4 | 1 | no | — |
| 679 | C23×C3 | — | 4 | 3 | no | — |
| 680 | C23×C3 | — | 4 | 1 | no | — |
| 681 | C23×C3 | — | 4 | 3 | no | — |
| 682 | C23×C3 | C2×#41 | 1 | 4 | yes | — |
| 683 | C23×C3 | C25 | 1 | 6 | yes | — |
| 684 | C23×C3 | C25 | 1 | 3 | yes | — |
| 685 | C22×D3 | — | 2 | 6 | no | — |
| 686 | C22×D3 | — | 4 | 3 | no | — |
| 687 | C22×D3 | — | 4 | 3 | no | — |
| 688 | C22×D3 | C25 | 1 | 6 | yes | — |
| 689 | C3×Q8 | — | 4 | 2 | no | — |
| 690 | C3×Q8 | — | 4 | 2 | no | — |
| 691 | C3×D4 | — | 2 | 24 | no | — |
| 692 | C3×D4 | — | 4 | 6 | no | — |
| 693 | C3×D4 | — | 4 | 6 | no | — |
| 694 | C2×C3×C4 | — | 2 | 6 | no | — |
| 695 | C2×C3×C4 | — | 2 | 6 | no | — |
| 696 | C2×C3×C4 | — | 2 | 12 | no | — |
| 697 | C2×C3×C4 | — | 4 | 3 | no | — |
| 698 | C2×C3×C4 | — | 4 | 3 | no | — |
| 699 | C2×C3×C4 | — | 4 | 6 | no | — |
| 700 | C2×C3×C4 | — | 4 | 3 | no | — |
| 701 | C2×C3×C4 | C25 | 1 | 3 | yes | — |
| 702 | C2×C3×C4 | C25 | 1 | 6 | yes | — |
| 703 | C2×C3×C4 | C25 | 1 | 6 | yes | — |
| 704 | C2×C3×C4 | C25 | 1 | 6 | yes | — |
| 705 | C2×C3×C4 | C25 | 1 | 1 | yes | characteristic |
| 706 | #67 | — | 2 | 24 | no | — |
| 707 | #67 | — | 2 | 24 | no | — |
| 708 | #67 | — | 4 | 12 | no | — |
| 709 | #67 | — | 4 | 12 | no | — |
| 710 | C2×Dic3 | — | 2 | 6 | no | — |
| 711 | C2×Dic3 | — | 2 | 12 | no | — |
| 712 | C2×Dic3 | — | 2 | 12 | no | — |
| 713 | C2×Dic3 | — | 2 | 6 | no | — |
| 714 | C2×Dic3 | — | 2 | 12 | no | — |
| 715 | C2×Dic3 | — | 4 | 3 | no | — |
| 716 | C2×Dic3 | — | 4 | 3 | no | — |
| 717 | C2×Dic3 | — | 4 | 6 | no | — |
| 718 | C2×Dic3 | — | 4 | 3 | no | — |
| 719 | C2×Dic3 | C2×#41 | 1 | 12 | yes | — |
| 720 | C2×Dic3 | C2×#41 | 1 | 12 | yes | — |
| 721 | C2×Dic3 | C25 | 1 | 3 | yes | — |
| 722 | C2×Dic3 | C25 | 1 | 6 | yes | — |
| 723 | C2×Dic3 | C25 | 1 | 6 | yes | — |
| 724 | C2×Dic3 | C25 | 1 | 6 | yes | — |
| 725 | C2×Dic3 | C25 | 1 | 1 | yes | characteristic |
| 726 | C2×Dic3 | C25 | 1 | 3 | yes | — |
| 727 | C2×Dic3 | C25 | 1 | 1 | yes | characteristic |
| 728 | D12 | — | 4 | 6 | no | — |
| 729 | D12 | — | 4 | 6 | no | — |
| 730 | C4×D3 | — | 2 | 12 | no | — |
| 731 | C4×D3 | — | 2 | 12 | no | — |
| 732 | C4×D3 | — | 2 | 12 | no | — |
| 733 | C4×D3 | — | 2 | 12 | no | — |
| 734 | C4×D3 | — | 4 | 6 | no | — |
| 735 | C4×D3 | — | 4 | 6 | no | — |
| 736 | Dic6 | — | 2 | 24 | no | — |
| 737 | Dic6 | — | 4 | 6 | no | — |
| 738 | Dic6 | — | 4 | 6 | no | — |
| 739 | C24 | — | 3 | 3 | no | — |
| 740 | C24 | C23×D3 | 1 | 3 | yes | — |
| 741 | C24 | C23×D3 | 1 | 1 | yes | characteristic |
| 742 | #41 | — | 4 | 4 | no | — |
| 743 | #41 | — | 6 | 48 | no | — |
| 744 | #41 | — | 6 | 48 | no | — |
| 745 | #41 | — | 12 | 12 | no | — |
| 746 | #41 | — | 12 | 12 | no | — |
| 747 | #41 | — | 12 | 4 | no | — |
| 748 | C2×Q8 | — | 3 | 12 | no | — |
| 749 | C2×Q8 | — | 3 | 6 | no | — |
| 750 | C2×Q8 | — | 3 | 6 | no | — |
| 751 | C2×Q8 | — | 6 | 12 | no | — |
| 752 | C2×Q8 | C23×D3 | 1 | 2 | yes | — |
| 753 | C2×Q8 | C23×D3 | 1 | 2 | yes | — |
| 754 | C2×D4 | — | 2 | 12 | no | — |
| 755 | C2×D4 | — | 3 | 12 | no | — |
| 756 | C2×D4 | — | 3 | 12 | no | — |
| 757 | C2×D4 | — | 3 | 12 | no | — |
| 758 | C2×D4 | — | 3 | 12 | no | — |
| 759 | C2×D4 | — | 3 | 6 | no | — |
| 760 | C2×D4 | — | 3 | 6 | no | — |
| 761 | C2×D4 | — | 6 | 12 | no | — |
| 762 | C2×D4 | — | 6 | 12 | no | — |
| 763 | C2×D4 | C23×D3 | 1 | 12 | yes | — |
| 764 | C2×D4 | C23×D3 | 1 | 6 | yes | — |
| 765 | C2×D4 | C23×D3 | 1 | 6 | yes | — |
| 766 | C22×C4 | — | 3 | 8 | no | — |
| 767 | C22×C4 | — | 3 | 3 | no | — |
| 768 | C22×C4 | — | 3 | 3 | no | — |
| 769 | C22×C4 | — | 3 | 3 | no | — |
| 770 | C22×C4 | — | 3 | 3 | no | — |
| 771 | C22×C4 | — | 3 | 6 | no | — |
| 772 | C22×C4 | — | 3 | 6 | no | — |
| 773 | C22×C4 | — | 3 | 6 | no | — |
| 774 | C22×C4 | — | 3 | 3 | no | — |
| 775 | C22×C4 | — | 3 | 3 | no | — |
| 776 | C22×C4 | — | 3 | 3 | no | — |
| 777 | C22×C4 | — | 3 | 6 | no | — |
| 778 | C22×C4 | — | 3 | 6 | no | — |
| 779 | C22×C4 | — | 3 | 6 | no | — |
| 780 | C22×C4 | — | 3 | 6 | no | — |
| 781 | C22×C4 | — | 3 | 6 | no | — |
| 782 | C22×C4 | — | 3 | 6 | no | — |
| 783 | C22×C4 | — | 3 | 6 | no | — |
| 784 | C22×C4 | — | 4 | 2 | no | — |
| 785 | C22×C4 | — | 4 | 6 | no | — |
| 786 | C22×C4 | — | 6 | 12 | no | — |
| 787 | C22×C4 | — | 6 | 12 | no | — |
| 788 | C22×C4 | — | 12 | 6 | no | — |
| 789 | C22×C4 | — | 12 | 6 | no | — |
| 790 | C22×C4 | — | 12 | 2 | no | — |
| 791 | C22×C4 | — | 12 | 6 | no | — |
| 792 | C22×C4 | C23×D3 | 1 | 3 | yes | — |
| 793 | C22×C4 | C23×D3 | 1 | 3 | yes | — |
| 794 | C22×C4 | C23×D3 | 1 | 6 | yes | — |
| 795 | C22×C4 | C23×D3 | 1 | 3 | yes | — |
| 796 | C22×C4 | C23×D3 | 1 | 3 | yes | — |
| 797 | C22×C4 | C23×D3 | 1 | 6 | yes | — |
| 798 | C22×C4 | C23×D3 | 1 | 3 | yes | — |
| 799 | C4⋊C4 | — | 3 | 12 | no | — |
| 800 | C4⋊C4 | — | 3 | 12 | no | — |
| 801 | C4⋊C4 | — | 3 | 12 | no | — |
| 802 | C4⋊C4 | — | 3 | 12 | no | — |
| 803 | C4⋊C4 | — | 3 | 12 | no | — |
| 804 | C4⋊C4 | — | 3 | 12 | no | — |
| 805 | C4⋊C4 | — | 3 | 12 | no | — |
| 806 | C4⋊C4 | — | 3 | 12 | no | — |
| 807 | C4⋊C4 | — | 3 | 12 | no | — |
| 808 | C4⋊C4 | — | 3 | 6 | no | — |
| 809 | C4⋊C4 | — | 3 | 6 | no | — |
| 810 | C4⋊C4 | — | 3 | 6 | no | — |
| 811 | C4⋊C4 | — | 3 | 6 | no | — |
| 812 | C4⋊C4 | C23×D3 | 1 | 12 | yes | — |
| 813 | C4⋊C4 | C23×D3 | 1 | 6 | yes | — |
| 814 | C4⋊C4 | C23×D3 | 1 | 6 | yes | — |
| 815 | C4⋊C4 | C23×D3 | 1 | 6 | yes | — |
| 816 | C4⋊C4 | C23×D3 | 1 | 6 | yes | — |
| 817 | C22⋊C4 | — | 3 | 12 | no | — |
| 818 | C22⋊C4 | — | 3 | 12 | no | — |
| 819 | C22⋊C4 | — | 3 | 12 | no | — |
| 820 | C22⋊C4 | — | 3 | 12 | no | — |
| 821 | C22⋊C4 | — | 3 | 12 | no | — |
| 822 | C22⋊C4 | — | 3 | 12 | no | — |
| 823 | C22⋊C4 | — | 3 | 12 | no | — |
| 824 | C22⋊C4 | — | 3 | 12 | no | — |
| 825 | C22⋊C4 | — | 3 | 12 | no | — |
| 826 | C22⋊C4 | — | 3 | 12 | no | — |
| 827 | C22⋊C4 | C23×D3 | 1 | 12 | yes | — |
| 828 | C22⋊C4 | C23×D3 | 1 | 12 | yes | — |
| 829 | C22⋊C4 | C23×D3 | 1 | 12 | yes | — |
| 830 | C22⋊C4 | C23×D3 | 1 | 12 | yes | — |
| 831 | C42 | — | 3 | 3 | no | — |
| 832 | C42 | — | 3 | 3 | no | — |
| 833 | C42 | — | 3 | 6 | no | — |
| 834 | C42 | — | 3 | 6 | no | — |
| 835 | C42 | — | 3 | 6 | no | — |
| 836 | C42 | — | 3 | 6 | no | — |
| 837 | C42 | — | 3 | 6 | no | — |
| 838 | C42 | — | 3 | 6 | no | — |
| 839 | C42 | — | 3 | 6 | no | — |
| 840 | C42 | — | 3 | 6 | no | — |
| 841 | C42 | — | 3 | 6 | no | — |
| 842 | C42 | — | 3 | 6 | no | — |
| 843 | C42 | — | 3 | 1 | no | — |
| 844 | C42 | — | 3 | 3 | no | — |
| 845 | C42 | — | 3 | 6 | no | — |
| 846 | C42 | C23×D3 | 1 | 6 | yes | — |
| 847 | C42 | C23×D3 | 1 | 6 | yes | — |
| 848 | C22×C3 | — | 2 | 3 | no | — |
| 849 | C22×C3 | — | 2 | 3 | no | — |
| 850 | C22×C3 | — | 2 | 6 | no | — |
| 851 | C22×C3 | — | 2 | 6 | no | — |
| 852 | C22×C3 | — | 2 | 6 | no | — |
| 853 | C22×C3 | — | 4 | 4 | no | — |
| 854 | C22×C3 | — | 4 | 12 | no | — |
| 855 | C22×C3 | C22×#41 | 1 | 6 | yes | — |
| 856 | C22×C3 | C26 | 1 | 1 | yes | characteristic |
| 857 | C2×D3 | — | 2 | 6 | no | — |
| 858 | C2×D3 | — | 2 | 6 | no | — |
| 859 | C2×D3 | — | 2 | 6 | no | — |
| 860 | C2×D3 | — | 4 | 12 | no | — |
| 861 | C3×C4 | — | 2 | 6 | no | — |
| 862 | C3×C4 | — | 2 | 6 | no | — |
| 863 | C3×C4 | — | 2 | 6 | no | — |
| 864 | C3×C4 | — | 2 | 3 | no | — |
| 865 | C3×C4 | #585 | 1 | 2 | yes | — |
| 866 | Dic3 | — | 2 | 6 | no | — |
| 867 | Dic3 | — | 2 | 6 | no | — |
| 868 | Dic3 | — | 2 | 6 | no | — |
| 869 | Dic3 | — | 2 | 3 | no | — |
| 870 | Dic3 | C22×#41 | 1 | 6 | yes | — |
| 871 | Dic3 | C22×#41 | 1 | 2 | yes | — |
| 872 | Dic3 | #585 | 1 | 2 | yes | — |
| 873 | C23 | — | 2 | 6 | no | — |
| 874 | C23 | — | 3 | 6 | no | — |
| 875 | C23 | — | 4 | 1 | no | — |
| 876 | C23 | — | 4 | 3 | no | — |
| 877 | C23 | — | 4 | 1 | no | — |
| 878 | C23 | — | 4 | 3 | no | — |
| 879 | C23 | — | 6 | 6 | no | — |
| 880 | C23 | — | 12 | 3 | no | — |
| 881 | C23 | — | 12 | 3 | no | — |
| 882 | C23 | D3×#41 | 1 | 4 | yes | — |
| 883 | C23 | C24×D3 | 1 | 6 | yes | — |
| 884 | C23 | C24×D3 | 1 | 3 | yes | — |
| 885 | Q8 | — | 4 | 2 | no | — |
| 886 | Q8 | — | 4 | 2 | no | — |
| 887 | Q8 | — | 6 | 24 | no | — |
| 888 | Q8 | — | 12 | 6 | no | — |
| 889 | Q8 | — | 12 | 6 | no | — |
| 890 | D4 | — | 2 | 24 | no | — |
| 891 | D4 | — | 4 | 6 | no | — |
| 892 | D4 | — | 4 | 6 | no | — |
| 893 | D4 | — | 6 | 24 | no | — |
| 894 | D4 | — | 6 | 24 | no | — |
| 895 | D4 | — | 12 | 6 | no | — |
| 896 | D4 | — | 12 | 6 | no | — |
| 897 | D4 | — | 12 | 12 | no | — |
| 898 | D4 | — | 12 | 12 | no | — |
| 899 | C2×C4 | — | 2 | 6 | no | — |
| 900 | C2×C4 | — | 2 | 6 | no | — |
| 901 | C2×C4 | — | 2 | 12 | no | — |
| 902 | C2×C4 | — | 3 | 12 | no | — |
| 903 | C2×C4 | — | 3 | 12 | no | — |
| 904 | C2×C4 | — | 3 | 1 | no | — |
| 905 | C2×C4 | — | 3 | 1 | no | — |
| 906 | C2×C4 | — | 3 | 3 | no | — |
| 907 | C2×C4 | — | 3 | 3 | no | — |
| 908 | C2×C4 | — | 3 | 6 | no | — |
| 909 | C2×C4 | — | 3 | 6 | no | — |
| 910 | C2×C4 | — | 3 | 6 | no | — |
| 911 | C2×C4 | — | 4 | 3 | no | — |
| 912 | C2×C4 | — | 4 | 6 | no | — |
| 913 | C2×C4 | — | 4 | 3 | no | — |
| 914 | C2×C4 | — | 4 | 3 | no | — |
| 915 | C2×C4 | — | 6 | 12 | no | — |
| 916 | C2×C4 | — | 6 | 12 | no | — |
| 917 | C2×C4 | — | 6 | 12 | no | — |
| 918 | C2×C4 | — | 6 | 12 | no | — |
| 919 | C2×C4 | — | 6 | 12 | no | — |
| 920 | C2×C4 | — | 6 | 6 | no | — |
| 921 | C2×C4 | — | 6 | 12 | no | — |
| 922 | C2×C4 | — | 6 | 6 | no | — |
| 923 | C2×C4 | — | 6 | 12 | no | — |
| 924 | C2×C4 | — | 12 | 6 | no | — |
| 925 | C2×C4 | — | 12 | 6 | no | — |
| 926 | C2×C4 | — | 12 | 3 | no | — |
| 927 | C2×C4 | — | 12 | 3 | no | — |
| 928 | C2×C4 | — | 12 | 6 | no | — |
| 929 | C2×C4 | — | 12 | 3 | no | — |
| 930 | C2×C4 | C24×D3 | 1 | 3 | yes | — |
| 931 | C2×C4 | C24×D3 | 1 | 6 | yes | — |
| 932 | C2×C4 | C24×D3 | 1 | 6 | yes | — |
| 933 | C2×C4 | C24×D3 | 1 | 6 | yes | — |
| 934 | C2×C4 | C24×D3 | 1 | 1 | yes | characteristic |
| 935 | C2×C3 | — | 2 | 6 | no | — |
| 936 | C2×C3 | — | 4 | 6 | no | — |
| 937 | C2×C3 | C23×#41 | 1 | 1 | yes | characteristic |
| 938 | C2×C3 | C2×#585 | 1 | 1 | yes | characteristic |
| 939 | C2×C3 | C2×#585 | 1 | 1 | yes | characteristic |
| 940 | D3 | — | 4 | 6 | no | — |
| 941 | C22 | — | 2 | 3 | no | — |
| 942 | C22 | — | 2 | 3 | no | — |
| 943 | C22 | — | 2 | 6 | no | — |
| 944 | C22 | — | 2 | 6 | no | — |
| 945 | C22 | — | 2 | 6 | no | — |
| 946 | C22 | — | 4 | 4 | no | — |
| 947 | C22 | — | 4 | 12 | no | — |
| 948 | C22 | — | 6 | 6 | no | — |
| 949 | C22 | — | 6 | 6 | no | — |
| 950 | C22 | — | 6 | 6 | no | — |
| 951 | C22 | — | 12 | 12 | no | — |
| 952 | C22 | C2×D3×#41 | 1 | 6 | yes | — |
| 953 | C22 | C25×D3 | 1 | 1 | yes | characteristic |
| 954 | C4 | — | 2 | 6 | no | — |
| 955 | C4 | — | 2 | 3 | no | — |
| 956 | C4 | — | 2 | 6 | no | — |
| 957 | C4 | — | 2 | 6 | no | — |
| 958 | C4 | — | 3 | 2 | no | — |
| 959 | C4 | — | 3 | 6 | no | — |
| 960 | C4 | — | 3 | 2 | no | — |
| 961 | C4 | — | 6 | 6 | no | — |
| 962 | C4 | — | 6 | 6 | no | — |
| 963 | C4 | — | 6 | 3 | no | — |
| 964 | C4 | — | 6 | 6 | no | — |
| 965 | C4 | #5966 | 1 | 2 | yes | — |
| 966 | C3 | #62686 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 967 | C2 | — | 2 | 6 | no | — |
| 968 | C2 | — | 4 | 6 | no | — |
| 969 | C2 | — | 12 | 6 | no | — |
| 970 | C2 | C22×D3×#41 | 1 | 1 | yes | characteristic |
| 971 | C2 | C2×#5966 | 1 | 1 | yes | characteristic |
| 972 | C2 | D3×#585 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C24×D3 |
| commutator, socle, cosocle | C22×C3 | C26 |
| Frattini | C22 | C25×D3 |
| Fitting | C3×#3459 | C2 |
| hypercenter | #3459 | D3 |
| hypocenter | C3 | #62686 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C2×C4 ◁ #3459 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×#3459 | C2 | semidirect |
| 2. #86572 | C2 | semidirect |
| 3. #86571 | C2 | semidirect |
| 4. #86429 | C2 | semidirect |
| 5. #86427 | C2 | semidirect |
| 6. #86389 | C2 | semidirect |
| 7. #86387 | C2 | semidirect |
| 8. #86295 | C2 | semidirect |
| 9. #86294 | C2 | semidirect |
| 10. #86120 | C2 | semidirect |
| 11. #86119 | C2 | semidirect |
| 12. #86020 | C2 | semidirect |
| 13. #86018 | C2 | semidirect |
| 14. #85776 | C2 | semidirect |
| 15. C2×C4×#237 | C2 | semidirect |
| 19. C3×#539 | C22 | semidirect |
| 20. C3×#538 | C22 | semidirect |
| 22. C3×#529 | C22 | semidirect |
| 23. C3×#525 | C22 | semidirect |
| 25. #5832 | C22 | semidirect |
| 26. Dic3×#41 | C22 | semidirect |
| 29. #5791 | C22 | semidirect |
| 31. C2×C4×#67 | C22 | semidirect |
| 33. C22×C4×Dic3 | C22 | semidirect |
| 34. #5710 | C22 | semidirect |
| 35. #5706 | C22 | semidirect |
| 36. #5706 | C22 | semidirect |
| 37. #5701 | C22 | semidirect |
| 38. #5696 | C22 | semidirect |
| 39. #5691 | C22 | semidirect |
| 40. #5688 | C22 | semidirect |
| 41. #5680 | C22 | semidirect |
| 42. #5669 | C22 | semidirect |
| 43. #5668 | C22 | semidirect |
| 44. #5665 | C22 | semidirect |
| 45. #5663 | C22 | semidirect |
| 46. #5662 | C22 | semidirect |
| 47. #5656 | C22 | semidirect |
| 48. #5649 | C22 | semidirect |
| 49. #5649 | C22 | semidirect |
| 50. #5649 | C22 | semidirect |
| 51. #5648 | C22 | semidirect |
| 52. #5645 | C22 | semidirect |
| 53. #5644 | C22 | semidirect |
| 54. #5640 | C22 | semidirect |
| 55. #5627 | C22 | semidirect |
| 56. #5624 | C22 | semidirect |
| 57. #5624 | C22 | semidirect |
| 58. #5623 | C22 | semidirect |
| 59. #5623 | C22 | semidirect |
| 60. #5622 | C22 | semidirect |
| 61. #5622 | C22 | semidirect |
| 62. #5622 | C22 | semidirect |
| 63. #5617 | C22 | semidirect |
| 64. #5615 | C22 | semidirect |
| 65. #5606 | C22 | semidirect |
| 66. #5602 | C22 | semidirect |
| 67. #5600 | C22 | semidirect |
| 68. #5600 | C22 | semidirect |
| 73. #5596 | C22 | semidirect |
| 74. #5593 | C22 | semidirect |
| 75. #5592 | C22 | semidirect |
| 76. #5586 | C22 | semidirect |
| 77. #5586 | C22 | semidirect |
| 78. #5578 | C22 | semidirect |
| 79. C4×#239 | C22 | semidirect |
| 80. #5564 | C22 | semidirect |
| 81. #5560 | C22 | semidirect |
| 82. #5548 | C22 | semidirect |
| 83. #5547 | C22 | semidirect |
| 84. #5538 | C22 | semidirect |
| 85. #5538 | C22 | semidirect |
| 86. C4×#237 | C22 | semidirect |
| 87. C4×#237 | C22 | semidirect |
| 88. C4×#237 | C22 | semidirect |
| 89. C4×#237 | C22 | semidirect |
| 90. C4×#237 | C22 | semidirect |
| 91. #5528 | C22 | semidirect |
| 92. #5522 | C22 | semidirect |
| 93. #5517 | C22 | semidirect |
| 94. #5515 | C22 | semidirect |
| 95. C2×#892 | C22 | semidirect |
| 96. C2×#887 | C22 | semidirect |
| 97. #5494 | C22 | semidirect |
| 100. C2×#67⋊C4 | C22 | semidirect |
| 103. C2×#877 | C22 | semidirect |
| 104. #5479 | C22 | semidirect |
| 105. C2×C42×D3 | C22 | semidirect |
| 106. C2×C4×Dic6 | C22 | semidirect |
| 114. #3459 | D3 | semidirect |
| 318. #539 | C2×D3 | semidirect |
| 324. #538 | C2×D3 | semidirect |
| 359. #529 | C2×D3 | semidirect |
| 367. #525 | C2×D3 | semidirect |
| 418. C22×Dic3 | #41 | semidirect |
| 966. C3 | #62686 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3459 | 2 |
| #86572 | 2 |
| #86571 | 2 |
| #86429 | 2 |
| #86427 | 2 |
| #86389 | 2 |
| #86387 | 2 |
| #86295 | 2 |
| #86294 | 2 |
| #86120 | 2 |
| #86119 | 2 |
| #86020 | 2 |
| #86018 | 2 |
| #85776 | 2 |
| C2×C4×#237 | 2 |
| #62686 | 3 |