Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
6974 conjugacy classes of subgroups.
The subgroup lattice has 918 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×C3×D4×Q8 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #87251 | C2 | 1 | 4 | yes | maximal, complemented |
| 3 | #86765 | C2 | 1 | 6 | yes | maximal, complemented |
| 4 | #86764 | C2 | 1 | 6 | yes | maximal, complemented |
| 5 | #86763 | C2 | 1 | 6 | yes | maximal, complemented |
| 6 | #86760 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #86755 | C2 | 1 | 6 | yes | maximal, complemented |
| 8 | #86753 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #86750 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #86746 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #86215 | C2 | 1 | 3 | yes | maximal, complemented |
| 12 | #86205 | C2 | 1 | 3 | yes | maximal, complemented |
| 13 | #85991 | C2 | 1 | 12 | yes | maximal, complemented |
| 14 | Q8×#235 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | #85802 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | #85788 | C2 | 1 | 3 | yes | maximal, complemented |
| 17 | #85777 | C2 | 1 | 3 | yes | maximal, complemented |
| 18 | #62913 | — | 3 | 1 | no | maximal, Sylow |
| 19 | C23×C3×Q8 | C22 | 1 | 2 | yes | — |
| 20 | C2×#1007 | C22 | 1 | 4 | yes | complemented |
| 21 | C3×D4×Q8 | C22 | 1 | 2 | yes | — |
| 22 | C3×D4×Q8 | C22 | 1 | 2 | yes | — |
| 23 | C3×D4×Q8 | C22 | 1 | 6 | yes | — |
| 24 | C3×D4×Q8 | C22 | 1 | 6 | yes | — |
| 25 | C2×C3×C4⋊Q8 | C22 | 1 | 3 | yes | — |
| 26 | C2×C3×C22⋊Q8 | C22 | 1 | 6 | yes | — |
| 27 | C2×C3×C4×Q8 | C22 | 1 | 1 | yes | characteristic |
| 28 | C2×C3×C4×D4 | C22 | 1 | 3 | yes | — |
| 29 | #5817 | C22 | 1 | 2 | yes | — |
| 30 | #5817 | C22 | 1 | 12 | yes | — |
| 31 | #5817 | C22 | 1 | 4 | yes | complemented |
| 32 | #5817 | C22 | 1 | 12 | yes | complemented |
| 33 | #5816 | C22 | 1 | 12 | yes | complemented |
| 34 | #5816 | C22 | 1 | 12 | yes | complemented |
| 35 | Q8×#67 | C22 | 1 | 2 | yes | — |
| 36 | Q8×#67 | C22 | 1 | 12 | yes | — |
| 37 | Q8×#67 | C22 | 1 | 4 | yes | complemented |
| 38 | Q8×#67 | C22 | 1 | 12 | yes | complemented |
| 39 | #5812 | C22 | 1 | 4 | yes | complemented |
| 40 | #5805 | C22 | 1 | 1 | yes | characteristic |
| 41 | #5805 | C22 | 1 | 3 | yes | — |
| 42 | #5791 | C22 | 1 | 12 | yes | — |
| 43 | #5791 | C22 | 1 | 12 | yes | — |
| 44 | #5734 | C22 | 1 | 6 | yes | complemented |
| 45 | #5733 | C22 | 1 | 12 | yes | complemented |
| 46 | #5732 | C22 | 1 | 6 | yes | complemented |
| 47 | #5730 | C22 | 1 | 6 | yes | complemented |
| 48 | #5730 | C22 | 1 | 6 | yes | complemented |
| 49 | #5729 | C22 | 1 | 12 | yes | complemented |
| 50 | #5728 | C22 | 1 | 6 | yes | complemented |
| 51 | #5728 | C22 | 1 | 6 | yes | complemented |
| 52 | #5727 | C22 | 1 | 6 | yes | complemented |
| 53 | #5726 | C22 | 1 | 6 | yes | complemented |
| 54 | #5725 | C22 | 1 | 6 | yes | complemented |
| 55 | D3×C4⋊Q8 | C22 | 1 | 6 | yes | complemented |
| 56 | #5722 | C22 | 1 | 6 | yes | complemented |
| 57 | #5721 | C22 | 1 | 6 | yes | complemented |
| 58 | #5647 | C22 | 1 | 24 | yes | complemented |
| 59 | #5646 | C22 | 1 | 24 | yes | complemented |
| 60 | #5643 | C22 | 1 | 12 | yes | complemented |
| 61 | #5641 | C22 | 1 | 12 | yes | complemented |
| 62 | #5640 | C22 | 1 | 24 | yes | complemented |
| 63 | #5639 | C22 | 1 | 12 | yes | complemented |
| 64 | #5638 | C22 | 1 | 24 | yes | complemented |
| 65 | #5633 | C22 | 1 | 12 | yes | complemented |
| 66 | #5631 | C22 | 1 | 12 | yes | complemented |
| 67 | #5629 | C22 | 1 | 12 | yes | complemented |
| 68 | #5628 | C22 | 1 | 12 | yes | complemented |
| 69 | #5625 | C22 | 1 | 12 | yes | complemented |
| 70 | #5585 | C22 | 1 | 3 | yes | complemented |
| 71 | #5584 | C22 | 1 | 3 | yes | complemented |
| 72 | #5580 | C22 | 1 | 6 | yes | complemented |
| 73 | #5579 | C22 | 1 | 3 | yes | complemented |
| 74 | #5578 | C22 | 1 | 6 | yes | complemented |
| 75 | #5577 | C22 | 1 | 1 | yes | characteristic, complemented |
| 76 | Q8×D12 | C22 | 1 | 1 | yes | characteristic, complemented |
| 77 | C4×#239 | C22 | 1 | 2 | yes | complemented |
| 78 | C4×D3×Q8 | C22 | 1 | 2 | yes | complemented |
| 79 | #5570 | C22 | 1 | 1 | yes | characteristic, complemented |
| 80 | #5567 | C22 | 1 | 3 | yes | complemented |
| 81 | Q8×Dic6 | C22 | 1 | 1 | yes | characteristic, complemented |
| 82 | #5563 | C22 | 1 | 6 | yes | — |
| 83 | #5562 | C22 | 1 | 6 | yes | — |
| 84 | #5562 | C22 | 1 | 6 | yes | — |
| 85 | #5561 | C22 | 1 | 6 | yes | — |
| 86 | #5561 | C22 | 1 | 6 | yes | — |
| 87 | #5559 | C22 | 1 | 12 | yes | — |
| 88 | #5558 | C22 | 1 | 12 | yes | — |
| 89 | #5557 | C22 | 1 | 6 | yes | — |
| 90 | #5557 | C22 | 1 | 6 | yes | — |
| 91 | #5553 | C22 | 1 | 6 | yes | — |
| 92 | #5551 | C22 | 1 | 6 | yes | — |
| 93 | #5548 | C22 | 1 | 6 | yes | — |
| 94 | #5548 | C22 | 1 | 6 | yes | — |
| 95 | #5542 | C22 | 1 | 6 | yes | — |
| 96 | #5514 | C22 | 1 | 6 | yes | — |
| 97 | #5514 | C22 | 1 | 12 | yes | — |
| 98 | #5511 | C22 | 1 | 6 | yes | — |
| 99 | #5511 | C22 | 1 | 12 | yes | — |
| 100 | #5510 | C22 | 1 | 3 | yes | — |
| 101 | #5504 | C22 | 1 | 6 | yes | — |
| 102 | #5500 | C22 | 1 | 3 | yes | — |
| 103 | #5494 | C22 | 1 | 12 | yes | — |
| 104 | #5494 | C22 | 1 | 12 | yes | — |
| 105 | #5477 | C22 | 1 | 3 | yes | — |
| 106 | C4×#235 | C22 | 1 | 3 | yes | — |
| 107 | C4×#235 | C22 | 1 | 3 | yes | — |
| 108 | #5470 | C22 | 1 | 3 | yes | — |
| 109 | #3554 | — | 3 | 6 | no | — |
| 110 | #3552 | — | 3 | 6 | no | — |
| 111 | #3550 | — | 3 | 6 | no | — |
| 112 | #3547 | — | 3 | 6 | no | — |
| 113 | #3541 | — | 3 | 12 | no | — |
| 114 | #3523 | — | 3 | 2 | no | — |
| 115 | #3518 | — | 3 | 2 | no | — |
| 116 | #3511 | — | 3 | 3 | no | — |
| 117 | #3506 | — | 3 | 3 | no | — |
| 118 | #3503 | — | 3 | 3 | no | — |
| 119 | #3499 | — | 3 | 2 | no | — |
| 120 | #3497 | — | 3 | 2 | no | — |
| 121 | #3486 | — | 3 | 4 | no | — |
| 122 | #3480 | — | 3 | 1 | no | — |
| 123 | Q8×#41 | — | 3 | 1 | no | — |
| 124 | C2×D4×Q8 | D3 | 1 | 1 | yes | characteristic, complemented |
| 125 | #3460 | — | 3 | 3 | no | — |
| 126 | C22×C3×Q8 | — | 4 | 8 | no | — |
| 127 | C22×C3×Q8 | C23 | 1 | 4 | yes | — |
| 128 | C22×C3×Q8 | C23 | 1 | 1 | yes | characteristic |
| 129 | C22×C3×Q8 | C23 | 1 | 6 | yes | — |
| 130 | C22×C3×Q8 | C23 | 1 | 12 | yes | — |
| 131 | C22×C3×D4 | C23 | 1 | 1 | yes | characteristic |
| 132 | C23×C3×C4 | C23 | 1 | 6 | yes | — |
| 133 | #1007 | — | 4 | 16 | no | — |
| 134 | C2×#239 | C23 | 1 | 2 | yes | — |
| 135 | C2×#239 | C23 | 1 | 12 | yes | — |
| 136 | C2×D3×Q8 | C23 | 1 | 2 | yes | — |
| 137 | C2×D3×Q8 | C23 | 1 | 12 | yes | — |
| 138 | C2×#235 | C23 | 1 | 1 | yes | characteristic |
| 139 | C2×#235 | C23 | 1 | 3 | yes | — |
| 140 | C2×#235 | C23 | 1 | 12 | yes | — |
| 141 | C2×#235 | C23 | 1 | 12 | yes | — |
| 142 | C3×C4⋊Q8 | C23 | 1 | 6 | yes | — |
| 143 | C3×C4⋊Q8 | C23 | 1 | 6 | yes | — |
| 144 | C3×C4⋊Q8 | C23 | 1 | 6 | yes | — |
| 145 | C3×C4⋊Q8 | C23 | 1 | 6 | yes | — |
| 146 | C3×C22⋊Q8 | C23 | 1 | 12 | yes | — |
| 147 | C3×C22⋊Q8 | C23 | 1 | 24 | yes | — |
| 148 | C3×C22⋊Q8 | C23 | 1 | 12 | yes | — |
| 149 | C3×C4×Q8 | C23 | 1 | 1 | yes | characteristic |
| 150 | C3×C4×Q8 | C23 | 1 | 3 | yes | — |
| 151 | C3×C4×Q8 | C23 | 1 | 1 | yes | characteristic |
| 152 | C3×C4×Q8 | C23 | 1 | 3 | yes | — |
| 153 | C3×C4×D4 | C23 | 1 | 6 | yes | — |
| 154 | C3×C4×D4 | C23 | 1 | 6 | yes | — |
| 155 | C3×C4×D4 | C23 | 1 | 6 | yes | — |
| 156 | C3×C4×D4 | C23 | 1 | 6 | yes | — |
| 157 | C2×C3×C4⋊C4 | C23 | 1 | 3 | yes | — |
| 158 | C2×C3×C4⋊C4 | C23 | 1 | 3 | yes | — |
| 159 | C2×C3×C4⋊C4 | C23 | 1 | 6 | yes | — |
| 160 | C2×C3×C22⋊C4 | C23 | 1 | 6 | yes | — |
| 161 | C2×C3×C42 | C23 | 1 | 3 | yes | — |
| 162 | #953 | C23 | 1 | 4 | yes | — |
| 163 | #953 | C23 | 1 | 12 | yes | — |
| 164 | #947 | C23 | 1 | 12 | yes | — |
| 165 | #947 | C23 | 1 | 24 | yes | — |
| 166 | #947 | C23 | 1 | 6 | yes | — |
| 167 | #946 | C23 | 1 | 24 | yes | — |
| 168 | #946 | C23 | 1 | 24 | yes | — |
| 169 | #946 | C23 | 1 | 12 | yes | — |
| 170 | #946 | C23 | 1 | 12 | yes | — |
| 171 | #946 | C23 | 1 | 6 | yes | — |
| 172 | #946 | C23 | 1 | 6 | yes | — |
| 173 | Q8×Dic3 | C23 | 1 | 12 | yes | — |
| 174 | Q8×Dic3 | C23 | 1 | 12 | yes | — |
| 175 | Q8×Dic3 | C23 | 1 | 2 | yes | — |
| 176 | Q8×Dic3 | C23 | 1 | 2 | yes | — |
| 177 | #944 | C23 | 1 | 24 | yes | — |
| 178 | #944 | C23 | 1 | 12 | yes | — |
| 179 | #944 | C23 | 1 | 6 | yes | — |
| 180 | #940 | C23 | 1 | 2 | yes | — |
| 181 | #940 | C23 | 1 | 6 | yes | — |
| 182 | #938 | C23 | 1 | 2 | yes | — |
| 183 | #938 | C23 | 1 | 6 | yes | — |
| 184 | #938 | C23 | 1 | 2 | yes | — |
| 185 | #938 | C23 | 1 | 6 | yes | — |
| 186 | #936 | C23 | 1 | 6 | yes | — |
| 187 | #936 | C23 | 1 | 2 | yes | — |
| 188 | #930 | C23 | 1 | 12 | yes | — |
| 189 | #930 | C23 | 1 | 12 | yes | — |
| 190 | #930 | C23 | 1 | 6 | yes | — |
| 191 | #930 | C23 | 1 | 6 | yes | — |
| 192 | #930 | C23 | 1 | 12 | yes | — |
| 193 | #929 | C23 | 1 | 12 | yes | — |
| 194 | #929 | C23 | 1 | 12 | yes | — |
| 195 | #929 | C23 | 1 | 24 | yes | — |
| 196 | C4×#67 | C23 | 1 | 12 | yes | — |
| 197 | C4×#67 | C23 | 1 | 24 | yes | — |
| 198 | C4×#67 | C23 | 1 | 12 | yes | — |
| 199 | C4×#67 | C23 | 1 | 6 | yes | — |
| 200 | C4×#67 | C23 | 1 | 6 | yes | — |
| 201 | C4×#67 | C23 | 1 | 6 | yes | — |
| 202 | C4×#67 | C23 | 1 | 6 | yes | — |
| 203 | C4×#67 | C23 | 1 | 24 | yes | — |
| 204 | #926 | C23 | 1 | 12 | yes | — |
| 205 | #926 | C23 | 1 | 12 | yes | — |
| 206 | #926 | C23 | 1 | 3 | yes | — |
| 207 | #926 | C23 | 1 | 1 | yes | characteristic |
| 208 | #924 | C23 | 1 | 12 | yes | — |
| 209 | #924 | C23 | 1 | 6 | yes | — |
| 210 | #924 | C23 | 1 | 6 | yes | — |
| 211 | #924 | C23 | 1 | 12 | yes | — |
| 212 | #924 | C23 | 1 | 12 | yes | — |
| 213 | #898 | C23 | 1 | 24 | yes | — |
| 214 | #898 | C23 | 1 | 12 | yes | — |
| 215 | #897 | C23 | 1 | 12 | yes | — |
| 216 | #897 | C23 | 1 | 6 | yes | — |
| 217 | #897 | C23 | 1 | 6 | yes | — |
| 218 | #897 | C23 | 1 | 6 | yes | — |
| 219 | #896 | C23 | 1 | 24 | yes | — |
| 220 | #896 | C23 | 1 | 12 | yes | — |
| 221 | #895 | C23 | 1 | 6 | yes | — |
| 222 | #895 | C23 | 1 | 12 | yes | — |
| 223 | #895 | C23 | 1 | 6 | yes | — |
| 224 | #895 | C23 | 1 | 6 | yes | — |
| 225 | #894 | C23 | 1 | 12 | yes | — |
| 226 | #894 | C23 | 1 | 24 | yes | — |
| 227 | #893 | C23 | 1 | 12 | yes | — |
| 228 | #893 | C23 | 1 | 6 | yes | — |
| 229 | #893 | C23 | 1 | 12 | yes | — |
| 230 | #892 | C23 | 1 | 12 | yes | — |
| 231 | #892 | C23 | 1 | 6 | yes | — |
| 232 | #892 | C23 | 1 | 12 | yes | — |
| 233 | D3×C4⋊C4 | C23 | 1 | 12 | yes | — |
| 234 | D3×C4⋊C4 | C23 | 1 | 6 | yes | — |
| 235 | D3×C4⋊C4 | C23 | 1 | 12 | yes | — |
| 236 | #890 | C23 | 1 | 6 | yes | — |
| 237 | #890 | C23 | 1 | 12 | yes | — |
| 238 | #890 | C23 | 1 | 6 | yes | — |
| 239 | #890 | C23 | 1 | 6 | yes | — |
| 240 | #889 | C23 | 1 | 12 | yes | — |
| 241 | #889 | C23 | 1 | 24 | yes | — |
| 242 | #888 | C23 | 1 | 6 | yes | — |
| 243 | #888 | C23 | 1 | 12 | yes | — |
| 244 | #888 | C23 | 1 | 6 | yes | — |
| 245 | #888 | C23 | 1 | 6 | yes | — |
| 246 | #887 | C23 | 1 | 6 | yes | — |
| 247 | #887 | C23 | 1 | 12 | yes | — |
| 248 | #887 | C23 | 1 | 12 | yes | — |
| 249 | #885 | C23 | 1 | 12 | yes | — |
| 250 | #885 | C23 | 1 | 12 | yes | — |
| 251 | #885 | C23 | 1 | 24 | yes | — |
| 252 | #884 | C23 | 1 | 24 | yes | — |
| 253 | #884 | C23 | 1 | 12 | yes | — |
| 254 | #884 | C23 | 1 | 12 | yes | — |
| 255 | #883 | C23 | 1 | 12 | yes | — |
| 256 | #883 | C23 | 1 | 24 | yes | — |
| 257 | #883 | C23 | 1 | 12 | yes | — |
| 258 | #879 | C23 | 1 | 12 | yes | — |
| 259 | #879 | C23 | 1 | 24 | yes | — |
| 260 | #879 | C23 | 1 | 12 | yes | — |
| 261 | #875 | C23 | 1 | 6 | yes | — |
| 262 | #874 | C23 | 1 | 3 | yes | — |
| 263 | C4×D12 | C23 | 1 | 3 | yes | — |
| 264 | C4×D12 | C23 | 1 | 6 | yes | — |
| 265 | C4×D12 | C23 | 1 | 3 | yes | — |
| 266 | C4×D12 | C23 | 1 | 3 | yes | — |
| 267 | C4×D12 | C23 | 1 | 3 | yes | — |
| 268 | C4×D12 | C23 | 1 | 6 | yes | — |
| 269 | #872 | C23 | 1 | 6 | yes | — |
| 270 | #872 | C23 | 1 | 6 | yes | — |
| 271 | C42×D3 | C23 | 1 | 6 | yes | — |
| 272 | C42×D3 | C23 | 1 | 6 | yes | — |
| 273 | #870 | C23 | 1 | 6 | yes | — |
| 274 | #869 | C23 | 1 | 3 | yes | — |
| 275 | #869 | C23 | 1 | 3 | yes | — |
| 276 | #869 | C23 | 1 | 3 | yes | — |
| 277 | C4×Dic6 | C23 | 1 | 3 | yes | — |
| 278 | C4×Dic6 | C23 | 1 | 6 | yes | — |
| 279 | C4×Dic6 | C23 | 1 | 3 | yes | — |
| 280 | C4×Dic6 | C23 | 1 | 6 | yes | — |
| 281 | C4×Dic6 | C23 | 1 | 3 | yes | — |
| 282 | C4×Dic6 | C23 | 1 | 3 | yes | — |
| 283 | C2×2−1+4 | — | 3 | 4 | no | — |
| 284 | C23×Q8 | C2×D3 | 1 | 2 | yes | — |
| 285 | #563 | — | 3 | 24 | no | — |
| 286 | #562 | — | 3 | 24 | no | — |
| 287 | #559 | — | 3 | 3 | no | — |
| 288 | #559 | — | 3 | 12 | no | — |
| 289 | Q82 | — | 3 | 6 | no | — |
| 290 | Q82 | — | 3 | 1 | no | — |
| 291 | #557 | — | 3 | 6 | no | — |
| 292 | #557 | — | 3 | 3 | no | — |
| 293 | #557 | — | 3 | 1 | no | — |
| 294 | #556 | — | 3 | 6 | no | — |
| 295 | #556 | — | 3 | 12 | no | — |
| 296 | #556 | — | 3 | 3 | no | — |
| 297 | #556 | — | 3 | 6 | no | — |
| 298 | #555 | — | 3 | 6 | no | — |
| 299 | #555 | — | 3 | 6 | no | — |
| 300 | #554 | — | 3 | 6 | no | — |
| 301 | #554 | — | 3 | 6 | no | — |
| 302 | #554 | — | 3 | 3 | no | — |
| 303 | #554 | — | 3 | 6 | no | — |
| 304 | #554 | — | 3 | 12 | no | — |
| 305 | #553 | — | 3 | 12 | no | — |
| 306 | #553 | — | 3 | 6 | no | — |
| 307 | #553 | — | 3 | 12 | no | — |
| 308 | #552 | — | 3 | 12 | no | — |
| 309 | #550 | — | 3 | 1 | no | — |
| 310 | #550 | — | 3 | 6 | no | — |
| 311 | D4×Q8 | — | 3 | 2 | no | — |
| 312 | D4×Q8 | — | 3 | 4 | no | — |
| 313 | D4×Q8 | — | 3 | 12 | no | — |
| 314 | D4×Q8 | — | 3 | 12 | no | — |
| 315 | D4×Q8 | — | 3 | 6 | no | — |
| 316 | D4×Q8 | — | 3 | 1 | no | — |
| 317 | D4×Q8 | C2×D3 | 1 | 2 | yes | — |
| 318 | D4×Q8 | C2×D3 | 1 | 2 | yes | — |
| 319 | D4×Q8 | C2×D3 | 1 | 6 | yes | — |
| 320 | D4×Q8 | C2×D3 | 1 | 6 | yes | — |
| 321 | #548 | — | 3 | 2 | no | — |
| 322 | #548 | — | 3 | 4 | no | — |
| 323 | #548 | — | 3 | 12 | no | — |
| 324 | #548 | — | 3 | 12 | no | — |
| 325 | #548 | — | 3 | 12 | no | — |
| 326 | #547 | — | 3 | 6 | no | — |
| 327 | #547 | — | 3 | 12 | no | — |
| 328 | #547 | — | 3 | 6 | no | — |
| 329 | #544 | — | 3 | 12 | no | — |
| 330 | #544 | — | 3 | 3 | no | — |
| 331 | #542 | — | 3 | 12 | no | — |
| 332 | #542 | — | 3 | 24 | no | — |
| 333 | #542 | — | 3 | 12 | no | — |
| 334 | #542 | — | 3 | 6 | no | — |
| 335 | #542 | — | 3 | 6 | no | — |
| 336 | #541 | — | 3 | 12 | no | — |
| 337 | #540 | — | 3 | 6 | no | — |
| 338 | #540 | — | 3 | 6 | no | — |
| 339 | #539 | — | 3 | 24 | no | — |
| 340 | #538 | — | 3 | 12 | no | — |
| 341 | #538 | — | 3 | 12 | no | — |
| 342 | #537 | — | 3 | 12 | no | — |
| 343 | #537 | — | 3 | 3 | no | — |
| 344 | #536 | — | 3 | 12 | no | — |
| 345 | #536 | — | 3 | 12 | no | — |
| 346 | #536 | — | 3 | 12 | no | — |
| 347 | #535 | — | 3 | 1 | no | — |
| 348 | #535 | — | 3 | 3 | no | — |
| 349 | #533 | — | 3 | 6 | no | — |
| 350 | #533 | — | 3 | 6 | no | — |
| 351 | #533 | — | 3 | 6 | no | — |
| 352 | #533 | — | 3 | 3 | no | — |
| 353 | #532 | — | 3 | 6 | no | — |
| 354 | #532 | — | 3 | 6 | no | — |
| 355 | #532 | — | 3 | 6 | no | — |
| 356 | #532 | — | 3 | 3 | no | — |
| 357 | C2×C4⋊Q8 | — | 3 | 6 | no | — |
| 358 | C2×C4⋊Q8 | C2×D3 | 1 | 3 | yes | — |
| 359 | #529 | — | 3 | 6 | no | — |
| 360 | #529 | — | 3 | 6 | no | — |
| 361 | #529 | — | 3 | 6 | no | — |
| 362 | #525 | — | 3 | 12 | no | — |
| 363 | #525 | — | 3 | 12 | no | — |
| 364 | C2×C22⋊Q8 | C2×D3 | 1 | 6 | yes | — |
| 365 | #520 | — | 3 | 6 | no | — |
| 366 | #519 | — | 3 | 4 | no | — |
| 367 | C4×#41 | — | 3 | 2 | no | — |
| 368 | C4×#41 | — | 3 | 3 | no | — |
| 369 | C4×#41 | — | 3 | 3 | no | — |
| 370 | C2×C4×Q8 | — | 3 | 2 | no | — |
| 371 | C2×C4×Q8 | C2×D3 | 1 | 1 | yes | characteristic |
| 372 | C2×C4×D4 | C2×D3 | 1 | 3 | yes | — |
| 373 | C24×C3 | C24 | 1 | 2 | yes | — |
| 374 | C2×C3×Q8 | — | 2 | 16 | no | — |
| 375 | C2×C3×Q8 | — | 2 | 4 | no | — |
| 376 | C2×C3×Q8 | — | 4 | 24 | no | — |
| 377 | C2×C3×Q8 | — | 4 | 12 | no | — |
| 378 | C2×C3×Q8 | C24 | 1 | 3 | yes | — |
| 379 | C2×C3×Q8 | C24 | 1 | 12 | yes | — |
| 380 | C2×C3×Q8 | C24 | 1 | 12 | yes | — |
| 381 | C2×C3×Q8 | C24 | 1 | 1 | yes | characteristic |
| 382 | C2×C3×D4 | — | 2 | 4 | no | — |
| 383 | C2×C3×D4 | C24 | 1 | 2 | yes | — |
| 384 | C2×C3×D4 | C24 | 1 | 2 | yes | — |
| 385 | C22×C3×C4 | — | 4 | 12 | no | — |
| 386 | C22×C3×C4 | C24 | 1 | 3 | yes | — |
| 387 | C22×C3×C4 | C24 | 1 | 12 | yes | — |
| 388 | C22×C3×C4 | C24 | 1 | 3 | yes | — |
| 389 | C22×C3×C4 | C24 | 1 | 6 | yes | — |
| 390 | C22×C3×C4 | C24 | 1 | 12 | yes | — |
| 391 | C22×C3×C4 | C24 | 1 | 1 | yes | characteristic |
| 392 | C2×#67 | C24 | 1 | 2 | yes | — |
| 393 | C2×#67 | C24 | 1 | 6 | yes | — |
| 394 | C2×#67 | C24 | 1 | 4 | yes | — |
| 395 | C2×#67 | C24 | 1 | 12 | yes | — |
| 396 | C2×#67 | C24 | 1 | 12 | yes | — |
| 397 | C2×#67 | C24 | 1 | 4 | yes | — |
| 398 | #239 | — | 2 | 8 | no | — |
| 399 | #239 | — | 4 | 24 | no | — |
| 400 | D3×Q8 | — | 2 | 8 | no | — |
| 401 | D3×Q8 | — | 4 | 24 | no | — |
| 402 | #235 | — | 2 | 4 | no | — |
| 403 | #235 | — | 2 | 12 | no | — |
| 404 | #235 | — | 4 | 24 | no | — |
| 405 | #235 | — | 4 | 24 | no | — |
| 406 | C2×D12 | C24 | 1 | 1 | yes | characteristic |
| 407 | C2×D12 | C24 | 1 | 3 | yes | — |
| 408 | C2×D12 | C24 | 1 | 6 | yes | — |
| 409 | C2×D12 | C24 | 1 | 6 | yes | — |
| 410 | C2×D12 | C24 | 1 | 12 | yes | — |
| 411 | C2×C4×D3 | C24 | 1 | 2 | yes | — |
| 412 | C2×C4×D3 | C24 | 1 | 6 | yes | — |
| 413 | C2×C4×D3 | C24 | 1 | 6 | yes | — |
| 414 | C2×C4×D3 | C24 | 1 | 6 | yes | — |
| 415 | C2×C4×D3 | C24 | 1 | 6 | yes | — |
| 416 | C2×C4×D3 | C24 | 1 | 6 | yes | — |
| 417 | C2×C4×D3 | C24 | 1 | 24 | yes | — |
| 418 | C2×Dic6 | C24 | 1 | 1 | yes | characteristic |
| 419 | C2×Dic6 | C24 | 1 | 3 | yes | — |
| 420 | C2×Dic6 | C24 | 1 | 6 | yes | — |
| 421 | C2×Dic6 | C24 | 1 | 6 | yes | — |
| 422 | C2×Dic6 | C24 | 1 | 12 | yes | — |
| 423 | C3×C4⋊C4 | C24 | 1 | 6 | yes | — |
| 424 | C3×C4⋊C4 | C24 | 1 | 3 | yes | — |
| 425 | C3×C4⋊C4 | C24 | 1 | 12 | yes | — |
| 426 | C3×C4⋊C4 | C24 | 1 | 3 | yes | — |
| 427 | C3×C4⋊C4 | C24 | 1 | 6 | yes | — |
| 428 | C3×C4⋊C4 | C24 | 1 | 12 | yes | — |
| 429 | C3×C4⋊C4 | C24 | 1 | 6 | yes | — |
| 430 | C3×C22⋊C4 | C24 | 1 | 12 | yes | — |
| 431 | C3×C22⋊C4 | C24 | 1 | 12 | yes | — |
| 432 | C3×C42 | C24 | 1 | 3 | yes | — |
| 433 | C3×C42 | C24 | 1 | 3 | yes | — |
| 434 | C3×C42 | C24 | 1 | 3 | yes | — |
| 435 | C3×C42 | C24 | 1 | 3 | yes | — |
| 436 | #217 | C24 | 1 | 4 | yes | — |
| 437 | #217 | C24 | 1 | 12 | yes | — |
| 438 | #217 | C24 | 1 | 12 | yes | — |
| 439 | #217 | C24 | 1 | 4 | yes | — |
| 440 | #217 | C24 | 1 | 6 | yes | — |
| 441 | #217 | C24 | 1 | 2 | yes | — |
| 442 | (C2×D3)⋊C4 | C24 | 1 | 6 | yes | — |
| 443 | (C2×D3)⋊C4 | C24 | 1 | 6 | yes | — |
| 444 | (C2×D3)⋊C4 | C24 | 1 | 6 | yes | — |
| 445 | (C2×D3)⋊C4 | C24 | 1 | 6 | yes | — |
| 446 | (C2×D3)⋊C4 | C24 | 1 | 12 | yes | — |
| 447 | (C2×D3)⋊C4 | C24 | 1 | 12 | yes | — |
| 448 | (C2×D3)⋊C4 | C24 | 1 | 12 | yes | — |
| 449 | (C2×D3)⋊C4 | C24 | 1 | 12 | yes | — |
| 450 | (C2×D3)⋊C4 | C24 | 1 | 24 | yes | — |
| 451 | C4⋊Dic3 | C24 | 1 | 1 | yes | characteristic |
| 452 | C4⋊Dic3 | C24 | 1 | 1 | yes | characteristic |
| 453 | C4⋊Dic3 | C24 | 1 | 3 | yes | — |
| 454 | C4⋊Dic3 | C24 | 1 | 3 | yes | — |
| 455 | C4⋊Dic3 | C24 | 1 | 6 | yes | — |
| 456 | C4⋊Dic3 | C24 | 1 | 6 | yes | — |
| 457 | C4⋊Dic3 | C24 | 1 | 6 | yes | — |
| 458 | C4⋊Dic3 | C24 | 1 | 6 | yes | — |
| 459 | C4⋊Dic3 | C24 | 1 | 12 | yes | — |
| 460 | C4⋊Dic3 | C24 | 1 | 12 | yes | — |
| 461 | Dic3⋊C4 | C24 | 1 | 12 | yes | — |
| 462 | Dic3⋊C4 | C24 | 1 | 12 | yes | — |
| 463 | Dic3⋊C4 | C24 | 1 | 6 | yes | — |
| 464 | Dic3⋊C4 | C24 | 1 | 6 | yes | — |
| 465 | Dic3⋊C4 | C24 | 1 | 6 | yes | — |
| 466 | Dic3⋊C4 | C24 | 1 | 6 | yes | — |
| 467 | Dic3⋊C4 | C24 | 1 | 24 | yes | — |
| 468 | Dic3⋊C4 | C24 | 1 | 12 | yes | — |
| 469 | Dic3⋊C4 | C24 | 1 | 12 | yes | — |
| 470 | C4×Dic3 | C24 | 1 | 6 | yes | — |
| 471 | C4×Dic3 | C24 | 1 | 6 | 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 | 2 | yes | — |
| 476 | C4×Dic3 | C24 | 1 | 24 | yes | — |
| 477 | 2−1+4 | — | 12 | 16 | no | — |
| 478 | C2×#41 | — | 3 | 2 | no | — |
| 479 | C2×#41 | — | 3 | 12 | no | — |
| 480 | C2×#41 | — | 3 | 1 | no | — |
| 481 | C2×#41 | — | 3 | 3 | no | — |
| 482 | C2×#41 | — | 3 | 12 | no | — |
| 483 | C2×#41 | — | 3 | 12 | no | — |
| 484 | C22×Q8 | — | 3 | 2 | no | — |
| 485 | C22×Q8 | — | 3 | 12 | no | — |
| 486 | C22×Q8 | — | 4 | 8 | no | — |
| 487 | C22×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 488 | C22×Q8 | C22×D3 | 1 | 4 | yes | — |
| 489 | C22×Q8 | C22×D3 | 1 | 6 | yes | — |
| 490 | C22×Q8 | C22×D3 | 1 | 12 | yes | — |
| 491 | C22×D4 | C22×D3 | 1 | 1 | yes | characteristic |
| 492 | C23×C4 | C22×D3 | 1 | 6 | yes | — |
| 493 | C4⋊Q8 | — | 3 | 12 | no | — |
| 494 | C4⋊Q8 | — | 3 | 6 | no | — |
| 495 | C4⋊Q8 | — | 3 | 24 | no | — |
| 496 | C4⋊Q8 | — | 3 | 6 | no | — |
| 497 | C4⋊Q8 | — | 3 | 12 | no | — |
| 498 | C4⋊Q8 | — | 3 | 6 | no | — |
| 499 | C4⋊Q8 | — | 3 | 6 | no | — |
| 500 | C4⋊Q8 | — | 3 | 3 | no | — |
| 501 | C4⋊Q8 | — | 3 | 3 | no | — |
| 502 | C4⋊Q8 | — | 3 | 3 | no | — |
| 503 | C4⋊Q8 | C22×D3 | 1 | 6 | yes | — |
| 504 | C4⋊Q8 | C22×D3 | 1 | 6 | yes | — |
| 505 | C4⋊Q8 | C22×D3 | 1 | 6 | yes | — |
| 506 | C4⋊Q8 | C22×D3 | 1 | 6 | yes | — |
| 507 | #127 | — | 3 | 2 | no | — |
| 508 | #127 | — | 3 | 6 | no | — |
| 509 | #127 | — | 3 | 3 | no | — |
| 510 | #126 | — | 3 | 12 | no | — |
| 511 | #126 | — | 3 | 24 | no | — |
| 512 | #126 | — | 3 | 12 | no | — |
| 513 | #126 | — | 3 | 12 | no | — |
| 514 | #126 | — | 3 | 24 | no | — |
| 515 | #125 | — | 3 | 6 | no | — |
| 516 | #125 | — | 3 | 6 | no | — |
| 517 | #125 | — | 3 | 6 | no | — |
| 518 | #125 | — | 3 | 12 | no | — |
| 519 | #125 | — | 3 | 12 | no | — |
| 520 | #125 | — | 3 | 24 | no | — |
| 521 | #125 | — | 3 | 6 | no | — |
| 522 | #124 | — | 3 | 6 | no | — |
| 523 | #124 | — | 3 | 12 | no | — |
| 524 | #124 | — | 3 | 24 | no | — |
| 525 | #124 | — | 3 | 2 | no | — |
| 526 | #124 | — | 3 | 6 | no | — |
| 527 | #124 | — | 3 | 12 | no | — |
| 528 | #124 | — | 3 | 12 | no | — |
| 529 | #124 | — | 3 | 24 | no | — |
| 530 | #124 | — | 3 | 6 | no | — |
| 531 | #123 | — | 3 | 12 | no | — |
| 532 | #123 | — | 3 | 12 | no | — |
| 533 | #123 | — | 3 | 24 | no | — |
| 534 | #123 | — | 3 | 12 | no | — |
| 535 | #123 | — | 3 | 24 | no | — |
| 536 | #123 | — | 3 | 12 | no | — |
| 537 | #123 | — | 3 | 12 | no | — |
| 538 | #123 | — | 3 | 24 | no | — |
| 539 | C22⋊Q8 | — | 3 | 6 | no | — |
| 540 | C22⋊Q8 | — | 3 | 12 | no | — |
| 541 | C22⋊Q8 | — | 3 | 6 | no | — |
| 542 | C22⋊Q8 | — | 3 | 12 | no | — |
| 543 | C22⋊Q8 | — | 3 | 24 | no | — |
| 544 | C22⋊Q8 | — | 3 | 24 | no | — |
| 545 | C22⋊Q8 | — | 3 | 6 | no | — |
| 546 | C22⋊Q8 | — | 3 | 12 | no | — |
| 547 | C22⋊Q8 | — | 3 | 12 | no | — |
| 548 | C22⋊Q8 | — | 3 | 12 | no | — |
| 549 | C22⋊Q8 | — | 3 | 6 | no | — |
| 550 | C22⋊Q8 | — | 3 | 6 | no | — |
| 551 | C22⋊Q8 | — | 3 | 6 | no | — |
| 552 | C22⋊Q8 | — | 3 | 6 | no | — |
| 553 | C22⋊Q8 | — | 3 | 12 | no | — |
| 554 | C22⋊Q8 | — | 3 | 12 | no | — |
| 555 | C22⋊Q8 | — | 3 | 24 | no | — |
| 556 | C22⋊Q8 | C22×D3 | 1 | 12 | yes | — |
| 557 | C22⋊Q8 | C22×D3 | 1 | 12 | yes | — |
| 558 | C22⋊Q8 | C22×D3 | 1 | 24 | yes | — |
| 559 | #121 | — | 3 | 2 | no | — |
| 560 | #121 | — | 3 | 6 | no | — |
| 561 | #121 | — | 3 | 2 | no | — |
| 562 | #121 | — | 3 | 6 | no | — |
| 563 | #121 | — | 3 | 6 | no | — |
| 564 | #121 | — | 3 | 12 | no | — |
| 565 | #121 | — | 3 | 12 | no | — |
| 566 | #121 | — | 3 | 12 | no | — |
| 567 | #121 | — | 3 | 6 | no | — |
| 568 | #121 | — | 3 | 6 | no | — |
| 569 | #121 | — | 3 | 6 | no | — |
| 570 | #121 | — | 3 | 12 | no | — |
| 571 | #121 | — | 3 | 6 | no | — |
| 572 | #121 | — | 3 | 12 | no | — |
| 573 | #121 | — | 3 | 12 | no | — |
| 574 | #121 | — | 3 | 24 | no | — |
| 575 | #120 | — | 3 | 4 | no | — |
| 576 | #120 | — | 3 | 12 | no | — |
| 577 | C4×Q8 | — | 3 | 2 | no | — |
| 578 | C4×Q8 | — | 3 | 2 | no | — |
| 579 | C4×Q8 | — | 3 | 12 | no | — |
| 580 | C4×Q8 | — | 3 | 12 | no | — |
| 581 | C4×Q8 | — | 3 | 6 | no | — |
| 582 | C4×Q8 | — | 3 | 12 | no | — |
| 583 | C4×Q8 | — | 3 | 12 | no | — |
| 584 | C4×Q8 | — | 3 | 6 | no | — |
| 585 | C4×Q8 | — | 3 | 3 | no | — |
| 586 | C4×Q8 | — | 3 | 3 | no | — |
| 587 | C4×Q8 | — | 3 | 3 | no | — |
| 588 | C4×Q8 | — | 3 | 3 | no | — |
| 589 | C4×Q8 | — | 3 | 6 | no | — |
| 590 | C4×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 591 | C4×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 592 | C4×Q8 | C22×D3 | 1 | 3 | yes | — |
| 593 | C4×Q8 | C22×D3 | 1 | 3 | yes | — |
| 594 | C4×D4 | — | 3 | 6 | no | — |
| 595 | C4×D4 | — | 3 | 6 | no | — |
| 596 | C4×D4 | — | 3 | 6 | no | — |
| 597 | C4×D4 | — | 3 | 6 | no | — |
| 598 | C4×D4 | — | 3 | 24 | no | — |
| 599 | C4×D4 | — | 3 | 12 | no | — |
| 600 | C4×D4 | — | 3 | 12 | no | — |
| 601 | C4×D4 | — | 3 | 24 | no | — |
| 602 | C4×D4 | — | 3 | 6 | no | — |
| 603 | C4×D4 | — | 3 | 12 | no | — |
| 604 | C4×D4 | — | 3 | 12 | no | — |
| 605 | C4×D4 | — | 3 | 6 | no | — |
| 606 | C4×D4 | — | 3 | 3 | no | — |
| 607 | C4×D4 | — | 3 | 3 | no | — |
| 608 | C4×D4 | — | 3 | 3 | no | — |
| 609 | C4×D4 | — | 3 | 3 | no | — |
| 610 | C4×D4 | — | 3 | 6 | no | — |
| 611 | C4×D4 | C22×D3 | 1 | 6 | yes | — |
| 612 | C4×D4 | C22×D3 | 1 | 6 | yes | — |
| 613 | C4×D4 | C22×D3 | 1 | 6 | yes | — |
| 614 | C4×D4 | C22×D3 | 1 | 6 | yes | — |
| 615 | #117 | — | 3 | 1 | no | — |
| 616 | #117 | — | 3 | 3 | no | — |
| 617 | #117 | — | 3 | 12 | no | — |
| 618 | #117 | — | 3 | 12 | no | — |
| 619 | #117 | — | 3 | 6 | no | — |
| 620 | #117 | — | 3 | 12 | no | — |
| 621 | #117 | — | 3 | 12 | no | — |
| 622 | #117 | — | 3 | 6 | no | — |
| 623 | #117 | — | 3 | 6 | no | — |
| 624 | C2×C4⋊C4 | — | 3 | 6 | no | — |
| 625 | C2×C4⋊C4 | — | 3 | 12 | no | — |
| 626 | C2×C4⋊C4 | — | 3 | 12 | no | — |
| 627 | C2×C4⋊C4 | C22×D3 | 1 | 3 | yes | — |
| 628 | C2×C4⋊C4 | C22×D3 | 1 | 3 | yes | — |
| 629 | C2×C4⋊C4 | C22×D3 | 1 | 6 | yes | — |
| 630 | C2×C22⋊C4 | C22×D3 | 1 | 6 | yes | — |
| 631 | C2×C42 | — | 3 | 6 | no | — |
| 632 | C2×C42 | — | 3 | 6 | no | — |
| 633 | C2×C42 | C22×D3 | 1 | 3 | yes | — |
| 634 | C23×C3 | — | 2 | 4 | no | — |
| 635 | C23×C3 | — | 4 | 2 | no | — |
| 636 | C23×C3 | — | 4 | 2 | no | — |
| 637 | C23×C3 | C25 | 1 | 4 | yes | — |
| 638 | C23×C3 | C25 | 1 | 1 | yes | characteristic |
| 639 | C22×D3 | C25 | 1 | 2 | yes | — |
| 640 | C22×D3 | C25 | 1 | 6 | yes | — |
| 641 | C3×Q8 | — | 2 | 24 | no | — |
| 642 | C3×Q8 | — | 2 | 6 | no | — |
| 643 | C3×Q8 | — | 4 | 12 | no | — |
| 644 | C3×Q8 | H(5,𝔽2) | 1 | 4 | yes | — |
| 645 | C3×D4 | — | 2 | 4 | no | — |
| 646 | C3×D4 | — | 2 | 4 | no | — |
| 647 | C2×C3×C4 | — | 2 | 24 | no | — |
| 648 | C2×C3×C4 | — | 2 | 6 | no | — |
| 649 | C2×C3×C4 | — | 4 | 6 | no | — |
| 650 | C2×C3×C4 | — | 4 | 12 | no | — |
| 651 | C2×C3×C4 | — | 4 | 3 | no | — |
| 652 | C2×C3×C4 | 2−1+4 | 1 | 4 | yes | complemented |
| 653 | C2×C3×C4 | C25 | 1 | 3 | yes | — |
| 654 | C2×C3×C4 | C25 | 1 | 12 | yes | — |
| 655 | C2×C3×C4 | C25 | 1 | 3 | yes | — |
| 656 | C2×C3×C4 | C25 | 1 | 3 | yes | — |
| 657 | C2×C3×C4 | C25 | 1 | 3 | yes | — |
| 658 | C2×C3×C4 | C25 | 1 | 1 | yes | characteristic |
| 659 | C2×C3×C4 | C25 | 1 | 1 | yes | characteristic |
| 660 | #67 | — | 2 | 4 | no | — |
| 661 | #67 | — | 2 | 12 | no | — |
| 662 | #67 | — | 4 | 12 | no | — |
| 663 | #67 | — | 4 | 4 | no | — |
| 664 | #67 | — | 4 | 12 | no | — |
| 665 | #67 | — | 4 | 4 | no | — |
| 666 | C2×Dic3 | C25 | 1 | 6 | yes | — |
| 667 | C2×Dic3 | C25 | 1 | 6 | yes | — |
| 668 | C2×Dic3 | C25 | 1 | 2 | yes | — |
| 669 | C2×Dic3 | C25 | 1 | 2 | yes | — |
| 670 | C2×Dic3 | C25 | 1 | 2 | yes | — |
| 671 | C2×Dic3 | C25 | 1 | 6 | yes | — |
| 672 | D12 | — | 2 | 12 | no | — |
| 673 | D12 | — | 2 | 6 | no | — |
| 674 | D12 | — | 2 | 2 | no | — |
| 675 | D12 | — | 4 | 6 | no | — |
| 676 | D12 | — | 4 | 12 | no | — |
| 677 | C4×D3 | — | 2 | 12 | no | — |
| 678 | C4×D3 | — | 2 | 12 | no | — |
| 679 | C4×D3 | — | 2 | 4 | no | — |
| 680 | C4×D3 | — | 2 | 12 | no | — |
| 681 | C4×D3 | — | 4 | 6 | no | — |
| 682 | C4×D3 | — | 4 | 6 | no | — |
| 683 | C4×D3 | — | 4 | 24 | no | — |
| 684 | Dic6 | — | 2 | 12 | no | — |
| 685 | Dic6 | — | 2 | 6 | no | — |
| 686 | Dic6 | — | 2 | 2 | no | — |
| 687 | Dic6 | — | 4 | 6 | no | — |
| 688 | Dic6 | — | 4 | 12 | no | — |
| 689 | C24 | C23×D3 | 1 | 2 | yes | — |
| 690 | #41 | — | 6 | 8 | no | — |
| 691 | #41 | — | 6 | 4 | no | — |
| 692 | #41 | — | 6 | 12 | no | — |
| 693 | #41 | — | 12 | 24 | no | — |
| 694 | #41 | — | 12 | 24 | no | — |
| 695 | #41 | — | 12 | 24 | no | — |
| 696 | C2×Q8 | — | 2 | 4 | no | — |
| 697 | C2×Q8 | — | 2 | 16 | no | — |
| 698 | C2×Q8 | — | 3 | 1 | no | — |
| 699 | C2×Q8 | — | 3 | 3 | no | — |
| 700 | C2×Q8 | — | 3 | 6 | no | — |
| 701 | C2×Q8 | — | 3 | 6 | no | — |
| 702 | C2×Q8 | — | 3 | 12 | no | — |
| 703 | C2×Q8 | — | 4 | 12 | no | — |
| 704 | C2×Q8 | — | 4 | 24 | no | — |
| 705 | C2×Q8 | — | 6 | 8 | no | — |
| 706 | C2×Q8 | — | 12 | 24 | no | — |
| 707 | C2×Q8 | C23×D3 | 1 | 12 | yes | — |
| 708 | C2×Q8 | C23×D3 | 1 | 3 | yes | — |
| 709 | C2×Q8 | C23×D3 | 1 | 12 | yes | — |
| 710 | C2×Q8 | C23×D3 | 1 | 1 | yes | characteristic |
| 711 | C2×D4 | — | 2 | 4 | no | — |
| 712 | C2×D4 | — | 3 | 2 | no | — |
| 713 | C2×D4 | — | 3 | 6 | no | — |
| 714 | C2×D4 | — | 3 | 4 | no | — |
| 715 | C2×D4 | — | 3 | 12 | no | — |
| 716 | C2×D4 | — | 3 | 12 | no | — |
| 717 | C2×D4 | — | 3 | 4 | no | — |
| 718 | C2×D4 | — | 3 | 1 | no | — |
| 719 | C2×D4 | — | 3 | 3 | no | — |
| 720 | C2×D4 | — | 3 | 6 | no | — |
| 721 | C2×D4 | — | 3 | 6 | no | — |
| 722 | C2×D4 | — | 3 | 12 | no | — |
| 723 | C2×D4 | C23×D3 | 1 | 2 | yes | — |
| 724 | C2×D4 | C23×D3 | 1 | 2 | yes | — |
| 725 | C22×C4 | — | 3 | 2 | no | — |
| 726 | C22×C4 | — | 3 | 6 | no | — |
| 727 | C22×C4 | — | 3 | 6 | no | — |
| 728 | C22×C4 | — | 3 | 6 | no | — |
| 729 | C22×C4 | — | 3 | 6 | no | — |
| 730 | C22×C4 | — | 3 | 6 | no | — |
| 731 | C22×C4 | — | 3 | 24 | no | — |
| 732 | C22×C4 | — | 4 | 12 | no | — |
| 733 | C22×C4 | C23×D3 | 1 | 3 | yes | — |
| 734 | C22×C4 | C23×D3 | 1 | 12 | yes | — |
| 735 | C22×C4 | C23×D3 | 1 | 3 | yes | — |
| 736 | C22×C4 | C23×D3 | 1 | 6 | yes | — |
| 737 | C22×C4 | C23×D3 | 1 | 12 | yes | — |
| 738 | C22×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 739 | C4⋊C4 | — | 3 | 3 | no | — |
| 740 | C4⋊C4 | — | 3 | 12 | no | — |
| 741 | C4⋊C4 | — | 3 | 6 | no | — |
| 742 | C4⋊C4 | — | 3 | 6 | no | — |
| 743 | C4⋊C4 | — | 3 | 24 | no | — |
| 744 | C4⋊C4 | — | 3 | 12 | no | — |
| 745 | C4⋊C4 | — | 3 | 3 | no | — |
| 746 | C4⋊C4 | — | 3 | 6 | no | — |
| 747 | C4⋊C4 | — | 3 | 6 | no | — |
| 748 | C4⋊C4 | — | 3 | 1 | no | — |
| 749 | C4⋊C4 | — | 3 | 1 | no | — |
| 750 | C4⋊C4 | — | 3 | 6 | no | — |
| 751 | C4⋊C4 | — | 3 | 6 | no | — |
| 752 | C4⋊C4 | — | 3 | 6 | no | — |
| 753 | C4⋊C4 | — | 3 | 6 | no | — |
| 754 | C4⋊C4 | — | 3 | 12 | no | — |
| 755 | C4⋊C4 | — | 3 | 12 | no | — |
| 756 | C4⋊C4 | — | 3 | 12 | no | — |
| 757 | C4⋊C4 | — | 3 | 12 | no | — |
| 758 | C4⋊C4 | C23×D3 | 1 | 6 | yes | — |
| 759 | C4⋊C4 | C23×D3 | 1 | 3 | yes | — |
| 760 | C4⋊C4 | C23×D3 | 1 | 12 | yes | — |
| 761 | C4⋊C4 | C23×D3 | 1 | 3 | yes | — |
| 762 | C4⋊C4 | C23×D3 | 1 | 12 | yes | — |
| 763 | C4⋊C4 | C23×D3 | 1 | 6 | yes | — |
| 764 | C4⋊C4 | C23×D3 | 1 | 6 | yes | — |
| 765 | C22⋊C4 | — | 3 | 4 | no | — |
| 766 | C22⋊C4 | — | 3 | 12 | no | — |
| 767 | C22⋊C4 | — | 3 | 6 | no | — |
| 768 | C22⋊C4 | — | 3 | 2 | no | — |
| 769 | C22⋊C4 | — | 3 | 12 | no | — |
| 770 | C22⋊C4 | — | 3 | 4 | no | — |
| 771 | C22⋊C4 | — | 3 | 12 | no | — |
| 772 | C22⋊C4 | — | 3 | 6 | no | — |
| 773 | C22⋊C4 | — | 3 | 24 | no | — |
| 774 | C22⋊C4 | — | 3 | 6 | no | — |
| 775 | C22⋊C4 | — | 3 | 6 | no | — |
| 776 | C22⋊C4 | — | 3 | 6 | no | — |
| 777 | C22⋊C4 | — | 3 | 12 | no | — |
| 778 | C22⋊C4 | — | 3 | 12 | no | — |
| 779 | C22⋊C4 | — | 3 | 12 | no | — |
| 780 | C22⋊C4 | C23×D3 | 1 | 12 | yes | — |
| 781 | C22⋊C4 | C23×D3 | 1 | 12 | yes | — |
| 782 | C42 | — | 3 | 2 | no | — |
| 783 | C42 | — | 3 | 6 | no | — |
| 784 | C42 | — | 3 | 6 | no | — |
| 785 | C42 | — | 3 | 6 | no | — |
| 786 | C42 | — | 3 | 6 | no | — |
| 787 | C42 | — | 3 | 6 | no | — |
| 788 | C42 | — | 3 | 24 | no | — |
| 789 | C42 | C23×D3 | 1 | 3 | yes | — |
| 790 | C42 | C23×D3 | 1 | 3 | yes | — |
| 791 | C42 | C23×D3 | 1 | 3 | yes | — |
| 792 | C42 | C23×D3 | 1 | 3 | yes | — |
| 793 | C22×C3 | — | 2 | 1 | no | — |
| 794 | C22×C3 | — | 2 | 1 | no | — |
| 795 | C22×C3 | — | 2 | 4 | no | — |
| 796 | C22×C3 | — | 2 | 4 | no | — |
| 797 | C22×C3 | — | 2 | 4 | no | — |
| 798 | C22×C3 | — | 4 | 8 | no | — |
| 799 | C22×C3 | C2×2−1+4 | 1 | 2 | yes | — |
| 800 | C22×C3 | C26 | 1 | 1 | yes | characteristic |
| 801 | C2×D3 | — | 2 | 2 | no | — |
| 802 | C2×D3 | — | 2 | 6 | no | — |
| 803 | C2×D3 | — | 2 | 2 | no | — |
| 804 | C2×D3 | — | 2 | 6 | no | — |
| 805 | C2×D3 | — | 2 | 2 | no | — |
| 806 | C2×D3 | — | 2 | 6 | no | — |
| 807 | C3×C4 | — | 2 | 12 | no | — |
| 808 | C3×C4 | — | 2 | 3 | no | — |
| 809 | C3×C4 | — | 2 | 3 | no | — |
| 810 | C3×C4 | — | 2 | 3 | no | — |
| 811 | C3×C4 | C2×H(5,𝔽2) | 1 | 6 | yes | — |
| 812 | C3×C4 | C2×2−1+4 | 1 | 2 | yes | — |
| 813 | C3×C4 | C2×2−1+4 | 1 | 2 | yes | — |
| 814 | Dic3 | — | 2 | 6 | no | — |
| 815 | Dic3 | — | 2 | 2 | no | — |
| 816 | Dic3 | — | 2 | 6 | no | — |
| 817 | Dic3 | — | 2 | 2 | no | — |
| 818 | Dic3 | — | 2 | 6 | no | — |
| 819 | Dic3 | — | 2 | 2 | no | — |
| 820 | C23 | — | 2 | 4 | no | — |
| 821 | C23 | — | 3 | 2 | no | — |
| 822 | C23 | — | 3 | 6 | no | — |
| 823 | C23 | — | 4 | 2 | no | — |
| 824 | C23 | — | 4 | 2 | no | — |
| 825 | C23 | C24×D3 | 1 | 4 | yes | — |
| 826 | C23 | C24×D3 | 1 | 1 | yes | characteristic |
| 827 | Q8 | — | 2 | 6 | no | — |
| 828 | Q8 | — | 2 | 24 | no | — |
| 829 | Q8 | — | 4 | 12 | no | — |
| 830 | Q8 | — | 6 | 12 | no | — |
| 831 | Q8 | — | 6 | 2 | no | — |
| 832 | Q8 | — | 6 | 6 | no | — |
| 833 | Q8 | — | 12 | 12 | no | — |
| 834 | Q8 | — | 12 | 6 | no | — |
| 835 | Q8 | #1004 | 1 | 4 | yes | — |
| 836 | D4 | — | 2 | 4 | no | — |
| 837 | D4 | — | 2 | 4 | no | — |
| 838 | D4 | — | 6 | 4 | no | — |
| 839 | D4 | — | 6 | 12 | no | — |
| 840 | D4 | — | 6 | 12 | no | — |
| 841 | D4 | — | 6 | 2 | no | — |
| 842 | D4 | — | 6 | 6 | no | — |
| 843 | D4 | — | 12 | 12 | no | — |
| 844 | D4 | — | 12 | 6 | no | — |
| 845 | D4 | — | 12 | 4 | no | — |
| 846 | D4 | — | 12 | 12 | no | — |
| 847 | D4 | — | 12 | 4 | no | — |
| 848 | D4 | — | 12 | 12 | no | — |
| 849 | C2×C4 | — | 2 | 6 | no | — |
| 850 | C2×C4 | — | 2 | 24 | no | — |
| 851 | C2×C4 | — | 3 | 6 | no | — |
| 852 | C2×C4 | — | 3 | 2 | no | — |
| 853 | C2×C4 | — | 3 | 6 | no | — |
| 854 | C2×C4 | — | 3 | 2 | no | — |
| 855 | C2×C4 | — | 3 | 2 | no | — |
| 856 | C2×C4 | — | 3 | 6 | no | — |
| 857 | C2×C4 | — | 4 | 12 | no | — |
| 858 | C2×C4 | — | 4 | 6 | no | — |
| 859 | C2×C4 | — | 4 | 3 | no | — |
| 860 | C2×C4 | — | 6 | 12 | no | — |
| 861 | C2×C4 | — | 6 | 12 | no | — |
| 862 | C2×C4 | — | 6 | 12 | no | — |
| 863 | C2×C4 | — | 6 | 4 | no | — |
| 864 | C2×C4 | — | 12 | 24 | no | — |
| 865 | C2×C4 | — | 12 | 6 | no | — |
| 866 | C2×C4 | — | 12 | 6 | no | — |
| 867 | C2×C4 | #1007 | 1 | 4 | yes | complemented |
| 868 | C2×C4 | C24×D3 | 1 | 3 | yes | — |
| 869 | C2×C4 | C24×D3 | 1 | 3 | yes | — |
| 870 | C2×C4 | C24×D3 | 1 | 12 | yes | — |
| 871 | C2×C4 | C24×D3 | 1 | 3 | yes | — |
| 872 | C2×C4 | C24×D3 | 1 | 3 | yes | — |
| 873 | C2×C4 | C24×D3 | 1 | 1 | yes | characteristic |
| 874 | C2×C4 | C24×D3 | 1 | 1 | yes | characteristic |
| 875 | C2×C3 | — | 2 | 2 | no | — |
| 876 | C2×C3 | — | 4 | 4 | no | — |
| 877 | C2×C3 | C22×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 878 | C2×C3 | C22×2−1+4 | 1 | 1 | yes | characteristic |
| 879 | C2×C3 | 2−1+6 | 1 | 1 | yes | characteristic |
| 880 | D3 | — | 4 | 2 | no | — |
| 881 | D3 | — | 4 | 6 | no | — |
| 882 | C22 | — | 2 | 1 | no | — |
| 883 | C22 | — | 2 | 1 | no | — |
| 884 | C22 | — | 2 | 4 | no | — |
| 885 | C22 | — | 2 | 4 | no | — |
| 886 | C22 | — | 2 | 4 | no | — |
| 887 | C22 | — | 4 | 8 | no | — |
| 888 | C22 | — | 6 | 2 | no | — |
| 889 | C22 | — | 6 | 6 | no | — |
| 890 | C22 | — | 6 | 2 | no | — |
| 891 | C22 | — | 6 | 6 | no | — |
| 892 | C22 | — | 6 | 2 | no | — |
| 893 | C22 | — | 6 | 6 | no | — |
| 894 | C22 | C2×#1007 | 1 | 2 | yes | — |
| 895 | C22 | C25×D3 | 1 | 1 | yes | characteristic |
| 896 | C4 | — | 2 | 3 | no | — |
| 897 | C4 | — | 2 | 12 | no | — |
| 898 | C4 | — | 2 | 3 | no | — |
| 899 | C4 | — | 2 | 3 | no | — |
| 900 | C4 | — | 6 | 2 | no | — |
| 901 | C4 | — | 6 | 6 | no | — |
| 902 | C4 | — | 6 | 6 | no | — |
| 903 | C4 | — | 6 | 2 | no | — |
| 904 | C4 | — | 6 | 2 | no | — |
| 905 | C4 | — | 6 | 6 | no | — |
| 906 | C4 | C2×#1004 | 1 | 6 | yes | — |
| 907 | C4 | C2×#1007 | 1 | 2 | yes | — |
| 908 | C4 | C2×#1007 | 1 | 2 | yes | — |
| 909 | C3 | #62913 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 910 | C2 | — | 2 | 2 | no | — |
| 911 | C2 | — | 4 | 4 | no | — |
| 912 | C2 | — | 12 | 2 | no | — |
| 913 | C2 | — | 12 | 6 | no | — |
| 914 | C2 | C22×#1004 | 1 | 1 | yes | characteristic |
| 915 | C2 | C22×#1007 | 1 | 1 | yes | characteristic |
| 916 | C2 | #87571 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C25×D3 |
| commutator, socle, cosocle | C22×C3 | C26 |
| Fitting | C2×C3×D4×Q8 | C2 |
| hypercenter | C2×D4×Q8 | D3 |
| hypocenter | C3 | #62913 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C22 ◁ C2×D4×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C3×D4×Q8 | C2 | semidirect |
| 2. #87251 | C2 | semidirect |
| 3. #86765 | C2 | semidirect |
| 4. #86764 | C2 | semidirect |
| 5. #86763 | C2 | semidirect |
| 6. #86760 | C2 | semidirect |
| 7. #86755 | C2 | semidirect |
| 8. #86753 | C2 | semidirect |
| 9. #86750 | C2 | semidirect |
| 10. #86746 | C2 | semidirect |
| 11. #86215 | C2 | semidirect |
| 12. #86205 | C2 | semidirect |
| 13. #85991 | C2 | semidirect |
| 14. Q8×#235 | C2 | semidirect |
| 15. #85802 | C2 | semidirect |
| 16. #85788 | C2 | semidirect |
| 17. #85777 | C2 | semidirect |
| 20. C2×#1007 | C22 | semidirect |
| 31. #5817 | C22 | semidirect |
| 32. #5817 | C22 | semidirect |
| 33. #5816 | C22 | semidirect |
| 34. #5816 | C22 | semidirect |
| 37. Q8×#67 | C22 | semidirect |
| 38. Q8×#67 | C22 | semidirect |
| 39. #5812 | C22 | semidirect |
| 44. #5734 | C22 | semidirect |
| 45. #5733 | C22 | semidirect |
| 46. #5732 | C22 | semidirect |
| 47. #5730 | C22 | semidirect |
| 48. #5730 | C22 | semidirect |
| 49. #5729 | C22 | semidirect |
| 50. #5728 | C22 | semidirect |
| 51. #5728 | C22 | semidirect |
| 52. #5727 | C22 | semidirect |
| 53. #5726 | C22 | semidirect |
| 54. #5725 | C22 | semidirect |
| 55. D3×C4⋊Q8 | C22 | semidirect |
| 56. #5722 | C22 | semidirect |
| 57. #5721 | C22 | semidirect |
| 58. #5647 | C22 | semidirect |
| 59. #5646 | C22 | semidirect |
| 60. #5643 | C22 | semidirect |
| 61. #5641 | C22 | semidirect |
| 62. #5640 | C22 | semidirect |
| 63. #5639 | C22 | semidirect |
| 64. #5638 | C22 | semidirect |
| 65. #5633 | C22 | semidirect |
| 66. #5631 | C22 | semidirect |
| 67. #5629 | C22 | semidirect |
| 68. #5628 | C22 | semidirect |
| 69. #5625 | C22 | semidirect |
| 70. #5585 | C22 | semidirect |
| 71. #5584 | C22 | semidirect |
| 72. #5580 | C22 | semidirect |
| 73. #5579 | C22 | semidirect |
| 74. #5578 | C22 | semidirect |
| 75. #5577 | C22 | semidirect |
| 76. Q8×D12 | C22 | semidirect |
| 77. C4×#239 | C22 | semidirect |
| 78. C4×D3×Q8 | C22 | semidirect |
| 79. #5570 | C22 | semidirect |
| 80. #5567 | C22 | semidirect |
| 81. Q8×Dic6 | C22 | semidirect |
| 124. C2×D4×Q8 | D3 | semidirect |
| 652. C2×C3×C4 | 2−1+4 | semidirect |
| 867. C2×C4 | #1007 | semidirect |
| 909. C3 | #62913 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D4×Q8 | 2 |
| #87251 | 2 |
| #86765 | 2 |
| #86764 | 2 |
| #86763 | 2 |
| #86760 | 2 |
| #86755 | 2 |
| #86753 | 2 |
| #86750 | 2 |
| #86746 | 2 |
| #86215 | 2 |
| #86205 | 2 |
| #85991 | 2 |
| Q8×#235 | 2 |
| #85802 | 2 |
| #85788 | 2 |
| #85777 | 2 |
| #62913 | 3 |