Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
994 conjugacy classes of subgroups.
The subgroup lattice has 788 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #87054 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #81777 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #80402 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #80382 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C3×#1620 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #71945 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #71281 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #71035 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #71029 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #68392 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #68384 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #68274 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #68251 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #68238 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | #68234 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | #18594 | — | 3 | 1 | no | maximal, Sylow |
| 17 | C3×#559 | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×#916 | — | 2 | 1 | no | — |
| 19 | #5717 | C22 | 1 | 1 | yes | characteristic |
| 20 | #5716 | C22 | 1 | 1 | yes | characteristic |
| 21 | #5716 | C22 | 1 | 1 | yes | characteristic, complemented |
| 22 | #5682 | — | 2 | 1 | no | — |
| 23 | #5677 | — | 2 | 1 | no | — |
| 24 | #5676 | — | 2 | 1 | no | — |
| 25 | D3×#124 | — | 2 | 1 | no | — |
| 26 | #5658 | — | 2 | 2 | no | — |
| 27 | #5657 | — | 2 | 2 | no | — |
| 28 | #5584 | C22 | 1 | 1 | yes | characteristic |
| 29 | #5580 | C22 | 1 | 1 | yes | characteristic |
| 30 | Q8×D12 | C22 | 1 | 1 | yes | characteristic |
| 31 | C4×#239 | C22 | 1 | 1 | yes | characteristic |
| 32 | #5563 | — | 2 | 1 | no | — |
| 33 | #5557 | — | 2 | 1 | no | — |
| 34 | #5554 | — | 2 | 1 | no | — |
| 35 | #5545 | — | 2 | 1 | no | — |
| 36 | C3×#493 | C22 | 1 | 1 | yes | characteristic |
| 37 | C3×#460 | C22 | 1 | 1 | yes | characteristic, complemented |
| 38 | C3×#460 | C22 | 1 | 1 | yes | characteristic, complemented |
| 39 | #5174 | — | 2 | 1 | no | — |
| 40 | #5166 | — | 2 | 1 | no | — |
| 41 | #5165 | — | 2 | 1 | no | — |
| 42 | #5159 | — | 2 | 2 | no | — |
| 43 | #5152 | — | 2 | 2 | no | — |
| 44 | #5072 | C22 | 1 | 1 | yes | characteristic |
| 45 | #5072 | C22 | 1 | 1 | yes | characteristic |
| 46 | #5070 | C22 | 1 | 1 | yes | characteristic |
| 47 | #5070 | C22 | 1 | 1 | yes | characteristic, complemented |
| 48 | #5031 | C22 | 1 | 1 | yes | characteristic, complemented |
| 49 | #5020 | C22 | 1 | 1 | yes | characteristic, complemented |
| 50 | #4846 | C22 | 1 | 1 | yes | characteristic |
| 51 | #4841 | C22 | 1 | 1 | yes | characteristic |
| 52 | #4837 | C22 | 1 | 1 | yes | characteristic, complemented |
| 53 | D3×C4⋊C8 | C22 | 1 | 1 | yes | characteristic, complemented |
| 54 | #4787 | — | 2 | 1 | no | — |
| 55 | #4782 | — | 2 | 1 | no | — |
| 56 | #4772 | — | 2 | 1 | no | — |
| 57 | #4766 | — | 2 | 1 | no | — |
| 58 | C4×ΓL(1,𝔽25) | C22 | 1 | 1 | yes | characteristic, complemented |
| 59 | #4680 | C22 | 1 | 1 | yes | characteristic, complemented |
| 60 | C3×#331 | C22 | 1 | 1 | yes | characteristic |
| 61 | C3×Q8⋊C8 | C22 | 1 | 1 | yes | characteristic, complemented |
| 62 | C3×Q8⋊C8 | C22 | 1 | 1 | yes | characteristic, complemented |
| 63 | #4544 | C22 | 1 | 1 | yes | characteristic |
| 64 | #4535 | C22 | 1 | 1 | yes | characteristic, complemented |
| 65 | #4535 | C22 | 1 | 1 | yes | characteristic, complemented |
| 66 | #4486 | C22 | 1 | 1 | yes | characteristic, complemented |
| 67 | #4483 | C22 | 1 | 1 | yes | characteristic |
| 68 | #4483 | C22 | 1 | 1 | yes | characteristic |
| 69 | #4482 | C22 | 1 | 1 | yes | characteristic, complemented |
| 70 | #4459 | C22 | 1 | 1 | yes | characteristic |
| 71 | #4459 | C22 | 1 | 1 | yes | characteristic |
| 72 | #3514 | — | 3 | 1 | no | — |
| 73 | #3251 | — | 3 | 1 | no | — |
| 74 | #3184 | — | 3 | 1 | no | — |
| 75 | #3035 | — | 3 | 1 | no | — |
| 76 | #1652 | — | 3 | 1 | no | — |
| 77 | #1651 | — | 3 | 1 | no | — |
| 78 | #1640 | — | 3 | 1 | no | — |
| 79 | #1639 | — | 3 | 1 | no | — |
| 80 | #1628 | — | 3 | 1 | no | — |
| 81 | #1627 | — | 3 | 1 | no | — |
| 82 | #1620 | D3 | 1 | 1 | yes | characteristic, complemented |
| 83 | #1619 | — | 3 | 1 | no | — |
| 84 | #1547 | — | 3 | 1 | no | — |
| 85 | #1489 | — | 3 | 1 | no | — |
| 86 | #1483 | — | 3 | 1 | no | — |
| 87 | C2×#239 | D4 | 1 | 1 | yes | characteristic |
| 88 | C2×D3×Q8 | — | 2 | 1 | no | — |
| 89 | C2×#237 | — | 2 | 1 | no | — |
| 90 | C2×#237 | — | 2 | 1 | no | — |
| 91 | C2×D3×D4 | — | 2 | 1 | no | — |
| 92 | C2×D3×D4 | — | 2 | 1 | no | — |
| 93 | C2×C3×SD16 | — | 2 | 1 | no | — |
| 94 | C2×C3×SD16 | — | 2 | 1 | no | — |
| 95 | C2×C3×D8 | — | 2 | 2 | no | — |
| 96 | C3×#127 | C23 | 1 | 1 | yes | characteristic |
| 97 | C3×#127 | C23 | 1 | 1 | yes | characteristic |
| 98 | C3×#124 | — | 2 | 1 | no | — |
| 99 | C3×#124 | — | 2 | 1 | no | — |
| 100 | C3×#123 | — | 2 | 2 | no | — |
| 101 | C3×C4×Q8 | C23 | 1 | 1 | yes | characteristic |
| 102 | C3×C4×Q8 | C23 | 1 | 1 | yes | characteristic |
| 103 | C3×C4×D4 | — | 2 | 1 | no | — |
| 104 | C3×C4×D4 | — | 2 | 1 | no | — |
| 105 | #947 | D4 | 1 | 1 | yes | characteristic |
| 106 | #946 | — | 2 | 1 | no | — |
| 107 | #946 | D4 | 1 | 1 | yes | characteristic |
| 108 | Q8×Dic3 | D4 | 1 | 1 | yes | characteristic |
| 109 | C2×#216 | — | 2 | 1 | no | — |
| 110 | #938 | — | 2 | 1 | no | — |
| 111 | #938 | — | 2 | 1 | no | — |
| 112 | #938 | — | 2 | 1 | no | — |
| 113 | #938 | — | 2 | 1 | no | — |
| 114 | #938 | — | 2 | 1 | no | — |
| 115 | #938 | D4 | 1 | 2 | yes | — |
| 116 | #937 | — | 2 | 2 | no | — |
| 117 | #936 | — | 2 | 1 | no | — |
| 118 | #936 | — | 2 | 1 | no | — |
| 119 | D4×Dic3 | — | 2 | 1 | no | — |
| 120 | D4×Dic3 | — | 2 | 1 | no | — |
| 121 | D4×Dic3 | — | 2 | 1 | no | — |
| 122 | D4×Dic3 | D4 | 1 | 2 | yes | — |
| 123 | C2×#213 | — | 2 | 1 | no | — |
| 124 | C2×#213 | — | 2 | 1 | no | — |
| 125 | #930 | — | 2 | 2 | no | — |
| 126 | C4×#67 | — | 2 | 2 | no | — |
| 127 | C2×(C2×D3)⋊C4 | — | 2 | 2 | no | — |
| 128 | #926 | — | 2 | 2 | no | — |
| 129 | #916 | — | 4 | 4 | no | — |
| 130 | C2×#204 | — | 2 | 1 | no | — |
| 131 | C2×ΓL(1,𝔽25) | — | 2 | 1 | no | — |
| 132 | C2×ΓL(1,𝔽25) | — | 2 | 1 | no | — |
| 133 | C2×D3×C8 | — | 2 | 1 | no | — |
| 134 | #898 | — | 2 | 2 | no | — |
| 135 | #898 | — | 2 | 1 | no | — |
| 136 | #897 | — | 2 | 1 | no | — |
| 137 | #897 | — | 2 | 2 | no | — |
| 138 | #895 | D4 | 1 | 1 | yes | characteristic |
| 139 | #894 | — | 2 | 1 | no | — |
| 140 | #893 | — | 2 | 1 | no | — |
| 141 | #893 | D4 | 1 | 1 | yes | characteristic |
| 142 | #892 | — | 2 | 1 | no | — |
| 143 | #892 | — | 2 | 1 | no | — |
| 144 | #892 | D4 | 1 | 1 | yes | characteristic |
| 145 | #890 | D4 | 1 | 1 | yes | characteristic |
| 146 | #886 | — | 2 | 2 | no | — |
| 147 | #885 | — | 2 | 2 | no | — |
| 148 | #885 | — | 2 | 2 | no | — |
| 149 | #885 | — | 2 | 2 | no | — |
| 150 | #884 | — | 2 | 2 | no | — |
| 151 | #883 | — | 2 | 2 | no | — |
| 152 | #882 | — | 2 | 2 | no | — |
| 153 | #67⋊C4 | — | 2 | 2 | no | — |
| 154 | D3×C22⋊C4 | — | 2 | 2 | no | — |
| 155 | D3×C22⋊C4 | — | 2 | 2 | no | — |
| 156 | #879 | — | 2 | 2 | no | — |
| 157 | #878 | — | 2 | 2 | no | — |
| 158 | #875 | — | 2 | 1 | no | — |
| 159 | C4×D12 | — | 2 | 1 | no | — |
| 160 | C4×D12 | — | 2 | 1 | no | — |
| 161 | C4×D12 | — | 2 | 1 | no | — |
| 162 | C4×D12 | C23 | 1 | 1 | yes | characteristic |
| 163 | C4×D12 | C23 | 1 | 1 | yes | characteristic |
| 164 | #872 | — | 2 | 1 | no | — |
| 165 | C42×D3 | — | 2 | 1 | no | — |
| 166 | C42×D3 | C23 | 1 | 1 | yes | characteristic |
| 167 | #869 | — | 2 | 1 | no | — |
| 168 | #869 | C23 | 1 | 1 | yes | characteristic |
| 169 | #869 | C23 | 1 | 1 | yes | characteristic |
| 170 | C4×Dic6 | — | 2 | 1 | no | — |
| 171 | C3×C4⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 172 | C3×C4⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 173 | C3×#102 | — | 2 | 1 | no | — |
| 174 | C3×#102 | — | 2 | 1 | no | — |
| 175 | C3×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 176 | #835 | — | 2 | 1 | no | — |
| 177 | #832 | — | 2 | 2 | no | — |
| 178 | #832 | — | 2 | 2 | no | — |
| 179 | #832 | — | 2 | 1 | no | — |
| 180 | #832 | — | 2 | 1 | no | — |
| 181 | #821 | — | 2 | 1 | no | — |
| 182 | #818 | — | 2 | 1 | no | — |
| 183 | #817 | — | 2 | 2 | no | — |
| 184 | #816 | — | 2 | 1 | no | — |
| 185 | #815 | — | 2 | 1 | no | — |
| 186 | Dic3⋊C8 | — | 2 | 1 | no | — |
| 187 | Dic3⋊C8 | — | 2 | 1 | no | — |
| 188 | #810 | — | 2 | 1 | no | — |
| 189 | #808 | — | 2 | 1 | no | — |
| 190 | C4⋊(C3⋊C8) | C23 | 1 | 1 | yes | characteristic |
| 191 | C4⋊(C3⋊C8) | C23 | 1 | 1 | yes | characteristic |
| 192 | C4×C3⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 193 | C2×#135 | — | 6 | 1 | no | — |
| 194 | #559 | C2×D3 | 1 | 1 | yes | characteristic |
| 195 | #556 | — | 3 | 1 | no | — |
| 196 | #555 | — | 6 | 1 | no | — |
| 197 | #551 | — | 6 | 2 | no | — |
| 198 | D4×Q8 | — | 3 | 1 | no | — |
| 199 | #548 | — | 6 | 1 | no | — |
| 200 | #546 | — | 6 | 1 | no | — |
| 201 | #546 | — | 6 | 1 | no | — |
| 202 | D42 | — | 3 | 1 | no | — |
| 203 | #542 | — | 6 | 1 | no | — |
| 204 | #538 | — | 6 | 2 | no | — |
| 205 | #532 | — | 3 | 1 | no | — |
| 206 | #532 | — | 3 | 1 | no | — |
| 207 | #529 | — | 3 | 1 | no | — |
| 208 | #529 | — | 6 | 1 | no | — |
| 209 | C2×#124 | — | 6 | 1 | no | — |
| 210 | #518 | — | 6 | 1 | no | — |
| 211 | C4×#41 | — | 3 | 1 | no | — |
| 212 | #498 | — | 3 | 1 | no | — |
| 213 | #493 | C2×D3 | 1 | 1 | yes | characteristic |
| 214 | #486 | — | 3 | 1 | no | — |
| 215 | #486 | — | 3 | 1 | no | — |
| 216 | #478 | — | 6 | 1 | no | — |
| 217 | #475 | — | 3 | 1 | no | — |
| 218 | #474 | — | 3 | 1 | no | — |
| 219 | #469 | — | 6 | 1 | no | — |
| 220 | #469 | — | 6 | 2 | no | — |
| 221 | #468 | — | 6 | 1 | no | — |
| 222 | #464 | — | 6 | 1 | no | — |
| 223 | #463 | — | 6 | 1 | no | — |
| 224 | #463 | — | 6 | 1 | no | — |
| 225 | #462 | — | 3 | 1 | no | — |
| 226 | #461 | — | 3 | 1 | no | — |
| 227 | #460 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 228 | #460 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 229 | #459 | — | 3 | 1 | no | — |
| 230 | #459 | — | 3 | 1 | no | — |
| 231 | #442 | — | 6 | 2 | no | — |
| 232 | #423 | — | 3 | 1 | no | — |
| 233 | C2×C4⋊C8 | — | 3 | 1 | no | — |
| 234 | #416 | — | 6 | 1 | no | — |
| 235 | C4×M16 | — | 3 | 1 | no | — |
| 236 | #332 | — | 3 | 1 | no | — |
| 237 | #332 | — | 3 | 1 | no | — |
| 238 | #331 | — | 3 | 1 | no | — |
| 239 | #331 | C2×D3 | 1 | 1 | yes | characteristic |
| 240 | Q8⋊C8 | — | 3 | 1 | no | — |
| 241 | Q8⋊C8 | — | 3 | 1 | no | — |
| 242 | Q8⋊C8 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 243 | Q8⋊C8 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 244 | D4⋊C8 | — | 3 | 1 | no | — |
| 245 | D4⋊C8 | — | 3 | 1 | no | — |
| 246 | D4⋊C8 | — | 3 | 1 | no | — |
| 247 | D4⋊C8 | — | 3 | 1 | no | — |
| 248 | C23×D3 | — | 2 | 2 | no | — |
| 249 | C2×C3×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 250 | C2×C3×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 251 | C2×C3×D4 | — | 2 | 1 | no | — |
| 252 | C2×C3×D4 | — | 2 | 1 | no | — |
| 253 | C2×C3×D4 | — | 2 | 1 | no | — |
| 254 | C2×C3×D4 | — | 2 | 1 | no | — |
| 255 | C2×C3×D4 | — | 2 | 1 | no | — |
| 256 | C2×C3×D4 | C2×D4 | 1 | 2 | yes | — |
| 257 | C22×C3×C4 | — | 2 | 2 | no | — |
| 258 | C2×#67 | — | 2 | 2 | no | — |
| 259 | C2×#67 | — | 2 | 2 | no | — |
| 260 | C2×#67 | — | 2 | 2 | no | — |
| 261 | C2×#67 | — | 4 | 1 | no | — |
| 262 | C22×Dic3 | — | 2 | 2 | no | — |
| 263 | C22×Dic3 | — | 4 | 1 | no | — |
| 264 | #239 | — | 2 | 2 | no | — |
| 265 | #239 | — | 4 | 1 | no | — |
| 266 | D3×Q8 | — | 8 | 1 | no | — |
| 267 | D3×Q8 | — | 8 | 1 | no | — |
| 268 | #237 | — | 4 | 2 | no | — |
| 269 | #237 | — | 4 | 2 | no | — |
| 270 | #237 | — | 8 | 1 | no | — |
| 271 | #237 | — | 8 | 1 | no | — |
| 272 | D3×D4 | — | 4 | 2 | no | — |
| 273 | D3×D4 | — | 4 | 2 | no | — |
| 274 | D3×D4 | — | 8 | 1 | no | — |
| 275 | D3×D4 | — | 8 | 1 | no | — |
| 276 | C2×D12 | — | 2 | 1 | no | — |
| 277 | C2×D12 | — | 2 | 1 | no | — |
| 278 | C2×D12 | C2×D4 | 1 | 1 | yes | characteristic |
| 279 | C2×D12 | C2×D4 | 1 | 1 | yes | characteristic |
| 280 | C2×C4×D3 | — | 2 | 1 | no | — |
| 281 | C2×C4×D3 | — | 2 | 1 | no | — |
| 282 | C2×C4×D3 | — | 2 | 1 | no | — |
| 283 | C2×C4×D3 | — | 2 | 2 | no | — |
| 284 | C2×C4×D3 | — | 2 | 1 | no | — |
| 285 | C2×C4×D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 286 | C2×C4×D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 287 | C2×C4×D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 288 | C2×Dic6 | — | 2 | 1 | no | — |
| 289 | C2×Dic6 | — | 2 | 1 | no | — |
| 290 | C2×Dic6 | — | 2 | 2 | no | — |
| 291 | C3×SD16 | — | 4 | 2 | no | — |
| 292 | C3×SD16 | — | 8 | 1 | no | — |
| 293 | C3×D8 | — | 4 | 4 | no | — |
| 294 | C2×C3×C8 | — | 2 | 1 | no | — |
| 295 | C2×C3×C8 | — | 2 | 1 | no | — |
| 296 | C2×C3×C8 | — | 2 | 1 | no | — |
| 297 | C3×C4⋊C4 | — | 2 | 1 | no | — |
| 298 | C3×C4⋊C4 | — | 2 | 1 | no | — |
| 299 | C3×C4⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 300 | C3×C4⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 301 | C3×C22⋊C4 | — | 2 | 2 | no | — |
| 302 | C3×C22⋊C4 | — | 2 | 2 | no | — |
| 303 | C3×C22⋊C4 | — | 2 | 2 | no | — |
| 304 | C3×C42 | — | 2 | 1 | no | — |
| 305 | C3×C42 | — | 2 | 1 | no | — |
| 306 | C3×C42 | C24 | 1 | 1 | yes | characteristic |
| 307 | #217 | — | 2 | 2 | no | — |
| 308 | #217 | — | 2 | 2 | no | — |
| 309 | #217 | — | 2 | 2 | no | — |
| 310 | #217 | — | 4 | 1 | no | — |
| 311 | #217 | — | 4 | 1 | no | — |
| 312 | #216 | — | 4 | 2 | no | — |
| 313 | #213 | — | 4 | 2 | no | — |
| 314 | #213 | — | 8 | 1 | no | — |
| 315 | (C2×D3)⋊C4 | — | 2 | 2 | no | — |
| 316 | (C2×D3)⋊C4 | — | 2 | 2 | no | — |
| 317 | (C2×D3)⋊C4 | — | 2 | 2 | no | — |
| 318 | (C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 319 | (C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 320 | (C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 321 | (C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 322 | (C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 323 | (C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 324 | (C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 325 | (C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 326 | C4⋊Dic3 | — | 2 | 2 | no | — |
| 327 | C4⋊Dic3 | — | 2 | 1 | no | — |
| 328 | C4⋊Dic3 | — | 2 | 1 | no | — |
| 329 | C4⋊Dic3 | — | 2 | 1 | no | — |
| 330 | C4⋊Dic3 | — | 2 | 1 | no | — |
| 331 | C4⋊Dic3 | — | 2 | 1 | no | — |
| 332 | C4⋊Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 333 | C4⋊Dic3 | C2×D4 | 1 | 2 | yes | — |
| 334 | C4⋊Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 335 | Dic3⋊C4 | — | 2 | 2 | no | — |
| 336 | Dic3⋊C4 | — | 2 | 1 | no | — |
| 337 | Dic3⋊C4 | — | 2 | 1 | no | — |
| 338 | C4×Dic3 | — | 2 | 2 | no | — |
| 339 | C4×Dic3 | — | 2 | 1 | no | — |
| 340 | C4×Dic3 | — | 2 | 1 | no | — |
| 341 | C4×Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 342 | C4×Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 343 | C4×Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 344 | C2×C3⋊C8 | — | 2 | 1 | no | — |
| 345 | C2×C3⋊C8 | — | 2 | 1 | no | — |
| 346 | C2×C3⋊C8 | — | 2 | 1 | no | — |
| 347 | #204 | — | 4 | 2 | no | — |
| 348 | ΓL(1,𝔽25) | — | 4 | 2 | no | — |
| 349 | ΓL(1,𝔽25) | — | 8 | 1 | no | — |
| 350 | D3×C8 | — | 4 | 2 | no | — |
| 351 | C2×#41 | — | 3 | 1 | no | — |
| 352 | C2×#41 | — | 6 | 1 | no | — |
| 353 | C2×#41 | — | 6 | 1 | no | — |
| 354 | C22×Q8 | — | 6 | 1 | no | — |
| 355 | C22×D4 | — | 6 | 1 | no | — |
| 356 | C22×D4 | — | 6 | 1 | no | — |
| 357 | #135 | — | 12 | 4 | no | — |
| 358 | C2×Q16 | — | 6 | 1 | no | — |
| 359 | C2×SD16 | — | 2 | 1 | no | — |
| 360 | C2×SD16 | — | 2 | 1 | no | — |
| 361 | C2×SD16 | — | 6 | 1 | no | — |
| 362 | C2×D8 | — | 2 | 2 | no | — |
| 363 | C2×D8 | — | 6 | 1 | no | — |
| 364 | C2×D8 | — | 6 | 1 | no | — |
| 365 | C2×M16 | — | 6 | 1 | no | — |
| 366 | C2×M16 | — | 6 | 1 | no | — |
| 367 | C22×C8 | — | 6 | 1 | no | — |
| 368 | C4⋊Q8 | — | 3 | 1 | no | — |
| 369 | C4⋊Q8 | — | 3 | 1 | no | — |
| 370 | C4⋊Q8 | — | 6 | 1 | no | — |
| 371 | #127 | C22×D3 | 1 | 1 | yes | characteristic |
| 372 | #127 | C22×D3 | 1 | 1 | yes | characteristic |
| 373 | #126 | — | 6 | 1 | no | — |
| 374 | #126 | — | 6 | 2 | no | — |
| 375 | #126 | — | 6 | 2 | no | — |
| 376 | #125 | — | 3 | 1 | no | — |
| 377 | #124 | — | 2 | 1 | no | — |
| 378 | #124 | — | 2 | 1 | no | — |
| 379 | #124 | — | 3 | 1 | no | — |
| 380 | #124 | — | 6 | 1 | no | — |
| 381 | #124 | — | 6 | 1 | no | — |
| 382 | #124 | — | 6 | 1 | no | — |
| 383 | #124 | — | 6 | 2 | no | — |
| 384 | #124 | — | 6 | 2 | no | — |
| 385 | #124 | — | 6 | 2 | no | — |
| 386 | #123 | — | 2 | 2 | no | — |
| 387 | #123 | — | 6 | 2 | no | — |
| 388 | #123 | — | 6 | 2 | no | — |
| 389 | #123 | — | 6 | 1 | no | — |
| 390 | C22⋊Q8 | — | 3 | 1 | no | — |
| 391 | C22⋊Q8 | — | 6 | 2 | no | — |
| 392 | C22⋊Q8 | — | 6 | 2 | no | — |
| 393 | C22⋊Q8 | — | 6 | 1 | no | — |
| 394 | C22⋊Q8 | — | 6 | 1 | no | — |
| 395 | #121 | — | 3 | 2 | no | — |
| 396 | #121 | — | 3 | 1 | no | — |
| 397 | #121 | — | 6 | 2 | no | — |
| 398 | #121 | — | 6 | 1 | no | — |
| 399 | #121 | — | 6 | 1 | no | — |
| 400 | #121 | — | 6 | 2 | no | — |
| 401 | #121 | — | 6 | 1 | no | — |
| 402 | #121 | — | 6 | 1 | no | — |
| 403 | #121 | — | 6 | 1 | no | — |
| 404 | #120 | — | 6 | 2 | no | — |
| 405 | #120 | — | 6 | 2 | no | — |
| 406 | C4×Q8 | — | 3 | 1 | no | — |
| 407 | C4×Q8 | — | 6 | 1 | no | — |
| 408 | C4×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 409 | C4×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 410 | C4×D4 | — | 2 | 1 | no | — |
| 411 | C4×D4 | — | 2 | 1 | no | — |
| 412 | C4×D4 | — | 3 | 2 | no | — |
| 413 | C4×D4 | — | 3 | 1 | no | — |
| 414 | C4×D4 | — | 3 | 1 | no | — |
| 415 | C4×D4 | — | 3 | 1 | no | — |
| 416 | C4×D4 | — | 6 | 1 | no | — |
| 417 | C4×D4 | — | 6 | 1 | no | — |
| 418 | C4×D4 | — | 6 | 1 | no | — |
| 419 | C4×D4 | — | 6 | 1 | no | — |
| 420 | C4×D4 | — | 6 | 1 | no | — |
| 421 | C4×D4 | — | 6 | 1 | no | — |
| 422 | C4×D4 | — | 6 | 2 | no | — |
| 423 | C4×D4 | — | 6 | 1 | no | — |
| 424 | C4×D4 | — | 6 | 2 | no | — |
| 425 | #117 | — | 3 | 1 | no | — |
| 426 | #117 | — | 6 | 1 | no | — |
| 427 | #117 | — | 6 | 1 | no | — |
| 428 | #117 | — | 6 | 2 | no | — |
| 429 | #117 | — | 6 | 1 | no | — |
| 430 | C2×C22⋊C4 | — | 6 | 2 | no | — |
| 431 | C2×C22⋊C4 | — | 6 | 2 | no | — |
| 432 | C2×C22⋊C4 | — | 6 | 2 | no | — |
| 433 | C2×C42 | — | 3 | 1 | no | — |
| 434 | C2×C42 | — | 6 | 1 | no | — |
| 435 | #107 | — | 6 | 1 | no | — |
| 436 | #106 | — | 6 | 2 | no | — |
| 437 | #106 | — | 6 | 1 | no | — |
| 438 | C4⋊C8 | — | 3 | 1 | no | — |
| 439 | C4⋊C8 | — | 3 | 1 | no | — |
| 440 | C4⋊C8 | — | 6 | 1 | no | — |
| 441 | C4⋊C8 | — | 6 | 1 | no | — |
| 442 | C4⋊C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 443 | C4⋊C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 444 | #103 | — | 6 | 1 | no | — |
| 445 | #103 | — | 6 | 1 | no | — |
| 446 | #103 | — | 6 | 1 | no | — |
| 447 | #102 | — | 2 | 1 | no | — |
| 448 | #102 | — | 2 | 1 | no | — |
| 449 | #102 | — | 6 | 1 | no | — |
| 450 | #102 | — | 6 | 2 | no | — |
| 451 | #102 | — | 6 | 1 | no | — |
| 452 | #102 | — | 6 | 1 | no | — |
| 453 | #102 | — | 6 | 2 | no | — |
| 454 | #97 | — | 6 | 1 | no | — |
| 455 | C4×C8 | — | 3 | 1 | no | — |
| 456 | C4×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 457 | C23×C3 | — | 2 | 2 | no | — |
| 458 | C23×C3 | — | 4 | 1 | no | — |
| 459 | C22×D3 | — | 2 | 1 | no | — |
| 460 | C22×D3 | — | 2 | 1 | no | — |
| 461 | C22×D3 | — | 4 | 4 | no | — |
| 462 | C22×D3 | — | 8 | 2 | no | — |
| 463 | C22×D3 | — | 8 | 2 | no | — |
| 464 | C22×D3 | #120 | 1 | 1 | yes | characteristic |
| 465 | C3×Q8 | — | 2 | 1 | no | — |
| 466 | C3×Q8 | — | 2 | 1 | no | — |
| 467 | C3×Q8 | — | 2 | 1 | no | — |
| 468 | C3×Q8 | — | 2 | 1 | no | — |
| 469 | C3×D4 | — | 4 | 2 | no | — |
| 470 | C3×D4 | — | 4 | 2 | no | — |
| 471 | C3×D4 | — | 4 | 1 | no | — |
| 472 | C3×D4 | — | 4 | 1 | no | — |
| 473 | C3×D4 | — | 4 | 1 | no | — |
| 474 | C3×D4 | — | 4 | 1 | no | — |
| 475 | C3×D4 | — | 4 | 1 | no | — |
| 476 | C3×D4 | — | 4 | 1 | no | — |
| 477 | C3×D4 | — | 4 | 1 | no | — |
| 478 | C3×D4 | — | 4 | 1 | no | — |
| 479 | C2×C3×C4 | — | 2 | 1 | no | — |
| 480 | C2×C3×C4 | — | 2 | 1 | no | — |
| 481 | C2×C3×C4 | — | 2 | 1 | no | — |
| 482 | C2×C3×C4 | — | 2 | 1 | no | — |
| 483 | C2×C3×C4 | — | 8 | 2 | no | — |
| 484 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 485 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 486 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 487 | #67 | — | 4 | 4 | no | — |
| 488 | #67 | — | 8 | 2 | no | — |
| 489 | #67 | — | 8 | 2 | no | — |
| 490 | #67 | — | 8 | 2 | no | — |
| 491 | C2×Dic3 | — | 2 | 1 | no | — |
| 492 | C2×Dic3 | — | 2 | 1 | no | — |
| 493 | C2×Dic3 | — | 2 | 2 | no | — |
| 494 | C2×Dic3 | — | 4 | 1 | no | — |
| 495 | C2×Dic3 | — | 8 | 2 | no | — |
| 496 | C2×Dic3 | — | 8 | 2 | no | — |
| 497 | C2×Dic3 | #120 | 1 | 1 | yes | characteristic |
| 498 | C2×Dic3 | #120 | 1 | 1 | yes | characteristic |
| 499 | C2×Dic3 | #120 | 1 | 1 | yes | characteristic |
| 500 | D12 | — | 2 | 1 | no | — |
| 501 | D12 | — | 2 | 1 | no | — |
| 502 | D12 | — | 2 | 1 | no | — |
| 503 | D12 | — | 4 | 2 | no | — |
| 504 | D12 | — | 8 | 1 | no | — |
| 505 | D12 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 506 | C4×D3 | — | 2 | 1 | no | — |
| 507 | C4×D3 | — | 2 | 1 | no | — |
| 508 | C4×D3 | — | 2 | 1 | no | — |
| 509 | C4×D3 | — | 2 | 1 | no | — |
| 510 | C4×D3 | — | 4 | 1 | no | — |
| 511 | C4×D3 | — | 4 | 2 | no | — |
| 512 | C4×D3 | — | 4 | 1 | no | — |
| 513 | C4×D3 | — | 4 | 1 | no | — |
| 514 | C4×D3 | — | 4 | 1 | no | — |
| 515 | C4×D3 | — | 4 | 1 | no | — |
| 516 | C4×D3 | — | 8 | 1 | no | — |
| 517 | C4×D3 | — | 8 | 2 | no | — |
| 518 | Dic6 | — | 4 | 1 | no | — |
| 519 | Dic6 | — | 4 | 1 | no | — |
| 520 | Dic6 | — | 4 | 1 | no | — |
| 521 | Dic6 | — | 4 | 1 | no | — |
| 522 | Dic6 | — | 8 | 2 | no | — |
| 523 | C3×C8 | — | 2 | 2 | no | — |
| 524 | C3×C8 | — | 4 | 1 | no | — |
| 525 | C3×C8 | — | 4 | 1 | no | — |
| 526 | C3⋊C8 | — | 4 | 1 | no | — |
| 527 | C3⋊C8 | — | 4 | 1 | no | — |
| 528 | C3⋊C8 | — | 4 | 1 | no | — |
| 529 | C24 | — | 6 | 2 | no | — |
| 530 | #41 | — | 6 | 2 | no | — |
| 531 | #41 | — | 12 | 1 | no | — |
| 532 | #41 | — | 12 | 2 | no | — |
| 533 | #41 | — | 12 | 2 | no | — |
| 534 | #41 | — | 24 | 1 | no | — |
| 535 | #41 | — | 24 | 1 | no | — |
| 536 | C2×Q8 | — | 6 | 2 | no | — |
| 537 | C2×Q8 | — | 6 | 1 | no | — |
| 538 | C2×Q8 | — | 6 | 1 | no | — |
| 539 | C2×Q8 | — | 24 | 1 | no | — |
| 540 | C2×Q8 | — | 24 | 1 | no | — |
| 541 | C2×Q8 | D3×D4 | 1 | 1 | yes | characteristic |
| 542 | C2×Q8 | D3×D4 | 1 | 1 | yes | characteristic |
| 543 | C2×D4 | — | 2 | 1 | no | — |
| 544 | C2×D4 | — | 2 | 1 | no | — |
| 545 | C2×D4 | — | 2 | 1 | no | — |
| 546 | C2×D4 | — | 2 | 1 | no | — |
| 547 | C2×D4 | — | 2 | 1 | no | — |
| 548 | C2×D4 | — | 3 | 1 | no | — |
| 549 | C2×D4 | — | 3 | 1 | no | — |
| 550 | C2×D4 | — | 6 | 1 | no | — |
| 551 | C2×D4 | — | 6 | 1 | no | — |
| 552 | C2×D4 | — | 6 | 2 | no | — |
| 553 | C2×D4 | — | 6 | 2 | no | — |
| 554 | C2×D4 | — | 6 | 2 | no | — |
| 555 | C2×D4 | — | 12 | 2 | no | — |
| 556 | C2×D4 | — | 12 | 2 | no | — |
| 557 | C2×D4 | — | 12 | 1 | no | — |
| 558 | C2×D4 | — | 24 | 1 | no | — |
| 559 | C2×D4 | — | 24 | 1 | no | — |
| 560 | C2×D4 | D3×D4 | 1 | 2 | yes | — |
| 561 | C22×C4 | — | 2 | 2 | no | — |
| 562 | C22×C4 | — | 3 | 1 | no | — |
| 563 | C22×C4 | — | 3 | 1 | no | — |
| 564 | C22×C4 | — | 3 | 1 | no | — |
| 565 | C22×C4 | — | 6 | 1 | no | — |
| 566 | C22×C4 | — | 6 | 1 | no | — |
| 567 | C22×C4 | — | 6 | 2 | no | — |
| 568 | C22×C4 | — | 6 | 2 | no | — |
| 569 | C22×C4 | — | 6 | 1 | no | — |
| 570 | C22×C4 | — | 6 | 1 | no | — |
| 571 | C22×C4 | — | 12 | 1 | no | — |
| 572 | Q16 | — | 12 | 2 | no | — |
| 573 | SD16 | — | 4 | 2 | no | — |
| 574 | SD16 | — | 8 | 1 | no | — |
| 575 | SD16 | — | 12 | 2 | no | — |
| 576 | D8 | — | 4 | 4 | no | — |
| 577 | D8 | — | 12 | 2 | no | — |
| 578 | D8 | — | 24 | 1 | no | — |
| 579 | M16 | — | 12 | 2 | no | — |
| 580 | M16 | — | 24 | 1 | no | — |
| 581 | C2×C8 | — | 2 | 1 | no | — |
| 582 | C2×C8 | — | 2 | 1 | no | — |
| 583 | C2×C8 | — | 2 | 1 | no | — |
| 584 | C2×C8 | — | 6 | 1 | no | — |
| 585 | C2×C8 | — | 6 | 1 | no | — |
| 586 | C2×C8 | — | 6 | 1 | no | — |
| 587 | C2×C8 | — | 12 | 2 | no | — |
| 588 | C4⋊C4 | — | 2 | 1 | no | — |
| 589 | C4⋊C4 | — | 2 | 1 | no | — |
| 590 | C4⋊C4 | — | 3 | 1 | no | — |
| 591 | C4⋊C4 | — | 3 | 2 | no | — |
| 592 | C4⋊C4 | — | 3 | 1 | no | — |
| 593 | C4⋊C4 | — | 6 | 1 | no | — |
| 594 | C4⋊C4 | — | 6 | 1 | no | — |
| 595 | C4⋊C4 | — | 6 | 1 | no | — |
| 596 | C4⋊C4 | — | 6 | 1 | no | — |
| 597 | C4⋊C4 | — | 6 | 2 | no | — |
| 598 | C4⋊C4 | — | 6 | 2 | no | — |
| 599 | C4⋊C4 | — | 6 | 1 | no | — |
| 600 | C4⋊C4 | — | 6 | 1 | no | — |
| 601 | C4⋊C4 | — | 6 | 1 | no | — |
| 602 | C4⋊C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 603 | C4⋊C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 604 | C22⋊C4 | — | 2 | 2 | no | — |
| 605 | C22⋊C4 | — | 2 | 2 | no | — |
| 606 | C22⋊C4 | — | 2 | 2 | no | — |
| 607 | C22⋊C4 | — | 6 | 1 | no | — |
| 608 | C22⋊C4 | — | 6 | 1 | no | — |
| 609 | C22⋊C4 | — | 6 | 1 | no | — |
| 610 | C22⋊C4 | — | 6 | 1 | no | — |
| 611 | C22⋊C4 | — | 6 | 1 | no | — |
| 612 | C22⋊C4 | — | 6 | 1 | no | — |
| 613 | C22⋊C4 | — | 6 | 2 | no | — |
| 614 | C22⋊C4 | — | 6 | 2 | no | — |
| 615 | C22⋊C4 | — | 6 | 2 | no | — |
| 616 | C22⋊C4 | — | 6 | 2 | no | — |
| 617 | C22⋊C4 | — | 6 | 2 | no | — |
| 618 | C22⋊C4 | — | 6 | 2 | no | — |
| 619 | C22⋊C4 | — | 6 | 1 | no | — |
| 620 | C22⋊C4 | — | 6 | 1 | no | — |
| 621 | C22⋊C4 | — | 12 | 1 | no | — |
| 622 | C22⋊C4 | — | 12 | 1 | no | — |
| 623 | C42 | — | 2 | 1 | no | — |
| 624 | C42 | — | 2 | 1 | no | — |
| 625 | C42 | — | 3 | 1 | no | — |
| 626 | C42 | — | 3 | 1 | no | — |
| 627 | C42 | — | 3 | 1 | no | — |
| 628 | C42 | — | 6 | 1 | no | — |
| 629 | C42 | — | 6 | 1 | no | — |
| 630 | C42 | — | 6 | 2 | no | — |
| 631 | C42 | C23×D3 | 1 | 1 | yes | characteristic |
| 632 | C22×C3 | — | 4 | 2 | no | — |
| 633 | C22×C3 | — | 4 | 2 | no | — |
| 634 | C22×C3 | — | 4 | 2 | no | — |
| 635 | C22×C3 | — | 8 | 1 | no | — |
| 636 | C22×C3 | — | 8 | 1 | no | — |
| 637 | C22×C3 | — | 8 | 1 | no | — |
| 638 | C22×C3 | C2×#120 | 1 | 1 | yes | characteristic |
| 639 | C2×D3 | — | 2 | 1 | no | — |
| 640 | C2×D3 | — | 2 | 2 | no | — |
| 641 | C2×D3 | — | 2 | 1 | no | — |
| 642 | C2×D3 | — | 2 | 1 | no | — |
| 643 | C2×D3 | — | 4 | 1 | no | — |
| 644 | C2×D3 | — | 4 | 1 | no | — |
| 645 | C2×D3 | — | 4 | 1 | no | — |
| 646 | C2×D3 | — | 4 | 1 | no | — |
| 647 | C2×D3 | — | 4 | 1 | no | — |
| 648 | C2×D3 | — | 16 | 4 | no | — |
| 649 | C3×C4 | — | 2 | 1 | no | — |
| 650 | C3×C4 | — | 4 | 1 | no | — |
| 651 | C3×C4 | — | 4 | 1 | no | — |
| 652 | C3×C4 | — | 4 | 1 | no | — |
| 653 | C3×C4 | — | 4 | 1 | no | — |
| 654 | C3×C4 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 655 | C3×C4 | #575 | 1 | 1 | yes | characteristic |
| 656 | C3×C4 | #576 | 1 | 1 | yes | characteristic |
| 657 | C3×C4 | #577 | 1 | 1 | yes | characteristic |
| 658 | Dic3 | — | 2 | 1 | no | — |
| 659 | Dic3 | — | 2 | 1 | no | — |
| 660 | Dic3 | — | 2 | 1 | no | — |
| 661 | Dic3 | — | 4 | 1 | no | — |
| 662 | Dic3 | — | 4 | 2 | no | — |
| 663 | Dic3 | — | 4 | 1 | no | — |
| 664 | Dic3 | — | 8 | 1 | no | — |
| 665 | C23 | — | 2 | 2 | no | — |
| 666 | C23 | — | 3 | 1 | no | — |
| 667 | C23 | — | 4 | 1 | no | — |
| 668 | C23 | — | 6 | 1 | no | — |
| 669 | C23 | — | 6 | 1 | no | — |
| 670 | C23 | — | 12 | 4 | no | — |
| 671 | C23 | — | 24 | 2 | no | — |
| 672 | C23 | — | 24 | 2 | no | — |
| 673 | Q8 | — | 2 | 1 | no | — |
| 674 | Q8 | — | 2 | 1 | no | — |
| 675 | Q8 | — | 2 | 1 | no | — |
| 676 | Q8 | — | 2 | 1 | no | — |
| 677 | Q8 | — | 12 | 1 | no | — |
| 678 | Q8 | — | 12 | 1 | no | — |
| 679 | Q8 | — | 12 | 1 | no | — |
| 680 | Q8 | — | 12 | 1 | no | — |
| 681 | Q8 | — | 24 | 2 | no | — |
| 682 | D4 | — | 3 | 2 | no | — |
| 683 | D4 | — | 4 | 2 | no | — |
| 684 | D4 | — | 4 | 2 | no | — |
| 685 | D4 | — | 4 | 1 | no | — |
| 686 | D4 | — | 4 | 1 | no | — |
| 687 | D4 | — | 4 | 1 | no | — |
| 688 | D4 | — | 4 | 1 | no | — |
| 689 | D4 | — | 4 | 1 | no | — |
| 690 | D4 | — | 4 | 1 | no | — |
| 691 | D4 | — | 4 | 1 | no | — |
| 692 | D4 | — | 4 | 1 | no | — |
| 693 | D4 | — | 6 | 1 | no | — |
| 694 | D4 | — | 6 | 1 | no | — |
| 695 | D4 | — | 6 | 1 | no | — |
| 696 | D4 | — | 12 | 2 | no | — |
| 697 | D4 | — | 12 | 4 | no | — |
| 698 | D4 | — | 24 | 1 | no | — |
| 699 | D4 | — | 24 | 2 | no | — |
| 700 | D4 | — | 24 | 2 | no | — |
| 701 | D4 | — | 24 | 2 | no | — |
| 702 | C2×C4 | — | 2 | 1 | no | — |
| 703 | C2×C4 | — | 2 | 1 | no | — |
| 704 | C2×C4 | — | 2 | 1 | no | — |
| 705 | C2×C4 | — | 2 | 1 | no | — |
| 706 | C2×C4 | — | 3 | 1 | no | — |
| 707 | C2×C4 | — | 3 | 1 | no | — |
| 708 | C2×C4 | — | 3 | 1 | no | — |
| 709 | C2×C4 | — | 6 | 1 | no | — |
| 710 | C2×C4 | — | 6 | 1 | no | — |
| 711 | C2×C4 | — | 6 | 1 | no | — |
| 712 | C2×C4 | — | 6 | 1 | no | — |
| 713 | C2×C4 | — | 6 | 1 | no | — |
| 714 | C2×C4 | — | 6 | 1 | no | — |
| 715 | C2×C4 | — | 6 | 2 | no | — |
| 716 | C2×C4 | — | 8 | 2 | no | — |
| 717 | C2×C4 | — | 12 | 1 | no | — |
| 718 | C2×C4 | — | 12 | 2 | no | — |
| 719 | C2×C4 | — | 12 | 1 | no | — |
| 720 | C2×C4 | — | 12 | 1 | no | — |
| 721 | C2×C4 | — | 12 | 1 | no | — |
| 722 | C2×C4 | — | 12 | 1 | no | — |
| 723 | C2×C4 | — | 12 | 1 | no | — |
| 724 | C2×C4 | — | 24 | 1 | no | — |
| 725 | C2×C4 | — | 24 | 2 | no | — |
| 726 | C2×C4 | — | 24 | 2 | no | — |
| 727 | C2×C4 | — | 24 | 2 | no | — |
| 728 | C2×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 729 | C2×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 730 | C2×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 731 | C8 | — | 2 | 2 | no | — |
| 732 | C8 | — | 4 | 1 | no | — |
| 733 | C8 | — | 4 | 1 | no | — |
| 734 | C8 | — | 12 | 1 | no | — |
| 735 | C8 | — | 12 | 1 | no | — |
| 736 | C8 | — | 12 | 1 | no | — |
| 737 | C2×C3 | — | 8 | 2 | no | — |
| 738 | C2×C3 | — | 16 | 1 | no | — |
| 739 | C2×C3 | #3006 | 1 | 1 | yes | characteristic |
| 740 | C2×C3 | #3012 | 1 | 1 | yes | characteristic |
| 741 | C2×C3 | #3018 | 1 | 1 | yes | characteristic |
| 742 | D3 | — | 4 | 1 | no | — |
| 743 | D3 | — | 4 | 2 | no | — |
| 744 | D3 | — | 8 | 1 | no | — |
| 745 | C22 | — | 4 | 2 | no | — |
| 746 | C22 | — | 4 | 2 | no | — |
| 747 | C22 | — | 4 | 2 | no | — |
| 748 | C22 | — | 6 | 1 | no | — |
| 749 | C22 | — | 6 | 1 | no | — |
| 750 | C22 | — | 6 | 2 | no | — |
| 751 | C22 | — | 6 | 1 | no | — |
| 752 | C22 | — | 8 | 1 | no | — |
| 753 | C22 | — | 8 | 1 | no | — |
| 754 | C22 | — | 8 | 1 | no | — |
| 755 | C22 | — | 12 | 1 | no | — |
| 756 | C22 | — | 12 | 1 | no | — |
| 757 | C22 | — | 12 | 1 | no | — |
| 758 | C22 | — | 12 | 1 | no | — |
| 759 | C22 | — | 12 | 1 | no | — |
| 760 | C22 | — | 48 | 4 | no | — |
| 761 | C22 | D3×#120 | 1 | 1 | yes | characteristic |
| 762 | C4 | — | 2 | 1 | no | — |
| 763 | C4 | — | 4 | 1 | no | — |
| 764 | C4 | — | 4 | 1 | no | — |
| 765 | C4 | — | 4 | 1 | no | — |
| 766 | C4 | — | 4 | 1 | no | — |
| 767 | C4 | — | 6 | 1 | no | — |
| 768 | C4 | — | 6 | 1 | no | — |
| 769 | C4 | — | 6 | 1 | no | — |
| 770 | C4 | — | 12 | 1 | no | — |
| 771 | C4 | — | 12 | 1 | no | — |
| 772 | C4 | — | 12 | 2 | no | — |
| 773 | C4 | — | 24 | 1 | no | — |
| 774 | C4 | #5768 | 1 | 1 | yes | characteristic |
| 775 | C4 | #5770 | 1 | 1 | yes | characteristic |
| 776 | C4 | D3×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 777 | C4 | #5774 | 1 | 1 | yes | characteristic |
| 778 | C3 | #18594 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 779 | C2 | — | 8 | 2 | no | — |
| 780 | C2 | — | 12 | 1 | no | — |
| 781 | C2 | — | 12 | 2 | no | — |
| 782 | C2 | — | 16 | 1 | no | — |
| 783 | C2 | — | 24 | 1 | no | — |
| 784 | C2 | #80084 | 1 | 1 | yes | characteristic |
| 785 | C2 | #80087 | 1 | 1 | yes | characteristic |
| 786 | C2 | #80277 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C22 | D3×#120 |
| commutator, cosocle | C3×C42 | C24 |
| Frattini | C42 | C23×D3 |
| Fitting | C3×#1620 | C2 |
| socle | C22×C3 | C2×#120 |
| hypercenter | #1620 | D3 |
| hypocenter | C3 | #18594 |
| LCS | G ▷ C3×C42 ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #1620 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #87054 | C2 | semidirect |
| 2. #81777 | C2 | semidirect |
| 3. #80402 | C2 | semidirect |
| 4. #80382 | C2 | semidirect |
| 5. C3×#1620 | C2 | semidirect |
| 6. #71945 | C2 | semidirect |
| 7. #71281 | C2 | semidirect |
| 8. #71035 | C2 | semidirect |
| 9. #71029 | C2 | semidirect |
| 10. #68392 | C2 | semidirect |
| 11. #68384 | C2 | semidirect |
| 12. #68274 | C2 | semidirect |
| 13. #68251 | C2 | semidirect |
| 14. #68238 | C2 | semidirect |
| 15. #68234 | C2 | semidirect |
| 21. #5716 | C22 | semidirect |
| 37. C3×#460 | C22 | semidirect |
| 38. C3×#460 | C22 | semidirect |
| 47. #5070 | C22 | semidirect |
| 48. #5031 | C22 | semidirect |
| 49. #5020 | C22 | semidirect |
| 52. #4837 | C22 | semidirect |
| 53. D3×C4⋊C8 | C22 | semidirect |
| 58. C4×ΓL(1,𝔽25) | C22 | semidirect |
| 59. #4680 | C22 | semidirect |
| 61. C3×Q8⋊C8 | C22 | semidirect |
| 62. C3×Q8⋊C8 | C22 | semidirect |
| 64. #4535 | C22 | semidirect |
| 65. #4535 | C22 | semidirect |
| 66. #4486 | C22 | semidirect |
| 69. #4482 | C22 | semidirect |
| 82. #1620 | D3 | semidirect |
| 227. #460 | C2×D3 | semidirect |
| 228. #460 | C2×D3 | semidirect |
| 242. Q8⋊C8 | C2×D3 | semidirect |
| 243. Q8⋊C8 | C2×D3 | semidirect |
| 778. C3 | #18594 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #87054 | 2 |
| #81777 | 2 |
| #80402 | 2 |
| #80382 | 2 |
| C3×#1620 | 2 |
| #71945 | 2 |
| #71281 | 2 |
| #71035 | 2 |
| #71029 | 2 |
| #68392 | 2 |
| #68384 | 2 |
| #68274 | 2 |
| #68251 | 2 |
| #68238 | 2 |
| #68234 | 2 |
| #18594 | 3 |