Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
930 conjugacy classes of subgroups.
The subgroup lattice has 748 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #87021 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #81559 | 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×#1626 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #71937 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #71196 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #71028 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #71028 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #68436 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #68423 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #68270 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #68249 | 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 | #18596 | — | 3 | 1 | no | maximal, Sylow |
| 17 | C3×#557 | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×#916 | — | 2 | 1 | no | — |
| 19 | #5731 | — | 2 | 1 | no | — |
| 20 | #5728 | C22 | 1 | 1 | yes | characteristic |
| 21 | #5726 | — | 2 | 1 | no | — |
| 22 | #5726 | C22 | 1 | 1 | yes | characteristic |
| 23 | #5716 | C22 | 1 | 1 | yes | characteristic |
| 24 | #5695 | — | 2 | 1 | no | — |
| 25 | #5693 | — | 2 | 2 | no | — |
| 26 | #5692 | — | 2 | 2 | no | — |
| 27 | D3×#125 | — | 2 | 1 | no | — |
| 28 | #5581 | — | 2 | 1 | no | — |
| 29 | #5581 | — | 2 | 1 | no | — |
| 30 | #5580 | — | 2 | 1 | no | — |
| 31 | #5580 | C22 | 1 | 1 | yes | characteristic |
| 32 | #5579 | C22 | 1 | 1 | yes | characteristic |
| 33 | #5579 | C22 | 1 | 1 | yes | characteristic |
| 34 | #5574 | — | 2 | 1 | no | — |
| 35 | C4×#239 | C22 | 1 | 1 | yes | characteristic |
| 36 | C3×#486 | C22 | 1 | 1 | yes | characteristic |
| 37 | C3×#460 | C22 | 1 | 1 | yes | characteristic |
| 38 | C3×#460 | C22 | 1 | 1 | yes | characteristic |
| 39 | #5174 | — | 2 | 1 | no | — |
| 40 | #5166 | — | 2 | 1 | no | — |
| 41 | #5165 | — | 2 | 1 | no | — |
| 42 | #5078 | C22 | 1 | 1 | yes | characteristic |
| 43 | #5076 | C22 | 1 | 1 | yes | characteristic |
| 44 | #5072 | C22 | 1 | 1 | yes | characteristic |
| 45 | #5072 | C22 | 1 | 1 | yes | characteristic |
| 46 | #5031 | C22 | 1 | 1 | yes | characteristic |
| 47 | #5020 | C22 | 1 | 1 | yes | characteristic |
| 48 | #4846 | C22 | 1 | 1 | yes | characteristic |
| 49 | #4841 | C22 | 1 | 1 | yes | characteristic |
| 50 | #4837 | C22 | 1 | 1 | yes | characteristic |
| 51 | D3×C4⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 52 | #4787 | — | 2 | 1 | no | — |
| 53 | #4782 | — | 2 | 1 | no | — |
| 54 | #4780 | — | 2 | 2 | no | — |
| 55 | #4772 | — | 2 | 1 | no | — |
| 56 | #4766 | — | 2 | 1 | no | — |
| 57 | #4757 | — | 2 | 2 | no | — |
| 58 | C4×ΓL(1,𝔽25) | C22 | 1 | 1 | yes | characteristic |
| 59 | #4681 | C22 | 1 | 1 | yes | characteristic |
| 60 | C3×#332 | C22 | 1 | 1 | yes | characteristic |
| 61 | C3×Q8⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 62 | C3×Q8⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 63 | #4547 | C22 | 1 | 1 | yes | characteristic |
| 64 | #4535 | C22 | 1 | 1 | yes | characteristic |
| 65 | #4535 | C22 | 1 | 1 | yes | characteristic |
| 66 | #4483 | C22 | 1 | 1 | yes | characteristic |
| 67 | #4483 | C22 | 1 | 1 | yes | characteristic |
| 68 | #4481 | C22 | 1 | 1 | yes | characteristic |
| 69 | #4481 | C22 | 1 | 1 | yes | characteristic |
| 70 | #4459 | C22 | 1 | 1 | yes | characteristic |
| 71 | #4459 | C22 | 1 | 1 | yes | characteristic |
| 72 | #3515 | — | 3 | 1 | no | — |
| 73 | #3251 | — | 3 | 1 | no | — |
| 74 | #3182 | — | 3 | 1 | no | — |
| 75 | #3035 | — | 3 | 1 | no | — |
| 76 | #1648 | — | 3 | 1 | no | — |
| 77 | #1647 | — | 3 | 1 | no | — |
| 78 | #1644 | — | 3 | 1 | no | — |
| 79 | #1643 | — | 3 | 1 | no | — |
| 80 | #1626 | D3 | 1 | 1 | yes | characteristic, complemented |
| 81 | #1625 | — | 3 | 1 | no | — |
| 82 | #1622 | — | 3 | 1 | no | — |
| 83 | #1622 | — | 3 | 1 | no | — |
| 84 | #1550 | — | 3 | 1 | no | — |
| 85 | #1489 | — | 3 | 1 | no | — |
| 86 | #1483 | — | 3 | 1 | no | — |
| 87 | C2×#239 | — | 2 | 1 | no | — |
| 88 | C2×#239 | D4 | 1 | 1 | yes | characteristic |
| 89 | C2×#237 | — | 2 | 1 | no | — |
| 90 | C2×C3×SD16 | — | 2 | 1 | no | — |
| 91 | C2×C3×SD16 | — | 2 | 1 | no | — |
| 92 | C3×C4⋊Q8 | — | 2 | 1 | no | — |
| 93 | C3×C4⋊Q8 | C23 | 1 | 1 | yes | characteristic |
| 94 | C3×#127 | C23 | 1 | 1 | yes | characteristic |
| 95 | C3×#125 | — | 2 | 1 | no | — |
| 96 | C3×#125 | — | 2 | 2 | no | — |
| 97 | C3×C4×Q8 | — | 2 | 1 | no | — |
| 98 | C3×C4×Q8 | — | 2 | 1 | no | — |
| 99 | C3×C4×Q8 | C23 | 1 | 1 | yes | characteristic |
| 100 | C3×C4×Q8 | C23 | 1 | 1 | yes | characteristic |
| 101 | #947 | D4 | 1 | 1 | yes | characteristic |
| 102 | #946 | — | 2 | 1 | no | — |
| 103 | #946 | — | 2 | 1 | no | — |
| 104 | #946 | — | 2 | 1 | no | — |
| 105 | #946 | — | 2 | 1 | no | — |
| 106 | #946 | D4 | 1 | 1 | yes | characteristic |
| 107 | Q8×Dic3 | — | 2 | 1 | no | — |
| 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 | #936 | — | 2 | 1 | no | — |
| 113 | D4×Dic3 | — | 2 | 1 | no | — |
| 114 | D4×Dic3 | — | 2 | 1 | no | — |
| 115 | C2×#214 | — | 2 | 2 | no | — |
| 116 | C2×#213 | — | 2 | 1 | no | — |
| 117 | C2×#213 | — | 2 | 1 | no | — |
| 118 | #916 | — | 4 | 4 | no | — |
| 119 | C2×#204 | — | 2 | 1 | no | — |
| 120 | C2×ΓL(1,𝔽25) | — | 2 | 1 | no | — |
| 121 | C2×ΓL(1,𝔽25) | — | 2 | 1 | no | — |
| 122 | C2×D3×C8 | — | 2 | 1 | no | — |
| 123 | #898 | — | 2 | 2 | no | — |
| 124 | #898 | — | 2 | 2 | no | — |
| 125 | #898 | — | 2 | 1 | no | — |
| 126 | #897 | D4 | 1 | 2 | yes | — |
| 127 | #896 | — | 2 | 2 | no | — |
| 128 | #896 | — | 2 | 2 | no | — |
| 129 | #895 | — | 2 | 2 | no | — |
| 130 | #895 | — | 2 | 1 | no | — |
| 131 | #895 | D4 | 1 | 1 | yes | characteristic |
| 132 | #894 | — | 2 | 2 | no | — |
| 133 | #894 | — | 2 | 2 | no | — |
| 134 | #894 | — | 2 | 2 | no | — |
| 135 | #894 | — | 2 | 1 | no | — |
| 136 | #894 | — | 2 | 2 | no | — |
| 137 | #893 | — | 2 | 2 | no | — |
| 138 | #893 | — | 2 | 1 | no | — |
| 139 | #893 | D4 | 1 | 1 | yes | characteristic |
| 140 | #892 | — | 2 | 1 | no | — |
| 141 | #892 | — | 2 | 1 | no | — |
| 142 | #892 | D4 | 1 | 1 | yes | characteristic |
| 143 | D3×C4⋊C4 | — | 2 | 2 | no | — |
| 144 | D3×C4⋊C4 | — | 2 | 2 | no | — |
| 145 | D3×C4⋊C4 | — | 2 | 1 | no | — |
| 146 | D3×C4⋊C4 | — | 2 | 1 | no | — |
| 147 | D3×C4⋊C4 | — | 2 | 1 | no | — |
| 148 | #890 | — | 2 | 1 | no | — |
| 149 | #890 | D4 | 1 | 1 | yes | characteristic |
| 150 | #889 | — | 2 | 2 | no | — |
| 151 | #889 | — | 2 | 2 | no | — |
| 152 | #889 | — | 2 | 2 | no | — |
| 153 | #887 | D4 | 1 | 2 | yes | — |
| 154 | #876 | — | 2 | 2 | no | — |
| 155 | C4×D12 | — | 2 | 2 | no | — |
| 156 | C4×D12 | — | 2 | 1 | no | — |
| 157 | C4×D12 | — | 2 | 1 | no | — |
| 158 | C4×D12 | — | 2 | 1 | no | — |
| 159 | C4×D12 | — | 2 | 1 | no | — |
| 160 | C4×D12 | C23 | 1 | 1 | yes | characteristic |
| 161 | C4×D12 | C23 | 1 | 1 | yes | characteristic |
| 162 | #872 | — | 2 | 2 | no | — |
| 163 | #872 | — | 2 | 2 | no | — |
| 164 | #872 | — | 2 | 1 | no | — |
| 165 | C42×D3 | — | 2 | 1 | no | — |
| 166 | C42×D3 | C23 | 1 | 1 | yes | characteristic |
| 167 | #870 | — | 2 | 1 | no | — |
| 168 | #870 | — | 2 | 1 | no | — |
| 169 | #869 | C23 | 1 | 1 | yes | characteristic |
| 170 | #869 | C23 | 1 | 1 | yes | characteristic |
| 171 | C3×C4⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 172 | C3×C4⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 173 | C3×#102 | — | 2 | 2 | no | — |
| 174 | C3×#102 | — | 2 | 1 | no | — |
| 175 | C3×#102 | — | 2 | 1 | no | — |
| 176 | C3×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 177 | #835 | — | 2 | 1 | no | — |
| 178 | #832 | — | 2 | 1 | no | — |
| 179 | #832 | — | 2 | 1 | no | — |
| 180 | #821 | — | 2 | 1 | no | — |
| 181 | #818 | — | 2 | 1 | no | — |
| 182 | #816 | — | 2 | 2 | no | — |
| 183 | #816 | — | 2 | 1 | no | — |
| 184 | #815 | — | 2 | 1 | no | — |
| 185 | Dic3⋊C8 | — | 2 | 1 | no | — |
| 186 | Dic3⋊C8 | — | 2 | 1 | no | — |
| 187 | #810 | — | 2 | 1 | no | — |
| 188 | #808 | — | 2 | 1 | no | — |
| 189 | #807 | — | 2 | 2 | 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 | #557 | C2×D3 | 1 | 1 | yes | characteristic |
| 195 | #554 | — | 3 | 1 | no | — |
| 196 | #554 | — | 3 | 1 | no | — |
| 197 | #553 | — | 6 | 1 | no | — |
| 198 | #552 | — | 6 | 1 | no | — |
| 199 | #552 | — | 6 | 1 | no | — |
| 200 | #552 | — | 6 | 2 | no | — |
| 201 | #547 | — | 3 | 1 | no | — |
| 202 | #547 | — | 6 | 1 | no | — |
| 203 | #541 | — | 6 | 1 | no | — |
| 204 | #539 | — | 6 | 2 | no | — |
| 205 | #533 | — | 3 | 1 | no | — |
| 206 | #532 | — | 3 | 1 | no | — |
| 207 | #529 | — | 3 | 1 | no | — |
| 208 | #529 | — | 6 | 1 | no | — |
| 209 | C2×#125 | — | 6 | 1 | no | — |
| 210 | #520 | — | 6 | 1 | no | — |
| 211 | C4×#41 | — | 3 | 1 | no | — |
| 212 | #500 | — | 3 | 1 | no | — |
| 213 | #492 | — | 3 | 1 | no | — |
| 214 | #487 | — | 3 | 1 | no | — |
| 215 | #486 | C2×D3 | 1 | 1 | yes | characteristic |
| 216 | #478 | — | 6 | 1 | no | — |
| 217 | #475 | — | 3 | 1 | no | — |
| 218 | #474 | — | 3 | 1 | no | — |
| 219 | #469 | — | 6 | 1 | no | — |
| 220 | #468 | — | 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 |
| 228 | #460 | C2×D3 | 1 | 1 | yes | characteristic |
| 229 | #459 | — | 3 | 1 | no | — |
| 230 | #459 | — | 3 | 1 | no | — |
| 231 | #440 | — | 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 | #333 | — | 3 | 1 | no | — |
| 237 | #333 | — | 3 | 1 | no | — |
| 238 | #332 | — | 3 | 1 | no | — |
| 239 | #332 | 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 |
| 243 | Q8⋊C8 | C2×D3 | 1 | 1 | yes | characteristic |
| 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 | C2×C3×Q8 | — | 2 | 1 | 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×#67 | — | 4 | 1 | no | — |
| 255 | C22×Dic3 | — | 4 | 1 | no | — |
| 256 | #239 | — | 2 | 2 | no | — |
| 257 | #239 | — | 4 | 1 | no | — |
| 258 | #239 | — | 4 | 2 | no | — |
| 259 | #239 | — | 4 | 2 | no | — |
| 260 | #237 | — | 4 | 2 | no | — |
| 261 | #237 | — | 4 | 2 | no | — |
| 262 | C2×D12 | — | 2 | 2 | no | — |
| 263 | C2×D12 | — | 2 | 1 | no | — |
| 264 | C2×D12 | — | 2 | 1 | no | — |
| 265 | C2×D12 | C2×D4 | 1 | 1 | yes | characteristic |
| 266 | C2×D12 | C2×D4 | 1 | 1 | yes | characteristic |
| 267 | C2×C4×D3 | — | 2 | 2 | no | — |
| 268 | C2×C4×D3 | — | 2 | 1 | no | — |
| 269 | C2×C4×D3 | — | 2 | 1 | no | — |
| 270 | C2×C4×D3 | — | 2 | 1 | no | — |
| 271 | C2×C4×D3 | — | 2 | 2 | no | — |
| 272 | C2×C4×D3 | — | 2 | 2 | no | — |
| 273 | C2×C4×D3 | — | 2 | 1 | no | — |
| 274 | C2×C4×D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 275 | C2×C4×D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 276 | C2×C4×D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 277 | C2×Dic6 | — | 2 | 1 | no | — |
| 278 | C2×Dic6 | C2×D4 | 1 | 2 | yes | — |
| 279 | C3×SD16 | — | 4 | 2 | no | — |
| 280 | C3×SD16 | — | 8 | 1 | no | — |
| 281 | C2×C3×C8 | — | 2 | 1 | no | — |
| 282 | C2×C3×C8 | — | 2 | 1 | no | — |
| 283 | C2×C3×C8 | — | 2 | 1 | no | — |
| 284 | C3×C4⋊C4 | — | 2 | 2 | no | — |
| 285 | C3×C4⋊C4 | — | 2 | 2 | no | — |
| 286 | C3×C4⋊C4 | — | 2 | 2 | no | — |
| 287 | C3×C4⋊C4 | — | 2 | 1 | no | — |
| 288 | C3×C4⋊C4 | — | 2 | 1 | no | — |
| 289 | C3×C4⋊C4 | — | 2 | 1 | no | — |
| 290 | C3×C4⋊C4 | C2×D4 | 1 | 2 | yes | — |
| 291 | C3×C4⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 292 | C3×C4⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 293 | C3×C42 | — | 2 | 2 | no | — |
| 294 | C3×C42 | — | 2 | 1 | no | — |
| 295 | C3×C42 | — | 2 | 1 | no | — |
| 296 | C3×C42 | C24 | 1 | 1 | yes | characteristic |
| 297 | #217 | — | 4 | 1 | no | — |
| 298 | #217 | — | 4 | 1 | no | — |
| 299 | #216 | — | 4 | 2 | no | — |
| 300 | #214 | — | 4 | 4 | no | — |
| 301 | #213 | — | 4 | 2 | no | — |
| 302 | #213 | — | 8 | 1 | no | — |
| 303 | (C2×D3)⋊C4 | — | 2 | 2 | no | — |
| 304 | (C2×D3)⋊C4 | — | 2 | 2 | no | — |
| 305 | (C2×D3)⋊C4 | — | 2 | 2 | no | — |
| 306 | (C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 307 | (C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 308 | (C2×D3)⋊C4 | — | 2 | 2 | no | — |
| 309 | (C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 310 | (C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 311 | (C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 312 | (C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 313 | (C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 314 | (C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 315 | C4⋊Dic3 | — | 2 | 1 | no | — |
| 316 | C4⋊Dic3 | — | 2 | 1 | no | — |
| 317 | C4⋊Dic3 | — | 2 | 1 | no | — |
| 318 | C4⋊Dic3 | — | 2 | 1 | no | — |
| 319 | C4⋊Dic3 | — | 2 | 2 | no | — |
| 320 | C4⋊Dic3 | — | 2 | 1 | no | — |
| 321 | C4⋊Dic3 | — | 2 | 1 | no | — |
| 322 | C4⋊Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 323 | C4⋊Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 324 | Dic3⋊C4 | — | 2 | 2 | no | — |
| 325 | Dic3⋊C4 | — | 2 | 2 | no | — |
| 326 | Dic3⋊C4 | — | 2 | 2 | no | — |
| 327 | Dic3⋊C4 | — | 2 | 2 | no | — |
| 328 | Dic3⋊C4 | — | 2 | 2 | no | — |
| 329 | Dic3⋊C4 | — | 2 | 1 | no | — |
| 330 | Dic3⋊C4 | — | 2 | 2 | no | — |
| 331 | Dic3⋊C4 | — | 2 | 1 | no | — |
| 332 | C4×Dic3 | — | 2 | 1 | no | — |
| 333 | C4×Dic3 | — | 2 | 1 | no | — |
| 334 | C4×Dic3 | — | 2 | 2 | no | — |
| 335 | C4×Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 336 | C4×Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 337 | C4×Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 338 | C2×C3⋊C8 | — | 2 | 1 | no | — |
| 339 | C2×C3⋊C8 | — | 2 | 1 | no | — |
| 340 | C2×C3⋊C8 | — | 2 | 1 | no | — |
| 341 | #204 | — | 4 | 2 | no | — |
| 342 | ΓL(1,𝔽25) | — | 4 | 2 | no | — |
| 343 | ΓL(1,𝔽25) | — | 8 | 1 | no | — |
| 344 | D3×C8 | — | 4 | 2 | no | — |
| 345 | C2×#41 | — | 3 | 1 | no | — |
| 346 | C2×#41 | — | 6 | 1 | no | — |
| 347 | C2×#41 | — | 6 | 1 | no | — |
| 348 | #135 | — | 12 | 4 | no | — |
| 349 | C2×Q16 | — | 6 | 1 | no | — |
| 350 | C2×SD16 | — | 2 | 1 | no | — |
| 351 | C2×SD16 | — | 2 | 1 | no | — |
| 352 | C2×SD16 | — | 6 | 1 | no | — |
| 353 | C2×SD16 | — | 6 | 2 | no | — |
| 354 | C2×D8 | — | 6 | 1 | no | — |
| 355 | C2×D8 | — | 6 | 1 | no | — |
| 356 | C2×M16 | — | 6 | 1 | no | — |
| 357 | C2×M16 | — | 6 | 1 | no | — |
| 358 | C22×C8 | — | 6 | 1 | no | — |
| 359 | C4⋊Q8 | — | 2 | 1 | no | — |
| 360 | C4⋊Q8 | — | 3 | 1 | no | — |
| 361 | C4⋊Q8 | — | 3 | 1 | no | — |
| 362 | C4⋊Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 363 | #127 | C22×D3 | 1 | 1 | yes | characteristic |
| 364 | #126 | — | 6 | 2 | no | — |
| 365 | #126 | — | 6 | 1 | no | — |
| 366 | #126 | — | 6 | 2 | no | — |
| 367 | #126 | — | 6 | 2 | no | — |
| 368 | #125 | — | 2 | 1 | no | — |
| 369 | #125 | — | 2 | 2 | no | — |
| 370 | #125 | — | 3 | 1 | no | — |
| 371 | #125 | — | 6 | 1 | no | — |
| 372 | #125 | — | 6 | 1 | no | — |
| 373 | #125 | — | 6 | 1 | no | — |
| 374 | #125 | — | 6 | 2 | no | — |
| 375 | #125 | — | 6 | 2 | no | — |
| 376 | #125 | — | 6 | 2 | no | — |
| 377 | #124 | — | 3 | 1 | no | — |
| 378 | #124 | — | 6 | 1 | no | — |
| 379 | #123 | — | 6 | 1 | no | — |
| 380 | #123 | — | 6 | 2 | no | — |
| 381 | #123 | — | 6 | 2 | no | — |
| 382 | #123 | — | 6 | 2 | no | — |
| 383 | #123 | — | 6 | 2 | no | — |
| 384 | C22⋊Q8 | — | 3 | 1 | no | — |
| 385 | C22⋊Q8 | — | 3 | 2 | no | — |
| 386 | C22⋊Q8 | — | 6 | 2 | no | — |
| 387 | C22⋊Q8 | — | 6 | 2 | no | — |
| 388 | C22⋊Q8 | — | 6 | 1 | no | — |
| 389 | C22⋊Q8 | — | 6 | 1 | no | — |
| 390 | C22⋊Q8 | — | 6 | 1 | no | — |
| 391 | C22⋊Q8 | — | 6 | 1 | no | — |
| 392 | #121 | — | 3 | 1 | no | — |
| 393 | #121 | — | 6 | 1 | no | — |
| 394 | #121 | — | 6 | 2 | no | — |
| 395 | #121 | — | 6 | 1 | no | — |
| 396 | #121 | — | 6 | 1 | no | — |
| 397 | C4×Q8 | — | 2 | 1 | no | — |
| 398 | C4×Q8 | — | 2 | 1 | no | — |
| 399 | C4×Q8 | — | 3 | 1 | no | — |
| 400 | C4×Q8 | — | 3 | 2 | no | — |
| 401 | C4×Q8 | — | 6 | 1 | no | — |
| 402 | C4×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 403 | C4×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 404 | C4×D4 | — | 3 | 1 | no | — |
| 405 | C4×D4 | — | 3 | 1 | no | — |
| 406 | C4×D4 | — | 3 | 1 | no | — |
| 407 | C4×D4 | — | 6 | 1 | no | — |
| 408 | C4×D4 | — | 6 | 1 | no | — |
| 409 | C4×D4 | — | 6 | 1 | no | — |
| 410 | C4×D4 | — | 6 | 1 | no | — |
| 411 | C4×D4 | — | 6 | 2 | no | — |
| 412 | C4×D4 | — | 6 | 1 | no | — |
| 413 | C4×D4 | — | 6 | 1 | no | — |
| 414 | C4×D4 | — | 6 | 1 | no | — |
| 415 | C4×D4 | — | 6 | 2 | no | — |
| 416 | #117 | — | 3 | 1 | no | — |
| 417 | #117 | — | 6 | 1 | no | — |
| 418 | #117 | — | 6 | 2 | no | — |
| 419 | #117 | — | 6 | 2 | no | — |
| 420 | #117 | — | 6 | 1 | no | — |
| 421 | #117 | — | 6 | 1 | no | — |
| 422 | C2×C4⋊C4 | — | 6 | 1 | no | — |
| 423 | C2×C4⋊C4 | — | 6 | 2 | no | — |
| 424 | C2×C4⋊C4 | — | 6 | 2 | no | — |
| 425 | C2×C4⋊C4 | — | 6 | 1 | no | — |
| 426 | C2×C4⋊C4 | — | 6 | 1 | no | — |
| 427 | C2×C42 | — | 3 | 1 | no | — |
| 428 | C2×C42 | — | 6 | 1 | no | — |
| 429 | #107 | — | 6 | 1 | no | — |
| 430 | #107 | — | 6 | 2 | no | — |
| 431 | #106 | — | 6 | 1 | no | — |
| 432 | C4⋊C8 | — | 3 | 1 | no | — |
| 433 | C4⋊C8 | — | 3 | 1 | no | — |
| 434 | C4⋊C8 | — | 6 | 1 | no | — |
| 435 | C4⋊C8 | — | 6 | 1 | no | — |
| 436 | C4⋊C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 437 | C4⋊C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 438 | #103 | — | 6 | 1 | no | — |
| 439 | #103 | — | 6 | 2 | no | — |
| 440 | #103 | — | 6 | 1 | no | — |
| 441 | #103 | — | 6 | 1 | no | — |
| 442 | #102 | — | 2 | 1 | no | — |
| 443 | #102 | — | 2 | 2 | no | — |
| 444 | #102 | — | 2 | 1 | no | — |
| 445 | #102 | — | 6 | 1 | no | — |
| 446 | #102 | — | 6 | 1 | no | — |
| 447 | #102 | — | 6 | 1 | no | — |
| 448 | #97 | — | 6 | 1 | no | — |
| 449 | C4×C8 | — | 3 | 1 | no | — |
| 450 | C4×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 451 | C23×C3 | — | 4 | 1 | no | — |
| 452 | C22×D3 | — | 2 | 1 | no | — |
| 453 | C22×D3 | — | 2 | 1 | no | — |
| 454 | C22×D3 | #120 | 1 | 1 | yes | characteristic |
| 455 | C3×Q8 | — | 2 | 1 | no | — |
| 456 | C3×Q8 | — | 2 | 1 | no | — |
| 457 | C3×Q8 | — | 2 | 1 | no | — |
| 458 | C3×Q8 | — | 2 | 1 | no | — |
| 459 | C3×Q8 | — | 4 | 1 | no | — |
| 460 | C3×Q8 | — | 4 | 1 | no | — |
| 461 | C3×D4 | — | 4 | 2 | no | — |
| 462 | C3×D4 | — | 4 | 1 | no | — |
| 463 | C3×D4 | — | 4 | 1 | no | — |
| 464 | C3×D4 | — | 4 | 1 | no | — |
| 465 | C3×D4 | — | 4 | 1 | no | — |
| 466 | C2×C3×C4 | — | 2 | 1 | no | — |
| 467 | C2×C3×C4 | — | 2 | 2 | no | — |
| 468 | C2×C3×C4 | — | 2 | 1 | no | — |
| 469 | C2×C3×C4 | — | 2 | 1 | no | — |
| 470 | C2×C3×C4 | — | 2 | 1 | no | — |
| 471 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 472 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 473 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 474 | #67 | — | 8 | 2 | no | — |
| 475 | C2×Dic3 | — | 2 | 1 | no | — |
| 476 | C2×Dic3 | — | 2 | 2 | no | — |
| 477 | C2×Dic3 | — | 2 | 1 | no | — |
| 478 | C2×Dic3 | — | 4 | 1 | no | — |
| 479 | C2×Dic3 | — | 8 | 2 | no | — |
| 480 | C2×Dic3 | #120 | 1 | 1 | yes | characteristic |
| 481 | C2×Dic3 | #120 | 1 | 1 | yes | characteristic |
| 482 | C2×Dic3 | #120 | 1 | 1 | yes | characteristic |
| 483 | D12 | — | 2 | 1 | no | — |
| 484 | D12 | — | 2 | 1 | no | — |
| 485 | D12 | — | 2 | 1 | no | — |
| 486 | D12 | — | 4 | 2 | no | — |
| 487 | D12 | — | 4 | 4 | no | — |
| 488 | D12 | — | 8 | 1 | no | — |
| 489 | D12 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 490 | C4×D3 | — | 2 | 1 | no | — |
| 491 | C4×D3 | — | 2 | 1 | no | — |
| 492 | C4×D3 | — | 2 | 1 | no | — |
| 493 | C4×D3 | — | 2 | 1 | no | — |
| 494 | C4×D3 | — | 4 | 1 | no | — |
| 495 | C4×D3 | — | 4 | 2 | no | — |
| 496 | C4×D3 | — | 4 | 4 | no | — |
| 497 | C4×D3 | — | 4 | 1 | no | — |
| 498 | C4×D3 | — | 4 | 1 | no | — |
| 499 | C4×D3 | — | 4 | 1 | no | — |
| 500 | C4×D3 | — | 4 | 1 | no | — |
| 501 | C4×D3 | — | 8 | 1 | no | — |
| 502 | C4×D3 | — | 8 | 2 | no | — |
| 503 | C4×D3 | — | 8 | 2 | no | — |
| 504 | Dic6 | — | 4 | 2 | no | — |
| 505 | Dic6 | — | 4 | 1 | no | — |
| 506 | Dic6 | — | 4 | 1 | no | — |
| 507 | C3×C8 | — | 4 | 1 | no | — |
| 508 | C3×C8 | — | 4 | 1 | no | — |
| 509 | C3×C8 | — | 4 | 1 | no | — |
| 510 | C3⋊C8 | — | 2 | 2 | no | — |
| 511 | C3⋊C8 | — | 4 | 1 | no | — |
| 512 | C3⋊C8 | — | 4 | 1 | no | — |
| 513 | #41 | — | 6 | 2 | no | — |
| 514 | #41 | — | 12 | 1 | no | — |
| 515 | #41 | — | 12 | 2 | no | — |
| 516 | #41 | — | 12 | 2 | no | — |
| 517 | #41 | — | 12 | 2 | no | — |
| 518 | #41 | — | 12 | 2 | no | — |
| 519 | C2×Q8 | — | 2 | 1 | no | — |
| 520 | C2×Q8 | — | 3 | 2 | no | — |
| 521 | C2×Q8 | — | 6 | 1 | no | — |
| 522 | C2×Q8 | D3×D4 | 1 | 1 | yes | characteristic |
| 523 | C2×Q8 | D3×D4 | 1 | 1 | yes | characteristic |
| 524 | C2×D4 | — | 2 | 1 | no | — |
| 525 | C2×D4 | — | 2 | 1 | no | — |
| 526 | C2×D4 | — | 2 | 1 | no | — |
| 527 | C2×D4 | — | 3 | 1 | no | — |
| 528 | C2×D4 | — | 3 | 1 | no | — |
| 529 | C2×D4 | — | 6 | 1 | no | — |
| 530 | C2×D4 | — | 6 | 2 | no | — |
| 531 | C2×D4 | — | 6 | 1 | no | — |
| 532 | C2×D4 | — | 12 | 1 | no | — |
| 533 | C22×C4 | — | 3 | 1 | no | — |
| 534 | C22×C4 | — | 3 | 1 | no | — |
| 535 | C22×C4 | — | 3 | 1 | no | — |
| 536 | C22×C4 | — | 6 | 1 | no | — |
| 537 | C22×C4 | — | 6 | 1 | no | — |
| 538 | C22×C4 | — | 6 | 2 | no | — |
| 539 | C22×C4 | — | 6 | 2 | no | — |
| 540 | C22×C4 | — | 6 | 2 | no | — |
| 541 | C22×C4 | — | 6 | 1 | no | — |
| 542 | C22×C4 | — | 6 | 1 | no | — |
| 543 | C22×C4 | — | 12 | 1 | no | — |
| 544 | Q16 | — | 12 | 2 | no | — |
| 545 | SD16 | — | 4 | 2 | no | — |
| 546 | SD16 | — | 8 | 1 | no | — |
| 547 | SD16 | — | 12 | 2 | no | — |
| 548 | SD16 | — | 12 | 4 | no | — |
| 549 | D8 | — | 12 | 2 | no | — |
| 550 | D8 | — | 24 | 1 | no | — |
| 551 | M16 | — | 12 | 2 | no | — |
| 552 | M16 | — | 24 | 1 | no | — |
| 553 | C2×C8 | — | 2 | 1 | no | — |
| 554 | C2×C8 | — | 2 | 1 | no | — |
| 555 | C2×C8 | — | 2 | 1 | no | — |
| 556 | C2×C8 | — | 6 | 1 | no | — |
| 557 | C2×C8 | — | 6 | 1 | no | — |
| 558 | C2×C8 | — | 6 | 1 | no | — |
| 559 | C2×C8 | — | 12 | 2 | no | — |
| 560 | C4⋊C4 | — | 2 | 2 | no | — |
| 561 | C4⋊C4 | — | 2 | 2 | no | — |
| 562 | C4⋊C4 | — | 2 | 2 | no | — |
| 563 | C4⋊C4 | — | 2 | 1 | no | — |
| 564 | C4⋊C4 | — | 2 | 1 | no | — |
| 565 | C4⋊C4 | — | 2 | 1 | no | — |
| 566 | C4⋊C4 | — | 3 | 1 | no | — |
| 567 | C4⋊C4 | — | 3 | 1 | no | — |
| 568 | C4⋊C4 | — | 6 | 1 | no | — |
| 569 | C4⋊C4 | — | 6 | 1 | no | — |
| 570 | C4⋊C4 | — | 6 | 2 | no | — |
| 571 | C4⋊C4 | — | 6 | 2 | no | — |
| 572 | C4⋊C4 | — | 6 | 1 | no | — |
| 573 | C4⋊C4 | — | 6 | 1 | no | — |
| 574 | C4⋊C4 | — | 6 | 2 | no | — |
| 575 | C4⋊C4 | — | 6 | 2 | no | — |
| 576 | C4⋊C4 | — | 6 | 2 | no | — |
| 577 | C4⋊C4 | — | 6 | 2 | no | — |
| 578 | C4⋊C4 | — | 6 | 2 | no | — |
| 579 | C4⋊C4 | — | 6 | 1 | no | — |
| 580 | C4⋊C4 | — | 6 | 1 | no | — |
| 581 | C4⋊C4 | — | 6 | 1 | no | — |
| 582 | C4⋊C4 | — | 6 | 1 | no | — |
| 583 | C4⋊C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 584 | C4⋊C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 585 | C4⋊C4 | D3×D4 | 1 | 2 | yes | — |
| 586 | C22⋊C4 | — | 6 | 1 | no | — |
| 587 | C22⋊C4 | — | 6 | 1 | no | — |
| 588 | C22⋊C4 | — | 6 | 1 | no | — |
| 589 | C22⋊C4 | — | 6 | 1 | no | — |
| 590 | C22⋊C4 | — | 6 | 1 | no | — |
| 591 | C22⋊C4 | — | 6 | 2 | no | — |
| 592 | C22⋊C4 | — | 6 | 1 | no | — |
| 593 | C22⋊C4 | — | 6 | 2 | no | — |
| 594 | C22⋊C4 | — | 6 | 2 | no | — |
| 595 | C22⋊C4 | — | 6 | 2 | no | — |
| 596 | C22⋊C4 | — | 6 | 1 | no | — |
| 597 | C22⋊C4 | — | 6 | 1 | no | — |
| 598 | C22⋊C4 | — | 12 | 1 | no | — |
| 599 | C22⋊C4 | — | 12 | 1 | no | — |
| 600 | C42 | — | 2 | 2 | no | — |
| 601 | C42 | — | 2 | 1 | no | — |
| 602 | C42 | — | 2 | 1 | no | — |
| 603 | C42 | — | 3 | 1 | no | — |
| 604 | C42 | — | 3 | 1 | no | — |
| 605 | C42 | — | 3 | 1 | no | — |
| 606 | C42 | — | 6 | 1 | no | — |
| 607 | C42 | — | 6 | 1 | no | — |
| 608 | C42 | — | 6 | 2 | no | — |
| 609 | C42 | C23×D3 | 1 | 1 | yes | characteristic |
| 610 | C22×C3 | — | 8 | 1 | no | — |
| 611 | C22×C3 | — | 8 | 1 | no | — |
| 612 | C22×C3 | — | 8 | 1 | no | — |
| 613 | C22×C3 | C2×#120 | 1 | 1 | yes | characteristic |
| 614 | C2×D3 | — | 2 | 1 | no | — |
| 615 | C2×D3 | — | 2 | 2 | no | — |
| 616 | C2×D3 | — | 2 | 1 | no | — |
| 617 | C2×D3 | — | 2 | 1 | no | — |
| 618 | C2×D3 | — | 4 | 1 | no | — |
| 619 | C2×D3 | — | 4 | 1 | no | — |
| 620 | C2×D3 | — | 4 | 1 | no | — |
| 621 | C2×D3 | — | 4 | 1 | no | — |
| 622 | C2×D3 | — | 4 | 1 | no | — |
| 623 | C3×C4 | — | 2 | 1 | no | — |
| 624 | C3×C4 | — | 4 | 1 | no | — |
| 625 | C3×C4 | — | 4 | 2 | no | — |
| 626 | C3×C4 | — | 4 | 1 | no | — |
| 627 | C3×C4 | — | 4 | 1 | no | — |
| 628 | C3×C4 | — | 4 | 1 | no | — |
| 629 | C3×C4 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 630 | C3×C4 | #575 | 1 | 1 | yes | characteristic |
| 631 | C3×C4 | #577 | 1 | 1 | yes | characteristic |
| 632 | C3×C4 | #578 | 1 | 1 | yes | characteristic |
| 633 | Dic3 | — | 2 | 1 | no | — |
| 634 | Dic3 | — | 2 | 1 | no | — |
| 635 | Dic3 | — | 2 | 1 | no | — |
| 636 | Dic3 | — | 4 | 1 | no | — |
| 637 | Dic3 | — | 4 | 1 | no | — |
| 638 | Dic3 | — | 4 | 2 | no | — |
| 639 | Dic3 | — | 8 | 1 | no | — |
| 640 | C23 | — | 3 | 1 | no | — |
| 641 | C23 | — | 4 | 1 | no | — |
| 642 | C23 | — | 6 | 1 | no | — |
| 643 | C23 | — | 6 | 1 | no | — |
| 644 | Q8 | — | 2 | 1 | no | — |
| 645 | Q8 | — | 2 | 1 | no | — |
| 646 | Q8 | — | 2 | 1 | no | — |
| 647 | Q8 | — | 2 | 1 | no | — |
| 648 | Q8 | — | 4 | 1 | no | — |
| 649 | Q8 | — | 4 | 1 | no | — |
| 650 | Q8 | — | 12 | 2 | no | — |
| 651 | Q8 | — | 12 | 1 | no | — |
| 652 | Q8 | — | 12 | 1 | no | — |
| 653 | D4 | — | 3 | 2 | no | — |
| 654 | D4 | — | 4 | 2 | no | — |
| 655 | D4 | — | 4 | 1 | no | — |
| 656 | D4 | — | 4 | 1 | no | — |
| 657 | D4 | — | 4 | 1 | no | — |
| 658 | D4 | — | 4 | 1 | no | — |
| 659 | D4 | — | 6 | 1 | no | — |
| 660 | D4 | — | 6 | 1 | no | — |
| 661 | D4 | — | 6 | 1 | no | — |
| 662 | D4 | — | 12 | 2 | no | — |
| 663 | D4 | — | 12 | 4 | no | — |
| 664 | D4 | — | 24 | 1 | no | — |
| 665 | D4 | — | 24 | 2 | no | — |
| 666 | C2×C4 | — | 2 | 1 | no | — |
| 667 | C2×C4 | — | 2 | 1 | no | — |
| 668 | C2×C4 | — | 2 | 1 | no | — |
| 669 | C2×C4 | — | 2 | 2 | no | — |
| 670 | C2×C4 | — | 2 | 1 | no | — |
| 671 | C2×C4 | — | 3 | 1 | no | — |
| 672 | C2×C4 | — | 3 | 1 | no | — |
| 673 | C2×C4 | — | 3 | 1 | no | — |
| 674 | C2×C4 | — | 6 | 1 | no | — |
| 675 | C2×C4 | — | 6 | 1 | no | — |
| 676 | C2×C4 | — | 6 | 1 | no | — |
| 677 | C2×C4 | — | 6 | 1 | no | — |
| 678 | C2×C4 | — | 6 | 1 | no | — |
| 679 | C2×C4 | — | 6 | 2 | no | — |
| 680 | C2×C4 | — | 6 | 1 | no | — |
| 681 | C2×C4 | — | 12 | 1 | no | — |
| 682 | C2×C4 | — | 12 | 2 | no | — |
| 683 | C2×C4 | — | 12 | 4 | no | — |
| 684 | C2×C4 | — | 12 | 1 | no | — |
| 685 | C2×C4 | — | 12 | 1 | no | — |
| 686 | C2×C4 | — | 12 | 1 | no | — |
| 687 | C2×C4 | — | 12 | 1 | no | — |
| 688 | C2×C4 | — | 12 | 1 | no | — |
| 689 | C2×C4 | — | 24 | 1 | no | — |
| 690 | C2×C4 | — | 24 | 2 | no | — |
| 691 | C2×C4 | — | 24 | 2 | no | — |
| 692 | C2×C4 | — | 24 | 2 | no | — |
| 693 | C2×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 694 | C2×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 695 | C2×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 696 | C8 | — | 4 | 1 | no | — |
| 697 | C8 | — | 4 | 1 | no | — |
| 698 | C8 | — | 4 | 1 | no | — |
| 699 | C8 | — | 6 | 2 | no | — |
| 700 | C8 | — | 12 | 1 | no | — |
| 701 | C8 | — | 12 | 1 | no | — |
| 702 | C2×C3 | — | 16 | 1 | no | — |
| 703 | C2×C3 | #3006 | 1 | 1 | yes | characteristic |
| 704 | C2×C3 | #3013 | 1 | 1 | yes | characteristic |
| 705 | C2×C3 | #3018 | 1 | 1 | yes | characteristic |
| 706 | D3 | — | 4 | 1 | no | — |
| 707 | D3 | — | 4 | 2 | no | — |
| 708 | D3 | — | 8 | 1 | no | — |
| 709 | C22 | — | 6 | 1 | no | — |
| 710 | C22 | — | 6 | 1 | no | — |
| 711 | C22 | — | 6 | 1 | no | — |
| 712 | C22 | — | 6 | 2 | no | — |
| 713 | C22 | — | 8 | 1 | no | — |
| 714 | C22 | — | 8 | 1 | no | — |
| 715 | C22 | — | 8 | 1 | no | — |
| 716 | C22 | — | 12 | 1 | no | — |
| 717 | C22 | — | 12 | 1 | no | — |
| 718 | C22 | — | 12 | 1 | no | — |
| 719 | C22 | — | 12 | 1 | no | — |
| 720 | C22 | — | 12 | 1 | no | — |
| 721 | C22 | D3×#120 | 1 | 1 | yes | characteristic |
| 722 | C4 | — | 2 | 1 | no | — |
| 723 | C4 | — | 4 | 1 | no | — |
| 724 | C4 | — | 4 | 1 | no | — |
| 725 | C4 | — | 4 | 1 | no | — |
| 726 | C4 | — | 4 | 1 | no | — |
| 727 | C4 | — | 4 | 2 | no | — |
| 728 | C4 | — | 6 | 1 | no | — |
| 729 | C4 | — | 6 | 1 | no | — |
| 730 | C4 | — | 6 | 1 | no | — |
| 731 | C4 | — | 12 | 2 | no | — |
| 732 | C4 | — | 12 | 1 | no | — |
| 733 | C4 | — | 12 | 1 | no | — |
| 734 | C4 | — | 24 | 1 | no | — |
| 735 | C4 | #5762 | 1 | 1 | yes | characteristic |
| 736 | C4 | #5768 | 1 | 1 | yes | characteristic |
| 737 | C4 | D3×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 738 | C4 | #5779 | 1 | 1 | yes | characteristic |
| 739 | C3 | #18596 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 740 | C2 | — | 12 | 1 | no | — |
| 741 | C2 | — | 12 | 2 | no | — |
| 742 | C2 | — | 16 | 1 | no | — |
| 743 | C2 | — | 24 | 1 | no | — |
| 744 | C2 | #80042 | 1 | 1 | yes | characteristic |
| 745 | C2 | #80084 | 1 | 1 | yes | characteristic |
| 746 | C2 | #80284 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C22 | D3×#120 |
| commutator, cosocle | C3×C42 | C24 |
| Frattini | C42 | C23×D3 |
| Fitting | C3×#1626 | C2 |
| socle | C22×C3 | C2×#120 |
| hypercenter | #1626 | D3 |
| hypocenter | C3 | #18596 |
| LCS | G ▷ C3×C42 ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #1626 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #87021 | C2 | semidirect |
| 2. #81559 | C2 | semidirect |
| 3. #80402 | C2 | semidirect |
| 4. #80382 | C2 | semidirect |
| 5. C3×#1626 | C2 | semidirect |
| 6. #71937 | C2 | semidirect |
| 7. #71196 | C2 | semidirect |
| 8. #71028 | C2 | semidirect |
| 9. #71028 | C2 | semidirect |
| 10. #68436 | C2 | semidirect |
| 11. #68423 | C2 | semidirect |
| 12. #68270 | C2 | semidirect |
| 13. #68249 | C2 | semidirect |
| 14. #68238 | C2 | semidirect |
| 15. #68234 | C2 | semidirect |
| 80. #1626 | D3 | semidirect |
| 739. C3 | #18596 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #87021 | 2 |
| #81559 | 2 |
| #80402 | 2 |
| #80382 | 2 |
| C3×#1626 | 2 |
| #71937 | 2 |
| #71196 | 2 |
| #71028 | 2 |
| #68436 | 2 |
| #68423 | 2 |
| #68270 | 2 |
| #68249 | 2 |
| #68238 | 2 |
| #68234 | 2 |
| #18596 | 3 |