Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
1034 conjugacy classes of subgroups.
The subgroup lattice has 942 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #87113 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #81958 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #81871 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #81685 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C3×#1661 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #71952 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #71392 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #71329 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #71244 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #68370 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #68364 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #68350 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #68350 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #68343 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | #68342 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | #19018 | — | 3 | 1 | no | maximal, Sylow |
| 17 | C3×#562 | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×#918 | — | 2 | 1 | no | — |
| 19 | C2×#914 | — | 2 | 1 | no | — |
| 20 | #5725 | C22 | 1 | 1 | yes | characteristic, complemented |
| 21 | #5700 | C22 | 1 | 1 | yes | characteristic |
| 22 | #5691 | C22 | 1 | 1 | yes | characteristic |
| 23 | #5683 | C22 | 1 | 1 | yes | characteristic |
| 24 | #5683 | C22 | 1 | 1 | yes | characteristic |
| 25 | D3×#124 | C22 | 1 | 1 | yes | characteristic |
| 26 | #5668 | C22 | 1 | 1 | yes | characteristic |
| 27 | #5664 | — | 2 | 1 | no | — |
| 28 | #5657 | — | 2 | 1 | no | — |
| 29 | #5654 | — | 2 | 1 | no | — |
| 30 | #5653 | — | 2 | 1 | no | — |
| 31 | #5644 | — | 2 | 1 | no | — |
| 32 | #5640 | — | 2 | 1 | no | — |
| 33 | #5633 | — | 2 | 1 | no | — |
| 34 | #5630 | — | 2 | 1 | no | — |
| 35 | #5613 | — | 2 | 1 | no | — |
| 36 | #5610 | — | 2 | 1 | no | — |
| 37 | #5609 | — | 2 | 1 | no | — |
| 38 | #5607 | — | 2 | 1 | no | — |
| 39 | C3×#501 | C22 | 1 | 1 | yes | characteristic, complemented |
| 40 | C3×#497 | C22 | 1 | 1 | yes | characteristic, complemented |
| 41 | C3×#489 | C22 | 1 | 1 | yes | characteristic, complemented |
| 42 | #5191 | — | 2 | 1 | no | — |
| 43 | #5168 | — | 2 | 1 | no | — |
| 44 | #5089 | C22 | 1 | 1 | yes | characteristic, complemented |
| 45 | #5089 | C22 | 1 | 1 | yes | characteristic, complemented |
| 46 | #5086 | C22 | 1 | 1 | yes | characteristic, complemented |
| 47 | #5067 | C22 | 1 | 1 | yes | characteristic, complemented |
| 48 | #5058 | C22 | 1 | 1 | yes | characteristic, complemented |
| 49 | #5058 | C22 | 1 | 1 | yes | characteristic, complemented |
| 50 | #4886 | — | 2 | 1 | no | — |
| 51 | #4872 | — | 2 | 1 | no | — |
| 52 | #4865 | — | 2 | 1 | no | — |
| 53 | #4852 | — | 2 | 1 | no | — |
| 54 | #4818 | — | 2 | 1 | no | — |
| 55 | #4810 | — | 2 | 1 | no | — |
| 56 | #4786 | — | 2 | 1 | no | — |
| 57 | #4781 | — | 2 | 1 | no | — |
| 58 | #4712 | C22 | 1 | 1 | yes | characteristic, complemented |
| 59 | #4712 | C22 | 1 | 1 | yes | characteristic, complemented |
| 60 | #4712 | C22 | 1 | 1 | yes | characteristic, complemented |
| 61 | #4707 | C22 | 1 | 1 | yes | characteristic, complemented |
| 62 | #4707 | C22 | 1 | 1 | yes | characteristic, complemented |
| 63 | #4705 | C22 | 1 | 1 | yes | characteristic, complemented |
| 64 | C3×#330 | C22 | 1 | 1 | yes | characteristic, complemented |
| 65 | C3×#329 | C22 | 1 | 1 | yes | characteristic, complemented |
| 66 | C3×#329 | C22 | 1 | 1 | yes | characteristic, complemented |
| 67 | #4543 | C22 | 1 | 1 | yes | characteristic, complemented |
| 68 | #4540 | C22 | 1 | 1 | yes | characteristic, complemented |
| 69 | #4540 | C22 | 1 | 1 | yes | characteristic, complemented |
| 70 | #4464 | C22 | 1 | 1 | yes | characteristic, complemented |
| 71 | #4464 | C22 | 1 | 1 | yes | characteristic, complemented |
| 72 | #4464 | C22 | 1 | 1 | yes | characteristic, complemented |
| 73 | #4464 | C22 | 1 | 1 | yes | characteristic, complemented |
| 74 | #4464 | C22 | 1 | 1 | yes | characteristic, complemented |
| 75 | #4464 | C22 | 1 | 1 | yes | characteristic, complemented |
| 76 | #3558 | — | 3 | 1 | no | — |
| 77 | #3214 | — | 3 | 1 | no | — |
| 78 | #3171 | — | 3 | 1 | no | — |
| 79 | #3153 | — | 3 | 1 | no | — |
| 80 | #1661 | — | 3 | 1 | no | — |
| 81 | #1661 | D3 | 1 | 1 | yes | characteristic, complemented |
| 82 | #1659 | — | 3 | 1 | no | — |
| 83 | #1659 | — | 3 | 1 | no | — |
| 84 | #1656 | — | 3 | 1 | no | — |
| 85 | #1656 | — | 3 | 1 | no | — |
| 86 | #1655 | — | 3 | 1 | no | — |
| 87 | #1655 | — | 3 | 1 | no | — |
| 88 | #1529 | — | 3 | 1 | no | — |
| 89 | #1527 | — | 3 | 1 | no | — |
| 90 | #1525 | — | 3 | 1 | no | — |
| 91 | C2×#239 | — | 2 | 1 | no | — |
| 92 | C2×#239 | D4 | 1 | 1 | yes | characteristic |
| 93 | C2×D3×Q8 | D4 | 1 | 1 | yes | characteristic |
| 94 | C2×#237 | D4 | 1 | 1 | yes | characteristic |
| 95 | C2×D3×D4 | — | 2 | 1 | no | — |
| 96 | C2×D3×D4 | — | 2 | 1 | no | — |
| 97 | C2×D3×D4 | D4 | 1 | 1 | yes | characteristic |
| 98 | C2×#235 | — | 2 | 1 | no | — |
| 99 | C22×D12 | — | 2 | 1 | no | — |
| 100 | C2×C3×Q16 | — | 2 | 1 | no | — |
| 101 | C2×C3×SD16 | — | 2 | 1 | no | — |
| 102 | C3×C4⋊Q8 | C23 | 1 | 1 | yes | characteristic |
| 103 | C3×#125 | C23 | 1 | 1 | yes | characteristic |
| 104 | C3×#124 | C23 | 1 | 1 | yes | characteristic |
| 105 | C3×#124 | C23 | 1 | 1 | yes | characteristic |
| 106 | C3×#123 | — | 2 | 1 | no | — |
| 107 | C3×#123 | — | 2 | 1 | no | — |
| 108 | C3×C22⋊Q8 | — | 2 | 1 | no | — |
| 109 | C3×C22⋊Q8 | — | 2 | 1 | no | — |
| 110 | C3×#121 | — | 2 | 1 | no | — |
| 111 | C3×#121 | — | 2 | 1 | no | — |
| 112 | #947 | — | 2 | 1 | no | — |
| 113 | #947 | — | 2 | 1 | no | — |
| 114 | #947 | — | 2 | 1 | no | — |
| 115 | #947 | D4 | 1 | 1 | yes | characteristic |
| 116 | #944 | D4 | 1 | 1 | yes | characteristic |
| 117 | C2×#216 | — | 2 | 1 | no | — |
| 118 | C2×#215 | — | 2 | 1 | no | — |
| 119 | C2×#215 | — | 2 | 1 | no | — |
| 120 | C2×#215 | — | 2 | 1 | no | — |
| 121 | #940 | — | 2 | 1 | no | — |
| 122 | #940 | D4 | 1 | 1 | yes | characteristic |
| 123 | #939 | — | 2 | 1 | no | — |
| 124 | #938 | — | 2 | 1 | no | — |
| 125 | #937 | — | 2 | 1 | no | — |
| 126 | #937 | — | 2 | 1 | no | — |
| 127 | #937 | — | 2 | 1 | no | — |
| 128 | #937 | — | 2 | 1 | no | — |
| 129 | #936 | D4 | 1 | 1 | yes | characteristic |
| 130 | #935 | — | 2 | 1 | no | — |
| 131 | C2×#213 | — | 2 | 1 | no | — |
| 132 | C2×#213 | — | 2 | 1 | no | — |
| 133 | #930 | — | 2 | 1 | no | — |
| 134 | #929 | — | 2 | 1 | no | — |
| 135 | C4×#67 | — | 2 | 1 | no | — |
| 136 | C4×#67 | — | 2 | 1 | no | — |
| 137 | C4×#67 | — | 2 | 1 | no | — |
| 138 | C2×(C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 139 | #918 | — | 4 | 4 | no | — |
| 140 | #914 | — | 4 | 4 | no | — |
| 141 | C2×D24 | — | 2 | 1 | no | — |
| 142 | C2×D24 | — | 2 | 1 | no | — |
| 143 | C2×D24 | — | 2 | 1 | no | — |
| 144 | C2×#204 | — | 2 | 1 | no | — |
| 145 | C2×#204 | — | 2 | 1 | no | — |
| 146 | C2×#204 | — | 2 | 1 | no | — |
| 147 | C2×ΓL(1,𝔽25) | — | 2 | 1 | no | — |
| 148 | C2×ΓL(1,𝔽25) | — | 2 | 1 | no | — |
| 149 | #898 | — | 2 | 1 | no | — |
| 150 | #898 | — | 2 | 1 | no | — |
| 151 | #897 | D4 | 1 | 1 | yes | characteristic |
| 152 | #896 | — | 2 | 1 | no | — |
| 153 | #896 | — | 2 | 1 | no | — |
| 154 | #896 | — | 2 | 1 | no | — |
| 155 | #895 | — | 2 | 1 | no | — |
| 156 | #895 | — | 2 | 1 | no | — |
| 157 | #895 | — | 2 | 1 | no | — |
| 158 | #895 | — | 2 | 1 | no | — |
| 159 | #895 | — | 2 | 1 | no | — |
| 160 | #895 | — | 2 | 1 | no | — |
| 161 | #895 | D4 | 1 | 1 | yes | characteristic |
| 162 | #894 | — | 2 | 1 | no | — |
| 163 | #894 | — | 2 | 1 | no | — |
| 164 | #894 | — | 2 | 1 | no | — |
| 165 | #894 | — | 2 | 1 | no | — |
| 166 | #894 | — | 2 | 1 | no | — |
| 167 | #893 | — | 2 | 1 | no | — |
| 168 | #893 | — | 2 | 1 | no | — |
| 169 | #893 | — | 2 | 1 | no | — |
| 170 | #893 | — | 2 | 1 | no | — |
| 171 | #893 | D4 | 1 | 1 | yes | characteristic |
| 172 | #892 | — | 2 | 1 | no | — |
| 173 | #887 | — | 2 | 1 | no | — |
| 174 | #887 | D4 | 1 | 1 | yes | characteristic |
| 175 | #885 | — | 2 | 1 | no | — |
| 176 | #885 | — | 2 | 1 | no | — |
| 177 | #885 | — | 2 | 1 | no | — |
| 178 | #885 | — | 2 | 1 | no | — |
| 179 | #885 | — | 2 | 1 | no | — |
| 180 | #885 | — | 2 | 1 | no | — |
| 181 | #885 | — | 2 | 1 | no | — |
| 182 | #884 | — | 2 | 1 | no | — |
| 183 | #884 | — | 2 | 1 | no | — |
| 184 | #884 | — | 2 | 1 | no | — |
| 185 | #884 | — | 2 | 1 | no | — |
| 186 | #882 | — | 2 | 1 | no | — |
| 187 | #882 | — | 2 | 1 | no | — |
| 188 | #882 | — | 2 | 1 | no | — |
| 189 | #882 | — | 2 | 1 | no | — |
| 190 | #882 | — | 2 | 1 | no | — |
| 191 | #882 | — | 2 | 1 | no | — |
| 192 | #67⋊C4 | — | 2 | 1 | no | — |
| 193 | #67⋊C4 | — | 2 | 1 | no | — |
| 194 | #67⋊C4 | — | 2 | 1 | no | — |
| 195 | D3×C22⋊C4 | — | 2 | 1 | no | — |
| 196 | D3×C22⋊C4 | — | 2 | 1 | no | — |
| 197 | D3×C22⋊C4 | — | 2 | 1 | no | — |
| 198 | #879 | — | 2 | 1 | no | — |
| 199 | #875 | C23 | 1 | 1 | yes | characteristic |
| 200 | #875 | C23 | 1 | 1 | yes | characteristic |
| 201 | #875 | C23 | 1 | 1 | yes | characteristic |
| 202 | #874 | C23 | 1 | 1 | yes | characteristic |
| 203 | C42×D3 | C23 | 1 | 1 | yes | characteristic |
| 204 | C3×#107 | — | 2 | 1 | no | — |
| 205 | C3×#106 | — | 2 | 1 | no | — |
| 206 | C3×#103 | — | 2 | 1 | no | — |
| 207 | C3×#102 | — | 2 | 1 | no | — |
| 208 | C3×#97 | C23 | 1 | 1 | yes | characteristic |
| 209 | C3×#97 | C23 | 1 | 1 | yes | characteristic |
| 210 | C3×#97 | C23 | 1 | 1 | yes | characteristic |
| 211 | (C2×D3)⋊C8 | — | 2 | 1 | no | — |
| 212 | Dic3⋊C8 | — | 2 | 1 | no | — |
| 213 | C8×Dic3 | — | 2 | 1 | no | — |
| 214 | C8×Dic3 | — | 2 | 1 | no | — |
| 215 | #810 | — | 2 | 1 | no | — |
| 216 | #810 | — | 2 | 1 | no | — |
| 217 | #809 | — | 2 | 1 | no | — |
| 218 | #809 | — | 2 | 1 | no | — |
| 219 | #809 | — | 2 | 1 | no | — |
| 220 | #809 | — | 2 | 1 | no | — |
| 221 | #803 | C23 | 1 | 1 | yes | characteristic |
| 222 | #803 | C23 | 1 | 1 | yes | characteristic |
| 223 | #803 | C23 | 1 | 1 | yes | characteristic |
| 224 | C2×#137 | — | 6 | 1 | no | — |
| 225 | C2×AGL(1,ℤ/8) | — | 6 | 1 | no | — |
| 226 | #562 | — | 3 | 1 | no | — |
| 227 | #562 | C2×D3 | 1 | 1 | yes | characteristic |
| 228 | H(3,𝔽4) | — | 3 | 1 | no | — |
| 229 | H(3,𝔽4) | — | 3 | 1 | no | — |
| 230 | #559 | — | 6 | 1 | no | — |
| 231 | #548 | — | 6 | 1 | no | — |
| 232 | #546 | — | 6 | 1 | no | — |
| 233 | #546 | — | 6 | 1 | no | — |
| 234 | #546 | — | 6 | 1 | no | — |
| 235 | D42 | — | 6 | 1 | no | — |
| 236 | #542 | — | 6 | 1 | no | — |
| 237 | #538 | — | 6 | 1 | no | — |
| 238 | #538 | — | 6 | 1 | no | — |
| 239 | #538 | — | 6 | 1 | no | — |
| 240 | #535 | — | 6 | 1 | no | — |
| 241 | #534 | — | 6 | 1 | no | — |
| 242 | #532 | — | 3 | 1 | no | — |
| 243 | #532 | — | 3 | 1 | no | — |
| 244 | #529 | — | 3 | 1 | no | — |
| 245 | C2×#124 | — | 3 | 1 | no | — |
| 246 | #501 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 247 | #497 | — | 3 | 1 | no | — |
| 248 | #497 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 249 | #496 | — | 3 | 1 | no | — |
| 250 | #496 | — | 3 | 1 | no | — |
| 251 | #496 | — | 3 | 1 | no | — |
| 252 | #496 | — | 3 | 1 | no | — |
| 253 | #496 | — | 3 | 1 | no | — |
| 254 | #495 | — | 6 | 1 | no | — |
| 255 | #495 | — | 6 | 1 | no | — |
| 256 | #490 | — | 3 | 1 | no | — |
| 257 | #489 | — | 3 | 1 | no | — |
| 258 | #489 | — | 3 | 1 | no | — |
| 259 | #489 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 260 | #469 | — | 6 | 1 | no | — |
| 261 | #468 | — | 6 | 1 | no | — |
| 262 | #461 | — | 6 | 1 | no | — |
| 263 | #459 | — | 6 | 1 | no | — |
| 264 | #449 | — | 6 | 1 | no | — |
| 265 | #449 | — | 6 | 1 | no | — |
| 266 | C4×SD16 | — | 6 | 1 | no | — |
| 267 | C4×D8 | — | 6 | 1 | no | — |
| 268 | #432 | — | 3 | 1 | no | — |
| 269 | C4×M16 | — | 3 | 1 | no | — |
| 270 | C4×M16 | — | 3 | 1 | no | — |
| 271 | #330 | — | 3 | 1 | no | — |
| 272 | #330 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 273 | #329 | — | 3 | 1 | no | — |
| 274 | #329 | — | 3 | 1 | no | — |
| 275 | #329 | — | 3 | 1 | no | — |
| 276 | #329 | — | 3 | 1 | no | — |
| 277 | #329 | — | 3 | 1 | no | — |
| 278 | #329 | — | 3 | 1 | no | — |
| 279 | #329 | — | 3 | 1 | no | — |
| 280 | #329 | — | 3 | 1 | no | — |
| 281 | #329 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 282 | #329 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 283 | C23×D3 | — | 2 | 1 | no | — |
| 284 | C23×D3 | — | 2 | 1 | no | — |
| 285 | C23×D3 | — | 2 | 1 | no | — |
| 286 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 287 | C2×C3×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 288 | C2×C3×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 289 | C2×C3×D4 | — | 2 | 1 | no | — |
| 290 | C2×C3×D4 | — | 2 | 1 | no | — |
| 291 | C2×C3×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 292 | C2×C3×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 293 | C22×C3×C4 | — | 2 | 1 | no | — |
| 294 | C22×C3×C4 | — | 2 | 1 | no | — |
| 295 | C2×#67 | — | 2 | 1 | no | — |
| 296 | C2×#67 | — | 2 | 1 | no | — |
| 297 | C2×#67 | — | 2 | 1 | no | — |
| 298 | C2×#67 | — | 2 | 1 | no | — |
| 299 | C2×#67 | — | 2 | 1 | no | — |
| 300 | C2×#67 | — | 2 | 1 | no | — |
| 301 | C2×#67 | — | 2 | 1 | no | — |
| 302 | C2×#67 | — | 2 | 1 | no | — |
| 303 | C22×Dic3 | — | 2 | 1 | no | — |
| 304 | #239 | — | 4 | 2 | no | — |
| 305 | #239 | — | 4 | 2 | no | — |
| 306 | #239 | — | 8 | 1 | no | — |
| 307 | D3×Q8 | — | 4 | 2 | no | — |
| 308 | #237 | — | 8 | 1 | no | — |
| 309 | D3×D4 | — | 4 | 2 | no | — |
| 310 | D3×D4 | — | 8 | 2 | no | — |
| 311 | D3×D4 | — | 8 | 2 | no | — |
| 312 | #235 | — | 8 | 2 | no | — |
| 313 | C2×D12 | — | 2 | 1 | no | — |
| 314 | C2×D12 | — | 2 | 1 | no | — |
| 315 | C2×D12 | — | 2 | 1 | no | — |
| 316 | C2×D12 | — | 2 | 1 | no | — |
| 317 | C2×D12 | — | 2 | 1 | no | — |
| 318 | C2×D12 | — | 2 | 1 | no | — |
| 319 | C2×D12 | — | 2 | 1 | no | — |
| 320 | C2×D12 | — | 2 | 1 | no | — |
| 321 | C2×D12 | — | 2 | 1 | no | — |
| 322 | C2×D12 | — | 4 | 1 | no | — |
| 323 | C2×D12 | — | 8 | 2 | no | — |
| 324 | C2×D12 | C2×D4 | 1 | 1 | yes | characteristic |
| 325 | C2×D12 | C2×D4 | 1 | 1 | yes | characteristic |
| 326 | C2×D12 | C2×D4 | 1 | 1 | yes | characteristic |
| 327 | C2×C4×D3 | — | 2 | 1 | no | — |
| 328 | C2×C4×D3 | — | 2 | 1 | no | — |
| 329 | C2×C4×D3 | — | 2 | 1 | no | — |
| 330 | C2×C4×D3 | — | 2 | 1 | no | — |
| 331 | C2×C4×D3 | — | 2 | 1 | no | — |
| 332 | C2×C4×D3 | — | 4 | 1 | no | — |
| 333 | C2×C4×D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 334 | C2×C4×D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 335 | C2×C4×D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 336 | C2×Dic6 | — | 2 | 1 | no | — |
| 337 | C2×Dic6 | C2×D4 | 1 | 1 | yes | characteristic |
| 338 | C2×Dic6 | C2×D4 | 1 | 1 | yes | characteristic |
| 339 | C2×Dic6 | C2×D4 | 1 | 1 | yes | characteristic |
| 340 | C3×Q16 | — | 4 | 2 | no | — |
| 341 | C3×SD16 | — | 4 | 2 | no | — |
| 342 | C2×C3×C8 | — | 2 | 1 | no | — |
| 343 | C2×C3×C8 | — | 2 | 1 | no | — |
| 344 | C2×C3×C8 | — | 2 | 1 | no | — |
| 345 | C3×C4⋊C4 | — | 2 | 1 | no | — |
| 346 | C3×C4⋊C4 | — | 2 | 1 | no | — |
| 347 | C3×C4⋊C4 | — | 2 | 1 | no | — |
| 348 | C3×C4⋊C4 | — | 2 | 1 | no | — |
| 349 | C3×C4⋊C4 | — | 2 | 1 | no | — |
| 350 | C3×C4⋊C4 | — | 2 | 1 | no | — |
| 351 | C3×C4⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 352 | C3×C4⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 353 | C3×C22⋊C4 | — | 2 | 1 | no | — |
| 354 | C3×C22⋊C4 | — | 2 | 1 | no | — |
| 355 | C3×C22⋊C4 | — | 2 | 1 | no | — |
| 356 | C3×C22⋊C4 | — | 2 | 1 | no | — |
| 357 | C3×C22⋊C4 | — | 2 | 1 | no | — |
| 358 | C3×C22⋊C4 | — | 2 | 1 | no | — |
| 359 | C3×C42 | C24 | 1 | 1 | yes | characteristic |
| 360 | #217 | — | 2 | 1 | no | — |
| 361 | #217 | — | 2 | 1 | no | — |
| 362 | #217 | — | 2 | 1 | no | — |
| 363 | #217 | — | 2 | 1 | no | — |
| 364 | #216 | — | 4 | 2 | no | — |
| 365 | #215 | — | 4 | 2 | no | — |
| 366 | #215 | — | 4 | 2 | no | — |
| 367 | #215 | — | 8 | 1 | no | — |
| 368 | #213 | — | 4 | 2 | no | — |
| 369 | #213 | — | 8 | 1 | no | — |
| 370 | (C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 371 | (C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 372 | (C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 373 | (C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 374 | (C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 375 | (C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 376 | (C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 377 | (C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 378 | (C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 379 | (C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 380 | (C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 381 | (C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 382 | (C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 383 | (C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 384 | (C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 385 | (C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 386 | (C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 387 | (C2×D3)⋊C4 | — | 4 | 1 | no | — |
| 388 | (C2×D3)⋊C4 | — | 4 | 1 | no | — |
| 389 | C4⋊Dic3 | — | 2 | 1 | no | — |
| 390 | Dic3⋊C4 | — | 2 | 1 | no | — |
| 391 | Dic3⋊C4 | — | 2 | 1 | no | — |
| 392 | Dic3⋊C4 | — | 2 | 1 | no | — |
| 393 | Dic3⋊C4 | — | 2 | 1 | no | — |
| 394 | Dic3⋊C4 | — | 2 | 1 | no | — |
| 395 | C4×Dic3 | — | 2 | 1 | no | — |
| 396 | C4×Dic3 | — | 2 | 1 | no | — |
| 397 | C4×Dic3 | — | 2 | 1 | no | — |
| 398 | C4×Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 399 | C4×Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 400 | C4×Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 401 | C2×C3⋊C8 | — | 2 | 1 | no | — |
| 402 | C2×C3⋊C8 | — | 2 | 1 | no | — |
| 403 | C2×C3⋊C8 | — | 2 | 1 | no | — |
| 404 | D24 | — | 4 | 2 | no | — |
| 405 | D24 | — | 4 | 2 | no | — |
| 406 | D24 | — | 8 | 1 | no | — |
| 407 | #204 | — | 4 | 2 | no | — |
| 408 | #204 | — | 4 | 2 | no | — |
| 409 | #204 | — | 8 | 1 | no | — |
| 410 | ΓL(1,𝔽25) | — | 2 | 4 | no | — |
| 411 | ΓL(1,𝔽25) | — | 4 | 2 | no | — |
| 412 | C2×#41 | — | 3 | 1 | no | — |
| 413 | C2×#41 | — | 3 | 1 | no | — |
| 414 | C2×#41 | — | 6 | 1 | no | — |
| 415 | C2×#41 | — | 6 | 1 | no | — |
| 416 | C22×Q8 | — | 3 | 1 | no | — |
| 417 | C22×D4 | — | 3 | 1 | no | — |
| 418 | C22×D4 | — | 6 | 1 | no | — |
| 419 | C22×D4 | — | 6 | 1 | no | — |
| 420 | C22×D4 | — | 6 | 1 | no | — |
| 421 | #137 | — | 12 | 4 | no | — |
| 422 | AGL(1,ℤ/8) | — | 12 | 4 | no | — |
| 423 | C2×Q16 | — | 2 | 1 | no | — |
| 424 | C2×Q16 | — | 6 | 1 | no | — |
| 425 | C2×SD16 | — | 2 | 1 | no | — |
| 426 | C2×SD16 | — | 6 | 1 | no | — |
| 427 | C2×SD16 | — | 6 | 1 | no | — |
| 428 | C2×SD16 | — | 6 | 1 | no | — |
| 429 | C2×SD16 | — | 6 | 1 | no | — |
| 430 | C2×SD16 | — | 6 | 1 | no | — |
| 431 | C2×SD16 | — | 6 | 1 | no | — |
| 432 | C2×D8 | — | 6 | 1 | no | — |
| 433 | C2×D8 | — | 6 | 1 | no | — |
| 434 | C2×D8 | — | 6 | 1 | no | — |
| 435 | C2×D8 | — | 6 | 1 | no | — |
| 436 | C2×D8 | — | 6 | 1 | no | — |
| 437 | C2×M16 | — | 6 | 1 | no | — |
| 438 | C2×M16 | — | 6 | 1 | no | — |
| 439 | C4⋊Q8 | — | 3 | 1 | no | — |
| 440 | C4⋊Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 441 | #127 | — | 3 | 1 | no | — |
| 442 | #127 | — | 3 | 1 | no | — |
| 443 | #127 | — | 6 | 1 | no | — |
| 444 | #126 | — | 6 | 1 | no | — |
| 445 | #126 | — | 6 | 1 | no | — |
| 446 | #126 | — | 6 | 1 | no | — |
| 447 | #125 | C22×D3 | 1 | 1 | yes | characteristic |
| 448 | #124 | — | 3 | 1 | no | — |
| 449 | #124 | — | 3 | 1 | no | — |
| 450 | #124 | — | 3 | 1 | no | — |
| 451 | #124 | — | 3 | 1 | no | — |
| 452 | #124 | — | 3 | 1 | no | — |
| 453 | #124 | — | 6 | 1 | no | — |
| 454 | #124 | — | 6 | 1 | no | — |
| 455 | #124 | — | 6 | 1 | no | — |
| 456 | #124 | — | 6 | 1 | no | — |
| 457 | #124 | — | 6 | 1 | no | — |
| 458 | #124 | — | 6 | 1 | no | — |
| 459 | #124 | — | 6 | 1 | no | — |
| 460 | #124 | — | 6 | 1 | no | — |
| 461 | #124 | — | 6 | 1 | no | — |
| 462 | #124 | — | 6 | 1 | no | — |
| 463 | #124 | C22×D3 | 1 | 1 | yes | characteristic |
| 464 | #124 | C22×D3 | 1 | 1 | yes | characteristic |
| 465 | #123 | — | 2 | 1 | no | — |
| 466 | #123 | — | 2 | 1 | no | — |
| 467 | #123 | — | 6 | 1 | no | — |
| 468 | #123 | — | 6 | 1 | no | — |
| 469 | #123 | — | 6 | 1 | no | — |
| 470 | #123 | — | 6 | 1 | no | — |
| 471 | #123 | — | 6 | 1 | no | — |
| 472 | #123 | — | 6 | 1 | no | — |
| 473 | #123 | — | 6 | 1 | no | — |
| 474 | C22⋊Q8 | — | 2 | 1 | no | — |
| 475 | C22⋊Q8 | — | 2 | 1 | no | — |
| 476 | C22⋊Q8 | — | 3 | 1 | no | — |
| 477 | C22⋊Q8 | — | 6 | 1 | no | — |
| 478 | C22⋊Q8 | — | 6 | 1 | no | — |
| 479 | C22⋊Q8 | — | 6 | 1 | no | — |
| 480 | #121 | — | 2 | 1 | no | — |
| 481 | #121 | — | 2 | 1 | no | — |
| 482 | #121 | — | 3 | 1 | no | — |
| 483 | #121 | — | 6 | 1 | no | — |
| 484 | #121 | — | 6 | 1 | no | — |
| 485 | #121 | — | 6 | 1 | no | — |
| 486 | #121 | — | 6 | 1 | no | — |
| 487 | #121 | — | 6 | 1 | no | — |
| 488 | #121 | — | 6 | 1 | no | — |
| 489 | #121 | — | 6 | 1 | no | — |
| 490 | #121 | — | 6 | 1 | no | — |
| 491 | #121 | — | 6 | 1 | no | — |
| 492 | #121 | — | 6 | 1 | no | — |
| 493 | #121 | — | 6 | 1 | no | — |
| 494 | #121 | — | 6 | 1 | no | — |
| 495 | #121 | — | 6 | 1 | no | — |
| 496 | #120 | — | 6 | 1 | no | — |
| 497 | #120 | — | 6 | 1 | no | — |
| 498 | #120 | — | 6 | 1 | no | — |
| 499 | #120 | — | 6 | 1 | no | — |
| 500 | #120 | — | 6 | 1 | no | — |
| 501 | #120 | — | 6 | 1 | no | — |
| 502 | #120 | — | 6 | 1 | no | — |
| 503 | #120 | — | 6 | 1 | no | — |
| 504 | #120 | — | 6 | 1 | no | — |
| 505 | #120 | — | 6 | 1 | no | — |
| 506 | C4×Q8 | — | 3 | 1 | no | — |
| 507 | C4×Q8 | — | 6 | 1 | no | — |
| 508 | C4×D4 | — | 3 | 1 | no | — |
| 509 | C4×D4 | — | 6 | 1 | no | — |
| 510 | C4×D4 | — | 6 | 1 | no | — |
| 511 | C4×D4 | — | 6 | 1 | no | — |
| 512 | C4×D4 | — | 6 | 1 | no | — |
| 513 | C4×D4 | — | 6 | 1 | no | — |
| 514 | C4×D4 | — | 6 | 1 | no | — |
| 515 | C4×D4 | — | 6 | 1 | no | — |
| 516 | C4×D4 | — | 6 | 1 | no | — |
| 517 | C4×D4 | — | 6 | 1 | no | — |
| 518 | C4×D4 | — | 6 | 1 | no | — |
| 519 | #117 | — | 6 | 1 | no | — |
| 520 | C2×C22⋊C4 | — | 6 | 1 | no | — |
| 521 | C2×C22⋊C4 | — | 6 | 1 | no | — |
| 522 | C2×C22⋊C4 | — | 6 | 1 | no | — |
| 523 | C2×C22⋊C4 | — | 6 | 1 | no | — |
| 524 | C2×C42 | — | 3 | 1 | no | — |
| 525 | #107 | — | 2 | 1 | no | — |
| 526 | #106 | — | 2 | 1 | no | — |
| 527 | C4⋊C8 | — | 6 | 1 | no | — |
| 528 | #103 | — | 2 | 1 | no | — |
| 529 | #103 | — | 6 | 1 | no | — |
| 530 | #103 | — | 6 | 1 | no | — |
| 531 | #102 | — | 2 | 1 | no | — |
| 532 | #102 | — | 6 | 1 | no | — |
| 533 | #102 | — | 6 | 1 | no | — |
| 534 | #102 | — | 6 | 1 | no | — |
| 535 | #102 | — | 6 | 1 | no | — |
| 536 | C22⋊C8 | — | 6 | 1 | no | — |
| 537 | #97 | — | 3 | 1 | no | — |
| 538 | #97 | — | 3 | 1 | no | — |
| 539 | #97 | — | 3 | 1 | no | — |
| 540 | #97 | C22×D3 | 1 | 1 | yes | characteristic |
| 541 | #97 | C22×D3 | 1 | 1 | yes | characteristic |
| 542 | #97 | C22×D3 | 1 | 1 | yes | characteristic |
| 543 | C4×C8 | — | 6 | 1 | no | — |
| 544 | C4×C8 | — | 6 | 1 | no | — |
| 545 | C23×C3 | — | 2 | 1 | no | — |
| 546 | C23×C3 | — | 2 | 1 | no | — |
| 547 | C22×D3 | — | 2 | 1 | no | — |
| 548 | C22×D3 | — | 2 | 1 | no | — |
| 549 | C22×D3 | — | 2 | 1 | no | — |
| 550 | C22×D3 | — | 4 | 2 | no | — |
| 551 | C22×D3 | — | 4 | 1 | no | — |
| 552 | C22×D3 | — | 8 | 1 | no | — |
| 553 | C22×D3 | — | 8 | 1 | no | — |
| 554 | C22×D3 | — | 8 | 1 | no | — |
| 555 | C22×D3 | — | 8 | 1 | no | — |
| 556 | C22×D3 | — | 8 | 1 | no | — |
| 557 | C22×D3 | — | 8 | 1 | no | — |
| 558 | C22×D3 | — | 8 | 1 | no | — |
| 559 | C22×D3 | — | 8 | 1 | no | — |
| 560 | C22×D3 | #120 | 1 | 1 | yes | characteristic |
| 561 | C3×Q8 | — | 4 | 1 | no | — |
| 562 | C3×Q8 | — | 4 | 1 | no | — |
| 563 | C3×Q8 | — | 4 | 1 | no | — |
| 564 | C3×Q8 | — | 4 | 1 | no | — |
| 565 | C3×D4 | — | 4 | 1 | no | — |
| 566 | C3×D4 | — | 4 | 1 | no | — |
| 567 | C3×D4 | — | 8 | 1 | no | — |
| 568 | C3×D4 | — | 8 | 1 | no | — |
| 569 | C2×C3×C4 | — | 2 | 1 | no | — |
| 570 | C2×C3×C4 | — | 2 | 1 | no | — |
| 571 | C2×C3×C4 | — | 2 | 1 | no | — |
| 572 | C2×C3×C4 | — | 2 | 1 | no | — |
| 573 | C2×C3×C4 | — | 4 | 1 | no | — |
| 574 | C2×C3×C4 | — | 8 | 1 | no | — |
| 575 | C2×C3×C4 | — | 8 | 1 | no | — |
| 576 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 577 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 578 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 579 | #67 | — | 4 | 2 | no | — |
| 580 | #67 | — | 4 | 2 | no | — |
| 581 | #67 | — | 4 | 2 | no | — |
| 582 | #67 | — | 8 | 1 | no | — |
| 583 | #67 | — | 8 | 1 | no | — |
| 584 | #67 | — | 8 | 1 | no | — |
| 585 | #67 | — | 8 | 1 | no | — |
| 586 | #67 | — | 8 | 1 | no | — |
| 587 | C2×Dic3 | — | 2 | 1 | no | — |
| 588 | C2×Dic3 | — | 2 | 1 | no | — |
| 589 | C2×Dic3 | — | 2 | 1 | no | — |
| 590 | C2×Dic3 | — | 8 | 1 | no | — |
| 591 | C2×Dic3 | #120 | 1 | 1 | yes | characteristic |
| 592 | C2×Dic3 | #120 | 1 | 1 | yes | characteristic |
| 593 | C2×Dic3 | #120 | 1 | 1 | yes | characteristic |
| 594 | D12 | — | 4 | 1 | no | — |
| 595 | D12 | — | 4 | 1 | no | — |
| 596 | D12 | — | 4 | 1 | no | — |
| 597 | D12 | — | 4 | 1 | no | — |
| 598 | D12 | — | 4 | 1 | no | — |
| 599 | D12 | — | 4 | 1 | no | — |
| 600 | D12 | — | 4 | 1 | no | — |
| 601 | D12 | — | 4 | 1 | no | — |
| 602 | D12 | — | 4 | 1 | no | — |
| 603 | D12 | — | 4 | 2 | no | — |
| 604 | D12 | — | 4 | 2 | no | — |
| 605 | D12 | — | 8 | 1 | no | — |
| 606 | D12 | — | 8 | 1 | no | — |
| 607 | D12 | — | 8 | 1 | no | — |
| 608 | D12 | — | 8 | 1 | no | — |
| 609 | D12 | — | 8 | 2 | no | — |
| 610 | C4×D3 | — | 2 | 2 | no | — |
| 611 | C4×D3 | — | 4 | 1 | no | — |
| 612 | C4×D3 | — | 4 | 1 | no | — |
| 613 | C4×D3 | — | 4 | 2 | no | — |
| 614 | C4×D3 | — | 8 | 1 | no | — |
| 615 | C4×D3 | — | 8 | 1 | no | — |
| 616 | C4×D3 | — | 8 | 1 | no | — |
| 617 | C4×D3 | — | 8 | 1 | no | — |
| 618 | C4×D3 | — | 8 | 2 | no | — |
| 619 | Dic6 | — | 4 | 2 | no | — |
| 620 | Dic6 | — | 4 | 1 | no | — |
| 621 | Dic6 | — | 4 | 1 | no | — |
| 622 | Dic6 | — | 4 | 1 | no | — |
| 623 | C3×C8 | — | 2 | 2 | no | — |
| 624 | C3×C8 | — | 2 | 2 | no | — |
| 625 | C3×C8 | — | 4 | 1 | no | — |
| 626 | C3⋊C8 | — | 2 | 2 | no | — |
| 627 | C3⋊C8 | — | 4 | 1 | no | — |
| 628 | C3⋊C8 | — | 4 | 1 | no | — |
| 629 | C24 | — | 6 | 1 | no | — |
| 630 | C24 | — | 6 | 1 | no | — |
| 631 | C24 | — | 6 | 1 | no | — |
| 632 | #41 | — | 12 | 2 | no | — |
| 633 | #41 | — | 12 | 2 | no | — |
| 634 | #41 | — | 24 | 2 | no | — |
| 635 | #41 | — | 24 | 1 | no | — |
| 636 | #41 | — | 24 | 1 | no | — |
| 637 | C2×Q8 | — | 2 | 1 | no | — |
| 638 | C2×Q8 | — | 3 | 1 | no | — |
| 639 | C2×Q8 | — | 3 | 1 | no | — |
| 640 | C2×Q8 | — | 3 | 1 | no | — |
| 641 | C2×Q8 | — | 6 | 1 | no | — |
| 642 | C2×Q8 | — | 12 | 2 | no | — |
| 643 | C2×Q8 | D3×D4 | 1 | 1 | yes | characteristic |
| 644 | C2×Q8 | D3×D4 | 1 | 1 | yes | characteristic |
| 645 | C2×D4 | — | 2 | 1 | no | — |
| 646 | C2×D4 | — | 2 | 1 | no | — |
| 647 | C2×D4 | — | 3 | 1 | no | — |
| 648 | C2×D4 | — | 3 | 1 | no | — |
| 649 | C2×D4 | — | 3 | 1 | no | — |
| 650 | C2×D4 | — | 6 | 1 | no | — |
| 651 | C2×D4 | — | 6 | 1 | no | — |
| 652 | C2×D4 | — | 6 | 1 | no | — |
| 653 | C2×D4 | — | 6 | 1 | no | — |
| 654 | C2×D4 | — | 6 | 1 | no | — |
| 655 | C2×D4 | — | 6 | 1 | no | — |
| 656 | C2×D4 | — | 6 | 1 | no | — |
| 657 | C2×D4 | — | 6 | 1 | no | — |
| 658 | C2×D4 | — | 6 | 1 | no | — |
| 659 | C2×D4 | — | 6 | 1 | no | — |
| 660 | C2×D4 | — | 6 | 1 | no | — |
| 661 | C2×D4 | — | 6 | 1 | no | — |
| 662 | C2×D4 | — | 6 | 1 | no | — |
| 663 | C2×D4 | — | 6 | 1 | no | — |
| 664 | C2×D4 | — | 6 | 1 | no | — |
| 665 | C2×D4 | — | 6 | 1 | no | — |
| 666 | C2×D4 | — | 6 | 1 | no | — |
| 667 | C2×D4 | — | 12 | 1 | no | — |
| 668 | C2×D4 | — | 12 | 2 | no | — |
| 669 | C2×D4 | — | 24 | 2 | no | — |
| 670 | C2×D4 | — | 24 | 2 | no | — |
| 671 | C2×D4 | — | 24 | 2 | no | — |
| 672 | C2×D4 | D3×D4 | 1 | 1 | yes | characteristic |
| 673 | C2×D4 | D3×D4 | 1 | 1 | yes | characteristic |
| 674 | C22×C4 | — | 2 | 1 | no | — |
| 675 | C22×C4 | — | 2 | 1 | no | — |
| 676 | C22×C4 | — | 3 | 1 | no | — |
| 677 | C22×C4 | — | 3 | 1 | no | — |
| 678 | C22×C4 | — | 3 | 1 | no | — |
| 679 | C22×C4 | — | 6 | 1 | no | — |
| 680 | C22×C4 | — | 6 | 1 | no | — |
| 681 | C22×C4 | — | 6 | 1 | no | — |
| 682 | C22×C4 | — | 6 | 1 | no | — |
| 683 | C22×C4 | — | 6 | 1 | no | — |
| 684 | C22×C4 | — | 6 | 1 | no | — |
| 685 | C22×C4 | — | 12 | 1 | no | — |
| 686 | Q16 | — | 4 | 2 | no | — |
| 687 | Q16 | — | 12 | 2 | no | — |
| 688 | SD16 | — | 4 | 2 | no | — |
| 689 | SD16 | — | 12 | 2 | no | — |
| 690 | SD16 | — | 12 | 2 | no | — |
| 691 | SD16 | — | 12 | 2 | no | — |
| 692 | SD16 | — | 12 | 2 | no | — |
| 693 | SD16 | — | 24 | 1 | no | — |
| 694 | SD16 | — | 24 | 1 | no | — |
| 695 | D8 | — | 12 | 2 | no | — |
| 696 | D8 | — | 12 | 2 | no | — |
| 697 | D8 | — | 12 | 2 | no | — |
| 698 | D8 | — | 24 | 1 | no | — |
| 699 | D8 | — | 24 | 1 | no | — |
| 700 | M16 | — | 6 | 4 | no | — |
| 701 | M16 | — | 12 | 2 | no | — |
| 702 | C2×C8 | — | 2 | 1 | no | — |
| 703 | C2×C8 | — | 2 | 1 | no | — |
| 704 | C2×C8 | — | 2 | 1 | no | — |
| 705 | C2×C8 | — | 6 | 1 | no | — |
| 706 | C2×C8 | — | 6 | 1 | no | — |
| 707 | C2×C8 | — | 6 | 1 | no | — |
| 708 | C4⋊C4 | — | 2 | 1 | no | — |
| 709 | C4⋊C4 | — | 2 | 1 | no | — |
| 710 | C4⋊C4 | — | 2 | 1 | no | — |
| 711 | C4⋊C4 | — | 2 | 1 | no | — |
| 712 | C4⋊C4 | — | 2 | 1 | no | — |
| 713 | C4⋊C4 | — | 2 | 1 | no | — |
| 714 | C4⋊C4 | — | 6 | 1 | no | — |
| 715 | C4⋊C4 | — | 6 | 1 | no | — |
| 716 | C4⋊C4 | — | 6 | 1 | no | — |
| 717 | C4⋊C4 | — | 6 | 1 | no | — |
| 718 | C4⋊C4 | — | 6 | 1 | no | — |
| 719 | C4⋊C4 | — | 6 | 1 | no | — |
| 720 | C4⋊C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 721 | C4⋊C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 722 | C22⋊C4 | — | 2 | 1 | no | — |
| 723 | C22⋊C4 | — | 2 | 1 | no | — |
| 724 | C22⋊C4 | — | 2 | 1 | no | — |
| 725 | C22⋊C4 | — | 2 | 1 | no | — |
| 726 | C22⋊C4 | — | 2 | 1 | no | — |
| 727 | C22⋊C4 | — | 2 | 1 | no | — |
| 728 | C22⋊C4 | — | 6 | 1 | no | — |
| 729 | C22⋊C4 | — | 6 | 1 | no | — |
| 730 | C22⋊C4 | — | 6 | 1 | no | — |
| 731 | C22⋊C4 | — | 6 | 1 | no | — |
| 732 | C22⋊C4 | — | 6 | 1 | no | — |
| 733 | C22⋊C4 | — | 6 | 1 | no | — |
| 734 | C22⋊C4 | — | 6 | 1 | no | — |
| 735 | C22⋊C4 | — | 6 | 1 | no | — |
| 736 | C22⋊C4 | — | 6 | 1 | no | — |
| 737 | C22⋊C4 | — | 6 | 1 | no | — |
| 738 | C22⋊C4 | — | 6 | 1 | no | — |
| 739 | C22⋊C4 | — | 6 | 1 | no | — |
| 740 | C22⋊C4 | — | 6 | 1 | no | — |
| 741 | C22⋊C4 | — | 6 | 1 | no | — |
| 742 | C22⋊C4 | — | 6 | 1 | no | — |
| 743 | C22⋊C4 | — | 6 | 1 | no | — |
| 744 | C22⋊C4 | — | 6 | 1 | no | — |
| 745 | C22⋊C4 | — | 6 | 1 | no | — |
| 746 | C22⋊C4 | — | 6 | 1 | no | — |
| 747 | C22⋊C4 | — | 6 | 1 | no | — |
| 748 | C22⋊C4 | — | 6 | 1 | no | — |
| 749 | C22⋊C4 | — | 12 | 1 | no | — |
| 750 | C22⋊C4 | — | 12 | 1 | no | — |
| 751 | C42 | — | 3 | 1 | no | — |
| 752 | C42 | — | 3 | 1 | no | — |
| 753 | C42 | — | 3 | 1 | no | — |
| 754 | C42 | — | 6 | 1 | no | — |
| 755 | C42 | — | 6 | 1 | no | — |
| 756 | C42 | — | 6 | 1 | no | — |
| 757 | C42 | C23×D3 | 1 | 1 | yes | characteristic |
| 758 | C22×C3 | — | 4 | 1 | no | — |
| 759 | C22×C3 | — | 4 | 1 | no | — |
| 760 | C22×C3 | — | 4 | 1 | no | — |
| 761 | C22×C3 | — | 4 | 1 | no | — |
| 762 | C22×C3 | — | 4 | 1 | no | — |
| 763 | C22×C3 | — | 4 | 1 | no | — |
| 764 | C22×C3 | C2×#120 | 1 | 1 | yes | characteristic |
| 765 | C2×D3 | — | 2 | 1 | no | — |
| 766 | C2×D3 | — | 2 | 1 | no | — |
| 767 | C2×D3 | — | 2 | 1 | no | — |
| 768 | C2×D3 | — | 4 | 1 | no | — |
| 769 | C2×D3 | — | 4 | 1 | no | — |
| 770 | C2×D3 | — | 4 | 1 | no | — |
| 771 | C2×D3 | — | 4 | 1 | no | — |
| 772 | C2×D3 | — | 4 | 1 | no | — |
| 773 | C2×D3 | — | 4 | 1 | no | — |
| 774 | C2×D3 | — | 4 | 1 | no | — |
| 775 | C2×D3 | — | 4 | 1 | no | — |
| 776 | C2×D3 | — | 4 | 1 | no | — |
| 777 | C2×D3 | — | 8 | 1 | no | — |
| 778 | C2×D3 | — | 8 | 1 | no | — |
| 779 | C2×D3 | — | 8 | 1 | no | — |
| 780 | C2×D3 | — | 16 | 2 | no | — |
| 781 | C2×D3 | — | 16 | 2 | no | — |
| 782 | C2×D3 | — | 16 | 2 | no | — |
| 783 | C3×C4 | — | 2 | 1 | no | — |
| 784 | C3×C4 | — | 2 | 1 | no | — |
| 785 | C3×C4 | — | 2 | 1 | no | — |
| 786 | C3×C4 | — | 4 | 1 | no | — |
| 787 | C3×C4 | — | 4 | 1 | no | — |
| 788 | C3×C4 | — | 4 | 1 | no | — |
| 789 | C3×C4 | — | 4 | 1 | no | — |
| 790 | C3×C4 | — | 8 | 1 | no | — |
| 791 | Dic3 | — | 2 | 1 | no | — |
| 792 | Dic3 | — | 2 | 1 | no | — |
| 793 | Dic3 | — | 4 | 1 | no | — |
| 794 | Dic3 | — | 4 | 1 | no | — |
| 795 | Dic3 | — | 4 | 1 | no | — |
| 796 | Dic3 | #453 | 1 | 2 | yes | — |
| 797 | C23 | — | 2 | 1 | no | — |
| 798 | C23 | — | 2 | 1 | no | — |
| 799 | C23 | — | 3 | 1 | no | — |
| 800 | C23 | — | 6 | 1 | no | — |
| 801 | C23 | — | 6 | 1 | no | — |
| 802 | C23 | — | 6 | 1 | no | — |
| 803 | C23 | — | 12 | 2 | no | — |
| 804 | C23 | — | 12 | 1 | no | — |
| 805 | C23 | — | 24 | 1 | no | — |
| 806 | C23 | — | 24 | 1 | no | — |
| 807 | C23 | — | 24 | 1 | no | — |
| 808 | C23 | — | 24 | 1 | no | — |
| 809 | C23 | — | 24 | 1 | no | — |
| 810 | C23 | — | 24 | 1 | no | — |
| 811 | C23 | — | 24 | 1 | no | — |
| 812 | C23 | — | 24 | 1 | no | — |
| 813 | Q8 | — | 4 | 1 | no | — |
| 814 | Q8 | — | 4 | 1 | no | — |
| 815 | Q8 | — | 4 | 1 | no | — |
| 816 | Q8 | — | 4 | 1 | no | — |
| 817 | Q8 | — | 12 | 1 | no | — |
| 818 | Q8 | — | 12 | 1 | no | — |
| 819 | Q8 | — | 12 | 1 | no | — |
| 820 | Q8 | — | 12 | 2 | no | — |
| 821 | D4 | — | 4 | 1 | no | — |
| 822 | D4 | — | 4 | 1 | no | — |
| 823 | D4 | — | 8 | 1 | no | — |
| 824 | D4 | — | 8 | 1 | no | — |
| 825 | D4 | — | 12 | 1 | no | — |
| 826 | D4 | — | 12 | 1 | no | — |
| 827 | D4 | — | 12 | 1 | no | — |
| 828 | D4 | — | 12 | 1 | no | — |
| 829 | D4 | — | 12 | 1 | no | — |
| 830 | D4 | — | 12 | 1 | no | — |
| 831 | D4 | — | 12 | 1 | no | — |
| 832 | D4 | — | 12 | 1 | no | — |
| 833 | D4 | — | 12 | 1 | no | — |
| 834 | D4 | — | 12 | 2 | no | — |
| 835 | D4 | — | 12 | 2 | no | — |
| 836 | D4 | — | 12 | 2 | no | — |
| 837 | D4 | — | 12 | 2 | no | — |
| 838 | D4 | — | 12 | 2 | no | — |
| 839 | D4 | — | 24 | 1 | no | — |
| 840 | D4 | — | 24 | 1 | no | — |
| 841 | D4 | — | 24 | 1 | no | — |
| 842 | D4 | — | 24 | 1 | no | — |
| 843 | D4 | — | 24 | 1 | no | — |
| 844 | D4 | — | 24 | 2 | no | — |
| 845 | D4 | — | 24 | 1 | no | — |
| 846 | D4 | — | 24 | 1 | no | — |
| 847 | D4 | — | 24 | 1 | no | — |
| 848 | D4 | — | 24 | 1 | no | — |
| 849 | C2×C4 | — | 2 | 1 | no | — |
| 850 | C2×C4 | — | 2 | 1 | no | — |
| 851 | C2×C4 | — | 2 | 1 | no | — |
| 852 | C2×C4 | — | 2 | 1 | no | — |
| 853 | C2×C4 | — | 3 | 1 | no | — |
| 854 | C2×C4 | — | 3 | 1 | no | — |
| 855 | C2×C4 | — | 3 | 1 | no | — |
| 856 | C2×C4 | — | 4 | 1 | no | — |
| 857 | C2×C4 | — | 6 | 2 | no | — |
| 858 | C2×C4 | — | 6 | 1 | no | — |
| 859 | C2×C4 | — | 6 | 1 | no | — |
| 860 | C2×C4 | — | 6 | 1 | no | — |
| 861 | C2×C4 | — | 8 | 1 | no | — |
| 862 | C2×C4 | — | 8 | 1 | no | — |
| 863 | C2×C4 | — | 12 | 1 | no | — |
| 864 | C2×C4 | — | 12 | 1 | no | — |
| 865 | C2×C4 | — | 12 | 2 | no | — |
| 866 | C2×C4 | — | 24 | 2 | no | — |
| 867 | C2×C4 | — | 24 | 1 | no | — |
| 868 | C2×C4 | — | 24 | 1 | no | — |
| 869 | C2×C4 | — | 24 | 1 | no | — |
| 870 | C2×C4 | — | 24 | 1 | no | — |
| 871 | C2×C4 | — | 24 | 1 | no | — |
| 872 | C2×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 873 | C2×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 874 | C2×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 875 | C8 | — | 2 | 2 | no | — |
| 876 | C8 | — | 2 | 2 | no | — |
| 877 | C8 | — | 4 | 1 | no | — |
| 878 | C8 | — | 6 | 2 | no | — |
| 879 | C8 | — | 12 | 1 | no | — |
| 880 | C8 | — | 12 | 1 | no | — |
| 881 | C2×C3 | — | 8 | 1 | no | — |
| 882 | C2×C3 | — | 8 | 1 | no | — |
| 883 | C2×C3 | C2×#453 | 1 | 1 | yes | characteristic |
| 884 | C2×C3 | #3018 | 1 | 1 | yes | characteristic |
| 885 | C2×C3 | #3019 | 1 | 1 | yes | characteristic |
| 886 | D3 | — | 4 | 1 | no | — |
| 887 | D3 | — | 8 | 1 | no | — |
| 888 | D3 | — | 8 | 1 | no | — |
| 889 | D3 | — | 8 | 1 | no | — |
| 890 | D3 | — | 16 | 1 | no | — |
| 891 | C22 | — | 4 | 1 | no | — |
| 892 | C22 | — | 4 | 1 | no | — |
| 893 | C22 | — | 4 | 1 | no | — |
| 894 | C22 | — | 4 | 1 | no | — |
| 895 | C22 | — | 4 | 1 | no | — |
| 896 | C22 | — | 4 | 1 | no | — |
| 897 | C22 | — | 6 | 1 | no | — |
| 898 | C22 | — | 6 | 1 | no | — |
| 899 | C22 | — | 6 | 1 | no | — |
| 900 | C22 | — | 12 | 1 | no | — |
| 901 | C22 | — | 12 | 1 | no | — |
| 902 | C22 | — | 12 | 1 | no | — |
| 903 | C22 | — | 12 | 1 | no | — |
| 904 | C22 | — | 12 | 1 | no | — |
| 905 | C22 | — | 12 | 1 | no | — |
| 906 | C22 | — | 12 | 1 | no | — |
| 907 | C22 | — | 12 | 1 | no | — |
| 908 | C22 | — | 12 | 1 | no | — |
| 909 | C22 | — | 24 | 1 | no | — |
| 910 | C22 | — | 24 | 1 | no | — |
| 911 | C22 | — | 24 | 1 | no | — |
| 912 | C22 | — | 48 | 2 | no | — |
| 913 | C22 | — | 48 | 2 | no | — |
| 914 | C22 | — | 48 | 2 | no | — |
| 915 | C22 | D3×#120 | 1 | 1 | yes | characteristic |
| 916 | C4 | — | 2 | 1 | no | — |
| 917 | C4 | — | 2 | 1 | no | — |
| 918 | C4 | — | 2 | 1 | no | — |
| 919 | C4 | — | 3 | 2 | no | — |
| 920 | C4 | — | 4 | 1 | no | — |
| 921 | C4 | — | 4 | 1 | no | — |
| 922 | C4 | — | 4 | 1 | no | — |
| 923 | C4 | — | 4 | 1 | no | — |
| 924 | C4 | — | 6 | 1 | no | — |
| 925 | C4 | — | 6 | 1 | no | — |
| 926 | C4 | — | 8 | 1 | no | — |
| 927 | C4 | — | 12 | 1 | no | — |
| 928 | C4 | — | 12 | 1 | no | — |
| 929 | C4 | — | 12 | 1 | no | — |
| 930 | C3 | #19018 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 931 | C2 | — | 8 | 1 | no | — |
| 932 | C2 | — | 8 | 1 | no | — |
| 933 | C2 | — | 12 | 1 | no | — |
| 934 | C2 | — | 24 | 1 | no | — |
| 935 | C2 | — | 24 | 1 | no | — |
| 936 | C2 | — | 24 | 1 | no | — |
| 937 | C2 | — | 48 | 1 | no | — |
| 938 | C2 | D3×#453 | 1 | 1 | yes | characteristic |
| 939 | C2 | #80292 | 1 | 1 | yes | characteristic |
| 940 | C2 | #80298 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C22 | D3×#120 |
| commutator, cosocle | C3×C42 | C24 |
| Frattini | C42 | C23×D3 |
| Fitting | C3×#1661 | C2 |
| socle | C22×C3 | C2×#120 |
| hypercenter | #1661 | D3 |
| hypocenter | C3 | #19018 |
| LCS | G ▷ C3×C42 ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #1661 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #87113 | C2 | semidirect |
| 2. #81958 | C2 | semidirect |
| 3. #81871 | C2 | semidirect |
| 4. #81685 | C2 | semidirect |
| 5. C3×#1661 | C2 | semidirect |
| 6. #71952 | C2 | semidirect |
| 7. #71392 | C2 | semidirect |
| 8. #71329 | C2 | semidirect |
| 9. #71244 | C2 | semidirect |
| 10. #68370 | C2 | semidirect |
| 11. #68364 | C2 | semidirect |
| 12. #68350 | C2 | semidirect |
| 13. #68350 | C2 | semidirect |
| 14. #68343 | C2 | semidirect |
| 15. #68342 | C2 | semidirect |
| 20. #5725 | C22 | semidirect |
| 39. C3×#501 | C22 | semidirect |
| 40. C3×#497 | C22 | semidirect |
| 41. C3×#489 | C22 | semidirect |
| 44. #5089 | C22 | semidirect |
| 45. #5089 | C22 | semidirect |
| 46. #5086 | C22 | semidirect |
| 47. #5067 | C22 | semidirect |
| 48. #5058 | C22 | semidirect |
| 49. #5058 | C22 | semidirect |
| 58. #4712 | C22 | semidirect |
| 59. #4712 | C22 | semidirect |
| 60. #4712 | C22 | semidirect |
| 61. #4707 | C22 | semidirect |
| 62. #4707 | C22 | semidirect |
| 63. #4705 | C22 | semidirect |
| 64. C3×#330 | C22 | semidirect |
| 65. C3×#329 | C22 | semidirect |
| 66. C3×#329 | C22 | semidirect |
| 67. #4543 | C22 | semidirect |
| 68. #4540 | C22 | semidirect |
| 69. #4540 | C22 | semidirect |
| 70. #4464 | C22 | semidirect |
| 71. #4464 | C22 | semidirect |
| 72. #4464 | C22 | semidirect |
| 73. #4464 | C22 | semidirect |
| 74. #4464 | C22 | semidirect |
| 75. #4464 | C22 | semidirect |
| 81. #1661 | D3 | semidirect |
| 246. #501 | C2×D3 | semidirect |
| 248. #497 | C2×D3 | semidirect |
| 259. #489 | C2×D3 | semidirect |
| 272. #330 | C2×D3 | semidirect |
| 281. #329 | C2×D3 | semidirect |
| 282. #329 | C2×D3 | semidirect |
| 930. C3 | #19018 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #87113 | 2 |
| #81958 | 2 |
| #81871 | 2 |
| #81685 | 2 |
| C3×#1661 | 2 |
| #71952 | 2 |
| #71392 | 2 |
| #71329 | 2 |
| #71244 | 2 |
| #68370 | 2 |
| #68364 | 2 |
| #68350 | 2 |
| #68343 | 2 |
| #68342 | 2 |
| #19018 | 3 |