Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
2068 conjugacy classes of subgroups.
The subgroup lattice has 852 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #85850 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #85818 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C3×C4×#137 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #83984 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #82525 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C2×#5020 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #79843 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #79805 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | #79739 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #79737 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #79687 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | #79678 | C2 | 1 | 2 | yes | maximal, complemented |
| 13 | #79222 | C2 | 1 | 2 | yes | maximal, complemented |
| 14 | #78957 | C2 | 1 | 2 | yes | maximal, complemented |
| 15 | #78890 | C2 | 1 | 2 | yes | maximal, complemented |
| 16 | #78528 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 17 | #78522 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 18 | #61202 | — | 3 | 1 | no | maximal, Sylow |
| 19 | C2×#1007 | C22 | 1 | 2 | yes | — |
| 20 | C2×C3×#137 | C22 | 1 | 1 | yes | characteristic |
| 21 | C3×C4×#41 | C22 | 1 | 1 | yes | characteristic |
| 22 | C2×C3×C4×Q8 | C22 | 1 | 1 | yes | characteristic |
| 23 | #5833 | C22 | 1 | 2 | yes | — |
| 24 | C2×#950 | C22 | 1 | 2 | yes | — |
| 25 | C2×#907 | C22 | 1 | 2 | yes | — |
| 26 | #5584 | C22 | 1 | 2 | yes | — |
| 27 | #5579 | C22 | 1 | 2 | yes | — |
| 28 | #5577 | — | 2 | 1 | no | — |
| 29 | #5577 | C22 | 1 | 2 | yes | — |
| 30 | #5576 | — | 2 | 2 | no | — |
| 31 | #5576 | C22 | 1 | 4 | yes | — |
| 32 | Q8×D12 | — | 2 | 1 | no | — |
| 33 | Q8×D12 | C22 | 1 | 2 | yes | — |
| 34 | #5565 | — | 2 | 2 | no | — |
| 35 | #5563 | C22 | 1 | 2 | yes | — |
| 36 | #5552 | — | 2 | 2 | no | — |
| 37 | #5551 | C22 | 1 | 2 | yes | — |
| 38 | #5534 | — | 2 | 2 | no | — |
| 39 | #5523 | C22 | 1 | 2 | yes | — |
| 40 | #5510 | — | 2 | 2 | no | — |
| 41 | #5510 | C22 | 1 | 2 | yes | — |
| 42 | #5477 | — | 2 | 2 | no | — |
| 43 | #5477 | — | 2 | 1 | no | — |
| 44 | #5477 | C22 | 1 | 1 | yes | characteristic |
| 45 | #5477 | C22 | 1 | 1 | yes | characteristic |
| 46 | #5470 | — | 2 | 1 | no | — |
| 47 | C2×#869 | C22 | 1 | 1 | yes | characteristic |
| 48 | C3×#441 | C22 | 1 | 2 | yes | — |
| 49 | C3×#440 | C22 | 1 | 2 | yes | — |
| 50 | C3×C4×Q16 | C22 | 1 | 2 | yes | — |
| 51 | C3×C4×SD16 | C22 | 1 | 2 | yes | — |
| 52 | C3×#428 | C22 | 1 | 1 | yes | characteristic |
| 53 | C3×#419 | C22 | 1 | 1 | yes | characteristic |
| 54 | C3×#417 | C22 | 1 | 1 | yes | characteristic |
| 55 | C3×C4×M16 | C22 | 1 | 1 | yes | characteristic |
| 56 | C2×#835 | C22 | 1 | 2 | yes | — |
| 57 | #5187 | C22 | 1 | 4 | yes | — |
| 58 | #5186 | C22 | 1 | 4 | yes | — |
| 59 | #5172 | C22 | 1 | 4 | yes | — |
| 60 | #5170 | C22 | 1 | 4 | yes | — |
| 61 | #5133 | C22 | 1 | 2 | yes | — |
| 62 | #5133 | C22 | 1 | 2 | yes | — |
| 63 | #5129 | C22 | 1 | 2 | yes | — |
| 64 | #5031 | C22 | 1 | 1 | yes | characteristic |
| 65 | #5028 | C22 | 1 | 2 | yes | — |
| 66 | #5027 | C22 | 1 | 1 | yes | characteristic |
| 67 | #5020 | C22 | 1 | 2 | yes | — |
| 68 | #5020 | C22 | 1 | 2 | yes | — |
| 69 | #5020 | C22 | 1 | 4 | yes | — |
| 70 | #5019 | C22 | 1 | 1 | yes | characteristic |
| 71 | #5016 | C22 | 1 | 2 | yes | — |
| 72 | #5015 | C22 | 1 | 1 | yes | characteristic |
| 73 | #5002 | C22 | 1 | 2 | yes | — |
| 74 | C2×#808 | C22 | 1 | 2 | yes | — |
| 75 | C2×C4⋊(C3⋊C8) | C22 | 1 | 1 | yes | characteristic |
| 76 | #4888 | C22 | 1 | 4 | yes | — |
| 77 | #4885 | C22 | 1 | 4 | yes | — |
| 78 | #4863 | C22 | 1 | 4 | yes | — |
| 79 | #4862 | C22 | 1 | 4 | yes | — |
| 80 | #4816 | C22 | 1 | 4 | yes | — |
| 81 | #4807 | C22 | 1 | 4 | yes | — |
| 82 | #4804 | C22 | 1 | 4 | yes | — |
| 83 | #4803 | C22 | 1 | 4 | yes | — |
| 84 | #4802 | C22 | 1 | 4 | yes | — |
| 85 | D3×#103 | C22 | 1 | 4 | yes | — |
| 86 | #4782 | C22 | 1 | 4 | yes | — |
| 87 | #4778 | C22 | 1 | 4 | yes | — |
| 88 | #4714 | C22 | 1 | 4 | yes | — |
| 89 | #4706 | C22 | 1 | 4 | yes | — |
| 90 | #4694 | C22 | 1 | 2 | yes | — |
| 91 | #4688 | C22 | 1 | 2 | yes | — |
| 92 | C8×D12 | C22 | 1 | 2 | yes | — |
| 93 | #4681 | C22 | 1 | 2 | yes | — |
| 94 | #3511 | — | 3 | 1 | no | — |
| 95 | #3497 | — | 3 | 1 | no | — |
| 96 | #3332 | — | 3 | 2 | no | — |
| 97 | #3328 | — | 3 | 2 | no | — |
| 98 | #3321 | — | 3 | 4 | no | — |
| 99 | #3316 | — | 3 | 4 | no | — |
| 100 | #3304 | — | 3 | 2 | no | — |
| 101 | #3298 | — | 3 | 2 | no | — |
| 102 | #3141 | — | 3 | 1 | no | — |
| 103 | #3099 | — | 3 | 2 | no | — |
| 104 | C2×#475 | — | 3 | 1 | no | — |
| 105 | #3060 | — | 3 | 2 | no | — |
| 106 | #3035 | — | 3 | 1 | no | — |
| 107 | #3013 | — | 3 | 2 | no | — |
| 108 | C4×#137 | D3 | 1 | 1 | yes | characteristic, complemented |
| 109 | #2935 | — | 3 | 1 | no | — |
| 110 | #2898 | — | 3 | 2 | no | — |
| 111 | C2×C3×#41 | C23 | 1 | 1 | yes | characteristic |
| 112 | C22×C3×Q8 | C23 | 1 | 1 | yes | characteristic |
| 113 | #1007 | — | 2 | 8 | no | — |
| 114 | #1007 | — | 4 | 4 | no | — |
| 115 | C2×#239 | — | 2 | 2 | no | — |
| 116 | C2×#239 | C23 | 1 | 4 | yes | — |
| 117 | C2×D3×Q8 | — | 2 | 2 | no | — |
| 118 | C2×D3×Q8 | C23 | 1 | 4 | yes | — |
| 119 | C2×#235 | — | 2 | 4 | no | — |
| 120 | C2×#235 | — | 2 | 2 | no | — |
| 121 | C2×#235 | C23 | 1 | 2 | yes | — |
| 122 | C2×#235 | C23 | 1 | 2 | yes | — |
| 123 | C22×Dic6 | — | 2 | 1 | no | — |
| 124 | C3×#137 | — | 2 | 4 | no | — |
| 125 | C2×C3×Q16 | C23 | 1 | 2 | yes | — |
| 126 | C2×C3×SD16 | C23 | 1 | 2 | yes | — |
| 127 | C2×C3×M16 | C23 | 1 | 1 | yes | characteristic |
| 128 | C2×C3×M16 | C23 | 1 | 1 | yes | characteristic |
| 129 | C3×C4×Q8 | — | 2 | 1 | no | — |
| 130 | C3×C4×Q8 | — | 2 | 1 | no | — |
| 131 | C3×C4×Q8 | C23 | 1 | 2 | yes | — |
| 132 | C3×C4×Q8 | C23 | 1 | 2 | yes | — |
| 133 | C3×C4×Q8 | C23 | 1 | 1 | yes | characteristic |
| 134 | C3×C4×Q8 | C23 | 1 | 1 | yes | characteristic |
| 135 | C3×C4×D4 | — | 2 | 1 | no | — |
| 136 | C3×C4×D4 | — | 2 | 1 | no | — |
| 137 | C3×C4×D4 | C23 | 1 | 1 | yes | characteristic |
| 138 | C3×C4×D4 | C23 | 1 | 1 | yes | characteristic |
| 139 | C3×#117 | — | 2 | 1 | no | — |
| 140 | C3×#117 | C23 | 1 | 1 | yes | characteristic |
| 141 | C2×C3×C4⋊C4 | — | 2 | 1 | no | — |
| 142 | C2×C3×C4⋊C4 | C23 | 1 | 1 | yes | characteristic |
| 143 | C2×C3×C42 | — | 2 | 1 | no | — |
| 144 | C2×C3×C42 | — | 2 | 1 | no | — |
| 145 | C2×C3×C42 | C23 | 1 | 1 | yes | characteristic |
| 146 | #950 | — | 4 | 4 | no | — |
| 147 | #946 | C23 | 1 | 4 | yes | — |
| 148 | C2×#216 | C23 | 1 | 2 | yes | — |
| 149 | C2×#215 | C23 | 1 | 2 | yes | — |
| 150 | #939 | — | 2 | 4 | no | — |
| 151 | #938 | C23 | 1 | 4 | yes | — |
| 152 | C2×#214 | C23 | 1 | 2 | yes | — |
| 153 | C2×#213 | C23 | 1 | 2 | yes | — |
| 154 | #930 | — | 2 | 1 | no | — |
| 155 | #930 | — | 2 | 1 | no | — |
| 156 | #930 | — | 2 | 4 | no | — |
| 157 | #930 | — | 2 | 2 | no | — |
| 158 | #930 | — | 2 | 2 | no | — |
| 159 | #930 | D4 | 1 | 2 | yes | — |
| 160 | #930 | D4 | 1 | 2 | yes | — |
| 161 | #926 | — | 2 | 2 | no | — |
| 162 | C2×C4⋊Dic3 | — | 2 | 1 | no | — |
| 163 | C2×C4⋊Dic3 | C23 | 1 | 2 | yes | — |
| 164 | #924 | — | 2 | 2 | no | — |
| 165 | #924 | — | 2 | 2 | no | — |
| 166 | C22×C3⋊C8 | C23 | 1 | 2 | yes | — |
| 167 | #907 | — | 4 | 4 | no | — |
| 168 | C2×ΓL(1,𝔽25) | C23 | 1 | 4 | yes | — |
| 169 | C2×D3×C8 | C23 | 1 | 4 | yes | — |
| 170 | #898 | — | 2 | 4 | no | — |
| 171 | #897 | — | 2 | 2 | no | — |
| 172 | #897 | — | 2 | 4 | no | — |
| 173 | #897 | — | 2 | 4 | no | — |
| 174 | #897 | C23 | 1 | 4 | yes | — |
| 175 | #896 | — | 2 | 4 | no | — |
| 176 | #895 | — | 2 | 4 | no | — |
| 177 | #895 | — | 2 | 2 | no | — |
| 178 | #895 | — | 2 | 4 | no | — |
| 179 | #895 | C23 | 1 | 4 | yes | — |
| 180 | #892 | C23 | 1 | 4 | yes | — |
| 181 | D3×C4⋊C4 | C23 | 1 | 4 | yes | — |
| 182 | #885 | — | 2 | 4 | no | — |
| 183 | #883 | — | 2 | 4 | no | — |
| 184 | #67⋊C4 | — | 2 | 4 | no | — |
| 185 | #875 | — | 2 | 2 | no | — |
| 186 | #875 | — | 2 | 4 | no | — |
| 187 | #875 | D4 | 1 | 2 | yes | — |
| 188 | #875 | C23 | 1 | 2 | yes | — |
| 189 | #874 | — | 2 | 2 | no | — |
| 190 | #874 | D4 | 1 | 1 | yes | characteristic |
| 191 | #874 | C23 | 1 | 1 | yes | characteristic |
| 192 | C4×D12 | — | 2 | 2 | no | — |
| 193 | C4×D12 | — | 2 | 2 | no | — |
| 194 | C4×D12 | — | 2 | 2 | no | — |
| 195 | C4×D12 | — | 2 | 1 | no | — |
| 196 | C4×D12 | — | 2 | 1 | no | — |
| 197 | C4×D12 | — | 2 | 4 | no | — |
| 198 | C4×D12 | — | 2 | 2 | no | — |
| 199 | C4×D12 | C23 | 1 | 2 | yes | — |
| 200 | C4×D12 | C23 | 1 | 2 | yes | — |
| 201 | #870 | — | 2 | 2 | no | — |
| 202 | #869 | — | 2 | 1 | no | — |
| 203 | #869 | — | 2 | 1 | no | — |
| 204 | #869 | — | 2 | 2 | no | — |
| 205 | #869 | D4 | 1 | 1 | yes | characteristic |
| 206 | #869 | C23 | 1 | 1 | yes | characteristic |
| 207 | #869 | C23 | 1 | 2 | yes | — |
| 208 | #869 | C23 | 1 | 2 | yes | — |
| 209 | C4×Dic6 | — | 2 | 2 | no | — |
| 210 | C4×Dic6 | — | 2 | 2 | no | — |
| 211 | C3×#107 | C23 | 1 | 2 | yes | — |
| 212 | C3×#106 | C23 | 1 | 2 | yes | — |
| 213 | C3×#103 | C23 | 1 | 2 | yes | — |
| 214 | C3×#103 | C23 | 1 | 2 | yes | — |
| 215 | C3×#103 | C23 | 1 | 2 | yes | — |
| 216 | C3×#102 | C23 | 1 | 2 | yes | — |
| 217 | C3×#97 | C23 | 1 | 2 | yes | — |
| 218 | C3×C4×C8 | C23 | 1 | 2 | yes | — |
| 219 | #835 | C23 | 1 | 4 | yes | — |
| 220 | #835 | C23 | 1 | 4 | yes | — |
| 221 | #821 | C23 | 1 | 4 | yes | — |
| 222 | #821 | C23 | 1 | 4 | yes | — |
| 223 | (C2×D3)⋊C8 | C23 | 1 | 4 | yes | — |
| 224 | (C2×D3)⋊C8 | C23 | 1 | 4 | yes | — |
| 225 | #816 | C23 | 1 | 4 | yes | — |
| 226 | #816 | C23 | 1 | 4 | yes | — |
| 227 | #810 | C23 | 1 | 2 | yes | — |
| 228 | #810 | C23 | 1 | 2 | yes | — |
| 229 | #809 | C23 | 1 | 2 | yes | — |
| 230 | #809 | C23 | 1 | 2 | yes | — |
| 231 | #808 | C23 | 1 | 4 | yes | — |
| 232 | #808 | C23 | 1 | 4 | yes | — |
| 233 | C4⋊(C3⋊C8) | C23 | 1 | 1 | yes | characteristic |
| 234 | C4⋊(C3⋊C8) | C23 | 1 | 1 | yes | characteristic |
| 235 | C4⋊(C3⋊C8) | C23 | 1 | 2 | yes | — |
| 236 | C2×2−1+4 | — | 3 | 2 | no | — |
| 237 | C2×#137 | C2×D3 | 1 | 1 | yes | characteristic |
| 238 | C2×#135 | — | 3 | 2 | no | — |
| 239 | C2×#131 | — | 3 | 2 | no | — |
| 240 | #556 | — | 3 | 2 | no | — |
| 241 | #555 | — | 3 | 2 | no | — |
| 242 | #554 | — | 3 | 2 | no | — |
| 243 | #553 | — | 6 | 2 | no | — |
| 244 | #550 | — | 3 | 2 | no | — |
| 245 | #550 | — | 6 | 1 | no | — |
| 246 | D4×Q8 | — | 3 | 2 | no | — |
| 247 | D4×Q8 | — | 6 | 1 | no | — |
| 248 | #548 | — | 3 | 4 | no | — |
| 249 | #548 | — | 6 | 2 | no | — |
| 250 | #548 | — | 6 | 2 | no | — |
| 251 | #547 | — | 3 | 2 | no | — |
| 252 | #542 | — | 6 | 2 | no | — |
| 253 | #537 | — | 3 | 2 | no | — |
| 254 | #537 | — | 3 | 2 | no | — |
| 255 | #537 | — | 6 | 2 | no | — |
| 256 | #533 | — | 6 | 1 | no | — |
| 257 | #532 | — | 3 | 1 | no | — |
| 258 | #532 | — | 3 | 1 | no | — |
| 259 | #532 | — | 6 | 2 | no | — |
| 260 | #532 | — | 6 | 1 | no | — |
| 261 | C2×C4⋊Q8 | — | 3 | 1 | no | — |
| 262 | #520 | — | 3 | 2 | no | — |
| 263 | C4×#41 | C2×D3 | 1 | 1 | yes | characteristic |
| 264 | C2×C4×Q8 | C2×D3 | 1 | 1 | yes | characteristic |
| 265 | #489 | — | 3 | 4 | no | — |
| 266 | #487 | — | 3 | 2 | no | — |
| 267 | #486 | — | 3 | 2 | no | — |
| 268 | #485 | — | 3 | 4 | no | — |
| 269 | #483 | — | 3 | 4 | no | — |
| 270 | #482 | — | 3 | 4 | no | — |
| 271 | #481 | — | 3 | 4 | no | — |
| 272 | #475 | — | 3 | 2 | no | — |
| 273 | #475 | — | 3 | 2 | no | — |
| 274 | #475 | — | 3 | 4 | no | — |
| 275 | #470 | — | 3 | 4 | no | — |
| 276 | #469 | — | 3 | 4 | no | — |
| 277 | #465 | — | 3 | 4 | no | — |
| 278 | #465 | — | 3 | 4 | no | — |
| 279 | #464 | — | 3 | 2 | no | — |
| 280 | #463 | — | 3 | 2 | no | — |
| 281 | #462 | — | 3 | 1 | no | — |
| 282 | #461 | — | 3 | 1 | no | — |
| 283 | #460 | — | 3 | 1 | no | — |
| 284 | #459 | — | 3 | 1 | no | — |
| 285 | #452 | — | 3 | 4 | no | — |
| 286 | #451 | — | 3 | 4 | no | — |
| 287 | #449 | — | 3 | 4 | no | — |
| 288 | #448 | — | 3 | 4 | no | — |
| 289 | #441 | C2×D3 | 1 | 2 | yes | — |
| 290 | #440 | C2×D3 | 1 | 2 | yes | — |
| 291 | C4×Q16 | C2×D3 | 1 | 2 | yes | — |
| 292 | C4×SD16 | C2×D3 | 1 | 2 | yes | — |
| 293 | #436 | — | 3 | 2 | no | — |
| 294 | #435 | — | 3 | 4 | no | — |
| 295 | C8×D4 | — | 3 | 2 | no | — |
| 296 | #428 | C2×D3 | 1 | 1 | yes | characteristic |
| 297 | C2×#106 | — | 3 | 2 | no | — |
| 298 | C2×C4⋊C8 | — | 3 | 1 | no | — |
| 299 | #419 | — | 3 | 4 | no | — |
| 300 | #419 | C2×D3 | 1 | 1 | yes | characteristic |
| 301 | #417 | — | 3 | 2 | no | — |
| 302 | #417 | — | 3 | 2 | no | — |
| 303 | #417 | — | 3 | 4 | no | — |
| 304 | #417 | C2×D3 | 1 | 1 | yes | characteristic |
| 305 | #416 | — | 3 | 2 | no | — |
| 306 | #416 | — | 3 | 4 | no | — |
| 307 | C2×#103 | — | 3 | 2 | no | — |
| 308 | C2×#103 | — | 3 | 4 | no | — |
| 309 | #408 | — | 3 | 2 | no | — |
| 310 | C4×M16 | C2×D3 | 1 | 1 | yes | characteristic |
| 311 | C3×#41 | — | 2 | 2 | no | — |
| 312 | C3×#41 | — | 2 | 2 | no | — |
| 313 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 314 | C2×C3×Q8 | — | 2 | 2 | no | — |
| 315 | C2×C3×Q8 | #41 | 1 | 4 | yes | complemented |
| 316 | C2×C3×Q8 | C24 | 1 | 1 | yes | characteristic |
| 317 | C2×C3×Q8 | C24 | 1 | 2 | yes | — |
| 318 | C2×C3×D4 | — | 2 | 1 | no | — |
| 319 | C2×C3×D4 | C24 | 1 | 1 | yes | characteristic |
| 320 | C22×C3×C4 | — | 2 | 1 | no | — |
| 321 | C22×C3×C4 | — | 2 | 1 | no | — |
| 322 | C22×C3×C4 | — | 2 | 1 | no | — |
| 323 | C22×C3×C4 | — | 2 | 1 | no | — |
| 324 | C22×C3×C4 | — | 2 | 1 | no | — |
| 325 | C22×C3×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 326 | C22×C3×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 327 | C22×C3×C4 | C24 | 1 | 1 | yes | characteristic |
| 328 | C2×#67 | — | 2 | 2 | no | — |
| 329 | C2×#67 | — | 2 | 4 | no | — |
| 330 | C2×#67 | C2×D4 | 1 | 4 | yes | — |
| 331 | C22×Dic3 | — | 2 | 2 | no | — |
| 332 | #239 | — | 2 | 8 | no | — |
| 333 | #239 | — | 4 | 4 | no | — |
| 334 | #239 | — | 4 | 8 | no | — |
| 335 | D3×Q8 | — | 2 | 8 | no | — |
| 336 | D3×Q8 | — | 4 | 4 | no | — |
| 337 | D3×Q8 | — | 4 | 8 | no | — |
| 338 | #235 | — | 2 | 4 | no | — |
| 339 | #235 | — | 2 | 4 | no | — |
| 340 | #235 | — | 2 | 4 | no | — |
| 341 | #235 | — | 2 | 4 | no | — |
| 342 | #235 | — | 4 | 16 | no | — |
| 343 | #235 | — | 8 | 4 | no | — |
| 344 | C2×D12 | — | 2 | 4 | no | — |
| 345 | C2×D12 | — | 2 | 1 | no | — |
| 346 | C2×D12 | — | 2 | 4 | no | — |
| 347 | C2×D12 | — | 2 | 1 | no | — |
| 348 | C2×D12 | C2×D4 | 1 | 2 | yes | — |
| 349 | C2×D12 | C2×D4 | 1 | 2 | yes | — |
| 350 | C2×D12 | C2×D4 | 1 | 2 | yes | — |
| 351 | C2×D12 | C24 | 1 | 2 | yes | — |
| 352 | C2×C4×D3 | — | 2 | 4 | no | — |
| 353 | C2×C4×D3 | — | 2 | 2 | no | — |
| 354 | C2×C4×D3 | — | 2 | 4 | no | — |
| 355 | C2×C4×D3 | — | 2 | 4 | no | — |
| 356 | C2×C4×D3 | C24 | 1 | 4 | yes | — |
| 357 | C2×Dic6 | — | 2 | 2 | no | — |
| 358 | C2×Dic6 | — | 2 | 4 | no | — |
| 359 | C2×Dic6 | — | 2 | 2 | no | — |
| 360 | C2×Dic6 | — | 8 | 2 | no | — |
| 361 | C2×Dic6 | C2×D4 | 1 | 2 | yes | — |
| 362 | C2×Dic6 | C24 | 1 | 2 | yes | — |
| 363 | C3×Q16 | — | 2 | 4 | no | — |
| 364 | C3×SD16 | — | 2 | 4 | no | — |
| 365 | C3×M16 | — | 2 | 2 | no | — |
| 366 | C3×M16 | — | 2 | 2 | no | — |
| 367 | C2×C3×C8 | C24 | 1 | 2 | yes | — |
| 368 | C2×C3×C8 | C24 | 1 | 2 | yes | — |
| 369 | C3×C4⋊C4 | — | 2 | 2 | no | — |
| 370 | C3×C4⋊C4 | — | 2 | 2 | no | — |
| 371 | C3×C4⋊C4 | — | 2 | 1 | no | — |
| 372 | C3×C4⋊C4 | — | 2 | 1 | no | — |
| 373 | C3×C4⋊C4 | — | 2 | 1 | no | — |
| 374 | C3×C4⋊C4 | C24 | 1 | 2 | yes | — |
| 375 | C3×C4⋊C4 | C24 | 1 | 1 | yes | characteristic |
| 376 | C3×C4⋊C4 | C24 | 1 | 1 | yes | characteristic |
| 377 | C3×C22⋊C4 | — | 2 | 1 | no | — |
| 378 | C3×C22⋊C4 | — | 2 | 1 | no | — |
| 379 | C3×C22⋊C4 | — | 2 | 1 | no | — |
| 380 | C3×C42 | — | 2 | 1 | no | — |
| 381 | C3×C42 | — | 2 | 1 | no | — |
| 382 | C3×C42 | — | 2 | 2 | no | — |
| 383 | C3×C42 | — | 2 | 1 | no | — |
| 384 | C3×C42 | — | 2 | 2 | no | — |
| 385 | C3×C42 | C2×D4 | 1 | 1 | yes | characteristic |
| 386 | C3×C42 | C2×D4 | 1 | 1 | yes | characteristic |
| 387 | C3×C42 | C24 | 1 | 1 | yes | characteristic |
| 388 | C3×C42 | C24 | 1 | 1 | yes | characteristic |
| 389 | #217 | — | 2 | 4 | no | — |
| 390 | #216 | — | 4 | 2 | no | — |
| 391 | #215 | — | 4 | 2 | no | — |
| 392 | #214 | — | 4 | 2 | no | — |
| 393 | #213 | — | 4 | 2 | no | — |
| 394 | (C2×D3)⋊C4 | — | 2 | 4 | no | — |
| 395 | (C2×D3)⋊C4 | — | 2 | 4 | no | — |
| 396 | (C2×D3)⋊C4 | — | 2 | 4 | no | — |
| 397 | (C2×D3)⋊C4 | — | 2 | 2 | no | — |
| 398 | (C2×D3)⋊C4 | — | 2 | 2 | no | — |
| 399 | (C2×D3)⋊C4 | — | 2 | 4 | no | — |
| 400 | (C2×D3)⋊C4 | C2×D4 | 1 | 4 | yes | — |
| 401 | (C2×D3)⋊C4 | C2×D4 | 1 | 4 | yes | — |
| 402 | C4⋊Dic3 | — | 2 | 2 | no | — |
| 403 | C4⋊Dic3 | — | 2 | 1 | no | — |
| 404 | C4⋊Dic3 | — | 2 | 2 | no | — |
| 405 | C4⋊Dic3 | — | 2 | 2 | no | — |
| 406 | C4⋊Dic3 | — | 2 | 1 | no | — |
| 407 | C4⋊Dic3 | — | 2 | 4 | no | — |
| 408 | C4⋊Dic3 | C2×D4 | 1 | 2 | yes | — |
| 409 | C4⋊Dic3 | C2×D4 | 1 | 2 | yes | — |
| 410 | C4⋊Dic3 | C24 | 1 | 4 | yes | — |
| 411 | Dic3⋊C4 | — | 2 | 4 | no | — |
| 412 | Dic3⋊C4 | — | 2 | 4 | no | — |
| 413 | C4×Dic3 | — | 2 | 4 | no | — |
| 414 | C2×C3⋊C8 | — | 2 | 4 | no | — |
| 415 | C2×C3⋊C8 | C24 | 1 | 2 | yes | — |
| 416 | C2×C3⋊C8 | C24 | 1 | 2 | yes | — |
| 417 | ΓL(1,𝔽25) | — | 4 | 4 | no | — |
| 418 | D3×C8 | — | 4 | 4 | no | — |
| 419 | 2−1+4 | — | 6 | 8 | no | — |
| 420 | 2−1+4 | — | 12 | 4 | no | — |
| 421 | C2×#41 | — | 3 | 2 | no | — |
| 422 | C2×#41 | — | 3 | 4 | no | — |
| 423 | C2×#41 | — | 3 | 2 | no | — |
| 424 | C2×#41 | — | 6 | 4 | no | — |
| 425 | C2×#41 | — | 6 | 2 | no | — |
| 426 | C2×#41 | — | 6 | 2 | no | — |
| 427 | C2×#41 | C22×D3 | 1 | 1 | yes | characteristic |
| 428 | C22×Q8 | — | 3 | 4 | no | — |
| 429 | C22×Q8 | — | 6 | 2 | no | — |
| 430 | C22×Q8 | — | 6 | 1 | no | — |
| 431 | C22×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 432 | #137 | — | 2 | 4 | no | — |
| 433 | #135 | — | 12 | 4 | no | — |
| 434 | C2×Q16 | — | 3 | 2 | no | — |
| 435 | C2×Q16 | C22×D3 | 1 | 2 | yes | — |
| 436 | C2×SD16 | — | 3 | 2 | no | — |
| 437 | C2×SD16 | — | 3 | 2 | no | — |
| 438 | C2×SD16 | C22×D3 | 1 | 2 | yes | — |
| 439 | C2×D8 | — | 3 | 2 | no | — |
| 440 | #131 | — | 12 | 4 | no | — |
| 441 | C2×M16 | — | 3 | 4 | no | — |
| 442 | C2×M16 | C22×D3 | 1 | 1 | yes | characteristic |
| 443 | C2×M16 | C22×D3 | 1 | 1 | yes | characteristic |
| 444 | C22×C8 | — | 3 | 2 | no | — |
| 445 | C22×C8 | — | 3 | 4 | no | — |
| 446 | C4⋊Q8 | — | 3 | 1 | no | — |
| 447 | C4⋊Q8 | — | 3 | 2 | no | — |
| 448 | C4⋊Q8 | — | 3 | 2 | no | — |
| 449 | C4⋊Q8 | — | 3 | 1 | no | — |
| 450 | C4⋊Q8 | — | 6 | 2 | no | — |
| 451 | C4⋊Q8 | — | 6 | 1 | no | — |
| 452 | C4⋊Q8 | — | 6 | 1 | no | — |
| 453 | #127 | — | 3 | 1 | no | — |
| 454 | #127 | — | 3 | 1 | no | — |
| 455 | #127 | — | 6 | 2 | no | — |
| 456 | #126 | — | 6 | 4 | no | — |
| 457 | #125 | — | 6 | 2 | no | — |
| 458 | #124 | — | 3 | 2 | no | — |
| 459 | #124 | — | 3 | 2 | no | — |
| 460 | #124 | — | 6 | 4 | no | — |
| 461 | #124 | — | 6 | 2 | no | — |
| 462 | #124 | — | 6 | 4 | no | — |
| 463 | #123 | — | 6 | 4 | no | — |
| 464 | C22⋊Q8 | — | 3 | 4 | no | — |
| 465 | C22⋊Q8 | — | 3 | 4 | no | — |
| 466 | C22⋊Q8 | — | 6 | 4 | no | — |
| 467 | C22⋊Q8 | — | 6 | 4 | no | — |
| 468 | C22⋊Q8 | — | 6 | 4 | no | — |
| 469 | C22⋊Q8 | — | 6 | 2 | no | — |
| 470 | C22⋊Q8 | — | 6 | 2 | no | — |
| 471 | C22⋊Q8 | — | 6 | 2 | no | — |
| 472 | #121 | — | 3 | 2 | no | — |
| 473 | #121 | — | 3 | 2 | no | — |
| 474 | #121 | — | 3 | 4 | no | — |
| 475 | #121 | — | 3 | 4 | no | — |
| 476 | #121 | — | 6 | 4 | no | — |
| 477 | #121 | — | 6 | 2 | no | — |
| 478 | #121 | — | 6 | 4 | no | — |
| 479 | #121 | — | 6 | 4 | no | — |
| 480 | #121 | — | 6 | 2 | no | — |
| 481 | #121 | — | 6 | 2 | no | — |
| 482 | #121 | — | 6 | 4 | no | — |
| 483 | #121 | — | 6 | 1 | no | — |
| 484 | #121 | — | 6 | 1 | no | — |
| 485 | C4×Q8 | — | 2 | 1 | no | — |
| 486 | C4×Q8 | — | 2 | 1 | no | — |
| 487 | C4×Q8 | — | 6 | 2 | no | — |
| 488 | C4×Q8 | — | 6 | 2 | no | — |
| 489 | C4×Q8 | C22×D3 | 1 | 2 | yes | — |
| 490 | C4×Q8 | C22×D3 | 1 | 2 | yes | — |
| 491 | C4×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 492 | C4×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 493 | C4×D4 | — | 2 | 1 | no | — |
| 494 | C4×D4 | — | 2 | 1 | no | — |
| 495 | C4×D4 | — | 3 | 2 | no | — |
| 496 | C4×D4 | — | 3 | 2 | no | — |
| 497 | C4×D4 | — | 6 | 4 | no | — |
| 498 | C4×D4 | — | 6 | 2 | no | — |
| 499 | C4×D4 | — | 6 | 2 | no | — |
| 500 | C4×D4 | — | 6 | 2 | no | — |
| 501 | C4×D4 | — | 6 | 2 | no | — |
| 502 | C4×D4 | — | 6 | 4 | no | — |
| 503 | C4×D4 | — | 6 | 1 | no | — |
| 504 | C4×D4 | — | 6 | 1 | no | — |
| 505 | C4×D4 | C22×D3 | 1 | 1 | yes | characteristic |
| 506 | C4×D4 | C22×D3 | 1 | 1 | yes | characteristic |
| 507 | #117 | — | 2 | 1 | no | — |
| 508 | #117 | — | 3 | 4 | no | — |
| 509 | #117 | — | 6 | 2 | no | — |
| 510 | #117 | C22×D3 | 1 | 1 | yes | characteristic |
| 511 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 512 | C2×C4⋊C4 | — | 3 | 2 | no | — |
| 513 | C2×C4⋊C4 | — | 3 | 4 | no | — |
| 514 | C2×C4⋊C4 | — | 6 | 1 | no | — |
| 515 | C2×C4⋊C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 516 | C2×C42 | — | 2 | 1 | no | — |
| 517 | C2×C42 | — | 2 | 1 | no | — |
| 518 | C2×C42 | C22×D3 | 1 | 1 | yes | characteristic |
| 519 | #107 | C22×D3 | 1 | 2 | yes | — |
| 520 | #106 | — | 3 | 4 | no | — |
| 521 | #106 | — | 3 | 4 | no | — |
| 522 | #106 | C22×D3 | 1 | 2 | yes | — |
| 523 | C4⋊C8 | — | 3 | 1 | no | — |
| 524 | C4⋊C8 | — | 3 | 2 | no | — |
| 525 | C4⋊C8 | — | 3 | 1 | no | — |
| 526 | #103 | — | 3 | 4 | no | — |
| 527 | #103 | — | 3 | 4 | no | — |
| 528 | #103 | — | 3 | 4 | no | — |
| 529 | #103 | — | 3 | 4 | no | — |
| 530 | #103 | — | 3 | 2 | no | — |
| 531 | #103 | — | 3 | 2 | no | — |
| 532 | #103 | C22×D3 | 1 | 2 | yes | — |
| 533 | #103 | C22×D3 | 1 | 2 | yes | — |
| 534 | #103 | C22×D3 | 1 | 2 | yes | — |
| 535 | #102 | — | 3 | 4 | no | — |
| 536 | #102 | — | 3 | 4 | no | — |
| 537 | #102 | — | 3 | 2 | no | — |
| 538 | #102 | — | 3 | 2 | no | — |
| 539 | #102 | C22×D3 | 1 | 2 | yes | — |
| 540 | C22⋊C8 | — | 3 | 4 | no | — |
| 541 | C22⋊C8 | — | 3 | 4 | no | — |
| 542 | #97 | C22×D3 | 1 | 2 | yes | — |
| 543 | C4×C8 | C22×D3 | 1 | 2 | yes | — |
| 544 | C23×C3 | — | 2 | 1 | no | — |
| 545 | C23×C3 | C22×D4 | 1 | 1 | yes | characteristic |
| 546 | C22×D3 | — | 2 | 2 | no | — |
| 547 | C22×D3 | C22×D4 | 1 | 4 | yes | — |
| 548 | C3×Q8 | — | 2 | 4 | no | — |
| 549 | C3×Q8 | — | 2 | 2 | no | — |
| 550 | C3×Q8 | — | 2 | 1 | no | — |
| 551 | C3×Q8 | — | 2 | 1 | no | — |
| 552 | C3×Q8 | C2×#41 | 1 | 4 | yes | — |
| 553 | C3×D4 | — | 2 | 1 | no | — |
| 554 | C3×D4 | — | 2 | 1 | no | — |
| 555 | C3×D4 | — | 4 | 2 | no | — |
| 556 | C2×C3×C4 | — | 2 | 4 | no | — |
| 557 | C2×C3×C4 | — | 2 | 2 | no | — |
| 558 | C2×C3×C4 | — | 2 | 2 | no | — |
| 559 | C2×C3×C4 | — | 2 | 1 | no | — |
| 560 | C2×C3×C4 | — | 2 | 1 | no | — |
| 561 | C2×C3×C4 | — | 2 | 1 | no | — |
| 562 | C2×C3×C4 | — | 2 | 2 | no | — |
| 563 | C2×C3×C4 | — | 4 | 1 | no | — |
| 564 | C2×C3×C4 | — | 4 | 2 | no | — |
| 565 | C2×C3×C4 | — | 4 | 2 | no | — |
| 566 | C2×C3×C4 | — | 4 | 2 | no | — |
| 567 | C2×C3×C4 | — | 8 | 1 | no | — |
| 568 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 569 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 570 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 571 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 572 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 573 | C2×C3×C4 | C2×#41 | 1 | 2 | yes | — |
| 574 | C2×C3×C4 | H(5,𝔽2) | 1 | 2 | yes | — |
| 575 | C2×C3×C4 | C25 | 1 | 1 | yes | characteristic |
| 576 | #67 | — | 2 | 8 | no | — |
| 577 | #67 | — | 4 | 4 | no | — |
| 578 | #67 | — | 8 | 4 | no | — |
| 579 | C2×Dic3 | — | 2 | 4 | no | — |
| 580 | C2×Dic3 | — | 2 | 2 | no | — |
| 581 | C2×Dic3 | — | 8 | 2 | no | — |
| 582 | C2×Dic3 | C22×D4 | 1 | 4 | yes | — |
| 583 | D12 | — | 2 | 4 | no | — |
| 584 | D12 | — | 2 | 4 | no | — |
| 585 | D12 | — | 2 | 2 | no | — |
| 586 | D12 | — | 2 | 2 | no | — |
| 587 | D12 | — | 4 | 2 | no | — |
| 588 | D12 | — | 4 | 8 | no | — |
| 589 | D12 | — | 4 | 2 | no | — |
| 590 | D12 | — | 8 | 1 | no | — |
| 591 | D12 | — | 8 | 4 | no | — |
| 592 | C4×D3 | — | 2 | 4 | no | — |
| 593 | C4×D3 | — | 2 | 4 | no | — |
| 594 | C4×D3 | — | 4 | 8 | no | — |
| 595 | C4×D3 | — | 4 | 8 | no | — |
| 596 | C4×D3 | — | 4 | 4 | no | — |
| 597 | C4×D3 | — | 8 | 4 | no | — |
| 598 | Dic6 | — | 2 | 4 | no | — |
| 599 | Dic6 | — | 2 | 2 | no | — |
| 600 | Dic6 | — | 2 | 2 | no | — |
| 601 | Dic6 | — | 4 | 8 | no | — |
| 602 | Dic6 | — | 4 | 4 | no | — |
| 603 | Dic6 | — | 8 | 2 | no | — |
| 604 | C3×C8 | — | 2 | 2 | no | — |
| 605 | C3×C8 | — | 2 | 2 | no | — |
| 606 | C3⋊C8 | — | 2 | 2 | no | — |
| 607 | C3⋊C8 | — | 2 | 2 | no | — |
| 608 | #41 | — | 2 | 2 | no | — |
| 609 | #41 | — | 2 | 2 | no | — |
| 610 | #41 | — | 6 | 4 | no | — |
| 611 | #41 | — | 6 | 4 | no | — |
| 612 | #41 | — | 6 | 8 | no | — |
| 613 | #41 | — | 6 | 4 | no | — |
| 614 | #41 | — | 6 | 4 | no | — |
| 615 | #41 | — | 12 | 16 | no | — |
| 616 | #41 | — | 12 | 4 | no | — |
| 617 | #41 | — | 12 | 8 | no | — |
| 618 | #41 | — | 24 | 4 | no | — |
| 619 | C2×Q8 | — | 2 | 1 | no | — |
| 620 | C2×Q8 | — | 2 | 2 | no | — |
| 621 | C2×Q8 | — | 3 | 2 | no | — |
| 622 | C2×Q8 | — | 3 | 2 | no | — |
| 623 | C2×Q8 | — | 6 | 4 | no | — |
| 624 | C2×Q8 | — | 6 | 2 | no | — |
| 625 | C2×Q8 | — | 6 | 2 | no | — |
| 626 | C2×Q8 | — | 6 | 8 | no | — |
| 627 | C2×Q8 | — | 12 | 4 | no | — |
| 628 | C2×Q8 | — | 12 | 8 | no | — |
| 629 | C2×Q8 | — | 24 | 2 | no | — |
| 630 | C2×Q8 | #235 | 1 | 4 | yes | complemented |
| 631 | C2×Q8 | C23×D3 | 1 | 1 | yes | characteristic |
| 632 | C2×Q8 | C23×D3 | 1 | 2 | yes | — |
| 633 | C2×D4 | — | 2 | 1 | no | — |
| 634 | C2×D4 | — | 3 | 4 | no | — |
| 635 | C2×D4 | — | 3 | 2 | no | — |
| 636 | C2×D4 | — | 3 | 2 | no | — |
| 637 | C2×D4 | — | 3 | 2 | no | — |
| 638 | C2×D4 | — | 3 | 2 | no | — |
| 639 | C2×D4 | — | 6 | 4 | no | — |
| 640 | C2×D4 | — | 6 | 4 | no | — |
| 641 | C2×D4 | — | 6 | 2 | no | — |
| 642 | C2×D4 | — | 6 | 4 | no | — |
| 643 | C2×D4 | — | 6 | 1 | no | — |
| 644 | C2×D4 | — | 6 | 1 | no | — |
| 645 | C2×D4 | C23×D3 | 1 | 1 | yes | characteristic |
| 646 | C22×C4 | — | 2 | 1 | no | — |
| 647 | C22×C4 | — | 2 | 1 | no | — |
| 648 | C22×C4 | — | 2 | 1 | no | — |
| 649 | C22×C4 | — | 2 | 1 | no | — |
| 650 | C22×C4 | — | 2 | 1 | no | — |
| 651 | C22×C4 | — | 3 | 4 | no | — |
| 652 | C22×C4 | — | 6 | 4 | no | — |
| 653 | C22×C4 | — | 6 | 4 | no | — |
| 654 | C22×C4 | — | 6 | 4 | no | — |
| 655 | C22×C4 | — | 6 | 2 | no | — |
| 656 | C22×C4 | — | 6 | 2 | no | — |
| 657 | C22×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 658 | C22×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 659 | C22×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 660 | Q16 | — | 2 | 4 | no | — |
| 661 | Q16 | — | 12 | 2 | no | — |
| 662 | SD16 | — | 2 | 4 | no | — |
| 663 | SD16 | — | 12 | 2 | no | — |
| 664 | SD16 | — | 12 | 2 | no | — |
| 665 | D8 | — | 12 | 2 | no | — |
| 666 | M16 | — | 2 | 2 | no | — |
| 667 | M16 | — | 2 | 2 | no | — |
| 668 | M16 | — | 12 | 4 | no | — |
| 669 | C2×C8 | — | 3 | 2 | no | — |
| 670 | C2×C8 | — | 3 | 2 | no | — |
| 671 | C2×C8 | — | 6 | 4 | no | — |
| 672 | C2×C8 | — | 12 | 4 | no | — |
| 673 | C2×C8 | C23×D3 | 1 | 2 | yes | — |
| 674 | C2×C8 | C23×D3 | 1 | 2 | yes | — |
| 675 | C4⋊C4 | — | 2 | 2 | no | — |
| 676 | C4⋊C4 | — | 2 | 2 | no | — |
| 677 | C4⋊C4 | — | 2 | 1 | no | — |
| 678 | C4⋊C4 | — | 2 | 1 | no | — |
| 679 | C4⋊C4 | — | 2 | 1 | no | — |
| 680 | C4⋊C4 | — | 3 | 2 | no | — |
| 681 | C4⋊C4 | — | 3 | 2 | no | — |
| 682 | C4⋊C4 | — | 3 | 4 | no | — |
| 683 | C4⋊C4 | — | 6 | 4 | no | — |
| 684 | C4⋊C4 | — | 6 | 4 | no | — |
| 685 | C4⋊C4 | — | 6 | 4 | no | — |
| 686 | C4⋊C4 | — | 6 | 2 | no | — |
| 687 | C4⋊C4 | — | 6 | 2 | no | — |
| 688 | C4⋊C4 | — | 6 | 2 | no | — |
| 689 | C4⋊C4 | — | 6 | 1 | no | — |
| 690 | C4⋊C4 | — | 6 | 1 | no | — |
| 691 | C4⋊C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 692 | C4⋊C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 693 | C4⋊C4 | C23×D3 | 1 | 2 | yes | — |
| 694 | C22⋊C4 | — | 2 | 1 | no | — |
| 695 | C22⋊C4 | — | 2 | 1 | no | — |
| 696 | C22⋊C4 | — | 2 | 1 | no | — |
| 697 | C22⋊C4 | — | 3 | 4 | no | — |
| 698 | C22⋊C4 | — | 3 | 4 | no | — |
| 699 | C22⋊C4 | — | 6 | 4 | no | — |
| 700 | C22⋊C4 | — | 6 | 4 | no | — |
| 701 | C22⋊C4 | — | 6 | 4 | no | — |
| 702 | C22⋊C4 | — | 6 | 4 | no | — |
| 703 | C22⋊C4 | — | 6 | 4 | no | — |
| 704 | C22⋊C4 | — | 6 | 2 | no | — |
| 705 | C22⋊C4 | — | 6 | 2 | no | — |
| 706 | C42 | — | 2 | 1 | no | — |
| 707 | C42 | — | 2 | 1 | no | — |
| 708 | C42 | — | 2 | 1 | no | — |
| 709 | C42 | — | 2 | 2 | no | — |
| 710 | C42 | — | 2 | 2 | no | — |
| 711 | C42 | — | 6 | 4 | no | — |
| 712 | C42 | D3×D4 | 1 | 1 | yes | characteristic |
| 713 | C42 | D3×D4 | 1 | 1 | yes | characteristic |
| 714 | C42 | C23×D3 | 1 | 1 | yes | characteristic |
| 715 | C42 | C23×D3 | 1 | 1 | yes | characteristic |
| 716 | C22×C3 | — | 2 | 1 | no | — |
| 717 | C22×C3 | — | 2 | 1 | no | — |
| 718 | C22×C3 | — | 4 | 1 | no | — |
| 719 | C22×C3 | — | 4 | 1 | no | — |
| 720 | C22×C3 | — | 4 | 1 | no | — |
| 721 | C22×C3 | #546 | 1 | 2 | yes | — |
| 722 | C22×C3 | C23×D4 | 1 | 1 | yes | characteristic |
| 723 | C2×D3 | — | 2 | 4 | no | — |
| 724 | C2×D3 | — | 2 | 4 | no | — |
| 725 | C2×D3 | — | 2 | 4 | no | — |
| 726 | C2×D3 | — | 4 | 2 | no | — |
| 727 | C2×D3 | — | 4 | 2 | no | — |
| 728 | C2×D3 | — | 4 | 2 | no | — |
| 729 | C3×C4 | — | 2 | 1 | no | — |
| 730 | C3×C4 | — | 2 | 1 | no | — |
| 731 | C3×C4 | — | 2 | 4 | no | — |
| 732 | C3×C4 | — | 2 | 1 | no | — |
| 733 | C3×C4 | — | 4 | 2 | no | — |
| 734 | C3×C4 | — | 4 | 1 | no | — |
| 735 | C3×C4 | — | 4 | 1 | no | — |
| 736 | C3×C4 | — | 4 | 1 | no | — |
| 737 | C3×C4 | #546 | 1 | 2 | yes | — |
| 738 | C3×C4 | #577 | 1 | 2 | yes | — |
| 739 | C3×C4 | C22×#41 | 1 | 1 | yes | characteristic |
| 740 | C3×C4 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 741 | Dic3 | — | 2 | 4 | no | — |
| 742 | Dic3 | — | 4 | 2 | no | — |
| 743 | Dic3 | — | 4 | 4 | no | — |
| 744 | C23 | — | 2 | 1 | no | — |
| 745 | C23 | — | 3 | 4 | no | — |
| 746 | C23 | — | 6 | 2 | no | — |
| 747 | C23 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 748 | Q8 | — | 2 | 2 | no | — |
| 749 | Q8 | — | 2 | 4 | no | — |
| 750 | Q8 | — | 2 | 1 | no | — |
| 751 | Q8 | — | 2 | 1 | no | — |
| 752 | Q8 | — | 6 | 4 | no | — |
| 753 | Q8 | — | 6 | 2 | no | — |
| 754 | Q8 | — | 6 | 2 | no | — |
| 755 | Q8 | — | 12 | 8 | no | — |
| 756 | Q8 | — | 12 | 4 | no | — |
| 757 | Q8 | — | 24 | 2 | no | — |
| 758 | Q8 | C2×#235 | 1 | 4 | yes | — |
| 759 | D4 | — | 2 | 1 | no | — |
| 760 | D4 | — | 2 | 1 | no | — |
| 761 | D4 | — | 4 | 2 | no | — |
| 762 | D4 | — | 6 | 8 | no | — |
| 763 | D4 | — | 6 | 2 | no | — |
| 764 | D4 | — | 6 | 2 | no | — |
| 765 | D4 | — | 6 | 4 | no | — |
| 766 | D4 | — | 6 | 4 | no | — |
| 767 | D4 | — | 12 | 2 | no | — |
| 768 | D4 | — | 12 | 8 | no | — |
| 769 | D4 | — | 12 | 4 | no | — |
| 770 | D4 | — | 12 | 2 | no | — |
| 771 | D4 | — | 24 | 1 | no | — |
| 772 | D4 | — | 24 | 4 | no | — |
| 773 | D4 | — | 24 | 4 | no | — |
| 774 | C2×C4 | — | 2 | 2 | no | — |
| 775 | C2×C4 | — | 2 | 4 | no | — |
| 776 | C2×C4 | — | 2 | 2 | no | — |
| 777 | C2×C4 | — | 2 | 1 | no | — |
| 778 | C2×C4 | — | 2 | 1 | no | — |
| 779 | C2×C4 | — | 2 | 2 | no | — |
| 780 | C2×C4 | — | 2 | 1 | no | — |
| 781 | C2×C4 | — | 3 | 4 | no | — |
| 782 | C2×C4 | — | 4 | 1 | no | — |
| 783 | C2×C4 | — | 4 | 2 | no | — |
| 784 | C2×C4 | — | 4 | 2 | no | — |
| 785 | C2×C4 | — | 4 | 2 | no | — |
| 786 | C2×C4 | — | 6 | 4 | no | — |
| 787 | C2×C4 | — | 6 | 4 | no | — |
| 788 | C2×C4 | — | 6 | 4 | no | — |
| 789 | C2×C4 | — | 6 | 2 | no | — |
| 790 | C2×C4 | — | 8 | 1 | no | — |
| 791 | C2×C4 | — | 12 | 8 | no | — |
| 792 | C2×C4 | — | 12 | 8 | no | — |
| 793 | C2×C4 | — | 12 | 4 | no | — |
| 794 | C2×C4 | — | 24 | 4 | no | — |
| 795 | C2×C4 | — | 24 | 2 | no | — |
| 796 | C2×C4 | C2×#235 | 1 | 2 | yes | — |
| 797 | C2×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 798 | C2×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 799 | C2×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 800 | C2×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 801 | C2×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 802 | C2×C4 | #1009 | 1 | 2 | yes | — |
| 803 | C2×C4 | C24×D3 | 1 | 1 | yes | characteristic |
| 804 | C8 | — | 2 | 2 | no | — |
| 805 | C8 | — | 2 | 2 | no | — |
| 806 | C8 | — | 6 | 2 | no | — |
| 807 | C8 | — | 6 | 2 | no | — |
| 808 | C2×C3 | — | 2 | 2 | no | — |
| 809 | C2×C3 | — | 8 | 1 | no | — |
| 810 | C2×C3 | C2×#546 | 1 | 1 | yes | characteristic |
| 811 | C2×C3 | C2×#577 | 1 | 1 | yes | characteristic |
| 812 | C2×C3 | #3586 | 1 | 1 | yes | characteristic |
| 813 | D3 | — | 4 | 4 | no | — |
| 814 | D3 | — | 8 | 2 | no | — |
| 815 | C22 | — | 2 | 1 | no | — |
| 816 | C22 | — | 2 | 1 | no | — |
| 817 | C22 | — | 4 | 1 | no | — |
| 818 | C22 | — | 4 | 1 | no | — |
| 819 | C22 | — | 4 | 1 | no | — |
| 820 | C22 | — | 6 | 4 | no | — |
| 821 | C22 | — | 6 | 4 | no | — |
| 822 | C22 | — | 6 | 4 | no | — |
| 823 | C22 | — | 12 | 2 | no | — |
| 824 | C22 | — | 12 | 2 | no | — |
| 825 | C22 | — | 12 | 2 | no | — |
| 826 | C22 | #5550 | 1 | 2 | yes | — |
| 827 | C22 | C22×D3×D4 | 1 | 1 | yes | characteristic |
| 828 | C4 | — | 2 | 4 | no | — |
| 829 | C4 | — | 2 | 1 | no | — |
| 830 | C4 | — | 2 | 1 | no | — |
| 831 | C4 | — | 2 | 1 | no | — |
| 832 | C4 | — | 4 | 1 | no | — |
| 833 | C4 | — | 4 | 1 | no | — |
| 834 | C4 | — | 4 | 1 | no | — |
| 835 | C4 | — | 4 | 2 | no | — |
| 836 | C4 | — | 6 | 4 | no | — |
| 837 | C4 | — | 12 | 2 | no | — |
| 838 | C4 | — | 12 | 4 | no | — |
| 839 | C4 | #5550 | 1 | 2 | yes | — |
| 840 | C4 | #5778 | 1 | 2 | yes | — |
| 841 | C4 | C22×#235 | 1 | 1 | yes | characteristic |
| 842 | C4 | C2×#1009 | 1 | 1 | yes | characteristic |
| 843 | C3 | #61202 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 844 | C2 | — | 2 | 2 | no | — |
| 845 | C2 | — | 8 | 1 | no | — |
| 846 | C2 | — | 12 | 4 | no | — |
| 847 | C2 | — | 24 | 2 | no | — |
| 848 | C2 | C2×#5550 | 1 | 1 | yes | characteristic |
| 849 | C2 | C2×#5778 | 1 | 1 | yes | characteristic |
| 850 | C2 | #87201 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #85850 | C2 | semidirect |
| 2. #85818 | C2 | semidirect |
| 3. C3×C4×#137 | C2 | semidirect |
| 4. #83984 | C2 | semidirect |
| 5. #82525 | C2 | semidirect |
| 6. C2×#5020 | C2 | semidirect |
| 7. #79843 | C2 | semidirect |
| 8. #79805 | C2 | semidirect |
| 9. #79739 | C2 | semidirect |
| 10. #79737 | C2 | semidirect |
| 11. #79687 | C2 | semidirect |
| 12. #79678 | C2 | semidirect |
| 13. #79222 | C2 | semidirect |
| 14. #78957 | C2 | semidirect |
| 15. #78890 | C2 | semidirect |
| 16. #78528 | C2 | semidirect |
| 17. #78522 | C2 | semidirect |
| 108. C4×#137 | D3 | semidirect |
| 315. C2×C3×Q8 | #41 | semidirect |
| 630. C2×Q8 | #235 | semidirect |
| 843. C3 | #61202 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #85850 | 2 |
| #85818 | 2 |
| C3×C4×#137 | 2 |
| #83984 | 2 |
| #82525 | 2 |
| C2×#5020 | 2 |
| #79843 | 2 |
| #79805 | 2 |
| #79739 | 2 |
| #79737 | 2 |
| #79687 | 2 |
| #79678 | 2 |
| #79222 | 2 |
| #78957 | 2 |
| #78890 | 2 |
| #78528 | 2 |
| #78522 | 2 |
| #61202 | 3 |