Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
2066 conjugacy classes of subgroups.
The subgroup lattice has 912 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #86281 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #86076 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | C3×#3140 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #83335 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C2×#5055 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #81683 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #81682 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #81679 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | D3×#489 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #81639 | C2 | 1 | 4 | yes | maximal, complemented |
| 11 | #81638 | C2 | 1 | 4 | yes | maximal, complemented |
| 12 | #78957 | C2 | 1 | 2 | yes | maximal, complemented |
| 13 | #78952 | C2 | 1 | 2 | yes | maximal, complemented |
| 14 | #78925 | C2 | 1 | 2 | yes | maximal, complemented |
| 15 | #78920 | C2 | 1 | 2 | yes | maximal, complemented |
| 16 | #78528 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 17 | #78516 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 18 | #60625 | — | 3 | 1 | no | maximal, Sylow |
| 19 | C2×#1007 | C22 | 1 | 1 | yes | characteristic |
| 20 | C2×#1004 | C22 | 1 | 1 | yes | characteristic |
| 21 | C3×#533 | C22 | 1 | 1 | yes | characteristic, complemented |
| 22 | C2×C3×#124 | C22 | 1 | 1 | yes | characteristic |
| 23 | #5816 | C22 | 1 | 1 | yes | characteristic |
| 24 | #5805 | C22 | 1 | 1 | yes | characteristic |
| 25 | C2×#907 | C22 | 1 | 2 | yes | — |
| 26 | #5728 | C22 | 1 | 2 | yes | complemented |
| 27 | D3×C4⋊Q8 | C22 | 1 | 2 | yes | complemented |
| 28 | #5689 | C22 | 1 | 4 | yes | complemented |
| 29 | #5677 | — | 2 | 1 | no | — |
| 30 | #5677 | — | 2 | 1 | no | — |
| 31 | #5676 | — | 2 | 1 | no | — |
| 32 | #5676 | — | 2 | 1 | no | — |
| 33 | #5675 | C22 | 1 | 2 | yes | — |
| 34 | #5674 | C22 | 1 | 2 | yes | — |
| 35 | D3×#124 | C22 | 1 | 2 | yes | — |
| 36 | #5668 | C22 | 1 | 2 | yes | — |
| 37 | #5635 | — | 2 | 2 | no | — |
| 38 | #5632 | — | 2 | 2 | no | — |
| 39 | #5579 | — | 2 | 1 | no | — |
| 40 | Q8×D12 | — | 2 | 1 | no | — |
| 41 | #5567 | — | 2 | 1 | no | — |
| 42 | Q8×Dic6 | — | 2 | 1 | no | — |
| 43 | #5523 | C22 | 1 | 2 | yes | — |
| 44 | #5519 | C22 | 1 | 2 | yes | complemented |
| 45 | #5490 | — | 2 | 2 | no | — |
| 46 | #5490 | — | 2 | 2 | no | — |
| 47 | #5477 | C22 | 1 | 1 | yes | characteristic |
| 48 | C4×#235 | C22 | 1 | 1 | yes | characteristic |
| 49 | C2×#869 | C22 | 1 | 1 | yes | characteristic, complemented |
| 50 | C3×#489 | C22 | 1 | 2 | yes | complemented |
| 51 | C3×#489 | C22 | 1 | 2 | yes | complemented |
| 52 | C3×#488 | C22 | 1 | 4 | yes | complemented |
| 53 | C3×#419 | C22 | 1 | 2 | yes | complemented |
| 54 | C3×#418 | C22 | 1 | 2 | yes | — |
| 55 | C3×C4×M16 | C22 | 1 | 1 | yes | characteristic, complemented |
| 56 | C2×#835 | C22 | 1 | 2 | yes | complemented |
| 57 | C2×#832 | C22 | 1 | 2 | yes | — |
| 58 | #5133 | C22 | 1 | 2 | yes | — |
| 59 | #5133 | C22 | 1 | 2 | yes | complemented |
| 60 | #5122 | C22 | 1 | 2 | yes | complemented |
| 61 | #5089 | C22 | 1 | 1 | yes | characteristic, complemented |
| 62 | #5089 | C22 | 1 | 1 | yes | characteristic, complemented |
| 63 | #5089 | C22 | 1 | 1 | yes | characteristic, complemented |
| 64 | #5089 | C22 | 1 | 1 | yes | characteristic, complemented |
| 65 | #5069 | C22 | 1 | 2 | yes | complemented |
| 66 | #5067 | C22 | 1 | 2 | yes | complemented |
| 67 | #5055 | C22 | 1 | 2 | yes | complemented |
| 68 | #5055 | C22 | 1 | 2 | yes | complemented |
| 69 | #5055 | C22 | 1 | 4 | yes | complemented |
| 70 | #5002 | C22 | 1 | 2 | yes | — |
| 71 | #5002 | C22 | 1 | 2 | yes | complemented |
| 72 | C2×#803 | C22 | 1 | 1 | yes | characteristic, complemented |
| 73 | #4804 | C22 | 1 | 4 | yes | complemented |
| 74 | #4803 | C22 | 1 | 4 | yes | complemented |
| 75 | #4802 | C22 | 1 | 4 | yes | complemented |
| 76 | D3×#103 | C22 | 1 | 4 | yes | complemented |
| 77 | #4800 | C22 | 1 | 4 | yes | complemented |
| 78 | #4797 | C22 | 1 | 4 | yes | complemented |
| 79 | #4794 | C22 | 1 | 4 | yes | complemented |
| 80 | #4792 | C22 | 1 | 4 | yes | complemented |
| 81 | #4772 | C22 | 1 | 4 | yes | — |
| 82 | #4771 | C22 | 1 | 4 | yes | — |
| 83 | #4770 | C22 | 1 | 4 | yes | — |
| 84 | D3×#102 | C22 | 1 | 4 | yes | — |
| 85 | #4768 | C22 | 1 | 4 | yes | complemented |
| 86 | #4765 | C22 | 1 | 4 | yes | complemented |
| 87 | #4764 | C22 | 1 | 4 | yes | complemented |
| 88 | #4760 | C22 | 1 | 4 | yes | complemented |
| 89 | #4714 | C22 | 1 | 2 | yes | complemented |
| 90 | #4714 | C22 | 1 | 2 | yes | complemented |
| 91 | #4707 | C22 | 1 | 2 | yes | complemented |
| 92 | D3×#97 | C22 | 1 | 2 | yes | complemented |
| 93 | #4694 | C22 | 1 | 2 | yes | complemented |
| 94 | #4689 | C22 | 1 | 4 | yes | complemented |
| 95 | #4681 | C22 | 1 | 2 | yes | complemented |
| 96 | #3503 | — | 3 | 1 | no | — |
| 97 | #3500 | — | 3 | 1 | no | — |
| 98 | #3141 | — | 3 | 2 | no | — |
| 99 | #3141 | — | 3 | 1 | no | — |
| 100 | #3140 | — | 3 | 2 | no | — |
| 101 | #3140 | D3 | 1 | 1 | yes | characteristic, complemented |
| 102 | #3137 | — | 3 | 4 | no | — |
| 103 | #3137 | — | 3 | 2 | no | — |
| 104 | #3136 | — | 3 | 4 | no | — |
| 105 | #3136 | — | 3 | 2 | no | — |
| 106 | #3135 | — | 3 | 2 | no | — |
| 107 | #3135 | — | 3 | 1 | no | — |
| 108 | C2×#489 | — | 3 | 2 | no | — |
| 109 | C2×#489 | — | 3 | 1 | no | — |
| 110 | #2898 | — | 3 | 2 | no | — |
| 111 | #2897 | — | 3 | 2 | no | — |
| 112 | #2875 | — | 3 | 1 | no | — |
| 113 | C22×C3×Q8 | C23 | 1 | 1 | yes | characteristic |
| 114 | C22×C3×D4 | C23 | 1 | 1 | yes | characteristic |
| 115 | C22×#67 | — | 2 | 2 | no | — |
| 116 | #1007 | — | 2 | 8 | no | — |
| 117 | C2×#239 | — | 2 | 1 | no | — |
| 118 | C2×#239 | C23 | 1 | 2 | yes | — |
| 119 | C2×D3×Q8 | — | 2 | 2 | no | — |
| 120 | C2×D3×Q8 | — | 2 | 1 | no | — |
| 121 | C2×D3×Q8 | C23 | 1 | 2 | yes | — |
| 122 | #1004 | — | 2 | 8 | no | — |
| 123 | C2×#237 | — | 2 | 1 | no | — |
| 124 | C2×#237 | C23 | 1 | 2 | yes | — |
| 125 | C2×D3×D4 | — | 2 | 1 | no | — |
| 126 | C2×D3×D4 | C23 | 1 | 2 | yes | — |
| 127 | C2×#235 | — | 2 | 2 | no | — |
| 128 | C2×#235 | C23 | 1 | 1 | yes | characteristic |
| 129 | C2×#235 | C23 | 1 | 1 | yes | characteristic |
| 130 | C2×#235 | C23 | 1 | 1 | yes | characteristic |
| 131 | C22×Dic6 | — | 2 | 1 | no | — |
| 132 | C2×C3×M16 | C23 | 1 | 2 | yes | — |
| 133 | C3×C4⋊Q8 | C23 | 1 | 1 | yes | characteristic |
| 134 | C3×C4⋊Q8 | C23 | 1 | 1 | yes | characteristic |
| 135 | C3×#125 | C23 | 1 | 2 | yes | — |
| 136 | C3×#124 | — | 2 | 1 | no | — |
| 137 | C3×#124 | — | 2 | 1 | no | — |
| 138 | C3×#124 | C23 | 1 | 2 | yes | — |
| 139 | C3×#124 | C23 | 1 | 2 | yes | — |
| 140 | C3×C22⋊Q8 | — | 2 | 1 | no | — |
| 141 | C3×C22⋊Q8 | — | 2 | 1 | no | — |
| 142 | C3×C4×Q8 | — | 2 | 1 | no | — |
| 143 | C3×C4×Q8 | — | 2 | 1 | no | — |
| 144 | C3×#117 | C23 | 1 | 2 | yes | — |
| 145 | C2×C3×C22⋊C4 | — | 2 | 1 | no | — |
| 146 | C2×C3×C22⋊C4 | — | 2 | 1 | no | — |
| 147 | C2×C3×C42 | C23 | 1 | 1 | yes | characteristic |
| 148 | #953 | — | 2 | 2 | no | — |
| 149 | #947 | C23 | 1 | 2 | yes | — |
| 150 | #946 | — | 2 | 2 | no | — |
| 151 | #946 | — | 2 | 1 | no | — |
| 152 | #946 | — | 2 | 1 | no | — |
| 153 | Q8×Dic3 | — | 2 | 2 | no | — |
| 154 | #944 | — | 2 | 2 | no | — |
| 155 | #944 | C23 | 1 | 2 | yes | — |
| 156 | #940 | C23 | 1 | 2 | yes | — |
| 157 | #938 | — | 2 | 1 | no | — |
| 158 | #938 | — | 2 | 1 | no | — |
| 159 | #936 | C23 | 1 | 2 | yes | — |
| 160 | #930 | — | 2 | 1 | no | — |
| 161 | #930 | — | 2 | 1 | no | — |
| 162 | #929 | — | 2 | 2 | no | — |
| 163 | C4×#67 | D4 | 1 | 2 | yes | — |
| 164 | C4×#67 | D4 | 1 | 2 | yes | — |
| 165 | #926 | C23 | 1 | 1 | yes | characteristic |
| 166 | C2×C4⋊Dic3 | — | 2 | 1 | no | — |
| 167 | C2×C4⋊Dic3 | C23 | 1 | 2 | yes | — |
| 168 | C22×C3⋊C8 | C23 | 1 | 2 | yes | — |
| 169 | #907 | — | 2 | 8 | no | — |
| 170 | C2×ΓL(1,𝔽25) | C23 | 1 | 4 | yes | — |
| 171 | C2×D3×C8 | C23 | 1 | 4 | yes | — |
| 172 | #897 | — | 2 | 2 | no | — |
| 173 | #897 | — | 2 | 4 | no | — |
| 174 | #896 | — | 2 | 4 | no | — |
| 175 | #892 | C23 | 1 | 4 | yes | — |
| 176 | D3×C4⋊C4 | — | 2 | 2 | no | — |
| 177 | D3×C4⋊C4 | C23 | 1 | 4 | yes | — |
| 178 | #890 | C23 | 1 | 4 | yes | — |
| 179 | #889 | — | 2 | 4 | no | — |
| 180 | #888 | — | 2 | 4 | no | — |
| 181 | #888 | — | 2 | 2 | no | — |
| 182 | #888 | C23 | 1 | 4 | yes | — |
| 183 | #887 | — | 2 | 2 | no | — |
| 184 | #885 | — | 2 | 2 | no | — |
| 185 | #885 | — | 2 | 2 | no | — |
| 186 | #884 | — | 2 | 2 | no | — |
| 187 | #884 | — | 2 | 2 | no | — |
| 188 | #884 | — | 2 | 2 | no | — |
| 189 | #884 | — | 2 | 2 | no | — |
| 190 | #883 | — | 2 | 2 | no | — |
| 191 | #883 | — | 2 | 2 | no | — |
| 192 | #882 | — | 2 | 2 | no | — |
| 193 | #882 | — | 2 | 2 | no | — |
| 194 | #67⋊C4 | — | 2 | 4 | no | — |
| 195 | #67⋊C4 | — | 2 | 2 | no | — |
| 196 | #67⋊C4 | — | 2 | 2 | no | — |
| 197 | D3×C22⋊C4 | — | 2 | 2 | no | — |
| 198 | D3×C22⋊C4 | — | 2 | 2 | no | — |
| 199 | #878 | — | 2 | 4 | no | — |
| 200 | #878 | — | 2 | 2 | no | — |
| 201 | #878 | — | 2 | 2 | no | — |
| 202 | #875 | C23 | 1 | 1 | yes | characteristic |
| 203 | #875 | C23 | 1 | 1 | yes | characteristic |
| 204 | #874 | C23 | 1 | 1 | yes | characteristic |
| 205 | C4×D12 | — | 2 | 2 | no | — |
| 206 | C4×D12 | — | 2 | 1 | no | — |
| 207 | C4×D12 | — | 2 | 1 | no | — |
| 208 | C4×D12 | D4 | 1 | 1 | yes | characteristic |
| 209 | C4×D12 | D4 | 1 | 1 | yes | characteristic |
| 210 | #872 | C23 | 1 | 2 | yes | — |
| 211 | C42×D3 | C23 | 1 | 2 | yes | — |
| 212 | #870 | — | 2 | 2 | no | — |
| 213 | #869 | — | 2 | 1 | no | — |
| 214 | #869 | — | 2 | 1 | no | — |
| 215 | #869 | — | 2 | 2 | no | — |
| 216 | #869 | C23 | 1 | 1 | yes | characteristic |
| 217 | #869 | C23 | 1 | 2 | yes | — |
| 218 | #869 | C23 | 1 | 2 | yes | — |
| 219 | C4×Dic6 | — | 2 | 2 | no | — |
| 220 | C4×Dic6 | D4 | 1 | 1 | yes | characteristic |
| 221 | C4×Dic6 | D4 | 1 | 1 | yes | characteristic |
| 222 | C3×#103 | C23 | 1 | 4 | yes | — |
| 223 | C3×#103 | C23 | 1 | 4 | yes | — |
| 224 | C3×#102 | C23 | 1 | 4 | yes | — |
| 225 | C3×#102 | C23 | 1 | 4 | yes | — |
| 226 | C3×#97 | C23 | 1 | 2 | yes | — |
| 227 | C3×C4×C8 | C23 | 1 | 2 | yes | — |
| 228 | #835 | C23 | 1 | 4 | yes | — |
| 229 | #835 | C23 | 1 | 4 | yes | — |
| 230 | #832 | C23 | 1 | 4 | yes | — |
| 231 | #832 | C23 | 1 | 4 | yes | — |
| 232 | #821 | C23 | 1 | 4 | yes | — |
| 233 | #821 | C23 | 1 | 4 | yes | — |
| 234 | #816 | C23 | 1 | 4 | yes | — |
| 235 | #816 | C23 | 1 | 4 | yes | — |
| 236 | #815 | C23 | 1 | 4 | yes | — |
| 237 | C8×Dic3 | C23 | 1 | 4 | yes | — |
| 238 | #810 | C23 | 1 | 2 | yes | — |
| 239 | #810 | C23 | 1 | 2 | yes | — |
| 240 | #810 | C23 | 1 | 2 | yes | — |
| 241 | #810 | C23 | 1 | 2 | yes | — |
| 242 | #809 | C23 | 1 | 2 | yes | — |
| 243 | #809 | C23 | 1 | 2 | yes | — |
| 244 | #809 | C23 | 1 | 2 | yes | — |
| 245 | #809 | C23 | 1 | 2 | yes | — |
| 246 | #803 | C23 | 1 | 2 | yes | — |
| 247 | #803 | C23 | 1 | 1 | yes | characteristic |
| 248 | #803 | C23 | 1 | 1 | yes | characteristic |
| 249 | C2×2−1+4 | — | 3 | 1 | no | — |
| 250 | C2×H(5,𝔽2) | — | 3 | 1 | no | — |
| 251 | C2×#131 | — | 3 | 2 | no | — |
| 252 | Q82 | — | 6 | 1 | no | — |
| 253 | #557 | — | 6 | 1 | no | — |
| 254 | #554 | — | 6 | 1 | no | — |
| 255 | #554 | — | 6 | 2 | no | — |
| 256 | D4×Q8 | — | 6 | 1 | no | — |
| 257 | D4×Q8 | — | 6 | 2 | no | — |
| 258 | #548 | — | 6 | 1 | no | — |
| 259 | #548 | — | 6 | 1 | no | — |
| 260 | #546 | — | 6 | 2 | no | — |
| 261 | #546 | — | 6 | 2 | no | — |
| 262 | #546 | — | 6 | 1 | no | — |
| 263 | #546 | — | 6 | 1 | no | — |
| 264 | #544 | — | 3 | 4 | no | — |
| 265 | #544 | — | 3 | 2 | no | — |
| 266 | #536 | — | 3 | 1 | no | — |
| 267 | #536 | — | 3 | 2 | no | — |
| 268 | #535 | — | 3 | 1 | no | — |
| 269 | #535 | — | 3 | 2 | no | — |
| 270 | #533 | — | 3 | 2 | no | — |
| 271 | #533 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 272 | #532 | — | 3 | 2 | no | — |
| 273 | #532 | — | 3 | 1 | no | — |
| 274 | C2×C4⋊Q8 | — | 3 | 2 | no | — |
| 275 | C2×C4⋊Q8 | — | 3 | 1 | no | — |
| 276 | C2×#124 | — | 3 | 2 | no | — |
| 277 | C2×#124 | C2×D3 | 1 | 1 | yes | characteristic |
| 278 | #520 | — | 3 | 2 | no | — |
| 279 | C4×#41 | — | 3 | 1 | no | — |
| 280 | #491 | — | 3 | 2 | no | — |
| 281 | #491 | — | 3 | 4 | no | — |
| 282 | #490 | — | 3 | 2 | no | — |
| 283 | #490 | — | 3 | 4 | no | — |
| 284 | #489 | — | 3 | 1 | no | — |
| 285 | #489 | — | 3 | 1 | no | — |
| 286 | #489 | — | 3 | 1 | no | — |
| 287 | #489 | — | 3 | 1 | no | — |
| 288 | #489 | — | 3 | 2 | no | — |
| 289 | #489 | — | 3 | 4 | no | — |
| 290 | #489 | — | 3 | 2 | no | — |
| 291 | #489 | — | 3 | 4 | no | — |
| 292 | #489 | — | 3 | 4 | no | — |
| 293 | #489 | — | 3 | 2 | no | — |
| 294 | #489 | — | 3 | 2 | no | — |
| 295 | #489 | C2×D3 | 1 | 2 | yes | complemented |
| 296 | #489 | C2×D3 | 1 | 2 | yes | complemented |
| 297 | #488 | — | 3 | 4 | no | — |
| 298 | #488 | — | 3 | 4 | no | — |
| 299 | #488 | C2×D3 | 1 | 4 | yes | complemented |
| 300 | #487 | — | 3 | 4 | no | — |
| 301 | #487 | — | 3 | 2 | no | — |
| 302 | #486 | — | 3 | 4 | no | — |
| 303 | #486 | — | 3 | 2 | no | — |
| 304 | #419 | — | 3 | 4 | no | — |
| 305 | #419 | C2×D3 | 1 | 2 | yes | complemented |
| 306 | #418 | — | 3 | 4 | no | — |
| 307 | #418 | C2×D3 | 1 | 2 | yes | — |
| 308 | #417 | — | 3 | 2 | no | — |
| 309 | #417 | — | 3 | 2 | no | — |
| 310 | #417 | — | 3 | 4 | no | — |
| 311 | #417 | — | 3 | 4 | no | — |
| 312 | #416 | — | 3 | 2 | no | — |
| 313 | #416 | — | 3 | 2 | no | — |
| 314 | #416 | — | 3 | 4 | no | — |
| 315 | #416 | — | 3 | 4 | no | — |
| 316 | C2×#103 | — | 3 | 2 | no | — |
| 317 | C2×#103 | — | 3 | 4 | no | — |
| 318 | C2×#102 | — | 3 | 2 | no | — |
| 319 | C2×#102 | — | 3 | 4 | no | — |
| 320 | #405 | — | 3 | 2 | no | — |
| 321 | #405 | — | 3 | 4 | no | — |
| 322 | C4×M16 | — | 3 | 2 | no | — |
| 323 | C4×M16 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 324 | C2×#97 | — | 3 | 1 | no | — |
| 325 | C2×#97 | — | 3 | 2 | no | — |
| 326 | C24×C3 | — | 2 | 1 | no | — |
| 327 | C23×D3 | — | 2 | 2 | no | — |
| 328 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 329 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 330 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 331 | C2×C3×Q8 | — | 2 | 4 | no | — |
| 332 | C2×C3×Q8 | C24 | 1 | 2 | yes | — |
| 333 | C2×C3×D4 | — | 2 | 1 | no | — |
| 334 | C2×C3×D4 | — | 2 | 4 | no | — |
| 335 | C2×C3×D4 | C24 | 1 | 2 | yes | — |
| 336 | C22×C3×C4 | — | 2 | 1 | no | — |
| 337 | C22×C3×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 338 | C22×C3×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 339 | C22×C3×C4 | C24 | 1 | 1 | yes | characteristic |
| 340 | C2×#67 | — | 2 | 1 | no | — |
| 341 | C2×#67 | — | 2 | 1 | no | — |
| 342 | C2×#67 | — | 2 | 2 | no | — |
| 343 | C2×#67 | — | 2 | 2 | no | — |
| 344 | C2×#67 | — | 2 | 2 | no | — |
| 345 | C2×#67 | — | 2 | 2 | no | — |
| 346 | C2×#67 | — | 4 | 8 | no | — |
| 347 | C2×#67 | C2×D4 | 1 | 2 | yes | — |
| 348 | C22×Dic3 | — | 2 | 2 | no | — |
| 349 | C22×Dic3 | — | 2 | 2 | no | — |
| 350 | #239 | — | 2 | 8 | no | — |
| 351 | #239 | — | 4 | 4 | no | — |
| 352 | D3×Q8 | — | 2 | 8 | no | — |
| 353 | D3×Q8 | — | 4 | 4 | no | — |
| 354 | D3×Q8 | — | 8 | 4 | no | — |
| 355 | #237 | — | 2 | 8 | no | — |
| 356 | #237 | — | 4 | 4 | no | — |
| 357 | D3×D4 | — | 2 | 8 | no | — |
| 358 | D3×D4 | — | 4 | 4 | no | — |
| 359 | #235 | — | 2 | 4 | no | — |
| 360 | #235 | — | 2 | 4 | no | — |
| 361 | #235 | — | 4 | 8 | no | — |
| 362 | #235 | #41 | 1 | 8 | yes | — |
| 363 | C2×D12 | — | 2 | 2 | no | — |
| 364 | C2×D12 | — | 2 | 1 | no | — |
| 365 | C2×D12 | — | 2 | 1 | no | — |
| 366 | C2×D12 | C2×D4 | 1 | 1 | yes | characteristic |
| 367 | C2×D12 | C24 | 1 | 1 | yes | characteristic |
| 368 | C2×D12 | C24 | 1 | 1 | yes | characteristic |
| 369 | C2×C4×D3 | — | 2 | 2 | no | — |
| 370 | C2×C4×D3 | — | 2 | 1 | no | — |
| 371 | C2×C4×D3 | — | 2 | 1 | no | — |
| 372 | C2×C4×D3 | — | 2 | 2 | no | — |
| 373 | C2×C4×D3 | — | 2 | 4 | no | — |
| 374 | C2×C4×D3 | C2×D4 | 1 | 2 | yes | — |
| 375 | C2×C4×D3 | C2×D4 | 1 | 2 | yes | — |
| 376 | C2×C4×D3 | C24 | 1 | 2 | yes | — |
| 377 | C2×Dic6 | — | 2 | 2 | no | — |
| 378 | C2×Dic6 | — | 2 | 2 | no | — |
| 379 | C2×Dic6 | — | 2 | 2 | no | — |
| 380 | C2×Dic6 | — | 2 | 4 | no | — |
| 381 | C2×Dic6 | — | 8 | 2 | no | — |
| 382 | C2×Dic6 | C2×D4 | 1 | 1 | yes | characteristic |
| 383 | C2×Dic6 | C24 | 1 | 1 | yes | characteristic |
| 384 | C2×Dic6 | C24 | 1 | 1 | yes | characteristic |
| 385 | C3×M16 | — | 2 | 4 | no | — |
| 386 | C2×C3×C8 | C24 | 1 | 4 | yes | — |
| 387 | C3×C4⋊C4 | — | 2 | 1 | no | — |
| 388 | C3×C4⋊C4 | — | 2 | 1 | no | — |
| 389 | C3×C4⋊C4 | — | 2 | 2 | no | — |
| 390 | C3×C4⋊C4 | — | 2 | 2 | no | — |
| 391 | C3×C4⋊C4 | C24 | 1 | 2 | yes | — |
| 392 | C3×C4⋊C4 | C24 | 1 | 2 | yes | — |
| 393 | C3×C22⋊C4 | — | 2 | 2 | no | — |
| 394 | C3×C22⋊C4 | — | 2 | 2 | no | — |
| 395 | C3×C22⋊C4 | — | 2 | 2 | no | — |
| 396 | C3×C22⋊C4 | — | 2 | 2 | no | — |
| 397 | C3×C22⋊C4 | — | 2 | 2 | no | — |
| 398 | C3×C42 | — | 2 | 2 | no | — |
| 399 | C3×C42 | C2×D4 | 1 | 1 | yes | characteristic |
| 400 | C3×C42 | C2×D4 | 1 | 1 | yes | characteristic |
| 401 | C3×C42 | C24 | 1 | 1 | yes | characteristic |
| 402 | C3×C42 | C24 | 1 | 1 | yes | characteristic |
| 403 | #217 | — | 2 | 2 | no | — |
| 404 | #217 | — | 2 | 2 | no | — |
| 405 | #217 | C2×D4 | 1 | 2 | yes | — |
| 406 | (C2×D3)⋊C4 | — | 2 | 4 | no | — |
| 407 | (C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 408 | (C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 409 | (C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 410 | (C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 411 | (C2×D3)⋊C4 | — | 2 | 2 | no | — |
| 412 | (C2×D3)⋊C4 | — | 2 | 2 | no | — |
| 413 | (C2×D3)⋊C4 | C2×D4 | 1 | 2 | yes | — |
| 414 | (C2×D3)⋊C4 | C2×D4 | 1 | 2 | yes | — |
| 415 | C4⋊Dic3 | — | 2 | 2 | no | — |
| 416 | C4⋊Dic3 | — | 2 | 2 | no | — |
| 417 | C4⋊Dic3 | — | 2 | 2 | no | — |
| 418 | C4⋊Dic3 | — | 2 | 1 | no | — |
| 419 | C4⋊Dic3 | — | 2 | 1 | no | — |
| 420 | C4⋊Dic3 | — | 2 | 4 | no | — |
| 421 | C4⋊Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 422 | C4⋊Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 423 | C4⋊Dic3 | C24 | 1 | 4 | yes | — |
| 424 | Dic3⋊C4 | — | 2 | 4 | no | — |
| 425 | Dic3⋊C4 | — | 2 | 4 | no | — |
| 426 | Dic3⋊C4 | — | 2 | 4 | no | — |
| 427 | Dic3⋊C4 | — | 2 | 2 | no | — |
| 428 | Dic3⋊C4 | — | 2 | 2 | no | — |
| 429 | Dic3⋊C4 | C2×D4 | 1 | 2 | yes | — |
| 430 | Dic3⋊C4 | C2×D4 | 1 | 2 | yes | — |
| 431 | C4×Dic3 | — | 2 | 4 | no | — |
| 432 | C4×Dic3 | C2×D4 | 1 | 2 | yes | — |
| 433 | C4×Dic3 | C2×D4 | 1 | 2 | yes | — |
| 434 | C4×Dic3 | C24 | 1 | 2 | yes | — |
| 435 | C2×C3⋊C8 | — | 2 | 4 | no | — |
| 436 | C2×C3⋊C8 | C24 | 1 | 2 | yes | — |
| 437 | C2×C3⋊C8 | C24 | 1 | 2 | yes | — |
| 438 | ΓL(1,𝔽25) | — | 2 | 8 | no | — |
| 439 | D3×C8 | — | 2 | 8 | no | — |
| 440 | 2−1+4 | — | 6 | 8 | no | — |
| 441 | H(5,𝔽2) | — | 6 | 8 | no | — |
| 442 | C2×#41 | — | 3 | 1 | no | — |
| 443 | C2×#41 | — | 3 | 2 | no | — |
| 444 | C2×#41 | — | 3 | 2 | no | — |
| 445 | C2×#41 | — | 3 | 1 | no | — |
| 446 | C2×#41 | — | 3 | 1 | no | — |
| 447 | C2×#41 | — | 6 | 2 | no | — |
| 448 | C2×#41 | — | 6 | 1 | no | — |
| 449 | C2×#41 | — | 6 | 1 | no | — |
| 450 | C22×Q8 | — | 3 | 2 | no | — |
| 451 | C22×Q8 | — | 6 | 2 | no | — |
| 452 | C22×Q8 | — | 6 | 1 | no | — |
| 453 | C22×Q8 | — | 6 | 1 | no | — |
| 454 | C22×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 455 | C22×D4 | — | 3 | 2 | no | — |
| 456 | C22×D4 | — | 6 | 1 | no | — |
| 457 | C22×D4 | — | 6 | 2 | no | — |
| 458 | C22×D4 | C22×D3 | 1 | 1 | yes | characteristic |
| 459 | #131 | — | 6 | 8 | no | — |
| 460 | C2×M16 | — | 3 | 4 | no | — |
| 461 | C2×M16 | C22×D3 | 1 | 2 | yes | — |
| 462 | C22×C8 | — | 3 | 2 | no | — |
| 463 | C22×C8 | — | 3 | 4 | no | — |
| 464 | C4⋊Q8 | — | 3 | 4 | no | — |
| 465 | C4⋊Q8 | — | 3 | 2 | no | — |
| 466 | C4⋊Q8 | — | 3 | 2 | no | — |
| 467 | C4⋊Q8 | — | 3 | 2 | no | — |
| 468 | C4⋊Q8 | — | 3 | 1 | no | — |
| 469 | C4⋊Q8 | — | 6 | 2 | no | — |
| 470 | C4⋊Q8 | — | 6 | 2 | no | — |
| 471 | C4⋊Q8 | — | 6 | 2 | no | — |
| 472 | C4⋊Q8 | — | 6 | 4 | no | — |
| 473 | C4⋊Q8 | — | 6 | 1 | no | — |
| 474 | C4⋊Q8 | — | 6 | 1 | no | — |
| 475 | C4⋊Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 476 | C4⋊Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 477 | #127 | — | 3 | 2 | no | — |
| 478 | #127 | — | 3 | 1 | no | — |
| 479 | #125 | — | 3 | 4 | no | — |
| 480 | #125 | — | 6 | 2 | no | — |
| 481 | #125 | — | 6 | 4 | no | — |
| 482 | #125 | C22×D3 | 1 | 2 | yes | — |
| 483 | #124 | — | 2 | 1 | no | — |
| 484 | #124 | — | 2 | 1 | no | — |
| 485 | #124 | — | 3 | 2 | no | — |
| 486 | #124 | — | 3 | 2 | no | — |
| 487 | #124 | — | 3 | 1 | no | — |
| 488 | #124 | — | 3 | 1 | no | — |
| 489 | #124 | — | 6 | 2 | no | — |
| 490 | #124 | — | 6 | 2 | no | — |
| 491 | #124 | C22×D3 | 1 | 2 | yes | — |
| 492 | #124 | C22×D3 | 1 | 2 | yes | — |
| 493 | #123 | — | 6 | 2 | no | — |
| 494 | #123 | — | 6 | 2 | no | — |
| 495 | #123 | — | 6 | 2 | no | — |
| 496 | C22⋊Q8 | — | 2 | 1 | no | — |
| 497 | C22⋊Q8 | — | 2 | 1 | no | — |
| 498 | C22⋊Q8 | — | 6 | 4 | no | — |
| 499 | C22⋊Q8 | — | 6 | 2 | no | — |
| 500 | C22⋊Q8 | — | 6 | 2 | no | — |
| 501 | C22⋊Q8 | — | 6 | 4 | no | — |
| 502 | C22⋊Q8 | — | 6 | 4 | no | — |
| 503 | C22⋊Q8 | — | 6 | 2 | no | — |
| 504 | C22⋊Q8 | — | 6 | 1 | no | — |
| 505 | C22⋊Q8 | — | 6 | 1 | no | — |
| 506 | C22⋊Q8 | — | 6 | 2 | no | — |
| 507 | #121 | — | 6 | 2 | no | — |
| 508 | #121 | — | 6 | 2 | no | — |
| 509 | #121 | — | 6 | 2 | no | — |
| 510 | #121 | — | 6 | 2 | no | — |
| 511 | #121 | — | 6 | 1 | no | — |
| 512 | #121 | — | 6 | 1 | no | — |
| 513 | #121 | — | 6 | 1 | no | — |
| 514 | #121 | — | 6 | 1 | no | — |
| 515 | #120 | — | 6 | 2 | no | — |
| 516 | #120 | — | 6 | 2 | no | — |
| 517 | #120 | — | 6 | 2 | no | — |
| 518 | C4×Q8 | — | 2 | 1 | no | — |
| 519 | C4×Q8 | — | 2 | 1 | no | — |
| 520 | C4×Q8 | — | 3 | 1 | no | — |
| 521 | C4×Q8 | — | 3 | 1 | no | — |
| 522 | C4×Q8 | — | 6 | 2 | no | — |
| 523 | C4×Q8 | — | 6 | 2 | no | — |
| 524 | C4×Q8 | — | 6 | 2 | no | — |
| 525 | C4×D4 | — | 3 | 2 | no | — |
| 526 | C4×D4 | — | 3 | 2 | no | — |
| 527 | C4×D4 | — | 3 | 1 | no | — |
| 528 | C4×D4 | — | 3 | 1 | no | — |
| 529 | C4×D4 | — | 6 | 2 | no | — |
| 530 | C4×D4 | — | 6 | 2 | no | — |
| 531 | C4×D4 | — | 6 | 2 | no | — |
| 532 | C4×D4 | — | 6 | 4 | no | — |
| 533 | C4×D4 | — | 6 | 1 | no | — |
| 534 | C4×D4 | — | 6 | 1 | no | — |
| 535 | #117 | — | 3 | 1 | no | — |
| 536 | #117 | — | 3 | 2 | no | — |
| 537 | #117 | — | 3 | 4 | no | — |
| 538 | #117 | C22×D3 | 1 | 2 | yes | — |
| 539 | C2×C4⋊C4 | — | 3 | 2 | no | — |
| 540 | C2×C4⋊C4 | — | 3 | 4 | no | — |
| 541 | C2×C4⋊C4 | — | 6 | 2 | no | — |
| 542 | C2×C4⋊C4 | — | 6 | 1 | no | — |
| 543 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 544 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 545 | C2×C22⋊C4 | — | 6 | 2 | no | — |
| 546 | C2×C22⋊C4 | — | 6 | 2 | no | — |
| 547 | C2×C42 | — | 3 | 2 | no | — |
| 548 | C2×C42 | C22×D3 | 1 | 1 | yes | characteristic |
| 549 | #103 | — | 3 | 4 | no | — |
| 550 | #103 | — | 3 | 4 | no | — |
| 551 | #103 | — | 3 | 4 | no | — |
| 552 | #103 | — | 3 | 4 | no | — |
| 553 | #103 | — | 3 | 2 | no | — |
| 554 | #103 | — | 3 | 2 | no | — |
| 555 | #103 | — | 3 | 2 | no | — |
| 556 | #103 | — | 3 | 2 | no | — |
| 557 | #103 | C22×D3 | 1 | 4 | yes | — |
| 558 | #103 | C22×D3 | 1 | 4 | yes | — |
| 559 | #102 | — | 3 | 4 | no | — |
| 560 | #102 | — | 3 | 4 | no | — |
| 561 | #102 | — | 3 | 4 | no | — |
| 562 | #102 | — | 3 | 4 | no | — |
| 563 | #102 | — | 3 | 2 | no | — |
| 564 | #102 | — | 3 | 2 | no | — |
| 565 | #102 | — | 3 | 2 | no | — |
| 566 | #102 | — | 3 | 2 | no | — |
| 567 | #102 | C22×D3 | 1 | 4 | yes | — |
| 568 | #102 | C22×D3 | 1 | 4 | yes | — |
| 569 | #97 | — | 3 | 4 | no | — |
| 570 | #97 | — | 3 | 1 | no | — |
| 571 | #97 | — | 3 | 1 | no | — |
| 572 | #97 | — | 3 | 2 | no | — |
| 573 | #97 | C22×D3 | 1 | 2 | yes | — |
| 574 | C4×C8 | — | 3 | 4 | no | — |
| 575 | C4×C8 | C22×D3 | 1 | 2 | yes | — |
| 576 | C23×C3 | — | 2 | 2 | no | — |
| 577 | C23×C3 | — | 4 | 2 | no | — |
| 578 | C23×C3 | — | 8 | 1 | no | — |
| 579 | C23×C3 | — | 8 | 1 | no | — |
| 580 | C23×C3 | C22×D4 | 1 | 1 | yes | characteristic |
| 581 | C22×D3 | — | 2 | 1 | no | — |
| 582 | C22×D3 | — | 2 | 1 | no | — |
| 583 | C22×D3 | — | 4 | 4 | no | — |
| 584 | C22×D3 | — | 8 | 2 | no | — |
| 585 | C22×D3 | — | 8 | 2 | no | — |
| 586 | C22×D3 | C22×D4 | 1 | 2 | yes | — |
| 587 | C3×Q8 | — | 2 | 4 | no | — |
| 588 | C3×Q8 | — | 4 | 2 | no | — |
| 589 | C3×Q8 | — | 4 | 2 | no | — |
| 590 | C3×Q8 | — | 4 | 2 | no | — |
| 591 | C3×D4 | — | 2 | 4 | no | — |
| 592 | C3×D4 | — | 4 | 2 | no | — |
| 593 | C2×C3×C4 | — | 2 | 2 | no | — |
| 594 | C2×C3×C4 | — | 2 | 2 | no | — |
| 595 | C2×C3×C4 | — | 2 | 2 | no | — |
| 596 | C2×C3×C4 | — | 4 | 1 | no | — |
| 597 | C2×C3×C4 | — | 4 | 1 | no | — |
| 598 | C2×C3×C4 | — | 4 | 2 | no | — |
| 599 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 600 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 601 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 602 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 603 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 604 | C2×C3×C4 | C2×#41 | 1 | 4 | yes | — |
| 605 | C2×C3×C4 | C25 | 1 | 1 | yes | characteristic |
| 606 | #67 | — | 4 | 2 | no | — |
| 607 | #67 | — | 4 | 2 | no | — |
| 608 | #67 | — | 4 | 4 | no | — |
| 609 | #67 | — | 4 | 4 | no | — |
| 610 | #67 | — | 8 | 2 | no | — |
| 611 | #67 | — | 8 | 2 | no | — |
| 612 | #67 | #124 | 1 | 8 | yes | — |
| 613 | C2×Dic3 | — | 2 | 4 | no | — |
| 614 | C2×Dic3 | — | 2 | 1 | no | — |
| 615 | C2×Dic3 | — | 2 | 1 | no | — |
| 616 | C2×Dic3 | — | 4 | 4 | no | — |
| 617 | C2×Dic3 | — | 8 | 2 | no | — |
| 618 | C2×Dic3 | C22×D4 | 1 | 2 | yes | — |
| 619 | C2×Dic3 | C22×D4 | 1 | 2 | yes | — |
| 620 | C2×Dic3 | C22×D4 | 1 | 2 | yes | — |
| 621 | D12 | — | 2 | 2 | no | — |
| 622 | D12 | — | 2 | 2 | no | — |
| 623 | D12 | — | 4 | 4 | no | — |
| 624 | D12 | — | 8 | 1 | no | — |
| 625 | D12 | — | 8 | 1 | no | — |
| 626 | D12 | #124 | 1 | 4 | yes | — |
| 627 | C4×D3 | — | 4 | 2 | no | — |
| 628 | C4×D3 | — | 4 | 2 | no | — |
| 629 | C4×D3 | — | 4 | 4 | no | — |
| 630 | C4×D3 | — | 4 | 2 | no | — |
| 631 | C4×D3 | — | 4 | 2 | no | — |
| 632 | C4×D3 | — | 4 | 4 | no | — |
| 633 | C4×D3 | — | 8 | 4 | no | — |
| 634 | C4×D3 | C2×#41 | 1 | 8 | yes | — |
| 635 | Dic6 | — | 2 | 2 | no | — |
| 636 | Dic6 | — | 2 | 2 | no | — |
| 637 | Dic6 | — | 4 | 4 | no | — |
| 638 | Dic6 | — | 4 | 4 | no | — |
| 639 | Dic6 | — | 8 | 4 | no | — |
| 640 | Dic6 | — | 8 | 2 | no | — |
| 641 | Dic6 | #124 | 1 | 4 | yes | — |
| 642 | C3×C8 | — | 2 | 4 | no | — |
| 643 | C3⋊C8 | — | 2 | 2 | no | — |
| 644 | C3⋊C8 | — | 2 | 2 | no | — |
| 645 | C24 | — | 2 | 1 | no | — |
| 646 | C24 | — | 6 | 2 | no | — |
| 647 | #41 | — | 3 | 8 | no | — |
| 648 | #41 | — | 6 | 8 | no | — |
| 649 | #41 | — | 6 | 8 | no | — |
| 650 | #41 | — | 6 | 4 | no | — |
| 651 | #41 | — | 6 | 4 | no | — |
| 652 | #41 | — | 12 | 8 | no | — |
| 653 | #41 | — | 12 | 4 | no | — |
| 654 | #41 | — | 12 | 4 | no | — |
| 655 | C2×Q8 | — | 2 | 1 | no | — |
| 656 | C2×Q8 | — | 2 | 1 | no | — |
| 657 | C2×Q8 | — | 2 | 1 | no | — |
| 658 | C2×Q8 | — | 2 | 4 | no | — |
| 659 | C2×Q8 | — | 3 | 1 | no | — |
| 660 | C2×Q8 | — | 3 | 1 | no | — |
| 661 | C2×Q8 | — | 3 | 1 | no | — |
| 662 | C2×Q8 | — | 6 | 2 | no | — |
| 663 | C2×Q8 | — | 6 | 4 | no | — |
| 664 | C2×Q8 | — | 6 | 8 | no | — |
| 665 | C2×Q8 | — | 6 | 2 | no | — |
| 666 | C2×Q8 | — | 6 | 2 | no | — |
| 667 | C2×Q8 | — | 12 | 4 | no | — |
| 668 | C2×Q8 | — | 24 | 2 | no | — |
| 669 | C2×Q8 | — | 24 | 4 | no | — |
| 670 | C2×Q8 | C23×D3 | 1 | 2 | yes | — |
| 671 | C2×D4 | — | 2 | 1 | no | — |
| 672 | C2×D4 | — | 2 | 4 | no | — |
| 673 | C2×D4 | — | 3 | 2 | no | — |
| 674 | C2×D4 | — | 3 | 1 | no | — |
| 675 | C2×D4 | — | 3 | 1 | no | — |
| 676 | C2×D4 | — | 3 | 1 | no | — |
| 677 | C2×D4 | — | 6 | 2 | no | — |
| 678 | C2×D4 | — | 6 | 8 | no | — |
| 679 | C2×D4 | — | 6 | 2 | no | — |
| 680 | C2×D4 | — | 6 | 2 | no | — |
| 681 | C2×D4 | — | 6 | 2 | no | — |
| 682 | C2×D4 | — | 6 | 2 | no | — |
| 683 | C2×D4 | — | 6 | 1 | no | — |
| 684 | C2×D4 | — | 6 | 1 | no | — |
| 685 | C2×D4 | — | 6 | 1 | no | — |
| 686 | C2×D4 | — | 6 | 1 | no | — |
| 687 | C2×D4 | — | 12 | 4 | no | — |
| 688 | C2×D4 | — | 12 | 8 | no | — |
| 689 | C2×D4 | C23×D3 | 1 | 2 | yes | — |
| 690 | C22×C4 | — | 2 | 1 | no | — |
| 691 | C22×C4 | — | 3 | 2 | no | — |
| 692 | C22×C4 | — | 3 | 2 | no | — |
| 693 | C22×C4 | — | 3 | 2 | no | — |
| 694 | C22×C4 | — | 6 | 2 | no | — |
| 695 | C22×C4 | — | 6 | 2 | no | — |
| 696 | C22×C4 | — | 6 | 4 | no | — |
| 697 | C22×C4 | — | 6 | 2 | no | — |
| 698 | C22×C4 | — | 6 | 2 | no | — |
| 699 | C22×C4 | — | 6 | 1 | no | — |
| 700 | C22×C4 | — | 6 | 1 | no | — |
| 701 | C22×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 702 | C22×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 703 | C22×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 704 | M16 | — | 2 | 4 | no | — |
| 705 | M16 | — | 6 | 8 | no | — |
| 706 | C2×C8 | — | 3 | 2 | no | — |
| 707 | C2×C8 | — | 3 | 2 | no | — |
| 708 | C2×C8 | — | 6 | 8 | no | — |
| 709 | C2×C8 | — | 6 | 4 | no | — |
| 710 | C2×C8 | C23×D3 | 1 | 4 | yes | — |
| 711 | C4⋊C4 | — | 2 | 1 | no | — |
| 712 | C4⋊C4 | — | 2 | 1 | no | — |
| 713 | C4⋊C4 | — | 2 | 2 | no | — |
| 714 | C4⋊C4 | — | 2 | 2 | no | — |
| 715 | C4⋊C4 | — | 3 | 2 | no | — |
| 716 | C4⋊C4 | — | 3 | 1 | no | — |
| 717 | C4⋊C4 | — | 3 | 2 | no | — |
| 718 | C4⋊C4 | — | 3 | 1 | no | — |
| 719 | C4⋊C4 | — | 3 | 4 | no | — |
| 720 | C4⋊C4 | — | 6 | 4 | no | — |
| 721 | C4⋊C4 | — | 6 | 4 | no | — |
| 722 | C4⋊C4 | — | 6 | 2 | no | — |
| 723 | C4⋊C4 | — | 6 | 2 | no | — |
| 724 | C4⋊C4 | — | 6 | 4 | no | — |
| 725 | C4⋊C4 | — | 6 | 4 | no | — |
| 726 | C4⋊C4 | — | 6 | 2 | no | — |
| 727 | C4⋊C4 | — | 6 | 2 | no | — |
| 728 | C4⋊C4 | — | 6 | 2 | no | — |
| 729 | C4⋊C4 | — | 6 | 1 | no | — |
| 730 | C4⋊C4 | — | 6 | 1 | no | — |
| 731 | C4⋊C4 | C23×D3 | 1 | 2 | yes | — |
| 732 | C4⋊C4 | C23×D3 | 1 | 2 | yes | — |
| 733 | C22⋊C4 | — | 2 | 2 | no | — |
| 734 | C22⋊C4 | — | 2 | 2 | no | — |
| 735 | C22⋊C4 | — | 2 | 2 | no | — |
| 736 | C22⋊C4 | — | 2 | 2 | no | — |
| 737 | C22⋊C4 | — | 2 | 2 | no | — |
| 738 | C22⋊C4 | — | 3 | 2 | no | — |
| 739 | C22⋊C4 | — | 3 | 2 | no | — |
| 740 | C22⋊C4 | — | 3 | 2 | no | — |
| 741 | C22⋊C4 | — | 6 | 2 | no | — |
| 742 | C22⋊C4 | — | 6 | 2 | no | — |
| 743 | C22⋊C4 | — | 6 | 4 | no | — |
| 744 | C22⋊C4 | — | 6 | 2 | no | — |
| 745 | C22⋊C4 | — | 6 | 2 | no | — |
| 746 | C22⋊C4 | — | 6 | 1 | no | — |
| 747 | C22⋊C4 | — | 6 | 1 | no | — |
| 748 | C22⋊C4 | — | 6 | 1 | no | — |
| 749 | C22⋊C4 | — | 6 | 1 | no | — |
| 750 | C42 | — | 2 | 2 | no | — |
| 751 | C42 | — | 3 | 2 | no | — |
| 752 | C42 | — | 3 | 2 | no | — |
| 753 | C42 | — | 3 | 2 | no | — |
| 754 | C42 | — | 6 | 4 | no | — |
| 755 | C42 | D3×D4 | 1 | 1 | yes | characteristic |
| 756 | C42 | D3×D4 | 1 | 1 | yes | characteristic |
| 757 | C42 | C23×D3 | 1 | 1 | yes | characteristic |
| 758 | C42 | C23×D3 | 1 | 1 | yes | characteristic |
| 759 | C22×C3 | — | 2 | 1 | no | — |
| 760 | C22×C3 | — | 2 | 1 | no | — |
| 761 | C22×C3 | — | 4 | 2 | no | — |
| 762 | C22×C3 | — | 4 | 2 | no | — |
| 763 | C22×C3 | — | 4 | 2 | no | — |
| 764 | C22×C3 | — | 16 | 2 | no | — |
| 765 | C22×C3 | C2×#124 | 1 | 2 | yes | — |
| 766 | C22×C3 | C23×D4 | 1 | 1 | yes | characteristic |
| 767 | C2×D3 | — | 2 | 2 | no | — |
| 768 | C2×D3 | — | 2 | 2 | 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 | — | 16 | 4 | no | — |
| 776 | C2×D3 | C2×#124 | 1 | 4 | yes | — |
| 777 | C3×C4 | — | 2 | 1 | no | — |
| 778 | C3×C4 | — | 2 | 1 | no | — |
| 779 | C3×C4 | — | 2 | 1 | no | — |
| 780 | C3×C4 | — | 2 | 1 | no | — |
| 781 | C3×C4 | — | 4 | 2 | no | — |
| 782 | C3×C4 | — | 4 | 2 | no | — |
| 783 | C3×C4 | — | 4 | 2 | no | — |
| 784 | C3×C4 | C2×#124 | 1 | 2 | yes | — |
| 785 | C3×C4 | C22×#41 | 1 | 2 | yes | — |
| 786 | Dic3 | — | 2 | 2 | no | — |
| 787 | Dic3 | — | 2 | 2 | no | — |
| 788 | Dic3 | — | 4 | 4 | no | — |
| 789 | Dic3 | — | 4 | 1 | no | — |
| 790 | Dic3 | — | 4 | 1 | no | — |
| 791 | Dic3 | C2×#124 | 1 | 4 | yes | — |
| 792 | C23 | — | 2 | 2 | no | — |
| 793 | C23 | — | 3 | 2 | no | — |
| 794 | C23 | — | 4 | 2 | no | — |
| 795 | C23 | — | 6 | 1 | no | — |
| 796 | C23 | — | 6 | 1 | no | — |
| 797 | C23 | — | 8 | 1 | no | — |
| 798 | C23 | — | 8 | 1 | no | — |
| 799 | C23 | — | 12 | 4 | no | — |
| 800 | C23 | — | 24 | 2 | no | — |
| 801 | C23 | — | 24 | 2 | no | — |
| 802 | C23 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 803 | Q8 | — | 2 | 4 | no | — |
| 804 | Q8 | — | 3 | 4 | no | — |
| 805 | Q8 | — | 4 | 2 | no | — |
| 806 | Q8 | — | 4 | 2 | no | — |
| 807 | Q8 | — | 4 | 2 | no | — |
| 808 | Q8 | — | 6 | 2 | no | — |
| 809 | Q8 | — | 6 | 2 | no | — |
| 810 | Q8 | — | 12 | 4 | no | — |
| 811 | Q8 | — | 12 | 4 | no | — |
| 812 | Q8 | — | 24 | 2 | no | — |
| 813 | Q8 | — | 24 | 4 | no | — |
| 814 | D4 | — | 2 | 4 | no | — |
| 815 | D4 | — | 3 | 8 | no | — |
| 816 | D4 | — | 3 | 4 | no | — |
| 817 | D4 | — | 4 | 2 | no | — |
| 818 | D4 | — | 6 | 2 | no | — |
| 819 | D4 | — | 6 | 2 | no | — |
| 820 | D4 | — | 12 | 4 | no | — |
| 821 | D4 | — | 12 | 4 | no | — |
| 822 | D4 | — | 12 | 4 | no | — |
| 823 | D4 | — | 12 | 2 | no | — |
| 824 | D4 | — | 12 | 2 | no | — |
| 825 | D4 | — | 24 | 1 | no | — |
| 826 | D4 | — | 24 | 1 | no | — |
| 827 | D4 | — | 24 | 2 | no | — |
| 828 | D4 | — | 24 | 2 | no | — |
| 829 | C2×C4 | — | 2 | 2 | no | — |
| 830 | C2×C4 | — | 2 | 2 | no | — |
| 831 | C2×C4 | — | 2 | 2 | no | — |
| 832 | C2×C4 | — | 3 | 2 | no | — |
| 833 | C2×C4 | — | 3 | 8 | no | — |
| 834 | C2×C4 | — | 3 | 2 | no | — |
| 835 | C2×C4 | — | 3 | 2 | no | — |
| 836 | C2×C4 | — | 4 | 1 | no | — |
| 837 | C2×C4 | — | 4 | 1 | no | — |
| 838 | C2×C4 | — | 4 | 2 | no | — |
| 839 | C2×C4 | — | 6 | 4 | no | — |
| 840 | C2×C4 | — | 6 | 1 | no | — |
| 841 | C2×C4 | — | 6 | 1 | no | — |
| 842 | C2×C4 | — | 12 | 2 | no | — |
| 843 | C2×C4 | — | 12 | 2 | no | — |
| 844 | C2×C4 | — | 12 | 4 | no | — |
| 845 | C2×C4 | — | 12 | 4 | no | — |
| 846 | C2×C4 | — | 12 | 4 | no | — |
| 847 | C2×C4 | — | 12 | 2 | no | — |
| 848 | C2×C4 | — | 12 | 2 | no | — |
| 849 | C2×C4 | — | 24 | 4 | no | — |
| 850 | C2×C4 | — | 24 | 2 | no | — |
| 851 | C2×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 852 | C2×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 853 | C2×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 854 | C2×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 855 | C2×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 856 | C2×C4 | D3×#41 | 1 | 4 | yes | — |
| 857 | C2×C4 | C24×D3 | 1 | 1 | yes | characteristic |
| 858 | C8 | — | 2 | 4 | no | — |
| 859 | C8 | — | 6 | 2 | no | — |
| 860 | C8 | — | 6 | 2 | no | — |
| 861 | C2×C3 | — | 2 | 2 | no | — |
| 862 | C2×C3 | — | 8 | 2 | no | — |
| 863 | C2×C3 | C22×#124 | 1 | 1 | yes | characteristic |
| 864 | C2×C3 | #3585 | 1 | 1 | yes | characteristic |
| 865 | C2×C3 | #3586 | 1 | 1 | yes | characteristic |
| 866 | D3 | — | 2 | 4 | no | — |
| 867 | D3 | — | 8 | 1 | no | — |
| 868 | D3 | — | 8 | 1 | no | — |
| 869 | C22 | — | 2 | 1 | no | — |
| 870 | C22 | — | 2 | 1 | no | — |
| 871 | C22 | — | 3 | 4 | no | — |
| 872 | C22 | — | 4 | 2 | no | — |
| 873 | C22 | — | 4 | 2 | no | — |
| 874 | C22 | — | 4 | 2 | no | — |
| 875 | C22 | — | 6 | 2 | no | — |
| 876 | C22 | — | 6 | 2 | no | — |
| 877 | C22 | — | 12 | 1 | no | — |
| 878 | C22 | — | 12 | 1 | no | — |
| 879 | C22 | — | 12 | 1 | no | — |
| 880 | C22 | — | 12 | 1 | no | — |
| 881 | C22 | — | 12 | 1 | no | — |
| 882 | C22 | — | 12 | 1 | no | — |
| 883 | C22 | — | 16 | 2 | no | — |
| 884 | C22 | — | 48 | 4 | no | — |
| 885 | C22 | D3×#124 | 1 | 2 | yes | — |
| 886 | C22 | C22×D3×D4 | 1 | 1 | yes | characteristic |
| 887 | C4 | — | 2 | 1 | no | — |
| 888 | C4 | — | 2 | 1 | no | — |
| 889 | C4 | — | 2 | 1 | no | — |
| 890 | C4 | — | 2 | 1 | no | — |
| 891 | C4 | — | 3 | 4 | no | — |
| 892 | C4 | — | 4 | 2 | no | — |
| 893 | C4 | — | 4 | 2 | no | — |
| 894 | C4 | — | 4 | 2 | no | — |
| 895 | C4 | — | 6 | 2 | no | — |
| 896 | C4 | — | 6 | 2 | no | — |
| 897 | C4 | — | 12 | 1 | no | — |
| 898 | C4 | — | 12 | 1 | no | — |
| 899 | C4 | — | 12 | 4 | no | — |
| 900 | C4 | D3×#124 | 1 | 2 | yes | — |
| 901 | C4 | C2×D3×#41 | 1 | 2 | yes | — |
| 902 | C3 | #60625 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 903 | C2 | — | 2 | 2 | no | — |
| 904 | C2 | — | 6 | 4 | no | — |
| 905 | C2 | — | 8 | 2 | no | — |
| 906 | C2 | — | 24 | 1 | no | — |
| 907 | C2 | — | 24 | 1 | no | — |
| 908 | C2 | C2×D3×#124 | 1 | 1 | yes | characteristic |
| 909 | C2 | #87200 | 1 | 1 | yes | characteristic |
| 910 | C2 | #87201 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #86281 | C2 | semidirect |
| 3. C3×#3140 | C2 | semidirect |
| 4. #83335 | C2 | semidirect |
| 5. C2×#5055 | C2 | semidirect |
| 6. #81683 | C2 | semidirect |
| 7. #81682 | C2 | semidirect |
| 8. #81679 | C2 | semidirect |
| 9. D3×#489 | C2 | semidirect |
| 10. #81639 | C2 | semidirect |
| 11. #81638 | C2 | semidirect |
| 12. #78957 | C2 | semidirect |
| 13. #78952 | C2 | semidirect |
| 14. #78925 | C2 | semidirect |
| 15. #78920 | C2 | semidirect |
| 16. #78528 | C2 | semidirect |
| 17. #78516 | C2 | semidirect |
| 21. C3×#533 | C22 | semidirect |
| 26. #5728 | C22 | semidirect |
| 27. D3×C4⋊Q8 | C22 | semidirect |
| 28. #5689 | C22 | semidirect |
| 44. #5519 | C22 | semidirect |
| 49. C2×#869 | C22 | semidirect |
| 50. C3×#489 | C22 | semidirect |
| 51. C3×#489 | C22 | semidirect |
| 52. C3×#488 | C22 | semidirect |
| 53. C3×#419 | C22 | semidirect |
| 55. C3×C4×M16 | C22 | semidirect |
| 56. C2×#835 | C22 | semidirect |
| 59. #5133 | C22 | semidirect |
| 60. #5122 | C22 | semidirect |
| 61. #5089 | C22 | semidirect |
| 62. #5089 | C22 | semidirect |
| 63. #5089 | C22 | semidirect |
| 64. #5089 | C22 | semidirect |
| 65. #5069 | C22 | semidirect |
| 66. #5067 | C22 | semidirect |
| 67. #5055 | C22 | semidirect |
| 68. #5055 | C22 | semidirect |
| 69. #5055 | C22 | semidirect |
| 71. #5002 | C22 | semidirect |
| 72. C2×#803 | C22 | semidirect |
| 73. #4804 | C22 | semidirect |
| 74. #4803 | C22 | semidirect |
| 75. #4802 | C22 | semidirect |
| 76. D3×#103 | C22 | semidirect |
| 77. #4800 | C22 | semidirect |
| 78. #4797 | C22 | semidirect |
| 79. #4794 | C22 | semidirect |
| 80. #4792 | C22 | semidirect |
| 85. #4768 | C22 | semidirect |
| 86. #4765 | C22 | semidirect |
| 87. #4764 | C22 | semidirect |
| 88. #4760 | C22 | semidirect |
| 89. #4714 | C22 | semidirect |
| 90. #4714 | C22 | semidirect |
| 91. #4707 | C22 | semidirect |
| 92. D3×#97 | C22 | semidirect |
| 93. #4694 | C22 | semidirect |
| 94. #4689 | C22 | semidirect |
| 95. #4681 | C22 | semidirect |
| 101. #3140 | D3 | semidirect |
| 271. #533 | C2×D3 | semidirect |
| 295. #489 | C2×D3 | semidirect |
| 296. #489 | C2×D3 | semidirect |
| 299. #488 | C2×D3 | semidirect |
| 305. #419 | C2×D3 | semidirect |
| 323. C4×M16 | C2×D3 | semidirect |
| 902. C3 | #60625 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #86281 | 2 |
| #86076 | 2 |
| C3×#3140 | 2 |
| #83335 | 2 |
| C2×#5055 | 2 |
| #81683 | 2 |
| #81682 | 2 |
| #81679 | 2 |
| D3×#489 | 2 |
| #81639 | 2 |
| #81638 | 2 |
| #78957 | 2 |
| #78952 | 2 |
| #78925 | 2 |
| #78920 | 2 |
| #78528 | 2 |
| #78516 | 2 |
| #60625 | 3 |