Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
2064 conjugacy classes of subgroups.
The subgroup lattice has 658 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #86767 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | D3×D4×Q8 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C3×#3358 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #83580 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #83568 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #81587 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | #81565 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | #80993 | C2 | 1 | 3 | yes | maximal, complemented |
| 9 | #80966 | C2 | 1 | 3 | yes | maximal, complemented |
| 10 | #80332 | C2 | 1 | 3 | yes | maximal, complemented |
| 11 | #80323 | C2 | 1 | 3 | yes | maximal, complemented |
| 12 | #79925 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | Q8×ΓL(1,𝔽25) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | C4×#911 | C2 | 1 | 3 | yes | maximal, complemented |
| 15 | #79571 | C2 | 1 | 3 | yes | maximal, complemented |
| 16 | #61317 | — | 3 | 1 | no | maximal, Sylow |
| 17 | C22×D3×Q8 | — | 2 | 1 | no | — |
| 18 | C3×#550 | C22 | 1 | 1 | yes | characteristic, complemented |
| 19 | C3×D4×Q8 | C22 | 1 | 1 | yes | characteristic |
| 20 | #5831 | — | 2 | 1 | no | — |
| 21 | Dic3×#41 | — | 2 | 1 | no | — |
| 22 | Q8×#67 | — | 2 | 1 | no | — |
| 23 | C2×#911 | C22 | 1 | 3 | yes | — |
| 24 | #5727 | C22 | 1 | 3 | yes | — |
| 25 | D3×C4⋊Q8 | C22 | 1 | 3 | yes | — |
| 26 | #5716 | C22 | 1 | 3 | yes | — |
| 27 | #5713 | C22 | 1 | 3 | yes | complemented |
| 28 | #5632 | — | 2 | 3 | no | — |
| 29 | D3×C22⋊Q8 | — | 2 | 3 | no | — |
| 30 | #5614 | — | 2 | 3 | no | — |
| 31 | #5600 | — | 2 | 3 | no | — |
| 32 | Q8×D12 | C22 | 1 | 1 | yes | characteristic |
| 33 | C4×D3×Q8 | C22 | 1 | 1 | yes | characteristic |
| 34 | #5570 | C22 | 1 | 1 | yes | characteristic, complemented |
| 35 | C4×D3×D4 | C22 | 1 | 3 | yes | — |
| 36 | #5542 | C22 | 1 | 3 | yes | complemented |
| 37 | D4×Dic6 | C22 | 1 | 3 | yes | — |
| 38 | C4×#237 | C22 | 1 | 3 | yes | — |
| 39 | C3×#486 | C22 | 1 | 3 | yes | complemented |
| 40 | C3×#474 | C22 | 1 | 3 | yes | complemented |
| 41 | C3×#459 | C22 | 1 | 3 | yes | — |
| 42 | C3×C8×Q8 | C22 | 1 | 1 | yes | characteristic, complemented |
| 43 | C3×C4×D8 | C22 | 1 | 3 | yes | — |
| 44 | #5153 | C22 | 1 | 6 | yes | — |
| 45 | #5152 | C22 | 1 | 3 | yes | — |
| 46 | #5094 | C22 | 1 | 3 | yes | complemented |
| 47 | #5093 | C22 | 1 | 3 | yes | complemented |
| 48 | #5072 | C22 | 1 | 3 | yes | — |
| 49 | #5070 | C22 | 1 | 3 | yes | complemented |
| 50 | Q8×C3⋊C8 | C22 | 1 | 1 | yes | characteristic, complemented |
| 51 | #5019 | C22 | 1 | 3 | yes | — |
| 52 | C4×#214 | C22 | 1 | 3 | yes | — |
| 53 | C4×#213 | C22 | 1 | 3 | yes | — |
| 54 | #5007 | C22 | 1 | 3 | yes | complemented |
| 55 | #4889 | C22 | 1 | 3 | yes | — |
| 56 | #4881 | C22 | 1 | 3 | yes | — |
| 57 | #4875 | C22 | 1 | 6 | yes | complemented |
| 58 | #4851 | C22 | 1 | 3 | yes | complemented |
| 59 | #4841 | C22 | 1 | 3 | yes | — |
| 60 | #4837 | C22 | 1 | 3 | yes | — |
| 61 | #4831 | C22 | 1 | 3 | yes | complemented |
| 62 | #4787 | C22 | 1 | 6 | yes | — |
| 63 | #4785 | C22 | 1 | 3 | yes | — |
| 64 | #4771 | C22 | 1 | 6 | yes | — |
| 65 | #4771 | C22 | 1 | 3 | yes | — |
| 66 | #4770 | C22 | 1 | 1 | yes | characteristic |
| 67 | #4765 | C22 | 1 | 6 | yes | complemented |
| 68 | #4765 | C22 | 1 | 6 | yes | complemented |
| 69 | #4761 | C22 | 1 | 6 | yes | complemented |
| 70 | #4757 | C22 | 1 | 3 | yes | — |
| 71 | C4×#204 | C22 | 1 | 3 | yes | — |
| 72 | C4×ΓL(1,𝔽25) | C22 | 1 | 3 | yes | — |
| 73 | #4681 | C22 | 1 | 3 | yes | complemented |
| 74 | #4679 | C22 | 1 | 3 | yes | complemented |
| 75 | #3480 | — | 3 | 1 | no | — |
| 76 | C2×D4×Q8 | — | 3 | 1 | no | — |
| 77 | #3373 | — | 3 | 3 | no | — |
| 78 | #3373 | — | 3 | 3 | no | — |
| 79 | #3367 | — | 3 | 3 | no | — |
| 80 | #3367 | — | 3 | 3 | no | — |
| 81 | #3359 | — | 3 | 1 | no | — |
| 82 | #3359 | — | 3 | 1 | no | — |
| 83 | #3358 | — | 3 | 1 | no | — |
| 84 | #3358 | D3 | 1 | 1 | yes | characteristic, complemented |
| 85 | #3141 | — | 3 | 3 | no | — |
| 86 | #3079 | — | 3 | 3 | no | — |
| 87 | #3036 | — | 3 | 3 | no | — |
| 88 | Q8×M16 | — | 3 | 1 | no | — |
| 89 | C4×AGL(1,ℤ/8) | — | 3 | 3 | no | — |
| 90 | C2×C3×#41 | — | 2 | 1 | no | — |
| 91 | C22×C3×Q8 | — | 2 | 1 | no | — |
| 92 | C2×D3×Q8 | — | 2 | 1 | no | — |
| 93 | C2×D3×Q8 | — | 2 | 3 | no | — |
| 94 | C2×D3×Q8 | — | 2 | 3 | no | — |
| 95 | C2×D3×Q8 | — | 4 | 8 | no | — |
| 96 | C2×D3×Q8 | D4 | 1 | 1 | yes | characteristic |
| 97 | C2×#237 | C23 | 1 | 3 | yes | — |
| 98 | C2×D3×D4 | C23 | 1 | 1 | yes | characteristic |
| 99 | C22×C4×D3 | — | 2 | 3 | no | — |
| 100 | C22×Dic6 | — | 2 | 3 | no | — |
| 101 | C2×C3×D8 | C23 | 1 | 3 | yes | — |
| 102 | C3×C4⋊Q8 | C23 | 1 | 3 | yes | — |
| 103 | C3×#127 | C23 | 1 | 3 | yes | — |
| 104 | C3×C22⋊Q8 | — | 2 | 3 | no | — |
| 105 | C3×#121 | — | 2 | 3 | no | — |
| 106 | C3×C4×Q8 | C23 | 1 | 1 | yes | characteristic |
| 107 | C3×C4×D4 | C23 | 1 | 3 | yes | — |
| 108 | C3×C4×D4 | C23 | 1 | 3 | yes | — |
| 109 | #946 | — | 2 | 3 | no | — |
| 110 | Q8×Dic3 | — | 2 | 1 | no | — |
| 111 | Q8×Dic3 | D4 | 1 | 1 | yes | characteristic |
| 112 | #944 | — | 2 | 3 | no | — |
| 113 | #938 | — | 2 | 3 | no | — |
| 114 | #938 | — | 2 | 3 | no | — |
| 115 | #936 | — | 2 | 3 | no | — |
| 116 | #936 | C23 | 1 | 6 | yes | — |
| 117 | #935 | — | 2 | 6 | no | — |
| 118 | D4×Dic3 | — | 2 | 3 | no | — |
| 119 | D4×Dic3 | — | 2 | 3 | no | — |
| 120 | D4×Dic3 | — | 2 | 3 | no | — |
| 121 | D4×Dic3 | C23 | 1 | 3 | yes | — |
| 122 | D4×Dic3 | C23 | 1 | 3 | yes | — |
| 123 | C2×#214 | C23 | 1 | 3 | yes | — |
| 124 | C2×#213 | C23 | 1 | 3 | yes | — |
| 125 | C4×#67 | — | 2 | 3 | no | — |
| 126 | C4×#67 | — | 2 | 3 | no | — |
| 127 | #926 | — | 2 | 3 | no | — |
| 128 | #924 | — | 2 | 3 | no | — |
| 129 | #924 | — | 2 | 3 | no | — |
| 130 | C2×C4×Dic3 | — | 2 | 3 | no | — |
| 131 | #911 | — | 2 | 12 | no | — |
| 132 | C2×#204 | C23 | 1 | 3 | yes | — |
| 133 | C2×ΓL(1,𝔽25) | C23 | 1 | 3 | yes | — |
| 134 | C2×ΓL(1,𝔽25) | C23 | 1 | 1 | yes | characteristic |
| 135 | #897 | — | 2 | 3 | no | — |
| 136 | #896 | — | 2 | 6 | no | — |
| 137 | #893 | C23 | 1 | 3 | yes | — |
| 138 | #892 | C23 | 1 | 1 | yes | characteristic |
| 139 | D3×C4⋊C4 | — | 2 | 3 | no | — |
| 140 | D3×C4⋊C4 | D4 | 1 | 3 | yes | — |
| 141 | D3×C4⋊C4 | C23 | 1 | 3 | yes | — |
| 142 | #890 | — | 2 | 3 | no | — |
| 143 | #888 | — | 2 | 3 | no | — |
| 144 | #888 | C23 | 1 | 6 | yes | — |
| 145 | #887 | D4 | 1 | 3 | yes | — |
| 146 | #887 | C23 | 1 | 3 | yes | — |
| 147 | #67⋊C4 | — | 2 | 3 | no | — |
| 148 | #67⋊C4 | — | 2 | 3 | no | — |
| 149 | D3×C22⋊C4 | — | 2 | 3 | no | — |
| 150 | #879 | — | 2 | 6 | no | — |
| 151 | #878 | — | 2 | 6 | no | — |
| 152 | #877 | — | 2 | 3 | no | — |
| 153 | C4×D12 | C23 | 1 | 3 | yes | — |
| 154 | C42×D3 | C23 | 1 | 3 | yes | — |
| 155 | #869 | C23 | 1 | 3 | yes | — |
| 156 | #869 | C23 | 1 | 3 | yes | — |
| 157 | C4×Dic6 | C23 | 1 | 3 | yes | — |
| 158 | C4×Dic6 | C23 | 1 | 3 | yes | — |
| 159 | C3×#107 | C23 | 1 | 3 | yes | — |
| 160 | C3×C4⋊C8 | C23 | 1 | 3 | yes | — |
| 161 | C3×#102 | C23 | 1 | 1 | yes | characteristic |
| 162 | C3×#102 | C23 | 1 | 6 | yes | — |
| 163 | C3×#102 | C23 | 1 | 3 | yes | — |
| 164 | C3×C4×C8 | C23 | 1 | 3 | yes | — |
| 165 | #832 | C23 | 1 | 1 | yes | characteristic |
| 166 | #832 | C23 | 1 | 3 | yes | — |
| 167 | #832 | C23 | 1 | 6 | yes | — |
| 168 | #821 | C23 | 1 | 1 | yes | characteristic |
| 169 | #817 | C23 | 1 | 3 | yes | — |
| 170 | #816 | C23 | 1 | 6 | yes | — |
| 171 | #816 | C23 | 1 | 3 | yes | — |
| 172 | #815 | C23 | 1 | 3 | yes | — |
| 173 | #815 | C23 | 1 | 3 | yes | — |
| 174 | Dic3⋊C8 | C23 | 1 | 6 | yes | — |
| 175 | #810 | C23 | 1 | 6 | yes | — |
| 176 | #810 | C23 | 1 | 3 | yes | — |
| 177 | #809 | C23 | 1 | 1 | yes | characteristic |
| 178 | #808 | C23 | 1 | 3 | yes | — |
| 179 | #807 | C23 | 1 | 3 | yes | — |
| 180 | C4⋊(C3⋊C8) | C23 | 1 | 3 | yes | — |
| 181 | C4×C3⋊C8 | C23 | 1 | 3 | yes | — |
| 182 | C23×Q8 | — | 6 | 1 | no | — |
| 183 | C2×AGL(1,ℤ/8) | — | 3 | 3 | no | — |
| 184 | #559 | — | 3 | 3 | no | — |
| 185 | #557 | — | 3 | 1 | no | — |
| 186 | #556 | — | 3 | 3 | no | — |
| 187 | #553 | — | 6 | 3 | no | — |
| 188 | #550 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 189 | D4×Q8 | — | 3 | 3 | no | — |
| 190 | D4×Q8 | — | 3 | 1 | no | — |
| 191 | D4×Q8 | — | 3 | 3 | no | — |
| 192 | D4×Q8 | — | 6 | 3 | no | — |
| 193 | D4×Q8 | — | 6 | 1 | no | — |
| 194 | D4×Q8 | C2×D3 | 1 | 1 | yes | characteristic |
| 195 | #548 | — | 6 | 1 | no | — |
| 196 | #532 | — | 3 | 3 | no | — |
| 197 | C2×C4⋊Q8 | — | 3 | 3 | no | — |
| 198 | #529 | — | 6 | 3 | no | — |
| 199 | C2×C22⋊Q8 | — | 6 | 3 | no | — |
| 200 | C4×#41 | — | 3 | 3 | no | — |
| 201 | C4×#41 | — | 6 | 1 | no | — |
| 202 | C2×C4×Q8 | — | 3 | 1 | no | — |
| 203 | C2×C4×D4 | — | 3 | 3 | no | — |
| 204 | #489 | — | 3 | 6 | no | — |
| 205 | #489 | — | 3 | 6 | no | — |
| 206 | #487 | — | 3 | 3 | no | — |
| 207 | #487 | — | 3 | 3 | no | — |
| 208 | #486 | — | 3 | 3 | no | — |
| 209 | #486 | C2×D3 | 1 | 3 | yes | complemented |
| 210 | #477 | — | 3 | 6 | no | — |
| 211 | #476 | — | 3 | 6 | no | — |
| 212 | #475 | — | 3 | 3 | no | — |
| 213 | #475 | — | 3 | 3 | no | — |
| 214 | #474 | — | 3 | 3 | no | — |
| 215 | #474 | C2×D3 | 1 | 3 | yes | complemented |
| 216 | #463 | — | 3 | 6 | no | — |
| 217 | #463 | — | 3 | 6 | no | — |
| 218 | #461 | — | 3 | 3 | no | — |
| 219 | #461 | — | 3 | 3 | no | — |
| 220 | #459 | — | 3 | 3 | no | — |
| 221 | #459 | C2×D3 | 1 | 3 | yes | — |
| 222 | #446 | — | 3 | 3 | no | — |
| 223 | #446 | — | 3 | 3 | no | — |
| 224 | C8×Q8 | — | 3 | 1 | no | — |
| 225 | C8×Q8 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 226 | #442 | — | 3 | 3 | no | — |
| 227 | #442 | — | 3 | 3 | no | — |
| 228 | #440 | — | 3 | 3 | no | — |
| 229 | #440 | — | 3 | 3 | no | — |
| 230 | C4×SD16 | — | 3 | 3 | no | — |
| 231 | C4×SD16 | — | 3 | 3 | no | — |
| 232 | C4×D8 | — | 3 | 3 | no | — |
| 233 | C4×D8 | C2×D3 | 1 | 3 | yes | — |
| 234 | #428 | — | 3 | 3 | no | — |
| 235 | #423 | — | 3 | 3 | no | — |
| 236 | #418 | — | 3 | 1 | no | — |
| 237 | #417 | — | 3 | 6 | no | — |
| 238 | #417 | — | 3 | 3 | no | — |
| 239 | C4×M16 | — | 3 | 3 | no | — |
| 240 | C23×D3 | — | 2 | 1 | no | — |
| 241 | C3×#41 | — | 4 | 4 | no | — |
| 242 | C2×C3×Q8 | — | 2 | 3 | no | — |
| 243 | C2×C3×Q8 | — | 4 | 4 | no | — |
| 244 | C2×C3×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 245 | C2×C3×D4 | — | 2 | 3 | no | — |
| 246 | C2×C3×D4 | — | 2 | 3 | no | — |
| 247 | C2×C3×D4 | C24 | 1 | 3 | yes | — |
| 248 | C2×C3×D4 | C24 | 1 | 1 | yes | characteristic |
| 249 | C22×C3×C4 | — | 2 | 3 | no | — |
| 250 | C22×C3×C4 | — | 2 | 3 | no | — |
| 251 | C2×#67 | — | 2 | 3 | no | — |
| 252 | C2×#67 | — | 2 | 1 | no | — |
| 253 | C22×Dic3 | — | 2 | 3 | no | — |
| 254 | C22×Dic3 | — | 2 | 3 | no | — |
| 255 | C22×Dic3 | — | 2 | 3 | no | — |
| 256 | D3×Q8 | — | 2 | 4 | no | — |
| 257 | D3×Q8 | — | 4 | 12 | no | — |
| 258 | D3×Q8 | — | 4 | 12 | no | — |
| 259 | D3×Q8 | — | 4 | 4 | no | — |
| 260 | #237 | — | 2 | 6 | no | — |
| 261 | #237 | — | 2 | 6 | no | — |
| 262 | D3×D4 | — | 2 | 2 | no | — |
| 263 | D3×D4 | #41 | 1 | 4 | yes | complemented |
| 264 | C2×D12 | C24 | 1 | 1 | yes | characteristic |
| 265 | C2×C4×D3 | — | 2 | 3 | no | — |
| 266 | C2×C4×D3 | — | 2 | 3 | no | — |
| 267 | C2×C4×D3 | — | 2 | 3 | no | — |
| 268 | C2×C4×D3 | — | 4 | 12 | no | — |
| 269 | C2×C4×D3 | C2×D4 | 1 | 3 | yes | — |
| 270 | C2×C4×D3 | C2×D4 | 1 | 3 | yes | — |
| 271 | C2×C4×D3 | C24 | 1 | 1 | yes | characteristic |
| 272 | C2×Dic6 | — | 2 | 3 | no | — |
| 273 | C2×Dic6 | — | 2 | 6 | no | — |
| 274 | C2×Dic6 | — | 4 | 12 | no | — |
| 275 | C2×Dic6 | C2×D4 | 1 | 3 | yes | — |
| 276 | C2×Dic6 | C24 | 1 | 3 | yes | — |
| 277 | C3×D8 | — | 2 | 6 | no | — |
| 278 | C2×C3×C8 | C24 | 1 | 3 | yes | — |
| 279 | C2×C3×C8 | C24 | 1 | 1 | yes | characteristic |
| 280 | C3×C4⋊C4 | — | 2 | 3 | no | — |
| 281 | C3×C4⋊C4 | C2×D4 | 1 | 3 | yes | — |
| 282 | C3×C4⋊C4 | C24 | 1 | 1 | yes | characteristic |
| 283 | C3×C4⋊C4 | C24 | 1 | 3 | yes | — |
| 284 | C3×C22⋊C4 | — | 2 | 3 | no | — |
| 285 | C3×C22⋊C4 | — | 2 | 3 | no | — |
| 286 | C3×C42 | C24 | 1 | 3 | yes | — |
| 287 | #217 | — | 2 | 3 | no | — |
| 288 | #217 | — | 2 | 3 | no | — |
| 289 | #217 | — | 2 | 6 | no | — |
| 290 | #217 | — | 2 | 6 | no | — |
| 291 | #214 | — | 2 | 6 | no | — |
| 292 | #213 | — | 2 | 6 | no | — |
| 293 | (C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 294 | (C2×D3)⋊C4 | — | 2 | 3 | no | — |
| 295 | (C2×D3)⋊C4 | — | 2 | 3 | no | — |
| 296 | C4⋊Dic3 | — | 2 | 3 | no | — |
| 297 | C4⋊Dic3 | — | 2 | 3 | no | — |
| 298 | C4⋊Dic3 | — | 2 | 3 | no | — |
| 299 | C4⋊Dic3 | C2×D4 | 1 | 3 | yes | — |
| 300 | C4⋊Dic3 | C24 | 1 | 3 | yes | — |
| 301 | C4⋊Dic3 | C24 | 1 | 1 | yes | characteristic |
| 302 | Dic3⋊C4 | — | 2 | 3 | no | — |
| 303 | Dic3⋊C4 | — | 2 | 3 | no | — |
| 304 | Dic3⋊C4 | — | 2 | 6 | no | — |
| 305 | Dic3⋊C4 | — | 2 | 3 | no | — |
| 306 | Dic3⋊C4 | C2×D4 | 1 | 6 | yes | — |
| 307 | C4×Dic3 | — | 2 | 3 | no | — |
| 308 | C4×Dic3 | — | 2 | 1 | no | — |
| 309 | C4×Dic3 | — | 2 | 3 | no | — |
| 310 | C4×Dic3 | C2×D4 | 1 | 3 | yes | — |
| 311 | C4×Dic3 | C2×D4 | 1 | 3 | yes | — |
| 312 | C4×Dic3 | C24 | 1 | 3 | yes | — |
| 313 | C2×C3⋊C8 | C24 | 1 | 1 | yes | characteristic |
| 314 | C2×C3⋊C8 | C24 | 1 | 3 | yes | — |
| 315 | #204 | — | 2 | 6 | no | — |
| 316 | ΓL(1,𝔽25) | — | 2 | 6 | no | — |
| 317 | ΓL(1,𝔽25) | — | 2 | 2 | no | — |
| 318 | C2×#41 | — | 2 | 1 | no | — |
| 319 | C2×#41 | — | 3 | 3 | no | — |
| 320 | C22×Q8 | — | 2 | 1 | no | — |
| 321 | C22×Q8 | — | 3 | 1 | no | — |
| 322 | C22×Q8 | — | 6 | 3 | no | — |
| 323 | C22×Q8 | — | 6 | 3 | no | — |
| 324 | C22×Q8 | — | 6 | 3 | no | — |
| 325 | C22×Q8 | — | 6 | 1 | no | — |
| 326 | C22×Q8 | — | 12 | 8 | no | — |
| 327 | C22×D4 | — | 3 | 1 | no | — |
| 328 | C23×C4 | — | 6 | 3 | no | — |
| 329 | AGL(1,ℤ/8) | — | 6 | 12 | no | — |
| 330 | C2×SD16 | — | 3 | 3 | no | — |
| 331 | C2×SD16 | — | 3 | 3 | no | — |
| 332 | C2×D8 | — | 3 | 3 | no | — |
| 333 | C2×D8 | C22×D3 | 1 | 3 | yes | — |
| 334 | C2×M16 | — | 3 | 3 | no | — |
| 335 | C2×M16 | — | 3 | 1 | no | — |
| 336 | C4⋊Q8 | — | 3 | 6 | no | — |
| 337 | C4⋊Q8 | — | 3 | 3 | no | — |
| 338 | C4⋊Q8 | — | 3 | 3 | no | — |
| 339 | C4⋊Q8 | — | 6 | 3 | no | — |
| 340 | C4⋊Q8 | — | 6 | 3 | no | — |
| 341 | C4⋊Q8 | C22×D3 | 1 | 3 | yes | — |
| 342 | #127 | C22×D3 | 1 | 3 | yes | — |
| 343 | #126 | — | 6 | 6 | no | — |
| 344 | #125 | — | 6 | 3 | no | — |
| 345 | #124 | — | 3 | 6 | no | — |
| 346 | #124 | — | 6 | 3 | no | — |
| 347 | #123 | — | 6 | 6 | no | — |
| 348 | C22⋊Q8 | — | 2 | 3 | no | — |
| 349 | C22⋊Q8 | — | 6 | 6 | no | — |
| 350 | C22⋊Q8 | — | 6 | 6 | no | — |
| 351 | C22⋊Q8 | — | 6 | 3 | no | — |
| 352 | C22⋊Q8 | — | 6 | 3 | no | — |
| 353 | C22⋊Q8 | — | 6 | 3 | no | — |
| 354 | C22⋊Q8 | — | 6 | 3 | no | — |
| 355 | #121 | — | 2 | 3 | no | — |
| 356 | #121 | — | 6 | 3 | no | — |
| 357 | #121 | — | 6 | 3 | no | — |
| 358 | C4×Q8 | — | 3 | 1 | no | — |
| 359 | C4×Q8 | — | 3 | 3 | no | — |
| 360 | C4×Q8 | — | 3 | 3 | no | — |
| 361 | C4×Q8 | — | 3 | 3 | no | — |
| 362 | C4×Q8 | — | 3 | 3 | no | — |
| 363 | C4×Q8 | — | 6 | 1 | no | — |
| 364 | C4×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 365 | C4×D4 | — | 3 | 3 | no | — |
| 366 | C4×D4 | — | 3 | 3 | no | — |
| 367 | C4×D4 | — | 3 | 3 | no | — |
| 368 | C4×D4 | — | 3 | 3 | no | — |
| 369 | C4×D4 | — | 6 | 3 | no | — |
| 370 | C4×D4 | — | 6 | 3 | no | — |
| 371 | C4×D4 | — | 6 | 3 | no | — |
| 372 | C4×D4 | — | 6 | 3 | no | — |
| 373 | C4×D4 | — | 6 | 3 | no | — |
| 374 | C4×D4 | — | 6 | 3 | no | — |
| 375 | C4×D4 | — | 6 | 3 | no | — |
| 376 | C4×D4 | C22×D3 | 1 | 3 | yes | — |
| 377 | C4×D4 | C22×D3 | 1 | 3 | yes | — |
| 378 | #117 | — | 3 | 1 | no | — |
| 379 | #117 | — | 6 | 3 | no | — |
| 380 | #117 | — | 6 | 3 | no | — |
| 381 | C2×C4⋊C4 | — | 3 | 3 | no | — |
| 382 | C2×C4⋊C4 | — | 3 | 3 | no | — |
| 383 | C2×C4⋊C4 | — | 6 | 3 | no | — |
| 384 | C2×C22⋊C4 | — | 6 | 3 | no | — |
| 385 | C2×C42 | — | 3 | 3 | no | — |
| 386 | C2×C42 | — | 6 | 3 | no | — |
| 387 | #107 | — | 3 | 3 | no | — |
| 388 | #107 | C22×D3 | 1 | 3 | yes | — |
| 389 | #106 | — | 3 | 3 | no | — |
| 390 | #106 | — | 3 | 3 | no | — |
| 391 | C4⋊C8 | — | 3 | 6 | no | — |
| 392 | C4⋊C8 | — | 3 | 3 | no | — |
| 393 | C4⋊C8 | C22×D3 | 1 | 3 | yes | — |
| 394 | #103 | — | 3 | 3 | no | — |
| 395 | #103 | — | 3 | 6 | no | — |
| 396 | #103 | — | 3 | 3 | no | — |
| 397 | #103 | — | 3 | 6 | no | — |
| 398 | #102 | — | 3 | 3 | no | — |
| 399 | #102 | — | 3 | 6 | no | — |
| 400 | #102 | — | 3 | 1 | no | — |
| 401 | #102 | — | 3 | 1 | no | — |
| 402 | #102 | — | 3 | 1 | no | — |
| 403 | #102 | C22×D3 | 1 | 3 | yes | — |
| 404 | #102 | C22×D3 | 1 | 6 | yes | — |
| 405 | #102 | C22×D3 | 1 | 1 | yes | characteristic |
| 406 | #97 | — | 3 | 3 | no | — |
| 407 | #97 | — | 3 | 3 | no | — |
| 408 | C4×C8 | — | 3 | 3 | no | — |
| 409 | C4×C8 | C22×D3 | 1 | 3 | yes | — |
| 410 | C23×C3 | — | 2 | 1 | no | — |
| 411 | C23×C3 | — | 2 | 3 | no | — |
| 412 | C22×D3 | — | 2 | 1 | no | — |
| 413 | C22×D3 | — | 2 | 4 | no | — |
| 414 | C22×D3 | — | 4 | 2 | no | — |
| 415 | C22×D3 | — | 4 | 2 | no | — |
| 416 | C22×D3 | C22×D4 | 1 | 1 | yes | characteristic |
| 417 | C3×Q8 | — | 4 | 6 | no | — |
| 418 | C3×Q8 | AGL(1,ℤ/8) | 1 | 4 | yes | complemented |
| 419 | C3×D4 | — | 2 | 3 | no | — |
| 420 | C3×D4 | — | 2 | 1 | no | — |
| 421 | C3×D4 | — | 2 | 3 | no | — |
| 422 | C3×D4 | — | 4 | 6 | no | — |
| 423 | C3×D4 | — | 8 | 3 | no | — |
| 424 | C3×D4 | C2×#41 | 1 | 2 | yes | — |
| 425 | C2×C3×C4 | — | 2 | 1 | no | — |
| 426 | C2×C3×C4 | — | 2 | 3 | no | — |
| 427 | C2×C3×C4 | — | 4 | 6 | no | — |
| 428 | C2×C3×C4 | — | 4 | 6 | no | — |
| 429 | C2×C3×C4 | C22×D4 | 1 | 3 | yes | — |
| 430 | C2×C3×C4 | C22×D4 | 1 | 3 | yes | — |
| 431 | C2×C3×C4 | C25 | 1 | 1 | yes | characteristic |
| 432 | #67 | — | 2 | 4 | no | — |
| 433 | #67 | — | 4 | 6 | no | — |
| 434 | C2×Dic3 | — | 2 | 1 | no | — |
| 435 | C2×Dic3 | — | 2 | 3 | no | — |
| 436 | C2×Dic3 | — | 2 | 3 | no | — |
| 437 | C2×Dic3 | — | 4 | 6 | no | — |
| 438 | C2×Dic3 | — | 4 | 6 | no | — |
| 439 | C2×Dic3 | — | 8 | 3 | no | — |
| 440 | C2×Dic3 | C22×D4 | 1 | 3 | yes | — |
| 441 | C2×Dic3 | C22×D4 | 1 | 3 | yes | — |
| 442 | C2×Dic3 | C22×D4 | 1 | 1 | yes | characteristic |
| 443 | D12 | — | 2 | 1 | no | — |
| 444 | D12 | C2×#41 | 1 | 2 | yes | — |
| 445 | C4×D3 | — | 2 | 6 | no | — |
| 446 | C4×D3 | — | 4 | 3 | no | — |
| 447 | C4×D3 | — | 4 | 6 | no | — |
| 448 | C4×D3 | — | 4 | 6 | no | — |
| 449 | C4×D3 | — | 4 | 6 | no | — |
| 450 | C4×D3 | C2×#41 | 1 | 2 | yes | — |
| 451 | C4×D3 | 2−1+4 | 1 | 2 | yes | — |
| 452 | Dic6 | — | 2 | 6 | no | — |
| 453 | Dic6 | — | 2 | 3 | no | — |
| 454 | Dic6 | — | 2 | 3 | no | — |
| 455 | Dic6 | — | 4 | 12 | no | — |
| 456 | Dic6 | — | 4 | 6 | no | — |
| 457 | C3×C8 | — | 2 | 3 | no | — |
| 458 | C3×C8 | — | 2 | 1 | no | — |
| 459 | C3⋊C8 | — | 2 | 3 | no | — |
| 460 | C3⋊C8 | — | 2 | 1 | no | — |
| 461 | C24 | — | 6 | 1 | no | — |
| 462 | #41 | — | 4 | 4 | no | — |
| 463 | #41 | — | 6 | 6 | no | — |
| 464 | #41 | — | 6 | 6 | no | — |
| 465 | C2×Q8 | — | 2 | 3 | no | — |
| 466 | C2×Q8 | — | 3 | 3 | no | — |
| 467 | C2×Q8 | — | 3 | 3 | no | — |
| 468 | C2×Q8 | — | 4 | 4 | no | — |
| 469 | C2×Q8 | — | 6 | 6 | no | — |
| 470 | C2×Q8 | — | 6 | 4 | no | — |
| 471 | C2×Q8 | — | 6 | 3 | no | — |
| 472 | C2×Q8 | — | 12 | 12 | no | — |
| 473 | C2×Q8 | — | 12 | 12 | no | — |
| 474 | C2×Q8 | — | 12 | 12 | no | — |
| 475 | C2×Q8 | — | 12 | 4 | no | — |
| 476 | C2×Q8 | D3×D4 | 1 | 1 | yes | characteristic |
| 477 | C2×D4 | — | 2 | 3 | no | — |
| 478 | C2×D4 | — | 2 | 3 | no | — |
| 479 | C2×D4 | — | 3 | 4 | no | — |
| 480 | C2×D4 | — | 3 | 1 | no | — |
| 481 | C2×D4 | — | 6 | 2 | no | — |
| 482 | C2×D4 | — | 6 | 1 | no | — |
| 483 | C2×D4 | — | 6 | 3 | no | — |
| 484 | C2×D4 | C23×D3 | 1 | 3 | yes | — |
| 485 | C2×D4 | C23×D3 | 1 | 1 | yes | characteristic |
| 486 | C22×C4 | — | 2 | 3 | no | — |
| 487 | C22×C4 | — | 2 | 3 | no | — |
| 488 | C22×C4 | — | 3 | 1 | no | — |
| 489 | C22×C4 | — | 3 | 3 | no | — |
| 490 | C22×C4 | — | 3 | 3 | no | — |
| 491 | C22×C4 | — | 6 | 3 | no | — |
| 492 | C22×C4 | — | 6 | 3 | no | — |
| 493 | C22×C4 | — | 6 | 3 | no | — |
| 494 | C22×C4 | — | 6 | 3 | no | — |
| 495 | C22×C4 | — | 6 | 3 | no | — |
| 496 | C22×C4 | — | 6 | 3 | no | — |
| 497 | C22×C4 | — | 12 | 12 | no | — |
| 498 | SD16 | — | 6 | 6 | no | — |
| 499 | SD16 | — | 6 | 6 | no | — |
| 500 | D8 | — | 2 | 6 | no | — |
| 501 | D8 | — | 6 | 6 | no | — |
| 502 | M16 | — | 6 | 6 | no | — |
| 503 | M16 | — | 6 | 2 | no | — |
| 504 | C2×C8 | — | 3 | 1 | no | — |
| 505 | C2×C8 | — | 3 | 3 | no | — |
| 506 | C2×C8 | C23×D3 | 1 | 1 | yes | characteristic |
| 507 | C2×C8 | C23×D3 | 1 | 3 | yes | — |
| 508 | C4⋊C4 | — | 2 | 3 | no | — |
| 509 | C4⋊C4 | — | 3 | 3 | no | — |
| 510 | C4⋊C4 | — | 3 | 6 | no | — |
| 511 | C4⋊C4 | — | 3 | 3 | no | — |
| 512 | C4⋊C4 | — | 3 | 1 | no | — |
| 513 | C4⋊C4 | — | 6 | 3 | no | — |
| 514 | C4⋊C4 | — | 6 | 6 | no | — |
| 515 | C4⋊C4 | — | 6 | 3 | no | — |
| 516 | C4⋊C4 | — | 6 | 3 | no | — |
| 517 | C4⋊C4 | — | 6 | 3 | no | — |
| 518 | C4⋊C4 | — | 6 | 3 | no | — |
| 519 | C4⋊C4 | — | 6 | 3 | no | — |
| 520 | C4⋊C4 | D3×D4 | 1 | 3 | yes | — |
| 521 | C4⋊C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 522 | C4⋊C4 | C23×D3 | 1 | 3 | yes | — |
| 523 | C22⋊C4 | — | 2 | 3 | no | — |
| 524 | C22⋊C4 | — | 2 | 3 | no | — |
| 525 | C22⋊C4 | — | 6 | 3 | no | — |
| 526 | C22⋊C4 | — | 6 | 1 | no | — |
| 527 | C22⋊C4 | — | 6 | 3 | no | — |
| 528 | C22⋊C4 | — | 6 | 3 | no | — |
| 529 | C22⋊C4 | — | 6 | 6 | no | — |
| 530 | C22⋊C4 | — | 6 | 6 | no | — |
| 531 | C22⋊C4 | — | 6 | 3 | no | — |
| 532 | C42 | — | 3 | 3 | no | — |
| 533 | C42 | — | 3 | 3 | no | — |
| 534 | C42 | — | 3 | 3 | no | — |
| 535 | C42 | — | 6 | 1 | no | — |
| 536 | C42 | — | 6 | 3 | no | — |
| 537 | C42 | — | 6 | 3 | no | — |
| 538 | C42 | C23×D3 | 1 | 3 | yes | — |
| 539 | C22×C3 | — | 2 | 2 | no | — |
| 540 | C22×C3 | — | 4 | 1 | no | — |
| 541 | C22×C3 | — | 4 | 1 | no | — |
| 542 | C22×C3 | — | 4 | 3 | no | — |
| 543 | C22×C3 | — | 4 | 3 | no | — |
| 544 | C22×C3 | — | 4 | 3 | no | — |
| 545 | C22×C3 | C23×D4 | 1 | 1 | yes | characteristic |
| 546 | C2×D3 | — | 2 | 1 | no | — |
| 547 | C2×D3 | — | 2 | 1 | no | — |
| 548 | C2×D3 | — | 2 | 2 | no | — |
| 549 | C2×D3 | — | 4 | 8 | no | — |
| 550 | C2×D3 | — | 4 | 1 | no | — |
| 551 | C2×D3 | — | 4 | 1 | no | — |
| 552 | C2×D3 | #548 | 1 | 2 | yes | — |
| 553 | C3×C4 | — | 2 | 3 | no | — |
| 554 | C3×C4 | — | 4 | 3 | no | — |
| 555 | C3×C4 | — | 4 | 1 | no | — |
| 556 | C3×C4 | C2×AGL(1,ℤ/8) | 1 | 6 | yes | — |
| 557 | C3×C4 | C22×#41 | 1 | 1 | yes | characteristic |
| 558 | C3×C4 | C2×2−1+4 | 1 | 1 | yes | characteristic |
| 559 | Dic3 | — | 2 | 3 | no | — |
| 560 | Dic3 | — | 2 | 3 | no | — |
| 561 | Dic3 | — | 4 | 1 | no | — |
| 562 | Dic3 | — | 4 | 3 | no | — |
| 563 | Dic3 | — | 4 | 3 | no | — |
| 564 | Dic3 | #548 | 1 | 2 | yes | — |
| 565 | C23 | — | 2 | 1 | no | — |
| 566 | C23 | — | 2 | 3 | no | — |
| 567 | C23 | — | 3 | 1 | no | — |
| 568 | C23 | — | 6 | 4 | no | — |
| 569 | C23 | — | 6 | 1 | no | — |
| 570 | C23 | — | 12 | 2 | no | — |
| 571 | C23 | — | 12 | 2 | no | — |
| 572 | Q8 | — | 4 | 6 | no | — |
| 573 | Q8 | — | 6 | 6 | no | — |
| 574 | Q8 | — | 6 | 3 | no | — |
| 575 | Q8 | — | 6 | 3 | no | — |
| 576 | Q8 | — | 12 | 12 | no | — |
| 577 | Q8 | — | 12 | 6 | no | — |
| 578 | Q8 | #911 | 1 | 4 | yes | complemented |
| 579 | D4 | — | 2 | 3 | no | — |
| 580 | D4 | — | 2 | 1 | no | — |
| 581 | D4 | — | 2 | 3 | no | — |
| 582 | D4 | — | 3 | 2 | no | — |
| 583 | D4 | — | 4 | 6 | no | — |
| 584 | D4 | — | 6 | 4 | no | — |
| 585 | D4 | — | 6 | 1 | no | — |
| 586 | D4 | — | 8 | 3 | no | — |
| 587 | D4 | — | 12 | 6 | no | — |
| 588 | D4 | D3×#41 | 1 | 2 | yes | — |
| 589 | C2×C4 | — | 2 | 1 | no | — |
| 590 | C2×C4 | — | 2 | 3 | no | — |
| 591 | C2×C4 | — | 3 | 1 | no | — |
| 592 | C2×C4 | — | 3 | 2 | no | — |
| 593 | C2×C4 | — | 3 | 2 | no | — |
| 594 | C2×C4 | — | 3 | 3 | no | — |
| 595 | C2×C4 | — | 3 | 3 | no | — |
| 596 | C2×C4 | — | 4 | 6 | no | — |
| 597 | C2×C4 | — | 4 | 6 | no | — |
| 598 | C2×C4 | — | 6 | 6 | no | — |
| 599 | C2×C4 | — | 6 | 1 | no | — |
| 600 | C2×C4 | — | 6 | 3 | no | — |
| 601 | C2×C4 | — | 6 | 3 | no | — |
| 602 | C2×C4 | — | 12 | 3 | no | — |
| 603 | C2×C4 | — | 12 | 6 | no | — |
| 604 | C2×C4 | — | 12 | 6 | no | — |
| 605 | C2×C4 | — | 12 | 6 | no | — |
| 606 | C2×C4 | — | 12 | 6 | no | — |
| 607 | C2×C4 | — | 12 | 6 | no | — |
| 608 | C2×C4 | — | 24 | 3 | no | — |
| 609 | C2×C4 | C2×D3×D4 | 1 | 3 | yes | — |
| 610 | C2×C4 | C2×D3×D4 | 1 | 3 | yes | — |
| 611 | C2×C4 | C24×D3 | 1 | 1 | yes | characteristic |
| 612 | C8 | — | 2 | 3 | no | — |
| 613 | C8 | — | 2 | 1 | no | — |
| 614 | C8 | — | 6 | 3 | no | — |
| 615 | C8 | — | 6 | 1 | no | — |
| 616 | C2×C3 | — | 4 | 2 | no | — |
| 617 | C2×C3 | — | 8 | 3 | no | — |
| 618 | C2×C3 | C2×#548 | 1 | 1 | yes | characteristic |
| 619 | C2×C3 | C22×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 620 | C2×C3 | #3586 | 1 | 1 | yes | characteristic |
| 621 | D3 | — | 2 | 2 | no | — |
| 622 | D3 | — | 4 | 2 | no | — |
| 623 | C22 | — | 2 | 2 | no | — |
| 624 | C22 | — | 3 | 2 | no | — |
| 625 | C22 | — | 4 | 1 | no | — |
| 626 | C22 | — | 4 | 1 | no | — |
| 627 | C22 | — | 4 | 3 | no | — |
| 628 | C22 | — | 4 | 3 | no | — |
| 629 | C22 | — | 4 | 3 | no | — |
| 630 | C22 | — | 6 | 1 | no | — |
| 631 | C22 | — | 6 | 1 | no | — |
| 632 | C22 | — | 6 | 2 | no | — |
| 633 | C22 | — | 12 | 8 | no | — |
| 634 | C22 | — | 12 | 1 | no | — |
| 635 | C22 | — | 12 | 1 | no | — |
| 636 | C22 | C22×D3×D4 | 1 | 1 | yes | characteristic |
| 637 | C4 | — | 2 | 3 | no | — |
| 638 | C4 | — | 3 | 2 | no | — |
| 639 | C4 | — | 4 | 1 | no | — |
| 640 | C4 | — | 4 | 3 | no | — |
| 641 | C4 | — | 6 | 3 | no | — |
| 642 | C4 | — | 6 | 3 | no | — |
| 643 | C4 | — | 12 | 3 | no | — |
| 644 | C4 | — | 12 | 1 | no | — |
| 645 | C4 | — | 12 | 3 | no | — |
| 646 | C4 | C2×#911 | 1 | 6 | yes | — |
| 647 | C4 | C2×D3×#41 | 1 | 1 | yes | characteristic |
| 648 | C4 | D3×2−1+4 | 1 | 1 | yes | characteristic |
| 649 | C3 | #61317 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 650 | C2 | — | 4 | 2 | no | — |
| 651 | C2 | — | 6 | 2 | no | — |
| 652 | C2 | — | 8 | 3 | no | — |
| 653 | C2 | — | 12 | 2 | no | — |
| 654 | C2 | D3×#548 | 1 | 1 | yes | characteristic |
| 655 | C2 | C22×#911 | 1 | 1 | yes | characteristic |
| 656 | C2 | #87208 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #86767 | C2 | semidirect |
| 2. D3×D4×Q8 | C2 | semidirect |
| 3. C3×#3358 | C2 | semidirect |
| 4. #83580 | C2 | semidirect |
| 5. #83568 | C2 | semidirect |
| 6. #81587 | C2 | semidirect |
| 7. #81565 | C2 | semidirect |
| 8. #80993 | C2 | semidirect |
| 9. #80966 | C2 | semidirect |
| 10. #80332 | C2 | semidirect |
| 11. #80323 | C2 | semidirect |
| 12. #79925 | C2 | semidirect |
| 13. Q8×ΓL(1,𝔽25) | C2 | semidirect |
| 14. C4×#911 | C2 | semidirect |
| 15. #79571 | C2 | semidirect |
| 18. C3×#550 | C22 | semidirect |
| 27. #5713 | C22 | semidirect |
| 34. #5570 | C22 | semidirect |
| 36. #5542 | C22 | semidirect |
| 39. C3×#486 | C22 | semidirect |
| 40. C3×#474 | C22 | semidirect |
| 42. C3×C8×Q8 | C22 | semidirect |
| 46. #5094 | C22 | semidirect |
| 47. #5093 | C22 | semidirect |
| 49. #5070 | C22 | semidirect |
| 50. Q8×C3⋊C8 | C22 | semidirect |
| 54. #5007 | C22 | semidirect |
| 57. #4875 | C22 | semidirect |
| 58. #4851 | C22 | semidirect |
| 61. #4831 | C22 | semidirect |
| 67. #4765 | C22 | semidirect |
| 68. #4765 | C22 | semidirect |
| 69. #4761 | C22 | semidirect |
| 73. #4681 | C22 | semidirect |
| 74. #4679 | C22 | semidirect |
| 84. #3358 | D3 | semidirect |
| 188. #550 | C2×D3 | semidirect |
| 209. #486 | C2×D3 | semidirect |
| 215. #474 | C2×D3 | semidirect |
| 225. C8×Q8 | C2×D3 | semidirect |
| 263. D3×D4 | #41 | semidirect |
| 418. C3×Q8 | AGL(1,ℤ/8) | semidirect |
| 578. Q8 | #911 | semidirect |
| 649. C3 | #61317 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #86767 | 2 |
| D3×D4×Q8 | 2 |
| C3×#3358 | 2 |
| #83580 | 2 |
| #83568 | 2 |
| #81587 | 2 |
| #81565 | 2 |
| #80993 | 2 |
| #80966 | 2 |
| #80332 | 2 |
| #80323 | 2 |
| #79925 | 2 |
| Q8×ΓL(1,𝔽25) | 2 |
| C4×#911 | 2 |
| #79571 | 2 |
| #61317 | 3 |