Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
1134 conjugacy classes of subgroups.
The subgroup lattice has 702 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #85877 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #82993 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #78943 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #78922 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C3×#1888 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #71730 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #71660 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #70324 | C2 | 1 | 1 | yes | maximal, characteristic |
| 9 | #70323 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #70119 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #70099 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #68762 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #68759 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #68731 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | #68728 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | #25592 | — | 3 | 1 | no | maximal, Sylow |
| 17 | C2×C3×#124 | C22 | 1 | 1 | yes | characteristic |
| 18 | C3×#519 | C22 | 1 | 1 | yes | characteristic |
| 19 | #5816 | C22 | 1 | 1 | yes | characteristic |
| 20 | C2×#947 | C22 | 1 | 1 | yes | characteristic |
| 21 | C2×#944 | C22 | 1 | 1 | yes | characteristic |
| 22 | C2×#940 | C22 | 1 | 1 | yes | characteristic |
| 23 | C2×#936 | C22 | 1 | 1 | yes | characteristic |
| 24 | C2×#932 | C22 | 1 | 1 | yes | characteristic |
| 25 | C2×#909 | C22 | 1 | 1 | yes | characteristic |
| 26 | #5585 | — | 2 | 2 | no | — |
| 27 | #5582 | — | 2 | 2 | no | — |
| 28 | #5580 | — | 2 | 2 | no | — |
| 29 | #5568 | — | 2 | 2 | no | — |
| 30 | #5527 | — | 2 | 4 | no | — |
| 31 | #5525 | C22 | 1 | 1 | yes | characteristic |
| 32 | #5522 | C22 | 1 | 1 | yes | characteristic |
| 33 | #5521 | C22 | 1 | 1 | yes | characteristic |
| 34 | #5517 | C22 | 1 | 1 | yes | characteristic |
| 35 | C2×#875 | C22 | 1 | 1 | yes | characteristic |
| 36 | C3×#418 | C22 | 1 | 1 | yes | characteristic |
| 37 | C3×#418 | C22 | 1 | 1 | yes | characteristic |
| 38 | C2×C3×#101 | C22 | 1 | 1 | yes | characteristic |
| 39 | C2×#836 | C22 | 1 | 1 | yes | characteristic |
| 40 | #5215 | C22 | 1 | 1 | yes | characteristic |
| 41 | C2×#825 | C22 | 1 | 1 | yes | characteristic |
| 42 | C2×#823 | C22 | 1 | 1 | yes | characteristic |
| 43 | C2×#823 | C22 | 1 | 1 | yes | characteristic |
| 44 | #5120 | C22 | 1 | 1 | yes | characteristic |
| 45 | #5118 | C22 | 1 | 1 | yes | characteristic |
| 46 | Dic3×M16 | C22 | 1 | 1 | yes | characteristic |
| 47 | #5004 | C22 | 1 | 1 | yes | characteristic |
| 48 | #5004 | C22 | 1 | 1 | yes | characteristic |
| 49 | #4957 | — | 2 | 4 | no | — |
| 50 | C42×Dic3 | C22 | 1 | 1 | yes | characteristic |
| 51 | C2×#805 | C22 | 1 | 1 | yes | characteristic |
| 52 | #4787 | — | 2 | 2 | no | — |
| 53 | #4768 | — | 2 | 2 | no | — |
| 54 | #4767 | — | 2 | 2 | no | — |
| 55 | #4765 | — | 2 | 2 | no | — |
| 56 | C3×#339 | C22 | 1 | 1 | yes | characteristic |
| 57 | C3×#339 | C22 | 1 | 1 | yes | characteristic |
| 58 | #4555 | C22 | 1 | 1 | yes | characteristic |
| 59 | #4532 | C22 | 1 | 1 | yes | characteristic |
| 60 | #4532 | C22 | 1 | 1 | yes | characteristic |
| 61 | #4523 | C22 | 1 | 1 | yes | characteristic |
| 62 | #3510 | — | 3 | 1 | no | — |
| 63 | #3140 | — | 3 | 1 | no | — |
| 64 | #3040 | — | 3 | 1 | no | — |
| 65 | #2858 | — | 3 | 1 | no | — |
| 66 | #2005 | — | 3 | 1 | no | — |
| 67 | #2004 | — | 3 | 1 | no | — |
| 68 | #2003 | — | 3 | 1 | no | — |
| 69 | #2002 | — | 3 | 1 | no | — |
| 70 | #1994 | — | 3 | 1 | no | — |
| 71 | #1967 | — | 3 | 1 | no | — |
| 72 | #1888 | D3 | 1 | 1 | yes | characteristic, complemented |
| 73 | #1887 | — | 3 | 1 | no | — |
| 74 | #1886 | — | 3 | 1 | no | — |
| 75 | #1885 | — | 3 | 1 | no | — |
| 76 | C4×#104 | — | 3 | 1 | no | — |
| 77 | C22×C3×Q8 | C23 | 1 | 1 | yes | characteristic |
| 78 | C22×C3×D4 | C23 | 1 | 1 | yes | characteristic |
| 79 | C22×#67 | — | 2 | 2 | no | — |
| 80 | C2×#235 | C23 | 1 | 1 | yes | characteristic |
| 81 | C22×D12 | C23 | 1 | 1 | yes | characteristic |
| 82 | C22×Dic6 | C23 | 1 | 1 | yes | characteristic |
| 83 | C2×C3×M16 | C23 | 1 | 1 | yes | characteristic |
| 84 | C2×C3×M16 | C23 | 1 | 1 | yes | characteristic |
| 85 | C3×#124 | — | 2 | 2 | no | — |
| 86 | C3×#124 | — | 4 | 1 | no | — |
| 87 | C3×C4×Q8 | — | 2 | 2 | no | — |
| 88 | C3×C4×Q8 | — | 2 | 2 | no | — |
| 89 | C3×#117 | — | 2 | 2 | no | — |
| 90 | C3×#117 | C23 | 1 | 1 | yes | characteristic |
| 91 | C3×#117 | C23 | 1 | 1 | yes | characteristic |
| 92 | C2×C3×C22⋊C4 | — | 2 | 2 | no | — |
| 93 | C2×C3×C42 | C23 | 1 | 1 | yes | characteristic |
| 94 | C2×#217 | — | 2 | 2 | no | — |
| 95 | #947 | — | 2 | 1 | no | — |
| 96 | #947 | — | 2 | 2 | no | — |
| 97 | #947 | — | 2 | 1 | no | — |
| 98 | #947 | — | 2 | 1 | no | — |
| 99 | #946 | — | 2 | 2 | no | — |
| 100 | #944 | — | 2 | 1 | no | — |
| 101 | #944 | — | 2 | 2 | no | — |
| 102 | #944 | — | 4 | 1 | no | — |
| 103 | #940 | — | 2 | 2 | no | — |
| 104 | #940 | — | 4 | 1 | no | — |
| 105 | #936 | — | 2 | 1 | no | — |
| 106 | #936 | — | 2 | 2 | no | — |
| 107 | #936 | — | 2 | 1 | no | — |
| 108 | C2×#214 | — | 2 | 1 | no | — |
| 109 | #932 | — | 4 | 1 | no | — |
| 110 | #932 | — | 4 | 1 | no | — |
| 111 | C2×#213 | — | 2 | 1 | no | — |
| 112 | #929 | — | 2 | 2 | no | — |
| 113 | C2×(C2×D3)⋊C4 | — | 2 | 2 | no | — |
| 114 | C2×(C2×D3)⋊C4 | D4 | 1 | 4 | yes | — |
| 115 | #926 | C23 | 1 | 1 | yes | characteristic |
| 116 | C2×Dic3⋊C4 | — | 2 | 2 | no | — |
| 117 | C2×C4×Dic3 | — | 2 | 2 | no | — |
| 118 | C2×C4×Dic3 | C23 | 1 | 1 | yes | characteristic |
| 119 | C2×C4×Dic3 | C23 | 1 | 1 | yes | characteristic |
| 120 | C2×#208 | C23 | 1 | 1 | yes | characteristic |
| 121 | C2×#208 | C23 | 1 | 1 | yes | characteristic |
| 122 | #909 | — | 4 | 1 | no | — |
| 123 | #909 | — | 4 | 1 | no | — |
| 124 | C2×Dic12 | — | 2 | 1 | no | — |
| 125 | C2×#204 | — | 2 | 1 | no | — |
| 126 | #898 | — | 2 | 4 | no | — |
| 127 | #896 | — | 2 | 4 | no | — |
| 128 | #895 | — | 2 | 2 | no | — |
| 129 | #894 | — | 2 | 4 | no | — |
| 130 | #894 | — | 2 | 4 | no | — |
| 131 | #893 | — | 2 | 2 | no | — |
| 132 | #893 | D4 | 1 | 2 | yes | complemented |
| 133 | #890 | D4 | 1 | 2 | yes | complemented |
| 134 | #888 | D4 | 1 | 2 | yes | complemented |
| 135 | #887 | D4 | 1 | 2 | yes | complemented |
| 136 | #882 | — | 2 | 2 | no | — |
| 137 | #67⋊C4 | — | 2 | 2 | no | — |
| 138 | D3×C22⋊C4 | — | 2 | 2 | no | — |
| 139 | #878 | — | 2 | 2 | no | — |
| 140 | #876 | — | 2 | 4 | no | — |
| 141 | #875 | — | 2 | 4 | no | — |
| 142 | #875 | — | 2 | 1 | no | — |
| 143 | #875 | — | 2 | 2 | no | — |
| 144 | #875 | — | 4 | 1 | no | — |
| 145 | #874 | — | 2 | 1 | no | — |
| 146 | C4×D12 | — | 2 | 4 | no | — |
| 147 | C4×D12 | — | 2 | 2 | no | — |
| 148 | #872 | — | 2 | 4 | no | — |
| 149 | #872 | — | 2 | 1 | no | — |
| 150 | C42×D3 | — | 2 | 1 | no | — |
| 151 | C4×Dic6 | — | 2 | 2 | no | — |
| 152 | C3×#102 | — | 2 | 2 | no | — |
| 153 | C3×#102 | — | 2 | 2 | no | — |
| 154 | C3×#101 | — | 4 | 1 | no | — |
| 155 | #836 | — | 4 | 1 | no | — |
| 156 | #832 | — | 2 | 2 | no | — |
| 157 | #825 | — | 2 | 2 | no | — |
| 158 | #823 | — | 4 | 1 | no | — |
| 159 | #823 | — | 4 | 1 | no | — |
| 160 | #816 | — | 2 | 2 | no | — |
| 161 | #815 | — | 2 | 1 | no | — |
| 162 | Dic3⋊C8 | — | 2 | 2 | no | — |
| 163 | C8×Dic3 | — | 2 | 1 | no | — |
| 164 | #810 | — | 2 | 2 | no | — |
| 165 | #810 | — | 2 | 2 | no | — |
| 166 | #805 | — | 2 | 2 | no | — |
| 167 | C2×#137 | — | 3 | 1 | no | — |
| 168 | C2×AGL(1,ℤ/8) | — | 3 | 1 | no | — |
| 169 | #559 | — | 6 | 2 | no | — |
| 170 | #556 | — | 6 | 2 | no | — |
| 171 | #551 | — | 6 | 4 | no | — |
| 172 | #542 | — | 6 | 2 | no | — |
| 173 | #536 | — | 3 | 1 | no | — |
| 174 | #535 | — | 3 | 1 | no | — |
| 175 | #533 | — | 3 | 1 | no | — |
| 176 | C2×C4⋊Q8 | — | 3 | 1 | no | — |
| 177 | C2×#127 | — | 3 | 1 | no | — |
| 178 | #529 | — | 6 | 2 | no | — |
| 179 | C2×#124 | — | 3 | 1 | no | — |
| 180 | C2×#124 | — | 3 | 1 | no | — |
| 181 | C2×#124 | — | 3 | 1 | no | — |
| 182 | C2×#124 | C2×D3 | 1 | 1 | yes | characteristic |
| 183 | #519 | C2×D3 | 1 | 1 | yes | characteristic |
| 184 | #518 | — | 3 | 1 | no | — |
| 185 | C4×#41 | — | 3 | 1 | no | — |
| 186 | #489 | — | 6 | 2 | no | — |
| 187 | #488 | — | 6 | 2 | no | — |
| 188 | #464 | — | 6 | 2 | no | — |
| 189 | #463 | — | 6 | 2 | no | — |
| 190 | #423 | — | 3 | 1 | no | — |
| 191 | C2×#104 | — | 3 | 1 | no | — |
| 192 | C2×#104 | — | 3 | 1 | no | — |
| 193 | #419 | — | 3 | 1 | no | — |
| 194 | #419 | — | 3 | 1 | no | — |
| 195 | #419 | — | 3 | 1 | no | — |
| 196 | #418 | — | 3 | 1 | no | — |
| 197 | #418 | C2×D3 | 1 | 1 | yes | characteristic |
| 198 | #418 | C2×D3 | 1 | 1 | yes | characteristic |
| 199 | C2×#101 | — | 3 | 1 | no | — |
| 200 | C2×#101 | C2×D3 | 1 | 1 | yes | characteristic |
| 201 | C2×#100 | — | 3 | 1 | no | — |
| 202 | C2×#100 | — | 3 | 1 | no | — |
| 203 | C4×M16 | — | 3 | 1 | no | — |
| 204 | #390 | — | 6 | 4 | no | — |
| 205 | C43 | — | 3 | 1 | no | — |
| 206 | #339 | — | 3 | 1 | no | — |
| 207 | #339 | — | 3 | 1 | no | — |
| 208 | #339 | — | 3 | 1 | no | — |
| 209 | #339 | — | 3 | 1 | no | — |
| 210 | #339 | C2×D3 | 1 | 1 | yes | characteristic |
| 211 | #339 | C2×D3 | 1 | 1 | yes | characteristic |
| 212 | C24×C3 | — | 2 | 1 | no | — |
| 213 | C23×D3 | C2×D4 | 1 | 2 | yes | — |
| 214 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 215 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 216 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 217 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 218 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 219 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 220 | C2×C3×D4 | — | 2 | 1 | no | — |
| 221 | C2×C3×D4 | — | 2 | 1 | no | — |
| 222 | C2×C3×D4 | — | 2 | 1 | no | — |
| 223 | C2×C3×D4 | — | 2 | 1 | no | — |
| 224 | C2×C3×D4 | — | 2 | 1 | no | — |
| 225 | C2×C3×D4 | — | 2 | 1 | no | — |
| 226 | C22×C3×C4 | — | 2 | 1 | no | — |
| 227 | C22×C3×C4 | C2×D4 | 1 | 2 | yes | — |
| 228 | C22×C3×C4 | C24 | 1 | 1 | yes | characteristic |
| 229 | C2×#67 | — | 2 | 1 | no | — |
| 230 | C2×#67 | — | 4 | 4 | no | — |
| 231 | C2×#67 | — | 4 | 8 | no | — |
| 232 | C22×Dic3 | — | 2 | 1 | no | — |
| 233 | C22×Dic3 | — | 2 | 1 | no | — |
| 234 | C22×Dic3 | C2×D4 | 1 | 2 | yes | — |
| 235 | #235 | — | 2 | 1 | no | — |
| 236 | #235 | — | 2 | 1 | no | — |
| 237 | #235 | — | 2 | 1 | no | — |
| 238 | #235 | — | 2 | 1 | no | — |
| 239 | C2×D12 | — | 2 | 1 | no | — |
| 240 | C2×D12 | — | 2 | 1 | no | — |
| 241 | C2×D12 | — | 2 | 1 | no | — |
| 242 | C2×D12 | — | 2 | 1 | no | — |
| 243 | C2×D12 | — | 2 | 1 | no | — |
| 244 | C2×D12 | — | 2 | 1 | no | — |
| 245 | C2×D12 | — | 2 | 4 | no | — |
| 246 | C2×D12 | C2×D4 | 1 | 1 | yes | characteristic |
| 247 | C2×C4×D3 | — | 2 | 1 | no | — |
| 248 | C2×C4×D3 | — | 2 | 4 | no | — |
| 249 | C2×C4×D3 | — | 2 | 2 | no | — |
| 250 | C2×Dic6 | — | 2 | 1 | no | — |
| 251 | C2×Dic6 | — | 2 | 1 | no | — |
| 252 | C2×Dic6 | — | 2 | 1 | no | — |
| 253 | C2×Dic6 | — | 2 | 1 | no | — |
| 254 | C2×Dic6 | — | 2 | 1 | no | — |
| 255 | C2×Dic6 | — | 2 | 1 | no | — |
| 256 | C2×Dic6 | — | 2 | 2 | no | — |
| 257 | C2×Dic6 | C2×D4 | 1 | 1 | yes | characteristic |
| 258 | C3×M16 | — | 2 | 1 | no | — |
| 259 | C3×M16 | — | 2 | 1 | no | — |
| 260 | C3×M16 | — | 2 | 1 | no | — |
| 261 | C3×M16 | — | 2 | 1 | no | — |
| 262 | C2×C3×C8 | — | 2 | 1 | no | — |
| 263 | C2×C3×C8 | — | 2 | 1 | no | — |
| 264 | C3×C4⋊C4 | — | 2 | 4 | no | — |
| 265 | C3×C4⋊C4 | C2×D4 | 1 | 2 | yes | — |
| 266 | C3×C4⋊C4 | C2×D4 | 1 | 2 | yes | — |
| 267 | C3×C22⋊C4 | — | 2 | 1 | no | — |
| 268 | C3×C22⋊C4 | — | 2 | 1 | no | — |
| 269 | C3×C22⋊C4 | — | 4 | 4 | no | — |
| 270 | C3×C42 | — | 2 | 4 | no | — |
| 271 | C3×C42 | — | 2 | 1 | no | — |
| 272 | C3×C42 | — | 2 | 1 | no | — |
| 273 | C3×C42 | — | 2 | 1 | no | — |
| 274 | C3×C42 | #41 | 1 | 2 | yes | — |
| 275 | #217 | — | 2 | 1 | no | — |
| 276 | #217 | — | 4 | 2 | no | — |
| 277 | #217 | — | 4 | 2 | no | — |
| 278 | #214 | — | 4 | 2 | no | — |
| 279 | #213 | — | 4 | 2 | no | — |
| 280 | (C2×D3)⋊C4 | — | 2 | 4 | no | — |
| 281 | (C2×D3)⋊C4 | — | 2 | 4 | no | — |
| 282 | (C2×D3)⋊C4 | — | 2 | 4 | no | — |
| 283 | (C2×D3)⋊C4 | — | 2 | 4 | no | — |
| 284 | (C2×D3)⋊C4 | — | 2 | 2 | no | — |
| 285 | (C2×D3)⋊C4 | — | 2 | 4 | no | — |
| 286 | (C2×D3)⋊C4 | — | 4 | 4 | no | — |
| 287 | C4⋊Dic3 | — | 2 | 2 | no | — |
| 288 | C4⋊Dic3 | C2×D4 | 1 | 2 | yes | — |
| 289 | Dic3⋊C4 | — | 2 | 4 | no | — |
| 290 | Dic3⋊C4 | — | 2 | 2 | no | — |
| 291 | Dic3⋊C4 | — | 2 | 2 | no | — |
| 292 | Dic3⋊C4 | — | 2 | 2 | no | — |
| 293 | Dic3⋊C4 | — | 4 | 4 | no | — |
| 294 | C4×Dic3 | — | 2 | 1 | no | — |
| 295 | C4×Dic3 | — | 2 | 1 | no | — |
| 296 | C4×Dic3 | — | 2 | 2 | no | — |
| 297 | C4×Dic3 | — | 4 | 4 | no | — |
| 298 | C4×Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 299 | C4×Dic3 | C2×D4 | 1 | 2 | yes | — |
| 300 | C4×Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 301 | C4×Dic3 | #41 | 1 | 2 | yes | — |
| 302 | #208 | — | 2 | 1 | no | — |
| 303 | #208 | — | 2 | 1 | no | — |
| 304 | #208 | — | 2 | 1 | no | — |
| 305 | #208 | — | 2 | 1 | no | — |
| 306 | C2×C3⋊C8 | — | 2 | 1 | no | — |
| 307 | C2×C3⋊C8 | — | 2 | 1 | no | — |
| 308 | Dic12 | — | 4 | 2 | no | — |
| 309 | #204 | — | 4 | 2 | no | — |
| 310 | C2×#41 | — | 3 | 1 | no | — |
| 311 | C22×Q8 | — | 3 | 1 | no | — |
| 312 | C22×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 313 | C22×D4 | — | 3 | 1 | no | — |
| 314 | C22×D4 | — | 6 | 2 | no | — |
| 315 | C22×D4 | C22×D3 | 1 | 1 | yes | characteristic |
| 316 | #137 | — | 12 | 1 | no | — |
| 317 | #137 | — | 12 | 1 | no | — |
| 318 | AGL(1,ℤ/8) | — | 12 | 1 | no | — |
| 319 | AGL(1,ℤ/8) | — | 12 | 1 | no | — |
| 320 | C2×Q16 | — | 6 | 1 | no | — |
| 321 | C2×SD16 | — | 6 | 1 | no | — |
| 322 | C2×SD16 | — | 6 | 1 | no | — |
| 323 | C2×D8 | — | 6 | 1 | no | — |
| 324 | C2×M16 | — | 3 | 1 | no | — |
| 325 | C2×M16 | — | 3 | 1 | no | — |
| 326 | C2×M16 | C22×D3 | 1 | 1 | yes | characteristic |
| 327 | C2×M16 | C22×D3 | 1 | 1 | yes | characteristic |
| 328 | C4⋊Q8 | — | 3 | 2 | no | — |
| 329 | C4⋊Q8 | — | 6 | 2 | no | — |
| 330 | C4⋊Q8 | — | 6 | 1 | no | — |
| 331 | C4⋊Q8 | — | 12 | 1 | no | — |
| 332 | #127 | — | 6 | 1 | no | — |
| 333 | #127 | — | 6 | 2 | no | — |
| 334 | #127 | — | 12 | 1 | no | — |
| 335 | #126 | — | 6 | 4 | no | — |
| 336 | #126 | — | 6 | 4 | no | — |
| 337 | #125 | — | 3 | 2 | no | — |
| 338 | #124 | — | 2 | 2 | no | — |
| 339 | #124 | — | 4 | 1 | no | — |
| 340 | #124 | — | 6 | 1 | no | — |
| 341 | #124 | — | 6 | 4 | no | — |
| 342 | #124 | — | 6 | 1 | no | — |
| 343 | #124 | — | 6 | 1 | no | — |
| 344 | #124 | — | 6 | 2 | no | — |
| 345 | #124 | — | 6 | 2 | no | — |
| 346 | #124 | — | 6 | 1 | no | — |
| 347 | #124 | — | 6 | 1 | no | — |
| 348 | #124 | — | 6 | 1 | no | — |
| 349 | #124 | — | 6 | 2 | no | — |
| 350 | #124 | — | 12 | 1 | no | — |
| 351 | #123 | — | 6 | 4 | no | — |
| 352 | #123 | — | 6 | 4 | no | — |
| 353 | #123 | — | 6 | 2 | no | — |
| 354 | C22⋊Q8 | — | 6 | 2 | no | — |
| 355 | C22⋊Q8 | — | 6 | 4 | no | — |
| 356 | C22⋊Q8 | — | 6 | 2 | no | — |
| 357 | #121 | — | 6 | 2 | no | — |
| 358 | #120 | — | 6 | 2 | no | — |
| 359 | C4×Q8 | — | 2 | 2 | no | — |
| 360 | C4×Q8 | — | 2 | 2 | no | — |
| 361 | C4×Q8 | — | 3 | 2 | no | — |
| 362 | C4×Q8 | — | 6 | 2 | no | — |
| 363 | C4×D4 | — | 3 | 2 | no | — |
| 364 | C4×D4 | — | 6 | 2 | no | — |
| 365 | C4×D4 | — | 6 | 4 | no | — |
| 366 | C4×D4 | — | 6 | 2 | no | — |
| 367 | C4×D4 | — | 6 | 2 | no | — |
| 368 | #117 | — | 2 | 2 | no | — |
| 369 | #117 | — | 3 | 1 | no | — |
| 370 | #117 | — | 6 | 1 | no | — |
| 371 | #117 | — | 6 | 4 | no | — |
| 372 | #117 | C22×D3 | 1 | 1 | yes | characteristic |
| 373 | #117 | C22×D3 | 1 | 1 | yes | characteristic |
| 374 | C2×C4⋊C4 | — | 6 | 2 | no | — |
| 375 | C2×C22⋊C4 | — | 2 | 2 | no | — |
| 376 | C2×C22⋊C4 | — | 3 | 4 | no | — |
| 377 | C2×C22⋊C4 | — | 6 | 2 | no | — |
| 378 | C2×C22⋊C4 | — | 6 | 2 | no | — |
| 379 | C2×C22⋊C4 | — | 6 | 2 | no | — |
| 380 | C2×C42 | — | 3 | 1 | no | — |
| 381 | C2×C42 | — | 3 | 1 | no | — |
| 382 | C2×C42 | — | 6 | 1 | no | — |
| 383 | C2×C42 | — | 6 | 2 | no | — |
| 384 | C2×C42 | C22×D3 | 1 | 1 | yes | characteristic |
| 385 | C4⋊C8 | — | 6 | 2 | no | — |
| 386 | #104 | — | 6 | 2 | no | — |
| 387 | #104 | — | 6 | 2 | no | — |
| 388 | #103 | — | 6 | 2 | no | — |
| 389 | #103 | — | 6 | 2 | no | — |
| 390 | #103 | — | 6 | 2 | no | — |
| 391 | #102 | — | 2 | 2 | no | — |
| 392 | #102 | — | 2 | 2 | no | — |
| 393 | #102 | — | 6 | 2 | no | — |
| 394 | #101 | — | 4 | 1 | no | — |
| 395 | #101 | — | 12 | 1 | no | — |
| 396 | #100 | — | 12 | 1 | no | — |
| 397 | #100 | — | 12 | 1 | no | — |
| 398 | #97 | — | 6 | 1 | no | — |
| 399 | C4×C8 | — | 6 | 1 | no | — |
| 400 | C23×C3 | — | 4 | 4 | no | — |
| 401 | C23×C3 | — | 4 | 1 | no | — |
| 402 | C23×C3 | — | 4 | 1 | no | — |
| 403 | C23×C3 | — | 4 | 1 | no | — |
| 404 | C23×C3 | C22×D4 | 1 | 1 | yes | characteristic |
| 405 | C22×D3 | — | 2 | 2 | no | — |
| 406 | C22×D3 | — | 2 | 1 | no | — |
| 407 | C22×D3 | — | 2 | 2 | no | — |
| 408 | C22×D3 | — | 2 | 2 | no | — |
| 409 | C22×D3 | — | 4 | 4 | no | — |
| 410 | C3×Q8 | — | 4 | 1 | no | — |
| 411 | C3×Q8 | — | 4 | 1 | no | — |
| 412 | C3×Q8 | — | 4 | 1 | no | — |
| 413 | C3×Q8 | — | 4 | 1 | no | — |
| 414 | C3×D4 | — | 4 | 1 | no | — |
| 415 | C3×D4 | — | 4 | 1 | no | — |
| 416 | C3×D4 | — | 4 | 1 | no | — |
| 417 | C3×D4 | — | 4 | 1 | no | — |
| 418 | C2×C3×C4 | — | 2 | 2 | no | — |
| 419 | C2×C3×C4 | — | 2 | 2 | no | — |
| 420 | C2×C3×C4 | — | 2 | 2 | no | — |
| 421 | C2×C3×C4 | — | 2 | 2 | no | — |
| 422 | C2×C3×C4 | — | 2 | 2 | no | — |
| 423 | C2×C3×C4 | — | 2 | 2 | no | — |
| 424 | C2×C3×C4 | — | 4 | 2 | no | — |
| 425 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 426 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 427 | C2×C3×C4 | C2×#41 | 1 | 1 | yes | characteristic |
| 428 | C2×C3×C4 | C2×#41 | 1 | 1 | yes | characteristic |
| 429 | C2×C3×C4 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 430 | C2×C3×C4 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 431 | #67 | — | 4 | 1 | no | — |
| 432 | #67 | — | 4 | 1 | no | — |
| 433 | #67 | — | 8 | 8 | no | — |
| 434 | C2×Dic3 | — | 2 | 4 | no | — |
| 435 | C2×Dic3 | — | 2 | 2 | no | — |
| 436 | C2×Dic3 | — | 2 | 1 | no | — |
| 437 | C2×Dic3 | — | 2 | 2 | no | — |
| 438 | C2×Dic3 | — | 4 | 2 | no | — |
| 439 | C2×Dic3 | — | 4 | 1 | no | — |
| 440 | C2×Dic3 | — | 4 | 1 | no | — |
| 441 | C2×Dic3 | — | 4 | 1 | no | — |
| 442 | C2×Dic3 | #120 | 1 | 2 | yes | — |
| 443 | C2×Dic3 | #120 | 1 | 2 | yes | — |
| 444 | D12 | — | 2 | 1 | no | — |
| 445 | D12 | — | 2 | 1 | no | — |
| 446 | D12 | — | 4 | 1 | no | — |
| 447 | D12 | — | 4 | 1 | no | — |
| 448 | D12 | — | 4 | 1 | no | — |
| 449 | D12 | — | 4 | 1 | no | — |
| 450 | D12 | — | 8 | 4 | no | — |
| 451 | C4×D3 | — | 4 | 1 | no | — |
| 452 | C4×D3 | — | 4 | 1 | no | — |
| 453 | C4×D3 | — | 8 | 2 | no | — |
| 454 | C4×D3 | — | 8 | 4 | no | — |
| 455 | Dic6 | — | 2 | 1 | no | — |
| 456 | Dic6 | — | 2 | 1 | no | — |
| 457 | Dic6 | — | 4 | 1 | no | — |
| 458 | Dic6 | — | 4 | 1 | no | — |
| 459 | Dic6 | — | 4 | 1 | no | — |
| 460 | Dic6 | — | 4 | 1 | no | — |
| 461 | Dic6 | — | 8 | 2 | no | — |
| 462 | C3×C8 | — | 4 | 1 | no | — |
| 463 | C3×C8 | — | 4 | 1 | no | — |
| 464 | C3⋊C8 | — | 4 | 1 | no | — |
| 465 | C3⋊C8 | — | 4 | 1 | no | — |
| 466 | C24 | — | 2 | 1 | no | — |
| 467 | C24 | — | 3 | 2 | no | — |
| 468 | #41 | — | 6 | 1 | no | — |
| 469 | #41 | — | 6 | 1 | no | — |
| 470 | #41 | — | 6 | 1 | no | — |
| 471 | #41 | — | 6 | 1 | no | — |
| 472 | C2×Q8 | — | 2 | 1 | no | — |
| 473 | C2×Q8 | — | 2 | 1 | no | — |
| 474 | C2×Q8 | — | 2 | 1 | no | — |
| 475 | C2×Q8 | — | 2 | 1 | no | — |
| 476 | C2×Q8 | — | 2 | 1 | no | — |
| 477 | C2×Q8 | — | 2 | 1 | no | — |
| 478 | C2×Q8 | — | 3 | 1 | no | — |
| 479 | C2×Q8 | — | 6 | 2 | no | — |
| 480 | C2×Q8 | — | 6 | 1 | no | — |
| 481 | C2×Q8 | — | 6 | 1 | no | — |
| 482 | C2×Q8 | — | 6 | 1 | no | — |
| 483 | C2×Q8 | — | 6 | 1 | no | — |
| 484 | C2×Q8 | — | 6 | 1 | no | — |
| 485 | C2×Q8 | — | 6 | 1 | no | — |
| 486 | C2×D4 | — | 2 | 1 | no | — |
| 487 | C2×D4 | — | 2 | 1 | no | — |
| 488 | C2×D4 | — | 2 | 1 | no | — |
| 489 | C2×D4 | — | 2 | 1 | no | — |
| 490 | C2×D4 | — | 2 | 1 | no | — |
| 491 | C2×D4 | — | 2 | 1 | no | — |
| 492 | C2×D4 | — | 3 | 1 | no | — |
| 493 | C2×D4 | — | 6 | 4 | no | — |
| 494 | C2×D4 | — | 6 | 1 | no | — |
| 495 | C2×D4 | — | 6 | 1 | no | — |
| 496 | C2×D4 | — | 6 | 1 | no | — |
| 497 | C2×D4 | — | 6 | 1 | no | — |
| 498 | C2×D4 | — | 6 | 1 | no | — |
| 499 | C2×D4 | — | 6 | 1 | no | — |
| 500 | C2×D4 | — | 6 | 1 | no | — |
| 501 | C2×D4 | — | 12 | 4 | no | — |
| 502 | C2×D4 | — | 12 | 8 | no | — |
| 503 | C22×C4 | — | 2 | 1 | no | — |
| 504 | C22×C4 | — | 3 | 2 | no | — |
| 505 | C22×C4 | — | 6 | 2 | no | — |
| 506 | C22×C4 | — | 6 | 4 | no | — |
| 507 | C22×C4 | — | 6 | 1 | no | — |
| 508 | C22×C4 | — | 6 | 1 | no | — |
| 509 | C22×C4 | — | 6 | 1 | no | — |
| 510 | C22×C4 | D3×D4 | 1 | 2 | yes | — |
| 511 | C22×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 512 | Q16 | — | 12 | 2 | no | — |
| 513 | SD16 | — | 12 | 2 | no | — |
| 514 | SD16 | — | 12 | 2 | no | — |
| 515 | D8 | — | 12 | 2 | no | — |
| 516 | M16 | — | 2 | 1 | no | — |
| 517 | M16 | — | 2 | 1 | no | — |
| 518 | M16 | — | 2 | 1 | no | — |
| 519 | M16 | — | 2 | 1 | no | — |
| 520 | M16 | — | 6 | 1 | no | — |
| 521 | M16 | — | 6 | 1 | no | — |
| 522 | M16 | — | 6 | 1 | no | — |
| 523 | M16 | — | 6 | 1 | no | — |
| 524 | C2×C8 | — | 2 | 1 | no | — |
| 525 | C2×C8 | — | 2 | 1 | no | — |
| 526 | C2×C8 | — | 6 | 1 | no | — |
| 527 | C2×C8 | — | 6 | 1 | no | — |
| 528 | C4⋊C4 | — | 2 | 4 | no | — |
| 529 | C4⋊C4 | — | 3 | 2 | no | — |
| 530 | C4⋊C4 | — | 6 | 2 | no | — |
| 531 | C4⋊C4 | — | 6 | 2 | no | — |
| 532 | C4⋊C4 | — | 6 | 2 | no | — |
| 533 | C4⋊C4 | — | 6 | 2 | no | — |
| 534 | C4⋊C4 | — | 6 | 4 | no | — |
| 535 | C4⋊C4 | — | 12 | 4 | no | — |
| 536 | C4⋊C4 | D3×D4 | 1 | 2 | yes | — |
| 537 | C4⋊C4 | D3×D4 | 1 | 2 | yes | — |
| 538 | C22⋊C4 | — | 2 | 1 | no | — |
| 539 | C22⋊C4 | — | 2 | 1 | no | — |
| 540 | C22⋊C4 | — | 4 | 4 | no | — |
| 541 | C22⋊C4 | — | 6 | 4 | no | — |
| 542 | C22⋊C4 | — | 6 | 4 | no | — |
| 543 | C22⋊C4 | — | 6 | 2 | no | — |
| 544 | C22⋊C4 | — | 6 | 4 | no | — |
| 545 | C22⋊C4 | — | 6 | 4 | no | — |
| 546 | C22⋊C4 | — | 6 | 4 | no | — |
| 547 | C22⋊C4 | — | 6 | 1 | no | — |
| 548 | C22⋊C4 | — | 12 | 4 | no | — |
| 549 | C22⋊C4 | — | 12 | 2 | no | — |
| 550 | C22⋊C4 | — | 12 | 2 | no | — |
| 551 | C42 | — | 2 | 4 | no | — |
| 552 | C42 | — | 2 | 1 | no | — |
| 553 | C42 | — | 2 | 1 | no | — |
| 554 | C42 | — | 2 | 1 | no | — |
| 555 | C42 | — | 3 | 1 | no | — |
| 556 | C42 | — | 3 | 1 | no | — |
| 557 | C42 | — | 3 | 2 | no | — |
| 558 | C42 | — | 3 | 2 | no | — |
| 559 | C42 | — | 6 | 2 | no | — |
| 560 | C42 | — | 6 | 1 | no | — |
| 561 | C42 | — | 6 | 1 | no | — |
| 562 | C42 | — | 12 | 4 | no | — |
| 563 | C42 | #235 | 1 | 2 | yes | — |
| 564 | C22×C3 | — | 2 | 2 | no | — |
| 565 | C22×C3 | — | 8 | 2 | no | — |
| 566 | C22×C3 | — | 8 | 2 | no | — |
| 567 | C22×C3 | — | 8 | 1 | no | — |
| 568 | C22×C3 | — | 8 | 2 | no | — |
| 569 | C22×C3 | C2×#120 | 1 | 1 | yes | characteristic |
| 570 | C22×C3 | #546 | 1 | 1 | yes | characteristic |
| 571 | C22×C3 | #546 | 1 | 1 | yes | characteristic |
| 572 | C2×D3 | — | 4 | 1 | no | — |
| 573 | C2×D3 | — | 4 | 2 | no | — |
| 574 | C2×D3 | — | 4 | 2 | no | — |
| 575 | C2×D3 | — | 4 | 4 | no | — |
| 576 | C2×D3 | — | 8 | 2 | no | — |
| 577 | C2×D3 | — | 8 | 2 | no | — |
| 578 | C3×C4 | — | 4 | 2 | no | — |
| 579 | C3×C4 | — | 4 | 2 | no | — |
| 580 | C3×C4 | — | 4 | 2 | no | — |
| 581 | C3×C4 | — | 4 | 2 | no | — |
| 582 | C3×C4 | #532 | 1 | 1 | yes | characteristic |
| 583 | C3×C4 | #535 | 1 | 1 | yes | characteristic |
| 584 | C3×C4 | #550 | 1 | 1 | yes | characteristic |
| 585 | C3×C4 | #550 | 1 | 1 | yes | characteristic |
| 586 | Dic3 | — | 2 | 4 | no | — |
| 587 | Dic3 | — | 2 | 2 | no | — |
| 588 | Dic3 | — | 2 | 2 | no | — |
| 589 | Dic3 | — | 4 | 1 | no | — |
| 590 | Dic3 | — | 4 | 2 | no | — |
| 591 | Dic3 | — | 8 | 1 | no | — |
| 592 | C23 | — | 4 | 4 | no | — |
| 593 | C23 | — | 4 | 1 | no | — |
| 594 | C23 | — | 4 | 1 | no | — |
| 595 | C23 | — | 4 | 1 | no | — |
| 596 | C23 | — | 6 | 2 | no | — |
| 597 | C23 | — | 6 | 1 | no | — |
| 598 | C23 | — | 6 | 2 | no | — |
| 599 | C23 | — | 6 | 2 | no | — |
| 600 | C23 | — | 12 | 4 | no | — |
| 601 | C23 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 602 | Q8 | — | 4 | 1 | no | — |
| 603 | Q8 | — | 4 | 1 | no | — |
| 604 | Q8 | — | 4 | 1 | no | — |
| 605 | Q8 | — | 4 | 1 | no | — |
| 606 | Q8 | — | 6 | 1 | no | — |
| 607 | Q8 | — | 6 | 1 | no | — |
| 608 | Q8 | — | 12 | 1 | no | — |
| 609 | Q8 | — | 12 | 1 | no | — |
| 610 | Q8 | — | 12 | 1 | no | — |
| 611 | Q8 | — | 12 | 1 | no | — |
| 612 | Q8 | — | 24 | 2 | no | — |
| 613 | D4 | — | 4 | 1 | no | — |
| 614 | D4 | — | 4 | 1 | no | — |
| 615 | D4 | — | 4 | 1 | no | — |
| 616 | D4 | — | 4 | 1 | no | — |
| 617 | D4 | — | 6 | 1 | no | — |
| 618 | D4 | — | 6 | 1 | no | — |
| 619 | D4 | — | 12 | 1 | no | — |
| 620 | D4 | — | 12 | 1 | no | — |
| 621 | D4 | — | 12 | 1 | no | — |
| 622 | D4 | — | 12 | 1 | no | — |
| 623 | D4 | — | 12 | 1 | no | — |
| 624 | D4 | — | 12 | 1 | no | — |
| 625 | D4 | — | 24 | 4 | no | — |
| 626 | D4 | — | 24 | 8 | no | — |
| 627 | C2×C4 | — | 2 | 2 | no | — |
| 628 | C2×C4 | — | 2 | 2 | no | — |
| 629 | C2×C4 | — | 2 | 2 | no | — |
| 630 | C2×C4 | — | 2 | 2 | no | — |
| 631 | C2×C4 | — | 2 | 2 | no | — |
| 632 | C2×C4 | — | 2 | 2 | no | — |
| 633 | C2×C4 | — | 3 | 2 | no | — |
| 634 | C2×C4 | — | 3 | 2 | no | — |
| 635 | C2×C4 | — | 4 | 2 | no | — |
| 636 | C2×C4 | — | 6 | 4 | no | — |
| 637 | C2×C4 | — | 6 | 2 | no | — |
| 638 | C2×C4 | — | 6 | 1 | no | — |
| 639 | C2×C4 | — | 6 | 2 | no | — |
| 640 | C2×C4 | — | 12 | 2 | no | — |
| 641 | C2×C4 | — | 12 | 1 | no | — |
| 642 | C2×C4 | — | 12 | 1 | no | — |
| 643 | C2×C4 | — | 12 | 1 | no | — |
| 644 | C2×C4 | — | 12 | 1 | no | — |
| 645 | C2×C4 | — | 12 | 1 | no | — |
| 646 | C2×C4 | — | 24 | 2 | no | — |
| 647 | C2×C4 | — | 24 | 4 | no | — |
| 648 | C2×C4 | C2×#235 | 1 | 1 | yes | characteristic |
| 649 | C2×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 650 | C2×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 651 | C2×C4 | #1004 | 1 | 1 | yes | characteristic |
| 652 | C2×C4 | D3×#41 | 1 | 1 | yes | characteristic |
| 653 | C2×C4 | #1009 | 1 | 1 | yes | characteristic |
| 654 | C8 | — | 4 | 1 | no | — |
| 655 | C8 | — | 4 | 1 | no | — |
| 656 | C8 | — | 12 | 1 | no | — |
| 657 | C8 | — | 12 | 1 | no | — |
| 658 | C2×C3 | — | 2 | 1 | no | — |
| 659 | C2×C3 | — | 2 | 1 | no | — |
| 660 | C2×C3 | — | 16 | 1 | no | — |
| 661 | C2×C3 | #2431 | 1 | 1 | yes | characteristic |
| 662 | C2×C3 | #3018 | 1 | 2 | yes | — |
| 663 | D3 | — | 8 | 1 | no | — |
| 664 | D3 | — | 8 | 2 | no | — |
| 665 | C22 | — | 2 | 2 | no | — |
| 666 | C22 | — | 8 | 2 | no | — |
| 667 | C22 | — | 8 | 2 | no | — |
| 668 | C22 | — | 8 | 2 | no | — |
| 669 | C22 | — | 8 | 1 | no | — |
| 670 | C22 | — | 12 | 2 | no | — |
| 671 | C22 | — | 12 | 4 | no | — |
| 672 | C22 | — | 12 | 1 | no | — |
| 673 | C22 | — | 12 | 2 | no | — |
| 674 | C22 | — | 24 | 2 | no | — |
| 675 | C22 | — | 24 | 2 | no | — |
| 676 | C22 | #5490 | 1 | 1 | yes | characteristic |
| 677 | C22 | D3×#120 | 1 | 1 | yes | characteristic |
| 678 | C22 | #5654 | 1 | 1 | yes | characteristic |
| 679 | C4 | — | 4 | 2 | no | — |
| 680 | C4 | — | 4 | 2 | no | — |
| 681 | C4 | — | 4 | 2 | no | — |
| 682 | C4 | — | 4 | 2 | no | — |
| 683 | C4 | — | 6 | 4 | no | — |
| 684 | C4 | — | 6 | 2 | no | — |
| 685 | C4 | — | 6 | 2 | no | — |
| 686 | C4 | — | 12 | 2 | no | — |
| 687 | C4 | — | 12 | 1 | no | — |
| 688 | C4 | — | 24 | 1 | no | — |
| 689 | C4 | #5548 | 1 | 1 | yes | characteristic |
| 690 | C4 | #5553 | 1 | 1 | yes | characteristic |
| 691 | C4 | #5599 | 1 | 1 | yes | characteristic |
| 692 | C4 | #5607 | 1 | 1 | yes | characteristic |
| 693 | C3 | #25592 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 694 | C2 | — | 2 | 1 | no | — |
| 695 | C2 | — | 2 | 1 | no | — |
| 696 | C2 | — | 16 | 1 | no | — |
| 697 | C2 | — | 24 | 2 | no | — |
| 698 | C2 | — | 24 | 1 | no | — |
| 699 | C2 | #74700 | 1 | 1 | yes | characteristic |
| 700 | C2 | #80284 | 1 | 2 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #85877 | C2 | semidirect |
| 2. #82993 | C2 | semidirect |
| 3. #78943 | C2 | semidirect |
| 4. #78922 | C2 | semidirect |
| 5. C3×#1888 | C2 | semidirect |
| 6. #71730 | C2 | semidirect |
| 7. #71660 | C2 | semidirect |
| 9. #70323 | C2 | semidirect |
| 10. #70119 | C2 | semidirect |
| 11. #70099 | C2 | semidirect |
| 12. #68762 | C2 | semidirect |
| 13. #68759 | C2 | semidirect |
| 14. #68731 | C2 | semidirect |
| 15. #68728 | C2 | semidirect |
| 72. #1888 | D3 | semidirect |
| 132. #893 | D4 | semidirect |
| 133. #890 | D4 | semidirect |
| 134. #888 | D4 | semidirect |
| 135. #887 | D4 | semidirect |
| 693. C3 | #25592 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #85877 | 2 |
| #82993 | 2 |
| #78943 | 2 |
| #78922 | 2 |
| C3×#1888 | 2 |
| #71730 | 2 |
| #71660 | 2 |
| #70324 | 2 |
| #70323 | 2 |
| #70119 | 2 |
| #70099 | 2 |
| #68762 | 2 |
| #68759 | 2 |
| #68731 | 2 |
| #68728 | 2 |
| #25592 | 3 |