Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
1470 conjugacy classes of subgroups.
The subgroup lattice has 978 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | #396 |
| commutator | C22×C4 | C2×C42 |
| Frattini, cosocle | C24×C4 | C23 |
| prime radical | C25 | C2×Q8 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C24×C4 ◁ G | |
| LECS | G ▷ C24×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 29. #1738 | C4 | semidirect |
| 35. C2×#338 | C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#343 | 2 |
| C2×#1738 | 2 |
| C22×#338 | 2 |