Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
478 conjugacy classes of subgroups.
The subgroup lattice has 395 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | #459 |
| commutator | C22×C8 | C22×C4 |
| Frattini, cosocle | C23×C8 | C23 |
| prime radical | C24 | AGL(1,ℤ/8) |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C23×C4 ◁ C22×C4×C8 ◁ G | |
| LECS | G ▷ C23×C8 ▷ C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 20. #1387 | C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#1387 | 2 |
| #12557 | 2 |
| C2×#1376 | 2 |
| #10862 | 2 |
| #10859 | 2 |