Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
762 conjugacy classes of subgroups; only the 242 normal subgroups are shown.
This group has 762 conjugacy classes of subgroups — too many to draw. Only its 242 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | C2×#121 |
| commutator, Frattini, cosocle | C23×C4 | C24 |
| prime radical | C24 | C2×#41 |
| LCS | G ▷ C23×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C22×C42 ◁ G | |
| LECS | G ▷ C23×C4 ▷ C2 ▷ C1 | |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21143 | 2 |
| C2×#1846 | 2 |
| #20765 | 2 |
| #11365 | 2 |
| #11238 | 2 |
| #10858 | 2 |
| C4×#341 | 2 |