Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
2450 conjugacy classes of subgroups; only the 1090 normal subgroups are shown.
This group has 2450 conjugacy classes of subgroups — too many to draw. Only its 1090 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23×C4 | C24 |
| commutator | C23 | C24×C4 |
| Frattini, cosocle | C22×C4 | C25 |
| socle | C24 | C23×C4 |
| prime radical | C25 | C22×C4 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C4 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #20773 | C2 | direct (N × H) |
| 3. C2×#1840 | C2 | semidirect |
| 12. #1840 | C22 | semidirect |
| 108. C2 | #20773 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#376 | 2 |
| #20773 | 2 |
| C2×#1840 | 2 |
| C2×#1728 | 2 |