Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
309 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 309 conjugacy classes of subgroups — too many to draw. Only its 100 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4 | #1972 |
| commutator | C2×C8 | C22×C8 |
| Frattini, cosocle | C2×C4×C8 | C23 |
| socle | C2 | #9659 |
| prime radical | C2×#508 | C4 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4 ◁ C22×C8 ◁ C4×M32 ◁ G | |
| LECS | G ▷ C2×C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #13197 | C2 | semidirect |
| 3. C2×#1369 | C2 | semidirect |
| 4. #11602 | C2 | semidirect |
| 5. #11405 | C2 | semidirect |
| 25. C2×Q32 | C8 | semidirect |
| 26. C2×SD32 | C8 | semidirect |
| 27. C2×D16 | C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#2179 | 2 |
| #13197 | 2 |
| C2×#1369 | 2 |
| #11602 | 2 |
| #11405 | 2 |