Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
460 conjugacy classes of subgroups; only the 280 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 280 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×D8 |
| commutator | C2×C8 | C23×C4 |
| Frattini, cosocle | C4×C8 | C24 |
| socle | C22 | C22×#107 |
| prime radical | C2×#41 | D8 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4 ◁ C4×#41 ◁ C8×#41 ◁ G | |
| LECS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #12033 | C2 | semidirect |
| 4. #12023 | C2 | semidirect |
| 5. C2×#1372 | C2 | semidirect |
| 101. C16 | #131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C16×#41 | 2 |
| #17828 | 2 |
| #12033 | 2 |
| #12023 | 2 |
| C2×#1372 | 2 |