Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
9058 conjugacy classes of subgroups; only the 4258 normal subgroups are shown.
This group has 9058 conjugacy classes of subgroups — too many to draw. Only its 4258 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C25 | C2×D4 |
| commutator, Frattini, cosocle | C2×C4 | C26 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C25 ◁ C23×C42 ◁ G | |
| LECS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C22×#487 | C2 | direct (N × H) |
| 18. C2×#487 | C22 | direct (N × H) |
| 44. #487 | C23 | direct (N × H) |
| 111. C23 | #487 | direct (N × H) |
| 132. C22 | C2×#487 | direct (N × H) |
| 143. C2 | C22×#487 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4⋊Q8 | 2 |
| C22×#487 | 2 |
| C23×#103 | 2 |
| C23×C4×C8 | 2 |