Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
484 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 134 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | #102 |
| commutator | C2×C8 | C2×C42 |
| Frattini, cosocle | C23×C8 | C23 |
| socle | C23 | C2×#102 |
| prime radical | C24 | C2×SD16 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4 ◁ C22×C42 ◁ C22×C4×C8 ◁ G | |
| LECS | G ▷ C23×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 23. #1350 | C4 | direct (N × H) |
| 287. C4 | #1350 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#467 | 2 |
| C4×C22⋊C16 | 2 |
| C2×#1350 | 2 |
| C4×#341 | 2 |
| #7259 | 2 |