Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
251 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 251 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C8 | #99 |
| commutator | C22×C4 | C4×C8 |
| Frattini, cosocle | C2×C8×D4 | C22 |
| socle | C22 | #1282 |
| prime radical | C22×D4 | M16 |
| LCS | G ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C8 ◁ C22×C8 ◁ C2×C8×D4 ◁ G | |
| LECS | G ▷ C2×C8×D4 ▷ C22×C4 ▷ C22 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 5. C2×C4⋊C16 | C4 | semidirect |
| 9. C2×#346 | C4 | semidirect |
| 13. #1322 | C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13190 | 2 |
| #11465 | 2 |
| C8×#99 | 2 |