Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
3250 conjugacy classes of subgroups; only the 970 normal subgroups are shown.
This group has 3250 conjugacy classes of subgroups — too many to draw. Only its 970 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, commutator, Frattini, socle, prime radical, cosocle | C24 | C25 |
| LCS | G ▷ C24 ▷ C1 | |
| UCS | C1 ◁ C24 ◁ G | |
| LECS | G ▷ C24 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 36. #384 | Q8 | semidirect |
| 43. C43 | Q8 | semidirect |
| 119. C42 | C4⋊Q8 | semidirect |
| 169. C4 | #2551 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#2551 | 2 |
| #17072 | 2 |
| #15128 | 2 |
| #14151 | 2 |
| C4×#384 | 2 |