Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
124 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 47 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C8 | #99 |
| commutator | C23 | C4×C8 |
| Frattini, cosocle | C2×#131 | C22 |
| socle | C2 | #1282 |
| prime radical | C2×#41 | C2×C4 |
| LCS | G ▷ C23 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8 ◁ C2×C8 ◁ C2×#131 ◁ G | |
| LECS | G ▷ C2×#131 ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 6. C2×M32 | C4 | semidirect |
| 7. C22×C16 | C4 | semidirect |
| 12. #349 | C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #2115 | 2 |
| #2113 | 2 |
| #1757 | 2 |