Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
201 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 201 conjugacy classes of subgroups — too many to draw. Only its 67 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | #102 |
| commutator | C2×C8 | C42 |
| Frattini, cosocle | C23×C8 | C22 |
| prime radical | C24 | D8 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C23×C4 ◁ C23×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 |
|---|---|---|
| 7. C2×#107 | C4 | semidirect |
| 10. C22⋊C16 | C4 | semidirect |
| 13. #340 | C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊C16 | 2 |
| #1808 | 2 |
| C2×#340 | 2 |