Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
561 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 561 conjugacy classes of subgroups — too many to draw. Only its 139 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 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24 |
| prime radical | C2×#466 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C4×C22⋊C4 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#481 | C2 | semidirect |
| 3. C2×#448 | C2 | semidirect |
| 4. C22×#103 | C2 | semidirect |
| 5. #2504 | C2 | semidirect |
| 6. #2436 | C2 | semidirect |
| 7. #2097 | C2 | semidirect |
| 8. #2012 | C2 | semidirect |
| 9. #1968 | C2 | semidirect |
| 10. #1958 | C2 | semidirect |
| 11. C8×C22⋊C4 | C2 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#481 | 2 |
| C2×#466 | 2 |
| C2×#448 | 2 |
| C22×#103 | 2 |
| #2504 | 2 |
| #2436 | 2 |
| #2097 | 2 |
| #2012 | 2 |
| #1968 | 2 |
| #1958 | 2 |
| C8×C22⋊C4 | 2 |