Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
585 conjugacy classes of subgroups; only the 195 normal subgroups are shown.
This group has 585 conjugacy classes of subgroups — too many to draw. Only its 195 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C42 | C2×D4 |
| commutator | C2×C4 | C23×C4 |
| Frattini, cosocle | C22×C4 | C24 |
| socle | C22 | C22×C22⋊C4 |
| prime radical | #3444 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C42 ◁ C22×C42 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #2920 | C2 | semidirect |
| 3. C4×#117 | C2 | semidirect |
| 4. #1995 | C2 | semidirect |
| 5. #1963 | C2 | semidirect |
| 6. #1897 | C2 | semidirect |
| 7. C4×#104 | C2 | semidirect |
| 8. #533 | C4 | semidirect |
| 10. #532 | C4 | semidirect |
| 14. #529 | C4 | semidirect |
| 139. C42 | #41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3444 | 2 |
| #2920 | 2 |
| C4×#117 | 2 |
| #1995 | 2 |
| #1963 | 2 |
| #1897 | 2 |
| C4×#104 | 2 |