Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
547 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 547 conjugacy classes of subgroups — too many to draw. Only its 191 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×D4 |
| commutator | C2×C4 | C23×C4 |
| Frattini, cosocle | C22×C4 | C24 |
| socle | C22 | C22×C22⋊C4 |
| prime radical | #3455 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4 ◁ C2×#117 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #2873 | C2 | semidirect |
| 3. #2298 | C2 | semidirect |
| 4. #1986 | C2 | semidirect |
| 5. #1980 | C2 | semidirect |
| 6. #1871 | C2 | semidirect |
| 7. #1759 | C2 | semidirect |
| 8. C4×#104 | C2 | semidirect |
| 10. #542 | C4 | semidirect |
| 11. #541 | C4 | semidirect |
| 12. #540 | C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3455 | 2 |
| #2873 | 2 |
| #2298 | 2 |
| #1986 | 2 |
| #1980 | 2 |
| #1871 | 2 |
| #1759 | 2 |
| C4×#104 | 2 |