Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
564 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 221 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2 | C22×#102 |
| commutator | C8 | C23×C4 |
| Frattini, cosocle | C2×C8 | C24 |
| prime radical | #3584 | C2 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2 ◁ C2×#41 ◁ C2×#131 ◁ G | |
| LECS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #3407 | C2 | semidirect |
| 3. #2912 | C2 | semidirect |
| 4. #2145 | C2 | semidirect |
| 5. C2×#360 | C2 | semidirect |
| 7. #578 | C4 | semidirect |
| 9. #576 | C4 | semidirect |
| 15. C2×M32 | C22 | semidirect |
| 17. #427 | C22 | semidirect |
| 18. C2×#106 | C22 | semidirect |
| 19. #360 | C22 | semidirect |
| 20. #360 | C22 | semidirect |
| 32. #135 | C2×C4 | semidirect |
| 34. C2×Q16 | C2×C4 | semidirect |
| 36. C2×D8 | C2×C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3584 | 2 |
| #3407 | 2 |
| #2912 | 2 |
| #2145 | 2 |
| C2×#360 | 2 |