Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
669 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 669 conjugacy classes of subgroups — too many to draw. Only its 185 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C22×C22⋊C4 |
| commutator | C2×C4 | C23×C4 |
| Frattini, cosocle | C22×C4 | C24 |
| prime radical | #3488 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C22×#41 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #2880 | C2 | semidirect |
| 3. #2341 | C2 | semidirect |
| 4. #1519 | C2 | semidirect |
| 5. #1513 | C2 | semidirect |
| 6. #1507 | C2 | semidirect |
| 7. #1501 | C2 | semidirect |
| 8. C2×H(5,𝔽2) | C4 | semidirect |
| 15. #537 | C4 | semidirect |
| 16. #535 | C4 | semidirect |
| 19. #520 | C4 | semidirect |
| 22. #407 | C22 | semidirect |
| 23. C2×C22⋊C8 | C22 | semidirect |
| 25. #380 | C22 | semidirect |
| 26. C4×C22⋊C4 | C22 | semidirect |
| 27. #328 | C22 | semidirect |
| 28. #328 | C22 | semidirect |
| 29. #327 | C22 | semidirect |
| 30. #327 | C22 | semidirect |
| 31. #327 | C22 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3488 | 2 |
| #2880 | 2 |
| #2341 | 2 |
| #1519 | 2 |
| #1513 | 2 |
| #1507 | 2 |
| #1501 | 2 |