Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
2405 conjugacy classes of subgroups; only the 991 normal subgroups are shown.
This group has 2405 conjugacy classes of subgroups — too many to draw. Only its 991 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 | C23×D4 |
| commutator | C4 | C24×C4 |
| Frattini, cosocle | C2×C4 | C25 |
| prime radical | C22×2−1+4 | C2 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C22×#41 ◁ G | |
| LECS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#568 | C2 | semidirect |
| 3. #3428 | C2 | semidirect |
| 4. #2898 | C2 | semidirect |
| 5. #2896 | C2 | semidirect |
| 6. C2×#419 | C2 | semidirect |
| 9. C2×2−1+4 | C4 | semidirect |
| 17. C2×#131 | C22 | semidirect |
| 19. #520 | C22 | semidirect |
| 25. #419 | C22 | semidirect |
| 27. #417 | C22 | semidirect |
| 28. #416 | C22 | semidirect |
| 29. C2×#103 | C22 | semidirect |
| 32. 2−1+4 | C2×C4 | semidirect |
| 38. C2×#41 | C2×C4 | semidirect |
| 48. C22×Q8 | C2×C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×2−1+4 | 2 |
| C2×#568 | 2 |
| #3428 | 2 |
| #2898 | 2 |
| #2896 | 2 |
| C2×#419 | 2 |