Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
675 conjugacy classes of subgroups; only the 223 normal subgroups are shown.
This group has 675 conjugacy classes of subgroups — too many to draw. Only its 223 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 | #3496 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C2×C4×D4 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #2972 | C2 | semidirect |
| 3. #2349 | C2 | semidirect |
| 4. #1519 | C2 | semidirect |
| 5. #1517 | C2 | semidirect |
| 6. #1502 | C2 | semidirect |
| 7. C2×#327 | C2 | semidirect |
| 9. #547 | C4 | semidirect |
| 11. D42 | C4 | semidirect |
| 19. #431 | C22 | semidirect |
| 20. C2×C22⋊C8 | C22 | semidirect |
| 23. #382 | C22 | semidirect |
| 24. #380 | C22 | semidirect |
| 25. C4×C4⋊C4 | C22 | semidirect |
| 26. C2×#95 | C22 | semidirect |
| 27. #327 | C22 | semidirect |
| 28. #327 | C22 | semidirect |
| 29. #327 | C22 | semidirect |
| 36. C22×D4 | C2×C4 | semidirect |
| 41. C4⋊Q8 | C2×C4 | semidirect |
| 42. #127 | C2×C4 | semidirect |
| 50. #121 | C2×C4 | semidirect |
| 56. C4×D4 | C2×C4 | semidirect |
| 61. C2×C4⋊C4 | C2×C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3496 | 2 |
| #2972 | 2 |
| #2349 | 2 |
| #1519 | 2 |
| #1517 | 2 |
| #1502 | 2 |
| C2×#327 | 2 |