Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
388 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 111 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 | C2×#121 |
| commutator, Frattini, cosocle | C42 | C24 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C2×C42 ◁ G | |
| LECS | G ▷ C42 ▷ C22 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #3217 | C2 | semidirect |
| 2. C2×#493 | C2 | semidirect |
| 3. #2966 | C2 | semidirect |
| 4. #1688 | C2 | semidirect |
| 5. #1687 | C2 | semidirect |
| 6. #1668 | C2 | semidirect |
| 7. #1667 | C2 | semidirect |
| 8. #1568 | C2 | semidirect |
| 9. #1555 | C2 | semidirect |
| 20. #460 | C22 | semidirect |
| 21. #459 | C22 | semidirect |
| 24. #446 | C22 | semidirect |
| 25. C8×Q8 | C22 | semidirect |
| 26. #436 | C22 | semidirect |
| 29. C8×D4 | C22 | semidirect |
| 35. #335 | C22 | semidirect |
| 36. #334 | C22 | semidirect |
| 37. #331 | C22 | semidirect |
| 38. #331 | C22 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3217 | 2 |
| C2×#493 | 2 |
| #2966 | 2 |
| #1688 | 2 |
| #1687 | 2 |
| #1668 | 2 |
| #1667 | 2 |
| #1568 | 2 |
| #1555 | 2 |