Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
659 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 659 conjugacy classes of subgroups — too many to draw. Only its 181 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 | #2308 |
| commutator | C23 | C23×C4 |
| Frattini, cosocle | C24 | C24 |
| prime radical | #3485 | C2 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2 ◁ C24 ◁ G | |
| LECS | G ▷ C24 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #2883 | C2 | semidirect |
| 3. #1913 | C2 | semidirect |
| 4. #1890 | C2 | semidirect |
| 5. #1828 | C2 | semidirect |
| 6. #1782 | C2 | semidirect |
| 11. #536 | C4 | semidirect |
| 12. #534 | C4 | semidirect |
| 14. #525 | C4 | semidirect |
| 15. C2×#123 | C4 | semidirect |
| 23. C2×#99 | C22 | semidirect |
| 24. #381 | C22 | semidirect |
| 25. #342 | C22 | semidirect |
| 31. C22×Q8 | C2×C4 | semidirect |
| 33. C22×D4 | C2×C4 | semidirect |
| 38. C23×C4 | C2×C4 | semidirect |
| 39. C23×C4 | C2×C4 | semidirect |
| 47. #123 | C2×C4 | semidirect |
| 48. #123 | C2×C4 | semidirect |
| 49. #123 | C2×C4 | semidirect |
| 57. #120 | C2×C4 | semidirect |
| 62. #117 | C2×C4 | semidirect |
| 68. C2×C22⋊C4 | C2×C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3485 | 2 |
| #2883 | 2 |
| #1913 | 2 |
| #1890 | 2 |
| #1828 | 2 |
| #1782 | 2 |