Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
1257 conjugacy classes of subgroups; only the 479 normal subgroups are shown.
This group has 1257 conjugacy classes of subgroups — too many to draw. Only its 479 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C22×C42 ◁ G | |
| LECS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#532 | C2 | semidirect |
| 2. #3184 | C2 | direct (N × H) |
| 3. C2×#498 | C2 | semidirect |
| 4. C2×#493 | C2 | semidirect |
| 5. C2×#486 | C2 | semidirect |
| 6. C2×#469 | C2 | semidirect |
| 7. C2×#442 | C2 | semidirect |
| 8. C2×C4×M16 | C2 | semidirect |
| 13. #532 | C22 | semidirect |
| 22. #498 | C22 | semidirect |
| 23. #493 | C22 | semidirect |
| 24. #486 | C22 | semidirect |
| 25. #469 | C22 | semidirect |
| 26. #442 | C22 | semidirect |
| 29. C4×M16 | C22 | semidirect |
| 103. C2×C8 | #41 | semidirect |
| 146. C8 | C2×#41 | semidirect |
| 165. C2 | #3184 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#532 | 2 |
| #3184 | 2 |
| C2×#498 | 2 |
| C2×#493 | 2 |
| C2×#486 | 2 |
| C2×#469 | 2 |
| C2×#442 | 2 |
| C2×C4×M16 | 2 |