Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
699 conjugacy classes of subgroups; only the 211 normal subgroups are shown.
This group has 699 conjugacy classes of subgroups — too many to draw. Only its 211 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 | C2×C4 | C23×C4 |
| Frattini, cosocle | C22×C4 | C24 |
| prime radical | C2×#493 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C43 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#442 | C2 | semidirect |
| 3. C4×#127 | C2 | semidirect |
| 4. #1972 | C2 | semidirect |
| 5. #1957 | C2 | semidirect |
| 6. #1844 | C2 | semidirect |
| 7. C4×#97 | C2 | semidirect |
| 12. #493 | C4 | semidirect |
| 29. C2×D8 | C2×C4 | semidirect |
| 33. #127 | C2×C4 | semidirect |
| 47. #97 | D4 | semidirect |
| 49. C4×C8 | C2×C4 | semidirect |
| 104. C8 | C4×D4 | semidirect |
| 117. C4 | #442 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#493 | 2 |
| C2×#442 | 2 |
| C4×#127 | 2 |
| #1972 | 2 |
| #1957 | 2 |
| #1844 | 2 |
| C4×#97 | 2 |