Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
415 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 415 conjugacy classes of subgroups — too many to draw. Only its 125 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 | #2416 |
| commutator, Frattini, cosocle | C22×C4 | C24 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2 ◁ C22×C4 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #3068 | C2 | semidirect |
| 2. C2×#472 | C2 | semidirect |
| 3. C2×#472 | C2 | semidirect |
| 4. #2955 | C2 | semidirect |
| 5. #2916 | C2 | semidirect |
| 6. #2069 | C2 | semidirect |
| 7. #2048 | C2 | semidirect |
| 8. #1978 | C2 | semidirect |
| 9. #1953 | C2 | semidirect |
| 10. #1903 | C2 | semidirect |
| 11. #1813 | C2 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3068 | 2 |
| C2×#472 | 2 |
| #2955 | 2 |
| #2916 | 2 |
| #2069 | 2 |
| #2048 | 2 |
| #1978 | 2 |
| #1953 | 2 |
| #1903 | 2 |
| #1813 | 2 |