Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
406 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 113 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 | #2535 |
| 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. C2×#472 | C2 | semidirect |
| 2. #3058 | C2 | semidirect |
| 3. #2955 | C2 | semidirect |
| 4. #2948 | C2 | semidirect |
| 5. #2081 | C2 | semidirect |
| 6. #2008 | C2 | semidirect |
| 7. #1911 | C2 | semidirect |
| 8. #1904 | C2 | semidirect |
| 9. #1833 | C2 | semidirect |
| 10. #1814 | C2 | semidirect |
| 11. #1812 | C2 | semidirect |
| 102. #97 | D4 | semidirect |
| 103. C4×C8 | D4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#472 | 2 |
| #3058 | 2 |
| #2955 | 2 |
| #2948 | 2 |
| #2081 | 2 |
| #2008 | 2 |
| #1911 | 2 |
| #1904 | 2 |
| #1833 | 2 |
| #1814 | 2 |
| #1812 | 2 |