Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
264 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 89 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 | #2749 |
| commutator, Frattini, cosocle | C22×C4 | C24 |
| prime radical | C2×#41 | C23 |
| 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. #2102 | C2 | semidirect |
| 2. #2082 | C2 | semidirect |
| 3. #2082 | C2 | semidirect |
| 4. #2070 | C2 | semidirect |
| 7. #1966 | C2 | semidirect |
| 12. #1886 | C2 | semidirect |
| 14. #1841 | C2 | semidirect |
| 15. #1830 | C2 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #2102 | 2 |
| #2082 | 2 |
| #2070 | 2 |
| #2049 | 2 |
| #2005 | 2 |
| #1966 | 2 |
| #1932 | 2 |
| #1915 | 2 |
| #1912 | 2 |
| #1902 | 2 |
| #1886 | 2 |
| #1861 | 2 |
| #1841 | 2 |
| #1830 | 2 |