Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
344 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 115 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 | C22×C4 | C24 |
| prime radical | C24 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C2×#117 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 5. #1960 | C2 | semidirect |
| 6. #1956 | C2 | semidirect |
| 7. #1928 | C2 | semidirect |
| 8. #1927 | C2 | semidirect |
| 9. #1846 | C2 | semidirect |
| 10. #1836 | C2 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #2621 | 2 |
| #2314 | 2 |
| #2036 | 2 |
| #2035 | 2 |
| #1960 | 2 |
| #1956 | 2 |
| #1928 | 2 |
| #1927 | 2 |
| #1846 | 2 |
| #1836 | 2 |
| #1750 | 2 |