Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
390 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 109 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 | #1999 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C4×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. #2490 | C2 | semidirect |
| 2. #2076 | C2 | semidirect |
| 3. #2054 | C2 | semidirect |
| 4. #2025 | C2 | semidirect |
| 6. #1989 | C2 | semidirect |
| 7. #1925 | C2 | semidirect |
| 8. #1893 | C2 | semidirect |
| 9. #1850 | C2 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #2490 | 2 |
| #2076 | 2 |
| #2054 | 2 |
| #2025 | 2 |
| #1999 | 2 |
| #1989 | 2 |
| #1925 | 2 |
| #1893 | 2 |
| #1850 | 2 |