Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
375 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 375 conjugacy classes of subgroups — too many to draw. Only its 131 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 | C22×D4 | C23 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C4×C4⋊C4 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #2551 | C2 | semidirect |
| 3. #2101 | C2 | semidirect |
| 5. #1993 | C2 | semidirect |
| 6. #1990 | C2 | semidirect |
| 7. #1987 | C2 | semidirect |
| 10. #1770 | C2 | semidirect |
| 76. #102 | Q8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #2563 | 2 |
| #2551 | 2 |
| #2101 | 2 |
| #2023 | 2 |
| #1993 | 2 |
| #1990 | 2 |
| #1987 | 2 |
| #1936 | 2 |
| #1802 | 2 |
| #1770 | 2 |
| C4×#102 | 2 |