Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
507 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 507 conjugacy classes of subgroups — too many to draw. Only its 167 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | D42 |
| commutator | C2×C4 | C23×C4 |
| Frattini, cosocle | C22×C4 | C24 |
| prime radical | C2×#493 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C22×C4 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #2948 | C2 | semidirect |
| 3. #1978 | C2 | semidirect |
| 4. #1887 | C2 | semidirect |
| 5. #1772 | C2 | semidirect |
| 9. #493 | C4 | semidirect |
| 24. C2×D8 | C2×C4 | semidirect |
| 28. #127 | C2×C4 | semidirect |
| 34. #107 | D4 | semidirect |
| 35. #106 | D4 | semidirect |
| 40. C4×C8 | C2×C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#493 | 2 |
| #2948 | 2 |
| #1978 | 2 |
| #1887 | 2 |
| #1772 | 2 |