Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
457 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 457 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 | C22×D8 | C22 |
| 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. #2950 | C2 | semidirect |
| 3. #2949 | C2 | semidirect |
| 5. #1979 | C2 | semidirect |
| 7. #1977 | C2 | semidirect |
| 8. #1888 | C2 | semidirect |
| 9. #1885 | C2 | semidirect |
| 10. #1772 | C2 | semidirect |
| 11. #1772 | C2 | semidirect |
| 18. #495 | C4 | semidirect |
| 47. C2×Q16 | C2×C4 | semidirect |
| 51. C2×SD16 | C2×C4 | semidirect |
| 62. #124 | C2×C4 | semidirect |
| 92. 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×#495 | 2 |
| #2950 | 2 |
| #2949 | 2 |
| #2948 | 2 |
| #1979 | 2 |
| #1978 | 2 |
| #1977 | 2 |
| #1888 | 2 |
| #1885 | 2 |
| #1772 | 2 |