Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
540 conjugacy classes of subgroups; only the 169 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 169 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 | C2×C4 | C23×C4 |
| Frattini, cosocle | C22×C4 | C24 |
| prime radical | C2×#121 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C22×C42 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×#391 | C2 | semidirect |
| 4. #1973 | C2 | semidirect |
| 5. #1935 | C2 | semidirect |
| 6. #1928 | C2 | semidirect |
| 7. #1877 | C2 | semidirect |
| 9. #1852 | C2 | semidirect |
| 10. #1787 | C2 | semidirect |
| 11. #1749 | C2 | semidirect |
| 19. #448 | C4 | semidirect |
| 48. C22×Q8 | C2×C4 | semidirect |
| 60. C2×SD16 | C2×C4 | semidirect |
| 88. #103 | C2×C4 | semidirect |
| 91. C22⋊C8 | C2×C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#448 | 2 |
| C4×#121 | 2 |
| C2×#391 | 2 |
| #1973 | 2 |
| #1935 | 2 |
| #1928 | 2 |
| #1877 | 2 |
| #1874 | 2 |
| #1852 | 2 |
| #1787 | 2 |
| #1749 | 2 |