Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
631 conjugacy classes of subgroups; only the 199 normal subgroups are shown.
This group has 631 conjugacy classes of subgroups — too many to draw. Only its 199 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×#496 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C43 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#442 | C2 | semidirect |
| 3. C2×#440 | C2 | semidirect |
| 4. C4×#127 | C2 | semidirect |
| 5. C4×#124 | C2 | semidirect |
| 6. #1970 | C2 | semidirect |
| 7. #1968 | C2 | semidirect |
| 8. #1961 | C2 | semidirect |
| 9. #1959 | C2 | semidirect |
| 10. #1847 | C2 | semidirect |
| 11. C4×#97 | C2 | semidirect |
| 20. #496 | C4 | semidirect |
| 50. C2×SD16 | C2×C4 | semidirect |
| 53. C2×D8 | C2×C4 | semidirect |
| 57. #127 | C2×C4 | semidirect |
| 59. #124 | C2×C4 | semidirect |
| 88. #97 | C2×C4 | semidirect |
| 89. #97 | D4 | semidirect |
| 197. C8 | C4×D4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#496 | 2 |
| C2×#442 | 2 |
| C2×#440 | 2 |
| C4×#127 | 2 |
| C4×#124 | 2 |
| #1970 | 2 |
| #1968 | 2 |
| #1961 | 2 |
| #1959 | 2 |
| #1847 | 2 |
| C4×#97 | 2 |