Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
519 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 519 conjugacy classes of subgroups — too many to draw. Only its 163 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×#469 | C2 |
| 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 |
|---|---|---|
| 2. C4×#121 | C2 | semidirect |
| 3. #1925 | C2 | semidirect |
| 4. #1920 | C2 | semidirect |
| 5. #1895 | C2 | semidirect |
| 6. #1879 | C2 | semidirect |
| 7. #1864 | C2 | semidirect |
| 8. #1809 | C2 | semidirect |
| 9. #1728 | C2 | semidirect |
| 17. #469 | C4 | semidirect |
| 43. C2×D8 | C2×C4 | semidirect |
| 49. C2×M16 | C2×C4 | semidirect |
| 54. #121 | C2×C4 | semidirect |
| 75. #106 | C2×C4 | semidirect |
| 78. #102 | C2×C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#469 | 2 |
| C4×#121 | 2 |
| #1925 | 2 |
| #1920 | 2 |
| #1895 | 2 |
| #1879 | 2 |
| #1864 | 2 |
| #1809 | 2 |
| #1728 | 2 |