Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
381 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 381 conjugacy classes of subgroups — too many to draw. Only its 191 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 | C24 | C2×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C2×#117 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #1949 | C2 | semidirect |
| 5. #1947 | C2 | semidirect |
| 8. #1847 | C2 | semidirect |
| 9. #1845 | C2 | semidirect |
| 10. #1836 | C2 | semidirect |
| 11. #1835 | C2 | semidirect |
| 15. #433 | C4 | semidirect |
| 70. C4⋊C8 | C2×C4 | semidirect |
| 72. #97 | C2×C4 | semidirect |
| 73. 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×#433 | 2 |
| #2317 | 2 |
| #2314 | 2 |
| #1949 | 2 |
| #1947 | 2 |
| #1854 | 2 |
| #1852 | 2 |
| #1847 | 2 |
| #1845 | 2 |
| #1836 | 2 |
| #1835 | 2 |