Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
491 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 491 conjugacy classes of subgroups — too many to draw. Only its 139 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, Frattini, cosocle | C22×C4 | C24 |
| prime radical | #2537 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C2×C4×D4 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#480 | C2 | semidirect |
| 3. D4×C4⋊C4 | C2 | semidirect |
| 4. #2075 | C2 | semidirect |
| 5. #2033 | C2 | semidirect |
| 6. #1954 | C2 | semidirect |
| 7. #1947 | C2 | semidirect |
| 8. #1852 | C2 | semidirect |
| 9. #1845 | C2 | semidirect |
| 10. #1802 | C2 | semidirect |
| 11. C4×#102 | C2 | semidirect |
| 85. #102 | D4 | semidirect |
| 248. C4 | #480 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#480 | 2 |
| #2537 | 2 |
| D4×C4⋊C4 | 2 |
| #2075 | 2 |
| #2033 | 2 |
| #1954 | 2 |
| #1947 | 2 |
| #1852 | 2 |
| #1845 | 2 |
| #1802 | 2 |
| C4×#102 | 2 |