Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
491 conjugacy classes of subgroups; only the 215 normal subgroups are shown.
This group has 491 conjugacy classes of subgroups — too many to draw. Only its 215 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 ◁ C22×C42 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #1948 | C2 | semidirect |
| 5. #1947 | C2 | semidirect |
| 8. #1776 | C2 | semidirect |
| 14. #432 | C4 | semidirect |
| 66. C4⋊C8 | C2×C4 | semidirect |
| 68. #97 | C2×C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#432 | 2 |
| #2285 | 2 |
| C2×C4×C4⋊C4 | 2 |
| #1948 | 2 |
| #1947 | 2 |
| #1853 | 2 |
| #1852 | 2 |
| #1776 | 2 |