Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
379 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 379 conjugacy classes of subgroups — too many to draw. Only its 127 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C2×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24 |
| socle | C23 | C22×D4 |
| prime radical | C22×D4 | C23 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4 ◁ C43 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C4×#125 | C2 | semidirect |
| 3. #2101 | C2 | semidirect |
| 4. #2074 | C2 | semidirect |
| 7. #2026 | C2 | semidirect |
| 9. C4×#103 | C2 | semidirect |
| 11. #1744 | C2 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#125 | 2 |
| C4×#124 | 2 |
| #2101 | 2 |
| #2074 | 2 |
| #2073 | 2 |
| #2042 | 2 |
| #2026 | 2 |
| #2025 | 2 |
| C4×#103 | 2 |
| C4×#102 | 2 |
| #1744 | 2 |