Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
499 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 499 conjugacy classes of subgroups — too many to draw. Only its 203 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C42 | C23 |
| commutator, socle | C23 | C23×C4 |
| Frattini, cosocle | C22×C4 | C24 |
| prime radical | C22×D4 | C2×C4 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C2×C42 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#431 | C2 | semidirect |
| 4. #1940 | C2 | semidirect |
| 5. #1924 | C2 | semidirect |
| 6. C4×C4⋊C8 | C2 | semidirect |
| 7. C4×C22⋊C8 | C2 | semidirect |
| 8. C4×#97 | C2 | semidirect |
| 62. C4×C8 | D4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#431 | 2 |
| C42×D4 | 2 |
| #1955 | 2 |
| #1940 | 2 |
| #1924 | 2 |
| C4×C4⋊C8 | 2 |
| C4×C22⋊C8 | 2 |
| C4×#97 | 2 |