Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
345 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 345 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, socle | C23 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24 |
| prime radical | C24 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C4×C22⋊C4 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #2099 | C2 | semidirect |
| 4. #1942 | C2 | semidirect |
| 5. #1942 | C2 | semidirect |
| 6. #1918 | C2 | semidirect |
| 7. #1845 | C2 | semidirect |
| 10. C4×#107 | C2 | semidirect |
| 177. C8 | #126 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #2496 | 2 |
| #2099 | 2 |
| #2075 | 2 |
| #1942 | 2 |
| #1918 | 2 |
| #1845 | 2 |
| #1808 | 2 |
| C4×#107 | 2 |
| C8×C22⋊C4 | 2 |