Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
805 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 805 conjugacy classes of subgroups — too many to draw. Only its 175 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 | C2×#535 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C22×#41 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#427 | C2 | semidirect |
| 3. C2×#418 | C2 | semidirect |
| 4. C22×#102 | C2 | semidirect |
| 5. C2×#408 | C2 | semidirect |
| 6. #2311 | C2 | semidirect |
| 7. #2034 | C2 | semidirect |
| 8. #2033 | C2 | semidirect |
| 9. #1736 | C2 | semidirect |
| 24. C2×#107 | C22 | semidirect |
| 25. C2×#106 | C22 | semidirect |
| 32. C2×C22⋊C8 | C22 | semidirect |
| 33. C2×C22⋊C8 | C22 | semidirect |
| 37. #380 | C22 | semidirect |
| 38. #340 | C22 | semidirect |
| 66. C22×C8 | D4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#535 | 2 |
| C2×#427 | 2 |
| C2×#418 | 2 |
| C22×#102 | 2 |
| C2×#408 | 2 |
| #2311 | 2 |
| #2034 | 2 |
| #2033 | 2 |
| #1736 | 2 |