Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
492 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 113 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 | C25 | D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C24×C4 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #2076 | C2 | semidirect |
| 3. #2036 | C2 | semidirect |
| 4. #2001 | C2 | semidirect |
| 7. C22×Q16 | C22 | semidirect |
| 9. C2×#107 | C22 | semidirect |
| 10. C2×#103 | C22 | semidirect |
| 16. #340 | C22 | semidirect |
| 17. #340 | C22 | semidirect |
| 40. C24 | Q16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #2848 | 2 |
| #2076 | 2 |
| #2036 | 2 |
| #2001 | 2 |
| #1779 | 2 |