Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
390 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24 |
| prime radical | #3153 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C2×C42 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #3141 | C2 | semidirect |
| 3. C2×#489 | C2 | semidirect |
| 4. #2932 | C2 | semidirect |
| 5. #2052 | C2 | semidirect |
| 6. #2051 | C2 | semidirect |
| 7. #1997 | C2 | semidirect |
| 8. #1967 | C2 | semidirect |
| 9. #1908 | C2 | semidirect |
| 10. #1907 | C2 | semidirect |
| 11. #1778 | C2 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3153 | 2 |
| #3141 | 2 |
| C2×#489 | 2 |
| #2932 | 2 |
| #2052 | 2 |
| #2051 | 2 |
| #1997 | 2 |
| #1967 | 2 |
| #1908 | 2 |
| #1907 | 2 |
| #1778 | 2 |