Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
242 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 67 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4 | #459 |
| commutator | C2×C8 | C22×C4 |
| Frattini, cosocle | C22×C8 | C23 |
| socle | C2 | #1879 |
| prime radical | #3414 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ C2×C4×C8 ◁ G | |
| LECS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C4×#135 | C2 | semidirect |
| 3. #2145 | C2 | semidirect |
| 4. #2143 | C2 | semidirect |
| 5. #1974 | C2 | semidirect |
| 6. #1389 | C2 | semidirect |
| 7. #1376 | C2 | semidirect |
| 12. #510 | C4 | semidirect |
| 14. #509 | C4 | semidirect |
| 39. C2×Q16 | C2×C4 | semidirect |
| 43. C2×D8 | C2×C4 | semidirect |
| 62. M32 | C2×C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3414 | 2 |
| C4×#135 | 2 |
| #2145 | 2 |
| #2143 | 2 |
| #1974 | 2 |
| #1389 | 2 |
| #1376 | 2 |