Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
387 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 387 conjugacy classes of subgroups — too many to draw. Only its 165 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C8 | C2×D4 |
| commutator | C2×C4 | C23×C4 |
| Frattini, cosocle | C42 | C24 |
| socle | C22 | C2×C4×D4 |
| prime radical | #3100 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C8 ◁ C2×C4×C8 ◁ G | |
| LECS | G ▷ C42 ▷ C22 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #2931 | C2 | semidirect |
| 3. C2×C8×D4 | C2 | semidirect |
| 4. #1581 | C2 | semidirect |
| 5. C8×D8 | C2 | semidirect |
| 6. #1571 | C2 | semidirect |
| 7. #1486 | C2 | semidirect |
| 8. #1480 | C2 | semidirect |
| 9. #1450 | C2 | semidirect |
| 20. #436 | C22 | semidirect |
| 26. C8×D4 | C22 | semidirect |
| 34. #335 | C22 | semidirect |
| 36. D4⋊C8 | C22 | semidirect |
| 37. #322 | C22 | semidirect |
| 38. C82 | C22 | semidirect |
| 119. C2×C8 | D8 | semidirect |
| 150. D4 | #131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3100 | 2 |
| #2931 | 2 |
| C2×C8×D4 | 2 |
| #1581 | 2 |
| C8×D8 | 2 |
| #1571 | 2 |
| #1486 | 2 |
| #1480 | 2 |
| #1450 | 2 |