Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
535 conjugacy classes of subgroups; only the 223 normal subgroups are shown.
This group has 535 conjugacy classes of subgroups — too many to draw. Only its 223 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 | C22×C22⋊C4 |
| commutator | C2×C4 | C23×C4 |
| Frattini, cosocle | C22×C4 | C24 |
| prime radical | C22×D4 | D4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C2×C4×D4 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #1520 | C2 | semidirect |
| 5. #1518 | C2 | semidirect |
| 6. #1503 | C2 | semidirect |
| 7. C2×#328 | C2 | semidirect |
| 9. #554 | C4 | semidirect |
| 10. D4×Q8 | C4 | semidirect |
| 30. C22×Q8 | C2×C4 | semidirect |
| 36. C4⋊Q8 | C2×C4 | semidirect |
| 37. C4⋊Q8 | C2×C4 | semidirect |
| 45. C22⋊Q8 | C2×C4 | semidirect |
| 48. C4×Q8 | C2×C4 | semidirect |
| 59. C2×C4⋊C4 | C2×C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3501 | 2 |
| #2972 | 2 |
| #2349 | 2 |
| #1520 | 2 |
| #1518 | 2 |
| #1503 | 2 |
| C2×#328 | 2 |