Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
355 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 355 conjugacy classes of subgroups — too many to draw. Only its 123 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 | C42 | C24 |
| prime radical | C2×#127 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C2×C42 ◁ G | |
| LECS | G ▷ C42 ▷ C22 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #3229 | C2 | semidirect |
| 4. #2960 | C2 | semidirect |
| 5. #1686 | C2 | semidirect |
| 6. #1666 | C2 | semidirect |
| 7. #1564 | C2 | semidirect |
| 8. #1546 | C2 | semidirect |
| 24. #475 | C22 | semidirect |
| 28. #446 | C22 | semidirect |
| 30. C8×Q8 | C22 | semidirect |
| 37. #335 | C22 | semidirect |
| 38. #334 | C22 | semidirect |
| 39. #332 | C22 | semidirect |
| 124. C2×C8 | SD16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3229 | 2 |
| #3208 | 2 |
| C2×#492 | 2 |
| #2960 | 2 |
| #1686 | 2 |
| #1666 | 2 |
| #1564 | 2 |
| #1546 | 2 |
| #1545 | 2 |