Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
559 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 559 conjugacy classes of subgroups — too many to draw. Only its 151 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24 |
| prime radical | C2×#127 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C4×C4⋊C4 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#497 | C2 | semidirect |
| 3. C2×#462 | C2 | semidirect |
| 5. C2×C4×Q16 | C2 | semidirect |
| 7. #2546 | C2 | semidirect |
| 8. #2015 | C2 | semidirect |
| 9. #2013 | C2 | semidirect |
| 10. #1973 | C2 | semidirect |
| 11. #1770 | C2 | semidirect |
| 55. C2×Q16 | D4 | semidirect |
| 244. C4 | #497 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#497 | 2 |
| C2×#492 | 2 |
| C2×#462 | 2 |
| C2×#460 | 2 |
| C2×C4×Q16 | 2 |
| #2548 | 2 |
| #2546 | 2 |
| #2015 | 2 |
| #2013 | 2 |
| #1973 | 2 |
| #1770 | 2 |