Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
1035 conjugacy classes of subgroups; only the 409 normal subgroups are shown.
This group has 1035 conjugacy classes of subgroups — too many to draw. Only its 409 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C24 |
| commutator, Frattini, socle, cosocle | C23 | C25 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4 ◁ G | |
| LECS | G ▷ C23 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #2840 | C2 | semidirect |
| 2. #2835 | C2 | semidirect |
| 3. #2824 | C2 | semidirect |
| 4. #2812 | C2 | semidirect |
| 5. #2398 | C2 | semidirect |
| 6. #2388 | C2 | semidirect |
| 7. C4×#120 | C2 | semidirect |
| 8. C22×#41 | C22 | semidirect |
| 11. C2×C4×Q8 | C22 | semidirect |
| 13. #400 | C22 | semidirect |
| 15. #397 | C22 | semidirect |
| 16. #395 | C22 | semidirect |
| 18. #394 | C22 | semidirect |
| 21. #393 | C22 | semidirect |
| 27. C4×C22⋊C4 | C22 | semidirect |
| 28. #376 | C22 | semidirect |
| 57. C24 | #41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #2840 | 2 |
| #2835 | 2 |
| #2824 | 2 |
| #2812 | 2 |
| #2398 | 2 |
| #2388 | 2 |
| C4×#120 | 2 |