Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
366 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2 | #2688 |
| commutator, Frattini, cosocle | C22×C4 | C24 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2 ◁ C22×C4 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #3068 | C2 | semidirect |
| 2. #3038 | C2 | semidirect |
| 3. #2102 | C2 | semidirect |
| 4. #2081 | C2 | semidirect |
| 5. #2081 | C2 | semidirect |
| 6. #2048 | C2 | semidirect |
| 7. #2008 | C2 | semidirect |
| 8. #2002 | C2 | semidirect |
| 9. #1910 | C2 | semidirect |
| 10. #1906 | C2 | semidirect |
| 11. #1904 | C2 | semidirect |
| 12. #1904 | C2 | semidirect |
| 13. #1887 | C2 | semidirect |
| 14. #1861 | C2 | semidirect |
| 15. #1827 | C2 | semidirect |
| 73. C2×SD16 | D4 | semidirect |
| 76. C2×D8 | D4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3068 | 2 |
| #3038 | 2 |
| #2102 | 2 |
| #2081 | 2 |
| #2048 | 2 |
| #2008 | 2 |
| #2002 | 2 |
| #1910 | 2 |
| #1906 | 2 |
| #1904 | 2 |
| #1887 | 2 |
| #1861 | 2 |
| #1827 | 2 |