Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
321 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 321 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | #121 |
| commutator, Frattini, cosocle | C42 | C24 |
| socle | C22 | C2×#121 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4 ◁ C2×C42 ◁ G | |
| LECS | G ▷ C42 ▷ C22 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #3169 | C2 | semidirect |
| 2. #3106 | C2 | semidirect |
| 3. #2965 | C2 | semidirect |
| 4. #1698 | C2 | semidirect |
| 5. #1697 | C2 | semidirect |
| 6. #1696 | C2 | semidirect |
| 7. #1695 | C2 | semidirect |
| 8. #1688 | C2 | semidirect |
| 9. #1687 | C2 | semidirect |
| 10. #1564 | C2 | semidirect |
| 11. #1543 | C2 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3169 | 2 |
| #3106 | 2 |
| #2965 | 2 |
| #1698 | 2 |
| #1697 | 2 |
| #1696 | 2 |
| #1695 | 2 |
| #1688 | 2 |
| #1687 | 2 |
| #1564 | 2 |
| #1543 | 2 |