Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
1809 conjugacy classes of subgroups; only the 595 normal subgroups are shown.
This group has 1809 conjugacy classes of subgroups — too many to draw. Only its 595 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, commutator, Frattini, socle, cosocle | C23 | C25 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ G | |
| LECS | G ▷ C23 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#547 | C2 | semidirect |
| 2. #2868 | C2 | semidirect |
| 3. #2856 | C2 | semidirect |
| 4. #2542 | C2 | semidirect |
| 5. #2501 | C2 | semidirect |
| 6. C4×#127 | C2 | semidirect |
| 7. C2×#384 | C2 | semidirect |
| 8. C42×D4 | C2 | semidirect |
| 44. C4×D4 | D4 | semidirect |
| 91. C42 | #41 | semidirect |
| 102. D4 | #127 | semidirect |
| 131. C4 | #547 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#547 | 2 |
| #2868 | 2 |
| #2856 | 2 |
| #2542 | 2 |
| #2501 | 2 |
| C4×#127 | 2 |
| C2×#384 | 2 |
| C42×D4 | 2 |