Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
1143 conjugacy classes of subgroups; only the 447 normal subgroups are shown.
This group has 1143 conjugacy classes of subgroups — too many to draw. Only its 447 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23×C4 | C23 |
| commutator | C22 | C22×C42 |
| Frattini, cosocle | C22×C4 | C24 |
| socle | C24 | C22×C4 |
| prime radical | C25 | C2×C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C4 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C22×#97 | C2 | semidirect |
| 4. #1749 | C2 | direct (N × H) |
| 5. C2×#336 | C2 | semidirect |
| 15. C2×C22⋊C8 | C4 | semidirect |
| 18. C2×#97 | C22 | semidirect |
| 19. #336 | C22 | semidirect |
| 36. C22×C8 | C2×C4 | semidirect |
| 48. C22⋊C8 | C2×C4 | semidirect |
| 88. C2×C8 | C22×C4 | semidirect |
| 101. C23 | #97 | semidirect |
| 140. C22 | C2×#97 | semidirect |
| 155. C2 | #1749 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C42 | 2 |
| C22×C22⋊C8 | 2 |
| C22×#97 | 2 |
| #1749 | 2 |
| C2×#336 | 2 |