Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
679 conjugacy classes of subgroups; only the 431 normal subgroups are shown.
This group has 679 conjugacy classes of subgroups — too many to draw. Only its 431 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 | D4 |
| commutator | C4 | C22×C42 |
| Frattini, cosocle | C22×C4 | C24 |
| socle, prime radical | C24 | C2×D4 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C4 ◁ C22×C42 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C4×#106 | C2 | direct (N × H) |
| 11. C2×#106 | C4 | direct (N × H) |
| 13. C2×C4×C8 | C4 | semidirect |
| 39. #106 | C2×C4 | direct (N × H) |
| 40. C4×C8 | C2×C4 | semidirect |
| 61. C2×C8 | C42 | semidirect |
| 83. C2×C4 | #106 | direct (N × H) |
| 97. C8 | C2×C42 | semidirect |
| 109. C4 | C2×#106 | direct (N × H) |
| 113. C2 | C4×#106 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#106 | 2 |
| C22×C4×C8 | 2 |
| C2×C4×C4⋊C4 | 2 |
| C4×#106 | 2 |
| C2×#340 | 2 |