Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
627 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 627 conjugacy classes of subgroups — too many to draw. Only its 183 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C22×C22⋊C4 |
| commutator | C23 | C23×C4 |
| Frattini, cosocle | C24 | C24 |
| prime radical | C2×#538 | C2 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C22×C22⋊C4 ◁ G | |
| LECS | G ▷ C24 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #2315 | C2 | semidirect |
| 3. #2312 | C2 | semidirect |
| 4. #1996 | C2 | semidirect |
| 5. #1964 | C2 | semidirect |
| 6. #1898 | C2 | semidirect |
| 7. #1799 | C2 | semidirect |
| 10. C2×#126 | C4 | semidirect |
| 11. C2×#124 | C4 | semidirect |
| 12. C2×#123 | C4 | semidirect |
| 14. C2×#121 | C4 | semidirect |
| 30. C22×Q8 | C2×C4 | semidirect |
| 33. C22×D4 | C2×C4 | semidirect |
| 36. C23×C4 | C2×C4 | semidirect |
| 54. C2×C4⋊C4 | C2×C4 | semidirect |
| 55. C2×C4⋊C4 | C2×C4 | semidirect |
| 56. C2×C4⋊C4 | C2×C4 | semidirect |
| 57. C2×C4⋊C4 | C2×C4 | semidirect |
| 66. C2×C22⋊C4 | C2×C4 | semidirect |
| 67. C2×C22⋊C4 | C2×C4 | semidirect |
| 74. C2×C42 | C2×C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#538 | 2 |
| #2315 | 2 |
| #2312 | 2 |
| #1996 | 2 |
| #1964 | 2 |
| #1898 | 2 |
| #1799 | 2 |