Finite Group DatabasebetaFinite Group DatabasebetaOrder 128.
210 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 88 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×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24 |
| prime radical | #525 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C23×C4 ◁ G | |
| LECS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C22⋊Q8 | C2 | semidirect |
| 3. #485 | C2 | semidirect |
| 4. #483 | C2 | semidirect |
| 5. #480 | C2 | semidirect |
| 6. #467 | C2 | semidirect |
| 7. #465 | C2 | semidirect |
| 8. #452 | C2 | semidirect |
| 9. #451 | C2 | semidirect |
| 10. #448 | C2 | semidirect |
| 11. C2×C22⋊C8 | C2 | semidirect |
| 15. C2×Q16 | C22 | semidirect |
| 16. C2×SD16 | C22 | semidirect |
| 34. #107 | C22 | semidirect |
| 35. #106 | C22 | semidirect |
| 36. #103 | C22 | semidirect |
| 37. #103 | C22 | semidirect |
| 38. #103 | C22 | semidirect |
| 39. #102 | C22 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #525 | 2 |
| C2×C22⋊Q8 | 2 |
| #485 | 2 |
| #483 | 2 |
| #480 | 2 |
| #467 | 2 |
| #465 | 2 |
| #452 | 2 |
| #451 | 2 |
| #448 | 2 |
| C2×C22⋊C8 | 2 |