Finite Group DatabasebetaFinite Group DatabasebetaOrder 128.
247 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 247 conjugacy classes of subgroups — too many to draw. Only its 96 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 | #546 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C4×D4 ◁ G | |
| LECS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#137 | C2 | semidirect |
| 2. C22×SD16 | C2 | semidirect |
| 3. D4×Q8 | C2 | semidirect |
| 5. #497 | C2 | semidirect |
| 6. #468 | C2 | semidirect |
| 7. #467 | C2 | semidirect |
| 8. #464 | C2 | semidirect |
| 9. #461 | C2 | semidirect |
| 10. #452 | C2 | semidirect |
| 11. #451 | C2 | semidirect |
| 12. #450 | C2 | semidirect |
| 13. #448 | C2 | semidirect |
| 14. #440 | C2 | semidirect |
| 15. #435 | C2 | semidirect |
| 18. C22×Q8 | C22 | semidirect |
| 21. C2×Q16 | C22 | semidirect |
| 22. C2×Q16 | C22 | semidirect |
| 23. C2×Q16 | C22 | semidirect |
| 31. C2×M16 | C22 | semidirect |
| 34. C4⋊Q8 | C22 | semidirect |
| 41. C22⋊Q8 | C22 | semidirect |
| 45. C4×Q8 | C22 | semidirect |
| 50. #107 | C22 | semidirect |
| 51. C4⋊C8 | C22 | semidirect |
| 52. #103 | C22 | semidirect |
| 53. #103 | C22 | semidirect |
| 54. #103 | C22 | semidirect |
| 55. #103 | C22 | semidirect |
| 59. C22⋊C8 | C22 | semidirect |
| 60. #97 | C22 | semidirect |
| 96. SD16 | D4 | semidirect |
| 183. C22 | #137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#137 | 2 |
| C22×SD16 | 2 |
| D4×Q8 | 2 |
| #546 | 2 |
| #497 | 2 |
| #468 | 2 |
| #467 | 2 |
| #464 | 2 |
| #461 | 2 |
| #452 | 2 |
| #451 | 2 |
| #450 | 2 |
| #448 | 2 |
| #440 | 2 |
| #435 | 2 |