Finite Group DatabasebetaFinite Group DatabasebetaOrder 1984.
294 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 151 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D31 |
| commutator | C2×C31 | C23×C4 |
| Fitting | C4×D4×C31 | C2 |
| socle, cosocle | C22×C31 | C24 |
| prime radical | C2×#92497 | C2 |
| hypercenter | C4×D4 | D31 |
| hypocenter | C31 | #520 |
| LCS | G ▷ C2×C31 ▷ C31 | |
| UCS | C1 ◁ C22 ◁ C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C4×D4×C31 | C2 | semidirect |
| 3. D4×Dic31 | C2 | semidirect |
| 4. C4×C22⋊D31 | C2 | semidirect |
| 5. C2×Dic31⋊C4 | C2 | semidirect |
| 6. C4⋊C4×D31 | C2 | semidirect |
| 7. #11758464 | C2 | semidirect |
| 8. (C22⋊D31)⋊C4 | C2 | semidirect |
| 9. #11758454 | C2 | semidirect |
| 10. #11758449 | C2 | semidirect |
| 11. C4×Dic62 | C2 | semidirect |
| 17. #92497 | C4 | semidirect |
| 38. D4×C31 | C2×C4 | semidirect |
| 44. C22⋊D31 | C2×C4 | semidirect |
| 46. C2×Dic31 | C2×C4 | semidirect |
| 53. C4×D31 | C2×C4 | semidirect |
| 54. Dic62 | C2×C4 | semidirect |
| 83. C4×D4 | D31 | semidirect |
| 88. C31 | #520 | semidirect |
| 117. D4 | C4×D31 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#92497 | 2 |
| C4×D4×C31 | 2 |
| D4×Dic31 | 2 |
| C4×C22⋊D31 | 2 |
| C2×Dic31⋊C4 | 2 |
| C4⋊C4×D31 | 2 |
| #11758464 | 2 |
| (C22⋊D31)⋊C4 | 2 |
| #11758454 | 2 |
| #11758449 | 2 |
| C4×Dic62 | 2 |
| #520 | 31 |