Finite Group DatabasebetaFinite Group DatabasebetaOrder 3008.
234 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 101 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×D47 |
| commutator, socle, cosocle | C22×C47 | C24 |
| Fitting | C22⋊Q8×C47 | C2 |
| prime radical | #13093998 | C2 |
| hypercenter | C22⋊Q8 | D47 |
| hypocenter | C47 | #529 |
| LCS | G ▷ C22×C47 ▷ C47 | |
| UCS | C1 ◁ C22 ◁ C22⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13094019 | C2 | semidirect |
| 2. #13094015 | C2 | semidirect |
| 3. #13094013 | C2 | semidirect |
| 4. #13094008 | C2 | semidirect |
| 6. Q8×Dic47 | C2 | semidirect |
| 7. #13093986 | C2 | semidirect |
| 8. (C22⋊D47)⋊C4 | C2 | semidirect |
| 9. #13093982 | C2 | semidirect |
| 10. C2×C4×Dic47 | C2 | semidirect |
| 11. C22⋊Q8×C47 | C2 | semidirect |
| 75. C47 | #529 | semidirect |
| 80. C22⋊Q8 | D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13094019 | 2 |
| #13094015 | 2 |
| #13094013 | 2 |
| #13094008 | 2 |
| #13093998 | 2 |
| Q8×Dic47 | 2 |
| #13093986 | 2 |
| (C22⋊D47)⋊C4 | 2 |
| #13093982 | 2 |
| C2×C4×Dic47 | 2 |
| C22⋊Q8×C47 | 2 |
| #529 | 47 |