Finite Group DatabasebetaFinite Group DatabasebetaOrder 3008.
334 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 111 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 | C2×#41×C47 | C2 |
| hypercenter | C2×#41 | D47 |
| hypocenter | C47 | #535 |
| LCS | G ▷ C22×C47 ▷ C47 | |
| UCS | C1 ◁ C22 ◁ C2×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×D188 | C2 | semidirect |
| 2. #13094020 | C2 | semidirect |
| 3. #13094013 | C2 | semidirect |
| 4. #13093998 | C2 | semidirect |
| 5. #13093992 | C2 | semidirect |
| 6. #13093983 | C2 | semidirect |
| 7. C2×#41×C47 | C2 | semidirect |
| 10. C2×Q8×C47 | C22 | semidirect |
| 12. C2×D4×C47 | C22 | semidirect |
| 14. C22×C4×C47 | C22 | semidirect |
| 15. C2×C22⋊D47 | C22 | semidirect |
| 20. (C2×D47)⋊C4 | C22 | semidirect |
| 21. C4⋊Dic47 | C22 | semidirect |
| 22. C4×Dic47 | C22 | semidirect |
| 32. C2×C4×C47 | D4 | semidirect |
| 58. C47 | #535 | semidirect |
| 59. C2×#41 | D47 | semidirect |
| 68. C2×Q8 | C2×D47 | semidirect |
| 74. C2×D4 | C2×D47 | semidirect |
| 76. C22×C4 | C2×D47 | semidirect |
| 94. C2×C4 | C22⋊D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D188 | 2 |
| #13094020 | 2 |
| #13094013 | 2 |
| #13093998 | 2 |
| #13093992 | 2 |
| #13093983 | 2 |
| C2×#41×C47 | 2 |
| #535 | 47 |