Finite Group DatabasebetaFinite Group DatabasebetaOrder 3008.
310 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 109 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 | #121×C47 | C2 |
| hypercenter | #121 | D47 |
| hypocenter | C47 | #532 |
| LCS | G ▷ C22×C47 ▷ C47 | |
| UCS | C1 ◁ C22 ◁ #121 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#10625352 | C2 | semidirect |
| 2. #13094023 | C2 | semidirect |
| 3. #13094020 | C2 | semidirect |
| 4. #13094010 | C2 | semidirect |
| 5. #13093998 | C2 | semidirect |
| 6. #13093996 | C2 | semidirect |
| 7. D4×Dic47 | C2 | semidirect |
| 8. #13093986 | C2 | semidirect |
| 9. (C22⋊D47)⋊C4 | C2 | semidirect |
| 10. C2×C4×Dic47 | C2 | semidirect |
| 11. #121×C47 | C2 | semidirect |
| 50. C2×Dic47 | D4 | semidirect |
| 71. C4×C47 | #41 | semidirect |
| 76. Dic47 | #41 | semidirect |
| 84. C47 | #532 | semidirect |
| 91. #121 | D47 | semidirect |
| 160. C4 | #10625352 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10625352 | 2 |
| #13094023 | 2 |
| #13094020 | 2 |
| #13094010 | 2 |
| #13093998 | 2 |
| #13093996 | 2 |
| D4×Dic47 | 2 |
| #13093986 | 2 |
| (C22⋊D47)⋊C4 | 2 |
| C2×C4×Dic47 | 2 |
| #121×C47 | 2 |
| #532 | 47 |