Finite Group DatabasebetaFinite Group DatabasebetaOrder 20032.
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×D313 |
| commutator, socle, cosocle | C22×C313 | C24 |
| Fitting | C2×#41×C313 | C2 |
| hypercenter | C2×#41 | D313 |
| hypocenter | C313 | #535 |
| LCS | G ▷ C22×C313 ▷ C313 | |
| UCS | C1 ◁ C22 ◁ C2×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×D1252 | C2 | semidirect |
| 2. #23756493 | C2 | semidirect |
| 3. #23756486 | C2 | semidirect |
| 4. #23756471 | C2 | semidirect |
| 5. #23756465 | C2 | semidirect |
| 6. #23756456 | C2 | semidirect |
| 7. C2×#41×C313 | C2 | semidirect |
| 12. C2×C22⋊D313 | C22 | semidirect |
| 13. C4⋊Dic313 | C22 | semidirect |
| 15. #19097538 | C22 | semidirect |
| 16. C4×Dic313 | C22 | semidirect |
| 18. C2×Q8×C313 | C22 | semidirect |
| 20. C2×D4×C313 | C22 | semidirect |
| 22. C22×C4×C313 | C22 | semidirect |
| 36. C2×C4×C313 | D4 | semidirect |
| 57. C313 | #535 | semidirect |
| 59. C2×#41 | D313 | semidirect |
| 68. C2×Q8 | C2×D313 | semidirect |
| 74. C2×D4 | C2×D313 | semidirect |
| 76. C22×C4 | C2×D313 | semidirect |
| 94. C2×C4 | C22⋊D313 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1252 | 2 |
| #23756493 | 2 |
| #23756486 | 2 |
| #23756471 | 2 |
| #23756465 | 2 |
| #23756456 | 2 |
| C2×#41×C313 | 2 |
| #535 | 313 |