Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
5314 conjugacy classes of subgroups; only the 1342 normal subgroups are shown.
This group has 5314 conjugacy classes of subgroups — too many to draw. Only its 1342 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C4 | #1044 |
| commutator, hypocenter | C52 | C24×C8 |
| Frattini | C2 | C24×#1044 |
| Fitting | C23×C4×C52 | C4 |
| socle | C24×C52 | C2×C4 |
| prime radical | C24×C5⋊D5 | C4 |
| cosocle | #1039 | C25 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C23×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C23×#6034 | C2 | semidirect |
| 3. C22×#87862 | C2 | direct (N × H) |
| 9. C22×#6034 | C22 | semidirect |
| 10. C2×#87862 | C22 | direct (N × H) |
| 13. C23×C5⋊D5 | C8 | semidirect |
| 20. C2×#6034 | C23 | semidirect |
| 21. #87862 | C23 | direct (N × H) |
| 26. C23×C52 | C2×C8 | semidirect |
| 28. C22×C5⋊D5 | C2×C8 | semidirect |
| 35. #6034 | C24 | semidirect |
| 49. C22×C52 | C22×C8 | semidirect |
| 51. C2×C5⋊D5 | C22×C8 | semidirect |
| 77. C2×C52 | C23×C8 | semidirect |
| 79. C5⋊D5 | C23×C8 | semidirect |
| 82. C23×C5 | D5⋊C8 | semidirect |
| 106. C52 | C24×C8 | semidirect |
| 109. C22×C5 | C2×D5⋊C8 | semidirect |
| 133. C2×C5 | C22×D5⋊C8 | semidirect |
| 139. C23 | #87862 | direct (N × H) |
| 148. C5 | C23×D5⋊C8 | semidirect |
| 151. C22 | C2×#87862 | direct (N × H) |
| 157. C2 | C22×#87862 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4×C5⋊D5 | 2 |
| C23×#6034 | 2 |
| C22×#87862 | 2 |
| C23×D5⋊C8 | 5 |