Finite Group DatabasebetaFinite Group DatabasebetaOrder 5248.
198 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 76 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C41 | #121 |
| commutator, Frattini, cosocle | C22×C4 | C23×C41 |
| prime radical | C2×#41×C41 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C41 ◁ C22×C4×C41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#107×C41 | C2 | semidirect |
| 4. C41×#343 | C2 | semidirect |
| 5. C41×#341 | C2 | semidirect |
| 61. #2078 | C41 | direct (N × H) |
| 67. C2×#107 | C2×C41 | semidirect |
| 70. #343 | C2×C41 | semidirect |
| 71. #341 | C2×C41 | semidirect |
| 72. C41 | #2078 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#107×C41 | 2 |
| C41×#417 | 2 |
| C41×#408 | 2 |
| C41×#343 | 2 |
| C41×#341 | 2 |
| #2078 | 41 |