Finite Group DatabasebetaFinite Group DatabasebetaOrder 5248.
402 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 108 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C41 | C2×D4 |
| commutator, Frattini, cosocle | C22×C4 | C23×C41 |
| prime radical | C2×#127×C41 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C41 ◁ C2×C42×C41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#102×C41 | C2 | semidirect |
| 3. C2×#102×C41 | C2 | semidirect |
| 4. C41×#389 | C2 | semidirect |
| 5. C41×#336 | C2 | semidirect |
| 42. C4⋊C4×C41 | D4 | semidirect |
| 95. #2041 | C41 | direct (N × H) |
| 105. C2×#102 | C2×C41 | semidirect |
| 106. C2×#102 | C2×C41 | semidirect |
| 107. #389 | C2×C41 | semidirect |
| 108. #336 | C2×C41 | semidirect |
| 109. C41 | #2041 | direct (N × H) |
| 146. C4⋊C4 | D4×C41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#127×C41 | 2 |
| C2×#102×C41 | 2 |
| C41×#389 | 2 |
| C41×#336 | 2 |
| #2041 | 41 |