Finite Group DatabasebetaFinite Group DatabasebetaOrder 5248.
316 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 104 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C41 | C2×D4 |
| commutator | C2×C4 | C22×C4×C41 |
| Frattini, cosocle | C42 | C23×C41 |
| socle | C22×C41 | C2×C22⋊C4 |
| prime radical | C22×D4×C41 | C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C41 ◁ C2×C42×C41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C41×#432 | C2 | semidirect |
| 3. C4×M16×C41 | C2 | semidirect |
| 4. C41×D4⋊C8 | C2 | semidirect |
| 15. C4⋊C8×C41 | C22 | semidirect |
| 19. C4×C8×C41 | C22 | semidirect |
| 49. D4×C41 | M16 | semidirect |
| 80. #1490 | C41 | direct (N × H) |
| 87. #432 | C2×C41 | semidirect |
| 88. C4×M16 | C2×C41 | semidirect |
| 89. D4⋊C8 | C2×C41 | semidirect |
| 90. C41 | #1490 | direct (N × H) |
| 101. C4⋊C8 | C22×C41 | semidirect |
| 105. C4×C8 | C22×C41 | semidirect |
| 135. D4 | M16×C41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D4×C41 | 2 |
| C41×#432 | 2 |
| C4×M16×C41 | 2 |
| C41×D4⋊C8 | 2 |
| #1490 | 41 |