Finite Group DatabasebetaFinite Group DatabasebetaOrder 5248.
240 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 64 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 | #120 |
| commutator, Frattini, cosocle | C22×C4 | C23×C41 |
| prime radical | C41×#538 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C41 ◁ C22×C4×C41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C41×#484 | C2 | semidirect |
| 3. C41×#481 | C2 | semidirect |
| 4. C41×#399 | C2 | semidirect |
| 5. C41×#328 | C2 | semidirect |
| 6. C41×#327 | C2 | semidirect |
| 7. C41×#323 | C2 | semidirect |
| 107. #1618 | C41 | direct (N × H) |
| 116. #484 | C2×C41 | semidirect |
| 117. #481 | C2×C41 | semidirect |
| 118. #399 | C2×C41 | semidirect |
| 119. #328 | C2×C41 | semidirect |
| 120. #327 | C2×C41 | semidirect |
| 121. #323 | C2×C41 | semidirect |
| 122. C41 | #1618 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C41×#538 | 2 |
| C41×#484 | 2 |
| C41×#481 | 2 |
| C41×#399 | 2 |
| C41×#328 | 2 |
| C41×#327 | 2 |
| C41×#323 | 2 |
| #1618 | 41 |