Finite Group DatabasebetaFinite Group DatabasebetaOrder 5248.
378 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 168 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 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C41 |
| prime radical | C2×#41×C41 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C41 ◁ C2×#41×C41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C41×#485 | C2 | semidirect |
| 3. C41×#470 | C2 | semidirect |
| 4. C41×#467 | C2 | semidirect |
| 5. C41×#451 | C2 | semidirect |
| 81. #3202 | C41 | direct (N × H) |
| 87. #485 | C2×C41 | semidirect |
| 88. #470 | C2×C41 | semidirect |
| 89. #467 | C2×C41 | semidirect |
| 90. #451 | C2×C41 | semidirect |
| 92. C41 | #3202 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C41×#536 | 2 |
| C41×#485 | 2 |
| C41×#470 | 2 |
| C41×#467 | 2 |
| C41×#451 | 2 |
| C41×#408 | 2 |
| #3202 | 41 |