Finite Group DatabasebetaFinite Group DatabasebetaOrder 5248.
360 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 360 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, socle | C23×C41 | C2×D4 |
| commutator, Frattini, cosocle | C22×C4 | C23×C41 |
| prime radical | C22×D8×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×C4⋊C8×C41 | C2 | semidirect |
| 3. C2×#102×C41 | C2 | semidirect |
| 4. C41×#390 | C2 | semidirect |
| 5. C41×#340 | C2 | semidirect |
| 58. C2×C4×C41 | D8 | semidirect |
| 83. #2054 | C41 | direct (N × H) |
| 91. C2×C4⋊C8 | C2×C41 | semidirect |
| 92. C2×#102 | C2×C41 | semidirect |
| 93. #390 | C2×C41 | semidirect |
| 94. #340 | C2×C41 | semidirect |
| 95. C41 | #2054 | direct (N × H) |
| 148. C2×C4 | D8×C41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D8×C41 | 2 |
| C2×C4⋊C8×C41 | 2 |
| C2×#102×C41 | 2 |
| C41×#390 | 2 |
| C41×#340 | 2 |
| #2054 | 41 |