Finite Group DatabasebetaFinite Group DatabasebetaOrder 5248.
284 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 284 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 | C2×C4×C41 | C22⋊C4 |
| commutator | C2×C4 | C22×C4×C41 |
| Frattini, cosocle | C22×C4 | C23×C41 |
| socle | C22×C41 | C2×C22⋊C4 |
| prime radical | C41×#532 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ 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×#431 | C2 | semidirect |
| 3. C4×C4⋊C4×C41 | C2 | semidirect |
| 4. C41×#327 | C2 | semidirect |
| 6. C4⋊Q8×C41 | C4 | semidirect |
| 7. #127×C41 | C4 | semidirect |
| 12. C4×D4×C41 | C4 | semidirect |
| 83. #1502 | C41 | direct (N × H) |
| 91. #431 | C2×C41 | semidirect |
| 92. C4×C4⋊C4 | C2×C41 | semidirect |
| 93. #327 | C2×C41 | semidirect |
| 94. C41 | #1502 | direct (N × H) |
| 96. C4⋊Q8 | C4×C41 | semidirect |
| 97. #127 | C4×C41 | semidirect |
| 102. C4×D4 | C4×C41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C41×#532 | 2 |
| C41×#431 | 2 |
| C4×C4⋊C4×C41 | 2 |
| C41×#327 | 2 |
| #1502 | 41 |