Finite Group DatabasebetaFinite Group DatabasebetaOrder 5248.
436 conjugacy classes of subgroups; only the 188 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 188 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 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C41 ◁ C2×C42×C41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C41×#532 | C2 | semidirect |
| 2. C41×#474 | C2 | semidirect |
| 3. C41×#466 | C2 | semidirect |
| 4. C41×#459 | C2 | semidirect |
| 5. C2×C4⋊C8×C41 | C2 | semidirect |
| 52. C2×C4×C41 | D8 | semidirect |
| 71. #3245 | C41 | direct (N × H) |
| 77. #532 | C2×C41 | semidirect |
| 78. #474 | C2×C41 | semidirect |
| 79. #466 | C2×C41 | semidirect |
| 80. #459 | C2×C41 | semidirect |
| 81. C2×C4⋊C8 | C2×C41 | semidirect |
| 82. C41 | #3245 | direct (N × H) |
| 129. C2×C4 | D8×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×#474 | 2 |
| C41×#466 | 2 |
| C41×#459 | 2 |
| C2×C4⋊C8×C41 | 2 |
| #3245 | 41 |