Finite Group DatabasebetaFinite Group DatabasebetaOrder 5248.
596 conjugacy classes of subgroups; only the 216 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 216 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 | C2×C4 | C24×C41 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C41 ◁ C23×C4×C41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×D8×C41 | C2 | semidirect |
| 2. C22×M16×C41 | C2 | semidirect |
| 3. C2×#121×C41 | C2 | semidirect |
| 4. C41×#469 | C2 | direct (N × H) |
| 5. C2×#106×C41 | C2 | semidirect |
| 6. C2×#102×C41 | C2 | semidirect |
| 11. C2×D8×C41 | C22 | semidirect |
| 13. C2×M16×C41 | C22 | semidirect |
| 17. #121×C41 | C22 | semidirect |
| 20. #106×C41 | C22 | semidirect |
| 21. #102×C41 | C22 | semidirect |
| 40. C2×C8×C41 | D4 | semidirect |
| 70. C8×C41 | C2×D4 | semidirect |
| 86. C2×#469 | C41 | direct (N × H) |
| 89. C2×C41 | #469 | direct (N × H) |
| 92. C22×D8 | C2×C41 | semidirect |
| 93. C22×M16 | C2×C41 | semidirect |
| 94. C2×#121 | C2×C41 | semidirect |
| 95. #469 | C2×C41 | direct (N × H) |
| 96. C2×#106 | C2×C41 | semidirect |
| 97. C2×#102 | C2×C41 | semidirect |
| 98. C41 | C2×#469 | direct (N × H) |
| 103. C2×D8 | C22×C41 | semidirect |
| 105. C2×M16 | C22×C41 | semidirect |
| 109. #121 | C22×C41 | semidirect |
| 112. #106 | C22×C41 | semidirect |
| 113. #102 | C22×C41 | semidirect |
| 132. C2×C8 | D4×C41 | semidirect |
| 162. C8 | C2×D4×C41 | semidirect |
| 180. C2 | C41×#469 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D8×C41 | 2 |
| C22×M16×C41 | 2 |
| C2×#121×C41 | 2 |
| C41×#469 | 2 |
| C2×#106×C41 | 2 |
| C2×#102×C41 | 2 |
| C2×#469 | 41 |