Finite Group DatabasebetaFinite Group DatabasebetaOrder 5248.
668 conjugacy classes of subgroups; only the 232 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 232 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 ◁ C2×C42×C41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×SD16×C41 | C2 | semidirect |
| 2. C22×D8×C41 | C2 | semidirect |
| 3. C2×#127×C41 | C2 | semidirect |
| 4. C2×#124×C41 | C2 | semidirect |
| 5. C41×#496 | C2 | direct (N × H) |
| 6. C2×#97×C41 | C2 | semidirect |
| 12. C2×SD16×C41 | C22 | semidirect |
| 14. C2×D8×C41 | C22 | semidirect |
| 17. #127×C41 | C22 | semidirect |
| 19. #124×C41 | C22 | semidirect |
| 22. #97×C41 | C22 | semidirect |
| 42. C2×C8×C41 | D4 | semidirect |
| 69. C8×C41 | C2×D4 | semidirect |
| 83. C2×#496 | C41 | direct (N × H) |
| 86. C2×C41 | #496 | direct (N × H) |
| 89. C22×SD16 | C2×C41 | semidirect |
| 90. C22×D8 | C2×C41 | semidirect |
| 91. C2×#127 | C2×C41 | semidirect |
| 92. C2×#124 | C2×C41 | semidirect |
| 93. #496 | C2×C41 | direct (N × H) |
| 94. C2×#97 | C2×C41 | semidirect |
| 95. C41 | C2×#496 | direct (N × H) |
| 101. C2×SD16 | C22×C41 | semidirect |
| 103. C2×D8 | C22×C41 | semidirect |
| 106. #127 | C22×C41 | semidirect |
| 108. #124 | C22×C41 | semidirect |
| 111. #97 | C22×C41 | semidirect |
| 131. C2×C8 | D4×C41 | semidirect |
| 158. C8 | C2×D4×C41 | semidirect |
| 174. C2 | C41×#496 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×SD16×C41 | 2 |
| C22×D8×C41 | 2 |
| C2×#127×C41 | 2 |
| C2×#124×C41 | 2 |
| C41×#496 | 2 |
| C2×#97×C41 | 2 |
| C2×#496 | 41 |