Finite Group DatabasebetaFinite Group DatabasebetaOrder 35584.
3598 conjugacy classes of subgroups.
The subgroup lattice has 156 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C139 | C24 |
| commutator | C2 | C23×C42×C139 |
| Frattini, cosocle | C23 | C25×C139 |
| socle | C23×C139 | C25 |
| prime radical | C22×#41×C139 | C22 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C139 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #2276×C139 | C2 | semidirect |
| 3. #2275×C139 | C2 | semidirect |
| 4. C4×#117×C139 | C2 | semidirect |
| 5. C2×#376×C139 | C2 | semidirect |
| 7. C4×#41×C139 | C4 | semidirect |
| 24. C4×Q8×C139 | C2×C4 | semidirect |
| 25. C4×D4×C139 | C2×C4 | semidirect |
| 26. #117×C139 | C2×C4 | semidirect |
| 29. C2×C42×C139 | C2×C4 | semidirect |
| 37. #41×C139 | C42 | semidirect |
| 77. #33999 | C139 | direct (N × H) |
| 78. C139 | #33999 | direct (N × H) |
| 80. #2276 | C2×C139 | semidirect |
| 81. #2275 | C2×C139 | semidirect |
| 82. C4×#117 | C2×C139 | semidirect |
| 83. C2×#376 | C2×C139 | semidirect |
| 85. C4×#41 | C4×C139 | semidirect |
| 102. C4×Q8 | C2×C4×C139 | semidirect |
| 103. C4×D4 | C2×C4×C139 | semidirect |
| 104. #117 | C2×C4×C139 | semidirect |
| 107. C2×C42 | C2×C4×C139 | semidirect |
| 115. #41 | C42×C139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#41×C139 | 2 |
| #2276×C139 | 2 |
| #2275×C139 | 2 |
| C4×#117×C139 | 2 |
| C2×#376×C139 | 2 |
| #33999 | 139 |