The fractional quantum Hall effect1–4 (FQHE) in an electron gas with multiple internal degrees of freedom provides a model system to study the interplay between symmetry breaking and emergent topological order5. In graphene, the structure of the honeycomb lattice endows the electron wave functions with an additional quantum number, termed valley isospin, which, combined with the usual electron spin, yields fourfold degenerate Landau levels (LLs; refs 6,7). This additional symmetry modifies the FQHE and is conjectured to produce new incompressible ground states in graphene8–17. Here we report multiterminal measurements of the FQHE in high mobility graphene devices fabricated on hexagonal boron nitride substrates18. The measured energy gaps are large, particularly in the second Landau level, where they are up to 10 times larger than those reported in the cleanest conventional systems. In the lowest Landau level the hierarchy of FQH states reflects the additional valley degeneracy.