The self-organization of strongly interacting electrons into superlattice
structures underlies the properties of many quantum materials. How these
electrons arrange within the superlattice dictates what symmetries are broken
and what ground states are stabilized. Here we show that cryogenic scanning
transmission electron microscopy enables direct mapping of local symmetries and
order at the intra-unit-cell level in the model charge-ordered system
Nd1/2​Sr1/2​MnO3​. In addition to imaging the prototypical
site-centered charge order, we discover the nanoscale coexistence of an exotic
intermediate state which mixes site and bond order and breaks inversion
symmetry. We further show that nonlinear coupling of distinct lattice modes
controls the selection between competing ground states. The results demonstrate
the importance of lattice coupling for understanding and manipulating the
character of electronic self-organization and highlight a novel method for
probing local order in a broad range of strongly correlated systems