<p>In this paper, we investigate classification and propagation of nonlinear wave patterns of the defocusing extended complex modified Korteweg–de Vries equation for its Riemann problem based on the Whitham theory. Firstly, the solutions and their corresponding Whitham equations for one, two-genus are obtained by the finite-gap integral approach. Secondly, we analyze the influence of dispersion on wave breaking which occur before the formation of dispersive shock waves (DSWs), by studying the breaking process of a simple wave. The dispersion effect makes the wave breaking behavior more complex, especially at the wave-breaking point existing a cubic root singularity. Compared with the cmKdV equation, the evolution of Riemann invariants in a quartic curve leads to the emergence of various new structures of evolution waves and the structures of Riemann problem solutions are more complex. For the basic wave structure, the rarefaction waves (RWs) are divided into three types with total 10 wave structures, and the DSWs are divided into two types with total 20 wave structures. Finally, we provided the full classification and propagation of Riemann problem solutions based on the basic wave structure with step-like initial values. The distributions and the corresponding situation of the initial data of Riemann invariants of each case are discussed and the propagation paths corresponding to the dynamic behaviors in the hydrodynamic system are taken into consideration. In particular, more two-genus DSW regions described roughly, which are produced from the collision of two one-genus DSWs. It is worth mentioning that there are more than 100 wave patterns in all, which is shocking and has not been described before.</p>