In this work, we study the superregular solitonic solutions of the higher-order nonlinear Schr\”{o}dinger equation (HNLSE) with nonvanishing boundary conditions. Solving the HNLSE with the dressing method, we obtain the explicit form of one-and two-solitonic solutions and discuss them in detail. These solutions can be used to describe the nonlinear stage of the modulation instability (MI) of the condensate. Moreover, we also find some novel features of the nonlinear stage of the MI arising from higher-order effects. This family of novel solutions include Peregrine soliton, Akhmediev breather, Kuznetsov-Ma breather, a symmetrical quasi-Akhmediev breather, coexistence of two symmetrical quasi-Akhmediev breather, coexistence of two nonsymmetrical quasi-Akhmediev breather, coexistence of a quasi-Akhmediev breather and a soliton, a bipolar-freak-wave etc. Finally, the main characteristics of these rational solutions are discussed with some graphics. These solutions would be of much importance in understanding and explaining rogue wave phenomena arising in nonlinear and complex systems.