The structure of the Taurid meteor complex based on photographic orbits available in the IAU Meteor database is studied. We have searched for potential sub-streams or filaments to be associated with the complex utilizing the Southworth-Hawkins D-criterion. Applying a strict limiting value for D=0.10, fifteen sub-streams or filaments, consisting of more than three members, could be separated out from the general complex. To confirm their mutual consistence as filaments, rather than fortuitous clumping at the present time, the orbital evolution over 5000 years of each member is studied. Utilizing the D-criterion we also searched for NEOs that might be associated with the streams and filaments of the complex and investigated the orbital evolution of potential members. Possible associations between 7 Taurid filaments and 9 NEOs were found. The most probable are for S Psc(b) -- 2003QC10, N Tau(a) -- 2004TG10, ο Ori -- 2003UL3 and N Tau(b) -- 2002XM35. Some of the potential parent objects could be either dormant comets or larger boulders moving within the complex. Three of the most populated filaments of the complex may have originated from 2P/Encke.