Not sure if there is a consensus prediction program which can predict various supersecondary structures (for example Helix-Turn-Helix, Beta-hairpins etc.) from sequence or structure information. Structure prediction is an area of active area research and various algorithms are available. I would recommend you to make a list of your supersecondary structures of interest and then search for servers/program which could predict such features from sequence information.
Helix-Turn-Helix prediction: http://npsa-pbil.ibcp.fr/cgi-bin/npsa_automat.pl?page=/NPSA/npsa_hth.html
Beta-hair pin prediction: http://www.imtech.res.in/raghava/bhairpred/supli.html
Also refer to Chou K. C's publications and various secondary structure prediction servers from G. P. S. Raghava's group for a good background reading on available supersecondary structure prediction algorithms.