The Collaborative International Dictionary of English v.0.48:

Subdiaconate \Sub`di*ac"o*nate\, a.
   Of or pertaining to a subdeacon, or to the office or rank of
   a subdeacon.
   [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

Subdiaconate \Sub`di*ac"o*nate\, n.
   The office or rank of a subdeacon.
   [1913 Webster]