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This family are described in Nicolas as the Parrys of Llwynynn, Llanrhaiadr, and Plas Newydd, (all in Denbighshire) and latterly of Warfield Hall, Berks. The first to take the name Parry was Richard Parry, the Bishop of St Asaph, and son of John ap Harry ap David ap Howel. The quarterings indicate many of the alliances of the family during the sixteenth and seventeenth centuries.
Nicolas lists some of the tribes and noble families represented by the quarterings, but not the families that they applied to at the time of writing (1872). Also he only lists sixteen names, whereas there are twenty-five quarterings. I have not yet been able to identify the correspondence between the names and image but, hopefully, after more research, I shall be able to do so.
Heraldry Index page
It will be noticed that nowhere do the arms "a fesse between three lozenges" appear. This is evidence towards the mis-identification by Meyrick of the portrait at Goodrich Court which, in his notes to Lewis Dwnn's Visitations of Wales, he describes as being of Bishop Richard Parry.
David Parry, son of Humphrey Parry of Pwllalog, Llwynynn, Llanrhaiadr and Plas Newydd, married Catherine Jane Okeden, daughter and heiress of Edmund Okeden of Little Critchell, Dorset. Their son, David Okeden Parry Okeden, assumed the name Okeden in pursuance of his maternal grandfather's Will. The following are the quartered Arms and crest given in Hutchins:

They are described as:
Arms: Quarterly; 1 and 4, Sable on a fess, between six acorns or, three oak leaves vert, Okeden; 2, Argent, a cross moline gules, Uvedale; 3, Gules, on a bend argent a lion passant guardant sable, Parry
Crest: A bear's paw erased sable, grasping an oak branch proper, fructed or, for Okeden; 2. Out of a ducal coronet or a demy lion gules, for Parry.
Motto: Tant que je puis
It will be noticed that the Parry Arms, "Gules, on a bend argent a lion passant guardant sable" appear in the first quartering of the Arms for the Parrys of Llwynynn above.