Peter, William was the son of John Bogan. William had several brothers and sisters but I don't know all of them. John Bogan came from South Carolina from a family who first settled in Pennsylvania, then moved to South Carolina.
William named his only son, John Washington Bogan. Some say William's father was named John Robert Bogan. I have not been able to find out about the "Robert" though, I have only found John L. Bogan on census records and just plain John.
John married in SC or NC and moved to Alabama by 1850 then to Arkansas later by 1862 where he raised his family and where William settled also.
The known brothers of William are George, Samuel and John (Jr. I guess) with sisters Anganetta (Nettie), Martha, Nancy and others whose names we don't know.
Where is the Plymouth you are talking about? Do you mean the east coast Plymouth?
Please write back soon. I'd love to find someone researching the same family lines. Carole