Some of his support in political matters came from family members. His mother's brother, Walter, was one of William's protectors during his minority. His half-sister, Adelaide (by a different mistress of Robert's), was married to Enguerrand II, Count of Ponthieu, giving William a powerful ally in upper Normandy (for a time: there were questions of legitimacy of the marriage that became too complex a story for right now). Of course his great-uncle Robert, Archbishop of Rouen, was a powerful support, though only for a couple years until his death.
After his father's death, his mother Herleva married Herluin de Conteville; he was a minor landowner on the banks of the Seine, and the title probably came to him from William after marrying Herleva. They had two sons, Odo and Robert. Odo became Bishop of Bayeux (and was involved in various matters here and here and here) and was one of William's most loyal and relied-upon supporters as well as one of the individuals specifically portrayed on the Bayeux Tapestry (he probably commissioned it). William's other half-brother, Robert of Mortain, was also one of the few individuals known to fight at the Battle of Hastings. In the Domesday Book, he is listed as one of the greatest landholders with 797 manors in his name. All this despite William of Malmesbury's description of him as a man crassi et hebetis ingenii ("of stupid & dull disposition"). (The illustration above shows William on the Bayeux Tapestry, flanked by Odo gesturing and Robert with a sword.)
William had some second cousins, descended from Gunnor, his great-grandfather's mistress/second wife. The three—William fitzOsbern, Roger de Beaumont, and Roger of Montgomery—became such powerful landowners in England and advisors to William that the speculation by Orderic Vitalis that William in his perilous minority was "hidden" among peasants to keep him safe from enemies may have arisen from his absence from court because he was with these distant cousins for safety. He certainly felt close to them and rewarded them greatly once he took over England.
Of course, the most important relative in one's life is one's spouse. William found his spouse in Matilda of Flanders, daughter of Baldwin V with whom William's father had a bit of a clash. Clearly that conflict was over with, but there were more issues with the union, issues that did not prevent the marriage. Let's look at William and Matilda tomorrow.