This is a jukugo word that uses the on'yomi readings of the kanji. You haven't learned this reading for 首 yet, so here's a mnemonic to help you:
When you need a radical to make a new kanji, you just press a button and the radical comes tumbling down the radical chute (しゅ). There's definitely no rhyme or reason to radical picking, it's just whatever pops out of the ol' chute.
What is this kanji’s radical?
Someone who laughs over radicals will eventually cry over radicals.
I remember all of the radicals.