  We classify subsystem symmetry-protected topological (SSPT) phases in $3+1$D
protected by planar subsystem symmetries, which are dual to abelian fracton
topological orders. We distinguish between weak SSPTs, which can be constructed
by stacking $2+1$D SPTs, and strong SSPTs, which cannot. We identify signatures
of strong phases, and show by explicit construction that such phases exist. A
classification of strong phases is presented for an arbitrary finite abelian
group. Finally, we show that fracton orders realizable via $p$-string
condensation are dual to weak SSPTs, while strong SSPTs do not admit such a
realization.
