Support, sustain, prop, bolster, buttress, brace are comparable when they mean to hold up either literally or figuratively, though they vary greatly in their specific senses and in the range of their applicability.
Support suggests the presence of a foundation or base and is applicable in diverse uses with the general meaning or suggestion of carrying from or as if from below, of maintaining or holding up the weight or pressure of, and of forestalling sinking or falling back, or sometimes, merely, of enduring the difficulties or rigors of without yielding and without undue distress.
Sustain may center attention on the fact of constantly holding up or of maintaining undiminished or it may more specifically imply an upholding by aiding or backing up or by supplying the physical or mental nutriments needed for strength.
Prop may imply a weakness, a tendency to fall, sink, or recede, or a need for strengthening or reinforcing on the part of the thing being treated.
Bolster blends the suggestions of sustain and prop ; it may suggest a supporting comparable to that afforded an invalid by pillows.
Buttress tends to suggest strengthening, reinforcing, or stabilizing, sometimes massive, at a stress point in the manner of an architectural buttress.
Brace may suggest supporting or strengthening so that the thing treated is made firm, unyielding, or rigid against pressure.