Every fingering that fits a hand
100x
open
1003
open
1403
easy
1443
moderate
x887
easy
What is true of it
A♭aug is A♭, C and E — 1, 3 and #5 counted from A♭.
The easiest of the 5 fingerings below is 100x: one finger, held at the 1st fret.
2 of them use open strings, which is what makes a shape quiet to change to.
1 string stays silent.
Where its notes are on the neck
The brass dots are A♭, the root. Everything else is a chord tone with its degree printed in it.
With a different note underneath
A♭aug/C
5047
A♭aug/E
x443
An inversion is the same chord with a different note lowest. The name changes to a slash name because the bass is what a listener hears as the foundation.