Every fingering that fits a hand
x002
open · no 5
5002
easy · no 5
5402
easy · no 5
5432
moderate
5777
moderate
What is true of it
Cmaj7 is C, E, G and B — 1, 3, 5 and 7 counted from C.
On an instrument that cannot reach all 4, the 5 goes first, in that order.
The easiest of the 5 fingerings below is x002: one finger, held at the 2nd fret.
1 of them use open strings, which is what makes a shape quiet to change to.
It leaves out the 5. 4 strings cannot carry 4 notes, and the 5 is the one this chord can lose without changing what it is.
1 string stays silent.
Where its notes are on the neck
The brass dots are C, the root. Everything else is a chord tone with its degree printed in it.
With a different note underneath
Cmaj7/E
9b8a
Cmaj7/G
0002
Cmaj7/B
400x
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.