Suspended chords (sus2 and sus4) are part of the major family and are an exception to the rule of never omitting the third. In either a Csus2 or a Csus4, the third is replaced by the second or fourth, respectively, however, the root, fifth, and any other intervals remain unchanged. Hence a Csus2 contains R, 2, P5 (C-D-G); and a Csus4 would contain R, 4, P5 (C-F-G). You can also combine a suspended second with a suspended fourth (ex. Csus2sus4 – C-D-F- G).
Suspended chords are also used in conjunction with other chord formations like sixth and seventh or even extensions, such as the ninth, eleventh, and thirteenth (ex. G7sus4 – G-C-D-F or C13sus2 – C-D-G-A). If there is no number following the sus notation, it’s assumed to be a suspended fourth.
7sus chords contain the root, fourth, fifth, flat seventh, and ninth intervals, substituting the third for the fourth (1st, 4th, 5th, b7 th, 9th). These chords may also contain a suspended second in tandem with the suspended fourth, in which case the ninth interval wouldn’t necessarily appear (since the second and ninth intervals are essentially the same note).