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, ♭7th, 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).