The 11th Chord is not as common as 7th and 9th chords, but it can create a nice sound in many styles like folk music, jazz and pop. The short story of theory is that the 11th chord is formed by adding the 11th note in the scale to a dominant ninth chord. In the case of C11 chord, the notes including C, E, G, Bb, D and F.
None for the moment in this category
There are also major and minor 11th chords for guitar. The abbreviations for these are maj11 (e.g. Cmaj11) and m11 (e.g. Cm11). In this case, the short abbreviations 11 mean it is an expanded dominant chord.
Alternative chord shapes
Besides the chord illustrated above there is like always other ways to form a specific chord. The 11th chord can also be played as a barre chord with this shape:
In this chord shape, the root is there you hold you index finger (the lowest note).