Actually, taking into account that the common clarinet is a Bb instrument and the soprano recorder is (I think) a C instrument, the fingerings for the clarinet and the recorder are identical for the notes of the same name, though not the same actual tones. You just have to keep the octave valve on the clarinet pressed, then the fingerings are otherwise the same up to B. Ten fingers for C, release one at a time...

(I play the clarinet as well. Couldn't get a note out of a flute if it killed me, though)

XWA