It looks like a cattail - Typha latifolia. - They will grow without being in water if the soil is moist enough.

and the leaves of Typha feel spongy if you squeeze them,

on a cross section off a leaf you should see two or three rows of somewhat airy cells

Seems to be quite a wet patch given the rushes in the second picture.

Ok would it be too late to dig them up and divide them and plant in an even boggier section of my yard? Will that kill it?