Hitomezashi sashiko is garnering increased attention in the mathematics community. This Japanese-style of em- broidery is as beautiful as it is mathematical—certain hitomezashi patterns can be encoded by two binary strings. In this paper, we define generalized hitomezashi patterns as those that can be generated by two binary strings. We provide properties on the generating binary strings that will produce symmetries in the resulting design and use these properties to prove which wallpaper groups are possible symmetry groups for periodic generalized hitomezashi patterns.