Coideal subalgebras of quantum SL2 at roots of unity

We classify right coideal subalgebras of the finite-dimensional quotient of the quantized enveloping algebra $U_q\left({\mathrm{sl}}_2\right)$ and that of the quantized coordinate algebra $O_q\left(S{L}_2\right)$ at a root of unity q of odd order. All those coideal subalgebras are described by generators and relations.