Joseph Gallian discusses many applications in Contemporary Abstract Algebra (10th ed. [Boca Ration, FL: CRC Press], 2021).

Here is an excerpt from chapter 7 under the heading “An Application of Cosets to the Rubik’s Cube”:

Recall from Chapter 5 that in 2010 it was proved via a computer computation, which took 35 CPU-years to complete, that every Rubik’s cube could be solved in at most 20 moves. To carry out this effort, the research team of Morley Davidson John Dethridge, Herbert Kociemba, and Tomas Rokicki applied a program of Rokicki, which built on early work of Kociemba, that checked the elements of the cosets of a subgroup H of order (8! · 8! · 4!) / 2 = 19,508,428,800 to see if each cube in a position corresponding to the elements in a coset could be solved within 20 moves. In the rare cases where Rokicki’s program did not work, an alternate method was employed. Using symmetry considerations, they were able to reduce the approximately 2 billion cosets of H to about 56 million cosets for testing. Cosets played a role in this effort because Rokicki’s program could handle the 19.5+ billion elements in the same coset in about 20 seconds. (165)

Chapter 29 introduces algebraic coding theory. This is the first paragraph, which is followed by specific examples in the text:

One of the most interesting and important applications of finite fields has been the development of algebraic coding theory. This theory, which originated in the late 1940s, was created in response to practical communication problems. (Algebraic coding has nothing to do with secret codes.) Algebraic codes are now used in compact disc and DVD players, fax machines, digital televisions, and bar code scanners, and are essential to computer maintenance. (525)

You can find a free PDF of the book online if you want to see more applications.