Is S = {0,4,8,12,16,24} a subring of Z₂₈ and is φ(x) = 8x mod 28 an isomorphism with Z₇?

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Show that the set S = { 0, 4, 8, 12, 16, 24} is a subring of Z subscript 28. Then prove that the map Ø: Z subscript 7 → S given by Ø(x) = 8x mod 28 is an isomorphism
 
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You need to show what you've tried before getting help.
 
dash: The usual definition of the word "ring" requires it to have a multiplicative identity. Are you using the usual definition? Or are you using an alternate definition that doesn't make such a requirement?

It doesn't really matter for what you're actually trying to do -- but if you are using the usual definition of ring, then the subset {0, 4, 8, 12, 16, 24} of Z / 28 is a ring, but not a subring of Z / 28.