I would say that DevOps is a peer of Agile, not a child. Agile methods apply largely within software development. DevOps, by contrast, applies the same Lean Manufacturing/Lean IT concepts across the software delivery lifecycle, which begins with the business and ends with business value delivered (code running in Production.)
I believe, after some thought on the subject, that there is also a dependent relationship between Agile and DevOps. DevOps is intensely focused on automation. There is limited benefit in automating a process that executes infrequently. Waterfall development methods are a perfect example of a slow, infrequent process.
Agile methods are focused on maintaining a constant flow of work through Development. This is a perfect, natural fit for DevOps, which keeps that flow going all the way from the business to the end state, which is code running in Production.