H-4 child of a domiciled H-1B parent Yes — by published rule
Published eligible list: PR/asylee/refugee or A, E, G, H, I, L, O, P, R, TC, TD, TN visa (unqualified H covers H-1B and H-4). B, F, J, M ineligible unless dependent of a qualifying supporting person. Burden: clear and convincing.