I cannot reproduce the issue by trying to create a tensor in a similar range:
x = torch.randn(5665, 48, device='cuda', dtype=torch.float16) * 100.
print(x)
with torch.cuda.amp.autocast():
    out = x - x.mean()
print(torch.isnan(out).any())

Output:
tensor([[  68.5000,   57.2188,  -15.8438,  ...,  -59.6562,  -81.4375,
          -58.6562],
        [  48.5938, -110.9375,  112.6250,  ..., -133.3750,   12.9766,
          -29.9062],
        [  -9.2812,  -36.3125,  -98.5000,  ...,  139.5000,  -30.3438,
           59.9062],
        ...,
        [ 114.8750,   89.8125,   23.7500,  ..., -150.6250,  -46.2500,
          -32.7500],
        [  42.2500,  -17.6406,  103.8750,  ...,  -55.9062,   38.0312,
          -62.6875],
        [  53.4688,  187.7500,   44.3125,  ...,  122.9375,   40.6875,
         -123.4375]], device='cuda:0', dtype=torch.float16)
tensor(False, device='cuda:0')