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Samir Rahamtalla
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To remove the spikes press Space search for "remove doubles" thenhit F6 to open the setting popover and adjust the merge distance to something like 0.03 to merge vertices that are very close to each other. That should take core of the spikes

Your main problem is that the overall topology of your mesh is not ideal for subdivision. For clean subdivision your model should be predominantly quads.

There is a good article on different types of modeling by Gleb Alexandrov that you can view Here

Samir Rahamtalla
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