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Another vote for miele cat and dog. It's only bagged, and there are also multiple filters. IIRC, my box of 4 bags come with one engine filter. And there's another box like filter that you should change every year. But it's all worth it because it really really removes that layer of grey fur my cat left on the carpet. I hoover once a week and have to change bag probably every two months.
I had a dyson and it wasn't good enough for my cat. Was great before cat though.