Hogan Interactive are an Italian fashion sneaker, released in the late 1990's. A popular model over the last 20 years, these premium sneakers include a small raised insole that boosts your height beyond the normal range of height most sneakers or shoes tend to provide.
In terms of thickness, I measured the Interactives to give 5.1cm, or a good 2 inches of height. That's a solid 1-1.25 inches more than your average sneaker gives. Whilst the model isn't designed as an elevator shoe, it provides enough of a boost to make it a comfortable alternative and is one of the thickest sneakers on the market.