Reddit mentions of HomeDone Drywall Anchor 50-Pack - 2 Different Sizes, Self-Drilling with Screws

Go to the local hardware store and get a larger screw in anchor, like these: Drywall Anchor.

They come in different sizes, get one slightly larger than the hole.

Alternatively you can use a toggle bolt.

Homedone Drywall Anchor 50-Pack - 2 Different Sizes, Self-Drilling with Screws https://www.amazon.com/dp/B01KVU4Z68/ref=cm_sw_r_cp_api_8PrxzbGDEQ8MP

I've used these with good results only downside is the huge hole they leave if you remove them.

They make smaller ones but I can't find them on Amazon that are rated for the 50 lbs and take a 7/32" drill bit to install.

I'd recommend just going to the hardware store they have a huge selection typically.

I agree with /u/niceflipflop that a couple of scale pics would be nice, but at a glance I'd definitely say you've got plaster walls. First thing's first, do you own or rent? That's going to make a big difference as to what advice I give as I've both owned and rented places with plaster walls.

If you rent, leave them the hell alone. Hell hath no fury like a rapidly deteriorating plaster wall and being a landlord myself who does all my own drywall/plaster you'll probably get charged a lot of money for those repairs. Stick to tape or 3M command strips and call it a day.

If you own the place, do yourself a favor and invest in a quality hammer drill. I bought a Dewalt because I knew I was going to abuse it, but for someone who is going to use it a few times a year, the model I linked will do fine. Some argue that you don't need a hammer drill to put a hole in masonry and they're wrong. Plus, it doubles as a standard, high power corded drill which is also an indispensable tool.

For interior (read: not masonry backed) walls, I've had good luck with these. They're low weight (~50 pounds or so) but great because you can avoid drilling and causing a mess like you have on your hands now. I never tried it, but I've heard putting a sturdy tape like duct tape can help prevent tear out as well. They also penetrate the slats and studs if you happen to hit one. This type of toggle fastener technically works, but I don't like them for plaster because of the size of hole you need to drill for them which generally causes more problems than it solves (1/2", if I remember). Definitely don't use anything like these as they'll just shred your plaster.

For exterior, structural, masonry walls, you need masonry screws and the 3/16" masonry bit to go with the 1/4" screws. If you have a hardware store near you, chances are they'll have them in packs far less than 100 and many stores sells Tapcons which often come with a bit included.

It seems daunting at first, drilling into a concrete/brick wall (I cut away an entire section to install a door. shudder) but once you get used to it it's just like mounting to any other wall surface. The thing you have to understand is just how thick your plaster is and subsequently how many threads you need to have inserted into the masonry to make it safe. Take this cross section for instance. If we look at the deepest your cabinet back is likely to be (.5") and add 1.5" for the plaster thickness that means the fastener has to penetrate 2" of material before it even hits the wall. The general rule is that for every length of fastener you have outside the functional threaded surface (the masonry wall), you need to have the same length of threads inside i.e. "A" has to equal "A". So, in this example, if you have 2" of material (.5" cabinet back and 1.5" plaster) you'd need ~4" masonry screws to safely hold your cabinet in place. For something as relatively light duty as a coat rack you could probably get away with 3.5" or so, but anything less and you're risking the fastener simply pulling out of the masonry walls, especially if your home is brick as the interior bricks are far softer than the exterior. Also I realize that not everyone is as tool hungry as I am, but an impact driver drives fasteners into masonry far better than a standard drill. You're more likely to strip them using a standard drill and frankly I use my impact more often than I do my drill, but we gutted our entire place so I understand not everyone wants a pile of tools.