Is it possible to study the subfield of Computer Programming and Hacking without being very good in Math? Apart from Cryptography and Computer Programming and Hacking - Are there any subfields of Information Security that don't (necessarily) involve Math?
Yes very much, the topic of information security is very broad. From networks, applications, operating systems, to more understandable and easy to grasp topics. Pretty much anything built, used or talked about involves security at some level.
Even if the entire technique behind all the systems is still too much or just plain boring, information security is also risk management. This is a subject withing the information security field closely related to management, governance and compliance.
Math is only part of the deal when you choose it to be. If you don't like it, avoid it. I would even argue you can be good/knowledgeable at crypto without understanding the deep mathematical material under the hood.
Sure, there is plenty of work to be done in the security field that does not need strong math skills.
First, math skills are helpful if you want to touch on the following:
Internals of Cryptography. If you want to know how encryption, hashing, signatures, etc works internally then you will need very strong math skills. That said, Many security professionals (and even many programmers / developers working with cryptography) are happy to treat crypto as a black-box; they know what it does and how to use it, but don't need to know how it works.
System / Vulnerability analysis: That is, looking at the proposed design of a piece of software, or a network and trying to find security holes in it. This does not involve math directly, but in my experience, people with advanced degrees in math have been trained to think very systematically, to break things down into classes of inputs, classes of use-cases, etc and very quickly zero in on which class is most likely to yield a vulnerability. In my experience, people without a formal training in math spend much more time doing trial-and-error to arrive at the same result.
(These are off the top of my head, I'm sure there are other examples)
That said, there are many areas of security programming and hacking that require almost no math knowledge. Really, a "security programmer" or "hacker"is someone who knows a particular technology so well that they can find little loopholes to exploit. For example, if you want to hack web pages, learn the HTTP and SQL protocols very well and find some web hacking tools that you like. If you want to hack linux servers, become very familiar with the linux command-line, the linux permission system, etc. If you know these things well enough, you'll start noticing when somebody has been sloppy is setting up a system, leaving you room to hack in. None of that needs very much math skill.