At the most abstract level, you can observe patterns in a model's activations and theorize that particular collections of components contribute to particular kinds of operations. There are many flavors of this intuition. In that sense, you can think of there being "submodels" within a model, insofar as different parts of the network can participate in specialized computations. Some reading that might interest you in this area would include things like mechanistic interpretability.
There are also Mixture of Expert models, which are a dominant architecture for LLMs now, in which you essentially have a bunch of smaller FFNs that get routed over/aggregated together when the LLM performs a forward pass. It would be a mistake to treat any single expert as a better task specific model though. They are trained as part of an ensemble, and they're almost always being combined with other experts in the forward pass, so they're more like (to use a loose analogy) regions of the brain that tend to correspond more towards particular actions than others. You couldn't just extract one and say "This is now our Chess model that performs as well as the larger LLM we took it from". You could potentially use the relevant experts as a basis for training a smaller task-specific model, and there is work around expert pruning and other distillation techniques, but it's not as simple as "This smaller inner model is a complete task-specific model as is". And more importantly, that ensemble of experts *is* the LLM you're comparing it to, at least in major part. It doesn't really make sense to treat the LLM as some foreign model that calls the expert. The experts themselves don't often correlate to easily interpretable task domains, as they've been learned via joint computation with the other experts and broader LLM.
Then there's tool calling. Today LLMs are trained to make tool calls (basically execute functions) for particular tasks. Those tools can be smaller specialized models, or deterministic code, or anything really that can be fired from a host environment.