Centriole is responsible for carrying out cell division but in neurons, centrioles are absent so they do not divide.

Why Neurons are the largest cells but do not undergo cell division?
Neurons are the largest cells in the human body, with complex structures that allow them to transmit electrical and chemical signals throughout the body. Despite their size and importance in the nervous system, neurons do not undergo cell division. There are several reasons for this:
Specialized function:
Neurons are highly specialized cells that have specific functions in transmitting information. Cell division could disrupt the intricate connections and structures that allow neurons to carry out their roles effectively.
Limited regenerative capacity:
Unlike other cells in the body that can divide and regenerate, neurons have limited regenerative capacity. Once neurons are damaged or lost, they are not easily replaced through cell division.
Post-mitotic state:
Neurons are in a post-mitotic state, meaning they have exited the cell cycle and no longer have the ability to divide. This state is necessary for the long-term stability and function of neurons in the nervous system.
Unique structure:
Neurons have a complex structure that includes long extensions called dendrites and axons. These structures are essential for transmitting signals over long distances and cannot be easily replicated through cell division.
Role of glial cells:
Instead of undergoing cell division, neurons rely on support cells called glial cells to maintain their health and function. Glial cells provide structural support, insulation, and nutrients to neurons, helping them carry out their functions effectively.
In conclusion, while neurons are the largest cells in the body, they do not undergo cell division due to their specialized function, limited regenerative capacity, post-mitotic state, unique structure, and reliance on glial cells for support.