**Core Concept**
Recurrent infections with encapsulated bacteria in a child are indicative of a specific immunodeficiency involving the complement system and antibody response. This condition is related to the subclass of IgG antibodies, which play a crucial role in providing long-term immunity against encapsulated bacteria.

**Why the Correct Answer is Right**
The correct subclass of IgG associated with this condition is IgG2. IgG2 is primarily responsible for providing immunity against encapsulated bacteria such as Streptococcus pneumoniae and Haemophilus influenzae type b. This subclass of IgG is crucial for the opsonization and clearance of these bacteria from the bloodstream. The deficiency of IgG2 leads to an increased susceptibility to infections with these encapsulated bacteria. IgG2 antibodies also activate the complement system, which further enhances the clearance of these pathogens.

**Why Each Wrong Option is Incorrect**
**Option A:** IgG1 is the most abundant subclass of IgG and plays a crucial role in providing immunity against a wide range of pathogens, including viruses and intracellular bacteria. However, it is not specifically associated with immunity against encapsulated bacteria.

**Option B:** IgG4 is involved in the regulation of immune responses and is not primarily associated with the clearance of encapsulated bacteria.

**Option C:** IgG3 is also involved in the clearance of pathogens but is not specifically associated with immunity against encapsulated bacteria.

**Clinical Pearl / High-Yield Fact**
The key to diagnosing IgG2 deficiency is to identify recurrent infections with encapsulated bacteria, particularly in children. This condition can be challenging to diagnose, and a high index of suspicion is required.

**Correct Answer:** C.