Yes, it applies to control groups. If I remember correctly common ownership rules are used to determine "Applicable Large Employer" status but if the time comes to owe a penalty, only the actual entity missing the mark will owe a penalty, not the entire control group.
This is an excerpt from Section 4980H (the section that lays out employer requirements and penalties)
(16) Employer. The term employer means the person that is the employer of an employee under the common-law standard. See § 31.3121(d)-1(c). For purposes of determining whether an employer is an applicable large employer, all persons treated as a single employer under section 414(b), (c), (m), or (o) are treated as a single employer. Thus, all employees of a controlled group of entities under section 414(b) or (c), an affiliated service group under section 414(m), or an entity in an arrangement described under section 414(o), are taken into account in determining whether the members of the controlled group or affiliated service group together are an applicable large employer. For purposes of determining applicable large employer status, the term employer also includes a predecessor employer (see paragraph (a)(36) of this section) and a successor employer.
Link to the Federal Register