Subgroup-conjugating not implies class-preserving

Statement
A subgroup-conjugating automorphism of a group (i.e., an automorphism that sends every subgroup to a conjugate subgroup) need not be class-preserving: it need not send every element to a conjugate element.

Stronger facts

 * Universal power not implies class-preserving
 * Universal power not implies IA
 * Universal power not implies center-fixing
 * Subgroup-conjugating not implies IA
 * Subgroup-conjugating not implies center-fixing

Weaker facts

 * Normal not implies class-preserving

Converse

 * Class-preserving not implies subgroup-conjugating

Facts used

 * 1) Universal power not implies class-preserving
 * 2) Universal power implies subgroup-conjugating

Proof
The proof follows directly from combining facts (1) and (2).