At the cathedral, bricks tend to be in a cmm pattern. Otherwise, the p4m symmetry group is ubiquitous. There are a good number of cm patterns. All of the rest are fairly hard to find.
pmSanctuary Dome.Patterns with pm symmetry cannot be rotated, and have reflection lines. 

cmNarthex, wall.Patterns with cm symmetry cannot be rotated, and have parallel reflection lines and glide reflection lines (giving a "staggered" look). 

cmAll Souls, window. Look carefully  it cannot be rotated. 

p2Narthex, wrapped around lamppost.Also visible is a nice cm pattern on the radiator grille. This p2 pattern is a stretch, but the only example I've found. 

pmmFrom outside, East wall.A pattern with pmm symmetry has only 180 degree rotations, with horizontal and vertical mirrors and no glide reflections. 

cmmAll Souls, floor. 

p4Central Dome, altar partition.A pattern with p4 symmetry can be turned 90 degrees, and has no reflection symmetry. This is the only example of p4 I've found at the Cathedral. 

p4gBlessed Virgin's Chapel, floor.A pattern with p4g symmetry can be turned 90 degrees, and has reflection symmetry horizontally and vertically. This is the only example of p4g I've found at the Cathedral, and it needs the color to count. 

p4mFront doorp4m symmetry is characterized by reflection symmetry in horizontal, vertical, and both 45degree diagonal directions. 

p4mEast Transept, window. 

p6mBlessed Virgin's Chapel, wall.p6m symmetry can be turned 1/6 of a rotation, and often looks like hexagons. I know only four examples of p6m symmetry at the cathedral (go and find the others!). 

p6mSanctuary Dome, latticework 