Lattices of Subgroups and Graph In Dummit and Foote´s Abstract Algebra, when talking about the lattice of subgroups of $A_4$, the authors make the statement that, unlike virtaully all groups, $A_4$ has a planar lattice? My question is

What do they mean when they say virtually all groups? Is there a reference for this statement?

On a somewhat different note, are there classes of graphs which can be realized as the subgroup lattice of some group?

Starr–Turner (2004) classifies abelian groups with planar subgroup lattices, and Schmidt (2006) and Bohanon–Reid (2006) complete the classification.  Dummit–Foote made this claim prior to this work, so it may have just been the observation that fairly small groups have non-planar lattices, so that it would intuitively be pretty hard for a large group to have a planar lattice.


*

*Starr, Colin L.; Turner, Galen E., III.
"Planar groups."
J. Algebraic Combin. 19 (2004), no. 3, 283–295.
MR2071475
DOI:10.1023/B:JACO.0000030704.77583.7b

*Schmidt, Roland.
"Planar subgroup lattices."
Algebra Universalis 55 (2006), no. 1, 3–12.
MR2217274
DOI:10.1007/s00012-006-1964-2

*Bohanon, Joseph P.; Reid, Les.
"Finite groups with planar subgroup lattices."
J. Algebraic Combin. 23 (2006), no. 3, 207–223.
MR2228925
DOI:10.1007/s10801-006-7392-8
James Wilson's catalog of groups by lattice (from 2004-2005) is mostly in tact at his new webpage.
