Subgroup Lattices of Groups of Small Order

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The subgroup lattice of a group is the Hasse diagram of the subgroups under the partial ordering of set inclusion. This Demonstration displays the subgroup lattice for each of the groups (up to isomorphism) of orders 2 through 12. You can highlight the cyclic subgroups, the normal subgroups, or the center of the group. Moving the cursor over a subgroup displays a description of the subgroup.
Contributed by: Marc Brodie (August 2012)
(Wheeling Jesuit University)
Open content licensed under CC BY-NC-SA
Snapshots
Details
A subgroup of a group
is normal in
if
for all elements
in
. The center
of a group
is the normal subgroup consisting of those elements in
that commute with all elements in
. A group
is Abelian iff
.
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