Group-subgroup graph

For a given group and supergroup, the program will give the lattice of maximal subgroups that relates these two groups. The group and supergroup can be specified by their space-group numbers, or you can start to type the space-group symbols (using _ before a subscript) and possible options to choose from will be shown. When the index is specified, all of the possible chains of maximal subgroups that relate the two groups are shown. In this case, it is also possible to obtain all of the different subgroups of the same type.

The graph of the maximal subgroups is interactive and you can select one subgroup and see all the chains that go through it.

The index and the transformation that correspond to each step in any chain are provided.

Example of a lattice of maximal subgroups

Supergroup number: 69 F m m m
Subgroup number: 42 F m m 2
See the result

The possible indices can be obtained from the lattice of maximal subgroups. In this example an index of 6 is possible.

Example of a graph of maximal subgroups for a specific index

Supergroup number: 69 F m m m
Subgroup number: 42 F m m 2
Index: 6
See the result