# gps_subgroup_search downloaded from the LMFDB on 16 April 2026.
# Search link: https://www.lmfdb.org/Groups/Abstract/?search_type=Subgroups&ambient=4.1
# Query "{'ambient': '4.1'}" returned 3 gps_subgroup_searchs, sorted by ambient order.

# Each entry in the following data list has the form:
#    [Label, Subgroup, Ambient, Quotient]
# For more details, see the definitions at the bottom of the file.



"4.1.1.a1.a1"	[["4.1", "C_4"], 4, 2, true, true, false, true, true, true, true, true, true, false, false, true, true, true, true]	[["4.1", "C_4"], 4]	[["1.1", "C_1"], 1, false, true, true, true, true, true, false, true, true]
"4.1.2.a1.a1"	[["2.1", "C_2"], 2, 0, true, true, true, true, true, true, true, true, true, false, true, true, true, true, true]	[["4.1", "C_4"], 4]	[["2.1", "C_2"], 2, true, true, true, true, true, true, true, true, true]
"4.1.4.a1.a1"	[["1.1", "C_1"], 1, 1, true, true, false, true, true, true, true, true, true, true, false, true, true, true, true]	[["4.1", "C_4"], 4]	[["4.1", "C_4"], 4, false, true, true, true, true, true, false, true, true]


# Label --
#    The full label of a subgroup is of the form $\mathtt{N.i.m.a}$ or $\mathtt{N.i.m.a.j}$.  In either case, $\mathtt{N.i}$ is the label of the ambient group, $\mathtt{m}$ is the index of the subgroup in the ambient group, $\mathtt{a}$ distinguishes subgroups up to automorphism and $\mathtt{j}$ distinguishes subgroups up to conjugacy.  Both $\mathtt{a}$ and $\mathtt{j}$ take the form of a sequence of letters followed by an ordinal. The letters are a base 26 (a=0, z=25) encoding of the ordering up to Gassmann-equivalence, and the integer following distinguishes groups in the same Gassmann class.  (For details on how we label Gassmann classes and order subgroups within a Gassmann class, see Computing labels of subgroups.) For some ambient groups, we only compute subgroups up to automorphism (in which case the first form is used, omitting the $\mathtt{j}$.

#    When the ambient group is clear from context, sometimes the short label $\mathtt{m.a}$ or $\mathtt{m.a.j}$ is used instead.