# gps_subgroup_search downloaded from the LMFDB on 23 July 2026.
# Search link: https://www.lmfdb.org/Groups/Abstract/Subgroups?subgroup=1296.3499
# Query "{'subgroup': '1296.3499'}" returned 354 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.



"1296.3499.1.a1.a1"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, true, true, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296]	[["1.1", "C_1"], 1, false, true, true, true, true, true, false, true, true]
"2592.fo.2.e1.a1"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, true, false, true, false, false, false, false, false, true, false, false, false, false, false, false]	[["2592.fo", "S_3^2:\\PSU(3,2)"], 2592]	[["2.1", "C_2"], 2, false, true, true, true, true, true, true, true, true]
"2592.fo.2.e1.b1"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, true, false, true, false, false, false, false, false, true, false, false, false, false, false, false]	[["2592.fo", "S_3^2:\\PSU(3,2)"], 2592]	[["2.1", "C_2"], 2, false, true, true, true, true, true, true, true, true]
"2592.lt.2.a1.a1"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, true, false, true, false, false, false, false, false, true, false, false, false, false, false, false]	[["2592.lt", "C_3^2\\wr C_2.\\SD_{16}"], 2592]	[["2.1", "C_2"], 2, false, true, true, true, true, true, true, true, true]
"2592.lt.2.a1.b1"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, true, false, true, false, false, false, false, false, true, false, false, false, false, false, false]	[["2592.lt", "C_3^2\\wr C_2.\\SD_{16}"], 2592]	[["2.1", "C_2"], 2, false, true, true, true, true, true, true, true, true]
"2592.pp.2.d1.a1"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, true, false, true, false, false, false, false, false, true, false, false, false, false, false, false]	[["2592.pp", "C_3^3:C_{12}:Q_8"], 2592]	[["2.1", "C_2"], 2, false, true, true, true, true, true, true, true, true]
"2592.pp.2.d1.b1"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, true, false, true, false, false, false, false, false, true, false, false, false, false, false, false]	[["2592.pp", "C_3^3:C_{12}:Q_8"], 2592]	[["2.1", "C_2"], 2, false, true, true, true, true, true, true, true, true]
"5184.cd.4.e1.a1"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["5184.cd", "C_3^4:D_8:C_4"], 5184]	[[NULL, NULL], 4, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"5184.ce.4.c1.a1"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["5184.ce", "C_3^4:C_{16}:C_4"], 5184]	[[NULL, NULL], 4, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"5184.gk.4.n1.a1"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["5184.gk", "(C_3^2\\times S_3^2):\\SD_{16}"], 5184]	[[NULL, NULL], 4, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"5184.qs.4.i1"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, true, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["5184.qs", "C_3^4:(D_4\\times Q_8)"], 5184]	[["4.2", "C_2^2"], 4, false, false, true, true, true, true, false, true, true]
"5184.sy.4.i1.a1"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["5184.sy", "C_3^3:C_{12}:\\SD_{16}"], 5184]	[[NULL, NULL], 4, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"5184.sz.4.i1.a1"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["5184.sz", "F_9:\\SOPlus(4,2)"], 5184]	[[NULL, NULL], 4, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"5184.ta.4.m1.a1"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["5184.ta", "F_9:\\SOPlus(4,2)"], 5184]	[[NULL, NULL], 4, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"6480.bm.5.a1.a1"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, true, false, false, false, false, false, true, false, false, false, false, false, false]	[["6480.bm", "C_3^4:C_{20}:C_4"], 6480]	[[NULL, NULL], 5, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"10368.bn.8.h1.a1"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["10368.bn", "C_3^4:D_8:Q_8"], 10368]	[[NULL, NULL], 8, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"10368.bn.8.h1.b1"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["10368.bn", "C_3^4:D_8:Q_8"], 10368]	[[NULL, NULL], 8, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"10368.ov.8.q1.a1"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["10368.ov", "C_3^4:\\OD_{32}:C_2^2"], 10368]	[[NULL, NULL], 8, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"10368.ov.8.q1.b1"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["10368.ov", "C_3^4:\\OD_{32}:C_2^2"], 10368]	[[NULL, NULL], 8, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"10368.ov.8.r1.a1"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["10368.ov", "C_3^4:\\OD_{32}:C_2^2"], 10368]	[[NULL, NULL], 8, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"10368.ow.8.m1.a1"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["10368.ow", "C_3^4:\\OD_{32}:C_4"], 10368]	[[NULL, NULL], 8, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"10368.ow.8.m1.b1"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["10368.ow", "C_3^4:\\OD_{32}:C_4"], 10368]	[[NULL, NULL], 8, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"10368.ow.8.n1.a1"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["10368.ow", "C_3^4:\\OD_{32}:C_4"], 10368]	[[NULL, NULL], 8, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"10368.ox.8.j1.a1"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["10368.ox", "C_3^2:F_9.C_4^2"], 10368]	[[NULL, NULL], 8, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"10368.ox.8.j1.b1"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["10368.ox", "C_3^2:F_9.C_4^2"], 10368]	[[NULL, NULL], 8, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"10368.ox.8.k1.a1"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["10368.ox", "C_3^2:F_9.C_4^2"], 10368]	[[NULL, NULL], 8, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"10368.oy.8.k1.a1"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["10368.oy", "C_3^4:\\OD_{32}:C_4"], 10368]	[[NULL, NULL], 8, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"10368.oy.8.k1.b1"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["10368.oy", "C_3^4:\\OD_{32}:C_4"], 10368]	[[NULL, NULL], 8, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"10368.oy.8.m1.a1"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["10368.oy", "C_3^4:\\OD_{32}:C_4"], 10368]	[[NULL, NULL], 8, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"10368.qo.8.bq1"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["10368.qo", "\\SOPlus(4,2)^2.C_2"], 10368]	[[NULL, NULL], 8, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"10368.qo.8.br1"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["10368.qo", "\\SOPlus(4,2)^2.C_2"], 10368]	[[NULL, NULL], 8, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"11664.dc.9.B"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, true, false, false, false, false, false, true, false, false, false, false, false, false]	[["11664.dc", "C_3^6.C_4:C_4"], 11664]	[[NULL, NULL], 9, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"11664.do.9.b1"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, true, false, false, false, false, false, true, false, false, false, false, false, false]	[["11664.do", "C_3^6.C_4:C_4"], 11664]	[[NULL, NULL], 9, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"12960.bx.10.a1.a1"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["12960.bx", "C_3^4:C_{40}:C_4"], 12960]	[[NULL, NULL], 10, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"12960.bx.10.a1.b1"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["12960.bx", "C_3^4:C_{40}:C_4"], 12960]	[[NULL, NULL], 10, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"15552.ll.12.p1.a1"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["15552.ll", "C_3^4:(D_4\\times \\SL(2,3))"], 15552]	[[NULL, NULL], 12, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"15552.ll.12.p1.a2"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["15552.ll", "C_3^4:(D_4\\times \\SL(2,3))"], 15552]	[[NULL, NULL], 12, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"20736.v.16.l1.a1"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["20736.v", "C_3^4:(C_8^2:C_4)"], 20736]	[[NULL, NULL], 16, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"20736.x.16.q1.a1"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["20736.x", "F_9\\wr C_2:C_2"], 20736]	[[NULL, NULL], 16, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"20736.ku.16.bv1.d1"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["20736.ku", "C_6^2:S_3^2.D_8"], 20736]	[[NULL, NULL], 16, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"20736.ku.16.bv1.a1"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["20736.ku", "C_6^2:S_3^2.D_8"], 20736]	[[NULL, NULL], 16, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"20736.ku.16.bv1.b1"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["20736.ku", "C_6^2:S_3^2.D_8"], 20736]	[[NULL, NULL], 16, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"20736.ku.16.bv1.c1"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["20736.ku", "C_6^2:S_3^2.D_8"], 20736]	[[NULL, NULL], 16, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"20736.ku.16.bx1.b1"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["20736.ku", "C_6^2:S_3^2.D_8"], 20736]	[[NULL, NULL], 16, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"20736.ku.16.bx1.a1"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["20736.ku", "C_6^2:S_3^2.D_8"], 20736]	[[NULL, NULL], 16, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"20736.ku.16.by1.b1"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["20736.ku", "C_6^2:S_3^2.D_8"], 20736]	[[NULL, NULL], 16, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"20736.ku.16.by1.d1"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["20736.ku", "C_6^2:S_3^2.D_8"], 20736]	[[NULL, NULL], 16, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"20736.ku.16.by1.a1"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["20736.ku", "C_6^2:S_3^2.D_8"], 20736]	[[NULL, NULL], 16, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"20736.ku.16.by1.c1"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["20736.ku", "C_6^2:S_3^2.D_8"], 20736]	[[NULL, NULL], 16, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"20736.kv.16.bf1.a1"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["20736.kv", "C_6^2:S_3^2.\\SD_{16}"], 20736]	[[NULL, NULL], 16, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"20736.kv.16.bf1.b1"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["20736.kv", "C_6^2:S_3^2.\\SD_{16}"], 20736]	[[NULL, NULL], 16, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"20736.kv.16.bf1.c1"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["20736.kv", "C_6^2:S_3^2.\\SD_{16}"], 20736]	[[NULL, NULL], 16, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"20736.kv.16.bf1.d1"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["20736.kv", "C_6^2:S_3^2.\\SD_{16}"], 20736]	[[NULL, NULL], 16, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"20736.kv.16.bi1.a1"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["20736.kv", "C_6^2:S_3^2.\\SD_{16}"], 20736]	[[NULL, NULL], 16, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"20736.kv.16.bi1.b1"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["20736.kv", "C_6^2:S_3^2.\\SD_{16}"], 20736]	[[NULL, NULL], 16, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"20736.kv.16.bk1.a1"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["20736.kv", "C_6^2:S_3^2.\\SD_{16}"], 20736]	[[NULL, NULL], 16, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"20736.kv.16.bk1.b1"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["20736.kv", "C_6^2:S_3^2.\\SD_{16}"], 20736]	[[NULL, NULL], 16, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"20736.kv.16.bk1.c1"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["20736.kv", "C_6^2:S_3^2.\\SD_{16}"], 20736]	[[NULL, NULL], 16, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"20736.kv.16.bk1.d1"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["20736.kv", "C_6^2:S_3^2.\\SD_{16}"], 20736]	[[NULL, NULL], 16, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"20736.lq.16.bf1.a1"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["20736.lq", "C_3^4:\\OD_{32}.C_2^3"], 20736]	[[NULL, NULL], 16, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"20736.lq.16.bf1.b1"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["20736.lq", "C_3^4:\\OD_{32}.C_2^3"], 20736]	[[NULL, NULL], 16, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
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"1119744.n.864.ee1"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["1119744.n", "C_3^5:S_3.(C_4^3.A_4)"], 1119744]	[[NULL, NULL], 864, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"1119744.n.864.ef1"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["1119744.n", "C_3^5:S_3.(C_4^3.A_4)"], 1119744]	[[NULL, NULL], 864, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"1119744.n.864.eh1"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["1119744.n", "C_3^5:S_3.(C_4^3.A_4)"], 1119744]	[[NULL, NULL], 864, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"1119744.n.864.ev1"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["1119744.n", "C_3^5:S_3.(C_4^3.A_4)"], 1119744]	[[NULL, NULL], 864, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"1119744.p.864.CM"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["1119744.p", "(C_3:S_3)^3.C_2^3:S_4"], 1119744]	[[NULL, NULL], 864, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"1119744.p.864.DC"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["1119744.p", "(C_3:S_3)^3.C_2^3:S_4"], 1119744]	[[NULL, NULL], 864, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"1119744.p.864.DG"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["1119744.p", "(C_3:S_3)^3.C_2^3:S_4"], 1119744]	[[NULL, NULL], 864, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"1119744.r.864.BZ"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["1119744.r", "C_3^6:((C_4\\times C_8^2):C_6)"], 1119744]	[[NULL, NULL], 864, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"1119744.r.864.CA"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["1119744.r", "C_3^6:((C_4\\times C_8^2):C_6)"], 1119744]	[[NULL, NULL], 864, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"1119744.r.864.CR"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["1119744.r", "C_3^6:((C_4\\times C_8^2):C_6)"], 1119744]	[[NULL, NULL], 864, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"1119744.r.864.CS"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["1119744.r", "C_3^6:((C_4\\times C_8^2):C_6)"], 1119744]	[[NULL, NULL], 864, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"1119744.r.864.GV"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["1119744.r", "C_3^6:((C_4\\times C_8^2):C_6)"], 1119744]	[[NULL, NULL], 864, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"1119744.r.864.HJ"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["1119744.r", "C_3^6:((C_4\\times C_8^2):C_6)"], 1119744]	[[NULL, NULL], 864, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"1119744.t.864.BZ"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["1119744.t", "C_3^6:(C_4^2.\\GL(2,\\mathbb{Z}/4))"], 1119744]	[[NULL, NULL], 864, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"1119744.t.864.CA"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["1119744.t", "C_3^6:(C_4^2.\\GL(2,\\mathbb{Z}/4))"], 1119744]	[[NULL, NULL], 864, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"1119744.t.864.GA"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["1119744.t", "C_3^6:(C_4^2.\\GL(2,\\mathbb{Z}/4))"], 1119744]	[[NULL, NULL], 864, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"1119744.t.864.GL"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["1119744.t", "C_3^6:(C_4^2.\\GL(2,\\mathbb{Z}/4))"], 1119744]	[[NULL, NULL], 864, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"1119744.u.864.CH"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["1119744.u", "(C_3:S_3)^3.C_2^3:S_4"], 1119744]	[[NULL, NULL], 864, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"1119744.v.864.BP"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["1119744.v", "C_3^6:(C_8^2:D_{12})"], 1119744]	[[NULL, NULL], 864, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"1119744.x.864.bm1"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["1119744.x", "C_3^5:S_3.C_8^2:D_6"], 1119744]	[[NULL, NULL], 864, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"1119744.x.864.bo1"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["1119744.x", "C_3^5:S_3.C_8^2:D_6"], 1119744]	[[NULL, NULL], 864, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"1119744.x.864.br1"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["1119744.x", "C_3^5:S_3.C_8^2:D_6"], 1119744]	[[NULL, NULL], 864, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"1119744.x.864.bv1"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["1119744.x", "C_3^5:S_3.C_8^2:D_6"], 1119744]	[[NULL, NULL], 864, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"1119744.x.864.bw1"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["1119744.x", "C_3^5:S_3.C_8^2:D_6"], 1119744]	[[NULL, NULL], 864, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"1119744.x.864.cr1"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["1119744.x", "C_3^5:S_3.C_8^2:D_6"], 1119744]	[[NULL, NULL], 864, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"1119744.x.864.cw1"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["1119744.x", "C_3^5:S_3.C_8^2:D_6"], 1119744]	[[NULL, NULL], 864, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"1119744.z.864.cv1"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["1119744.z", "C_3^6:(C_8^2:(C_4\\times S_3))"], 1119744]	[[NULL, NULL], 864, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"1119744.z.864.cy1"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["1119744.z", "C_3^6:(C_8^2:(C_4\\times S_3))"], 1119744]	[[NULL, NULL], 864, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"1119744.bb.864.cm1"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["1119744.bb", "C_3^6:(C_4^3.S_4)"], 1119744]	[[NULL, NULL], 864, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"1119744.bb.864.cn1"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["1119744.bb", "C_3^6:(C_4^3.S_4)"], 1119744]	[[NULL, NULL], 864, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"1119744.bb.864.cu1"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["1119744.bb", "C_3^6:(C_4^3.S_4)"], 1119744]	[[NULL, NULL], 864, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"1119744.bi.864.bk1"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["1119744.bi", "C_3^6:(C_8^2:(C_3\\times Q_8))"], 1119744]	[[NULL, NULL], 864, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"1119744.bi.864.bm1"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["1119744.bi", "C_3^6:(C_8^2:(C_3\\times Q_8))"], 1119744]	[[NULL, NULL], 864, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"1119744.bi.864.cm1"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["1119744.bi", "C_3^6:(C_8^2:(C_3\\times Q_8))"], 1119744]	[[NULL, NULL], 864, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"1119744.bi.864.co1"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["1119744.bi", "C_3^6:(C_8^2:(C_3\\times Q_8))"], 1119744]	[[NULL, NULL], 864, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"1119744.bi.864.dw1"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["1119744.bi", "C_3^6:(C_8^2:(C_3\\times Q_8))"], 1119744]	[[NULL, NULL], 864, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"1119744.bi.864.ec1"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["1119744.bi", "C_3^6:(C_8^2:(C_3\\times Q_8))"], 1119744]	[[NULL, NULL], 864, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"1679616.hj.1296.V"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["1679616.hj", "C_3^5:D_6.\\SOPlus(4,3)"], 1679616]	[[NULL, NULL], 1296, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"2073600.d.1600.O"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["2073600.d", "\\PGL(2,9)\\wr C_2:C_2"], 2073600]	[[NULL, NULL], 1600, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"2073600.e.1600.M"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["2073600.e", "A_6:S_6.D_4"], 2073600]	[[NULL, NULL], 1600, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"2073600.z.1600.Z"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["2073600.z", "C_2\\times A_6^2.D_4"], 2073600]	[[NULL, NULL], 1600, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"2073600.z.1600.BF"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["2073600.z", "C_2\\times A_6^2.D_4"], 2073600]	[[NULL, NULL], 1600, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"2073600.ba.1600.Z"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["2073600.ba", "A_6^2.D_8"], 2073600]	[[NULL, NULL], 1600, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"2073600.ba.1600.BC"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["2073600.ba", "A_6^2.D_8"], 2073600]	[[NULL, NULL], 1600, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"2073600.bb.1600.X"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["2073600.bb", "(C_2\\times A_6^2).D_4"], 2073600]	[[NULL, NULL], 1600, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"2073600.bb.1600.BC"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["2073600.bb", "(C_2\\times A_6^2).D_4"], 2073600]	[[NULL, NULL], 1600, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"2073600.bc.1600.X"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["2073600.bc", "A_6^2.\\SD_{16}"], 2073600]	[[NULL, NULL], 1600, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"2073600.bc.1600.Y"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["2073600.bc", "A_6^2.\\SD_{16}"], 2073600]	[[NULL, NULL], 1600, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"2099520.d.1620.DS"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["2099520.d", "C_3^6.(A_6.D_4)"], 2099520]	[[NULL, NULL], 1620, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"2099520.d.1620.DX"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["2099520.d", "C_3^6.(A_6.D_4)"], 2099520]	[[NULL, NULL], 1620, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"2099520.d.1620.DY"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["2099520.d", "C_3^6.(A_6.D_4)"], 2099520]	[[NULL, NULL], 1620, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"125452800.a.96800._.V"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["125452800.a", "M_{11}\\wr C_2"], 125452800]	[[NULL, NULL], 96800, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"125452800.a.96800._.CG"	[["1296.3499", "C_3^2\\wr C_2.D_4"], 1296, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["125452800.a", "M_{11}\\wr C_2"], 125452800]	[[NULL, NULL], 96800, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]


# 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.