
# gps_subgroup_search downloaded from the LMFDB on 25 July 2026.
# Search link: https://www.lmfdb.org/Groups/Abstract/Subgroups?ambient=384.12440+
# Query "{'ambient': '384.12440'}" returned 230 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.



"384.12440.1.a1"	[["384.12440", "D_8:(C_4\\times S_3)"], 384, 0, true, true, false, false, false, false, false, true, true, false, false, false, false, true, false]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[["1.1", "C_1"], 1, false, true, true, true, true, true, false, true, true]
"384.12440.2.a1"	[["192.1095", "C_4^2.D_6"], 192, 0, true, false, true, false, false, false, false, true, true, false, false, false, false, true, false]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[["2.1", "C_2"], 2, false, true, true, true, true, true, true, true, true]
"384.12440.2.b1"	[["192.331", "(C_8\\times D_6):C_2"], 192, 0, true, false, true, false, false, false, false, true, true, false, false, false, false, true, false]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[["2.1", "C_2"], 2, false, true, true, true, true, true, true, true, true]
"384.12440.2.c1"	[["192.577", "C_4^2.D_6"], 192, 0, true, false, true, false, false, false, false, true, true, false, false, false, false, true, false]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[["2.1", "C_2"], 2, false, true, true, true, true, true, true, true, true]
"384.12440.2.d1"	[["192.316", "C_4.(C_4\\times D_6)"], 192, 0, true, false, true, false, false, false, false, true, true, false, false, false, false, true, false]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[["2.1", "C_2"], 2, false, true, true, true, true, true, true, true, true]
"384.12440.2.e1"	[["192.1315", "D_8:D_6"], 192, 0, true, true, true, false, false, false, false, true, true, false, false, false, false, true, false]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[["2.1", "C_2"], 2, false, true, true, true, true, true, true, true, true]
"384.12440.2.f1"	[["192.875", "D_8:C_{12}"], 192, 0, true, true, true, false, false, false, true, true, true, false, false, false, false, true, false]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[["2.1", "C_2"], 2, false, true, true, true, true, true, true, true, true]
"384.12440.2.g1"	[["192.711", "C_{24}:(C_2\\times C_4)"], 192, 0, true, true, true, false, false, false, false, true, true, false, false, false, false, true, false]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[["2.1", "C_2"], 2, false, true, true, true, true, true, true, true, true]
"384.12440.2.h1"	[["192.263", "D_6.C_4^2"], 192, 0, true, true, true, false, false, false, false, true, true, false, false, false, false, true, false]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[["2.1", "C_2"], 2, false, true, true, true, true, true, true, true, true]
"384.12440.2.i1"	[["192.419", "(S_3\\times C_8):C_4"], 192, 0, true, true, true, false, false, false, false, true, true, false, false, false, false, true, false]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[["2.1", "C_2"], 2, false, true, true, true, true, true, true, true, true]
"384.12440.2.j1"	[["192.275", "C_4^2.D_6"], 192, 0, true, true, true, false, false, false, false, true, true, false, false, false, false, true, false]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[["2.1", "C_2"], 2, false, true, true, true, true, true, true, true, true]
"384.12440.2.k1"	[["192.412", "C_8.(C_4\\times S_3)"], 192, 0, true, true, true, false, false, false, false, true, true, false, false, false, false, true, false]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[["2.1", "C_2"], 2, false, true, true, true, true, true, true, true, true]
"384.12440.3.a1"	[["128.1675", "C_4^2.D_4"], 128, 2, false, false, true, false, false, false, true, true, true, false, false, false, false, true, false]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[[NULL, NULL], 3, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"384.12440.4.a1"	[["96.210", "D_4:D_6"], 96, 0, true, false, false, false, false, false, false, true, true, false, false, false, false, true, false]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[["4.2", "C_2^2"], 4, false, false, true, true, true, true, false, true, true]
"384.12440.4.b1"	[["96.165", "D_4\\times C_{12}"], 96, 0, true, false, false, false, false, false, true, true, true, false, false, false, false, true, false]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[["4.2", "C_2^2"], 4, false, false, true, true, true, true, false, true, true]
"384.12440.4.c1"	[["96.52", "D_4:C_{12}"], 96, 0, true, false, false, false, false, false, true, true, true, false, false, false, false, true, NULL]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[["4.2", "C_2^2"], 4, false, false, true, true, true, true, false, true, true]
"384.12440.4.d1"	[["96.141", "C_2^3.D_6"], 96, 0, true, false, false, false, false, false, false, true, true, false, false, false, false, true, false]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[["4.2", "C_2^2"], 4, false, false, true, true, true, true, false, true, true]
"384.12440.4.e1"	[["96.140", "C_6:\\SD_{16}"], 96, 0, true, false, false, false, false, false, false, true, true, false, false, false, false, true, false]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[["4.2", "C_2^2"], 4, false, false, true, true, true, true, false, true, true]
"384.12440.4.f1"	[["96.39", "C_6.D_8"], 96, 0, true, false, false, false, false, false, false, true, true, false, false, false, false, true, NULL]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[["4.2", "C_2^2"], 4, false, false, true, true, true, true, false, true, true]
"384.12440.4.g1"	[["96.179", "C_6\\times D_8"], 96, 0, true, true, false, false, false, false, true, true, true, false, false, false, false, true, false]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[["4.2", "C_2^2"], 4, false, false, true, true, true, true, false, true, true]
"384.12440.4.h1"	[["96.78", "S_3\\times C_4^2"], 96, 0, true, true, false, false, false, false, false, true, true, false, false, true, false, true, false]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[["4.2", "C_2^2"], 4, false, false, true, true, true, true, false, true, true]
"384.12440.4.i1"	[["96.99", "(C_4\\times S_3):C_4"], 96, 0, true, false, false, false, false, false, false, true, true, false, false, false, false, true, false]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[["4.2", "C_2^2"], 4, false, false, true, true, true, true, false, true, true]
"384.12440.4.j1"	[["96.106", "C_8\\times D_6"], 96, 0, true, true, false, false, false, false, false, true, true, false, false, true, false, true, false]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[["4.2", "C_2^2"], 4, false, false, true, true, true, true, false, true, true]
"384.12440.4.k1"	[["96.106", "C_8\\times D_6"], 96, 0, true, true, false, false, false, false, false, true, true, false, false, true, false, true, false]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[["4.2", "C_2^2"], 4, false, false, true, true, true, true, false, true, true]
"384.12440.4.l1"	[["96.75", "C_{12}:Q_8"], 96, 0, true, false, false, false, false, false, false, true, true, false, false, false, false, true, false]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[["4.2", "C_2^2"], 4, false, false, true, true, true, true, false, true, true]
"384.12440.4.m1"	[["96.47", "C_8:C_{12}"], 96, 0, true, true, false, false, false, false, true, true, true, false, false, false, false, true, NULL]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[["4.2", "C_2^2"], 4, false, false, true, true, true, true, false, true, true]
"384.12440.4.n1"	[["96.10", "C_6.C_4^2"], 96, 0, true, true, false, false, false, false, false, true, true, false, false, false, false, true, NULL]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[["4.2", "C_2^2"], 4, false, false, true, true, true, true, false, true, true]
"384.12440.4.o1"	[["96.94", "C_3:(C_4\\times Q_8)"], 96, 0, true, false, false, false, false, false, false, true, true, false, false, false, false, true, false]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[["4.2", "C_2^2"], 4, false, false, true, true, true, true, false, true, true]
"384.12440.4.p1"	[["96.17", "C_4.D_{12}"], 96, 0, true, false, false, false, false, false, false, true, true, false, false, false, false, true, NULL]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[["4.2", "C_2^2"], 4, false, false, true, true, true, true, false, true, true]
"384.12440.4.q1"	[["96.14", "C_6.D_8"], 96, 0, true, false, false, false, false, false, false, true, true, false, false, false, false, true, NULL]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[["4.2", "C_2^2"], 4, false, false, true, true, true, true, false, true, true]
"384.12440.4.r1"	[["96.56", "C_8:C_{12}"], 96, 0, true, true, false, false, false, false, true, true, true, false, false, false, false, true, NULL]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[["4.2", "C_2^2"], 4, false, false, true, true, true, true, false, true, true]
"384.12440.4.s1"	[["96.22", "C_{24}:C_4"], 96, 0, true, true, false, false, false, false, false, true, true, false, false, false, false, true, NULL]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[["4.2", "C_2^2"], 4, false, false, true, true, true, true, false, true, true]
"384.12440.4.t1"	[["96.22", "C_{24}:C_4"], 96, 0, true, true, false, false, false, false, false, true, true, false, false, false, false, true, NULL]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[["4.2", "C_2^2"], 4, false, false, true, true, true, true, false, true, true]
"384.12440.4.u1"	[["96.23", "C_6.Q_{16}"], 96, 0, true, false, false, false, false, false, false, true, true, false, false, false, false, true, NULL]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[["4.2", "C_2^2"], 4, false, false, true, true, true, true, false, true, true]
"384.12440.4.v1"	[["96.112", "C_6:Q_{16}"], 96, 0, true, true, false, false, false, false, false, true, true, false, false, false, false, true, false]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[["4.2", "C_2^2"], 4, false, false, true, true, true, true, false, true, true]
"384.12440.4.w1"	[["96.24", "C_{24}:C_4"], 96, 0, true, true, false, false, false, false, false, true, true, false, false, false, false, true, NULL]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[["4.2", "C_2^2"], 4, false, false, true, true, true, true, false, true, true]
"384.12440.4.x1"	[["96.119", "D_8:S_3"], 96, 0, true, false, false, false, false, false, false, true, true, false, false, false, false, true, false]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[["4.1", "C_4"], 4, false, true, true, true, true, true, false, true, true]
"384.12440.4.y1"	[["96.88", "C_2^3.D_6"], 96, 0, false, false, false, false, false, false, false, true, true, false, false, false, false, true, false]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[[NULL, NULL], 4, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"384.12440.4.y2"	[["96.135", "C_{12}:D_4"], 96, 0, false, false, false, false, false, false, false, true, true, false, false, false, false, true, false]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[[NULL, NULL], 4, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"384.12440.4.z1"	[["96.129", "C_6:C_4^2"], 96, 0, false, false, false, false, false, false, false, true, true, false, false, true, false, true, false]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[[NULL, NULL], 4, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"384.12440.4.z2"	[["96.84", "C_2^3.D_6"], 96, 0, false, false, false, false, false, false, false, true, true, false, false, false, false, true, false]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[[NULL, NULL], 4, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"384.12440.6.a1"	[["64.123", "D_8:C_4"], 64, 0, true, true, false, false, false, false, true, true, true, false, false, false, false, true, false]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[["6.1", "S_3"], 6, false, false, false, false, true, true, false, true, true]
"384.12440.6.b1"	[["64.198", "C_4^2.C_2^2"], 64, 0, false, false, false, false, false, false, true, true, true, false, false, false, false, true, false]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[[NULL, NULL], 6, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"384.12440.6.c1"	[["64.97", "C_2^3.D_4"], 64, 0, false, false, false, false, false, false, true, true, true, false, false, false, false, true, false]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[[NULL, NULL], 6, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"384.12440.6.d1"	[["64.121", "\\SD_{16}:C_4"], 64, 0, false, false, false, false, false, false, true, true, true, false, false, false, false, true, false]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[[NULL, NULL], 6, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"384.12440.6.e1"	[["64.121", "\\SD_{16}:C_4"], 64, 0, false, false, false, false, false, false, true, true, true, false, false, false, false, true, false]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[[NULL, NULL], 6, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"384.12440.6.f1"	[["64.253", "D_8:C_2^2"], 64, 0, false, false, false, false, false, false, true, true, true, false, false, false, false, true, false]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[[NULL, NULL], 6, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"384.12440.6.g1"	[["64.123", "D_8:C_4"], 64, 0, false, false, false, false, false, false, true, true, true, false, false, false, false, true, false]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[[NULL, NULL], 6, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"384.12440.6.h1"	[["64.84", "C_4.C_4^2"], 64, 0, false, false, false, false, false, false, true, true, true, false, false, false, false, true, false]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[[NULL, NULL], 6, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"384.12440.6.i1"	[["64.108", "C_2^3.D_4"], 64, 0, false, false, false, false, false, false, true, true, true, false, false, false, false, true, false]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[[NULL, NULL], 6, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"384.12440.6.j1"	[["64.122", "Q_{16}:C_4"], 64, 0, false, false, false, false, false, false, true, true, true, false, false, false, false, true, false]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[[NULL, NULL], 6, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"384.12440.6.k1"	[["64.122", "Q_{16}:C_4"], 64, 0, false, false, false, false, false, false, true, true, true, false, false, false, false, true, false]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[[NULL, NULL], 6, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"384.12440.8.a1"	[["48.45", "C_6\\times D_4"], 48, 0, true, false, false, false, false, false, true, true, true, false, false, false, false, true, false]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[["8.5", "C_2^3"], 8, false, false, true, true, true, true, false, true, true]
"384.12440.8.b1"	[["48.35", "C_4\\times D_6"], 48, 0, true, true, false, false, false, false, false, true, true, false, false, true, false, true, false]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[["8.5", "C_2^3"], 8, false, false, true, true, true, true, false, true, true]
"384.12440.8.c1"	[["48.35", "C_4\\times D_6"], 48, 0, true, false, false, false, false, false, false, true, true, false, false, true, false, true, false]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[["8.3", "D_4"], 8, false, false, false, true, true, true, false, false, true]
"384.12440.8.d1"	[["48.20", "C_4\\times C_{12}"], 48, 0, true, true, false, false, false, true, true, true, true, false, false, true, false, true, true]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[["8.5", "C_2^3"], 8, false, false, true, true, true, true, false, true, true]
"384.12440.8.e1"	[["48.22", "C_4:C_{12}"], 48, 0, true, false, false, false, false, false, true, true, true, false, false, false, false, true, NULL]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[["8.5", "C_2^3"], 8, false, false, true, true, true, true, false, true, true]
"384.12440.8.f1"	[["48.11", "C_{12}:C_4"], 48, 0, true, true, false, false, false, false, false, true, true, false, false, true, false, true, NULL]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[["8.5", "C_2^3"], 8, false, false, true, true, true, true, false, true, true]
"384.12440.8.g1"	[["48.34", "C_6:Q_8"], 48, 0, true, false, false, false, false, false, false, true, true, false, false, false, false, true, false]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[["8.5", "C_2^3"], 8, false, false, true, true, true, true, false, true, true]
"384.12440.8.h1"	[["48.13", "C_{12}:C_4"], 48, 0, true, false, false, false, false, false, false, true, true, false, false, false, false, true, NULL]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[["8.5", "C_2^3"], 8, false, false, true, true, true, true, false, true, true]
"384.12440.8.i1"	[["48.23", "C_2\\times C_{24}"], 48, 0, true, true, false, false, false, true, true, true, true, false, false, true, false, true, true]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[["8.5", "C_2^3"], 8, false, false, true, true, true, true, false, true, true]
"384.12440.8.j1"	[["48.23", "C_2\\times C_{24}"], 48, 0, true, true, false, false, false, true, true, true, true, false, false, true, false, true, true]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[["8.5", "C_2^3"], 8, false, false, true, true, true, true, false, true, true]
"384.12440.8.k1"	[["48.9", "C_6:C_8"], 48, 0, true, true, false, false, false, false, false, true, true, false, false, true, false, true, NULL]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[["8.5", "C_2^3"], 8, false, false, true, true, true, true, false, true, true]
"384.12440.8.l1"	[["48.9", "C_6:C_8"], 48, 0, true, true, false, false, false, false, false, true, true, false, false, true, false, true, NULL]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[["8.5", "C_2^3"], 8, false, false, true, true, true, true, false, true, true]
"384.12440.8.m1"	[["48.11", "C_{12}:C_4"], 48, 0, true, false, false, false, false, false, false, true, true, false, false, true, false, true, NULL]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[["8.3", "D_4"], 8, false, false, false, true, true, true, false, false, true]
"384.12440.8.n1"	[["48.39", "D_4:S_3"], 48, 0, true, false, false, false, false, false, false, true, true, false, false, false, false, true, false]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[["8.2", "C_2\\times C_4"], 8, false, false, true, true, true, true, false, true, true]
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"384.12440.48.r1"	[["8.1", "C_8"], 8, 0, false, false, false, false, true, true, true, true, true, false, false, true, true, true, true]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[[NULL, NULL], 48, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"384.12440.48.s1"	[["8.4", "Q_8"], 8, 0, false, false, false, false, false, false, true, true, true, false, false, false, false, true, true]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[[NULL, NULL], 48, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"384.12440.48.t1"	[["8.1", "C_8"], 8, 0, false, false, false, false, true, true, true, true, true, false, false, true, true, true, true]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[[NULL, NULL], 48, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"384.12440.48.u1"	[["8.1", "C_8"], 8, 0, false, false, false, false, true, true, true, true, true, false, false, true, true, true, true]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[[NULL, NULL], 48, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"384.12440.48.v1"	[["8.2", "C_2\\times C_4"], 8, 0, false, false, false, false, false, true, true, true, true, false, false, true, false, true, true]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[[NULL, NULL], 48, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"384.12440.48.w1"	[["8.2", "C_2\\times C_4"], 8, 0, false, false, false, false, false, true, true, true, true, false, false, true, false, true, true]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[[NULL, NULL], 48, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"384.12440.48.x1"	[["8.2", "C_2\\times C_4"], 8, 0, false, false, false, false, false, true, true, true, true, false, false, true, false, true, true]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[[NULL, NULL], 48, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"384.12440.64.a1"	[["6.2", "C_6"], 6, 0, true, true, false, false, true, true, true, true, true, false, false, true, true, true, true]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[["64.196", "C_4^2:C_2^2"], 64, false, false, false, true, true, true, false, false, true]
"384.12440.64.b1"	[["6.2", "C_6"], 6, 0, true, false, false, false, true, true, true, true, true, false, false, true, true, true, true]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[["64.256", "D_8:C_2^2"], 64, false, false, false, true, true, true, false, false, true]
"384.12440.64.c1"	[["6.2", "C_6"], 6, 0, false, false, false, false, true, true, true, true, true, false, false, true, true, true, true]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[[NULL, NULL], 64, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"384.12440.64.d1"	[["6.1", "S_3"], 6, 0, false, false, false, false, false, false, false, true, true, false, false, true, true, true, true]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[[NULL, NULL], 64, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"384.12440.96.a1"	[["4.2", "C_2^2"], 4, 0, true, true, false, true, false, true, true, true, true, false, false, true, false, true, true]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[["96.209", "D_4\\times D_6"], 96, false, false, false, false, true, true, false, false, true]
"384.12440.96.b1"	[["4.1", "C_4"], 4, 0, true, true, false, false, true, true, true, true, true, false, false, true, true, true, true]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[["96.206", "C_{12}:C_2^3"], 96, false, false, false, false, true, true, false, true, true]
"384.12440.96.c1"	[["4.1", "C_4"], 4, 0, true, true, false, false, true, true, true, true, true, false, false, true, true, true, true]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[["96.215", "D_4:D_6"], 96, false, false, false, false, true, true, false, false, true]
"384.12440.96.d1"	[["4.2", "C_2^2"], 4, 0, false, false, false, false, false, true, true, true, true, false, false, true, false, true, true]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[[NULL, NULL], 96, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"384.12440.96.e1"	[["4.2", "C_2^2"], 4, 0, false, false, false, false, false, true, true, true, true, false, false, true, false, true, true]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[[NULL, NULL], 96, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"384.12440.96.f1"	[["4.1", "C_4"], 4, 0, false, false, false, false, true, true, true, true, true, false, false, true, true, true, true]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[[NULL, NULL], 96, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"384.12440.96.g1"	[["4.1", "C_4"], 4, 0, false, false, false, false, true, true, true, true, true, false, false, true, true, true, true]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[[NULL, NULL], 96, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"384.12440.96.h1"	[["4.2", "C_2^2"], 4, 0, false, false, false, false, false, true, true, true, true, false, false, true, false, true, true]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[[NULL, NULL], 96, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"384.12440.96.h2"	[["4.2", "C_2^2"], 4, 0, false, false, false, false, false, true, true, true, true, false, false, true, false, true, true]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[[NULL, NULL], 96, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"384.12440.96.i1"	[["4.2", "C_2^2"], 4, 0, false, false, false, false, false, true, true, true, true, false, false, true, false, true, true]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[[NULL, NULL], 96, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"384.12440.96.j1"	[["4.1", "C_4"], 4, 0, false, false, false, false, true, true, true, true, true, false, false, true, true, true, true]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[[NULL, NULL], 96, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"384.12440.96.k1"	[["4.1", "C_4"], 4, 0, false, false, false, false, true, true, true, true, true, false, false, true, true, true, true]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[[NULL, NULL], 96, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"384.12440.96.l1"	[["4.1", "C_4"], 4, 0, false, false, false, false, true, true, true, true, true, false, false, true, true, true, true]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[[NULL, NULL], 96, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"384.12440.96.m1"	[["4.1", "C_4"], 4, 0, false, false, false, false, true, true, true, true, true, false, false, true, true, true, true]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[[NULL, NULL], 96, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"384.12440.128.a1"	[["3.1", "C_3"], 3, 3, true, true, false, false, true, true, true, true, true, false, true, true, true, true, true]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[["128.1675", "C_4^2.D_4"], 128, true, false, false, true, true, true, false, false, true]
"384.12440.192.a1"	[["2.1", "C_2"], 2, 0, true, true, false, true, true, true, true, true, true, false, true, true, true, true, true]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[["192.1103", "C_4^2:D_6"], 192, true, false, false, false, true, true, false, false, true]
"384.12440.192.b1"	[["2.1", "C_2"], 2, 0, true, false, false, true, true, true, true, true, true, false, true, true, true, true, true]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[["192.1332", "D_8:D_6"], 192, true, false, false, false, true, true, false, false, true]
"384.12440.192.c1"	[["2.1", "C_2"], 2, 0, false, false, false, false, true, true, true, true, true, false, true, true, true, true, true]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[[NULL, NULL], 192, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"384.12440.192.d1"	[["2.1", "C_2"], 2, 0, false, false, false, false, true, true, true, true, true, false, true, true, true, true, true]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[[NULL, NULL], 192, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"384.12440.384.a1"	[["1.1", "C_1"], 1, 1, true, true, false, true, true, true, true, true, true, true, false, true, true, true, true]	[["384.12440", "D_8:(C_4\\times S_3)"], 384]	[["384.12440", "D_8:(C_4\\times S_3)"], 384, false, false, false, false, true, true, false, false, 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.


