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Note: Search results may be incomplete due to uncomputed quantities: Subgroup label (103813812 objects)

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Subgroup label Subgroup order Cyclic Abelian Solvable
Normal Characteristic Perfect Maximal Central
Ambient label Ambient order Direct product Semidirect product
Quotient label Subgroup index Cyclic quotient Abelian quotient Solvable quotient
Maximal quotient Non-trivial proper Hall subgroup Sylow subgroup
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Results (1-50 of 70 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
384.171.1.a1.a1 $C_{16}.D_{12}$ $2^{7} \cdot 3$ ✓ ✓ $C_{16}.D_{12}$ $2^{7} \cdot 3$ $C_1$ $1$ ✓
768.90133.2.b1.a1 $C_{16}.D_{12}$ $2^{7} \cdot 3$ ✓ ✓ $C_{32}.D_{12}$ $2^{8} \cdot 3$ $C_2$ $2$ ✓
768.90133.2.b1.b1 $C_{16}.D_{12}$ $2^{7} \cdot 3$ ✓ ✓ $C_{32}.D_{12}$ $2^{8} \cdot 3$ $C_2$ $2$ ✓
1152.6722.3.a1.a1 $C_{16}.D_{12}$ $2^{7} \cdot 3$ ✓ $C_{16}.D_{36}$ $2^{7} \cdot 3^{2}$ $3$ $-$
1152.6724.3.a1.a1 $C_{16}.D_{12}$ $2^{7} \cdot 3$ ✓ ✓ ✓ $D_{12}.C_{48}$ $2^{7} \cdot 3^{2}$ $C_3$ $3$ ✓
1536.10499001.4.e1.a1 $C_{16}.D_{12}$ $2^{7} \cdot 3$ $C_{32}.D_{24}$ $2^{9} \cdot 3$ $2^{2}$ $-$
1536.10829877.4.j1.a1 $C_{16}.D_{12}$ $2^{7} \cdot 3$ $C_{32}.D_{24}$ $2^{9} \cdot 3$ $2^{2}$ $-$
1536.10829877.4.j1.b1 $C_{16}.D_{12}$ $2^{7} \cdot 3$ $C_{32}.D_{24}$ $2^{9} \cdot 3$ $2^{2}$ $-$
1536.10843710.4.b1.a1 $C_{16}.D_{12}$ $2^{7} \cdot 3$ ✓ $C_{192}.D_4$ $2^{9} \cdot 3$ $C_4$ $2^{2}$ ✓
1536.10843710.4.b1.b1 $C_{16}.D_{12}$ $2^{7} \cdot 3$ ✓ $C_{192}.D_4$ $2^{9} \cdot 3$ $C_4$ $2^{2}$ ✓
2304.by.6.b1.a1 $C_{16}.D_{12}$ $2^{7} \cdot 3$ ✓ $D_{24}.C_{48}$ $2^{8} \cdot 3^{2}$ $C_6$ $2 \cdot 3$ ✓
2304.by.6.b1.b1 $C_{16}.D_{12}$ $2^{7} \cdot 3$ ✓ $D_{24}.C_{48}$ $2^{8} \cdot 3^{2}$ $C_6$ $2 \cdot 3$ ✓
2304.cv.6.c1.a1 $C_{16}.D_{12}$ $2^{7} \cdot 3$ $C_{32}.D_{36}$ $2^{8} \cdot 3^{2}$ $2 \cdot 3$ $-$
2304.cv.6.c1.b1 $C_{16}.D_{12}$ $2^{7} \cdot 3$ $C_{32}.D_{36}$ $2^{8} \cdot 3^{2}$ $2 \cdot 3$ $-$
3072.co.8.l1.b1 $C_{16}.D_{12}$ $2^{7} \cdot 3$ $D_{96}:C_{16}$ $2^{10} \cdot 3$ $2^{3}$ $-$
3072.co.8.l1.a1 $C_{16}.D_{12}$ $2^{7} \cdot 3$ $D_{96}:C_{16}$ $2^{10} \cdot 3$ $2^{3}$ $-$
3072.db.8.l1.a1 $C_{16}.D_{12}$ $2^{7} \cdot 3$ $C_{192}.D_8$ $2^{10} \cdot 3$ $2^{3}$ $-$
3072.db.8.l1.b1 $C_{16}.D_{12}$ $2^{7} \cdot 3$ $C_{192}.D_8$ $2^{10} \cdot 3$ $2^{3}$ $-$
3072.dd.8.g1.a1 $C_{16}.D_{12}$ $2^{7} \cdot 3$ $C_{32}.D_{48}$ $2^{10} \cdot 3$ $2^{3}$ $-$
3456.j.9.a1.a1 $C_{16}.D_{12}$ $2^{7} \cdot 3$ ✓ ✓ $D_{12}.C_{144}$ $2^{7} \cdot 3^{3}$ $C_9$ $3^{2}$ ✓
3456.v.9.b1.a1 $C_{16}.D_{12}$ $2^{7} \cdot 3$ $C_{48}.D_{36}$ $2^{7} \cdot 3^{3}$ $3^{2}$ $-$
4608.n.12.q1.a1 $C_{16}.D_{12}$ $2^{7} \cdot 3$ $C_{96}.D_{24}$ $2^{9} \cdot 3^{2}$ $2^{2} \cdot 3$ $-$
4608.n.12.q1.b1 $C_{16}.D_{12}$ $2^{7} \cdot 3$ $C_{96}.D_{24}$ $2^{9} \cdot 3^{2}$ $2^{2} \cdot 3$ $-$
4608.t.12.i1.a1 $C_{16}.D_{12}$ $2^{7} \cdot 3$ $D_{24}.C_{96}$ $2^{9} \cdot 3^{2}$ $2^{2} \cdot 3$ $-$
4608.v.12._.C $C_{16}.D_{12}$ $2^{7} \cdot 3$ ✓ $D_{24}.C_{96}$ $2^{9} \cdot 3^{2}$ $C_{12}$ $2^{2} \cdot 3$ ✓
4608.v.12._.D $C_{16}.D_{12}$ $2^{7} \cdot 3$ ✓ $D_{24}.C_{96}$ $2^{9} \cdot 3^{2}$ $C_{12}$ $2^{2} \cdot 3$ ✓
4608.bg.12.e1.a1 $C_{16}.D_{12}$ $2^{7} \cdot 3$ $C_{32}.D_{72}$ $2^{9} \cdot 3^{2}$ $2^{2} \cdot 3$ $-$
4608.bg.12.e1.b1 $C_{16}.D_{12}$ $2^{7} \cdot 3$ $C_{32}.D_{72}$ $2^{9} \cdot 3^{2}$ $2^{2} \cdot 3$ $-$
6144.cb.16.i1.a1 $C_{16}.D_{12}$ $2^{7} \cdot 3$ $D_{96}:C_{32}$ $2^{11} \cdot 3$ $2^{4}$ $-$
6144.cf.16._.R $C_{16}.D_{12}$ $2^{7} \cdot 3$ $C_{64}.D_{48}$ $2^{11} \cdot 3$ $2^{4}$ $-$
6144.cf.16._.S $C_{16}.D_{12}$ $2^{7} \cdot 3$ $C_{64}.D_{48}$ $2^{11} \cdot 3$ $2^{4}$ $-$
6144.ch.16._.R $C_{16}.D_{12}$ $2^{7} \cdot 3$ $D_{192}:C_{16}$ $2^{11} \cdot 3$ $2^{4}$ $-$
6144.ch.16._.S $C_{16}.D_{12}$ $2^{7} \cdot 3$ $D_{192}:C_{16}$ $2^{11} \cdot 3$ $2^{4}$ $-$
6912.d.18.b1.a1 $C_{16}.D_{12}$ $2^{7} \cdot 3$ ✓ $D_{24}.C_{144}$ $2^{8} \cdot 3^{3}$ $C_{18}$ $2 \cdot 3^{2}$ ✓
6912.d.18.b1.b1 $C_{16}.D_{12}$ $2^{7} \cdot 3$ ✓ $D_{24}.C_{144}$ $2^{8} \cdot 3^{3}$ $C_{18}$ $2 \cdot 3^{2}$ ✓
6912.l.18.g1.a1 $C_{16}.D_{12}$ $2^{7} \cdot 3$ $C_{96}.D_{36}$ $2^{8} \cdot 3^{3}$ $2 \cdot 3^{2}$ $-$
6912.l.18.g1.b1 $C_{16}.D_{12}$ $2^{7} \cdot 3$ $C_{96}.D_{36}$ $2^{8} \cdot 3^{3}$ $2 \cdot 3^{2}$ $-$
9216.c.24._.BR $C_{16}.D_{12}$ $2^{7} \cdot 3$ $C_{96}.D_{48}$ $2^{10} \cdot 3^{2}$ $2^{3} \cdot 3$ $-$
9216.c.24._.BS $C_{16}.D_{12}$ $2^{7} \cdot 3$ $C_{96}.D_{48}$ $2^{10} \cdot 3^{2}$ $2^{3} \cdot 3$ $-$
9216.i.24._.Z $C_{16}.D_{12}$ $2^{7} \cdot 3$ $C_{96}.D_{48}$ $2^{10} \cdot 3^{2}$ $2^{3} \cdot 3$ $-$
9216.j.24.U $C_{16}.D_{12}$ $2^{7} \cdot 3$ $D_{48}.C_{96}$ $2^{10} \cdot 3^{2}$ $2^{3} \cdot 3$ $-$
9216.p.24.g1.a1 $C_{16}.D_{12}$ $2^{7} \cdot 3$ $D_{288}:C_{16}$ $2^{10} \cdot 3^{2}$ $2^{3} \cdot 3$ $-$
9216.p.24.g1.b1 $C_{16}.D_{12}$ $2^{7} \cdot 3$ $D_{288}:C_{16}$ $2^{10} \cdot 3^{2}$ $2^{3} \cdot 3$ $-$
10368.h.27.b1.a1 $C_{16}.D_{12}$ $2^{7} \cdot 3$ $D_{36}.C_{144}$ $2^{7} \cdot 3^{4}$ $3^{3}$ $-$
12288.bt.32._.T $C_{16}.D_{12}$ $2^{7} \cdot 3$ $D_{192}:C_{32}$ $2^{12} \cdot 3$ $2^{5}$ $-$
12288.bt.32._.U $C_{16}.D_{12}$ $2^{7} \cdot 3$ $D_{192}:C_{32}$ $2^{12} \cdot 3$ $2^{5}$ $-$
13824.b.36._.Y $C_{16}.D_{12}$ $2^{7} \cdot 3$ $D_{48}.C_{144}$ $2^{9} \cdot 3^{3}$ $2^{2} \cdot 3^{2}$ $-$
13824.b.36._.Z $C_{16}.D_{12}$ $2^{7} \cdot 3$ $D_{48}.C_{144}$ $2^{9} \cdot 3^{3}$ $2^{2} \cdot 3^{2}$ $-$
13824.i.36.l1.a1 $C_{16}.D_{12}$ $2^{7} \cdot 3$ $C_{96}.D_{72}$ $2^{9} \cdot 3^{3}$ $2^{2} \cdot 3^{2}$ $-$
13824.i.36.l1.b1 $C_{16}.D_{12}$ $2^{7} \cdot 3$ $C_{96}.D_{72}$ $2^{9} \cdot 3^{3}$ $2^{2} \cdot 3^{2}$ $-$
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