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 354 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
1296.3499.1.a1.a1 $C_3^2\wr C_2.D_4$ $2^{4} \cdot 3^{4}$ ✓ ✓ $C_3^2\wr C_2.D_4$ $2^{4} \cdot 3^{4}$ $C_1$ $1$ ✓
2592.fo.2.e1.a1 $C_3^2\wr C_2.D_4$ $2^{4} \cdot 3^{4}$ ✓ ✓ $S_3^2:\PSU(3,2)$ $2^{5} \cdot 3^{4}$ $C_2$ $2$ ✓
2592.fo.2.e1.b1 $C_3^2\wr C_2.D_4$ $2^{4} \cdot 3^{4}$ ✓ ✓ $S_3^2:\PSU(3,2)$ $2^{5} \cdot 3^{4}$ $C_2$ $2$ ✓
2592.lt.2.a1.a1 $C_3^2\wr C_2.D_4$ $2^{4} \cdot 3^{4}$ ✓ ✓ $C_3^2\wr C_2.\SD_{16}$ $2^{5} \cdot 3^{4}$ $C_2$ $2$ ✓
2592.lt.2.a1.b1 $C_3^2\wr C_2.D_4$ $2^{4} \cdot 3^{4}$ ✓ ✓ $C_3^2\wr C_2.\SD_{16}$ $2^{5} \cdot 3^{4}$ $C_2$ $2$ ✓
2592.pp.2.d1.a1 $C_3^2\wr C_2.D_4$ $2^{4} \cdot 3^{4}$ ✓ ✓ $C_3^3:C_{12}:Q_8$ $2^{5} \cdot 3^{4}$ $C_2$ $2$ ✓
2592.pp.2.d1.b1 $C_3^2\wr C_2.D_4$ $2^{4} \cdot 3^{4}$ ✓ ✓ $C_3^3:C_{12}:Q_8$ $2^{5} \cdot 3^{4}$ $C_2$ $2$ ✓
5184.cd.4.e1.a1 $C_3^2\wr C_2.D_4$ $2^{4} \cdot 3^{4}$ $C_3^4:D_8:C_4$ $2^{6} \cdot 3^{4}$ $2^{2}$ $-$
5184.ce.4.c1.a1 $C_3^2\wr C_2.D_4$ $2^{4} \cdot 3^{4}$ $C_3^4:C_{16}:C_4$ $2^{6} \cdot 3^{4}$ $2^{2}$ $-$
5184.gk.4.n1.a1 $C_3^2\wr C_2.D_4$ $2^{4} \cdot 3^{4}$ $(C_3^2\times S_3^2):\SD_{16}$ $2^{6} \cdot 3^{4}$ $2^{2}$ $-$
5184.qs.4.i1 $C_3^2\wr C_2.D_4$ $2^{4} \cdot 3^{4}$ ✓ $C_3^4:(D_4\times Q_8)$ $2^{6} \cdot 3^{4}$ $C_2^2$ $2^{2}$ ✓
5184.sy.4.i1.a1 $C_3^2\wr C_2.D_4$ $2^{4} \cdot 3^{4}$ $C_3^3:C_{12}:\SD_{16}$ $2^{6} \cdot 3^{4}$ $2^{2}$ $-$
5184.sz.4.i1.a1 $C_3^2\wr C_2.D_4$ $2^{4} \cdot 3^{4}$ $F_9:\SOPlus(4,2)$ $2^{6} \cdot 3^{4}$ $2^{2}$ $-$
5184.ta.4.m1.a1 $C_3^2\wr C_2.D_4$ $2^{4} \cdot 3^{4}$ $F_9:\SOPlus(4,2)$ $2^{6} \cdot 3^{4}$ $2^{2}$ $-$
6480.bm.5.a1.a1 $C_3^2\wr C_2.D_4$ $2^{4} \cdot 3^{4}$ ✓ $C_3^4:C_{20}:C_4$ $2^{4} \cdot 3^{4} \cdot 5$ $5$ $-$
10368.bn.8.h1.a1 $C_3^2\wr C_2.D_4$ $2^{4} \cdot 3^{4}$ $C_3^4:D_8:Q_8$ $2^{7} \cdot 3^{4}$ $2^{3}$ $-$
10368.bn.8.h1.b1 $C_3^2\wr C_2.D_4$ $2^{4} \cdot 3^{4}$ $C_3^4:D_8:Q_8$ $2^{7} \cdot 3^{4}$ $2^{3}$ $-$
10368.ov.8.q1.a1 $C_3^2\wr C_2.D_4$ $2^{4} \cdot 3^{4}$ $C_3^4:\OD_{32}:C_2^2$ $2^{7} \cdot 3^{4}$ $2^{3}$ $-$
10368.ov.8.q1.b1 $C_3^2\wr C_2.D_4$ $2^{4} \cdot 3^{4}$ $C_3^4:\OD_{32}:C_2^2$ $2^{7} \cdot 3^{4}$ $2^{3}$ $-$
10368.ov.8.r1.a1 $C_3^2\wr C_2.D_4$ $2^{4} \cdot 3^{4}$ $C_3^4:\OD_{32}:C_2^2$ $2^{7} \cdot 3^{4}$ $2^{3}$ $-$
10368.ow.8.m1.a1 $C_3^2\wr C_2.D_4$ $2^{4} \cdot 3^{4}$ $C_3^4:\OD_{32}:C_4$ $2^{7} \cdot 3^{4}$ $2^{3}$ $-$
10368.ow.8.m1.b1 $C_3^2\wr C_2.D_4$ $2^{4} \cdot 3^{4}$ $C_3^4:\OD_{32}:C_4$ $2^{7} \cdot 3^{4}$ $2^{3}$ $-$
10368.ow.8.n1.a1 $C_3^2\wr C_2.D_4$ $2^{4} \cdot 3^{4}$ $C_3^4:\OD_{32}:C_4$ $2^{7} \cdot 3^{4}$ $2^{3}$ $-$
10368.ox.8.j1.a1 $C_3^2\wr C_2.D_4$ $2^{4} \cdot 3^{4}$ $C_3^2:F_9.C_4^2$ $2^{7} \cdot 3^{4}$ $2^{3}$ $-$
10368.ox.8.j1.b1 $C_3^2\wr C_2.D_4$ $2^{4} \cdot 3^{4}$ $C_3^2:F_9.C_4^2$ $2^{7} \cdot 3^{4}$ $2^{3}$ $-$
10368.ox.8.k1.a1 $C_3^2\wr C_2.D_4$ $2^{4} \cdot 3^{4}$ $C_3^2:F_9.C_4^2$ $2^{7} \cdot 3^{4}$ $2^{3}$ $-$
10368.oy.8.k1.a1 $C_3^2\wr C_2.D_4$ $2^{4} \cdot 3^{4}$ $C_3^4:\OD_{32}:C_4$ $2^{7} \cdot 3^{4}$ $2^{3}$ $-$
10368.oy.8.k1.b1 $C_3^2\wr C_2.D_4$ $2^{4} \cdot 3^{4}$ $C_3^4:\OD_{32}:C_4$ $2^{7} \cdot 3^{4}$ $2^{3}$ $-$
10368.oy.8.m1.a1 $C_3^2\wr C_2.D_4$ $2^{4} \cdot 3^{4}$ $C_3^4:\OD_{32}:C_4$ $2^{7} \cdot 3^{4}$ $2^{3}$ $-$
10368.qo.8.bq1 $C_3^2\wr C_2.D_4$ $2^{4} \cdot 3^{4}$ $\SOPlus(4,2)^2.C_2$ $2^{7} \cdot 3^{4}$ $2^{3}$ $-$
10368.qo.8.br1 $C_3^2\wr C_2.D_4$ $2^{4} \cdot 3^{4}$ $\SOPlus(4,2)^2.C_2$ $2^{7} \cdot 3^{4}$ $2^{3}$ $-$
11664.dc.9.B $C_3^2\wr C_2.D_4$ $2^{4} \cdot 3^{4}$ ✓ $C_3^6.C_4:C_4$ $2^{4} \cdot 3^{6}$ $3^{2}$ $-$
11664.do.9.b1 $C_3^2\wr C_2.D_4$ $2^{4} \cdot 3^{4}$ ✓ $C_3^6.C_4:C_4$ $2^{4} \cdot 3^{6}$ $3^{2}$ $-$
12960.bx.10.a1.a1 $C_3^2\wr C_2.D_4$ $2^{4} \cdot 3^{4}$ $C_3^4:C_{40}:C_4$ $2^{5} \cdot 3^{4} \cdot 5$ $2 \cdot 5$ $-$
12960.bx.10.a1.b1 $C_3^2\wr C_2.D_4$ $2^{4} \cdot 3^{4}$ $C_3^4:C_{40}:C_4$ $2^{5} \cdot 3^{4} \cdot 5$ $2 \cdot 5$ $-$
15552.ll.12.p1.a1 $C_3^2\wr C_2.D_4$ $2^{4} \cdot 3^{4}$ $C_3^4:(D_4\times \SL(2,3))$ $2^{6} \cdot 3^{5}$ $2^{2} \cdot 3$ $-$
15552.ll.12.p1.a2 $C_3^2\wr C_2.D_4$ $2^{4} \cdot 3^{4}$ $C_3^4:(D_4\times \SL(2,3))$ $2^{6} \cdot 3^{5}$ $2^{2} \cdot 3$ $-$
20736.v.16.l1.a1 $C_3^2\wr C_2.D_4$ $2^{4} \cdot 3^{4}$ $C_3^4:(C_8^2:C_4)$ $2^{8} \cdot 3^{4}$ $2^{4}$ $-$
20736.x.16.q1.a1 $C_3^2\wr C_2.D_4$ $2^{4} \cdot 3^{4}$ $F_9\wr C_2:C_2$ $2^{8} \cdot 3^{4}$ $2^{4}$ $-$
20736.ku.16.bv1.d1 $C_3^2\wr C_2.D_4$ $2^{4} \cdot 3^{4}$ $C_6^2:S_3^2.D_8$ $2^{8} \cdot 3^{4}$ $2^{4}$ $-$
20736.ku.16.bv1.a1 $C_3^2\wr C_2.D_4$ $2^{4} \cdot 3^{4}$ $C_6^2:S_3^2.D_8$ $2^{8} \cdot 3^{4}$ $2^{4}$ $-$
20736.ku.16.bv1.b1 $C_3^2\wr C_2.D_4$ $2^{4} \cdot 3^{4}$ $C_6^2:S_3^2.D_8$ $2^{8} \cdot 3^{4}$ $2^{4}$ $-$
20736.ku.16.bv1.c1 $C_3^2\wr C_2.D_4$ $2^{4} \cdot 3^{4}$ $C_6^2:S_3^2.D_8$ $2^{8} \cdot 3^{4}$ $2^{4}$ $-$
20736.ku.16.bx1.b1 $C_3^2\wr C_2.D_4$ $2^{4} \cdot 3^{4}$ $C_6^2:S_3^2.D_8$ $2^{8} \cdot 3^{4}$ $2^{4}$ $-$
20736.ku.16.bx1.a1 $C_3^2\wr C_2.D_4$ $2^{4} \cdot 3^{4}$ $C_6^2:S_3^2.D_8$ $2^{8} \cdot 3^{4}$ $2^{4}$ $-$
20736.ku.16.by1.b1 $C_3^2\wr C_2.D_4$ $2^{4} \cdot 3^{4}$ $C_6^2:S_3^2.D_8$ $2^{8} \cdot 3^{4}$ $2^{4}$ $-$
20736.ku.16.by1.d1 $C_3^2\wr C_2.D_4$ $2^{4} \cdot 3^{4}$ $C_6^2:S_3^2.D_8$ $2^{8} \cdot 3^{4}$ $2^{4}$ $-$
20736.ku.16.by1.a1 $C_3^2\wr C_2.D_4$ $2^{4} \cdot 3^{4}$ $C_6^2:S_3^2.D_8$ $2^{8} \cdot 3^{4}$ $2^{4}$ $-$
20736.ku.16.by1.c1 $C_3^2\wr C_2.D_4$ $2^{4} \cdot 3^{4}$ $C_6^2:S_3^2.D_8$ $2^{8} \cdot 3^{4}$ $2^{4}$ $-$
20736.kv.16.bf1.a1 $C_3^2\wr C_2.D_4$ $2^{4} \cdot 3^{4}$ $C_6^2:S_3^2.\SD_{16}$ $2^{8} \cdot 3^{4}$ $2^{4}$ $-$
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