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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 68 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
26244.hm.1.a1.a1 $C_3^6.D_{18}$ $2^{2} \cdot 3^{8}$ ✓ ✓ $C_3^6.D_{18}$ $2^{2} \cdot 3^{8}$ $C_1$ $1$ ✓
26244.hm.2._.A $C_3^7.C_6$ $2 \cdot 3^{8}$ ✓ ✓ ✓ $C_3^6.D_{18}$ $2^{2} \cdot 3^{8}$ $C_2$ $2$ ✓
26244.hm.2._.B $C_3^6.C_3.C_6$ $2 \cdot 3^{8}$ ✓ ✓ $C_3^6.D_{18}$ $2^{2} \cdot 3^{8}$ $C_2$ $2$ ✓
26244.hm.2._.C $C_3^6.C_3.C_6$ $2 \cdot 3^{8}$ ✓ ✓ $C_3^6.D_{18}$ $2^{2} \cdot 3^{8}$ $C_2$ $2$ ✓
26244.hm.4.a1.a1 $C_3^7.C_3$ $3^{8}$ $3$ ✓ ✓ $C_3^6.D_{18}$ $2^{2} \cdot 3^{8}$ $C_2^2$ $2^{2}$ ✓
26244.hm.6._.A $C_3^6.S_3$ $2 \cdot 3^{7}$ ✓ $C_3^6.D_{18}$ $2^{2} \cdot 3^{8}$ $S_3$ $2 \cdot 3$
26244.hm.6._.B $C_3^7.C_2$ $2 \cdot 3^{7}$ ✓ ✓ $C_3^6.D_{18}$ $2^{2} \cdot 3^{8}$ $S_3$ $2 \cdot 3$
26244.hm.6._.C $C_3^6.S_3$ $2 \cdot 3^{7}$ ✓ $C_3^6.D_{18}$ $2^{2} \cdot 3^{8}$ $S_3$ $2 \cdot 3$
26244.hm.12._.A $C_3^7$ $3^{7}$ ✓ ✓ ✓ $C_3^6.D_{18}$ $2^{2} \cdot 3^{8}$ $D_6$ $2^{2} \cdot 3$
26244.hm.12._.B $C_3^6.C_3$ $3^{7}$ ✓ $C_3^6.D_{18}$ $2^{2} \cdot 3^{8}$ $D_6$ $2^{2} \cdot 3$
26244.hm.12._.C $C_3^6.C_3$ $3^{7}$ ✓ $C_3^6.D_{18}$ $2^{2} \cdot 3^{8}$ $D_6$ $2^{2} \cdot 3$
26244.hm.18._.A $C_3^5:S_3$ $2 \cdot 3^{6}$ ✓ ✓ $C_3^6.D_{18}$ $2^{2} \cdot 3^{8}$ $D_9$ $2 \cdot 3^{2}$
26244.hm.36._.A $C_3^6$ $3^{6}$ ✓ ✓ $C_3^6.D_{18}$ $2^{2} \cdot 3^{8}$ $S_3^2$ $2^{2} \cdot 3^{2}$
26244.hm.36._.B $C_3^6$ $3^{6}$ ✓ ✓ $C_3^6.D_{18}$ $2^{2} \cdot 3^{8}$ $S_3^2$ $2^{2} \cdot 3^{2}$
26244.hm.36._.C $C_3^4:C_9$ $3^{6}$ ✓ ✓ $C_3^6.D_{18}$ $2^{2} \cdot 3^{8}$ $S_3^2$ $2^{2} \cdot 3^{2}$
26244.hm.36._.D $C_3^6$ $3^{6}$ ✓ ✓ ✓ $C_3^6.D_{18}$ $2^{2} \cdot 3^{8}$ $D_{18}$ $2^{2} \cdot 3^{2}$
26244.hm.108._.A $C_3^5$ $3^{5}$ ✓ ✓ $C_3^6.D_{18}$ $2^{2} \cdot 3^{8}$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$
26244.hm.108._.B $C_3^5$ $3^{5}$ ✓ ✓ $C_3^6.D_{18}$ $2^{2} \cdot 3^{8}$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$
26244.hm.108._.C $C_3^5$ $3^{5}$ ✓ ✓ $C_3^6.D_{18}$ $2^{2} \cdot 3^{8}$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$
26244.hm.108._.D $C_3^5$ $3^{5}$ ✓ ✓ ✓ $C_3^6.D_{18}$ $2^{2} \cdot 3^{8}$ $C_3:S_3^2$ $2^{2} \cdot 3^{3}$
26244.hm.108._.E $C_3^5$ $3^{5}$ ✓ ✓ $C_3^6.D_{18}$ $2^{2} \cdot 3^{8}$ $S_3\times D_9$ $2^{2} \cdot 3^{3}$
26244.hm.108._.F $C_3^5$ $3^{5}$ ✓ ✓ $C_3^6.D_{18}$ $2^{2} \cdot 3^{8}$ $S_3\times D_9$ $2^{2} \cdot 3^{3}$
26244.hm.108._.G $C_3^5$ $3^{5}$ ✓ ✓ $C_3^6.D_{18}$ $2^{2} \cdot 3^{8}$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$
26244.hm.108._.H $C_3^5$ $3^{5}$ ✓ ✓ $C_3^6.D_{18}$ $2^{2} \cdot 3^{8}$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$
26244.hm.108._.I $C_3^5$ $3^{5}$ ✓ ✓ $C_3^6.D_{18}$ $2^{2} \cdot 3^{8}$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$
26244.hm.324._.A $C_3^4$ $3^{4}$ ✓ ✓ $C_3^6.D_{18}$ $2^{2} \cdot 3^{8}$ $C_3^3:D_6$ $2^{2} \cdot 3^{4}$
26244.hm.324._.B $C_3^4$ $3^{4}$ ✓ ✓ $C_3^6.D_{18}$ $2^{2} \cdot 3^{8}$ $C_3^3:D_6$ $2^{2} \cdot 3^{4}$
26244.hm.324._.C $C_3^4$ $3^{4}$ ✓ ✓ $C_3^6.D_{18}$ $2^{2} \cdot 3^{8}$ $C_3^3:D_6$ $2^{2} \cdot 3^{4}$
26244.hm.324._.D $C_3^4$ $3^{4}$ ✓ ✓ $C_3^6.D_{18}$ $2^{2} \cdot 3^{8}$ $C_3^2:D_{18}$ $2^{2} \cdot 3^{4}$
26244.hm.324._.E $C_3^4$ $3^{4}$ ✓ ✓ $C_3^6.D_{18}$ $2^{2} \cdot 3^{8}$ $C_3^2:D_{18}$ $2^{2} \cdot 3^{4}$
26244.hm.324._.F $C_3^4$ $3^{4}$ ✓ ✓ $C_3^6.D_{18}$ $2^{2} \cdot 3^{8}$ $C_3^2:D_{18}$ $2^{2} \cdot 3^{4}$
26244.hm.324._.G $C_3^4$ $3^{4}$ ✓ ✓ $C_3^6.D_{18}$ $2^{2} \cdot 3^{8}$ $C_3^2:D_{18}$ $2^{2} \cdot 3^{4}$
26244.hm.324._.H $C_3^4$ $3^{4}$ ✓ ✓ $C_3^6.D_{18}$ $2^{2} \cdot 3^{8}$ $C_3^2:S_3^2$ $2^{2} \cdot 3^{4}$
26244.hm.324._.I $C_3^4$ $3^{4}$ ✓ ✓ $C_3^6.D_{18}$ $2^{2} \cdot 3^{8}$ $C_3^2:S_3^2$ $2^{2} \cdot 3^{4}$
26244.hm.324._.J $C_3^4$ $3^{4}$ ✓ ✓ $C_3^6.D_{18}$ $2^{2} \cdot 3^{8}$ $C_3^3:D_6$ $2^{2} \cdot 3^{4}$
26244.hm.324._.K $C_3^4$ $3^{4}$ ✓ ✓ ✓ $C_3^6.D_{18}$ $2^{2} \cdot 3^{8}$ $C_9:S_3^2$ $2^{2} \cdot 3^{4}$
26244.hm.324._.L $C_3^4$ $3^{4}$ ✓ ✓ $C_3^6.D_{18}$ $2^{2} \cdot 3^{8}$ $C_3^3:D_6$ $2^{2} \cdot 3^{4}$
26244.hm.324._.M $C_3^4$ $3^{4}$ ✓ ✓ $C_3^6.D_{18}$ $2^{2} \cdot 3^{8}$ $C_3^2:D_{18}$ $2^{2} \cdot 3^{4}$
26244.hm.324._.N $C_3^4$ $3^{4}$ ✓ ✓ $C_3^6.D_{18}$ $2^{2} \cdot 3^{8}$ $C_3^2:D_{18}$ $2^{2} \cdot 3^{4}$
26244.hm.324._.O $C_3^4$ $3^{4}$ ✓ ✓ $C_3^6.D_{18}$ $2^{2} \cdot 3^{8}$ $C_3^3:D_6$ $2^{2} \cdot 3^{4}$
26244.hm.972._.A $C_3^3$ $3^{3}$ ✓ ✓ $C_3^6.D_{18}$ $2^{2} \cdot 3^{8}$ $C_3^3:D_{18}$ $2^{2} \cdot 3^{5}$
26244.hm.972._.B $C_3^3$ $3^{3}$ ✓ ✓ $C_3^6.D_{18}$ $2^{2} \cdot 3^{8}$ $C_3^3:D_{18}$ $2^{2} \cdot 3^{5}$
26244.hm.972._.C $C_3^3$ $3^{3}$ ✓ ✓ $C_3^6.D_{18}$ $2^{2} \cdot 3^{8}$ $C_3^3:D_{18}$ $2^{2} \cdot 3^{5}$
26244.hm.972._.D $C_3^3$ $3^{3}$ ✓ ✓ $C_3^6.D_{18}$ $2^{2} \cdot 3^{8}$ $C_3^3:D_{18}$ $2^{2} \cdot 3^{5}$
26244.hm.972._.E $C_3^3$ $3^{3}$ ✓ ✓ $C_3^6.D_{18}$ $2^{2} \cdot 3^{8}$ $C_3^3:D_{18}$ $2^{2} \cdot 3^{5}$
26244.hm.972._.F $C_3^3$ $3^{3}$ ✓ ✓ $C_3^6.D_{18}$ $2^{2} \cdot 3^{8}$ $C_3^3:D_{18}$ $2^{2} \cdot 3^{5}$
26244.hm.972._.G $C_3^3$ $3^{3}$ ✓ ✓ $C_3^6.D_{18}$ $2^{2} \cdot 3^{8}$ $C_3^3:S_3^2$ $2^{2} \cdot 3^{5}$
26244.hm.972._.H $C_3^3$ $3^{3}$ ✓ ✓ $C_3^6.D_{18}$ $2^{2} \cdot 3^{8}$ $C_3^3:S_3^2$ $2^{2} \cdot 3^{5}$
26244.hm.972._.I $C_3^3$ $3^{3}$ ✓ ✓ $C_3^6.D_{18}$ $2^{2} \cdot 3^{8}$ $C_3^3:S_3^2$ $2^{2} \cdot 3^{5}$
26244.hm.972._.J $C_3^3$ $3^{3}$ ✓ ✓ $C_3^6.D_{18}$ $2^{2} \cdot 3^{8}$ $C_3^3:S_3^2$ $2^{2} \cdot 3^{5}$
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