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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 (30 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
705277476864.ie.1.a1.a1 $C_3^{12}.C_2^8.C_3^4.D_4:D_4$ $2^{14} \cdot 3^{16}$ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.D_4:D_4$ $2^{14} \cdot 3^{16}$ $C_1$ $1$ ✓
705277476864.ie.2._.A $C_3^{12}.C_2^8.C_3^4.D_8.C_2$ $2^{13} \cdot 3^{16}$ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.D_4:D_4$ $2^{14} \cdot 3^{16}$ $C_2$ $2$ ✓
705277476864.ie.2._.B $C_3^{12}.C_2^8.C_3^4.C_4\wr C_2$ $2^{13} \cdot 3^{16}$ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.D_4:D_4$ $2^{14} \cdot 3^{16}$ $C_2$ $2$ ✓
705277476864.ie.2._.C $C_3^{12}.C_2^8.C_3^4.\OD_{16}.C_2$ $2^{13} \cdot 3^{16}$ ✓ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.D_4:D_4$ $2^{14} \cdot 3^{16}$ $C_2$ $2$ ✓
705277476864.ie.2._.D $C_3^{12}.C_2^8.C_3^4.D_8.C_2$ $2^{13} \cdot 3^{16}$ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.D_4:D_4$ $2^{14} \cdot 3^{16}$ $C_2$ $2$ ✓
705277476864.ie.2._.E $C_3^{12}.C_2^8.C_3.S_3^3.C_2^2$ $2^{13} \cdot 3^{16}$ ✓ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.D_4:D_4$ $2^{14} \cdot 3^{16}$ $C_2$ $2$ ✓
705277476864.ie.2._.F $C_3^{12}.C_2^8.C_3^4.C_4\wr C_2$ $2^{13} \cdot 3^{16}$ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.D_4:D_4$ $2^{14} \cdot 3^{16}$ $C_2$ $2$ ✓
705277476864.ie.2._.G $C_3^{12}.C_2^4.A_4^2.C_4:S_3\wr C_2$ $2^{13} \cdot 3^{16}$ ✓ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.D_4:D_4$ $2^{14} \cdot 3^{16}$ $C_2$ $2$ ✓
705277476864.ie.4._.A $C_3^{12}.C_2^4.C_2^4.C_3^4.C_2^3.C_2$ $2^{12} \cdot 3^{16}$ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.D_4:D_4$ $2^{14} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
705277476864.ie.4._.B $C_3^{12}.C_2^8.C_3^4.\OD_{16}$ $2^{12} \cdot 3^{16}$ ✓ $C_3^{12}.C_2^8.C_3^4.D_4:D_4$ $2^{14} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
705277476864.ie.4._.C $C_3^{12}.C_2^8.C_3^4.D_4:C_2$ $2^{12} \cdot 3^{16}$ ✓ $C_3^{12}.C_2^8.C_3^4.D_4:D_4$ $2^{14} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
705277476864.ie.4._.D $C_3^{12}.C_2^4.C_2^4.C_3^4.C_2^3.C_2$ $2^{12} \cdot 3^{16}$ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.D_4:D_4$ $2^{14} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
705277476864.ie.4._.E $C_3^{12}.C_2^8.C_3^4.D_4:C_2$ $2^{12} \cdot 3^{16}$ ✓ $C_3^{12}.C_2^8.C_3^4.D_4:D_4$ $2^{14} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
705277476864.ie.4._.F $C_3^{12}.C_2^4.A_4^2.C_3^2.C_4^2$ $2^{12} \cdot 3^{16}$ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.D_4:D_4$ $2^{14} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
705277476864.ie.4._.G $C_3^{12}.C_2^8.C_3^4.\OD_{16}$ $2^{12} \cdot 3^{16}$ ✓ $C_3^{12}.C_2^8.C_3^4.D_4:D_4$ $2^{14} \cdot 3^{16}$ $C_2^2$ $2^{2}$ ✓
705277476864.ie.8._.A $C_3^{12}.C_2^8.C_3^4.Q_8$ $2^{11} \cdot 3^{16}$ ✓ $C_3^{12}.C_2^8.C_3^4.D_4:D_4$ $2^{14} \cdot 3^{16}$ $D_4$ $2^{3}$
705277476864.ie.8._.B $C_3^{12}.C_2^4.C_2^4.C_3^4.C_2^2.C_2$ $2^{11} \cdot 3^{16}$ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.D_4:D_4$ $2^{14} \cdot 3^{16}$ $C_2^3$ $2^{3}$ ✓
705277476864.ie.8._.C $C_3^{12}.C_2^4.C_2^4.C_3.S_3^3$ $2^{11} \cdot 3^{16}$ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.D_4:D_4$ $2^{14} \cdot 3^{16}$ $D_4$ $2^{3}$
705277476864.ie.8._.D $C_3^{12}.C_2^6.C_2^2.C_3.S_3^3$ $2^{11} \cdot 3^{16}$ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.D_4:D_4$ $2^{14} \cdot 3^{16}$ $D_4$ $2^{3}$
705277476864.ie.8._.E $C_3^{12}.C_2^8.C_3^4.Q_8$ $2^{11} \cdot 3^{16}$ ✓ $C_3^{12}.C_2^8.C_3^4.D_4:D_4$ $2^{14} \cdot 3^{16}$ $D_4$ $2^{3}$
705277476864.ie.8._.F $C_3^{12}.C_2^8.C_3^4.D_4$ $2^{11} \cdot 3^{16}$ ✓ $C_3^{12}.C_2^8.C_3^4.D_4:D_4$ $2^{14} \cdot 3^{16}$ $D_4$ $2^{3}$
705277476864.ie.8._.G $C_3^{12}.C_2^8.C_3^4.D_4$ $2^{11} \cdot 3^{16}$ ✓ $C_3^{12}.C_2^8.C_3^4.D_4:D_4$ $2^{14} \cdot 3^{16}$ $D_4$ $2^{3}$
705277476864.ie.16._.A $C_3^{12}.C_2^6.C_6^2.S_3^2$ $2^{10} \cdot 3^{16}$ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.D_4:D_4$ $2^{14} \cdot 3^{16}$ $C_2\times D_4$ $2^{4}$
705277476864.ie.16._.B $C_3^{12}.C_2^4.A_4^2.C_3^2.C_4$ $2^{10} \cdot 3^{16}$ ✓ $C_3^{12}.C_2^8.C_3^4.D_4:D_4$ $2^{14} \cdot 3^{16}$ $C_2\times D_4$ $2^{4}$
705277476864.ie.16._.C $C_3^{12}.C_2^4.A_4^2.C_3^2.C_4$ $2^{10} \cdot 3^{16}$ ✓ $C_3^{12}.C_2^8.C_3^4.D_4:D_4$ $2^{14} \cdot 3^{16}$ $C_2\times D_4$ $2^{4}$
705277476864.ie.32._.A $C_3^{12}.C_2^6.C_6^2.C_3.S_3$ $2^{9} \cdot 3^{16}$ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.D_4:D_4$ $2^{14} \cdot 3^{16}$ $C_2^2\wr C_2$ $2^{5}$
705277476864.ie.64._.A $C_3^{12}.C_2^6.C_6^2.C_3^2$ $2^{8} \cdot 3^{16}$ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.D_4:D_4$ $2^{14} \cdot 3^{16}$ $D_4:D_4$ $2^{6}$
705277476864.ie.5184._.A $C_3^{11}.D_6.C_2^6$ $2^{8} \cdot 3^{12}$ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.D_4:D_4$ $2^{14} \cdot 3^{16}$ $C_3^4:D_4:D_4$ $2^{6} \cdot 3^{4}$
705277476864.ie.1327104._.A $C_3^{12}$ $3^{12}$ ✓ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.D_4:D_4$ $2^{14} \cdot 3^{16}$ $A_4^2\wr C_2.C_2^2.D_4$ $2^{14} \cdot 3^{4}$ ✓
705277476864.ie.705277476864.a1.a1 $C_1$ $1$ ✓ ✓ ✓ ✓ $C_3^{12}.C_2^8.C_3^4.D_4:D_4$ $2^{14} \cdot 3^{16}$ $C_3^{12}.C_2^8.C_3^4.D_4:D_4$ $2^{14} \cdot 3^{16}$
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