Subgroups — C₁₁×C₃₂×C₅₃ #72196444

Order 18656.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×C₁₆×C₅₃	C₂	1	1	yes	maximal, characteristic
2	C₈×C₁₁×C₅₃	C₄	1	1	yes	characteristic
3	C₄×C₁₁×C₅₃	C₈	1	1	yes	characteristic
4	C₃₂×C₅₃	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₁₁×C₅₃	C₁₆	1	1	yes	characteristic
6	C₁₆×C₅₃	C₂×C₁₁	1	1	yes	characteristic
7	C₁₁×C₅₃	C₃₂	1	1	yes	characteristic, direct product factor, Hall
8	C₈×C₅₃	C₄×C₁₁	1	1	yes	characteristic
9	C₁₁×C₃₂	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₄×C₅₃	C₈×C₁₁	1	1	yes	characteristic
11	C₁₁×C₁₆	C₂×C₅₃	1	1	yes	characteristic
12	C₂×C₅₃	C₁₁×C₁₆	1	1	yes	characteristic
13	C₈×C₁₁	C₄×C₅₃	1	1	yes	characteristic
14	C₅₃	C₁₁×C₃₂	1	1	yes	characteristic, direct product factor, Sylow
15	C₄×C₁₁	C₈×C₅₃	1	1	yes	characteristic
16	C₃₂	C₁₁×C₅₃	1	1	yes	characteristic, direct product factor, Sylow
17	C₂×C₁₁	C₁₆×C₅₃	1	1	yes	characteristic
18	C₁₆	C₂×C₁₁×C₅₃	1	1	yes	characteristic
19	C₁₁	C₃₂×C₅₃	1	1	yes	characteristic, direct product factor, Sylow
20	C₈	C₄×C₁₁×C₅₃	1	1	yes	characteristic
21	C₄	C₈×C₁₁×C₅₃	1	1	yes	characteristic
22	C₂	C₁₁×C₁₆×C₅₃	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.