Subgroups — C₁₇×C₄₃×Dic₁₁ #44565482

Order 32164.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×C₁₇×C₄₃	C₂	1	1	yes	maximal, characteristic
2	C₁₁×C₁₇×C₄₃	C₄	1	1	yes	characteristic, complemented, Hall
3	C₄×C₁₇×C₄₃	—	11	1	no	maximal, Hall
4	C₄₃×Dic₁₁	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₁₇×C₄₃	D₁₁	1	1	yes	characteristic
6	C₂×C₁₁×C₄₃	C₂×C₁₇	1	1	yes	characteristic
7	C₁₇×Dic₁₁	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₁₇×C₄₃	Dic₁₁	1	1	yes	characteristic, direct product factor, Hall
9	C₁₁×C₄₃	C₄×C₁₇	1	1	yes	characteristic, complemented, Hall
10	C₂×C₁₁×C₁₇	C₂×C₄₃	1	1	yes	characteristic
11	C₁₁×C₁₇	C₄×C₄₃	1	1	yes	characteristic, complemented, Hall
12	C₄×C₄₃	—	11	1	no	Hall
13	C₂×C₄₃	C₁₇×D₁₁	1	1	yes	characteristic
14	C₄×C₁₇	—	11	1	no	Hall
15	Dic₁₁	C₁₇×C₄₃	1	1	yes	characteristic, direct product factor, Hall
16	C₄₃	C₁₇×Dic₁₁	1	1	yes	characteristic, direct product factor, Sylow
17	C₂×C₁₇	D₁₁×C₄₃	1	1	yes	characteristic
18	C₂×C₁₁	C₂×C₁₇×C₄₃	1	1	yes	characteristic
19	C₁₇	C₄₃×Dic₁₁	1	1	yes	characteristic, direct product factor, Sylow
20	C₁₁	C₄×C₁₇×C₄₃	1	1	yes	characteristic, complemented, Sylow
21	C₄	—	11	1	no	Sylow
22	C₂	C₁₇×D₁₁×C₄₃	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.