Subgroups — Dic₈₀₄₁ #44565485

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	Dic₇₃₁	—	11	1	no	maximal, Hall
4	Dic₄₇₃	—	17	1	no	maximal, Hall
5	C₂×C₁₇×C₄₃	D₁₁	1	1	yes	characteristic
6	C₂×C₁₁×C₄₃	D₁₇	1	1	yes	characteristic
7	Dic₁₈₇	—	43	1	no	maximal, Hall
8	C₁₇×C₄₃	Dic₁₁	1	1	yes	characteristic, complemented, Hall
9	C₁₁×C₄₃	Dic₁₇	1	1	yes	characteristic, complemented, Hall
10	C₂×C₁₁×C₁₇	D₄₃	1	1	yes	characteristic
11	C₁₁×C₁₇	Dic₄₃	1	1	yes	characteristic, complemented, Hall
12	Dic₄₃	—	187	1	no	Hall
13	C₂×C₄₃	D₁₈₇	1	1	yes	characteristic
14	Dic₁₇	—	473	1	no	Hall
15	Dic₁₁	—	731	1	no	Hall
16	C₄₃	Dic₁₈₇	1	1	yes	characteristic, complemented, Sylow
17	C₂×C₁₇	D₄₇₃	1	1	yes	characteristic
18	C₂×C₁₁	D₇₃₁	1	1	yes	characteristic
19	C₁₇	Dic₄₇₃	1	1	yes	characteristic, complemented, Sylow
20	C₁₁	Dic₇₃₁	1	1	yes	characteristic, complemented, Sylow
21	C₄	—	8041	1	no	Sylow
22	C₂	D₈₀₄₁	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₈₀₄₁
commutator, hypocenter	C₁₁×C₁₇×C₄₃	C₄
Fitting, socle, prime radical, cosocle	C₂×C₁₁×C₁₇×C₄₃	C₂
LCS	G ▷ C₁₁×C₁₇×C₄₃
UCS	C₁ ◁ C₂

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.