Subgroups — Dic₂₁₆₃ #22575739

Order 8652.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₇×C₁₀₃	C₂	1	1	yes	maximal, characteristic
2	Dic₇₂₁	—	3	1	no	maximal, Hall
3	C₃×C₇×C₁₀₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₇×C₁₀₃	D₃	1	1	yes	characteristic
5	Dic₃₀₉	—	7	1	no	maximal, Hall
6	C₇×C₁₀₃	Dic₃	1	1	yes	characteristic, complemented, Hall
7	C₂×C₃×C₁₀₃	D₇	1	1	yes	characteristic
8	Dic₁₀₃	—	21	1	no	Hall
9	C₃×C₁₀₃	Dic₇	1	1	yes	characteristic, complemented, Hall
10	C₂×C₁₀₃	D₂₁	1	1	yes	characteristic
11	C₁₀₃	Dic₂₁	1	1	yes	characteristic, complemented, Sylow
12	Dic₂₁	—	103	1	no	maximal, Hall
13	C₂×C₃×C₇	D₁₀₃	1	1	yes	characteristic
14	Dic₇	—	309	1	no	Hall
15	C₃×C₇	Dic₁₀₃	1	1	yes	characteristic, complemented, Hall
16	C₂×C₇	D₃₀₉	1	1	yes	characteristic
17	Dic₃	—	721	1	no	Hall
18	C₇	Dic₃₀₉	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₃	D₇₂₁	1	1	yes	characteristic
20	C₄	—	2163	1	no	Sylow
21	C₃	Dic₇₂₁	1	1	yes	characteristic, complemented, Sylow
22	C₂	D₂₁₆₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₂₁₆₃
commutator, hypocenter	C₃×C₇×C₁₀₃	C₄
Fitting, socle	C₂×C₃×C₇×C₁₀₃	C₂
LCS	G ▷ C₃×C₇×C₁₀₃
UCS	C₁ ◁ C₂

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