Subgroups — Dic₂₇₀₃ #24925199

Order 10812.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₁₇×C₅₃	C₂	1	1	yes	maximal, characteristic
2	Dic₉₀₁	—	3	1	no	maximal, Hall
3	C₃×C₁₇×C₅₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₇×C₅₃	D₃	1	1	yes	characteristic
5	C₁₇×C₅₃	Dic₃	1	1	yes	characteristic, complemented, Hall
6	Dic₁₅₉	—	17	1	no	maximal, Hall
7	C₂×C₃×C₅₃	D₁₇	1	1	yes	characteristic
8	Dic₅₃	—	51	1	no	Hall
9	Dic₅₁	—	53	1	no	maximal, Hall
10	C₃×C₅₃	Dic₁₇	1	1	yes	characteristic, complemented, Hall
11	C₂×C₅₃	D₅₁	1	1	yes	characteristic
12	C₂×C₃×C₁₇	D₅₃	1	1	yes	characteristic
13	Dic₁₇	—	159	1	no	Hall
14	C₅₃	Dic₅₁	1	1	yes	characteristic, complemented, Sylow
15	C₃×C₁₇	Dic₅₃	1	1	yes	characteristic, complemented, Hall
16	C₂×C₁₇	D₁₅₉	1	1	yes	characteristic
17	C₁₇	Dic₁₅₉	1	1	yes	characteristic, complemented, Sylow
18	Dic₃	—	901	1	no	Hall
19	C₂×C₃	D₉₀₁	1	1	yes	characteristic
20	C₄	—	2703	1	no	Sylow
21	C₃	Dic₉₀₁	1	1	yes	characteristic, complemented, Sylow
22	C₂	D₂₇₀₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₂₇₀₃
commutator, hypocenter	C₃×C₁₇×C₅₃	C₄
Fitting, socle, prime radical, cosocle	C₂×C₃×C₁₇×C₅₃	C₂
LCS	G ▷ C₃×C₁₇×C₅₃
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.