Subgroups — Dic₆₀₆₃ #37564639

Order 24252.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄₃×C₄₇	C₂	1	1	yes	maximal, characteristic
2	Dic₂₀₂₁	—	3	1	no	maximal, Hall
3	C₃×C₄₃×C₄₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₄₃×C₄₇	D₃	1	1	yes	characteristic
5	C₄₃×C₄₇	Dic₃	1	1	yes	characteristic, complemented, Hall
6	Dic₁₄₁	—	43	1	no	maximal, Hall
7	Dic₁₂₉	—	47	1	no	maximal, Hall
8	C₂×C₃×C₄₇	D₄₃	1	1	yes	characteristic
9	C₂×C₃×C₄₃	D₄₇	1	1	yes	characteristic
10	Dic₄₇	—	129	1	no	Hall
11	Dic₄₃	—	141	1	no	Hall
12	C₃×C₄₇	Dic₄₃	1	1	yes	characteristic, complemented, Hall
13	C₃×C₄₃	Dic₄₇	1	1	yes	characteristic, complemented, Hall
14	C₂×C₄₇	D₁₂₉	1	1	yes	characteristic
15	C₂×C₄₃	D₁₄₁	1	1	yes	characteristic
16	C₄₇	Dic₁₂₉	1	1	yes	characteristic, complemented, Sylow
17	C₄₃	Dic₁₄₁	1	1	yes	characteristic, complemented, Sylow
18	Dic₃	—	2021	1	no	Hall
19	C₂×C₃	D₂₀₂₁	1	1	yes	characteristic
20	C₄	—	6063	1	no	Sylow
21	C₃	Dic₂₀₂₁	1	1	yes	characteristic, complemented, Sylow
22	C₂	D₆₀₆₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₆₀₆₃
commutator, hypocenter	C₃×C₄₃×C₄₇	C₄
Fitting, socle, prime radical, cosocle	C₂×C₃×C₄₃×C₄₇	C₂
LCS	G ▷ C₃×C₄₃×C₄₇
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.