Subgroups — Dic₆₀₆₁ #37564607

Order 24244.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×C₁₉×C₂₉	C₂	1	1	yes	maximal, characteristic
2	C₁₁×C₁₉×C₂₉	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₅₅₁	—	11	1	no	maximal, Hall
4	Dic₃₁₉	—	19	1	no	maximal, Hall
5	C₂×C₁₉×C₂₉	D₁₁	1	1	yes	characteristic
6	Dic₂₀₉	—	29	1	no	maximal, Hall
7	C₂×C₁₁×C₂₉	D₁₉	1	1	yes	characteristic
8	C₁₉×C₂₉	Dic₁₁	1	1	yes	characteristic, complemented, Hall
9	C₂×C₁₁×C₁₉	D₂₉	1	1	yes	characteristic
10	C₁₁×C₂₉	Dic₁₉	1	1	yes	characteristic, complemented, Hall
11	C₁₁×C₁₉	Dic₂₉	1	1	yes	characteristic, complemented, Hall
12	Dic₂₉	—	209	1	no	Hall
13	Dic₁₉	—	319	1	no	Hall
14	C₂×C₂₉	D₂₀₉	1	1	yes	characteristic
15	Dic₁₁	—	551	1	no	Hall
16	C₂×C₁₉	D₃₁₉	1	1	yes	characteristic
17	C₂₉	Dic₂₀₉	1	1	yes	characteristic, complemented, Sylow
18	C₂×C₁₁	D₅₅₁	1	1	yes	characteristic
19	C₁₉	Dic₃₁₉	1	1	yes	characteristic, complemented, Sylow
20	C₁₁	Dic₅₅₁	1	1	yes	characteristic, complemented, Sylow
21	C₄	—	6061	1	no	Sylow
22	C₂	D₆₀₆₁	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₆₀₆₁
commutator, hypocenter	C₁₁×C₁₉×C₂₉	C₄
Fitting, socle, prime radical, cosocle	C₂×C₁₁×C₁₉×C₂₉	C₂
LCS	G ▷ C₁₁×C₁₉×C₂₉
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.