Subgroups — C₄₇⋊#10621729 #44540969

Order 31772.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₇×C₁₃⋊D₁₃	C₂	1	1	yes	maximal, characteristic
2	C₁₃²×C₄₇	C₄	1	1	yes	characteristic, complemented, Hall
3	C₄₇⋊#261	—	13	2	no	maximal
4	D₁₃×C₄₇	—	13	2	no	—
5	D₁₃×C₄₇	—	26	6	no	—
6	#10621729	—	47	1	no	maximal, Hall
7	C₁₃×C₄₇	—	2	6	no	—
8	C₁₃×C₄₇	#261	1	2	yes	complemented
9	C₁₃⋊D₁₃	D₄₇	1	1	yes	characteristic
10	Dic₄₇	—	169	1	no	Hall
11	C₁₃²	Dic₄₇	1	1	yes	characteristic, complemented, Sylow
12	C₂×C₄₇	—	169	1	no	—
13	#261	—	611	2	no	—
14	C₄₇	#10621729	1	1	yes	characteristic, complemented, Sylow
15	D₁₃	—	13	2	no	—
16	D₁₃	—	26	6	no	—
17	C₁₃	—	2	6	no	—
18	C₁₃	C₄₇⋊#261	1	2	yes	complemented
19	C₄	—	7943	1	no	Sylow
20	C₂	—	169	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₁₃²×C₄₇	C₄
prime radical, cosocle	C₄₇×C₁₃⋊D₁₃	C₂
LCS	G ▷ C₁₃²×C₄₇
UCS	C₁

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.