Subgroups — C₄₇⋊#10625191 #46851997

Order 34780.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₇×D₁₈₅	C₂	1	1	yes	maximal, characteristic
2	C₅×C₃₇×C₄₇	C₄	1	1	yes	characteristic, complemented, Hall
3	C₄₇⋊#3866	—	5	1	no	maximal, Hall
4	C₄₇×D₃₇	—	5	1	no	—
5	C₃₇×C₄₇	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
6	C₄₇⋊AGL(1,𝔽₅)	—	37	1	no	maximal, Hall
7	#10625191	—	47	1	no	maximal, Hall
8	D₅×C₄₇	—	37	1	no	—
9	D₁₈₅	D₄₇	1	1	yes	characteristic
10	C₅×C₄₇	#3866	1	1	yes	characteristic, complemented, Hall
11	Dic₄₇	—	185	1	no	Hall
12	C₅×C₃₇	Dic₄₇	1	1	yes	characteristic, complemented, Hall
13	#3866	—	235	1	no	Hall
14	C₂×C₄₇	—	185	1	no	—
15	D₃₇	—	5	1	no	—
16	C₄₇	#10625191	1	1	yes	characteristic, complemented, Sylow
17	C₃₇	C₄₇⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
18	AGL(1,𝔽₅)	—	1739	1	no	Hall
19	D₅	—	37	1	no	—
20	C₅	C₄₇⋊#3866	1	1	yes	characteristic, complemented, Sylow
21	C₄	—	8695	1	no	Sylow
22	C₂	—	185	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅×C₃₇×C₄₇	C₄
prime radical, cosocle	C₄₇×D₁₈₅	C₂
LCS	G ▷ C₅×C₃₇×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.