Subgroups — C₇₁⋊(#3866⋊C₃) #44538613

Order 31524.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₁×D₃₇⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₇₁⋊#3866	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇₁×C₃₇⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₇₁×D₃₇	C₂×C₃	1	1	yes	characteristic
5	C₃₇×C₇₁	C₃×C₄	1	1	yes	characteristic, complemented, Hall
6	C₃×Dic₇₁	—	37	1	no	maximal, Hall
7	#3866⋊C₃	—	71	1	no	maximal, Hall
8	C₂×C₃×C₇₁	—	37	1	no	—
9	Dic₇₁	—	37	1	no	Hall
10	D₃₇⋊C₃	D₇₁	1	1	yes	characteristic
11	C₃×C₇₁	—	37	1	no	Hall
12	#3866	—	71	1	no	Hall
13	C₂×C₇₁	—	37	1	no	—
14	C₃₇⋊C₃	Dic₇₁	1	1	yes	characteristic, complemented, Hall
15	D₃₇	C₃×D₇₁	1	1	yes	characteristic
16	C₇₁	#3866⋊C₃	1	1	yes	characteristic, complemented, Sylow
17	C₃₇	C₃×Dic₇₁	1	1	yes	characteristic, complemented, Sylow
18	C₃×C₄	—	2627	1	no	Hall
19	C₂×C₃	—	37	1	no	—
20	C₄	—	2627	1	no	Sylow
21	C₃	—	37	1	no	Sylow
22	C₂	—	37	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃₇×C₇₁	C₃×C₄
prime radical	C₇₁×D₃₇⋊C₃	C₂
cosocle	C₇₁×D₃₇	C₂×C₃
LCS	G ▷ C₃₇×C₇₁
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.