Subgroups — C₃₇⋊C₃×Dic₇₁ #44538608

Order 31524.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇₁×C₃₇⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₃₇×Dic₇₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇₁×C₃₇⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃₇×C₇₁	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	C₄×C₃₇⋊C₃	—	71	1	no	maximal, Hall
8	C₂×C₃×C₇₁	—	37	1	no	—
9	Dic₇₁	C₃₇⋊C₃	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₃₇⋊C₃	D₇₁	1	1	yes	characteristic
11	C₃×C₇₁	—	37	1	no	Hall
12	C₄×C₃₇	—	71	1	no	Hall
13	C₂×C₇₁	C₂×C₃₇⋊C₃	1	1	yes	characteristic
14	C₃₇⋊C₃	Dic₇₁	1	1	yes	characteristic, direct product factor, Hall
15	C₂×C₃₇	C₃×D₇₁	1	1	yes	characteristic
16	C₇₁	C₄×C₃₇⋊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	—	71	1	no	Sylow
21	C₃	—	37	1	no	Sylow
22	C₂	C₃₇⋊C₃×D₇₁	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₃₇⋊C₃×D₇₁
commutator, hypocenter	C₃₇×C₇₁	C₃×C₄
Fitting, socle, cosocle	C₂×C₃₇×C₇₁	C₂×C₃
prime radical	C₂×C₇₁×C₃₇⋊C₃	C₂
LCS	G ▷ C₃₇×C₇₁
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.