Subgroups — C₃⋊(C₃₁⋊#6157) #34089324

Order 19716.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₃₁×D₅₃	C₂	1	1	yes	maximal, characteristic
2	C₃₁⋊#6157	—	3	1	no	maximal, Hall
3	C₃×C₃₁×C₅₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃₁×D₅₃	D₃	1	1	yes	characteristic
5	C₃₁×C₅₃	Dic₃	1	1	yes	characteristic, complemented, Hall
6	C₃⋊#6157	—	31	1	no	maximal, Hall
7	Dic₉₃	—	53	1	no	maximal, Hall
8	C₃×D₅₃	D₃₁	1	1	yes	characteristic
9	#6157	—	93	1	no	Hall
10	C₂×C₃×C₃₁	—	53	1	no	—
11	C₃×C₅₃	Dic₃₁	1	1	yes	characteristic, complemented, Hall
12	Dic₃₁	—	159	1	no	Hall
13	D₅₃	D₉₃	1	1	yes	characteristic
14	C₃×C₃₁	#6157	1	1	yes	characteristic, complemented, Hall
15	C₂×C₃₁	—	53	1	no	—
16	C₅₃	Dic₉₃	1	1	yes	characteristic, complemented, Sylow
17	C₃₁	C₃⋊#6157	1	1	yes	characteristic, complemented, Sylow
18	Dic₃	—	1643	1	no	Hall
19	C₂×C₃	—	53	1	no	—
20	C₄	—	4929	1	no	Sylow
21	C₃	C₃₁⋊#6157	1	1	yes	characteristic, complemented, Sylow
22	C₂	—	53	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃×C₃₁×C₅₃	C₄
prime radical, cosocle	C₃×C₃₁×D₅₃	C₂
LCS	G ▷ C₃×C₃₁×C₅₃
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.