Subgroups — C₃⋊(C₄₃⋊#3866) #34061883

Order 19092.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄₃×D₃₇	C₂	1	1	yes	maximal, characteristic
2	C₄₃⋊#3866	—	3	1	no	maximal, Hall
3	C₃×C₃₇×C₄₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₄₃×D₃₇	D₃	1	1	yes	characteristic
5	C₃₇×C₄₃	Dic₃	1	1	yes	characteristic, complemented, Hall
6	Dic₁₂₉	—	37	1	no	maximal, Hall
7	C₃⋊#3866	—	43	1	no	maximal, Hall
8	C₂×C₃×C₄₃	—	37	1	no	—
9	C₃×D₃₇	D₄₃	1	1	yes	characteristic
10	Dic₄₃	—	111	1	no	Hall
11	#3866	—	129	1	no	Hall
12	C₃×C₄₃	#3866	1	1	yes	characteristic, complemented, Hall
13	C₃×C₃₇	Dic₄₃	1	1	yes	characteristic, complemented, Hall
14	C₂×C₄₃	—	37	1	no	—
15	D₃₇	D₁₂₉	1	1	yes	characteristic
16	C₄₃	C₃⋊#3866	1	1	yes	characteristic, complemented, Sylow
17	C₃₇	Dic₁₂₉	1	1	yes	characteristic, complemented, Sylow
18	Dic₃	—	1591	1	no	Hall
19	C₂×C₃	—	37	1	no	—
20	C₄	—	4773	1	no	Sylow
21	C₃	C₄₃⋊#3866	1	1	yes	characteristic, complemented, Sylow
22	C₂	—	37	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃×C₃₇×C₄₃	C₄
prime radical, cosocle	C₃×C₄₃×D₃₇	C₂
LCS	G ▷ C₃×C₃₇×C₄₃
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.