Subgroups — C₁₁⋊(C₁₉⋊#3866) #44525823

Order 30932.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×C₁₉×D₃₇	C₂	1	1	yes	maximal, characteristic
2	C₁₁×C₁₉×C₃₇	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₉⋊#3866	—	11	1	no	maximal, Hall
4	C₁₁⋊#3866	—	19	1	no	maximal, Hall
5	C₁₉×D₃₇	D₁₁	1	1	yes	characteristic
6	Dic₂₀₉	—	37	1	no	maximal, Hall
7	C₁₁×D₃₇	D₁₉	1	1	yes	characteristic
8	C₁₉×C₃₇	Dic₁₁	1	1	yes	characteristic, complemented, Hall
9	C₂×C₁₁×C₁₉	—	37	1	no	—
10	C₁₁×C₃₇	Dic₁₉	1	1	yes	characteristic, complemented, Hall
11	C₁₁×C₁₉	#3866	1	1	yes	characteristic, complemented, Hall
12	#3866	—	209	1	no	Hall
13	Dic₁₉	—	407	1	no	Hall
14	D₃₇	D₂₀₉	1	1	yes	characteristic
15	Dic₁₁	—	703	1	no	Hall
16	C₂×C₁₉	—	37	1	no	—
17	C₃₇	Dic₂₀₉	1	1	yes	characteristic, complemented, Sylow
18	C₂×C₁₁	—	37	1	no	—
19	C₁₉	C₁₁⋊#3866	1	1	yes	characteristic, complemented, Sylow
20	C₁₁	C₁₉⋊#3866	1	1	yes	characteristic, complemented, Sylow
21	C₄	—	7733	1	no	Sylow
22	C₂	—	37	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₁₁×C₁₉×C₃₇	C₄
prime radical, cosocle	C₁₁×C₁₉×D₃₇	C₂
LCS	G ▷ C₁₁×C₁₉×C₃₇
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.