Subgroups — C₃⋊(C₁₁⋊(C₁₉⋊D₁₉)) #37558554

Order 23826.

176 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₁×C₁₉²	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₁⋊(C₁₉⋊D₁₉)	—	3	1	no	maximal, Hall
3	C₁₁×C₁₉²	D₃	1	1	yes	characteristic, complemented, Hall
4	C₃⋊(C₁₉⋊D₁₉)	—	11	1	no	maximal, Hall
5	D₆₂₇	—	19	20	no	maximal
6	C₃×C₁₉²	D₁₁	1	1	yes	characteristic, complemented, Hall
7	C₁₉⋊D₁₉	—	33	1	no	Hall
8	C₃×C₁₁×C₁₉	D₁₉	1	20	yes	complemented
9	D₂₀₉	—	57	20	no	—
10	C₁₉²	D₃₃	1	1	yes	characteristic, complemented, Sylow
11	C₁₁×C₁₉	D₅₇	1	20	yes	complemented
12	D₅₇	—	209	20	no	—
13	D₃₃	—	361	1	no	Hall
14	C₃×C₁₉	D₂₀₉	1	20	yes	complemented
15	D₁₉	—	627	20	no	—
16	C₃×C₁₁	C₁₉⋊D₁₉	1	1	yes	characteristic, complemented, Hall
17	D₁₁	—	1083	1	no	Hall
18	C₁₉	D₆₂₇	1	20	yes	complemented
19	C₁₁	C₃⋊(C₁₉⋊D₁₉)	1	1	yes	characteristic, complemented, Sylow
20	D₃	—	3971	1	no	Hall
21	C₃	C₁₁⋊(C₁₉⋊D₁₉)	1	1	yes	characteristic, complemented, Sylow
22	C₂	—	11913	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₁₁×C₁₉²	C₂
LCS	G ▷ C₃×C₁₁×C₁₉²
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.