Subgroups — C₄₇⋊((C₁₉⋊C₃)⋊C₄) #24924269

Order 10716.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×C₁₉⋊C₃	C₂	1	1	yes	maximal, characteristic
2	Dic₈₉₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₄₇×C₁₉⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₉×C₄₇	C₂×C₃	1	1	yes	characteristic
5	C₁₉×C₄₇	C₃×C₄	1	1	yes	characteristic, complemented, Hall
6	C₃×Dic₄₇	—	19	1	no	maximal, Hall
7	C₂×C₃×C₄₇	—	19	1	no	—
8	(C₁₉⋊C₃)⋊C₄	—	47	1	no	maximal, Hall
9	Dic₄₇	—	19	1	no	Hall
10	C₃×C₄₇	—	19	1	no	Hall
11	C₂×C₁₉⋊C₃	D₄₇	1	1	yes	characteristic
12	C₂×C₄₇	D₁₉⋊C₃	1	1	yes	characteristic
13	Dic₁₉	—	47	1	no	Hall
14	C₁₉⋊C₃	Dic₄₇	1	1	yes	characteristic, complemented, Hall
15	C₄₇	(C₁₉⋊C₃)⋊C₄	1	1	yes	characteristic, complemented, Sylow
16	C₂×C₁₉	C₃×D₄₇	1	1	yes	characteristic
17	C₁₉	C₃×Dic₄₇	1	1	yes	characteristic, complemented, Sylow
18	C₃×C₄	—	893	1	no	Hall
19	C₂×C₃	—	19	1	no	—
20	C₄	—	893	1	no	Sylow
21	C₃	—	19	1	no	Sylow
22	C₂	C₄₇⋊(D₁₉⋊C₃)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₄₇⋊(D₁₉⋊C₃)
commutator, hypocenter	C₁₉×C₄₇	C₃×C₄
Fitting, socle, cosocle	C₂×C₁₉×C₄₇	C₂×C₃
prime radical	C₂×C₄₇×C₁₉⋊C₃	C₂
LCS	G ▷ C₁₉×C₄₇
UCS	C₁ ◁ C₂

Splittings G = N ⋊ H with N normal; H ≅ G/N.