Subgroups — C₂²×C₄₇×C₁₉⋊C₃ #24924284

Order 10716.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×C₁₉⋊C₃	C₂	1	3	yes	maximal, direct product factor
2	C₂²×C₁₉×C₄₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₄₇×C₁₉⋊C₃	C₂²	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₁₉×C₄₇	C₂×C₃	1	3	yes	complemented
5	C₁₉×C₄₇	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
6	C₂²×C₃×C₄₇	—	19	1	no	maximal, Hall
7	C₂×C₃×C₄₇	—	19	3	no	—
8	C₂²×C₁₉⋊C₃	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂²×C₄₇	C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Hall
10	C₃×C₄₇	—	19	1	no	Hall
11	C₂×C₁₉⋊C₃	C₂×C₄₇	1	3	yes	direct product factor
12	C₂×C₄₇	C₂×C₁₉⋊C₃	1	3	yes	direct product factor
13	C₂²×C₁₉	C₃×C₄₇	1	1	yes	characteristic, complemented, Hall
14	C₁₉⋊C₃	C₂²×C₄₇	1	1	yes	characteristic, direct product factor, Hall
15	C₄₇	C₂²×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
16	C₂×C₁₉	C₂×C₃×C₄₇	1	3	yes	complemented
17	C₁₉	C₂²×C₃×C₄₇	1	1	yes	characteristic, complemented, Sylow
18	C₂²×C₃	—	19	1	no	Hall
19	C₂×C₃	—	19	3	no	—
20	C₂²	C₄₇×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
21	C₃	—	19	1	no	Sylow
22	C₂	C₂×C₄₇×C₁₉⋊C₃	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²×C₄₇	C₁₉⋊C₃
commutator, cosocle, hypocenter	C₁₉	C₂²×C₃×C₄₇
Frattini	C₁	G
Fitting, socle	C₂²×C₁₉×C₄₇	C₃
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄₇

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