Subgroups — (C₄₃⋊C₉)⋊D₇ #19129331

Order 5418.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₄₃⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×D₃₀₁	C₃	1	1	yes	maximal, characteristic
3	C₃×C₇×C₄₃	C₂×C₃	1	1	yes	characteristic
4	D₄₃⋊C₉	—	7	1	no	maximal, Hall
5	D₃₀₁	C₉	1	1	yes	characteristic, complemented, Hall
6	C₄₃⋊C₉	D₇	1	1	yes	characteristic, complemented, Hall
7	C₇×C₄₃	C₂×C₉	1	1	yes	characteristic, complemented, Hall
8	C₃×D₄₃	—	7	1	no	—
9	C₃×C₄₃	C₃×D₇	1	1	yes	characteristic
10	C₉×D₇	—	43	1	no	maximal, Hall
11	D₄₃	—	7	1	no	Hall
12	C₇×C₉	—	43	1	no	Hall
13	C₄₃	C₉×D₇	1	1	yes	characteristic, complemented, Sylow
14	C₃×D₇	—	43	1	no	—
15	C₃×C₇	D₄₃⋊C₃	1	1	yes	characteristic
16	C₂×C₉	—	301	1	no	Hall
17	D₇	—	43	1	no	Hall
18	C₉	—	43	1	no	Sylow
19	C₇	D₄₃⋊C₉	1	1	yes	characteristic, complemented, Sylow
20	C₂×C₃	—	301	1	no	—
21	C₃	(C₄₃⋊C₃)⋊D₇	1	1	yes	characteristic
22	C₂	—	301	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₃	(C₄₃⋊C₃)⋊D₇
commutator, hypocenter	C₇×C₄₃	C₂×C₉
Fitting, socle	C₃×C₇×C₄₃	C₂×C₃
LCS	G ▷ C₇×C₄₃
UCS	C₁ ◁ C₃

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