Subgroups — C₄₁⋊(D₄₃⋊C₉) #44540622

Order 31734.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×C₄₃⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×D₁₇₆₃	C₃	1	1	yes	maximal, characteristic
3	C₃×C₄₁×C₄₃	C₂×C₃	1	1	yes	characteristic
4	D₁₇₆₃	C₉	1	1	yes	characteristic, complemented, Hall
5	C₄₁×C₄₃	C₂×C₉	1	1	yes	characteristic, complemented, Hall
6	D₄₃⋊C₉	—	41	1	no	maximal, Hall
7	C₉×D₄₁	—	43	1	no	maximal, Hall
8	C₄₃⋊C₉	D₄₁	1	1	yes	characteristic, complemented, Hall
9	C₉×C₄₁	—	43	1	no	Hall
10	C₃×D₄₃	—	41	1	no	—
11	C₃×D₄₁	—	43	1	no	—
12	C₃×C₄₃	C₃×D₄₁	1	1	yes	characteristic
13	C₃×C₄₁	D₄₃⋊C₃	1	1	yes	characteristic
14	D₄₃	—	41	1	no	Hall
15	D₄₁	—	43	1	no	Hall
16	C₄₃	C₉×D₄₁	1	1	yes	characteristic, complemented, Sylow
17	C₄₁	D₄₃⋊C₉	1	1	yes	characteristic, complemented, Sylow
18	C₂×C₉	—	1763	1	no	Hall
19	C₉	—	43	1	no	Sylow
20	C₂×C₃	—	1763	1	no	—
21	C₃	C₄₁⋊(D₄₃⋊C₃)	1	1	yes	characteristic
22	C₂	—	1763	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₃	C₄₁⋊(D₄₃⋊C₃)
commutator, hypocenter	C₄₁×C₄₃	C₂×C₉
Fitting, socle, cosocle	C₃×C₄₁×C₄₃	C₂×C₃
prime radical	C₃×D₁₇₆₃	C₃
LCS	G ▷ C₄₁×C₄₃
UCS	C₁ ◁ C₃

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.