Subgroups — C₄₃×D₃₆₉ #44540618

Order 31734.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₄₁×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₄₃×D₁₂₃	—	3	1	no	maximal
3	C₃×C₄₁×C₄₃	D₃	1	1	yes	characteristic
4	C₄₃×D₄₁	—	9	1	no	Hall
5	C₄₁×C₄₃	D₉	1	1	yes	characteristic, complemented, Hall
6	D₉×C₄₃	—	41	1	no	maximal, Hall
7	D₃₆₉	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₉×C₄₃	D₄₁	1	1	yes	characteristic, complemented, Hall
9	C₉×C₄₁	C₂×C₄₃	1	1	yes	characteristic, complemented, Hall
10	D₃×C₄₃	—	123	1	no	—
11	D₁₂₃	—	3	1	no	—
12	C₃×C₄₃	D₁₂₃	1	1	yes	characteristic
13	C₃×C₄₁	D₃×C₄₃	1	1	yes	characteristic
14	C₂×C₄₃	—	369	1	no	Hall
15	D₄₁	—	9	1	no	Hall
16	C₄₃	D₃₆₉	1	1	yes	characteristic, direct product factor, Sylow
17	C₄₁	D₉×C₄₃	1	1	yes	characteristic, complemented, Sylow
18	D₉	—	41	1	no	Hall
19	C₉	C₄₃×D₄₁	1	1	yes	characteristic, complemented, Sylow
20	D₃	—	123	1	no	—
21	C₃	C₄₃×D₁₂₃	1	1	yes	characteristic
22	C₂	—	369	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₄₃	D₃₆₉
commutator, cosocle, hypocenter	C₉×C₄₁	C₂×C₄₃
Frattini	C₃	C₄₃×D₁₂₃
Fitting	C₉×C₄₁×C₄₃	C₂
socle	C₃×C₄₁×C₄₃	D₃
LCS	G ▷ C₉×C₄₁
UCS	C₁ ◁ C₄₃

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.