Subgroups — C₄₃×C₃⋊D₁₂₃ #44540641

Order 31734.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₄₁×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₄₃×D₁₂₃	—	3	4	no	maximal
3	C₃×C₄₁×C₄₃	D₃	1	4	yes	complemented
4	C₄₃×D₄₁	—	9	1	no	Hall
5	C₄₁×C₄₃	C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
6	C₃⋊D₃×C₄₃	—	41	1	no	maximal, Hall
7	C₃⋊D₁₂₃	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₃²×C₄₃	D₄₁	1	1	yes	characteristic, complemented, Hall
9	C₃²×C₄₁	C₂×C₄₃	1	1	yes	characteristic, complemented, Hall
10	D₃×C₄₃	—	123	4	no	—
11	D₁₂₃	—	3	4	no	—
12	C₃×C₄₃	D₁₂₃	1	4	yes	complemented
13	C₃×C₄₁	D₃×C₄₃	1	4	yes	complemented
14	C₂×C₄₃	—	369	1	no	Hall
15	D₄₁	—	9	1	no	Hall
16	C₄₃	C₃⋊D₁₂₃	1	1	yes	characteristic, direct product factor, Sylow
17	C₄₁	C₃⋊D₃×C₄₃	1	1	yes	characteristic, complemented, Sylow
18	C₃⋊D₃	—	41	1	no	Hall
19	C₃²	C₄₃×D₄₁	1	1	yes	characteristic, complemented, Sylow
20	D₃	—	123	4	no	—
21	C₃	C₄₃×D₁₂₃	1	4	yes	complemented
22	C₂	—	369	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₄₃	C₃⋊D₁₂₃
commutator, cosocle, hypocenter	C₃²×C₄₁	C₂×C₄₃
Frattini	C₁	G
Fitting, socle	C₃²×C₄₁×C₄₃	C₂
LCS	G ▷ C₃²×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.