Subgroups — C₃²×C₄₁×D₄₃ #44540632

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	C₃×C₄₁×D₄₃	C₃	1	4	yes	maximal, direct product factor
3	C₃×C₄₁×C₄₃	C₂×C₃	1	4	yes	complemented
4	C₄₁×D₄₃	C₃²	1	1	yes	characteristic, direct product factor, Hall
5	C₄₁×C₄₃	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
6	C₃²×D₄₃	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₃²×C₄₁	—	43	1	no	maximal, Hall
8	C₃²×C₄₃	C₂×C₄₁	1	1	yes	characteristic, complemented, Hall
9	C₃²×C₄₁	D₄₃	1	1	yes	characteristic, direct product factor, Hall
10	C₃×D₄₃	C₃×C₄₁	1	4	yes	direct product factor
11	C₂×C₃×C₄₁	—	43	4	no	—
12	C₃×C₄₃	C₂×C₃×C₄₁	1	4	yes	complemented
13	C₃×C₄₁	C₃×D₄₃	1	4	yes	direct product factor
14	D₄₃	C₃²×C₄₁	1	1	yes	characteristic, direct product factor, Hall
15	C₂×C₄₁	—	43	1	no	Hall
16	C₄₃	C₂×C₃²×C₄₁	1	1	yes	characteristic, complemented, Sylow
17	C₄₁	C₃²×D₄₃	1	1	yes	characteristic, direct product factor, Sylow
18	C₂×C₃²	—	43	1	no	Hall
19	C₃²	C₄₁×D₄₃	1	1	yes	characteristic, direct product factor, Sylow
20	C₂×C₃	—	43	4	no	—
21	C₃	C₃×C₄₁×D₄₃	1	4	yes	direct product factor
22	C₂	—	43	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃²×C₄₁	D₄₃
commutator, cosocle, hypocenter	C₄₃	C₂×C₃²×C₄₁
Frattini	C₁	G
Fitting, socle	C₃²×C₄₁×C₄₃	C₂
LCS	G ▷ C₄₃
UCS	C₁ ◁ C₃²×C₄₁

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.