Subgroups — C₃²×C₄₃×D₄₁ #44540633

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×C₄₃×D₄₁	C₃	1	4	yes	maximal, direct product factor
3	C₃×C₄₁×C₄₃	C₂×C₃	1	4	yes	complemented
4	C₄₃×D₄₁	C₃²	1	1	yes	characteristic, direct product factor, Hall
5	C₄₁×C₄₃	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₃²×C₄₃	—	41	1	no	maximal, Hall
7	C₃²×D₄₁	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₃²×C₄₃	D₄₁	1	1	yes	characteristic, direct product factor, Hall
9	C₃²×C₄₁	C₂×C₄₃	1	1	yes	characteristic, complemented, Hall
10	C₂×C₃×C₄₃	—	41	4	no	—
11	C₃×D₄₁	C₃×C₄₃	1	4	yes	direct product factor
12	C₃×C₄₃	C₃×D₄₁	1	4	yes	direct product factor
13	C₃×C₄₁	C₂×C₃×C₄₃	1	4	yes	complemented
14	C₂×C₄₃	—	41	1	no	Hall
15	D₄₁	C₃²×C₄₃	1	1	yes	characteristic, direct product factor, Hall
16	C₄₃	C₃²×D₄₁	1	1	yes	characteristic, direct product factor, Sylow
17	C₄₁	C₂×C₃²×C₄₃	1	1	yes	characteristic, complemented, Sylow
18	C₂×C₃²	—	41	1	no	Hall
19	C₃²	C₄₃×D₄₁	1	1	yes	characteristic, direct product factor, Sylow
20	C₂×C₃	—	41	4	no	—
21	C₃	C₃×C₄₃×D₄₁	1	4	yes	direct product factor
22	C₂	—	41	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃²×C₄₃	D₄₁
commutator, cosocle, hypocenter	C₄₁	C₂×C₃²×C₄₃
Frattini	C₁	G
Fitting, socle	C₃²×C₄₁×C₄₃	C₂
LCS	G ▷ C₄₁
UCS	C₁ ◁ C₃²×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.