Subgroups — C₃⋊D₃×C₄₁×C₄₃ #44540639

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	D₃×C₄₁×C₄₃	—	3	4	no	maximal
3	C₃×C₄₁×C₄₃	D₃	1	4	yes	complemented
4	C₂×C₄₁×C₄₃	—	9	1	no	Hall
5	C₄₁×C₄₃	C₃⋊D₃	1	1	yes	characteristic, direct product factor, Hall
6	C₃⋊D₃×C₄₃	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₃⋊D₃×C₄₁	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₃²×C₄₃	C₂×C₄₁	1	1	yes	characteristic, complemented, Hall
9	C₃²×C₄₁	C₂×C₄₃	1	1	yes	characteristic, complemented, Hall
10	D₃×C₄₃	—	3	4	no	—
11	D₃×C₄₁	—	3	4	no	—
12	C₃×C₄₃	D₃×C₄₁	1	4	yes	complemented
13	C₃×C₄₁	D₃×C₄₃	1	4	yes	complemented
14	C₂×C₄₃	—	9	1	no	Hall
15	C₂×C₄₁	—	9	1	no	Hall
16	C₄₃	C₃⋊D₃×C₄₁	1	1	yes	characteristic, direct product factor, Sylow
17	C₄₁	C₃⋊D₃×C₄₃	1	1	yes	characteristic, direct product factor, Sylow
18	C₃⋊D₃	C₄₁×C₄₃	1	1	yes	characteristic, direct product factor, Hall
19	C₃²	C₂×C₄₁×C₄₃	1	1	yes	characteristic, complemented, Sylow
20	D₃	—	3	4	no	—
21	C₃	D₃×C₄₁×C₄₃	1	4	yes	complemented
22	C₂	—	9	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₄₁×C₄₃	C₃⋊D₃
commutator, cosocle, hypocenter	C₃²	C₂×C₄₁×C₄₃
Frattini	C₁	G
Fitting, socle	C₃²×C₄₁×C₄₃	C₂
LCS	G ▷ C₃²
UCS	C₁ ◁ C₄₁×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.