Subgroups — C₄₁×C₃⋊D₁₂₉ #44540640

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	C₄₁×D₁₂₉	—	3	4	no	maximal
3	C₃×C₄₁×C₄₃	D₃	1	4	yes	complemented
4	C₄₁×D₄₃	—	9	1	no	Hall
5	C₄₁×C₄₃	C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
6	C₃⋊D₁₂₉	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₃⋊D₃×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, complemented, Hall
10	D₁₂₉	—	3	4	no	—
11	D₃×C₄₁	—	129	4	no	—
12	C₃×C₄₃	D₃×C₄₁	1	4	yes	complemented
13	C₃×C₄₁	D₁₂₉	1	4	yes	complemented
14	D₄₃	—	9	1	no	Hall
15	C₂×C₄₁	—	387	1	no	Hall
16	C₄₃	C₃⋊D₃×C₄₁	1	1	yes	characteristic, complemented, Sylow
17	C₄₁	C₃⋊D₁₂₉	1	1	yes	characteristic, direct product factor, Sylow
18	C₃⋊D₃	—	43	1	no	Hall
19	C₃²	C₄₁×D₄₃	1	1	yes	characteristic, complemented, Sylow
20	D₃	—	129	4	no	—
21	C₃	C₄₁×D₁₂₉	1	4	yes	complemented
22	C₂	—	387	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₄₁	C₃⋊D₁₂₉
commutator, cosocle, hypocenter	C₃²×C₄₃	C₂×C₄₁
Frattini	C₁	G
Fitting, socle	C₃²×C₄₁×C₄₃	C₂
LCS	G ▷ C₃²×C₄₃
UCS	C₁ ◁ 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.