Subgroups — C₃⋊(C₄₁⋊(D₄₃⋊C₃)) #44540629

Order 31734.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄₁×C₄₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₄₁⋊(D₄₃⋊C₃)	—	3	1	no	maximal
3	D₅₂₈₉	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₄₁×C₄₃	C₂×C₃	1	1	yes	characteristic, complemented
5	C₄₁×C₄₃⋊C₃	—	2	1	no	—
6	C₄₁×C₄₃⋊C₃	D₃	1	1	yes	characteristic, complemented
7	D₁₇₆₃	—	3	1	no	Hall
8	C₄₁×C₄₃	C₃×D₃	1	1	yes	characteristic, complemented, Hall
9	C₃⋊(D₄₃⋊C₃)	—	41	1	no	maximal, Hall
10	C₃×D₁₂₃	—	43	1	no	maximal, Hall
11	C₃×C₄₃⋊C₃	D₄₁	1	1	yes	characteristic, complemented, Hall
12	C₃²×C₄₁	—	43	1	no	Hall
13	D₁₂₉	—	41	1	no	—
14	D₄₃⋊C₃	—	123	1	no	—
15	D₁₂₃	—	43	1	no	—
16	C₃×D₄₁	—	129	1	no	—
17	C₃×C₄₃	C₃×D₄₁	1	1	yes	characteristic, complemented
18	C₄₃⋊C₃	—	2	1	no	—
19	C₄₃⋊C₃	D₁₂₃	1	1	yes	characteristic, complemented
20	C₃×C₄₁	—	43	1	no	—
21	C₃×C₄₁	—	86	1	no	—
22	C₃×C₄₁	D₄₃⋊C₃	1	1	yes	characteristic, complemented
23	D₄₃	—	123	1	no	Hall
24	D₄₁	—	129	1	no	Hall
25	C₄₃	C₃×D₁₂₃	1	1	yes	characteristic, complemented, Sylow
26	C₄₁	C₃⋊(D₄₃⋊C₃)	1	1	yes	characteristic, complemented, Sylow
27	C₃×D₃	—	1763	1	no	Hall
28	C₃²	—	43	1	no	Sylow
29	C₂×C₃	—	5289	1	no	—
30	D₃	—	1763	1	no	—
31	C₃	—	43	1	no	—
32	C₃	—	86	1	no	—
33	C₃	C₄₁⋊(D₄₃⋊C₃)	1	1	yes	characteristic, complemented
34	C₂	—	5289	1	no	Sylow

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

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.