Subgroups — C₃×#10620282 #14520121

Order 1968.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₄×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₁₆₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#66491	C₂	1	1	yes	maximal, characteristic, complemented
4	#10620282	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂²×C₃×C₄₁	—	2	1	no	—
6	C₂×C₃×D₄₁	—	2	1	no	—
7	C₃×C₄×C₄₁	C₂²	1	1	yes	characteristic
8	D₄×C₄₁	C₂×C₃	1	1	yes	characteristic, complemented
9	D₁₆₄	C₂×C₃	1	1	yes	characteristic, complemented
10	#66491	C₂×C₃	1	1	yes	characteristic, complemented
11	C₂×C₃×C₄₁	—	4	1	no	—
12	C₂×C₃×C₄₁	D₄	1	1	yes	characteristic
13	C₃×D₄₁	—	4	1	no	—
14	C₂²×C₄₁	—	2	1	no	—
15	C₂×D₄₁	—	2	1	no	—
16	C₄×C₄₁	C₂²×C₃	1	1	yes	characteristic
17	C₃×C₄₁	D₈	1	1	yes	characteristic, complemented, Hall
18	C₂×C₄₁	—	4	1	no	—
19	C₂×C₄₁	C₃×D₄	1	1	yes	characteristic
20	D₄₁	—	4	1	no	—
21	C₃×D₈	—	41	1	no	maximal, Hall
22	C₄₁	C₃×D₈	1	1	yes	characteristic, complemented, Sylow
23	C₃×D₄	—	41	1	no	—
24	C₃×D₄	D₄₁	1	1	yes	characteristic, complemented
25	C₃×C₈	—	41	1	no	—
26	D₈	—	41	1	no	Sylow
27	C₂²×C₃	—	2	1	no	—
28	C₂²×C₃	—	82	1	no	—
29	C₃×C₄	C₂×D₄₁	1	1	yes	characteristic
30	D₄	—	41	1	no	—
31	D₄	C₃×D₄₁	1	1	yes	characteristic, complemented
32	C₈	—	41	1	no	—
33	C₂×C₃	—	4	1	no	—
34	C₂×C₃	—	164	1	no	—
35	C₂×C₃	C₂²⋊D₄₁	1	1	yes	characteristic
36	C₂²	—	2	1	no	—
37	C₂²	—	82	1	no	—
38	C₄	C₂×C₃×D₄₁	1	1	yes	characteristic
39	C₃	#10620282	1	1	yes	characteristic, direct product factor, Sylow
40	C₂	—	4	1	no	—
41	C₂	—	164	1	no	—
42	C₂	C₃×C₂²⋊D₄₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	C₂²⋊D₄₁
commutator, cosocle	C₄×C₄₁	C₂²×C₃
Frattini	C₄	C₂×C₃×D₄₁
Fitting	C₃×D₄×C₄₁	C₂
socle	C₂×C₃×C₄₁	D₄
hypercenter	C₃×D₄	D₄₁
hypocenter	C₄₁	C₃×D₈
LCS	G ▷ C₄×C₄₁ ▷ C₂×C₄₁ ▷ C₄₁
UCS	C₁ ◁ C₂×C₃ ◁ C₃×C₄ ◁ C₃×D₄

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₃×D₄×C₄₁	C₂	semidirect
2. C₃×D₁₆₄	C₂	semidirect
3. C₃×#66491	C₂	semidirect
4. #10620282	C₃	direct (N × H)
8. D₄×C₄₁	C₂×C₃	semidirect
9. D₁₆₄	C₂×C₃	semidirect
10. #66491	C₂×C₃	semidirect
17. C₃×C₄₁	D₈	semidirect
22. C₄₁	C₃×D₈	semidirect
24. C₃×D₄	D₄₁	semidirect
31. D₄	C₃×D₄₁	semidirect
39. C₃	#10620282	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×D₄×C₄₁	2
C₃×D₁₆₄	2
C₃×#66491	2
#10620282	3
C₃×D₈	41

Subgroups — C3×#10620282 #14520121

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10620282 #14520121