Subgroups — C₃×#41×C₄₁ #14520261

Order 1968.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×Q₈×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₄×C₄₁	C₂	1	3	yes	maximal, complemented
3	C₂×C₃×C₄×C₄₁	C₂	1	3	yes	maximal, complemented
4	#41×C₄₁	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂²×C₃×C₄₁	C₂²	1	3	yes	—
6	C₃×C₄×C₄₁	C₂²	1	3	yes	—
7	C₃×C₄×C₄₁	C₂²	1	1	yes	characteristic
8	Q₈×C₄₁	C₂×C₃	1	1	yes	characteristic, complemented
9	D₄×C₄₁	C₂×C₃	1	3	yes	complemented
10	C₂×C₄×C₄₁	C₂×C₃	1	3	yes	complemented
11	C₂×C₃×C₄₁	—	2	3	no	—
12	C₂×C₃×C₄₁	C₂³	1	1	yes	characteristic
13	C₂²×C₄₁	C₂²×C₃	1	3	yes	—
14	C₄×C₄₁	C₂²×C₃	1	3	yes	—
15	C₄×C₄₁	C₂²×C₃	1	1	yes	characteristic
16	C₃×C₄₁	#41	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₄₁	—	2	3	no	—
18	C₂×C₄₁	C₂³×C₃	1	1	yes	characteristic
19	C₃×#41	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Hall
20	C₄₁	C₃×#41	1	1	yes	characteristic, direct product factor, Sylow
21	C₃×Q₈	C₂×C₄₁	1	1	yes	characteristic, complemented
22	C₃×D₄	C₂×C₄₁	1	3	yes	complemented
23	C₂×C₃×C₄	C₂×C₄₁	1	3	yes	complemented
24	#41	C₃×C₄₁	1	1	yes	characteristic, direct product factor, Sylow
25	C₂²×C₃	C₂²×C₄₁	1	3	yes	—
26	C₃×C₄	C₂²×C₄₁	1	3	yes	—
27	C₃×C₄	C₂²×C₄₁	1	1	yes	characteristic
28	Q₈	C₂×C₃×C₄₁	1	1	yes	characteristic, complemented
29	D₄	C₂×C₃×C₄₁	1	3	yes	complemented
30	C₂×C₄	C₂×C₃×C₄₁	1	3	yes	complemented
31	C₂×C₃	—	2	3	no	—
32	C₂×C₃	C₂³×C₄₁	1	1	yes	characteristic
33	C₂²	C₂²×C₃×C₄₁	1	3	yes	—
34	C₄	C₂²×C₃×C₄₁	1	1	yes	characteristic
35	C₄	C₂²×C₃×C₄₁	1	3	yes	—
36	C₃	#41×C₄₁	1	1	yes	characteristic, direct product factor, Sylow
37	C₂	—	2	3	no	—
38	C₂	C₂³×C₃×C₄₁	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄×C₄₁	C₂²
commutator, Frattini, cosocle	C₂	C₂³×C₃×C₄₁
socle	C₂×C₃×C₄₁	C₂³
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₃×C₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×Q₈×C₄₁	C₂	semidirect
2. C₃×D₄×C₄₁	C₂	semidirect
3. C₂×C₃×C₄×C₄₁	C₂	semidirect
4. #41×C₄₁	C₃	direct (N × H)
8. Q₈×C₄₁	C₂×C₃	semidirect
9. D₄×C₄₁	C₂×C₃	semidirect
10. C₂×C₄×C₄₁	C₂×C₃	semidirect
16. C₃×C₄₁	#41	direct (N × H)
19. C₃×#41	C₄₁	direct (N × H)
20. C₄₁	C₃×#41	direct (N × H)
21. C₃×Q₈	C₂×C₄₁	semidirect
22. C₃×D₄	C₂×C₄₁	semidirect
23. C₂×C₃×C₄	C₂×C₄₁	semidirect
24. #41	C₃×C₄₁	direct (N × H)
28. Q₈	C₂×C₃×C₄₁	semidirect
29. D₄	C₂×C₃×C₄₁	semidirect
30. C₂×C₄	C₂×C₃×C₄₁	semidirect
36. C₃	#41×C₄₁	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×Q₈×C₄₁	2
C₃×D₄×C₄₁	2
C₂×C₃×C₄×C₄₁	2
#41×C₄₁	3
C₃×#41	41

Subgroups — C3×#41×C41 #14520261

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#41×C₄₁ #14520261