Subgroups — D₃×C₆₁×D₄₃ #44538381

Order 31476.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×D₁₂₉	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃×C₄₃×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₆₁×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₆₁×D₄₃	—	3	1	no	maximal, Hall
5	C₃×C₄₃×C₆₁	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₄₃×C₆₁	—	3	1	no	—
7	C₆₁×D₄₃	—	3	1	no	—
8	C₆₁×D₄₃	D₃	1	1	yes	characteristic, direct product factor
9	C₄₃×C₆₁	C₂×D₃	1	1	yes	characteristic, complemented, Hall
10	C₂×D₃×C₆₁	—	43	1	no	maximal, Hall
11	D₃×D₄₃	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₂×C₃×C₆₁	—	43	1	no	—
13	D₃×C₆₁	—	43	1	no	—
14	D₃×C₆₁	D₄₃	1	1	yes	characteristic, direct product factor
15	D₁₂₉	C₂×C₆₁	1	1	yes	characteristic, complemented
16	C₃×D₄₃	C₂×C₆₁	1	1	yes	characteristic, complemented
17	D₃×C₄₃	C₂×C₆₁	1	1	yes	characteristic, complemented
18	C₂²×C₆₁	—	129	1	no	Hall
19	C₃×C₆₁	C₂×D₄₃	1	1	yes	characteristic, complemented, Hall
20	C₂×D₄₃	—	3	1	no	Hall
21	C₃×C₄₃	C₂²×C₆₁	1	1	yes	characteristic, complemented, Hall
22	C₂×C₆₁	—	3	1	no	—
23	C₂×C₆₁	—	43	1	no	—
24	C₂×C₆₁	—	129	1	no	—
25	C₂×C₄₃	—	3	1	no	—
26	D₄₃	—	3	1	no	—
27	D₄₃	D₃×C₆₁	1	1	yes	characteristic, direct product factor
28	C₆₁	D₃×D₄₃	1	1	yes	characteristic, direct product factor, Sylow
29	C₄₃	C₂×D₃×C₆₁	1	1	yes	characteristic, complemented, Sylow
30	C₂×D₃	—	43	1	no	Hall
31	C₂×C₃	—	43	1	no	—
32	D₃	—	43	1	no	—
33	D₃	C₆₁×D₄₃	1	1	yes	characteristic, direct product factor
34	C₂²	—	129	1	no	Sylow
35	C₃	C₂×C₆₁×D₄₃	1	1	yes	characteristic, complemented, Sylow
36	C₂	—	3	1	no	—
37	C₂	—	43	1	no	—
38	C₂	—	129	1	no	—

	subgroup	G/H
center, hypercenter	C₆₁	D₃×D₄₃
commutator, cosocle, hypocenter	C₃×C₄₃	C₂²×C₆₁
Frattini	C₁	G
Fitting, socle	C₃×C₄₃×C₆₁	C₂²
LCS	G ▷ C₃×C₄₃
UCS	C₁ ◁ C₆₁

Complements

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

N	H ≅ G/N	type
1. C₆₁×D₁₂₉	C₂	semidirect
2. D₃×C₄₃×C₆₁	C₂	semidirect
3. C₃×C₆₁×D₄₃	C₂	semidirect
5. C₃×C₄₃×C₆₁	C₂²	semidirect
8. C₆₁×D₄₃	D₃	direct (N × H)
9. C₄₃×C₆₁	C₂×D₃	semidirect
11. D₃×D₄₃	C₆₁	direct (N × H)
14. D₃×C₆₁	D₄₃	direct (N × H)
15. D₁₂₉	C₂×C₆₁	semidirect
16. C₃×D₄₃	C₂×C₆₁	semidirect
17. D₃×C₄₃	C₂×C₆₁	semidirect
19. C₃×C₆₁	C₂×D₄₃	semidirect
21. C₃×C₄₃	C₂²×C₆₁	semidirect
27. D₄₃	D₃×C₆₁	direct (N × H)
28. C₆₁	D₃×D₄₃	direct (N × H)
29. C₄₃	C₂×D₃×C₆₁	semidirect
33. D₃	C₆₁×D₄₃	direct (N × H)
35. C₃	C₂×C₆₁×D₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₆₁×D₁₂₉	2
D₃×C₄₃×C₆₁	2
C₃×C₆₁×D₄₃	2
C₂×C₆₁×D₄₃	3
C₂×D₃×C₆₁	43
D₃×D₄₃	61

Subgroups — D3×C61×D43 #44538381

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×C₆₁×D₄₃ #44538381