Subgroups — C₂×C₃×C₄₇×D₄₁ #37528867

Order 23124.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄₇×D₄₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₄₁×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₇×D₄₁	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₄₁×C₄₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₄₁×C₄₇	C₂×C₃	1	1	yes	characteristic, complemented
6	C₄₇×D₄₁	C₂×C₃	1	2	yes	direct product factor
7	C₄₁×C₄₇	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
8	C₂²×C₃×C₄₇	—	41	1	no	maximal, Hall
9	C₂×C₃×D₄₁	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₃×C₄₇	—	41	2	no	—
11	C₂×C₃×C₄₇	D₄₁	1	1	yes	characteristic, direct product factor
12	C₂×C₃×C₄₁	C₂×C₄₇	1	1	yes	characteristic, complemented
13	C₃×D₄₁	C₂×C₄₇	1	2	yes	direct product factor
14	C₂²×C₄₇	—	41	1	no	Hall
15	C₂×D₄₁	C₃×C₄₇	1	1	yes	characteristic, direct product factor, Hall
16	C₃×C₄₇	C₂×D₄₁	1	1	yes	characteristic, direct product factor, Hall
17	C₃×C₄₁	C₂²×C₄₇	1	1	yes	characteristic, complemented, Hall
18	C₂×C₄₇	—	41	2	no	—
19	C₂×C₄₇	C₃×D₄₁	1	1	yes	characteristic, direct product factor
20	C₂×C₄₁	C₂×C₃×C₄₇	1	1	yes	characteristic, complemented
21	D₄₁	C₂×C₃×C₄₇	1	2	yes	direct product factor
22	C₄₇	C₂×C₃×D₄₁	1	1	yes	characteristic, direct product factor, Sylow
23	C₄₁	C₂²×C₃×C₄₇	1	1	yes	characteristic, complemented, Sylow
24	C₂²×C₃	—	41	1	no	Hall
25	C₂×C₃	—	41	2	no	—
26	C₂×C₃	C₄₇×D₄₁	1	1	yes	characteristic, direct product factor
27	C₂²	—	41	1	no	Sylow
28	C₃	C₂×C₄₇×D₄₁	1	1	yes	characteristic, direct product factor, Sylow
29	C₂	—	41	2	no	—
30	C₂	C₃×C₄₇×D₄₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₄₇	D₄₁
commutator, cosocle, hypocenter	C₄₁	C₂²×C₃×C₄₇
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₄₁×C₄₇	C₂
LCS	G ▷ C₄₁
UCS	C₁ ◁ C₂×C₃×C₄₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₄₇×D₄₁	C₂	direct (N × H)
2. C₂×C₃×C₄₁×C₄₇	C₂	semidirect
3. C₂×C₄₇×D₄₁	C₃	direct (N × H)
4. C₃×C₄₁×C₄₇	C₂²	semidirect
5. C₂×C₄₁×C₄₇	C₂×C₃	semidirect
6. C₄₇×D₄₁	C₂×C₃	direct (N × H)
7. C₄₁×C₄₇	C₂²×C₃	semidirect
9. C₂×C₃×D₄₁	C₄₇	direct (N × H)
11. C₂×C₃×C₄₇	D₄₁	direct (N × H)
12. C₂×C₃×C₄₁	C₂×C₄₇	semidirect
13. C₃×D₄₁	C₂×C₄₇	direct (N × H)
15. C₂×D₄₁	C₃×C₄₇	direct (N × H)
16. C₃×C₄₇	C₂×D₄₁	direct (N × H)
17. C₃×C₄₁	C₂²×C₄₇	semidirect
19. C₂×C₄₇	C₃×D₄₁	direct (N × H)
20. C₂×C₄₁	C₂×C₃×C₄₇	semidirect
21. D₄₁	C₂×C₃×C₄₇	direct (N × H)
22. C₄₇	C₂×C₃×D₄₁	direct (N × H)
23. C₄₁	C₂²×C₃×C₄₇	semidirect
26. C₂×C₃	C₄₇×D₄₁	direct (N × H)
28. C₃	C₂×C₄₇×D₄₁	direct (N × H)
30. C₂	C₃×C₄₇×D₄₁	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×C₄₇×D₄₁	2
C₂×C₃×C₄₁×C₄₇	2
C₂×C₄₇×D₄₁	3
C₂²×C₃×C₄₇	41
C₂×C₃×D₄₁	47

Subgroups — C2×C3×C47×D41 #37528867

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₄₇×D₄₁ #37528867