Subgroups — C₂×C₄₃×C₃⋊D₂₁ #24925674

Order 10836.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₃×C₃⋊D₂₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₇×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₂₁×C₄₃	—	3	4	no	maximal
4	C₃²×C₇×C₄₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×C₇×C₄₃	D₃	1	4	yes	complemented
6	D₂₁×C₄₃	—	3	8	no	—
7	C₂×C₃⋊D₃×C₄₃	—	7	1	no	maximal, Hall
8	C₂×D₇×C₄₃	—	9	1	no	Hall
9	C₃×C₇×C₄₃	C₂×D₃	1	4	yes	complemented
10	C₂×C₃²×C₄₃	D₇	1	1	yes	characteristic, complemented
11	C₃⋊D₃×C₄₃	—	7	2	no	—
12	C₂×C₇×C₄₃	C₃⋊D₃	1	1	yes	characteristic, complemented
13	D₇×C₄₃	—	9	2	no	—
14	C₂×D₃×C₄₃	—	21	4	no	—
15	C₃²×C₄₃	C₂×D₇	1	1	yes	characteristic, complemented, Hall
16	C₇×C₄₃	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
17	C₂×C₃×C₄₃	D₂₁	1	4	yes	complemented
18	D₃×C₄₃	—	21	8	no	—
19	C₂×C₃⋊D₂₁	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Hall
20	C₂²×C₄₃	—	63	1	no	Hall
21	C₃×C₄₃	C₂×D₂₁	1	4	yes	complemented
22	C₂×C₃²×C₇	C₂×C₄₃	1	1	yes	characteristic, complemented
23	C₃⋊D₂₁	C₂×C₄₃	1	2	yes	direct product factor
24	C₂×C₄₃	—	63	2	no	—
25	C₂×C₄₃	C₃⋊D₂₁	1	1	yes	characteristic, direct product factor
26	C₂×D₂₁	—	3	4	no	—
27	C₃²×C₇	C₂²×C₄₃	1	1	yes	characteristic, complemented, Hall
28	C₄₃	C₂×C₃⋊D₂₁	1	1	yes	characteristic, direct product factor, Sylow
29	C₂×C₃×C₇	D₃×C₄₃	1	4	yes	complemented
30	D₂₁	—	3	8	no	—
31	C₂×C₃⋊D₃	—	7	1	no	Hall
32	C₂×D₇	—	9	1	no	Hall
33	C₃×C₇	C₂×D₃×C₄₃	1	4	yes	complemented
34	C₂×C₃²	D₇×C₄₃	1	1	yes	characteristic, complemented
35	C₃⋊D₃	—	7	2	no	—
36	C₂×C₇	C₃⋊D₃×C₄₃	1	1	yes	characteristic, complemented
37	D₇	—	9	2	no	—
38	C₂×D₃	—	21	4	no	—
39	C₃²	C₂×D₇×C₄₃	1	1	yes	characteristic, complemented, Sylow
40	C₇	C₂×C₃⋊D₃×C₄₃	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₃	D₂₁×C₄₃	1	4	yes	complemented
42	D₃	—	21	8	no	—
43	C₂²	—	63	1	no	Sylow
44	C₃	C₂×D₂₁×C₄₃	1	4	yes	complemented
45	C₂	—	63	2	no	—
46	C₂	C₄₃×C₃⋊D₂₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₄₃	C₃⋊D₂₁
commutator, cosocle, hypocenter	C₃²×C₇	C₂²×C₄₃
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₇×C₄₃	C₂
LCS	G ▷ C₃²×C₇
UCS	C₁ ◁ C₂×C₄₃

Complements

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

N	H ≅ G/N	type
1. C₄₃×C₃⋊D₂₁	C₂	direct (N × H)
2. C₂×C₃²×C₇×C₄₃	C₂	semidirect
4. C₃²×C₇×C₄₃	C₂²	semidirect
5. C₂×C₃×C₇×C₄₃	D₃	semidirect
9. C₃×C₇×C₄₃	C₂×D₃	semidirect
10. C₂×C₃²×C₄₃	D₇	semidirect
12. C₂×C₇×C₄₃	C₃⋊D₃	semidirect
15. C₃²×C₄₃	C₂×D₇	semidirect
16. C₇×C₄₃	C₂×C₃⋊D₃	semidirect
17. C₂×C₃×C₄₃	D₂₁	semidirect
19. C₂×C₃⋊D₂₁	C₄₃	direct (N × H)
21. C₃×C₄₃	C₂×D₂₁	semidirect
22. C₂×C₃²×C₇	C₂×C₄₃	semidirect
23. C₃⋊D₂₁	C₂×C₄₃	direct (N × H)
25. C₂×C₄₃	C₃⋊D₂₁	direct (N × H)
27. C₃²×C₇	C₂²×C₄₃	semidirect
28. C₄₃	C₂×C₃⋊D₂₁	direct (N × H)
29. C₂×C₃×C₇	D₃×C₄₃	semidirect
33. C₃×C₇	C₂×D₃×C₄₃	semidirect
34. C₂×C₃²	D₇×C₄₃	semidirect
36. C₂×C₇	C₃⋊D₃×C₄₃	semidirect
39. C₃²	C₂×D₇×C₄₃	semidirect
40. C₇	C₂×C₃⋊D₃×C₄₃	semidirect
41. C₂×C₃	D₂₁×C₄₃	semidirect
44. C₃	C₂×D₂₁×C₄₃	semidirect
46. C₂	C₄₃×C₃⋊D₂₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄₃×C₃⋊D₂₁	2
C₂×C₃²×C₇×C₄₃	2
C₂×D₂₁×C₄₃	3
C₂×C₃⋊D₃×C₄₃	7
C₂×C₃⋊D₂₁	43

Subgroups — C2×C43×C3⋊D21 #24925674

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₃×C₃⋊D₂₁ #24925674