Subgroups — D₃×C₇²×D₄₁ #37563141

Order 24108.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇²×D₄₁	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃×C₇²×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇²×D₁₂₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₇²×D₄₁	—	3	1	no	maximal, Hall
5	C₃×C₇²×C₄₁	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₇²×D₄₁	—	3	1	no	—
7	C₇²×D₄₁	D₃	1	1	yes	characteristic, direct product factor
8	C₂×C₇²×C₄₁	—	3	1	no	—
9	D₃×C₇×D₄₁	C₇	1	8	yes	maximal, direct product factor
10	C₇²×C₄₁	C₂×D₃	1	1	yes	characteristic, complemented, Hall
11	C₇×D₁₂₃	C₂×C₇	1	8	yes	complemented
12	D₃×C₇×C₄₁	C₂×C₇	1	8	yes	complemented
13	C₃×C₇×D₄₁	C₂×C₇	1	8	yes	complemented
14	C₂×C₇×D₄₁	—	3	8	no	—
15	C₃×C₇×C₄₁	C₂²×C₇	1	8	yes	complemented
16	C₂×D₃×C₇²	—	41	1	no	maximal, Hall
17	C₂×C₇×C₄₁	—	3	8	no	—
18	C₇×D₄₁	—	3	8	no	—
19	C₇×D₄₁	D₃×C₇	1	8	yes	direct product factor
20	D₃×D₄₁	C₇²	1	1	yes	characteristic, direct product factor, Hall
21	C₂×C₃×C₇²	—	41	1	no	—
22	D₃×C₇²	—	41	1	no	—
23	D₃×C₇²	D₄₁	1	1	yes	characteristic, direct product factor
24	C₇×C₄₁	C₂×D₃×C₇	1	8	yes	complemented
25	D₁₂₃	C₂×C₇²	1	1	yes	characteristic, complemented
26	C₃×D₄₁	C₂×C₇²	1	1	yes	characteristic, complemented
27	D₃×C₄₁	C₂×C₇²	1	1	yes	characteristic, complemented
28	C₂²×C₇²	—	123	1	no	Hall
29	C₂×D₄₁	—	3	1	no	Hall
30	C₃×C₇²	C₂×D₄₁	1	1	yes	characteristic, complemented, Hall
31	C₃×C₄₁	C₂²×C₇²	1	1	yes	characteristic, complemented, Hall
32	C₂×C₇²	—	3	1	no	—
33	C₂×C₇²	—	41	1	no	—
34	C₂×C₇²	—	123	1	no	—
35	C₂×D₃×C₇	—	41	8	no	—
36	C₂×C₄₁	—	3	1	no	—
37	D₄₁	—	3	1	no	—
38	D₄₁	D₃×C₇²	1	1	yes	characteristic, direct product factor
39	C₇²	D₃×D₄₁	1	1	yes	characteristic, direct product factor, Sylow
40	C₂×C₃×C₇	—	41	8	no	—
41	D₃×C₇	—	41	8	no	—
42	D₃×C₇	C₇×D₄₁	1	8	yes	direct product factor
43	C₄₁	C₂×D₃×C₇²	1	1	yes	characteristic, complemented, Sylow
44	C₂²×C₇	—	123	8	no	—
45	C₃×C₇	C₂×C₇×D₄₁	1	8	yes	complemented
46	C₂×C₇	—	3	8	no	—
47	C₂×C₇	—	41	8	no	—
48	C₂×C₇	—	123	8	no	—
49	C₂×D₃	—	41	1	no	Hall
50	C₇	D₃×C₇×D₄₁	1	8	yes	direct product factor
51	C₂×C₃	—	41	1	no	—
52	D₃	—	41	1	no	—
53	D₃	C₇²×D₄₁	1	1	yes	characteristic, direct product factor
54	C₂²	—	123	1	no	Sylow
55	C₃	C₂×C₇²×D₄₁	1	1	yes	characteristic, complemented, Sylow
56	C₂	—	3	1	no	—
57	C₂	—	41	1	no	—
58	C₂	—	123	1	no	—

	subgroup	G/H
center, hypercenter	C₇²	D₃×D₄₁
commutator, cosocle, hypocenter	C₃×C₄₁	C₂²×C₇²
Frattini	C₁	G
Fitting, socle	C₃×C₇²×C₄₁	C₂²
LCS	G ▷ C₃×C₄₁
UCS	C₁ ◁ C₇²

Complements

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

N	H ≅ G/N	type
1. C₃×C₇²×D₄₁	C₂	semidirect
2. D₃×C₇²×C₄₁	C₂	semidirect
3. C₇²×D₁₂₃	C₂	semidirect
5. C₃×C₇²×C₄₁	C₂²	semidirect
7. C₇²×D₄₁	D₃	direct (N × H)
9. D₃×C₇×D₄₁	C₇	direct (N × H)
10. C₇²×C₄₁	C₂×D₃	semidirect
11. C₇×D₁₂₃	C₂×C₇	semidirect
12. D₃×C₇×C₄₁	C₂×C₇	semidirect
13. C₃×C₇×D₄₁	C₂×C₇	semidirect
15. C₃×C₇×C₄₁	C₂²×C₇	semidirect
19. C₇×D₄₁	D₃×C₇	direct (N × H)
20. D₃×D₄₁	C₇²	direct (N × H)
23. D₃×C₇²	D₄₁	direct (N × H)
24. C₇×C₄₁	C₂×D₃×C₇	semidirect
25. D₁₂₃	C₂×C₇²	semidirect
26. C₃×D₄₁	C₂×C₇²	semidirect
27. D₃×C₄₁	C₂×C₇²	semidirect
30. C₃×C₇²	C₂×D₄₁	semidirect
31. C₃×C₄₁	C₂²×C₇²	semidirect
38. D₄₁	D₃×C₇²	direct (N × H)
39. C₇²	D₃×D₄₁	direct (N × H)
42. D₃×C₇	C₇×D₄₁	direct (N × H)
43. C₄₁	C₂×D₃×C₇²	semidirect
45. C₃×C₇	C₂×C₇×D₄₁	semidirect
50. C₇	D₃×C₇×D₄₁	direct (N × H)
53. D₃	C₇²×D₄₁	direct (N × H)
55. C₃	C₂×C₇²×D₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₇²×D₄₁	2
D₃×C₇²×C₄₁	2
C₇²×D₁₂₃	2
C₂×C₇²×D₄₁	3
D₃×C₇×D₄₁	7
C₂×D₃×C₇²	41

Subgroups — D3×C72×D41 #37563141

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×C₇²×D₄₁ #37563141