Subgroups — C₇×C₃⋊D₃×D₄₁ #23780211

Order 10332.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₃⋊D₁₂₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×C₃⋊D₃×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×C₇×D₄₁	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×C₇×D₄₁	—	3	4	no	maximal
5	C₃²×C₇×C₄₁	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₇×D₁₂₃	—	3	4	no	—
7	D₃×C₇×C₄₁	—	3	4	no	—
8	C₃×C₇×D₄₁	D₃	1	4	yes	complemented
9	C₃⋊D₃×D₄₁	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₇×D₄₁	—	9	1	no	Hall
11	C₃×C₇×C₄₁	C₂×D₃	1	4	yes	complemented
12	C₃⋊D₁₂₃	C₂×C₇	1	1	yes	characteristic, complemented
13	C₃⋊D₃×C₄₁	C₂×C₇	1	1	yes	characteristic, complemented
14	C₃²×D₄₁	C₂×C₇	1	1	yes	characteristic, complemented
15	C₂×C₇×C₄₁	—	9	1	no	—
16	C₇×D₄₁	—	9	1	no	—
17	C₇×D₄₁	C₃⋊D₃	1	1	yes	characteristic, direct product factor
18	D₃×D₄₁	—	3	4	no	—
19	C₃²×C₄₁	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
20	C₇×C₄₁	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
21	C₂×C₇×C₃⋊D₃	—	41	1	no	maximal, Hall
22	D₁₂₃	—	3	4	no	—
23	C₃×D₄₁	D₃×C₇	1	4	yes	complemented
24	D₃×C₄₁	—	3	4	no	—
25	C₂×D₄₁	—	9	1	no	Hall
26	C₂×C₃²×C₇	—	41	1	no	—
27	C₇×C₃⋊D₃	—	41	1	no	—
28	C₇×C₃⋊D₃	D₄₁	1	1	yes	characteristic, direct product factor
29	C₃×C₄₁	C₂×D₃×C₇	1	4	yes	complemented
30	C₂×D₃×C₇	—	123	4	no	—
31	C₂×C₄₁	—	9	1	no	—
32	D₄₁	—	9	1	no	—
33	D₄₁	C₇×C₃⋊D₃	1	1	yes	characteristic, direct product factor
34	C₃²×C₇	C₂×D₄₁	1	1	yes	characteristic, complemented, Hall
35	C₂×C₃×C₇	—	41	4	no	—
36	D₃×C₇	—	3	4	no	—
37	D₃×C₇	—	123	4	no	—
38	C₄₁	C₂×C₇×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
39	C₂×C₃⋊D₃	—	41	1	no	Hall
40	C₂²×C₇	—	369	1	no	Hall
41	C₃×C₇	D₃×D₄₁	1	4	yes	complemented
42	C₂×C₃²	—	41	1	no	—
43	C₃⋊D₃	—	41	1	no	—
44	C₃⋊D₃	C₇×D₄₁	1	1	yes	characteristic, direct product factor
45	C₂×C₇	—	9	1	no	—
46	C₂×C₇	—	41	1	no	—
47	C₂×C₇	—	369	1	no	—
48	C₂×D₃	—	123	4	no	—
49	C₃²	C₂×C₇×D₄₁	1	1	yes	characteristic, complemented, Sylow
50	C₇	C₃⋊D₃×D₄₁	1	1	yes	characteristic, direct product factor, Sylow
51	C₂×C₃	—	41	4	no	—
52	D₃	—	3	4	no	—
53	D₃	—	123	4	no	—
54	C₂²	—	369	1	no	Sylow
55	C₃	D₃×C₇×D₄₁	1	4	yes	complemented
56	C₂	—	9	1	no	—
57	C₂	—	41	1	no	—
58	C₂	—	369	1	no	—

	subgroup	G/H
center, hypercenter	C₇	C₃⋊D₃×D₄₁
commutator, cosocle, hypocenter	C₃²×C₄₁	C₂²×C₇
Frattini	C₁	G
Fitting, socle	C₃²×C₇×C₄₁	C₂²
LCS	G ▷ C₃²×C₄₁
UCS	C₁ ◁ C₇

Complements

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

N	H ≅ G/N	type
1. C₇×C₃⋊D₁₂₃	C₂	semidirect
2. C₇×C₃⋊D₃×C₄₁	C₂	semidirect
3. C₃²×C₇×D₄₁	C₂	semidirect
5. C₃²×C₇×C₄₁	C₂²	semidirect
8. C₃×C₇×D₄₁	D₃	semidirect
9. C₃⋊D₃×D₄₁	C₇	direct (N × H)
11. C₃×C₇×C₄₁	C₂×D₃	semidirect
12. C₃⋊D₁₂₃	C₂×C₇	semidirect
13. C₃⋊D₃×C₄₁	C₂×C₇	semidirect
14. C₃²×D₄₁	C₂×C₇	semidirect
17. C₇×D₄₁	C₃⋊D₃	direct (N × H)
19. C₃²×C₄₁	C₂²×C₇	semidirect
20. C₇×C₄₁	C₂×C₃⋊D₃	semidirect
23. C₃×D₄₁	D₃×C₇	semidirect
28. C₇×C₃⋊D₃	D₄₁	direct (N × H)
29. C₃×C₄₁	C₂×D₃×C₇	semidirect
33. D₄₁	C₇×C₃⋊D₃	direct (N × H)
34. C₃²×C₇	C₂×D₄₁	semidirect
38. C₄₁	C₂×C₇×C₃⋊D₃	semidirect
41. C₃×C₇	D₃×D₄₁	semidirect
44. C₃⋊D₃	C₇×D₄₁	direct (N × H)
49. C₃²	C₂×C₇×D₄₁	semidirect
50. C₇	C₃⋊D₃×D₄₁	direct (N × H)
55. C₃	D₃×C₇×D₄₁	semidirect

Subgroups — C7×C3⋊D3×D41 #23780211

Conjugacy classes of subgroups

Complements

Subgroups — C₇×C₃⋊D₃×D₄₁ #23780211