Subgroups — C₃×C₁₁×C₁₃×D₂₁ #31825088

Order 18018.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₇×C₁₁×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₁×C₁₃×D₂₁	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×C₁₁×C₁₃×D₇	—	3	1	no	maximal
4	C₃×C₇×C₁₁×C₁₃	—	2	1	no	—
5	C₃×C₇×C₁₁×C₁₃	D₃	1	1	yes	characteristic, complemented
6	C₃×C₇×C₁₁×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented
7	C₃×D₃×C₁₁×C₁₃	—	7	1	no	maximal, Hall
8	C₁₁×C₁₃×D₇	—	3	1	no	Hall
9	C₃×C₁₃×D₂₁	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₃×C₁₁×D₂₁	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₃²×C₁₁×C₁₃	D₇	1	1	yes	characteristic, complemented, Hall
12	C₇×C₁₁×C₁₃	C₃×D₃	1	1	yes	characteristic, complemented, Hall
13	C₂×C₃×C₁₁×C₁₃	—	21	1	no	—
14	D₃×C₁₁×C₁₃	—	7	1	no	—
15	C₃²×C₇×C₁₃	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
16	C₃²×C₇×C₁₁	C₂×C₁₃	1	1	yes	characteristic, complemented, Hall
17	C₁₃×D₂₁	C₃×C₁₁	1	1	yes	characteristic, direct product factor
18	C₃×C₁₃×D₇	—	3	1	no	—
19	C₁₁×D₂₁	C₃×C₁₃	1	1	yes	characteristic, direct product factor
20	C₃×C₁₁×D₇	—	3	1	no	—
21	C₃×C₁₁×C₁₃	—	2	1	no	—
22	C₃×C₁₁×C₁₃	C₃×D₇	1	1	yes	characteristic, complemented
23	C₃×C₁₁×C₁₃	D₂₁	1	1	yes	characteristic, direct product factor
24	C₂×C₁₁×C₁₃	—	21	1	no	Hall
25	C₃×C₇×C₁₃	—	2	1	no	—
26	C₃×C₇×C₁₃	D₃×C₁₁	1	1	yes	characteristic, complemented
27	C₃×C₇×C₁₃	C₂×C₃×C₁₁	1	1	yes	characteristic, complemented
28	C₃×D₃×C₁₃	—	7	1	no	Hall
29	C₃×C₇×C₁₁	—	2	1	no	—
30	C₃×C₇×C₁₁	D₃×C₁₃	1	1	yes	characteristic, complemented
31	C₃×C₇×C₁₁	C₂×C₃×C₁₃	1	1	yes	characteristic, complemented
32	C₃×D₃×C₁₁	—	7	1	no	Hall
33	C₁₃×D₇	—	3	1	no	Hall
34	C₁₁×D₇	—	3	1	no	Hall
35	C₁₁×C₁₃	C₃×D₂₁	1	1	yes	characteristic, direct product factor, Hall
36	C₃×D₂₁	C₁₁×C₁₃	1	1	yes	characteristic, direct product factor, Hall
37	C₃²×C₁₃	C₁₁×D₇	1	1	yes	characteristic, complemented, Hall
38	C₃²×C₁₁	C₁₃×D₇	1	1	yes	characteristic, complemented, Hall
39	C₇×C₁₃	C₃×D₃×C₁₁	1	1	yes	characteristic, complemented, Hall
40	C₂×C₃×C₁₃	—	21	1	no	—
41	D₃×C₁₃	—	7	1	no	—
42	C₇×C₁₁	C₃×D₃×C₁₃	1	1	yes	characteristic, complemented, Hall
43	C₂×C₃×C₁₁	—	21	1	no	—
44	D₃×C₁₁	—	7	1	no	—
45	C₃²×C₇	C₂×C₁₁×C₁₃	1	1	yes	characteristic, complemented, Hall
46	D₂₁	C₃×C₁₁×C₁₃	1	1	yes	characteristic, direct product factor
47	C₃×D₇	—	3	1	no	—
48	C₃×C₁₃	—	2	1	no	—
49	C₃×C₁₃	C₃×C₁₁×D₇	1	1	yes	characteristic, complemented
50	C₃×C₁₃	C₁₁×D₂₁	1	1	yes	characteristic, direct product factor
51	C₃×C₁₁	—	2	1	no	—
52	C₃×C₁₁	C₃×C₁₃×D₇	1	1	yes	characteristic, complemented
53	C₃×C₁₁	C₁₃×D₂₁	1	1	yes	characteristic, direct product factor
54	C₂×C₁₃	—	21	1	no	Hall
55	C₂×C₁₁	—	21	1	no	Hall
56	C₃×C₇	—	2	1	no	—
57	C₃×C₇	D₃×C₁₁×C₁₃	1	1	yes	characteristic, complemented
58	C₃×C₇	C₂×C₃×C₁₁×C₁₃	1	1	yes	characteristic, complemented
59	C₃×D₃	—	7	1	no	Hall
60	D₇	—	3	1	no	Hall
61	C₁₃	C₃×C₁₁×D₂₁	1	1	yes	characteristic, direct product factor, Sylow
62	C₁₁	C₃×C₁₃×D₂₁	1	1	yes	characteristic, direct product factor, Sylow
63	C₃²	C₁₁×C₁₃×D₇	1	1	yes	characteristic, complemented, Sylow
64	C₇	C₃×D₃×C₁₁×C₁₃	1	1	yes	characteristic, complemented, Sylow
65	C₂×C₃	—	21	1	no	—
66	D₃	—	7	1	no	—
67	C₃	—	2	1	no	—
68	C₃	C₃×C₁₁×C₁₃×D₇	1	1	yes	characteristic, complemented
69	C₃	C₁₁×C₁₃×D₂₁	1	1	yes	characteristic, direct product factor
70	C₂	—	21	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₁₁×C₁₃	D₂₁
commutator, cosocle, hypocenter	C₃×C₇	C₂×C₃×C₁₁×C₁₃
Frattini	C₁	G
Fitting, socle	C₃²×C₇×C₁₁×C₁₃	C₂
LCS	G ▷ C₃×C₇
UCS	C₁ ◁ C₃×C₁₁×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₃²×C₇×C₁₁×C₁₃	C₂	semidirect
2. C₁₁×C₁₃×D₂₁	C₃	direct (N × H)
5. C₃×C₇×C₁₁×C₁₃	D₃	semidirect
6. C₃×C₇×C₁₁×C₁₃	C₂×C₃	semidirect
9. C₃×C₁₃×D₂₁	C₁₁	direct (N × H)
10. C₃×C₁₁×D₂₁	C₁₃	direct (N × H)
11. C₃²×C₁₁×C₁₃	D₇	semidirect
12. C₇×C₁₁×C₁₃	C₃×D₃	semidirect
15. C₃²×C₇×C₁₃	C₂×C₁₁	semidirect
16. C₃²×C₇×C₁₁	C₂×C₁₃	semidirect
17. C₁₃×D₂₁	C₃×C₁₁	direct (N × H)
19. C₁₁×D₂₁	C₃×C₁₃	direct (N × H)
22. C₃×C₁₁×C₁₃	C₃×D₇	semidirect
23. C₃×C₁₁×C₁₃	D₂₁	direct (N × H)
26. C₃×C₇×C₁₃	D₃×C₁₁	semidirect
27. C₃×C₇×C₁₃	C₂×C₃×C₁₁	semidirect
30. C₃×C₇×C₁₁	D₃×C₁₃	semidirect
31. C₃×C₇×C₁₁	C₂×C₃×C₁₃	semidirect
35. C₁₁×C₁₃	C₃×D₂₁	direct (N × H)
36. C₃×D₂₁	C₁₁×C₁₃	direct (N × H)
37. C₃²×C₁₃	C₁₁×D₇	semidirect
38. C₃²×C₁₁	C₁₃×D₇	semidirect
39. C₇×C₁₃	C₃×D₃×C₁₁	semidirect
42. C₇×C₁₁	C₃×D₃×C₁₃	semidirect
45. C₃²×C₇	C₂×C₁₁×C₁₃	semidirect
46. D₂₁	C₃×C₁₁×C₁₃	direct (N × H)
49. C₃×C₁₃	C₃×C₁₁×D₇	semidirect
50. C₃×C₁₃	C₁₁×D₂₁	direct (N × H)
52. C₃×C₁₁	C₃×C₁₃×D₇	semidirect
53. C₃×C₁₁	C₁₃×D₂₁	direct (N × H)
57. C₃×C₇	D₃×C₁₁×C₁₃	semidirect
58. C₃×C₇	C₂×C₃×C₁₁×C₁₃	semidirect
61. C₁₃	C₃×C₁₁×D₂₁	direct (N × H)
62. C₁₁	C₃×C₁₃×D₂₁	direct (N × H)
63. C₃²	C₁₁×C₁₃×D₇	semidirect
64. C₇	C₃×D₃×C₁₁×C₁₃	semidirect
68. C₃	C₃×C₁₁×C₁₃×D₇	semidirect
69. C₃	C₁₁×C₁₃×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
C₃²×C₇×C₁₁×C₁₃	2
C₁₁×C₁₃×D₂₁	3
C₃×C₁₁×C₁₃×D₇	3
C₃×D₃×C₁₁×C₁₃	7
C₃×C₁₃×D₂₁	11
C₃×C₁₁×D₂₁	13

Subgroups — C3×C11×C13×D21 #31825088

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₁₁×C₁₃×D₂₁ #31825088