Subgroups — C₉×C₁₃×D₇² #37524564

Order 22932.

156 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₁₃×C₇⋊D₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×C₉×C₁₃×D₇	C₂	1	2	yes	maximal, complemented
3	C₃×C₁₃×D₇²	C₃	1	1	yes	maximal, characteristic
4	C₇²×C₉×C₁₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₃×C₇⋊D₇	C₂×C₃	1	1	yes	characteristic
6	C₃×C₇×C₁₃×D₇	C₂×C₃	1	2	yes	—
7	C₂×C₉×C₁₃×D₇	—	7	2	no	maximal
8	C₁₃×D₇²	C₉	1	1	yes	characteristic, direct product factor, Hall
9	C₃×C₇²×C₁₃	C₂²×C₃	1	1	yes	characteristic
10	C₉×D₇²	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₇×C₉×C₁₃	—	7	2	no	—
12	C₉×C₁₃×D₇	—	7	2	no	—
13	C₉×C₁₃×D₇	—	14	3	no	—
14	C₉×C₁₃×D₇	D₇	1	2	yes	direct product factor
15	C₁₃×C₇⋊D₇	C₂×C₉	1	1	yes	characteristic, complemented
16	C₇×C₁₃×D₇	C₂×C₉	1	2	yes	complemented
17	C₂×C₃×C₁₃×D₇	—	7	2	no	—
18	C₉×C₇⋊D₇	C₂×C₁₃	1	1	yes	characteristic, complemented
19	C₇×C₉×D₇	C₂×C₁₃	1	2	yes	complemented
20	C₇×C₉×C₁₃	—	2	3	no	—
21	C₇×C₉×C₁₃	C₂×D₇	1	2	yes	complemented
22	C₇²×C₁₃	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
23	C₃×D₇²	C₃×C₁₃	1	1	yes	characteristic
24	C₂×C₃×C₇×C₁₃	—	7	2	no	—
25	C₃×C₁₃×D₇	—	7	2	no	—
26	C₃×C₁₃×D₇	—	14	3	no	—
27	C₃×C₁₃×D₇	C₃×D₇	1	2	yes	—
28	C₂²×C₉×C₁₃	—	49	1	no	Hall
29	C₇²×C₉	C₂²×C₁₃	1	1	yes	characteristic, complemented, Hall
30	C₂×C₁₃×D₇	—	7	2	no	—
31	C₃×C₇⋊D₇	C₂×C₃×C₁₃	1	1	yes	characteristic
32	C₃×C₇×D₇	C₂×C₃×C₁₃	1	2	yes	—
33	C₃×C₇×C₁₃	—	2	3	no	—
34	C₃×C₇×C₁₃	C₂×C₃×D₇	1	2	yes	—
35	C₂×C₉×D₇	—	7	2	no	—
36	C₂×C₉×C₁₃	—	7	2	no	—
37	C₂×C₉×C₁₃	—	49	1	no	—
38	D₇²	C₉×C₁₃	1	1	yes	characteristic, direct product factor, Hall
39	C₂×C₇×C₁₃	—	7	2	no	—
40	C₁₃×D₇	—	7	2	no	—
41	C₁₃×D₇	—	14	3	no	—
42	C₁₃×D₇	C₉×D₇	1	2	yes	direct product factor
43	C₂²×C₃×C₁₃	—	49	1	no	—
44	C₃×C₇²	C₂²×C₃×C₁₃	1	1	yes	characteristic
45	C₂×C₇×C₉	—	7	2	no	—
46	C₉×D₇	—	7	2	no	—
47	C₉×D₇	—	14	3	no	—
48	C₉×D₇	C₁₃×D₇	1	2	yes	direct product factor
49	C₉×C₁₃	D₇²	1	1	yes	characteristic, direct product factor, Hall
50	C₇⋊D₇	C₂×C₉×C₁₃	1	1	yes	characteristic, complemented
51	C₇×D₇	C₂×C₉×C₁₃	1	2	yes	complemented
52	C₇×C₁₃	—	2	3	no	—
53	C₇×C₁₃	C₂×C₉×D₇	1	2	yes	complemented
54	C₂×C₃×D₇	—	7	2	no	—
55	C₂×C₃×C₁₃	—	7	2	no	—
56	C₂×C₃×C₁₃	—	49	1	no	—
57	C₇×C₉	—	2	3	no	—
58	C₇×C₉	C₂×C₁₃×D₇	1	2	yes	complemented
59	C₂²×C₁₃	—	49	1	no	Hall
60	C₇²	C₂²×C₉×C₁₃	1	1	yes	characteristic, complemented, Sylow
61	C₂×C₃×C₇	—	7	2	no	—
62	C₃×D₇	—	7	2	no	—
63	C₃×D₇	—	14	3	no	—
64	C₃×D₇	C₃×C₁₃×D₇	1	2	yes	—
65	C₃×C₁₃	C₃×D₇²	1	1	yes	characteristic
66	C₂²×C₉	—	49	1	no	Hall
67	C₂×D₇	—	7	2	no	—
68	C₂×C₁₃	—	7	2	no	—
69	C₂×C₁₃	—	49	1	no	—
70	C₃×C₇	—	2	3	no	—
71	C₃×C₇	C₂×C₃×C₁₃×D₇	1	2	yes	—
72	C₂×C₉	—	7	2	no	—
73	C₂×C₉	—	49	1	no	—
74	C₂×C₇	—	7	2	no	—
75	D₇	—	7	2	no	—
76	D₇	—	14	3	no	—
77	D₇	C₉×C₁₃×D₇	1	2	yes	direct product factor
78	C₁₃	C₉×D₇²	1	1	yes	characteristic, direct product factor, Sylow
79	C₂²×C₃	—	49	1	no	—
80	C₉	C₁₃×D₇²	1	1	yes	characteristic, direct product factor, Sylow
81	C₇	—	2	3	no	—
82	C₇	C₂×C₉×C₁₃×D₇	1	2	yes	complemented
83	C₂×C₃	—	7	2	no	—
84	C₂×C₃	—	49	1	no	—
85	C₂²	—	49	1	no	Sylow
86	C₃	C₃×C₁₃×D₇²	1	1	yes	characteristic
87	C₂	—	7	2	no	—
88	C₂	—	49	1	no	—

	subgroup	G/H
center, hypercenter	C₉×C₁₃	D₇²
commutator, hypocenter	C₇²	C₂²×C₉×C₁₃
Frattini	C₃	C₃×C₁₃×D₇²
Fitting	C₇²×C₉×C₁₃	C₂²
socle	C₃×C₇²×C₁₃	C₂²×C₃
prime radical	C₃×C₁₃×D₇²	C₃
cosocle	C₃×C₇²	C₂²×C₃×C₁₃
LCS	G ▷ C₇²
UCS	C₁ ◁ C₉×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₉×C₁₃×C₇⋊D₇	C₂	semidirect
2. C₇×C₉×C₁₃×D₇	C₂	semidirect
4. C₇²×C₉×C₁₃	C₂²	semidirect
8. C₁₃×D₇²	C₉	direct (N × H)
10. C₉×D₇²	C₁₃	direct (N × H)
14. C₉×C₁₃×D₇	D₇	direct (N × H)
15. C₁₃×C₇⋊D₇	C₂×C₉	semidirect
16. C₇×C₁₃×D₇	C₂×C₉	semidirect
18. C₉×C₇⋊D₇	C₂×C₁₃	semidirect
19. C₇×C₉×D₇	C₂×C₁₃	semidirect
21. C₇×C₉×C₁₃	C₂×D₇	semidirect
22. C₇²×C₁₃	C₂²×C₉	semidirect
29. C₇²×C₉	C₂²×C₁₃	semidirect
38. D₇²	C₉×C₁₃	direct (N × H)
42. C₁₃×D₇	C₉×D₇	direct (N × H)
48. C₉×D₇	C₁₃×D₇	direct (N × H)
49. C₉×C₁₃	D₇²	direct (N × H)
50. C₇⋊D₇	C₂×C₉×C₁₃	semidirect
51. C₇×D₇	C₂×C₉×C₁₃	semidirect
53. C₇×C₁₃	C₂×C₉×D₇	semidirect
58. C₇×C₉	C₂×C₁₃×D₇	semidirect
60. C₇²	C₂²×C₉×C₁₃	semidirect
77. D₇	C₉×C₁₃×D₇	direct (N × H)
78. C₁₃	C₉×D₇²	direct (N × H)
80. C₉	C₁₃×D₇²	direct (N × H)
82. C₇	C₂×C₉×C₁₃×D₇	semidirect

Maximal subgroups

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

subgroup	index
C₉×C₁₃×C₇⋊D₇	2
C₇×C₉×C₁₃×D₇	2
C₃×C₁₃×D₇²	3
C₂×C₉×C₁₃×D₇	7
C₉×D₇²	13

Subgroups — C9×C13×D72 #37524564

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×C₁₃×D₇² #37524564