Subgroups — C₃²×C₇×C₇⋊#261 #37525571

Order 22932.

216 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₇²×D₁₃	C₂	1	1	yes	maximal, characteristic
2	C₃×C₇×C₇⋊#261	C₃	1	4	yes	maximal, direct product factor
3	C₃²×C₇²×C₁₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₇²×D₁₃	C₂×C₃	1	4	yes	—
5	C₃²×C₇⋊#261	C₇	1	1	yes	maximal, characteristic, direct product factor
6	C₃²×C₇×#261	—	7	1	no	maximal
7	C₇×C₇⋊#261	C₃²	1	1	yes	characteristic, direct product factor, Hall
8	C₃×C₇²×C₁₃	C₃×C₄	1	4	yes	complemented
9	C₃²×C₇×Dic₇	—	13	1	no	maximal, Hall
10	C₃²×C₇×D₁₃	—	2	3	no	—
11	C₃²×C₇×D₁₃	D₇	1	1	yes	characteristic
12	C₃²×C₇×D₁₃	C₂×C₇	1	1	yes	characteristic
13	C₇²×D₁₃	C₂×C₃²	1	1	yes	characteristic
14	C₃×C₇⋊#261	C₃×C₇	1	4	yes	direct product factor
15	C₃×C₇×#261	—	7	4	no	—
16	C₂×C₃²×C₇²	—	13	1	no	—
17	C₃²×C₇×C₁₃	—	2	3	no	—
18	C₃²×C₇×C₁₃	Dic₇	1	1	yes	characteristic, complemented
19	C₃²×C₇×C₁₃	C₄×C₇	1	1	yes	characteristic, complemented
20	C₇²×C₁₃	C₃²×C₄	1	1	yes	characteristic, complemented, Hall
21	C₃×C₇×Dic₇	—	13	4	no	—
22	C₃×C₇×D₁₃	—	2	12	no	—
23	C₃×C₇×D₁₃	C₃×D₇	1	4	yes	—
24	C₃×C₇×D₁₃	C₂×C₃×C₇	1	4	yes	—
25	C₃²×#261	—	7	1	no	Hall
26	C₃²×C₇²	#261	1	1	yes	characteristic, complemented, Hall
27	C₇⋊#261	C₃²×C₇	1	1	yes	characteristic, direct product factor
28	C₇×#261	—	7	1	no	—
29	C₂×C₃×C₇²	—	13	4	no	—
30	C₃×C₇×C₁₃	—	2	12	no	—
31	C₃×C₇×C₁₃	C₃×Dic₇	1	4	yes	complemented
32	C₃×C₇×C₁₃	C₃×C₄×C₇	1	4	yes	complemented
33	C₃²×C₄×C₇	—	91	1	no	—
34	C₃²×Dic₇	—	13	1	no	—
35	C₃²×D₁₃	C₇×D₇	1	1	yes	characteristic
36	C₇×Dic₇	—	13	1	no	Hall
37	C₇×D₁₃	—	2	3	no	—
38	C₇×D₁₃	C₃²×D₇	1	1	yes	characteristic
39	C₇×D₁₃	C₂×C₃²×C₇	1	1	yes	characteristic
40	C₃×#261	—	7	4	no	—
41	C₃×C₇²	C₃×#261	1	4	yes	complemented
42	C₂×C₃²×C₇	—	13	1	no	—
43	C₂×C₃²×C₇	—	13	1	no	—
44	C₂×C₃²×C₇	—	26	3	no	—
45	C₃²×C₁₃	C₇×Dic₇	1	1	yes	characteristic, complemented, Hall
46	C₂×C₇²	—	13	1	no	—
47	C₇×C₁₃	—	2	3	no	—
48	C₇×C₁₃	C₃²×Dic₇	1	1	yes	characteristic, complemented
49	C₇×C₁₃	C₃²×C₄×C₇	1	1	yes	characteristic, complemented
50	C₃×C₄×C₇	—	91	4	no	—
51	C₃×Dic₇	—	13	4	no	—
52	C₃×D₁₃	C₃×C₇×D₇	1	4	yes	—
53	C₃²×C₇	—	2	3	no	—
54	C₃²×C₇	C₇×#261	1	1	yes	characteristic, complemented
55	C₃²×C₇	C₇⋊#261	1	1	yes	characteristic, direct product factor
56	#261	—	7	1	no	Hall
57	C₇²	C₃²×#261	1	1	yes	characteristic, complemented, Sylow
58	C₂×C₃×C₇	—	13	4	no	—
59	C₂×C₃×C₇	—	13	4	no	—
60	C₂×C₃×C₇	—	26	12	no	—
61	C₃×C₁₃	C₃×C₇×Dic₇	1	4	yes	complemented
62	C₃²×C₄	—	91	1	no	Hall
63	C₄×C₇	—	91	1	no	—
64	Dic₇	—	13	1	no	—
65	D₁₃	C₃²×C₇×D₇	1	1	yes	characteristic
66	C₃×C₇	—	2	12	no	—
67	C₃×C₇	C₃×C₇×#261	1	4	yes	complemented
68	C₃×C₇	C₃×C₇⋊#261	1	4	yes	direct product factor
69	C₂×C₃²	—	13	1	no	—
70	C₂×C₇	—	13	1	no	—
71	C₂×C₇	—	13	1	no	—
72	C₂×C₇	—	26	3	no	—
73	C₁₃	C₃²×C₇×Dic₇	1	1	yes	characteristic, complemented, Sylow
74	C₃×C₄	—	91	4	no	—
75	C₃²	C₇×C₇⋊#261	1	1	yes	characteristic, direct product factor, Sylow
76	C₇	—	2	3	no	—
77	C₇	C₃²×C₇×#261	1	1	yes	characteristic, complemented
78	C₇	C₃²×C₇⋊#261	1	1	yes	characteristic, direct product factor
79	C₂×C₃	—	13	4	no	—
80	C₄	—	91	1	no	Sylow
81	C₃	C₃×C₇×C₇⋊#261	1	4	yes	direct product factor
82	C₂	—	13	1	no	—

	subgroup	G/H
center, hypercenter	C₃²×C₇	C₇⋊#261
commutator, hypocenter	C₇×C₁₃	C₃²×C₄×C₇
Frattini	C₁	G
Fitting, socle	C₃²×C₇²×C₁₃	C₄
prime radical	C₃²×C₇²×D₁₃	C₂
cosocle	C₇×D₁₃	C₂×C₃²×C₇
LCS	G ▷ C₇×C₁₃
UCS	C₁ ◁ C₃²×C₇

Complements

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

N	H ≅ G/N	type
2. C₃×C₇×C₇⋊#261	C₃	direct (N × H)
3. C₃²×C₇²×C₁₃	C₄	semidirect
5. C₃²×C₇⋊#261	C₇	direct (N × H)
7. C₇×C₇⋊#261	C₃²	direct (N × H)
8. C₃×C₇²×C₁₃	C₃×C₄	semidirect
14. C₃×C₇⋊#261	C₃×C₇	direct (N × H)
18. C₃²×C₇×C₁₃	Dic₇	semidirect
19. C₃²×C₇×C₁₃	C₄×C₇	semidirect
20. C₇²×C₁₃	C₃²×C₄	semidirect
26. C₃²×C₇²	#261	semidirect
27. C₇⋊#261	C₃²×C₇	direct (N × H)
31. C₃×C₇×C₁₃	C₃×Dic₇	semidirect
32. C₃×C₇×C₁₃	C₃×C₄×C₇	semidirect
41. C₃×C₇²	C₃×#261	semidirect
45. C₃²×C₁₃	C₇×Dic₇	semidirect
48. C₇×C₁₃	C₃²×Dic₇	semidirect
49. C₇×C₁₃	C₃²×C₄×C₇	semidirect
54. C₃²×C₇	C₇×#261	semidirect
55. C₃²×C₇	C₇⋊#261	direct (N × H)
57. C₇²	C₃²×#261	semidirect
61. C₃×C₁₃	C₃×C₇×Dic₇	semidirect
67. C₃×C₇	C₃×C₇×#261	semidirect
68. C₃×C₇	C₃×C₇⋊#261	direct (N × H)
73. C₁₃	C₃²×C₇×Dic₇	semidirect
75. C₃²	C₇×C₇⋊#261	direct (N × H)
77. C₇	C₃²×C₇×#261	semidirect
78. C₇	C₃²×C₇⋊#261	direct (N × H)
81. C₃	C₃×C₇×C₇⋊#261	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×C₇²×D₁₃	2
C₃×C₇×C₇⋊#261	3
C₃²×C₇⋊#261	7
C₃²×C₇×#261	7
C₃²×C₇×Dic₇	13

Subgroups — C32×C7×C7⋊#261 #37525571

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×C₇×C₇⋊#261 #37525571