Subgroups — C₃×C₃⋊(C₇⋊(C₇⋊#261)) #37525596

Order 22932.

280 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	1	yes	maximal, characteristic, direct product factor
3	C₃×C₇⋊(C₇⋊#261)	—	3	1	no	maximal
4	C₃²×C₇²×C₁₃	C₄	1	1	yes	characteristic, complemented, Hall
5	C₃×C₇²×D₁₃	—	2	1	no	—
6	C₃×C₇²×D₁₃	D₃	1	1	yes	characteristic
7	C₃×C₇²×D₁₃	C₂×C₃	1	1	yes	characteristic
8	C₃×C₃⋊(C₇⋊#261)	—	7	8	no	maximal
9	C₇⋊(C₇⋊#261)	—	3	1	no	Hall
10	C₃×C₇²×C₁₃	—	2	1	no	—
11	C₃×C₇²×C₁₃	Dic₃	1	1	yes	characteristic, complemented
12	C₃×C₇²×C₁₃	C₃×C₄	1	1	yes	characteristic, complemented
13	C₃×C₃⋊(C₇⋊Dic₇)	—	13	1	no	maximal, Hall
14	C₃²×C₇×D₁₃	D₇	1	8	yes	—
15	C₇²×D₁₃	C₃×D₃	1	1	yes	characteristic
16	C₃⋊(C₇⋊#261)	—	7	8	no	—
17	C₃×C₇⋊#261	—	21	8	no	—
18	C₂×C₃²×C₇²	—	13	1	no	—
19	C₃²×C₇×C₁₃	Dic₇	1	8	yes	complemented
20	C₇²×C₁₃	C₃×Dic₃	1	1	yes	characteristic, complemented, Hall
21	C₃⋊(C₇⋊Dic₇)	—	13	1	no	—
22	C₃×C₇⋊Dic₇	—	39	1	no	—
23	C₃×C₇×D₁₃	—	2	8	no	—
24	C₃×C₇×D₁₃	C₃×D₇	1	8	yes	—
25	C₃×C₇×D₁₃	D₂₁	1	8	yes	—
26	C₃×C₃⋊#261	—	49	1	no	Hall
27	C₃²×C₇²	#261	1	1	yes	characteristic, complemented, Hall
28	C₇⋊#261	—	21	8	no	—
29	C₂×C₃×C₇²	—	13	1	no	—
30	C₂×C₃×C₇²	—	13	1	no	—
31	C₂×C₃×C₇²	—	26	1	no	—
32	C₃×C₇×C₁₃	—	2	8	no	—
33	C₃×C₇×C₁₃	C₃×Dic₇	1	8	yes	complemented
34	C₃×C₇×C₁₃	Dic₂₁	1	8	yes	complemented
35	C₃×Dic₂₁	—	91	8	no	—
36	C₃²×D₁₃	C₇⋊D₇	1	1	yes	characteristic
37	C₇⋊Dic₇	—	39	1	no	Hall
38	C₇×D₁₃	C₃×D₂₁	1	8	yes	—
39	C₃⋊#261	—	49	1	no	—
40	C₃×#261	—	147	1	no	—
41	C₃×C₇²	—	2	1	no	—
42	C₃×C₇²	C₃×#261	1	1	yes	characteristic, complemented
43	C₃×C₇²	C₃⋊#261	1	1	yes	characteristic, complemented
44	C₂×C₃²×C₇	—	13	8	no	—
45	C₃²×C₁₃	C₇⋊Dic₇	1	1	yes	characteristic, complemented, Hall
46	C₂×C₇²	—	13	1	no	—
47	C₇×C₁₃	C₃×Dic₂₁	1	8	yes	complemented
48	Dic₂₁	—	91	8	no	—
49	C₃×Dic₇	—	273	8	no	—
50	C₃×D₁₃	—	2	1	no	—
51	C₃×D₁₃	C₃×C₇⋊D₇	1	1	yes	characteristic
52	C₃×D₁₃	C₃⋊(C₇⋊D₇)	1	1	yes	characteristic
53	C₃²×C₇	C₇⋊#261	1	8	yes	complemented
54	#261	—	147	1	no	Hall
55	C₇²	C₃×C₃⋊#261	1	1	yes	characteristic, complemented, Sylow
56	C₂×C₃×C₇	—	13	8	no	—
57	C₂×C₃×C₇	—	13	8	no	—
58	C₂×C₃×C₇	—	26	8	no	—
59	C₃×C₁₃	—	2	1	no	—
60	C₃×C₁₃	C₃×C₇⋊Dic₇	1	1	yes	characteristic, complemented
61	C₃×C₁₃	C₃⋊(C₇⋊Dic₇)	1	1	yes	characteristic, complemented
62	C₃×Dic₃	—	637	1	no	Hall
63	Dic₇	—	273	8	no	—
64	D₁₃	C₃×C₃⋊(C₇⋊D₇)	1	1	yes	characteristic
65	C₃×C₇	—	2	8	no	—
66	C₃×C₇	C₃×C₇⋊#261	1	8	yes	complemented
67	C₃×C₇	C₃⋊(C₇⋊#261)	1	8	yes	complemented
68	C₂×C₃²	—	13	1	no	—
69	C₂×C₇	—	13	8	no	—
70	C₁₃	C₃×C₃⋊(C₇⋊Dic₇)	1	1	yes	characteristic, complemented, Sylow
71	C₃×C₄	—	1911	1	no	—
72	Dic₃	—	637	1	no	—
73	C₃²	C₇⋊(C₇⋊#261)	1	1	yes	characteristic, complemented, Sylow
74	C₇	C₃×C₃⋊(C₇⋊#261)	1	8	yes	complemented
75	C₂×C₃	—	13	1	no	—
76	C₂×C₃	—	13	1	no	—
77	C₂×C₃	—	26	1	no	—
78	C₄	—	1911	1	no	Sylow
79	C₃	—	2	1	no	—
80	C₃	C₃×C₇⋊(C₇⋊#261)	1	1	yes	characteristic, complemented
81	C₃	C₃⋊(C₇⋊(C₇⋊#261))	1	1	yes	characteristic, direct product factor
82	C₂	—	13	1	no	—

	subgroup	G/H
center, hypercenter	C₃	C₃⋊(C₇⋊(C₇⋊#261))
commutator, hypocenter	C₃×C₇²×C₁₃	C₃×C₄
Frattini	C₁	G
Fitting, socle	C₃²×C₇²×C₁₃	C₄
prime radical	C₃²×C₇²×D₁₃	C₂
cosocle	C₃×C₇²×D₁₃	C₂×C₃
LCS	G ▷ C₃×C₇²×C₁₃
UCS	C₁ ◁ C₃

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)
4. C₃²×C₇²×C₁₃	C₄	semidirect
11. C₃×C₇²×C₁₃	Dic₃	semidirect
12. C₃×C₇²×C₁₃	C₃×C₄	semidirect
19. C₃²×C₇×C₁₃	Dic₇	semidirect
20. C₇²×C₁₃	C₃×Dic₃	semidirect
27. C₃²×C₇²	#261	semidirect
33. C₃×C₇×C₁₃	C₃×Dic₇	semidirect
34. C₃×C₇×C₁₃	Dic₂₁	semidirect
42. C₃×C₇²	C₃×#261	semidirect
43. C₃×C₇²	C₃⋊#261	semidirect
45. C₃²×C₁₃	C₇⋊Dic₇	semidirect
47. C₇×C₁₃	C₃×Dic₂₁	semidirect
53. C₃²×C₇	C₇⋊#261	semidirect
55. C₇²	C₃×C₃⋊#261	semidirect
60. C₃×C₁₃	C₃×C₇⋊Dic₇	semidirect
61. C₃×C₁₃	C₃⋊(C₇⋊Dic₇)	semidirect
66. C₃×C₇	C₃×C₇⋊#261	semidirect
67. C₃×C₇	C₃⋊(C₇⋊#261)	semidirect
70. C₁₃	C₃×C₃⋊(C₇⋊Dic₇)	semidirect
73. C₃²	C₇⋊(C₇⋊#261)	semidirect
74. C₇	C₃×C₃⋊(C₇⋊#261)	semidirect
80. C₃	C₃×C₇⋊(C₇⋊#261)	semidirect
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
C₃×C₇⋊(C₇⋊#261)	3
C₃×C₃⋊(C₇⋊#261)	7
C₃×C₃⋊(C₇⋊Dic₇)	13

Subgroups — C3×C3⋊(C7⋊(C7⋊#261)) #37525596

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₃⋊(C₇⋊(C₇⋊#261)) #37525596