Subgroups — C₃×C₃⋊(C₇⋊#1181) #20300647

Order 7308.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₇×D₂₉	C₂	1	1	yes	maximal, characteristic
2	C₃⋊(C₇⋊#1181)	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×C₇⋊#1181	—	3	1	no	maximal
4	C₃²×C₇×C₂₉	C₄	1	1	yes	characteristic, complemented, Hall
5	C₃×C₇×D₂₉	—	2	1	no	—
6	C₃×C₇×D₂₉	D₃	1	1	yes	characteristic
7	C₃×C₇×D₂₉	C₂×C₃	1	1	yes	characteristic
8	C₃×C₃⋊#1181	—	7	1	no	maximal, Hall
9	C₇⋊#1181	—	3	1	no	Hall
10	C₃×C₇×C₂₉	—	2	1	no	—
11	C₃×C₇×C₂₉	Dic₃	1	1	yes	characteristic, complemented
12	C₃×C₇×C₂₉	C₃×C₄	1	1	yes	characteristic, complemented
13	C₃²×D₂₉	D₇	1	1	yes	characteristic
14	C₇×D₂₉	C₃×D₃	1	1	yes	characteristic
15	C₃⋊#1181	—	7	1	no	—
16	C₃×#1181	—	21	1	no	—
17	C₃²×C₂₉	Dic₇	1	1	yes	characteristic, complemented, Hall
18	C₃×Dic₂₁	—	29	1	no	maximal, Hall
19	C₇×C₂₉	C₃×Dic₃	1	1	yes	characteristic, complemented, Hall
20	C₃×D₂₉	—	2	1	no	—
21	C₃×D₂₉	C₃×D₇	1	1	yes	characteristic
22	C₃×D₂₉	D₂₁	1	1	yes	characteristic
23	C₂×C₃²×C₇	—	29	1	no	—
24	#1181	—	21	1	no	Hall
25	C₃×C₂₉	—	2	1	no	—
26	C₃×C₂₉	C₃×Dic₇	1	1	yes	characteristic, complemented
27	C₃×C₂₉	Dic₂₁	1	1	yes	characteristic, complemented
28	Dic₂₁	—	29	1	no	—
29	C₃×Dic₇	—	87	1	no	—
30	C₃²×C₇	#1181	1	1	yes	characteristic, complemented, Hall
31	D₂₉	C₃×D₂₁	1	1	yes	characteristic
32	C₂×C₃×C₇	—	29	1	no	—
33	C₂×C₃×C₇	—	29	1	no	—
34	C₂×C₃×C₇	—	58	1	no	—
35	C₃×Dic₃	—	203	1	no	Hall
36	C₂₉	C₃×Dic₂₁	1	1	yes	characteristic, complemented, Sylow
37	Dic₇	—	87	1	no	Hall
38	C₃×C₇	—	2	1	no	—
39	C₃×C₇	C₃×#1181	1	1	yes	characteristic, complemented
40	C₃×C₇	C₃⋊#1181	1	1	yes	characteristic, complemented
41	C₂×C₃²	—	29	1	no	—
42	C₂×C₇	—	29	1	no	—
43	C₃×C₄	—	609	1	no	—
44	Dic₃	—	203	1	no	—
45	C₃²	C₇⋊#1181	1	1	yes	characteristic, complemented, Sylow
46	C₇	C₃×C₃⋊#1181	1	1	yes	characteristic, complemented, Sylow
47	C₂×C₃	—	29	1	no	—
48	C₂×C₃	—	29	1	no	—
49	C₂×C₃	—	58	1	no	—
50	C₄	—	609	1	no	Sylow
51	C₃	—	2	1	no	—
52	C₃	C₃×C₇⋊#1181	1	1	yes	characteristic, complemented
53	C₃	C₃⋊(C₇⋊#1181)	1	1	yes	characteristic, direct product factor
54	C₂	—	29	1	no	—

	subgroup	G/H
center, hypercenter	C₃	C₃⋊(C₇⋊#1181)
commutator, hypocenter	C₃×C₇×C₂₉	C₃×C₄
Frattini	C₁	G
Fitting, socle	C₃²×C₇×C₂₉	C₄
LCS	G ▷ C₃×C₇×C₂₉
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
2. C₃⋊(C₇⋊#1181)	C₃	direct (N × H)
4. C₃²×C₇×C₂₉	C₄	semidirect
11. C₃×C₇×C₂₉	Dic₃	semidirect
12. C₃×C₇×C₂₉	C₃×C₄	semidirect
17. C₃²×C₂₉	Dic₇	semidirect
19. C₇×C₂₉	C₃×Dic₃	semidirect
26. C₃×C₂₉	C₃×Dic₇	semidirect
27. C₃×C₂₉	Dic₂₁	semidirect
30. C₃²×C₇	#1181	semidirect
36. C₂₉	C₃×Dic₂₁	semidirect
39. C₃×C₇	C₃×#1181	semidirect
40. C₃×C₇	C₃⋊#1181	semidirect
45. C₃²	C₇⋊#1181	semidirect
46. C₇	C₃×C₃⋊#1181	semidirect
52. C₃	C₃×C₇⋊#1181	semidirect
53. C₃	C₃⋊(C₇⋊#1181)	direct (N × H)

Subgroups — C3×C3⋊(C7⋊#1181) #20300647

Conjugacy classes of subgroups

Complements

Subgroups — C₃×C₃⋊(C₇⋊#1181) #20300647