Subgroups — C₃×C₇×C₃⋊#1181 #20300645

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	C₇×C₃⋊#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	C₇	1	1	yes	maximal, characteristic, direct product factor, 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	C₂×C₇	1	1	yes	characteristic
14	C₇×D₂₉	C₃×D₃	1	1	yes	characteristic
15	C₃⋊#1181	C₃×C₇	1	1	yes	characteristic, direct product factor
16	C₃×#1181	—	3	1	no	—
17	C₃²×C₂₉	C₄×C₇	1	1	yes	characteristic, complemented, Hall
18	C₃×C₇×Dic₃	—	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	D₃×C₇	1	1	yes	characteristic
22	C₃×D₂₉	C₂×C₃×C₇	1	1	yes	characteristic
23	C₂×C₃²×C₇	—	29	1	no	—
24	#1181	—	3	1	no	Hall
25	C₃×C₂₉	—	2	1	no	—
26	C₃×C₂₉	C₇×Dic₃	1	1	yes	characteristic, complemented
27	C₃×C₂₉	C₃×C₄×C₇	1	1	yes	characteristic, complemented
28	C₃×C₄×C₇	—	87	1	no	—
29	C₇×Dic₃	—	29	1	no	—
30	C₃²×C₇	#1181	1	1	yes	characteristic, complemented, Hall
31	D₂₉	C₃×D₃×C₇	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	—	29	1	no	Hall
36	C₂₉	C₃×C₇×Dic₃	1	1	yes	characteristic, complemented, Sylow
37	C₄×C₇	—	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, direct product factor
41	C₂×C₃²	—	29	1	no	—
42	C₂×C₇	—	29	1	no	—
43	C₃×C₄	—	87	1	no	—
44	Dic₃	—	29	1	no	—
45	C₃²	C₇×#1181	1	1	yes	characteristic, complemented, Sylow
46	C₇	C₃×C₃⋊#1181	1	1	yes	characteristic, direct product factor, Sylow
47	C₂×C₃	—	29	1	no	—
48	C₂×C₃	—	29	1	no	—
49	C₂×C₃	—	58	1	no	—
50	C₄	—	87	1	no	Sylow
51	C₃	—	2	1	no	—
52	C₃	C₃×C₇×#1181	1	1	yes	characteristic, complemented
53	C₃	C₇×C₃⋊#1181	1	1	yes	characteristic, direct product factor
54	C₂	—	29	1	no	—

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

Complements

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

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

Subgroups — C3×C7×C3⋊#1181 #20300645

Conjugacy classes of subgroups

Complements

Subgroups — C₃×C₇×C₃⋊#1181 #20300645