Subgroups — C₃×C₁₁×C₇⋊#595 #30628126

Order 15708.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₁₁×D₁₇	C₂	1	1	yes	maximal, characteristic
2	C₁₁×C₇⋊#595	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₇×C₁₁×C₁₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₇×C₁₁×D₁₇	C₂×C₃	1	1	yes	characteristic
5	C₃×C₁₁×#595	—	7	1	no	maximal, Hall
6	C₃×C₇⋊#595	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₇×C₁₁×C₁₇	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	C₃×C₁₁×D₁₇	D₇	1	1	yes	characteristic
9	C₃×C₁₁×Dic₇	—	17	1	no	maximal, Hall
10	C₁₁×#595	—	7	1	no	Hall
11	C₃×C₇×D₁₇	C₂×C₁₁	1	1	yes	characteristic
12	C₃×C₁₁×C₁₇	Dic₇	1	1	yes	characteristic, complemented, Hall
13	C₇⋊#595	C₃×C₁₁	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₃×C₇×C₁₁	—	17	1	no	—
15	C₁₁×D₁₇	C₃×D₇	1	1	yes	characteristic
16	C₃×C₇×C₁₇	C₄×C₁₁	1	1	yes	characteristic, complemented, Hall
17	C₁₁×Dic₇	—	17	1	no	Hall
18	C₇×D₁₇	C₂×C₃×C₁₁	1	1	yes	characteristic
19	C₃×C₇×C₁₁	#595	1	1	yes	characteristic, complemented, Hall
20	C₃×#595	—	7	1	no	Hall
21	C₁₁×C₁₇	C₃×Dic₇	1	1	yes	characteristic, complemented, Hall
22	C₂×C₇×C₁₁	—	17	1	no	—
23	C₃×C₄×C₁₁	—	119	1	no	Hall
24	C₇×C₁₇	C₃×C₄×C₁₁	1	1	yes	characteristic, complemented, Hall
25	C₃×D₁₇	C₁₁×D₇	1	1	yes	characteristic
26	C₃×Dic₇	—	17	1	no	Hall
27	C₇×C₁₁	C₃×#595	1	1	yes	characteristic, complemented, Hall
28	#595	—	7	1	no	Hall
29	C₂×C₃×C₁₁	—	17	1	no	—
30	C₃×C₁₇	C₁₁×Dic₇	1	1	yes	characteristic, complemented, Hall
31	C₄×C₁₁	—	119	1	no	Hall
32	C₂×C₃×C₇	—	17	1	no	—
33	D₁₇	C₃×C₁₁×D₇	1	1	yes	characteristic
34	C₃×C₁₁	C₇⋊#595	1	1	yes	characteristic, direct product factor, Hall
35	Dic₇	—	17	1	no	Hall
36	C₂×C₁₁	—	17	1	no	—
37	C₃×C₇	C₁₁×#595	1	1	yes	characteristic, complemented, Hall
38	C₁₇	C₃×C₁₁×Dic₇	1	1	yes	characteristic, complemented, Sylow
39	C₂×C₇	—	17	1	no	—
40	C₃×C₄	—	119	1	no	Hall
41	C₁₁	C₃×C₇⋊#595	1	1	yes	characteristic, direct product factor, Sylow
42	C₇	C₃×C₁₁×#595	1	1	yes	characteristic, complemented, Sylow
43	C₂×C₃	—	17	1	no	—
44	C₄	—	119	1	no	Sylow
45	C₃	C₁₁×C₇⋊#595	1	1	yes	characteristic, direct product factor, Sylow
46	C₂	—	17	1	no	—

	subgroup	G/H
center, hypercenter	C₃×C₁₁	C₇⋊#595
commutator, hypocenter	C₇×C₁₇	C₃×C₄×C₁₁
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₁×C₁₇	C₄
prime radical	C₃×C₇×C₁₁×D₁₇	C₂
cosocle	C₇×D₁₇	C₂×C₃×C₁₁
LCS	G ▷ C₇×C₁₇
UCS	C₁ ◁ C₃×C₁₁

Complements

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

N	H ≅ G/N	type
2. C₁₁×C₇⋊#595	C₃	direct (N × H)
3. C₃×C₇×C₁₁×C₁₇	C₄	semidirect
6. C₃×C₇⋊#595	C₁₁	direct (N × H)
7. C₇×C₁₁×C₁₇	C₃×C₄	semidirect
12. C₃×C₁₁×C₁₇	Dic₇	semidirect
13. C₇⋊#595	C₃×C₁₁	direct (N × H)
16. C₃×C₇×C₁₇	C₄×C₁₁	semidirect
19. C₃×C₇×C₁₁	#595	semidirect
21. C₁₁×C₁₇	C₃×Dic₇	semidirect
24. C₇×C₁₇	C₃×C₄×C₁₁	semidirect
27. C₇×C₁₁	C₃×#595	semidirect
30. C₃×C₁₇	C₁₁×Dic₇	semidirect
34. C₃×C₁₁	C₇⋊#595	direct (N × H)
37. C₃×C₇	C₁₁×#595	semidirect
38. C₁₇	C₃×C₁₁×Dic₇	semidirect
41. C₁₁	C₃×C₇⋊#595	direct (N × H)
42. C₇	C₃×C₁₁×#595	semidirect
45. C₃	C₁₁×C₇⋊#595	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₇×C₁₁×D₁₇	2
C₁₁×C₇⋊#595	3
C₃×C₁₁×#595	7
C₃×C₇⋊#595	11
C₃×C₁₁×Dic₇	17

Subgroups — C3×C11×C7⋊#595 #30628126

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₁₁×C₇⋊#595 #30628126