Subgroups — C₃₇×C₃⋊#66772 #49179878

Order 37740.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×D₁₇×C₃₇	C₂	1	1	yes	maximal, characteristic
2	C₃₇×#66772	—	3	1	no	maximal, Hall
3	C₃×C₅×C₁₇×C₃₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃₇×C₃⋊#595	—	5	1	no	maximal, Hall
5	C₅×D₁₇×C₃₇	D₃	1	1	yes	characteristic
6	C₃×D₁₇×C₃₇	D₅	1	1	yes	characteristic
7	C₅×C₁₇×C₃₇	Dic₃	1	1	yes	characteristic, complemented, Hall
8	C₃₇×#595	—	15	1	no	Hall
9	C₃₇×Dic₁₅	—	17	1	no	maximal, Hall
10	C₃×C₁₇×C₃₇	Dic₅	1	1	yes	characteristic, complemented, Hall
11	D₁₇×C₃₇	D₁₅	1	1	yes	characteristic
12	C₂×C₃×C₅×C₃₇	—	17	1	no	—
13	C₃⋊#66772	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
14	Dic₅×C₃₇	—	51	1	no	Hall
15	C₁₇×C₃₇	Dic₁₅	1	1	yes	characteristic, complemented, Hall
16	C₃×C₅×C₃₇	#595	1	1	yes	characteristic, complemented, Hall
17	C₃×C₅×D₁₇	C₂×C₃₇	1	1	yes	characteristic
18	Dic₃×C₃₇	—	85	1	no	Hall
19	C₂×C₅×C₃₇	—	17	1	no	—
20	#66772	—	3	1	no	Hall
21	C₃×C₅×C₁₇	C₄×C₃₇	1	1	yes	characteristic, complemented, Hall
22	C₂×C₃×C₃₇	—	17	1	no	—
23	C₃⋊#595	—	5	1	no	Hall
24	C₅×C₃₇	C₃⋊#595	1	1	yes	characteristic, complemented, Hall
25	C₅×D₁₇	D₃×C₃₇	1	1	yes	characteristic
26	C₄×C₃₇	—	255	1	no	Hall
27	C₃×C₃₇	#66772	1	1	yes	characteristic, complemented, Hall
28	C₃×D₁₇	D₅×C₃₇	1	1	yes	characteristic
29	C₅×C₁₇	Dic₃×C₃₇	1	1	yes	characteristic, complemented, Hall
30	C₂×C₃₇	—	17	1	no	—
31	#595	—	15	1	no	Hall
32	Dic₁₅	—	17	1	no	Hall
33	C₃×C₁₇	Dic₅×C₃₇	1	1	yes	characteristic, complemented, Hall
34	C₃₇	C₃⋊#66772	1	1	yes	characteristic, direct product factor, Sylow
35	D₁₇	D₁₅×C₃₇	1	1	yes	characteristic
36	C₂×C₃×C₅	—	17	1	no	—
37	Dic₅	—	51	1	no	Hall
38	C₁₇	C₃₇×Dic₁₅	1	1	yes	characteristic, complemented, Sylow
39	C₃×C₅	C₃₇×#595	1	1	yes	characteristic, complemented, Hall
40	Dic₃	—	85	1	no	Hall
41	C₂×C₅	—	17	1	no	—
42	C₂×C₃	—	17	1	no	—
43	C₅	C₃₇×C₃⋊#595	1	1	yes	characteristic, complemented, Sylow
44	C₄	—	255	1	no	Sylow
45	C₃	C₃₇×#66772	1	1	yes	characteristic, complemented, Sylow
46	C₂	—	17	1	no	—

	subgroup	G/H
center, hypercenter	C₃₇	C₃⋊#66772
commutator, hypocenter	C₃×C₅×C₁₇	C₄×C₃₇
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₇×C₃₇	C₄
prime radical	C₃×C₅×D₁₇×C₃₇	C₂
cosocle	C₃×C₅×D₁₇	C₂×C₃₇
LCS	G ▷ C₃×C₅×C₁₇
UCS	C₁ ◁ C₃₇

Complements

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

N	H ≅ G/N	type
3. C₃×C₅×C₁₇×C₃₇	C₄	semidirect
7. C₅×C₁₇×C₃₇	Dic₃	semidirect
10. C₃×C₁₇×C₃₇	Dic₅	semidirect
13. C₃⋊#66772	C₃₇	direct (N × H)
15. C₁₇×C₃₇	Dic₁₅	semidirect
16. C₃×C₅×C₃₇	#595	semidirect
21. C₃×C₅×C₁₇	C₄×C₃₇	semidirect
24. C₅×C₃₇	C₃⋊#595	semidirect
27. C₃×C₃₇	#66772	semidirect
29. C₅×C₁₇	Dic₃×C₃₇	semidirect
33. C₃×C₁₇	Dic₅×C₃₇	semidirect
34. C₃₇	C₃⋊#66772	direct (N × H)
38. C₁₇	C₃₇×Dic₁₅	semidirect
39. C₃×C₅	C₃₇×#595	semidirect
43. C₅	C₃₇×C₃⋊#595	semidirect
45. C₃	C₃₇×#66772	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×D₁₇×C₃₇	2
C₃₇×#66772	3
C₃₇×C₃⋊#595	5
C₃₇×Dic₁₅	17
C₃⋊#66772	37

Subgroups — C37×C3⋊#66772 #49179878

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×C₃⋊#66772 #49179878