Subgroups — C₃₇×C₃⋊(C₃⋊#1043) #45686495

Order 33300.

288 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₃₇×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic
2	C₃₇×C₃⋊#1043	—	3	4	no	maximal
3	C₃²×C₅²×C₃₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃₇×C₃⋊ΓL(1,𝔽₁₆)	—	5	6	no	maximal
5	C₃×C₃₇×C₅⋊D₅	D₃	1	4	yes	—
6	C₃₇×#1043	—	9	1	no	Hall
7	C₃²×D₅×C₃₇	—	5	6	no	—
8	C₃×C₅²×C₃₇	Dic₃	1	4	yes	complemented
9	C₃₇×ΓL(1,𝔽₁₆)	—	15	24	no	—
10	C₃₇×C₅⋊D₅	C₃⋊D₃	1	1	yes	characteristic
11	C₃²×C₅×C₃₇	AGL(1,𝔽₅)	1	6	yes	complemented
12	C₃⋊Dic₃×C₃₇	—	25	1	no	Hall
13	C₃×D₅×C₃₇	—	5	24	no	—
14	C₅²×C₃₇	C₃⋊Dic₃	1	1	yes	characteristic, complemented, Hall
15	C₃⋊(C₃⋊#1043)	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
16	AGL(1,𝔽₅)×C₃₇	—	45	6	no	—
17	C₂×C₃²×C₃₇	—	25	1	no	—
18	C₃×C₅×C₃₇	ΓL(1,𝔽₁₆)	1	24	yes	complemented
19	C₃²×C₅⋊D₅	C₂×C₃₇	1	1	yes	characteristic
20	Dic₃×C₃₇	—	75	4	no	—
21	D₅×C₃₇	—	5	6	no	—
22	C₃²×C₃₇	#1043	1	1	yes	characteristic, complemented, Hall
23	C₃⋊#1043	—	3	4	no	—
24	C₃²×C₅²	C₄×C₃₇	1	1	yes	characteristic, complemented, Hall
25	C₂×C₃×C₃₇	—	25	4	no	—
26	C₅×C₃₇	C₃⋊ΓL(1,𝔽₁₆)	1	6	yes	complemented
27	C₃⋊ΓL(1,𝔽₁₆)	—	5	6	no	—
28	C₃×C₅⋊D₅	D₃×C₃₇	1	4	yes	—
29	C₄×C₃₇	—	225	1	no	Hall
30	C₃×C₃₇	C₃⋊#1043	1	4	yes	complemented
31	#1043	—	9	1	no	Hall
32	C₃²×D₅	—	5	6	no	—
33	C₃×C₅²	Dic₃×C₃₇	1	4	yes	complemented
34	C₂×C₃₇	—	25	1	no	—
35	ΓL(1,𝔽₁₆)	—	15	24	no	—
36	C₅⋊D₅	C₃⋊D₃×C₃₇	1	1	yes	characteristic
37	C₃²×C₅	AGL(1,𝔽₅)×C₃₇	1	6	yes	complemented
38	C₃₇	C₃⋊(C₃⋊#1043)	1	1	yes	characteristic, direct product factor, Sylow
39	C₃⋊Dic₃	—	25	1	no	Hall
40	C₃×D₅	—	5	24	no	—
41	C₅²	C₃⋊Dic₃×C₃₇	1	1	yes	characteristic, complemented, Sylow
42	AGL(1,𝔽₅)	—	45	6	no	—
43	C₂×C₃²	—	25	1	no	—
44	C₃×C₅	C₃₇×ΓL(1,𝔽₁₆)	1	24	yes	complemented
45	Dic₃	—	75	4	no	—
46	D₅	—	5	6	no	—
47	C₃²	C₃₇×#1043	1	1	yes	characteristic, complemented, Sylow
48	C₂×C₃	—	25	4	no	—
49	C₅	C₃₇×C₃⋊ΓL(1,𝔽₁₆)	1	6	yes	complemented
50	C₄	—	225	1	no	Sylow
51	C₃	C₃₇×C₃⋊#1043	1	4	yes	complemented
52	C₂	—	25	1	no	—

	subgroup	G/H
center, hypercenter	C₃₇	C₃⋊(C₃⋊#1043)
commutator, hypocenter	C₃²×C₅²	C₄×C₃₇
Frattini	C₁	G
Fitting, socle	C₃²×C₅²×C₃₇	C₄
prime radical	C₃²×C₃₇×C₅⋊D₅	C₂
cosocle	C₃²×C₅⋊D₅	C₂×C₃₇
LCS	G ▷ C₃²×C₅²
UCS	C₁ ◁ C₃₇

Complements

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

N	H ≅ G/N	type
3. C₃²×C₅²×C₃₇	C₄	semidirect
8. C₃×C₅²×C₃₇	Dic₃	semidirect
11. C₃²×C₅×C₃₇	AGL(1,𝔽₅)	semidirect
14. C₅²×C₃₇	C₃⋊Dic₃	semidirect
15. C₃⋊(C₃⋊#1043)	C₃₇	direct (N × H)
18. C₃×C₅×C₃₇	ΓL(1,𝔽₁₆)	semidirect
22. C₃²×C₃₇	#1043	semidirect
24. C₃²×C₅²	C₄×C₃₇	semidirect
26. C₅×C₃₇	C₃⋊ΓL(1,𝔽₁₆)	semidirect
30. C₃×C₃₇	C₃⋊#1043	semidirect
33. C₃×C₅²	Dic₃×C₃₇	semidirect
37. C₃²×C₅	AGL(1,𝔽₅)×C₃₇	semidirect
38. C₃₇	C₃⋊(C₃⋊#1043)	direct (N × H)
41. C₅²	C₃⋊Dic₃×C₃₇	semidirect
44. C₃×C₅	C₃₇×ΓL(1,𝔽₁₆)	semidirect
47. C₃²	C₃₇×#1043	semidirect
49. C₅	C₃₇×C₃⋊ΓL(1,𝔽₁₆)	semidirect
51. C₃	C₃₇×C₃⋊#1043	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₃₇×C₅⋊D₅	2
C₃₇×C₃⋊#1043	3
C₃₇×C₃⋊ΓL(1,𝔽₁₆)	5
C₃⋊(C₃⋊#1043)	37

Subgroups — C37×C3⋊(C3⋊#1043) #45686495

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×C₃⋊(C₃⋊#1043) #45686495