Subgroups — C₃₇×C₃⋊(C₃⋊#1044) #45686499

Order 33300.

192 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⋊#1044	—	3	4	no	maximal
3	C₃²×C₅²×C₃₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃₇×C₃⋊ΓL(1,𝔽₁₆)	—	5	2	no	maximal
5	C₃×C₃₇×C₅⋊D₅	D₃	1	4	yes	—
6	C₃₇×#1044	—	9	1	no	Hall
7	C₃²×D₅×C₃₇	—	5	2	no	—
8	C₃²×D₅×C₃₇	—	10	2	no	—
9	C₃×C₅²×C₃₇	Dic₃	1	4	yes	complemented
10	C₃₇×ΓL(1,𝔽₁₆)	—	15	8	no	—
11	C₃₇×C₅⋊D₅	C₃⋊D₃	1	1	yes	characteristic
12	C₃²×C₅×C₃₇	—	2	2	no	—
13	C₃²×C₅×C₃₇	AGL(1,𝔽₅)	1	2	yes	complemented
14	C₃⋊Dic₃×C₃₇	—	25	1	no	Hall
15	C₃×D₅×C₃₇	—	5	8	no	—
16	C₃×D₅×C₃₇	—	10	8	no	—
17	C₅²×C₃₇	C₃⋊Dic₃	1	1	yes	characteristic, complemented, Hall
18	C₃⋊(C₃⋊#1044)	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
19	AGL(1,𝔽₅)×C₃₇	—	45	2	no	—
20	C₂×C₃²×C₃₇	—	25	1	no	—
21	C₃×C₅×C₃₇	—	2	8	no	—
22	C₃×C₅×C₃₇	ΓL(1,𝔽₁₆)	1	8	yes	complemented
23	C₃²×C₅⋊D₅	C₂×C₃₇	1	1	yes	characteristic
24	Dic₃×C₃₇	—	75	4	no	—
25	D₅×C₃₇	—	5	2	no	—
26	D₅×C₃₇	—	10	2	no	—
27	C₃²×C₃₇	#1044	1	1	yes	characteristic, complemented, Hall
28	C₃⋊#1044	—	3	4	no	—
29	C₃²×C₅²	C₄×C₃₇	1	1	yes	characteristic, complemented, Hall
30	C₂×C₃×C₃₇	—	25	4	no	—
31	C₅×C₃₇	—	2	2	no	—
32	C₅×C₃₇	C₃⋊ΓL(1,𝔽₁₆)	1	2	yes	complemented
33	C₃⋊ΓL(1,𝔽₁₆)	—	5	2	no	—
34	C₃×C₅⋊D₅	D₃×C₃₇	1	4	yes	—
35	C₄×C₃₇	—	225	1	no	Hall
36	C₃×C₃₇	C₃⋊#1044	1	4	yes	complemented
37	#1044	—	9	1	no	Hall
38	C₃²×D₅	—	5	2	no	—
39	C₃²×D₅	—	10	2	no	—
40	C₃×C₅²	Dic₃×C₃₇	1	4	yes	complemented
41	C₂×C₃₇	—	25	1	no	—
42	ΓL(1,𝔽₁₆)	—	15	8	no	—
43	C₅⋊D₅	C₃⋊D₃×C₃₇	1	1	yes	characteristic
44	C₃²×C₅	—	2	2	no	—
45	C₃²×C₅	AGL(1,𝔽₅)×C₃₇	1	2	yes	complemented
46	C₃₇	C₃⋊(C₃⋊#1044)	1	1	yes	characteristic, direct product factor, Sylow
47	C₃⋊Dic₃	—	25	1	no	Hall
48	C₃×D₅	—	5	8	no	—
49	C₃×D₅	—	10	8	no	—
50	C₅²	C₃⋊Dic₃×C₃₇	1	1	yes	characteristic, complemented, Sylow
51	AGL(1,𝔽₅)	—	45	2	no	—
52	C₂×C₃²	—	25	1	no	—
53	C₃×C₅	—	2	8	no	—
54	C₃×C₅	C₃₇×ΓL(1,𝔽₁₆)	1	8	yes	complemented
55	Dic₃	—	75	4	no	—
56	D₅	—	5	2	no	—
57	D₅	—	10	2	no	—
58	C₃²	C₃₇×#1044	1	1	yes	characteristic, complemented, Sylow
59	C₂×C₃	—	25	4	no	—
60	C₅	—	2	2	no	—
61	C₅	C₃₇×C₃⋊ΓL(1,𝔽₁₆)	1	2	yes	complemented
62	C₄	—	225	1	no	Sylow
63	C₃	C₃₇×C₃⋊#1044	1	4	yes	complemented
64	C₂	—	25	1	no	—

	subgroup	G/H
center, hypercenter	C₃₇	C₃⋊(C₃⋊#1044)
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
9. C₃×C₅²×C₃₇	Dic₃	semidirect
13. C₃²×C₅×C₃₇	AGL(1,𝔽₅)	semidirect
17. C₅²×C₃₇	C₃⋊Dic₃	semidirect
18. C₃⋊(C₃⋊#1044)	C₃₇	direct (N × H)
22. C₃×C₅×C₃₇	ΓL(1,𝔽₁₆)	semidirect
27. C₃²×C₃₇	#1044	semidirect
29. C₃²×C₅²	C₄×C₃₇	semidirect
32. C₅×C₃₇	C₃⋊ΓL(1,𝔽₁₆)	semidirect
36. C₃×C₃₇	C₃⋊#1044	semidirect
40. C₃×C₅²	Dic₃×C₃₇	semidirect
45. C₃²×C₅	AGL(1,𝔽₅)×C₃₇	semidirect
46. C₃₇	C₃⋊(C₃⋊#1044)	direct (N × H)
50. C₅²	C₃⋊Dic₃×C₃₇	semidirect
54. C₃×C₅	C₃₇×ΓL(1,𝔽₁₆)	semidirect
58. C₃²	C₃₇×#1044	semidirect
61. C₅	C₃₇×C₃⋊ΓL(1,𝔽₁₆)	semidirect
63. C₃	C₃₇×C₃⋊#1044	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⋊#1044	3
C₃₇×C₃⋊ΓL(1,𝔽₁₆)	5
C₃⋊(C₃⋊#1044)	37

Subgroups — C37×C3⋊(C3⋊#1044) #45686499

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×C₃⋊(C₃⋊#1044) #45686499