Subgroups — C₃₇×#64418⋊C₃ #45657384

Order 32634.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	ΓL(1,𝔽₈)²×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃₇×#64418	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃₇×#64423	—	3	1	no	maximal
4	C₃₇×#3862	C₂×C₃	1	1	yes	characteristic, complemented
5	C₃₇×#3861	D₃	1	1	yes	characteristic, complemented
6	C₇×ΓL(1,𝔽₈)×C₃₇	—	2	1	no	—
7	C₇×D₇×C₃₇	—	3	1	no	Hall
8	C₃×ΓL(1,𝔽₈)×C₃₇	—	14	1	no	—
9	C₇²×C₃₇	C₃×D₃	1	1	yes	characteristic, complemented, Hall
10	C₂×ΓL(1,𝔽₈)×C₃₇	—	21	1	no	—
11	C₃₇×AGL(1,𝔽₇)	—	21	1	no	—
12	#64418⋊C₃	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₃×C₇×C₃₇	—	14	1	no	—
14	ΓL(1,𝔽₈)×C₃₇	—	2	1	no	—
15	ΓL(1,𝔽₈)×C₃₇	—	14	1	no	—
16	ΓL(1,𝔽₈)×C₃₇	—	14	1	no	—
17	ΓL(1,𝔽₈)×C₃₇	—	21	1	no	—
18	ΓL(1,𝔽₈)×C₃₇	—	21	1	no	—
19	C₃×D₃×C₃₇	—	49	1	no	maximal, Hall
20	C₂×C₇×C₃₇	—	21	1	no	—
21	D₇×C₃₇	—	3	1	no	—
22	ΓL(1,𝔽₈)²	C₂×C₃₇	1	1	yes	characteristic, complemented, Hall
23	C₃²×C₃₇	—	49	1	no	Hall
24	#64423	—	3	1	no	—
25	#64418	C₃×C₃₇	1	1	yes	characteristic, complemented
26	C₇×C₃₇	—	2	1	no	—
27	C₇×C₃₇	—	3	1	no	—
28	C₇×C₃₇	—	3	1	no	—
29	C₂×C₃×C₃₇	—	147	1	no	—
30	D₃×C₃₇	—	49	1	no	—
31	#3862	C₂×C₃×C₃₇	1	1	yes	characteristic, complemented
32	#3861	D₃×C₃₇	1	1	yes	characteristic, complemented
33	C₇×ΓL(1,𝔽₈)	—	2	1	no	—
34	C₃×C₃₇	—	14	1	no	—
35	C₃×C₃₇	—	49	1	no	—
36	C₃×C₃₇	—	49	1	no	—
37	C₇×D₇	—	3	1	no	Hall
38	C₂×C₃₇	—	21	1	no	Hall
39	C₃×ΓL(1,𝔽₈)	—	14	1	no	—
40	C₇²	C₃×D₃×C₃₇	1	1	yes	characteristic, complemented, Sylow
41	C₂×ΓL(1,𝔽₈)	—	21	1	no	—
42	AGL(1,𝔽₇)	—	21	1	no	—
43	C₃₇	#64418⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
44	C₃×C₇	—	14	1	no	—
45	ΓL(1,𝔽₈)	—	2	1	no	—
46	ΓL(1,𝔽₈)	—	14	1	no	—
47	ΓL(1,𝔽₈)	—	14	1	no	—
48	ΓL(1,𝔽₈)	—	21	1	no	—
49	ΓL(1,𝔽₈)	—	21	1	no	—
50	C₃×D₃	—	49	1	no	Hall
51	C₂×C₇	—	21	1	no	—
52	D₇	—	3	1	no	—
53	C₃²	—	49	1	no	Sylow
54	C₇	—	2	1	no	—
55	C₇	—	3	1	no	—
56	C₇	—	3	1	no	—
57	C₂×C₃	—	147	1	no	—
58	D₃	—	49	1	no	—
59	C₃	—	14	1	no	—
60	C₃	—	49	1	no	—
61	C₃	—	49	1	no	—
62	C₂	—	21	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃₇	#64418⋊C₃
commutator, cosocle, hypocenter	#3862	C₂×C₃×C₃₇
Frattini	C₁	G
Fitting, socle	C₇²×C₃₇	C₃×D₃
LCS	G ▷ #3862
UCS	C₁ ◁ C₃₇

Complements

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

N	H ≅ G/N	type
1. ΓL(1,𝔽₈)²×C₃₇	C₂	semidirect
2. C₃₇×#64418	C₃	semidirect
4. C₃₇×#3862	C₂×C₃	semidirect
5. C₃₇×#3861	D₃	semidirect
9. C₇²×C₃₇	C₃×D₃	semidirect
12. #64418⋊C₃	C₃₇	direct (N × H)
22. ΓL(1,𝔽₈)²	C₂×C₃₇	semidirect
25. #64418	C₃×C₃₇	semidirect
31. #3862	C₂×C₃×C₃₇	semidirect
32. #3861	D₃×C₃₇	semidirect
40. C₇²	C₃×D₃×C₃₇	semidirect
43. C₃₇	#64418⋊C₃	direct (N × H)

Maximal subgroups

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

subgroup	index
ΓL(1,𝔽₈)²×C₃₇	2
C₃₇×#64418	3
C₃₇×#64423	3
#64418⋊C₃	37
C₃×D₃×C₃₇	49

Subgroups — C37×#64418⋊C3 #45657384

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#64418⋊C₃ #45657384