Subgroups — C₂×C₇×#14556423 #45657481

Order 32634.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#14556423	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₇²×C₃₇⋊C₃	C₃	1	1	yes	maximal, characteristic
3	C₇²×C₃₇⋊C₃	C₂×C₃	1	1	yes	characteristic
4	C₂×#14556423	C₇	1	1	yes	maximal, characteristic, direct product factor
5	C₂×C₇×#66526	—	7	1	no	maximal
6	C₂×C₇²×C₃₇	C₉	1	1	yes	characteristic, complemented, Hall
7	#14556423	C₂×C₇	1	1	yes	characteristic, direct product factor
8	C₇×#66526	—	7	1	no	—
9	C₇²×C₃₇	C₂×C₉	1	1	yes	characteristic, complemented, Hall
10	C₂×C₇×C₃₇⋊C₃	—	3	2	no	—
11	C₂×C₇×C₃₇⋊C₃	ΓL(1,𝔽₈)	1	1	yes	characteristic
12	C₂×C₇×C₃₇⋊C₃	C₃×C₇	1	1	yes	characteristic
13	C₂×C₇×C₇⋊C₉	—	37	1	no	maximal, Hall
14	C₇×C₃₇⋊C₃	—	3	2	no	—
15	C₇×C₃₇⋊C₃	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic
16	C₇×C₃₇⋊C₃	C₂×C₃×C₇	1	1	yes	characteristic
17	C₂×#66526	—	7	1	no	Hall
18	C₂×C₇×C₃₇	—	3	2	no	—
19	C₂×C₇×C₃₇	C₇⋊C₉	1	1	yes	characteristic, complemented
20	C₂×C₇×C₃₇	C₇×C₉	1	1	yes	characteristic, complemented
21	C₇×C₇⋊C₉	—	37	1	no	Hall
22	#66526	—	7	1	no	Hall
23	C₂×C₃×C₇²	—	37	1	no	—
24	C₇×C₃₇	—	3	2	no	—
25	C₇×C₃₇	C₂×C₇⋊C₉	1	1	yes	characteristic, complemented
26	C₇×C₃₇	C₂×C₇×C₉	1	1	yes	characteristic, complemented
27	C₂×C₃₇⋊C₃	C₇×ΓL(1,𝔽₈)	1	1	yes	characteristic
28	C₃×C₇²	—	37	1	no	—
29	C₂×C₇×C₉	—	259	1	no	—
30	C₂×C₇⋊C₉	—	37	1	no	—
31	C₃₇⋊C₃	C₂×C₇×ΓL(1,𝔽₈)	1	1	yes	characteristic
32	C₂×C₇²	#66526	1	1	yes	characteristic, complemented, Hall
33	C₂×C₃₇	C₇×C₇⋊C₉	1	1	yes	characteristic, complemented, Hall
34	C₇×C₉	—	259	1	no	—
35	C₇⋊C₉	—	37	1	no	—
36	C₇²	C₂×#66526	1	1	yes	characteristic, complemented, Sylow
37	C₂×C₃×C₇	—	37	1	no	—
38	C₂×C₃×C₇	—	37	1	no	—
39	C₂×C₃×C₇	—	111	2	no	—
40	C₃₇	C₂×C₇×C₇⋊C₉	1	1	yes	characteristic, complemented, Sylow
41	C₃×C₇	—	37	1	no	—
42	C₃×C₇	—	37	1	no	—
43	C₃×C₇	—	111	2	no	—
44	C₂×C₉	—	259	1	no	Hall
45	C₂×C₇	—	3	2	no	—
46	C₂×C₇	C₇×#66526	1	1	yes	characteristic, complemented
47	C₂×C₇	#14556423	1	1	yes	characteristic, direct product factor
48	C₉	—	259	1	no	Sylow
49	C₇	—	3	2	no	—
50	C₇	C₂×C₇×#66526	1	1	yes	characteristic, complemented
51	C₇	C₂×#14556423	1	1	yes	characteristic, direct product factor
52	C₂×C₃	—	37	1	no	—
53	C₃	—	37	1	no	—
54	C₂	C₇×#14556423	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂×C₇	#14556423
commutator, hypocenter	C₇×C₃₇	C₂×C₇×C₉
Frattini	C₁	G
Fitting, socle	C₂×C₇²×C₃₇	C₉
prime radical	C₂×C₇²×C₃₇⋊C₃	C₃
cosocle	C₇×C₃₇⋊C₃	C₂×C₃×C₇
LCS	G ▷ C₇×C₃₇
UCS	C₁ ◁ C₂×C₇

Complements

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

N	H ≅ G/N	type
1. C₇×#14556423	C₂	direct (N × H)
4. C₂×#14556423	C₇	direct (N × H)
6. C₂×C₇²×C₃₇	C₉	semidirect
7. #14556423	C₂×C₇	direct (N × H)
9. C₇²×C₃₇	C₂×C₉	semidirect
19. C₂×C₇×C₃₇	C₇⋊C₉	semidirect
20. C₂×C₇×C₃₇	C₇×C₉	semidirect
25. C₇×C₃₇	C₂×C₇⋊C₉	semidirect
26. C₇×C₃₇	C₂×C₇×C₉	semidirect
32. C₂×C₇²	#66526	semidirect
33. C₂×C₃₇	C₇×C₇⋊C₉	semidirect
36. C₇²	C₂×#66526	semidirect
40. C₃₇	C₂×C₇×C₇⋊C₉	semidirect
46. C₂×C₇	C₇×#66526	semidirect
47. C₂×C₇	#14556423	direct (N × H)
50. C₇	C₂×C₇×#66526	semidirect
51. C₇	C₂×#14556423	direct (N × H)
54. C₂	C₇×#14556423	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×#14556423	2
C₂×C₇²×C₃₇⋊C₃	3
C₂×#14556423	7
C₂×C₇×#66526	7
C₂×C₇×C₇⋊C₉	37

Subgroups — C2×C7×#14556423 #45657481

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#14556423 #45657481