Subgroups — C₃×#24925969 #45657507

Order 32634.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×#11715913	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₇⋊D₂₅₉	C₃	1	1	yes	maximal, characteristic, complemented
3	#24925969	C₃	1	3	yes	maximal, direct product factor
4	C₇×#11715913	C₂×C₃	1	3	yes	complemented
5	C₃×C₇²×C₃₇	C₂×C₃	1	1	yes	characteristic, complemented
6	C₃×(C₃₇⋊C₃)⋊D₇	—	7	1	no	maximal
7	C₃×#13095537	—	7	1	no	maximal
8	C₇⋊D₂₅₉	C₃²	1	1	yes	characteristic, complemented, Hall
9	C₃×C₇×C₃₇⋊C₃	—	7	1	no	—
10	C₃×#11715913	D₇	1	1	yes	characteristic, complemented
11	C₇²×C₃₇	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
12	C₃×D₂₅₉	—	7	1	no	—
13	C₃×D₂₅₉	—	7	1	no	—
14	C₃×D₂₅₉	—	21	2	no	—
15	#13095537	—	7	3	no	—
16	(C₃₇⋊C₃)⋊D₇	—	7	3	no	—
17	C₃×ΓL(1,𝔽₈)⋊D₇	—	37	1	no	maximal, Hall
18	C₃×C₇×C₃₇	—	3	2	no	—
19	C₃×C₇×C₃₇	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
20	C₃×C₇×C₃₇	C₃×D₇	1	1	yes	characteristic, complemented
21	#11715913	C₃×D₇	1	3	yes	complemented
22	C₇×C₃₇⋊C₃	—	7	3	no	—
23	C₃×D₃₇⋊C₃	—	49	1	no	Hall
24	D₂₅₉	—	7	1	no	—
25	D₂₅₉	—	7	1	no	—
26	D₂₅₉	—	21	2	no	—
27	C₃×C₇×ΓL(1,𝔽₈)	—	37	1	no	Hall
28	C₃×C₃₇⋊C₃	—	7	1	no	Hall
29	C₃×C₇⋊D₇	—	37	1	no	—
30	ΓL(1,𝔽₈)⋊D₇	—	37	3	no	—
31	C₇×C₃₇	—	3	2	no	—
32	C₇×C₃₇	C₃×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
33	C₇×C₃₇	C₃²×D₇	1	1	yes	characteristic, complemented
34	C₃×D₃₇	—	49	1	no	—
35	D₃₇⋊C₃	—	49	3	no	—
36	C₃×C₇²	D₃₇⋊C₃	1	1	yes	characteristic, complemented
37	C₇×ΓL(1,𝔽₈)	—	37	3	no	—
38	C₃²×D₇	—	259	1	no	—
39	C₃×AGL(1,𝔽₇)	—	259	1	no	—
40	C₃×C₃₇	ΓL(1,𝔽₈)⋊D₇	1	1	yes	characteristic, complemented
41	C₃₇⋊C₃	—	7	3	no	—
42	C₇⋊D₇	—	37	1	no	Hall
43	D₃₇	—	49	1	no	Hall
44	C₃²×C₇	—	259	1	no	—
45	C₃×ΓL(1,𝔽₈)	—	37	1	no	—
46	C₇²	C₃×D₃₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
47	C₃×D₇	—	259	3	no	—
48	C₃×D₇	—	259	1	no	—
49	C₃×D₇	—	259	1	no	—
50	C₃×D₇	—	777	2	no	—
51	AGL(1,𝔽₇)	—	259	3	no	—
52	C₃₇	C₃×ΓL(1,𝔽₈)⋊D₇	1	1	yes	characteristic, complemented, Sylow
53	C₃×C₇	—	3	2	no	—
54	C₃×C₇	—	259	3	no	—
55	C₃×C₇	(C₃₇⋊C₃)⋊D₇	1	1	yes	characteristic, complemented
56	C₃×C₇	#13095537	1	1	yes	characteristic, complemented
57	ΓL(1,𝔽₈)	—	37	3	no	—
58	C₂×C₃²	—	1813	1	no	Hall
59	D₇	—	259	1	no	—
60	D₇	—	259	1	no	—
61	D₇	—	777	2	no	—
62	C₃²	—	259	1	no	Sylow
63	C₇	—	3	2	no	—
64	C₇	C₃×#13095537	1	1	yes	characteristic, complemented
65	C₇	C₃×(C₃₇⋊C₃)⋊D₇	1	1	yes	characteristic, complemented
66	C₂×C₃	—	1813	3	no	—
67	C₂×C₃	—	1813	1	no	—
68	C₃	—	259	3	no	—
69	C₃	#24925969	1	1	yes	characteristic, direct product factor
70	C₂	—	1813	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	#24925969
commutator, cosocle, hypocenter	C₇²×C₃₇	C₂×C₃²
Frattini	C₁	G
Fitting, socle	C₃×C₇²×C₃₇	C₂×C₃
LCS	G ▷ C₇²×C₃₇
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₇×#11715913	C₂	semidirect
2. C₃×C₇⋊D₂₅₉	C₃	semidirect
3. #24925969	C₃	direct (N × H)
4. C₇×#11715913	C₂×C₃	semidirect
5. C₃×C₇²×C₃₇	C₂×C₃	semidirect
8. C₇⋊D₂₅₉	C₃²	semidirect
10. C₃×#11715913	D₇	semidirect
11. C₇²×C₃₇	C₂×C₃²	semidirect
19. C₃×C₇×C₃₇	AGL(1,𝔽₇)	semidirect
20. C₃×C₇×C₃₇	C₃×D₇	semidirect
21. #11715913	C₃×D₇	semidirect
32. C₇×C₃₇	C₃×AGL(1,𝔽₇)	semidirect
33. C₇×C₃₇	C₃²×D₇	semidirect
36. C₃×C₇²	D₃₇⋊C₃	semidirect
40. C₃×C₃₇	ΓL(1,𝔽₈)⋊D₇	semidirect
46. C₇²	C₃×D₃₇⋊C₃	semidirect
52. C₃₇	C₃×ΓL(1,𝔽₈)⋊D₇	semidirect
55. C₃×C₇	(C₃₇⋊C₃)⋊D₇	semidirect
56. C₃×C₇	#13095537	semidirect
64. C₇	C₃×#13095537	semidirect
65. C₇	C₃×(C₃₇⋊C₃)⋊D₇	semidirect
69. C₃	#24925969	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₇×#11715913	2
C₃×C₇⋊D₂₅₉	3
#24925969	3
C₃×(C₃₇⋊C₃)⋊D₇	7
C₃×#13095537	7
C₃×ΓL(1,𝔽₈)⋊D₇	37

Subgroups — C3×#24925969 #45657507

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#24925969 #45657507