Subgroups — C₃×#24925957 #45657530

Order 32634.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#19129588	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₇×D₂₅₉	C₃	1	1	yes	maximal, characteristic, complemented
3	#24925957	C₃	1	3	yes	maximal, direct product factor
4	#19129588	C₂×C₃	1	3	yes	complemented
5	C₃×C₇²×C₃₇	C₂×C₃	1	1	yes	characteristic, complemented
6	C₃×#13095531	—	7	1	no	maximal
7	C₃×#13095537	—	7	1	no	maximal
8	C₇×D₂₅₉	C₃²	1	1	yes	characteristic, complemented, Hall
9	C₃×#11715913	—	7	1	no	—
10	C₃×#11715913	—	7	1	no	—
11	C₃×#11715913	—	14	3	no	—
12	C₇²×C₃₇	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
13	C₃×D₂₅₉	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
14	C₃×C₇×D₃₇	—	7	1	no	—
15	#13095537	—	7	3	no	—
16	#13095531	—	7	3	no	—
17	C₃×#64423	—	37	1	no	maximal, Hall
18	C₃×C₇×C₃₇	—	2	3	no	—
19	C₃×C₇×C₃₇	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
20	C₃×C₇×C₃₇	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
21	#11715913	—	7	3	no	—
22	#11715913	—	7	3	no	—
23	#11715913	—	14	9	no	—
24	C₃×D₃₇⋊C₃	—	49	1	no	Hall
25	D₂₅₉	C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
26	C₇×D₃₇	—	7	1	no	—
27	C₃×#3861	—	37	1	no	Hall
28	C₃×C₃₇⋊C₃	—	49	1	no	Hall
29	C₃×C₇×D₇	—	37	1	no	—
30	#64423	—	37	3	no	—
31	C₇×C₃₇	—	2	3	no	—
32	C₇×C₃₇	C₃×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
33	C₇×C₃₇	C₂×C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
34	C₃×D₃₇	—	7	1	no	—
35	D₃₇⋊C₃	—	49	3	no	—
36	C₃×C₇²	D₃₇⋊C₃	1	1	yes	characteristic, complemented
37	#3861	—	37	3	no	—
38	C₂×C₃×ΓL(1,𝔽₈)	—	259	1	no	—
39	C₃×AGL(1,𝔽₇)	—	259	1	no	—
40	C₃×C₃₇	#64423	1	1	yes	characteristic, complemented
41	C₃₇⋊C₃	—	49	3	no	—
42	C₇×D₇	—	37	1	no	Hall
43	D₃₇	—	7	1	no	Hall
44	C₃×ΓL(1,𝔽₈)	—	259	1	no	—
45	C₃×ΓL(1,𝔽₈)	—	259	1	no	—
46	C₃×ΓL(1,𝔽₈)	—	518	3	no	—
47	C₇²	C₃×D₃₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
48	C₂×C₃×C₇	—	259	1	no	—
49	C₃×D₇	—	37	1	no	—
50	C₂×ΓL(1,𝔽₈)	—	259	3	no	—
51	AGL(1,𝔽₇)	—	259	3	no	—
52	C₃₇	C₃×#64423	1	1	yes	characteristic, complemented, Sylow
53	C₃×C₇	—	2	3	no	—
54	C₃×C₇	#13095531	1	1	yes	characteristic, complemented
55	C₃×C₇	#13095537	1	1	yes	characteristic, complemented
56	ΓL(1,𝔽₈)	—	259	3	no	—
57	ΓL(1,𝔽₈)	—	259	3	no	—
58	ΓL(1,𝔽₈)	—	518	9	no	—
59	C₂×C₃²	—	1813	1	no	Hall
60	C₂×C₇	—	259	1	no	—
61	D₇	—	37	1	no	—
62	C₃²	—	1813	1	no	Sylow
63	C₇	—	2	3	no	—
64	C₇	C₃×#13095537	1	1	yes	characteristic, complemented
65	C₇	C₃×#13095531	1	1	yes	characteristic, complemented
66	C₂×C₃	—	259	1	no	—
67	C₂×C₃	—	1813	3	no	—
68	C₃	—	1813	3	no	—
69	C₃	#24925957	1	1	yes	characteristic, direct product factor
70	C₂	—	259	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	#24925957
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×#19129588	C₂	semidirect
2. C₃×C₇×D₂₅₉	C₃	semidirect
3. #24925957	C₃	direct (N × H)
4. #19129588	C₂×C₃	semidirect
5. C₃×C₇²×C₃₇	C₂×C₃	semidirect
8. C₇×D₂₅₉	C₃²	semidirect
12. C₇²×C₃₇	C₂×C₃²	semidirect
13. C₃×D₂₅₉	ΓL(1,𝔽₈)	semidirect
19. C₃×C₇×C₃₇	AGL(1,𝔽₇)	semidirect
20. C₃×C₇×C₃₇	C₂×ΓL(1,𝔽₈)	semidirect
25. D₂₅₉	C₃×ΓL(1,𝔽₈)	semidirect
32. C₇×C₃₇	C₃×AGL(1,𝔽₇)	semidirect
33. C₇×C₃₇	C₂×C₃×ΓL(1,𝔽₈)	semidirect
36. C₃×C₇²	D₃₇⋊C₃	semidirect
40. C₃×C₃₇	#64423	semidirect
47. C₇²	C₃×D₃₇⋊C₃	semidirect
52. C₃₇	C₃×#64423	semidirect
54. C₃×C₇	#13095531	semidirect
55. C₃×C₇	#13095537	semidirect
64. C₇	C₃×#13095537	semidirect
65. C₇	C₃×#13095531	semidirect
69. C₃	#24925957	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×#19129588	2
C₃×C₇×D₂₅₉	3
#24925957	3
C₃×#13095531	7
C₃×#13095537	7
C₃×#64423	37

Subgroups — C3×#24925957 #45657530

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#24925957 #45657530