Subgroups — C₂×C₇×#11924780 #30660733

Order 16758.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#11924780	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₇²×C₁₉⋊C₃	C₃	1	1	yes	maximal, characteristic
3	C₇²×C₁₉⋊C₃	C₂×C₃	1	1	yes	characteristic
4	C₂×#11924780	C₇	1	1	yes	maximal, characteristic, direct product factor
5	C₂×C₇×#4296	—	7	1	no	maximal
6	C₂×C₇²×C₁₉	C₉	1	1	yes	characteristic, complemented, Hall
7	#11924780	C₂×C₇	1	1	yes	characteristic, direct product factor
8	C₇×#4296	—	7	1	no	—
9	C₇²×C₁₉	C₂×C₉	1	1	yes	characteristic, complemented, Hall
10	C₂×C₇×C₇⋊C₉	—	19	1	no	maximal, Hall
11	C₂×C₇×C₁₉⋊C₃	—	3	2	no	—
12	C₂×C₇×C₁₉⋊C₃	ΓL(1,𝔽₈)	1	1	yes	characteristic
13	C₂×C₇×C₁₉⋊C₃	C₃×C₇	1	1	yes	characteristic
14	C₇×C₇⋊C₉	—	19	1	no	Hall
15	C₇×C₁₉⋊C₃	—	3	2	no	—
16	C₇×C₁₉⋊C₃	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic
17	C₇×C₁₉⋊C₃	C₂×C₃×C₇	1	1	yes	characteristic
18	C₂×#4296	—	7	1	no	Hall
19	C₂×C₃×C₇²	—	19	1	no	—
20	C₂×C₇×C₁₉	—	3	2	no	—
21	C₂×C₇×C₁₉	C₇⋊C₉	1	1	yes	characteristic, complemented
22	C₂×C₇×C₁₉	C₇×C₉	1	1	yes	characteristic, complemented
23	#4296	—	7	1	no	Hall
24	C₃×C₇²	—	19	1	no	—
25	C₇×C₁₉	—	3	2	no	—
26	C₇×C₁₉	C₂×C₇⋊C₉	1	1	yes	characteristic, complemented
27	C₇×C₁₉	C₂×C₇×C₉	1	1	yes	characteristic, complemented
28	C₂×C₇×C₉	—	133	1	no	—
29	C₂×C₇⋊C₉	—	19	1	no	—
30	C₂×C₁₉⋊C₃	C₇×ΓL(1,𝔽₈)	1	1	yes	characteristic
31	C₂×C₇²	#4296	1	1	yes	characteristic, complemented, Hall
32	C₇×C₉	—	133	1	no	—
33	C₇⋊C₉	—	19	1	no	—
34	C₁₉⋊C₃	C₂×C₇×ΓL(1,𝔽₈)	1	1	yes	characteristic
35	C₇²	C₂×#4296	1	1	yes	characteristic, complemented, Sylow
36	C₂×C₃×C₇	—	19	1	no	—
37	C₂×C₃×C₇	—	19	1	no	—
38	C₂×C₃×C₇	—	57	2	no	—
39	C₂×C₁₉	C₇×C₇⋊C₉	1	1	yes	characteristic, complemented, Hall
40	C₃×C₇	—	19	1	no	—
41	C₃×C₇	—	19	1	no	—
42	C₃×C₇	—	57	2	no	—
43	C₁₉	C₂×C₇×C₇⋊C₉	1	1	yes	characteristic, complemented, Sylow
44	C₂×C₉	—	133	1	no	Hall
45	C₂×C₇	—	3	2	no	—
46	C₂×C₇	C₇×#4296	1	1	yes	characteristic, complemented
47	C₂×C₇	#11924780	1	1	yes	characteristic, direct product factor
48	C₉	—	133	1	no	Sylow
49	C₇	—	3	2	no	—
50	C₇	C₂×C₇×#4296	1	1	yes	characteristic, complemented
51	C₇	C₂×#11924780	1	1	yes	characteristic, direct product factor
52	C₂×C₃	—	19	1	no	—
53	C₃	—	19	1	no	—
54	C₂	C₇×#11924780	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂×C₇	#11924780
commutator, hypocenter	C₇×C₁₉	C₂×C₇×C₉
Frattini	C₁	G
Fitting, socle	C₂×C₇²×C₁₉	C₉
prime radical	C₂×C₇²×C₁₉⋊C₃	C₃
cosocle	C₇×C₁₉⋊C₃	C₂×C₃×C₇
LCS	G ▷ C₇×C₁₉
UCS	C₁ ◁ C₂×C₇

Complements

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

N	H ≅ G/N	type
1. C₇×#11924780	C₂	direct (N × H)
4. C₂×#11924780	C₇	direct (N × H)
6. C₂×C₇²×C₁₉	C₉	semidirect
7. #11924780	C₂×C₇	direct (N × H)
9. C₇²×C₁₉	C₂×C₉	semidirect
21. C₂×C₇×C₁₉	C₇⋊C₉	semidirect
22. C₂×C₇×C₁₉	C₇×C₉	semidirect
26. C₇×C₁₉	C₂×C₇⋊C₉	semidirect
27. C₇×C₁₉	C₂×C₇×C₉	semidirect
31. C₂×C₇²	#4296	semidirect
35. C₇²	C₂×#4296	semidirect
39. C₂×C₁₉	C₇×C₇⋊C₉	semidirect
43. C₁₉	C₂×C₇×C₇⋊C₉	semidirect
46. C₂×C₇	C₇×#4296	semidirect
47. C₂×C₇	#11924780	direct (N × H)
50. C₇	C₂×C₇×#4296	semidirect
51. C₇	C₂×#11924780	direct (N × H)
54. C₂	C₇×#11924780	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×#11924780	2
C₂×C₇²×C₁₉⋊C₃	3
C₂×#11924780	7
C₂×C₇×#4296	7
C₂×C₇×C₇⋊C₉	19

Subgroups — C2×C7×#11924780 #30660733

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#11924780 #30660733