Subgroups — C₇×#14558808 #30660643

Order 16758.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#11924781	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇²×D₁₉⋊C₃	C₃	1	1	yes	maximal, characteristic
3	C₇²×C₁₉⋊C₃	C₂×C₃	1	1	yes	characteristic
4	#14558808	C₇	1	1	yes	maximal, characteristic, direct product factor
5	C₇×AGL(1,𝔽₁₉)	—	7	1	no	maximal
6	C₇²×D₁₉	C₉	1	1	yes	characteristic, complemented, Hall
7	#11924781	C₂×C₇	1	1	yes	characteristic, complemented
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	C₇×D₁₉⋊C₃	—	3	2	no	—
12	C₇×D₁₉⋊C₃	ΓL(1,𝔽₈)	1	1	yes	characteristic
13	C₇×D₁₉⋊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	AGL(1,𝔽₁₉)	—	7	1	no	Hall
19	C₂×C₃×C₇²	—	19	1	no	—
20	C₇×D₁₉	—	3	2	no	—
21	C₇×D₁₉	C₇⋊C₉	1	1	yes	characteristic, complemented
22	C₇×D₁₉	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	D₁₉⋊C₃	C₇×ΓL(1,𝔽₈)	1	1	yes	characteristic
31	C₂×C₇²	—	19	1	no	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	AGL(1,𝔽₁₉)	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	D₁₉	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	—	171	2	no	—
46	C₂×C₇	—	171	1	no	—
47	C₂×C₇	—	171	1	no	—
48	C₉	—	133	1	no	Sylow
49	C₇	—	3	2	no	—
50	C₇	C₇×AGL(1,𝔽₁₉)	1	1	yes	characteristic, complemented
51	C₇	#14558808	1	1	yes	characteristic, direct product factor
52	C₂×C₃	—	19	1	no	—
53	C₃	—	19	1	no	—
54	C₂	—	171	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇	#14558808
commutator, hypocenter	C₇×C₁₉	C₂×C₇×C₉
Frattini	C₁	G
Fitting, socle	C₇²×C₁₉	C₂×C₉
prime radical	C₇²×D₁₉⋊C₃	C₃
cosocle	C₇×C₁₉⋊C₃	C₂×C₃×C₇
LCS	G ▷ C₇×C₁₉
UCS	C₁ ◁ C₇

Complements

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

N	H ≅ G/N	type
1. C₇×#11924781	C₂	semidirect
4. #14558808	C₇	direct (N × H)
6. C₇²×D₁₉	C₉	semidirect
7. #11924781	C₂×C₇	semidirect
9. C₇²×C₁₉	C₂×C₉	semidirect
21. C₇×D₁₉	C₇⋊C₉	semidirect
22. C₇×D₁₉	C₇×C₉	semidirect
26. C₇×C₁₉	C₂×C₇⋊C₉	semidirect
27. C₇×C₁₉	C₂×C₇×C₉	semidirect
35. C₇²	AGL(1,𝔽₁₉)	semidirect
39. D₁₉	C₇×C₇⋊C₉	semidirect
43. C₁₉	C₂×C₇×C₇⋊C₉	semidirect
50. C₇	C₇×AGL(1,𝔽₁₉)	semidirect
51. C₇	#14558808	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×#11924781	2
C₇²×D₁₉⋊C₃	3
#14558808	7
C₇×AGL(1,𝔽₁₉)	7
C₂×C₇×C₇⋊C₉	19

Subgroups — C7×#14558808 #30660643

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#14558808 #30660643