Subgroups — #4296⋊(C₇⋊D₇) #30660722

Order 16758.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇²×#4296	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	(C₁₉⋊C₃)⋊(C₇⋊D₇)	C₃	1	1	yes	maximal, characteristic
3	C₇²×C₁₉⋊C₃	C₂×C₃	1	1	yes	characteristic
4	#4296⋊D₇	—	7	1	no	maximal
5	#4296⋊D₇	—	7	7	no	maximal
6	C₇⋊D₁₃₃	C₉	1	1	yes	characteristic, complemented, Hall
7	C₇×#4296	D₇	1	1	yes	characteristic, complemented
8	C₇×#4296	D₇	1	7	yes	complemented
9	C₇²×C₁₉	C₂×C₉	1	1	yes	characteristic, complemented, Hall
10	C₉×C₇⋊D₇	—	19	1	no	maximal, Hall
11	(C₁₉⋊C₃)⋊D₇	—	7	1	no	—
12	(C₁₉⋊C₃)⋊D₇	—	7	7	no	—
13	C₇²×C₉	—	19	1	no	Hall
14	C₇×C₁₉⋊C₃	C₃×D₇	1	1	yes	characteristic
15	C₇×C₁₉⋊C₃	C₃×D₇	1	7	yes	—
16	AGL(1,𝔽₁₉)	—	49	1	no	Hall
17	C₃×C₇⋊D₇	—	19	1	no	—
18	D₁₃₃	—	7	1	no	—
19	D₁₃₃	—	7	7	no	—
20	#4296	C₇⋊D₇	1	1	yes	characteristic, complemented, Hall
21	C₃×C₇²	—	19	1	no	—
22	C₇×C₁₉	C₉×D₇	1	1	yes	characteristic, complemented
23	C₇×C₁₉	C₉×D₇	1	7	yes	complemented
24	C₉×D₇	—	133	1	no	—
25	C₉×D₇	—	133	7	no	—
26	D₁₉⋊C₃	—	49	1	no	—
27	C₇⋊D₇	—	171	1	no	Hall
28	C₇×C₉	—	19	1	no	—
29	C₇×C₉	—	19	7	no	—
30	C₁₉⋊C₃	C₃×C₇⋊D₇	1	1	yes	characteristic
31	C₇²	AGL(1,𝔽₁₉)	1	1	yes	characteristic, complemented, Sylow
32	C₃×D₇	—	133	1	no	—
33	C₃×D₇	—	133	7	no	—
34	D₁₉	—	49	1	no	Hall
35	C₃×C₇	—	19	1	no	—
36	C₃×C₇	—	19	7	no	—
37	C₁₉	C₉×C₇⋊D₇	1	1	yes	characteristic, complemented, Sylow
38	C₂×C₉	—	931	1	no	Hall
39	D₇	—	133	1	no	—
40	D₇	—	1197	7	no	—
41	C₉	—	19	1	no	Sylow
42	C₇	#4296⋊D₇	1	1	yes	characteristic, complemented
43	C₇	#4296⋊D₇	1	7	yes	complemented
44	C₂×C₃	—	931	1	no	—
45	C₃	—	19	1	no	—
46	C₂	—	8379	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₇²×C₁₉	C₂×C₉
prime radical	(C₁₉⋊C₃)⋊(C₇⋊D₇)	C₃
cosocle	C₇²×C₁₉⋊C₃	C₂×C₃
LCS	G ▷ C₇²×C₁₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₇²×#4296	C₂	semidirect
6. C₇⋊D₁₃₃	C₉	semidirect
7. C₇×#4296	D₇	semidirect
8. C₇×#4296	D₇	semidirect
9. C₇²×C₁₉	C₂×C₉	semidirect
20. #4296	C₇⋊D₇	semidirect
22. C₇×C₁₉	C₉×D₇	semidirect
23. C₇×C₁₉	C₉×D₇	semidirect
31. C₇²	AGL(1,𝔽₁₉)	semidirect
37. C₁₉	C₉×C₇⋊D₇	semidirect
42. C₇	#4296⋊D₇	semidirect
43. C₇	#4296⋊D₇	semidirect

Maximal subgroups

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

subgroup	index
C₇²×#4296	2
(C₁₉⋊C₃)⋊(C₇⋊D₇)	3
#4296⋊D₇	7
C₉×C₇⋊D₇	19

Subgroups — #4296⋊(C7⋊D7) #30660722

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #4296⋊(C₇⋊D₇) #30660722