Subgroups — D₇×#11924777 #30660608

Order 16758.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#11924777	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₇×D₇×C₁₉	C₃	1	1	yes	maximal, characteristic
3	C₃×C₇²×C₁₉	C₂×C₃	1	1	yes	characteristic
4	C₂×#11924777	—	7	1	no	maximal
5	D₇×#4294	—	7	1	no	maximal
6	C₇×D₇×C₁₉	C₉	1	1	yes	characteristic, complemented, Hall
7	#11924777	D₇	1	1	yes	characteristic, direct product factor
8	C₇×#4294	—	7	1	no	—
9	C₇²×C₁₉	C₂×C₉	1	1	yes	characteristic, complemented, Hall
10	D₇×C₇⋊C₉	—	19	1	no	maximal, Hall
11	C₂×C₃×C₇×C₁₉	—	7	1	no	—
12	C₃×D₇×C₁₉	ΓL(1,𝔽₈)	1	1	yes	characteristic
13	C₇×C₇⋊C₉	—	19	1	no	Hall
14	C₃×C₇×C₁₉	—	6	1	no	—
15	C₃×C₇×C₁₉	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic
16	C₃×C₇×C₁₉	C₃×D₇	1	1	yes	characteristic
17	C₂×#4294	—	49	1	no	Hall
18	C₃×C₇×D₇	C₁₉⋊C₃	1	1	yes	characteristic
19	C₂×C₇×C₁₉	—	7	1	no	—
20	D₇×C₁₉	C₇⋊C₉	1	1	yes	characteristic, complemented
21	#4294	—	7	1	no	Hall
22	C₃×C₇²	C₂×C₁₉⋊C₃	1	1	yes	characteristic
23	C₇×C₁₉	—	6	1	no	—
24	C₇×C₁₉	C₂×C₇⋊C₉	1	1	yes	characteristic, complemented
25	C₇×C₁₉	C₉×D₇	1	1	yes	characteristic, complemented
26	C₉×D₇	—	133	1	no	—
27	C₂×C₇⋊C₉	—	133	1	no	—
28	C₂×C₃×C₁₉	—	7	1	no	—
29	C₇×D₇	#4294	1	1	yes	characteristic, complemented, Hall
30	C₇×C₉	—	133	1	no	—
31	C₇⋊C₉	—	19	1	no	—
32	C₃×C₁₉	D₇×ΓL(1,𝔽₈)	1	1	yes	characteristic
33	C₇²	C₂×#4294	1	1	yes	characteristic, complemented, Sylow
34	C₂×C₃×C₇	—	7	1	no	—
35	C₃×D₇	#87705	1	1	yes	characteristic
36	C₂×C₁₉	—	7	1	no	Hall
37	C₃×C₇	—	6	1	no	—
38	C₃×C₇	D₇×C₁₉⋊C₃	1	1	yes	characteristic
39	C₃×C₇	C₂×#87705	1	1	yes	characteristic
40	C₁₉	D₇×C₇⋊C₉	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₉	—	931	1	no	Hall
42	C₂×C₇	—	7	1	no	—
43	D₇	#11924777	1	1	yes	characteristic, direct product factor
44	C₉	—	133	1	no	Sylow
45	C₇	—	6	1	no	—
46	C₇	D₇×#4294	1	1	yes	characteristic, complemented
47	C₇	C₂×#11924777	1	1	yes	characteristic, complemented
48	C₂×C₃	—	7	1	no	—
49	C₃	D₇×#87705	1	1	yes	characteristic
50	C₂	—	7	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₃	D₇×#87705
commutator, hypocenter	C₇²×C₁₉	C₂×C₉
Fitting, socle, cosocle	C₃×C₇²×C₁₉	C₂×C₃
prime radical	C₃×C₇×D₇×C₁₉	C₃
LCS	G ▷ C₇²×C₁₉
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₇×#11924777	C₂	semidirect
6. C₇×D₇×C₁₉	C₉	semidirect
7. #11924777	D₇	direct (N × H)
9. C₇²×C₁₉	C₂×C₉	semidirect
20. D₇×C₁₉	C₇⋊C₉	semidirect
24. C₇×C₁₉	C₂×C₇⋊C₉	semidirect
25. C₇×C₁₉	C₉×D₇	semidirect
29. C₇×D₇	#4294	semidirect
33. C₇²	C₂×#4294	semidirect
40. C₁₉	D₇×C₇⋊C₉	semidirect
43. D₇	#11924777	direct (N × H)
46. C₇	D₇×#4294	semidirect
47. C₇	C₂×#11924777	semidirect

Maximal subgroups

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

subgroup	index
C₇×#11924777	2
C₃×C₇×D₇×C₁₉	3
C₂×#11924777	7
D₇×#4294	7
D₇×C₇⋊C₉	19

Subgroups — D7×#11924777 #30660608

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₇×#11924777 #30660608