Subgroups — Dic₇×#87704 #26013852

Order 11172.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#87704	C₂	1	1	yes	maximal, characteristic
2	C₇×C₁₉×Dic₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇×#87704	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₇²×C₁₉	C₂×C₃	1	1	yes	characteristic
5	C₄×#87704	—	7	1	no	maximal
6	Dic₇×C₁₉⋊C₃	—	7	1	no	maximal
7	C₇²×C₁₉	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	C₂×#87704	D₇	1	1	yes	characteristic
9	C₂×C₇×C₁₉⋊C₃	—	7	1	no	—
10	ΓL(1,𝔽₈)×Dic₇	—	19	1	no	maximal, Hall
11	C₄×C₇×C₁₉	—	7	1	no	—
12	C₁₉×Dic₇	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
13	#87704	Dic₇	1	1	yes	characteristic, direct product factor
14	C₇×C₁₉⋊C₃	—	7	1	no	—
15	C₂×C₇×ΓL(1,𝔽₈)	—	19	1	no	—
16	C₂×C₇×C₁₉	—	6	1	no	—
17	C₂×C₇×C₁₉	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic
18	C₂×C₇×C₁₉	C₃×D₇	1	1	yes	characteristic
19	C₄×C₁₉⋊C₃	—	49	1	no	Hall
20	C₇×Dic₇	C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
21	C₇×ΓL(1,𝔽₈)	—	19	1	no	Hall
22	C₇×C₁₉	—	6	1	no	—
23	C₇×C₁₉	C₄×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
24	C₇×C₁₉	C₃×Dic₇	1	1	yes	characteristic, complemented
25	C₂×C₁₉⋊C₃	—	7	1	no	—
26	C₂×C₇²	C₂×C₁₉⋊C₃	1	1	yes	characteristic
27	C₃×Dic₇	—	133	1	no	—
28	C₄×ΓL(1,𝔽₈)	—	133	1	no	—
29	C₄×C₁₉	—	7	1	no	Hall
30	C₁₉⋊C₃	—	7	1	no	Hall
31	C₇²	C₄×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
32	C₂×C₃×C₇	—	133	1	no	—
33	C₂×ΓL(1,𝔽₈)	—	19	1	no	—
34	C₂×C₁₉	D₇×ΓL(1,𝔽₈)	1	1	yes	characteristic
35	C₄×C₇	—	7	1	no	—
36	Dic₇	#87704	1	1	yes	characteristic, direct product factor
37	C₃×C₇	—	133	1	no	—
38	ΓL(1,𝔽₈)	—	19	1	no	—
39	C₁₉	ΓL(1,𝔽₈)×Dic₇	1	1	yes	characteristic, complemented, Sylow
40	C₂×C₇	—	6	1	no	—
41	C₂×C₇	D₇×C₁₉⋊C₃	1	1	yes	characteristic
42	C₂×C₇	C₂×#87704	1	1	yes	characteristic
43	C₃×C₄	—	931	1	no	Hall
44	C₇	—	6	1	no	—
45	C₇	Dic₇×C₁₉⋊C₃	1	1	yes	characteristic, complemented
46	C₇	C₄×#87704	1	1	yes	characteristic, complemented
47	C₂×C₃	—	133	1	no	—
48	C₄	—	7	1	no	Sylow
49	C₃	—	133	1	no	Sylow
50	C₂	D₇×#87704	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₇×#87704
commutator, hypocenter	C₇²×C₁₉	C₃×C₄
Fitting, socle, cosocle	C₂×C₇²×C₁₉	C₂×C₃
prime radical	C₂×C₇×#87704	C₂
LCS	G ▷ C₇²×C₁₉
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
2. C₇×C₁₉×Dic₇	C₃	semidirect
3. C₇×#87704	C₄	semidirect
7. C₇²×C₁₉	C₃×C₄	semidirect
12. C₁₉×Dic₇	ΓL(1,𝔽₈)	semidirect
13. #87704	Dic₇	direct (N × H)
20. C₇×Dic₇	C₁₉⋊C₃	semidirect
23. C₇×C₁₉	C₄×ΓL(1,𝔽₈)	semidirect
24. C₇×C₁₉	C₃×Dic₇	semidirect
31. C₇²	C₄×C₁₉⋊C₃	semidirect
36. Dic₇	#87704	direct (N × H)
39. C₁₉	ΓL(1,𝔽₈)×Dic₇	semidirect
45. C₇	Dic₇×C₁₉⋊C₃	semidirect
46. C₇	C₄×#87704	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₇×#87704	2
C₇×C₁₉×Dic₇	3
C₄×#87704	7
Dic₇×C₁₉⋊C₃	7
ΓL(1,𝔽₈)×Dic₇	19

Subgroups — Dic7×#87704 #26013852

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₇×#87704 #26013852