Subgroups — C₄×C₇×#87704 #26013861

Order 11172.

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

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

Complements

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

N	H ≅ G/N	type
2. C₄×C₇²×C₁₉	C₃	semidirect
3. C₇×#87704	C₄	direct (N × H)
5. C₄×#87704	C₇	direct (N × H)
7. C₇²×C₁₉	C₃×C₄	semidirect
12. C₄×C₇×C₁₉	ΓL(1,𝔽₈)	semidirect
13. C₄×C₇×C₁₉	C₃×C₇	semidirect
14. #87704	C₄×C₇	direct (N × H)
21. C₄×C₇²	C₁₉⋊C₃	semidirect
24. C₇×C₁₉	C₄×ΓL(1,𝔽₈)	semidirect
25. C₇×C₁₉	C₃×C₄×C₇	semidirect
30. C₄×C₁₉	C₇×ΓL(1,𝔽₈)	semidirect
32. C₇²	C₄×C₁₉⋊C₃	semidirect
37. C₄×C₇	C₇×C₁₉⋊C₃	semidirect
38. C₄×C₇	#87704	direct (N × H)
41. C₁₉	C₄×C₇×ΓL(1,𝔽₈)	semidirect
47. C₇	C₄×C₇×C₁₉⋊C₃	semidirect
48. C₇	C₄×#87704	direct (N × H)
50. C₄	C₇×#87704	direct (N × H)

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
C₄×C₇²×C₁₉	3
C₄×#87704	7
C₄×C₇×C₁₉⋊C₃	7
C₄×C₇×ΓL(1,𝔽₈)	19

Subgroups — C4×C7×#87704 #26013861

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₇×#87704 #26013861