Subgroups — C₂²×C₇×#87705 #26014042

Order 11172.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#87705	C₂	1	3	yes	maximal, direct product factor
2	C₂²×C₇²×C₁₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇×#87705	C₂²	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₇²×C₁₉	C₂×C₃	1	3	yes	complemented
5	C₂²×#87705	C₇	1	1	yes	maximal, characteristic, direct product factor
6	C₂²×C₇×C₁₉⋊C₃	—	7	1	no	maximal
7	C₇²×C₁₉	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
8	C₂×#87705	C₂×C₇	1	3	yes	direct product factor
9	C₂×C₇×C₁₉⋊C₃	—	7	3	no	—
10	C₂²×C₇×ΓL(1,𝔽₈)	—	19	1	no	maximal, Hall
11	C₂²×C₇×C₁₉	—	3	2	no	—
12	C₂²×C₇×C₁₉	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
13	C₂²×C₇×C₁₉	C₃×C₇	1	1	yes	characteristic, complemented
14	#87705	C₂²×C₇	1	1	yes	characteristic, direct product factor
15	C₇×C₁₉⋊C₃	—	7	1	no	—
16	C₂×C₇×ΓL(1,𝔽₈)	—	19	3	no	—
17	C₂×C₇×C₁₉	—	3	6	no	—
18	C₂×C₇×C₁₉	C₂×ΓL(1,𝔽₈)	1	3	yes	complemented
19	C₂×C₇×C₁₉	C₂×C₃×C₇	1	3	yes	complemented
20	C₂²×C₁₉⋊C₃	—	7	1	no	Hall
21	C₂²×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	C₂²×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
25	C₇×C₁₉	C₂²×C₃×C₇	1	1	yes	characteristic, complemented
26	C₂×C₁₉⋊C₃	—	7	3	no	—
27	C₂×C₇²	C₂×C₁₉⋊C₃	1	3	yes	complemented
28	C₂²×C₃×C₇	—	133	1	no	—
29	C₂²×ΓL(1,𝔽₈)	—	19	1	no	—
30	C₂²×C₁₉	C₇×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
31	C₁₉⋊C₃	—	7	1	no	Hall
32	C₇²	C₂²×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
33	C₂×C₃×C₇	—	133	3	no	—
34	C₂×ΓL(1,𝔽₈)	—	19	3	no	—
35	C₂×C₁₉	C₂×C₇×ΓL(1,𝔽₈)	1	3	yes	complemented
36	C₂²×C₇	—	3	2	no	—
37	C₂²×C₇	C₇×C₁₉⋊C₃	1	1	yes	characteristic, complemented
38	C₂²×C₇	#87705	1	1	yes	characteristic, direct product factor
39	C₃×C₇	—	133	1	no	—
40	ΓL(1,𝔽₈)	—	19	1	no	—
41	C₁₉	C₂²×C₇×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Sylow
42	C₂×C₇	—	3	6	no	—
43	C₂×C₇	C₂×C₇×C₁₉⋊C₃	1	3	yes	complemented
44	C₂×C₇	C₂×#87705	1	3	yes	direct product factor
45	C₂²×C₃	—	133	1	no	Hall
46	C₇	—	3	2	no	—
47	C₇	C₂²×C₇×C₁₉⋊C₃	1	1	yes	characteristic, complemented
48	C₇	C₂²×#87705	1	1	yes	characteristic, direct product factor
49	C₂×C₃	—	133	3	no	—
50	C₂²	C₇×#87705	1	1	yes	characteristic, direct product factor, Sylow
51	C₃	—	133	1	no	Sylow
52	C₂	C₂×C₇×#87705	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²×C₇	#87705
commutator, cosocle, hypocenter	C₇×C₁₉	C₂²×C₃×C₇
Frattini	C₁	G
Fitting, socle	C₂²×C₇²×C₁₉	C₃
LCS	G ▷ C₇×C₁₉
UCS	C₁ ◁ C₂²×C₇

Complements

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

N	H ≅ G/N	type
1. C₂×C₇×#87705	C₂	direct (N × H)
2. C₂²×C₇²×C₁₉	C₃	semidirect
3. C₇×#87705	C₂²	direct (N × H)
4. C₂×C₇²×C₁₉	C₂×C₃	semidirect
5. C₂²×#87705	C₇	direct (N × H)
7. C₇²×C₁₉	C₂²×C₃	semidirect
8. C₂×#87705	C₂×C₇	direct (N × H)
12. C₂²×C₇×C₁₉	ΓL(1,𝔽₈)	semidirect
13. C₂²×C₇×C₁₉	C₃×C₇	semidirect
14. #87705	C₂²×C₇	direct (N × H)
18. C₂×C₇×C₁₉	C₂×ΓL(1,𝔽₈)	semidirect
19. C₂×C₇×C₁₉	C₂×C₃×C₇	semidirect
21. C₂²×C₇²	C₁₉⋊C₃	semidirect
24. C₇×C₁₉	C₂²×ΓL(1,𝔽₈)	semidirect
25. C₇×C₁₉	C₂²×C₃×C₇	semidirect
27. C₂×C₇²	C₂×C₁₉⋊C₃	semidirect
30. C₂²×C₁₉	C₇×ΓL(1,𝔽₈)	semidirect
32. C₇²	C₂²×C₁₉⋊C₃	semidirect
35. C₂×C₁₉	C₂×C₇×ΓL(1,𝔽₈)	semidirect
37. C₂²×C₇	C₇×C₁₉⋊C₃	semidirect
38. C₂²×C₇	#87705	direct (N × H)
41. C₁₉	C₂²×C₇×ΓL(1,𝔽₈)	semidirect
43. C₂×C₇	C₂×C₇×C₁₉⋊C₃	semidirect
44. C₂×C₇	C₂×#87705	direct (N × H)
47. C₇	C₂²×C₇×C₁₉⋊C₃	semidirect
48. C₇	C₂²×#87705	direct (N × H)
50. C₂²	C₇×#87705	direct (N × H)
52. C₂	C₂×C₇×#87705	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×#87705	2
C₂²×C₇²×C₁₉	3
C₂²×#87705	7
C₂²×C₇×C₁₉⋊C₃	7
C₂²×C₇×ΓL(1,𝔽₈)	19

Subgroups — C22×C7×#87705 #26014042

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₇×#87705 #26014042