Subgroups — C₁₁×#64422⋊C₂ #20266341

Order 6468.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#64422	C₂	1	2	yes	maximal, complemented
2	C₁₁×#64425	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×D₇²	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₁₁×#3862	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₁₁×C₇⋊D₇	C₂×C₃	1	1	yes	characteristic, complemented
6	C₇×C₁₁×D₇	C₂×C₃	1	2	yes	complemented
7	C₂×C₁₁×AGL(1,𝔽₇)	—	7	2	no	maximal
8	#64422⋊C₂	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₇²×C₁₁	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
10	C₂×C₁₁×ΓL(1,𝔽₈)	—	7	2	no	—
11	C₁₁×AGL(1,𝔽₇)	—	7	2	no	—
12	C₁₁×AGL(1,𝔽₇)	—	7	2	no	—
13	C₂×C₁₁×D₇	—	7	2	no	—
14	#64425	C₂×C₁₁	1	1	yes	characteristic, complemented
15	#64422	C₂×C₁₁	1	2	yes	complemented
16	C₁₁×ΓL(1,𝔽₈)	—	7	2	no	—
17	D₇²	C₃×C₁₁	1	1	yes	characteristic, complemented, Hall
18	C₂×C₇×C₁₁	—	7	2	no	—
19	C₁₁×D₇	—	7	2	no	—
20	C₁₁×D₇	—	42	1	no	—
21	C₁₁×D₇	AGL(1,𝔽₇)	1	2	yes	complemented
22	#3862	C₂²×C₁₁	1	1	yes	characteristic, complemented, Hall
23	C₂²×C₃×C₁₁	—	49	1	no	Hall
24	C₇⋊D₇	C₂×C₃×C₁₁	1	1	yes	characteristic, complemented
25	C₇×D₇	C₂×C₃×C₁₁	1	2	yes	complemented
26	C₂×AGL(1,𝔽₇)	—	7	2	no	—
27	C₇×C₁₁	—	6	1	no	—
28	C₇×C₁₁	C₂×AGL(1,𝔽₇)	1	2	yes	complemented
29	C₂×C₃×C₁₁	—	49	2	no	—
30	C₂×C₃×C₁₁	—	49	1	no	—
31	C₇²	C₂²×C₃×C₁₁	1	1	yes	characteristic, complemented, Sylow
32	C₂²×C₁₁	—	49	1	no	Hall
33	C₂×ΓL(1,𝔽₈)	—	7	2	no	—
34	AGL(1,𝔽₇)	—	7	2	no	—
35	AGL(1,𝔽₇)	—	7	2	no	—
36	C₃×C₁₁	—	49	1	no	Hall
37	C₂×D₇	—	7	2	no	—
38	C₂×C₁₁	—	7	2	no	—
39	C₂×C₁₁	—	49	1	no	—
40	ΓL(1,𝔽₈)	—	7	2	no	—
41	C₂×C₇	—	7	2	no	—
42	D₇	—	7	2	no	—
43	D₇	—	42	1	no	—
44	D₇	C₁₁×AGL(1,𝔽₇)	1	2	yes	complemented
45	C₂²×C₃	—	49	1	no	Hall
46	C₁₁	#64422⋊C₂	1	1	yes	characteristic, direct product factor, Sylow
47	C₇	—	6	1	no	—
48	C₇	C₂×C₁₁×AGL(1,𝔽₇)	1	2	yes	complemented
49	C₂×C₃	—	49	2	no	—
50	C₂×C₃	—	49	1	no	—
51	C₂²	—	49	1	no	Sylow
52	C₃	—	49	1	no	Sylow
53	C₂	—	7	2	no	—
54	C₂	—	49	1	no	—

	subgroup	G/H
center, hypercenter	C₁₁	#64422⋊C₂
commutator, hypocenter	C₇²	C₂²×C₃×C₁₁
Frattini	C₁	G
Fitting, socle	C₇²×C₁₁	C₂²×C₃
LCS	G ▷ C₇²
UCS	C₁ ◁ C₁₁

Complements

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

N	H ≅ G/N	type
1. C₁₁×#64422	C₂	semidirect
2. C₁₁×#64425	C₂	semidirect
3. C₁₁×D₇²	C₃	semidirect
4. C₁₁×#3862	C₂²	semidirect
5. C₁₁×C₇⋊D₇	C₂×C₃	semidirect
6. C₇×C₁₁×D₇	C₂×C₃	semidirect
8. #64422⋊C₂	C₁₁	direct (N × H)
9. C₇²×C₁₁	C₂²×C₃	semidirect
14. #64425	C₂×C₁₁	semidirect
15. #64422	C₂×C₁₁	semidirect
17. D₇²	C₃×C₁₁	semidirect
21. C₁₁×D₇	AGL(1,𝔽₇)	semidirect
22. #3862	C₂²×C₁₁	semidirect
24. C₇⋊D₇	C₂×C₃×C₁₁	semidirect
25. C₇×D₇	C₂×C₃×C₁₁	semidirect
28. C₇×C₁₁	C₂×AGL(1,𝔽₇)	semidirect
31. C₇²	C₂²×C₃×C₁₁	semidirect
44. D₇	C₁₁×AGL(1,𝔽₇)	semidirect
46. C₁₁	#64422⋊C₂	direct (N × H)
48. C₇	C₂×C₁₁×AGL(1,𝔽₇)	semidirect

Subgroups — C11×#64422⋊C2 #20266341

Conjugacy classes of subgroups

Complements

Subgroups — C₁₁×#64422⋊C₂ #20266341