Subgroups — C₂×D₁₁×#3862 #20266374

Order 6468.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#3862	C₂	1	1	yes	maximal, characteristic, complemented
2	D₁₁×#3862	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₇²×D₁₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₁₁×#3862	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₇²×C₁₁	C₂×C₃	1	1	yes	characteristic, complemented
6	C₇²×D₁₁	C₂×C₃	1	2	yes	complemented
7	C₂×ΓL(1,𝔽₈)×D₁₁	—	7	2	no	maximal
8	C₂²×#3862	—	11	1	no	maximal, Hall
9	C₇²×C₁₁	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
10	C₂×C₁₁×ΓL(1,𝔽₈)	—	7	2	no	—
11	ΓL(1,𝔽₈)×D₁₁	—	7	4	no	—
12	C₂×C₇×D₁₁	—	3	2	no	—
13	C₂×C₇×D₁₁	ΓL(1,𝔽₈)	1	2	yes	complemented
14	C₂×#3862	—	11	2	no	—
15	C₂×#3862	D₁₁	1	1	yes	characteristic, direct product factor
16	C₁₁×ΓL(1,𝔽₈)	—	7	2	no	—
17	C₂²×C₇²	—	11	1	no	Hall
18	C₂×C₇×C₁₁	—	3	2	no	—
19	C₂×C₇×C₁₁	C₂×ΓL(1,𝔽₈)	1	2	yes	complemented
20	C₇×D₁₁	—	3	4	no	—
21	C₇×D₁₁	C₂×ΓL(1,𝔽₈)	1	4	yes	complemented
22	#3862	C₂×D₁₁	1	1	yes	characteristic, direct product factor, Hall
23	C₂×C₃×D₁₁	—	49	1	no	Hall
24	C₂×C₇²	—	11	2	no	—
25	C₂×C₇²	C₃×D₁₁	1	1	yes	characteristic, complemented
26	C₂²×ΓL(1,𝔽₈)	—	77	2	no	—
27	C₇×C₁₁	—	3	2	no	—
28	C₇×C₁₁	C₂²×ΓL(1,𝔽₈)	1	2	yes	complemented
29	C₂×C₃×C₁₁	—	49	1	no	—
30	C₃×D₁₁	—	49	2	no	—
31	C₇²	C₂×C₃×D₁₁	1	1	yes	characteristic, complemented, Sylow
32	C₂×D₁₁	#3862	1	1	yes	characteristic, direct product factor, Hall
33	C₂×ΓL(1,𝔽₈)	—	7	2	no	—
34	C₂×ΓL(1,𝔽₈)	—	77	4	no	—
35	C₃×C₁₁	—	49	1	no	Hall
36	C₂²×C₇	—	11	2	no	—
37	C₂²×C₇	—	33	2	no	—
38	C₂×C₁₁	C₂×#3862	1	1	yes	characteristic, complemented
39	D₁₁	C₂×#3862	1	2	yes	direct product factor
40	ΓL(1,𝔽₈)	—	7	2	no	—
41	C₂×C₇	—	3	2	no	—
42	C₂×C₇	—	11	4	no	—
43	C₂×C₇	—	33	4	no	—
44	C₂×C₇	ΓL(1,𝔽₈)×D₁₁	1	2	yes	complemented
45	C₂²×C₃	—	539	1	no	Hall
46	C₁₁	C₂²×#3862	1	1	yes	characteristic, complemented, Sylow
47	C₇	—	3	2	no	—
48	C₇	C₂×ΓL(1,𝔽₈)×D₁₁	1	2	yes	complemented
49	C₂×C₃	—	539	2	no	—
50	C₂×C₃	—	49	1	no	—
51	C₂²	—	11	1	no	Sylow
52	C₃	—	49	1	no	Sylow
53	C₂	—	11	2	no	—
54	C₂	D₁₁×#3862	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₁₁×#3862
commutator, hypocenter	C₇²×C₁₁	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₇²×C₁₁	C₂×C₃
LCS	G ▷ C₇²×C₁₁
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₁×#3862	C₂	semidirect
2. D₁₁×#3862	C₂	direct (N × H)
3. C₂×C₇²×D₁₁	C₃	semidirect
4. C₁₁×#3862	C₂²	semidirect
5. C₂×C₇²×C₁₁	C₂×C₃	semidirect
6. C₇²×D₁₁	C₂×C₃	semidirect
9. C₇²×C₁₁	C₂²×C₃	semidirect
13. C₂×C₇×D₁₁	ΓL(1,𝔽₈)	semidirect
15. C₂×#3862	D₁₁	direct (N × H)
19. C₂×C₇×C₁₁	C₂×ΓL(1,𝔽₈)	semidirect
21. C₇×D₁₁	C₂×ΓL(1,𝔽₈)	semidirect
22. #3862	C₂×D₁₁	direct (N × H)
25. C₂×C₇²	C₃×D₁₁	semidirect
28. C₇×C₁₁	C₂²×ΓL(1,𝔽₈)	semidirect
31. C₇²	C₂×C₃×D₁₁	semidirect
32. C₂×D₁₁	#3862	direct (N × H)
38. C₂×C₁₁	C₂×#3862	semidirect
39. D₁₁	C₂×#3862	direct (N × H)
44. C₂×C₇	ΓL(1,𝔽₈)×D₁₁	semidirect
46. C₁₁	C₂²×#3862	semidirect
48. C₇	C₂×ΓL(1,𝔽₈)×D₁₁	semidirect
54. C₂	D₁₁×#3862	direct (N × H)

Subgroups — C2×D11×#3862 #20266374

Conjugacy classes of subgroups

Complements

Subgroups — C₂×D₁₁×#3862 #20266374