Subgroups — C₂×C₁₁⋊(#4294⋊C₂) #21418972

Order 7524.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#4294	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₁⋊(#4294⋊C₂)	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃×D₂₀₉	C₃	1	1	yes	maximal, characteristic
4	C₁₁×#4294	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×C₁₁×C₁₉	C₂×C₃	1	1	yes	characteristic
6	C₃×D₂₀₉	C₂×C₃	1	2	yes	—
7	C₂×D₂₀₉	C₉	1	1	yes	characteristic, complemented, Hall
8	C₂×#4294⋊C₂	—	11	1	no	maximal, Hall
9	C₃×C₁₁×C₁₉	C₂²×C₃	1	1	yes	characteristic
10	C₂×C₁₁×C₁₉	C₂×C₉	1	1	yes	characteristic, complemented
11	D₂₀₉	C₂×C₉	1	2	yes	complemented
12	C₂×C₉×D₁₁	—	19	1	no	maximal, Hall
13	C₂×#4294	D₁₁	1	1	yes	characteristic, complemented
14	#4294⋊C₂	—	11	2	no	—
15	C₂×C₃×D₁₉	—	11	1	no	—
16	C₁₁×C₁₉	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
17	C₂×C₉×C₁₁	—	19	1	no	—
18	C₉×D₁₁	—	19	2	no	—
19	#4294	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
20	C₂×C₃×D₁₁	—	19	1	no	—
21	C₂×C₃×C₁₉	C₃×D₁₁	1	1	yes	characteristic
22	C₃×D₁₉	—	11	2	no	—
23	C₉×C₁₁	—	19	1	no	Hall
24	C₂×D₁₉	—	11	1	no	Hall
25	C₂×C₃×C₁₁	D₁₉⋊C₃	1	1	yes	characteristic
26	C₃×D₁₁	—	19	2	no	—
27	C₃×C₁₉	C₂×C₃×D₁₁	1	1	yes	characteristic
28	C₂×D₁₁	—	19	1	no	Hall
29	C₂×C₁₉	C₉×D₁₁	1	1	yes	characteristic, complemented
30	D₁₉	—	11	2	no	—
31	C₂²×C₉	—	209	1	no	Hall
32	C₃×C₁₁	C₂×D₁₉⋊C₃	1	1	yes	characteristic
33	C₂×C₁₁	#4294⋊C₂	1	1	yes	characteristic, complemented
34	D₁₁	—	19	2	no	—
35	C₁₉	C₂×C₉×D₁₁	1	1	yes	characteristic, complemented, Sylow
36	C₂×C₉	—	19	1	no	—
37	C₂×C₉	—	209	2	no	—
38	C₂²×C₃	—	209	1	no	—
39	C₁₁	C₂×#4294⋊C₂	1	1	yes	characteristic, complemented, Sylow
40	C₉	—	19	1	no	Sylow
41	C₂×C₃	—	209	2	no	—
42	C₂×C₃	C₁₁⋊(D₁₉⋊C₃)	1	1	yes	characteristic
43	C₂²	—	209	1	no	Sylow
44	C₃	C₂×C₁₁⋊(D₁₉⋊C₃)	1	1	yes	characteristic
45	C₂	—	209	2	no	—
46	C₂	C₁₁⋊(#4294⋊C₂)	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃	C₁₁⋊(D₁₉⋊C₃)
commutator, hypocenter	C₁₁×C₁₉	C₂²×C₉
Frattini	C₃	C₂×C₁₁⋊(D₁₉⋊C₃)
Fitting, socle	C₂×C₃×C₁₁×C₁₉	C₂×C₃
LCS	G ▷ C₁₁×C₁₉
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₁×#4294	C₂	semidirect
2. C₁₁⋊(#4294⋊C₂)	C₂	direct (N × H)
4. C₁₁×#4294	C₂²	semidirect
7. C₂×D₂₀₉	C₉	semidirect
10. C₂×C₁₁×C₁₉	C₂×C₉	semidirect
11. D₂₀₉	C₂×C₉	semidirect
13. C₂×#4294	D₁₁	semidirect
16. C₁₁×C₁₉	C₂²×C₉	semidirect
19. #4294	C₂×D₁₁	semidirect
29. C₂×C₁₉	C₉×D₁₁	semidirect
33. C₂×C₁₁	#4294⋊C₂	semidirect
35. C₁₉	C₂×C₉×D₁₁	semidirect
39. C₁₁	C₂×#4294⋊C₂	semidirect
46. C₂	C₁₁⋊(#4294⋊C₂)	direct (N × H)

Subgroups — C2×C11⋊(#4294⋊C2) #21418972

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₁₁⋊(#4294⋊C₂) #21418972