Subgroups — C₂×C₁₁×C₃⋊D₂₁ #14583946

Order 2772.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₇×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₁×C₃⋊D₂₁	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₁₁×D₂₁	—	3	4	no	maximal
4	C₃²×C₇×C₁₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×C₇×C₁₁	D₃	1	4	yes	complemented
6	C₁₁×D₂₁	—	3	8	no	—
7	C₂×C₁₁×C₃⋊D₃	—	7	1	no	maximal, Hall
8	C₂×C₁₁×D₇	—	9	1	no	Hall
9	C₂×C₃⋊D₂₁	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₃×C₇×C₁₁	C₂×D₃	1	4	yes	complemented
11	C₂×C₃²×C₁₁	D₇	1	1	yes	characteristic, complemented
12	C₁₁×C₃⋊D₃	—	7	2	no	—
13	C₂×C₇×C₁₁	C₃⋊D₃	1	1	yes	characteristic, complemented
14	C₁₁×D₇	—	9	2	no	—
15	C₂×D₃×C₁₁	—	21	4	no	—
16	C₂×C₃²×C₇	C₂×C₁₁	1	1	yes	characteristic, complemented
17	C₃⋊D₂₁	C₂×C₁₁	1	2	yes	direct product factor
18	C₃²×C₁₁	C₂×D₇	1	1	yes	characteristic, complemented, Hall
19	C₂×D₂₁	—	3	4	no	—
20	C₇×C₁₁	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
21	C₂×C₃×C₁₁	D₂₁	1	4	yes	complemented
22	D₃×C₁₁	—	21	8	no	—
23	C₃²×C₇	C₂²×C₁₁	1	1	yes	characteristic, complemented, Hall
24	C₂²×C₁₁	—	63	1	no	Hall
25	C₂×C₃×C₇	D₃×C₁₁	1	4	yes	complemented
26	D₂₁	—	3	8	no	—
27	C₂×C₃⋊D₃	—	7	1	no	Hall
28	C₃×C₁₁	C₂×D₂₁	1	4	yes	complemented
29	C₂×D₇	—	9	1	no	Hall
30	C₂×C₁₁	—	63	2	no	—
31	C₂×C₁₁	C₃⋊D₂₁	1	1	yes	characteristic, direct product factor
32	C₃×C₇	C₂×D₃×C₁₁	1	4	yes	complemented
33	C₂×C₃²	C₁₁×D₇	1	1	yes	characteristic, complemented
34	C₃⋊D₃	—	7	2	no	—
35	C₂×C₇	C₁₁×C₃⋊D₃	1	1	yes	characteristic, complemented
36	D₇	—	9	2	no	—
37	C₂×D₃	—	21	4	no	—
38	C₁₁	C₂×C₃⋊D₂₁	1	1	yes	characteristic, direct product factor, Sylow
39	C₃²	C₂×C₁₁×D₇	1	1	yes	characteristic, complemented, Sylow
40	C₇	C₂×C₁₁×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₃	C₁₁×D₂₁	1	4	yes	complemented
42	D₃	—	21	8	no	—
43	C₂²	—	63	1	no	Sylow
44	C₃	C₂×C₁₁×D₂₁	1	4	yes	complemented
45	C₂	—	63	2	no	—
46	C₂	C₁₁×C₃⋊D₂₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₁	C₃⋊D₂₁
commutator, cosocle, hypocenter	C₃²×C₇	C₂²×C₁₁
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₇×C₁₁	C₂
LCS	G ▷ C₃²×C₇
UCS	C₁ ◁ C₂×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₂×C₃²×C₇×C₁₁	C₂	semidirect
2. C₁₁×C₃⋊D₂₁	C₂	direct (N × H)
4. C₃²×C₇×C₁₁	C₂²	semidirect
5. C₂×C₃×C₇×C₁₁	D₃	semidirect
9. C₂×C₃⋊D₂₁	C₁₁	direct (N × H)
10. C₃×C₇×C₁₁	C₂×D₃	semidirect
11. C₂×C₃²×C₁₁	D₇	semidirect
13. C₂×C₇×C₁₁	C₃⋊D₃	semidirect
16. C₂×C₃²×C₇	C₂×C₁₁	semidirect
17. C₃⋊D₂₁	C₂×C₁₁	direct (N × H)
18. C₃²×C₁₁	C₂×D₇	semidirect
20. C₇×C₁₁	C₂×C₃⋊D₃	semidirect
21. C₂×C₃×C₁₁	D₂₁	semidirect
23. C₃²×C₇	C₂²×C₁₁	semidirect
25. C₂×C₃×C₇	D₃×C₁₁	semidirect
28. C₃×C₁₁	C₂×D₂₁	semidirect
31. C₂×C₁₁	C₃⋊D₂₁	direct (N × H)
32. C₃×C₇	C₂×D₃×C₁₁	semidirect
33. C₂×C₃²	C₁₁×D₇	semidirect
35. C₂×C₇	C₁₁×C₃⋊D₃	semidirect
38. C₁₁	C₂×C₃⋊D₂₁	direct (N × H)
39. C₃²	C₂×C₁₁×D₇	semidirect
40. C₇	C₂×C₁₁×C₃⋊D₃	semidirect
41. C₂×C₃	C₁₁×D₂₁	semidirect
44. C₃	C₂×C₁₁×D₂₁	semidirect
46. C₂	C₁₁×C₃⋊D₂₁	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×C₃²×C₇×C₁₁	2
C₁₁×C₃⋊D₂₁	2
C₂×C₁₁×D₂₁	3
C₂×C₁₁×C₃⋊D₃	7
C₂×C₃⋊D₂₁	11

Subgroups — C2×C11×C3⋊D21 #14583946

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×C₃⋊D₂₁ #14583946