Subgroups — C₁₁×C₁₃×C₃⋊D₂₁ #31825080

Order 18018.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₇×C₁₁×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₁×C₁₃×D₂₁	—	3	4	no	maximal
3	C₃×C₇×C₁₁×C₁₃	D₃	1	4	yes	complemented
4	C₁₁×C₁₃×C₃⋊D₃	—	7	1	no	maximal, Hall
5	C₁₁×C₁₃×D₇	—	9	1	no	Hall
6	C₁₃×C₃⋊D₂₁	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₁₁×C₃⋊D₂₁	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₃²×C₁₁×C₁₃	D₇	1	1	yes	characteristic, complemented, Hall
9	C₇×C₁₁×C₁₃	C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
10	D₃×C₁₁×C₁₃	—	21	4	no	—
11	C₃²×C₇×C₁₃	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
12	C₃²×C₇×C₁₁	C₂×C₁₃	1	1	yes	characteristic, complemented, Hall
13	C₁₃×D₂₁	—	3	4	no	—
14	C₁₁×D₂₁	—	3	4	no	—
15	C₃×C₁₁×C₁₃	D₂₁	1	4	yes	complemented
16	C₂×C₁₁×C₁₃	—	63	1	no	Hall
17	C₃×C₇×C₁₃	D₃×C₁₁	1	4	yes	complemented
18	C₁₃×C₃⋊D₃	—	7	1	no	Hall
19	C₃×C₇×C₁₁	D₃×C₁₃	1	4	yes	complemented
20	C₁₁×C₃⋊D₃	—	7	1	no	Hall
21	C₁₃×D₇	—	9	1	no	Hall
22	C₁₁×D₇	—	9	1	no	Hall
23	C₁₁×C₁₃	C₃⋊D₂₁	1	1	yes	characteristic, direct product factor, Hall
24	C₃⋊D₂₁	C₁₁×C₁₃	1	1	yes	characteristic, direct product factor, Hall
25	C₃²×C₁₃	C₁₁×D₇	1	1	yes	characteristic, complemented, Hall
26	C₃²×C₁₁	C₁₃×D₇	1	1	yes	characteristic, complemented, Hall
27	C₇×C₁₃	C₁₁×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
28	D₃×C₁₃	—	21	4	no	—
29	C₇×C₁₁	C₁₃×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
30	D₃×C₁₁	—	21	4	no	—
31	C₃²×C₇	C₂×C₁₁×C₁₃	1	1	yes	characteristic, complemented, Hall
32	D₂₁	—	3	4	no	—
33	C₃×C₁₃	C₁₁×D₂₁	1	4	yes	complemented
34	C₃×C₁₁	C₁₃×D₂₁	1	4	yes	complemented
35	C₂×C₁₃	—	63	1	no	Hall
36	C₂×C₁₁	—	63	1	no	Hall
37	C₃×C₇	D₃×C₁₁×C₁₃	1	4	yes	complemented
38	C₃⋊D₃	—	7	1	no	Hall
39	D₇	—	9	1	no	Hall
40	C₁₃	C₁₁×C₃⋊D₂₁	1	1	yes	characteristic, direct product factor, Sylow
41	C₁₁	C₁₃×C₃⋊D₂₁	1	1	yes	characteristic, direct product factor, Sylow
42	C₃²	C₁₁×C₁₃×D₇	1	1	yes	characteristic, complemented, Sylow
43	C₇	C₁₁×C₁₃×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
44	D₃	—	21	4	no	—
45	C₃	C₁₁×C₁₃×D₂₁	1	4	yes	complemented
46	C₂	—	63	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₁×C₁₃	C₃⋊D₂₁
commutator, cosocle, hypocenter	C₃²×C₇	C₂×C₁₁×C₁₃
Frattini	C₁	G
Fitting, socle	C₃²×C₇×C₁₁×C₁₃	C₂
LCS	G ▷ C₃²×C₇
UCS	C₁ ◁ C₁₁×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₃²×C₇×C₁₁×C₁₃	C₂	semidirect
3. C₃×C₇×C₁₁×C₁₃	D₃	semidirect
6. C₁₃×C₃⋊D₂₁	C₁₁	direct (N × H)
7. C₁₁×C₃⋊D₂₁	C₁₃	direct (N × H)
8. C₃²×C₁₁×C₁₃	D₇	semidirect
9. C₇×C₁₁×C₁₃	C₃⋊D₃	semidirect
11. C₃²×C₇×C₁₃	C₂×C₁₁	semidirect
12. C₃²×C₇×C₁₁	C₂×C₁₃	semidirect
15. C₃×C₁₁×C₁₃	D₂₁	semidirect
17. C₃×C₇×C₁₃	D₃×C₁₁	semidirect
19. C₃×C₇×C₁₁	D₃×C₁₃	semidirect
23. C₁₁×C₁₃	C₃⋊D₂₁	direct (N × H)
24. C₃⋊D₂₁	C₁₁×C₁₃	direct (N × H)
25. C₃²×C₁₃	C₁₁×D₇	semidirect
26. C₃²×C₁₁	C₁₃×D₇	semidirect
27. C₇×C₁₃	C₁₁×C₃⋊D₃	semidirect
29. C₇×C₁₁	C₁₃×C₃⋊D₃	semidirect
31. C₃²×C₇	C₂×C₁₁×C₁₃	semidirect
33. C₃×C₁₃	C₁₁×D₂₁	semidirect
34. C₃×C₁₁	C₁₃×D₂₁	semidirect
37. C₃×C₇	D₃×C₁₁×C₁₃	semidirect
40. C₁₃	C₁₁×C₃⋊D₂₁	direct (N × H)
41. C₁₁	C₁₃×C₃⋊D₂₁	direct (N × H)
42. C₃²	C₁₁×C₁₃×D₇	semidirect
43. C₇	C₁₁×C₁₃×C₃⋊D₃	semidirect
45. C₃	C₁₁×C₁₃×D₂₁	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃²×C₇×C₁₁×C₁₃	2
C₁₁×C₁₃×D₂₁	3
C₁₁×C₁₃×C₃⋊D₃	7
C₁₃×C₃⋊D₂₁	11
C₁₁×C₃⋊D₂₁	13

Subgroups — C11×C13×C3⋊D21 #31825080

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×C₁₃×C₃⋊D₂₁ #31825080