Subgroups — C₃×C₄₇×C₂²⋊(C₁₃⋊C₃) #36347276

Order 21996.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₇×C₂²⋊(C₁₃⋊C₃)	C₃	1	3	yes	maximal, direct product factor
2	C₂²×C₃×C₁₃×C₄₇	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃×C₁₃⋊C₃×C₄₇	—	4	1	no	maximal, Hall
4	C₂×C₃×C₁₃×C₄₇	—	3	1	no	—
5	C₂²×C₁₃×C₄₇	C₃²	1	1	yes	characteristic, complemented, Hall
6	C₃×C₁₃×C₄₇	A₄	1	1	yes	characteristic, complemented
7	C₁₃⋊C₃×C₄₇	—	4	3	no	—
8	C₃×A₄×C₄₇	—	13	1	no	maximal, Hall
9	C₂×C₁₃×C₄₇	—	3	1	no	—
10	C₁₃×C₄₇	C₃×A₄	1	1	yes	characteristic, complemented, Hall
11	C₂²×C₃×C₄₇	C₁₃⋊C₃	1	1	yes	characteristic, complemented
12	A₄×C₄₇	—	13	3	no	—
13	C₃×C₂²⋊(C₁₃⋊C₃)	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₃²×C₄₇	—	52	1	no	Hall
15	C₂×C₃×C₄₇	—	3	1	no	—
16	C₂²×C₄₇	C₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
17	C₂²×C₃×C₁₃	C₃×C₄₇	1	1	yes	characteristic, complemented
18	C₂²⋊(C₁₃⋊C₃)	C₃×C₄₇	1	3	yes	direct product factor
19	C₃×C₄₇	—	52	3	no	—
20	C₃×C₄₇	C₂²⋊(C₁₃⋊C₃)	1	1	yes	characteristic, direct product factor
21	C₃×C₁₃⋊C₃	—	4	1	no	Hall
22	C₂×C₄₇	—	3	1	no	—
23	C₂×C₃×C₁₃	—	3	1	no	—
24	C₂²×C₁₃	C₃²×C₄₇	1	1	yes	characteristic, complemented, Hall
25	C₄₇	C₃×C₂²⋊(C₁₃⋊C₃)	1	1	yes	characteristic, direct product factor, Sylow
26	C₃×C₁₃	A₄×C₄₇	1	1	yes	characteristic, complemented
27	C₁₃⋊C₃	—	4	3	no	—
28	C₃×A₄	—	13	1	no	Hall
29	C₂×C₁₃	—	3	1	no	—
30	C₁₃	C₃×A₄×C₄₇	1	1	yes	characteristic, complemented, Sylow
31	C₂²×C₃	C₁₃⋊C₃×C₄₇	1	1	yes	characteristic, complemented
32	A₄	—	13	3	no	—
33	C₃²	—	52	1	no	Sylow
34	C₂×C₃	—	3	1	no	—
35	C₂²	C₃×C₁₃⋊C₃×C₄₇	1	1	yes	characteristic, complemented, Sylow
36	C₃	—	52	3	no	—
37	C₃	C₄₇×C₂²⋊(C₁₃⋊C₃)	1	1	yes	characteristic, direct product factor
38	C₂	—	3	1	no	—

	subgroup	G/H
center, hypercenter	C₃×C₄₇	C₂²⋊(C₁₃⋊C₃)
commutator, cosocle, hypocenter	C₂²×C₁₃	C₃²×C₄₇
Frattini	C₁	G
Fitting, socle	C₂²×C₃×C₁₃×C₄₇	C₃
LCS	G ▷ C₂²×C₁₃
UCS	C₁ ◁ C₃×C₄₇

Complements

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

N	H ≅ G/N	type
1. C₄₇×C₂²⋊(C₁₃⋊C₃)	C₃	direct (N × H)
2. C₂²×C₃×C₁₃×C₄₇	C₃	semidirect
5. C₂²×C₁₃×C₄₇	C₃²	semidirect
6. C₃×C₁₃×C₄₇	A₄	semidirect
10. C₁₃×C₄₇	C₃×A₄	semidirect
11. C₂²×C₃×C₄₇	C₁₃⋊C₃	semidirect
13. C₃×C₂²⋊(C₁₃⋊C₃)	C₄₇	direct (N × H)
16. C₂²×C₄₇	C₃×C₁₃⋊C₃	semidirect
17. C₂²×C₃×C₁₃	C₃×C₄₇	semidirect
18. C₂²⋊(C₁₃⋊C₃)	C₃×C₄₇	direct (N × H)
20. C₃×C₄₇	C₂²⋊(C₁₃⋊C₃)	direct (N × H)
24. C₂²×C₁₃	C₃²×C₄₇	semidirect
25. C₄₇	C₃×C₂²⋊(C₁₃⋊C₃)	direct (N × H)
26. C₃×C₁₃	A₄×C₄₇	semidirect
30. C₁₃	C₃×A₄×C₄₇	semidirect
31. C₂²×C₃	C₁₃⋊C₃×C₄₇	semidirect
35. C₂²	C₃×C₁₃⋊C₃×C₄₇	semidirect
37. C₃	C₄₇×C₂²⋊(C₁₃⋊C₃)	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄₇×C₂²⋊(C₁₃⋊C₃)	3
C₂²×C₃×C₁₃×C₄₇	3
C₃×C₁₃⋊C₃×C₄₇	4
C₃×A₄×C₄₇	13
C₃×C₂²⋊(C₁₃⋊C₃)	47

Subgroups — C3×C47×C22⋊(C13⋊C3) #36347276

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄₇×C₂²⋊(C₁₃⋊C₃) #36347276