Subgroups — C₃×C₂₉×C₂²⋊(C₃₁⋊C₃) #44569131

Order 32364.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×C₂²⋊(C₃₁⋊C₃)	C₃	1	3	yes	maximal, direct product factor
2	C₂²×C₃×C₂₉×C₃₁	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃×C₂₉×C₃₁⋊C₃	—	4	1	no	maximal, Hall
4	C₂×C₃×C₂₉×C₃₁	—	3	1	no	—
5	C₂²×C₂₉×C₃₁	C₃²	1	1	yes	characteristic, complemented, Hall
6	C₃×C₂₉×C₃₁	A₄	1	1	yes	characteristic, complemented
7	C₂₉×C₃₁⋊C₃	—	4	3	no	—
8	C₂×C₂₉×C₃₁	—	3	1	no	—
9	C₃×C₂²⋊(C₃₁⋊C₃)	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₃×A₄×C₂₉	—	31	1	no	maximal, Hall
11	C₂₉×C₃₁	C₃×A₄	1	1	yes	characteristic, complemented, Hall
12	C₂²×C₃×C₃₁	C₃×C₂₉	1	1	yes	characteristic, complemented
13	C₂²⋊(C₃₁⋊C₃)	C₃×C₂₉	1	3	yes	direct product factor
14	C₂²×C₃×C₂₉	C₃₁⋊C₃	1	1	yes	characteristic, complemented
15	A₄×C₂₉	—	31	3	no	—
16	C₃×C₃₁⋊C₃	—	4	1	no	Hall
17	C₃²×C₂₉	—	124	1	no	Hall
18	C₂×C₃×C₃₁	—	3	1	no	—
19	C₂×C₃×C₂₉	—	3	1	no	—
20	C₂²×C₃₁	C₃²×C₂₉	1	1	yes	characteristic, complemented, Hall
21	C₂²×C₂₉	C₃×C₃₁⋊C₃	1	1	yes	characteristic, complemented, Hall
22	C₃×C₃₁	A₄×C₂₉	1	1	yes	characteristic, complemented
23	C₃₁⋊C₃	—	4	3	no	—
24	C₃×C₂₉	—	124	3	no	—
25	C₃×C₂₉	C₂²⋊(C₃₁⋊C₃)	1	1	yes	characteristic, direct product factor
26	C₂×C₃₁	—	3	1	no	—
27	C₂×C₂₉	—	3	1	no	—
28	C₃×A₄	—	31	1	no	Hall
29	C₃₁	C₃×A₄×C₂₉	1	1	yes	characteristic, complemented, Sylow
30	C₂₉	C₃×C₂²⋊(C₃₁⋊C₃)	1	1	yes	characteristic, direct product factor, Sylow
31	C₂²×C₃	C₂₉×C₃₁⋊C₃	1	1	yes	characteristic, complemented
32	A₄	—	31	3	no	—
33	C₃²	—	124	1	no	Sylow
34	C₂×C₃	—	3	1	no	—
35	C₂²	C₃×C₂₉×C₃₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
36	C₃	—	124	3	no	—
37	C₃	C₂₉×C₂²⋊(C₃₁⋊C₃)	1	1	yes	characteristic, direct product factor
38	C₂	—	3	1	no	—

	subgroup	G/H
center, hypercenter	C₃×C₂₉	C₂²⋊(C₃₁⋊C₃)
commutator, cosocle, hypocenter	C₂²×C₃₁	C₃²×C₂₉
Frattini	C₁	G
Fitting, socle	C₂²×C₃×C₂₉×C₃₁	C₃
LCS	G ▷ C₂²×C₃₁
UCS	C₁ ◁ C₃×C₂₉

Complements

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

N	H ≅ G/N	type
1. C₂₉×C₂²⋊(C₃₁⋊C₃)	C₃	direct (N × H)
2. C₂²×C₃×C₂₉×C₃₁	C₃	semidirect
5. C₂²×C₂₉×C₃₁	C₃²	semidirect
6. C₃×C₂₉×C₃₁	A₄	semidirect
9. C₃×C₂²⋊(C₃₁⋊C₃)	C₂₉	direct (N × H)
11. C₂₉×C₃₁	C₃×A₄	semidirect
12. C₂²×C₃×C₃₁	C₃×C₂₉	semidirect
13. C₂²⋊(C₃₁⋊C₃)	C₃×C₂₉	direct (N × H)
14. C₂²×C₃×C₂₉	C₃₁⋊C₃	semidirect
20. C₂²×C₃₁	C₃²×C₂₉	semidirect
21. C₂²×C₂₉	C₃×C₃₁⋊C₃	semidirect
22. C₃×C₃₁	A₄×C₂₉	semidirect
25. C₃×C₂₉	C₂²⋊(C₃₁⋊C₃)	direct (N × H)
29. C₃₁	C₃×A₄×C₂₉	semidirect
30. C₂₉	C₃×C₂²⋊(C₃₁⋊C₃)	direct (N × H)
31. C₂²×C₃	C₂₉×C₃₁⋊C₃	semidirect
35. C₂²	C₃×C₂₉×C₃₁⋊C₃	semidirect
37. C₃	C₂₉×C₂²⋊(C₃₁⋊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
C₂₉×C₂²⋊(C₃₁⋊C₃)	3
C₂²×C₃×C₂₉×C₃₁	3
C₃×C₂₉×C₃₁⋊C₃	4
C₃×C₂²⋊(C₃₁⋊C₃)	29
C₃×A₄×C₂₉	31

Subgroups — C3×C29×C22⋊(C31⋊C3) #44569131

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₂₉×C₂²⋊(C₃₁⋊C₃) #44569131