Subgroups — C₃²×D₂₉×D₃₁ #44569103

Order 32364.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₂₉×D₃₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃²×C₃₁×D₂₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×D₈₉₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×D₂₉×D₃₁	C₃	1	4	yes	maximal, direct product factor
5	C₃²×C₂₉×C₃₁	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₃×D₈₉₉	C₂×C₃	1	4	yes	complemented
7	C₃×C₃₁×D₂₉	C₂×C₃	1	4	yes	complemented
8	C₃×C₂₉×D₃₁	C₂×C₃	1	4	yes	complemented
9	D₂₉×D₃₁	C₃²	1	1	yes	characteristic, direct product factor, Hall
10	C₃×C₂₉×C₃₁	C₂²×C₃	1	4	yes	complemented
11	D₈₉₉	C₂×C₃²	1	1	yes	characteristic, complemented
12	C₂₉×D₃₁	C₂×C₃²	1	1	yes	characteristic, complemented
13	C₃₁×D₂₉	C₂×C₃²	1	1	yes	characteristic, complemented
14	C₂×C₃²×D₃₁	—	29	1	no	maximal, Hall
15	C₂×C₃²×D₂₉	—	31	1	no	maximal, Hall
16	C₂₉×C₃₁	C₂²×C₃²	1	1	yes	characteristic, complemented, Hall
17	C₂×C₃²×C₃₁	—	29	1	no	—
18	C₃²×D₃₁	—	29	1	no	—
19	C₃²×D₃₁	D₂₉	1	1	yes	characteristic, direct product factor
20	C₂×C₃²×C₂₉	—	31	1	no	—
21	C₃²×D₂₉	—	31	1	no	—
22	C₃²×D₂₉	D₃₁	1	1	yes	characteristic, direct product factor
23	C₂×C₃×D₃₁	—	29	4	no	—
24	C₂×C₃×D₂₉	—	31	4	no	—
25	C₃²×C₃₁	C₂×D₂₉	1	1	yes	characteristic, complemented, Hall
26	C₃²×C₂₉	C₂×D₃₁	1	1	yes	characteristic, complemented, Hall
27	C₂×C₃×C₃₁	—	29	4	no	—
28	C₃×D₃₁	—	29	4	no	—
29	C₃×D₃₁	C₃×D₂₉	1	4	yes	direct product factor
30	C₂×C₃×C₂₉	—	31	4	no	—
31	C₃×D₂₉	—	31	4	no	—
32	C₃×D₂₉	C₃×D₃₁	1	4	yes	direct product factor
33	C₂×D₃₁	—	29	1	no	Hall
34	C₂×D₂₉	—	31	1	no	Hall
35	C₃×C₃₁	C₂×C₃×D₂₉	1	4	yes	complemented
36	C₃×C₂₉	C₂×C₃×D₃₁	1	4	yes	complemented
37	C₂×C₃₁	—	29	1	no	—
38	D₃₁	—	29	1	no	—
39	D₃₁	C₃²×D₂₉	1	1	yes	characteristic, direct product factor
40	C₂×C₂₉	—	31	1	no	—
41	D₂₉	—	31	1	no	—
42	D₂₉	C₃²×D₃₁	1	1	yes	characteristic, direct product factor
43	C₂²×C₃²	—	899	1	no	Hall
44	C₃₁	C₂×C₃²×D₂₉	1	1	yes	characteristic, complemented, Sylow
45	C₂₉	C₂×C₃²×D₃₁	1	1	yes	characteristic, complemented, Sylow
46	C₂×C₃²	—	29	1	no	—
47	C₂×C₃²	—	31	1	no	—
48	C₂×C₃²	—	899	1	no	—
49	C₂²×C₃	—	899	4	no	—
50	C₃²	D₂₉×D₃₁	1	1	yes	characteristic, direct product factor, Sylow
51	C₂×C₃	—	29	4	no	—
52	C₂×C₃	—	31	4	no	—
53	C₂×C₃	—	899	4	no	—
54	C₂²	—	899	1	no	Sylow
55	C₃	C₃×D₂₉×D₃₁	1	4	yes	direct product factor
56	C₂	—	29	1	no	—
57	C₂	—	31	1	no	—
58	C₂	—	899	1	no	—

	subgroup	G/H
center, hypercenter	C₃²	D₂₉×D₃₁
commutator, cosocle, hypocenter	C₂₉×C₃₁	C₂²×C₃²
Frattini	C₁	G
Fitting, socle	C₃²×C₂₉×C₃₁	C₂²
LCS	G ▷ C₂₉×C₃₁
UCS	C₁ ◁ C₃²

Complements

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

N	H ≅ G/N	type
1. C₃²×C₂₉×D₃₁	C₂	semidirect
2. C₃²×C₃₁×D₂₉	C₂	semidirect
3. C₃²×D₈₉₉	C₂	semidirect
4. C₃×D₂₉×D₃₁	C₃	direct (N × H)
5. C₃²×C₂₉×C₃₁	C₂²	semidirect
6. C₃×D₈₉₉	C₂×C₃	semidirect
7. C₃×C₃₁×D₂₉	C₂×C₃	semidirect
8. C₃×C₂₉×D₃₁	C₂×C₃	semidirect
9. D₂₉×D₃₁	C₃²	direct (N × H)
10. C₃×C₂₉×C₃₁	C₂²×C₃	semidirect
11. D₈₉₉	C₂×C₃²	semidirect
12. C₂₉×D₃₁	C₂×C₃²	semidirect
13. C₃₁×D₂₉	C₂×C₃²	semidirect
16. C₂₉×C₃₁	C₂²×C₃²	semidirect
19. C₃²×D₃₁	D₂₉	direct (N × H)
22. C₃²×D₂₉	D₃₁	direct (N × H)
25. C₃²×C₃₁	C₂×D₂₉	semidirect
26. C₃²×C₂₉	C₂×D₃₁	semidirect
29. C₃×D₃₁	C₃×D₂₉	direct (N × H)
32. C₃×D₂₉	C₃×D₃₁	direct (N × H)
35. C₃×C₃₁	C₂×C₃×D₂₉	semidirect
36. C₃×C₂₉	C₂×C₃×D₃₁	semidirect
39. D₃₁	C₃²×D₂₉	direct (N × H)
42. D₂₉	C₃²×D₃₁	direct (N × H)
44. C₃₁	C₂×C₃²×D₂₉	semidirect
45. C₂₉	C₂×C₃²×D₃₁	semidirect
50. C₃²	D₂₉×D₃₁	direct (N × H)
55. C₃	C₃×D₂₉×D₃₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×C₂₉×D₃₁	2
C₃²×C₃₁×D₂₉	2
C₃²×D₈₉₉	2
C₃×D₂₉×D₃₁	3
C₂×C₃²×D₃₁	29
C₂×C₃²×D₂₉	31

Subgroups — C32×D29×D31 #44569103

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×D₂₉×D₃₁ #44569103