Subgroups — C₂×D₃×C₃₁×C₃₁⋊C₃ #46829421

Order 34596.

188 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₃₁×C₃₁⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃×C₃₁×C₃₁⋊C₃	C₂	1	2	yes	maximal, direct product factor
3	C₂×D₃×C₃₁²	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₃₁×C₃₁⋊C₃	—	3	1	no	maximal
5	C₃×C₃₁×C₃₁⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₃×C₃₁²	C₂×C₃	1	2	yes	complemented
7	C₂×C₃₁×C₃₁⋊C₃	—	2	1	no	—
8	C₂×C₃₁×C₃₁⋊C₃	—	3	2	no	—
9	C₂×C₃₁×C₃₁⋊C₃	D₃	1	1	yes	characteristic, direct product factor
10	C₂×C₃×C₃₁²	C₂×C₃	1	1	yes	characteristic, complemented
11	C₂²×C₃₁²	—	3	1	no	Hall
12	C₃×C₃₁²	C₂²×C₃	1	1	yes	characteristic, complemented
13	C₃₁×C₃₁⋊C₃	—	2	1	no	—
14	C₃₁×C₃₁⋊C₃	C₂×D₃	1	1	yes	characteristic, direct product factor
15	C₂×C₃₁²	—	3	2	no	—
16	C₂×C₃₁²	C₃×D₃	1	1	yes	characteristic, complemented
17	C₂×C₃×D₃×C₃₁	—	31	1	no	maximal
18	C₂×D₃×C₃₁⋊C₃	C₃₁	1	1	yes	maximal, characteristic, direct product factor
19	C₃₁²	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Sylow
20	C₂×C₃²×C₃₁	—	31	1	no	—
21	C₃×D₃×C₃₁	—	31	2	no	—
22	C₂×C₃×C₃₁⋊C₃	C₂×C₃₁	1	1	yes	characteristic, complemented
23	D₃×C₃₁⋊C₃	C₂×C₃₁	1	2	yes	direct product factor
24	C₂²×C₃×C₃₁	—	93	1	no	—
25	C₂×D₃×C₃₁	—	3	10	no	—
26	C₂×D₃×C₃₁	C₃₁⋊C₃	1	1	yes	characteristic, direct product factor
27	C₂×D₃×C₃₁	C₃×C₃₁	1	1	yes	characteristic, complemented
28	C₂²×C₃₁⋊C₃	—	3	1	no	—
29	C₃²×C₃₁	—	31	1	no	—
30	C₃×C₃₁⋊C₃	C₂²×C₃₁	1	1	yes	characteristic, complemented
31	C₂×C₃×C₃₁	—	3	10	no	—
32	C₂×C₃×C₃₁	—	31	1	no	—
33	C₂×C₃×C₃₁	—	62	1	no	—
34	C₂×C₃×C₃₁	—	93	2	no	—
35	C₂×C₃×C₃₁	C₂×C₃₁⋊C₃	1	1	yes	characteristic, complemented
36	C₂×C₃×C₃₁	C₂×C₃×C₃₁	1	1	yes	characteristic, complemented
37	D₃×C₃₁	—	3	20	no	—
38	D₃×C₃₁	C₂×C₃₁⋊C₃	1	2	yes	direct product factor
39	D₃×C₃₁	C₂×C₃×C₃₁	1	2	yes	complemented
40	C₂×C₃₁⋊C₃	—	2	1	no	—
41	C₂×C₃₁⋊C₃	—	3	2	no	—
42	C₂×C₃₁⋊C₃	D₃×C₃₁	1	1	yes	characteristic, direct product factor
43	C₂²×C₃₁	—	3	1	no	—
44	C₂²×C₃₁	—	3	1	no	—
45	C₂²×C₃₁	—	9	10	no	—
46	C₃×C₃₁	—	3	10	no	—
47	C₃×C₃₁	—	31	1	no	—
48	C₃×C₃₁	—	62	1	no	—
49	C₃×C₃₁	C₂²×C₃₁⋊C₃	1	1	yes	characteristic, complemented
50	C₃×C₃₁	C₂²×C₃×C₃₁	1	1	yes	characteristic, complemented
51	C₃₁⋊C₃	—	2	1	no	—
52	C₃₁⋊C₃	C₂×D₃×C₃₁	1	1	yes	characteristic, direct product factor
53	C₂×C₃₁	—	3	2	no	—
54	C₂×C₃₁	—	3	2	no	—
55	C₂×C₃₁	—	3	10	no	—
56	C₂×C₃₁	—	9	20	no	—
57	C₂×C₃₁	D₃×C₃₁⋊C₃	1	1	yes	characteristic, direct product factor
58	C₂×C₃₁	C₃×D₃×C₃₁	1	1	yes	characteristic, complemented
59	C₂×C₃×D₃	—	31	1	no	Hall
60	C₃₁	—	3	10	no	—
61	C₃₁	C₂×D₃×C₃₁⋊C₃	1	1	yes	characteristic, direct product factor
62	C₃₁	C₂×C₃×D₃×C₃₁	1	1	yes	characteristic, complemented
63	C₂×C₃²	—	31	1	no	—
64	C₃×D₃	—	31	2	no	—
65	C₂²×C₃	—	93	1	no	—
66	C₂×D₃	C₃₁×C₃₁⋊C₃	1	1	yes	characteristic, direct product factor
67	C₃²	—	31	1	no	Sylow
68	C₂×C₃	—	31	1	no	—
69	C₂×C₃	—	62	1	no	—
70	C₂×C₃	—	93	2	no	—
71	C₂×C₃	C₂×C₃₁×C₃₁⋊C₃	1	1	yes	characteristic, complemented
72	D₃	C₂×C₃₁×C₃₁⋊C₃	1	2	yes	direct product factor
73	C₂²	—	3	1	no	Sylow
74	C₃	—	31	1	no	—
75	C₃	—	62	1	no	—
76	C₃	C₂²×C₃₁×C₃₁⋊C₃	1	1	yes	characteristic, complemented
77	C₂	—	3	2	no	—
78	C₂	D₃×C₃₁×C₃₁⋊C₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃₁	D₃×C₃₁⋊C₃
commutator, cosocle, hypocenter	C₃×C₃₁	C₂²×C₃×C₃₁
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₃₁²	C₂×C₃
LCS	G ▷ C₃×C₃₁
UCS	C₁ ◁ C₂×C₃₁

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₃₁×C₃₁⋊C₃	C₂	semidirect
2. D₃×C₃₁×C₃₁⋊C₃	C₂	direct (N × H)
3. C₂×D₃×C₃₁²	C₃	semidirect
5. C₃×C₃₁×C₃₁⋊C₃	C₂²	semidirect
6. D₃×C₃₁²	C₂×C₃	semidirect
9. C₂×C₃₁×C₃₁⋊C₃	D₃	direct (N × H)
10. C₂×C₃×C₃₁²	C₂×C₃	semidirect
12. C₃×C₃₁²	C₂²×C₃	semidirect
14. C₃₁×C₃₁⋊C₃	C₂×D₃	direct (N × H)
16. C₂×C₃₁²	C₃×D₃	semidirect
18. C₂×D₃×C₃₁⋊C₃	C₃₁	direct (N × H)
19. C₃₁²	C₂×C₃×D₃	semidirect
22. C₂×C₃×C₃₁⋊C₃	C₂×C₃₁	semidirect
23. D₃×C₃₁⋊C₃	C₂×C₃₁	direct (N × H)
26. C₂×D₃×C₃₁	C₃₁⋊C₃	direct (N × H)
27. C₂×D₃×C₃₁	C₃×C₃₁	semidirect
30. C₃×C₃₁⋊C₃	C₂²×C₃₁	semidirect
35. C₂×C₃×C₃₁	C₂×C₃₁⋊C₃	semidirect
36. C₂×C₃×C₃₁	C₂×C₃×C₃₁	semidirect
38. D₃×C₃₁	C₂×C₃₁⋊C₃	direct (N × H)
39. D₃×C₃₁	C₂×C₃×C₃₁	semidirect
42. C₂×C₃₁⋊C₃	D₃×C₃₁	direct (N × H)
49. C₃×C₃₁	C₂²×C₃₁⋊C₃	semidirect
50. C₃×C₃₁	C₂²×C₃×C₃₁	semidirect
52. C₃₁⋊C₃	C₂×D₃×C₃₁	direct (N × H)
57. C₂×C₃₁	D₃×C₃₁⋊C₃	direct (N × H)
58. C₂×C₃₁	C₃×D₃×C₃₁	semidirect
61. C₃₁	C₂×D₃×C₃₁⋊C₃	direct (N × H)
62. C₃₁	C₂×C₃×D₃×C₃₁	semidirect
66. C₂×D₃	C₃₁×C₃₁⋊C₃	direct (N × H)
71. C₂×C₃	C₂×C₃₁×C₃₁⋊C₃	semidirect
72. D₃	C₂×C₃₁×C₃₁⋊C₃	direct (N × H)
76. C₃	C₂²×C₃₁×C₃₁⋊C₃	semidirect
78. C₂	D₃×C₃₁×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
C₂×C₃×C₃₁×C₃₁⋊C₃	2
D₃×C₃₁×C₃₁⋊C₃	2
C₂×D₃×C₃₁²	3
C₂²×C₃₁×C₃₁⋊C₃	3
C₂×C₃×D₃×C₃₁	31
C₂×D₃×C₃₁⋊C₃	31

Subgroups — C2×D3×C31×C31⋊C3 #46829421

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₃×C₃₁×C₃₁⋊C₃ #46829421