Subgroups — D₃×C₇₃×D₃₉ #46802987

Order 34164.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₃×C₁₃×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₇₃×D₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₃×C₃⋊D₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₇₃×D₃₉	—	3	1	no	maximal
5	D₃×D₁₃×C₇₃	—	3	1	no	maximal
6	C₃²×C₁₃×C₇₃	C₂²	1	1	yes	characteristic, complemented, Hall
7	C₇₃×D₃₉	—	3	1	no	—
8	C₇₃×D₃₉	—	3	1	no	—
9	C₇₃×D₃₉	—	6	1	no	—
10	C₇₃×D₃₉	D₃	1	1	yes	characteristic, direct product factor
11	D₃×C₁₃×C₇₃	D₃	1	1	yes	characteristic, complemented
12	C₃×D₁₃×C₇₃	—	3	1	no	—
13	C₂×C₃×C₁₃×C₇₃	—	3	1	no	—
14	C₂×D₁₃×C₇₃	—	9	1	no	Hall
15	C₃×C₁₃×C₇₃	—	2	1	no	—
16	C₃×C₁₃×C₇₃	C₂×D₃	1	1	yes	characteristic, complemented
17	C₃×C₁₃×C₇₃	C₂×D₃	1	1	yes	characteristic, complemented
18	D₃²×C₇₃	—	13	1	no	maximal, Hall
19	C₂×C₁₃×C₇₃	—	3	1	no	—
20	D₁₃×C₇₃	—	3	1	no	—
21	D₁₃×C₇₃	—	9	1	no	—
22	C₃⋊D₃×C₇₃	—	13	1	no	—
23	C₃×D₃×C₇₃	—	13	1	no	—
24	C₃×D₃×C₇₃	D₁₃	1	1	yes	characteristic, complemented
25	C₁₃×C₇₃	D₃²	1	1	yes	characteristic, complemented, Hall
26	C₂×D₃×C₇₃	—	39	1	no	—
27	C₂×D₃×C₇₃	—	39	1	no	—
28	C₃²×C₇₃	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
29	D₃×D₃₉	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Hall
30	C₂×C₃×C₇₃	—	3	1	no	—
31	C₂×C₃×C₇₃	—	39	1	no	—
32	D₃×C₇₃	—	13	1	no	—
33	D₃×C₇₃	—	39	1	no	—
34	D₃×C₇₃	—	39	1	no	—
35	D₃×C₇₃	—	78	1	no	—
36	D₃×C₇₃	D₃₉	1	1	yes	characteristic, direct product factor
37	C₂²×C₇₃	—	117	1	no	Hall
38	C₃⋊D₃₉	C₂×C₇₃	1	1	yes	characteristic, complemented
39	C₃×D₃₉	C₂×C₇₃	1	1	yes	characteristic, complemented
40	C₃×D₃×C₁₃	C₂×C₇₃	1	1	yes	characteristic, complemented
41	C₃×C₇₃	—	2	1	no	—
42	C₃×C₇₃	D₃×D₁₃	1	1	yes	characteristic, complemented
43	C₃×C₇₃	C₂×D₃₉	1	1	yes	characteristic, complemented
44	C₂×D₃₉	—	3	1	no	—
45	D₃×D₁₃	—	3	1	no	—
46	C₂×C₇₃	—	3	1	no	—
47	C₂×C₇₃	—	39	1	no	—
48	C₂×C₇₃	—	117	1	no	—
49	C₃²×C₁₃	C₂²×C₇₃	1	1	yes	characteristic, complemented, Hall
50	C₂×C₃×C₁₃	—	3	1	no	—
51	D₃₉	—	3	1	no	—
52	D₃₉	—	3	1	no	—
53	D₃₉	—	6	1	no	—
54	D₃₉	D₃×C₇₃	1	1	yes	characteristic, direct product factor
55	C₃×D₁₃	—	3	1	no	—
56	D₃×C₁₃	D₃×C₇₃	1	1	yes	characteristic, complemented
57	C₇₃	D₃×D₃₉	1	1	yes	characteristic, direct product factor, Sylow
58	C₂×D₁₃	—	9	1	no	Hall
59	C₃×C₁₃	—	2	1	no	—
60	C₃×C₁₃	C₂×D₃×C₇₃	1	1	yes	characteristic, complemented
61	C₃×C₁₃	C₂×D₃×C₇₃	1	1	yes	characteristic, complemented
62	D₃²	—	13	1	no	Hall
63	C₂×C₁₃	—	3	1	no	—
64	D₁₃	—	3	1	no	—
65	D₁₃	—	9	1	no	—
66	C₃⋊D₃	—	13	1	no	—
67	C₃×D₃	—	13	1	no	—
68	C₃×D₃	D₁₃×C₇₃	1	1	yes	characteristic, complemented
69	C₁₃	D₃²×C₇₃	1	1	yes	characteristic, complemented, Sylow
70	C₂×D₃	—	39	1	no	—
71	C₂×D₃	—	39	1	no	—
72	C₃²	C₂×D₁₃×C₇₃	1	1	yes	characteristic, complemented, Sylow
73	C₂×C₃	—	3	1	no	—
74	C₂×C₃	—	39	1	no	—
75	D₃	—	13	1	no	—
76	D₃	—	39	1	no	—
77	D₃	—	39	1	no	—
78	D₃	—	78	1	no	—
79	D₃	C₇₃×D₃₉	1	1	yes	characteristic, direct product factor
80	C₂²	—	117	1	no	Sylow
81	C₃	—	2	1	no	—
82	C₃	D₃×D₁₃×C₇₃	1	1	yes	characteristic, complemented
83	C₃	C₂×C₇₃×D₃₉	1	1	yes	characteristic, complemented
84	C₂	—	3	1	no	—
85	C₂	—	39	1	no	—
86	C₂	—	117	1	no	—

	subgroup	G/H
center, hypercenter	C₇₃	D₃×D₃₉
commutator, cosocle, hypocenter	C₃²×C₁₃	C₂²×C₇₃
Frattini	C₁	G
Fitting, socle	C₃²×C₁₃×C₇₃	C₂²
LCS	G ▷ C₃²×C₁₃
UCS	C₁ ◁ C₇₃

Complements

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

N	H ≅ G/N	type
1. C₃×D₃×C₁₃×C₇₃	C₂	semidirect
2. C₃×C₇₃×D₃₉	C₂	semidirect
3. C₇₃×C₃⋊D₃₉	C₂	semidirect
6. C₃²×C₁₃×C₇₃	C₂²	semidirect
10. C₇₃×D₃₉	D₃	direct (N × H)
11. D₃×C₁₃×C₇₃	D₃	semidirect
16. C₃×C₁₃×C₇₃	C₂×D₃	semidirect
17. C₃×C₁₃×C₇₃	C₂×D₃	semidirect
24. C₃×D₃×C₇₃	D₁₃	semidirect
25. C₁₃×C₇₃	D₃²	semidirect
28. C₃²×C₇₃	C₂×D₁₃	semidirect
29. D₃×D₃₉	C₇₃	direct (N × H)
36. D₃×C₇₃	D₃₉	direct (N × H)
38. C₃⋊D₃₉	C₂×C₇₃	semidirect
39. C₃×D₃₉	C₂×C₇₃	semidirect
40. C₃×D₃×C₁₃	C₂×C₇₃	semidirect
42. C₃×C₇₃	D₃×D₁₃	semidirect
43. C₃×C₇₃	C₂×D₃₉	semidirect
49. C₃²×C₁₃	C₂²×C₇₃	semidirect
54. D₃₉	D₃×C₇₃	direct (N × H)
56. D₃×C₁₃	D₃×C₇₃	semidirect
57. C₇₃	D₃×D₃₉	direct (N × H)
60. C₃×C₁₃	C₂×D₃×C₇₃	semidirect
61. C₃×C₁₃	C₂×D₃×C₇₃	semidirect
68. C₃×D₃	D₁₃×C₇₃	semidirect
69. C₁₃	D₃²×C₇₃	semidirect
72. C₃²	C₂×D₁₃×C₇₃	semidirect
79. D₃	C₇₃×D₃₉	direct (N × H)
82. C₃	D₃×D₁₃×C₇₃	semidirect
83. C₃	C₂×C₇₃×D₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₃×D₃×C₁₃×C₇₃	2
C₃×C₇₃×D₃₉	2
C₇₃×C₃⋊D₃₉	2
C₂×C₇₃×D₃₉	3
D₃×D₁₃×C₇₃	3
D₃²×C₇₃	13
D₃×D₃₉	73

Subgroups — D3×C73×D39 #46802987

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×C₇₃×D₃₉ #46802987