Subgroups — C₉×C₄₇×#733 #46804360

Order 34263.

274 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄₇×#733	C₃	1	1	yes	maximal, characteristic
2	C₉×3₋¹⁺²×C₄₇	C₃	1	3	yes	maximal
3	C₃×C₉²×C₄₇	C₃	1	1	yes	maximal, characteristic
4	C₄₇×3₋¹⁺²⋊C₉	C₃	1	6	yes	maximal
5	C₄₇×#6868	C₃	1	2	yes	maximal
6	C₃×3₋¹⁺²×C₄₇	C₃²	1	3	yes	—
7	C₃²×C₉×C₄₇	C₃²	1	2	yes	—
8	C₃²×C₉×C₄₇	C₃²	1	1	yes	characteristic
9	C₃²×C₉×C₄₇	C₃²	1	1	yes	characteristic
10	C₄₇×#733	C₉	1	9	yes	direct product factor
11	C₄₇×C₉⋊C₉	—	3	6	no	—
12	C₄₇×C₃²⋊C₉	C₃²	1	6	yes	—
13	C₉²×C₄₇	—	3	2	no	—
14	C₉²×C₄₇	—	3	1	no	—
15	C₉²×C₄₇	—	3	3	no	—
16	C₃³×C₄₇	C₃³	1	1	yes	characteristic
17	3₋¹⁺²×C₄₇	—	3	6	no	—
18	3₋¹⁺²×C₄₇	C₃×C₉	1	9	yes	—
19	C₃×C₉×C₄₇	—	3	1	no	—
20	C₃×C₉×C₄₇	—	3	2	no	—
21	C₃×C₉×C₄₇	—	3	3	no	—
22	C₃×C₉×C₄₇	—	3	2	no	—
23	C₃×C₉×C₄₇	—	3	3	no	—
24	C₃×C₉×C₄₇	—	3	6	no	—
25	C₃×C₉×C₄₇	—	3	6	no	—
26	C₃×C₉×C₄₇	C₃×C₉	1	3	yes	—
27	C₃×C₉×C₄₇	H(3,𝔽₃)	1	2	yes	—
28	C₃×C₉×C₄₇	H(3,𝔽₃)	1	1	yes	characteristic
29	C₉×#733	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
30	C₃²×C₄₇	—	3	1	no	—
31	C₃²×C₄₇	—	3	2	no	—
32	C₃²×C₄₇	C₃²×C₉	1	1	yes	characteristic
33	C₃²×C₄₇	C₃×H(3,𝔽₃)	1	1	yes	characteristic
34	C₃²×C₄₇	#737	1	2	yes	—
35	C₉×C₄₇	—	3	3	no	—
36	C₉×C₄₇	—	3	9	no	—
37	C₉×C₄₇	—	3	2	no	—
38	C₉×C₄₇	—	3	6	no	—
39	C₉×C₄₇	—	9	6	no	—
40	C₉×C₄₇	#733	1	3	yes	direct product factor
41	C₃×#733	C₃×C₄₇	1	1	yes	characteristic
42	C₉×3₋¹⁺²	C₃×C₄₇	1	3	yes	—
43	C₃×C₉²	C₃×C₄₇	1	1	yes	characteristic
44	3₋¹⁺²⋊C₉	C₃×C₄₇	1	6	yes	—
45	#6868	C₃×C₄₇	1	2	yes	—
46	C₃×C₄₇	—	3	1	no	—
47	C₃×C₄₇	—	3	2	no	—
48	C₃×C₄₇	C₉×H(3,𝔽₃)	1	1	yes	characteristic
49	C₃×C₄₇	C₃×#733	1	1	yes	characteristic
50	C₃×C₄₇	#6908	1	2	yes	—
51	C₃×3₋¹⁺²	C₃²×C₄₇	1	3	yes	—
52	C₃²×C₉	C₃²×C₄₇	1	2	yes	—
53	C₃²×C₉	C₃²×C₄₇	1	1	yes	characteristic
54	C₃²×C₉	C₃²×C₄₇	1	1	yes	characteristic
55	#733	C₉×C₄₇	1	9	yes	direct product factor
56	C₉⋊C₉	—	3	6	no	—
57	C₃²⋊C₉	C₃²×C₄₇	1	6	yes	—
58	C₉²	—	3	2	no	—
59	C₉²	—	3	1	no	—
60	C₉²	—	3	3	no	—
61	C₄₇	C₉×#733	1	1	yes	characteristic, direct product factor, Sylow
62	C₃³	C₃³×C₄₇	1	1	yes	characteristic
63	3₋¹⁺²	—	3	6	no	—
64	3₋¹⁺²	C₃×C₉×C₄₇	1	9	yes	—
65	C₃×C₉	—	3	1	no	—
66	C₃×C₉	—	3	2	no	—
67	C₃×C₉	—	3	3	no	—
68	C₃×C₉	—	3	2	no	—
69	C₃×C₉	—	3	3	no	—
70	C₃×C₉	—	3	6	no	—
71	C₃×C₉	—	3	6	no	—
72	C₃×C₉	C₃×C₉×C₄₇	1	3	yes	—
73	C₃×C₉	H(3,𝔽₃)×C₄₇	1	2	yes	—
74	C₃×C₉	H(3,𝔽₃)×C₄₇	1	1	yes	characteristic
75	C₃²	—	3	1	no	—
76	C₃²	—	3	2	no	—
77	C₃²	C₃²×C₉×C₄₇	1	1	yes	characteristic
78	C₃²	C₃×H(3,𝔽₃)×C₄₇	1	1	yes	characteristic
79	C₃²	C₄₇×#737	1	2	yes	—
80	C₉	—	3	3	no	—
81	C₉	—	3	9	no	—
82	C₉	—	3	2	no	—
83	C₉	—	3	6	no	—
84	C₉	—	9	6	no	—
85	C₉	C₄₇×#733	1	3	yes	direct product factor
86	C₃	—	3	1	no	—
87	C₃	—	3	2	no	—
88	C₃	C₉×H(3,𝔽₃)×C₄₇	1	1	yes	characteristic
89	C₃	C₃×C₄₇×#733	1	1	yes	characteristic
90	C₃	C₄₇×#6908	1	2	yes	—

	subgroup	G/H
center	C₃×C₉×C₄₇	H(3,𝔽₃)
commutator	C₃²	C₃²×C₉×C₄₇
Frattini, cosocle	C₃³	C₃³×C₄₇
socle	C₃²×C₄₇	C₃×H(3,𝔽₃)
prime radical	C₃³×C₄₇	C₃³
LCS	G ▷ C₃² ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃×C₉×C₄₇ ◁ C₃²×C₉×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
10. C₄₇×#733	C₉	direct (N × H)
29. C₉×#733	C₄₇	direct (N × H)
40. C₉×C₄₇	#733	direct (N × H)
55. #733	C₉×C₄₇	direct (N × H)
61. C₄₇	C₉×#733	direct (N × H)
85. C₉	C₄₇×#733	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₄₇×#733	3
C₉×3₋¹⁺²×C₄₇	3
C₃×C₉²×C₄₇	3
C₄₇×3₋¹⁺²⋊C₉	3
C₄₇×#6868	3
C₉×#733	47

Subgroups — C9×C47×#733 #46804360

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×C₄₇×#733 #46804360