Subgroups — D₉×#737 #13091374

Order 1458.

395 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#737	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	D₃×#737	—	3	1	no	maximal
3	D₉×3₋¹⁺²	C₃	1	8	yes	maximal, complemented
4	D₉×H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic
5	C₃×C₉×D₉	C₃	1	4	yes	maximal, complemented
6	C₃×#737	D₃	1	1	yes	characteristic
7	C₉×3₋¹⁺²	—	2	8	no	—
8	C₉×3₋¹⁺²	C₂×C₃	1	8	yes	complemented
9	C₉×H(3,𝔽₃)	—	2	1	no	—
10	C₉×H(3,𝔽₃)	C₂×C₃	1	1	yes	characteristic
11	#6887	—	2	4	no	—
12	C₃×C₉²	C₂×C₃	1	4	yes	complemented
13	C₂×#737	—	9	1	no	—
14	D₃×3₋¹⁺²	—	3	8	no	—
15	D₃×H(3,𝔽₃)	—	3	1	no	—
16	C₃×D₃×C₉	—	3	4	no	—
17	C₃²×D₉	C₃²	1	4	yes	—
18	C₉×D₉	C₃²	1	1	yes	characteristic
19	C₉×D₉	C₃²	1	8	yes	—
20	#737	—	2	8	no	—
21	#737	—	2	1	no	—
22	#737	—	2	4	no	—
23	#737	D₉	1	1	yes	characteristic, direct product factor
24	C₃×3₋¹⁺²	C₃×D₃	1	8	yes	—
25	C₃×H(3,𝔽₃)	C₃×D₃	1	1	yes	characteristic
26	C₃²×C₉	—	2	4	no	—
27	C₃²×C₉	C₃×D₃	1	4	yes	—
28	C₃²×C₉	C₂×C₃²	1	4	yes	—
29	C₉⋊C₉	—	2	24	no	—
30	C₃²⋊C₉	—	2	8	no	—
31	C₃²⋊C₉	—	2	4	no	—
32	C₉²	—	2	4	no	—
33	C₉²	—	2	8	no	—
34	C₉²	C₂×C₃²	1	1	yes	characteristic
35	C₉²	C₂×C₃²	1	8	yes	—
36	C₃²×D₃	—	3	4	no	—
37	C₂×3₋¹⁺²	—	9	8	no	—
38	C₂×H(3,𝔽₃)	—	9	1	no	—
39	C₂×C₃×C₉	—	9	4	no	—
40	D₃×C₉	—	3	1	no	—
41	D₃×C₉	—	3	8	no	—
42	C₃×D₉	—	3	4	no	—
43	C₃×D₉	C₃³	1	1	yes	characteristic
44	C₃³	C₃²×D₃	1	4	yes	—
45	3₋¹⁺²	—	2	8	no	—
46	3₋¹⁺²	—	2	24	no	—
47	3₋¹⁺²	C₃×D₉	1	8	yes	complemented
48	H(3,𝔽₃)	—	2	4	no	—
49	H(3,𝔽₃)	C₃×D₉	1	1	yes	characteristic
50	C₃×C₉	—	2	4	no	—
51	C₃×C₉	—	2	1	no	—
52	C₃×C₉	—	2	8	no	—
53	C₃×C₉	—	2	4	no	—
54	C₃×C₉	—	2	4	no	—
55	C₃×C₉	—	2	8	no	—
56	C₃×C₉	—	3	4	no	—
57	C₃×C₉	—	6	12	no	—
58	C₃×C₉	—	6	4	no	—
59	C₃×C₉	C₃×D₉	1	4	yes	complemented
60	C₃×C₉	C₃²×D₃	1	8	yes	—
61	C₃×C₉	C₃²×D₃	1	1	yes	characteristic
62	C₃×C₉	C₂×C₃³	1	1	yes	characteristic
63	C₂×C₃²	—	9	4	no	—
64	C₃×D₃	—	3	1	no	—
65	C₃×D₃	—	9	4	no	—
66	C₂×C₉	—	9	8	no	—
67	C₂×C₉	—	9	1	no	—
68	D₉	#737	1	1	yes	characteristic, direct product factor
69	C₃²	—	2	4	no	—
70	C₃²	—	3	4	no	—
71	C₃²	—	6	4	no	—
72	C₃²	C₃²×D₉	1	4	yes	—
73	C₃²	C₃³×D₃	1	1	yes	characteristic
74	C₉	—	2	3	no	—
75	C₉	—	2	1	no	—
76	C₉	—	2	8	no	—
77	C₉	—	2	1	no	—
78	C₉	—	6	8	no	—
79	C₉	—	6	4	no	—
80	C₉	C₃²×D₉	1	8	yes	—
81	C₉	C₃²×D₉	1	1	yes	characteristic
82	C₉	C₂×#737	1	1	yes	characteristic, complemented
83	C₂×C₃	—	9	1	no	—
84	C₂×C₃	—	27	4	no	—
85	D₃	—	3	1	no	—
86	C₃	—	2	1	no	—
87	C₃	—	3	4	no	—
88	C₃	—	6	4	no	—
89	C₃	C₃³×D₉	1	1	yes	characteristic
90	C₃	D₃×#737	1	1	yes	characteristic
91	C₂	—	9	1	no	Sylow

	subgroup	G/H
center	C₉	C₃²×D₉
commutator, cosocle	C₃×C₉	C₂×C₃³
Frattini, socle	C₃²	C₃³×D₃
Fitting	C₉×#737	C₂
prime radical	D₉×H(3,𝔽₃)	C₃
hypercenter	#737	D₉
hypocenter	C₉	C₂×#737
LCS	G ▷ C₃×C₉ ▷ C₉
UCS	C₁ ◁ C₉ ◁ #737

Complements

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

N	H ≅ G/N	type
1. C₉×#737	C₂	semidirect
3. D₉×3₋¹⁺²	C₃	semidirect
5. C₃×C₉×D₉	C₃	semidirect
8. C₉×3₋¹⁺²	C₂×C₃	semidirect
12. C₃×C₉²	C₂×C₃	semidirect
23. #737	D₉	direct (N × H)
47. 3₋¹⁺²	C₃×D₉	semidirect
59. C₃×C₉	C₃×D₉	semidirect
68. D₉	#737	direct (N × H)
82. C₉	C₂×#737	semidirect

Maximal subgroups

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

subgroup	index
C₉×#737	2
D₃×#737	3
D₉×3₋¹⁺²	3
D₉×H(3,𝔽₃)	3
C₃×C₉×D₉	3

Subgroups — D9×#737 #13091374

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₉×#737 #13091374