Subgroups — C₉×#6180 #14516331

Order 1944.

284 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₉×H(3,𝔽₃)	C₂	1	1	yes	maximal, characteristic
2	C₃×#6180	C₃	1	1	yes	maximal, characteristic
3	C₃×C₉×C₃⋊C₈	—	3	4	no	maximal
4	C₂×C₉×H(3,𝔽₃)	C₄	1	1	yes	characteristic
5	C₃×C₄×H(3,𝔽₃)	C₂×C₃	1	1	yes	characteristic
6	C₃²×C₄×C₉	D₃	1	4	yes	—
7	C₄×C₃²⋊C₉	—	2	4	no	—
8	C₉×H(3,𝔽₃)	C₈	1	1	yes	characteristic, complemented, Sylow
9	C₃²×C₃⋊C₈	—	3	4	no	—
10	C₃×C₈×C₉	—	9	1	no	—
11	#6180	C₉	1	1	yes	characteristic, direct product factor
12	C₉×C₃⋊C₈	—	3	12	no	—
13	C₂×C₃×H(3,𝔽₃)	C₃×C₄	1	1	yes	characteristic
14	C₂×C₃²×C₉	Dic₃	1	4	yes	—
15	C₂×C₃²⋊C₉	—	2	4	no	—
16	C₃³×C₄	C₃×D₃	1	4	yes	—
17	C₄×H(3,𝔽₃)	—	2	4	no	—
18	C₄×H(3,𝔽₃)	C₂×C₉	1	1	yes	characteristic
19	C₃×C₄×C₉	—	2	4	no	—
20	C₃×C₄×C₉	—	3	12	no	—
21	C₃×C₄×C₉	C₃⋊D₃	1	1	yes	characteristic
22	C₃×H(3,𝔽₃)	C₃×C₈	1	1	yes	characteristic
23	C₃²×C₉	C₃⋊C₈	1	4	yes	complemented
24	C₃²⋊C₉	—	2	4	no	—
25	C₃²×C₈	—	9	1	no	—
26	C₃×C₃⋊C₈	—	3	4	no	—
27	C₃×C₃⋊C₈	—	3	8	no	—
28	C₃×C₃⋊C₈	—	3	4	no	—
29	C₈×C₉	—	9	3	no	—
30	C₂×C₃³	C₃×Dic₃	1	4	yes	—
31	C₂×H(3,𝔽₃)	—	2	4	no	—
32	C₂×H(3,𝔽₃)	C₄×C₉	1	1	yes	characteristic
33	C₂×C₃×C₉	—	2	4	no	—
34	C₂×C₃×C₉	—	3	12	no	—
35	C₂×C₃×C₉	C₃⋊Dic₃	1	1	yes	characteristic
36	C₃²×C₄	—	2	4	no	—
37	C₃²×C₄	—	3	4	no	—
38	C₃²×C₄	—	3	8	no	—
39	C₃²×C₄	D₃×C₉	1	4	yes	—
40	C₃²×C₄	C₃×C₃⋊D₃	1	1	yes	characteristic
41	C₄×C₉	—	6	4	no	—
42	C₄×C₉	#272	1	3	yes	—
43	C₃³	C₃×C₃⋊C₈	1	4	yes	—
44	H(3,𝔽₃)	—	2	4	no	—
45	H(3,𝔽₃)	C₈×C₉	1	1	yes	characteristic, complemented
46	C₃×C₉	—	2	4	no	—
47	C₃×C₉	—	3	12	no	—
48	C₃×C₉	C₃⋊(C₃⋊C₈)	1	1	yes	characteristic
49	C₃×C₈	—	9	1	no	—
50	C₃×C₈	—	9	1	no	—
51	C₃×C₈	—	9	2	no	—
52	C₃⋊C₈	—	3	4	no	—
53	C₂×C₃²	—	2	4	no	—
54	C₂×C₃²	—	3	4	no	—
55	C₂×C₃²	—	3	8	no	—
56	C₂×C₃²	C₉×Dic₃	1	4	yes	—
57	C₂×C₃²	C₃×C₃⋊Dic₃	1	1	yes	characteristic
58	C₂×C₉	—	6	4	no	—
59	C₂×C₉	#1084	1	3	yes	—
60	C₃×C₄	—	3	4	no	—
61	C₃×C₄	—	6	4	no	—
62	C₃×C₄	C₉×C₃⋊D₃	1	1	yes	characteristic
63	C₃×C₄	C₃×#272	1	1	yes	characteristic
64	C₃×C₄	#4208	1	2	yes	—
65	C₃²	—	2	4	no	—
66	C₃²	—	3	4	no	—
67	C₃²	—	3	8	no	—
68	C₃²	C₉×C₃⋊C₈	1	4	yes	complemented
69	C₃²	C₃×C₃⋊(C₃⋊C₈)	1	1	yes	characteristic
70	C₉	—	6	4	no	—
71	C₉	#6180	1	3	yes	direct product factor
72	C₈	—	9	1	no	Sylow
73	C₂×C₃	—	3	4	no	—
74	C₂×C₃	—	6	4	no	—
75	C₂×C₃	C₉×C₃⋊Dic₃	1	1	yes	characteristic
76	C₂×C₃	C₃×#1084	1	1	yes	characteristic
77	C₂×C₃	#66410	1	2	yes	—
78	C₄	C₉×#272	1	1	yes	characteristic
79	C₃	—	3	4	no	—
80	C₃	—	6	4	no	—
81	C₃	C₉×C₃⋊(C₃⋊C₈)	1	1	yes	characteristic
82	C₃	C₃×#6180	1	1	yes	characteristic
83	C₃	#10619725	1	2	yes	—
84	C₂	C₉×#1084	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₃×C₄×C₉	C₃⋊D₃
commutator, hypocenter	H(3,𝔽₃)	C₈×C₉
Frattini	C₃²×C₄	C₃×C₃⋊D₃
Fitting	C₄×C₉×H(3,𝔽₃)	C₂
socle	C₂×C₃²	C₃×C₃⋊Dic₃
prime radical	C₂×C₃×H(3,𝔽₃)	C₃×C₄
cosocle	C₃×C₄×H(3,𝔽₃)	C₂×C₃
LCS	G ▷ H(3,𝔽₃)
UCS	C₁ ◁ C₃×C₄×C₉

Complements

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

N	H ≅ G/N	type
8. C₉×H(3,𝔽₃)	C₈	semidirect
11. #6180	C₉	direct (N × H)
23. C₃²×C₉	C₃⋊C₈	semidirect
45. H(3,𝔽₃)	C₈×C₉	semidirect
68. C₃²	C₉×C₃⋊C₈	semidirect
71. C₉	#6180	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₉×H(3,𝔽₃)	2
C₃×#6180	3
C₃×C₉×C₃⋊C₈	3

Subgroups — C9×#6180 #14516331

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#6180 #14516331