Subgroups — #13090778

Order 1458.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10624620	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	#92302	C₃	1	1	yes	maximal, characteristic, complemented
3	(C₃⋊D₃)⋊H(3,𝔽₃)	—	3	1	no	maximal
4	#92163	C₃	1	3	yes	maximal, complemented
5	#6891	C₂×C₃	1	1	yes	characteristic, complemented
6	C₃²⋊H(3,𝔽₃)	D₃	1	1	yes	characteristic
7	C₃×C₃²⋊C₉	—	2	1	no	—
8	#6859	—	2	3	no	—
9	#6859	C₂×C₃	1	3	yes	complemented
10	C₃²×C₃⋊D₃	—	3	1	no	—
11	C₃×AGL(1,ℤ/9)	—	9	1	no	—
12	D₃×H(3,𝔽₃)	—	9	1	no	—
13	C₃×(C₃⋊D₃)⋊C₃	—	3	3	no	—
14	#4181	C₃²	1	1	yes	characteristic
15	C₃⁴	C₃×D₃	1	1	yes	characteristic
16	C₃×3₋¹⁺²	—	3	1	no	—
17	C₃×H(3,𝔽₃)	—	3	1	no	—
18	C₃×H(3,𝔽₃)	—	6	1	no	—
19	C₃×H(3,𝔽₃)	C₃×D₃	1	3	yes	—
20	C₃²×C₉	—	6	1	no	—
21	C₃²⋊C₉	—	2	1	no	—
22	C₃²⋊C₉	—	2	3	no	—
23	C₃²⋊C₉	—	6	1	no	—
24	C₃²⋊C₉	—	6	1	no	—
25	C₃²⋊C₉	—	6	1	no	—
26	C₃²⋊C₉	C₂×C₃²	1	1	yes	characteristic
27	C₃×C₃⋊D₃	—	3	1	no	—
28	C₃×C₃⋊D₃	—	9	1	no	—
29	C₃²×D₃	—	9	3	no	—
30	C₃²×D₃	—	9	1	no	—
31	C₃²×D₃	—	27	1	no	—
32	C₂×H(3,𝔽₃)	—	27	1	no	—
33	AGL(1,ℤ/9)	—	9	3	no	—
34	(C₃⋊D₃)⋊C₃	—	9	3	no	—
35	C₃×D₉	—	9	1	no	—
36	C₃³	—	2	1	no	—
37	C₃³	—	3	3	no	—
38	C₃³	—	6	3	no	—
39	C₃³	—	9	1	no	—
40	C₃³	—	9	1	no	—
41	C₃³	(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
42	C₃³	C₃²×D₃	1	1	yes	characteristic
43	3₋¹⁺²	—	9	3	no	—
44	H(3,𝔽₃)	—	9	3	no	—
45	H(3,𝔽₃)	—	9	1	no	—
46	H(3,𝔽₃)	—	18	3	no	—
47	H(3,𝔽₃)	—	18	1	no	—
48	C₃×C₉	—	3	1	no	—
49	C₃×C₉	—	6	3	no	—
50	C₃×C₉	—	6	1	no	—
51	C₃×C₉	—	18	3	no	—
52	C₂×C₃²	—	27	1	no	—
53	C₂×C₃²	—	27	3	no	—
54	C₃⋊D₃	—	3	1	no	—
55	C₃×D₃	—	9	1	no	—
56	C₃×D₃	—	27	1	no	—
57	C₃×D₃	—	27	3	no	—
58	C₃×D₃	—	27	1	no	—
59	C₃×D₃	—	27	3	no	—
60	D₉	—	9	1	no	—
61	C₃²	—	2	3	no	—
62	C₃²	—	3	1	no	—
63	C₃²	—	3	1	no	—
64	C₃²	—	3	1	no	—
65	C₃²	—	3	1	no	—
66	C₃²	—	6	1	no	—
67	C₃²	—	6	1	no	—
68	C₃²	—	6	1	no	—
69	C₃²	—	6	1	no	—
70	C₃²	—	6	1	no	—
71	C₃²	—	9	3	no	—
72	C₃²	—	9	3	no	—
73	C₃²	—	9	3	no	—
74	C₃²	—	18	3	no	—
75	C₃²	—	18	3	no	—
76	C₃²	C₃×(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
77	C₉	—	9	1	no	—
78	C₉	—	18	1	no	—
79	C₉	—	18	3	no	—
80	C₂×C₃	—	27	1	no	—
81	C₂×C₃	—	81	1	no	—
82	C₂×C₃	—	81	3	no	—
83	D₃	—	9	1	no	—
84	D₃	—	27	1	no	—
85	C₃	—	2	1	no	—
86	C₃	—	6	3	no	—
87	C₃	—	9	1	no	—
88	C₃	—	9	1	no	—
89	C₃	—	27	3	no	—
90	C₃	#92281	1	1	yes	characteristic
91	C₃	#4179⋊C₃	1	1	yes	characteristic
92	C₂	—	27	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	#4179⋊C₃
commutator, cosocle, hypocenter	C₃²⋊C₉	C₂×C₃²
Frattini	C₃³	C₃²×D₃
Fitting	#10624620	C₂
socle	C₃²	C₃×(C₃⋊D₃)⋊C₃
LCS	G ▷ C₃²⋊C₉
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. #10624620	C₂	semidirect
2. #92302	C₃	semidirect
4. #92163	C₃	semidirect
5. #6891	C₂×C₃	semidirect
9. #6859	C₂×C₃	semidirect

Maximal subgroups

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

subgroup	index
#10624620	2
#92302	3
(C₃⋊D₃)⋊H(3,𝔽₃)	3
#92163	3