Subgroups — #13091524

Order 1458.

379 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10624900	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	C₃⋊#4208	—	3	1	no	maximal
3	C₉⋊#272	C₃	1	1	yes	maximal, characteristic
4	#6895⋊C₂	—	3	8	no	maximal
5	C₃⋊(D₉⋊C₉)	—	3	4	no	maximal
6	C₃×#737	D₃	1	1	yes	characteristic
7	#6895	D₃	1	8	yes	complemented
8	#6894	—	2	4	no	—
9	#6894	—	2	8	no	—
10	C₉×H(3,𝔽₃)	—	2	1	no	—
11	C₉×H(3,𝔽₃)	C₂×C₃	1	1	yes	characteristic
12	C₃×C₉⋊C₉	D₃	1	4	yes	complemented
13	C₃⋊#272	—	3	1	no	—
14	#4208	—	9	9	no	—
15	C₉×C₃⋊D₃	—	9	4	no	—
16	C₃×C₃⋊D₉	—	3	4	no	—
17	#4181	—	3	8	no	—
18	D₉⋊C₉	—	9	1	no	—
19	D₉⋊C₉	—	9	8	no	—
20	#737	—	3	9	no	—
21	C₃×3₋¹⁺²	—	2	4	no	—
22	C₃×H(3,𝔽₃)	C₃×D₃	1	1	yes	characteristic
23	C₃²×C₉	—	2	4	no	—
24	C₃²×C₉	C₃×D₃	1	4	yes	—
25	C₃²×C₉	C₃⋊D₃	1	4	yes	—
26	C₉⋊C₉	—	2	4	no	—
27	C₉⋊C₉	—	2	8	no	—
28	C₉⋊C₉	—	2	24	no	—
29	C₉⋊C₉	C₃⋊D₃	1	1	yes	characteristic
30	C₉⋊C₉	C₃⋊D₃	1	8	yes	—
31	C₃²⋊C₉	—	2	8	no	—
32	C₃²⋊C₉	C₃×D₃	1	8	yes	—
33	C₃×C₃⋊D₃	—	9	4	no	—
34	#272	—	9	9	no	—
35	C₃⋊D₉	—	3	4	no	—
36	D₃×C₉	—	27	12	no	—
37	D₃×C₉	—	27	1	no	—
38	C₃×D₉	—	9	8	no	—
39	C₃×D₉	—	9	1	no	—
40	C₃³	C₃×C₃⋊D₃	1	4	yes	—
41	3₋¹⁺²	—	6	12	no	—
42	H(3,𝔽₃)	AGL(1,ℤ/9)	1	9	yes	—
43	C₃×C₉	—	2	8	no	—
44	C₃×C₉	—	2	4	no	—
45	C₃×C₉	—	2	1	no	—
46	C₃×C₉	—	3	4	no	—
47	C₃×C₉	—	3	12	no	—
48	C₃×C₉	—	6	4	no	—
49	C₃×C₉	—	18	4	no	—
50	C₃×C₉	C₃×C₃⋊D₃	1	1	yes	characteristic
51	C₃×C₉	C₃×C₃⋊D₃	1	8	yes	—
52	C₃×C₉	C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
53	C₃⋊D₃	—	9	4	no	—
54	C₃×D₃	—	27	12	no	—
55	C₃×D₃	—	27	1	no	—
56	C₂×C₉	—	81	1	no	—
57	D₉	—	9	8	no	—
58	D₉	—	9	1	no	—
59	C₃²	—	3	4	no	—
60	C₃²	—	6	4	no	—
61	C₃²	C₃⋊AGL(1,ℤ/9)	1	12	yes	—
62	C₃²	C₃×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
63	C₉	—	2	1	no	—
64	C₉	—	3	1	no	—
65	C₉	—	3	8	no	—
66	C₉	—	6	8	no	—
67	C₉	—	6	1	no	—
68	C₉	—	6	4	no	—
69	C₉	#4208	1	1	yes	characteristic, complemented
70	C₂×C₃	—	81	1	no	—
71	D₃	—	27	12	no	—
72	D₃	—	27	1	no	—
73	C₃	—	2	1	no	—
74	C₃	—	3	12	no	—
75	C₃	C₃⋊(C₃⋊AGL(1,ℤ/9))	1	1	yes	characteristic
76	C₃	C₃⋊#4208	1	1	yes	characteristic
77	C₂	—	81	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	C₃⋊(C₃⋊AGL(1,ℤ/9))
commutator, cosocle, hypocenter	C₉×H(3,𝔽₃)	C₂×C₃
Frattini, socle	C₃²	C₃×C₃⋊(C₃⋊D₃)
Fitting	#10624900	C₂
prime radical	C₉⋊#272	C₃
LCS	G ▷ C₉×H(3,𝔽₃)
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. #10624900	C₂	semidirect
7. #6895	D₃	semidirect
12. C₃×C₉⋊C₉	D₃	semidirect
69. C₉	#4208	semidirect

Maximal subgroups

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

subgroup	index
#10624900	2
C₃⋊#4208	3
C₉⋊#272	3
#6895⋊C₂	3
C₃⋊(D₉⋊C₉)	3