Subgroups — C₉×#4208 #13091377

Order 1458.

434 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	C₃×#4208	C₃	1	1	yes	maximal, characteristic
3	C₉×#272	C₃	1	3	yes	maximal
4	D₃×C₉²	—	3	4	no	maximal
5	C₃×#737	C₂×C₃	1	1	yes	characteristic
6	C₉×3₋¹⁺²	—	2	12	no	—
7	C₉×H(3,𝔽₃)	C₂×C₃	1	3	yes	—
8	#6887	—	2	4	no	—
9	C₃×C₉²	D₃	1	4	yes	complemented
10	#4208	C₉	1	3	yes	direct product factor
11	C₃×#272	C₃²	1	1	yes	characteristic
12	C₃×D₃×C₉	—	3	12	no	—
13	C₃×D₃×C₉	—	3	4	no	—
14	C₂×C₉²	—	9	1	no	—
15	#737	—	2	12	no	—
16	#737	C₂×C₉	1	3	yes	complemented
17	C₃×3₋¹⁺²	—	2	4	no	—
18	C₃×H(3,𝔽₃)	C₂×C₃²	1	1	yes	characteristic
19	C₃²×C₉	C₃×D₃	1	4	yes	—
20	C₃²×C₉	C₃×D₃	1	12	yes	—
21	C₉⋊C₉	—	2	24	no	—
22	C₃²⋊C₉	—	2	12	no	—
23	C₉²	—	2	4	no	—
24	C₉²	—	2	12	no	—
25	C₉²	C₃⋊D₃	1	1	yes	characteristic
26	C₃²×D₃	—	3	4	no	—
27	C₂×C₃×C₉	—	9	1	no	—
28	C₂×C₃×C₉	—	9	3	no	—
29	#272	C₃×C₉	1	1	yes	characteristic
30	D₃×C₉	—	3	36	no	—
31	D₃×C₉	—	3	12	no	—
32	C₃³	C₃²×D₃	1	4	yes	—
33	3₋¹⁺²	—	2	24	no	—
34	3₋¹⁺²	—	2	12	no	—
35	H(3,𝔽₃)	—	2	4	no	—
36	H(3,𝔽₃)	C₂×C₃×C₉	1	1	yes	characteristic
37	C₃×C₉	—	2	4	no	—
38	C₃×C₉	—	2	12	no	—
39	C₃×C₉	—	2	12	no	—
40	C₃×C₉	—	3	36	no	—
41	C₃×C₉	D₃×C₉	1	12	yes	complemented
42	C₃×C₉	C₃×C₃⋊D₃	1	1	yes	characteristic
43	C₃×C₉	C₃×C₃⋊D₃	1	3	yes	—
44	C₂×C₃²	—	9	1	no	—
45	C₃×D₃	—	3	12	no	—
46	C₃×D₃	—	3	4	no	—
47	C₂×C₉	—	9	3	no	—
48	C₂×C₉	—	9	9	no	—
49	C₃²	—	2	4	no	—
50	C₃²	—	3	12	no	—
51	C₃²	C₃×D₃×C₉	1	4	yes	—
52	C₃²	C₃²×C₃⋊D₃	1	1	yes	characteristic
53	C₉	—	2	12	no	—
54	C₉	—	6	12	no	—
55	C₉	C₉×C₃⋊D₃	1	3	yes	—
56	C₉	#4208	1	9	yes	direct product factor
57	C₂×C₃	—	9	1	no	—
58	C₂×C₃	—	9	3	no	—
59	D₃	—	3	4	no	—
60	C₃	—	3	4	no	—
61	C₃	—	6	4	no	—
62	C₃	C₃×C₉×C₃⋊D₃	1	1	yes	characteristic
63	C₃	C₃×#4208	1	3	yes	—
64	C₂	—	9	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₉²	C₃⋊D₃
commutator, hypocenter	H(3,𝔽₃)	C₂×C₃×C₉
Frattini, socle	C₃²	C₃²×C₃⋊D₃
Fitting	C₉×#737	C₂
prime radical	C₃×#272	C₃²
cosocle	C₃×H(3,𝔽₃)	C₂×C₃²
LCS	G ▷ H(3,𝔽₃)
UCS	C₁ ◁ C₉²

Complements

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

N	H ≅ G/N	type
1. C₉×#737	C₂	semidirect
9. C₃×C₉²	D₃	semidirect
10. #4208	C₉	direct (N × H)
16. #737	C₂×C₉	semidirect
41. C₃×C₉	D₃×C₉	semidirect
56. C₉	#4208	direct (N × H)

Maximal subgroups

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

subgroup	index
C₉×#737	2
C₃×#4208	3
C₉×#272	3
D₃×C₉²	3

Subgroups — C9×#4208 #13091377

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#4208 #13091377