Subgroups — C₉×#4430 #13133536

Order 1701.

148 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₇×C₉	C₃	1	1	yes	maximal, characteristic
2	C₃×#4430	C₃	1	1	yes	maximal, characteristic
3	C₃²⋊(C₇⋊C₉)	C₃	1	2	yes	maximal
4	(C₇⋊C₉)⋊C₉	C₃	1	6	yes	maximal, complemented
5	C₉×C₇⋊C₉	C₃	1	3	yes	maximal, complemented
6	C₉×3₋¹⁺²	—	7	1	no	maximal, Sylow
7	C₃³×C₇	C₃²	1	1	yes	characteristic
8	C₃×C₇×C₉	—	3	3	no	—
9	C₃×C₇×C₉	C₃²	1	2	yes	—
10	C₃×C₇×C₉	C₃²	1	1	yes	characteristic
11	#4430	C₉	1	9	yes	direct product factor
12	C₃×C₇⋊C₉	C₃²	1	6	yes	—
13	C₃×C₇⋊C₉	C₃²	1	3	yes	—
14	C₃×3₋¹⁺²	—	7	1	no	—
15	C₃²×C₉	ΓL(1,𝔽₈)	1	1	yes	characteristic
16	C₉⋊C₉	—	7	6	no	—
17	C₃²⋊C₉	—	7	2	no	—
18	C₉²	—	7	3	no	—
19	C₃²×C₇	—	3	1	no	—
20	C₃²×C₇	—	3	2	no	—
21	C₃²×C₇	C₃×C₉	1	3	yes	—
22	C₃²×C₇	C₃³	1	1	yes	characteristic
23	C₇×C₉	—	3	2	no	—
24	C₇×C₉	3₋¹⁺²	1	3	yes	complemented
25	C₇⋊C₉	—	3	6	no	—
26	C₇⋊C₉	C₃×C₉	1	9	yes	complemented
27	C₃³	C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic
28	3₋¹⁺²	—	7	9	no	—
29	C₃×C₉	—	3	3	no	—
30	C₃×C₉	—	7	3	no	—
31	C₃×C₉	—	7	6	no	—
32	C₃×C₉	C₃×ΓL(1,𝔽₈)	1	2	yes	—
33	C₃×C₉	C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic
34	C₃×C₇	—	3	3	no	—
35	C₃×C₇	C₃²×C₉	1	1	yes	characteristic
36	C₃×C₇	C₃×3₋¹⁺²	1	1	yes	characteristic
37	C₃×C₇	#737	1	2	yes	—
38	C₃²	—	3	2	no	—
39	C₃²	—	3	1	no	—
40	C₃²	C₉×ΓL(1,𝔽₈)	1	3	yes	—
41	C₃²	C₃²×ΓL(1,𝔽₈)	1	1	yes	characteristic
42	C₉	—	3	2	no	—
43	C₉	—	7	9	no	—
44	C₉	—	21	6	no	—
45	C₉	#4430	1	3	yes	direct product factor
46	C₇	C₉×3₋¹⁺²	1	1	yes	characteristic, complemented, Sylow
47	C₃	—	3	3	no	—
48	C₃	C₃×C₉×ΓL(1,𝔽₈)	1	1	yes	characteristic
49	C₃	#10588061	1	2	yes	—
50	C₃	C₃×#4430	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₉	C₃×ΓL(1,𝔽₈)
commutator	C₃×C₇	C₃²×C₉
Frattini	C₃²	C₃²×ΓL(1,𝔽₈)
Fitting	C₃²×C₇×C₉	C₃
socle, cosocle	C₃²×C₇	C₃³
prime radical	C₃³×C₇	C₃²
hypercenter	C₃²×C₉	ΓL(1,𝔽₈)
hypocenter	C₇	C₉×3₋¹⁺²
LCS	G ▷ C₃×C₇ ▷ C₇
UCS	C₁ ◁ C₃×C₉ ◁ C₃²×C₉

Complements

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

N	H ≅ G/N	type
4. (C₇⋊C₉)⋊C₉	C₃	semidirect
5. C₉×C₇⋊C₉	C₃	semidirect
11. #4430	C₉	direct (N × H)
24. C₇×C₉	3₋¹⁺²	semidirect
26. C₇⋊C₉	C₃×C₉	semidirect
45. C₉	#4430	direct (N × H)
46. C₇	C₉×3₋¹⁺²	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₇×C₉	3
C₃×#4430	3
C₃²⋊(C₇⋊C₉)	3
(C₇⋊C₉)⋊C₉	3
C₉×C₇⋊C₉	3
C₉×3₋¹⁺²	7

Subgroups — C9×#4430 #13133536

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#4430 #13133536