Subgroups — C₃×(C₇⋊C₉)⋊C₉ #13133524

Order 1701.

180 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	C₃²×C₇⋊C₉	C₃	1	1	yes	maximal, characteristic
3	C₃²×C₇⋊C₉	C₃	1	1	yes	maximal, characteristic
4	C₃²×C₇⋊C₉	C₃	1	1	yes	maximal, characteristic
5	(C₇⋊C₉)⋊C₉	C₃	1	9	yes	maximal, direct product factor
6	C₃×C₉⋊C₉	—	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	3	yes	—
10	C₃×C₇⋊C₉	—	3	3	no	—
11	C₃×C₇⋊C₉	—	3	3	no	—
12	C₃×C₇⋊C₉	C₉	1	9	yes	complemented
13	C₃×C₇⋊C₉	C₃²	1	3	yes	—
14	C₃×C₇⋊C₉	C₃²	1	3	yes	—
15	C₃×C₇⋊C₉	C₃²	1	3	yes	—
16	C₃²×C₉	—	7	1	no	—
17	C₃²×C₉	—	7	1	no	—
18	C₃²×C₉	—	7	1	no	—
19	C₃²×C₉	ΓL(1,𝔽₈)	1	1	yes	characteristic
20	C₉⋊C₉	—	7	9	no	—
21	C₃²×C₇	C₃×C₉	1	3	yes	—
22	C₃²×C₇	3₋¹⁺²	1	3	yes	—
23	C₃²×C₇	3₋¹⁺²	1	3	yes	—
24	C₃²×C₇	3₋¹⁺²	1	3	yes	—
25	C₃²×C₇	C₃³	1	1	yes	characteristic
26	C₇×C₉	—	3	3	no	—
27	C₇⋊C₉	—	3	3	no	—
28	C₇⋊C₉	—	3	3	no	—
29	C₇⋊C₉	C₃×C₉	1	9	yes	complemented
30	C₃³	C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic
31	C₃×C₉	—	3	3	no	—
32	C₃×C₉	—	7	9	no	—
33	C₃×C₉	—	7	3	no	—
34	C₃×C₉	—	7	3	no	—
35	C₃×C₉	—	7	3	no	—
36	C₃×C₉	—	21	3	no	—
37	C₃×C₉	—	21	3	no	—
38	C₃×C₉	C₃×ΓL(1,𝔽₈)	1	3	yes	—
39	C₃×C₇	C₉⋊C₉	1	9	yes	complemented
40	C₃×C₇	C₃²×C₉	1	1	yes	characteristic
41	C₃×C₇	C₃×3₋¹⁺²	1	1	yes	characteristic
42	C₃×C₇	C₃×3₋¹⁺²	1	1	yes	characteristic
43	C₃×C₇	C₃×3₋¹⁺²	1	1	yes	characteristic
44	C₃²	C₉×ΓL(1,𝔽₈)	1	3	yes	—
45	C₃²	#4427	1	3	yes	—
46	C₃²	#4428	1	3	yes	—
47	C₃²	#4430	1	3	yes	—
48	C₃²	C₃²×ΓL(1,𝔽₈)	1	1	yes	characteristic
49	C₉	—	3	3	no	—
50	C₉	—	7	9	no	—
51	C₉	—	21	3	no	—
52	C₉	—	21	3	no	—
53	C₇	C₃×C₉⋊C₉	1	1	yes	characteristic, complemented, Sylow
54	C₃	(C₇⋊C₉)⋊C₉	1	9	yes	direct product factor
55	C₃	C₃×C₉×ΓL(1,𝔽₈)	1	1	yes	characteristic
56	C₃	C₃×#4427	1	1	yes	characteristic
57	C₃	C₃×#4428	1	1	yes	characteristic
58	C₃	C₃×#4430	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
5. (C₇⋊C₉)⋊C₉	C₃	direct (N × H)
12. C₃×C₇⋊C₉	C₉	semidirect
29. C₇⋊C₉	C₃×C₉	semidirect
39. C₃×C₇	C₉⋊C₉	semidirect
53. C₇	C₃×C₉⋊C₉	semidirect
54. C₃	(C₇⋊C₉)⋊C₉	direct (N × H)

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
C₃²×C₇⋊C₉	3
(C₇⋊C₉)⋊C₉	3
C₃×C₉⋊C₉	7

Subgroups — C3×(C7⋊C9)⋊C9 #13133524

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×(C₇⋊C₉)⋊C₉ #13133524