Subgroups — C₃×C₃²⋊(C₇⋊C₉) #13133522

Order 1701.

288 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⁴×C₇	C₃	1	1	yes	maximal, characteristic
2	C₃²×C₇⋊C₉	C₃	1	3	yes	maximal, complemented
3	C₃²⋊(C₇⋊C₉)	C₃	1	9	yes	maximal, direct product factor
4	C₃×C₃²⋊C₉	—	7	1	no	maximal, Sylow
5	C₃³×C₇	—	3	3	no	—
6	C₃³×C₇	—	3	6	no	—
7	C₃³×C₇	C₉	1	9	yes	complemented
8	C₃³×C₇	C₃²	1	3	yes	—
9	C₃³×C₇	C₃²	1	1	yes	characteristic
10	C₃×C₇⋊C₉	—	3	9	no	—
11	C₃×C₇⋊C₉	C₃²	1	9	yes	complemented
12	C₃⁴	ΓL(1,𝔽₈)	1	1	yes	characteristic
13	C₃²×C₉	—	7	3	no	—
14	C₃²⋊C₉	—	7	9	no	—
15	C₃²×C₇	—	3	27	no	—
16	C₃²×C₇	—	3	3	no	—
17	C₃²×C₇	—	3	6	no	—
18	C₃²×C₇	C₃×C₉	1	3	yes	—
19	C₃²×C₇	C₃×C₉	1	9	yes	complemented
20	C₃²×C₇	H(3,𝔽₃)	1	3	yes	—
21	C₃²×C₇	3₋¹⁺²	1	6	yes	—
22	C₃²×C₇	C₃³	1	1	yes	characteristic
23	C₇⋊C₉	—	3	9	no	—
24	C₃³	—	3	6	no	—
25	C₃³	—	3	3	no	—
26	C₃³	C₇⋊C₉	1	9	yes	complemented
27	C₃³	C₃×ΓL(1,𝔽₈)	1	3	yes	—
28	C₃³	C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic
29	C₃×C₉	—	7	9	no	—
30	C₃×C₉	—	21	9	no	—
31	C₃×C₇	—	3	9	no	—
32	C₃×C₇	C₃²⋊C₉	1	9	yes	complemented
33	C₃×C₇	C₃²×C₉	1	1	yes	characteristic
34	C₃×C₇	C₃×H(3,𝔽₃)	1	1	yes	characteristic
35	C₃×C₇	C₃×3₋¹⁺²	1	2	yes	—
36	C₃²	—	3	27	no	—
37	C₃²	—	3	6	no	—
38	C₃²	—	3	3	no	—
39	C₃²	C₃×C₇⋊C₉	1	3	yes	—
40	C₃²	C₃×C₇⋊C₉	1	9	yes	complemented
41	C₃²	#4430	1	6	yes	—
42	C₃²	C₇⋊H(3,𝔽₃)	1	3	yes	—
43	C₃²	C₃²×ΓL(1,𝔽₈)	1	1	yes	characteristic
44	C₉	—	21	9	no	—
45	C₇	C₃×C₃²⋊C₉	1	1	yes	characteristic, complemented, Sylow
46	C₃	—	3	9	no	—
47	C₃	C₃²⋊(C₇⋊C₉)	1	9	yes	direct product factor
48	C₃	C₃²×C₇⋊C₉	1	1	yes	characteristic
49	C₃	C₃×#4430	1	2	yes	—
50	C₃	C₃×C₇⋊H(3,𝔽₃)	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, prime radical	C₃⁴×C₇	C₃
socle	C₃³×C₇	C₃²
cosocle	C₃²×C₇	C₃³
hypercenter	C₃⁴	ΓL(1,𝔽₈)
hypocenter	C₇	C₃×C₃²⋊C₉
LCS	G ▷ C₃×C₇ ▷ C₇
UCS	C₁ ◁ C₃³ ◁ C₃⁴

Complements

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

N	H ≅ G/N	type
2. C₃²×C₇⋊C₉	C₃	semidirect
3. C₃²⋊(C₇⋊C₉)	C₃	direct (N × H)
7. C₃³×C₇	C₉	semidirect
11. C₃×C₇⋊C₉	C₃²	semidirect
19. C₃²×C₇	C₃×C₉	semidirect
26. C₃³	C₇⋊C₉	semidirect
32. C₃×C₇	C₃²⋊C₉	semidirect
40. C₃²	C₃×C₇⋊C₉	semidirect
45. C₇	C₃×C₃²⋊C₉	semidirect
47. C₃	C₃²⋊(C₇⋊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
C₃⁴×C₇	3
C₃²×C₇⋊C₉	3
C₃²⋊(C₇⋊C₉)	3
C₃×C₃²⋊C₉	7

Subgroups — C3×C32⋊(C7⋊C9) #13133522

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₃²⋊(C₇⋊C₉) #13133522