Subgroups — C₃×#22552470 #38736607

Order 25029.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#14584009	C₃	1	3	yes	maximal
2	#22552470	C₃	1	9	yes	maximal, direct product factor
3	C₃²×C₉×C₁₀₃	C₃	1	1	yes	maximal, characteristic
4	#14584009	—	3	6	no	—
5	#14584009	C₃²	1	9	yes	—
6	C₃×C₁₀₃⋊C₉	—	3	3	no	—
7	C₃³×C₁₀₃	C₃²	1	1	yes	characteristic
8	C₃×C₉×C₁₀₃	—	3	2	no	—
9	C₃×C₉×C₁₀₃	—	3	1	no	—
10	C₃×C₉×C₁₀₃	C₃²	1	3	yes	—
11	C₃²×C₁₀₃	—	3	3	no	—
12	C₃²×C₁₀₃	H(3,𝔽₃)	1	2	yes	—
13	C₃²×C₁₀₃	H(3,𝔽₃)	1	1	yes	characteristic
14	C₃²×C₁₀₃	C₃³	1	1	yes	characteristic
15	C₉×C₁₀₃	—	3	3	no	—
16	C₁₀₃⋊C₉	—	3	9	no	—
17	C₃×C₁₀₃	—	3	2	no	—
18	C₃×C₁₀₃	—	3	1	no	—
19	C₃×C₁₀₃	#733	1	3	yes	complemented
20	C₃×C₁₀₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
21	C₃×#733	—	103	1	no	maximal, Sylow
22	C₁₀₃	C₃×#733	1	1	yes	characteristic, complemented, Sylow
23	C₃×3₋¹⁺²	—	103	3	no	—
24	C₃²×C₉	C₁₀₃⋊C₃	1	1	yes	characteristic
25	#733	—	103	9	no	—
26	C₃³	C₃×C₁₀₃⋊C₃	1	1	yes	characteristic
27	3₋¹⁺²	—	309	6	no	—
28	3₋¹⁺²	—	103	9	no	—
29	C₃×C₉	—	3	2	no	—
30	C₃×C₉	—	3	1	no	—
31	C₃×C₉	—	309	3	no	—
32	C₃×C₉	C₃×C₁₀₃⋊C₃	1	3	yes	—
33	C₃²	—	3	3	no	—
34	C₃²	C₃²⋊(C₁₀₃⋊C₃)	1	2	yes	—
35	C₃²	C₃²⋊(C₁₀₃⋊C₃)	1	1	yes	characteristic
36	C₃²	C₃²×C₁₀₃⋊C₃	1	1	yes	characteristic
37	C₉	—	3	3	no	—
38	C₉	—	309	9	no	—
39	C₃	—	3	2	no	—
40	C₃	—	3	1	no	—
41	C₃	#22552470	1	3	yes	direct product factor
42	C₃	C₃×C₃²⋊(C₁₀₃⋊C₃)	1	1	yes	characteristic

	subgroup	G/H
center	C₃²	C₃²⋊(C₁₀₃⋊C₃)
commutator, cosocle	C₃²×C₁₀₃	C₃³
Frattini	C₃²	C₃²×C₁₀₃⋊C₃
Fitting	C₃²×C₉×C₁₀₃	C₃
socle	C₃²×C₁₀₃	H(3,𝔽₃)
prime radical	C₃³×C₁₀₃	C₃²
hypercenter	C₃²×C₉	C₁₀₃⋊C₃
hypocenter	C₁₀₃	C₃×#733
LCS	G ▷ C₃²×C₁₀₃ ▷ C₃×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₃² ◁ C₃³ ◁ C₃²×C₉

Complements

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

N	H ≅ G/N	type
2. #22552470	C₃	direct (N × H)
19. C₃×C₁₀₃	#733	semidirect
22. C₁₀₃	C₃×#733	semidirect
41. C₃	#22552470	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×#14584009	3
#22552470	3
C₃²×C₉×C₁₀₃	3
C₃×#733	103

Subgroups — C3×#22552470 #38736607

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#22552470 #38736607