Subgroups — C₃×#22552465 #38736600

Order 25029.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#14584009	C₃	1	2	yes	maximal, complemented
2	C₃×C₃²⋊(C₁₀₃⋊C₃)	C₃	1	1	yes	maximal, characteristic
3	#22552465	C₃	1	9	yes	maximal, direct product factor
4	C₃²×C₉×C₁₀₃	C₃	1	1	yes	maximal, characteristic, complemented
5	C₃²×C₁₀₃⋊C₃	—	3	1	no	—
6	#14584009	—	3	4	no	—
7	#14584009	C₃²	1	6	yes	complemented
8	C₃²⋊(C₁₀₃⋊C₃)	—	3	2	no	—
9	C₃²⋊(C₁₀₃⋊C₃)	C₃²	1	3	yes	—
10	C₃×C₁₀₃⋊C₉	—	3	2	no	—
11	C₃³×C₁₀₃	C₃²	1	1	yes	characteristic
12	C₃×C₉×C₁₀₃	—	3	2	no	—
13	C₃×C₉×C₁₀₃	—	3	1	no	—
14	C₃×C₉×C₁₀₃	C₃²	1	3	yes	complemented
15	C₃²×C₁₀₃	—	3	3	no	—
16	C₃²×C₁₀₃	H(3,𝔽₃)	1	2	yes	—
17	C₃²×C₁₀₃	H(3,𝔽₃)	1	1	yes	characteristic
18	C₃²×C₁₀₃	C₃³	1	1	yes	characteristic
19	C₃×C₁₀₃⋊C₃	—	3	3	no	—
20	C₃×C₁₀₃⋊C₃	—	9	3	no	—
21	C₉×C₁₀₃	—	3	3	no	—
22	C₁₀₃⋊C₉	—	3	6	no	—
23	C₃×C₁₀₃	—	3	2	no	—
24	C₃×C₁₀₃	—	3	1	no	—
25	C₃×C₁₀₃	#731	1	3	yes	complemented
26	C₃×C₁₀₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
27	C₁₀₃⋊C₃	—	9	3	no	—
28	C₃×#731	—	103	1	no	maximal, Sylow
29	C₁₀₃	C₃×#731	1	1	yes	characteristic, complemented, Sylow
30	C₃×3₋¹⁺²	—	103	2	no	—
31	C₃×H(3,𝔽₃)	—	103	1	no	—
32	C₃²×C₉	C₁₀₃⋊C₃	1	1	yes	characteristic, complemented
33	#731	—	103	9	no	—
34	C₃³	—	309	1	no	—
35	C₃³	C₃×C₁₀₃⋊C₃	1	1	yes	characteristic
36	3₋¹⁺²	—	309	4	no	—
37	3₋¹⁺²	—	103	6	no	—
38	H(3,𝔽₃)	—	309	2	no	—
39	H(3,𝔽₃)	—	103	3	no	—
40	C₃×C₉	—	3	2	no	—
41	C₃×C₉	—	3	1	no	—
42	C₃×C₉	—	309	2	no	—
43	C₃×C₉	C₃×C₁₀₃⋊C₃	1	3	yes	complemented
44	C₃²	—	3	3	no	—
45	C₃²	—	309	3	no	—
46	C₃²	—	927	3	no	—
47	C₃²	C₃²⋊(C₁₀₃⋊C₃)	1	2	yes	—
48	C₃²	C₃²⋊(C₁₀₃⋊C₃)	1	1	yes	characteristic
49	C₃²	C₃²×C₁₀₃⋊C₃	1	1	yes	characteristic
50	C₉	—	3	3	no	—
51	C₉	—	309	6	no	—
52	C₃	—	3	2	no	—
53	C₃	—	3	1	no	—
54	C₃	—	927	3	no	—
55	C₃	#22552465	1	3	yes	direct product factor
56	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	C₃×C₃²⋊(C₁₀₃⋊C₃)	C₃
hypercenter	C₃²×C₉	C₁₀₃⋊C₃
hypocenter	C₁₀₃	C₃×#731
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
1. C₃×#14584009	C₃	semidirect
3. #22552465	C₃	direct (N × H)
4. C₃²×C₉×C₁₀₃	C₃	semidirect
7. #14584009	C₃²	semidirect
14. C₃×C₉×C₁₀₃	C₃²	semidirect
25. C₃×C₁₀₃	#731	semidirect
29. C₁₀₃	C₃×#731	semidirect
32. C₃²×C₉	C₁₀₃⋊C₃	semidirect
43. C₃×C₉	C₃×C₁₀₃⋊C₃	semidirect
55. C₃	#22552465	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
C₃×C₃²⋊(C₁₀₃⋊C₃)	3
#22552465	3
C₃²×C₉×C₁₀₃	3
C₃×#731	103

Subgroups — C3×#22552465 #38736600

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#22552465 #38736600