Subgroups — C₃×#732×C₁₀₃ #38736404

Order 25029.

168 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×H(3,𝔽₃)×C₁₀₃	C₃	1	3	yes	maximal, complemented
2	C₃²×C₉×C₁₀₃	C₃	1	1	yes	maximal, characteristic, complemented
3	#732×C₁₀₃	C₃	1	9	yes	maximal, direct product factor
4	C₃³×C₁₀₃	—	3	3	no	—
5	C₃³×C₁₀₃	C₃²	1	1	yes	characteristic
6	H(3,𝔽₃)×C₁₀₃	—	3	6	no	—
7	H(3,𝔽₃)×C₁₀₃	C₃²	1	9	yes	complemented
8	C₃×C₉×C₁₀₃	—	3	2	no	—
9	C₃×C₉×C₁₀₃	—	3	1	no	—
10	C₃×C₉×C₁₀₃	C₃²	1	3	yes	complemented
11	C₃²×C₁₀₃	—	3	3	no	—
12	C₃²×C₁₀₃	—	3	9	no	—
13	C₃²×C₁₀₃	—	9	9	no	—
14	C₃²×C₁₀₃	H(3,𝔽₃)	1	2	yes	—
15	C₃²×C₁₀₃	H(3,𝔽₃)	1	1	yes	characteristic
16	C₃²×C₁₀₃	C₃³	1	1	yes	characteristic
17	C₉×C₁₀₃	—	3	3	no	—
18	C₃×C₁₀₃	—	3	2	no	—
19	C₃×C₁₀₃	—	3	1	no	—
20	C₃×C₁₀₃	—	9	9	no	—
21	C₃×C₁₀₃	#732	1	3	yes	direct product factor
22	C₃×C₁₀₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
23	C₃×#732	C₁₀₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
24	C₁₀₃	C₃×#732	1	1	yes	characteristic, direct product factor, Sylow
25	C₃×H(3,𝔽₃)	C₃×C₁₀₃	1	3	yes	complemented
26	C₃²×C₉	C₃×C₁₀₃	1	1	yes	characteristic, complemented
27	#732	C₃×C₁₀₃	1	9	yes	direct product factor
28	C₃³	—	3	3	no	—
29	C₃³	C₃²×C₁₀₃	1	1	yes	characteristic
30	H(3,𝔽₃)	—	3	6	no	—
31	H(3,𝔽₃)	C₃²×C₁₀₃	1	9	yes	complemented
32	C₃×C₉	—	3	2	no	—
33	C₃×C₉	—	3	1	no	—
34	C₃×C₉	C₃²×C₁₀₃	1	3	yes	complemented
35	C₃²	—	3	3	no	—
36	C₃²	—	3	9	no	—
37	C₃²	—	9	9	no	—
38	C₃²	H(3,𝔽₃)×C₁₀₃	1	2	yes	—
39	C₃²	H(3,𝔽₃)×C₁₀₃	1	1	yes	characteristic
40	C₃²	C₃³×C₁₀₃	1	1	yes	characteristic
41	C₉	—	3	3	no	—
42	C₃	—	3	2	no	—
43	C₃	—	3	1	no	—
44	C₃	—	9	9	no	—
45	C₃	#732×C₁₀₃	1	3	yes	direct product factor
46	C₃	C₃×H(3,𝔽₃)×C₁₀₃	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₃²×C₁₀₃	H(3,𝔽₃)
commutator, Frattini, cosocle	C₃²	C₃³×C₁₀₃
LCS	G ▷ C₃² ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃²×C₁₀₃ ◁ C₃³×C₁₀₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×H(3,𝔽₃)×C₁₀₃	C₃	semidirect
2. C₃²×C₉×C₁₀₃	C₃	semidirect
3. #732×C₁₀₃	C₃	direct (N × H)
7. H(3,𝔽₃)×C₁₀₃	C₃²	semidirect
10. C₃×C₉×C₁₀₃	C₃²	semidirect
21. C₃×C₁₀₃	#732	direct (N × H)
23. C₃×#732	C₁₀₃	direct (N × H)
24. C₁₀₃	C₃×#732	direct (N × H)
25. C₃×H(3,𝔽₃)	C₃×C₁₀₃	semidirect
26. C₃²×C₉	C₃×C₁₀₃	semidirect
27. #732	C₃×C₁₀₃	direct (N × H)
31. H(3,𝔽₃)	C₃²×C₁₀₃	semidirect
34. C₃×C₉	C₃²×C₁₀₃	semidirect
45. C₃	#732×C₁₀₃	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×H(3,𝔽₃)×C₁₀₃	3
C₃²×C₉×C₁₀₃	3
#732×C₁₀₃	3
C₃×#732	103

Subgroups — C3×#732×C103 #38736404

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#732×C₁₀₃ #38736404