Subgroups — #731×C₁₀₃⋊C₃ #38736598

Order 25029.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	3₋¹⁺²×C₁₀₃⋊C₃	C₃	1	2	yes	maximal, complemented
2	H(3,𝔽₃)×C₁₀₃⋊C₃	C₃	1	1	yes	maximal, characteristic
3	C₃×C₉×C₁₀₃⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
4	#22552466	C₃	1	4	yes	maximal, complemented
5	#22552465	C₃	1	2	yes	maximal, complemented
6	#22552464	C₃	1	2	yes	maximal, complemented
7	#731×C₁₀₃	C₃	1	1	yes	maximal, characteristic, complemented
8	C₃²×C₁₀₃⋊C₃	—	3	1	no	—
9	C₃²×C₁₀₃⋊C₃	C₃²	1	1	yes	characteristic
10	#14584009	C₃²	1	4	yes	complemented
11	#14584008	—	3	2	no	—
12	#14584007	—	3	2	no	—
13	C₃²⋊(C₁₀₃⋊C₃)	—	3	2	no	—
14	C₃²⋊(C₁₀₃⋊C₃)	C₃²	1	2	yes	—
15	C₃×C₁₀₃⋊C₉	C₃²	1	2	yes	complemented
16	C₉×C₁₀₃⋊C₃	—	3	2	no	—
17	C₉×C₁₀₃⋊C₃	—	3	1	no	—
18	C₉×C₁₀₃⋊C₃	—	3	2	no	—
19	3₋¹⁺²×C₁₀₃	C₃²	1	2	yes	complemented
20	H(3,𝔽₃)×C₁₀₃	C₃²	1	1	yes	characteristic
21	C₃×C₉×C₁₀₃	C₃²	1	1	yes	characteristic, complemented
22	C₃²×C₁₀₃	—	3	1	no	—
23	C₃²×C₁₀₃	C₃³	1	1	yes	characteristic
24	C₃×C₁₀₃⋊C₃	—	3	3	no	—
25	C₃×C₁₀₃⋊C₃	—	3	2	no	—
26	C₃×C₁₀₃⋊C₃	—	9	3	no	—
27	C₃×C₁₀₃⋊C₃	H(3,𝔽₃)	1	2	yes	—
28	C₃×C₁₀₃⋊C₃	H(3,𝔽₃)	1	1	yes	characteristic
29	C₉×C₁₀₃	—	3	1	no	—
30	C₉×C₁₀₃	—	3	2	no	—
31	C₁₀₃⋊C₉	—	3	2	no	—
32	C₁₀₃⋊C₉	—	3	4	no	—
33	C₃×C₁₀₃	—	3	1	no	—
34	C₃×C₁₀₃	—	9	1	no	—
35	C₃×C₁₀₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
36	C₁₀₃⋊C₃	—	3	2	no	—
37	C₁₀₃⋊C₃	—	9	2	no	—
38	C₁₀₃⋊C₃	#731	1	3	yes	direct product factor
39	C₃×#731	—	103	1	no	maximal, Sylow
40	C₁₀₃	C₃×#731	1	1	yes	characteristic, complemented, Sylow
41	C₃×3₋¹⁺²	—	103	2	no	—
42	C₃×H(3,𝔽₃)	—	103	1	no	—
43	C₃²×C₉	—	103	1	no	—
44	#731	—	103	4	no	—
45	#731	—	103	2	no	—
46	#731	—	103	2	no	—
47	#731	C₁₀₃⋊C₃	1	1	yes	characteristic, direct product factor
48	C₃³	—	309	1	no	—
49	C₃³	—	103	1	no	—
50	3₋¹⁺²	—	309	2	no	—
51	3₋¹⁺²	—	309	2	no	—
52	3₋¹⁺²	—	103	4	no	—
53	3₋¹⁺²	C₃×C₁₀₃⋊C₃	1	2	yes	complemented
54	H(3,𝔽₃)	—	309	2	no	—
55	H(3,𝔽₃)	—	103	2	no	—
56	H(3,𝔽₃)	C₃×C₁₀₃⋊C₃	1	1	yes	characteristic
57	C₃×C₉	—	309	2	no	—
58	C₃×C₉	—	309	1	no	—
59	C₃×C₉	—	309	2	no	—
60	C₃×C₉	—	103	2	no	—
61	C₃×C₉	C₃×C₁₀₃⋊C₃	1	1	yes	characteristic, complemented
62	C₃²	—	3	1	no	—
63	C₃²	—	309	3	no	—
64	C₃²	—	309	2	no	—
65	C₃²	—	103	2	no	—
66	C₃²	—	103	1	no	—
67	C₃²	—	927	3	no	—
68	C₃²	C₃²×C₁₀₃⋊C₃	1	1	yes	characteristic
69	C₉	—	3	1	no	—
70	C₉	—	3	2	no	—
71	C₉	—	309	2	no	—
72	C₉	—	309	4	no	—
73	C₃	—	3	1	no	—
74	C₃	—	9	1	no	—
75	C₃	—	309	2	no	—
76	C₃	—	103	3	no	—
77	C₃	—	927	2	no	—
78	C₃	H(3,𝔽₃)×C₁₀₃⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center	C₃	H(3,𝔽₃)×C₁₀₃⋊C₃
commutator, cosocle	C₃²×C₁₀₃	C₃³
Frattini	C₃²	C₃²×C₁₀₃⋊C₃
Fitting	#731×C₁₀₃	C₃
socle	C₃×C₁₀₃	C₃×H(3,𝔽₃)
prime radical	H(3,𝔽₃)×C₁₀₃⋊C₃	C₃
hypercenter	#731	C₁₀₃⋊C₃
hypocenter	C₁₀₃	C₃×#731
LCS	G ▷ C₃²×C₁₀₃ ▷ C₃×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₃ ◁ C₃² ◁ #731

Complements

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

N	H ≅ G/N	type
1. 3₋¹⁺²×C₁₀₃⋊C₃	C₃	semidirect
3. C₃×C₉×C₁₀₃⋊C₃	C₃	semidirect
4. #22552466	C₃	semidirect
5. #22552465	C₃	semidirect
6. #22552464	C₃	semidirect
7. #731×C₁₀₃	C₃	semidirect
10. #14584009	C₃²	semidirect
15. C₃×C₁₀₃⋊C₉	C₃²	semidirect
19. 3₋¹⁺²×C₁₀₃	C₃²	semidirect
21. C₃×C₉×C₁₀₃	C₃²	semidirect
38. C₁₀₃⋊C₃	#731	direct (N × H)
40. C₁₀₃	C₃×#731	semidirect
47. #731	C₁₀₃⋊C₃	direct (N × H)
53. 3₋¹⁺²	C₃×C₁₀₃⋊C₃	semidirect
61. C₃×C₉	C₃×C₁₀₃⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
3₋¹⁺²×C₁₀₃⋊C₃	3
H(3,𝔽₃)×C₁₀₃⋊C₃	3
C₃×C₉×C₁₀₃⋊C₃	3
#22552466	3
#22552465	3
#22552464	3
#731×C₁₀₃	3
C₃×#731	103

Subgroups — #731×C103⋊C3 #38736598

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #731×C₁₀₃⋊C₃ #38736598