Subgroups — C₃×#14578897 #21419379

Order 7533.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#11719689	C₃	1	2	yes	maximal, complemented
2	C₃×C₃²⋊(C₃₁⋊C₃)	C₃	1	1	yes	maximal, characteristic
3	#14578897	C₃	1	9	yes	maximal, direct product factor
4	C₃²×C₉×C₃₁	C₃	1	1	yes	maximal, characteristic, complemented
5	C₃³×C₃₁	C₃²	1	1	yes	characteristic
6	C₃²×C₃₁⋊C₃	—	3	1	no	—
7	C₃×C₉×C₃₁	—	3	2	no	—
8	C₃×C₉×C₃₁	—	3	1	no	—
9	C₃×C₉×C₃₁	C₃²	1	3	yes	complemented
10	C₃²⋊(C₃₁⋊C₃)	—	3	2	no	—
11	C₃²⋊(C₃₁⋊C₃)	C₃²	1	3	yes	—
12	#11719689	—	3	4	no	—
13	#11719689	C₃²	1	6	yes	complemented
14	C₃×C₃₁⋊C₉	—	3	2	no	—
15	C₃²×C₃₁	—	3	3	no	—
16	C₃²×C₃₁	H(3,𝔽₃)	1	2	yes	—
17	C₃²×C₃₁	H(3,𝔽₃)	1	1	yes	characteristic
18	C₃²×C₃₁	C₃³	1	1	yes	characteristic
19	C₃×C₃₁⋊C₃	—	3	3	no	—
20	C₃×C₃₁⋊C₃	—	9	3	no	—
21	C₉×C₃₁	—	3	3	no	—
22	C₃₁⋊C₉	—	3	6	no	—
23	C₃×#731	—	31	1	no	maximal, Sylow
24	C₃×C₃₁	—	3	2	no	—
25	C₃×C₃₁	—	3	1	no	—
26	C₃×C₃₁	#731	1	3	yes	complemented
27	C₃×C₃₁	C₃×H(3,𝔽₃)	1	1	yes	characteristic
28	C₃₁⋊C₃	—	9	3	no	—
29	C₃×3₋¹⁺²	—	31	2	no	—
30	C₃×H(3,𝔽₃)	—	31	1	no	—
31	C₃²×C₉	C₃₁⋊C₃	1	1	yes	characteristic, complemented
32	#731	—	31	9	no	—
33	C₃₁	C₃×#731	1	1	yes	characteristic, complemented, Sylow
34	C₃³	—	93	1	no	—
35	C₃³	C₃×C₃₁⋊C₃	1	1	yes	characteristic
36	3₋¹⁺²	—	31	6	no	—
37	3₋¹⁺²	—	93	4	no	—
38	H(3,𝔽₃)	—	31	3	no	—
39	H(3,𝔽₃)	—	93	2	no	—
40	C₃×C₉	—	3	2	no	—
41	C₃×C₉	—	3	1	no	—
42	C₃×C₉	—	93	2	no	—
43	C₃×C₉	C₃×C₃₁⋊C₃	1	3	yes	complemented
44	C₃²	—	3	3	no	—
45	C₃²	—	279	3	no	—
46	C₃²	—	93	3	no	—
47	C₃²	C₃²⋊(C₃₁⋊C₃)	1	2	yes	—
48	C₃²	C₃²⋊(C₃₁⋊C₃)	1	1	yes	characteristic
49	C₃²	C₃²×C₃₁⋊C₃	1	1	yes	characteristic
50	C₉	—	3	3	no	—
51	C₉	—	93	6	no	—
52	C₃	—	3	2	no	—
53	C₃	—	3	1	no	—
54	C₃	—	279	3	no	—
55	C₃	#14578897	1	3	yes	direct product factor
56	C₃	C₃×C₃²⋊(C₃₁⋊C₃)	1	1	yes	characteristic

	subgroup	G/H
center	C₃²	C₃²⋊(C₃₁⋊C₃)
commutator	C₃²×C₃₁	C₃³
Frattini	C₃²	C₃²×C₃₁⋊C₃
Fitting	C₃²×C₉×C₃₁	C₃
socle	C₃²×C₃₁	H(3,𝔽₃)
hypercenter	C₃²×C₉	C₃₁⋊C₃
hypocenter	C₃₁	C₃×#731
LCS	G ▷ C₃²×C₃₁ ▷ C₃×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₃² ◁ C₃³ ◁ C₃²×C₉

Complements

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

N	H ≅ G/N	type
1. C₃×#11719689	C₃	semidirect
3. #14578897	C₃	direct (N × H)
4. C₃²×C₉×C₃₁	C₃	semidirect
9. C₃×C₉×C₃₁	C₃²	semidirect
13. #11719689	C₃²	semidirect
26. C₃×C₃₁	#731	semidirect
31. C₃²×C₉	C₃₁⋊C₃	semidirect
33. C₃₁	C₃×#731	semidirect
43. C₃×C₉	C₃×C₃₁⋊C₃	semidirect
55. C₃	#14578897	direct (N × H)

Subgroups — C3×#14578897 #21419379

Conjugacy classes of subgroups

Complements

Subgroups — C₃×#14578897 #21419379