Subgroups — C₃×#14578893 #21419374

Order 7533.

252 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₃₁⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
2	C₃×#11719689	C₃	1	2	yes	maximal, complemented
3	#14578893	C₃	1	9	yes	maximal, direct product factor
4	C₃×H(3,𝔽₃)×C₃₁	C₃	1	1	yes	maximal, characteristic, complemented
5	C₃³×C₃₁	—	3	1	no	—
6	C₃³×C₃₁	C₃²	1	1	yes	characteristic
7	C₃²×C₃₁⋊C₃	—	3	2	no	—
8	C₃²×C₃₁⋊C₃	—	3	1	no	—
9	C₃²×C₃₁⋊C₃	—	3	9	no	—
10	C₃²×C₃₁⋊C₃	C₃²	1	3	yes	complemented
11	H(3,𝔽₃)×C₃₁	—	3	2	no	—
12	H(3,𝔽₃)×C₃₁	C₃²	1	3	yes	complemented
13	#11719689	—	3	4	no	—
14	#11719689	C₃²	1	6	yes	complemented
15	C₃×C₃₁⋊C₉	—	3	2	no	—
16	C₃²×C₃₁	—	3	3	no	—
17	C₃²×C₃₁	—	3	3	no	—
18	C₃²×C₃₁	—	9	3	no	—
19	C₃²×C₃₁	H(3,𝔽₃)	1	2	yes	—
20	C₃²×C₃₁	H(3,𝔽₃)	1	1	yes	characteristic
21	C₃²×C₃₁	C₃³	1	1	yes	characteristic
22	C₃×C₃₁⋊C₃	—	3	18	no	—
23	C₃×C₃₁⋊C₃	—	3	9	no	—
24	C₃×C₃₁⋊C₃	—	3	3	no	—
25	C₃×C₃₁⋊C₃	—	3	9	no	—
26	C₃₁⋊C₉	—	3	6	no	—
27	C₃×AΣL(1,𝔽₂₇)	—	31	1	no	maximal, Sylow
28	C₃×C₃₁	—	3	2	no	—
29	C₃×C₃₁	—	3	1	no	—
30	C₃×C₃₁	—	9	3	no	—
31	C₃×C₃₁	AΣL(1,𝔽₂₇)	1	3	yes	complemented
32	C₃×C₃₁	C₃×H(3,𝔽₃)	1	1	yes	characteristic
33	C₃₁⋊C₃	—	3	9	no	—
34	C₃⁴	—	31	1	no	—
35	C₃×3₋¹⁺²	—	31	2	no	—
36	C₃×H(3,𝔽₃)	C₃₁⋊C₃	1	1	yes	characteristic, complemented
37	AΣL(1,𝔽₂₇)	—	31	9	no	—
38	C₃₁	C₃×AΣL(1,𝔽₂₇)	1	1	yes	characteristic, complemented, Sylow
39	C₃³	—	3	1	no	—
40	C₃³	—	31	3	no	—
41	C₃³	—	93	9	no	—
42	C₃³	—	93	2	no	—
43	C₃³	—	93	1	no	—
44	C₃³	C₃×C₃₁⋊C₃	1	1	yes	characteristic
45	3₋¹⁺²	—	31	6	no	—
46	3₋¹⁺²	—	93	4	no	—
47	H(3,𝔽₃)	—	3	2	no	—
48	H(3,𝔽₃)	C₃×C₃₁⋊C₃	1	3	yes	complemented
49	C₃×C₉	—	93	2	no	—
50	C₃²	—	3	3	no	—
51	C₃²	—	3	3	no	—
52	C₃²	—	9	3	no	—
53	C₃²	—	93	9	no	—
54	C₃²	—	93	18	no	—
55	C₃²	—	93	9	no	—
56	C₃²	—	93	3	no	—
57	C₃²	C₃²⋊(C₃₁⋊C₃)	1	2	yes	—
58	C₃²	C₃²⋊(C₃₁⋊C₃)	1	1	yes	characteristic
59	C₃²	C₃²×C₃₁⋊C₃	1	1	yes	characteristic
60	C₉	—	93	6	no	—
61	C₃	—	3	2	no	—
62	C₃	—	3	1	no	—
63	C₃	—	9	3	no	—
64	C₃	—	93	9	no	—
65	C₃	#14578893	1	3	yes	direct product factor
66	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	C₃×H(3,𝔽₃)×C₃₁	C₃
socle	C₃²×C₃₁	H(3,𝔽₃)
hypercenter	C₃×H(3,𝔽₃)	C₃₁⋊C₃
hypocenter	C₃₁	C₃×AΣL(1,𝔽₂₇)
LCS	G ▷ C₃²×C₃₁ ▷ C₃×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₃² ◁ C₃³ ◁ C₃×H(3,𝔽₃)

Complements

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

N	H ≅ G/N	type
1. C₃³×C₃₁⋊C₃	C₃	semidirect
2. C₃×#11719689	C₃	semidirect
3. #14578893	C₃	direct (N × H)
4. C₃×H(3,𝔽₃)×C₃₁	C₃	semidirect
10. C₃²×C₃₁⋊C₃	C₃²	semidirect
12. H(3,𝔽₃)×C₃₁	C₃²	semidirect
14. #11719689	C₃²	semidirect
31. C₃×C₃₁	AΣL(1,𝔽₂₇)	semidirect
36. C₃×H(3,𝔽₃)	C₃₁⋊C₃	semidirect
38. C₃₁	C₃×AΣL(1,𝔽₂₇)	semidirect
48. H(3,𝔽₃)	C₃×C₃₁⋊C₃	semidirect
65. C₃	#14578893	direct (N × H)

Subgroups — C3×#14578893 #21419374

Conjugacy classes of subgroups

Complements

Subgroups — C₃×#14578893 #21419374