Subgroups — #21419408

Order 7533.

124 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#11719687	C₃	1	1	yes	maximal, characteristic
2	3₋¹⁺²×C₃₁⋊C₃	C₃	1	3	yes	maximal
3	#14578902	C₃	1	2	yes	maximal, complemented
4	#14578901	C₃	1	6	yes	maximal, complemented
5	C₃₁×#733	C₃	1	1	yes	maximal, characteristic, complemented
6	C₃²×C₃₁⋊C₃	C₃²	1	1	yes	characteristic
7	3₋¹⁺²×C₃₁	C₃²	1	3	yes	—
8	C₃×C₉×C₃₁	C₃²	1	1	yes	characteristic
9	#11719689	C₃²	1	6	yes	—
10	C₃×C₃₁⋊C₉	C₃²	1	2	yes	—
11	#11719687	—	3	3	no	—
12	#11719687	—	3	3	no	—
13	#11719686	—	3	3	no	—
14	C₉×C₃₁⋊C₃	—	3	3	no	—
15	C₃²×C₃₁	C₃³	1	1	yes	characteristic
16	C₃×C₃₁⋊C₃	—	9	1	no	—
17	C₃×C₃₁⋊C₃	H(3,𝔽₃)	1	3	yes	—
18	C₉×C₃₁	—	3	3	no	—
19	C₉×C₃₁	—	3	1	no	—
20	C₃₁⋊C₉	—	3	6	no	—
21	C₃₁⋊C₉	—	3	2	no	—
22	#6912	—	31	1	no	maximal, Sylow
23	C₃×C₃₁	—	3	1	no	—
24	C₃×C₃₁	C₃×H(3,𝔽₃)	1	1	yes	characteristic
25	C₃₁⋊C₃	—	3	3	no	—
26	C₃×3₋¹⁺²	—	31	1	no	—
27	C₃×3₋¹⁺²	—	31	3	no	—
28	#733	—	31	6	no	—
29	#733	—	31	2	no	—
30	#733	C₃₁⋊C₃	1	1	yes	characteristic, complemented
31	C₃₁	#6912	1	1	yes	characteristic, complemented, Sylow
32	C₃³	—	31	1	no	—
33	3₋¹⁺²	—	31	6	no	—
34	3₋¹⁺²	—	93	3	no	—
35	3₋¹⁺²	—	93	3	no	—
36	3₋¹⁺²	—	93	3	no	—
37	3₋¹⁺²	C₃×C₃₁⋊C₃	1	3	yes	—
38	C₃×C₉	—	31	2	no	—
39	C₃×C₉	—	93	3	no	—
40	C₃×C₉	C₃×C₃₁⋊C₃	1	1	yes	characteristic
41	C₃²	—	279	1	no	—
42	C₃²	—	31	3	no	—
43	C₃²	C₃²×C₃₁⋊C₃	1	1	yes	characteristic
44	C₉	—	3	3	no	—
45	C₉	—	3	1	no	—
46	C₉	—	93	2	no	—
47	C₉	—	93	6	no	—
48	C₃	—	3	1	no	—
49	C₃	—	93	3	no	—
50	C₃	H(3,𝔽₃)×C₃₁⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center	C₃	H(3,𝔽₃)×C₃₁⋊C₃
commutator	C₃²×C₃₁	C₃³
Frattini	C₃²	C₃²×C₃₁⋊C₃
Fitting	C₃₁×#733	C₃
socle	C₃×C₃₁	C₃×H(3,𝔽₃)
hypercenter	#733	C₃₁⋊C₃
hypocenter	C₃₁	#6912
LCS	G ▷ C₃²×C₃₁ ▷ C₃×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₃ ◁ C₃² ◁ #733

Complements

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

N	H ≅ G/N	type
3. #14578902	C₃	semidirect
4. #14578901	C₃	semidirect
5. C₃₁×#733	C₃	semidirect
30. #733	C₃₁⋊C₃	semidirect
31. C₃₁	#6912	semidirect