Subgroups — #21419415

Order 7533.

126 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14578911	C₃	1	3	yes	maximal, complemented
2	C₃×#11719686	C₃	1	1	yes	maximal, characteristic, complemented
3	#14578902	C₃	1	2	yes	maximal, complemented
4	#14578896	C₃	1	3	yes	maximal, complemented
5	#14578893	C₃	1	3	yes	maximal, complemented
6	C₃₁×#732	C₃	1	1	yes	maximal, characteristic, complemented
7	C₃²×C₃₁⋊C₃	C₃²	1	1	yes	characteristic
8	H(3,𝔽₃)×C₃₁	C₃²	1	3	yes	—
9	C₃×C₉×C₃₁	C₃²	1	1	yes	characteristic
10	#11719689	—	3	6	no	—
11	#11719689	C₃²	1	6	yes	—
12	C₃×C₃₁⋊C₉	—	3	3	no	—
13	C₃×C₃₁⋊C₉	C₃²	1	1	yes	characteristic
14	C₃×C₃₁⋊C₉	C₃²	1	1	yes	characteristic
15	#11719686	—	3	3	no	—
16	C₃²×C₃₁	—	3	3	no	—
17	C₃²×C₃₁	C₃³	1	1	yes	characteristic
18	C₃×C₃₁⋊C₃	—	3	1	no	—
19	C₃×C₃₁⋊C₃	—	9	1	no	—
20	C₉×C₃₁	—	3	1	no	—
21	C₃₁⋊C₉	—	3	1	no	—
22	C₃₁⋊C₉	—	3	6	no	—
23	C₃₁⋊C₉	H(3,𝔽₃)	1	3	yes	—
24	#6913	—	31	1	no	maximal, Sylow
25	C₃×C₃₁	—	3	1	no	—
26	C₃×C₃₁	—	9	3	no	—
27	C₃×C₃₁	C₃×H(3,𝔽₃)	1	1	yes	characteristic
28	C₃₁⋊C₃	—	9	1	no	—
29	#737	—	31	3	no	—
30	C₃×3₋¹⁺²	—	31	1	no	—
31	#733	—	31	2	no	—
32	#732	C₃₁⋊C₃	1	1	yes	characteristic, complemented
33	#731	—	31	3	no	—
34	AΣL(1,𝔽₂₇)	—	31	3	no	—
35	C₃₁	#6913	1	1	yes	characteristic, complemented, Sylow
36	C₃³	—	31	1	no	—
37	3₋¹⁺²	—	31	6	no	—
38	3₋¹⁺²	—	93	3	no	—
39	3₋¹⁺²	—	93	6	no	—
40	H(3,𝔽₃)	C₃×C₃₁⋊C₃	1	3	yes	—
41	C₃×C₉	—	31	1	no	—
42	C₃×C₉	—	31	1	no	—
43	C₃×C₉	—	93	3	no	—
44	C₃×C₉	C₃×C₃₁⋊C₃	1	1	yes	characteristic
45	C₃²	—	3	3	no	—
46	C₃²	—	279	1	no	—
47	C₃²	—	93	1	no	—
48	C₃²	C₃²×C₃₁⋊C₃	1	1	yes	characteristic
49	C₉	—	3	1	no	—
50	C₉	—	31	3	no	—
51	C₉	—	93	1	no	—
52	C₉	—	93	6	no	—
53	C₃	—	3	1	no	—
54	C₃	—	9	3	no	—
55	C₃	—	279	1	no	—
56	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×#732	C₃
socle	C₃×C₃₁	C₃×H(3,𝔽₃)
hypercenter	#732	C₃₁⋊C₃
hypocenter	C₃₁	#6913
LCS	G ▷ C₃²×C₃₁ ▷ C₃×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₃ ◁ C₃² ◁ #732

Complements

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

N	H ≅ G/N	type
1. #14578911	C₃	semidirect
2. C₃×#11719686	C₃	semidirect
3. #14578902	C₃	semidirect
4. #14578896	C₃	semidirect
5. #14578893	C₃	semidirect
6. C₃₁×#732	C₃	semidirect
32. #732	C₃₁⋊C₃	semidirect
35. C₃₁	#6913	semidirect