Subgroups — #21419389

Order 7533.

134 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×C₉×C₃₁⋊C₃	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	C₉×C₃₁⋊C₃	—	3	1	no	—
16	C₉×C₃₁⋊C₃	—	3	2	no	—
17	C₃²×C₃₁	—	3	3	no	—
18	C₃²×C₃₁	C₃³	1	1	yes	characteristic
19	C₃×C₃₁⋊C₃	—	3	1	no	—
20	C₃×C₃₁⋊C₃	—	3	3	no	—
21	C₉×C₃₁	—	3	1	no	—
22	C₃₁⋊C₉	—	3	1	no	—
23	C₃₁⋊C₉	—	3	6	no	—
24	C₃₁⋊C₉	H(3,𝔽₃)	1	1	yes	characteristic
25	C₃₁⋊C₉	H(3,𝔽₃)	1	2	yes	—
26	#6908	—	31	1	no	maximal, Sylow
27	C₃×C₃₁	—	3	1	no	—
28	C₃×C₃₁	—	9	3	no	—
29	C₃×C₃₁	C₃×H(3,𝔽₃)	1	1	yes	characteristic
30	C₃₁⋊C₃	—	3	3	no	—
31	#737	—	31	3	no	—
32	C₃²×C₉	—	31	1	no	—
33	#733	—	31	2	no	—
34	#732	C₃₁⋊C₃	1	1	yes	characteristic, complemented
35	#731	—	31	3	no	—
36	AΣL(1,𝔽₂₇)	—	31	3	no	—
37	C₃₁	#6908	1	1	yes	characteristic, complemented, Sylow
38	C₃³	—	31	1	no	—
39	3₋¹⁺²	—	31	6	no	—
40	3₋¹⁺²	—	93	6	no	—
41	H(3,𝔽₃)	C₃×C₃₁⋊C₃	1	3	yes	—
42	C₃×C₉	—	31	1	no	—
43	C₃×C₉	—	31	1	no	—
44	C₃×C₉	—	93	1	no	—
45	C₃×C₉	—	93	2	no	—
46	C₃×C₉	—	93	3	no	—
47	C₃×C₉	C₃×C₃₁⋊C₃	1	1	yes	characteristic
48	C₃²	—	3	3	no	—
49	C₃²	—	93	3	no	—
50	C₃²	—	93	1	no	—
51	C₃²	C₃²×C₃₁⋊C₃	1	1	yes	characteristic
52	C₉	—	3	1	no	—
53	C₉	—	31	1	no	—
54	C₉	—	31	2	no	—
55	C₉	—	93	1	no	—
56	C₉	—	93	6	no	—
57	C₃	—	3	1	no	—
58	C₃	—	9	3	no	—
59	C₃	—	93	3	no	—
60	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	#6908
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×C₉×C₃₁⋊C₃	C₃	semidirect
3. #14578902	C₃	semidirect
4. #14578896	C₃	semidirect
5. #14578893	C₃	semidirect
6. C₃₁×#732	C₃	semidirect
34. #732	C₃₁⋊C₃	semidirect
37. C₃₁	#6908	semidirect