Subgroups — #21419391

Order 7533.

134 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14578912	C₃	1	3	yes	maximal, complemented
2	#14578902	C₃	1	2	yes	maximal, complemented
3	#14578900	C₃	1	1	yes	maximal, characteristic, complemented
4	#14578897	C₃	1	3	yes	maximal, complemented
5	#14578894	C₃	1	3	yes	maximal, complemented
6	C₃²×C₉×C₃₁	C₃	1	1	yes	maximal, characteristic, complemented
7	C₃³×C₃₁	C₃²	1	1	yes	characteristic
8	C₃×C₉×C₃₁	—	3	1	no	—
9	C₃×C₉×C₃₁	—	3	1	no	—
10	C₃×C₉×C₃₁	—	3	1	no	—
11	C₃×C₉×C₃₁	C₃²	1	1	yes	characteristic
12	C₃×C₉×C₃₁	C₃²	1	1	yes	characteristic
13	C₃×C₉×C₃₁	C₃²	1	1	yes	characteristic
14	C₃²⋊(C₃₁⋊C₃)	C₃²	1	3	yes	—
15	#11719689	C₃²	1	6	yes	—
16	#11719687	—	3	3	no	—
17	#11719686	—	3	3	no	—
18	C₉×C₃₁⋊C₃	—	3	3	no	—
19	C₃²×C₃₁	—	3	3	no	—
20	C₃²×C₃₁	—	3	1	no	—
21	C₃²×C₃₁	C₃³	1	1	yes	characteristic
22	C₃×C₃₁⋊C₃	—	3	3	no	—
23	C₉×C₃₁	—	3	1	no	—
24	C₉×C₃₁	—	3	1	no	—
25	C₉×C₃₁	H(3,𝔽₃)	1	1	yes	characteristic
26	C₉×C₃₁	H(3,𝔽₃)	1	1	yes	characteristic
27	C₉×C₃₁	H(3,𝔽₃)	1	1	yes	characteristic
28	C₃₁⋊C₉	—	3	6	no	—
29	#6908	—	31	1	no	maximal, Sylow
30	C₃×C₃₁	—	3	3	no	—
31	C₃×C₃₁	—	3	1	no	—
32	C₃×C₃₁	C₃×H(3,𝔽₃)	1	1	yes	characteristic
33	C₃₁⋊C₃	—	9	3	no	—
34	#737	—	31	3	no	—
35	C₃²×C₉	C₃₁⋊C₃	1	1	yes	characteristic, complemented
36	#733	—	31	2	no	—
37	#732	—	31	1	no	—
38	#731	—	31	3	no	—
39	AΣL(1,𝔽₂₇)	—	31	3	no	—
40	C₃₁	#6908	1	1	yes	characteristic, complemented, Sylow
41	C₃³	C₃×C₃₁⋊C₃	1	1	yes	characteristic
42	3₋¹⁺²	—	31	6	no	—
43	3₋¹⁺²	—	93	3	no	—
44	3₋¹⁺²	—	93	3	no	—
45	H(3,𝔽₃)	—	31	3	no	—
46	C₃×C₉	—	3	1	no	—
47	C₃×C₉	—	3	1	no	—
48	C₃×C₉	—	3	1	no	—
49	C₃×C₉	—	93	3	no	—
50	C₃×C₉	C₃×C₃₁⋊C₃	1	1	yes	characteristic
51	C₃×C₉	C₃×C₃₁⋊C₃	1	1	yes	characteristic
52	C₃×C₉	C₃×C₃₁⋊C₃	1	1	yes	characteristic
53	C₃²	—	3	3	no	—
54	C₃²	—	3	1	no	—
55	C₃²	—	93	3	no	—
56	C₃²	C₃²×C₃₁⋊C₃	1	1	yes	characteristic
57	C₉	—	3	1	no	—
58	C₉	—	3	1	no	—
59	C₉	—	93	6	no	—
60	C₉	C₃²⋊(C₃₁⋊C₃)	1	1	yes	characteristic
61	C₉	C₃²⋊(C₃₁⋊C₃)	1	1	yes	characteristic
62	C₉	C₃²⋊(C₃₁⋊C₃)	1	1	yes	characteristic
63	C₃	—	3	1	no	—
64	C₃	—	3	3	no	—
65	C₃	—	279	3	no	—
66	C₃	C₃×C₃²⋊(C₃₁⋊C₃)	1	1	yes	characteristic

	subgroup	G/H
center	C₉	C₃²⋊(C₃₁⋊C₃)
commutator	C₃²×C₃₁	C₃³
Frattini	C₃²	C₃²×C₃₁⋊C₃
Fitting	C₃²×C₉×C₃₁	C₃
socle	C₃×C₃₁	C₃×H(3,𝔽₃)
hypercenter	C₃²×C₉	C₃₁⋊C₃
hypocenter	C₃₁	#6908
LCS	G ▷ C₃²×C₃₁ ▷ C₃×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₉ ◁ C₃×C₉ ◁ C₃²×C₉

Complements

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

N	H ≅ G/N	type
1. #14578912	C₃	semidirect
2. #14578902	C₃	semidirect
3. #14578900	C₃	semidirect
4. #14578897	C₃	semidirect
5. #14578894	C₃	semidirect
6. C₃²×C₉×C₃₁	C₃	semidirect
35. C₃²×C₉	C₃₁⋊C₃	semidirect
40. C₃₁	#6908	semidirect