Subgroups — #21419392

Order 7533.

134 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14578913	C₃	1	3	yes	maximal, complemented
2	C₃×C₉×C₃₁⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
3	#14578902	C₃	1	1	yes	maximal, characteristic, complemented
4	#14578900	C₃	1	1	yes	maximal, characteristic, complemented
5	#14578898	C₃	1	3	yes	maximal, complemented
6	#14578895	C₃	1	3	yes	maximal, complemented
7	C₃₁×#733	C₃	1	1	yes	maximal, characteristic, complemented
8	C₃²×C₃₁⋊C₃	C₃²	1	1	yes	characteristic
9	3₋¹⁺²×C₃₁	C₃²	1	3	yes	—
10	C₃×C₉×C₃₁	C₃²	1	1	yes	characteristic
11	C₃²⋊(C₃₁⋊C₃)	C₃²	1	3	yes	—
12	#11719689	C₃²	1	3	yes	—
13	C₃×C₃₁⋊C₉	C₃²	1	1	yes	characteristic
14	C₃×C₃₁⋊C₉	C₃²	1	1	yes	characteristic
15	#11719687	—	3	3	no	—
16	#11719686	—	3	3	no	—
17	C₉×C₃₁⋊C₃	—	3	1	no	—
18	C₉×C₃₁⋊C₃	—	3	1	no	—
19	C₉×C₃₁⋊C₃	—	3	1	no	—
20	C₉×C₃₁⋊C₃	—	3	3	no	—
21	C₃²×C₃₁	C₃³	1	1	yes	characteristic
22	C₃×C₃₁⋊C₃	—	3	1	no	—
23	C₃×C₃₁⋊C₃	—	3	3	no	—
24	C₃×C₃₁⋊C₃	—	3	3	no	—
25	C₉×C₃₁	—	3	1	no	—
26	C₉×C₃₁	—	3	3	no	—
27	C₃₁⋊C₉	—	3	1	no	—
28	C₃₁⋊C₉	—	3	3	no	—
29	C₃₁⋊C₉	H(3,𝔽₃)	1	1	yes	characteristic
30	C₃₁⋊C₉	H(3,𝔽₃)	1	1	yes	characteristic
31	C₃₁⋊C₉	H(3,𝔽₃)	1	1	yes	characteristic
32	#6908	—	31	1	no	maximal, Sylow
33	C₃×C₃₁	—	3	1	no	—
34	C₃×C₃₁	C₃×H(3,𝔽₃)	1	1	yes	characteristic
35	C₃₁⋊C₃	—	3	3	no	—
36	C₃₁⋊C₃	—	9	3	no	—
37	#737	—	31	3	no	—
38	C₃²×C₉	—	31	1	no	—
39	#733	—	31	1	no	—
40	#733	C₃₁⋊C₃	1	1	yes	characteristic, complemented
41	#732	—	31	1	no	—
42	#731	—	31	3	no	—
43	AΣL(1,𝔽₂₇)	—	31	3	no	—
44	C₃₁	#6908	1	1	yes	characteristic, complemented, Sylow
45	C₃³	—	31	1	no	—
46	3₋¹⁺²	—	31	3	no	—
47	3₋¹⁺²	—	93	3	no	—
48	3₋¹⁺²	—	93	3	no	—
49	3₋¹⁺²	C₃×C₃₁⋊C₃	1	3	yes	—
50	H(3,𝔽₃)	—	31	3	no	—
51	C₃×C₉	—	31	1	no	—
52	C₃×C₉	—	31	1	no	—
53	C₃×C₉	—	93	1	no	—
54	C₃×C₉	—	93	1	no	—
55	C₃×C₉	—	93	1	no	—
56	C₃×C₉	—	93	3	no	—
57	C₃×C₉	C₃×C₃₁⋊C₃	1	1	yes	characteristic
58	C₃²	—	93	3	no	—
59	C₃²	—	93	3	no	—
60	C₃²	—	93	1	no	—
61	C₃²	C₃²×C₃₁⋊C₃	1	1	yes	characteristic
62	C₉	—	3	1	no	—
63	C₉	—	3	3	no	—
64	C₉	—	31	1	no	—
65	C₉	—	31	1	no	—
66	C₉	—	31	1	no	—
67	C₉	—	93	1	no	—
68	C₉	—	93	3	no	—
69	C₃	—	3	1	no	—
70	C₃	—	279	3	no	—
71	C₃	—	93	3	no	—
72	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	#6908
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
1. #14578913	C₃	semidirect
2. C₃×C₉×C₃₁⋊C₃	C₃	semidirect
3. #14578902	C₃	semidirect
4. #14578900	C₃	semidirect
5. #14578898	C₃	semidirect
6. #14578895	C₃	semidirect
7. C₃₁×#733	C₃	semidirect
40. #733	C₃₁⋊C₃	semidirect
44. C₃₁	#6908	semidirect