Subgroups — #23748640

Order 9477.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×(C₃³⋊C₁₃)⋊C₃	C₃	1	1	yes	maximal, characteristic
2	(C₃³⋊C₁₃)⋊C₉	C₃	1	2	yes	maximal, complemented
3	C₉×C₃³⋊C₁₃	C₃	1	1	yes	maximal, characteristic, complemented
4	(C₃³⋊C₁₃)⋊C₃	—	3	1	no	—
5	C₃×C₃³⋊C₁₃	C₃²	1	1	yes	characteristic
6	#10624784	—	13	1	no	maximal, Sylow
7	C₃³⋊C₁₃	3₋¹⁺²	1	1	yes	characteristic, complemented
8	#66849	—	27	1	no	maximal
9	C₃³×C₉	C₁₃⋊C₃	1	1	yes	characteristic, complemented
10	C₃×AΣL(1,𝔽₂₇)	—	13	1	no	—
11	#6894	—	13	2	no	—
12	C₉⋊H(3,𝔽₃)	—	13	1	no	—
13	3₋¹⁺²⋊C₉	—	13	4	no	—
14	H(3,𝔽₃)⋊C₉	—	13	2	no	—
15	#6866	—	13	2	no	—
16	C₃×C₁₃⋊C₃	—	27	1	no	—
17	C₉×C₁₃	—	27	1	no	—
18	C₁₃⋊C₉	—	27	2	no	—
19	C₃⁴	C₃×C₁₃⋊C₃	1	1	yes	characteristic
20	C₃×3₋¹⁺²	—	13	2	no	—
21	C₃×3₋¹⁺²	—	39	1	no	—
22	C₃×H(3,𝔽₃)	—	13	1	no	—
23	C₃²×C₉	—	13	1	no	—
24	C₃²×C₉	—	13	2	no	—
25	AΣL(1,𝔽₂₇)	—	39	2	no	—
26	AΣL(1,𝔽₂₇)	—	39	1	no	—
27	C₉⋊C₉	—	39	2	no	—
28	C₉⋊C₉	—	39	4	no	—
29	C₃²⋊C₉	—	13	4	no	—
30	C₃²⋊C₉	—	13	2	no	—
31	C₃²⋊C₉	—	39	2	no	—
32	C₃×C₁₃	—	27	1	no	—
33	C₁₃⋊C₃	—	81	1	no	—
34	C₃³	—	13	1	no	—
35	C₃³	—	13	2	no	—
36	C₃³	—	39	1	no	—
37	C₃³	#66849	1	1	yes	characteristic, complemented
38	3₋¹⁺²	—	39	2	no	—
39	3₋¹⁺²	—	39	4	no	—
40	3₋¹⁺²	—	117	2	no	—
41	3₋¹⁺²	—	117	1	no	—
42	H(3,𝔽₃)	—	39	1	no	—
43	H(3,𝔽₃)	—	39	2	no	—
44	C₃×C₉	—	13	1	no	—
45	C₃×C₉	—	13	2	no	—
46	C₃×C₉	—	39	2	no	—
47	C₃×C₉	—	39	2	no	—
48	C₃×C₉	—	39	4	no	—
49	C₃×C₉	—	39	2	no	—
50	C₁₃	—	27	1	no	Sylow
51	C₃²	—	13	1	no	—
52	C₃²	—	13	2	no	—
53	C₃²	—	13	1	no	—
54	C₃²	—	39	2	no	—
55	C₃²	—	117	1	no	—
56	C₃²	—	117	2	no	—
57	C₃²	—	117	1	no	—
58	C₉	—	13	2	no	—
59	C₉	—	117	4	no	—
60	C₉	—	117	2	no	—
61	C₉	—	117	2	no	—
62	C₉	(C₃³⋊C₁₃)⋊C₃	1	1	yes	characteristic, complemented
63	C₃	—	13	1	no	—
64	C₃	—	13	2	no	—
65	C₃	—	351	1	no	—
66	C₃	C₃×(C₃³⋊C₁₃)⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₃	C₃×(C₃³⋊C₁₃)⋊C₃
commutator, cosocle	C₃×C₃³⋊C₁₃	C₃²
Fitting	C₃³×C₉	C₁₃⋊C₃
socle	C₃⁴	C₃×C₁₃⋊C₃
prime radical	C₃×(C₃³⋊C₁₃)⋊C₃	C₃
hypercenter	C₉	(C₃³⋊C₁₃)⋊C₃
hypocenter	C₃³⋊C₁₃	3₋¹⁺²
LCS	G ▷ C₃×C₃³⋊C₁₃ ▷ C₃³⋊C₁₃
UCS	C₁ ◁ C₃ ◁ C₉

Complements

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

N	H ≅ G/N	type
2. (C₃³⋊C₁₃)⋊C₉	C₃	semidirect
3. C₉×C₃³⋊C₁₃	C₃	semidirect
7. C₃³⋊C₁₃	3₋¹⁺²	semidirect
9. C₃³×C₉	C₁₃⋊C₃	semidirect
37. C₃³	#66849	semidirect
62. C₉	(C₃³⋊C₁₃)⋊C₃	semidirect