Subgroups — #15691681

Order 3159.

126 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11760454	C₃	1	3	yes	maximal, complemented
2	C₃×#66849	C₃	1	1	yes	maximal, characteristic, complemented
3	#11760443	C₃	1	1	yes	maximal, characteristic, complemented
4	#11760441	C₃	1	1	yes	maximal, characteristic, complemented
5	#11760439	C₃	1	3	yes	maximal, complemented
6	#11760436	C₃	1	3	yes	maximal, complemented
7	C₁₃×#733	C₃	1	1	yes	maximal, characteristic, complemented
8	C₃²×C₁₃⋊C₃	C₃²	1	1	yes	characteristic
9	C₁₃×3₋¹⁺²	C₃²	1	3	yes	—
10	C₃×C₉×C₁₃	C₃²	1	1	yes	characteristic
11	C₃²⋊(C₁₃⋊C₃)	C₃²	1	3	yes	—
12	#66851	C₃²	1	3	yes	—
13	C₃×C₁₃⋊C₉	C₃²	1	1	yes	characteristic
14	C₃×C₁₃⋊C₉	C₃²	1	1	yes	characteristic
15	#66849	—	3	3	no	—
16	#66849	—	3	3	no	—
17	#66848	—	3	3	no	—
18	C₉×C₁₃⋊C₃	—	3	3	no	—
19	#6913	—	13	1	no	maximal, Sylow
20	C₃²×C₁₃	C₃³	1	1	yes	characteristic
21	C₃×C₁₃⋊C₃	—	3	3	no	—
22	C₃×C₁₃⋊C₃	—	3	1	no	—
23	C₃×C₁₃⋊C₃	—	9	1	no	—
24	C₉×C₁₃	—	3	3	no	—
25	C₉×C₁₃	—	3	1	no	—
26	C₁₃⋊C₉	—	3	3	no	—
27	C₁₃⋊C₉	—	3	1	no	—
28	C₁₃⋊C₉	H(3,𝔽₃)	1	3	yes	—
29	#737	—	13	3	no	—
30	C₃×3₋¹⁺²	—	13	1	no	—
31	#733	—	13	1	no	—
32	#733	C₁₃⋊C₃	1	1	yes	characteristic, complemented
33	#732	—	13	1	no	—
34	#731	—	13	3	no	—
35	AΣL(1,𝔽₂₇)	—	13	3	no	—
36	C₃×C₁₃	—	3	1	no	—
37	C₃×C₁₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
38	C₁₃⋊C₃	—	9	3	no	—
39	C₁₃⋊C₃	—	9	1	no	—
40	C₃³	—	13	1	no	—
41	3₋¹⁺²	—	13	3	no	—
42	3₋¹⁺²	—	39	3	no	—
43	3₋¹⁺²	—	39	3	no	—
44	3₋¹⁺²	—	39	3	no	—
45	3₋¹⁺²	C₃×C₁₃⋊C₃	1	3	yes	—
46	H(3,𝔽₃)	—	13	3	no	—
47	C₃×C₉	—	13	1	no	—
48	C₃×C₉	—	13	1	no	—
49	C₃×C₉	—	39	3	no	—
50	C₃×C₉	C₃×C₁₃⋊C₃	1	1	yes	characteristic
51	C₁₃	#6913	1	1	yes	characteristic, complemented, Sylow
52	C₃²	—	39	3	no	—
53	C₃²	—	39	1	no	—
54	C₃²	—	117	1	no	—
55	C₃²	C₃²×C₁₃⋊C₃	1	1	yes	characteristic
56	C₉	—	3	3	no	—
57	C₉	—	3	1	no	—
58	C₉	—	13	3	no	—
59	C₉	—	39	1	no	—
60	C₉	—	39	3	no	—
61	C₃	—	3	1	no	—
62	C₃	—	117	1	no	—
63	C₃	—	117	3	no	—
64	C₃	H(3,𝔽₃)×C₁₃⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center	C₃	H(3,𝔽₃)×C₁₃⋊C₃
commutator, cosocle	C₃²×C₁₃	C₃³
Frattini	C₃²	C₃²×C₁₃⋊C₃
Fitting	C₁₃×#733	C₃
socle	C₃×C₁₃	C₃×H(3,𝔽₃)
hypercenter	#733	C₁₃⋊C₃
hypocenter	C₁₃	#6913
LCS	G ▷ C₃²×C₁₃ ▷ C₃×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₃ ◁ C₃² ◁ #733

Complements

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

N	H ≅ G/N	type
1. #11760454	C₃	semidirect
2. C₃×#66849	C₃	semidirect
3. #11760443	C₃	semidirect
4. #11760441	C₃	semidirect
5. #11760439	C₃	semidirect
6. #11760436	C₃	semidirect
7. C₁₃×#733	C₃	semidirect
32. #733	C₁₃⋊C₃	semidirect
51. C₁₃	#6913	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#11760454	3
C₃×#66849	3
#11760443	3
#11760441	3
#11760439	3
#11760436	3
C₁₃×#733	3
#6913	13