Subgroups — C₃×#22582554 #41007537

Order 26973.

2636 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#11758608	C₃	1	3	yes	maximal, complemented
2	#22582554	C₃	1	27	yes	maximal, direct product factor
3	C₃×C₃²⋊#66524	C₃	1	9	yes	maximal, complemented
4	C₃⁵×C₃₇	C₃	1	1	yes	maximal, characteristic
5	C₃×#11758608	—	3	27	no	—
6	C₃×#11758608	C₃²	1	27	yes	complemented
7	C₃²×#66524	C₃²	1	9	yes	complemented
8	C₃²⋊#66524	C₃²	1	81	yes	complemented
9	C₃⁴×C₃₇	—	3	9	no	—
10	C₃⁴×C₃₇	—	3	27	no	—
11	C₃⁴×C₃₇	C₃²	1	9	yes	—
12	C₃⁴×C₃₇	C₃²	1	1	yes	characteristic
13	C₃⁴×C₃₇	C₃²	1	3	yes	—
14	C₃³×C₃₇	—	3	243	no	—
15	C₃³×C₃₇	—	3	27	no	—
16	C₃³×C₃₇	—	3	9	no	—
17	C₃³×C₃₇	—	3	9	no	—
18	C₃³×C₃₇	—	3	18	no	—
19	C₃³×C₃₇	—	3	81	no	—
20	C₃³×C₃₇	H(3,𝔽₃)	1	9	yes	—
21	C₃³×C₃₇	3₋¹⁺²	1	27	yes	complemented
22	C₃³×C₃₇	C₃³	1	3	yes	—
23	C₃³×C₃₇	C₃³	1	9	yes	—
24	C₃³×C₃₇	C₃³	1	1	yes	characteristic
25	#11758608	—	3	81	no	—
26	C₃×#66524	—	3	27	no	—
27	C₃×#66524	C₃³	1	27	yes	complemented
28	C₃×#6891	—	37	1	no	maximal, Sylow
29	C₃²×C₃₇	—	3	243	no	—
30	C₃²×C₃₇	—	3	9	no	—
31	C₃²×C₃₇	—	3	9	no	—
32	C₃²×C₃₇	—	3	18	no	—
33	C₃²×C₃₇	—	3	27	no	—
34	C₃²×C₃₇	—	3	81	no	—
35	C₃²×C₃₇	C₃×H(3,𝔽₃)	1	9	yes	—
36	C₃²×C₃₇	C₃×H(3,𝔽₃)	1	3	yes	—
37	C₃²×C₃₇	C₃×3₋¹⁺²	1	9	yes	—
38	C₃²×C₃₇	C₃×3₋¹⁺²	1	27	yes	complemented
39	C₃²×C₃₇	C₃⁴	1	1	yes	characteristic
40	#66524	—	3	27	no	—
41	C₃⁵	C₃₇⋊C₃	1	1	yes	characteristic
42	C₃²×3₋¹⁺²	—	37	3	no	—
43	#6891	—	37	27	no	—
44	C₃×C₃²⋊C₉	—	37	9	no	—
45	C₃×C₃₇	—	3	9	no	—
46	C₃×C₃₇	—	3	27	no	—
47	C₃×C₃₇	#6891	1	9	yes	complemented
48	C₃×C₃₇	C₃²×H(3,𝔽₃)	1	1	yes	characteristic
49	C₃×C₃₇	C₃²×3₋¹⁺²	1	3	yes	—
50	C₃⁴	—	3	27	no	—
51	C₃⁴	—	3	9	no	—
52	C₃⁴	C₃×C₃₇⋊C₃	1	9	yes	—
53	C₃⁴	C₃×C₃₇⋊C₃	1	3	yes	—
54	C₃⁴	C₃×C₃₇⋊C₃	1	1	yes	characteristic
55	C₃×3₋¹⁺²	—	37	27	no	—
56	C₃×3₋¹⁺²	—	111	27	no	—
57	C₃²×C₉	—	37	9	no	—
58	C₃²⋊C₉	—	37	81	no	—
59	C₃₇	C₃×#6891	1	1	yes	characteristic, complemented, Sylow
60	C₃³	—	3	243	no	—
61	C₃³	—	3	27	no	—
62	C₃³	—	3	9	no	—
63	C₃³	—	3	18	no	—
64	C₃³	—	3	9	no	—
65	C₃³	—	3	81	no	—
66	C₃³	#11758608	1	27	yes	complemented
67	C₃³	C₃²⋊(C₃₇⋊C₃)	1	9	yes	—
68	C₃³	C₃²×C₃₇⋊C₃	1	3	yes	—
69	C₃³	C₃²×C₃₇⋊C₃	1	9	yes	—
70	C₃³	C₃²×C₃₇⋊C₃	1	1	yes	characteristic
71	3₋¹⁺²	—	111	81	no	—
72	C₃×C₉	—	37	27	no	—
73	C₃×C₉	—	111	27	no	—
74	C₃²	—	3	243	no	—
75	C₃²	—	3	81	no	—
76	C₃²	—	3	27	no	—
77	C₃²	—	3	9	no	—
78	C₃²	—	3	9	no	—
79	C₃²	—	3	18	no	—
80	C₃²	C₃×C₃²⋊(C₃₇⋊C₃)	1	9	yes	—
81	C₃²	C₃×C₃²⋊(C₃₇⋊C₃)	1	3	yes	—
82	C₃²	C₃×#11758608	1	9	yes	—
83	C₃²	C₃×#11758608	1	27	yes	complemented
84	C₃²	C₃³×C₃₇⋊C₃	1	1	yes	characteristic
85	C₉	—	111	27	no	—
86	C₃	—	3	9	no	—
87	C₃	—	3	27	no	—
88	C₃	#22582554	1	9	yes	direct product factor
89	C₃	C₃²×C₃²⋊(C₃₇⋊C₃)	1	1	yes	characteristic
90	C₃	C₃²×#11758608	1	3	yes	—

	subgroup	G/H
center	C₃³	C₃²×C₃₇⋊C₃
commutator, cosocle	C₃²×C₃₇	C₃⁴
Frattini	C₃²	C₃³×C₃₇⋊C₃
Fitting, prime radical	C₃⁵×C₃₇	C₃
socle	C₃³×C₃₇	C₃³
hypercenter	C₃⁵	C₃₇⋊C₃
hypocenter	C₃₇	C₃×#6891
LCS	G ▷ C₃²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₃³ ◁ C₃⁵

Complements

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

N	H ≅ G/N	type
1. C₃²×#11758608	C₃	semidirect
2. #22582554	C₃	direct (N × H)
3. C₃×C₃²⋊#66524	C₃	semidirect
6. C₃×#11758608	C₃²	semidirect
7. C₃²×#66524	C₃²	semidirect
8. C₃²⋊#66524	C₃²	semidirect
21. C₃³×C₃₇	3₋¹⁺²	semidirect
27. C₃×#66524	C₃³	semidirect
38. C₃²×C₃₇	C₃×3₋¹⁺²	semidirect
47. C₃×C₃₇	#6891	semidirect
59. C₃₇	C₃×#6891	semidirect
66. C₃³	#11758608	semidirect
83. C₃²	C₃×#11758608	semidirect
88. C₃	#22582554	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×#11758608	3
#22582554	3
C₃×C₃²⋊#66524	3
C₃⁵×C₃₇	3
C₃×#6891	37

Subgroups — C3×#22582554 #41007537

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#22582554 #41007537