Subgroups — C₃²×#15688506 #41007492

Order 26973.

1484 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×#66524	C₃	1	3	yes	maximal
2	C₃×#15688506	C₃	1	36	yes	maximal, direct product factor
3	C₃³×C₉×C₃₇	C₃	1	1	yes	maximal, characteristic
4	C₃²×#66524	—	3	27	no	—
5	C₃²×#66524	C₃²	1	36	yes	—
6	#15688506	C₃²	1	81	yes	direct product factor
7	C₃⁴×C₃₇	C₃²	1	1	yes	characteristic
8	C₃²×C₉×C₃₇	C₉	1	27	yes	complemented
9	C₃²×C₉×C₃₇	C₃²	1	12	yes	—
10	C₃³×C₃₇	C₃×C₉	1	9	yes	—
11	C₃³×C₃₇	3₋¹⁺²	1	27	yes	—
12	C₃³×C₃₇	C₃³	1	4	yes	—
13	C₃×C₉×C₃₇	C₃×C₉	1	108	yes	complemented
14	C₃×C₉×C₃₇	C₃³	1	9	yes	—
15	C₃×#66524	—	3	108	no	—
16	C₃×#66524	C₃³	1	27	yes	—
17	C₃²×C₉⋊C₉	—	37	1	no	maximal, Sylow
18	C₃²×C₃₇	C₉⋊C₉	1	81	yes	complemented
19	C₃²×C₃₇	C₃²×C₉	1	12	yes	—
20	C₃²×C₃₇	C₃×3₋¹⁺²	1	36	yes	—
21	C₃²×C₃₇	C₃⁴	1	1	yes	characteristic
22	C₉×C₃₇	C₃²×C₉	1	27	yes	complemented
23	#66524	—	3	27	no	—
24	C₃³×C₉	—	37	3	no	—
25	C₃³×C₉	C₃₇⋊C₃	1	1	yes	characteristic
26	C₃×C₉⋊C₉	—	37	36	no	—
27	C₃×C₃₇	C₃×C₉⋊C₉	1	36	yes	complemented
28	C₃×C₃₇	C₃³×C₉	1	1	yes	characteristic
29	C₃×C₃₇	C₃²×3₋¹⁺²	1	3	yes	—
30	C₃⁴	C₃×C₃₇⋊C₃	1	1	yes	characteristic
31	C₃²×C₉	—	37	36	no	—
32	C₃²×C₉	—	111	27	no	—
33	C₃²×C₉	#66524	1	27	yes	complemented
34	C₃²×C₉	C₃×C₃₇⋊C₃	1	12	yes	—
35	C₉⋊C₉	—	37	81	no	—
36	C₃₇	C₃²×C₉⋊C₉	1	1	yes	characteristic, complemented, Sylow
37	C₃³	#11758606	1	27	yes	—
38	C₃³	C₃×#66524	1	9	yes	—
39	C₃³	C₃²×C₃₇⋊C₃	1	4	yes	—
40	C₃×C₉	—	37	27	no	—
41	C₃×C₉	—	111	108	no	—
42	C₃×C₉	C₃×#66524	1	108	yes	complemented
43	C₃×C₉	C₃²×C₃₇⋊C₃	1	9	yes	—
44	C₃²	#15688506	1	81	yes	direct product factor
45	C₃²	C₃²×#66524	1	12	yes	—
46	C₃²	C₃×#11758606	1	36	yes	—
47	C₃²	C₃³×C₃₇⋊C₃	1	1	yes	characteristic
48	C₉	—	111	27	no	—
49	C₉	C₃²×#66524	1	27	yes	complemented
50	C₃	C₃×#15688506	1	36	yes	direct product factor
51	C₃	C₃³×#66524	1	1	yes	characteristic
52	C₃	C₃²×#11758606	1	3	yes	—

	subgroup	G/H
center	C₃⁴	C₃×C₃₇⋊C₃
commutator	C₃×C₃₇	C₃³×C₉
Frattini	C₃²	C₃³×C₃₇⋊C₃
Fitting	C₃³×C₉×C₃₇	C₃
socle, prime radical	C₃⁴×C₃₇	C₃²
cosocle	C₃²×C₃₇	C₃⁴
hypercenter	C₃³×C₉	C₃₇⋊C₃
hypocenter	C₃₇	C₃²×C₉⋊C₉
LCS	G ▷ C₃×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₃⁴ ◁ C₃³×C₉

Complements

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

N	H ≅ G/N	type
2. C₃×#15688506	C₃	direct (N × H)
6. #15688506	C₃²	direct (N × H)
8. C₃²×C₉×C₃₇	C₉	semidirect
13. C₃×C₉×C₃₇	C₃×C₉	semidirect
18. C₃²×C₃₇	C₉⋊C₉	semidirect
22. C₉×C₃₇	C₃²×C₉	semidirect
27. C₃×C₃₇	C₃×C₉⋊C₉	semidirect
33. C₃²×C₉	#66524	semidirect
36. C₃₇	C₃²×C₉⋊C₉	semidirect
42. C₃×C₉	C₃×#66524	semidirect
44. C₃²	#15688506	direct (N × H)
49. C₉	C₃²×#66524	semidirect
50. C₃	C₃×#15688506	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃³×#66524	3
C₃×#15688506	3
C₃³×C₉×C₃₇	3
C₃²×C₉⋊C₉	37

Subgroups — C32×#15688506 #41007492

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#15688506 #41007492