Subgroups — C₃²×C₃₇×C₉⋊C₉ #41004646

Order 26973.

1484 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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

Complements

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

N	H ≅ G/N	type
3. C₃×C₃₇×C₉⋊C₉	C₃	direct (N × H)
6. C₃²×C₉×C₃₇	C₉	semidirect
9. C₃₇×C₉⋊C₉	C₃²	direct (N × H)
14. C₃×C₉×C₃₇	C₃×C₉	semidirect
17. C₃²×C₉⋊C₉	C₃₇	direct (N × H)
18. C₃²×C₃₇	C₉⋊C₉	direct (N × H)
23. C₉×C₃₇	C₃²×C₉	semidirect
26. C₃×C₉⋊C₉	C₃×C₃₇	direct (N × H)
27. C₃×C₃₇	C₃×C₉⋊C₉	direct (N × H)
32. C₃²×C₉	C₉×C₃₇	semidirect
35. C₉⋊C₉	C₃²×C₃₇	direct (N × H)
36. C₃₇	C₃²×C₉⋊C₉	direct (N × H)
41. C₃×C₉	C₃×C₉×C₃₇	semidirect
44. C₃²	C₃₇×C₉⋊C₉	direct (N × H)
49. C₉	C₃²×C₉×C₃₇	semidirect
50. C₃	C₃×C₃₇×C₉⋊C₉	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×C₉×C₃₇	3
C₃×C₃₇×C₉⋊C₉	3
C₃²×C₉⋊C₉	37

Subgroups — C32×C37×C9⋊C9 #41004646

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×C₃₇×C₉⋊C₉ #41004646