Subgroups — C₃×C₉²×C₃₇⋊C₃ #41007484

Order 26973.

2132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₉×C₃₇⋊C₃	C₃	1	4	yes	maximal
2	C₃×C₉×#66524	C₃	1	8	yes	maximal, complemented
3	C₉²×C₃₇⋊C₃	C₃	1	27	yes	maximal, direct product factor
4	C₃×C₉²×C₃₇	C₃	1	1	yes	maximal, characteristic, complemented
5	C₃³×C₃₇⋊C₃	C₃²	1	1	yes	characteristic
6	C₃²×#66524	C₃²	1	8	yes	—
7	C₃×C₉×C₃₇⋊C₃	C₉	1	108	yes	direct product factor
8	C₃×C₉×C₃₇⋊C₃	C₃²	1	36	yes	—
9	C₉×#66524	C₃²	1	72	yes	complemented
10	C₃²×C₉×C₃₇	C₃²	1	4	yes	—
11	C₉²×C₃₇	C₃²	1	9	yes	complemented
12	C₃³×C₃₇	C₃³	1	1	yes	characteristic
13	C₃²×C₃₇⋊C₃	C₃×C₉	1	36	yes	—
14	C₃²×C₃₇⋊C₃	C₃³	1	3	yes	—
15	C₃×C₉×C₃₇	C₃×C₉	1	36	yes	complemented
16	C₃×C₉×C₃₇	C₃³	1	12	yes	—
17	C₃×#66524	C₃×C₉	1	72	yes	complemented
18	C₃×#66524	C₃³	1	24	yes	—
19	C₉×C₃₇⋊C₃	C₃×C₉	1	324	yes	direct product factor
20	C₃²×C₉²	—	37	1	no	maximal, Sylow
21	C₃²×C₃₇	C₃²×C₉	1	12	yes	—
22	C₃²×C₃₇	C₃⁴	1	1	yes	characteristic
23	C₃×C₃₇⋊C₃	C₉²	1	81	yes	direct product factor
24	C₃×C₃₇⋊C₃	C₃²×C₉	1	36	yes	—
25	C₉×C₃₇	C₃²×C₉	1	36	yes	complemented
26	#66524	C₃²×C₉	1	72	yes	complemented
27	C₃³×C₉	—	37	4	no	—
28	C₃×C₉²	—	37	8	no	—
29	C₃×C₉²	—	37	27	no	—
30	C₃×C₉²	C₃₇⋊C₃	1	1	yes	characteristic, direct product factor
31	C₃×C₃₇	C₃×C₉²	1	9	yes	complemented
32	C₃×C₃₇	C₃³×C₉	1	4	yes	—
33	C₃₇⋊C₃	C₃×C₉²	1	27	yes	direct product factor
34	C₃⁴	—	37	1	no	—
35	C₃²×C₉	—	37	8	no	—
36	C₃²×C₉	—	37	108	no	—
37	C₃²×C₉	—	37	36	no	—
38	C₃²×C₉	C₃×C₃₇⋊C₃	1	4	yes	—
39	C₉²	—	37	72	no	—
40	C₉²	C₃×C₃₇⋊C₃	1	9	yes	direct product factor
41	C₃₇	C₃²×C₉²	1	1	yes	characteristic, complemented, Sylow
42	C₃³	—	37	36	no	—
43	C₃³	—	37	3	no	—
44	C₃³	C₃²×C₃₇⋊C₃	1	1	yes	characteristic
45	C₃×C₉	—	37	72	no	—
46	C₃×C₉	—	37	24	no	—
47	C₃×C₉	—	37	324	no	—
48	C₃×C₉	C₉×C₃₇⋊C₃	1	36	yes	direct product factor
49	C₃×C₉	C₃²×C₃₇⋊C₃	1	12	yes	—
50	C₃²	—	37	36	no	—
51	C₃²	—	37	81	no	—
52	C₃²	C₃×C₉×C₃₇⋊C₃	1	12	yes	—
53	C₃²	C₃³×C₃₇⋊C₃	1	1	yes	characteristic
54	C₉	—	37	72	no	—
55	C₉	C₃×C₉×C₃₇⋊C₃	1	36	yes	direct product factor
56	C₃	—	37	27	no	—
57	C₃	C₉²×C₃₇⋊C₃	1	9	yes	direct product factor
58	C₃	C₃²×C₉×C₃₇⋊C₃	1	4	yes	—

	subgroup	G/H
center, hypercenter	C₃×C₉²	C₃₇⋊C₃
commutator, hypocenter	C₃₇	C₃²×C₉²
Frattini	C₃²	C₃³×C₃₇⋊C₃
Fitting	C₃×C₉²×C₃₇	C₃
socle	C₃³×C₃₇	C₃³
prime radical	C₃³×C₃₇⋊C₃	C₃²
cosocle	C₃²×C₃₇	C₃⁴
LCS	G ▷ C₃₇
UCS	C₁ ◁ C₃×C₉²

Complements

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

N	H ≅ G/N	type
2. C₃×C₉×#66524	C₃	semidirect
3. C₉²×C₃₇⋊C₃	C₃	direct (N × H)
4. C₃×C₉²×C₃₇	C₃	semidirect
7. C₃×C₉×C₃₇⋊C₃	C₉	direct (N × H)
9. C₉×#66524	C₃²	semidirect
11. C₉²×C₃₇	C₃²	semidirect
15. C₃×C₉×C₃₇	C₃×C₉	semidirect
17. C₃×#66524	C₃×C₉	semidirect
19. C₉×C₃₇⋊C₃	C₃×C₉	direct (N × H)
23. C₃×C₃₇⋊C₃	C₉²	direct (N × H)
25. C₉×C₃₇	C₃²×C₉	semidirect
26. #66524	C₃²×C₉	semidirect
30. C₃×C₉²	C₃₇⋊C₃	direct (N × H)
31. C₃×C₃₇	C₃×C₉²	semidirect
33. C₃₇⋊C₃	C₃×C₉²	direct (N × H)
40. C₉²	C₃×C₃₇⋊C₃	direct (N × H)
41. C₃₇	C₃²×C₉²	semidirect
48. C₃×C₉	C₉×C₃₇⋊C₃	direct (N × H)
55. C₉	C₃×C₉×C₃₇⋊C₃	direct (N × H)
57. C₃	C₉²×C₃₇⋊C₃	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×C₉×C₃₇⋊C₃	3
C₃×C₉×#66524	3
C₉²×C₃₇⋊C₃	3
C₃×C₉²×C₃₇	3
C₃²×C₉²	37

Subgroups — C3×C92×C37⋊C3 #41007484

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₉²×C₃₇⋊C₃ #41007484