Subgroups — C₃×#22582602 #41007623

Order 26973.

1076 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#11758605	C₃	1	4	yes	maximal
2	#22582602	C₃	1	27	yes	maximal, direct product factor
3	C₃×#15688505	C₃	1	8	yes	maximal, complemented
4	C₃×C₉²×C₃₇	C₃	1	1	yes	maximal, characteristic, complemented
5	C₃³×C₃₇⋊C₃	C₃²	1	1	yes	characteristic
6	C₃×#11758605	—	3	36	no	—
7	C₃×#11758605	C₃²	1	36	yes	—
8	C₃²×#66524	C₃²	1	8	yes	—
9	#15688505	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	—	3	12	no	—
14	C₃²×C₃₇⋊C₃	C₃³	1	3	yes	—
15	C₃×C₉×C₃₇	3₋¹⁺²	1	36	yes	complemented
16	C₃×C₉×C₃₇	C₃³	1	12	yes	—
17	C₃×#66524	—	3	24	no	—
18	C₃×#66524	C₃³	1	24	yes	—
19	#11758605	—	3	108	no	—
20	C₃×#6900	—	37	1	no	maximal, Sylow
21	C₃²×C₃₇	C₃×3₋¹⁺²	1	12	yes	—
22	C₃²×C₃₇	C₃⁴	1	1	yes	characteristic
23	C₃×C₃₇⋊C₃	—	3	12	no	—
24	C₃×C₃₇⋊C₃	—	9	9	no	—
25	C₉×C₃₇	C₃×3₋¹⁺²	1	36	yes	complemented
26	#66524	—	3	24	no	—
27	C₃²×3₋¹⁺²	—	37	4	no	—
28	#6900	—	37	27	no	—
29	C₃×C₉⋊C₉	—	37	8	no	—
30	C₃×C₉²	C₃₇⋊C₃	1	1	yes	characteristic, complemented
31	C₃×C₃₇	#6900	1	9	yes	complemented
32	C₃×C₃₇	C₃²×3₋¹⁺²	1	4	yes	—
33	C₃₇⋊C₃	—	9	3	no	—
34	C₃⁴	—	37	1	no	—
35	C₃×3₋¹⁺²	—	37	36	no	—
36	C₃×3₋¹⁺²	—	111	36	no	—
37	C₃²×C₉	—	37	8	no	—
38	C₃²×C₉	C₃×C₃₇⋊C₃	1	4	yes	—
39	C₉⋊C₉	—	37	72	no	—
40	C₉²	C₃×C₃₇⋊C₃	1	9	yes	complemented
41	C₃₇	C₃×#6900	1	1	yes	characteristic, complemented, Sylow
42	C₃³	—	37	3	no	—
43	C₃³	—	111	12	no	—
44	C₃³	C₃²×C₃₇⋊C₃	1	1	yes	characteristic
45	3₋¹⁺²	—	111	108	no	—
46	C₃×C₉	—	37	24	no	—
47	C₃×C₉	—	111	24	no	—
48	C₃×C₉	#11758605	1	36	yes	complemented
49	C₃×C₉	C₃²×C₃₇⋊C₃	1	12	yes	—
50	C₃²	—	333	9	no	—
51	C₃²	—	111	12	no	—
52	C₃²	C₃×#11758605	1	12	yes	—
53	C₃²	C₃³×C₃₇⋊C₃	1	1	yes	characteristic
54	C₉	—	111	24	no	—
55	C₉	C₃×#11758605	1	36	yes	complemented
56	C₃	—	333	3	no	—
57	C₃	#22582602	1	9	yes	direct product factor
58	C₃	C₃²×#11758605	1	4	yes	—

	subgroup	G/H
center	C₃³	C₃²×C₃₇⋊C₃
commutator, cosocle	C₃²×C₃₇	C₃⁴
Frattini	C₃²	C₃³×C₃₇⋊C₃
Fitting	C₃×C₉²×C₃₇	C₃
socle	C₃³×C₃₇	C₃³
prime radical	C₃³×C₃₇⋊C₃	C₃²
hypercenter	C₃×C₉²	C₃₇⋊C₃
hypocenter	C₃₇	C₃×#6900
LCS	G ▷ C₃²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₃³ ◁ C₃×C₉²

Complements

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

N	H ≅ G/N	type
2. #22582602	C₃	direct (N × H)
3. C₃×#15688505	C₃	semidirect
4. C₃×C₉²×C₃₇	C₃	semidirect
9. #15688505	C₃²	semidirect
11. C₉²×C₃₇	C₃²	semidirect
15. C₃×C₉×C₃₇	3₋¹⁺²	semidirect
25. C₉×C₃₇	C₃×3₋¹⁺²	semidirect
30. C₃×C₉²	C₃₇⋊C₃	semidirect
31. C₃×C₃₇	#6900	semidirect
40. C₉²	C₃×C₃₇⋊C₃	semidirect
41. C₃₇	C₃×#6900	semidirect
48. C₃×C₉	#11758605	semidirect
55. C₉	C₃×#11758605	semidirect
57. C₃	#22582602	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×#11758605	3
#22582602	3
C₃×#15688505	3
C₃×C₉²×C₃₇	3
C₃×#6900	37

Subgroups — C3×#22582602 #41007623

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#22582602 #41007623