Subgroups — C₃³×#11758608 #41008247

Order 26973.

7208 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#11758608	C₃	1	117	yes	maximal, direct product factor
2	C₃³×#66524	C₃	1	3	yes	maximal, complemented
3	C₃⁵×C₃₇	C₃	1	1	yes	maximal, characteristic
4	C₃×#11758608	C₃²	1	1053	yes	direct product factor
5	C₃²×#66524	C₃²	1	117	yes	complemented
6	C₃⁴×C₃₇	—	3	27	no	—
7	C₃⁴×C₃₇	C₃²	1	39	yes	—
8	C₃⁴×C₃₇	C₃²	1	1	yes	characteristic
9	C₃³×C₃₇	—	3	351	no	—
10	C₃³×C₃₇	3₋¹⁺²	1	27	yes	complemented
11	C₃³×C₃₇	C₃³	1	117	yes	—
12	C₃³×C₃₇	C₃³	1	13	yes	—
13	#11758608	C₃³	1	729	yes	direct product factor
14	C₃×#66524	C₃³	1	351	yes	complemented
15	C₃³×3₋¹⁺²	—	37	1	no	maximal, Sylow
16	C₃²×C₃₇	—	3	351	no	—
17	C₃²×C₃₇	C₃×3₋¹⁺²	1	117	yes	complemented
18	C₃²×C₃₇	C₃⁴	1	27	yes	—
19	C₃²×C₃₇	C₃⁴	1	13	yes	—
20	#66524	C₃⁴	1	81	yes	complemented
21	C₃⁵	C₃₇⋊C₃	1	1	yes	characteristic
22	C₃²×3₋¹⁺²	—	37	117	no	—
23	C₃³×C₉	—	37	3	no	—
24	C₃×C₃₇	—	3	27	no	—
25	C₃×C₃₇	C₃²×3₋¹⁺²	1	39	yes	complemented
26	C₃×C₃₇	C₃⁵	1	1	yes	characteristic
27	C₃⁴	—	3	27	no	—
28	C₃⁴	C₃×C₃₇⋊C₃	1	39	yes	—
29	C₃⁴	C₃×C₃₇⋊C₃	1	1	yes	characteristic
30	C₃×3₋¹⁺²	—	37	1053	no	—
31	C₃²×C₉	—	37	117	no	—
32	C₃₇	C₃³×3₋¹⁺²	1	1	yes	characteristic, complemented, Sylow
33	C₃³	—	3	351	no	—
34	C₃³	#11758608	1	27	yes	direct product factor
35	C₃³	C₃²×C₃₇⋊C₃	1	117	yes	—
36	C₃³	C₃²×C₃₇⋊C₃	1	13	yes	—
37	3₋¹⁺²	—	37	729	no	—
38	C₃×C₉	—	37	351	no	—
39	C₃²	—	3	351	no	—
40	C₃²	C₃×#11758608	1	117	yes	direct product factor
41	C₃²	C₃³×C₃₇⋊C₃	1	27	yes	—
42	C₃²	C₃³×C₃₇⋊C₃	1	13	yes	—
43	C₉	—	37	81	no	—
44	C₃	—	3	27	no	—
45	C₃	C₃²×#11758608	1	39	yes	direct product factor
46	C₃	C₃⁴×C₃₇⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center	C₃⁴	C₃×C₃₇⋊C₃
commutator, cosocle	C₃×C₃₇	C₃⁵
Frattini	C₃	C₃⁴×C₃₇⋊C₃
Fitting, prime radical	C₃⁵×C₃₇	C₃
socle	C₃⁴×C₃₇	C₃²
hypercenter	C₃⁵	C₃₇⋊C₃
hypocenter	C₃₇	C₃³×3₋¹⁺²
LCS	G ▷ C₃×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₃⁴ ◁ C₃⁵

Complements

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

N	H ≅ G/N	type
1. C₃²×#11758608	C₃	direct (N × H)
2. C₃³×#66524	C₃	semidirect
4. C₃×#11758608	C₃²	direct (N × H)
5. C₃²×#66524	C₃²	semidirect
10. C₃³×C₃₇	3₋¹⁺²	semidirect
13. #11758608	C₃³	direct (N × H)
14. C₃×#66524	C₃³	semidirect
17. C₃²×C₃₇	C₃×3₋¹⁺²	semidirect
20. #66524	C₃⁴	semidirect
25. C₃×C₃₇	C₃²×3₋¹⁺²	semidirect
32. C₃₇	C₃³×3₋¹⁺²	semidirect
34. C₃³	#11758608	direct (N × H)
40. C₃²	C₃×#11758608	direct (N × H)
45. C₃	C₃²×#11758608	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
C₃³×#66524	3
C₃⁵×C₃₇	3
C₃³×3₋¹⁺²	37

Subgroups — C33×#11758608 #41008247

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃³×#11758608 #41008247