Subgroups — C₃×C₃²⋊#66526 #22582719

Order 8991.

288 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#66526	C₃	1	3	yes	maximal, complemented
2	C₃²⋊#66526	C₃	1	9	yes	maximal, direct product factor
3	C₃³×C₃₇⋊C₃	C₃	1	1	yes	maximal, characteristic
4	C₃³×C₃₇	C₉	1	1	yes	characteristic, complemented
5	C₃²×C₃₇⋊C₃	—	3	3	no	—
6	C₃²×C₃₇⋊C₃	—	3	6	no	—
7	C₃²×C₃₇⋊C₃	C₉	1	6	yes	complemented
8	C₃²×C₃₇⋊C₃	C₉	1	2	yes	complemented
9	C₃²×C₃₇⋊C₃	C₃²	1	3	yes	—
10	C₃²×C₃₇⋊C₃	C₃²	1	1	yes	characteristic
11	C₃×#66526	—	3	9	no	—
12	C₃×#66526	C₃²	1	9	yes	complemented
13	C₃²×C₃₇	—	3	3	no	—
14	C₃²×C₃₇	C₃×C₉	1	1	yes	characteristic
15	C₃²×C₃₇	C₃×C₉	1	3	yes	complemented
16	C₃×C₃₇⋊C₃	—	3	6	no	—
17	C₃×C₃₇⋊C₃	—	3	18	no	—
18	C₃×C₃₇⋊C₃	—	3	3	no	—
19	C₃×C₃₇⋊C₃	—	3	6	no	—
20	C₃×C₃₇⋊C₃	C₃×C₉	1	2	yes	—
21	C₃×C₃₇⋊C₃	C₃×C₉	1	6	yes	complemented
22	C₃×C₃₇⋊C₃	H(3,𝔽₃)	1	3	yes	—
23	C₃×C₃₇⋊C₃	3₋¹⁺²	1	6	yes	—
24	C₃×C₃₇⋊C₃	C₃³	1	1	yes	characteristic
25	#66526	—	3	9	no	—
26	C₃×C₃²⋊C₉	—	37	1	no	maximal, Sylow
27	C₃×C₃₇	—	3	3	no	—
28	C₃×C₃₇	C₃²⋊C₉	1	3	yes	complemented
29	C₃×C₃₇	C₃²×C₉	1	1	yes	characteristic
30	C₃₇⋊C₃	—	3	6	no	—
31	C₃₇⋊C₃	C₃²⋊C₉	1	6	yes	complemented
32	C₃₇⋊C₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
33	C₃₇⋊C₃	C₃×3₋¹⁺²	1	2	yes	—
34	C₃⁴	—	37	1	no	—
35	C₃²×C₉	—	37	3	no	—
36	C₃²⋊C₉	—	37	9	no	—
37	C₃₇	C₃×C₃²⋊C₉	1	1	yes	characteristic, complemented, Sylow
38	C₃³	—	37	1	no	—
39	C₃³	—	37	2	no	—
40	C₃³	—	37	6	no	—
41	C₃³	—	37	3	no	—
42	C₃³	—	111	3	no	—
43	C₃³	—	111	6	no	—
44	C₃³	#66526	1	1	yes	characteristic, complemented
45	C₃×C₉	—	37	9	no	—
46	C₃×C₉	—	111	9	no	—
47	C₃²	—	3	3	no	—
48	C₃²	—	37	3	no	—
49	C₃²	—	37	6	no	—
50	C₃²	—	37	1	no	—
51	C₃²	—	37	2	no	—
52	C₃²	—	37	6	no	—
53	C₃²	—	111	3	no	—
54	C₃²	—	111	18	no	—
55	C₃²	—	111	6	no	—
56	C₃²	—	111	6	no	—
57	C₃²	C₃×#66526	1	1	yes	characteristic
58	C₃²	C₃×#66526	1	3	yes	complemented
59	C₉	—	111	9	no	—
60	C₃	—	3	3	no	—
61	C₃	—	37	1	no	—
62	C₃	—	37	6	no	—
63	C₃	—	37	2	no	—
64	C₃	—	111	6	no	—
65	C₃	C₃²⋊#66526	1	3	yes	direct product factor
66	C₃	C₃²×#66526	1	1	yes	characteristic

	subgroup	G/H
center	C₃²	C₃×#66526
commutator	C₃×C₃₇	C₃²×C₉
Frattini	C₃	C₃²×#66526
Fitting	C₃³×C₃₇	C₉
socle	C₃²×C₃₇	C₃×C₉
hypercenter	C₃³	#66526
hypocenter	C₃₇	C₃×C₃²⋊C₉
LCS	G ▷ C₃×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₃² ◁ C₃³

Complements

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

N	H ≅ G/N	type
1. C₃²×#66526	C₃	semidirect
2. C₃²⋊#66526	C₃	direct (N × H)
4. C₃³×C₃₇	C₉	semidirect
7. C₃²×C₃₇⋊C₃	C₉	semidirect
8. C₃²×C₃₇⋊C₃	C₉	semidirect
12. C₃×#66526	C₃²	semidirect
15. C₃²×C₃₇	C₃×C₉	semidirect
21. C₃×C₃₇⋊C₃	C₃×C₉	semidirect
28. C₃×C₃₇	C₃²⋊C₉	semidirect
31. C₃₇⋊C₃	C₃²⋊C₉	semidirect
37. C₃₇	C₃×C₃²⋊C₉	semidirect
44. C₃³	#66526	semidirect
58. C₃²	C₃×#66526	semidirect
65. C₃	C₃²⋊#66526	direct (N × H)

Subgroups — C3×C32⋊#66526 #22582719

Conjugacy classes of subgroups

Complements

Subgroups — C₃×C₃²⋊#66526 #22582719