Subgroups — C₃×#22582704 #41008526

Order 26973.

284 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#11758603	C₃	1	3	yes	maximal
2	#22582704	C₃	1	9	yes	maximal, direct product factor
3	C₃×C₉×#66524	C₃	1	1	yes	maximal, characteristic
4	C₃×#11758603	—	3	9	no	—
5	C₃×#11758603	C₃²	1	9	yes	—
6	C₃²×#66524	C₉	1	2	yes	—
7	C₃²×#66524	C₃²	1	1	yes	characteristic
8	C₉×#66524	C₉	1	6	yes	—
9	C₉×#66524	C₃²	1	3	yes	—
10	C₃²×C₉×C₃₇	C₉	1	1	yes	characteristic
11	C₃³×C₃₇	C₃×C₉	1	1	yes	characteristic
12	C₃×C₉×C₃₇	C₂₇	1	9	yes	complemented
13	C₃×C₉×C₃₇	C₃×C₉	1	3	yes	—
14	C₃×#66524	—	3	6	no	—
15	C₃×#66524	C₃×C₉	1	6	yes	—
16	C₃×#66524	C₃×C₉	1	2	yes	—
17	C₃×#66524	3₋¹⁺²	1	9	yes	—
18	C₃×#66524	C₃³	1	1	yes	characteristic
19	#11758603	—	3	9	no	—
20	C₃×C₉⋊C₂₇	—	37	1	no	maximal, Sylow
21	C₃²×C₃₇	C₉⋊C₉	1	3	yes	—
22	C₃²×C₃₇	C₃×C₂₇	1	3	yes	—
23	C₃²×C₃₇	C₂₇⋊C₃	1	6	yes	—
24	C₃²×C₃₇	C₃²×C₉	1	1	yes	characteristic
25	C₉×C₃₇	C₃×C₂₇	1	9	yes	complemented
26	#66524	—	3	6	no	—
27	#66524	C₉⋊C₉	1	6	yes	—
28	#66524	C₃×3₋¹⁺²	1	3	yes	—
29	C₃²×C₂₇	—	37	3	no	—
30	C₃×C₉²	—	37	1	no	—
31	C₉⋊C₂₇	—	37	9	no	—
32	C₃×C₃₇	C₉⋊C₂₇	1	9	yes	complemented
33	C₃×C₃₇	C₃×C₉⋊C₉	1	1	yes	characteristic
34	C₃×C₃₇	C₃²×C₂₇	1	1	yes	characteristic
35	C₃×C₃₇	C₃×C₂₇⋊C₃	1	2	yes	—
36	C₃²×C₉	—	37	1	no	—
37	C₃²×C₉	—	37	2	no	—
38	C₃²×C₉	#66526	1	1	yes	characteristic
39	C₃×C₂₇	—	37	9	no	—
40	C₃×C₂₇	—	111	9	no	—
41	C₉²	—	37	6	no	—
42	C₉²	—	37	3	no	—
43	C₃₇	C₃×C₉⋊C₂₇	1	1	yes	characteristic, complemented, Sylow
44	C₃³	C₃×#66526	1	1	yes	characteristic
45	C₃×C₉	—	37	9	no	—
46	C₃×C₉	—	37	2	no	—
47	C₃×C₉	—	37	1	no	—
48	C₃×C₉	—	37	6	no	—
49	C₃×C₉	—	111	6	no	—
50	C₃×C₉	#11758603	1	9	yes	complemented
51	C₃×C₉	C₃×#66526	1	3	yes	—
52	C₂₇	—	111	9	no	—
53	C₃²	#15688538	1	3	yes	—
54	C₃²	C₃×#11758603	1	3	yes	—
55	C₃²	#15688543	1	6	yes	—
56	C₃²	C₃²×#66526	1	1	yes	characteristic
57	C₉	—	37	3	no	—
58	C₉	—	37	6	no	—
59	C₉	—	111	6	no	—
60	C₉	C₃×#11758603	1	9	yes	complemented
61	C₃	#22582704	1	9	yes	direct product factor
62	C₃	C₃×#15688538	1	1	yes	characteristic
63	C₃	C₃²×#11758603	1	1	yes	characteristic
64	C₃	C₃×#15688543	1	2	yes	—

	subgroup	G/H
center	C₃³	C₃×#66526
commutator	C₃×C₃₇	C₃²×C₂₇
Frattini	C₃²	C₃²×#66526
Fitting	C₃²×C₉×C₃₇	C₉
socle, prime radical	C₃³×C₃₇	C₃×C₉
cosocle	C₃×#66524	C₃³
hypercenter	C₃²×C₉	#66526
hypocenter	C₃₇	C₃×C₉⋊C₂₇
LCS	G ▷ C₃×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₃³ ◁ C₃²×C₉

Complements

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

N	H ≅ G/N	type
2. #22582704	C₃	direct (N × H)
12. C₃×C₉×C₃₇	C₂₇	semidirect
25. C₉×C₃₇	C₃×C₂₇	semidirect
32. C₃×C₃₇	C₉⋊C₂₇	semidirect
43. C₃₇	C₃×C₉⋊C₂₇	semidirect
50. C₃×C₉	#11758603	semidirect
60. C₉	C₃×#11758603	semidirect
61. C₃	#22582704	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×#11758603	3
#22582704	3
C₃×C₉×#66524	3
C₃×C₉⋊C₂₇	37

Subgroups — C3×#22582704 #41008526

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#22582704 #41008526