Subgroups — C₃×#22582709 #41008545

Order 26973.

212 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#15688542	C₃	1	2	yes	maximal
2	C₃×#15688537	C₃	1	1	yes	maximal, characteristic
3	#22582709	C₃	1	9	yes	maximal, direct product factor
4	C₃×#15688510	C₃	1	1	yes	maximal, characteristic
5	C₃²×#66526	—	3	1	no	—
6	#15688542	—	3	4	no	—
7	#15688542	C₃²	1	6	yes	—
8	C₃×#11758603	—	3	2	no	—
9	#15688537	—	3	2	no	—
10	#15688537	C₃²	1	3	yes	—
11	C₃×C₉×C₃₇⋊C₃	C₃²	1	1	yes	characteristic
12	#15688510	C₉	1	6	yes	complemented
13	#15688510	C₃²	1	3	yes	—
14	C₃×#11758601	C₉	1	2	yes	complemented
15	C₃×C₂₇×C₃₇	C₉	1	1	yes	characteristic, complemented
16	C₃²×C₃₇⋊C₃	3₋¹⁺²	1	1	yes	characteristic
17	C₃×#66526	—	3	3	no	—
18	C₃×#66526	—	9	3	no	—
19	C₃×C₉×C₃₇	C₃×C₉	1	1	yes	characteristic
20	C₃×#66524	3₋¹⁺²	1	2	yes	—
21	C₉×C₃₇⋊C₃	C₃×C₉	1	2	yes	—
22	C₉×C₃₇⋊C₃	3₋¹⁺²	1	2	yes	—
23	C₉×C₃₇⋊C₃	3₋¹⁺²	1	4	yes	—
24	C₉×C₃₇⋊C₃	C₃³	1	1	yes	characteristic
25	#11758603	—	3	6	no	—
26	C₂₇×C₃₇	C₃×C₉	1	3	yes	complemented
27	#11758601	C₃×C₉	1	6	yes	complemented
28	C₃×#6875	—	37	1	no	maximal, Sylow
29	C₃²×C₃₇	C₉⋊C₉	1	1	yes	characteristic
30	C₃×C₃₇⋊C₃	—	3	3	no	—
31	C₃×C₃₇⋊C₃	C₉⋊C₉	1	2	yes	—
32	C₃×C₃₇⋊C₃	C₃×3₋¹⁺²	1	1	yes	characteristic
33	#66526	—	9	3	no	—
34	C₉×C₃₇	C₉⋊C₉	1	2	yes	—
35	C₉×C₃₇	C₃²×C₉	1	1	yes	characteristic
36	#66524	C₉⋊C₉	1	4	yes	—
37	#66524	C₃×3₋¹⁺²	1	2	yes	—
38	C₃×C₂₇⋊C₃	—	37	1	no	—
39	C₃×C₂₇⋊C₃	—	37	2	no	—
40	C₃×C₉⋊C₉	—	37	1	no	—
41	#6875	—	37	9	no	—
42	C₃×C₃₇	#6875	1	3	yes	complemented
43	C₃×C₃₇	C₃×C₉⋊C₉	1	1	yes	characteristic
44	C₃₇⋊C₃	—	3	1	no	—
45	C₃₇⋊C₃	—	3	2	no	—
46	C₃²×C₉	—	37	1	no	—
47	C₃²×C₉	—	111	1	no	—
48	C₂₇⋊C₃	—	37	6	no	—
49	C₂₇⋊C₃	—	37	3	no	—
50	C₂₇⋊C₃	—	37	6	no	—
51	C₂₇⋊C₃	—	111	4	no	—
52	C₃×C₂₇	—	37	2	no	—
53	C₃×C₂₇	—	111	2	no	—
54	C₃×C₂₇	#66526	1	1	yes	characteristic, complemented
55	C₉⋊C₉	—	37	3	no	—
56	C₉⋊C₉	—	111	2	no	—
57	C₃₇	C₃×#6875	1	1	yes	characteristic, complemented, Sylow
58	C₃³	—	37	1	no	—
59	C₃×C₉	—	37	2	no	—
60	C₃×C₉	—	37	2	no	—
61	C₃×C₉	—	37	4	no	—
62	C₃×C₉	—	37	2	no	—
63	C₃×C₉	—	37	1	no	—
64	C₃×C₉	—	333	3	no	—
65	C₃×C₉	—	111	3	no	—
66	C₃×C₉	C₃×#66526	1	1	yes	characteristic
67	C₂₇	—	37	6	no	—
68	C₂₇	—	111	6	no	—
69	C₂₇	C₃×#66526	1	3	yes	complemented
70	C₃²	—	37	1	no	—
71	C₃²	—	37	2	no	—
72	C₃²	—	111	3	no	—
73	C₃²	#15688537	1	1	yes	characteristic
74	C₉	—	37	2	no	—
75	C₉	—	37	4	no	—
76	C₉	—	333	3	no	—
77	C₉	#15688537	1	2	yes	—
78	C₉	C₃²×#66526	1	1	yes	characteristic
79	C₃	—	111	1	no	—
80	C₃	—	111	2	no	—
81	C₃	#22582709	1	3	yes	direct product factor
82	C₃	C₃×#15688537	1	1	yes	characteristic

	subgroup	G/H
center	C₃²	#15688537
commutator	C₉×C₃₇	C₃²×C₉
Frattini	C₉	C₃²×#66526
Fitting	C₃×C₂₇×C₃₇	C₉
socle	C₃²×C₃₇	C₉⋊C₉
prime radical	C₃²×C₃₇⋊C₃	3₋¹⁺²
cosocle	C₉×C₃₇⋊C₃	C₃³
hypercenter	C₃×C₂₇	#66526
hypocenter	C₃₇	C₃×#6875
LCS	G ▷ C₉×C₃₇ ▷ C₃×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₃² ◁ C₃×C₉ ◁ C₃×C₂₇

Complements

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

N	H ≅ G/N	type
3. #22582709	C₃	direct (N × H)
12. #15688510	C₉	semidirect
14. C₃×#11758601	C₉	semidirect
15. C₃×C₂₇×C₃₇	C₉	semidirect
26. C₂₇×C₃₇	C₃×C₉	semidirect
27. #11758601	C₃×C₉	semidirect
42. C₃×C₃₇	#6875	semidirect
54. C₃×C₂₇	#66526	semidirect
57. C₃₇	C₃×#6875	semidirect
69. C₂₇	C₃×#66526	semidirect
81. C₃	#22582709	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×#15688542	3
C₃×#15688537	3
#22582709	3
C₃×#15688510	3
C₃×#6875	37

Subgroups — C3×#22582709 #41008545

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#22582709 #41008545