Subgroups — C₃×#22582491 #41006328

Order 26973.

212 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#15688511	C₃	1	1	yes	maximal, characteristic
2	C₃×#15688511	C₃	1	1	yes	maximal, characteristic
3	C₃×#15688511	C₃	1	1	yes	maximal, characteristic
4	#22582491	C₃	1	9	yes	maximal, direct product factor
5	C₃×C₃₇×C₉⋊C₉	C₃	1	1	yes	maximal, characteristic
6	#15688511	—	3	2	no	—
7	#15688511	—	3	2	no	—
8	#15688511	C₉	1	6	yes	complemented
9	#15688511	C₃²	1	3	yes	—
10	#15688511	C₃²	1	3	yes	—
11	#15688511	C₃²	1	3	yes	—
12	C₃×#11758601	—	3	1	no	—
13	C₃×#11758601	—	3	1	no	—
14	C₃×#11758601	C₉	1	3	yes	complemented
15	C₃²×C₉×C₃₇	—	3	1	no	—
16	C₃²×C₉×C₃₇	C₃²	1	1	yes	characteristic
17	C₃₇×C₉⋊C₉	—	3	2	no	—
18	C₃₇×C₉⋊C₉	C₃²	1	3	yes	—
19	C₃³×C₃₇	3₋¹⁺²	1	1	yes	characteristic
20	C₃×C₉×C₃₇	—	3	3	no	—
21	C₃×C₉×C₃₇	—	9	3	no	—
22	C₃×C₉×C₃₇	C₃×C₉	1	1	yes	characteristic
23	C₃×C₉×C₃₇	C₃×C₉	1	2	yes	—
24	C₃×C₉×C₃₇	3₋¹⁺²	1	1	yes	characteristic
25	C₃×C₉×C₃₇	3₋¹⁺²	1	2	yes	—
26	C₃×C₉×C₃₇	3₋¹⁺²	1	1	yes	characteristic
27	C₃×C₉×C₃₇	3₋¹⁺²	1	2	yes	—
28	C₃×C₉×C₃₇	3₋¹⁺²	1	2	yes	—
29	C₃×C₉×C₃₇	C₃³	1	1	yes	characteristic
30	#11758601	—	3	3	no	—
31	#11758601	—	3	3	no	—
32	#11758601	C₃×C₉	1	9	yes	complemented
33	C₃×#6875	—	37	1	no	maximal, Sylow
34	C₃²×C₃₇	—	3	3	no	—
35	C₃²×C₃₇	C₉⋊C₉	1	2	yes	—
36	C₃²×C₃₇	C₉⋊C₉	1	1	yes	characteristic
37	C₃²×C₃₇	C₃×3₋¹⁺²	1	1	yes	characteristic
38	C₉×C₃₇	—	9	3	no	—
39	C₉×C₃₇	C₉⋊C₉	1	2	yes	—
40	C₉×C₃₇	C₉⋊C₉	1	2	yes	—
41	C₉×C₃₇	C₉⋊C₉	1	2	yes	—
42	C₉×C₃₇	C₃²×C₉	1	1	yes	characteristic
43	C₉×C₃₇	C₃×3₋¹⁺²	1	1	yes	characteristic
44	C₉×C₃₇	C₃×3₋¹⁺²	1	1	yes	characteristic
45	C₃×C₂₇⋊C₃	—	37	1	no	—
46	C₃×C₂₇⋊C₃	—	37	1	no	—
47	C₃×C₂₇⋊C₃	—	37	1	no	—
48	C₃×C₉⋊C₉	C₃₇⋊C₃	1	1	yes	characteristic
49	#6875	—	37	9	no	—
50	C₃×C₃₇	—	3	1	no	—
51	C₃×C₃₇	—	3	2	no	—
52	C₃×C₃₇	#6875	1	3	yes	complemented
53	C₃×C₃₇	C₃×C₉⋊C₉	1	1	yes	characteristic
54	C₃²×C₉	—	3	1	no	—
55	C₃²×C₉	C₃×C₃₇⋊C₃	1	1	yes	characteristic
56	C₂₇⋊C₃	—	37	6	no	—
57	C₂₇⋊C₃	—	37	3	no	—
58	C₂₇⋊C₃	—	37	3	no	—
59	C₂₇⋊C₃	—	37	3	no	—
60	C₂₇⋊C₃	—	111	2	no	—
61	C₂₇⋊C₃	—	111	2	no	—
62	C₃×C₂₇	—	37	3	no	—
63	C₃×C₂₇	—	111	1	no	—
64	C₃×C₂₇	—	111	1	no	—
65	C₉⋊C₉	—	3	2	no	—
66	C₉⋊C₉	C₃×C₃₇⋊C₃	1	3	yes	—
67	C₃₇	C₃×#6875	1	1	yes	characteristic, complemented, Sylow
68	C₃³	#11758608	1	1	yes	characteristic
69	C₃×C₉	—	3	3	no	—
70	C₃×C₉	—	9	3	no	—
71	C₃×C₉	C₉×C₃₇⋊C₃	1	2	yes	—
72	C₃×C₉	C₉×C₃₇⋊C₃	1	1	yes	characteristic
73	C₃×C₉	#11758605	1	2	yes	—
74	C₃×C₉	#11758605	1	1	yes	characteristic
75	C₃×C₉	#11758606	1	2	yes	—
76	C₃×C₉	#11758606	1	1	yes	characteristic
77	C₃×C₉	#11758608	1	2	yes	—
78	C₃×C₉	C₃²×C₃₇⋊C₃	1	1	yes	characteristic
79	C₂₇	—	37	9	no	—
80	C₂₇	—	111	3	no	—
81	C₂₇	—	111	3	no	—
82	C₃²	—	3	3	no	—
83	C₃²	#15688504	1	2	yes	—
84	C₃²	#15688504	1	1	yes	characteristic
85	C₃²	C₃×#11758608	1	1	yes	characteristic
86	C₉	—	9	3	no	—
87	C₉	#15688504	1	2	yes	—
88	C₉	#15688504	1	2	yes	—
89	C₉	#15688504	1	2	yes	—
90	C₉	C₃×C₉×C₃₇⋊C₃	1	1	yes	characteristic
91	C₉	C₃×#11758606	1	1	yes	characteristic
92	C₉	C₃×#11758605	1	1	yes	characteristic
93	C₃	—	3	1	no	—
94	C₃	—	3	2	no	—
95	C₃	#22582491	1	3	yes	direct product factor
96	C₃	C₃×#15688504	1	1	yes	characteristic

	subgroup	G/H
center	C₃²	#15688504
commutator	C₉×C₃₇	C₃²×C₉
Frattini	C₃×C₉	C₃²×C₃₇⋊C₃
Fitting	C₃×C₃₇×C₉⋊C₉	C₃
socle	C₃²×C₃₇	C₉⋊C₉
prime radical	C₃³×C₃₇	3₋¹⁺²
cosocle	C₃×C₉×C₃₇	C₃³
hypercenter	C₃×C₉⋊C₉	C₃₇⋊C₃
hypocenter	C₃₇	C₃×#6875
LCS	G ▷ C₉×C₃₇ ▷ C₃×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₃² ◁ C₃²×C₉ ◁ C₃×C₉⋊C₉

Complements

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

N	H ≅ G/N	type
4. #22582491	C₃	direct (N × H)
8. #15688511	C₉	semidirect
14. C₃×#11758601	C₉	semidirect
32. #11758601	C₃×C₉	semidirect
52. C₃×C₃₇	#6875	semidirect
67. C₃₇	C₃×#6875	semidirect
95. C₃	#22582491	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×#15688511	3
#22582491	3
C₃×C₃₇×C₉⋊C₉	3
C₃×#6875	37

Subgroups — C3×#22582491 #41006328

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#22582491 #41006328