Subgroups — C₃×#22582538 #41007497

Order 26973.

1052 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22582538	C₃	1	27	yes	maximal, direct product factor
2	C₃×#15688506	C₃	1	3	yes	maximal, complemented
3	C₃×#15688505	C₃	1	3	yes	maximal, complemented
4	C₃×C₃²⋊#66524	C₃	1	3	yes	maximal
5	C₃×C₉×#66524	C₃	1	3	yes	maximal, complemented
6	C₃³×C₉×C₃₇	C₃	1	1	yes	maximal, characteristic
7	C₃²×#66524	C₃²	1	9	yes	—
8	#15688506	C₃²	1	27	yes	complemented
9	#15688505	C₃²	1	27	yes	complemented
10	C₃²⋊#66524	C₃²	1	27	yes	—
11	C₉×#66524	C₃²	1	27	yes	complemented
12	C₃⁴×C₃₇	C₃²	1	1	yes	characteristic
13	C₃²×C₉×C₃₇	C₉	1	27	yes	complemented
14	C₃²×C₉×C₃₇	C₃²	1	1	yes	characteristic
15	C₃²×C₉×C₃₇	C₃²	1	1	yes	characteristic
16	C₃²×C₉×C₃₇	C₃²	1	1	yes	characteristic
17	C₃²×C₉×C₃₇	C₃²	1	9	yes	—
18	C₃³×C₃₇	—	3	9	no	—
19	C₃³×C₃₇	C₃×C₉	1	9	yes	—
20	C₃³×C₃₇	C₃³	1	3	yes	—
21	C₃³×C₃₇	C₃³	1	1	yes	characteristic
22	C₃×C₉×C₃₇	C₃×C₉	1	9	yes	—
23	C₃×C₉×C₃₇	C₃×C₉	1	9	yes	—
24	C₃×C₉×C₃₇	C₃×C₉	1	9	yes	—
25	C₃×C₉×C₃₇	C₃×C₉	1	81	yes	complemented
26	C₃×C₉×C₃₇	C₃³	1	3	yes	—
27	C₃×C₉×C₃₇	C₃³	1	3	yes	—
28	C₃×C₉×C₃₇	C₃³	1	3	yes	—
29	C₃×#66524	—	3	27	no	—
30	C₃×#66524	C₃³	1	27	yes	—
31	C₃×#6887	—	37	1	no	maximal, Sylow
32	C₃²×C₃₇	—	3	9	no	—
33	C₃²×C₃₇	—	3	27	no	—
34	C₃²×C₃₇	C₃²×C₉	1	9	yes	—
35	C₃²×C₃₇	C₃²×C₉	1	3	yes	—
36	C₃²×C₃₇	#737	1	9	yes	—
37	C₃²×C₃₇	C₃⁴	1	1	yes	characteristic
38	C₉×C₃₇	C₃²×C₉	1	9	yes	—
39	C₉×C₃₇	C₃²×C₉	1	9	yes	—
40	C₉×C₃₇	C₃²×C₉	1	9	yes	—
41	#66524	—	3	27	no	—
42	C₃³×C₉	C₃₇⋊C₃	1	1	yes	characteristic
43	#6887	—	37	27	no	—
44	C₃×C₉⋊C₉	—	37	3	no	—
45	C₃×C₉⋊C₉	—	37	3	no	—
46	C₃×C₃²⋊C₉	—	37	3	no	—
47	C₃×C₉²	—	37	3	no	—
48	C₃×C₃₇	—	3	9	no	—
49	C₃×C₃₇	#6887	1	9	yes	complemented
50	C₃×C₃₇	C₃³×C₉	1	1	yes	characteristic
51	C₃×C₃₇	C₃×#737	1	3	yes	—
52	C₃⁴	C₃×C₃₇⋊C₃	1	1	yes	characteristic
53	C₃²×C₉	—	37	9	no	—
54	C₃²×C₉	#66524	1	27	yes	complemented
55	C₃²×C₉	C₃×C₃₇⋊C₃	1	1	yes	characteristic
56	C₃²×C₉	C₃×C₃₇⋊C₃	1	1	yes	characteristic
57	C₃²×C₉	C₃×C₃₇⋊C₃	1	9	yes	—
58	C₃²×C₉	C₃×C₃₇⋊C₃	1	1	yes	characteristic
59	C₉⋊C₉	—	37	27	no	—
60	C₉⋊C₉	—	37	27	no	—
61	C₃²⋊C₉	—	37	27	no	—
62	C₉²	—	37	27	no	—
63	C₃₇	C₃×#6887	1	1	yes	characteristic, complemented, Sylow
64	C₃³	—	3	9	no	—
65	C₃³	C₃×#66524	1	9	yes	—
66	C₃³	C₃²×C₃₇⋊C₃	1	3	yes	—
67	C₃³	C₃²×C₃₇⋊C₃	1	1	yes	characteristic
68	C₃×C₉	—	37	27	no	—
69	C₃×C₉	—	111	27	no	—
70	C₃×C₉	C₃×#66524	1	9	yes	—
71	C₃×C₉	C₃×#66524	1	9	yes	—
72	C₃×C₉	C₃×#66524	1	9	yes	—
73	C₃×C₉	C₃×#66524	1	81	yes	complemented
74	C₃×C₉	C₃²×C₃₇⋊C₃	1	3	yes	—
75	C₃×C₉	C₃²×C₃₇⋊C₃	1	3	yes	—
76	C₃×C₉	C₃²×C₃₇⋊C₃	1	3	yes	—
77	C₃²	—	3	27	no	—
78	C₃²	—	3	9	no	—
79	C₃²	C₃²×#66524	1	9	yes	—
80	C₃²	C₃²×#66524	1	3	yes	—
81	C₃²	#15688531	1	9	yes	—
82	C₃²	C₃³×C₃₇⋊C₃	1	1	yes	characteristic
83	C₉	—	111	27	no	—
84	C₉	C₃²×#66524	1	9	yes	—
85	C₉	C₃²×#66524	1	9	yes	—
86	C₉	C₃²×#66524	1	9	yes	—
87	C₃	—	3	9	no	—
88	C₃	#22582538	1	9	yes	direct product factor
89	C₃	C₃³×#66524	1	1	yes	characteristic
90	C₃	C₃×#15688531	1	3	yes	—

	subgroup	G/H
center	C₃²×C₉	C₃×C₃₇⋊C₃
commutator	C₃×C₃₇	C₃³×C₉
Frattini	C₃²	C₃³×C₃₇⋊C₃
Fitting	C₃³×C₉×C₃₇	C₃
socle	C₃³×C₃₇	C₃³
prime radical	C₃⁴×C₃₇	C₃²
cosocle	C₃²×C₃₇	C₃⁴
hypercenter	C₃³×C₉	C₃₇⋊C₃
hypocenter	C₃₇	C₃×#6887
LCS	G ▷ C₃×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₃²×C₉ ◁ C₃³×C₉

Complements

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

N	H ≅ G/N	type
1. #22582538	C₃	direct (N × H)
2. C₃×#15688506	C₃	semidirect
3. C₃×#15688505	C₃	semidirect
5. C₃×C₉×#66524	C₃	semidirect
8. #15688506	C₃²	semidirect
9. #15688505	C₃²	semidirect
11. C₉×#66524	C₃²	semidirect
13. C₃²×C₉×C₃₇	C₉	semidirect
25. C₃×C₉×C₃₇	C₃×C₉	semidirect
49. C₃×C₃₇	#6887	semidirect
54. C₃²×C₉	#66524	semidirect
63. C₃₇	C₃×#6887	semidirect
73. C₃×C₉	C₃×#66524	semidirect
88. C₃	#22582538	direct (N × H)

Maximal subgroups

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

subgroup	index
#22582538	3
C₃×#15688506	3
C₃×#15688505	3
C₃×C₃²⋊#66524	3
C₃×C₉×#66524	3
C₃³×C₉×C₃₇	3
C₃×#6887	37

Subgroups — C3×#22582538 #41007497

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#22582538 #41007497