Subgroups — C₃×#22582517 #41007367

Order 26973.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#15688521	C₃	1	2	yes	maximal
2	C₃×#15688505	C₃	1	1	yes	maximal, characteristic
3	#22582517	C₃	1	9	yes	maximal, direct product factor
4	C₃×C₃₇×#733	C₃	1	1	yes	maximal, characteristic
5	C₃×#11758608	—	3	2	no	—
6	C₃²×#66524	—	3	1	no	—
7	#15688521	—	3	4	no	—
8	#15688521	C₃²	1	6	yes	—
9	#15688505	—	3	2	no	—
10	#15688505	C₃²	1	3	yes	—
11	C₃×3₋¹⁺²×C₃₇	—	3	1	no	—
12	C₃²×C₉×C₃₇	C₃²	1	1	yes	characteristic
13	C₃₇×#733	—	3	2	no	—
14	C₃₇×#733	C₃²	1	3	yes	—
15	C₃³×C₃₇	H(3,𝔽₃)	1	1	yes	characteristic
16	3₋¹⁺²×C₃₇	—	3	3	no	—
17	3₋¹⁺²×C₃₇	—	9	2	no	—
18	C₃×C₉×C₃₇	—	3	2	no	—
19	C₃×C₉×C₃₇	—	3	1	no	—
20	C₃×C₉×C₃₇	—	9	1	no	—
21	C₃×C₉×C₃₇	H(3,𝔽₃)	1	2	yes	—
22	C₃×C₉×C₃₇	C₃³	1	1	yes	characteristic
23	#11758608	—	3	6	no	—
24	#11758608	—	9	4	no	—
25	C₃×#66524	—	3	3	no	—
26	C₃×#66524	—	9	3	no	—
27	C₃×#66524	—	9	2	no	—
28	C₃×#6882	—	37	1	no	maximal, Sylow
29	C₃²×C₃₇	—	3	3	no	—
30	C₃²×C₃₇	#732	1	2	yes	—
31	C₃²×C₃₇	#732	1	1	yes	characteristic
32	C₃²×C₃₇	C₃×H(3,𝔽₃)	1	1	yes	characteristic
33	C₉×C₃₇	—	3	2	no	—
34	C₉×C₃₇	—	3	1	no	—
35	C₉×C₃₇	—	9	3	no	—
36	#66524	—	9	3	no	—
37	#66524	—	9	6	no	—
38	C₃×#733	—	37	2	no	—
39	C₃×#733	C₃₇⋊C₃	1	1	yes	characteristic
40	C₃×C₉⋊C₉	—	37	1	no	—
41	#6882	—	37	9	no	—
42	C₃×C₃₇	—	3	1	no	—
43	C₃×C₃₇	—	3	2	no	—
44	C₃×C₃₇	#6882	1	3	yes	complemented
45	C₃×C₃₇	C₃×#732	1	1	yes	characteristic
46	C₃×3₋¹⁺²	—	3	1	no	—
47	C₃×3₋¹⁺²	—	111	2	no	—
48	C₃²×C₉	—	111	1	no	—
49	C₃²×C₉	C₃×C₃₇⋊C₃	1	1	yes	characteristic
50	#733	—	3	2	no	—
51	#733	—	37	6	no	—
52	#733	—	111	4	no	—
53	#733	C₃×C₃₇⋊C₃	1	3	yes	—
54	C₉⋊C₉	—	37	3	no	—
55	C₉⋊C₉	—	111	2	no	—
56	C₃₇	C₃×#6882	1	1	yes	characteristic, complemented, Sylow
57	C₃³	C₃²⋊(C₃₇⋊C₃)	1	1	yes	characteristic
58	3₋¹⁺²	—	3	3	no	—
59	3₋¹⁺²	—	9	2	no	—
60	3₋¹⁺²	—	333	4	no	—
61	3₋¹⁺²	—	111	6	no	—
62	C₃×C₉	—	3	2	no	—
63	C₃×C₉	—	3	1	no	—
64	C₃×C₉	—	9	1	no	—
65	C₃×C₉	—	333	3	no	—
66	C₃×C₉	—	333	2	no	—
67	C₃×C₉	—	111	3	no	—
68	C₃×C₉	C₃²⋊(C₃₇⋊C₃)	1	2	yes	—
69	C₃×C₉	C₃²×C₃₇⋊C₃	1	1	yes	characteristic
70	C₃²	—	3	3	no	—
71	C₃²	#15688518	1	2	yes	—
72	C₃²	#15688518	1	1	yes	characteristic
73	C₃²	C₃×C₃²⋊(C₃₇⋊C₃)	1	1	yes	characteristic
74	C₉	—	3	2	no	—
75	C₉	—	3	1	no	—
76	C₉	—	9	3	no	—
77	C₉	—	333	3	no	—
78	C₉	—	333	6	no	—
79	C₃	—	3	1	no	—
80	C₃	—	3	2	no	—
81	C₃	#22582517	1	3	yes	direct product factor
82	C₃	C₃×#15688518	1	1	yes	characteristic

	subgroup	G/H
center	C₃²	#15688518
commutator, cosocle	C₃×C₉×C₃₇	C₃³
Frattini	C₃×C₉	C₃²×C₃₇⋊C₃
Fitting	C₃×C₃₇×#733	C₃
socle	C₃²×C₃₇	#732
prime radical	C₃³×C₃₇	H(3,𝔽₃)
hypercenter	C₃×#733	C₃₇⋊C₃
hypocenter	C₃₇	C₃×#6882
LCS	G ▷ C₃×C₉×C₃₇ ▷ C₃²×C₃₇ ▷ C₃×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₃² ◁ C₃³ ◁ C₃²×C₉ ◁ C₃×#733

Complements

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

N	H ≅ G/N	type
3. #22582517	C₃	direct (N × H)
44. C₃×C₃₇	#6882	semidirect
56. C₃₇	C₃×#6882	semidirect
81. C₃	#22582517	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×#15688521	3
C₃×#15688505	3
#22582517	3
C₃×C₃₇×#733	3
C₃×#6882	37

Subgroups — C3×#22582517 #41007367

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#22582517 #41007367