Subgroups — #41008502

Order 26973.

312 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#15688541	C₃	1	3	yes	maximal, complemented
2	#22582695	C₃	1	9	yes	maximal, complemented
3	C₃×#15688532	C₃	1	1	yes	maximal, characteristic
4	#15688541	—	3	6	no	—
5	#15688541	C₃²	1	9	yes	—
6	C₃×#11758603	—	3	3	no	—
7	#15688532	—	3	3	no	—
8	#15688532	—	3	6	no	—
9	C₃×#11758608	C₉	1	1	yes	characteristic
10	C₃×#11758605	C₉	1	3	yes	—
11	C₃×#11758606	C₉	1	3	yes	—
12	C₃×C₃²⋊(C₃₇⋊C₃)	C₉	1	1	yes	characteristic
13	C₃²×#66524	C₃²	1	1	yes	characteristic
14	C₃×C₉×C₃₇⋊C₃	C₃²	1	3	yes	—
15	C₃×3₋¹⁺²×C₃₇	C₉	1	1	yes	characteristic
16	C₃³×C₃₇	C₃×C₉	1	1	yes	characteristic
17	C₃²×C₃₇⋊C₃	C₃×C₉	1	3	yes	—
18	3₋¹⁺²×C₃₇	—	3	3	no	—
19	C₃×C₉×C₃₇	C₃×C₉	1	3	yes	—
20	C₃²⋊(C₃₇⋊C₃)	—	3	3	no	—
21	#11758608	—	3	3	no	—
22	C₃×#66524	C₃×C₉	1	3	yes	—
23	C₃×#66524	C₃×C₉	1	1	yes	characteristic
24	C₃×#66524	C₃×C₉	1	1	yes	characteristic
25	C₃×#66524	H(3,𝔽₃)	1	3	yes	—
26	C₃×#66524	3₋¹⁺²	1	6	yes	—
27	C₃×#66524	C₃³	1	1	yes	characteristic
28	#11758606	—	3	9	no	—
29	#11758605	—	3	9	no	—
30	C₉×C₃₇⋊C₃	—	3	3	no	—
31	C₉×C₃₇⋊C₃	—	3	6	no	—
32	#11758603	—	3	9	no	—
33	#10624694	—	37	1	no	maximal, Sylow
34	C₃²×C₃₇	—	9	1	no	—
35	C₃²×C₃₇	C₃²⋊C₉	1	3	yes	—
36	C₃²×C₃₇	C₃²×C₉	1	1	yes	characteristic
37	C₃×C₃₇⋊C₃	—	3	3	no	—
38	C₃×C₃₇⋊C₃	—	9	3	no	—
39	C₉×C₃₇	—	3	3	no	—
40	#66524	—	3	3	no	—
41	#66524	C₃²⋊C₉	1	3	yes	—
42	#66524	C₃²⋊C₉	1	3	yes	—
43	#66524	C₃×H(3,𝔽₃)	1	1	yes	characteristic
44	#66524	C₃×3₋¹⁺²	1	2	yes	—
45	C₃×#737	—	37	1	no	—
46	C₃×C₂₇⋊C₃	—	37	3	no	—
47	#6869	—	37	9	no	—
48	C₃×C₃₇	—	3	1	no	—
49	C₃×C₃₇	—	3	3	no	—
50	C₃×C₃₇	C₃×C₃²⋊C₉	1	1	yes	characteristic
51	C₃₇⋊C₃	—	9	3	no	—
52	#737	—	111	3	no	—
53	#737	—	111	6	no	—
54	C₃×3₋¹⁺²	—	37	1	no	—
55	C₃×3₋¹⁺²	—	37	3	no	—
56	C₃×3₋¹⁺²	—	37	3	no	—
57	C₃×3₋¹⁺²	#66526	1	1	yes	characteristic
58	C₃×H(3,𝔽₃)	—	37	1	no	—
59	C₃²×C₉	—	37	1	no	—
60	C₃²×C₉	—	37	3	no	—
61	C₂₇⋊C₃	—	37	9	no	—
62	C₂₇⋊C₃	—	111	6	no	—
63	C₃×C₂₇	—	111	3	no	—
64	C₃₇	#10624694	1	1	yes	characteristic, complemented, Sylow
65	C₃³	—	37	3	no	—
66	C₃³	C₃×#66526	1	1	yes	characteristic
67	3₋¹⁺²	—	3	3	no	—
68	3₋¹⁺²	—	111	9	no	—
69	3₋¹⁺²	—	111	9	no	—
70	3₋¹⁺²	—	111	3	no	—
71	H(3,𝔽₃)	—	111	3	no	—
72	C₃×C₉	—	37	3	no	—
73	C₃×C₉	—	37	6	no	—
74	C₃×C₉	—	37	1	no	—
75	C₃×C₉	—	37	1	no	—
76	C₃×C₉	—	37	1	no	—
77	C₃×C₉	—	37	3	no	—
78	C₃×C₉	—	111	3	no	—
79	C₃×C₉	—	111	6	no	—
80	C₃×C₉	C₃×#66526	1	3	yes	—
81	C₂₇	—	111	9	no	—
82	C₃²	—	9	1	no	—
83	C₃²	—	333	3	no	—
84	C₃²	—	111	3	no	—
85	C₃²	C₃²⋊#66526	1	3	yes	—
86	C₃²	C₃²×#66526	1	1	yes	characteristic
87	C₉	—	3	3	no	—
88	C₉	—	37	1	no	—
89	C₉	—	37	2	no	—
90	C₉	—	37	3	no	—
91	C₉	—	37	3	no	—
92	C₉	—	111	3	no	—
93	C₃	—	3	1	no	—
94	C₃	—	3	3	no	—
95	C₃	—	333	3	no	—
96	C₃	C₃×C₃²⋊#66526	1	1	yes	characteristic

	subgroup	G/H
center	C₃	C₃×C₃²⋊#66526
commutator	C₃²×C₃₇	C₃²×C₉
Frattini	C₃²	C₃²×#66526
Fitting	C₃×3₋¹⁺²×C₃₇	C₉
socle	C₃×C₃₇	C₃×C₃²⋊C₉
prime radical	C₃×C₃²⋊(C₃₇⋊C₃)	C₉
cosocle	C₃×#66524	C₃³
hypercenter	C₃×3₋¹⁺²	#66526
hypocenter	C₃₇	#10624694
LCS	G ▷ C₃²×C₃₇ ▷ C₃×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₃ ◁ C₃³ ◁ C₃×3₋¹⁺²

Complements

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

N	H ≅ G/N	type
1. C₃×#15688541	C₃	semidirect
2. #22582695	C₃	semidirect
64. C₃₇	#10624694	semidirect

Maximal subgroups

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

subgroup	index
C₃×#15688541	3
#22582695	3
C₃×#15688532	3
#10624694	37