Subgroups — #41008317

Order 26973.

194 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#15688541	C₃	1	3	yes	maximal
2	C₃×C₉×#66524	C₃	1	1	yes	maximal, characteristic
3	#15688541	—	3	3	no	—
4	#15688541	—	3	3	no	—
5	#15688541	C₉	1	9	yes	complemented
6	C₃×#11758603	—	3	3	no	—
7	C₃²×#66524	C₉	1	1	yes	characteristic
8	C₃²×#66524	C₉	1	1	yes	characteristic
9	C₃²×#66524	C₃²	1	1	yes	characteristic
10	C₉×#66524	—	3	1	no	—
11	C₉×#66524	—	3	2	no	—
12	C₃²×C₉×C₃₇	C₉	1	1	yes	characteristic
13	C₃³×C₃₇	C₃×C₉	1	1	yes	characteristic
14	C₃×C₉×C₃₇	—	3	1	no	—
15	C₃×C₉×C₃₇	—	3	3	no	—
16	C₃×#66524	—	3	1	no	—
17	C₃×#66524	—	3	1	no	—
18	C₃×#66524	—	3	3	no	—
19	C₃×#66524	—	3	3	no	—
20	C₃×#66524	C₃×C₉	1	3	yes	—
21	C₃×#66524	H(3,𝔽₃)	1	1	yes	characteristic
22	C₃×#66524	3₋¹⁺²	1	3	yes	—
23	C₃×#66524	3₋¹⁺²	1	3	yes	—
24	C₃×#66524	3₋¹⁺²	1	2	yes	—
25	#11758603	—	3	9	no	—
26	#10624467	—	37	1	no	maximal, Sylow
27	C₃²×C₃₇	—	3	1	no	—
28	C₃²×C₃₇	—	3	1	no	—
29	C₃²×C₃₇	—	3	1	no	—
30	C₃²×C₃₇	C₉²	1	1	yes	characteristic
31	C₃²×C₃₇	C₃²⋊C₉	1	1	yes	characteristic
32	C₃²×C₃₇	C₉⋊C₉	1	1	yes	characteristic
33	C₃²×C₃₇	C₉⋊C₉	1	1	yes	characteristic
34	C₉×C₃₇	—	3	3	no	—
35	#66524	—	3	3	no	—
36	#66524	—	3	3	no	—
37	#66524	C₃²⋊C₉	1	3	yes	—
38	#66524	C₉⋊C₉	1	6	yes	—
39	C₃×C₂₇⋊C₃	—	37	3	no	—
40	C₃×C₉²	—	37	1	no	—
41	C₃×C₃₇	—	3	1	no	—
42	C₃×C₃₇	—	3	1	no	—
43	C₃×C₃₇	—	3	1	no	—
44	C₃×C₃₇	#6855	1	1	yes	characteristic
45	C₃×C₃₇	#6869	1	1	yes	characteristic
46	C₃×C₃₇	#6869	1	1	yes	characteristic
47	C₃×C₃₇	#6869	1	1	yes	characteristic
48	C₃²×C₉	—	37	1	no	—
49	C₃²×C₉	—	37	1	no	—
50	C₃²×C₉	—	37	1	no	—
51	C₃²×C₉	#66526	1	1	yes	characteristic
52	C₂₇⋊C₃	—	37	9	no	—
53	C₂₇⋊C₃	—	111	3	no	—
54	C₂₇⋊C₃	—	111	3	no	—
55	C₃×C₂₇	—	111	3	no	—
56	C₉²	—	111	1	no	—
57	C₉²	—	111	2	no	—
58	C₃₇	#10624467	1	1	yes	characteristic, complemented, Sylow
59	C₃³	C₃×#66526	1	1	yes	characteristic
60	C₃×C₉	—	3	1	no	—
61	C₃×C₉	—	3	3	no	—
62	C₃×C₉	—	37	3	no	—
63	C₃×C₉	—	37	1	no	—
64	C₃×C₉	—	37	2	no	—
65	C₃×C₉	—	37	3	no	—
66	C₃×C₉	—	37	3	no	—
67	C₃×C₉	—	111	1	no	—
68	C₃×C₉	—	111	1	no	—
69	C₃×C₉	—	111	3	no	—
70	C₃×C₉	—	111	3	no	—
71	C₂₇	—	111	9	no	—
72	C₃²	—	3	1	no	—
73	C₃²	—	3	1	no	—
74	C₃²	—	3	1	no	—
75	C₃²	C₉×#66526	1	1	yes	characteristic
76	C₃²	C₃²⋊#66526	1	1	yes	characteristic
77	C₃²	#15688537	1	1	yes	characteristic
78	C₃²	#15688538	1	1	yes	characteristic
79	C₉	—	3	3	no	—
80	C₉	—	37	3	no	—
81	C₉	—	37	6	no	—
82	C₉	—	111	3	no	—
83	C₉	—	111	3	no	—
84	C₃	—	3	1	no	—
85	C₃	—	3	1	no	—
86	C₃	—	3	1	no	—
87	C₃	(C₃×#66526)⋊C₉	1	1	yes	characteristic
88	C₃	#22582694	1	1	yes	characteristic
89	C₃	#22582695	1	1	yes	characteristic
90	C₃	#22582696	1	1	yes	characteristic

	subgroup	G/H
center	C₃²	C₃²⋊#66526
commutator	C₃²×C₃₇	C₉²
Frattini	C₃³	C₃×#66526
Fitting	C₃²×C₉×C₃₇	C₉
socle	C₃²×C₃₇	C₃²⋊C₉
prime radical	C₃³×C₃₇	C₃×C₉
cosocle	C₃²×#66524	C₃²
hypercenter	C₃²×C₉	#66526
hypocenter	C₃₇	#10624467
LCS	G ▷ C₃²×C₃₇ ▷ C₃×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₃² ◁ C₃³ ◁ C₃²×C₉

Complements

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

N	H ≅ G/N	type
5. #15688541	C₉	semidirect
58. C₃₇	#10624467	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
C₃×C₉×#66524	3
#10624467	37