Group #41005266 — subgroups

Subgroups — #41005266

Order 26973.

296 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 103 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#15688506	C₃	1	1	yes	maximal, characteristic
2	C₃×#15688504	C₃	1	3	yes	maximal
3	#22582441	C₃	1	3	yes	maximal
4	#22582441	C₃	1	3	yes	maximal
5	#22582441	C₃	1	1	yes	maximal, characteristic
6	#22582441	C₃	1	1	yes	maximal, characteristic
7	C₃₇×#6855	C₃	1	1	yes	maximal, characteristic
8	C₃²×#66524	C₃²	1	1	yes	characteristic
9	C₃²×#66524	C₃²	1	3	yes	—
10	C₃²×#66524	C₃²	1	1	yes	characteristic
11	C₃²×#66524	C₃²	1	1	yes	characteristic
12	C₃²×#66524	C₃²	1	3	yes	—
13	#15688506	—	3	3	no	—
14	#15688504	—	3	9	no	—
15	C₃²×C₉×C₃₇	C₃²	1	3	yes	—
16	C₃²×C₉×C₃₇	C₃²	1	1	yes	characteristic
17	C₃³×C₃₇	C₃³	1	1	yes	characteristic
18	C₃×C₉×C₃₇	—	3	1	no	—
19	C₃×C₉×C₃₇	—	3	1	no	—
20	C₃×C₉×C₃₇	—	3	1	no	—
21	C₃×C₉×C₃₇	—	3	3	no	—
22	C₃×C₉×C₃₇	—	3	3	no	—
23	C₃×C₉×C₃₇	—	3	3	no	—
24	C₃×C₉×C₃₇	—	3	3	no	—
25	C₃×C₉×C₃₇	3₋¹⁺²	1	3	yes	—
26	C₃×#66524	—	3	3	no	—
27	C₃×#66524	—	3	3	no	—
28	C₃×#66524	—	3	3	no	—
29	C₃×#66524	—	3	3	no	—
30	C₃×#66524	—	3	3	no	—
31	C₃×#66524	—	3	1	no	—
32	C₃×#66524	—	3	1	no	—
33	C₃×#66524	—	3	1	no	—
34	C₃×#66524	—	3	3	no	—
35	C₃×#66524	—	3	3	no	—
36	C₃×#66524	—	3	3	no	—
37	C₃×#66524	—	3	3	no	—
38	C₃×#66524	—	3	3	no	—
39	C₃×#66524	3₋¹⁺²	1	9	yes	—
40	#10624577	—	37	1	no	maximal, Sylow
41	C₃²×C₃₇	C₃×3₋¹⁺²	1	3	yes	—
42	C₃²×C₃₇	C₃×3₋¹⁺²	1	1	yes	characteristic
43	C₃²×C₃₇	#737	1	1	yes	characteristic
44	C₃²×C₃₇	#737	1	3	yes	—
45	C₃²×C₃₇	#737	1	1	yes	characteristic
46	C₃²×C₃₇	#737	1	1	yes	characteristic
47	C₃²×C₃₇	#737	1	3	yes	—
48	C₉×C₃₇	—	3	3	no	—
49	C₉×C₃₇	—	9	3	no	—
50	#66524	—	3	9	no	—
51	#66524	—	9	1	no	—
52	#66524	—	9	3	no	—
53	#66524	—	9	1	no	—
54	#66524	—	9	1	no	—
55	C₃×C₉⋊C₉	—	37	3	no	—
56	C₃×C₉⋊C₉	—	37	1	no	—
57	#6855	—	37	1	no	—
58	#6855	—	37	3	no	—
59	#6855	—	37	3	no	—
60	#6855	—	37	1	no	—
61	#6855	C₃₇⋊C₃	1	1	yes	characteristic
62	C₃×C₃₇	#6895	1	1	yes	characteristic
63	C₃×C₃₇	#6895	1	3	yes	—
64	C₃×C₃₇	#6899	1	3	yes	—
65	C₃×C₃₇	#6899	1	1	yes	characteristic
66	C₃×C₃₇	#6899	1	3	yes	—
67	C₃×C₃₇	#6899	1	1	yes	characteristic
68	C₃×C₃₇	#6900	1	1	yes	characteristic
69	C₃²×C₉	—	37	3	no	—
70	C₃²×C₉	—	37	3	no	—
71	C₃²×C₉	—	37	1	no	—
72	C₃²×C₉	—	37	1	no	—
73	C₃²×C₉	—	37	1	no	—
74	C₃²×C₉	C₃×C₃₇⋊C₃	1	3	yes	—
75	C₃²×C₉	C₃×C₃₇⋊C₃	1	1	yes	characteristic
76	C₉⋊C₉	—	111	9	no	—
77	C₉⋊C₉	—	111	3	no	—
78	C₃₇	#10624577	1	1	yes	characteristic, complemented, Sylow
79	C₃³	C₃²×C₃₇⋊C₃	1	1	yes	characteristic
80	C₃×C₉	—	3	1	no	—
81	C₃×C₉	—	3	1	no	—
82	C₃×C₉	—	3	1	no	—
83	C₃×C₉	—	3	3	no	—
84	C₃×C₉	—	3	3	no	—
85	C₃×C₉	—	3	3	no	—
86	C₃×C₉	—	3	3	no	—
87	C₃×C₉	—	37	9	no	—
88	C₃×C₉	—	111	3	no	—
89	C₃×C₉	—	111	3	no	—
90	C₃×C₉	—	111	1	no	—
91	C₃×C₉	—	111	1	no	—
92	C₃×C₉	—	111	1	no	—
93	C₃×C₉	—	111	3	no	—
94	C₃×C₉	—	111	3	no	—
95	C₃×C₉	—	111	3	no	—
96	C₃×C₉	—	111	3	no	—
97	C₃×C₉	—	111	3	no	—
98	C₃×C₉	—	111	3	no	—
99	C₃×C₉	—	111	3	no	—
100	C₃×C₉	—	111	3	no	—
101	C₃×C₉	#11758606	1	3	yes	—
102	C₃²	3₋¹⁺²×C₃₇⋊C₃	1	3	yes	—
103	C₃²	C₃×#11758606	1	1	yes	characteristic
104	C₃²	#15688530	1	1	yes	characteristic
105	C₃²	#15688531	1	3	yes	—
106	C₃²	#15688532	1	1	yes	characteristic
107	C₃²	#15688532	1	1	yes	characteristic
108	C₃²	#15688532	1	3	yes	—
109	C₉	—	3	3	no	—
110	C₉	—	9	3	no	—
111	C₉	—	333	1	no	—
112	C₉	—	333	3	no	—
113	C₉	—	333	1	no	—
114	C₉	—	333	1	no	—
115	C₉	—	111	9	no	—
116	C₃	#22582575	1	1	yes	characteristic
117	C₃	#22582577	1	3	yes	—
118	C₃	#22582593	1	3	yes	—
119	C₃	#22582595	1	1	yes	characteristic
120	C₃	#22582597	1	3	yes	—
121	C₃	#22582600	1	1	yes	characteristic
122	C₃	#22582604	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₃×#15688506

C₃

yes

maximal, characteristic

C₃×#15688504

C₃

yes

maximal

#22582441

C₃

yes

maximal

#22582441

C₃

yes

maximal

#22582441

C₃

yes

maximal, characteristic

#22582441

C₃

yes

maximal, characteristic

C₃₇×#6855

C₃

yes

maximal, characteristic

C₃²×#66524

C₃²

yes

characteristic

C₃²×#66524

C₃²

yes

—

C₃²×#66524

C₃²

yes

characteristic

C₃²×#66524

C₃²

yes

characteristic

C₃²×#66524

C₃²

yes

—

#15688506

—

#15688504

—

C₃²×C₉×C₃₇

C₃²

yes

—

C₃²×C₉×C₃₇

C₃²

yes

characteristic

C₃³×C₃₇

C₃³

yes

characteristic

C₃×C₉×C₃₇

—

C₃×C₉×C₃₇

—

C₃×C₉×C₃₇

—

C₃×C₉×C₃₇

—

C₃×C₉×C₃₇

—

C₃×C₉×C₃₇

—

C₃×C₉×C₃₇

—

C₃×C₉×C₃₇

3₋¹⁺²

yes

—

—

—

—

—

—

—

—

—

—

—

—

—

—

3₋¹⁺²

yes

—

#10624577

—

maximal, Sylow

C₃²×C₃₇

C₃×3₋¹⁺²

yes

—

C₃²×C₃₇

C₃×3₋¹⁺²

yes

C₃²×C₃₇

yes

C₃²×C₃₇

yes

—

C₃²×C₃₇

yes

C₃²×C₃₇

yes

C₃²×C₃₇

yes

—

C₉×C₃₇

—

C₉×C₃₇

—

—

—

—

—

—

C₃×C₉⋊C₉

—

C₃×C₉⋊C₉

—

—

—

—

—

C₃₇⋊C₃

yes

C₃×C₃₇

yes

C₃×C₃₇

yes

—

C₃×C₃₇

#6899

yes

—

C₃×C₃₇

#6899

yes

characteristic

C₃×C₃₇

#6899

yes

—

C₃×C₃₇

yes

C₃×C₃₇

yes

C₃²×C₉

—

C₃²×C₉

—

C₃²×C₉

—

C₃²×C₉

—

C₃²×C₉

—

C₃²×C₉

C₃×C₃₇⋊C₃

yes

—

C₃²×C₉

C₃×C₃₇⋊C₃

yes

characteristic

C₉⋊C₉

—

111

—

C₉⋊C₉

—

111

—

C₃₇

#10624577

yes

characteristic, complemented, Sylow

C₃³

C₃²×C₃₇⋊C₃

yes

characteristic

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

111

—

C₃×C₉

—

111

—

C₃×C₉

—

111

—

C₃×C₉

—

111

—

C₃×C₉

—

111

—

C₃×C₉

—

111

—

C₃×C₉

—

111

—

C₃×C₉

—

111

—

C₃×C₉

—

111

—

C₃×C₉

—

111

—

C₃×C₉

—

111

—

C₃×C₉

—

111

—

100

C₃×C₉

—

111

—

101

C₃×C₉

#11758606

yes

—

102

C₃²

3₋¹⁺²×C₃₇⋊C₃

yes

—

103

C₃²

C₃×#11758606

yes

characteristic

104

C₃²

#15688530

yes

characteristic

105

C₃²

#15688531

yes

—

106

C₃²

#15688532

yes

characteristic

107

C₃²

#15688532

yes

characteristic

108

C₃²

#15688532

yes

—

109

C₉

—

110

C₉

—

111

C₉

—

333

—

112

C₉

—

333

—

113

C₉

—

333

—

114

C₉

—

333

—

115

C₉

—

111

—

116

C₃

#22582575

yes

characteristic

117

C₃

#22582577

yes

—

118

C₃

#22582593

yes

—

119

C₃

#22582595

yes

characteristic

120

C₃

#22582597

yes

—

121

C₃

#22582600

yes

characteristic

122

C₃

#22582604

yes

characteristic

	subgroup	G/H
center, Frattini	C₃³	C₃²×C₃₇⋊C₃
commutator, socle, prime radical, cosocle	C₃³×C₃₇	C₃³
Fitting	C₃₇×#6855	C₃
hypercenter	#6855	C₃₇⋊C₃
hypocenter	C₃₇	#10624577
LCS	G ▷ C₃³×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₃³ ◁ #6855

subgroup

G/H

center, Frattini

C₃³

C₃²×C₃₇⋊C₃

commutator, socle, prime radical, cosocle

C₃³×C₃₇

C₃³

Fitting

C₃₇×#6855

C₃

C₃₇⋊C₃

C₃₇

G ▷ C₃³×C₃₇ ▷ C₃₇

C₁ ◁ C₃³ ◁ #6855

N	H ≅ G/N	type
78. C₃₇	#10624577	semidirect

H ≅ G/N

type

78. C₃₇

#10624577

semidirect

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

subgroup	index
C₃×#15688506	3
C₃×#15688504	3
#22582441	3
C₃₇×#6855	3
#10624577	37

subgroup

index

C₃₇×#6855

Subgroups — #41005266

Conjugacy classes of subgroups

Complements

Maximal subgroups