Group #14547115 — subgroups

Subgroups — #14547115

Order 2187.

359 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 359 conjugacy classes of subgroups — too many to draw. Only its 59 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×C₉×3₋¹⁺²	C₃	1	1	yes	maximal, characteristic
2	#10624807	C₃	1	3	yes	maximal
3	#10624768	C₃	1	1	yes	maximal, characteristic
4	#10624768	C₃	1	1	yes	maximal, characteristic
5	C₃×#6868	C₃	1	1	yes	maximal, characteristic
6	#10624605	C₃	1	3	yes	maximal
7	#10624594	C₃	1	3	yes	maximal
8	C₃²×3₋¹⁺²	C₃²	1	1	yes	characteristic
9	C₃³×C₉	C₃²	1	1	yes	characteristic
10	#6891	C₃²	1	3	yes	—
11	#6891	C₃²	1	3	yes	—
12	C₉×3₋¹⁺²	—	3	3	no	—
13	C₉×3₋¹⁺²	—	3	3	no	—
14	C₉×3₋¹⁺²	—	3	3	no	—
15	C₃×C₉⋊C₉	—	3	2	no	—
16	C₃×C₃²⋊C₉	C₃²	1	3	yes	—
17	C₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
18	C₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
19	C₃×C₉²	—	3	1	no	—
20	#6868	—	3	2	no	—
21	#6868	—	3	2	no	—
22	#6868	—	3	1	no	—
23	#6868	—	3	1	no	—
24	#6868	—	3	2	no	—
25	#6868	—	3	1	no	—
26	#6868	—	3	9	no	—
27	#6860	—	3	9	no	—
28	#6858	—	3	9	no	—
29	C₃⁴	C₃³	1	1	yes	characteristic
30	C₃×3₋¹⁺²	—	3	1	no	—
31	C₃×3₋¹⁺²	—	3	1	no	—
32	C₃×3₋¹⁺²	—	3	9	no	—
33	C₃×3₋¹⁺²	—	3	3	no	—
34	C₃×3₋¹⁺²	—	3	3	no	—
35	C₃×3₋¹⁺²	H(3,𝔽₃)	1	3	yes	—
36	C₃²×C₉	—	3	1	no	—
37	C₃²×C₉	—	3	1	no	—
38	C₃²×C₉	—	3	1	no	—
39	C₃²×C₉	—	3	1	no	—
40	C₃²×C₉	—	3	1	no	—
41	C₃²×C₉	—	3	1	no	—
42	C₃²×C₉	—	3	3	no	—
43	C₃²×C₉	—	3	3	no	—
44	C₃²×C₉	—	9	2	no	—
45	C₃²×C₉	H(3,𝔽₃)	1	2	yes	—
46	C₃²×C₉	H(3,𝔽₃)	1	1	yes	characteristic
47	C₉⋊C₉	—	3	18	no	—
48	C₃²⋊C₉	—	3	1	no	—
49	C₃²⋊C₉	—	3	1	no	—
50	C₃²⋊C₉	—	3	1	no	—
51	C₃²⋊C₉	—	3	1	no	—
52	C₃²⋊C₉	—	3	3	no	—
53	C₃²⋊C₉	—	3	3	no	—
54	C₃²⋊C₉	—	3	3	no	—
55	C₃²⋊C₉	—	3	3	no	—
56	C₃²⋊C₉	—	3	3	no	—
57	C₃²⋊C₉	—	3	3	no	—
58	C₃²⋊C₉	—	3	3	no	—
59	C₃²⋊C₉	—	3	3	no	—
60	C₃²⋊C₉	—	3	3	no	—
61	C₃²⋊C₉	H(3,𝔽₃)	1	3	yes	—
62	C₃²⋊C₉	H(3,𝔽₃)	1	3	yes	—
63	C₉²	—	3	9	no	—
64	C₃³	—	3	2	no	—
65	C₃³	—	3	1	no	—
66	C₃³	—	3	3	no	—
67	C₃³	—	9	1	no	—
68	C₃³	—	9	1	no	—
69	C₃³	C₃×H(3,𝔽₃)	1	1	yes	characteristic
70	C₃³	C₃×H(3,𝔽₃)	1	1	yes	characteristic
71	C₃³	C₃×H(3,𝔽₃)	1	1	yes	characteristic
72	C₃³	C₃×H(3,𝔽₃)	1	1	yes	characteristic
73	3₋¹⁺²	—	3	9	no	—
74	3₋¹⁺²	—	3	9	no	—
75	3₋¹⁺²	—	3	9	no	—
76	3₋¹⁺²	—	27	3	no	—
77	3₋¹⁺²	—	27	3	no	—
78	C₃×C₉	—	3	9	no	—
79	C₃×C₉	—	3	2	no	—
80	C₃×C₉	—	3	1	no	—
81	C₃×C₉	—	3	3	no	—
82	C₃×C₉	—	3	4	no	—
83	C₃×C₉	—	3	3	no	—
84	C₃×C₉	—	3	3	no	—
85	C₃×C₉	—	3	2	no	—
86	C₃×C₉	—	3	2	no	—
87	C₃×C₉	—	9	3	no	—
88	C₃×C₉	—	9	3	no	—
89	C₃×C₉	—	9	3	no	—
90	C₃×C₉	—	9	3	no	—
91	C₃×C₉	—	9	3	no	—
92	C₃×C₉	—	9	3	no	—
93	C₃×C₉	—	9	3	no	—
94	C₃×C₉	—	9	3	no	—
95	C₃×C₉	—	9	9	no	—
96	C₃×C₉	#733	1	3	yes	—
97	C₃²	—	3	1	no	—
98	C₃²	—	3	1	no	—
99	C₃²	—	3	1	no	—
100	C₃²	—	3	1	no	—
101	C₃²	—	3	1	no	—
102	C₃²	—	3	1	no	—
103	C₃²	—	3	1	no	—
104	C₃²	—	3	1	no	—
105	C₃²	—	3	1	no	—
106	C₃²	—	3	1	no	—
107	C₃²	—	3	1	no	—
108	C₃²	—	3	1	no	—
109	C₃²	—	3	1	no	—
110	C₃²	—	3	1	no	—
111	C₃²	—	9	6	no	—
112	C₃²	—	9	3	no	—
113	C₃²	C₃²⋊H(3,𝔽₃)	1	1	yes	characteristic
114	C₃²	C₃×#733	1	1	yes	characteristic
115	C₃²	#6908	1	3	yes	—
116	C₃²	#6912	1	2	yes	—
117	C₉	—	3	9	no	—
118	C₉	—	3	3	no	—
119	C₉	—	9	2	no	—
120	C₉	—	9	3	no	—
121	C₉	—	9	3	no	—
122	C₉	—	27	3	no	—
123	C₉	—	27	3	no	—
124	C₉	—	27	3	no	—
125	C₃	—	3	2	no	—
126	C₃	—	3	1	no	—
127	C₃	—	3	3	no	—
128	C₃	—	9	1	no	—
129	C₃	—	9	1	no	—
130	C₃	#10624734	1	1	yes	characteristic
131	C₃	#10624744	1	1	yes	characteristic
132	C₃	#10624757	1	1	yes	characteristic
133	C₃	#10624758	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₃×C₉×3₋¹⁺²

C₃

yes

maximal, characteristic

#10624807

C₃

yes

maximal

#10624768

C₃

yes

maximal, characteristic

#10624768

C₃

yes

maximal, characteristic

C₃×#6868

C₃

yes

maximal, characteristic

#10624605

C₃

yes

maximal

#10624594

C₃

yes

maximal

C₃²×3₋¹⁺²

C₃²

yes

characteristic

C₃³×C₉

C₃²

yes

characteristic

#6891

C₃²

yes

—

#6891

C₃²

yes

—

C₉×3₋¹⁺²

—

C₉×3₋¹⁺²

—

C₉×3₋¹⁺²

—

C₃×C₉⋊C₉

—

C₃×C₃²⋊C₉

C₃²

yes

—

C₃×C₃²⋊C₉

C₃²

yes

characteristic

C₃×C₃²⋊C₉

C₃²

yes

characteristic

C₃×C₉²

—

—

—

—

—

—

—

—

—

—

C₃⁴

C₃³

yes

characteristic

C₃×3₋¹⁺²

—

C₃×3₋¹⁺²

—

C₃×3₋¹⁺²

—

C₃×3₋¹⁺²

—

C₃×3₋¹⁺²

—

C₃×3₋¹⁺²

H(3,𝔽₃)

yes

—

C₃²×C₉

—

C₃²×C₉

—

C₃²×C₉

—

C₃²×C₉

—

C₃²×C₉

—

C₃²×C₉

—

C₃²×C₉

—

C₃²×C₉

—

C₃²×C₉

—

C₃²×C₉

H(3,𝔽₃)

yes

—

C₃²×C₉

H(3,𝔽₃)

yes

characteristic

C₉⋊C₉

—

C₃²⋊C₉

—

C₃²⋊C₉

—

C₃²⋊C₉

—

C₃²⋊C₉

—

C₃²⋊C₉

—

C₃²⋊C₉

—

C₃²⋊C₉

—

C₃²⋊C₉

—

C₃²⋊C₉

—

C₃²⋊C₉

—

C₃²⋊C₉

—

C₃²⋊C₉

—

C₃²⋊C₉

—

C₃²⋊C₉

H(3,𝔽₃)

yes

—

C₃²⋊C₉

H(3,𝔽₃)

yes

—

C₉²

—

C₃³

—

C₃³

—

C₃³

—

C₃³

—

C₃³

—

C₃³

C₃×H(3,𝔽₃)

yes

characteristic

C₃³

C₃×H(3,𝔽₃)

yes

characteristic

C₃³

C₃×H(3,𝔽₃)

yes

characteristic

C₃³

C₃×H(3,𝔽₃)

yes

characteristic

3₋¹⁺²

—

3₋¹⁺²

—

3₋¹⁺²

—

3₋¹⁺²

—

3₋¹⁺²

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

#733

yes

—

C₃²

—

C₃²

—

C₃²

—

100

C₃²

—

101

C₃²

—

102

C₃²

—

103

C₃²

—

104

C₃²

—

105

C₃²

—

106

C₃²

—

107

C₃²

—

108

C₃²

—

109

C₃²

—

110

C₃²

—

111

C₃²

—

112

C₃²

—

113

C₃²

C₃²⋊H(3,𝔽₃)

yes

characteristic

114

C₃²

C₃×#733

yes

characteristic

115

C₃²

#6908

yes

—

116

C₃²

#6912

yes

—

117

C₉

—

118

C₉

—

119

C₉

—

120

C₉

—

121

C₉

—

122

C₉

—

123

C₉

—

124

C₉

—

125

C₃

—

126

C₃

—

127

C₃

—

128

C₃

—

129

C₃

—

130

C₃

#10624734

yes

characteristic

131

C₃

#10624744

yes

characteristic

132

C₃

#10624757

yes

characteristic

133

C₃

#10624758

yes

characteristic

	subgroup	G/H
center, socle	C₃²	C₃²⋊H(3,𝔽₃)
commutator, Frattini, prime radical, cosocle	C₃⁴	C₃³
LCS	G ▷ C₃⁴ ▷ C₃² ▷ C₁
UCS	C₁ ◁ C₃² ◁ C₃⁴ ◁ G
LECS	G ▷ C₃⁴ ▷ C₃² ▷ C₁

subgroup

G/H

center, socle

C₃²

C₃²⋊H(3,𝔽₃)

commutator, Frattini, prime radical, cosocle

C₃⁴

C₃³

LCS

G ▷ C₃⁴ ▷ C₃² ▷ C₁

UCS

C₁ ◁ C₃² ◁ C₃⁴ ◁ G

LECS

G ▷ C₃⁴ ▷ C₃² ▷ C₁

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

subgroup	index
C₃×C₉×3₋¹⁺²	3
#10624807	3
#10624768	3
C₃×#6868	3
#10624605	3
#10624594	3

subgroup

index

C₃×C₉×3₋¹⁺²

Subgroups — #14547115

Conjugacy classes of subgroups

Maximal subgroups