Group #14550920 — subgroups

Subgroups — #14550920

Order 2187.

332 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 50 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	C₃²×#733	C₃	1	1	yes	maximal, characteristic
2	#10624768	C₃	1	1	yes	maximal, characteristic
3	#10624733	C₃	1	1	yes	maximal, characteristic
4	C₉×C₃²⋊C₉	C₃	1	1	yes	maximal, characteristic
5	#10624482	C₃	1	9	yes	maximal, complemented
6	C₃²×3₋¹⁺²	—	3	1	no	—
7	C₃³×C₉	C₃²	1	1	yes	characteristic
8	C₃×#733	—	3	1	no	—
9	C₃×#733	—	3	1	no	—
10	C₃×#733	—	3	9	no	—
11	C₃×#733	—	3	1	no	—
12	C₃×#733	—	3	1	no	—
13	C₃×#733	C₃²	1	3	yes	—
14	C₃×#733	C₃²	1	3	yes	—
15	#6891	—	3	1	no	—
16	#6891	—	3	1	no	—
17	C₃×C₃²⋊C₉	—	3	1	no	—
18	C₃×C₉²	—	3	1	no	—
19	#6868	—	3	1	no	—
20	#6868	—	3	1	no	—
21	#6868	C₃²	1	3	yes	—
22	#6855	—	3	1	no	—
23	#6855	C₃²	1	3	yes	—
24	C₃⁴	H(3,𝔽₃)	1	1	yes	characteristic
25	C₃×3₋¹⁺²	—	3	9	no	—
26	C₃×3₋¹⁺²	—	3	3	no	—
27	C₃×3₋¹⁺²	—	3	3	no	—
28	C₃×3₋¹⁺²	—	9	3	no	—
29	C₃×3₋¹⁺²	—	9	3	no	—
30	C₃×3₋¹⁺²	—	9	1	no	—
31	C₃×3₋¹⁺²	—	9	1	no	—
32	C₃×3₋¹⁺²	—	9	1	no	—
33	C₃²×C₉	—	3	1	no	—
34	C₃²×C₉	—	3	1	no	—
35	C₃²×C₉	—	3	1	no	—
36	C₃²×C₉	—	3	3	no	—
37	C₃²×C₉	—	3	3	no	—
38	C₃²×C₉	—	9	1	no	—
39	C₃²×C₉	—	9	1	no	—
40	C₃²×C₉	—	9	1	no	—
41	C₃²×C₉	H(3,𝔽₃)	1	1	yes	characteristic
42	C₃²×C₉	H(3,𝔽₃)	1	1	yes	characteristic
43	C₃²×C₉	C₃³	1	1	yes	characteristic
44	#733	—	3	9	no	—
45	#733	—	3	9	no	—
46	#733	—	3	9	no	—
47	#733	—	9	3	no	—
48	#733	—	9	3	no	—
49	#733	—	9	3	no	—
50	C₃²⋊C₉	—	3	9	no	—
51	C₃²⋊C₉	—	3	3	no	—
52	C₃²⋊C₉	—	9	1	no	—
53	C₃²⋊C₉	—	9	1	no	—
54	C₃²⋊C₉	—	9	1	no	—
55	C₃²⋊C₉	—	9	1	no	—
56	C₃²⋊C₉	—	9	1	no	—
57	C₉²	—	9	3	no	—
58	C₃³	—	3	3	no	—
59	C₃³	—	3	1	no	—
60	C₃³	—	3	1	no	—
61	C₃³	—	3	1	no	—
62	C₃³	—	9	1	no	—
63	C₃³	—	9	1	no	—
64	C₃³	#732	1	1	yes	characteristic
65	C₃³	#732	1	1	yes	characteristic
66	C₃³	#732	1	1	yes	characteristic
67	C₃³	C₃×H(3,𝔽₃)	1	1	yes	characteristic
68	3₋¹⁺²	—	3	9	no	—
69	3₋¹⁺²	—	9	9	no	—
70	3₋¹⁺²	—	9	9	no	—
71	3₋¹⁺²	—	9	3	no	—
72	3₋¹⁺²	—	9	3	no	—
73	3₋¹⁺²	—	9	3	no	—
74	3₋¹⁺²	—	9	3	no	—
75	3₋¹⁺²	—	9	3	no	—
76	3₋¹⁺²	—	27	3	no	—
77	C₃×C₉	—	3	1	no	—
78	C₃×C₉	—	3	1	no	—
79	C₃×C₉	—	3	1	no	—
80	C₃×C₉	—	3	9	no	—
81	C₃×C₉	—	3	1	no	—
82	C₃×C₉	—	3	1	no	—
83	C₃×C₉	—	3	1	no	—
84	C₃×C₉	—	3	1	no	—
85	C₃×C₉	—	3	1	no	—
86	C₃×C₉	—	3	1	no	—
87	C₃×C₉	—	3	1	no	—
88	C₃×C₉	—	3	1	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	9	no	—
95	C₃×C₉	—	9	3	no	—
96	C₃×C₉	—	9	3	no	—
97	C₃×C₉	—	9	3	no	—
98	C₃×C₉	—	9	3	no	—
99	C₃×C₉	AΣL(1,𝔽₂₇)	1	3	yes	—
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	—	3	1	no	—
112	C₃²	—	3	1	no	—
113	C₃²	—	3	1	no	—
114	C₃²	—	9	3	no	—
115	C₃²	—	9	3	no	—
116	C₃²	—	9	3	no	—
117	C₃²	#6880	1	3	yes	—
118	C₃²	C₃×AΣL(1,𝔽₂₇)	1	1	yes	characteristic
119	C₃²	C₃×#732	1	1	yes	characteristic
120	C₃²	#6909	1	1	yes	characteristic
121	C₃²	#6911	1	1	yes	characteristic
122	C₉	—	3	3	no	—
123	C₉	—	9	9	no	—
124	C₉	—	9	1	no	—
125	C₉	—	9	1	no	—
126	C₉	—	9	9	no	—
127	C₉	—	27	3	no	—
128	C₉	—	27	3	no	—
129	C₃	—	3	1	no	—
130	C₃	—	3	3	no	—
131	C₃	—	3	1	no	—
132	C₃	—	3	1	no	—
133	C₃	—	9	1	no	—
134	C₃	—	9	1	no	—
135	C₃	#10624596	1	1	yes	characteristic
136	C₃	C₃×#6880	1	1	yes	characteristic
137	C₃	#10624847	1	1	yes	characteristic
138	C₃	#10624848	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₃²×#733

C₃

yes

maximal, characteristic

#10624768

C₃

yes

maximal, characteristic

#10624733

C₃

yes

maximal, characteristic

C₉×C₃²⋊C₉

C₃

yes

maximal, characteristic

#10624482

C₃

yes

maximal, complemented

C₃²×3₋¹⁺²

—

C₃³×C₉

C₃²

yes

—

—

—

—

—

C₃²

yes

—

C₃×#733

C₃²

yes

—

#6891

—

#6891

—

C₃×C₃²⋊C₉

—

C₃×C₉²

—

#6868

—

#6868

—

#6868

C₃²

yes

—

#6855

—

#6855

C₃²

yes

—

C₃⁴

H(3,𝔽₃)

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

—

C₃×3₋¹⁺²

—

C₃×3₋¹⁺²

—

C₃²×C₉

—

C₃²×C₉

—

C₃²×C₉

—

C₃²×C₉

—

C₃²×C₉

—

C₃²×C₉

—

C₃²×C₉

—

C₃²×C₉

—

C₃²×C₉

yes

C₃²×C₉

yes

C₃²×C₉

C₃³

yes

—

—

—

—

—

—

C₃²⋊C₉

—

C₃²⋊C₉

—

C₃²⋊C₉

—

C₃²⋊C₉

—

C₃²⋊C₉

—

C₃²⋊C₉

—

C₃²⋊C₉

—

C₉²

—

C₃³

—

C₃³

—

C₃³

—

C₃³

—

C₃³

—

C₃³

—

C₃³

yes

C₃³

yes

C₃³

yes

C₃³

C₃×H(3,𝔽₃)

yes

characteristic

3₋¹⁺²

—

3₋¹⁺²

—

3₋¹⁺²

—

3₋¹⁺²

—

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

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

AΣL(1,𝔽₂₇)

yes

—

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

—

114

C₃²

—

115

C₃²

—

116

C₃²

—

117

C₃²

#6880

yes

—

118

C₃²

C₃×AΣL(1,𝔽₂₇)

yes

characteristic

119

C₃²

C₃×#732

yes

characteristic

120

C₃²

#6909

yes

characteristic

121

C₃²

#6911

yes

characteristic

122

C₉

—

123

C₉

—

124

C₉

—

125

C₉

—

126

C₉

—

127

C₉

—

128

C₉

—

129

C₃

—

130

C₃

—

131

C₃

—

132

C₃

—

133

C₃

—

134

C₃

—

135

C₃

#10624596

yes

characteristic

136

C₃

C₃×#6880

yes

characteristic

137

C₃

#10624847

yes

characteristic

138

C₃

#10624848

yes

characteristic

	subgroup	G/H
center, socle	C₃²	C₃×#732
commutator, Frattini, cosocle	C₃²×C₉	C₃³
prime radical	C₃⁴	H(3,𝔽₃)
LCS	G ▷ C₃²×C₉ ▷ C₃³ ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃² ◁ C₃⁴ ◁ C₃³×C₉ ◁ G
LECS	G ▷ C₃²×C₉ ▷ C₃³ ▷ C₃ ▷ C₁

subgroup

G/H

center, socle

C₃²

C₃×#732

commutator, Frattini, cosocle

C₃²×C₉

C₃³

prime radical

C₃⁴

H(3,𝔽₃)

LCS

G ▷ C₃²×C₉ ▷ C₃³ ▷ C₃ ▷ C₁

UCS

C₁ ◁ C₃² ◁ C₃⁴ ◁ C₃³×C₉ ◁ G

LECS

G ▷ C₃²×C₉ ▷ C₃³ ▷ C₃ ▷ C₁

N	H ≅ G/N	type
5. #10624482	C₃	semidirect

H ≅ G/N

type

5. #10624482

C₃

semidirect

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

subgroup	index
C₃²×#733	3
#10624768	3
#10624733	3
C₉×C₃²⋊C₉	3
#10624482	3

subgroup

index

C₃²×#733

#10624768

#10624733

C₉×C₃²⋊C₉

#10624482

Subgroups — #14550920

Conjugacy classes of subgroups

Complements

Maximal subgroups