Group #44532590 — subgroups

Subgroups — #44532590

Order 31347.

452 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 64 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×#11923958	C₃	1	1	yes	maximal, characteristic
2	C₃²×#11923958	C₃	1	1	yes	maximal, characteristic
3	#23782798	C₃	1	1	yes	maximal, characteristic
4	#23782699	C₃	1	9	yes	maximal, complemented
5	C₄₃×#6891	C₃	1	1	yes	maximal, characteristic
6	C₃×#11923958	—	3	9	no	—
7	C₃×#11923958	—	3	9	no	—
8	C₃×#11923958	—	3	1	no	—
9	C₃×#11923958	—	3	1	no	—
10	C₃×#11923958	—	3	1	no	—
11	C₃×#11923958	—	3	1	no	—
12	C₃×#11923958	—	3	1	no	—
13	C₃×#11923958	C₃²	1	3	yes	—
14	C₃×#11923958	C₃²	1	3	yes	—
15	C₃²×C₄₃⋊C₉	—	3	1	no	—
16	C₃²×C₄₃⋊C₉	—	3	1	no	—
17	C₃²⋊(C₄₃⋊C₉)	—	3	1	no	—
18	C₃²⋊(C₄₃⋊C₉)	—	3	1	no	—
19	C₃²⋊(C₄₃⋊C₉)	C₃²	1	3	yes	—
20	C₃⁴×C₄₃	C₃²	1	1	yes	characteristic
21	C₃×3₋¹⁺²×C₄₃	—	3	1	no	—
22	C₄₃×C₃²⋊C₉	—	3	1	no	—
23	C₄₃×C₃²⋊C₉	—	3	1	no	—
24	C₄₃×C₃²⋊C₉	C₃²	1	3	yes	—
25	#11923958	—	3	9	no	—
26	#11923958	—	3	9	no	—
27	#11923958	—	3	9	no	—
28	#11923958	—	3	9	no	—
29	#11923958	—	3	9	no	—
30	#11923958	—	3	9	no	—
31	#11923958	—	9	3	no	—
32	C₃×C₄₃⋊C₉	—	3	9	no	—
33	C₃×C₄₃⋊C₉	—	3	9	no	—
34	C₃×C₄₃⋊C₉	—	3	3	no	—
35	C₃×C₄₃⋊C₉	—	3	3	no	—
36	C₃×C₄₃⋊C₉	—	3	3	no	—
37	C₃³×C₄₃	—	3	3	no	—
38	C₃³×C₄₃	—	3	3	no	—
39	C₃³×C₄₃	—	9	1	no	—
40	C₃³×C₄₃	—	9	1	no	—
41	C₃³×C₄₃	H(3,𝔽₃)	1	1	yes	characteristic
42	C₃³×C₄₃	H(3,𝔽₃)	1	1	yes	characteristic
43	C₃³×C₄₃	H(3,𝔽₃)	1	1	yes	characteristic
44	C₃³×C₄₃	C₃³	1	1	yes	characteristic
45	3₋¹⁺²×C₄₃	—	9	3	no	—
46	C₃×C₉×C₄₃	—	3	3	no	—
47	#10624607	—	43	1	no	maximal, Sylow
48	C₃²×C₄₃	—	3	1	no	—
49	C₃²×C₄₃	—	3	1	no	—
50	C₃²×C₄₃	—	3	1	no	—
51	C₃²×C₄₃	—	3	1	no	—
52	C₃²×C₄₃	—	3	1	no	—
53	C₃²×C₄₃	—	3	1	no	—
54	C₃²×C₄₃	—	3	1	no	—
55	C₃²×C₄₃	—	3	1	no	—
56	C₃²×C₄₃	—	3	1	no	—
57	C₃²×C₄₃	—	3	1	no	—
58	C₃²×C₄₃	—	3	1	no	—
59	C₃²×C₄₃	—	3	1	no	—
60	C₃²×C₄₃	—	3	1	no	—
61	C₃²×C₄₃	—	3	1	no	—
62	C₃²×C₄₃	—	9	9	no	—
63	C₃²×C₄₃	AΣL(1,𝔽₂₇)	1	3	yes	—
64	C₃²×C₄₃	AΣL(1,𝔽₂₇)	1	3	yes	—
65	C₃²×C₄₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
66	C₉×C₄₃	—	9	3	no	—
67	C₄₃⋊C₉	—	3	9	no	—
68	C₄₃⋊C₉	—	3	9	no	—
69	C₄₃⋊C₉	—	9	3	no	—
70	C₃²×3₋¹⁺²	—	43	1	no	—
71	C₃²×3₋¹⁺²	—	43	1	no	—
72	#6891	—	43	1	no	—
73	#6891	C₄₃⋊C₃	1	1	yes	characteristic
74	#6860	—	43	9	no	—
75	C₃×C₄₃	—	3	3	no	—
76	C₃×C₄₃	—	3	3	no	—
77	C₃×C₄₃	—	9	1	no	—
78	C₃×C₄₃	—	9	1	no	—
79	C₃×C₄₃	C₃×AΣL(1,𝔽₂₇)	1	1	yes	characteristic
80	C₃×C₄₃	C₃×AΣL(1,𝔽₂₇)	1	1	yes	characteristic
81	C₃×C₄₃	#6912	1	1	yes	characteristic
82	C₃×C₄₃	#6912	1	1	yes	characteristic
83	C₃⁴	C₃×C₄₃⋊C₃	1	1	yes	characteristic
84	C₃×3₋¹⁺²	—	3	1	no	—
85	C₃×3₋¹⁺²	—	43	3	no	—
86	C₃×3₋¹⁺²	—	43	3	no	—
87	C₃×3₋¹⁺²	—	129	1	no	—
88	C₃×3₋¹⁺²	—	129	1	no	—
89	C₃×3₋¹⁺²	—	129	1	no	—
90	C₃×3₋¹⁺²	—	129	1	no	—
91	C₃×3₋¹⁺²	—	129	9	no	—
92	C₃×3₋¹⁺²	—	129	9	no	—
93	C₃×3₋¹⁺²	—	129	1	no	—
94	C₃²×C₉	—	129	1	no	—
95	C₃²×C₉	—	129	1	no	—
96	C₃²⋊C₉	—	3	1	no	—
97	C₃²⋊C₉	—	3	1	no	—
98	C₃²⋊C₉	—	43	3	no	—
99	C₃²⋊C₉	—	129	1	no	—
100	C₃²⋊C₉	—	129	1	no	—
101	C₃²⋊C₉	C₃×C₄₃⋊C₃	1	3	yes	—
102	C₄₃	#10624607	1	1	yes	characteristic, complemented, Sylow
103	C₃³	—	3	3	no	—
104	C₃³	—	3	3	no	—
105	C₃³	—	9	1	no	—
106	C₃³	—	9	1	no	—
107	C₃³	C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
108	C₃³	C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
109	C₃³	C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
110	C₃³	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
111	3₋¹⁺²	—	9	3	no	—
112	3₋¹⁺²	—	129	9	no	—
113	3₋¹⁺²	—	129	9	no	—
114	3₋¹⁺²	—	129	9	no	—
115	3₋¹⁺²	—	129	9	no	—
116	3₋¹⁺²	—	129	9	no	—
117	3₋¹⁺²	—	129	9	no	—
118	3₋¹⁺²	—	387	3	no	—
119	C₃×C₉	—	3	3	no	—
120	C₃×C₉	—	129	9	no	—
121	C₃×C₉	—	129	9	no	—
122	C₃×C₉	—	129	3	no	—
123	C₃×C₉	—	129	3	no	—
124	C₃×C₉	—	129	3	no	—
125	C₃²	—	3	1	no	—
126	C₃²	—	3	1	no	—
127	C₃²	—	3	1	no	—
128	C₃²	—	3	1	no	—
129	C₃²	—	3	1	no	—
130	C₃²	—	3	1	no	—
131	C₃²	—	3	1	no	—
132	C₃²	—	3	1	no	—
133	C₃²	—	3	1	no	—
134	C₃²	—	3	1	no	—
135	C₃²	—	3	1	no	—
136	C₃²	—	3	1	no	—
137	C₃²	—	3	1	no	—
138	C₃²	—	3	1	no	—
139	C₃²	—	9	9	no	—
140	C₃²	#16812506	1	3	yes	—
141	C₃²	#16812508	1	3	yes	—
142	C₃²	C₃×C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
143	C₉	—	9	3	no	—
144	C₉	—	129	9	no	—
145	C₉	—	129	9	no	—
146	C₉	—	387	3	no	—
147	C₃	—	3	3	no	—
148	C₃	—	3	3	no	—
149	C₃	—	9	1	no	—
150	C₃	—	9	1	no	—
151	C₃	C₃×#16812506	1	1	yes	characteristic
152	C₃	C₃×#16812508	1	1	yes	characteristic
153	C₃	#23782895	1	1	yes	characteristic
154	C₃	#23782896	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₃²×#11923958

C₃

yes

maximal, characteristic

C₃²×#11923958

C₃

yes

maximal, characteristic

#23782798

C₃

yes

maximal, characteristic

#23782699

C₃

yes

maximal, complemented

C₄₃×#6891

C₃

yes

maximal, characteristic

—

—

—

—

—

—

—

C₃²

yes

—

C₃×#11923958

C₃²

yes

—

C₃²×C₄₃⋊C₉

—

C₃²×C₄₃⋊C₉

—

C₃²⋊(C₄₃⋊C₉)

—

C₃²⋊(C₄₃⋊C₉)

—

C₃²⋊(C₄₃⋊C₉)

C₃²

yes

—

C₃⁴×C₄₃

C₃²

yes

characteristic

C₃×3₋¹⁺²×C₄₃

—

C₄₃×C₃²⋊C₉

—

C₄₃×C₃²⋊C₉

—

C₄₃×C₃²⋊C₉

C₃²

yes

—

—

—

—

—

—

—

—

C₃×C₄₃⋊C₉

—

C₃×C₄₃⋊C₉

—

C₃×C₄₃⋊C₉

—

C₃×C₄₃⋊C₉

—

C₃×C₄₃⋊C₉

—

C₃³×C₄₃

—

C₃³×C₄₃

—

C₃³×C₄₃

—

C₃³×C₄₃

—

C₃³×C₄₃

yes

C₃³×C₄₃

yes

C₃³×C₄₃

yes

C₃³×C₄₃

C₃³

yes

characteristic

3₋¹⁺²×C₄₃

—

C₃×C₉×C₄₃

—

#10624607

—

maximal, Sylow

C₃²×C₄₃

—

C₃²×C₄₃

—

C₃²×C₄₃

—

C₃²×C₄₃

—

C₃²×C₄₃

—

C₃²×C₄₃

—

C₃²×C₄₃

—

C₃²×C₄₃

—

C₃²×C₄₃

—

C₃²×C₄₃

—

C₃²×C₄₃

—

C₃²×C₄₃

—

C₃²×C₄₃

—

C₃²×C₄₃

—

C₃²×C₄₃

—

C₃²×C₄₃

AΣL(1,𝔽₂₇)

yes

—

C₃²×C₄₃

AΣL(1,𝔽₂₇)

yes

—

C₃²×C₄₃

C₃×H(3,𝔽₃)

yes

characteristic

C₉×C₄₃

—

C₄₃⋊C₉

—

C₄₃⋊C₉

—

C₄₃⋊C₉

—

C₃²×3₋¹⁺²

—

C₃²×3₋¹⁺²

—

#6891

—

#6891

C₄₃⋊C₃

yes

characteristic

#6860

—

C₃×C₄₃

—

C₃×C₄₃

—

C₃×C₄₃

—

C₃×C₄₃

—

C₃×C₄₃

C₃×AΣL(1,𝔽₂₇)

yes

characteristic

C₃×C₄₃

C₃×AΣL(1,𝔽₂₇)

yes

C₃×C₄₃

yes

C₃×C₄₃

yes

C₃⁴

C₃×C₄₃⋊C₃

yes

characteristic

C₃×3₋¹⁺²

—

C₃×3₋¹⁺²

—

C₃×3₋¹⁺²

—

C₃×3₋¹⁺²

—

129

—

C₃×3₋¹⁺²

—

129

—

C₃×3₋¹⁺²

—

129

—

C₃×3₋¹⁺²

—

129

—

C₃×3₋¹⁺²

—

129

—

C₃×3₋¹⁺²

—

129

—

C₃×3₋¹⁺²

—

129

—

C₃²×C₉

—

129

—

C₃²×C₉

—

129

—

C₃²⋊C₉

—

C₃²⋊C₉

—

C₃²⋊C₉

—

C₃²⋊C₉

—

129

—

100

C₃²⋊C₉

—

129

—

101

C₃²⋊C₉

C₃×C₄₃⋊C₃

yes

—

102

C₄₃

#10624607

yes

characteristic, complemented, Sylow

103

C₃³

—

104

C₃³

—

105

C₃³

—

106

C₃³

—

107

C₃³

C₃²⋊(C₄₃⋊C₃)

yes

characteristic

108

C₃³

C₃²⋊(C₄₃⋊C₃)

yes

characteristic

109

C₃³

C₃²⋊(C₄₃⋊C₃)

yes

characteristic

110

C₃³

C₃²×C₄₃⋊C₃

yes

characteristic

111

3₋¹⁺²

—

112

3₋¹⁺²

—

129

—

113

3₋¹⁺²

—

129

—

114

3₋¹⁺²

—

129

—

115

3₋¹⁺²

—

129

—

116

3₋¹⁺²

—

129

—

117

3₋¹⁺²

—

129

—

118

3₋¹⁺²

—

387

—

119

C₃×C₉

—

120

C₃×C₉

—

129

—

121

C₃×C₉

—

129

—

122

C₃×C₉

—

129

—

123

C₃×C₉

—

129

—

124

C₃×C₉

—

129

—

125

C₃²

—

126

C₃²

—

127

C₃²

—

128

C₃²

—

129

C₃²

—

130

C₃²

—

131

C₃²

—

132

C₃²

—

133

C₃²

—

134

C₃²

—

135

C₃²

—

136

C₃²

—

137

C₃²

—

138

C₃²

—

139

C₃²

—

140

C₃²

#16812506

yes

—

141

C₃²

#16812508

yes

—

142

C₃²

C₃×C₃²⋊(C₄₃⋊C₃)

yes

characteristic

143

C₉

—

144

C₉

—

129

—

145

C₉

—

129

—

146

C₉

—

387

—

147

C₃

—

148

C₃

—

149

C₃

—

150

C₃

—

151

C₃

C₃×#16812506

yes

characteristic

152

C₃

C₃×#16812508

yes

characteristic

153

C₃

#23782895

yes

characteristic

154

C₃

#23782896

yes

characteristic

	subgroup	G/H
center	C₃²	C₃×C₃²⋊(C₄₃⋊C₃)
commutator, cosocle	C₃³×C₄₃	C₃³
Frattini	C₃³	C₃²×C₄₃⋊C₃
Fitting	C₄₃×#6891	C₃
socle	C₃²×C₄₃	C₃×H(3,𝔽₃)
prime radical	C₃⁴×C₄₃	C₃²
hypercenter	#6891	C₄₃⋊C₃
hypocenter	C₄₃	#10624607
LCS	G ▷ C₃³×C₄₃ ▷ C₃²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃² ◁ C₃⁴ ◁ #6891

subgroup

G/H

center

C₃²

C₃×C₃²⋊(C₄₃⋊C₃)

commutator, cosocle

C₃³×C₄₃

C₃³

Frattini

C₃³

C₃²×C₄₃⋊C₃

Fitting

C₄₃×#6891

C₃

socle

C₃²×C₄₃

C₃×H(3,𝔽₃)

prime radical

C₃⁴×C₄₃

C₃²

C₄₃⋊C₃

C₄₃

G ▷ C₃³×C₄₃ ▷ C₃²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₃² ◁ C₃⁴ ◁ #6891

N	H ≅ G/N	type
4. #23782699	C₃	semidirect
102. C₄₃	#10624607	semidirect

H ≅ G/N

type

4. #23782699

C₃

semidirect

102. C₄₃

#10624607

semidirect

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

subgroup	index
C₃²×#11923958	3
#23782798	3
#23782699	3
C₄₃×#6891	3
#10624607	43

subgroup

index

C₄₃×#6891

Subgroups — #44532590

Conjugacy classes of subgroups

Complements

Maximal subgroups