Group #19134078 — subgroups

Subgroups — #19134078

Order 5504.

184 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 51 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	#14583275	C₂	1	1	yes	maximal, characteristic
2	#14583100	C₂	1	1	yes	maximal, characteristic, complemented
3	#14583096	C₂	1	1	yes	maximal, characteristic, complemented
4	#14583026	C₂	1	1	yes	maximal, characteristic, complemented
5	#14582649	C₂	1	1	yes	maximal, characteristic, complemented
6	#14582642	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#331	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#10621873	—	2	1	no	—
9	C₂×#10621883	—	2	1	no	—
10	C₂×#10621882	—	2	1	no	—
11	C₂×#10621882	—	2	1	no	—
12	#13063322	C₂²	1	1	yes	characteristic
13	C₄×Dic₈₆	C₂²	1	1	yes	characteristic
14	C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
15	Dic₄₃⋊C₈	—	2	1	no	—
16	#13063247	—	2	1	no	—
17	#13063246	—	2	1	no	—
18	#13063235	—	2	1	no	—
19	C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
20	#127×C₄₃	C₂²	1	1	yes	characteristic
21	C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
22	C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
23	C₂×D₄×C₄₃	—	2	1	no	—
24	C₂×D₄×C₄₃	—	2	1	no	—
25	C₂×D₄×C₄₃	—	2	1	no	—
26	C₂×D₁₇₂	—	2	1	no	—
27	C₂×D₁₇₂	—	2	1	no	—
28	C₂×D₁₇₂	—	2	1	no	—
29	C₂×Dic₈₆	D₄	1	1	yes	characteristic
30	C₂×C₈×C₄₃	—	2	1	no	—
31	C₂×C₈×C₄₃	—	2	1	no	—
32	C₄²×C₄₃	C₂³	1	1	yes	characteristic
33	#10621883	—	4	2	no	—
34	#10621882	—	4	2	no	—
35	#10621882	—	4	2	no	—
36	C₄⋊Dic₄₃	D₄	1	1	yes	characteristic
37	Dic₄₃⋊C₄	—	2	1	no	—
38	C₄×Dic₄₃	—	2	1	no	—
39	C₂×C₄₃⋊C₈	—	2	1	no	—
40	C₂×C₄₃⋊C₈	D₄	1	1	yes	characteristic
41	C₂×C₄₃⋊C₈	D₄	1	1	yes	characteristic
42	#10621873	—	4	2	no	—
43	C₂³×C₄₃	—	4	1	no	—
44	C₂²×D₄₃	—	4	1	no	—
45	D₄×C₄₃	—	4	1	no	—
46	D₄×C₄₃	—	4	1	no	—
47	D₄×C₄₃	—	4	1	no	—
48	D₄×C₄₃	—	4	1	no	—
49	D₄×C₄₃	—	8	1	no	—
50	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
51	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
52	C₂×C₄×C₄₃	#41	1	1	yes	characteristic
53	C₂×Dic₄₃	—	2	1	no	—
54	C₂×Dic₄₃	—	2	1	no	—
55	D₁₇₂	—	4	1	no	—
56	D₁₇₂	—	4	1	no	—
57	D₁₇₂	—	4	1	no	—
58	D₁₇₂	—	4	1	no	—
59	D₁₇₂	—	8	1	no	—
60	Dic₈₆	—	2	1	no	—
61	Dic₈₆	—	2	1	no	—
62	C₈×C₄₃	—	4	1	no	—
63	C₈×C₄₃	—	4	1	no	—
64	C₄₃⋊C₈	—	2	1	no	—
65	C₄₃⋊C₈	—	4	1	no	—
66	C₄₃⋊C₈	SD₁₆	1	2	yes	complemented
67	C₂²×C₄₃	—	8	1	no	—
68	C₂²×C₄₃	—	8	1	no	—
69	C₂²×C₄₃	—	8	1	no	—
70	C₂²×C₄₃	#121	1	1	yes	characteristic
71	C₂×D₄₃	—	8	1	no	—
72	C₂×D₄₃	—	8	1	no	—
73	C₂×D₄₃	—	8	1	no	—
74	C₄×C₄₃	—	2	1	no	—
75	C₄×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
76	C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
77	C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
78	C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
79	Dic₄₃	—	4	1	no	—
80	Dic₄₃	—	4	1	no	—
81	#1688	—	43	1	no	maximal, Sylow
82	C₂×C₄₃	—	16	1	no	—
83	C₂×C₄₃	#460	1	1	yes	characteristic
84	C₂×C₄₃	#469	1	1	yes	characteristic
85	C₂×C₄₃	#472	1	1	yes	characteristic
86	D₄₃	—	16	1	no	—
87	#493	—	43	1	no	—
88	#460	—	43	1	no	—
89	#460	—	43	1	no	—
90	#446	—	43	1	no	—
91	#334	—	43	1	no	—
92	#331	—	43	1	no	—
93	#331	D₄₃	1	1	yes	characteristic, complemented
94	C₄₃	#1688	1	1	yes	characteristic, complemented, Sylow
95	C₂×SD₁₆	—	86	1	no	—
96	C₂×SD₁₆	—	86	1	no	—
97	C₂×D₈	—	86	1	no	—
98	C₂×D₈	—	86	1	no	—
99	#127	—	43	1	no	—
100	#127	C₂×D₄₃	1	1	yes	characteristic
101	C₄×Q₈	—	43	1	no	—
102	C₄⋊C₈	—	43	1	no	—
103	C₄⋊C₈	—	86	1	no	—
104	C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
105	C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
106	#102	—	86	1	no	—
107	#102	—	86	1	no	—
108	#97	—	86	1	no	—
109	C₄×C₈	—	43	1	no	—
110	C₂×Q₈	—	43	1	no	—
111	C₂×D₄	—	2	1	no	—
112	C₂×D₄	—	2	1	no	—
113	C₂×D₄	—	2	1	no	—
114	C₂×D₄	—	86	1	no	—
115	C₂×D₄	—	86	1	no	—
116	C₂×D₄	—	86	1	no	—
117	SD₁₆	—	172	2	no	—
118	SD₁₆	—	172	2	no	—
119	D₈	—	172	2	no	—
120	D₈	—	172	2	no	—
121	C₂×C₈	—	2	1	no	—
122	C₂×C₈	—	2	1	no	—
123	C₂×C₈	—	43	1	no	—
124	C₂×C₈	—	43	1	no	—
125	C₂×C₈	—	86	1	no	—
126	C₄⋊C₄	—	43	1	no	—
127	C₄⋊C₄	—	86	1	no	—
128	C₄²	—	86	1	no	—
129	C₄²	C₂²×D₄₃	1	1	yes	characteristic
130	C₂³	—	4	1	no	—
131	C₂³	—	172	1	no	—
132	Q₈	—	86	1	no	—
133	Q₈	—	86	1	no	—
134	D₄	—	4	1	no	—
135	D₄	—	4	1	no	—
136	D₄	—	4	1	no	—
137	D₄	—	4	1	no	—
138	D₄	—	8	1	no	—
139	D₄	—	344	1	no	—
140	D₄	—	172	1	no	—
141	D₄	—	172	1	no	—
142	D₄	—	172	1	no	—
143	D₄	—	172	1	no	—
144	C₂×C₄	—	86	1	no	—
145	C₂×C₄	—	86	1	no	—
146	C₂×C₄	#10621898	1	1	yes	characteristic
147	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
148	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
149	C₈	—	4	1	no	—
150	C₈	—	4	1	no	—
151	C₈	—	43	2	no	—
152	C₈	—	86	1	no	—
153	C₈	—	172	1	no	—
154	C₂²	—	8	1	no	—
155	C₂²	—	8	1	no	—
156	C₂²	—	8	1	no	—
157	C₂²	—	344	1	no	—
158	C₂²	—	344	1	no	—
159	C₂²	—	344	1	no	—
160	C₂²	#13063298	1	1	yes	characteristic
161	C₄	—	2	1	no	—
162	C₄	—	172	1	no	—
163	C₄	—	172	1	no	—
164	C₄	SD₁₆×D₄₃	1	1	yes	characteristic
165	C₄	#13063349	1	1	yes	characteristic
166	C₄	#13063349	1	1	yes	characteristic
167	C₄	#13063352	1	1	yes	characteristic
168	C₂	—	16	1	no	—
169	C₂	—	688	1	no	—
170	C₂	#14583098	1	1	yes	characteristic
171	C₂	#14583151	1	1	yes	characteristic
172	C₂	#14583168	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14583275

C₂

yes

maximal, characteristic

#14583100

C₂

yes

maximal, characteristic, complemented

#14583096

C₂

yes

maximal, characteristic, complemented

#14583026

C₂

yes

maximal, characteristic, complemented

#14582649

C₂

yes

maximal, characteristic, complemented

#14582642

C₂

yes

maximal, characteristic, complemented

C₄₃×#331

C₂

yes

maximal, characteristic, complemented

—

—

—

—

C₂²

yes

characteristic

C₄×Dic₈₆

C₂²

yes

characteristic

C₄⋊(C₄₃⋊C₈)

C₂²

yes

characteristic

Dic₄₃⋊C₈

—

#13063247

—

#13063246

—

#13063235

—

C₄×C₄₃⋊C₈

C₂²

yes

characteristic

#127×C₄₃

C₂²

yes

characteristic

C₄⋊C₈×C₄₃

C₂²

yes

characteristic

C₄⋊C₈×C₄₃

C₂²

yes

characteristic

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×Dic₈₆

D₄

yes

characteristic

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₄²×C₄₃

C₂³

yes

—

—

—

C₄⋊Dic₄₃

D₄

yes

characteristic

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

D₄

yes

characteristic

C₂×C₄₃⋊C₈

D₄

yes

characteristic

#10621873

—

C₂³×C₄₃

—

C₂²×D₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

#41

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

—

D₁₇₂

—

D₁₇₂

—

D₁₇₂

—

D₁₇₂

—

D₁₇₂

—

Dic₈₆

—

Dic₈₆

—

C₈×C₄₃

—

C₈×C₄₃

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

C₄₃⋊C₈

SD₁₆

yes

complemented

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

#121

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

C₂×SD₁₆

yes

C₄×C₄₃

yes

C₄×C₄₃

yes

C₄×C₄₃

yes

Dic₄₃

—

Dic₄₃

—

#1688

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

D₄₃

—

—

—

—

—

—

—

D₄₃

yes

characteristic, complemented

C₄₃

#1688

yes

characteristic, complemented, Sylow

C₂×SD₁₆

—

C₂×SD₁₆

—

C₂×D₈

—

C₂×D₈

—

#127

—

100

#127

C₂×D₄₃

yes

characteristic

101

C₄×Q₈

—

102

C₄⋊C₈

—

103

C₄⋊C₈

—

104

C₄⋊C₈

C₂×D₄₃

yes

characteristic

105

C₄⋊C₈

C₂×D₄₃

yes

characteristic

106

#102

—

107

#102

—

108

#97

—

109

C₄×C₈

—

110

C₂×Q₈

—

111

C₂×D₄

—

112

C₂×D₄

—

113

C₂×D₄

—

114

C₂×D₄

—

115

C₂×D₄

—

116

C₂×D₄

—

117

SD₁₆

—

172

—

118

SD₁₆

—

172

—

119

D₈

—

172

—

120

D₈

—

172

—

121

C₂×C₈

—

122

C₂×C₈

—

123

C₂×C₈

—

124

C₂×C₈

—

125

C₂×C₈

—

126

C₄⋊C₄

—

127

C₄⋊C₄

—

128

C₄²

—

129

C₄²

C₂²×D₄₃

yes

characteristic

130

C₂³

—

131

C₂³

—

172

—

132

Q₈

—

133

Q₈

—

134

D₄

—

135

D₄

—

136

D₄

—

137

D₄

—

138

D₄

—

139

D₄

—

344

—

140

D₄

—

172

—

141

D₄

—

172

—

142

D₄

—

172

—

143

D₄

—

172

—

144

C₂×C₄

—

145

C₂×C₄

—

146

C₂×C₄

#10621898

yes

characteristic

147

C₂×C₄

D₄×D₄₃

yes

characteristic

148

C₂×C₄

D₄×D₄₃

yes

characteristic

149

C₈

—

150

C₈

—

151

C₈

—

152

C₈

—

153

C₈

—

172

—

154

C₂²

—

155

C₂²

—

156

C₂²

—

157

C₂²

—

344

—

158

C₂²

—

344

—

159

C₂²

—

344

—

160

C₂²

#13063298

yes

characteristic

161

C₄

—

162

C₄

—

172

—

163

C₄

—

172

—

164

C₄

SD₁₆×D₄₃

yes

characteristic

165

C₄

#13063349

yes

characteristic

166

C₄

#13063349

yes

characteristic

167

C₄

#13063352

yes

characteristic

168

C₂

—

169

C₂

—

688

—

170

C₂

#14583098

yes

characteristic

171

C₂

#14583151

yes

characteristic

172

C₂

#14583168

yes

characteristic

	subgroup	G/H
center	C₂²	#13063298
commutator	C₄²×C₄₃	C₂³
Frattini	C₄²	C₂²×D₄₃
Fitting	C₄₃×#331	C₂
socle	C₂²×C₄₃	#121
hypercenter	#331	D₄₃
hypocenter	C₄₃	#1688
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #331

subgroup

G/H

center

C₂²

#13063298

commutator

C₄²×C₄₃

C₂³

Frattini

C₄²

C₂²×D₄₃

Fitting

C₄₃×#331

C₂

C₂²×C₄₃

D₄₃

C₄₃

G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #331

N	H ≅ G/N	type
2. #14583100	C₂	semidirect
3. #14583096	C₂	semidirect
4. #14583026	C₂	semidirect
5. #14582649	C₂	semidirect
6. #14582642	C₂	semidirect
7. C₄₃×#331	C₂	semidirect
66. C₄₃⋊C₈	SD₁₆	semidirect
93. #331	D₄₃	semidirect
94. C₄₃	#1688	semidirect

H ≅ G/N

type

2. #14583100

C₂

semidirect

3. #14583096

C₂

semidirect

4. #14583026

C₂

semidirect

5. #14582649

C₂

semidirect

6. #14582642

C₂

semidirect

7. C₄₃×#331

C₂

semidirect

66. C₄₃⋊C₈

SD₁₆

semidirect

93. #331

D₄₃

semidirect

94. C₄₃

#1688

semidirect

Subgroups — #19134078

Conjugacy classes of subgroups

Complements