Group #19136337 — subgroups

Subgroups — #362×D₄₃ #19136337

Order 5504.

216 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 67 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	C₂×Q₁₆×D₄₃	C₂	1	1	yes	maximal, characteristic
2	M₃₂×D₄₃	C₂	1	1	yes	maximal, characteristic
3	#108×D₄₃	C₂	1	1	yes	maximal, characteristic
4	#14582716	C₂	1	1	yes	maximal, characteristic, complemented
5	#14582715	C₂	1	1	yes	maximal, characteristic, complemented
6	#14582714	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#362	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×Q₈×D₄₃	—	2	1	no	—
9	C₂×Dic₁₇₂	C₂²	1	1	yes	characteristic
10	C₂×#10621885	—	2	1	no	—
11	Q₁₆×D₄₃	—	2	1	no	—
12	Q₁₆×D₄₃	—	2	1	no	—
13	Q₁₆×D₄₃	C₄	1	2	yes	—
14	Q₁₆×D₄₃	C₄	1	2	yes	—
15	M₁₆×D₄₃	—	2	1	no	—
16	C₂×C₈×D₄₃	C₂²	1	1	yes	characteristic
17	#13063265	C₂²	1	1	yes	characteristic
18	#13063264	—	2	1	no	—
19	C₁₆×D₄₃	—	2	1	no	—
20	#13063261	C₂²	1	1	yes	characteristic
21	#13063260	—	2	1	no	—
22	C₂×Q₁₆×C₄₃	C₂²	1	1	yes	characteristic
23	M₃₂×C₄₃	C₂²	1	1	yes	characteristic
24	#108×C₄₃	C₂²	1	1	yes	characteristic
25	C₂×Q₈×C₄₃	—	2	1	no	—
26	Q₈×D₄₃	—	2	2	no	—
27	Q₈×D₄₃	—	2	2	no	—
28	Q₈×D₄₃	—	4	1	no	—
29	Q₈×D₄₃	—	4	1	no	—
30	C₂×C₄×D₄₃	—	4	1	no	—
31	C₂×C₄×D₄₃	D₄	1	1	yes	characteristic
32	C₂×Dic₈₆	—	2	1	no	—
33	C₂×Dic₈₆	—	4	1	no	—
34	Q₁₆×C₄₃	—	2	1	no	—
35	Q₁₆×C₄₃	C₂×C₄	1	2	yes	—
36	M₁₆×C₄₃	—	2	1	no	—
37	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
38	#10621885	—	2	2	no	—
39	#10621885	—	2	2	no	—
40	#10621877	—	2	1	no	—
41	C₂×C₄₃⋊C₈	D₄	1	1	yes	characteristic
42	Dic₁₇₂	—	2	1	no	—
43	Dic₁₇₂	C₂×C₄	1	2	yes	—
44	#10621872	—	4	1	no	—
45	C₈×D₄₃	—	4	1	no	—
46	C₈×D₄₃	C₂×C₄	1	1	yes	characteristic
47	C₈×D₄₃	C₂×C₄	1	1	yes	characteristic
48	C₈×D₄₃	D₄	1	1	yes	characteristic
49	C₈×D₄₃	D₄	1	1	yes	characteristic
50	C₁₆×C₄₃	—	2	1	no	—
51	C₄₃⋊C₁₆	—	2	1	no	—
52	C₂²×D₄₃	SD₁₆	1	1	yes	characteristic
53	Q₈×C₄₃	—	2	2	no	—
54	Q₈×C₄₃	—	4	1	no	—
55	C₂×C₄×C₄₃	—	4	1	no	—
56	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
57	C₂×Dic₄₃	—	4	1	no	—
58	C₂×Dic₄₃	SD₁₆	1	1	yes	characteristic
59	C₄×D₄₃	—	4	2	no	—
60	C₄×D₄₃	—	4	2	no	—
61	C₄×D₄₃	C₂²⋊C₄	1	1	yes	characteristic
62	C₄×D₄₃	C₂²⋊C₄	1	1	yes	characteristic
63	C₄×D₄₃	D₈	1	1	yes	characteristic
64	C₄×D₄₃	D₈	1	1	yes	characteristic
65	Dic₈₆	—	2	2	no	—
66	Dic₈₆	—	4	1	no	—
67	Dic₈₆	—	4	2	no	—
68	Dic₈₆	—	4	2	no	—
69	C₈×C₄₃	—	4	1	no	—
70	C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
71	C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
72	C₄₃⋊C₈	—	4	1	no	—
73	C₄₃⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
74	C₄₃⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
75	C₂²×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
76	C₂×D₄₃	—	2	2	no	—
77	C₂×D₄₃	#102	1	1	yes	characteristic
78	C₂×D₄₃	#102	1	1	yes	characteristic
79	C₄×C₄₃	—	4	2	no	—
80	C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
81	C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
82	Dic₄₃	—	4	2	no	—
83	Dic₄₃	#102	1	1	yes	characteristic
84	Dic₄₃	#102	1	1	yes	characteristic
85	C₂×#362	—	43	1	no	maximal, Sylow
86	C₂×C₄₃	—	2	1	no	—
87	C₂×C₄₃	C₂×#102	1	1	yes	characteristic
88	D₄₃	—	2	1	no	—
89	D₄₃	#362	1	2	yes	direct product factor
90	C₂²×Q₁₆	—	43	1	no	—
91	C₂×M₃₂	—	43	1	no	—
92	C₂×#108	—	43	1	no	—
93	#362	—	43	1	no	—
94	#362	—	43	1	no	—
95	#362	—	43	1	no	—
96	#362	D₄₃	1	1	yes	characteristic, direct product factor
97	C₄₃	C₂×#362	1	1	yes	characteristic, complemented, Sylow
98	C₂²×Q₈	—	86	1	no	—
99	C₂×Q₁₆	—	43	2	no	—
100	C₂×Q₁₆	—	43	2	no	—
101	C₂×Q₁₆	—	43	1	no	—
102	C₂×Q₁₆	—	86	1	no	—
103	C₂×Q₁₆	—	86	1	no	—
104	C₂×Q₁₆	—	86	1	no	—
105	C₂×Q₁₆	C₂×D₄₃	1	1	yes	characteristic
106	C₂×M₁₆	—	86	1	no	—
107	C₂²×C₈	—	43	1	no	—
108	M₃₂	—	43	1	no	—
109	M₃₂	—	86	1	no	—
110	M₃₂	C₂×D₄₃	1	1	yes	characteristic
111	C₂×C₁₆	—	86	1	no	—
112	#108	—	43	1	no	—
113	#108	—	86	1	no	—
114	#108	C₂×D₄₃	1	1	yes	characteristic
115	C₂×Q₈	—	2	1	no	—
116	C₂×Q₈	—	86	2	no	—
117	C₂×Q₈	—	86	2	no	—
118	C₂×Q₈	—	86	1	no	—
119	C₂×Q₈	—	172	1	no	—
120	C₂×Q₈	—	172	1	no	—
121	C₂×Q₈	—	172	1	no	—
122	C₂²×C₄	—	43	1	no	—
123	C₂²×C₄	—	172	1	no	—
124	Q₁₆	—	2	1	no	—
125	Q₁₆	—	43	2	no	—
126	Q₁₆	—	86	2	no	—
127	Q₁₆	—	86	2	no	—
128	Q₁₆	—	86	1	no	—
129	Q₁₆	C₄×D₄₃	1	2	yes	—
130	M₁₆	—	2	1	no	—
131	M₁₆	—	86	1	no	—
132	M₁₆	—	172	1	no	—
133	C₂×C₈	—	43	1	no	—
134	C₂×C₈	—	43	1	no	—
135	C₂×C₈	—	43	1	no	—
136	C₂×C₈	—	43	1	no	—
137	C₂×C₈	—	43	1	no	—
138	C₂×C₈	—	172	1	no	—
139	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
140	C₁₆	—	2	1	no	—
141	C₁₆	—	86	1	no	—
142	C₂³	—	43	1	no	—
143	Q₈	—	2	2	no	—
144	Q₈	—	4	1	no	—
145	Q₈	—	86	2	no	—
146	Q₈	—	172	2	no	—
147	Q₈	—	172	2	no	—
148	Q₈	—	172	1	no	—
149	C₂×C₄	—	4	1	no	—
150	C₂×C₄	—	43	1	no	—
151	C₂×C₄	—	43	1	no	—
152	C₂×C₄	—	43	1	no	—
153	C₂×C₄	—	43	1	no	—
154	C₂×C₄	—	43	1	no	—
155	C₂×C₄	—	172	2	no	—
156	C₂×C₄	—	172	2	no	—
157	C₂×C₄	—	172	1	no	—
158	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
159	C₈	—	4	1	no	—
160	C₈	—	43	1	no	—
161	C₈	—	43	1	no	—
162	C₈	—	172	1	no	—
163	C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
164	C₈	D₄×D₄₃	1	1	yes	characteristic
165	C₂²	—	43	1	no	—
166	C₂²	—	43	1	no	—
167	C₂²	—	86	2	no	—
168	C₂²	SD₁₆×D₄₃	1	1	yes	characteristic
169	C₄	—	4	2	no	—
170	C₄	—	43	1	no	—
171	C₄	—	43	1	no	—
172	C₄	—	172	2	no	—
173	C₄	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
174	C₄	D₈×D₄₃	1	1	yes	characteristic
175	C₂	—	2	1	no	—
176	C₂	—	43	2	no	—
177	C₂	—	86	1	no	—
178	C₂	#102×D₄₃	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×Q₁₆×D₄₃

C₂

yes

maximal, characteristic

M₃₂×D₄₃

C₂

yes

maximal, characteristic

#108×D₄₃

C₂

yes

maximal, characteristic

#14582716

C₂

yes

maximal, characteristic, complemented

#14582715

C₂

yes

maximal, characteristic, complemented

#14582714

C₂

yes

maximal, characteristic, complemented

C₄₃×#362

C₂

yes

maximal, characteristic, complemented

C₂×Q₈×D₄₃

—

C₂×Dic₁₇₂

C₂²

yes

characteristic

C₂×#10621885

—

Q₁₆×D₄₃

—

Q₁₆×D₄₃

—

Q₁₆×D₄₃

C₄

yes

—

Q₁₆×D₄₃

C₄

yes

—

M₁₆×D₄₃

—

C₂×C₈×D₄₃

C₂²

yes

characteristic

#13063265

C₂²

yes

characteristic

#13063264

—

C₁₆×D₄₃

—

#13063261

C₂²

yes

characteristic

#13063260

—

C₂×Q₁₆×C₄₃

C₂²

yes

characteristic

M₃₂×C₄₃

C₂²

yes

characteristic

#108×C₄₃

C₂²

yes

characteristic

C₂×Q₈×C₄₃

—

Q₈×D₄₃

—

Q₈×D₄₃

—

Q₈×D₄₃

—

Q₈×D₄₃

—

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

D₄

yes

characteristic

C₂×Dic₈₆

—

C₂×Dic₈₆

—

Q₁₆×C₄₃

—

Q₁₆×C₄₃

C₂×C₄

yes

—

M₁₆×C₄₃

—

C₂×C₈×C₄₃

C₂³

yes

—

—

—

C₂×C₄₃⋊C₈

D₄

yes

characteristic

Dic₁₇₂

—

Dic₁₇₂

C₂×C₄

yes

—

#10621872

—

C₈×D₄₃

—

C₈×D₄₃

C₂×C₄

yes

characteristic

C₈×D₄₃

C₂×C₄

yes

characteristic

C₈×D₄₃

D₄

yes

characteristic

C₈×D₄₃

D₄

yes

characteristic

C₁₆×C₄₃

—

C₄₃⋊C₁₆

—

C₂²×D₄₃

SD₁₆

yes

characteristic

Q₈×C₄₃

—

Q₈×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

SD₁₆

yes

characteristic

C₄×D₄₃

—

C₄×D₄₃

—

C₄×D₄₃

C₂²⋊C₄

yes

characteristic

C₄×D₄₃

C₂²⋊C₄

yes

characteristic

C₄×D₄₃

D₈

yes

characteristic

C₄×D₄₃

D₈

yes

characteristic

Dic₈₆

—

Dic₈₆

—

Dic₈₆

—

Dic₈₆

—

C₈×C₄₃

—

C₈×C₄₃

C₂²×C₄

yes

characteristic

C₈×C₄₃

C₂×D₄

yes

characteristic

C₄₃⋊C₈

—

C₄₃⋊C₈

C₂²⋊C₄

yes

characteristic

C₄₃⋊C₈

C₂²⋊C₄

yes

characteristic

C₂²×C₄₃

C₂×SD₁₆

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

yes

C₂×D₄₃

yes

C₄×C₄₃

—

C₄×C₄₃

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₄₃

C₂×D₈

yes

characteristic

Dic₄₃

—

Dic₄₃

yes

Dic₄₃

yes

—

C₂×C₄₃

—

C₂×C₄₃

C₂×#102

yes

characteristic

D₄₃

—

D₄₃

#362

yes

direct product factor

C₂²×Q₁₆

—

C₂×M₃₂

—

—

—

—

—

D₄₃

yes

characteristic, direct product factor

C₄₃

C₂×#362

yes

characteristic, complemented, Sylow

C₂²×Q₈

—

C₂×Q₁₆

—

100

C₂×Q₁₆

—

101

C₂×Q₁₆

—

102

C₂×Q₁₆

—

103

C₂×Q₁₆

—

104

C₂×Q₁₆

—

105

C₂×Q₁₆

C₂×D₄₃

yes

characteristic

106

C₂×M₁₆

—

107

C₂²×C₈

—

108

M₃₂

—

109

M₃₂

—

110

M₃₂

C₂×D₄₃

yes

characteristic

111

C₂×C₁₆

—

112

#108

—

113

#108

—

114

#108

C₂×D₄₃

yes

characteristic

115

C₂×Q₈

—

116

C₂×Q₈

—

117

C₂×Q₈

—

118

C₂×Q₈

—

119

C₂×Q₈

—

172

—

120

C₂×Q₈

—

172

—

121

C₂×Q₈

—

172

—

122

C₂²×C₄

—

123

C₂²×C₄

—

172

—

124

Q₁₆

—

125

Q₁₆

—

126

Q₁₆

—

127

Q₁₆

—

128

Q₁₆

—

129

Q₁₆

C₄×D₄₃

yes

—

130

M₁₆

—

131

M₁₆

—

132

M₁₆

—

172

—

133

C₂×C₈

—

134

C₂×C₈

—

135

C₂×C₈

—

136

C₂×C₈

—

137

C₂×C₈

—

138

C₂×C₈

—

172

—

139

C₂×C₈

C₂²×D₄₃

yes

characteristic

140

C₁₆

—

141

C₁₆

—

142

C₂³

—

143

Q₈

—

144

Q₈

—

145

Q₈

—

146

Q₈

—

172

—

147

Q₈

—

172

—

148

Q₈

—

172

—

149

C₂×C₄

—

150

C₂×C₄

—

151

C₂×C₄

—

152

C₂×C₄

—

153

C₂×C₄

—

154

C₂×C₄

—

155

C₂×C₄

—

172

—

156

C₂×C₄

—

172

—

157

C₂×C₄

—

172

—

158

C₂×C₄

D₄×D₄₃

yes

characteristic

159

C₈

—

160

C₈

—

161

C₈

—

162

C₈

—

172

—

163

C₈

C₂×C₄×D₄₃

yes

characteristic

164

C₈

D₄×D₄₃

yes

characteristic

165

C₂²

—

166

C₂²

—

167

C₂²

—

168

C₂²

SD₁₆×D₄₃

yes

characteristic

169

C₄

—

170

C₄

—

171

C₄

—

172

C₄

—

172

—

173

C₄

C₂²⋊C₄×D₄₃

yes

characteristic

174

C₄

D₈×D₄₃

yes

characteristic

175

C₂

—

176

C₂

—

177

C₂

—

178

C₂

#102×D₄₃

yes

characteristic

	subgroup	G/H
center	C₂	#102×D₄₃
commutator	C₈×C₄₃	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₄₃
Fitting	C₄₃×#362	C₂
socle	C₂×C₄₃	C₂×#102
hypercenter	#362	D₄₃
hypocenter	C₄₃	C₂×#362
LCS	G ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #362

subgroup

G/H

center

C₂

#102×D₄₃

commutator

C₈×C₄₃

C₂²×C₄

Frattini

C₂×C₈

C₂²×D₄₃

Fitting

C₄₃×#362

C₂

C₂×C₄₃

D₄₃

C₄₃

G ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #362

N	H ≅ G/N	type
4. #14582716	C₂	semidirect
5. #14582715	C₂	semidirect
6. #14582714	C₂	semidirect
7. C₄₃×#362	C₂	semidirect
89. D₄₃	#362	direct (N × H)
96. #362	D₄₃	direct (N × H)
97. C₄₃	C₂×#362	semidirect

H ≅ G/N

type

4. #14582716

C₂

semidirect

5. #14582715

C₂

semidirect

6. #14582714

C₂

semidirect

7. C₄₃×#362

C₂

semidirect

89. D₄₃

#362

direct (N × H)

96. #362

D₄₃

direct (N × H)

97. C₄₃

C₂×#362

semidirect

Subgroups — #362×D₄₃ #19136337

Conjugacy classes of subgroups

Complements

Subgroups — #362×D43 #19136337

Conjugacy classes of subgroups

Complements

Subgroups — #362×D₄₃ #19136337