Group #19136323 — subgroups

Subgroups — #19136323

Order 5504.

220 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 89 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×#13063265	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#13063261	C₂	1	1	yes	maximal, characteristic, complemented
3	#14582706	C₂	1	4	yes	maximal, complemented
4	C₂×#135×C₄₃	C₂	1	1	yes	maximal, characteristic
5	C₂×#10621877	—	2	1	no	—
6	#13063265	—	2	1	no	—
7	#13063265	—	2	1	no	—
8	C₂×C₄₃⋊C₁₆	C₂²	1	2	yes	complemented
9	#13063261	—	2	1	no	—
10	#13063261	C₂²	1	2	yes	complemented
11	C₂×#41×C₄₃	—	2	1	no	—
12	#135×C₄₃	—	2	1	no	—
13	#135×C₄₃	—	2	1	no	—
14	#135×C₄₃	C₄	1	2	yes	—
15	#135×C₄₃	C₂²	1	2	yes	—
16	C₂×Q₁₆×C₄₃	C₄	1	1	yes	characteristic
17	C₂×SD₁₆×C₄₃	—	2	1	no	—
18	C₂×D₈×C₄₃	C₄	1	1	yes	characteristic
19	C₂²×C₈×C₄₃	C₂²	1	1	yes	characteristic
20	#41×C₄₃	—	2	2	no	—
21	#41×C₄₃	—	2	2	no	—
22	#41×C₄₃	—	4	1	no	—
23	#41×C₄₃	—	4	1	no	—
24	C₂×Q₈×C₄₃	—	2	1	no	—
25	C₂×D₄×C₄₃	—	2	1	no	—
26	C₂×D₄×C₄₃	—	4	1	no	—
27	C₂²×C₄×C₄₃	—	4	1	no	—
28	C₂²×C₄×C₄₃	D₄	1	1	yes	characteristic
29	Q₁₆×C₄₃	—	2	1	no	—
30	Q₁₆×C₄₃	C₂×C₄	1	2	yes	—
31	SD₁₆×C₄₃	—	2	2	no	—
32	SD₁₆×C₄₃	—	2	2	no	—
33	D₈×C₄₃	—	2	1	no	—
34	D₈×C₄₃	C₂×C₄	1	2	yes	—
35	C₂×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
36	C₂×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
37	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
38	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
39	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
40	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
41	#10621877	—	2	2	no	—
42	#10621877	—	4	1	no	—
43	C₂×C₄₃⋊C₈	—	4	1	no	—
44	C₄₃⋊C₁₆	—	2	2	no	—
45	C₂³×C₄₃	—	4	1	no	—
46	C₂³×C₄₃	SD₁₆	1	1	yes	characteristic
47	Q₈×C₄₃	—	2	2	no	—
48	Q₈×C₄₃	—	4	1	no	—
49	D₄×C₄₃	—	2	2	no	—
50	D₄×C₄₃	—	4	2	no	—
51	D₄×C₄₃	—	4	2	no	—
52	D₄×C₄₃	—	4	1	no	—
53	C₂×C₄×C₄₃	—	4	1	no	—
54	C₂×C₄×C₄₃	—	4	2	no	—
55	C₂×C₄×C₄₃	—	4	2	no	—
56	C₂×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
57	C₂×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
58	C₂×C₄×C₄₃	D₈	1	1	yes	characteristic
59	C₂×C₄×C₄₃	D₈	1	1	yes	characteristic
60	C₂×C₄×C₄₃	SD₁₆	1	1	yes	characteristic
61	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
62	C₈×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
63	C₈×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
64	C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
65	C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
66	C₄₃⋊C₈	—	4	2	no	—
67	C₂²×C₄₃	—	4	1	no	—
68	C₂²×C₄₃	—	4	2	no	—
69	C₂²×C₄₃	—	8	2	no	—
70	C₂²×C₄₃	#102	1	1	yes	characteristic
71	C₂²×C₄₃	#102	1	1	yes	characteristic
72	C₂²×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
73	C₄×C₄₃	—	4	2	no	—
74	C₄×C₄₃	#102	1	1	yes	characteristic
75	C₄×C₄₃	#102	1	1	yes	characteristic
76	C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
77	C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
78	#2143	—	43	1	no	maximal, Sylow
79	C₂×C₄₃	—	2	1	no	—
80	C₂×C₄₃	—	2	1	no	—
81	C₂×C₄₃	—	2	1	no	—
82	C₂×C₄₃	—	8	2	no	—
83	C₂×C₄₃	C₂×#102	1	1	yes	characteristic
84	C₂×#135	D₄₃	1	1	yes	characteristic
85	C₂×M₃₂	—	43	1	no	—
86	C₂×#108	—	43	1	no	—
87	#359	—	43	4	no	—
88	C₄₃	#2143	1	1	yes	characteristic, complemented, Sylow
89	C₂×#41	—	2	1	no	—
90	#135	—	2	1	no	—
91	#135	—	2	1	no	—
92	#135	Dic₄₃	1	2	yes	—
93	#135	C₂×D₄₃	1	2	yes	—
94	C₂×Q₁₆	Dic₄₃	1	1	yes	characteristic
95	C₂×SD₁₆	—	2	1	no	—
96	C₂×D₈	Dic₄₃	1	1	yes	characteristic
97	C₂×M₁₆	—	86	1	no	—
98	C₂²×C₈	C₂×D₄₃	1	1	yes	characteristic
99	M₃₂	—	86	1	no	—
100	M₃₂	—	86	1	no	—
101	C₂×C₁₆	—	43	2	no	—
102	#108	—	43	2	no	—
103	#108	—	86	1	no	—
104	#41	—	2	2	no	—
105	#41	—	2	2	no	—
106	#41	—	4	1	no	—
107	#41	—	4	1	no	—
108	C₂×Q₈	—	2	1	no	—
109	C₂×D₄	—	2	1	no	—
110	C₂×D₄	—	4	1	no	—
111	C₂²×C₄	—	4	1	no	—
112	C₂²×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
113	Q₁₆	—	2	1	no	—
114	Q₁₆	C₂×Dic₄₃	1	2	yes	—
115	SD₁₆	—	2	2	no	—
116	SD₁₆	—	2	2	no	—
117	D₈	—	2	1	no	—
118	D₈	C₂×Dic₄₃	1	2	yes	—
119	M₁₆	—	86	2	no	—
120	M₁₆	—	172	1	no	—
121	C₂×C₈	—	172	1	no	—
122	C₂×C₈	C₂×Dic₄₃	1	1	yes	characteristic
123	C₂×C₈	C₂×Dic₄₃	1	1	yes	characteristic
124	C₂×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
125	C₂×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
126	C₂×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
127	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
128	C₁₆	—	86	2	no	—
129	C₂³	—	4	1	no	—
130	C₂³	#10621883	1	1	yes	characteristic
131	Q₈	—	2	2	no	—
132	Q₈	—	4	1	no	—
133	D₄	—	2	2	no	—
134	D₄	—	4	2	no	—
135	D₄	—	4	2	no	—
136	D₄	—	4	1	no	—
137	C₂×C₄	—	4	1	no	—
138	C₂×C₄	—	4	2	no	—
139	C₂×C₄	—	4	2	no	—
140	C₂×C₄	#10621882	1	1	yes	characteristic
141	C₂×C₄	#10621882	1	1	yes	characteristic
142	C₂×C₄	#10621883	1	1	yes	characteristic
143	C₂×C₄	C₂²⋊Dic₄₃	1	1	yes	characteristic
144	C₂×C₄	C₂²⋊Dic₄₃	1	1	yes	characteristic
145	C₂×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
146	C₈	—	172	2	no	—
147	C₈	C₂²⋊Dic₄₃	1	1	yes	characteristic
148	C₈	C₂²⋊Dic₄₃	1	1	yes	characteristic
149	C₈	C₂²×Dic₄₃	1	1	yes	characteristic
150	C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
151	C₂²	—	4	1	no	—
152	C₂²	—	4	2	no	—
153	C₂²	—	8	2	no	—
154	C₂²	#13063246	1	1	yes	characteristic
155	C₂²	#13063246	1	1	yes	characteristic
156	C₂²	C₂×#10621883	1	1	yes	characteristic
157	C₄	—	4	2	no	—
158	C₄	#13063246	1	1	yes	characteristic
159	C₄	#13063246	1	1	yes	characteristic
160	C₄	C₂×C₂²⋊Dic₄₃	1	1	yes	characteristic
161	C₄	C₂×#10621882	1	1	yes	characteristic
162	C₂	—	2	1	no	—
163	C₂	—	2	1	no	—
164	C₂	—	2	1	no	—
165	C₂	—	8	2	no	—
166	C₂	C₂×#13063246	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063265

C₂

yes

maximal, characteristic, complemented

C₂×#13063261

C₂

yes

maximal, characteristic, complemented

#14582706

C₂

yes

maximal, complemented

C₂×#135×C₄₃

C₂

yes

maximal, characteristic

C₂×#10621877

—

#13063265

—

#13063265

—

C₂×C₄₃⋊C₁₆

C₂²

yes

complemented

#13063261

—

#13063261

C₂²

yes

complemented

C₂×#41×C₄₃

—

#135×C₄₃

—

#135×C₄₃

—

#135×C₄₃

C₄

yes

—

#135×C₄₃

C₂²

yes

—

C₂×Q₁₆×C₄₃

C₄

yes

characteristic

C₂×SD₁₆×C₄₃

—

C₂×D₈×C₄₃

C₄

yes

characteristic

C₂²×C₈×C₄₃

C₂²

yes

characteristic

#41×C₄₃

—

#41×C₄₃

—

#41×C₄₃

—

#41×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

D₄

yes

characteristic

Q₁₆×C₄₃

—

Q₁₆×C₄₃

C₂×C₄

yes

—

SD₁₆×C₄₃

—

SD₁₆×C₄₃

—

D₈×C₄₃

—

D₈×C₄₃

C₂×C₄

yes

—

C₂×C₈×C₄₃

C₂×C₄

yes

characteristic

C₂×C₈×C₄₃

C₂×C₄

yes

characteristic

C₂×C₈×C₄₃

D₄

yes

characteristic

C₂×C₈×C₄₃

D₄

yes

characteristic

C₂×C₈×C₄₃

D₄

yes

characteristic

C₂×C₈×C₄₃

C₂³

yes

characteristic

#10621877

—

#10621877

—

C₂×C₄₃⋊C₈

—

C₄₃⋊C₁₆

—

C₂³×C₄₃

—

C₂³×C₄₃

SD₁₆

yes

characteristic

Q₈×C₄₃

—

Q₈×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₃

D₈

yes

characteristic

C₂×C₄×C₄₃

D₈

yes

characteristic

C₂×C₄×C₄₃

SD₁₆

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₈×C₄₃

C₂²⋊C₄

yes

characteristic

C₈×C₄₃

C₂²⋊C₄

yes

characteristic

C₈×C₄₃

C₂²×C₄

yes

characteristic

C₈×C₄₃

C₂×D₄

yes

characteristic

C₄₃⋊C₈

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

yes

C₂²×C₄₃

yes

C₂²×C₄₃

C₂×SD₁₆

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

yes

C₄×C₄₃

yes

C₄×C₄₃

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₄₃

C₂×D₈

yes

characteristic

#2143

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

C₂×#102

yes

characteristic

C₂×#135

D₄₃

yes

characteristic

C₂×M₃₂

—

C₂×#108

—

#359

—

C₄₃

#2143

yes

characteristic, complemented, Sylow

C₂×#41

—

#135

—

#135

—

#135

Dic₄₃

yes

—

#135

C₂×D₄₃

yes

—

C₂×Q₁₆

Dic₄₃

yes

characteristic

C₂×SD₁₆

—

C₂×D₈

Dic₄₃

yes

characteristic

C₂×M₁₆

—

C₂²×C₈

C₂×D₄₃

yes

characteristic

M₃₂

—

100

M₃₂

—

101

C₂×C₁₆

—

102

#108

—

103

#108

—

104

#41

—

105

#41

—

106

#41

—

107

#41

—

108

C₂×Q₈

—

109

C₂×D₄

—

110

C₂×D₄

—

111

C₂²×C₄

—

112

C₂²×C₄

C₂²⋊D₄₃

yes

characteristic

113

Q₁₆

—

114

Q₁₆

C₂×Dic₄₃

yes

—

115

SD₁₆

—

116

SD₁₆

—

117

D₈

—

118

D₈

C₂×Dic₄₃

yes

—

119

M₁₆

—

120

M₁₆

—

172

—

121

C₂×C₈

—

172

—

122

C₂×C₈

C₂×Dic₄₃

yes

characteristic

123

C₂×C₈

C₂×Dic₄₃

yes

characteristic

124

C₂×C₈

C₂²⋊D₄₃

yes

characteristic

125

C₂×C₈

C₂²⋊D₄₃

yes

characteristic

126

C₂×C₈

C₂²⋊D₄₃

yes

characteristic

127

C₂×C₈

C₂²×D₄₃

yes

characteristic

128

C₁₆

—

129

C₂³

—

130

C₂³

#10621883

yes

characteristic

131

Q₈

—

132

Q₈

—

133

D₄

—

134

D₄

—

135

D₄

—

136

D₄

—

137

C₂×C₄

—

138

C₂×C₄

—

139

C₂×C₄

—

140

C₂×C₄

#10621882

yes

characteristic

141

C₂×C₄

#10621882

yes

characteristic

142

C₂×C₄

#10621883

yes

characteristic

143

C₂×C₄

C₂²⋊Dic₄₃

yes

characteristic

144

C₂×C₄

C₂²⋊Dic₄₃

yes

characteristic

145

C₂×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

146

C₈

—

172

—

147

C₈

C₂²⋊Dic₄₃

yes

characteristic

148

C₈

C₂²⋊Dic₄₃

yes

characteristic

149

C₈

C₂²×Dic₄₃

yes

characteristic

150

C₈

C₂×C₂²⋊D₄₃

yes

characteristic

151

C₂²

—

152

C₂²

—

153

C₂²

—

154

C₂²

#13063246

yes

characteristic

155

C₂²

#13063246

yes

characteristic

156

C₂²

C₂×#10621883

yes

characteristic

157

C₄

—

158

C₄

#13063246

yes

characteristic

159

C₄

#13063246

yes

characteristic

160

C₄

C₂×C₂²⋊Dic₄₃

yes

characteristic

161

C₄

C₂×#10621882

yes

characteristic

162

C₂

—

163

C₂

—

164

C₂

—

165

C₂

—

166

C₂

C₂×#13063246

yes

characteristic

	subgroup	G/H
center	C₄	C₂×#10621882
commutator	C₈×C₄₃	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₄₃
Fitting	C₂×#135×C₄₃	C₂
socle	C₂×C₄₃	C₂×#102
hypercenter	C₂×#135	D₄₃
hypocenter	C₄₃	#2143
LCS	G ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#135

subgroup

G/H

center

C₄

C₂×#10621882

commutator

C₈×C₄₃

C₂²×C₄

Frattini

C₂×C₈

C₂²×D₄₃

Fitting

C₂×#135×C₄₃

C₂

C₂×C₄₃

D₄₃

C₄₃

G ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#135

N	H ≅ G/N	type
1. C₂×#13063265	C₂	semidirect
2. C₂×#13063261	C₂	semidirect
3. #14582706	C₂	semidirect
8. C₂×C₄₃⋊C₁₆	C₂²	semidirect
10. #13063261	C₂²	semidirect
88. C₄₃	#2143	semidirect

H ≅ G/N

type

1. C₂×#13063265

C₂

semidirect

2. C₂×#13063261

C₂

semidirect

3. #14582706

C₂

semidirect

8. C₂×C₄₃⋊C₁₆

C₂²

semidirect

10. #13063261

C₂²

semidirect

88. C₄₃

#2143

semidirect

Subgroups — #19136323

Conjugacy classes of subgroups

Complements