Group #19134061 — subgroups

Subgroups — #19134061

Order 5504.

182 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 182 conjugacy classes of subgroups — too many to draw. Only its 55 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	#14583272	C₂	1	1	yes	maximal, characteristic, complemented
2	#14583180	C₂	1	1	yes	maximal, characteristic, complemented
3	#14583095	C₂	1	1	yes	maximal, characteristic
4	#14582978	C₂	1	1	yes	maximal, characteristic, complemented
5	#14582644	C₂	1	1	yes	maximal, characteristic, complemented
6	#14582642	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#335	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#10621873	—	2	1	no	—
9	C₂×#10621873	—	2	1	no	—
10	C₂×D₃₄₄	—	2	1	no	—
11	C₂×#10621872	—	2	1	no	—
12	#13063325	C₂²	1	1	yes	characteristic
13	#13063322	C₂²	1	1	yes	characteristic
14	C₄×D₁₇₂	C₂²	1	1	yes	characteristic
15	#13063259	—	2	1	no	—
16	C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
17	#13063247	—	2	1	no	—
18	#13063247	—	2	1	no	—
19	(C₂×D₄₃)⋊C₈	—	2	1	no	—
20	C₄⋊C₈×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×D₁₇₂	—	2	1	no	—
24	C₂×D₁₇₂	—	2	1	no	—
25	C₂×D₁₇₂	—	2	1	no	—
26	C₂×D₁₇₂	D₄	1	1	yes	characteristic
27	C₂×C₄×D₄₃	—	2	1	no	—
28	C₂×Dic₈₆	—	2	1	no	—
29	C₂×C₈×C₄₃	—	2	1	no	—
30	C₂×C₈×C₄₃	—	2	1	no	—
31	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
32	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
33	C₄²×C₄₃	C₂³	1	1	yes	characteristic
34	(C₂×D₄₃)⋊C₄	—	2	1	no	—
35	C₄⋊Dic₄₃	—	2	1	no	—
36	C₄⋊Dic₄₃	—	2	1	no	—
37	C₄⋊Dic₄₃	D₄	1	1	yes	characteristic
38	C₂×C₄₃⋊C₈	—	2	1	no	—
39	D₃₄₄	—	4	2	no	—
40	#10621873	—	4	2	no	—
41	#10621873	—	4	2	no	—
42	#10621872	—	4	2	no	—
43	C₂²×D₄₃	—	2	1	no	—
44	C₂²×D₄₃	—	4	1	no	—
45	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
46	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
47	C₂×C₄×C₄₃	#41	1	1	yes	characteristic
48	C₂×Dic₄₃	—	2	1	no	—
49	C₂×Dic₄₃	—	4	1	no	—
50	D₁₇₂	—	2	1	no	—
51	D₁₇₂	—	2	1	no	—
52	D₁₇₂	—	4	1	no	—
53	D₁₇₂	—	4	1	no	—
54	D₁₇₂	—	4	1	no	—
55	D₁₇₂	—	4	1	no	—
56	D₁₇₂	—	8	1	no	—
57	C₄×D₄₃	—	4	1	no	—
58	C₄×D₄₃	—	4	1	no	—
59	Dic₈₆	—	4	1	no	—
60	Dic₈₆	—	4	1	no	—
61	C₈×C₄₃	—	2	1	no	—
62	C₈×C₄₃	—	4	1	no	—
63	C₈×C₄₃	—	4	1	no	—
64	C₈×C₄₃	D₈	1	2	yes	complemented
65	C₄₃⋊C₈	—	4	1	no	—
66	C₂²×C₄₃	#121	1	1	yes	characteristic
67	C₂×D₄₃	—	4	1	no	—
68	C₂×D₄₃	—	4	1	no	—
69	C₂×D₄₃	—	4	1	no	—
70	C₂×D₄₃	—	8	1	no	—
71	C₂×D₄₃	—	8	1	no	—
72	C₂×D₄₃	—	8	1	no	—
73	C₄×C₄₃	—	2	1	no	—
74	C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
75	C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
76	C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
77	C₄×C₄₃	#137	1	1	yes	characteristic
78	Dic₄₃	—	4	1	no	—
79	Dic₄₃	—	8	1	no	—
80	#1685	—	43	1	no	maximal, Sylow
81	C₂×C₄₃	#459	1	1	yes	characteristic
82	C₂×C₄₃	#468	1	1	yes	characteristic
83	C₂×C₄₃	#471	1	1	yes	characteristic
84	D₄₃	—	8	1	no	—
85	D₄₃	—	16	1	no	—
86	#492	—	43	1	no	—
87	#474	—	43	1	no	—
88	#459	—	43	1	no	—
89	#436	—	43	1	no	—
90	#335	D₄₃	1	1	yes	characteristic, complemented
91	#332	—	43	1	no	—
92	#331	—	43	1	no	—
93	C₄₃	#1685	1	1	yes	characteristic, complemented, Sylow
94	C₂×SD₁₆	—	86	1	no	—
95	C₂×SD₁₆	—	86	1	no	—
96	C₂×D₈	—	86	1	no	—
97	C₂×M₁₆	—	86	1	no	—
98	C₄⋊Q₈	—	43	1	no	—
99	#127	—	43	1	no	—
100	C₄×D₄	—	43	1	no	—
101	#107	—	86	1	no	—
102	C₄⋊C₈	—	43	1	no	—
103	C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
104	C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
105	#102	—	86	1	no	—
106	#102	—	86	1	no	—
107	C₂²⋊C₈	—	86	1	no	—
108	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
109	C₂×Q₈	—	86	1	no	—
110	C₂×D₄	—	43	1	no	—
111	C₂×D₄	—	86	1	no	—
112	C₂×D₄	—	86	1	no	—
113	C₂×D₄	—	86	1	no	—
114	C₂²×C₄	—	86	1	no	—
115	SD₁₆	—	172	2	no	—
116	SD₁₆	—	172	2	no	—
117	D₈	—	172	2	no	—
118	M₁₆	—	172	2	no	—
119	C₂×C₈	—	2	1	no	—
120	C₂×C₈	—	2	1	no	—
121	C₂×C₈	—	86	1	no	—
122	C₂×C₈	D₁₇₂	1	1	yes	characteristic
123	C₂×C₈	D₁₇₂	1	1	yes	characteristic
124	C₄⋊C₄	—	43	1	no	—
125	C₄⋊C₄	—	86	1	no	—
126	C₄⋊C₄	—	86	1	no	—
127	C₂²⋊C₄	—	86	1	no	—
128	C₄²	C₂²×D₄₃	1	1	yes	characteristic
129	C₂³	—	86	1	no	—
130	C₂³	—	172	1	no	—
131	Q₈	—	172	1	no	—
132	Q₈	—	172	1	no	—
133	D₄	—	86	1	no	—
134	D₄	—	86	1	no	—
135	D₄	—	344	1	no	—
136	D₄	—	172	1	no	—
137	D₄	—	172	1	no	—
138	D₄	—	172	1	no	—
139	D₄	—	172	1	no	—
140	C₂×C₄	—	86	1	no	—
141	C₂×C₄	—	172	1	no	—
142	C₂×C₄	—	172	1	no	—
143	C₂×C₄	—	172	1	no	—
144	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
145	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
146	C₂×C₄	#10621902	1	1	yes	characteristic
147	C₈	—	2	1	no	—
148	C₈	—	4	1	no	—
149	C₈	—	4	1	no	—
150	C₈	—	172	1	no	—
151	C₈	D₃₄₄	1	2	yes	complemented
152	C₂²	—	344	1	no	—
153	C₂²	—	344	1	no	—
154	C₂²	—	344	1	no	—
155	C₂²	—	172	1	no	—
156	C₂²	—	172	1	no	—
157	C₂²	—	172	1	no	—
158	C₂²	#13063300	1	1	yes	characteristic
159	C₄	—	2	1	no	—
160	C₄	—	344	1	no	—
161	C₄	—	172	1	no	—
162	C₄	C₂×D₃₄₄	1	1	yes	characteristic
163	C₄	#13063349	1	1	yes	characteristic
164	C₄	#13063353	1	1	yes	characteristic
165	C₄	#13063357	1	1	yes	characteristic
166	C₂	—	344	1	no	—
167	C₂	—	688	1	no	—
168	C₂	#14583095	1	1	yes	characteristic
169	C₂	#14583146	1	1	yes	characteristic
170	C₂	#14583163	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14583272

C₂

yes

maximal, characteristic, complemented

#14583180

C₂

yes

maximal, characteristic, complemented

#14583095

C₂

yes

maximal, characteristic

#14582978

C₂

yes

maximal, characteristic, complemented

#14582644

C₂

yes

maximal, characteristic, complemented

#14582642

C₂

yes

maximal, characteristic, complemented

C₄₃×#335

C₂

yes

maximal, characteristic, complemented

C₂×#10621873

—

C₂×#10621873

—

C₂×D₃₄₄

—

C₂×#10621872

—

#13063325

C₂²

yes

characteristic

#13063322

C₂²

yes

characteristic

C₄×D₁₇₂

C₂²

yes

characteristic

#13063259

—

C₄⋊(C₄₃⋊C₈)

C₂²

yes

characteristic

#13063247

—

#13063247

—

(C₂×D₄₃)⋊C₈

—

C₄⋊C₈×C₄₃

C₂²

yes

characteristic

C₄⋊C₈×C₄₃

C₂²

yes

characteristic

C₄×C₈×C₄₃

C₂²

yes

characteristic

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

D₄

yes

characteristic

C₂×C₄×D₄₃

—

C₂×Dic₈₆

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

D₄

yes

characteristic

C₂×C₈×C₄₃

D₄

yes

characteristic

C₄²×C₄₃

C₂³

yes

characteristic

(C₂×D₄₃)⋊C₄

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

D₄

yes

characteristic

C₂×C₄₃⋊C₈

—

D₃₄₄

—

#10621873

—

#10621873

—

#10621872

—

C₂²×D₄₃

—

C₂²×D₄₃

—

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

—

D₁₇₂

—

D₁₇₂

—

C₄×D₄₃

—

C₄×D₄₃

—

Dic₈₆

—

Dic₈₆

—

C₈×C₄₃

—

C₈×C₄₃

—

C₈×C₄₃

—

C₈×C₄₃

D₈

yes

complemented

C₄₃⋊C₈

—

C₂²×C₄₃

#121

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

C₂×D₈

yes

C₄×C₄₃

yes

C₄×C₄₃

yes

C₄×C₄₃

yes

Dic₄₃

—

Dic₄₃

—

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

D₄₃

—

D₄₃

—

—

—

—

—

D₄₃

yes

characteristic, complemented

#332

—

#331

—

C₄₃

#1685

yes

characteristic, complemented, Sylow

C₂×SD₁₆

—

C₂×SD₁₆

—

C₂×D₈

—

C₂×M₁₆

—

C₄⋊Q₈

—

#127

—

100

C₄×D₄

—

101

#107

—

102

C₄⋊C₈

—

103

C₄⋊C₈

C₂×D₄₃

yes

characteristic

104

C₄⋊C₈

C₂×D₄₃

yes

characteristic

105

#102

—

106

#102

—

107

C₂²⋊C₈

—

108

C₄×C₈

C₂×D₄₃

yes

characteristic

109

C₂×Q₈

—

110

C₂×D₄

—

111

C₂×D₄

—

112

C₂×D₄

—

113

C₂×D₄

—

114

C₂²×C₄

—

115

SD₁₆

—

172

—

116

SD₁₆

—

172

—

117

D₈

—

172

—

118

M₁₆

—

172

—

119

C₂×C₈

—

120

C₂×C₈

—

121

C₂×C₈

—

122

C₂×C₈

D₁₇₂

yes

characteristic

123

C₂×C₈

D₁₇₂

yes

characteristic

124

C₄⋊C₄

—

125

C₄⋊C₄

—

126

C₄⋊C₄

—

127

C₂²⋊C₄

—

128

C₄²

C₂²×D₄₃

yes

characteristic

129

C₂³

—

130

C₂³

—

172

—

131

Q₈

—

172

—

132

Q₈

—

172

—

133

D₄

—

134

D₄

—

135

D₄

—

344

—

136

D₄

—

172

—

137

D₄

—

172

—

138

D₄

—

172

—

139

D₄

—

172

—

140

C₂×C₄

—

141

C₂×C₄

—

172

—

142

C₂×C₄

—

172

—

143

C₂×C₄

—

172

—

144

C₂×C₄

C₂×D₁₇₂

yes

characteristic

145

C₂×C₄

D₄×D₄₃

yes

characteristic

146

C₂×C₄

#10621902

yes

characteristic

147

C₈

—

148

C₈

—

149

C₈

—

150

C₈

—

172

—

151

C₈

D₃₄₄

yes

complemented

152

C₂²

—

344

—

153

C₂²

—

344

—

154

C₂²

—

344

—

155

C₂²

—

172

—

156

C₂²

—

172

—

157

C₂²

—

172

—

158

C₂²

#13063300

yes

characteristic

159

C₄

—

160

C₄

—

344

—

161

C₄

—

172

—

162

C₄

C₂×D₃₄₄

yes

characteristic

163

C₄

#13063349

yes

characteristic

164

C₄

#13063353

yes

characteristic

165

C₄

#13063357

yes

characteristic

166

C₂

—

344

—

167

C₂

—

688

—

168

C₂

#14583095

yes

characteristic

169

C₂

#14583146

yes

characteristic

170

C₂

#14583163

yes

characteristic

	subgroup	G/H
center	C₂²	#13063300
commutator	C₄²×C₄₃	C₂³
Frattini	C₄²	C₂²×D₄₃
Fitting	C₄₃×#335	C₂
socle	C₂²×C₄₃	#121
hypercenter	#335	D₄₃
hypocenter	C₄₃	#1685
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #335

subgroup

G/H

center

C₂²

#13063300

commutator

C₄²×C₄₃

C₂³

Frattini

C₄²

C₂²×D₄₃

Fitting

C₄₃×#335

C₂

C₂²×C₄₃

D₄₃

C₄₃

G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #335

N	H ≅ G/N	type
1. #14583272	C₂	semidirect
2. #14583180	C₂	semidirect
4. #14582978	C₂	semidirect
5. #14582644	C₂	semidirect
6. #14582642	C₂	semidirect
7. C₄₃×#335	C₂	semidirect
64. C₈×C₄₃	D₈	semidirect
90. #335	D₄₃	semidirect
93. C₄₃	#1685	semidirect
151. C₈	D₃₄₄	semidirect

H ≅ G/N

type

1. #14583272

C₂

semidirect

2. #14583180

C₂

semidirect

4. #14582978

C₂

semidirect

5. #14582644

C₂

semidirect

6. #14582642

C₂

semidirect

7. C₄₃×#335

C₂

semidirect

64. C₈×C₄₃

D₈

semidirect

90. #335

D₄₃

semidirect

93. C₄₃

#1685

semidirect

151. C₈

D₃₄₄

semidirect

Subgroups — #19134061

Conjugacy classes of subgroups

Complements