Group #19135683 — subgroups

Subgroups — #19135683

Order 5504.

474 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 474 conjugacy classes of subgroups — too many to draw. Only its 99 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	C₂²×#10621883	C₂	1	2	yes	maximal, complemented
2	C₂×#13063246	C₂	1	2	yes	maximal, complemented
3	#14582805	C₂	1	1	yes	maximal, characteristic, complemented
4	#14582654	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#127×C₄₃	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₈₆	C₂²	1	1	yes	characteristic
7	C₂×#10621883	—	2	4	no	—
8	C₂×#10621883	—	2	4	no	—
9	C₂×#10621883	—	2	4	no	—
10	C₂²×C₄₃⋊C₈	C₂²	1	2	yes	—
11	C₂×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
12	#13063246	—	2	4	no	—
13	C₄₃⋊#95	—	2	2	no	—
14	C₂²×D₄×C₄₃	—	2	2	no	—
15	C₂²×D₄×C₄₃	C₂²	1	2	yes	—
16	#127×C₄₃	—	2	4	no	—
17	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
18	C₂⁴×C₄₃	—	2	2	no	—
19	C₂×D₄×C₄₃	—	2	8	no	—
20	C₂×D₄×C₄₃	—	2	2	no	—
21	C₂×D₄×C₄₃	—	2	2	no	—
22	C₂×D₄×C₄₃	—	2	2	no	—
23	C₂×D₄×C₄₃	—	2	2	no	—
24	C₂×D₄×C₄₃	—	2	2	no	—
25	C₂×D₄×C₄₃	—	4	4	no	—
26	C₂×D₄×C₄₃	—	4	4	no	—
27	C₂×D₄×C₄₃	D₄	1	4	yes	—
28	C₂²×C₄×C₄₃	D₄	1	2	yes	—
29	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
30	C₂²×Dic₄₃	—	2	1	no	—
31	C₂²×Dic₄₃	—	2	1	no	—
32	C₂×Dic₈₆	—	2	2	no	—
33	C₂×Dic₈₆	—	2	2	no	—
34	C₂×Dic₈₆	—	2	1	no	—
35	C₂×Dic₈₆	D₄	1	2	yes	complemented
36	C₄²×C₄₃	—	2	2	no	—
37	#10621883	—	2	16	no	—
38	C₄⋊Dic₄₃	—	2	2	no	—
39	C₂×C₄₃⋊C₈	—	2	2	no	—
40	C₂×C₄₃⋊C₈	—	2	2	no	—
41	C₂×C₄₃⋊C₈	D₄	1	4	yes	complemented
42	C₂³×C₄₃	—	2	4	no	—
43	C₂³×C₄₃	—	4	2	no	—
44	C₂³×C₄₃	—	4	2	no	—
45	C₂³×C₄₃	—	4	4	no	—
46	C₂³×C₄₃	—	4	4	no	—
47	C₂³×C₄₃	C₂×D₄	1	1	yes	characteristic
48	D₄×C₄₃	—	2	4	no	—
49	D₄×C₄₃	—	2	4	no	—
50	D₄×C₄₃	—	4	16	no	—
51	D₄×C₄₃	—	4	2	no	—
52	D₄×C₄₃	—	4	2	no	—
53	C₂×C₄×C₄₃	—	2	2	no	—
54	C₂×C₄×C₄₃	—	2	2	no	—
55	C₂×C₄×C₄₃	SD₁₆	1	4	yes	complemented
56	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
57	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
58	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
59	C₂×C₄×C₄₃	#41	1	1	yes	characteristic
60	C₂×Dic₄₃	—	2	2	no	—
61	C₂×Dic₄₃	—	4	1	no	—
62	C₂×Dic₄₃	—	4	1	no	—
63	C₂×Dic₄₃	—	4	1	no	—
64	C₂×Dic₄₃	—	4	2	no	—
65	Dic₈₆	—	2	4	no	—
66	Dic₈₆	—	4	2	no	—
67	C₄₃⋊C₈	—	2	4	no	—
68	C₂²×C₄₃	—	4	4	no	—
69	C₂²×C₄₃	—	4	8	no	—
70	C₂²×C₄₃	—	8	4	no	—
71	C₂²×C₄₃	—	8	2	no	—
72	C₂²×C₄₃	—	8	2	no	—
73	C₂²×C₄₃	#120	1	1	yes	characteristic
74	C₂²×C₄₃	#121	1	1	yes	characteristic
75	C₂²×C₄₃	#127	1	1	yes	characteristic
76	C₂²×C₄₃	C₂×SD₁₆	1	2	yes	—
77	C₂²×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
78	C₄×C₄₃	—	2	4	no	—
79	C₄×C₄₃	#120	1	2	yes	—
80	C₄×C₄₃	#121	1	2	yes	—
81	Dic₄₃	—	4	2	no	—
82	Dic₄₃	—	8	1	no	—
83	#2014	—	43	1	no	maximal, Sylow
84	C₂×C₄₃	—	8	4	no	—
85	C₂×C₄₃	#392	1	1	yes	characteristic
86	C₂×C₄₃	#450	1	2	yes	—
87	C₂×C₄₃	#460	1	2	yes	—
88	C₂×C₄₃	#492	1	1	yes	characteristic
89	C₂×C₄₃	#496	1	1	yes	characteristic
90	C₂²×SD₁₆	—	43	2	no	—
91	C₂×#127	D₄₃	1	1	yes	characteristic
92	C₂×#102	—	43	2	no	—
93	#391	—	43	1	no	—
94	#336	—	43	1	no	—
95	C₄₃	#2014	1	1	yes	characteristic, complemented, Sylow
96	C₂²×Q₈	—	43	1	no	—
97	C₂²×D₄	—	2	2	no	—
98	C₂²×D₄	C₂×D₄₃	1	2	yes	—
99	C₂×SD₁₆	—	86	4	no	—
100	C₂×SD₁₆	—	86	4	no	—
101	C₂×SD₁₆	—	86	4	no	—
102	C₂²×C₈	—	43	2	no	—
103	#127	—	2	4	no	—
104	C₂×C₄⋊C₄	—	43	1	no	—
105	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
106	#102	—	86	4	no	—
107	#95	—	86	2	no	—
108	C₂⁴	—	2	2	no	—
109	C₂×Q₈	—	43	2	no	—
110	C₂×Q₈	—	86	1	no	—
111	C₂×Q₈	—	86	2	no	—
112	C₂×Q₈	—	86	2	no	—
113	C₂×D₄	—	2	8	no	—
114	C₂×D₄	—	2	2	no	—
115	C₂×D₄	—	2	2	no	—
116	C₂×D₄	—	2	2	no	—
117	C₂×D₄	—	2	2	no	—
118	C₂×D₄	—	2	2	no	—
119	C₂×D₄	—	4	4	no	—
120	C₂×D₄	—	4	4	no	—
121	C₂×D₄	C₂²⋊D₄₃	1	4	yes	—
122	C₂²×C₄	—	86	1	no	—
123	C₂²×C₄	—	86	1	no	—
124	C₂²×C₄	C₂²⋊D₄₃	1	2	yes	—
125	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
126	SD₁₆	—	86	16	no	—
127	C₂×C₈	—	43	4	no	—
128	C₂×C₈	—	86	2	no	—
129	C₂×C₈	—	86	2	no	—
130	C₄⋊C₄	—	86	2	no	—
131	C₄²	—	2	2	no	—
132	C₂³	—	2	4	no	—
133	C₂³	—	4	2	no	—
134	C₂³	—	4	2	no	—
135	C₂³	—	4	4	no	—
136	C₂³	—	4	4	no	—
137	C₂³	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
138	Q₈	—	86	4	no	—
139	Q₈	—	172	2	no	—
140	D₄	—	2	4	no	—
141	D₄	—	2	4	no	—
142	D₄	—	4	16	no	—
143	D₄	—	4	2	no	—
144	D₄	—	4	2	no	—
145	C₂×C₄	—	2	2	no	—
146	C₂×C₄	—	2	2	no	—
147	C₂×C₄	—	86	2	no	—
148	C₂×C₄	—	172	1	no	—
149	C₂×C₄	—	172	2	no	—
150	C₂×C₄	—	172	1	no	—
151	C₂×C₄	—	172	1	no	—
152	C₂×C₄	#10621883	1	4	yes	complemented
153	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
154	C₂×C₄	D₄×D₄₃	1	2	yes	—
155	C₂×C₄	#10621900	1	1	yes	characteristic
156	C₂×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
157	C₈	—	86	4	no	—
158	C₂²	—	4	8	no	—
159	C₂²	—	4	4	no	—
160	C₂²	—	8	4	no	—
161	C₂²	—	8	2	no	—
162	C₂²	—	8	2	no	—
163	C₂²	#13063294	1	1	yes	characteristic
164	C₂²	#13063296	1	1	yes	characteristic
165	C₂²	#13063321	1	1	yes	characteristic
166	C₂²	C₂×#10621883	1	2	yes	—
167	C₂²	#13063351	1	2	yes	—
168	C₄	—	2	4	no	—
169	C₄	—	344	1	no	—
170	C₄	—	172	2	no	—
171	C₄	#13063293	1	2	yes	—
172	C₄	#13063297	1	2	yes	—
173	C₂	—	8	4	no	—
174	C₂	#14582807	1	1	yes	characteristic
175	C₂	#14583050	1	2	yes	—
176	C₂	#14583096	1	2	yes	—
177	C₂	#14583271	1	1	yes	characteristic
178	C₂	#14583286	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#10621883

C₂

yes

maximal, complemented

C₂×#13063246

C₂

yes

maximal, complemented

#14582805

C₂

yes

maximal, characteristic, complemented

#14582654

C₂

yes

maximal, characteristic, complemented

C₂×#127×C₄₃

C₂

yes

maximal, characteristic

C₂²×Dic₈₆

C₂²

yes

—

—

—

C₂²×C₄₃⋊C₈

C₂²

yes

—

C₂×C₄⋊Dic₄₃

C₂²

yes

characteristic

#13063246

—

C₄₃⋊#95

—

C₂²×D₄×C₄₃

—

C₂²×D₄×C₄₃

C₂²

yes

—

#127×C₄₃

—

C₂×C₄²×C₄₃

C₂²

yes

characteristic

C₂⁴×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

D₄

yes

—

C₂²×C₄×C₄₃

D₄

yes

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

—

C₂²×Dic₄₃

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

D₄

yes

complemented

C₄²×C₄₃

—

#10621883

—

C₄⋊Dic₄₃

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

D₄

yes

complemented

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

C₂×D₄

yes

characteristic

D₄×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

SD₁₆

yes

complemented

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₄×C₄₃

#41

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

Dic₈₆

—

Dic₈₆

—

C₄₃⋊C₈

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

yes

C₂²×C₄₃

yes

C₂²×C₄₃

yes

C₂²×C₄₃

C₂×SD₁₆

yes

—

C₂²×C₄₃

AGL(1,ℤ/8)

yes

—

C₄×C₄₃

—

C₄×C₄₃

#120

yes

—

C₄×C₄₃

#121

yes

—

Dic₄₃

—

Dic₄₃

—

#2014

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

#392

yes

characteristic

C₂×C₄₃

#450

yes

—

C₂×C₄₃

#460

yes

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂²×SD₁₆

—

C₂×#127

D₄₃

yes

—

—

—

C₄₃

#2014

yes

characteristic, complemented, Sylow

C₂²×Q₈

—

C₂²×D₄

—

C₂²×D₄

C₂×D₄₃

yes

—

C₂×SD₁₆

—

100

C₂×SD₁₆

—

101

C₂×SD₁₆

—

102

C₂²×C₈

—

103

#127

—

104

C₂×C₄⋊C₄

—

105

C₂×C₄²

C₂×D₄₃

yes

characteristic

106

#102

—

107

#95

—

108

C₂⁴

—

109

C₂×Q₈

—

110

C₂×Q₈

—

111

C₂×Q₈

—

112

C₂×Q₈

—

113

C₂×D₄

—

114

C₂×D₄

—

115

C₂×D₄

—

116

C₂×D₄

—

117

C₂×D₄

—

118

C₂×D₄

—

119

C₂×D₄

—

120

C₂×D₄

—

121

C₂×D₄

C₂²⋊D₄₃

yes

—

122

C₂²×C₄

—

123

C₂²×C₄

—

124

C₂²×C₄

C₂²⋊D₄₃

yes

—

125

C₂²×C₄

C₂²×D₄₃

yes

characteristic

126

SD₁₆

—

127

C₂×C₈

—

128

C₂×C₈

—

129

C₂×C₈

—

130

C₄⋊C₄

—

131

C₄²

—

132

C₂³

—

133

C₂³

—

134

C₂³

—

135

C₂³

—

136

C₂³

—

137

C₂³

C₂×C₂²⋊D₄₃

yes

characteristic

138

Q₈

—

139

Q₈

—

172

—

140

D₄

—

141

D₄

—

142

D₄

—

143

D₄

—

144

D₄

—

145

C₂×C₄

—

146

C₂×C₄

—

147

C₂×C₄

—

148

C₂×C₄

—

172

—

149

C₂×C₄

—

172

—

150

C₂×C₄

—

172

—

151

C₂×C₄

—

172

—

152

C₂×C₄

#10621883

yes

complemented

153

C₂×C₄

D₄×D₄₃

yes

characteristic

154

C₂×C₄

D₄×D₄₃

yes

—

155

C₂×C₄

#10621900

yes

characteristic

156

C₂×C₄

C₂×C₂²⋊D₄₃

yes

—

157

C₈

—

158

C₂²

—

159

C₂²

—

160

C₂²

—

161

C₂²

—

162

C₂²

—

163

C₂²

#13063294

yes

characteristic

164

C₂²

#13063296

yes

characteristic

165

C₂²

#13063321

yes

characteristic

166

C₂²

C₂×#10621883

yes

—

167

C₂²

#13063351

yes

—

168

C₄

—

169

C₄

—

344

—

170

C₄

—

172

—

171

C₄

#13063293

yes

—

172

C₄

#13063297

yes

—

173

C₂

—

174

C₂

#14582807

yes

characteristic

175

C₂

#14583050

yes

—

176

C₂

#14583096

yes

—

177

C₂

#14583271

yes

characteristic

178

C₂

#14583286

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₄₃
commutator	C₂²×C₄×C₄₃	C₂³
Frattini	C₂²×C₄	C₂²×D₄₃
Fitting	C₂×#127×C₄₃	C₂
socle	C₂³×C₄₃	C₂×D₄
hypercenter	C₂×#127	D₄₃
hypocenter	C₄₃	#2014
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#127

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₄₃

commutator

C₂²×C₄×C₄₃

C₂³

Frattini

C₂²×C₄

C₂²×D₄₃

Fitting

C₂×#127×C₄₃

C₂

socle

C₂³×C₄₃

C₂×D₄

D₄₃

C₄₃

G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#127

N	H ≅ G/N	type
1. C₂²×#10621883	C₂	semidirect
2. C₂×#13063246	C₂	semidirect
3. #14582805	C₂	semidirect
4. #14582654	C₂	semidirect
35. C₂×Dic₈₆	D₄	semidirect
41. C₂×C₄₃⋊C₈	D₄	semidirect
55. C₂×C₄×C₄₃	SD₁₆	semidirect
95. C₄₃	#2014	semidirect
152. C₂×C₄	#10621883	semidirect

H ≅ G/N

type

1. C₂²×#10621883

C₂

semidirect

2. C₂×#13063246

C₂

semidirect

3. #14582805

C₂

semidirect

4. #14582654

C₂

semidirect

35. C₂×Dic₈₆

D₄

semidirect

41. C₂×C₄₃⋊C₈

D₄

semidirect

55. C₂×C₄×C₄₃

SD₁₆

semidirect

95. C₄₃

#2014

semidirect

152. C₂×C₄

#10621883

semidirect

Subgroups — #19135683

Conjugacy classes of subgroups

Complements