Group #19133728 — subgroups

Subgroups — #19133728

Order 5504.

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

normal subgroups only

This group has 214 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	#14583609	C₂	1	1	yes	maximal, characteristic
2	#14583278	C₂	1	1	yes	maximal, characteristic, complemented
3	#14583186	C₂	1	1	yes	maximal, characteristic
4	#14582647	C₂	1	1	yes	maximal, characteristic, complemented
5	Q₈⋊(C₄₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
6	#14582626	C₂	1	1	yes	maximal, characteristic
7	C₄₃×#477	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#10621885	—	2	2	no	—
9	#13063325	C₂²	1	1	yes	characteristic
10	#13063317	—	2	1	no	—
11	#13063303	—	2	2	no	—
12	#13063301	—	2	1	no	—
13	C₄×D₁₇₂	—	2	1	no	—
14	C₄×D₁₇₂	C₂²	1	1	yes	characteristic
15	C₄⋊C₄×D₄₃	—	2	1	no	—
16	#13063256	—	2	1	no	—
17	C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
18	#13063245	—	2	1	no	—
19	C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
20	C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
21	C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
22	#107×C₄₃	—	2	1	no	—
23	C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
24	#103×C₄₃	—	2	1	no	—
25	C₂×Q₈×C₄₃	—	2	1	no	—
26	C₂×Q₈×C₄₃	D₄	1	1	yes	characteristic
27	C₂×D₁₇₂	D₄	1	1	yes	characteristic
28	C₂×C₄×D₄₃	—	2	1	no	—
29	C₂×C₄×D₄₃	—	2	2	no	—
30	C₂×Dic₈₆	D₄	1	2	yes	—
31	C₂×C₈×C₄₃	—	2	1	no	—
32	C₄⋊C₄×C₄₃	—	2	1	no	—
33	C₄⋊C₄×C₄₃	—	2	1	no	—
34	C₄⋊C₄×C₄₃	—	2	1	no	—
35	C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
36	C₄²×C₄₃	—	2	1	no	—
37	C₄²×C₄₃	C₂³	1	1	yes	characteristic
38	#10621885	—	4	4	no	—
39	(C₂×D₄₃)⋊C₄	—	2	2	no	—
40	(C₂×D₄₃)⋊C₄	—	2	1	no	—
41	C₄⋊Dic₄₃	—	2	1	no	—
42	C₄⋊Dic₄₃	—	2	1	no	—
43	C₄⋊Dic₄₃	D₄	1	1	yes	characteristic
44	Dic₄₃⋊C₄	—	2	2	no	—
45	Dic₄₃⋊C₄	—	2	2	no	—
46	C₂×C₄₃⋊C₈	—	2	1	no	—
47	C₂×C₄₃⋊C₈	—	2	1	no	—
48	C₂²×D₄₃	—	2	1	no	—
49	Q₈×C₄₃	—	2	1	no	—
50	Q₈×C₄₃	—	2	1	no	—
51	Q₈×C₄₃	—	4	2	no	—
52	C₂×C₄×C₄₃	—	2	1	no	—
53	C₂×C₄×C₄₃	—	2	1	no	—
54	C₂×C₄×C₄₃	—	4	1	no	—
55	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
56	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
57	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
58	C₂×Dic₄₃	—	2	1	no	—
59	C₂×Dic₄₃	—	2	2	no	—
60	D₁₇₂	—	2	1	no	—
61	D₁₇₂	Q₁₆	1	2	yes	complemented
62	C₄×D₄₃	—	4	1	no	—
63	C₄×D₄₃	—	4	1	no	—
64	C₄×D₄₃	—	8	2	no	—
65	Dic₈₆	—	4	2	no	—
66	C₈×C₄₃	—	4	1	no	—
67	C₄₃⋊C₈	—	2	2	no	—
68	C₄₃⋊C₈	—	4	1	no	—
69	C₂²×C₄₃	#120	1	1	yes	characteristic
70	C₂×D₄₃	—	2	2	no	—
71	C₂×D₄₃	—	4	1	no	—
72	C₂×D₄₃	—	4	1	no	—
73	C₄×C₄₃	—	2	1	no	—
74	C₄×C₄₃	—	4	1	no	—
75	C₄×C₄₃	—	4	1	no	—
76	C₄×C₄₃	—	8	1	no	—
77	C₄×C₄₃	C₂×Q₁₆	1	1	yes	characteristic
78	C₄×C₄₃	#135	1	1	yes	characteristic
79	C₄×C₄₃	#137	1	1	yes	characteristic
80	C₄×C₄₃	#137	1	1	yes	characteristic
81	Dic₄₃	—	4	1	no	—
82	Dic₄₃	—	4	2	no	—
83	#1632	—	43	1	no	maximal, Sylow
84	C₂×C₄₃	#451	1	1	yes	characteristic
85	C₂×C₄₃	#452	1	1	yes	characteristic
86	C₂×C₄₃	#453	1	1	yes	characteristic
87	D₄₃	—	4	2	no	—
88	#554	—	43	1	no	—
89	#494	—	43	1	no	—
90	#477	D₄₃	1	1	yes	characteristic, complemented
91	#476	—	43	1	no	—
92	#333	—	43	1	no	—
93	Q₈⋊C₈	—	43	1	no	—
94	D₄⋊C₈	—	43	1	no	—
95	C₄₃	#1632	1	1	yes	characteristic, complemented, Sylow
96	C₂×Q₁₆	—	86	2	no	—
97	C₄⋊Q₈	—	43	1	no	—
98	C₄⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
99	#125	—	86	1	no	—
100	C₂²⋊Q₈	—	86	2	no	—
101	C₂²⋊Q₈	—	86	1	no	—
102	C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic
103	C₄×D₄	—	43	1	no	—
104	C₄×D₄	—	86	1	no	—
105	C₂×C₄⋊C₄	—	86	1	no	—
106	#107	—	2	1	no	—
107	#106	—	86	1	no	—
108	C₄⋊C₈	—	43	1	no	—
109	C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
110	#103	—	2	1	no	—
111	#102	—	86	1	no	—
112	C₄×C₈	—	43	1	no	—
113	C₂×Q₈	—	2	1	no	—
114	C₂×Q₈	—	43	2	no	—
115	C₂×Q₈	C₂²⋊D₄₃	1	1	yes	characteristic
116	C₂×D₄	—	43	1	no	—
117	C₂²×C₄	—	86	2	no	—
118	C₂²×C₄	—	86	1	no	—
119	Q₁₆	—	172	4	no	—
120	C₂×C₈	—	2	1	no	—
121	C₂×C₈	—	86	1	no	—
122	C₂×C₈	—	86	1	no	—
123	C₄⋊C₄	—	2	1	no	—
124	C₄⋊C₄	—	2	1	no	—
125	C₄⋊C₄	—	2	1	no	—
126	C₄⋊C₄	—	43	1	no	—
127	C₄⋊C₄	—	86	2	no	—
128	C₄⋊C₄	—	86	2	no	—
129	C₄⋊C₄	—	86	1	no	—
130	C₄⋊C₄	—	86	1	no	—
131	C₄⋊C₄	C₂²⋊D₄₃	1	1	yes	characteristic
132	C₂²⋊C₄	—	86	2	no	—
133	C₂²⋊C₄	—	86	1	no	—
134	C₄²	—	2	1	no	—
135	C₄²	C₂²×D₄₃	1	1	yes	characteristic
136	C₂³	—	86	1	no	—
137	Q₈	—	2	1	no	—
138	Q₈	—	2	1	no	—
139	Q₈	—	4	2	no	—
140	Q₈	—	172	2	no	—
141	D₄	—	43	2	no	—
142	D₄	—	86	1	no	—
143	C₂×C₄	—	2	1	no	—
144	C₂×C₄	—	2	1	no	—
145	C₂×C₄	—	4	1	no	—
146	C₂×C₄	—	86	1	no	—
147	C₂×C₄	—	86	2	no	—
148	C₂×C₄	—	344	2	no	—
149	C₂×C₄	—	172	1	no	—
150	C₂×C₄	—	172	1	no	—
151	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
152	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
153	C₂×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
154	C₈	—	4	1	no	—
155	C₈	—	86	2	no	—
156	C₈	—	172	1	no	—
157	C₂²	—	86	2	no	—
158	C₂²	—	172	1	no	—
159	C₂²	—	172	1	no	—
160	C₂²	#13063293	1	1	yes	characteristic
161	C₄	—	2	1	no	—
162	C₄	—	4	1	no	—
163	C₄	—	4	1	no	—
164	C₄	—	8	1	no	—
165	C₄	—	172	1	no	—
166	C₄	—	172	2	no	—
167	C₄	Q₁₆×D₄₃	1	1	yes	characteristic
168	C₄	#13063345	1	1	yes	characteristic
169	C₄	#13063356	1	1	yes	characteristic
170	C₄	#13063357	1	1	yes	characteristic
171	C₂	—	172	2	no	—
172	C₂	#14583053	1	1	yes	characteristic
173	C₂	#14583059	1	1	yes	characteristic
174	C₂	#14583065	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14583609

C₂

yes

maximal, characteristic

#14583278

C₂

yes

maximal, characteristic, complemented

#14583186

C₂

yes

maximal, characteristic

#14582647

C₂

yes

maximal, characteristic, complemented

Q₈⋊(C₄₃⋊C₈)

C₂

yes

maximal, characteristic, complemented

#14582626

C₂

yes

maximal, characteristic

C₄₃×#477

C₂

yes

maximal, characteristic, complemented

C₂×#10621885

—

#13063325

C₂²

yes

—

—

—

C₄×D₁₇₂

—

C₄×D₁₇₂

C₂²

yes

characteristic

C₄⋊C₄×D₄₃

—

#13063256

—

C₄⋊(C₄₃⋊C₈)

C₂²

yes

characteristic

#13063245

—

C₄×C₄₃⋊C₈

C₂²

yes

characteristic

C₄⋊Q₈×C₄₃

C₂²

yes

characteristic

C₄×Q₈×C₄₃

C₂²

yes

characteristic

#107×C₄₃

—

C₄⋊C₈×C₄₃

C₂²

yes

characteristic

#103×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

D₄

yes

characteristic

C₂×D₁₇₂

D₄

yes

characteristic

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

—

C₂×Dic₈₆

D₄

yes

—

C₂×C₈×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

D₄

yes

characteristic

C₄²×C₄₃

—

C₄²×C₄₃

C₂³

yes

characteristic

#10621885

—

(C₂×D₄₃)⋊C₄

—

(C₂×D₄₃)⋊C₄

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

D₄

yes

characteristic

Dic₄₃⋊C₄

—

Dic₄₃⋊C₄

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂²×D₄₃

—

Q₈×C₄₃

—

Q₈×C₄₃

—

Q₈×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

—

D₁₇₂

—

D₁₇₂

Q₁₆

yes

complemented

C₄×D₄₃

—

C₄×D₄₃

—

C₄×D₄₃

—

Dic₈₆

—

C₈×C₄₃

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

C₂²×C₄₃

#120

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

C₂×Q₁₆

yes

C₄×C₄₃

yes

C₄×C₄₃

yes

C₄×C₄₃

yes

Dic₄₃

—

Dic₄₃

—

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

D₄₃

—

#554

—

#494

—

#477

D₄₃

yes

characteristic, complemented

#476

—

#333

—

Q₈⋊C₈

—

D₄⋊C₈

—

C₄₃

#1632

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

C₄⋊Q₈

—

C₄⋊Q₈

C₂×D₄₃

yes

characteristic

#125

—

100

C₂²⋊Q₈

—

101

C₂²⋊Q₈

—

102

C₄×Q₈

C₂×D₄₃

yes

characteristic

103

C₄×D₄

—

104

C₄×D₄

—

105

C₂×C₄⋊C₄

—

106

#107

—

107

#106

—

108

C₄⋊C₈

—

109

C₄⋊C₈

C₂×D₄₃

yes

characteristic

110

#103

—

111

#102

—

112

C₄×C₈

—

113

C₂×Q₈

—

114

C₂×Q₈

—

115

C₂×Q₈

C₂²⋊D₄₃

yes

characteristic

116

C₂×D₄

—

117

C₂²×C₄

—

118

C₂²×C₄

—

119

Q₁₆

—

172

—

120

C₂×C₈

—

121

C₂×C₈

—

122

C₂×C₈

—

123

C₄⋊C₄

—

124

C₄⋊C₄

—

125

C₄⋊C₄

—

126

C₄⋊C₄

—

127

C₄⋊C₄

—

128

C₄⋊C₄

—

129

C₄⋊C₄

—

130

C₄⋊C₄

—

131

C₄⋊C₄

C₂²⋊D₄₃

yes

characteristic

132

C₂²⋊C₄

—

133

C₂²⋊C₄

—

134

C₄²

—

135

C₄²

C₂²×D₄₃

yes

characteristic

136

C₂³

—

137

Q₈

—

138

Q₈

—

139

Q₈

—

140

Q₈

—

172

—

141

D₄

—

142

D₄

—

143

C₂×C₄

—

144

C₂×C₄

—

145

C₂×C₄

—

146

C₂×C₄

—

147

C₂×C₄

—

148

C₂×C₄

—

344

—

149

C₂×C₄

—

172

—

150

C₂×C₄

—

172

—

151

C₂×C₄

D₄×D₄₃

yes

characteristic

152

C₂×C₄

D₄×D₄₃

yes

characteristic

153

C₂×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

154

C₈

—

155

C₈

—

156

C₈

—

172

—

157

C₂²

—

158

C₂²

—

172

—

159

C₂²

—

172

—

160

C₂²

#13063293

yes

characteristic

161

C₄

—

162

C₄

—

163

C₄

—

164

C₄

—

165

C₄

—

172

—

166

C₄

—

172

—

167

C₄

Q₁₆×D₄₃

yes

characteristic

168

C₄

#13063345

yes

characteristic

169

C₄

#13063356

yes

characteristic

170

C₄

#13063357

yes

characteristic

171

C₂

—

172

—

172

C₂

#14583053

yes

characteristic

173

C₂

#14583059

yes

characteristic

174

C₂

#14583065

yes

characteristic

	subgroup	G/H
center	C₂²	#13063293
commutator	C₄²×C₄₃	C₂³
Frattini	C₄²	C₂²×D₄₃
Fitting	C₄₃×#477	C₂
socle	C₂²×C₄₃	#120
hypercenter	#477	D₄₃
hypocenter	C₄₃	#1632
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #477

subgroup

G/H

center

C₂²

#13063293

commutator

C₄²×C₄₃

C₂³

Frattini

C₄²

C₂²×D₄₃

Fitting

C₄₃×#477

C₂

C₂²×C₄₃

D₄₃

C₄₃

G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #477

N	H ≅ G/N	type
2. #14583278	C₂	semidirect
4. #14582647	C₂	semidirect
5. Q₈⋊(C₄₃⋊C₈)	C₂	semidirect
7. C₄₃×#477	C₂	semidirect
61. D₁₇₂	Q₁₆	semidirect
90. #477	D₄₃	semidirect
95. C₄₃	#1632	semidirect

H ≅ G/N

type

2. #14583278

C₂

semidirect

4. #14582647

C₂

semidirect

5. Q₈⋊(C₄₃⋊C₈)

C₂

semidirect

7. C₄₃×#477

C₂

semidirect

61. D₁₇₂

Q₁₆

semidirect

90. #477

D₄₃

semidirect

95. C₄₃

#1632

semidirect

Subgroups — #19133728

Conjugacy classes of subgroups

Complements