Group #19133807 — subgroups

Subgroups — #19133807

Order 5504.

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

normal subgroups only

This group has 208 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	#14583251	C₂	1	1	yes	maximal, characteristic, complemented
3	#14583176	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×#462	C₂	1	1	yes	maximal, characteristic, complemented
8	#13063325	C₂²	1	1	yes	characteristic
9	#13063317	—	2	1	no	—
10	#13063303	—	2	2	no	—
11	#13063301	—	2	1	no	—
12	C₄×D₁₇₂	—	2	1	no	—
13	C₄×D₁₇₂	C₂²	1	1	yes	characteristic
14	C₄⋊C₄×D₄₃	—	2	1	no	—
15	#13063258	—	2	1	no	—
16	C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
17	#13063248	—	2	2	no	—
18	#13063245	—	2	1	no	—
19	C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×Q₁₆×C₄₃	—	2	1	no	—
21	C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
22	C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
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	Q₁₆×C₄₃	—	4	2	no	—
32	C₂×C₈×C₄₃	—	2	1	no	—
33	C₄⋊C₄×C₄₃	—	2	1	no	—
34	C₄⋊C₄×C₄₃	—	2	1	no	—
35	C₄⋊C₄×C₄₃	—	2	1	no	—
36	C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
37	C₄²×C₄₃	—	2	1	no	—
38	C₄²×C₄₃	C₂³	1	1	yes	characteristic
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	1	no	—
52	Q₈×C₄₃	—	4	1	no	—
53	C₂×C₄×C₄₃	—	2	1	no	—
54	C₂×C₄×C₄₃	—	2	1	no	—
55	C₂×C₄×C₄₃	—	4	1	no	—
56	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
57	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
58	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
59	C₂×Dic₄₃	—	2	1	no	—
60	C₂×Dic₄₃	—	2	2	no	—
61	D₁₇₂	—	2	1	no	—
62	D₁₇₂	Q₁₆	1	2	yes	complemented
63	C₄×D₄₃	—	4	1	no	—
64	C₄×D₄₃	—	4	1	no	—
65	C₄×D₄₃	—	8	2	no	—
66	Dic₈₆	—	4	2	no	—
67	C₈×C₄₃	—	4	1	no	—
68	C₄₃⋊C₈	—	4	1	no	—
69	C₄₃⋊C₈	—	4	1	no	—
70	C₂²×C₄₃	#120	1	1	yes	characteristic
71	C₂×D₄₃	—	2	2	no	—
72	C₂×D₄₃	—	4	1	no	—
73	C₂×D₄₃	—	4	1	no	—
74	C₄×C₄₃	—	2	1	no	—
75	C₄×C₄₃	—	4	1	no	—
76	C₄×C₄₃	—	4	1	no	—
77	C₄×C₄₃	—	8	1	no	—
78	C₄×C₄₃	C₂×Q₁₆	1	1	yes	characteristic
79	C₄×C₄₃	#135	1	1	yes	characteristic
80	C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
81	C₄×C₄₃	#137	1	1	yes	characteristic
82	Dic₄₃	—	4	1	no	—
83	Dic₄₃	—	4	2	no	—
84	#1644	—	43	1	no	maximal, Sylow
85	C₂×C₄₃	#449	1	1	yes	characteristic
86	C₂×C₄₃	#451	1	1	yes	characteristic
87	C₂×C₄₃	#455	1	1	yes	characteristic
88	D₄₃	—	4	2	no	—
89	#554	—	43	1	no	—
90	#487	—	43	1	no	—
91	#474	—	43	1	no	—
92	#462	D₄₃	1	1	yes	characteristic, complemented
93	#333	—	43	1	no	—
94	Q₈⋊C₈	—	43	1	no	—
95	D₄⋊C₈	—	43	1	no	—
96	C₄₃	#1644	1	1	yes	characteristic, complemented, Sylow
97	C₂×Q₁₆	—	2	1	no	—
98	C₄⋊Q₈	—	43	1	no	—
99	C₄⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
100	#125	—	86	1	no	—
101	C₂²⋊Q₈	—	86	2	no	—
102	C₂²⋊Q₈	—	86	1	no	—
103	C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic
104	C₄×D₄	—	43	1	no	—
105	C₄×D₄	—	86	1	no	—
106	C₂×C₄⋊C₄	—	86	1	no	—
107	#107	—	86	1	no	—
108	C₄⋊C₈	—	43	1	no	—
109	C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
110	#103	—	2	1	no	—
111	#103	—	86	2	no	—
112	#102	—	86	1	no	—
113	C₄×C₈	—	43	1	no	—
114	C₂×Q₈	—	2	1	no	—
115	C₂×Q₈	—	43	2	no	—
116	C₂×Q₈	C₂²⋊D₄₃	1	1	yes	characteristic
117	C₂×D₄	—	43	1	no	—
118	C₂²×C₄	—	86	2	no	—
119	C₂²×C₄	—	86	1	no	—
120	Q₁₆	—	4	2	no	—
121	C₂×C₈	—	2	1	no	—
122	C₂×C₈	—	86	1	no	—
123	C₂×C₈	—	86	1	no	—
124	C₄⋊C₄	—	2	1	no	—
125	C₄⋊C₄	—	2	1	no	—
126	C₄⋊C₄	—	2	1	no	—
127	C₄⋊C₄	—	43	1	no	—
128	C₄⋊C₄	—	86	2	no	—
129	C₄⋊C₄	—	86	2	no	—
130	C₄⋊C₄	—	86	1	no	—
131	C₄⋊C₄	—	86	1	no	—
132	C₄⋊C₄	C₂²⋊D₄₃	1	1	yes	characteristic
133	C₂²⋊C₄	—	86	2	no	—
134	C₂²⋊C₄	—	86	1	no	—
135	C₄²	—	2	1	no	—
136	C₄²	C₂²×D₄₃	1	1	yes	characteristic
137	C₂³	—	86	1	no	—
138	Q₈	—	2	1	no	—
139	Q₈	—	2	1	no	—
140	Q₈	—	4	1	no	—
141	Q₈	—	4	1	no	—
142	Q₈	—	172	2	no	—
143	D₄	—	43	2	no	—
144	D₄	—	86	1	no	—
145	C₂×C₄	—	2	1	no	—
146	C₂×C₄	—	2	1	no	—
147	C₂×C₄	—	4	1	no	—
148	C₂×C₄	—	86	1	no	—
149	C₂×C₄	—	86	2	no	—
150	C₂×C₄	—	344	2	no	—
151	C₂×C₄	—	172	1	no	—
152	C₂×C₄	—	172	1	no	—
153	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
154	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
155	C₂×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
156	C₈	—	4	1	no	—
157	C₈	—	172	1	no	—
158	C₈	—	172	1	no	—
159	C₂²	—	86	2	no	—
160	C₂²	—	172	1	no	—
161	C₂²	—	172	1	no	—
162	C₂²	#13063293	1	1	yes	characteristic
163	C₄	—	2	1	no	—
164	C₄	—	4	1	no	—
165	C₄	—	4	1	no	—
166	C₄	—	8	1	no	—
167	C₄	—	172	1	no	—
168	C₄	—	172	2	no	—
169	C₄	Q₁₆×D₄₃	1	1	yes	characteristic
170	C₄	#13063345	1	1	yes	characteristic
171	C₄	#13063351	1	1	yes	characteristic
172	C₄	#13063357	1	1	yes	characteristic
173	C₂	—	172	2	no	—
174	C₂	#14583042	1	1	yes	characteristic
175	C₂	#14583053	1	1	yes	characteristic
176	C₂	#14583075	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14583609

C₂

yes

maximal, characteristic

#14583251

C₂

yes

maximal, characteristic, complemented

#14583176

C₂

yes

maximal, characteristic

#14582647

C₂

yes

maximal, characteristic, complemented

Q₈⋊(C₄₃⋊C₈)

C₂

yes

maximal, characteristic, complemented

#14582626

C₂

yes

maximal, characteristic

C₄₃×#462

C₂

yes

maximal, characteristic, complemented

#13063325

C₂²

yes

—

—

—

C₄×D₁₇₂

—

C₄×D₁₇₂

C₂²

yes

characteristic

C₄⋊C₄×D₄₃

—

#13063258

—

C₄⋊(C₄₃⋊C₈)

C₂²

yes

characteristic

#13063248

—

#13063245

—

C₄×C₄₃⋊C₈

C₂²

yes

characteristic

C₂×Q₁₆×C₄₃

—

C₄⋊Q₈×C₄₃

C₂²

yes

characteristic

C₄×Q₈×C₄₃

C₂²

yes

characteristic

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

—

Q₁₆×C₄₃

—

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

(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

—

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

—

—

—

—

D₄₃

yes

characteristic, complemented

#333

—

Q₈⋊C₈

—

D₄⋊C₈

—

C₄₃

#1644

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

C₄⋊Q₈

—

C₄⋊Q₈

C₂×D₄₃

yes

characteristic

100

#125

—

101

C₂²⋊Q₈

—

102

C₂²⋊Q₈

—

103

C₄×Q₈

C₂×D₄₃

yes

characteristic

104

C₄×D₄

—

105

C₄×D₄

—

106

C₂×C₄⋊C₄

—

107

#107

—

108

C₄⋊C₈

—

109

C₄⋊C₈

C₂×D₄₃

yes

characteristic

110

#103

—

111

#103

—

112

#102

—

113

C₄×C₈

—

114

C₂×Q₈

—

115

C₂×Q₈

—

116

C₂×Q₈

C₂²⋊D₄₃

yes

characteristic

117

C₂×D₄

—

118

C₂²×C₄

—

119

C₂²×C₄

—

120

Q₁₆

—

121

C₂×C₈

—

122

C₂×C₈

—

123

C₂×C₈

—

124

C₄⋊C₄

—

125

C₄⋊C₄

—

126

C₄⋊C₄

—

127

C₄⋊C₄

—

128

C₄⋊C₄

—

129

C₄⋊C₄

—

130

C₄⋊C₄

—

131

C₄⋊C₄

—

132

C₄⋊C₄

C₂²⋊D₄₃

yes

characteristic

133

C₂²⋊C₄

—

134

C₂²⋊C₄

—

135

C₄²

—

136

C₄²

C₂²×D₄₃

yes

characteristic

137

C₂³

—

138

Q₈

—

139

Q₈

—

140

Q₈

—

141

Q₈

—

142

Q₈

—

172

—

143

D₄

—

144

D₄

—

145

C₂×C₄

—

146

C₂×C₄

—

147

C₂×C₄

—

148

C₂×C₄

—

149

C₂×C₄

—

150

C₂×C₄

—

344

—

151

C₂×C₄

—

172

—

152

C₂×C₄

—

172

—

153

C₂×C₄

D₄×D₄₃

yes

characteristic

154

C₂×C₄

D₄×D₄₃

yes

characteristic

155

C₂×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

156

C₈

—

157

C₈

—

172

—

158

C₈

—

172

—

159

C₂²

—

160

C₂²

—

172

—

161

C₂²

—

172

—

162

C₂²

#13063293

yes

characteristic

163

C₄

—

164

C₄

—

165

C₄

—

166

C₄

—

167

C₄

—

172

—

168

C₄

—

172

—

169

C₄

Q₁₆×D₄₃

yes

characteristic

170

C₄

#13063345

yes

characteristic

171

C₄

#13063351

yes

characteristic

172

C₄

#13063357

yes

characteristic

173

C₂

—

172

—

174

C₂

#14583042

yes

characteristic

175

C₂

#14583053

yes

characteristic

176

C₂

#14583075

yes

characteristic

	subgroup	G/H
center	C₂²	#13063293
commutator	C₄²×C₄₃	C₂³
Frattini	C₄²	C₂²×D₄₃
Fitting	C₄₃×#462	C₂
socle	C₂²×C₄₃	#120
hypercenter	#462	D₄₃
hypocenter	C₄₃	#1644
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #462

subgroup

G/H

center

C₂²

#13063293

commutator

C₄²×C₄₃

C₂³

Frattini

C₄²

C₂²×D₄₃

Fitting

C₄₃×#462

C₂

C₂²×C₄₃

D₄₃

C₄₃

G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #462

N	H ≅ G/N	type
2. #14583251	C₂	semidirect
4. #14582647	C₂	semidirect
5. Q₈⋊(C₄₃⋊C₈)	C₂	semidirect
7. C₄₃×#462	C₂	semidirect
62. D₁₇₂	Q₁₆	semidirect
92. #462	D₄₃	semidirect
96. C₄₃	#1644	semidirect

H ≅ G/N

type

2. #14583251

C₂

semidirect

4. #14582647

C₂

semidirect

5. Q₈⋊(C₄₃⋊C₈)

C₂

semidirect

7. C₄₃×#462

C₂

semidirect

62. D₁₇₂

Q₁₆

semidirect

92. #462

D₄₃

semidirect

96. C₄₃

#1644

semidirect

Subgroups — #19133807

Conjugacy classes of subgroups

Complements