Group #19135838 — subgroups

Subgroups — #19135838

Order 5504.

298 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 298 conjugacy classes of subgroups — too many to draw. Only its 95 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×#13063249	C₂	1	2	yes	maximal
2	C₂×#13063249	C₂	1	2	yes	maximal
3	#14582797	C₂	1	1	yes	maximal, characteristic
4	#14582654	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄⋊Q₈×C₄₃	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₄₃⋊C₈	C₂²	1	2	yes	—
7	C₂×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
8	C₂×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
9	C₂×Dic₄₃⋊C₄	—	2	1	no	—
10	#13063249	—	2	4	no	—
11	#13063249	—	2	4	no	—
12	C₄₃⋊#95	—	2	1	no	—
13	C₂²×Q₈×C₄₃	C₂²	1	2	yes	—
14	C₄⋊Q₈×C₄₃	—	2	4	no	—
15	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
16	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
17	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
18	C₂×Q₈×C₄₃	—	2	2	no	—
19	C₂×Q₈×C₄₃	—	2	2	no	—
20	C₂×Q₈×C₄₃	—	2	2	no	—
21	C₂×Q₈×C₄₃	—	2	2	no	—
22	C₂×Q₈×C₄₃	—	2	2	no	—
23	C₂×Q₈×C₄₃	D₄	1	4	yes	—
24	C₂²×C₄×C₄₃	—	2	2	no	—
25	C₂²×C₄×C₄₃	D₄	1	1	yes	characteristic
26	C₂²×C₄×C₄₃	D₄	1	1	yes	characteristic
27	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
28	C₂²×Dic₄₃	—	2	1	no	—
29	C₂²×Dic₄₃	—	2	1	no	—
30	C₄⋊C₄×C₄₃	—	2	4	no	—
31	C₄⋊C₄×C₄₃	—	2	4	no	—
32	C₄²×C₄₃	—	2	2	no	—
33	C₄⋊Dic₄₃	—	2	1	no	—
34	C₄⋊Dic₄₃	—	2	2	no	—
35	C₄⋊Dic₄₃	D₄	1	2	yes	—
36	Dic₄₃⋊C₄	—	4	2	no	—
37	C₂×C₄₃⋊C₈	—	2	2	no	—
38	C₂×C₄₃⋊C₈	—	2	2	no	—
39	C₂×C₄₃⋊C₈	—	2	2	no	—
40	C₂³×C₄₃	C₂×D₄	1	1	yes	characteristic
41	Q₈×C₄₃	—	2	4	no	—
42	Q₈×C₄₃	—	2	4	no	—
43	Q₈×C₄₃	—	4	2	no	—
44	Q₈×C₄₃	—	4	2	no	—
45	C₂×C₄×C₄₃	—	2	1	no	—
46	C₂×C₄×C₄₃	—	2	1	no	—
47	C₂×C₄×C₄₃	—	2	1	no	—
48	C₂×C₄×C₄₃	—	2	1	no	—
49	C₂×C₄×C₄₃	—	2	4	no	—
50	C₂×C₄×C₄₃	—	4	2	no	—
51	C₂×C₄×C₄₃	—	4	2	no	—
52	C₂×C₄×C₄₃	SD₁₆	1	2	yes	—
53	C₂×C₄×C₄₃	Q₁₆	1	2	yes	—
54	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
55	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
56	C₂×C₄×C₄₃	#41	1	2	yes	—
57	C₂×C₄×C₄₃	#41	1	1	yes	characteristic
58	C₂×Dic₄₃	—	2	2	no	—
59	C₂×Dic₄₃	—	4	1	no	—
60	C₂×Dic₄₃	—	4	1	no	—
61	C₂×Dic₄₃	—	4	1	no	—
62	C₂×Dic₄₃	—	4	1	no	—
63	C₂×Dic₄₃	—	4	1	no	—
64	C₄₃⋊C₈	—	4	2	no	—
65	C₂²×C₄₃	#120	1	1	yes	characteristic
66	C₂²×C₄₃	#121	1	1	yes	characteristic
67	C₂²×C₄₃	#124	1	1	yes	characteristic
68	C₂²×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
69	C₂²×C₄₃	C₂×Q₁₆	1	1	yes	characteristic
70	C₂²×C₄₃	#137	1	1	yes	characteristic
71	C₂²×C₄₃	#137	1	1	yes	characteristic
72	C₄×C₄₃	—	2	2	no	—
73	C₄×C₄₃	—	2	2	no	—
74	C₄×C₄₃	—	4	4	no	—
75	C₄×C₄₃	#121	1	2	yes	—
76	C₄×C₄₃	#123	1	2	yes	—
77	Dic₄₃	—	4	2	no	—
78	Dic₄₃	—	8	1	no	—
79	#2043	—	43	1	no	maximal, Sylow
80	C₂×C₄₃	#394	1	1	yes	characteristic
81	C₂×C₄₃	#448	1	1	yes	characteristic
82	C₂×C₄₃	#451	1	1	yes	characteristic
83	C₂×C₄₃	#461	1	1	yes	characteristic
84	C₂×C₄₃	#462	1	1	yes	characteristic
85	C₂×C₄₃	#487	1	1	yes	characteristic
86	C₂×C₄₃	#491	1	1	yes	characteristic
87	C₂×C₄⋊Q₈	D₄₃	1	1	yes	characteristic
88	C₂×#103	—	43	2	no	—
89	C₂×#103	—	43	2	no	—
90	#389	—	43	1	no	—
91	#336	—	43	1	no	—
92	C₄₃	#2043	1	1	yes	characteristic, complemented, Sylow
93	C₂²×Q₈	C₂×D₄₃	1	2	yes	—
94	C₂²×C₈	—	43	2	no	—
95	C₄⋊Q₈	—	2	4	no	—
96	C₂×C₄⋊C₄	—	2	1	no	—
97	C₂×C₄⋊C₄	—	2	1	no	—
98	C₂×C₄⋊C₄	—	43	1	no	—
99	C₂×C₄⋊C₄	—	43	1	no	—
100	C₂×C₄⋊C₄	—	86	1	no	—
101	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
102	#103	—	86	4	no	—
103	#103	—	86	4	no	—
104	#95	—	86	1	no	—
105	C₂×Q₈	—	2	2	no	—
106	C₂×Q₈	—	2	2	no	—
107	C₂×Q₈	—	2	2	no	—
108	C₂×Q₈	—	2	2	no	—
109	C₂×Q₈	—	2	2	no	—
110	C₂×Q₈	C₂²⋊D₄₃	1	4	yes	—
111	C₂²×C₄	—	2	2	no	—
112	C₂²×C₄	—	86	1	no	—
113	C₂²×C₄	—	86	1	no	—
114	C₂²×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
115	C₂²×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
116	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
117	C₂×C₈	—	86	2	no	—
118	C₂×C₈	—	86	2	no	—
119	C₂×C₈	—	86	2	no	—
120	C₄⋊C₄	—	2	4	no	—
121	C₄⋊C₄	—	2	4	no	—
122	C₄⋊C₄	—	43	2	no	—
123	C₄⋊C₄	—	86	1	no	—
124	C₄⋊C₄	—	86	2	no	—
125	C₄⋊C₄	—	172	2	no	—
126	C₄²	—	2	2	no	—
127	C₂³	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
128	Q₈	—	2	4	no	—
129	Q₈	—	2	4	no	—
130	Q₈	—	4	2	no	—
131	Q₈	—	4	2	no	—
132	C₂×C₄	—	2	1	no	—
133	C₂×C₄	—	2	1	no	—
134	C₂×C₄	—	2	1	no	—
135	C₂×C₄	—	2	1	no	—
136	C₂×C₄	—	2	4	no	—
137	C₂×C₄	—	4	2	no	—
138	C₂×C₄	—	4	2	no	—
139	C₂×C₄	—	86	2	no	—
140	C₂×C₄	—	172	1	no	—
141	C₂×C₄	—	172	1	no	—
142	C₂×C₄	—	172	1	no	—
143	C₂×C₄	—	172	1	no	—
144	C₂×C₄	—	172	1	no	—
145	C₂×C₄	#10621884	1	2	yes	—
146	C₂×C₄	#10621885	1	2	yes	—
147	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
148	C₂×C₄	#10621900	1	2	yes	—
149	C₂×C₄	#10621900	1	1	yes	characteristic
150	C₂×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
151	C₈	—	172	2	no	—
152	C₂²	#13063294	1	1	yes	characteristic
153	C₂²	#13063296	1	1	yes	characteristic
154	C₂²	#13063312	1	1	yes	characteristic
155	C₂²	C₂×#10621884	1	1	yes	characteristic
156	C₂²	C₂×#10621885	1	1	yes	characteristic
157	C₂²	#13063356	1	1	yes	characteristic
158	C₂²	#13063356	1	1	yes	characteristic
159	C₄	—	2	2	no	—
160	C₄	—	2	2	no	—
161	C₄	—	4	4	no	—
162	C₄	—	344	1	no	—
163	C₄	—	172	2	no	—
164	C₄	#13063297	1	2	yes	—
165	C₄	#13063306	1	2	yes	—
166	C₂	#14582813	1	1	yes	characteristic
167	C₂	#14583038	1	1	yes	characteristic
168	C₂	#14583055	1	1	yes	characteristic
169	C₂	#14583101	1	1	yes	characteristic
170	C₂	#14583106	1	1	yes	characteristic
171	C₂	#14583249	1	1	yes	characteristic
172	C₂	#14583267	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063249

C₂

yes

maximal

C₂×#13063249

C₂

yes

maximal

#14582797

C₂

yes

maximal, characteristic

#14582654

C₂

yes

maximal, characteristic

C₂×C₄⋊Q₈×C₄₃

C₂

yes

maximal, characteristic

C₂²×C₄₃⋊C₈

C₂²

yes

—

C₂×C₄⋊Dic₄₃

C₂²

yes

characteristic

C₂×C₄⋊Dic₄₃

C₂²

yes

characteristic

C₂×Dic₄₃⋊C₄

—

#13063249

—

#13063249

—

C₄₃⋊#95

—

C₂²×Q₈×C₄₃

C₂²

yes

—

C₄⋊Q₈×C₄₃

—

C₂×C₄⋊C₄×C₄₃

—

C₂×C₄⋊C₄×C₄₃

—

C₂×C₄²×C₄₃

C₂²

yes

characteristic

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

D₄

yes

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

D₄

yes

characteristic

C₂²×C₄×C₄₃

D₄

yes

characteristic

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

—

C₂²×Dic₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄²×C₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

D₄

yes

—

Dic₄₃⋊C₄

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

C₂×D₄

yes

characteristic

Q₈×C₄₃

—

Q₈×C₄₃

—

Q₈×C₄₃

—

Q₈×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

SD₁₆

yes

—

C₂×C₄×C₄₃

Q₁₆

yes

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₄×C₄₃

#41

yes

—

C₂×C₄×C₄₃

#41

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₄₃⋊C₈

—

C₂²×C₄₃

yes

C₂²×C₄₃

yes

C₂²×C₄₃

yes

C₂²×C₄₃

C₂×SD₁₆

yes

characteristic

C₂²×C₄₃

C₂×Q₁₆

yes

C₂²×C₄₃

yes

C₂²×C₄₃

yes

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

#121

yes

—

C₄×C₄₃

#123

yes

—

Dic₄₃

—

Dic₄₃

—

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄⋊Q₈

D₄₃

yes

—

—

—

—

C₄₃

#2043

yes

characteristic, complemented, Sylow

C₂²×Q₈

C₂×D₄₃

yes

—

C₂²×C₈

—

C₄⋊Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

100

C₂×C₄⋊C₄

—

101

C₂×C₄²

C₂×D₄₃

yes

characteristic

102

#103

—

103

#103

—

104

#95

—

105

C₂×Q₈

—

106

C₂×Q₈

—

107

C₂×Q₈

—

108

C₂×Q₈

—

109

C₂×Q₈

—

110

C₂×Q₈

C₂²⋊D₄₃

yes

—

111

C₂²×C₄

—

112

C₂²×C₄

—

113

C₂²×C₄

—

114

C₂²×C₄

C₂²⋊D₄₃

yes

characteristic

115

C₂²×C₄

C₂²⋊D₄₃

yes

characteristic

116

C₂²×C₄

C₂²×D₄₃

yes

characteristic

117

C₂×C₈

—

118

C₂×C₈

—

119

C₂×C₈

—

120

C₄⋊C₄

—

121

C₄⋊C₄

—

122

C₄⋊C₄

—

123

C₄⋊C₄

—

124

C₄⋊C₄

—

125

C₄⋊C₄

—

172

—

126

C₄²

—

127

C₂³

C₂×C₂²⋊D₄₃

yes

characteristic

128

Q₈

—

129

Q₈

—

130

Q₈

—

131

Q₈

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

—

137

C₂×C₄

—

138

C₂×C₄

—

139

C₂×C₄

—

140

C₂×C₄

—

172

—

141

C₂×C₄

—

172

—

142

C₂×C₄

—

172

—

143

C₂×C₄

—

172

—

144

C₂×C₄

—

172

—

145

C₂×C₄

#10621884

yes

—

146

C₂×C₄

#10621885

yes

—

147

C₂×C₄

D₄×D₄₃

yes

characteristic

148

C₂×C₄

#10621900

yes

—

149

C₂×C₄

#10621900

yes

characteristic

150

C₂×C₄

C₂×C₂²⋊D₄₃

yes

—

151

C₈

—

172

—

152

C₂²

#13063294

yes

characteristic

153

C₂²

#13063296

yes

characteristic

154

C₂²

#13063312

yes

characteristic

155

C₂²

C₂×#10621884

yes

characteristic

156

C₂²

C₂×#10621885

yes

characteristic

157

C₂²

#13063356

yes

characteristic

158

C₂²

#13063356

yes

characteristic

159

C₄

—

160

C₄

—

161

C₄

—

162

C₄

—

344

—

163

C₄

—

172

—

164

C₄

#13063297

yes

—

165

C₄

#13063306

yes

—

166

C₂

#14582813

yes

characteristic

167

C₂

#14583038

yes

characteristic

168

C₂

#14583055

yes

characteristic

169

C₂

#14583101

yes

characteristic

170

C₂

#14583106

yes

characteristic

171

C₂

#14583249

yes

characteristic

172

C₂

#14583267

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₄₃
commutator	C₂²×C₄×C₄₃	C₂³
Frattini	C₂²×C₄	C₂²×D₄₃
Fitting	C₂×C₄⋊Q₈×C₄₃	C₂
socle	C₂³×C₄₃	C₂×D₄
hypercenter	C₂×C₄⋊Q₈	D₄₃
hypocenter	C₄₃	#2043
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄⋊Q₈

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₄₃

commutator

C₂²×C₄×C₄₃

C₂³

Frattini

C₂²×C₄

C₂²×D₄₃

Fitting

C₂×C₄⋊Q₈×C₄₃

C₂

socle

C₂³×C₄₃

C₂×D₄

hypercenter

C₂×C₄⋊Q₈

D₄₃

hypocenter

C₄₃

#2043

LCS

G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄⋊Q₈

N	H ≅ G/N	type
92. C₄₃	#2043	semidirect

H ≅ G/N

type

92. C₄₃

#2043

semidirect

Subgroups — #19135838

Conjugacy classes of subgroups

Complements