Group #19136059 — subgroups

Subgroups — #19136059

Order 5504.

184 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 61 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	#14582948	C₂	1	1	yes	maximal, characteristic
2	#14582908	C₂	1	1	yes	maximal, characteristic
3	C₂×#13063244	C₂	1	1	yes	maximal, characteristic
4	#14582670	C₂	1	1	yes	maximal, characteristic
5	#14582669	C₂	1	1	yes	maximal, characteristic
6	#14582655	C₂	1	1	yes	maximal, characteristic
7	C₄₃×#419	C₂	1	1	yes	maximal, characteristic
8	C₂×#10621877	C₂²	1	1	yes	characteristic
9	C₂×#10621877	C₂²	1	1	yes	characteristic
10	C₂×#10621877	C₂²	1	1	yes	characteristic
11	#13063284	C₂²	1	1	yes	characteristic
12	#13063261	—	2	2	no	—
13	#13063249	—	2	2	no	—
14	#13063244	—	2	2	no	—
15	C₂²×Q₈×C₄₃	C₂²	1	1	yes	characteristic
16	C₂×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
17	#117×C₄₃	C₂²	1	1	yes	characteristic
18	#103×C₄₃	—	2	2	no	—
19	C₂×Q₈×C₄₃	—	2	1	no	—
20	C₂×Q₈×C₄₃	—	2	1	no	—
21	C₂×Q₈×C₄₃	—	2	1	no	—
22	C₂×Q₈×C₄₃	—	2	1	no	—
23	C₂×Q₈×C₄₃	—	2	1	no	—
24	C₂×Q₈×C₄₃	D₄	1	2	yes	—
25	C₂²×C₄×C₄₃	—	2	1	no	—
26	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
27	M₁₆×C₄₃	—	2	1	no	—
28	M₁₆×C₄₃	—	2	1	no	—
29	C₂×C₈×C₄₃	D₄	1	2	yes	—
30	C₄⋊C₄×C₄₃	—	2	1	no	—
31	C₂²⋊C₄×C₄₃	—	2	1	no	—
32	C₄²×C₄₃	—	2	1	no	—
33	C₂²⋊Dic₄₃	—	2	1	no	—
34	C₄⋊Dic₄₃	—	2	1	no	—
35	C₄×Dic₄₃	—	2	1	no	—
36	#10621877	—	2	1	no	—
37	#10621877	—	2	1	no	—
38	#10621877	—	2	1	no	—
39	#10621877	—	2	1	no	—
40	#10621877	—	2	1	no	—
41	#10621877	—	2	1	no	—
42	C₂×C₄₃⋊C₈	—	2	1	no	—
43	C₂×C₄₃⋊C₈	—	2	1	no	—
44	C₂×C₄₃⋊C₈	—	2	1	no	—
45	C₂³×C₄₃	#41	1	1	yes	characteristic
46	Q₈×C₄₃	—	2	2	no	—
47	Q₈×C₄₃	—	2	2	no	—
48	Q₈×C₄₃	—	4	1	no	—
49	Q₈×C₄₃	—	4	1	no	—
50	C₂×C₄×C₄₃	—	2	2	no	—
51	C₂×C₄×C₄₃	—	4	1	no	—
52	C₂×C₄×C₄₃	—	4	1	no	—
53	C₂×C₄×C₄₃	—	4	1	no	—
54	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
55	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
56	C₂×C₄×C₄₃	#41	1	1	yes	characteristic
57	C₂×C₄×C₄₃	#41	1	1	yes	characteristic
58	C₂×C₄×C₄₃	#41	1	1	yes	characteristic
59	C₂×C₄×C₄₃	#41	1	1	yes	characteristic
60	C₂×Dic₄₃	—	4	1	no	—
61	C₈×C₄₃	—	2	2	no	—
62	C₄₃⋊C₈	—	4	1	no	—
63	C₄₃⋊C₈	—	4	1	no	—
64	C₄₃⋊C₈	—	4	1	no	—
65	C₂²×C₄₃	—	4	1	no	—
66	C₂²×C₄₃	#123	1	1	yes	characteristic
67	C₂²×C₄₃	#124	1	1	yes	characteristic
68	C₂²×C₄₃	#126	1	1	yes	characteristic
69	C₄×C₄₃	—	4	2	no	—
70	C₄×C₄₃	—	8	1	no	—
71	C₄×C₄₃	#121	1	1	yes	characteristic
72	C₄×C₄₃	#123	1	1	yes	characteristic
73	C₄×C₄₃	#123	1	1	yes	characteristic
74	C₄×C₄₃	#126	1	1	yes	characteristic
75	Dic₄₃	—	8	1	no	—
76	#2082	—	43	1	no	maximal, Sylow
77	C₂×C₄₃	—	2	1	no	—
78	C₂×C₄₃	—	2	1	no	—
79	C₂×C₄₃	—	2	1	no	—
80	C₂×C₄₃	#397	1	1	yes	characteristic
81	#430	—	43	1	no	—
82	#419	—	43	1	no	—
83	#419	D₄₃	1	1	yes	characteristic
84	C₂×#101	—	43	1	no	—
85	#344	—	43	1	no	—
86	#344	—	43	1	no	—
87	H(3,ℤ/4)	—	43	1	no	—
88	C₄₃	#2082	1	1	yes	characteristic, complemented, Sylow
89	C₂²×Q₈	C₂×D₄₃	1	1	yes	characteristic
90	C₂×M₁₆	—	43	1	no	—
91	C₂×M₁₆	—	43	1	no	—
92	C₂×M₁₆	—	43	1	no	—
93	C₂×M₁₆	C₂×D₄₃	1	1	yes	characteristic
94	#117	—	43	1	no	—
95	#117	C₂×D₄₃	1	1	yes	characteristic
96	#108	—	86	2	no	—
97	#103	—	2	2	no	—
98	#103	—	86	2	no	—
99	#101	—	86	2	no	—
100	C₂×Q₈	—	2	1	no	—
101	C₂×Q₈	—	2	1	no	—
102	C₂×Q₈	—	2	1	no	—
103	C₂×Q₈	—	2	1	no	—
104	C₂×Q₈	—	2	1	no	—
105	C₂×Q₈	D₁₇₂	1	2	yes	—
106	C₂²×C₄	—	2	1	no	—
107	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
108	M₁₆	—	2	1	no	—
109	M₁₆	—	2	1	no	—
110	M₁₆	—	86	1	no	—
111	M₁₆	—	86	1	no	—
112	M₁₆	—	86	1	no	—
113	M₁₆	—	86	1	no	—
114	M₁₆	—	86	1	no	—
115	M₁₆	—	86	1	no	—
116	C₂×C₈	—	86	1	no	—
117	C₂×C₈	—	86	1	no	—
118	C₂×C₈	—	86	1	no	—
119	C₂×C₈	C₂²⋊D₄₃	1	2	yes	—
120	C₄⋊C₄	—	2	1	no	—
121	C₄⋊C₄	—	86	1	no	—
122	C₂²⋊C₄	—	2	1	no	—
123	C₂²⋊C₄	—	86	1	no	—
124	C₄²	—	2	1	no	—
125	C₄²	—	86	1	no	—
126	C₂³	#10621900	1	1	yes	characteristic
127	Q₈	—	2	2	no	—
128	Q₈	—	2	2	no	—
129	Q₈	—	4	1	no	—
130	Q₈	—	4	1	no	—
131	C₂×C₄	—	2	2	no	—
132	C₂×C₄	—	4	1	no	—
133	C₂×C₄	—	4	1	no	—
134	C₂×C₄	—	4	1	no	—
135	C₂×C₄	—	172	1	no	—
136	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
137	C₂×C₄	#10621898	1	1	yes	characteristic
138	C₂×C₄	#10621900	1	1	yes	characteristic
139	C₂×C₄	#10621900	1	1	yes	characteristic
140	C₂×C₄	#10621900	1	1	yes	characteristic
141	C₂×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
142	C₈	—	2	2	no	—
143	C₈	—	172	1	no	—
144	C₈	—	172	1	no	—
145	C₈	—	172	1	no	—
146	C₂²	—	4	1	no	—
147	C₂²	#13063309	1	1	yes	characteristic
148	C₂²	#13063312	1	1	yes	characteristic
149	C₂²	#13063318	1	1	yes	characteristic
150	C₄	—	4	2	no	—
151	C₄	—	8	1	no	—
152	C₄	—	344	1	no	—
153	C₄	#13063299	1	1	yes	characteristic
154	C₄	#13063306	1	1	yes	characteristic
155	C₄	#13063309	1	1	yes	characteristic
156	C₄	#13063318	1	1	yes	characteristic
157	C₂	—	2	1	no	—
158	C₂	—	2	1	no	—
159	C₂	—	2	1	no	—
160	C₂	#14582824	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14582948

C₂

yes

maximal, characteristic

#14582908

C₂

yes

maximal, characteristic

C₂×#13063244

C₂

yes

maximal, characteristic

#14582670

C₂

yes

maximal, characteristic

#14582669

C₂

yes

maximal, characteristic

#14582655

C₂

yes

maximal, characteristic

C₄₃×#419

C₂

yes

maximal, characteristic

C₂×#10621877

C₂²

yes

characteristic

C₂×#10621877

C₂²

yes

characteristic

C₂×#10621877

C₂²

yes

characteristic

#13063284

C₂²

yes

—

—

—

C₂²×Q₈×C₄₃

C₂²

yes

characteristic

C₂×M₁₆×C₄₃

C₂²

yes

characteristic

#117×C₄₃

C₂²

yes

characteristic

#103×C₄₃

—

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

C₂³

yes

characteristic

M₁₆×C₄₃

—

M₁₆×C₄₃

—

C₂×C₈×C₄₃

D₄

yes

—

C₄⋊C₄×C₄₃

—

C₂²⋊C₄×C₄₃

—

C₄²×C₄₃

—

C₂²⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄×Dic₄₃

—

—

—

—

—

—

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

#41

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×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₂×Dic₄₃

—

C₈×C₄₃

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

C₂²×C₄₃

—

C₂²×C₄₃

yes

C₂²×C₄₃

yes

C₂²×C₄₃

yes

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

yes

C₄×C₄₃

yes

C₄×C₄₃

yes

C₄×C₄₃

yes

Dic₄₃

—

#2082

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

yes

—

—

D₄₃

yes

—

—

—

—

C₄₃

#2082

yes

characteristic, complemented, Sylow

C₂²×Q₈

C₂×D₄₃

yes

characteristic

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₄₃

yes

characteristic

#117

—

#117

C₂×D₄₃

yes

—

—

—

—

100

C₂×Q₈

—

101

C₂×Q₈

—

102

C₂×Q₈

—

103

C₂×Q₈

—

104

C₂×Q₈

—

105

C₂×Q₈

D₁₇₂

yes

—

106

C₂²×C₄

—

107

C₂²×C₄

C₂²×D₄₃

yes

characteristic

108

M₁₆

—

109

M₁₆

—

110

M₁₆

—

111

M₁₆

—

112

M₁₆

—

113

M₁₆

—

114

M₁₆

—

115

M₁₆

—

116

C₂×C₈

—

117

C₂×C₈

—

118

C₂×C₈

—

119

C₂×C₈

C₂²⋊D₄₃

yes

—

120

C₄⋊C₄

—

121

C₄⋊C₄

—

122

C₂²⋊C₄

—

123

C₂²⋊C₄

—

124

C₄²

—

125

C₄²

—

126

C₂³

#10621900

yes

characteristic

127

Q₈

—

128

Q₈

—

129

Q₈

—

130

Q₈

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

172

—

136

C₂×C₄

C₂×D₁₇₂

yes

characteristic

137

C₂×C₄

#10621898

yes

characteristic

138

C₂×C₄

#10621900

yes

characteristic

139

C₂×C₄

#10621900

yes

characteristic

140

C₂×C₄

#10621900

yes

characteristic

141

C₂×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

142

C₈

—

143

C₈

—

172

—

144

C₈

—

172

—

145

C₈

—

172

—

146

C₂²

—

147

C₂²

#13063309

yes

characteristic

148

C₂²

#13063312

yes

characteristic

149

C₂²

#13063318

yes

characteristic

150

C₄

—

151

C₄

—

152

C₄

—

344

—

153

C₄

#13063299

yes

characteristic

154

C₄

#13063306

yes

characteristic

155

C₄

#13063309

yes

characteristic

156

C₄

#13063318

yes

characteristic

157

C₂

—

158

C₂

—

159

C₂

—

160

C₂

#14582824

yes

characteristic

	subgroup	G/H
center	C₂	#14582824
commutator	C₂²×C₄×C₄₃	C₂³
Frattini	C₂²×C₄	C₂²×D₄₃
Fitting	C₄₃×#419	C₂
socle	C₂×C₄₃	#397
hypercenter	#419	D₄₃
hypocenter	C₄₃	#2082
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #419

subgroup

G/H

center

C₂

#14582824

commutator

C₂²×C₄×C₄₃

C₂³

Frattini

C₂²×C₄

C₂²×D₄₃

Fitting

C₄₃×#419

C₂

C₂×C₄₃

D₄₃

C₄₃

G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #419

N	H ≅ G/N	type
88. C₄₃	#2082	semidirect

H ≅ G/N

type

88. C₄₃

#2082

semidirect

Subgroups — #19136059

Conjugacy classes of subgroups

Complements