Group #19134691 — subgroups

Subgroups — #19134691

Order 5504.

300 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 300 conjugacy classes of subgroups — too many to draw. Only its 101 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×#13063284	C₂	1	1	yes	maximal, characteristic
2	#14582759	C₂	1	1	yes	maximal, characteristic
3	#14582662	C₂	1	2	yes	maximal, complemented
4	#14582662	C₂	1	2	yes	maximal, complemented
5	C₂×C₂²⋊C₈×C₄₃	C₂	1	1	yes	maximal, characteristic
6	#13063284	—	2	2	no	—
7	#13063284	C₄	1	4	yes	complemented
8	C₂×C₄⋊Dic₄₃	C₂²	1	2	yes	—
9	C₂×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
11	C₂×C₂²⋊Dic₄₃	—	2	1	no	—
12	C₂×C₂²⋊Dic₄₃	—	2	1	no	—
13	C₂×C₄×Dic₄₃	—	2	1	no	—
14	C₄₃⋊#95	—	2	1	no	—
15	C₂³×C₄×C₄₃	C₂²	1	1	yes	characteristic
16	C₂²×C₈×C₄₃	C₂²	1	2	yes	—
17	C₂²⋊C₈×C₄₃	—	2	2	no	—
18	C₂⁴×C₄₃	D₄	1	1	yes	characteristic
19	C₂²×C₄×C₄₃	—	2	4	no	—
20	C₂²×C₄×C₄₃	C₂×C₄	1	2	yes	—
21	C₂²×C₄×C₄₃	D₄	1	2	yes	—
22	C₂²×C₄×C₄₃	D₄	1	1	yes	characteristic
23	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
24	C₂²×Dic₄₃	—	2	1	no	—
25	C₂²×Dic₄₃	—	2	1	no	—
26	C₂²×Dic₄₃	—	2	2	no	—
27	C₂×C₈×C₄₃	—	2	2	no	—
28	C₂×C₈×C₄₃	—	2	4	no	—
29	C₂²⋊Dic₄₃	—	2	4	no	—
30	C₂²⋊Dic₄₃	—	4	2	no	—
31	C₄⋊Dic₄₃	—	2	1	no	—
32	C₄⋊Dic₄₃	—	2	1	no	—
33	C₄⋊Dic₄₃	—	2	4	no	—
34	C₄⋊Dic₄₃	C₂×C₄	1	2	yes	—
35	C₄⋊Dic₄₃	C₂×C₄	1	2	yes	—
36	C₄×Dic₄₃	—	2	4	no	—
37	C₂³×C₄₃	—	2	2	no	—
38	C₂³×C₄₃	—	2	2	no	—
39	C₂³×C₄₃	—	2	1	no	—
40	C₂³×C₄₃	—	2	1	no	—
41	C₂³×C₄₃	C₂²⋊C₄	1	2	yes	—
42	C₂³×C₄₃	C₂×D₄	1	1	yes	characteristic
43	C₂×C₄×C₄₃	—	2	2	no	—
44	C₂×C₄×C₄₃	—	2	4	no	—
45	C₂×C₄×C₄₃	—	2	4	no	—
46	C₂×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
47	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
48	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
49	C₂×C₄×C₄₃	#41	1	4	yes	—
50	C₂×Dic₄₃	—	2	2	no	—
51	C₂×Dic₄₃	—	2	2	no	—
52	C₂×Dic₄₃	—	4	2	no	—
53	C₂×Dic₄₃	—	4	1	no	—
54	C₂×Dic₄₃	—	4	1	no	—
55	C₂×Dic₄₃	—	4	2	no	—
56	C₂×Dic₄₃	—	4	2	no	—
57	C₂×Dic₄₃	—	4	2	no	—
58	C₈×C₄₃	—	4	2	no	—
59	C₂²×C₄₃	—	2	2	no	—
60	C₂²×C₄₃	—	2	2	no	—
61	C₂²×C₄₃	—	2	2	no	—
62	C₂²×C₄₃	—	4	2	no	—
63	C₂²×C₄₃	—	4	2	no	—
64	C₂²×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
65	C₂²×C₄₃	#123	1	2	yes	—
66	C₂²×C₄₃	#135	1	2	yes	—
67	C₂²×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
68	C₂²×C₄₃	#137	1	1	yes	characteristic
69	C₄×C₄₃	—	2	2	no	—
70	C₄×C₄₃	#117	1	2	yes	—
71	C₄×C₄₃	#123	1	2	yes	—
72	Dic₄₃	—	4	2	no	—
73	Dic₄₃	—	4	2	no	—
74	Dic₄₃	—	8	2	no	—
75	#1825	—	43	1	no	maximal, Sylow
76	C₂×C₄₃	—	4	2	no	—
77	C₂×C₄₃	#381	1	1	yes	characteristic
78	C₂×C₄₃	#416	1	1	yes	characteristic
79	C₂×C₄₃	#417	1	1	yes	characteristic
80	C₂×C₄₃	#482	1	2	yes	—
81	C₂×C₄₃	#485	1	2	yes	—
82	C₂×#117	—	43	1	no	—
83	C₂×C₂²⋊C₈	D₄₃	1	1	yes	characteristic
84	#380	—	43	1	no	—
85	#340	—	43	2	no	—
86	#340	—	43	2	no	—
87	C₄₃	#1825	1	1	yes	characteristic, complemented, Sylow
88	C₂³×C₄	C₂×D₄₃	1	1	yes	characteristic
89	C₂²×C₈	C₂×D₄₃	1	2	yes	—
90	#117	—	43	4	no	—
91	#117	—	86	2	no	—
92	C₂×C₄⋊C₄	—	43	1	no	—
93	C₂×C₄⋊C₄	—	43	1	no	—
94	C₂×C₄⋊C₄	—	43	2	no	—
95	C₂×C₂²⋊C₄	—	86	1	no	—
96	C₂×C₂²⋊C₄	—	86	1	no	—
97	C₂×C₄²	—	86	1	no	—
98	C₂²⋊C₈	—	2	2	no	—
99	#95	—	86	1	no	—
100	C₂⁴	D₁₇₂	1	1	yes	characteristic
101	C₂²×C₄	—	2	4	no	—
102	C₂²×C₄	—	86	1	no	—
103	C₂²×C₄	—	86	1	no	—
104	C₂²×C₄	—	86	2	no	—
105	C₂²×C₄	C₄×D₄₃	1	2	yes	—
106	C₂²×C₄	D₁₇₂	1	1	yes	characteristic
107	C₂²×C₄	C₂²⋊D₄₃	1	2	yes	—
108	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
109	C₂×C₈	—	2	4	no	—
110	C₂×C₈	—	2	2	no	—
111	C₄⋊C₄	—	43	2	no	—
112	C₄⋊C₄	—	43	2	no	—
113	C₄⋊C₄	—	86	1	no	—
114	C₄⋊C₄	—	86	1	no	—
115	C₄⋊C₄	—	86	4	no	—
116	C₂²⋊C₄	—	86	4	no	—
117	C₂²⋊C₄	—	172	2	no	—
118	C₄²	—	86	4	no	—
119	C₂³	—	2	2	no	—
120	C₂³	—	2	2	no	—
121	C₂³	—	2	1	no	—
122	C₂³	—	2	1	no	—
123	C₂³	(C₂×D₄₃)⋊C₄	1	2	yes	—
124	C₂³	C₂×D₁₇₂	1	1	yes	characteristic
125	C₂×C₄	—	2	2	no	—
126	C₂×C₄	—	2	4	no	—
127	C₂×C₄	—	2	4	no	—
128	C₂×C₄	—	86	2	no	—
129	C₂×C₄	—	86	2	no	—
130	C₂×C₄	—	172	2	no	—
131	C₂×C₄	—	172	2	no	—
132	C₂×C₄	—	172	2	no	—
133	C₂×C₄	—	172	2	no	—
134	C₂×C₄	—	172	1	no	—
135	C₂×C₄	—	172	1	no	—
136	C₂×C₄	(C₂×D₄₃)⋊C₄	1	2	yes	—
137	C₂×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
138	C₂×C₄	#10621900	1	4	yes	—
139	C₂×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
140	C₈	—	4	2	no	—
141	C₂²	—	2	2	no	—
142	C₂²	—	2	2	no	—
143	C₂²	—	2	2	no	—
144	C₂²	—	4	2	no	—
145	C₂²	—	4	2	no	—
146	C₂²	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
147	C₂²	#13063309	1	2	yes	—
148	C₂²	#13063347	1	2	yes	—
149	C₂²	#13063353	1	1	yes	characteristic
150	C₂²	#13063358	1	1	yes	characteristic
151	C₄	—	2	2	no	—
152	C₄	—	344	2	no	—
153	C₄	—	172	2	no	—
154	C₄	—	172	2	no	—
155	C₄	#13063281	1	2	yes	—
156	C₄	#13063306	1	2	yes	—
157	C₂	—	4	2	no	—
158	C₂	#14582760	1	1	yes	characteristic
159	C₂	#14582896	1	1	yes	characteristic
160	C₂	#14582901	1	1	yes	characteristic
161	C₂	#14583224	1	2	yes	—
162	C₂	#14583241	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063284

C₂

yes

maximal, characteristic

#14582759

C₂

yes

maximal, characteristic

#14582662

C₂

yes

maximal, complemented

#14582662

C₂

yes

maximal, complemented

C₂×C₂²⋊C₈×C₄₃

C₂

yes

maximal, characteristic

#13063284

—

#13063284

C₄

yes

complemented

C₂×C₄⋊Dic₄₃

C₂²

yes

—

C₂×C₄⋊Dic₄₃

C₂²

yes

characteristic

C₂×C₄⋊Dic₄₃

C₂²

yes

characteristic

C₂×C₂²⋊Dic₄₃

—

C₂×C₂²⋊Dic₄₃

—

C₂×C₄×Dic₄₃

—

C₄₃⋊#95

—

C₂³×C₄×C₄₃

C₂²

yes

characteristic

C₂²×C₈×C₄₃

C₂²

yes

—

C₂²⋊C₈×C₄₃

—

C₂⁴×C₄₃

D₄

yes

characteristic

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₂×C₄

yes

—

C₂²×C₄×C₄₃

D₄

yes

—

C₂²×C₄×C₄₃

D₄

yes

characteristic

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

—

C₂²×Dic₄₃

—

C₂²×Dic₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂²⋊Dic₄₃

—

C₂²⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

C₂×C₄

yes

—

C₄⋊Dic₄₃

C₂×C₄

yes

—

C₄×Dic₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

C₂²⋊C₄

yes

—

C₂³×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²⋊C₄

yes

—

C₂×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

#41

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₈×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₄₃

#123

yes

—

C₂²×C₄₃

#135

yes

—

C₂²×C₄₃

yes

C₂²×C₄₃

yes

C₄×C₄₃

—

C₄×C₄₃

#117

yes

—

C₄×C₄₃

#123

yes

—

Dic₄₃

—

Dic₄₃

—

Dic₄₃

—

#1825

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

—

C₂×C₄₃

#485

yes

—

C₂×#117

—

C₂×C₂²⋊C₈

D₄₃

yes

—

—

—

C₄₃

#1825

yes

characteristic, complemented, Sylow

C₂³×C₄

C₂×D₄₃

yes

characteristic

C₂²×C₈

C₂×D₄₃

yes

—

#117

—

#117

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₄²

—

C₂²⋊C₈

—

#95

—

100

C₂⁴

D₁₇₂

yes

characteristic

101

C₂²×C₄

—

102

C₂²×C₄

—

103

C₂²×C₄

—

104

C₂²×C₄

—

105

C₂²×C₄

C₄×D₄₃

yes

—

106

C₂²×C₄

D₁₇₂

yes

characteristic

107

C₂²×C₄

C₂²⋊D₄₃

yes

—

108

C₂²×C₄

C₂²×D₄₃

yes

characteristic

109

C₂×C₈

—

110

C₂×C₈

—

111

C₄⋊C₄

—

112

C₄⋊C₄

—

113

C₄⋊C₄

—

114

C₄⋊C₄

—

115

C₄⋊C₄

—

116

C₂²⋊C₄

—

117

C₂²⋊C₄

—

172

—

118

C₄²

—

119

C₂³

—

120

C₂³

—

121

C₂³

—

122

C₂³

—

123

C₂³

(C₂×D₄₃)⋊C₄

yes

—

124

C₂³

C₂×D₁₇₂

yes

characteristic

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

172

—

131

C₂×C₄

—

172

—

132

C₂×C₄

—

172

—

133

C₂×C₄

—

172

—

134

C₂×C₄

—

172

—

135

C₂×C₄

—

172

—

136

C₂×C₄

(C₂×D₄₃)⋊C₄

yes

—

137

C₂×C₄

C₂×C₄×D₄₃

yes

characteristic

138

C₂×C₄

#10621900

yes

—

139

C₂×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

140

C₈

—

141

C₂²

—

142

C₂²

—

143

C₂²

—

144

C₂²

—

145

C₂²

—

146

C₂²

C₂×(C₂×D₄₃)⋊C₄

yes

characteristic

147

C₂²

#13063309

yes

—

148

C₂²

#13063347

yes

—

149

C₂²

#13063353

yes

characteristic

150

C₂²

#13063358

yes

characteristic

151

C₄

—

152

C₄

—

344

—

153

C₄

—

172

—

154

C₄

—

172

—

155

C₄

#13063281

yes

—

156

C₄

#13063306

yes

—

157

C₂

—

158

C₂

#14582760

yes

characteristic

159

C₂

#14582896

yes

characteristic

160

C₂

#14582901

yes

characteristic

161

C₂

#14583224

yes

—

162

C₂

#14583241

yes

—

	subgroup	G/H
center	C₂³	C₂×D₁₇₂
commutator	C₂×C₄×C₄₃	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₄₃
Fitting	C₂×C₂²⋊C₈×C₄₃	C₂
socle	C₂³×C₄₃	C₂×D₄
hypercenter	C₂×C₂²⋊C₈	D₄₃
hypocenter	C₄₃	#1825
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂×C₂²⋊C₈

subgroup

G/H

center

C₂³

C₂×D₁₇₂

commutator

C₂×C₄×C₄₃

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₄₃

Fitting

C₂×C₂²⋊C₈×C₄₃

C₂

socle

C₂³×C₄₃

C₂×D₄

hypercenter

C₂×C₂²⋊C₈

D₄₃

hypocenter

C₄₃

#1825

LCS

G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂×C₂²⋊C₈

N	H ≅ G/N	type
3. #14582662	C₂	semidirect
4. #14582662	C₂	semidirect
7. #13063284	C₄	semidirect
87. C₄₃	#1825	semidirect

H ≅ G/N

type

3. #14582662

C₂

semidirect

4. #14582662

C₂

semidirect

7. #13063284

C₄

semidirect

87. C₄₃

#1825

semidirect

Subgroups — #19134691

Conjugacy classes of subgroups

Complements