Group #19133632 — subgroups

Subgroups — #19133632

Order 5504.

246 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 57 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	#14583215	C₂	1	2	yes	maximal, complemented
2	#14582838	C₂	1	1	yes	maximal, characteristic, complemented
3	#14582633	C₂	1	2	yes	maximal, complemented
4	#14582625	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#537	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
7	#13063256	—	2	2	no	—
8	#13063246	—	2	2	no	—
9	C₂²⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
10	C₄₃⋊#95	—	2	1	no	—
11	C₄₃⋊#95	—	2	1	no	—
12	C₄₃⋊#95	C₂²	1	1	yes	characteristic
13	C₂×#41×C₄₃	—	2	1	no	—
14	C₂²⋊Q₈×C₄₃	—	2	2	no	—
15	#121×C₄₃	—	2	2	no	—
16	#121×C₄₃	—	2	1	no	—
17	#121×C₄₃	C₂²	1	2	yes	—
18	C₂×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
19	#41×C₄₃	—	4	2	no	—
20	#41×C₄₃	—	4	2	no	—
21	C₂×Q₈×C₄₃	—	2	1	no	—
22	C₂×D₄×C₄₃	—	2	1	no	—
23	C₂×D₄×C₄₃	—	2	1	no	—
24	C₂×D₄×C₄₃	—	2	2	no	—
25	C₂×D₄×C₄₃	D₄	1	2	yes	—
26	C₂²×C₄×C₄₃	—	2	2	no	—
27	C₂²×C₄×C₄₃	D₄	1	1	yes	characteristic
28	C₂²×C₄×C₄₃	D₄	1	1	yes	characteristic
29	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
30	C₂²×Dic₄₃	—	2	1	no	—
31	C₂²×Dic₄₃	—	2	1	no	—
32	C₄⋊C₄×C₄₃	—	2	1	no	—
33	C₄⋊C₄×C₄₃	—	2	2	no	—
34	C₄⋊C₄×C₄₃	D₄	1	2	yes	—
35	C₂²⋊C₄×C₄₃	—	2	2	no	—
36	C₂²⋊C₄×C₄₃	—	2	2	no	—
37	C₄⋊Dic₄₃	—	2	2	no	—
38	C₂×C₄₃⋊C₈	—	2	2	no	—
39	C₂³×C₄₃	—	2	2	no	—
40	C₂³×C₄₃	C₂×D₄	1	1	yes	characteristic
41	Q₈×C₄₃	—	4	2	no	—
42	D₄×C₄₃	—	4	2	no	—
43	D₄×C₄₃	—	4	2	no	—
44	D₄×C₄₃	—	4	2	no	—
45	D₄×C₄₃	—	4	2	no	—
46	D₄×C₄₃	—	8	1	no	—
47	C₂×C₄×C₄₃	—	2	1	no	—
48	C₂×C₄×C₄₃	—	2	1	no	—
49	C₂×C₄×C₄₃	—	2	1	no	—
50	C₂×C₄×C₄₃	—	2	2	no	—
51	C₂×C₄×C₄₃	—	4	1	no	—
52	C₂×C₄×C₄₃	—	4	4	no	—
53	C₂×C₄×C₄₃	—	4	1	no	—
54	C₂×C₄×C₄₃	SD₁₆	1	2	yes	—
55	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
56	C₂×Dic₄₃	—	4	1	no	—
57	C₂×Dic₄₃	—	4	1	no	—
58	C₂×Dic₄₃	—	4	2	no	—
59	C₂×Dic₄₃	—	4	1	no	—
60	C₂×Dic₄₃	—	4	1	no	—
61	C₄₃⋊C₈	—	4	2	no	—
62	C₂²×C₄₃	—	2	1	no	—
63	C₂²×C₄₃	—	2	1	no	—
64	C₂²×C₄₃	—	4	2	no	—
65	C₂²×C₄₃	—	4	2	no	—
66	C₂²×C₄₃	—	4	2	no	—
67	C₂²×C₄₃	#120	1	1	yes	characteristic
68	C₂²×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
69	C₂²×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
70	C₄×C₄₃	—	2	2	no	—
71	C₄×C₄₃	—	2	2	no	—
72	C₄×C₄₃	—	4	2	no	—
73	C₄×C₄₃	—	4	1	no	—
74	Dic₄₃	—	8	1	no	—
75	Dic₄₃	—	8	1	no	—
76	#1616	—	43	1	no	maximal, Sylow
77	C₂×C₄₃	—	2	1	no	—
78	C₂×C₄₃	—	2	1	no	—
79	C₂×C₄₃	—	8	2	no	—
80	C₂×C₄₃	#450	1	1	yes	characteristic
81	C₂×C₄₃	#454	1	1	yes	characteristic
82	C₂×C₄₃	#458	1	1	yes	characteristic
83	#537	D₄₃	1	1	yes	characteristic
84	#481	—	43	2	no	—
85	#400	—	43	1	no	—
86	#327	—	43	2	no	—
87	#324	—	43	1	no	—
88	C₄₃	#1616	1	1	yes	characteristic, complemented, Sylow
89	C₂×#41	—	2	1	no	—
90	C₂²⋊Q₈	—	2	2	no	—
91	#121	—	2	2	no	—
92	#121	—	2	1	no	—
93	#121	C₂×D₄₃	1	2	yes	—
94	C₂×C₄⋊C₄	—	43	1	no	—
95	C₂×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
96	#106	—	86	2	no	—
97	#102	—	86	2	no	—
98	C₂²⋊C₈	—	43	2	no	—
99	#95	—	43	1	no	—
100	#95	—	86	1	no	—
101	#95	—	86	1	no	—
102	#41	—	4	2	no	—
103	#41	—	4	2	no	—
104	C₂×Q₈	—	2	1	no	—
105	C₂×D₄	—	2	1	no	—
106	C₂×D₄	—	2	2	no	—
107	C₂×D₄	—	2	1	no	—
108	C₂×D₄	C₂²⋊D₄₃	1	2	yes	—
109	C₂²×C₄	—	2	2	no	—
110	C₂²×C₄	—	86	1	no	—
111	C₂²×C₄	—	86	1	no	—
112	C₂²×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
113	C₂²×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
114	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
115	C₂×C₈	—	86	2	no	—
116	C₄⋊C₄	—	2	1	no	—
117	C₄⋊C₄	—	2	2	no	—
118	C₄⋊C₄	—	86	2	no	—
119	C₄⋊C₄	C₂²⋊D₄₃	1	2	yes	—
120	C₂²⋊C₄	—	2	2	no	—
121	C₂²⋊C₄	—	2	2	no	—
122	C₂³	—	2	2	no	—
123	C₂³	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
124	Q₈	—	4	2	no	—
125	D₄	—	4	2	no	—
126	D₄	—	4	2	no	—
127	D₄	—	4	2	no	—
128	D₄	—	4	2	no	—
129	D₄	—	8	1	no	—
130	C₂×C₄	—	2	1	no	—
131	C₂×C₄	—	2	1	no	—
132	C₂×C₄	—	2	1	no	—
133	C₂×C₄	—	2	2	no	—
134	C₂×C₄	—	4	1	no	—
135	C₂×C₄	—	4	4	no	—
136	C₂×C₄	—	4	1	no	—
137	C₂×C₄	—	172	1	no	—
138	C₂×C₄	—	172	1	no	—
139	C₂×C₄	—	172	2	no	—
140	C₂×C₄	—	172	1	no	—
141	C₂×C₄	—	172	1	no	—
142	C₂×C₄	#10621883	1	2	yes	—
143	C₂×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
144	C₈	—	172	2	no	—
145	C₂²	—	2	1	no	—
146	C₂²	—	2	1	no	—
147	C₂²	—	4	2	no	—
148	C₂²	—	4	2	no	—
149	C₂²	—	4	2	no	—
150	C₂²	#13063294	1	1	yes	characteristic
151	C₂²	C₂×#10621883	1	1	yes	characteristic
152	C₂²	#13063351	1	1	yes	characteristic
153	C₄	—	2	2	no	—
154	C₄	—	2	2	no	—
155	C₄	—	4	2	no	—
156	C₄	—	4	1	no	—
157	C₄	—	344	1	no	—
158	C₄	—	344	1	no	—
159	C₂	—	2	1	no	—
160	C₂	—	2	1	no	—
161	C₂	—	8	2	no	—
162	C₂	#14583050	1	1	yes	characteristic
163	C₂	#14583072	1	1	yes	characteristic
164	C₂	#14583089	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14583215

C₂

yes

maximal, complemented

#14582838

C₂

yes

maximal, characteristic, complemented

#14582633

C₂

yes

maximal, complemented

#14582625

C₂

yes

maximal, characteristic, complemented

C₄₃×#537

C₂

yes

maximal, characteristic

C₂×C₄⋊Dic₄₃

C₂²

yes

characteristic

#13063256

—

#13063246

—

C₂²⋊(C₄₃⋊C₈)

C₂²

yes

—

C₄₃⋊#95

—

C₄₃⋊#95

—

C₄₃⋊#95

C₂²

yes

characteristic

C₂×#41×C₄₃

—

C₂²⋊Q₈×C₄₃

—

#121×C₄₃

—

#121×C₄₃

—

#121×C₄₃

C₂²

yes

—

C₂×C₄⋊C₄×C₄₃

C₂²

yes

characteristic

#41×C₄₃

—

#41×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×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

—

C₄⋊C₄×C₄₃

D₄

yes

—

C₂²⋊C₄×C₄₃

—

C₂²⋊C₄×C₄₃

—

C₄⋊Dic₄₃

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

—

C₂³×C₄₃

C₂×D₄

yes

characteristic

Q₈×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

D₄×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

C₂×D₄

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₄₃⋊C₈

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

#120

yes

characteristic

C₂²×C₄₃

C₂×SD₁₆

yes

characteristic

C₂²×C₄₃

AGL(1,ℤ/8)

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

Dic₄₃

—

Dic₄₃

—

#1616

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

D₄₃

yes

—

—

—

—

C₄₃

#1616

yes

characteristic, complemented, Sylow

C₂×#41

—

C₂²⋊Q₈

—

#121

—

#121

—

#121

C₂×D₄₃

yes

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₄₃

yes

characteristic

#106

—

#102

—

C₂²⋊C₈

—

#95

—

100

#95

—

101

#95

—

102

#41

—

103

#41

—

104

C₂×Q₈

—

105

C₂×D₄

—

106

C₂×D₄

—

107

C₂×D₄

—

108

C₂×D₄

C₂²⋊D₄₃

yes

—

109

C₂²×C₄

—

110

C₂²×C₄

—

111

C₂²×C₄

—

112

C₂²×C₄

C₂²⋊D₄₃

yes

characteristic

113

C₂²×C₄

C₂²⋊D₄₃

yes

characteristic

114

C₂²×C₄

C₂²×D₄₃

yes

characteristic

115

C₂×C₈

—

116

C₄⋊C₄

—

117

C₄⋊C₄

—

118

C₄⋊C₄

—

119

C₄⋊C₄

C₂²⋊D₄₃

yes

—

120

C₂²⋊C₄

—

121

C₂²⋊C₄

—

122

C₂³

—

123

C₂³

C₂×C₂²⋊D₄₃

yes

characteristic

124

Q₈

—

125

D₄

—

126

D₄

—

127

D₄

—

128

D₄

—

129

D₄

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

—

137

C₂×C₄

—

172

—

138

C₂×C₄

—

172

—

139

C₂×C₄

—

172

—

140

C₂×C₄

—

172

—

141

C₂×C₄

—

172

—

142

C₂×C₄

#10621883

yes

—

143

C₂×C₄

C₂×C₂²⋊D₄₃

yes

—

144

C₈

—

172

—

145

C₂²

—

146

C₂²

—

147

C₂²

—

148

C₂²

—

149

C₂²

—

150

C₂²

#13063294

yes

characteristic

151

C₂²

C₂×#10621883

yes

characteristic

152

C₂²

#13063351

yes

characteristic

153

C₄

—

154

C₄

—

155

C₄

—

156

C₄

—

157

C₄

—

344

—

158

C₄

—

344

—

159

C₂

—

160

C₂

—

161

C₂

—

162

C₂

#14583050

yes

characteristic

163

C₂

#14583072

yes

characteristic

164

C₂

#14583089

yes

characteristic

	subgroup	G/H
center	C₂²	#13063294
commutator	C₂²×C₄×C₄₃	C₂³
Frattini	C₂²×C₄	C₂²×D₄₃
Fitting	C₄₃×#537	C₂
socle	C₂²×C₄₃	#120
hypercenter	#537	D₄₃
hypocenter	C₄₃	#1616
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #537

subgroup

G/H

center

C₂²

#13063294

commutator

C₂²×C₄×C₄₃

C₂³

Frattini

C₂²×C₄

C₂²×D₄₃

Fitting

C₄₃×#537

C₂

C₂²×C₄₃

D₄₃

C₄₃

G ▷ C₂²×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #537

N	H ≅ G/N	type
1. #14583215	C₂	semidirect
2. #14582838	C₂	semidirect
3. #14582633	C₂	semidirect
4. #14582625	C₂	semidirect
88. C₄₃	#1616	semidirect

H ≅ G/N

type

1. #14583215

C₂

semidirect

2. #14582838

C₂

semidirect

3. #14582633

C₂

semidirect

4. #14582625

C₂

semidirect

88. C₄₃

#1616

semidirect

Subgroups — #19133632

Conjugacy classes of subgroups

Complements