Group #19134778 — subgroups

Subgroups — #19134778

Order 5504.

324 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 113 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×Dic₄₃⋊C₈	C₂	1	2	yes	maximal, complemented
2	C₂×C₂²⋊(C₄₃⋊C₈)	C₂	1	1	yes	maximal, characteristic
3	C₄×C₂²⋊Dic₄₃	C₂	1	1	yes	maximal, characteristic
4	#14582653	C₂	1	2	yes	maximal, complemented
5	C₂²×M₁₆×C₄₃	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
7	C₂²×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
8	C₂×C₂²⋊Dic₄₃	C₄	1	2	yes	—
9	C₂×C₄×Dic₄₃	C₂²	1	2	yes	—
10	Dic₄₃⋊C₈	—	2	4	no	—
11	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
12	C₄₃⋊#95	C₄	1	1	yes	characteristic
13	C₄₃⋊#95	C₄	1	1	yes	characteristic
14	C₂³×C₄×C₄₃	C₂²	1	1	yes	characteristic
15	C₂×M₁₆×C₄₃	—	2	2	no	—
16	C₂×M₁₆×C₄₃	—	2	4	no	—
17	C₂²×C₈×C₄₃	C₂²	1	2	yes	—
18	C₂⁴×C₄₃	C₂×C₄	1	1	yes	characteristic
19	C₂²×C₄×C₄₃	—	2	2	no	—
20	C₂²×C₄×C₄₃	—	2	2	no	—
21	C₂²×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
22	C₂²×C₄×C₄₃	D₄	1	2	yes	—
23	C₂²×C₄×C₄₃	Q₈	1	2	yes	—
24	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
25	C₂²×Dic₄₃	C₂×C₄	1	2	yes	—
26	C₂²×Dic₄₃	C₂×C₄	1	2	yes	—
27	M₁₆×C₄₃	—	2	8	no	—
28	C₂×C₈×C₄₃	—	2	2	no	—
29	C₂×C₈×C₄₃	—	2	2	no	—
30	C₂×C₈×C₄₃	D₄	1	4	yes	—
31	C₂²⋊Dic₄₃	—	2	4	no	—
32	C₄×Dic₄₃	—	2	2	no	—
33	C₄×Dic₄₃	—	2	2	no	—
34	C₂×C₄₃⋊C₈	—	2	1	no	—
35	C₂×C₄₃⋊C₈	—	2	1	no	—
36	C₂×C₄₃⋊C₈	—	2	2	no	—
37	C₂×C₄₃⋊C₈	—	2	2	no	—
38	C₂³×C₄₃	—	2	2	no	—
39	C₂³×C₄₃	—	2	2	no	—
40	C₂³×C₄₃	—	2	1	no	—
41	C₂³×C₄₃	—	2	1	no	—
42	C₂³×C₄₃	C₄⋊C₄	1	2	yes	—
43	C₂³×C₄₃	C₂²×C₄	1	1	yes	characteristic
44	C₂×C₄×C₄₃	—	2	2	no	—
45	C₂×C₄×C₄₃	—	2	2	no	—
46	C₂×C₄×C₄₃	—	2	4	no	—
47	C₂×C₄×C₄₃	—	2	2	no	—
48	C₂×C₄×C₄₃	C₄⋊C₄	1	2	yes	—
49	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
50	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
51	C₂×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
52	C₂×C₄×C₄₃	#41	1	2	yes	—
53	C₂×Dic₄₃	—	2	2	no	—
54	C₂×Dic₄₃	—	2	2	no	—
55	C₂×Dic₄₃	—	2	2	no	—
56	C₂×Dic₄₃	—	2	2	no	—
57	C₂×Dic₄₃	—	2	2	no	—
58	C₂×Dic₄₃	M₁₆	1	4	yes	complemented
59	C₈×C₄₃	—	2	4	no	—
60	C₄₃⋊C₈	—	4	1	no	—
61	C₄₃⋊C₈	—	4	1	no	—
62	C₂²×C₄₃	—	2	2	no	—
63	C₂²×C₄₃	—	2	2	no	—
64	C₂²×C₄₃	—	2	2	no	—
65	C₂²×C₄₃	—	4	2	no	—
66	C₂²×C₄₃	—	4	2	no	—
67	C₂²×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
68	C₂²×C₄₃	C₄×D₄	1	2	yes	—
69	C₂²×C₄₃	C₂×M₁₆	1	2	yes	—
70	C₂²×C₄₃	#131	1	1	yes	characteristic
71	C₂²×C₄₃	#131	1	1	yes	characteristic
72	C₄×C₄₃	—	2	2	no	—
73	C₄×C₄₃	#120	1	1	yes	characteristic
74	C₄×C₄₃	C₂²⋊Q₈	1	2	yes	—
75	C₄×C₄₃	#123	1	1	yes	characteristic
76	Dic₄₃	—	2	4	no	—
77	Dic₄₃	—	4	2	no	—
78	#1851	—	43	1	no	maximal, Sylow
79	C₂×C₄₃	—	4	2	no	—
80	C₂×C₄₃	#385	1	1	yes	characteristic
81	C₂×C₄₃	#423	1	1	yes	characteristic
82	C₂×C₄₃	#424	1	1	yes	characteristic
83	C₂×C₄₃	#435	1	2	yes	—
84	C₂×C₄₃	#436	1	2	yes	—
85	C₂²×M₁₆	D₄₃	1	1	yes	characteristic
86	C₂×C₄⋊C₈	—	43	2	no	—
87	C₂×C₂²⋊C₈	—	43	1	no	—
88	C₄×C₂²⋊C₄	—	43	1	no	—
89	#336	—	43	2	no	—
90	C₄₃	#1851	1	1	yes	characteristic, complemented, Sylow
91	C₂³×C₄	C₂×D₄₃	1	1	yes	characteristic
92	C₂×M₁₆	—	2	2	no	—
93	C₂×M₁₆	—	2	4	no	—
94	C₂²×C₈	—	43	1	no	—
95	C₂²×C₈	—	43	1	no	—
96	C₂²×C₈	C₂×D₄₃	1	2	yes	—
97	C₂×C₂²⋊C₄	—	43	2	no	—
98	C₂×C₄²	—	43	2	no	—
99	C₄⋊C₈	—	86	4	no	—
100	C₂²⋊C₈	—	86	2	no	—
101	#95	—	43	1	no	—
102	#95	—	43	1	no	—
103	C₂⁴	C₄×D₄₃	1	1	yes	characteristic
104	C₂²×C₄	—	2	2	no	—
105	C₂²×C₄	—	2	2	no	—
106	C₂²×C₄	—	43	2	no	—
107	C₂²×C₄	—	43	2	no	—
108	C₂²×C₄	Dic₈₆	1	2	yes	—
109	C₂²×C₄	C₄×D₄₃	1	1	yes	characteristic
110	C₂²×C₄	C₂²⋊D₄₃	1	2	yes	—
111	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
112	M₁₆	—	2	8	no	—
113	C₂×C₈	—	2	2	no	—
114	C₂×C₈	—	2	2	no	—
115	C₂×C₈	—	86	2	no	—
116	C₂×C₈	—	86	1	no	—
117	C₂×C₈	—	86	1	no	—
118	C₂×C₈	—	86	2	no	—
119	C₂×C₈	C₂²⋊D₄₃	1	4	yes	—
120	C₂²⋊C₄	—	86	4	no	—
121	C₄²	—	86	2	no	—
122	C₄²	—	86	2	no	—
123	C₂³	—	2	2	no	—
124	C₂³	—	2	2	no	—
125	C₂³	—	2	1	no	—
126	C₂³	—	2	1	no	—
127	C₂³	Dic₄₃⋊C₄	1	2	yes	—
128	C₂³	C₂×C₄×D₄₃	1	1	yes	characteristic
129	C₂×C₄	—	2	2	no	—
130	C₂×C₄	—	2	2	no	—
131	C₂×C₄	—	2	4	no	—
132	C₂×C₄	—	2	2	no	—
133	C₂×C₄	—	43	4	no	—
134	C₂×C₄	—	86	2	no	—
135	C₂×C₄	—	86	2	no	—
136	C₂×C₄	—	86	2	no	—
137	C₂×C₄	—	86	2	no	—
138	C₂×C₄	—	86	2	no	—
139	C₂×C₄	Dic₄₃⋊C₄	1	2	yes	—
140	C₂×C₄	C₂×Dic₈₆	1	1	yes	characteristic
141	C₂×C₄	#10621898	1	2	yes	—
142	C₂×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
143	C₂×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
144	C₈	—	2	4	no	—
145	C₈	—	172	1	no	—
146	C₈	—	172	1	no	—
147	C₂²	—	2	2	no	—
148	C₂²	—	2	2	no	—
149	C₂²	—	2	2	no	—
150	C₂²	—	4	2	no	—
151	C₂²	—	4	2	no	—
152	C₂²	C₂×Dic₄₃⋊C₄	1	1	yes	characteristic
153	C₂²	C₄×C₂²⋊D₄₃	1	2	yes	—
154	C₂²	M₁₆×D₄₃	1	2	yes	—
155	C₂²	#13063333	1	1	yes	characteristic
156	C₂²	#13063333	1	1	yes	characteristic
157	C₄	—	2	2	no	—
158	C₄	—	86	4	no	—
159	C₄	—	172	2	no	—
160	C₄	#13063294	1	1	yes	characteristic
161	C₄	#13063304	1	2	yes	—
162	C₄	#13063308	1	1	yes	characteristic
163	C₂	—	4	2	no	—
164	C₂	#14582772	1	1	yes	characteristic
165	C₂	#14582922	1	1	yes	characteristic
166	C₂	#14582927	1	1	yes	characteristic
167	C₂	#14582968	1	2	yes	—
168	C₂	#14582975	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×Dic₄₃⋊C₈

C₂

yes

maximal, complemented

C₂×C₂²⋊(C₄₃⋊C₈)

C₂

yes

maximal, characteristic

C₄×C₂²⋊Dic₄₃

C₂

yes

maximal, characteristic

#14582653

C₂

yes

maximal, complemented

C₂²×M₁₆×C₄₃

C₂

yes

maximal, characteristic

C₂²×C₄₃⋊C₈

C₂²

yes

characteristic

C₂²×C₄₃⋊C₈

C₂²

yes

characteristic

C₂×C₂²⋊Dic₄₃

C₄

yes

—

C₂×C₄×Dic₄₃

C₂²

yes

—

Dic₄₃⋊C₈

—

C₂²⋊(C₄₃⋊C₈)

—

C₄₃⋊#95

C₄

yes

characteristic

C₄₃⋊#95

C₄

yes

characteristic

C₂³×C₄×C₄₃

C₂²

yes

characteristic

C₂×M₁₆×C₄₃

—

C₂×M₁₆×C₄₃

—

C₂²×C₈×C₄₃

C₂²

yes

—

C₂⁴×C₄₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₄₃

D₄

yes

—

C₂²×C₄×C₄₃

Q₈

yes

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

C₂×C₄

yes

—

C₂²×Dic₄₃

C₂×C₄

yes

—

M₁₆×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

D₄

yes

—

C₂²⋊Dic₄₃

—

C₄×Dic₄₃

—

C₄×Dic₄₃

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

C₄⋊C₄

yes

—

C₂³×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₄⋊C₄

yes

—

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×Q₈

yes

characteristic

C₂×C₄×C₄₃

#41

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

M₁₆

yes

complemented

C₈×C₄₃

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₄₃

C₄×D₄

yes

—

C₂²×C₄₃

C₂×M₁₆

yes

—

C₂²×C₄₃

yes

C₂²×C₄₃

yes

C₄×C₄₃

—

C₄×C₄₃

#120

yes

characteristic

C₄×C₄₃

C₂²⋊Q₈

yes

—

C₄×C₄₃

#123

yes

characteristic

Dic₄₃

—

Dic₄₃

—

#1851

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

—

C₂×C₄₃

#436

yes

—

C₂²×M₁₆

D₄₃

yes

characteristic

C₂×C₄⋊C₈

—

C₂×C₂²⋊C₈

—

C₄×C₂²⋊C₄

—

#336

—

C₄₃

#1851

yes

characteristic, complemented, Sylow

C₂³×C₄

C₂×D₄₃

yes

characteristic

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

C₂×D₄₃

yes

—

C₂×C₂²⋊C₄

—

C₂×C₄²

—

C₄⋊C₈

—

100

C₂²⋊C₈

—

101

#95

—

102

#95

—

103

C₂⁴

C₄×D₄₃

yes

characteristic

104

C₂²×C₄

—

105

C₂²×C₄

—

106

C₂²×C₄

—

107

C₂²×C₄

—

108

C₂²×C₄

Dic₈₆

yes

—

109

C₂²×C₄

C₄×D₄₃

yes

characteristic

110

C₂²×C₄

C₂²⋊D₄₃

yes

—

111

C₂²×C₄

C₂²×D₄₃

yes

characteristic

112

M₁₆

—

113

C₂×C₈

—

114

C₂×C₈

—

115

C₂×C₈

—

116

C₂×C₈

—

117

C₂×C₈

—

118

C₂×C₈

—

119

C₂×C₈

C₂²⋊D₄₃

yes

—

120

C₂²⋊C₄

—

121

C₄²

—

122

C₄²

—

123

C₂³

—

124

C₂³

—

125

C₂³

—

126

C₂³

—

127

C₂³

Dic₄₃⋊C₄

yes

—

128

C₂³

C₂×C₄×D₄₃

yes

characteristic

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

—

137

C₂×C₄

—

138

C₂×C₄

—

139

C₂×C₄

Dic₄₃⋊C₄

yes

—

140

C₂×C₄

C₂×Dic₈₆

yes

characteristic

141

C₂×C₄

#10621898

yes

—

142

C₂×C₄

C₂×C₂²⋊D₄₃

yes

—

143

C₂×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

144

C₈

—

145

C₈

—

172

—

146

C₈

—

172

—

147

C₂²

—

148

C₂²

—

149

C₂²

—

150

C₂²

—

151

C₂²

—

152

C₂²

C₂×Dic₄₃⋊C₄

yes

characteristic

153

C₂²

C₄×C₂²⋊D₄₃

yes

—

154

C₂²

M₁₆×D₄₃

yes

—

155

C₂²

#13063333

yes

characteristic

156

C₂²

#13063333

yes

characteristic

157

C₄

—

158

C₄

—

159

C₄

—

172

—

160

C₄

#13063294

yes

characteristic

161

C₄

#13063304

yes

—

162

C₄

#13063308

yes

characteristic

163

C₂

—

164

C₂

#14582772

yes

characteristic

165

C₂

#14582922

yes

characteristic

166

C₂

#14582927

yes

characteristic

167

C₂

#14582968

yes

—

168

C₂

#14582975

yes

—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₄₃
commutator, socle	C₂³×C₄₃	C₂²×C₄
Fitting	C₂²×M₁₆×C₄₃	C₂
hypercenter	C₂²×M₁₆	D₄₃
hypocenter	C₄₃	#1851
LCS	G ▷ C₂³×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×M₁₆

subgroup

G/H

center, Frattini

C₂²×C₄

C₂²×D₄₃

commutator, socle

C₂³×C₄₃

C₂²×C₄

Fitting

C₂²×M₁₆×C₄₃

C₂

hypercenter

C₂²×M₁₆

D₄₃

C₄₃

G ▷ C₂³×C₄₃ ▷ C₄₃

C₁ ◁ C₂²×C₄ ◁ C₂²×M₁₆

N	H ≅ G/N	type
1. C₂×Dic₄₃⋊C₈	C₂	semidirect
4. #14582653	C₂	semidirect
58. C₂×Dic₄₃	M₁₆	semidirect
90. C₄₃	#1851	semidirect

H ≅ G/N

type

1. C₂×Dic₄₃⋊C₈

C₂

semidirect

4. #14582653

C₂

semidirect

58. C₂×Dic₄₃

M₁₆

semidirect

90. C₄₃

#1851

semidirect

Subgroups — #19134778

Conjugacy classes of subgroups

Complements