Group #19142907 — subgroups

Subgroups — #19142907

Order 5504.

582 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 582 conjugacy classes of subgroups — too many to draw. Only its 149 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×C₄²×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
2	#14582787	C₂	1	3	yes	maximal, complemented
3	#14582780	C₂	1	3	yes	maximal, complemented
4	#14582775	C₂	1	3	yes	maximal
5	#14582770	C₂	1	3	yes	maximal, complemented
6	#14582767	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#126×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₂²⋊D₄₃	C₂²	1	1	yes	characteristic
9	C₂²×C₄×D₄₃	C₂²	1	3	yes	—
10	C₂×Dic₄₃⋊C₄	C₂²	1	3	yes	—
11	C₂×C₂²⋊Dic₄₃	C₂²	1	3	yes	—
12	C₂×(C₂×D₄₃)⋊C₄	C₂²	1	3	yes	—
13	C₂×C₄×Dic₄₃	C₂²	1	3	yes	—
14	C₄²×D₄₃	—	2	4	no	—
15	C₄₃⋊#95	C₂²	1	3	yes	—
16	C₄₃⋊#95	C₂²	1	3	yes	—
17	C₄₃⋊#95	C₂²	1	3	yes	—
18	C₄₃⋊#95	C₂²	1	3	yes	—
19	#126×C₄₃	—	2	4	no	—
20	C₂×C₄⋊C₄×C₄₃	C₂²	1	3	yes	—
21	C₂×C₂²⋊C₄×C₄₃	C₂²	1	3	yes	—
22	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
23	C₂⁴×C₄₃	C₂³	1	1	yes	characteristic
24	C₂³×D₄₃	C₂³	1	1	yes	characteristic
25	C₂²×C₄×C₄₃	C₂³	1	3	yes	—
26	C₂²×C₄×C₄₃	C₂³	1	3	yes	—
27	C₂×C₂²⋊D₄₃	—	2	6	no	—
28	C₂²×Dic₄₃	C₂³	1	1	yes	characteristic
29	C₂²×Dic₄₃	C₂³	1	3	yes	—
30	C₂²×Dic₄₃	C₂³	1	3	yes	—
31	C₂×C₄×D₄₃	—	2	6	no	—
32	C₂×C₄×D₄₃	—	2	6	no	—
33	C₂×C₄×D₄₃	—	2	6	no	—
34	C₄⋊C₄×C₄₃	—	2	6	no	—
35	C₂²⋊C₄×C₄₃	—	2	6	no	—
36	C₄²×C₄₃	D₄	1	4	yes	complemented
37	C₂²⋊Dic₄₃	—	2	6	no	—
38	(C₂×D₄₃)⋊C₄	—	2	6	no	—
39	Dic₄₃⋊C₄	—	2	6	no	—
40	C₄×Dic₄₃	—	2	6	no	—
41	C₂³×C₄₃	—	2	1	no	—
42	C₂³×C₄₃	—	2	3	no	—
43	C₂³×C₄₃	—	2	3	no	—
44	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
45	C₂²×D₄₃	—	2	1	no	—
46	C₂²×D₄₃	—	2	3	no	—
47	C₂²×D₄₃	#41	1	6	yes	—
48	C₂×C₄×C₄₃	—	2	3	no	—
49	C₂×C₄×C₄₃	—	2	3	no	—
50	C₂×C₄×C₄₃	—	2	3	no	—
51	C₂×C₄×C₄₃	—	2	3	no	—
52	C₂×C₄×C₄₃	—	2	3	no	—
53	C₂×C₄×C₄₃	C₂×D₄	1	6	yes	—
54	C₂²⋊D₄₃	—	4	4	no	—
55	C₂×Dic₄₃	—	2	3	no	—
56	C₂×Dic₄₃	—	2	3	no	—
57	C₂×Dic₄₃	—	2	3	no	—
58	C₂×Dic₄₃	—	2	3	no	—
59	C₂×Dic₄₃	—	2	3	no	—
60	C₂×Dic₄₃	—	2	3	no	—
61	C₂×Dic₄₃	#41	1	6	yes	—
62	C₄×D₄₃	—	2	24	no	—
63	C₂²×C₄₃	—	4	3	no	—
64	C₂²×C₄₃	—	4	1	no	—
65	C₂²×C₄₃	—	4	3	no	—
66	C₂²×C₄₃	C₂²×D₄	1	1	yes	characteristic
67	C₂²×C₄₃	C₂×#41	1	3	yes	—
68	C₂²×C₄₃	C₂×#41	1	3	yes	—
69	C₂×D₄₃	—	2	6	no	—
70	C₂×D₄₃	—	2	6	no	—
71	C₂×D₄₃	#126	1	4	yes	complemented
72	C₄×C₄₃	—	2	6	no	—
73	C₄×C₄₃	—	4	3	no	—
74	Dic₄₃	—	2	6	no	—
75	Dic₄₃	—	4	1	no	—
76	Dic₄₃	—	4	3	no	—
77	#2852	—	43	1	no	maximal, Sylow
78	C₂×C₄₃	—	8	1	no	—
79	C₂×C₄₃	#525	1	3	yes	—
80	C₂×C₄₃	C₂×#126	1	1	yes	characteristic
81	C₂×C₄₃	#529	1	3	yes	—
82	D₄₃	—	2	4	no	—
83	C₂×#126	D₄₃	1	1	yes	characteristic, complemented
84	C₂²×C₄²	—	43	1	no	—
85	#388	—	43	3	no	—
86	#387	—	43	3	no	—
87	#386	—	43	3	no	—
88	#385	—	43	3	no	—
89	#383	—	43	1	no	—
90	C₄₃	#2852	1	1	yes	characteristic, complemented, Sylow
91	C₂²×D₄	—	43	1	no	—
92	C₂³×C₄	—	43	3	no	—
93	#126	—	2	4	no	—
94	C₂×C₄⋊C₄	—	43	3	no	—
95	C₂×C₄⋊C₄	C₂×D₄₃	1	3	yes	—
96	C₂×C₂²⋊C₄	—	43	3	no	—
97	C₂×C₂²⋊C₄	—	43	3	no	—
98	C₂×C₂²⋊C₄	C₂×D₄₃	1	3	yes	—
99	C₂×C₄²	—	43	3	no	—
100	C₂×C₄²	—	86	4	no	—
101	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
102	#95	—	43	3	no	—
103	#95	—	43	3	no	—
104	#95	—	43	3	no	—
105	#95	—	43	3	no	—
106	C₂⁴	—	43	1	no	—
107	C₂⁴	C₂²×D₄₃	1	1	yes	characteristic
108	C₂×D₄	—	86	6	no	—
109	C₂²×C₄	—	43	3	no	—
110	C₂²×C₄	—	43	1	no	—
111	C₂²×C₄	—	43	3	no	—
112	C₂²×C₄	—	86	6	no	—
113	C₂²×C₄	—	86	6	no	—
114	C₂²×C₄	—	86	6	no	—
115	C₂²×C₄	C₂²×D₄₃	1	3	yes	—
116	C₂²×C₄	C₂²×D₄₃	1	3	yes	—
117	C₄⋊C₄	—	2	6	no	—
118	C₄⋊C₄	—	86	6	no	—
119	C₂²⋊C₄	—	2	6	no	—
120	C₂²⋊C₄	—	86	6	no	—
121	C₂²⋊C₄	—	86	6	no	—
122	C₄²	—	86	6	no	—
123	C₄²	C₂²⋊D₄₃	1	4	yes	complemented
124	C₂³	—	2	1	no	—
125	C₂³	—	2	3	no	—
126	C₂³	—	2	3	no	—
127	C₂³	—	43	6	no	—
128	C₂³	—	86	1	no	—
129	C₂³	—	86	3	no	—
130	C₂³	C₂³×D₄₃	1	1	yes	characteristic
131	D₄	—	172	4	no	—
132	C₂×C₄	—	2	3	no	—
133	C₂×C₄	—	2	3	no	—
134	C₂×C₄	—	2	3	no	—
135	C₂×C₄	—	2	3	no	—
136	C₂×C₄	—	2	3	no	—
137	C₂×C₄	—	43	6	no	—
138	C₂×C₄	—	86	24	no	—
139	C₂×C₄	—	86	3	no	—
140	C₂×C₄	—	86	3	no	—
141	C₂×C₄	—	86	3	no	—
142	C₂×C₄	—	86	3	no	—
143	C₂×C₄	—	86	3	no	—
144	C₂×C₄	—	86	3	no	—
145	C₂×C₄	C₂×C₂²⋊D₄₃	1	6	yes	—
146	C₂²	—	4	3	no	—
147	C₂²	—	4	1	no	—
148	C₂²	—	4	3	no	—
149	C₂²	—	43	4	no	—
150	C₂²	—	86	6	no	—
151	C₂²	—	86	6	no	—
152	C₂²	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
153	C₂²	#41×D₄₃	1	3	yes	—
154	C₂²	#41×D₄₃	1	3	yes	—
155	C₄	—	2	6	no	—
156	C₄	—	4	3	no	—
157	C₄	—	86	6	no	—
158	C₄	—	172	1	no	—
159	C₄	—	172	3	no	—
160	C₂	—	8	1	no	—
161	C₂	—	86	4	no	—
162	C₂	#14583406	1	3	yes	—
163	C₂	#126×D₄₃	1	1	yes	characteristic
164	C₂	#14583432	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄²×D₄₃

C₂

yes

maximal, characteristic, complemented

#14582787

C₂

yes

maximal, complemented

#14582780

C₂

yes

maximal, complemented

#14582775

C₂

yes

maximal

#14582770

C₂

yes

maximal, complemented

#14582767

C₂

yes

maximal, characteristic, complemented

C₂×#126×C₄₃

C₂

yes

maximal, characteristic, complemented

C₂²×C₂²⋊D₄₃

C₂²

yes

characteristic

C₂²×C₄×D₄₃

C₂²

yes

—

C₂×Dic₄₃⋊C₄

C₂²

yes

—

C₂×C₂²⋊Dic₄₃

C₂²

yes

—

C₂×(C₂×D₄₃)⋊C₄

C₂²

yes

—

C₂×C₄×Dic₄₃

C₂²

yes

—

C₄²×D₄₃

—

C₄₃⋊#95

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

—

#126×C₄₃

—

C₂×C₄⋊C₄×C₄₃

C₂²

yes

—

C₂×C₂²⋊C₄×C₄₃

C₂²

yes

—

C₂×C₄²×C₄₃

C₂²

yes

characteristic

C₂⁴×C₄₃

C₂³

yes

characteristic

C₂³×D₄₃

C₂³

yes

characteristic

C₂²×C₄×C₄₃

C₂³

yes

—

C₂²×C₄×C₄₃

C₂³

yes

—

C₂×C₂²⋊D₄₃

—

C₂²×Dic₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

C₂³

yes

—

C₂²×Dic₄₃

C₂³

yes

—

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

—

C₄⋊C₄×C₄₃

—

C₂²⋊C₄×C₄₃

—

C₄²×C₄₃

D₄

yes

complemented

C₂²⋊Dic₄₃

—

(C₂×D₄₃)⋊C₄

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

C₂⁴

yes

characteristic

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

#41

yes

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂²⋊D₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

#41

yes

—

C₄×D₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

C₂²×D₄

yes

characteristic

C₂²×C₄₃

C₂×#41

yes

—

C₂²×C₄₃

C₂×#41

yes

—

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

#126

yes

complemented

C₄×C₄₃

—

C₄×C₄₃

—

Dic₄₃

—

Dic₄₃

—

Dic₄₃

—

#2852

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

#525

yes

—

C₂×C₄₃

C₂×#126

yes

characteristic

C₂×C₄₃

#529

yes

—

D₄₃

—

C₂×#126

D₄₃

yes

characteristic, complemented

C₂²×C₄²

—

—

—

—

—

—

C₄₃

#2852

yes

characteristic, complemented, Sylow

C₂²×D₄

—

C₂³×C₄

—

#126

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₄₃

yes

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

C₂×D₄₃

yes

—

C₂×C₄²

—

100

C₂×C₄²

—

101

C₂×C₄²

C₂×D₄₃

yes

characteristic

102

#95

—

103

#95

—

104

#95

—

105

#95

—

106

C₂⁴

—

107

C₂⁴

C₂²×D₄₃

yes

characteristic

108

C₂×D₄

—

109

C₂²×C₄

—

110

C₂²×C₄

—

111

C₂²×C₄

—

112

C₂²×C₄

—

113

C₂²×C₄

—

114

C₂²×C₄

—

115

C₂²×C₄

C₂²×D₄₃

yes

—

116

C₂²×C₄

C₂²×D₄₃

yes

—

117

C₄⋊C₄

—

118

C₄⋊C₄

—

119

C₂²⋊C₄

—

120

C₂²⋊C₄

—

121

C₂²⋊C₄

—

122

C₄²

—

123

C₄²

C₂²⋊D₄₃

yes

complemented

124

C₂³

—

125

C₂³

—

126

C₂³

—

127

C₂³

—

128

C₂³

—

129

C₂³

—

130

C₂³

C₂³×D₄₃

yes

characteristic

131

D₄

—

172

—

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

—

141

C₂×C₄

—

142

C₂×C₄

—

143

C₂×C₄

—

144

C₂×C₄

—

145

C₂×C₄

C₂×C₂²⋊D₄₃

yes

—

146

C₂²

—

147

C₂²

—

148

C₂²

—

149

C₂²

—

150

C₂²

—

151

C₂²

—

152

C₂²

C₂²×C₂²⋊D₄₃

yes

characteristic

153

C₂²

#41×D₄₃

yes

—

154

C₂²

#41×D₄₃

yes

—

155

C₄

—

156

C₄

—

157

C₄

—

158

C₄

—

172

—

159

C₄

—

172

—

160

C₂

—

161

C₂

—

162

C₂

#14583406

yes

—

163

C₂

#126×D₄₃

yes

characteristic

164

C₂

#14583432

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₄₃
commutator, socle	C₂³×C₄₃	C₂⁴
Fitting	C₂×#126×C₄₃	C₂
hypercenter	C₂×#126	D₄₃
hypocenter	C₄₃	#2852
LCS	G ▷ C₂³×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×#126

subgroup

G/H

center, Frattini

C₂³

C₂³×D₄₃

commutator, socle

C₂³×C₄₃

C₂⁴

Fitting

C₂×#126×C₄₃

C₂

D₄₃

C₄₃

G ▷ C₂³×C₄₃ ▷ C₄₃

C₁ ◁ C₂³ ◁ C₂×#126

N	H ≅ G/N	type
1. C₂×C₄²×D₄₃	C₂	semidirect
2. #14582787	C₂	semidirect
3. #14582780	C₂	semidirect
5. #14582770	C₂	semidirect
6. #14582767	C₂	semidirect
7. C₂×#126×C₄₃	C₂	semidirect
36. C₄²×C₄₃	D₄	semidirect
71. C₂×D₄₃	#126	semidirect
83. C₂×#126	D₄₃	semidirect
90. C₄₃	#2852	semidirect
123. C₄²	C₂²⋊D₄₃	semidirect

H ≅ G/N

type

1. C₂×C₄²×D₄₃

C₂

semidirect

2. #14582787

C₂

semidirect

3. #14582780

C₂

semidirect

5. #14582770

C₂

semidirect

6. #14582767

C₂

semidirect

7. C₂×#126×C₄₃

C₂

semidirect

36. C₄²×C₄₃

D₄

semidirect

71. C₂×D₄₃

#126

semidirect

83. C₂×#126

D₄₃

semidirect

90. C₄₃

#2852

semidirect

123. C₄²

C₂²⋊D₄₃

semidirect

Subgroups — #19142907

Conjugacy classes of subgroups

Complements