Group #19135409 — subgroups

Subgroups — #19135409

Order 5504.

344 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 105 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×#13063313	C₂	1	1	yes	maximal, characteristic
2	C₂×#13063248	C₂	1	2	yes	maximal, complemented
3	C₂×#13063245	C₂	1	2	yes	maximal
4	C₂×#13063236	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#384	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×Dic₈₆	C₂²	1	1	yes	characteristic
7	C₂²×D₁₇₂	C₂²	1	1	yes	characteristic
8	C₂²×C₄₃⋊C₈	C₂²	1	2	yes	—
9	#13063313	—	2	2	no	—
10	#13063313	C₄	1	4	yes	complemented
11	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
12	#13063248	—	2	4	no	—
13	#13063245	—	2	4	no	—
14	#13063236	—	2	2	no	—
15	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
16	C₂×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
17	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
18	C₂³×D₄₃	—	2	1	no	—
19	C₂²×C₄×C₄₃	—	2	2	no	—
20	C₂²×C₄×C₄₃	D₄	1	2	yes	—
21	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
22	C₂²×Dic₄₃	—	2	1	no	—
23	C₂×D₁₇₂	—	2	1	no	—
24	C₂×D₁₇₂	—	2	2	no	—
25	C₂×D₁₇₂	—	2	2	no	—
26	C₂×D₁₇₂	C₂×C₄	1	2	yes	—
27	C₂×Dic₈₆	—	2	2	no	—
28	C₂×Dic₈₆	—	2	2	no	—
29	C₂×Dic₈₆	—	2	1	no	—
30	C₂×Dic₈₆	C₂×C₄	1	2	yes	—
31	C₄⋊C₄×C₄₃	—	2	2	no	—
32	C₄⋊C₄×C₄₃	—	2	2	no	—
33	C₄⋊C₄×C₄₃	—	4	4	no	—
34	C₄²×C₄₃	C₂×C₄	1	2	yes	—
35	C₄²×C₄₃	D₄	1	2	yes	—
36	(C₂×D₄₃)⋊C₄	—	2	8	no	—
37	C₂×C₄₃⋊C₈	—	2	2	no	—
38	C₂×C₄₃⋊C₈	—	2	2	no	—
39	C₂×C₄₃⋊C₈	D₄	1	4	yes	—
40	C₂³×C₄₃	C₂×D₄	1	1	yes	characteristic
41	C₂²×D₄₃	—	2	2	no	—
42	C₂²×D₄₃	—	4	1	no	—
43	C₂²×D₄₃	—	4	1	no	—
44	C₂²×D₄₃	—	4	2	no	—
45	C₂²×D₄₃	—	4	2	no	—
46	C₂×C₄×C₄₃	—	2	2	no	—
47	C₂×C₄×C₄₃	—	2	2	no	—
48	C₂×C₄×C₄₃	—	4	2	no	—
49	C₂×C₄×C₄₃	—	4	4	no	—
50	C₂×C₄×C₄₃	C₂²⋊C₄	1	4	yes	—
51	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
52	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
53	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
54	C₂×C₄×C₄₃	#41	1	2	yes	—
55	C₂×Dic₄₃	—	2	2	no	—
56	C₂×Dic₄₃	—	4	1	no	—
57	C₂×Dic₄₃	—	4	1	no	—
58	D₁₇₂	—	2	4	no	—
59	D₁₇₂	—	4	2	no	—
60	Dic₈₆	—	2	4	no	—
61	Dic₈₆	—	4	2	no	—
62	C₄₃⋊C₈	—	2	4	no	—
63	C₂²×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
64	C₂²×C₄₃	#124	1	1	yes	characteristic
65	C₂²×C₄₃	#127	1	1	yes	characteristic
66	C₂²×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
67	C₂²×C₄₃	#137	1	2	yes	—
68	C₂×D₄₃	—	4	2	no	—
69	C₂×D₄₃	—	4	4	no	—
70	C₂×D₄₃	—	8	2	no	—
71	C₂×D₄₃	—	8	1	no	—
72	C₂×D₄₃	—	8	1	no	—
73	C₄×C₄₃	—	2	4	no	—
74	C₄×C₄₃	—	8	2	no	—
75	C₄×C₄₃	C₄×D₄	1	2	yes	—
76	C₄×C₄₃	#121	1	2	yes	—
77	Dic₄₃	—	4	2	no	—
78	#1959	—	43	1	no	maximal, Sylow
79	C₂×C₄₃	#390	1	1	yes	characteristic
80	C₂×C₄₃	#417	1	2	yes	—
81	C₂×C₄₃	#489	1	2	yes	—
82	C₂×C₄₃	#496	1	1	yes	characteristic
83	C₂×C₄₃	#497	1	1	yes	characteristic
84	D₄₃	—	8	2	no	—
85	C₂×#124	—	43	1	no	—
86	C₂×#103	—	43	2	no	—
87	C₂×#102	—	43	2	no	—
88	C₂×#97	—	43	1	no	—
89	#384	D₄₃	1	1	yes	characteristic, complemented
90	C₄₃	#1959	1	1	yes	characteristic, complemented, Sylow
91	C₂²×Q₈	—	43	1	no	—
92	C₂²×D₄	—	43	1	no	—
93	C₂²×C₈	—	43	2	no	—
94	#124	—	43	4	no	—
95	#124	—	86	2	no	—
96	C₂×C₄⋊C₄	—	2	2	no	—
97	C₂×C₄⋊C₄	C₂×D₄₃	1	2	yes	—
98	C₂×C₂²⋊C₄	—	86	2	no	—
99	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
100	#103	—	86	4	no	—
101	#102	—	86	4	no	—
102	#97	—	86	2	no	—
103	C₂⁴	—	86	1	no	—
104	C₂×Q₈	—	43	2	no	—
105	C₂×Q₈	—	86	1	no	—
106	C₂×Q₈	—	86	2	no	—
107	C₂×Q₈	—	86	2	no	—
108	C₂×D₄	—	43	2	no	—
109	C₂×D₄	—	86	1	no	—
110	C₂×D₄	—	86	2	no	—
111	C₂×D₄	—	86	2	no	—
112	C₂²×C₄	—	2	2	no	—
113	C₂²×C₄	—	86	1	no	—
114	C₂²×C₄	C₂²⋊D₄₃	1	2	yes	—
115	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
116	C₂×C₈	—	43	4	no	—
117	C₂×C₈	—	86	2	no	—
118	C₂×C₈	—	86	2	no	—
119	C₄⋊C₄	—	2	2	no	—
120	C₄⋊C₄	—	2	2	no	—
121	C₄⋊C₄	—	4	4	no	—
122	C₂²⋊C₄	—	86	8	no	—
123	C₄²	C₄×D₄₃	1	2	yes	—
124	C₄²	D₁₇₂	1	2	yes	—
125	C₂³	—	86	2	no	—
126	C₂³	—	172	1	no	—
127	C₂³	—	172	1	no	—
128	C₂³	—	172	2	no	—
129	C₂³	—	172	2	no	—
130	C₂³	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
131	Q₈	—	86	4	no	—
132	Q₈	—	172	2	no	—
133	D₄	—	86	4	no	—
134	D₄	—	172	2	no	—
135	C₂×C₄	—	2	2	no	—
136	C₂×C₄	—	2	2	no	—
137	C₂×C₄	—	4	2	no	—
138	C₂×C₄	—	4	4	no	—
139	C₂×C₄	—	86	2	no	—
140	C₂×C₄	—	172	1	no	—
141	C₂×C₄	—	172	1	no	—
142	C₂×C₄	(C₂×D₄₃)⋊C₄	1	4	yes	—
143	C₂×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
144	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
145	C₂×C₄	D₄×D₄₃	1	2	yes	—
146	C₂×C₄	#10621902	1	2	yes	—
147	C₈	—	86	4	no	—
148	C₂²	—	344	2	no	—
149	C₂²	—	344	1	no	—
150	C₂²	—	344	1	no	—
151	C₂²	—	172	2	no	—
152	C₂²	—	172	4	no	—
153	C₂²	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
154	C₂²	#13063314	1	1	yes	characteristic
155	C₂²	#13063321	1	1	yes	characteristic
156	C₂²	#13063351	1	2	yes	—
157	C₂²	#13063356	1	2	yes	—
158	C₄	—	2	4	no	—
159	C₄	—	8	2	no	—
160	C₄	—	172	2	no	—
161	C₄	#13063287	1	2	yes	—
162	C₄	#13063300	1	2	yes	—
163	C₂	—	344	2	no	—
164	C₂	#14582800	1	1	yes	characteristic
165	C₂	#14582898	1	2	yes	—
166	C₂	#14583261	1	2	yes	—
167	C₂	#14583286	1	1	yes	characteristic
168	C₂	#14583291	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063313

C₂

yes

maximal, characteristic

C₂×#13063248

C₂

yes

maximal, complemented

C₂×#13063245

C₂

yes

maximal

C₂×#13063236

C₂

yes

maximal, characteristic, complemented

C₄₃×#384

C₂

yes

maximal, characteristic, complemented

C₂²×Dic₈₆

C₂²

yes

characteristic

C₂²×D₁₇₂

C₂²

yes

characteristic

C₂²×C₄₃⋊C₈

C₂²

yes

—

#13063313

—

#13063313

C₄

yes

complemented

C₂×(C₂×D₄₃)⋊C₄

—

#13063248

—

#13063245

—

#13063236

—

C₂×C₄⋊C₄×C₄₃

—

C₂×C₄⋊C₄×C₄₃

C₂²

yes

—

C₂×C₄²×C₄₃

C₂²

yes

characteristic

C₂³×D₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

D₄

yes

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

C₂×C₄

yes

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

C₂×C₄

yes

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄²×C₄₃

C₂×C₄

yes

—

C₄²×C₄₃

D₄

yes

—

(C₂×D₄₃)⋊C₄

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

D₄

yes

—

C₂³×C₄₃

C₂×D₄

yes

characteristic

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂×C₄×C₄₃

—

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

C₂×D₄

yes

—

C₂×C₄×C₄₃

#41

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

D₁₇₂

—

D₁₇₂

—

Dic₈₆

—

Dic₈₆

—

C₄₃⋊C₈

—

C₂²×C₄₃

C₂×C₂²⋊C₄

yes

C₂²×C₄₃

yes

C₂²×C₄₃

yes

C₂²×C₄₃

yes

—

C₂²×C₄₃

#137

yes

—

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

C₄×D₄

yes

—

C₄×C₄₃

#121

yes

—

Dic₄₃

—

—

C₂×C₄₃

yes

C₂×C₄₃

yes

—

C₂×C₄₃

#489

yes

—

C₂×C₄₃

yes

C₂×C₄₃

yes

D₄₃

—

C₂×#124

—

C₂×#103

—

C₂×#102

—

C₂×#97

—

#384

D₄₃

yes

characteristic, complemented

C₄₃

#1959

yes

characteristic, complemented, Sylow

C₂²×Q₈

—

C₂²×D₄

—

C₂²×C₈

—

#124

—

#124

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₄₃

yes

—

C₂×C₂²⋊C₄

—

C₂×C₄²

C₂×D₄₃

yes

characteristic

100

#103

—

101

#102

—

102

#97

—

103

C₂⁴

—

104

C₂×Q₈

—

105

C₂×Q₈

—

106

C₂×Q₈

—

107

C₂×Q₈

—

108

C₂×D₄

—

109

C₂×D₄

—

110

C₂×D₄

—

111

C₂×D₄

—

112

C₂²×C₄

—

113

C₂²×C₄

—

114

C₂²×C₄

C₂²⋊D₄₃

yes

—

115

C₂²×C₄

C₂²×D₄₃

yes

characteristic

116

C₂×C₈

—

117

C₂×C₈

—

118

C₂×C₈

—

119

C₄⋊C₄

—

120

C₄⋊C₄

—

121

C₄⋊C₄

—

122

C₂²⋊C₄

—

123

C₄²

C₄×D₄₃

yes

—

124

C₄²

D₁₇₂

yes

—

125

C₂³

—

126

C₂³

—

172

—

127

C₂³

—

172

—

128

C₂³

—

172

—

129

C₂³

—

172

—

130

C₂³

C₂×C₂²⋊D₄₃

yes

characteristic

131

Q₈

—

132

Q₈

—

172

—

133

D₄

—

134

D₄

—

172

—

135

C₂×C₄

—

136

C₂×C₄

—

137

C₂×C₄

—

138

C₂×C₄

—

139

C₂×C₄

—

140

C₂×C₄

—

172

—

141

C₂×C₄

—

172

—

142

C₂×C₄

(C₂×D₄₃)⋊C₄

yes

—

143

C₂×C₄

C₂×C₄×D₄₃

yes

characteristic

144

C₂×C₄

C₂×D₁₇₂

yes

characteristic

145

C₂×C₄

D₄×D₄₃

yes

—

146

C₂×C₄

#10621902

yes

—

147

C₈

—

148

C₂²

—

344

—

149

C₂²

—

344

—

150

C₂²

—

344

—

151

C₂²

—

172

—

152

C₂²

—

172

—

153

C₂²

C₂×(C₂×D₄₃)⋊C₄

yes

characteristic

154

C₂²

#13063314

yes

characteristic

155

C₂²

#13063321

yes

characteristic

156

C₂²

#13063351

yes

—

157

C₂²

#13063356

yes

—

158

C₄

—

159

C₄

—

160

C₄

—

172

—

161

C₄

#13063287

yes

—

162

C₄

#13063300

yes

—

163

C₂

—

344

—

164

C₂

#14582800

yes

characteristic

165

C₂

#14582898

yes

—

166

C₂

#14583261

yes

—

167

C₂

#14583286

yes

characteristic

168

C₂

#14583291

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₄₃
commutator	C₂×C₄×C₄₃	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₄₃
Fitting	C₄₃×#384	C₂
socle	C₂³×C₄₃	C₂×D₄
hypercenter	#384	D₄₃
hypocenter	C₄₃	#1959
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #384

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₄₃

commutator

C₂×C₄×C₄₃

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₄₃

Fitting

C₄₃×#384

C₂

socle

C₂³×C₄₃

C₂×D₄

D₄₃

C₄₃

G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #384

N	H ≅ G/N	type
2. C₂×#13063248	C₂	semidirect
4. C₂×#13063236	C₂	semidirect
5. C₄₃×#384	C₂	semidirect
10. #13063313	C₄	semidirect
89. #384	D₄₃	semidirect
90. C₄₃	#1959	semidirect

H ≅ G/N

type

2. C₂×#13063248

C₂

semidirect

4. C₂×#13063236

C₂

semidirect

5. C₄₃×#384

C₂

semidirect

10. #13063313

C₄

semidirect

89. #384

D₄₃

semidirect

90. C₄₃

#1959

semidirect

Subgroups — #19135409

Conjugacy classes of subgroups

Complements