Group #19134996 — subgroups

Subgroups — #19134996

Order 5504.

344 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 89 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×#13063314	C₂	1	1	yes	maximal, characteristic
2	#14583377	C₂	1	1	yes	maximal, characteristic, complemented
3	#14582905	C₂	1	2	yes	maximal
4	#14582660	C₂	1	2	yes	maximal, complemented
5	C₂×#101×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₁₇₂	C₂²	1	1	yes	characteristic
7	#13063314	—	2	2	no	—
8	#13063314	C₄	1	4	yes	complemented
9	Q₈×Dic₄₃	—	2	4	no	—
10	#13063284	—	2	2	no	—
11	#13063284	C₂²	1	2	yes	—
12	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
13	C₂×C₄×Dic₄₃	C₂²	1	1	yes	characteristic
14	#13063247	—	2	4	no	—
15	C₂²×Q₈×C₄₃	C₂²	1	1	yes	characteristic
16	C₂×M₁₆×C₄₃	C₂²	1	2	yes	—
17	#101×C₄₃	—	2	2	no	—
18	C₂³×D₄₃	—	2	1	no	—
19	C₂×Q₈×C₄₃	—	2	2	no	—
20	C₂×Q₈×C₄₃	—	2	2	no	—
21	C₂×Q₈×C₄₃	C₂×C₄	1	2	yes	—
22	C₂×Q₈×C₄₃	D₄	1	2	yes	—
23	C₂²×C₄×C₄₃	D₄	1	2	yes	—
24	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
25	C₂²×Dic₄₃	—	2	1	no	—
26	C₂×D₁₇₂	—	2	1	no	—
27	C₂×D₁₇₂	—	2	2	no	—
28	C₂×D₁₇₂	—	2	2	no	—
29	C₂×D₁₇₂	C₂×C₄	1	2	yes	—
30	M₁₆×C₄₃	—	2	2	no	—
31	M₁₆×C₄₃	—	2	2	no	—
32	C₂×C₈×C₄₃	—	2	2	no	—
33	C₂²⋊Dic₄₃	—	2	2	no	—
34	(C₂×D₄₃)⋊C₄	—	2	8	no	—
35	C₄⋊Dic₄₃	—	2	4	no	—
36	C₄⋊Dic₄₃	D₄	1	4	yes	—
37	C₄×Dic₄₃	—	2	4	no	—
38	C₄×Dic₄₃	—	2	1	no	—
39	C₄×Dic₄₃	—	2	2	no	—
40	C₄×Dic₄₃	C₂×C₄	1	2	yes	—
41	C₂³×C₄₃	C₂×D₄	1	1	yes	characteristic
42	C₂²×D₄₃	—	2	2	no	—
43	C₂²×D₄₃	—	4	4	no	—
44	C₂²×D₄₃	—	4	1	no	—
45	C₂²×D₄₃	—	4	1	no	—
46	Q₈×C₄₃	—	2	4	no	—
47	Q₈×C₄₃	—	2	4	no	—
48	C₂×C₄×C₄₃	—	2	2	no	—
49	C₂×C₄×C₄₃	—	2	2	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	2	yes	—
53	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
54	C₂×C₄×C₄₃	#41	1	2	yes	—
55	C₂×Dic₄₃	—	2	2	no	—
56	C₂×Dic₄₃	—	2	4	no	—
57	C₂×Dic₄₃	—	4	2	no	—
58	D₁₇₂	—	2	4	no	—
59	D₁₇₂	—	4	2	no	—
60	C₈×C₄₃	—	4	2	no	—
61	C₂²×C₄₃	—	2	2	no	—
62	C₂²×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
63	C₂²×C₄₃	#120	1	1	yes	characteristic
64	C₂²×C₄₃	#123	1	1	yes	characteristic
65	C₂×D₄₃	—	4	4	no	—
66	C₂×D₄₃	—	4	2	no	—
67	C₂×D₄₃	—	8	2	no	—
68	C₂×D₄₃	—	8	2	no	—
69	C₄×C₄₃	—	2	4	no	—
70	C₄×C₄₃	C₄×D₄	1	2	yes	—
71	C₄×C₄₃	#121	1	2	yes	—
72	Dic₄₃	—	4	2	no	—
73	Dic₄₃	—	4	4	no	—
74	#1888	—	43	1	no	maximal, Sylow
75	C₂×C₄₃	—	2	1	no	—
76	C₂×C₄₃	—	2	1	no	—
77	C₂×C₄₃	#386	1	1	yes	characteristic
78	C₂×C₄₃	#454	1	2	yes	—
79	D₄₃	—	8	2	no	—
80	C₂×#124	—	43	1	no	—
81	#519	—	43	1	no	—
82	#418	—	43	2	no	—
83	C₂×#101	D₄₃	1	1	yes	characteristic, complemented
84	#339	—	43	2	no	—
85	C₄₃	#1888	1	1	yes	characteristic, complemented, Sylow
86	C₂²×Q₈	C₂×D₄₃	1	1	yes	characteristic
87	C₂²×D₄	—	43	1	no	—
88	C₂×M₁₆	C₂×D₄₃	1	2	yes	—
89	#124	—	43	4	no	—
90	#124	—	86	2	no	—
91	C₄×Q₈	—	86	4	no	—
92	#117	—	43	2	no	—
93	#117	—	86	2	no	—
94	C₂×C₂²⋊C₄	—	86	2	no	—
95	C₂×C₄²	—	43	1	no	—
96	#102	—	86	4	no	—
97	#101	—	2	2	no	—
98	C₂⁴	—	86	1	no	—
99	C₂×Q₈	—	2	2	no	—
100	C₂×Q₈	—	2	2	no	—
101	C₂×Q₈	C₄×D₄₃	1	2	yes	—
102	C₂×Q₈	C₂²⋊D₄₃	1	2	yes	—
103	C₂×D₄	—	43	2	no	—
104	C₂×D₄	—	86	2	no	—
105	C₂×D₄	—	86	2	no	—
106	C₂×D₄	—	86	1	no	—
107	C₂²×C₄	—	86	1	no	—
108	C₂²×C₄	D₁₇₂	1	2	yes	—
109	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
110	M₁₆	—	2	2	no	—
111	M₁₆	—	2	2	no	—
112	C₂×C₈	—	2	2	no	—
113	C₄⋊C₄	—	43	4	no	—
114	C₄⋊C₄	—	86	4	no	—
115	C₂²⋊C₄	—	86	2	no	—
116	C₂²⋊C₄	—	86	8	no	—
117	C₄²	—	43	2	no	—
118	C₄²	—	86	4	no	—
119	C₄²	—	86	2	no	—
120	C₄²	—	86	1	no	—
121	C₂³	—	86	2	no	—
122	C₂³	—	172	4	no	—
123	C₂³	—	172	1	no	—
124	C₂³	—	172	1	no	—
125	C₂³	C₂×D₁₇₂	1	1	yes	characteristic
126	Q₈	—	2	4	no	—
127	Q₈	—	2	4	no	—
128	D₄	—	86	4	no	—
129	D₄	—	172	2	no	—
130	C₂×C₄	—	2	2	no	—
131	C₂×C₄	—	2	2	no	—
132	C₂×C₄	—	86	2	no	—
133	C₂×C₄	—	86	4	no	—
134	C₂×C₄	—	172	2	no	—
135	C₂×C₄	(C₂×D₄₃)⋊C₄	1	4	yes	—
136	C₂×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
137	C₂×C₄	D₄×D₄₃	1	2	yes	—
138	C₂×C₄	#10621900	1	2	yes	—
139	C₂×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
140	C₈	—	4	2	no	—
141	C₂²	—	2	2	no	—
142	C₂²	—	344	2	no	—
143	C₂²	—	344	2	no	—
144	C₂²	—	172	4	no	—
145	C₂²	—	172	2	no	—
146	C₂²	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
147	C₂²	#13063295	1	1	yes	characteristic
148	C₂²	#13063309	1	1	yes	characteristic
149	C₄	—	2	4	no	—
150	C₄	—	172	2	no	—
151	C₄	—	172	4	no	—
152	C₄	(C₂²⋊D₄₃)⋊C₄	1	2	yes	—
153	C₄	#13063297	1	2	yes	—
154	C₂	—	2	1	no	—
155	C₂	—	2	1	no	—
156	C₂	—	344	2	no	—
157	C₂	#14582776	1	1	yes	characteristic
158	C₂	#14583074	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063314

C₂

yes

maximal, characteristic

#14583377

C₂

yes

maximal, characteristic, complemented

#14582905

C₂

yes

maximal

#14582660

C₂

yes

maximal, complemented

C₂×#101×C₄₃

C₂

yes

maximal, characteristic, complemented

C₂²×D₁₇₂

C₂²

yes

characteristic

#13063314

—

#13063314

C₄

yes

complemented

Q₈×Dic₄₃

—

#13063284

—

#13063284

C₂²

yes

—

C₂×(C₂×D₄₃)⋊C₄

—

C₂×C₄×Dic₄₃

C₂²

yes

characteristic

#13063247

—

C₂²×Q₈×C₄₃

C₂²

yes

characteristic

C₂×M₁₆×C₄₃

C₂²

yes

—

#101×C₄₃

—

C₂³×D₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

C₂×C₄

yes

—

C₂×Q₈×C₄₃

D₄

yes

—

C₂²×C₄×C₄₃

D₄

yes

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

C₂×C₄

yes

—

M₁₆×C₄₃

—

M₁₆×C₄₃

—

C₂×C₈×C₄₃

—

C₂²⋊Dic₄₃

—

(C₂×D₄₃)⋊C₄

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

D₄

yes

—

C₄×Dic₄₃

—

C₄×Dic₄₃

—

C₄×Dic₄₃

—

C₄×Dic₄₃

C₂×C₄

yes

—

C₂³×C₄₃

C₂×D₄

yes

characteristic

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

Q₈×C₄₃

—

Q₈×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

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

#41

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

D₁₇₂

—

D₁₇₂

—

C₈×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

C₂×C₂²⋊C₄

yes

C₂²×C₄₃

yes

C₂²×C₄₃

yes

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

C₄×D₄

yes

—

C₄×C₄₃

#121

yes

—

Dic₄₃

—

Dic₄₃

—

#1888

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

#386

yes

characteristic

C₂×C₄₃

#454

yes

—

D₄₃

—

—

—

—

D₄₃

yes

characteristic, complemented

#339

—

C₄₃

#1888

yes

characteristic, complemented, Sylow

C₂²×Q₈

C₂×D₄₃

yes

characteristic

C₂²×D₄

—

C₂×M₁₆

C₂×D₄₃

yes

—

#124

—

#124

—

C₄×Q₈

—

#117

—

#117

—

C₂×C₂²⋊C₄

—

C₂×C₄²

—

#102

—

#101

—

C₂⁴

—

C₂×Q₈

—

100

C₂×Q₈

—

101

C₂×Q₈

C₄×D₄₃

yes

—

102

C₂×Q₈

C₂²⋊D₄₃

yes

—

103

C₂×D₄

—

104

C₂×D₄

—

105

C₂×D₄

—

106

C₂×D₄

—

107

C₂²×C₄

—

108

C₂²×C₄

D₁₇₂

yes

—

109

C₂²×C₄

C₂²×D₄₃

yes

characteristic

110

M₁₆

—

111

M₁₆

—

112

C₂×C₈

—

113

C₄⋊C₄

—

114

C₄⋊C₄

—

115

C₂²⋊C₄

—

116

C₂²⋊C₄

—

117

C₄²

—

118

C₄²

—

119

C₄²

—

120

C₄²

—

121

C₂³

—

122

C₂³

—

172

—

123

C₂³

—

172

—

124

C₂³

—

172

—

125

C₂³

C₂×D₁₇₂

yes

characteristic

126

Q₈

—

127

Q₈

—

128

D₄

—

129

D₄

—

172

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

—

172

—

135

C₂×C₄

(C₂×D₄₃)⋊C₄

yes

—

136

C₂×C₄

C₂×C₄×D₄₃

yes

characteristic

137

C₂×C₄

D₄×D₄₃

yes

—

138

C₂×C₄

#10621900

yes

—

139

C₂×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

140

C₈

—

141

C₂²

—

142

C₂²

—

344

—

143

C₂²

—

344

—

144

C₂²

—

172

—

145

C₂²

—

172

—

146

C₂²

C₂×(C₂×D₄₃)⋊C₄

yes

characteristic

147

C₂²

#13063295

yes

characteristic

148

C₂²

#13063309

yes

characteristic

149

C₄

—

150

C₄

—

172

—

151

C₄

—

172

—

152

C₄

(C₂²⋊D₄₃)⋊C₄

yes

—

153

C₄

#13063297

yes

—

154

C₂

—

155

C₂

—

156

C₂

—

344

—

157

C₂

#14582776

yes

characteristic

158

C₂

#14583074

yes

—

	subgroup	G/H
center	C₂²	#13063295
commutator	C₂×C₄×C₄₃	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₄₃
Fitting	C₂×#101×C₄₃	C₂
socle	C₂²×C₄₃	#120
hypercenter	C₂×#101	D₄₃
hypocenter	C₄₃	#1888
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#101

subgroup

G/H

center

C₂²

#13063295

commutator

C₂×C₄×C₄₃

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₄₃

Fitting

C₂×#101×C₄₃

C₂

C₂²×C₄₃

D₄₃

C₄₃

G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#101

N	H ≅ G/N	type
2. #14583377	C₂	semidirect
4. #14582660	C₂	semidirect
5. C₂×#101×C₄₃	C₂	semidirect
8. #13063314	C₄	semidirect
83. C₂×#101	D₄₃	semidirect
85. C₄₃	#1888	semidirect

H ≅ G/N

type

2. #14583377

C₂

semidirect

4. #14582660

C₂

semidirect

5. C₂×#101×C₄₃

C₂

semidirect

8. #13063314

C₄

semidirect

83. C₂×#101

D₄₃

semidirect

85. C₄₃

#1888

semidirect

Subgroups — #19134996

Conjugacy classes of subgroups

Complements