Group #19132937 — subgroups

Subgroups — #19132937

Order 5504.

236 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 69 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×#13063290	C₂	1	1	yes	maximal, characteristic
2	#14582953	C₂	1	2	yes	maximal
3	#14582625	C₂	1	1	yes	maximal, characteristic
4	#14582624	C₂	1	2	yes	maximal
5	C₄₃×#324	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₈₆	C₄	1	1	yes	characteristic
7	#13063290	—	2	2	no	—
8	#13063290	—	2	2	no	—
9	C₂×Dic₄₃⋊C₄	C₄	1	1	yes	characteristic
10	C₂×Dic₄₃⋊C₄	C₂²	1	1	yes	characteristic
11	C₂×C₄×Dic₄₃	C₄	1	1	yes	characteristic
12	C₂×C₄×Dic₄₃	C₄	1	1	yes	characteristic
13	C₂×C₄×Dic₄₃	C₂²	1	1	yes	characteristic
14	Dic₄₃⋊C₈	—	2	2	no	—
15	C₂²⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
16	#13063235	—	2	2	no	—
17	C₂×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
18	C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
19	C₂²×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
20	C₂²×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
21	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
22	C₂²×Dic₄₃	C₂×C₄	1	1	yes	characteristic
23	C₂²×Dic₄₃	C₂×C₄	1	1	yes	characteristic
24	C₂²×Dic₄₃	C₂×C₄	1	1	yes	characteristic
25	C₂²×Dic₄₃	C₂×C₄	1	1	yes	characteristic
26	C₂×Dic₈₆	—	2	2	no	—
27	C₂×Dic₈₆	—	2	2	no	—
28	C₂×Dic₈₆	—	2	2	no	—
29	C₂×C₈×C₄₃	—	2	2	no	—
30	C₄⋊C₄×C₄₃	—	2	2	no	—
31	Dic₄₃⋊C₄	—	2	2	no	—
32	Dic₄₃⋊C₄	—	2	2	no	—
33	C₄×Dic₄₃	—	2	1	no	—
34	C₄×Dic₄₃	—	2	1	no	—
35	C₄×Dic₄₃	—	2	1	no	—
36	C₄×Dic₄₃	—	2	1	no	—
37	C₄×Dic₄₃	D₄	1	2	yes	—
38	C₄×Dic₄₃	D₄	1	2	yes	—
39	C₂×C₄₃⋊C₈	—	2	2	no	—
40	C₂³×C₄₃	C₂²×C₄	1	1	yes	characteristic
41	C₂×C₄×C₄₃	—	2	1	no	—
42	C₂×C₄×C₄₃	—	2	1	no	—
43	C₂×C₄×C₄₃	—	2	1	no	—
44	C₂×C₄×C₄₃	—	4	1	no	—
45	C₂×C₄×C₄₃	—	4	1	no	—
46	C₂×C₄×C₄₃	M₁₆	1	2	yes	—
47	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
48	C₂×Dic₄₃	—	2	1	no	—
49	C₂×Dic₄₃	—	2	1	no	—
50	C₂×Dic₄₃	—	2	1	no	—
51	C₂×Dic₄₃	—	2	1	no	—
52	C₂×Dic₄₃	—	2	2	no	—
53	C₂×Dic₄₃	—	2	1	no	—
54	C₂×Dic₄₃	—	4	1	no	—
55	C₂×Dic₄₃	C₂²⋊C₄	1	1	yes	characteristic
56	C₂×Dic₄₃	C₂²⋊C₄	1	2	yes	—
57	C₂×Dic₄₃	C₂²⋊C₄	1	1	yes	characteristic
58	C₂×Dic₄₃	M₁₆	1	2	yes	—
59	Dic₈₆	—	2	8	no	—
60	C₈×C₄₃	—	4	2	no	—
61	C₄₃⋊C₈	—	4	2	no	—
62	C₂²×C₄₃	—	2	1	no	—
63	C₂²×C₄₃	—	2	1	no	—
64	C₂²×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
65	C₂²×C₄₃	C₂×M₁₆	1	1	yes	characteristic
66	C₂²×C₄₃	C₂×M₁₆	1	1	yes	characteristic
67	C₄×C₄₃	—	2	2	no	—
68	C₄×C₄₃	—	2	2	no	—
69	C₄×C₄₃	—	4	1	no	—
70	Dic₄₃	—	2	2	no	—
71	Dic₄₃	—	2	2	no	—
72	Dic₄₃	—	2	1	no	—
73	Dic₄₃	—	4	1	no	—
74	Dic₄₃	#101	1	2	yes	—
75	#1467	—	43	1	no	maximal, Sylow
76	C₂×C₄₃	—	2	1	no	—
77	C₂×C₄₃	—	2	1	no	—
78	C₂×C₄₃	#407	1	1	yes	characteristic
79	C₂×C₄₃	#410	1	1	yes	characteristic
80	C₂×C₄₃	C₂×#101	1	1	yes	characteristic
81	C₂×C₄×Q₈	—	43	1	no	—
82	#432	—	43	2	no	—
83	#324	—	43	1	no	—
84	#324	—	43	2	no	—
85	#324	D₄₃	1	1	yes	characteristic
86	C₄₃	#1467	1	1	yes	characteristic, complemented, Sylow
87	C₂²×Q₈	—	43	1	no	—
88	C₄×Q₈	—	86	2	no	—
89	C₄×Q₈	—	86	2	no	—
90	C₂×C₄⋊C₄	—	43	1	no	—
91	C₂×C₄⋊C₄	—	43	1	no	—
92	C₂×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
93	C₂×C₄²	—	43	1	no	—
94	C₂×C₄²	—	43	1	no	—
95	C₂×C₄²	—	43	1	no	—
96	C₄⋊C₈	—	86	2	no	—
97	C₂²⋊C₈	—	43	2	no	—
98	C₂²⋊C₈	C₂×D₄₃	1	2	yes	—
99	#97	—	86	2	no	—
100	C₂×Q₈	—	86	2	no	—
101	C₂×Q₈	—	86	2	no	—
102	C₂×Q₈	—	86	2	no	—
103	C₂²×C₄	—	43	1	no	—
104	C₂²×C₄	—	43	1	no	—
105	C₂²×C₄	—	43	1	no	—
106	C₂²×C₄	—	43	1	no	—
107	C₂²×C₄	C₄×D₄₃	1	1	yes	characteristic
108	C₂²×C₄	C₄×D₄₃	1	1	yes	characteristic
109	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
110	C₂×C₈	—	2	2	no	—
111	C₂×C₈	—	86	2	no	—
112	C₄⋊C₄	—	2	2	no	—
113	C₄⋊C₄	—	86	2	no	—
114	C₄⋊C₄	—	86	2	no	—
115	C₄²	—	43	2	no	—
116	C₄²	—	43	2	no	—
117	C₄²	—	86	1	no	—
118	C₄²	—	86	1	no	—
119	C₄²	—	86	1	no	—
120	C₄²	—	86	1	no	—
121	C₂³	C₂×C₄×D₄₃	1	1	yes	characteristic
122	Q₈	—	86	8	no	—
123	C₂×C₄	—	2	1	no	—
124	C₂×C₄	—	2	1	no	—
125	C₂×C₄	—	2	1	no	—
126	C₂×C₄	—	4	1	no	—
127	C₂×C₄	—	4	1	no	—
128	C₂×C₄	—	43	1	no	—
129	C₂×C₄	—	43	1	no	—
130	C₂×C₄	—	43	2	no	—
131	C₂×C₄	—	43	2	no	—
132	C₂×C₄	—	86	2	no	—
133	C₂×C₄	—	86	1	no	—
134	C₂×C₄	—	86	1	no	—
135	C₂×C₄	—	86	1	no	—
136	C₂×C₄	—	86	1	no	—
137	C₂×C₄	—	86	1	no	—
138	C₂×C₄	—	172	1	no	—
139	C₂×C₄	#10621872	1	2	yes	—
140	C₂×C₄	D₄×D₄₃	1	2	yes	—
141	C₈	—	4	2	no	—
142	C₈	—	172	2	no	—
143	C₂²	—	2	1	no	—
144	C₂²	—	2	1	no	—
145	C₂²	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
146	C₂²	M₁₆×D₄₃	1	1	yes	characteristic
147	C₂²	C₂×#10621872	1	1	yes	characteristic
148	C₄	—	2	2	no	—
149	C₄	—	2	2	no	—
150	C₄	—	4	1	no	—
151	C₄	—	43	2	no	—
152	C₄	—	86	2	no	—
153	C₄	—	86	2	no	—
154	C₄	—	86	1	no	—
155	C₄	—	172	1	no	—
156	C₂	—	2	1	no	—
157	C₂	—	2	1	no	—
158	C₂	#14582861	1	1	yes	characteristic
159	C₂	#14582871	1	1	yes	characteristic
160	C₂	#101×D₄₃	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063290

C₂

yes

maximal, characteristic

#14582953

C₂

yes

maximal

#14582625

C₂

yes

maximal, characteristic

#14582624

C₂

yes

maximal

C₄₃×#324

C₂

yes

maximal, characteristic

C₂²×Dic₈₆

C₄

yes

characteristic

#13063290

—

#13063290

—

C₂×Dic₄₃⋊C₄

C₄

yes

characteristic

C₂×Dic₄₃⋊C₄

C₂²

yes

characteristic

C₂×C₄×Dic₄₃

C₄

yes

characteristic

C₂×C₄×Dic₄₃

C₄

yes

characteristic

C₂×C₄×Dic₄₃

C₂²

yes

characteristic

Dic₄₃⋊C₈

—

C₂²⋊(C₄₃⋊C₈)

C₂²

yes

—

#13063235

—

C₂×C₄⋊C₄×C₄₃

C₂²

yes

characteristic

C₂²⋊C₈×C₄₃

C₂²

yes

—

C₂²×C₄×C₄₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₄₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

C₂×C₄

yes

characteristic

C₂²×Dic₄₃

C₂×C₄

yes

characteristic

C₂²×Dic₄₃

C₂×C₄

yes

characteristic

C₂²×Dic₄₃

C₂×C₄

yes

characteristic

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×C₈×C₄₃

—

C₄⋊C₄×C₄₃

—

Dic₄₃⋊C₄

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

C₄×Dic₄₃

—

C₄×Dic₄₃

—

C₄×Dic₄₃

—

C₄×Dic₄₃

D₄

yes

—

C₄×Dic₄₃

D₄

yes

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

M₁₆

yes

—

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

C₂²⋊C₄

yes

characteristic

C₂×Dic₄₃

C₂²⋊C₄

yes

—

C₂×Dic₄₃

C₂²⋊C₄

yes

characteristic

C₂×Dic₄₃

M₁₆

yes

—

Dic₈₆

—

C₈×C₄₃

—

C₄₃⋊C₈

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₄₃

C₂×M₁₆

yes

characteristic

C₂²×C₄₃

C₂×M₁₆

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

Dic₄₃

—

Dic₄₃

—

Dic₄₃

—

Dic₄₃

—

Dic₄₃

#101

yes

—

#1467

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄×Q₈

—

—

—

—

D₄₃

yes

characteristic

C₄₃

#1467

yes

characteristic, complemented, Sylow

C₂²×Q₈

—

C₄×Q₈

—

C₄×Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₄₃

yes

characteristic

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₄⋊C₈

—

C₂²⋊C₈

—

C₂²⋊C₈

C₂×D₄₃

yes

—

#97

—

100

C₂×Q₈

—

101

C₂×Q₈

—

102

C₂×Q₈

—

103

C₂²×C₄

—

104

C₂²×C₄

—

105

C₂²×C₄

—

106

C₂²×C₄

—

107

C₂²×C₄

C₄×D₄₃

yes

characteristic

108

C₂²×C₄

C₄×D₄₃

yes

characteristic

109

C₂²×C₄

C₂²×D₄₃

yes

characteristic

110

C₂×C₈

—

111

C₂×C₈

—

112

C₄⋊C₄

—

113

C₄⋊C₄

—

114

C₄⋊C₄

—

115

C₄²

—

116

C₄²

—

117

C₄²

—

118

C₄²

—

119

C₄²

—

120

C₄²

—

121

C₂³

C₂×C₄×D₄₃

yes

characteristic

122

Q₈

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

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

—

172

—

139

C₂×C₄

#10621872

yes

—

140

C₂×C₄

D₄×D₄₃

yes

—

141

C₈

—

142

C₈

—

172

—

143

C₂²

—

144

C₂²

—

145

C₂²

C₂²⋊C₄×D₄₃

yes

characteristic

146

C₂²

M₁₆×D₄₃

yes

characteristic

147

C₂²

C₂×#10621872

yes

characteristic

148

C₄

—

149

C₄

—

150

C₄

—

151

C₄

—

152

C₄

—

153

C₄

—

154

C₄

—

155

C₄

—

172

—

156

C₂

—

157

C₂

—

158

C₂

#14582861

yes

characteristic

159

C₂

#14582871

yes

characteristic

160

C₂

#101×D₄₃

yes

characteristic

	subgroup	G/H
center	C₂²	C₂²⋊C₄×D₄₃
commutator	C₂³×C₄₃	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₄₃
Fitting	C₄₃×#324	C₂
socle	C₂²×C₄₃	C₂×C₂²⋊C₄
hypercenter	#324	D₄₃
hypocenter	C₄₃	#1467
LCS	G ▷ C₂³×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #324

subgroup

G/H

center

C₂²

C₂²⋊C₄×D₄₃

commutator

C₂³×C₄₃

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₄₃

Fitting

C₄₃×#324

C₂

socle

C₂²×C₄₃

C₂×C₂²⋊C₄

D₄₃

C₄₃

G ▷ C₂³×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #324

N	H ≅ G/N	type
86. C₄₃	#1467	semidirect

H ≅ G/N

type

86. C₄₃

#1467

semidirect

Subgroups — #19132937

Conjugacy classes of subgroups

Complements