Group #19136004 — subgroups

Subgroups — #19136004

Order 5504.

238 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 87 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×#13063248	C₂	1	2	yes	maximal
2	#14582805	C₂	1	1	yes	maximal, characteristic
3	#14582661	C₂	1	2	yes	maximal
4	#14582654	C₂	1	1	yes	maximal, characteristic
5	C₄₃×#384	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₈₆	C₂²	1	1	yes	characteristic
7	C₂²×C₄₃⋊C₈	C₂²	1	2	yes	—
8	C₂×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
9	#13063248	—	2	4	no	—
10	C₄₃⋊#95	—	2	1	no	—
11	C₄₃⋊#95	—	2	1	no	—
12	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
13	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
14	C₂×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
15	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
16	C₂²×C₄×C₄₃	—	2	2	no	—
17	C₂²×C₄×C₄₃	D₄	1	1	yes	characteristic
18	C₂²×C₄×C₄₃	D₄	1	1	yes	characteristic
19	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
20	C₂²×Dic₄₃	—	2	1	no	—
21	C₂²×Dic₄₃	—	2	1	no	—
22	C₂×Dic₈₆	—	2	2	no	—
23	C₂×Dic₈₆	—	2	2	no	—
24	C₂×Dic₈₆	—	2	1	no	—
25	C₂×Dic₈₆	D₄	1	2	yes	—
26	C₄⋊C₄×C₄₃	—	2	2	no	—
27	C₄⋊C₄×C₄₃	—	2	2	no	—
28	C₄⋊C₄×C₄₃	—	4	2	no	—
29	C₄⋊C₄×C₄₃	—	4	2	no	—
30	C₄²×C₄₃	—	2	2	no	—
31	C₄⋊Dic₄₃	—	2	2	no	—
32	C₂×C₄₃⋊C₈	—	2	2	no	—
33	C₂×C₄₃⋊C₈	—	2	2	no	—
34	C₂×C₄₃⋊C₈	—	2	2	no	—
35	C₂³×C₄₃	C₂×D₄	1	1	yes	characteristic
36	C₂×C₄×C₄₃	—	2	1	no	—
37	C₂×C₄×C₄₃	—	2	1	no	—
38	C₂×C₄×C₄₃	—	2	1	no	—
39	C₂×C₄×C₄₃	—	2	1	no	—
40	C₂×C₄×C₄₃	—	4	2	no	—
41	C₂×C₄×C₄₃	—	4	2	no	—
42	C₂×C₄×C₄₃	—	4	2	no	—
43	C₂×C₄×C₄₃	SD₁₆	1	2	yes	—
44	C₂×C₄×C₄₃	Q₁₆	1	2	yes	—
45	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
46	C₂×C₄×C₄₃	#41	1	2	yes	—
47	C₂×C₄×C₄₃	#41	1	1	yes	characteristic
48	C₂×C₄×C₄₃	#41	1	2	yes	—
49	C₂×Dic₄₃	—	2	2	no	—
50	C₂×Dic₄₃	—	4	1	no	—
51	C₂×Dic₄₃	—	4	1	no	—
52	C₂×Dic₄₃	—	4	1	no	—
53	C₂×Dic₄₃	—	4	1	no	—
54	C₂×Dic₄₃	—	4	1	no	—
55	Dic₈₆	—	2	4	no	—
56	Dic₈₆	—	4	2	no	—
57	C₄₃⋊C₈	—	4	2	no	—
58	C₂²×C₄₃	#121	1	1	yes	characteristic
59	C₂²×C₄₃	#123	1	1	yes	characteristic
60	C₂²×C₄₃	#124	1	1	yes	characteristic
61	C₂²×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
62	C₂²×C₄₃	C₂×Q₁₆	1	1	yes	characteristic
63	C₂²×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
64	C₂²×C₄₃	#137	1	1	yes	characteristic
65	C₄×C₄₃	—	2	2	no	—
66	C₄×C₄₃	—	2	2	no	—
67	C₄×C₄₃	—	8	2	no	—
68	C₄×C₄₃	#123	1	2	yes	—
69	C₄×C₄₃	#126	1	2	yes	—
70	Dic₄₃	—	4	2	no	—
71	Dic₄₃	—	8	1	no	—
72	#2072	—	43	1	no	maximal, Sylow
73	C₂×C₄₃	#397	1	1	yes	characteristic
74	C₂×C₄₃	#460	1	1	yes	characteristic
75	C₂×C₄₃	#462	1	1	yes	characteristic
76	C₂×C₄₃	#483	1	1	yes	characteristic
77	C₂×C₄₃	#484	1	1	yes	characteristic
78	C₂×C₄₃	#487	1	1	yes	characteristic
79	C₂×C₄₃	#489	1	1	yes	characteristic
80	C₂×#103	—	43	2	no	—
81	#391	—	43	1	no	—
82	#384	D₄₃	1	1	yes	characteristic
83	#340	—	43	2	no	—
84	#336	—	43	1	no	—
85	C₄₃	#2072	1	1	yes	characteristic, complemented, Sylow
86	C₂²×Q₈	—	43	1	no	—
87	C₂²×C₈	—	43	2	no	—
88	C₂×C₄⋊C₄	—	2	1	no	—
89	C₂×C₄⋊C₄	—	2	1	no	—
90	C₂×C₄⋊C₄	—	43	1	no	—
91	C₂×C₄⋊C₄	C₂×D₄₃	1	2	yes	—
92	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
93	#103	—	86	4	no	—
94	#95	—	86	1	no	—
95	#95	—	86	1	no	—
96	C₂×Q₈	—	43	2	no	—
97	C₂×Q₈	—	86	1	no	—
98	C₂×Q₈	—	86	2	no	—
99	C₂×Q₈	—	86	2	no	—
100	C₂²×C₄	—	2	2	no	—
101	C₂²×C₄	—	86	1	no	—
102	C₂²×C₄	—	86	1	no	—
103	C₂²×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
104	C₂²×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
105	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
106	C₂×C₈	—	86	2	no	—
107	C₂×C₈	—	86	2	no	—
108	C₂×C₈	—	86	2	no	—
109	C₄⋊C₄	—	2	2	no	—
110	C₄⋊C₄	—	2	2	no	—
111	C₄⋊C₄	—	4	2	no	—
112	C₄⋊C₄	—	4	2	no	—
113	C₄⋊C₄	—	86	2	no	—
114	C₄²	—	2	2	no	—
115	C₂³	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
116	Q₈	—	86	4	no	—
117	Q₈	—	172	2	no	—
118	C₂×C₄	—	2	1	no	—
119	C₂×C₄	—	2	1	no	—
120	C₂×C₄	—	2	1	no	—
121	C₂×C₄	—	2	1	no	—
122	C₂×C₄	—	4	2	no	—
123	C₂×C₄	—	4	2	no	—
124	C₂×C₄	—	4	2	no	—
125	C₂×C₄	—	86	2	no	—
126	C₂×C₄	—	172	1	no	—
127	C₂×C₄	—	172	1	no	—
128	C₂×C₄	—	172	1	no	—
129	C₂×C₄	—	172	1	no	—
130	C₂×C₄	—	172	1	no	—
131	C₂×C₄	#10621883	1	2	yes	—
132	C₂×C₄	#10621885	1	2	yes	—
133	C₂×C₄	#10621898	1	2	yes	—
134	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
135	C₂×C₄	#10621900	1	1	yes	characteristic
136	C₂×C₄	#10621902	1	2	yes	—
137	C₈	—	172	2	no	—
138	C₂²	#13063296	1	1	yes	characteristic
139	C₂²	#13063308	1	1	yes	characteristic
140	C₂²	#13063314	1	1	yes	characteristic
141	C₂²	C₂×#10621883	1	1	yes	characteristic
142	C₂²	C₂×#10621885	1	1	yes	characteristic
143	C₂²	#13063351	1	1	yes	characteristic
144	C₂²	#13063356	1	1	yes	characteristic
145	C₄	—	2	2	no	—
146	C₄	—	2	2	no	—
147	C₄	—	8	2	no	—
148	C₄	—	344	1	no	—
149	C₄	—	172	2	no	—
150	C₄	#13063310	1	2	yes	—
151	C₄	#13063320	1	2	yes	—
152	C₂	#14582825	1	1	yes	characteristic
153	C₂	#14583096	1	1	yes	characteristic
154	C₂	#14583106	1	1	yes	characteristic
155	C₂	#14583229	1	1	yes	characteristic
156	C₂	#14583234	1	1	yes	characteristic
157	C₂	#14583251	1	1	yes	characteristic
158	C₂	#14583261	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063248

C₂

yes

maximal

#14582805

C₂

yes

maximal, characteristic

#14582661

C₂

yes

maximal

#14582654

C₂

yes

maximal, characteristic

C₄₃×#384

C₂

yes

maximal, characteristic

C₂²×Dic₈₆

C₂²

yes

characteristic

C₂²×C₄₃⋊C₈

C₂²

yes

—

C₂×C₄⋊Dic₄₃

C₂²

yes

characteristic

#13063248

—

C₄₃⋊#95

—

C₄₃⋊#95

—

C₂×C₄⋊C₄×C₄₃

—

C₂×C₄⋊C₄×C₄₃

—

C₂×C₄⋊C₄×C₄₃

C₂²

yes

—

C₂×C₄²×C₄₃

C₂²

yes

characteristic

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

D₄

yes

characteristic

C₂²×C₄×C₄₃

D₄

yes

characteristic

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

—

C₂²×Dic₄₃

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

D₄

yes

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄²×C₄₃

—

C₄⋊Dic₄₃

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

SD₁₆

yes

—

C₂×C₄×C₄₃

Q₁₆

yes

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

#41

yes

—

C₂×C₄×C₄₃

#41

yes

characteristic

C₂×C₄×C₄₃

#41

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

Dic₈₆

—

Dic₈₆

—

C₄₃⋊C₈

—

C₂²×C₄₃

yes

C₂²×C₄₃

yes

C₂²×C₄₃

yes

C₂²×C₄₃

C₂×SD₁₆

yes

characteristic

C₂²×C₄₃

C₂×Q₁₆

yes

C₂²×C₄₃

yes

C₂²×C₄₃

yes

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

#123

yes

—

C₄×C₄₃

#126

yes

—

Dic₄₃

—

Dic₄₃

—

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

—

—

D₄₃

yes

characteristic

#340

—

#336

—

C₄₃

#2072

yes

characteristic, complemented, Sylow

C₂²×Q₈

—

C₂²×C₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₄₃

yes

—

C₂×C₄²

C₂×D₄₃

yes

—

—

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

100

C₂²×C₄

—

101

C₂²×C₄

—

102

C₂²×C₄

—

103

C₂²×C₄

C₂²⋊D₄₃

yes

characteristic

104

C₂²×C₄

C₂²⋊D₄₃

yes

characteristic

105

C₂²×C₄

C₂²×D₄₃

yes

characteristic

106

C₂×C₈

—

107

C₂×C₈

—

108

C₂×C₈

—

109

C₄⋊C₄

—

110

C₄⋊C₄

—

111

C₄⋊C₄

—

112

C₄⋊C₄

—

113

C₄⋊C₄

—

114

C₄²

—

115

C₂³

C₂×C₂²⋊D₄₃

yes

characteristic

116

Q₈

—

117

Q₈

—

172

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

172

—

127

C₂×C₄

—

172

—

128

C₂×C₄

—

172

—

129

C₂×C₄

—

172

—

130

C₂×C₄

—

172

—

131

C₂×C₄

#10621883

yes

—

132

C₂×C₄

#10621885

yes

—

133

C₂×C₄

#10621898

yes

—

134

C₂×C₄

D₄×D₄₃

yes

characteristic

135

C₂×C₄

#10621900

yes

characteristic

136

C₂×C₄

#10621902

yes

—

137

C₈

—

172

—

138

C₂²

#13063296

yes

characteristic

139

C₂²

#13063308

yes

characteristic

140

C₂²

#13063314

yes

characteristic

141

C₂²

C₂×#10621883

yes

characteristic

142

C₂²

C₂×#10621885

yes

characteristic

143

C₂²

#13063351

yes

characteristic

144

C₂²

#13063356

yes

characteristic

145

C₄

—

146

C₄

—

147

C₄

—

148

C₄

—

344

—

149

C₄

—

172

—

150

C₄

#13063310

yes

—

151

C₄

#13063320

yes

—

152

C₂

#14582825

yes

characteristic

153

C₂

#14583096

yes

characteristic

154

C₂

#14583106

yes

characteristic

155

C₂

#14583229

yes

characteristic

156

C₂

#14583234

yes

characteristic

157

C₂

#14583251

yes

characteristic

158

C₂

#14583261

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₄₃
commutator	C₂²×C₄×C₄₃	C₂³
Frattini	C₂²×C₄	C₂²×D₄₃
Fitting	C₄₃×#384	C₂
socle	C₂³×C₄₃	C₂×D₄
hypercenter	#384	D₄₃
hypocenter	C₄₃	#2072
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #384

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₄₃

commutator

C₂²×C₄×C₄₃

C₂³

Frattini

C₂²×C₄

C₂²×D₄₃

Fitting

C₄₃×#384

C₂

socle

C₂³×C₄₃

C₂×D₄

D₄₃

C₄₃

G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #384

N	H ≅ G/N	type
85. C₄₃	#2072	semidirect

H ≅ G/N

type

85. C₄₃

#2072

semidirect

Subgroups — #19136004

Conjugacy classes of subgroups

Complements