Group #24983640 — subgroups

Subgroups — #24983640

Order 11008.

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

normal subgroups only

This group has 196 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	#19134733	C₂	1	1	yes	maximal, characteristic
2	#19133351	C₂	1	1	yes	maximal, characteristic
3	C₄₃×#2162	C₂	1	1	yes	maximal, characteristic
4	#14582923	—	2	1	no	—
5	#14582923	—	2	1	no	—
6	#14582664	—	2	1	no	—
7	#14582664	C₄	1	2	yes	—
8	#14582650	—	2	1	no	—
9	#14582650	C₄	1	2	yes	—
10	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
11	C₄₃×C₄⋊C₁₆	—	2	1	no	—
12	C₄₃×C₂²⋊C₁₆	—	2	1	no	—
13	C₄×C₁₆×C₄₃	C₄	1	2	yes	—
14	C₂×#10621877	—	2	2	no	—
15	C₂×#10621877	—	4	1	no	—
16	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
17	C₄⋊(C₄₃⋊C₈)	—	4	1	no	—
18	C₄⋊(C₄₃⋊C₈)	—	4	1	no	—
19	C₄⋊(C₄₃⋊C₈)	—	4	1	no	—
20	C₂²×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
21	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
22	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
23	C₂×C₁₆×C₄₃	—	2	2	no	—
24	C₄×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
25	C₄×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
26	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
27	C₄×C₈×C₄₃	Q₈	1	1	yes	characteristic
28	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
29	C₂²×C₄×C₄₃	SD₁₆	1	1	yes	characteristic
30	C₂²×C₄×C₄₃	Q₁₆	1	1	yes	characteristic
31	C₂×C₈×C₄₃	—	4	1	no	—
32	C₂×C₈×C₄₃	—	4	1	no	—
33	C₂×C₈×C₄₃	C₄²	1	1	yes	characteristic
34	C₂×C₈×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
35	C₂×C₈×C₄₃	C₄⋊C₄	1	1	yes	characteristic
36	C₂×C₈×C₄₃	C₄⋊C₄	1	1	yes	characteristic
37	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
38	C₄²×C₄₃	C₄⋊C₄	1	1	yes	characteristic
39	C₄²×C₄₃	D₈	1	1	yes	characteristic
40	C₄²×C₄₃	SD₁₆	1	1	yes	characteristic
41	#10621877	—	4	2	no	—
42	#10621877	—	4	2	no	—
43	#10621877	—	8	2	no	—
44	C₂×C₄₃⋊C₈	—	4	2	no	—
45	C₂×C₄₃⋊C₈	—	4	2	no	—
46	C₁₆×C₄₃	—	4	2	no	—
47	C₂³×C₄₃	#103	1	1	yes	characteristic
48	C₂×C₄×C₄₃	—	2	1	no	—
49	C₂×C₄×C₄₃	—	2	1	no	—
50	C₂×C₄×C₄₃	—	2	2	no	—
51	C₂×C₄×C₄₃	—	2	2	no	—
52	C₂×C₄×C₄₃	#95	1	1	yes	characteristic
53	C₂×C₄×C₄₃	#102	1	1	yes	characteristic
54	C₂×C₄×C₄₃	#102	1	1	yes	characteristic
55	C₂×C₄×C₄₃	#103	1	1	yes	characteristic
56	C₂×C₄×C₄₃	#106	1	1	yes	characteristic
57	C₂×C₄×C₄₃	#107	1	1	yes	characteristic
58	C₈×C₄₃	—	2	1	no	—
59	C₈×C₄₃	—	2	1	no	—
60	C₈×C₄₃	—	2	1	no	—
61	C₈×C₄₃	—	2	1	no	—
62	C₄₃⋊C₈	—	8	2	no	—
63	C₄₃⋊C₈	—	8	2	no	—
64	#7219	—	43	1	no	maximal, Sylow
65	C₂²×C₄₃	—	2	1	no	—
66	C₂²×C₄₃	—	2	1	no	—
67	C₂²×C₄₃	—	2	1	no	—
68	C₂²×C₄₃	#340	1	1	yes	characteristic
69	C₄×C₄₃	—	2	1	no	—
70	C₄×C₄₃	—	2	1	no	—
71	C₄×C₄₃	—	2	1	no	—
72	C₄×C₄₃	H(3,ℤ/4)	1	1	yes	characteristic
73	C₄×C₄₃	#344	1	1	yes	characteristic
74	C₄×C₄₃	#365	1	2	yes	—
75	C₄×C₄₃	#368	1	2	yes	—
76	#2162	D₄₃	1	1	yes	characteristic
77	#1837	—	43	1	no	—
78	#1566	—	43	1	no	—
79	C₂×C₄₃	—	4	1	no	—
80	C₂×C₄₃	#1286	1	1	yes	characteristic
81	C₂×C₄₃	#1381	1	1	yes	characteristic
82	C₂×C₄₃	#1383	1	1	yes	characteristic
83	#423	—	86	1	no	—
84	#423	—	86	1	no	—
85	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
86	C₄⋊C₁₆	—	2	1	no	—
87	C₂²⋊C₁₆	—	2	1	no	—
88	C₄×C₁₆	Dic₄₃	1	2	yes	—
89	#341	—	43	2	no	—
90	#341	—	86	1	no	—
91	#334	—	43	2	no	—
92	#334	—	86	1	no	—
93	C₄₃	#7219	1	1	yes	characteristic, complemented, Sylow
94	C₂×M₁₆	—	86	2	no	—
95	C₂×M₁₆	—	172	1	no	—
96	C₂²×C₈	C₄×D₄₃	1	1	yes	characteristic
97	C₂²×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
98	C₂×C₄²	D₁₇₂	1	1	yes	characteristic
99	C₂×C₁₆	—	2	2	no	—
100	C₄⋊C₈	—	86	2	no	—
101	C₄⋊C₈	—	172	1	no	—
102	C₄⋊C₈	—	172	1	no	—
103	C₄⋊C₈	—	172	1	no	—
104	C₄×C₈	Dic₈₆	1	1	yes	characteristic
105	C₄×C₈	C₄×D₄₃	1	1	yes	characteristic
106	C₄×C₈	C₂×Dic₄₃	1	1	yes	characteristic
107	C₄×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
108	C₂²×C₄	#10621873	1	1	yes	characteristic
109	C₂²×C₄	Dic₁₇₂	1	1	yes	characteristic
110	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
111	M₁₆	—	344	2	no	—
112	M₁₆	—	172	2	no	—
113	M₁₆	—	172	2	no	—
114	C₂×C₈	—	4	1	no	—
115	C₂×C₈	—	4	1	no	—
116	C₂×C₈	—	172	2	no	—
117	C₂×C₈	—	172	2	no	—
118	C₂×C₈	C₄×Dic₄₃	1	1	yes	characteristic
119	C₂×C₈	Dic₄₃⋊C₄	1	1	yes	characteristic
120	C₂×C₈	Dic₄₃⋊C₄	1	1	yes	characteristic
121	C₂×C₈	C₂²⋊Dic₄₃	1	1	yes	characteristic
122	C₄²	#10621873	1	1	yes	characteristic
123	C₄²	D₃₄₄	1	1	yes	characteristic
124	C₄²	C₄⋊Dic₄₃	1	1	yes	characteristic
125	C₄²	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
126	C₁₆	—	4	2	no	—
127	C₂³	#13063250	1	1	yes	characteristic
128	C₂×C₄	—	2	1	no	—
129	C₂×C₄	—	2	1	no	—
130	C₂×C₄	—	2	2	no	—
131	C₂×C₄	—	2	2	no	—
132	C₂×C₄	C₄₃⋊#95	1	1	yes	characteristic
133	C₂×C₄	#13063247	1	1	yes	characteristic
134	C₂×C₄	#13063247	1	1	yes	characteristic
135	C₂×C₄	#13063250	1	1	yes	characteristic
136	C₂×C₄	#13063257	1	1	yes	characteristic
137	C₂×C₄	#13063259	1	1	yes	characteristic
138	C₈	—	2	1	no	—
139	C₈	—	2	1	no	—
140	C₈	—	2	1	no	—
141	C₈	—	2	1	no	—
142	C₈	—	344	2	no	—
143	C₈	—	344	2	no	—
144	C₂²	—	2	1	no	—
145	C₂²	—	2	1	no	—
146	C₂²	—	2	1	no	—
147	C₂²	#14582662	1	1	yes	characteristic
148	C₄	—	2	1	no	—
149	C₄	—	2	1	no	—
150	C₄	—	2	1	no	—
151	C₄	#14582655	1	1	yes	characteristic
152	C₄	#14582670	1	1	yes	characteristic
153	C₄	#14582722	1	2	yes	—
154	C₄	#14582729	1	2	yes	—
155	C₂	—	4	1	no	—
156	C₂	#19132454	1	1	yes	characteristic
157	C₂	#19132689	1	1	yes	characteristic
158	C₂	#19132694	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19134733

C₂

yes

maximal, characteristic

#19133351

C₂

yes

maximal, characteristic

C₄₃×#2162

C₂

yes

maximal, characteristic

—

—

—

C₄

yes

—

#14582650

—

#14582650

C₄

yes

—

C₂×C₄×C₈×C₄₃

C₂²

yes

characteristic

C₄₃×C₄⋊C₁₆

—

C₄₃×C₂²⋊C₁₆

—

C₄×C₁₆×C₄₃

C₄

yes

—

C₂×#10621877

—

C₂×#10621877

—

C₄⋊(C₄₃⋊C₈)

—

C₄⋊(C₄₃⋊C₈)

—

C₄⋊(C₄₃⋊C₈)

—

C₄⋊(C₄₃⋊C₈)

—

C₂²×C₈×C₄₃

C₂×C₄

yes

characteristic

C₂²×C₈×C₄₃

D₄

yes

characteristic

C₂×C₄²×C₄₃

D₄

yes

characteristic

C₂×C₁₆×C₄₃

—

C₄×C₈×C₄₃

C₂×C₄

yes

characteristic

C₄×C₈×C₄₃

C₂×C₄

yes

characteristic

C₄×C₈×C₄₃

D₄

yes

characteristic

C₄×C₈×C₄₃

Q₈

yes

characteristic

C₂²×C₄×C₄₃

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₄₃

SD₁₆

yes

characteristic

C₂²×C₄×C₄₃

Q₁₆

yes

characteristic

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

C₄²

yes

characteristic

C₂×C₈×C₄₃

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₄₃

C₄⋊C₄

yes

characteristic

C₂×C₈×C₄₃

C₄⋊C₄

yes

characteristic

C₄²×C₄₃

C₂²⋊C₄

yes

characteristic

C₄²×C₄₃

C₄⋊C₄

yes

characteristic

C₄²×C₄₃

D₈

yes

characteristic

C₄²×C₄₃

SD₁₆

yes

—

—

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₁₆×C₄₃

—

C₂³×C₄₃

#103

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₈×C₄₃

—

C₈×C₄₃

—

C₈×C₄₃

—

C₈×C₄₃

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

#7219

—

maximal, Sylow

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

#340

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

yes

C₄×C₄₃

yes

C₄×C₄₃

yes

—

C₄×C₄₃

#368

yes

—

#2162

D₄₃

yes

characteristic

#1837

—

#1566

—

C₂×C₄₃

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

—

—

C₂×C₄×C₈

C₂×D₄₃

yes

characteristic

C₄⋊C₁₆

—

C₂²⋊C₁₆

—

C₄×C₁₆

Dic₄₃

yes

—

—

—

—

—

C₄₃

#7219

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂×M₁₆

—

172

—

C₂²×C₈

C₄×D₄₃

yes

characteristic

C₂²×C₈

C₂²⋊D₄₃

yes

characteristic

C₂×C₄²

D₁₇₂

yes

characteristic

C₂×C₁₆

—

100

C₄⋊C₈

—

101

C₄⋊C₈

—

172

—

102

C₄⋊C₈

—

172

—

103

C₄⋊C₈

—

172

—

104

C₄×C₈

Dic₈₆

yes

characteristic

105

C₄×C₈

C₄×D₄₃

yes

characteristic

106

C₄×C₈

C₂×Dic₄₃

yes

characteristic

107

C₄×C₈

C₂²⋊D₄₃

yes

characteristic

108

C₂²×C₄

#10621873

yes

characteristic

109

C₂²×C₄

Dic₁₇₂

yes

characteristic

110

C₂²×C₄

(C₂×D₄₃)⋊C₄

yes

characteristic

111

M₁₆

—

344

—

112

M₁₆

—

172

—

113

M₁₆

—

172

—

114

C₂×C₈

—

115

C₂×C₈

—

116

C₂×C₈

—

172

—

117

C₂×C₈

—

172

—

118

C₂×C₈

C₄×Dic₄₃

yes

characteristic

119

C₂×C₈

Dic₄₃⋊C₄

yes

characteristic

120

C₂×C₈

Dic₄₃⋊C₄

yes

characteristic

121

C₂×C₈

C₂²⋊Dic₄₃

yes

characteristic

122

C₄²

#10621873

yes

characteristic

123

C₄²

D₃₄₄

yes

characteristic

124

C₄²

C₄⋊Dic₄₃

yes

characteristic

125

C₄²

(C₂×D₄₃)⋊C₄

yes

characteristic

126

C₁₆

—

127

C₂³

#13063250

yes

characteristic

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

C₄₃⋊#95

yes

characteristic

133

C₂×C₄

#13063247

yes

characteristic

134

C₂×C₄

#13063247

yes

characteristic

135

C₂×C₄

#13063250

yes

characteristic

136

C₂×C₄

#13063257

yes

characteristic

137

C₂×C₄

#13063259

yes

characteristic

138

C₈

—

139

C₈

—

140

C₈

—

141

C₈

—

142

C₈

—

344

—

143

C₈

—

344

—

144

C₂²

—

145

C₂²

—

146

C₂²

—

147

C₂²

#14582662

yes

characteristic

148

C₄

—

149

C₄

—

150

C₄

—

151

C₄

#14582655

yes

characteristic

152

C₄

#14582670

yes

characteristic

153

C₄

#14582722

yes

—

154

C₄

#14582729

yes

—

155

C₂

—

156

C₂

#19132454

yes

characteristic

157

C₂

#19132689

yes

characteristic

158

C₂

#19132694

yes

characteristic

	subgroup	G/H
center	C₂²	#14582662
commutator	C₂×C₈×C₄₃	C₄²
Frattini	C₂×C₄×C₈	C₂×D₄₃
Fitting	C₄₃×#2162	C₂
socle	C₂²×C₄₃	#340
prime radical	C₂³×C₄₃	#103
cosocle	C₂×C₄×C₈×C₄₃	C₂²
hypercenter	#2162	D₄₃
hypocenter	C₄₃	#7219
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ #2162

subgroup

G/H

center

C₂²

#14582662

commutator

C₂×C₈×C₄₃

C₄²

Frattini

C₂×C₄×C₈

C₂×D₄₃

Fitting

C₄₃×#2162

C₂

C₂²×C₄₃

C₂³×C₄₃

C₂×C₄×C₈×C₄₃

C₂²

D₄₃

C₄₃

G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ #2162

N	H ≅ G/N	type
93. C₄₃	#7219	semidirect

H ≅ G/N

type

93. C₄₃

#7219

semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#19134733	2
#19133351	2
C₄₃×#2162	2
#7219	43

subgroup

index

#19134733

#19133351

C₄₃×#2162

#7219

Subgroups — #24983640

Conjugacy classes of subgroups

Complements

Maximal subgroups