Group #24983980 — subgroups

Subgroups — #24983980

Order 11008.

268 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 268 conjugacy classes of subgroups — too many to draw. Only its 47 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	#19132541	C₂	1	2	yes	maximal, complemented
2	C₄₃×#1957	C₂	1	1	yes	maximal, characteristic
3	#14582625	—	2	2	no	—
4	C₂×#127×C₄₃	C₄	1	1	yes	characteristic
5	C₂×#102×C₄₃	—	2	2	no	—
6	C₂×C₄×C₈×C₄₃	C₄	1	1	yes	characteristic
7	C₄₃×#384	C₂²	1	1	yes	characteristic
8	C₂²⋊(C₄₃⋊C₈)	—	4	2	no	—
9	C₂²×D₄×C₄₃	—	2	1	no	—
10	C₂²×D₄×C₄₃	—	4	1	no	—
11	C₂²×C₈×C₄₃	—	2	1	no	—
12	#127×C₄₃	—	2	1	no	—
13	#127×C₄₃	—	4	1	no	—
14	#127×C₄₃	C₈	1	2	yes	complemented
15	C₂×C₄⋊C₄×C₄₃	—	4	1	no	—
16	C₂×C₄⋊C₄×C₄₃	D₄	1	2	yes	—
17	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
18	#102×C₄₃	—	4	4	no	—
19	C₄×C₈×C₄₃	—	4	1	no	—
20	C₂⁴×C₄₃	—	4	1	no	—
21	C₂×D₄×C₄₃	—	2	2	no	—
22	C₂×D₄×C₄₃	—	4	2	no	—
23	C₂×D₄×C₄₃	—	4	1	no	—
24	C₂×D₄×C₄₃	—	4	2	no	—
25	C₂×D₄×C₄₃	—	4	2	no	—
26	C₂×D₄×C₄₃	—	4	2	no	—
27	C₂×D₄×C₄₃	—	8	2	no	—
28	C₂×D₄×C₄₃	—	8	2	no	—
29	C₂²×C₄×C₄₃	—	2	1	no	—
30	C₂²×C₄×C₄₃	—	2	2	no	—
31	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
32	C₂×C₈×C₄₃	—	2	2	no	—
33	C₂×C₈×C₄₃	—	4	1	no	—
34	C₂×C₈×C₄₃	—	4	1	no	—
35	C₄⋊C₄×C₄₃	—	4	2	no	—
36	C₄⋊C₄×C₄₃	—	8	2	no	—
37	C₄²×C₄₃	—	2	1	no	—
38	C₄²×C₄₃	C₂×C₈	1	1	yes	characteristic
39	C₄²×C₄₃	M₁₆	1	1	yes	characteristic
40	C₂×C₄₃⋊C₈	—	8	2	no	—
41	C₂³×C₄₃	—	4	2	no	—
42	C₂³×C₄₃	—	8	2	no	—
43	C₂³×C₄₃	—	8	2	no	—
44	C₂³×C₄₃	—	8	1	no	—
45	C₂³×C₄₃	—	8	1	no	—
46	C₂³×C₄₃	#99	1	1	yes	characteristic
47	D₄×C₄₃	—	4	4	no	—
48	D₄×C₄₃	—	8	2	no	—
49	D₄×C₄₃	—	8	4	no	—
50	D₄×C₄₃	—	8	4	no	—
51	C₂×C₄×C₄₃	—	2	2	no	—
52	C₂×C₄×C₄₃	—	2	2	no	—
53	C₂×C₄×C₄₃	—	2	1	no	—
54	C₂×C₄×C₄₃	—	2	1	no	—
55	C₂×C₄×C₄₃	—	2	1	no	—
56	C₂×C₄×C₄₃	—	2	1	no	—
57	C₂×C₄×C₄₃	—	4	2	no	—
58	C₂×C₄×C₄₃	—	8	2	no	—
59	C₂×C₄×C₄₃	C₂²⋊C₈	1	1	yes	characteristic
60	C₂×C₄×C₄₃	#100	1	1	yes	characteristic
61	C₈×C₄₃	—	4	2	no	—
62	C₄₃⋊C₈	—	16	2	no	—
63	#7354	—	43	1	no	maximal, Sylow
64	C₂²×C₄₃	—	2	1	no	—
65	C₂²×C₄₃	—	2	1	no	—
66	C₂²×C₄₃	—	8	4	no	—
67	C₂²×C₄₃	—	8	2	no	—
68	C₂²×C₄₃	—	16	2	no	—
69	C₂²×C₄₃	—	16	1	no	—
70	C₂²×C₄₃	—	16	1	no	—
71	C₂²×C₄₃	#323	1	1	yes	characteristic
72	C₂²×C₄₃	#353	1	1	yes	characteristic
73	C₂²×C₄₃	#355	1	1	yes	characteristic
74	C₄×C₄₃	—	2	2	no	—
75	C₄×C₄₃	—	2	2	no	—
76	C₄×C₄₃	—	2	1	no	—
77	C₄×C₄₃	—	2	1	no	—
78	C₄×C₄₃	—	8	2	no	—
79	#1957	D₄₃	1	1	yes	characteristic
80	#1325	—	43	2	no	—
81	C₂×C₄₃	—	2	1	no	—
82	C₂×C₄₃	—	2	1	no	—
83	C₂×C₄₃	—	16	2	no	—
84	C₂×C₄₃	#1318	1	1	yes	characteristic
85	C₂×C₄₃	#1408	1	1	yes	characteristic
86	C₂×C₄₃	#1410	1	1	yes	characteristic
87	C₂×#127	Dic₄₃	1	1	yes	characteristic
88	C₂×#102	—	2	2	no	—
89	C₂×C₄×C₈	Dic₄₃	1	1	yes	characteristic
90	#384	C₂×D₄₃	1	1	yes	characteristic
91	#324	—	86	2	no	—
92	C₄₃	#7354	1	1	yes	characteristic, complemented, Sylow
93	C₂²×D₄	—	2	1	no	—
94	C₂²×D₄	—	4	1	no	—
95	C₂²×C₈	—	2	1	no	—
96	#127	—	2	1	no	—
97	#127	—	4	1	no	—
98	#127	C₄₃⋊C₈	1	2	yes	complemented
99	C₂×C₄⋊C₄	—	4	1	no	—
100	C₂×C₄⋊C₄	C₂²⋊D₄₃	1	2	yes	—
101	C₂×C₄²	C₂×Dic₄₃	1	1	yes	characteristic
102	#102	—	4	4	no	—
103	C₂²⋊C₈	—	172	2	no	—
104	C₄×C₈	—	4	1	no	—
105	C₂⁴	—	4	1	no	—
106	C₂×D₄	—	2	2	no	—
107	C₂×D₄	—	4	2	no	—
108	C₂×D₄	—	4	2	no	—
109	C₂×D₄	—	4	2	no	—
110	C₂×D₄	—	4	2	no	—
111	C₂×D₄	—	4	1	no	—
112	C₂×D₄	—	8	2	no	—
113	C₂×D₄	—	8	2	no	—
114	C₂²×C₄	—	2	1	no	—
115	C₂²×C₄	—	2	2	no	—
116	C₂²×C₄	C₂²⋊Dic₄₃	1	1	yes	characteristic
117	C₂×C₈	—	2	2	no	—
118	C₂×C₈	—	4	1	no	—
119	C₂×C₈	—	4	1	no	—
120	C₂×C₈	—	344	2	no	—
121	C₄⋊C₄	—	4	2	no	—
122	C₄⋊C₄	—	8	2	no	—
123	C₄²	—	2	1	no	—
124	C₄²	C₂×C₄₃⋊C₈	1	1	yes	characteristic
125	C₄²	#10621877	1	1	yes	characteristic
126	C₂³	—	4	2	no	—
127	C₂³	—	8	2	no	—
128	C₂³	—	8	2	no	—
129	C₂³	—	8	1	no	—
130	C₂³	—	8	1	no	—
131	C₂³	#13063240	1	1	yes	characteristic
132	D₄	—	4	4	no	—
133	D₄	—	8	2	no	—
134	D₄	—	8	4	no	—
135	D₄	—	8	4	no	—
136	C₂×C₄	—	2	2	no	—
137	C₂×C₄	—	2	2	no	—
138	C₂×C₄	—	2	1	no	—
139	C₂×C₄	—	2	1	no	—
140	C₂×C₄	—	2	1	no	—
141	C₂×C₄	—	2	1	no	—
142	C₂×C₄	—	4	2	no	—
143	C₂×C₄	—	8	2	no	—
144	C₂×C₄	C₂²⋊(C₄₃⋊C₈)	1	1	yes	characteristic
145	C₂×C₄	#13063242	1	1	yes	characteristic
146	C₈	—	4	2	no	—
147	C₈	—	688	2	no	—
148	C₂²	—	2	1	no	—
149	C₂²	—	2	1	no	—
150	C₂²	—	8	4	no	—
151	C₂²	—	8	2	no	—
152	C₂²	—	16	2	no	—
153	C₂²	—	16	1	no	—
154	C₂²	—	16	1	no	—
155	C₂²	#14582623	1	1	yes	characteristic
156	C₂²	#14582692	1	1	yes	characteristic
157	C₂²	#14582696	1	1	yes	characteristic
158	C₄	—	2	2	no	—
159	C₄	—	2	2	no	—
160	C₄	—	2	1	no	—
161	C₄	—	2	1	no	—
162	C₄	—	8	2	no	—
163	C₂	—	2	1	no	—
164	C₂	—	2	1	no	—
165	C₂	—	16	2	no	—
166	C₂	#19132527	1	1	yes	characteristic
167	C₂	#19132758	1	1	yes	characteristic
168	C₂	#19132762	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19132541

C₂

yes

maximal, complemented

C₄₃×#1957

C₂

yes

maximal, characteristic

#14582625

—

C₂×#127×C₄₃

C₄

yes

characteristic

C₂×#102×C₄₃

—

C₂×C₄×C₈×C₄₃

C₄

yes

characteristic

C₄₃×#384

C₂²

yes

characteristic

C₂²⋊(C₄₃⋊C₈)

—

C₂²×D₄×C₄₃

—

C₂²×D₄×C₄₃

—

C₂²×C₈×C₄₃

—

#127×C₄₃

—

#127×C₄₃

—

#127×C₄₃

C₈

yes

complemented

C₂×C₄⋊C₄×C₄₃

—

C₂×C₄⋊C₄×C₄₃

D₄

yes

—

C₂×C₄²×C₄₃

C₂×C₄

yes

characteristic

#102×C₄₃

—

C₄×C₈×C₄₃

—

C₂⁴×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

C₂×C₈

yes

characteristic

C₄²×C₄₃

M₁₆

yes

characteristic

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

#99

yes

characteristic

D₄×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²⋊C₈

yes

characteristic

C₂×C₄×C₄₃

#100

yes

characteristic

C₈×C₄₃

—

C₄₃⋊C₈

—

#7354

—

maximal, Sylow

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

yes

C₂²×C₄₃

yes

C₂²×C₄₃

yes

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

#1957

D₄₃

yes

characteristic

#1325

—

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

Dic₄₃

yes

characteristic

C₂×#102

—

C₂×C₄×C₈

Dic₄₃

yes

characteristic

#384

C₂×D₄₃

yes

characteristic

#324

—

C₄₃

#7354

yes

characteristic, complemented, Sylow

C₂²×D₄

—

C₂²×D₄

—

C₂²×C₈

—

#127

—

#127

—

#127

C₄₃⋊C₈

yes

complemented

C₂×C₄⋊C₄

—

100

C₂×C₄⋊C₄

C₂²⋊D₄₃

yes

—

101

C₂×C₄²

C₂×Dic₄₃

yes

characteristic

102

#102

—

103

C₂²⋊C₈

—

172

—

104

C₄×C₈

—

105

C₂⁴

—

106

C₂×D₄

—

107

C₂×D₄

—

108

C₂×D₄

—

109

C₂×D₄

—

110

C₂×D₄

—

111

C₂×D₄

—

112

C₂×D₄

—

113

C₂×D₄

—

114

C₂²×C₄

—

115

C₂²×C₄

—

116

C₂²×C₄

C₂²⋊Dic₄₃

yes

characteristic

117

C₂×C₈

—

118

C₂×C₈

—

119

C₂×C₈

—

120

C₂×C₈

—

344

—

121

C₄⋊C₄

—

122

C₄⋊C₄

—

123

C₄²

—

124

C₄²

C₂×C₄₃⋊C₈

yes

characteristic

125

C₄²

#10621877

yes

characteristic

126

C₂³

—

127

C₂³

—

128

C₂³

—

129

C₂³

—

130

C₂³

—

131

C₂³

#13063240

yes

characteristic

132

D₄

—

133

D₄

—

134

D₄

—

135

D₄

—

136

C₂×C₄

—

137

C₂×C₄

—

138

C₂×C₄

—

139

C₂×C₄

—

140

C₂×C₄

—

141

C₂×C₄

—

142

C₂×C₄

—

143

C₂×C₄

—

144

C₂×C₄

C₂²⋊(C₄₃⋊C₈)

yes

characteristic

145

C₂×C₄

#13063242

yes

characteristic

146

C₈

—

147

C₈

—

688

—

148

C₂²

—

149

C₂²

—

150

C₂²

—

151

C₂²

—

152

C₂²

—

153

C₂²

—

154

C₂²

—

155

C₂²

#14582623

yes

characteristic

156

C₂²

#14582692

yes

characteristic

157

C₂²

#14582696

yes

characteristic

158

C₄

—

159

C₄

—

160

C₄

—

161

C₄

—

162

C₄

—

163

C₂

—

164

C₂

—

165

C₂

—

166

C₂

#19132527

yes

characteristic

167

C₂

#19132758

yes

characteristic

168

C₂

#19132762

yes

characteristic

	subgroup	G/H
center	C₂²	#14582692
commutator	C₄²×C₄₃	C₂×C₈
Frattini	#384	C₂×D₄₃
Fitting	C₄₃×#1957	C₂
socle	C₂²×C₄₃	#353
prime radical	C₂×#127×C₄₃	C₄
cosocle	C₄₃×#384	C₂²
hypercenter	#1957	D₄₃
hypocenter	C₄₃	#7354
LCS	G ▷ C₄²×C₄₃ ▷ C₂×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂³ ◁ C₂²×C₄ ◁ #384 ◁ #1957

subgroup

G/H

center

C₂²

#14582692

commutator

C₄²×C₄₃

C₂×C₈

Frattini

#384

C₂×D₄₃

Fitting

C₄₃×#1957

C₂

socle

C₂²×C₄₃

#353

prime radical

C₂×#127×C₄₃

C₄

cosocle

C₄₃×#384

C₂²

D₄₃

C₄₃

G ▷ C₄²×C₄₃ ▷ C₂×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₂³ ◁ C₂²×C₄ ◁ #384 ◁ #1957

N	H ≅ G/N	type
1. #19132541	C₂	semidirect
14. #127×C₄₃	C₈	semidirect
92. C₄₃	#7354	semidirect
98. #127	C₄₃⋊C₈	semidirect

H ≅ G/N

type

1. #19132541

C₂

semidirect

14. #127×C₄₃

C₈

semidirect

92. C₄₃

#7354

semidirect

98. #127

C₄₃⋊C₈

semidirect

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

subgroup	index
#19132541	2
C₄₃×#1957	2
#7354	43

subgroup

index

#19132541

C₄₃×#1957

#7354

Subgroups — #24983980

Conjugacy classes of subgroups

Complements

Maximal subgroups