Group #25012978 — subgroups

Subgroups — #25012978

Order 11008.

310 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 131 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×C₁₆×Dic₄₃	C₂	1	1	yes	maximal, characteristic
2	#19134758	C₂	1	2	yes	maximal
3	#19132687	C₂	1	1	yes	maximal, characteristic
4	#19132686	C₂	1	2	yes	maximal
5	C₄₃×#1380	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₄₃⋊C₁₆	C₂²	1	1	yes	characteristic
7	C₂×#13063259	C₂²	1	2	yes	—
8	C₂×#13063256	—	2	2	no	—
9	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
10	#14582764	—	2	2	no	—
11	C₁₆×Dic₄₃	C₄	1	4	yes	complemented
12	C₂²×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
13	C₂×#107×C₄₃	C₂²	1	2	yes	—
14	C₂²×C₄₃⋊C₈	D₄	1	1	yes	characteristic
15	C₂×C₄⋊Dic₄₃	—	2	2	no	—
16	C₂×C₄×Dic₄₃	D₄	1	1	yes	characteristic
17	C₂×C₄₃⋊C₁₆	—	2	2	no	—
18	C₂×C₄₃⋊C₁₆	C₂×C₄	1	2	yes	—
19	#13063259	—	2	2	no	—
20	#13063259	—	2	2	no	—
21	#13063256	—	4	4	no	—
22	C₈×Dic₄₃	C₂×C₄	1	2	yes	—
23	C₈×Dic₄₃	Q₈	1	2	yes	—
24	C₄₃⋊#95	—	4	2	no	—
25	C₄₃⋊#95	—	4	2	no	—
26	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
27	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
28	C₂×C₁₆×C₄₃	—	2	2	no	—
29	C₂×C₁₆×C₄₃	C₂×C₄	1	2	yes	—
30	#107×C₄₃	—	2	2	no	—
31	#107×C₄₃	—	2	2	no	—
32	C₂²×C₄×C₄₃	—	4	2	no	—
33	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
34	C₂²×Dic₄₃	—	4	2	no	—
35	C₂²×Dic₄₃	D₈	1	1	yes	characteristic
36	C₂²×Dic₄₃	D₈	1	1	yes	characteristic
37	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
38	C₂×C₈×C₄₃	C₂×Q₈	1	1	yes	characteristic
39	C₂×C₈×C₄₃	#41	1	2	yes	—
40	C₂×C₈×C₄₃	#41	1	2	yes	—
41	C₄⋊C₄×C₄₃	—	4	2	no	—
42	C₄⋊C₄×C₄₃	—	4	2	no	—
43	C₄⋊Dic₄₃	—	4	2	no	—
44	C₄⋊Dic₄₃	—	4	2	no	—
45	C₄×Dic₄₃	C₄⋊C₄	1	2	yes	—
46	C₄×Dic₄₃	Q₁₆	1	2	yes	—
47	C₂×C₄₃⋊C₈	C₄⋊C₄	1	2	yes	—
48	C₂×C₄₃⋊C₈	SD₁₆	1	4	yes	—
49	C₁₆×C₄₃	—	2	2	no	—
50	C₄₃⋊C₁₆	—	2	2	no	—
51	C₂³×C₄₃	C₂×D₈	1	1	yes	characteristic
52	C₂×C₄×C₄₃	—	8	2	no	—
53	C₂×C₄×C₄₃	—	8	2	no	—
54	C₂×C₄×C₄₃	—	8	2	no	—
55	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
56	C₂×C₄×C₄₃	#124	1	2	yes	—
57	C₂×C₄×C₄₃	C₂×SD₁₆	1	2	yes	—
58	C₂×C₄×C₄₃	C₂×Q₁₆	1	1	yes	characteristic
59	C₂×Dic₄₃	—	2	1	no	—
60	C₂×Dic₄₃	—	2	2	no	—
61	C₂×Dic₄₃	—	2	1	no	—
62	C₂×Dic₄₃	—	8	2	no	—
63	C₂×Dic₄₃	—	8	2	no	—
64	C₂×Dic₄₃	—	8	2	no	—
65	C₂×Dic₄₃	#107	1	2	yes	—
66	C₂×Dic₄₃	#107	1	2	yes	—
67	C₈×C₄₃	#117	1	1	yes	characteristic
68	C₈×C₄₃	#117	1	1	yes	characteristic
69	C₈×C₄₃	#125	1	2	yes	—
70	C₄₃⋊C₈	#106	1	4	yes	—
71	#12889	—	43	1	no	maximal, Sylow
72	C₂²×C₄₃	C₂×#107	1	1	yes	characteristic
73	C₂²×C₄₃	#486	1	2	yes	—
74	C₂²×C₄₃	#508	1	1	yes	characteristic
75	C₂²×C₄₃	#508	1	2	yes	—
76	C₂²×C₄₃	#508	1	1	yes	characteristic
77	C₄×C₄₃	—	16	2	no	—
78	C₄×C₄₃	#382	1	1	yes	characteristic
79	C₄×C₄₃	C₂×#106	1	1	yes	characteristic
80	C₄×C₄₃	#487	1	2	yes	—
81	Dic₄₃	—	2	2	no	—
82	Dic₄₃	—	2	2	no	—
83	Dic₄₃	—	16	2	no	—
84	C₂×C₄×C₁₆	—	43	1	no	—
85	#1846	—	43	2	no	—
86	#1380	—	43	1	no	—
87	#1380	—	43	2	no	—
88	#1380	D₄₃	1	1	yes	characteristic
89	C₂×C₄₃	#1834	1	1	yes	characteristic
90	C₂×C₄₃	#2158	1	1	yes	characteristic
91	C₂×C₄₃	#2158	1	1	yes	characteristic
92	C₂×C₄₃	#2242	1	2	yes	—
93	C₂×C₄₃	#2242	1	2	yes	—
94	C₂²×C₁₆	—	43	1	no	—
95	C₂²×C₁₆	C₂×D₄₃	1	1	yes	characteristic
96	C₂×#107	—	43	2	no	—
97	C₂×#107	C₂×D₄₃	1	2	yes	—
98	C₂×#106	—	86	2	no	—
99	C₂×C₄×C₈	—	43	1	no	—
100	#382	—	86	2	no	—
101	C₄×C₁₆	—	43	4	no	—
102	C₄₃	#12889	1	1	yes	characteristic, complemented, Sylow
103	C₂²×C₈	—	43	1	no	—
104	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
105	C₂×C₄⋊C₄	—	2	2	no	—
106	C₂×C₄⋊C₄	—	86	2	no	—
107	C₂×C₄²	—	43	1	no	—
108	C₂×C₁₆	—	2	2	no	—
109	C₂×C₁₆	—	43	2	no	—
110	C₂×C₁₆	—	86	2	no	—
111	C₂×C₁₆	C₄×D₄₃	1	2	yes	—
112	#107	—	2	2	no	—
113	#107	—	2	2	no	—
114	#107	—	86	2	no	—
115	#107	—	86	2	no	—
116	#106	—	172	4	no	—
117	C₄×C₈	—	43	2	no	—
118	C₄×C₈	—	43	2	no	—
119	#95	—	172	2	no	—
120	#95	—	172	2	no	—
121	C₂²×C₄	—	4	2	no	—
122	C₂²×C₄	—	43	1	no	—
123	C₂²×C₄	—	43	1	no	—
124	C₂²×C₄	—	172	2	no	—
125	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
126	C₂×C₈	—	43	2	no	—
127	C₂×C₈	—	43	4	no	—
128	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
129	C₂×C₈	#10621898	1	2	yes	—
130	C₂×C₈	#10621900	1	2	yes	—
131	C₂×C₈	Q₈×D₄₃	1	1	yes	characteristic
132	C₄⋊C₄	—	4	2	no	—
133	C₄⋊C₄	—	4	2	no	—
134	C₄⋊C₄	—	172	2	no	—
135	C₄⋊C₄	—	172	2	no	—
136	C₄²	—	43	2	no	—
137	C₄²	—	43	2	no	—
138	C₁₆	—	2	2	no	—
139	C₁₆	—	86	2	no	—
140	C₂³	D₈×D₄₃	1	1	yes	characteristic
141	C₂×C₄	—	8	2	no	—
142	C₂×C₄	—	8	2	no	—
143	C₂×C₄	—	8	2	no	—
144	C₂×C₄	—	43	2	no	—
145	C₂×C₄	—	43	2	no	—
146	C₂×C₄	—	86	1	no	—
147	C₂×C₄	—	86	2	no	—
148	C₂×C₄	—	86	1	no	—
149	C₂×C₄	—	344	2	no	—
150	C₂×C₄	—	344	2	no	—
151	C₂×C₄	—	344	2	no	—
152	C₂×C₄	C₄⋊C₄×D₄₃	1	1	yes	characteristic
153	C₂×C₄	#13063311	1	2	yes	—
154	C₂×C₄	SD₁₆×D₄₃	1	2	yes	—
155	C₂×C₄	Q₁₆×D₄₃	1	1	yes	characteristic
156	C₈	—	43	4	no	—
157	C₈	#13063281	1	1	yes	characteristic
158	C₈	#13063282	1	1	yes	characteristic
159	C₈	#13063315	1	2	yes	—
160	C₂²	#107×D₄₃	1	1	yes	characteristic
161	C₂²	#14583244	1	2	yes	—
162	C₂²	#14583328	1	1	yes	characteristic
163	C₂²	#14583330	1	2	yes	—
164	C₂²	#14583332	1	1	yes	characteristic
165	C₄	—	16	2	no	—
166	C₄	—	86	2	no	—
167	C₄	—	86	2	no	—
168	C₄	—	688	2	no	—
169	C₄	#14582763	1	1	yes	characteristic
170	C₄	#106×D₄₃	1	1	yes	characteristic
171	C₄	#14583248	1	2	yes	—
172	C₂	#19134721	1	1	yes	characteristic
173	C₂	#19136376	1	1	yes	characteristic
174	C₂	#19136378	1	1	yes	characteristic
175	C₂	#19136825	1	2	yes	—
176	C₂	#19136828	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₁₆×Dic₄₃

C₂

yes

maximal, characteristic

#19134758

C₂

yes

maximal

#19132687

C₂

yes

maximal, characteristic

#19132686

C₂

yes

maximal

C₄₃×#1380

C₂

yes

maximal, characteristic

C₂²×C₄₃⋊C₁₆

C₂²

yes

characteristic

C₂×#13063259

C₂²

yes

—

C₂×#13063256

—

C₂×C₈×Dic₄₃

C₂²

yes

characteristic

#14582764

—

C₁₆×Dic₄₃

C₄

yes

complemented

C₂²×C₁₆×C₄₃

C₂²

yes

characteristic

C₂×#107×C₄₃

C₂²

yes

—

C₂²×C₄₃⋊C₈

D₄

yes

characteristic

C₂×C₄⋊Dic₄₃

—

C₂×C₄×Dic₄₃

D₄

yes

characteristic

C₂×C₄₃⋊C₁₆

—

C₂×C₄₃⋊C₁₆

C₂×C₄

yes

—

#13063259

—

#13063259

—

#13063256

—

C₈×Dic₄₃

C₂×C₄

yes

—

C₈×Dic₄₃

Q₈

yes

—

C₄₃⋊#95

—

C₄₃⋊#95

—

C₂²×C₈×C₄₃

C₂³

yes

characteristic

C₂×C₄⋊C₄×C₄₃

—

C₂×C₁₆×C₄₃

—

C₂×C₁₆×C₄₃

C₂×C₄

yes

—

#107×C₄₃

—

#107×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²×Dic₄₃

—

C₂²×Dic₄₃

D₈

yes

characteristic

C₂²×Dic₄₃

D₈

yes

characteristic

C₂×C₈×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₈×C₄₃

C₂×Q₈

yes

characteristic

C₂×C₈×C₄₃

#41

yes

—

C₂×C₈×C₄₃

#41

yes

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄×Dic₄₃

C₄⋊C₄

yes

—

C₄×Dic₄₃

Q₁₆

yes

—

C₂×C₄₃⋊C₈

C₄⋊C₄

yes

—

C₂×C₄₃⋊C₈

SD₁₆

yes

—

C₁₆×C₄₃

—

C₄₃⋊C₁₆

—

C₂³×C₄₃

C₂×D₈

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₄₃

#124

yes

—

C₂×C₄×C₄₃

C₂×SD₁₆

yes

—

C₂×C₄×C₄₃

C₂×Q₁₆

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

#107

yes

—

C₂×Dic₄₃

#107

yes

—

C₈×C₄₃

yes

C₈×C₄₃

yes

C₈×C₄₃

yes

—

C₄₃⋊C₈

#106

yes

—

—

C₂²×C₄₃

yes

C₂²×C₄₃

yes

—

C₂²×C₄₃

#508

yes

characteristic

C₂²×C₄₃

#508

yes

—

C₂²×C₄₃

#508

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

yes

C₄×C₄₃

yes

C₄×C₄₃

yes

—

Dic₄₃

—

Dic₄₃

—

Dic₄₃

—

C₂×C₄×C₁₆

—

—

—

—

D₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

—

C₂×C₄₃

#2242

yes

—

C₂²×C₁₆

—

C₂²×C₁₆

C₂×D₄₃

yes

characteristic

C₂×#107

—

C₂×#107

C₂×D₄₃

yes

—

C₂×#106

—

C₂×C₄×C₈

—

100

#382

—

101

C₄×C₁₆

—

102

C₄₃

#12889

yes

characteristic, complemented, Sylow

103

C₂²×C₈

—

104

C₂²×C₈

C₂²×D₄₃

yes

characteristic

105

C₂×C₄⋊C₄

—

106

C₂×C₄⋊C₄

—

107

C₂×C₄²

—

108

C₂×C₁₆

—

109

C₂×C₁₆

—

110

C₂×C₁₆

—

111

C₂×C₁₆

C₄×D₄₃

yes

—

112

#107

—

113

#107

—

114

#107

—

115

#107

—

116

#106

—

172

—

117

C₄×C₈

—

118

C₄×C₈

—

119

#95

—

172

—

120

#95

—

172

—

121

C₂²×C₄

—

122

C₂²×C₄

—

123

C₂²×C₄

—

124

C₂²×C₄

—

172

—

125

C₂²×C₄

D₄×D₄₃

yes

characteristic

126

C₂×C₈

—

127

C₂×C₈

—

128

C₂×C₈

C₂×C₄×D₄₃

yes

characteristic

129

C₂×C₈

#10621898

yes

—

130

C₂×C₈

#10621900

yes

—

131

C₂×C₈

Q₈×D₄₃

yes

characteristic

132

C₄⋊C₄

—

133

C₄⋊C₄

—

134

C₄⋊C₄

—

172

—

135

C₄⋊C₄

—

172

—

136

C₄²

—

137

C₄²

—

138

C₁₆

—

139

C₁₆

—

140

C₂³

D₈×D₄₃

yes

characteristic

141

C₂×C₄

—

142

C₂×C₄

—

143

C₂×C₄

—

144

C₂×C₄

—

145

C₂×C₄

—

146

C₂×C₄

—

147

C₂×C₄

—

148

C₂×C₄

—

149

C₂×C₄

—

344

—

150

C₂×C₄

—

344

—

151

C₂×C₄

—

344

—

152

C₂×C₄

C₄⋊C₄×D₄₃

yes

characteristic

153

C₂×C₄

#13063311

yes

—

154

C₂×C₄

SD₁₆×D₄₃

yes

—

155

C₂×C₄

Q₁₆×D₄₃

yes

characteristic

156

C₈

—

157

C₈

#13063281

yes

characteristic

158

C₈

#13063282

yes

characteristic

159

C₈

#13063315

yes

—

160

C₂²

#107×D₄₃

yes

characteristic

161

C₂²

#14583244

yes

—

162

C₂²

#14583328

yes

characteristic

163

C₂²

#14583330

yes

—

164

C₂²

#14583332

yes

characteristic

165

C₄

—

166

C₄

—

167

C₄

—

168

C₄

—

688

—

169

C₄

#14582763

yes

characteristic

170

C₄

#106×D₄₃

yes

characteristic

171

C₄

#14583248

yes

—

172

C₂

#19134721

yes

characteristic

173

C₂

#19136376

yes

characteristic

174

C₂

#19136378

yes

characteristic

175

C₂

#19136825

yes

—

176

C₂

#19136828

yes

—

	subgroup	G/H
center	C₂³	D₈×D₄₃
commutator	C₂×C₈×C₄₃	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₄₃
Fitting	C₄₃×#1380	C₂
socle, prime radical	C₂³×C₄₃	C₂×D₈
cosocle	C₂²×C₈×C₄₃	C₂³
hypercenter	#1380	D₄₃
hypocenter	C₄₃	#12889
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #1380

subgroup

G/H

center

C₂³

D₈×D₄₃

commutator

C₂×C₈×C₄₃

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₄₃

Fitting

C₄₃×#1380

C₂

socle, prime radical

C₂³×C₄₃

C₂×D₈

cosocle

C₂²×C₈×C₄₃

C₂³

D₄₃

C₄₃

G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #1380

N	H ≅ G/N	type
11. C₁₆×Dic₄₃	C₄	semidirect
102. C₄₃	#12889	semidirect

H ≅ G/N

type

11. C₁₆×Dic₄₃

C₄

semidirect

102. C₄₃

#12889

semidirect

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

subgroup	index
C₂×C₁₆×Dic₄₃	2
#19134758	2
#19132687	2
#19132686	2
C₄₃×#1380	2
#12889	43

subgroup

index

C₂×C₁₆×Dic₄₃

C₄₃×#1380

Subgroups — #25012978

Conjugacy classes of subgroups

Complements

Maximal subgroups