Group #25249186 — subgroups

Subgroups — #25249186

Order 11008.

806 conjugacy classes of subgroups; only the 267 normal subgroups are shown.

normal subgroups only

This group has 806 conjugacy classes of subgroups — too many to draw. Only its 267 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×#14583298	C₂	1	4	yes	maximal
2	#19142958	C₂	1	1	yes	maximal, characteristic
3	#19134764	C₂	1	4	yes	maximal
4	#19134761	C₂	1	4	yes	maximal
5	C₄×#13063236	C₂	1	1	yes	maximal, characteristic
6	C₄₃×#2859	C₂	1	1	yes	maximal, characteristic
7	C₂×#13063317	C₂²	1	2	yes	—
8	#14583298	—	2	16	no	—
9	C₂×#13063258	C₂²	1	8	yes	—
10	C₂×#13063256	C₂²	1	8	yes	—
11	C₂×#13063236	C₂²	1	2	yes	—
12	C₂×#13063236	C₂²	1	2	yes	—
13	C₂×C₄×C₄₃⋊C₈	C₂²	1	2	yes	—
14	#14582797	—	2	4	no	—
15	#14582769	C₂²	1	2	yes	—
16	#14582765	C₂²	1	2	yes	—
17	C₂×#125×C₄₃	C₂²	1	2	yes	—
18	C₄₃×#389	—	2	4	no	—
19	C₄₃×#384	C₂²	1	2	yes	—
20	C₄₃×#382	C₂²	1	2	yes	—
21	C₄³×C₄₃	C₂²	1	1	yes	characteristic
22	C₂²×C₄₃⋊C₈	C₂³	1	4	yes	—
23	#13063317	—	2	8	no	—
24	C₂×C₄⋊Dic₄₃	—	2	4	no	—
25	C₂×C₄⋊Dic₄₃	C₂³	1	4	yes	—
26	C₂×Dic₄₃⋊C₄	—	2	4	no	—
27	#13063258	—	2	16	no	—
28	#13063256	—	2	16	no	—
29	#13063236	Q₈	1	8	yes	—
30	#13063236	Q₈	1	8	yes	—
31	C₄×C₄₃⋊C₈	D₄	1	8	yes	—
32	C₄₃⋊#95	—	2	4	no	—
33	#125×C₄₃	—	2	8	no	—
34	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
35	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
36	C₂×C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
37	C₂×C₄²×C₄₃	D₄	1	4	yes	—
38	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
39	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
40	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
41	#95×C₄₃	—	2	4	no	—
42	C₂²×C₄×C₄₃	—	2	4	no	—
43	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
44	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
45	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
46	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
47	C₂²×Dic₄₃	—	2	4	no	—
48	C₄⋊C₄×C₄₃	—	2	8	no	—
49	C₄⋊C₄×C₄₃	—	4	8	no	—
50	C₄⋊C₄×C₄₃	—	4	8	no	—
51	C₄²×C₄₃	—	4	4	no	—
52	C₄²×C₄₃	C₂×D₄	1	4	yes	—
53	C₄²×C₄₃	C₂×Q₈	1	4	yes	—
54	C₄²×C₄₃	C₂×Q₈	1	4	yes	—
55	C₄⋊Dic₄₃	—	2	8	no	—
56	C₄⋊Dic₄₃	—	4	8	no	—
57	Dic₄₃⋊C₄	—	4	8	no	—
58	C₂×C₄₃⋊C₈	C₂×D₄	1	8	yes	—
59	C₂×C₄₃⋊C₈	C₂×Q₈	1	8	yes	—
60	C₂×C₄₃⋊C₈	C₂×Q₈	1	8	yes	—
61	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
62	C₂×C₄×C₄₃	—	2	4	no	—
63	C₂×C₄×C₄₃	—	2	4	no	—
64	C₂×C₄×C₄₃	—	2	4	no	—
65	C₂×C₄×C₄₃	—	4	4	no	—
66	C₂×C₄×C₄₃	—	4	8	no	—
67	C₂×C₄×C₄₃	#127	1	4	yes	—
68	C₂×C₄×C₄₃	C₄⋊Q₈	1	4	yes	—
69	C₂×C₄×C₄₃	C₄⋊Q₈	1	4	yes	—
70	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
71	C₂×C₄×C₄₃	C₂²×Q₈	1	2	yes	—
72	C₂×C₄×C₄₃	C₂²×Q₈	1	2	yes	—
73	C₂×Dic₄₃	—	4	4	no	—
74	C₂×Dic₄₃	—	4	8	no	—
75	C₄₃⋊C₈	C₄⋊Q₈	1	16	yes	—
76	#33315	—	43	1	no	maximal, Sylow
77	C₂²×C₄₃	C₂×#127	1	1	yes	characteristic
78	C₂²×C₄₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
79	C₂²×C₄₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
80	C₂²×C₄₃	#575	1	4	yes	—
81	C₄×C₄₃	—	2	4	no	—
82	C₄×C₄₃	—	2	4	no	—
83	C₄×C₄₃	—	2	4	no	—
84	C₄×C₄₃	—	8	4	no	—
85	C₄×C₄₃	C₂×C₄⋊Q₈	1	4	yes	—
86	Dic₄₃	—	8	4	no	—
87	C₂×#499	—	43	4	no	—
88	#2859	—	43	1	no	—
89	#2859	D₄₃	1	1	yes	characteristic
90	#1847	—	43	4	no	—
91	#1847	—	43	4	no	—
92	C₄×#97	—	43	1	no	—
93	C₂×C₄₃	#2868	1	1	yes	characteristic
94	C₂×C₄₃	#3150	1	2	yes	—
95	C₂×C₄₃	#3166	1	2	yes	—
96	C₂×C₄₃	#3166	1	2	yes	—
97	C₂×#125	—	43	2	no	—
98	C₂×#125	C₂×D₄₃	1	2	yes	—
99	#499	—	86	16	no	—
100	C₂×#107	—	43	8	no	—
101	C₂×#106	—	43	8	no	—
102	C₂×#97	—	43	2	no	—
103	C₂×#97	—	43	2	no	—
104	C₂×C₄×C₈	—	43	2	no	—
105	#389	—	2	4	no	—
106	#389	—	86	4	no	—
107	#384	—	43	2	no	—
108	#384	C₂×D₄₃	1	2	yes	—
109	#382	—	43	2	no	—
110	#382	C₂×D₄₃	1	2	yes	—
111	C₄³	C₂×D₄₃	1	1	yes	characteristic
112	C₄₃	#33315	1	1	yes	characteristic, complemented, Sylow
113	C₂²×C₈	—	43	4	no	—
114	#125	—	2	8	no	—
115	#125	—	86	8	no	—
116	C₂×C₄⋊C₄	—	2	4	no	—
117	C₂×C₄⋊C₄	—	2	4	no	—
118	C₂×C₄⋊C₄	—	43	4	no	—
119	C₂×C₄⋊C₄	—	86	4	no	—
120	C₂×C₄⋊C₄	—	86	4	no	—
121	C₂×C₄⋊C₄	C₂²×D₄₃	1	4	yes	—
122	C₂×C₄²	C₂²⋊D₄₃	1	4	yes	—
123	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
124	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
125	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
126	#107	—	86	16	no	—
127	#106	—	86	16	no	—
128	#97	—	43	8	no	—
129	#97	—	43	8	no	—
130	C₄×C₈	—	43	8	no	—
131	#95	—	2	4	no	—
132	#95	—	86	4	no	—
133	C₂²×C₄	—	2	4	no	—
134	C₂²×C₄	—	86	4	no	—
135	C₂²×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
136	C₂²×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
137	C₂²×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
138	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
139	C₂×C₈	—	43	8	no	—
140	C₂×C₈	—	43	8	no	—
141	C₂×C₈	—	43	8	no	—
142	C₄⋊C₄	—	2	8	no	—
143	C₄⋊C₄	—	4	8	no	—
144	C₄⋊C₄	—	4	8	no	—
145	C₄⋊C₄	—	86	8	no	—
146	C₄⋊C₄	—	172	8	no	—
147	C₄⋊C₄	—	172	8	no	—
148	C₄²	—	4	4	no	—
149	C₄²	D₄×D₄₃	1	4	yes	—
150	C₄²	Q₈×D₄₃	1	4	yes	—
151	C₄²	Q₈×D₄₃	1	4	yes	—
152	C₂³	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
153	C₂×C₄	—	2	4	no	—
154	C₂×C₄	—	2	4	no	—
155	C₂×C₄	—	2	4	no	—
156	C₂×C₄	—	4	4	no	—
157	C₂×C₄	—	4	8	no	—
158	C₂×C₄	—	172	4	no	—
159	C₂×C₄	—	172	8	no	—
160	C₂×C₄	#13063321	1	4	yes	—
161	C₂×C₄	#13063323	1	4	yes	—
162	C₂×C₄	#13063323	1	4	yes	—
163	C₂×C₄	C₂×D₄×D₄₃	1	2	yes	—
164	C₂×C₄	C₂×Q₈×D₄₃	1	2	yes	—
165	C₂×C₄	C₂×Q₈×D₄₃	1	2	yes	—
166	C₈	—	43	16	no	—
167	C₂²	C₂×#13063321	1	1	yes	characteristic
168	C₂²	C₂×#13063323	1	1	yes	characteristic
169	C₂²	C₂×#13063323	1	1	yes	characteristic
170	C₂²	#14583697	1	4	yes	—
171	C₄	—	2	4	no	—
172	C₄	—	2	4	no	—
173	C₄	—	2	4	no	—
174	C₄	—	8	4	no	—
175	C₄	—	344	4	no	—
176	C₄	C₄⋊Q₈×D₄₃	1	4	yes	—
177	C₂	#19142991	1	1	yes	characteristic
178	C₂	#19145040	1	2	yes	—
179	C₂	#19145144	1	2	yes	—
180	C₂	#19145148	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14583298

C₂

yes

maximal

#19142958

C₂

yes

maximal, characteristic

#19134764

C₂

yes

maximal

#19134761

C₂

yes

maximal

C₄×#13063236

C₂

yes

maximal, characteristic

C₄₃×#2859

C₂

yes

maximal, characteristic

C₂×#13063317

C₂²

yes

—

#14583298

—

C₂×#13063258

C₂²

yes

—

C₂×#13063256

C₂²

yes

—

C₂×#13063236

C₂²

yes

—

C₂×#13063236

C₂²

yes

—

C₂×C₄×C₄₃⋊C₈

C₂²

yes

—

#14582797

—

#14582769

C₂²

yes

—

#14582765

C₂²

yes

—

C₂×#125×C₄₃

C₂²

yes

—

C₄₃×#389

—

C₄₃×#384

C₂²

yes

—

C₄₃×#382

C₂²

yes

—

C₄³×C₄₃

C₂²

yes

characteristic

C₂²×C₄₃⋊C₈

C₂³

yes

—

#13063317

—

C₂×C₄⋊Dic₄₃

—

C₂×C₄⋊Dic₄₃

C₂³

yes

—

C₂×Dic₄₃⋊C₄

—

#13063258

—

#13063256

—

#13063236

Q₈

yes

—

#13063236

Q₈

yes

—

C₄×C₄₃⋊C₈

D₄

yes

—

C₄₃⋊#95

—

#125×C₄₃

—

C₂×C₄⋊C₄×C₄₃

—

C₂×C₄⋊C₄×C₄₃

—

C₂×C₄⋊C₄×C₄₃

C₂³

yes

—

C₂×C₄²×C₄₃

D₄

yes

—

C₂×C₄²×C₄₃

C₂³

yes

characteristic

C₂×C₄²×C₄₃

C₂³

yes

characteristic

C₂×C₄²×C₄₃

C₂³

yes

characteristic

#95×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₂×D₄

yes

—

C₂²×C₄×C₄₃

C₂×D₄

yes

—

C₂²×C₄×C₄₃

C₂×D₄

yes

—

C₂²×C₄×C₄₃

C₂⁴

yes

characteristic

C₂²×Dic₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

C₂×D₄

yes

—

C₄²×C₄₃

C₂×Q₈

yes

—

C₄²×C₄₃

C₂×Q₈

yes

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

Dic₄₃⋊C₄

—

C₂×C₄₃⋊C₈

C₂×D₄

yes

—

C₂×C₄₃⋊C₈

C₂×Q₈

yes

—

C₂×C₄₃⋊C₈

C₂×Q₈

yes

—

C₂³×C₄₃

C₂²×D₄

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

#127

yes

—

C₂×C₄×C₄₃

C₄⋊Q₈

yes

—

C₂×C₄×C₄₃

C₄⋊Q₈

yes

—

C₂×C₄×C₄₃

C₂²×D₄

yes

—

C₂×C₄×C₄₃

C₂²×Q₈

yes

—

C₂×C₄×C₄₃

C₂²×Q₈

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₄₃⋊C₈

C₄⋊Q₈

yes

—

—

C₂²×C₄₃

yes

C₂²×C₄₃

C₂×C₄⋊Q₈

yes

characteristic

C₂²×C₄₃

C₂×C₄⋊Q₈

yes

characteristic

C₂²×C₄₃

#575

yes

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

C₂×C₄⋊Q₈

yes

—

Dic₄₃

—

C₂×#499

—

#2859

—

#2859

D₄₃

yes

characteristic

#1847

—

#1847

—

C₄×#97

—

C₂×C₄₃

#2868

yes

characteristic

C₂×C₄₃

#3150

yes

—

C₂×C₄₃

#3166

yes

—

C₂×C₄₃

#3166

yes

—

C₂×#125

—

C₂×#125

C₂×D₄₃

yes

—

#499

—

100

C₂×#107

—

101

C₂×#106

—

102

C₂×#97

—

103

C₂×#97

—

104

C₂×C₄×C₈

—

105

#389

—

106

#389

—

107

#384

—

108

#384

C₂×D₄₃

yes

—

109

#382

—

110

#382

C₂×D₄₃

yes

—

111

C₄³

C₂×D₄₃

yes

characteristic

112

C₄₃

#33315

yes

characteristic, complemented, Sylow

113

C₂²×C₈

—

114

#125

—

115

#125

—

116

C₂×C₄⋊C₄

—

117

C₂×C₄⋊C₄

—

118

C₂×C₄⋊C₄

—

119

C₂×C₄⋊C₄

—

120

C₂×C₄⋊C₄

—

121

C₂×C₄⋊C₄

C₂²×D₄₃

yes

—

122

C₂×C₄²

C₂²⋊D₄₃

yes

—

123

C₂×C₄²

C₂²×D₄₃

yes

characteristic

124

C₂×C₄²

C₂²×D₄₃

yes

characteristic

125

C₂×C₄²

C₂²×D₄₃

yes

characteristic

126

#107

—

127

#106

—

128

#97

—

129

#97

—

130

C₄×C₈

—

131

#95

—

132

#95

—

133

C₂²×C₄

—

134

C₂²×C₄

—

135

C₂²×C₄

C₂×C₂²⋊D₄₃

yes

—

136

C₂²×C₄

C₂×C₂²⋊D₄₃

yes

—

137

C₂²×C₄

C₂×C₂²⋊D₄₃

yes

—

138

C₂²×C₄

C₂³×D₄₃

yes

characteristic

139

C₂×C₈

—

140

C₂×C₈

—

141

C₂×C₈

—

142

C₄⋊C₄

—

143

C₄⋊C₄

—

144

C₄⋊C₄

—

145

C₄⋊C₄

—

146

C₄⋊C₄

—

172

—

147

C₄⋊C₄

—

172

—

148

C₄²

—

149

C₄²

D₄×D₄₃

yes

—

150

C₄²

Q₈×D₄₃

yes

—

151

C₄²

Q₈×D₄₃

yes

—

152

C₂³

C₂²×C₂²⋊D₄₃

yes

characteristic

153

C₂×C₄

—

154

C₂×C₄

—

155

C₂×C₄

—

156

C₂×C₄

—

157

C₂×C₄

—

158

C₂×C₄

—

172

—

159

C₂×C₄

—

172

—

160

C₂×C₄

#13063321

yes

—

161

C₂×C₄

#13063323

yes

—

162

C₂×C₄

#13063323

yes

—

163

C₂×C₄

C₂×D₄×D₄₃

yes

—

164

C₂×C₄

C₂×Q₈×D₄₃

yes

—

165

C₂×C₄

C₂×Q₈×D₄₃

yes

—

166

C₈

—

167

C₂²

C₂×#13063321

yes

characteristic

168

C₂²

C₂×#13063323

yes

characteristic

169

C₂²

C₂×#13063323

yes

characteristic

170

C₂²

#14583697

yes

—

171

C₄

—

172

C₄

—

173

C₄

—

174

C₄

—

175

C₄

—

344

—

176

C₄

C₄⋊Q₈×D₄₃

yes

—

177

C₂

#19142991

yes

characteristic

178

C₂

#19145040

yes

—

179

C₂

#19145144

yes

—

180

C₂

#19145148

yes

—

	subgroup	G/H
center	C₂³	C₂²×C₂²⋊D₄₃
commutator, cosocle	C₂²×C₄×C₄₃	C₂⁴
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₄₃×#2859	C₂
socle, prime radical	C₂³×C₄₃	C₂²×D₄
hypercenter	#2859	D₄₃
hypocenter	C₄₃	#33315
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ #2859

subgroup

G/H

center

C₂³

C₂²×C₂²⋊D₄₃

commutator, cosocle

C₂²×C₄×C₄₃

C₂⁴

Frattini

C₂²×C₄

C₂³×D₄₃

Fitting

C₄₃×#2859

C₂

socle, prime radical

C₂³×C₄₃

C₂²×D₄

D₄₃

C₄₃

G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂³ ◁ C₄³ ◁ #2859

N	H ≅ G/N	type
112. C₄₃	#33315	semidirect

H ≅ G/N

type

112. C₄₃

#33315

semidirect

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

subgroup	index
C₂×#14583298	2
#19142958	2
#19134764	2
#19134761	2
C₄×#13063236	2
C₄₃×#2859	2
#33315	43

subgroup

index

C₄₃×#2859

Subgroups — #25249186

Conjugacy classes of subgroups

Complements

Maximal subgroups