Group #24991551 — subgroups

Subgroups — #24991551

Order 11008.

376 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 99 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	#19145117	C₂	1	1	yes	maximal, characteristic
2	#19133260	C₂	1	1	yes	maximal, characteristic
3	#19133067	C₂	1	2	yes	maximal
4	#19132493	C₂	1	2	yes	maximal
5	C₄₃×#2987	C₂	1	1	yes	maximal, characteristic
6	#14583456	C₂²	1	1	yes	characteristic
7	#14583309	C₄	1	4	yes	—
8	#14583305	—	2	2	no	—
9	#14582952	C₂²	1	2	yes	—
10	#14582935	—	2	2	no	—
11	C₂×#13063236	C₂²	1	1	yes	characteristic
12	#14582645	—	2	2	no	—
13	#14582629	—	2	4	no	—
14	C₄₃×#533	C₂²	1	1	yes	characteristic
15	C₄₃×#446	—	2	4	no	—
16	C₄₃×#433	—	2	2	no	—
17	C₄₃×#432	C₂²	1	2	yes	—
18	C₂²×C₄₃⋊C₈	—	2	1	no	—
19	#13063325	C₂×C₄	1	2	yes	—
20	#13063317	—	2	1	no	—
21	#13063304	—	2	2	no	—
22	C₄×Dic₈₆	—	2	2	no	—
23	#13063284	—	2	1	no	—
24	#13063258	—	2	4	no	—
25	#13063256	—	2	4	no	—
26	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
27	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
28	#13063236	—	2	1	no	—
29	#13063236	C₂×C₄	1	2	yes	—
30	C₄×C₄₃⋊C₈	—	2	2	no	—
31	C₄⋊Q₈×C₄₃	D₄	1	2	yes	—
32	#125×C₄₃	C₂×C₄	1	2	yes	—
33	C₂²⋊Q₈×C₄₃	—	2	2	no	—
34	C₄×Q₈×C₄₃	—	2	2	no	—
35	#117×C₄₃	D₄	1	2	yes	—
36	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
37	C₄⋊C₈×C₄₃	—	2	4	no	—
38	C₄⋊C₈×C₄₃	D₄	1	4	yes	—
39	C₂²⋊C₈×C₄₃	—	2	2	no	—
40	#97×C₄₃	—	2	2	no	—
41	#97×C₄₃	—	2	2	no	—
42	C₄×C₈×C₄₃	—	2	2	no	—
43	C₂×Q₈×C₄₃	—	2	2	no	—
44	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
45	C₂²×C₄×C₄₃	#41	1	2	yes	—
46	C₂×Dic₈₆	—	2	2	no	—
47	C₂×C₈×C₄₃	—	2	4	no	—
48	C₄⋊C₄×C₄₃	—	2	4	no	—
49	C₄⋊C₄×C₄₃	—	2	2	no	—
50	C₄⋊C₄×C₄₃	C₂²⋊C₄	1	4	yes	—
51	C₂²⋊C₄×C₄₃	—	2	2	no	—
52	C₄²×C₄₃	—	2	2	no	—
53	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
54	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
55	C₄²×C₄₃	C₂×D₄	1	2	yes	—
56	C₂²⋊Dic₄₃	—	4	1	no	—
57	C₄⋊Dic₄₃	—	2	2	no	—
58	C₄⋊Dic₄₃	—	2	2	no	—
59	Dic₄₃⋊C₄	—	4	2	no	—
60	C₄×Dic₄₃	—	4	1	no	—
61	C₂×C₄₃⋊C₈	—	2	4	no	—
62	C₂×C₄₃⋊C₈	—	2	2	no	—
63	C₂×C₄₃⋊C₈	—	4	2	no	—
64	C₂³×C₄₃	#123	1	1	yes	characteristic
65	Q₈×C₄₃	—	8	2	no	—
66	C₂×C₄×C₄₃	—	2	2	no	—
67	C₂×C₄×C₄₃	—	2	4	no	—
68	C₂×C₄×C₄₃	—	4	2	no	—
69	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
70	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
71	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
72	C₂×C₄×C₄₃	#121	1	2	yes	—
73	C₂×Dic₄₃	—	4	2	no	—
74	Dic₈₆	—	4	4	no	—
75	C₈×C₄₃	—	4	4	no	—
76	C₄₃⋊C₈	—	2	4	no	—
77	C₄₃⋊C₈	—	8	2	no	—
78	#9006	—	43	1	no	maximal, Sylow
79	C₂²×C₄₃	—	2	2	no	—
80	C₂²×C₄₃	—	2	1	no	—
81	C₂²×C₄₃	#386	1	1	yes	characteristic
82	C₄×C₄₃	—	2	2	no	—
83	C₄×C₄₃	—	2	2	no	—
84	C₄×C₄₃	—	2	1	no	—
85	C₄×C₄₃	—	4	4	no	—
86	C₄×C₄₃	#456	1	2	yes	—
87	Dic₄₃	—	8	2	no	—
88	#3162	—	43	1	no	—
89	#2987	D₄₃	1	1	yes	characteristic
90	#1544	—	43	1	no	—
91	#1497	—	43	2	no	—
92	#1302	—	43	2	no	—
93	C₂×C₄₃	—	4	1	no	—
94	C₂×C₄₃	#1881	1	2	yes	—
95	C₂×C₄₃	#1886	1	1	yes	characteristic
96	#533	—	43	1	no	—
97	#533	C₂×D₄₃	1	1	yes	characteristic
98	#501	—	43	4	no	—
99	#501	—	86	2	no	—
100	#446	—	2	4	no	—
101	#433	—	2	2	no	—
102	#432	C₂×D₄₃	1	2	yes	—
103	#431	—	43	2	no	—
104	#427	—	86	2	no	—
105	C₂×#97	—	43	1	no	—
106	#332	—	86	2	no	—
107	Q₈⋊C₈	—	86	4	no	—
108	C₄₃	#9006	1	1	yes	characteristic, complemented, Sylow
109	C₂²×C₈	—	86	1	no	—
110	C₄⋊Q₈	—	43	2	no	—
111	C₄⋊Q₈	D₁₇₂	1	2	yes	—
112	#125	—	86	1	no	—
113	#125	C₄×D₄₃	1	2	yes	—
114	C₂²⋊Q₈	—	2	2	no	—
115	C₂²⋊Q₈	—	86	2	no	—
116	C₄×Q₈	—	2	2	no	—
117	C₄×Q₈	—	86	2	no	—
118	#117	—	86	1	no	—
119	#117	C₂²⋊D₄₃	1	2	yes	—
120	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
121	#107	—	86	4	no	—
122	#106	—	86	4	no	—
123	C₄⋊C₈	—	2	4	no	—
124	C₄⋊C₈	—	86	2	no	—
125	C₄⋊C₈	C₂²⋊D₄₃	1	4	yes	—
126	C₂²⋊C₈	—	2	2	no	—
127	C₂²⋊C₈	—	86	2	no	—
128	#97	—	2	2	no	—
129	#97	—	2	2	no	—
130	#97	—	43	2	no	—
131	#97	—	86	1	no	—
132	C₄×C₈	—	2	2	no	—
133	C₄×C₈	—	86	2	no	—
134	C₂×Q₈	—	2	2	no	—
135	C₂×Q₈	—	86	2	no	—
136	C₂²×C₄	#10621898	1	2	yes	—
137	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
138	C₂×C₈	—	2	4	no	—
139	C₂×C₈	—	86	4	no	—
140	C₂×C₈	—	86	2	no	—
141	C₂×C₈	—	172	2	no	—
142	C₄⋊C₄	—	2	4	no	—
143	C₄⋊C₄	—	2	2	no	—
144	C₄⋊C₄	—	86	2	no	—
145	C₄⋊C₄	—	86	2	no	—
146	C₄⋊C₄	—	172	2	no	—
147	C₄⋊C₄	(C₂×D₄₃)⋊C₄	1	4	yes	—
148	C₂²⋊C₄	—	2	2	no	—
149	C₂²⋊C₄	—	172	1	no	—
150	C₄²	—	2	2	no	—
151	C₄²	—	172	1	no	—
152	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
153	C₄²	C₂×D₁₇₂	1	1	yes	characteristic
154	C₄²	C₂×C₂²⋊D₄₃	1	2	yes	—
155	C₂³	#13063308	1	1	yes	characteristic
156	Q₈	—	8	2	no	—
157	Q₈	—	172	4	no	—
158	C₂×C₄	—	2	2	no	—
159	C₂×C₄	—	2	4	no	—
160	C₂×C₄	—	4	2	no	—
161	C₂×C₄	—	172	2	no	—
162	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
163	C₂×C₄	C₄×C₂²⋊D₄₃	1	2	yes	—
164	C₂×C₄	#13063294	1	1	yes	characteristic
165	C₂×C₄	#13063299	1	2	yes	—
166	C₈	—	4	4	no	—
167	C₈	—	86	4	no	—
168	C₈	—	344	2	no	—
169	C₂²	—	2	1	no	—
170	C₂²	—	2	2	no	—
171	C₂²	#14582778	1	1	yes	characteristic
172	C₄	—	2	1	no	—
173	C₄	—	2	2	no	—
174	C₄	—	2	2	no	—
175	C₄	—	4	4	no	—
176	C₄	—	344	2	no	—
177	C₄	#14583082	1	2	yes	—
178	C₂	—	4	1	no	—
179	C₂	#19134957	1	2	yes	—
180	C₂	#19134988	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19145117

C₂

yes

maximal, characteristic

#19133260

C₂

yes

maximal, characteristic

#19133067

C₂

yes

maximal

#19132493

C₂

yes

maximal

C₄₃×#2987

C₂

yes

maximal, characteristic

#14583456

C₂²

yes

characteristic

#14583309

C₄

yes

—

#14583305

—

#14582952

C₂²

yes

—

#14582935

—

C₂×#13063236

C₂²

yes

characteristic

#14582645

—

#14582629

—

C₄₃×#533

C₂²

yes

characteristic

C₄₃×#446

—

C₄₃×#433

—

C₄₃×#432

C₂²

yes

—

C₂²×C₄₃⋊C₈

—

#13063325

C₂×C₄

yes

—

#13063317

—

#13063304

—

C₄×Dic₈₆

—

#13063284

—

#13063258

—

#13063256

—

C₄⋊(C₄₃⋊C₈)

—

C₂²⋊(C₄₃⋊C₈)

—

#13063236

—

#13063236

C₂×C₄

yes

—

C₄×C₄₃⋊C₈

—

C₄⋊Q₈×C₄₃

D₄

yes

—

#125×C₄₃

C₂×C₄

yes

—

C₂²⋊Q₈×C₄₃

—

C₄×Q₈×C₄₃

—

#117×C₄₃

D₄

yes

—

C₂×C₄²×C₄₃

C₂³

yes

characteristic

C₄⋊C₈×C₄₃

—

C₄⋊C₈×C₄₃

D₄

yes

—

C₂²⋊C₈×C₄₃

—

#97×C₄₃

—

#97×C₄₃

—

C₄×C₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂²×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₃

#41

yes

—

C₂×Dic₈₆

—

C₂×C₈×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

C₂²⋊C₄

yes

—

C₂²⋊C₄×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

C₂²×C₄

yes

characteristic

C₄²×C₄₃

C₂×D₄

yes

characteristic

C₄²×C₄₃

C₂×D₄

yes

—

C₂²⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

#123

yes

characteristic

Q₈×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₃

C₄×D₄

yes

—

C₂×C₄×C₄₃

#120

yes

characteristic

C₂×C₄×C₄₃

#121

yes

—

C₂×Dic₄₃

—

Dic₈₆

—

C₈×C₄₃

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

#9006

—

maximal, Sylow

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

#386

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

#456

yes

—

Dic₄₃

—

#3162

—

#2987

D₄₃

yes

—

—

—

C₂×C₄₃

—

C₂×C₄₃

#1881

yes

—

C₂×C₄₃

yes

—

C₂×D₄₃

yes

characteristic

#501

—

#501

—

100

#446

—

101

#433

—

102

#432

C₂×D₄₃

yes

—

103

#431

—

104

#427

—

105

C₂×#97

—

106

#332

—

107

Q₈⋊C₈

—

108

C₄₃

#9006

yes

characteristic, complemented, Sylow

109

C₂²×C₈

—

110

C₄⋊Q₈

—

111

C₄⋊Q₈

D₁₇₂

yes

—

112

#125

—

113

#125

C₄×D₄₃

yes

—

114

C₂²⋊Q₈

—

115

C₂²⋊Q₈

—

116

C₄×Q₈

—

117

C₄×Q₈

—

118

#117

—

119

#117

C₂²⋊D₄₃

yes

—

120

C₂×C₄²

C₂²×D₄₃

yes

characteristic

121

#107

—

122

#106

—

123

C₄⋊C₈

—

124

C₄⋊C₈

—

125

C₄⋊C₈

C₂²⋊D₄₃

yes

—

126

C₂²⋊C₈

—

127

C₂²⋊C₈

—

128

#97

—

129

#97

—

130

#97

—

131

#97

—

132

C₄×C₈

—

133

C₄×C₈

—

134

C₂×Q₈

—

135

C₂×Q₈

—

136

C₂²×C₄

#10621898

yes

—

137

C₂²×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

138

C₂×C₈

—

139

C₂×C₈

—

140

C₂×C₈

—

141

C₂×C₈

—

172

—

142

C₄⋊C₄

—

143

C₄⋊C₄

—

144

C₄⋊C₄

—

145

C₄⋊C₄

—

146

C₄⋊C₄

—

172

—

147

C₄⋊C₄

(C₂×D₄₃)⋊C₄

yes

—

148

C₂²⋊C₄

—

149

C₂²⋊C₄

—

172

—

150

C₄²

—

151

C₄²

—

172

—

152

C₄²

C₂×C₄×D₄₃

yes

characteristic

153

C₄²

C₂×D₁₇₂

yes

characteristic

154

C₄²

C₂×C₂²⋊D₄₃

yes

—

155

C₂³

#13063308

yes

characteristic

156

Q₈

—

157

Q₈

—

172

—

158

C₂×C₄

—

159

C₂×C₄

—

160

C₂×C₄

—

161

C₂×C₄

—

172

—

162

C₂×C₄

C₂×(C₂×D₄₃)⋊C₄

yes

characteristic

163

C₂×C₄

C₄×C₂²⋊D₄₃

yes

—

164

C₂×C₄

#13063294

yes

characteristic

165

C₂×C₄

#13063299

yes

—

166

C₈

—

167

C₈

—

168

C₈

—

344

—

169

C₂²

—

170

C₂²

—

171

C₂²

#14582778

yes

characteristic

172

C₄

—

173

C₄

—

174

C₄

—

175

C₄

—

176

C₄

—

344

—

177

C₄

#14583082

yes

—

178

C₂

—

179

C₂

#19134957

yes

—

180

C₂

#19134988

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#13063294
commutator	C₄²×C₄₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄₃×#2987	C₂
socle	C₂²×C₄₃	#386
prime radical	C₂³×C₄₃	#123
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	#2987	D₄₃
hypocenter	C₄₃	#9006
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #2987

subgroup

G/H

center

C₂×C₄

#13063294

commutator

C₄²×C₄₃

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₄₃

Fitting

C₄₃×#2987

C₂

C₂²×C₄₃

C₂³×C₄₃

C₂×C₄²×C₄₃

C₂³

D₄₃

C₄₃

G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #2987

N	H ≅ G/N	type
108. C₄₃	#9006	semidirect

H ≅ G/N

type

108. C₄₃

#9006

semidirect

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

subgroup	index
#19145117	2
#19133260	2
#19133067	2
#19132493	2
C₄₃×#2987	2
#9006	43

subgroup

index

C₄₃×#2987

Subgroups — #24991551

Conjugacy classes of subgroups

Complements

Maximal subgroups