Group #24987608 — subgroups

Subgroups — #24987608

Order 11008.

384 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 133 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	#19143530	C₂	1	1	yes	maximal, characteristic
2	#19133190	C₂	1	1	yes	maximal, characteristic
3	#19132876	C₂	1	2	yes	maximal
4	#19132486	C₂	1	2	yes	maximal
5	C₄₃×#1544	C₂	1	1	yes	maximal, characteristic
6	#14583030	—	2	2	no	—
7	Q₈×C₄₃⋊C₈	—	2	2	no	—
8	#14582926	C₄	1	2	yes	—
9	#14582923	C₂²	1	1	yes	characteristic
10	#14582855	C₄	1	2	yes	—
11	C₄×#10621877	C₂²	1	2	yes	—
12	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
13	#14582641	C₄	1	4	yes	—
14	#14582621	—	2	2	no	—
15	C₈×C₄₃⋊C₈	—	2	2	no	—
16	C₄₃×#533	C₂²	1	1	yes	characteristic
17	C₄₃×#431	C₂²	1	2	yes	—
18	C₄₃×#332	C₄	1	4	yes	—
19	C₂×#10621877	—	2	2	no	—
20	C₂×#10621877	C₂×C₄	1	2	yes	—
21	C₂²×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
22	C₂²×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
23	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
24	C₄⋊(C₄₃⋊C₈)	—	2	4	no	—
25	#13063236	—	2	2	no	—
26	#13063236	C₂×C₄	1	4	yes	—
27	C₄×C₄₃⋊C₈	—	2	2	no	—
28	C₄×C₄₃⋊C₈	—	2	2	no	—
29	C₄×C₄₃⋊C₈	D₄	1	2	yes	—
30	C₄×C₄₃⋊C₈	D₄	1	2	yes	—
31	C₄⋊Q₈×C₄₃	C₂×C₄	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	C₂×C₄	1	2	yes	—
36	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
37	C₄⋊C₈×C₄₃	C₂×C₄	1	4	yes	—
38	C₂²⋊C₈×C₄₃	—	2	2	no	—
39	C₄×C₈×C₄₃	—	2	2	no	—
40	C₂×Q₈×C₄₃	—	2	2	no	—
41	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
42	C₂²×C₄×C₄₃	#41	1	2	yes	—
43	C₂×C₈×C₄₃	—	2	4	no	—
44	C₄⋊C₄×C₄₃	—	2	4	no	—
45	C₄⋊C₄×C₄₃	—	2	2	no	—
46	C₄⋊C₄×C₄₃	C₄²	1	4	yes	—
47	C₂²⋊C₄×C₄₃	—	2	2	no	—
48	C₄²×C₄₃	—	2	2	no	—
49	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
50	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
51	C₄²×C₄₃	C₂×D₄	1	2	yes	—
52	#10621877	—	2	8	no	—
53	#10621877	—	4	2	no	—
54	C₂×C₄₃⋊C₈	—	2	4	no	—
55	C₂×C₄₃⋊C₈	—	2	2	no	—
56	C₂×C₄₃⋊C₈	—	2	2	no	—
57	C₂×C₄₃⋊C₈	—	4	1	no	—
58	C₂×C₄₃⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
59	C₂×C₄₃⋊C₈	C₂²⋊C₄	1	2	yes	—
60	C₂×C₄₃⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
61	C₂³×C₄₃	#117	1	1	yes	characteristic
62	Q₈×C₄₃	—	4	4	no	—
63	C₂×C₄×C₄₃	—	2	1	no	—
64	C₂×C₄×C₄₃	—	2	1	no	—
65	C₂×C₄×C₄₃	—	2	4	no	—
66	C₂×C₄×C₄₃	—	2	4	no	—
67	C₂×C₄×C₄₃	C₂×C₄²	1	1	yes	characteristic
68	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
69	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
70	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
71	C₈×C₄₃	—	4	4	no	—
72	C₄₃⋊C₈	—	2	8	no	—
73	C₄₃⋊C₈	—	2	1	no	—
74	C₄₃⋊C₈	—	2	2	no	—
75	C₄₃⋊C₈	—	4	2	no	—
76	C₄₃⋊C₈	#101	1	2	yes	—
77	#8242	—	43	1	no	maximal, Sylow
78	C₂²×C₄₃	—	2	1	no	—
79	C₂²×C₄₃	—	2	2	no	—
80	C₂²×C₄₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
81	C₄×C₄₃	—	2	1	no	—
82	C₄×C₄₃	—	2	2	no	—
83	C₄×C₄₃	—	4	4	no	—
84	C₄×C₄₃	C₂×#101	1	1	yes	characteristic
85	C₄×C₄₃	#413	1	1	yes	characteristic
86	C₄×C₄₃	#443	1	4	yes	—
87	#2960	—	43	1	no	—
88	#1544	D₄₃	1	1	yes	characteristic
89	#1526	—	43	1	no	—
90	C₈×M₁₆	—	43	2	no	—
91	#1299	—	43	2	no	—
92	C₂×C₄₃	—	4	1	no	—
93	C₂×C₄₃	C₄×#101	1	1	yes	characteristic
94	C₂×C₄₃	#1764	1	2	yes	—
95	#533	C₂×D₄₃	1	1	yes	characteristic
96	#446	—	86	2	no	—
97	C₈×Q₈	—	86	2	no	—
98	#431	C₂×D₄₃	1	2	yes	—
99	#424	—	43	2	no	—
100	#423	—	43	1	no	—
101	#405	—	43	2	no	—
102	C₄×M₁₆	—	43	2	no	—
103	C₂×C₄×C₈	—	43	1	no	—
104	#332	Dic₄₃	1	4	yes	—
105	#330	—	43	4	no	—
106	#322	—	86	2	no	—
107	C₈²	—	86	2	no	—
108	C₄₃	#8242	1	1	yes	characteristic, complemented, Sylow
109	C₂×M₁₆	—	43	2	no	—
110	C₂×M₁₆	—	86	2	no	—
111	C₂²×C₈	—	43	1	no	—
112	C₂²×C₈	—	43	1	no	—
113	C₄⋊Q₈	C₂×Dic₄₃	1	2	yes	—
114	#125	C₄×D₄₃	1	2	yes	—
115	C₂²⋊Q₈	—	2	2	no	—
116	C₄×Q₈	—	2	2	no	—
117	#117	C₄×D₄₃	1	2	yes	—
118	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
119	C₄⋊C₈	—	86	4	no	—
120	C₄⋊C₈	—	86	2	no	—
121	C₄⋊C₈	C₂×Dic₄₃	1	4	yes	—
122	C₂²⋊C₈	—	2	2	no	—
123	#97	—	43	4	no	—
124	#97	—	86	2	no	—
125	C₄×C₈	—	2	2	no	—
126	C₄×C₈	—	43	2	no	—
127	C₄×C₈	—	43	2	no	—
128	C₄×C₈	—	86	2	no	—
129	C₄×C₈	—	86	2	no	—
130	C₂×Q₈	—	2	2	no	—
131	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
132	C₂²×C₄	#10621900	1	2	yes	—
133	M₁₆	—	86	8	no	—
134	M₁₆	—	172	2	no	—
135	C₂×C₈	—	2	4	no	—
136	C₂×C₈	—	43	1	no	—
137	C₂×C₈	—	43	1	no	—
138	C₂×C₈	—	43	2	no	—
139	C₂×C₈	—	86	2	no	—
140	C₂×C₈	—	86	4	no	—
141	C₂×C₈	—	86	2	no	—
142	C₂×C₈	—	172	1	no	—
143	C₄⋊C₄	—	2	4	no	—
144	C₄⋊C₄	—	2	2	no	—
145	C₄⋊C₄	C₄×Dic₄₃	1	4	yes	—
146	C₂²⋊C₄	—	2	2	no	—
147	C₄²	—	2	2	no	—
148	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
149	C₄²	D₄×D₄₃	1	2	yes	—
150	C₄²	C₂²×Dic₄₃	1	1	yes	characteristic
151	C₂³	#13063281	1	1	yes	characteristic
152	Q₈	—	4	4	no	—
153	C₂×C₄	—	2	1	no	—
154	C₂×C₄	—	2	1	no	—
155	C₂×C₄	—	2	4	no	—
156	C₂×C₄	—	2	4	no	—
157	C₂×C₄	C₂×C₄×Dic₄₃	1	1	yes	characteristic
158	C₂×C₄	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
159	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	2	yes	—
160	C₂×C₄	D₄×Dic₄₃	1	2	yes	—
161	C₈	—	4	4	no	—
162	C₈	—	43	2	no	—
163	C₈	—	86	8	no	—
164	C₈	—	86	1	no	—
165	C₈	—	86	2	no	—
166	C₈	—	172	2	no	—
167	C₂²	—	2	1	no	—
168	C₂²	—	2	2	no	—
169	C₂²	C₂²⋊C₄×Dic₄₃	1	1	yes	characteristic
170	C₄	—	2	1	no	—
171	C₄	—	2	2	no	—
172	C₄	—	4	4	no	—
173	C₄	#101×D₄₃	1	1	yes	characteristic
174	C₄	#14582882	1	1	yes	characteristic
175	C₄	#14583016	1	4	yes	—
176	C₂	—	4	1	no	—
177	C₂	#101×Dic₄₃	1	1	yes	characteristic
178	C₂	#19134435	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#19143530

C₂

yes

maximal, characteristic

#19133190

C₂

yes

maximal, characteristic

#19132876

C₂

yes

maximal

#19132486

C₂

yes

maximal

C₄₃×#1544

C₂

yes

maximal, characteristic

#14583030

—

Q₈×C₄₃⋊C₈

—

#14582926

C₄

yes

—

#14582923

C₂²

yes

characteristic

#14582855

C₄

yes

—

C₄×#10621877

C₂²

yes

—

C₂×C₄×C₄₃⋊C₈

C₂²

yes

characteristic

#14582641

C₄

yes

—

#14582621

—

C₈×C₄₃⋊C₈

—

C₄₃×#533

C₂²

yes

characteristic

C₄₃×#431

C₂²

yes

—

C₄₃×#332

C₄

yes

—

C₂×#10621877

—

C₂×#10621877

C₂×C₄

yes

—

C₂²×C₄₃⋊C₈

C₂×C₄

yes

characteristic

C₂²×C₄₃⋊C₈

C₂×C₄

yes

characteristic

C₄⋊(C₄₃⋊C₈)

—

C₄⋊(C₄₃⋊C₈)

—

#13063236

—

#13063236

C₂×C₄

yes

—

C₄×C₄₃⋊C₈

—

C₄×C₄₃⋊C₈

—

C₄×C₄₃⋊C₈

D₄

yes

—

C₄×C₄₃⋊C₈

D₄

yes

—

C₄⋊Q₈×C₄₃

C₂×C₄

yes

—

#125×C₄₃

C₂×C₄

yes

—

C₂²⋊Q₈×C₄₃

—

C₄×Q₈×C₄₃

—

#117×C₄₃

C₂×C₄

yes

—

C₂×C₄²×C₄₃

C₂³

yes

characteristic

C₄⋊C₈×C₄₃

C₂×C₄

yes

—

C₂²⋊C₈×C₄₃

—

C₄×C₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂²×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂²×C₄×C₄₃

#41

yes

—

C₂×C₈×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

C₄²

yes

—

C₂²⋊C₄×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

C₂²×C₄

yes

characteristic

C₄²×C₄₃

C₂²×C₄

yes

characteristic

C₄²×C₄₃

C₂×D₄

yes

—

#10621877

—

#10621877

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

C₂²⋊C₄

yes

characteristic

C₂×C₄₃⋊C₈

C₂²⋊C₄

yes

—

C₂×C₄₃⋊C₈

C₂²⋊C₄

yes

characteristic

C₂³×C₄₃

#117

yes

characteristic

Q₈×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×C₄²

yes

characteristic

C₂×C₄×C₄₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₃

C₄×D₄

yes

—

C₂×C₄×C₄₃

C₄×D₄

yes

—

C₈×C₄₃

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

C₄₃⋊C₈

#101

yes

—

#8242

—

maximal, Sylow

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

C₄×C₂²⋊C₄

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

yes

C₄×C₄₃

yes

C₄×C₄₃

yes

—

#2960

—

#1544

D₄₃

yes

characteristic

#1526

—

C₈×M₁₆

—

#1299

—

C₂×C₄₃

—

C₂×C₄₃

C₄×#101

yes

characteristic

C₂×C₄₃

#1764

yes

—

#533

C₂×D₄₃

yes

characteristic

#446

—

C₈×Q₈

—

#431

C₂×D₄₃

yes

—

#424

—

100

#423

—

101

#405

—

102

C₄×M₁₆

—

103

C₂×C₄×C₈

—

104

#332

Dic₄₃

yes

—

105

#330

—

106

#322

—

107

C₈²

—

108

C₄₃

#8242

yes

characteristic, complemented, Sylow

109

C₂×M₁₆

—

110

C₂×M₁₆

—

111

C₂²×C₈

—

112

C₂²×C₈

—

113

C₄⋊Q₈

C₂×Dic₄₃

yes

—

114

#125

C₄×D₄₃

yes

—

115

C₂²⋊Q₈

—

116

C₄×Q₈

—

117

#117

C₄×D₄₃

yes

—

118

C₂×C₄²

C₂²×D₄₃

yes

characteristic

119

C₄⋊C₈

—

120

C₄⋊C₈

—

121

C₄⋊C₈

C₂×Dic₄₃

yes

—

122

C₂²⋊C₈

—

123

#97

—

124

#97

—

125

C₄×C₈

—

126

C₄×C₈

—

127

C₄×C₈

—

128

C₄×C₈

—

129

C₄×C₈

—

130

C₂×Q₈

—

131

C₂²×C₄

C₂×C₄×D₄₃

yes

characteristic

132

C₂²×C₄

#10621900

yes

—

133

M₁₆

—

134

M₁₆

—

172

—

135

C₂×C₈

—

136

C₂×C₈

—

137

C₂×C₈

—

138

C₂×C₈

—

139

C₂×C₈

—

140

C₂×C₈

—

141

C₂×C₈

—

142

C₂×C₈

—

172

—

143

C₄⋊C₄

—

144

C₄⋊C₄

—

145

C₄⋊C₄

C₄×Dic₄₃

yes

—

146

C₂²⋊C₄

—

147

C₄²

—

148

C₄²

C₂×C₄×D₄₃

yes

characteristic

149

C₄²

D₄×D₄₃

yes

—

150

C₄²

C₂²×Dic₄₃

yes

characteristic

151

C₂³

#13063281

yes

characteristic

152

Q₈

—

153

C₂×C₄

—

154

C₂×C₄

—

155

C₂×C₄

—

156

C₂×C₄

—

157

C₂×C₄

C₂×C₄×Dic₄₃

yes

characteristic

158

C₂×C₄

C₂²⋊C₄×D₄₃

yes

characteristic

159

C₂×C₄

(C₂²⋊D₄₃)⋊C₄

yes

—

160

C₂×C₄

D₄×Dic₄₃

yes

—

161

C₈

—

162

C₈

—

163

C₈

—

164

C₈

—

165

C₈

—

166

C₈

—

172

—

167

C₂²

—

168

C₂²

—

169

C₂²

C₂²⋊C₄×Dic₄₃

yes

characteristic

170

C₄

—

171

C₄

—

172

C₄

—

173

C₄

#101×D₄₃

yes

characteristic

174

C₄

#14582882

yes

characteristic

175

C₄

#14583016

yes

—

176

C₂

—

177

C₂

#101×Dic₄₃

yes

characteristic

178

C₂

#19134435

yes

—

	subgroup	G/H
center	C₂×C₄	C₂²⋊C₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄₃×#1544	C₂
socle	C₂²×C₄₃	C₄×C₂²⋊C₄
prime radical	C₂³×C₄₃	#117
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	#1544	D₄₃
hypocenter	C₄₃	#8242
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1544

subgroup

G/H

center

C₂×C₄

C₂²⋊C₄×D₄₃

commutator

C₂×C₄×C₄₃

C₂×C₄²

Frattini

C₂×C₄²

C₂²×D₄₃

Fitting

C₄₃×#1544

C₂

socle

C₂²×C₄₃

C₄×C₂²⋊C₄

prime radical

C₂³×C₄₃

#117

cosocle

C₂×C₄²×C₄₃

C₂³

D₄₃

C₄₃

G ▷ C₂×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1544

N	H ≅ G/N	type
108. C₄₃	#8242	semidirect

H ≅ G/N

type

108. C₄₃

#8242

semidirect

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

subgroup	index
#19143530	2
#19133190	2
#19132876	2
#19132486	2
C₄₃×#1544	2
#8242	43

subgroup

index

C₄₃×#1544

Subgroups — #24987608

Conjugacy classes of subgroups

Complements

Maximal subgroups