Group #23790371 — subgroups

Subgroups — C₄₁×#14170 #23790371

Order 10496.

1494 conjugacy classes of subgroups; only the 494 normal subgroups are shown.

normal subgroups only

This group has 1494 conjugacy classes of subgroups — too many to draw. Only its 494 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	C₂²×#125×C₄₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₁×#376	C₂	1	2	yes	maximal
3	C₄₁×#1445	C₂	1	4	yes	maximal
4	C₄₁×#1436	C₂	1	8	yes	maximal
5	C₂×#125×C₄₁	—	2	8	no	—
6	C₂×#125×C₄₁	C₄	1	8	yes	complemented
7	C₂²×C₄⋊C₄×C₄₁	C₂²	1	4	yes	—
8	C₂²×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
9	C₂²×C₄²×C₄₁	C₂²	1	4	yes	—
10	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
11	C₄₁×#376	—	2	8	no	—
12	C₂×#95×C₄₁	C₂²	1	16	yes	—
13	C₂×#95×C₄₁	C₂²	1	4	yes	—
14	C₂×#95×C₄₁	C₂²	1	4	yes	—
15	C₂³×C₄×C₄₁	C₂³	1	4	yes	—
16	C₂³×C₄×C₄₁	C₂³	1	8	yes	—
17	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
18	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
19	#125×C₄₁	—	2	32	no	—
20	C₂×C₄⋊C₄×C₄₁	—	2	8	no	—
21	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
22	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
23	C₂×C₄⋊C₄×C₄₁	—	2	8	no	—
24	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	16	yes	—
25	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	8	yes	—
26	C₂×C₄²×C₄₁	—	2	8	no	—
27	C₂×C₄²×C₄₁	—	2	16	no	—
28	C₂×C₄²×C₄₁	C₂×C₄	1	4	yes	—
29	C₂×C₄²×C₄₁	D₄	1	8	yes	—
30	#95×C₄₁	—	2	8	no	—
31	#95×C₄₁	—	2	8	no	—
32	#95×C₄₁	—	2	32	no	—
33	C₂⁴×C₄₁	C₂⁴	1	1	yes	characteristic
34	C₂²×C₄×C₄₁	—	2	8	no	—
35	C₂²×C₄×C₄₁	—	2	4	no	—
36	C₂²×C₄×C₄₁	—	2	8	no	—
37	C₂²×C₄×C₄₁	—	2	4	no	—
38	C₂²×C₄×C₄₁	—	2	4	no	—
39	C₂²×C₄×C₄₁	—	2	16	no	—
40	C₂²×C₄×C₄₁	—	2	16	no	—
41	C₂²×C₄×C₄₁	—	2	8	no	—
42	C₂²×C₄×C₄₁	—	2	16	no	—
43	C₂²×C₄×C₄₁	C₂²×C₄	1	8	yes	—
44	C₂²×C₄×C₄₁	C₂²×C₄	1	4	yes	—
45	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
46	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
47	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
48	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
49	C₂²×C₄×C₄₁	#41	1	16	yes	—
50	C₄⋊C₄×C₄₁	—	2	16	no	—
51	C₄⋊C₄×C₄₁	—	2	32	no	—
52	C₄²×C₄₁	—	2	32	no	—
53	C₄²×C₄₁	C₂²⋊C₄	1	16	yes	—
54	C₂³×C₄₁	C₂³×C₄	1	1	yes	characteristic
55	C₂³×C₄₁	C₂²×D₄	1	2	yes	—
56	C₂³×C₄₁	C₂×#41	1	8	yes	—
57	C₂³×C₄₁	2₋¹⁺⁴	1	4	yes	—
58	C₂×C₄×C₄₁	—	2	8	no	—
59	C₂×C₄×C₄₁	—	2	4	no	—
60	C₂×C₄×C₄₁	—	2	8	no	—
61	C₂×C₄×C₄₁	—	2	8	no	—
62	C₂×C₄×C₄₁	—	2	8	no	—
63	C₂×C₄×C₄₁	—	2	8	no	—
64	C₂×C₄×C₄₁	—	2	16	no	—
65	C₂×C₄×C₄₁	—	2	16	no	—
66	C₂×C₄×C₄₁	—	2	32	no	—
67	C₂×C₄×C₄₁	—	4	8	no	—
68	C₂×C₄×C₄₁	—	4	8	no	—
69	C₂×C₄×C₄₁	—	4	8	no	—
70	C₂×C₄×C₄₁	—	4	8	no	—
71	C₂×C₄×C₄₁	—	4	16	no	—
72	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	4	yes	—
73	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	8	yes	—
74	#14170	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
75	C₂²×C₄₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
76	C₂²×C₄₁	C₄×#41	1	4	yes	—
77	C₂²×C₄₁	#519	1	2	yes	—
78	C₂²×C₄₁	#525	1	4	yes	—
79	C₂²×C₄₁	#532	1	4	yes	—
80	C₂²×C₄₁	#536	1	4	yes	—
81	C₂²×C₄₁	#552	1	16	yes	—
82	C₄×C₄₁	—	2	4	no	—
83	C₄×C₄₁	—	2	8	no	—
84	C₄×C₄₁	—	4	16	no	—
85	C₄×C₄₁	—	4	8	no	—
86	C₂²×#125	C₂×C₄₁	1	1	yes	characteristic
87	C₂×#376	C₂×C₄₁	1	2	yes	—
88	#1445	C₂×C₄₁	1	4	yes	—
89	#1436	C₂×C₄₁	1	8	yes	—
90	C₂×C₄₁	#2297	1	2	yes	—
91	C₂×C₄₁	#2310	1	1	yes	characteristic
92	C₂×C₄₁	#2371	1	4	yes	—
93	C₂×C₄₁	#2611	1	8	yes	—
94	C₂×#125	—	2	8	no	—
95	C₂×#125	C₄×C₄₁	1	8	yes	complemented
96	C₂²×C₄⋊C₄	C₂²×C₄₁	1	4	yes	—
97	C₂²×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
98	C₂²×C₄²	C₂²×C₄₁	1	4	yes	—
99	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
100	#376	—	2	8	no	—
101	C₂×#95	C₂²×C₄₁	1	16	yes	—
102	C₂×#95	C₂²×C₄₁	1	4	yes	—
103	C₂×#95	C₂²×C₄₁	1	4	yes	—
104	C₄₁	#14170	1	1	yes	characteristic, direct product factor, Sylow
105	C₂³×C₄	C₂³×C₄₁	1	4	yes	—
106	C₂³×C₄	C₂³×C₄₁	1	8	yes	—
107	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
108	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
109	#125	—	2	32	no	—
110	C₂×C₄⋊C₄	—	2	8	no	—
111	C₂×C₄⋊C₄	—	2	4	no	—
112	C₂×C₄⋊C₄	—	2	4	no	—
113	C₂×C₄⋊C₄	—	2	8	no	—
114	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	16	yes	—
115	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	8	yes	—
116	C₂×C₄²	—	2	8	no	—
117	C₂×C₄²	—	2	16	no	—
118	C₂×C₄²	C₂×C₄×C₄₁	1	4	yes	—
119	C₂×C₄²	D₄×C₄₁	1	8	yes	—
120	#95	—	2	8	no	—
121	#95	—	2	8	no	—
122	#95	—	2	32	no	—
123	C₂⁴	C₂⁴×C₄₁	1	1	yes	characteristic
124	C₂²×C₄	—	2	8	no	—
125	C₂²×C₄	—	2	4	no	—
126	C₂²×C₄	—	2	8	no	—
127	C₂²×C₄	—	2	4	no	—
128	C₂²×C₄	—	2	4	no	—
129	C₂²×C₄	—	2	16	no	—
130	C₂²×C₄	—	2	16	no	—
131	C₂²×C₄	—	2	8	no	—
132	C₂²×C₄	—	2	16	no	—
133	C₂²×C₄	C₂²×C₄×C₄₁	1	8	yes	—
134	C₂²×C₄	C₂²×C₄×C₄₁	1	4	yes	—
135	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
136	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
137	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
138	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
139	C₂²×C₄	#41×C₄₁	1	16	yes	—
140	C₄⋊C₄	—	2	32	no	—
141	C₄⋊C₄	—	2	16	no	—
142	C₄²	—	2	32	no	—
143	C₄²	C₂²⋊C₄×C₄₁	1	16	yes	—
144	C₂³	C₂³×C₄×C₄₁	1	1	yes	characteristic
145	C₂³	C₂²×D₄×C₄₁	1	2	yes	—
146	C₂³	C₂×#41×C₄₁	1	8	yes	—
147	C₂³	2₋¹⁺⁴×C₄₁	1	4	yes	—
148	C₂×C₄	—	2	8	no	—
149	C₂×C₄	—	2	4	no	—
150	C₂×C₄	—	2	8	no	—
151	C₂×C₄	—	2	8	no	—
152	C₂×C₄	—	2	8	no	—
153	C₂×C₄	—	2	8	no	—
154	C₂×C₄	—	2	16	no	—
155	C₂×C₄	—	2	16	no	—
156	C₂×C₄	—	2	32	no	—
157	C₂×C₄	—	4	8	no	—
158	C₂×C₄	—	4	8	no	—
159	C₂×C₄	—	4	8	no	—
160	C₂×C₄	—	4	8	no	—
161	C₂×C₄	—	4	16	no	—
162	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	8	yes	—
163	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	4	yes	—
164	C₂²	C₂²×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
165	C₂²	C₄×#41×C₄₁	1	4	yes	—
166	C₂²	C₄₁×#519	1	2	yes	—
167	C₂²	C₄₁×#525	1	4	yes	—
168	C₂²	C₄₁×#532	1	4	yes	—
169	C₂²	C₄₁×#536	1	4	yes	—
170	C₂²	C₄₁×#552	1	16	yes	—
171	C₄	—	2	8	no	—
172	C₄	—	2	4	no	—
173	C₄	—	4	8	no	—
174	C₄	—	4	16	no	—
175	C₂	C₄₁×#2297	1	2	yes	—
176	C₂	C₄₁×#2310	1	1	yes	characteristic
177	C₂	C₄₁×#2371	1	4	yes	—
178	C₂	C₄₁×#2611	1	8	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#125×C₄₁

C₂

yes

maximal, characteristic

C₂×C₄₁×#376

C₂

yes

maximal

C₄₁×#1445

C₂

yes

maximal

C₄₁×#1436

C₂

yes

maximal

C₂×#125×C₄₁

—

C₂×#125×C₄₁

C₄

yes

complemented

C₂²×C₄⋊C₄×C₄₁

C₂²

yes

—

C₂²×C₄⋊C₄×C₄₁

C₂²

yes

—

C₂²×C₄²×C₄₁

C₂²

yes

—

C₂²×C₄²×C₄₁

C₂²

yes

characteristic

C₄₁×#376

—

C₂×#95×C₄₁

C₂²

yes

—

C₂×#95×C₄₁

C₂²

yes

—

C₂×#95×C₄₁

C₂²

yes

—

C₂³×C₄×C₄₁

C₂³

yes

—

C₂³×C₄×C₄₁

C₂³

yes

—

C₂³×C₄×C₄₁

C₂³

yes

—

C₂³×C₄×C₄₁

C₂³

yes

characteristic

#125×C₄₁

—

C₂×C₄⋊C₄×C₄₁

—

C₂×C₄⋊C₄×C₄₁

—

C₂×C₄⋊C₄×C₄₁

—

C₂×C₄⋊C₄×C₄₁

—

C₂×C₄⋊C₄×C₄₁

C₂×C₄

yes

—

C₂×C₄⋊C₄×C₄₁

C₂×C₄

yes

—

C₂×C₄²×C₄₁

—

C₂×C₄²×C₄₁

—

C₂×C₄²×C₄₁

C₂×C₄

yes

—

C₂×C₄²×C₄₁

D₄

yes

—

#95×C₄₁

—

#95×C₄₁

—

#95×C₄₁

—

C₂⁴×C₄₁

C₂⁴

yes

characteristic

C₂²×C₄×C₄₁

—

C₂²×C₄×C₄₁

—

C₂²×C₄×C₄₁

—

C₂²×C₄×C₄₁

—

C₂²×C₄×C₄₁

—

C₂²×C₄×C₄₁

—

C₂²×C₄×C₄₁

—

C₂²×C₄×C₄₁

—

C₂²×C₄×C₄₁

—

C₂²×C₄×C₄₁

C₂²×C₄

yes

—

C₂²×C₄×C₄₁

C₂²×C₄

yes

—

C₂²×C₄×C₄₁

C₂²×C₄

yes

—

C₂²×C₄×C₄₁

C₂×D₄

yes

—

C₂²×C₄×C₄₁

C₂×D₄

yes

—

C₂²×C₄×C₄₁

C₂×D₄

yes

—

C₂²×C₄×C₄₁

#41

yes

—

C₄⋊C₄×C₄₁

—

C₄⋊C₄×C₄₁

—

C₄²×C₄₁

—

C₄²×C₄₁

C₂²⋊C₄

yes

—

C₂³×C₄₁

C₂³×C₄

yes

characteristic

C₂³×C₄₁

C₂²×D₄

yes

—

C₂³×C₄₁

C₂×#41

yes

—

C₂³×C₄₁

2₋¹⁺⁴

yes

—

C₂×C₄×C₄₁

—

C₂×C₄×C₄₁

—

C₂×C₄×C₄₁

—

C₂×C₄×C₄₁

—

C₂×C₄×C₄₁

—

C₂×C₄×C₄₁

—

C₂×C₄×C₄₁

—

C₂×C₄×C₄₁

—

C₂×C₄×C₄₁

—

C₂×C₄×C₄₁

—

C₂×C₄×C₄₁

—

C₂×C₄×C₄₁

—

C₂×C₄×C₄₁

—

C₂×C₄×C₄₁

—

C₂×C₄×C₄₁

C₂×C₂²⋊C₄

yes

—

C₂×C₄×C₄₁

C₂×C₂²⋊C₄

yes

—

#14170

C₄₁

yes

maximal, characteristic, direct product factor, Sylow

C₂²×C₄₁

C₂²×C₂²⋊C₄

yes

characteristic

C₂²×C₄₁

C₄×#41

yes

—

C₂²×C₄₁

#519

yes

—

C₂²×C₄₁

#525

yes

—

C₂²×C₄₁

#532

yes

—

C₂²×C₄₁

#536

yes

—

C₂²×C₄₁

#552

yes

—

C₄×C₄₁

—

C₄×C₄₁

—

C₄×C₄₁

—

C₄×C₄₁

—

C₂²×#125

C₂×C₄₁

yes

characteristic

C₂×#376

C₂×C₄₁

yes

—

#1445

C₂×C₄₁

yes

—

#1436

C₂×C₄₁

yes

—

C₂×C₄₁

#2297

yes

—

C₂×C₄₁

#2310

yes

characteristic

C₂×C₄₁

#2371

yes

—

C₂×C₄₁

#2611

yes

—

C₂×#125

—

C₂×#125

C₄×C₄₁

yes

complemented

C₂²×C₄⋊C₄

C₂²×C₄₁

yes

—

C₂²×C₄⋊C₄

C₂²×C₄₁

yes

—

C₂²×C₄²

C₂²×C₄₁

yes

—

C₂²×C₄²

C₂²×C₄₁

yes

characteristic

100

#376

—

101

C₂×#95

C₂²×C₄₁

yes

—

102

C₂×#95

C₂²×C₄₁

yes

—

103

C₂×#95

C₂²×C₄₁

yes

—

104

C₄₁

#14170

yes

characteristic, direct product factor, Sylow

105

C₂³×C₄

C₂³×C₄₁

yes

—

106

C₂³×C₄

C₂³×C₄₁

yes

—

107

C₂³×C₄

C₂³×C₄₁

yes

characteristic

108

C₂³×C₄

C₂³×C₄₁

yes

—

109

#125

—

110

C₂×C₄⋊C₄

—

111

C₂×C₄⋊C₄

—

112

C₂×C₄⋊C₄

—

113

C₂×C₄⋊C₄

—

114

C₂×C₄⋊C₄

C₂×C₄×C₄₁

yes

—

115

C₂×C₄⋊C₄

C₂×C₄×C₄₁

yes

—

116

C₂×C₄²

—

117

C₂×C₄²

—

118

C₂×C₄²

C₂×C₄×C₄₁

yes

—

119

C₂×C₄²

D₄×C₄₁

yes

—

120

#95

—

121

#95

—

122

#95

—

123

C₂⁴

C₂⁴×C₄₁

yes

characteristic

124

C₂²×C₄

—

125

C₂²×C₄

—

126

C₂²×C₄

—

127

C₂²×C₄

—

128

C₂²×C₄

—

129

C₂²×C₄

—

130

C₂²×C₄

—

131

C₂²×C₄

—

132

C₂²×C₄

—

133

C₂²×C₄

C₂²×C₄×C₄₁

yes

—

134

C₂²×C₄

C₂²×C₄×C₄₁

yes

—

135

C₂²×C₄

C₂²×C₄×C₄₁

yes

—

136

C₂²×C₄

C₂×D₄×C₄₁

yes

—

137

C₂²×C₄

C₂×D₄×C₄₁

yes

—

138

C₂²×C₄

C₂×D₄×C₄₁

yes

—

139

C₂²×C₄

#41×C₄₁

yes

—

140

C₄⋊C₄

—

141

C₄⋊C₄

—

142

C₄²

—

143

C₄²

C₂²⋊C₄×C₄₁

yes

—

144

C₂³

C₂³×C₄×C₄₁

yes

characteristic

145

C₂³

C₂²×D₄×C₄₁

yes

—

146

C₂³

C₂×#41×C₄₁

yes

—

147

C₂³

2₋¹⁺⁴×C₄₁

yes

—

148

C₂×C₄

—

149

C₂×C₄

—

150

C₂×C₄

—

151

C₂×C₄

—

152

C₂×C₄

—

153

C₂×C₄

—

154

C₂×C₄

—

155

C₂×C₄

—

156

C₂×C₄

—

157

C₂×C₄

—

158

C₂×C₄

—

159

C₂×C₄

—

160

C₂×C₄

—

161

C₂×C₄

—

162

C₂×C₄

C₂×C₂²⋊C₄×C₄₁

yes

—

163

C₂×C₄

C₂×C₂²⋊C₄×C₄₁

yes

—

164

C₂²

C₂²×C₂²⋊C₄×C₄₁

yes

characteristic

165

C₂²

C₄×#41×C₄₁

yes

—

166

C₂²

C₄₁×#519

yes

—

167

C₂²

C₄₁×#525

yes

—

168

C₂²

C₄₁×#532

yes

—

169

C₂²

C₄₁×#536

yes

—

170

C₂²

C₄₁×#552

yes

—

171

C₄

—

172

C₄

—

173

C₄

—

174

C₄

—

175

C₂

C₄₁×#2297

yes

—

176

C₂

C₄₁×#2310

yes

characteristic

177

C₂

C₄₁×#2371

yes

—

178

C₂

C₄₁×#2611

yes

—

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₄₁	C₂⁴
commutator	C₂³	C₂³×C₄×C₄₁
Frattini, cosocle	C₂⁴	C₂⁴×C₄₁
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₄₁ ◁ G

subgroup

G/H

center, socle, prime radical

C₂⁴×C₄₁

C₂⁴

commutator

C₂³

C₂³×C₄×C₄₁

Frattini, cosocle

C₂⁴

C₂⁴×C₄₁

LCS

G ▷ C₂³ ▷ C₁

UCS

C₁ ◁ C₂⁴×C₄₁ ◁ G

N	H ≅ G/N	type
6. C₂×#125×C₄₁	C₄	semidirect
74. #14170	C₄₁	direct (N × H)
95. C₂×#125	C₄×C₄₁	semidirect
104. C₄₁	#14170	direct (N × H)

H ≅ G/N

type

6. C₂×#125×C₄₁

C₄

semidirect

74. #14170

C₄₁

direct (N × H)

95. C₂×#125

C₄×C₄₁

semidirect

104. C₄₁

#14170

direct (N × H)

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

subgroup	index
C₂²×#125×C₄₁	2
C₂×C₄₁×#376	2
C₄₁×#1445	2
C₄₁×#1436	2
#14170	41

subgroup

index

C₂²×#125×C₄₁

C₂×C₄₁×#376

C₄₁×#1445

C₄₁×#1436

#14170

Subgroups — C₄₁×#14170 #23790371

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C41×#14170 #23790371

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#14170 #23790371