Group #23787584 — subgroups

Subgroups — C₄₁×#11383 #23787584

Order 10496.

926 conjugacy classes of subgroups; only the 270 normal subgroups are shown.

normal subgroups only

This group has 926 conjugacy classes of subgroups — too many to draw. Only its 270 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×#343	C₂	1	4	yes	maximal
3	C₄₁×#1728	C₂	1	2	yes	maximal
4	C₂²×M₁₆×C₄₁	C₂²	1	4	yes	—
5	C₂×#125×C₄₁	—	2	8	no	—
6	C₂×#125×C₄₁	—	2	4	no	—
7	C₂²×C₄⋊C₄×C₄₁	C₄	1	4	yes	—
8	C₂²×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
9	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
10	C₄₁×#343	—	2	8	no	—
11	C₄₁×#336	—	2	4	no	—
12	C₂³×C₄×C₄₁	C₂×C₄	1	2	yes	—
13	C₂³×C₄×C₄₁	C₂×C₄	1	4	yes	—
14	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
15	C₂×M₁₆×C₄₁	—	2	4	no	—
16	C₂×M₁₆×C₄₁	—	2	8	no	—
17	C₂×M₁₆×C₄₁	—	2	8	no	—
18	C₂×M₁₆×C₄₁	Q₈	1	8	yes	—
19	C₂²×C₈×C₄₁	—	2	4	no	—
20	#125×C₄₁	—	2	32	no	—
21	C₂×C₄⋊C₄×C₄₁	—	2	8	no	—
22	C₂×C₄⋊C₄×C₄₁	—	2	8	no	—
23	C₂×C₄⋊C₄×C₄₁	—	2	8	no	—
24	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
25	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
26	C₂×C₄⋊C₄×C₄₁	D₄	1	8	yes	—
27	C₂×C₄²×C₄₁	—	2	4	no	—
28	C₂×C₄²×C₄₁	D₄	1	4	yes	—
29	C₂⁴×C₄₁	C₂²×C₄	1	1	yes	characteristic
30	C₂²×C₄×C₄₁	—	2	2	no	—
31	C₂²×C₄×C₄₁	—	2	2	no	—
32	C₂²×C₄×C₄₁	—	2	4	no	—
33	C₂²×C₄×C₄₁	—	2	4	no	—
34	C₂²×C₄×C₄₁	—	4	4	no	—
35	C₂²×C₄×C₄₁	—	4	8	no	—
36	C₂²×C₄×C₄₁	C₂²⋊C₄	1	4	yes	—
37	C₂²×C₄×C₄₁	C₂²⋊C₄	1	8	yes	—
38	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
39	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
40	C₂²×C₄×C₄₁	C₂×Q₈	1	4	yes	—
41	C₂²×C₄×C₄₁	#41	1	4	yes	—
42	M₁₆×C₄₁	—	2	16	no	—
43	M₁₆×C₄₁	—	4	8	no	—
44	C₂×C₈×C₄₁	—	2	8	no	—
45	C₂×C₈×C₄₁	—	4	4	no	—
46	C₂×C₈×C₄₁	—	4	4	no	—
47	C₄⋊C₄×C₄₁	—	2	32	no	—
48	C₄⋊C₄×C₄₁	—	2	16	no	—
49	C₄²×C₄₁	—	2	8	no	—
50	C₂³×C₄₁	—	2	4	no	—
51	C₂³×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
52	C₂³×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
53	C₂³×C₄₁	C₄×Q₈	1	4	yes	—
54	C₂×C₄×C₄₁	—	2	4	no	—
55	C₂×C₄×C₄₁	—	2	8	no	—
56	C₂×C₄×C₄₁	—	2	8	no	—
57	C₂×C₄×C₄₁	—	4	4	no	—
58	C₂×C₄×C₄₁	—	4	4	no	—
59	C₂×C₄×C₄₁	—	4	8	no	—
60	C₂×C₄×C₄₁	—	4	8	no	—
61	C₂×C₄×C₄₁	—	4	8	no	—
62	C₂×C₄×C₄₁	#120	1	4	yes	—
63	C₂×C₄×C₄₁	C₂²⋊Q₈	1	4	yes	—
64	C₂×C₄×C₄₁	C₂²⋊Q₈	1	8	yes	—
65	C₂×C₄×C₄₁	#124	1	2	yes	—
66	C₂×C₄×C₄₁	#124	1	4	yes	—
67	C₂×C₄×C₄₁	C₄⋊Q₈	1	4	yes	—
68	C₂×C₄×C₄₁	C₄⋊Q₈	1	2	yes	—
69	C₈×C₄₁	—	4	8	no	—
70	#11383	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
71	C₂²×C₄₁	—	2	8	no	—
72	C₂²×C₄₁	—	2	2	no	—
73	C₂²×C₄₁	—	2	2	no	—
74	C₂²×C₄₁	#379	1	1	yes	characteristic
75	C₂²×C₄₁	#391	1	4	yes	—
76	C₂²×C₄₁	#391	1	2	yes	—
77	C₂²×C₄₁	#413	1	4	yes	—
78	C₄×C₄₁	—	4	4	no	—
79	C₄×C₄₁	—	4	8	no	—
80	C₄×C₄₁	#393	1	4	yes	—
81	C₄×C₄₁	#395	1	4	yes	—
82	C₂²×#125	C₂×C₄₁	1	1	yes	characteristic
83	C₂×#343	C₂×C₄₁	1	4	yes	—
84	#1728	C₂×C₄₁	1	2	yes	—
85	C₂×C₄₁	—	2	4	no	—
86	C₂×C₄₁	#1446	1	1	yes	characteristic
87	C₂×C₄₁	#1785	1	2	yes	—
88	C₂×C₄₁	#1998	1	4	yes	—
89	C₂²×M₁₆	C₂²×C₄₁	1	4	yes	—
90	C₂×#125	—	2	8	no	—
91	C₂×#125	—	2	4	no	—
92	C₂²×C₄⋊C₄	C₄×C₄₁	1	4	yes	—
93	C₂²×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
94	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
95	#343	—	2	8	no	—
96	#336	—	2	4	no	—
97	C₄₁	#11383	1	1	yes	characteristic, direct product factor, Sylow
98	C₂³×C₄	C₂×C₄×C₄₁	1	4	yes	—
99	C₂³×C₄	C₂×C₄×C₄₁	1	2	yes	—
100	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
101	C₂×M₁₆	—	2	4	no	—
102	C₂×M₁₆	—	2	8	no	—
103	C₂×M₁₆	—	2	8	no	—
104	C₂×M₁₆	Q₈×C₄₁	1	8	yes	—
105	C₂²×C₈	—	2	4	no	—
106	#125	—	2	32	no	—
107	C₂×C₄⋊C₄	—	2	8	no	—
108	C₂×C₄⋊C₄	—	2	8	no	—
109	C₂×C₄⋊C₄	—	2	8	no	—
110	C₂×C₄⋊C₄	—	2	4	no	—
111	C₂×C₄⋊C₄	—	2	4	no	—
112	C₂×C₄⋊C₄	D₄×C₄₁	1	8	yes	—
113	C₂×C₄²	—	2	4	no	—
114	C₂×C₄²	D₄×C₄₁	1	4	yes	—
115	C₂⁴	C₂²×C₄×C₄₁	1	1	yes	characteristic
116	C₂²×C₄	—	2	2	no	—
117	C₂²×C₄	—	2	2	no	—
118	C₂²×C₄	—	2	4	no	—
119	C₂²×C₄	—	2	4	no	—
120	C₂²×C₄	—	4	4	no	—
121	C₂²×C₄	—	4	8	no	—
122	C₂²×C₄	C₂²⋊C₄×C₄₁	1	4	yes	—
123	C₂²×C₄	C₂²⋊C₄×C₄₁	1	8	yes	—
124	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
125	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
126	C₂²×C₄	C₂×Q₈×C₄₁	1	4	yes	—
127	C₂²×C₄	#41×C₄₁	1	4	yes	—
128	M₁₆	—	2	16	no	—
129	M₁₆	—	4	8	no	—
130	C₂×C₈	—	2	8	no	—
131	C₂×C₈	—	4	4	no	—
132	C₂×C₈	—	4	4	no	—
133	C₄⋊C₄	—	2	32	no	—
134	C₄⋊C₄	—	2	16	no	—
135	C₄²	—	2	8	no	—
136	C₂³	—	2	4	no	—
137	C₂³	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
138	C₂³	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
139	C₂³	C₄×Q₈×C₄₁	1	4	yes	—
140	C₂×C₄	—	2	4	no	—
141	C₂×C₄	—	2	8	no	—
142	C₂×C₄	—	2	8	no	—
143	C₂×C₄	—	4	4	no	—
144	C₂×C₄	—	4	4	no	—
145	C₂×C₄	—	4	8	no	—
146	C₂×C₄	—	4	8	no	—
147	C₂×C₄	—	4	8	no	—
148	C₂×C₄	#120×C₄₁	1	4	yes	—
149	C₂×C₄	C₂²⋊Q₈×C₄₁	1	4	yes	—
150	C₂×C₄	C₂²⋊Q₈×C₄₁	1	8	yes	—
151	C₂×C₄	#124×C₄₁	1	2	yes	—
152	C₂×C₄	#124×C₄₁	1	4	yes	—
153	C₂×C₄	C₄⋊Q₈×C₄₁	1	4	yes	—
154	C₂×C₄	C₄⋊Q₈×C₄₁	1	2	yes	—
155	C₈	—	4	8	no	—
156	C₂²	—	2	2	no	—
157	C₂²	—	2	2	no	—
158	C₂²	—	2	8	no	—
159	C₂²	C₄₁×#379	1	1	yes	characteristic
160	C₂²	C₄₁×#391	1	4	yes	—
161	C₂²	C₄₁×#391	1	2	yes	—
162	C₂²	C₄₁×#413	1	4	yes	—
163	C₄	—	4	4	no	—
164	C₄	—	4	8	no	—
165	C₄	C₄₁×#393	1	4	yes	—
166	C₄	C₄₁×#395	1	4	yes	—
167	C₂	—	2	4	no	—
168	C₂	C₄₁×#1446	1	1	yes	characteristic
169	C₂	C₄₁×#1785	1	2	yes	—
170	C₂	C₄₁×#1998	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#125×C₄₁

C₂

yes

maximal, characteristic

C₂×C₄₁×#343

C₂

yes

maximal

C₄₁×#1728

C₂

yes

maximal

C₂²×M₁₆×C₄₁

C₂²

yes

—

C₂×#125×C₄₁

—

C₂×#125×C₄₁

—

C₂²×C₄⋊C₄×C₄₁

C₄

yes

—

C₂²×C₄⋊C₄×C₄₁

C₂²

yes

—

C₂²×C₄²×C₄₁

C₂²

yes

characteristic

C₄₁×#343

—

C₄₁×#336

—

C₂³×C₄×C₄₁

C₂×C₄

yes

—

C₂³×C₄×C₄₁

C₂×C₄

yes

—

C₂³×C₄×C₄₁

C₂³

yes

characteristic

C₂×M₁₆×C₄₁

—

C₂×M₁₆×C₄₁

—

C₂×M₁₆×C₄₁

—

C₂×M₁₆×C₄₁

Q₈

yes

—

C₂²×C₈×C₄₁

—

#125×C₄₁

—

C₂×C₄⋊C₄×C₄₁

—

C₂×C₄⋊C₄×C₄₁

—

C₂×C₄⋊C₄×C₄₁

—

C₂×C₄⋊C₄×C₄₁

—

C₂×C₄⋊C₄×C₄₁

—

C₂×C₄⋊C₄×C₄₁

D₄

yes

—

C₂×C₄²×C₄₁

—

C₂×C₄²×C₄₁

D₄

yes

—

C₂⁴×C₄₁

C₂²×C₄

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

yes

—

C₂²×C₄×C₄₁

C₂²⋊C₄

yes

—

C₂²×C₄×C₄₁

C₂×D₄

yes

—

C₂²×C₄×C₄₁

C₂×D₄

yes

—

C₂²×C₄×C₄₁

C₂×Q₈

yes

—

C₂²×C₄×C₄₁

#41

yes

—

M₁₆×C₄₁

—

M₁₆×C₄₁

—

C₂×C₈×C₄₁

—

C₂×C₈×C₄₁

—

C₂×C₈×C₄₁

—

C₄⋊C₄×C₄₁

—

C₄⋊C₄×C₄₁

—

C₄²×C₄₁

—

C₂³×C₄₁

—

C₂³×C₄₁

C₂×C₂²⋊C₄

yes

—

C₂³×C₄₁

C₂×C₂²⋊C₄

yes

characteristic

C₂³×C₄₁

C₄×Q₈

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

#120

yes

—

C₂×C₄×C₄₁

C₂²⋊Q₈

yes

—

C₂×C₄×C₄₁

C₂²⋊Q₈

yes

—

C₂×C₄×C₄₁

#124

yes

—

C₂×C₄×C₄₁

#124

yes

—

C₂×C₄×C₄₁

C₄⋊Q₈

yes

—

C₂×C₄×C₄₁

C₄⋊Q₈

yes

—

C₈×C₄₁

—

#11383

C₄₁

yes

maximal, characteristic, direct product factor, Sylow

C₂²×C₄₁

—

C₂²×C₄₁

—

C₂²×C₄₁

—

C₂²×C₄₁

#379

yes

characteristic

C₂²×C₄₁

#391

yes

—

C₂²×C₄₁

#391

yes

—

C₂²×C₄₁

#413

yes

—

C₄×C₄₁

—

C₄×C₄₁

—

C₄×C₄₁

#393

yes

—

C₄×C₄₁

#395

yes

—

C₂²×#125

C₂×C₄₁

yes

characteristic

C₂×#343

C₂×C₄₁

yes

—

#1728

C₂×C₄₁

yes

—

C₂×C₄₁

—

C₂×C₄₁

#1446

yes

characteristic

C₂×C₄₁

#1785

yes

—

C₂×C₄₁

#1998

yes

—

C₂²×M₁₆

C₂²×C₄₁

yes

—

C₂×#125

—

C₂×#125

—

C₂²×C₄⋊C₄

C₄×C₄₁

yes

—

C₂²×C₄⋊C₄

C₂²×C₄₁

yes

—

C₂²×C₄²

C₂²×C₄₁

yes

characteristic

#343

—

#336

—

C₄₁

#11383

yes

characteristic, direct product factor, Sylow

C₂³×C₄

C₂×C₄×C₄₁

yes

—

C₂³×C₄

C₂×C₄×C₄₁

yes

—

100

C₂³×C₄

C₂³×C₄₁

yes

characteristic

101

C₂×M₁₆

—

102

C₂×M₁₆

—

103

C₂×M₁₆

—

104

C₂×M₁₆

Q₈×C₄₁

yes

—

105

C₂²×C₈

—

106

#125

—

107

C₂×C₄⋊C₄

—

108

C₂×C₄⋊C₄

—

109

C₂×C₄⋊C₄

—

110

C₂×C₄⋊C₄

—

111

C₂×C₄⋊C₄

—

112

C₂×C₄⋊C₄

D₄×C₄₁

yes

—

113

C₂×C₄²

—

114

C₂×C₄²

D₄×C₄₁

yes

—

115

C₂⁴

C₂²×C₄×C₄₁

yes

characteristic

116

C₂²×C₄

—

117

C₂²×C₄

—

118

C₂²×C₄

—

119

C₂²×C₄

—

120

C₂²×C₄

—

121

C₂²×C₄

—

122

C₂²×C₄

C₂²⋊C₄×C₄₁

yes

—

123

C₂²×C₄

C₂²⋊C₄×C₄₁

yes

—

124

C₂²×C₄

C₂×D₄×C₄₁

yes

—

125

C₂²×C₄

C₂×D₄×C₄₁

yes

—

126

C₂²×C₄

C₂×Q₈×C₄₁

yes

—

127

C₂²×C₄

#41×C₄₁

yes

—

128

M₁₆

—

129

M₁₆

—

130

C₂×C₈

—

131

C₂×C₈

—

132

C₂×C₈

—

133

C₄⋊C₄

—

134

C₄⋊C₄

—

135

C₄²

—

136

C₂³

—

137

C₂³

C₂×C₂²⋊C₄×C₄₁

yes

—

138

C₂³

C₂×C₂²⋊C₄×C₄₁

yes

characteristic

139

C₂³

C₄×Q₈×C₄₁

yes

—

140

C₂×C₄

—

141

C₂×C₄

—

142

C₂×C₄

—

143

C₂×C₄

—

144

C₂×C₄

—

145

C₂×C₄

—

146

C₂×C₄

—

147

C₂×C₄

—

148

C₂×C₄

#120×C₄₁

yes

—

149

C₂×C₄

C₂²⋊Q₈×C₄₁

yes

—

150

C₂×C₄

C₂²⋊Q₈×C₄₁

yes

—

151

C₂×C₄

#124×C₄₁

yes

—

152

C₂×C₄

#124×C₄₁

yes

—

153

C₂×C₄

C₄⋊Q₈×C₄₁

yes

—

154

C₂×C₄

C₄⋊Q₈×C₄₁

yes

—

155

C₈

—

156

C₂²

—

157

C₂²

—

158

C₂²

—

159

C₂²

C₄₁×#379

yes

characteristic

160

C₂²

C₄₁×#391

yes

—

161

C₂²

C₄₁×#391

yes

—

162

C₂²

C₄₁×#413

yes

—

163

C₄

—

164

C₄

—

165

C₄

C₄₁×#393

yes

—

166

C₄

C₄₁×#395

yes

—

167

C₂

—

168

C₂

C₄₁×#1446

yes

characteristic

169

C₂

C₄₁×#1785

yes

—

170

C₂

C₄₁×#1998

yes

—

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂×C₂²⋊C₄
commutator	C₂⁴	C₂²×C₄×C₄₁
Frattini, cosocle	C₂³×C₄	C₂³×C₄₁
prime radical	C₂⁴×C₄₁	C₂²×C₄
LCS	G ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₂²×C₄²×C₄₁ ◁ G

subgroup

G/H

center, socle

C₂³×C₄₁

C₂×C₂²⋊C₄

commutator

C₂⁴

C₂²×C₄×C₄₁

Frattini, cosocle

C₂³×C₄

C₂³×C₄₁

prime radical

C₂⁴×C₄₁

C₂²×C₄

LCS

G ▷ C₂⁴ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂³×C₄₁ ◁ C₂²×C₄²×C₄₁ ◁ G

N	H ≅ G/N	type
70. #11383	C₄₁	direct (N × H)
97. C₄₁	#11383	direct (N × H)

H ≅ G/N

type

70. #11383

C₄₁

direct (N × H)

97. C₄₁

#11383

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×#343	2
C₄₁×#1728	2
#11383	41

subgroup

index

C₂²×#125×C₄₁

C₂×C₄₁×#343

C₄₁×#1728

#11383

Subgroups — C₄₁×#11383 #23787584

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C41×#11383 #23787584

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#11383 #23787584