Group #23763159 — subgroups

Subgroups — C₄×(C₂×D₇₉)⋊C₈ #23763159

Order 10112.

436 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 181 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×C₄²×D₇₉	C₂	1	1	yes	maximal, characteristic
2	C₂×(C₂×D₇₉)⋊C₈	C₂	1	2	yes	maximal
3	C₂×C₄×C₇₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#19098317	C₂	1	2	yes	maximal, complemented
5	C₂×C₄×C₈×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₄×D₇₉	C₄	1	2	yes	—
7	C₂²×C₄×D₇₉	C₂²	1	1	yes	characteristic
8	C₂²×C₇₉⋊C₈	C₂²	1	2	yes	—
9	C₂×C₄×Dic₇₉	C₄	1	2	yes	—
10	C₂×C₄×Dic₇₉	C₂²	1	1	yes	characteristic
11	C₄²×D₇₉	—	2	2	no	—
12	C₄²×D₇₉	—	2	2	no	—
13	(C₂×D₇₉)⋊C₈	C₄	1	8	yes	direct product factor
14	C₄×C₇₉⋊C₈	—	2	2	no	—
15	C₂²×C₈×C₇₉	C₂²	1	2	yes	—
16	C₂×C₄²×C₇₉	C₂²	1	1	yes	characteristic
17	C₄×C₈×C₇₉	—	2	2	no	—
18	C₂³×D₇₉	C₂×C₄	1	1	yes	characteristic
19	C₂²×Dic₇₉	C₂×C₄	1	1	yes	characteristic
20	C₂²×Dic₇₉	C₂×C₄	1	2	yes	—
21	C₂×C₄×D₇₉	—	2	4	no	—
22	C₂×C₄×D₇₉	—	2	4	no	—
23	C₂×C₄×D₇₉	—	2	1	no	—
24	C₂×C₄×D₇₉	—	2	1	no	—
25	C₂×C₄×D₇₉	—	2	2	no	—
26	C₂×C₄×D₇₉	C₈	1	8	yes	complemented
27	C₂×C₄×D₇₉	C₂×C₄	1	4	yes	—
28	C₂×C₇₉⋊C₈	—	2	2	no	—
29	C₂×C₇₉⋊C₈	—	2	2	no	—
30	C₂×C₇₉⋊C₈	C₂×C₄	1	4	yes	complemented
31	C₄×Dic₇₉	—	2	4	no	—
32	C₄×Dic₇₉	—	2	1	no	—
33	C₄×Dic₇₉	—	2	1	no	—
34	C₂²×C₄×C₇₉	C₂×C₄	1	2	yes	—
35	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
36	C₂×C₈×C₇₉	—	2	2	no	—
37	C₂×C₈×C₇₉	—	2	2	no	—
38	C₂×C₈×C₇₉	C₂×C₄	1	4	yes	complemented
39	C₄²×C₇₉	D₄	1	2	yes	—
40	C₄²×C₇₉	D₄	1	2	yes	—
41	C₂³×C₇₉	C₂²×C₄	1	1	yes	characteristic
42	C₂²×D₇₉	—	2	1	no	—
43	C₂²×D₇₉	—	2	1	no	—
44	C₂²×D₇₉	—	2	2	no	—
45	C₂²×D₇₉	C₄²	1	2	yes	—
46	C₂²×D₇₉	C₂×C₈	1	4	yes	—
47	C₂×C₄×C₇₉	C₂²⋊C₄	1	4	yes	—
48	C₂×C₄×C₇₉	C₂×C₈	1	4	yes	—
49	C₂×C₄×C₇₉	M₁₆	1	4	yes	—
50	C₂×C₄×C₇₉	C₂²×C₄	1	2	yes	—
51	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
52	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
53	C₂×C₄×C₇₉	#41	1	2	yes	—
54	C₂×Dic₇₉	—	2	1	no	—
55	C₂×Dic₇₉	—	2	2	no	—
56	C₂×Dic₇₉	—	2	1	no	—
57	C₂×Dic₇₉	—	2	2	no	—
58	C₂×Dic₇₉	C₄²	1	2	yes	—
59	C₂×Dic₇₉	C₂×C₈	1	4	yes	—
60	C₄×D₇₉	—	2	16	no	—
61	C₄×D₇₉	—	2	4	no	—
62	C₄×D₇₉	—	2	4	no	—
63	C₈×C₇₉	—	2	4	no	—
64	C₇₉⋊C₈	—	2	4	no	—
65	C₂²×C₇₉	C₂×C₄²	1	1	yes	characteristic
66	C₂²×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
67	C₂²×C₇₉	#117	1	1	yes	characteristic
68	C₂²×C₇₉	C₂²×C₈	1	2	yes	—
69	C₂²×C₇₉	C₂×M₁₆	1	2	yes	—
70	C₂×D₇₉	—	2	2	no	—
71	C₂×D₇₉	—	2	2	no	—
72	C₂×D₇₉	—	2	4	no	—
73	C₂×D₇₉	—	2	4	no	—
74	C₂×D₇₉	C₄×C₈	1	4	yes	complemented
75	C₄×C₇₉	C₂²⋊C₈	1	8	yes	complemented
76	C₄×C₇₉	C₄×D₄	1	2	yes	—
77	C₄×C₇₉	C₄×D₄	1	2	yes	—
78	Dic₇₉	—	2	2	no	—
79	Dic₇₉	—	2	4	no	—
80	C₂×C₇₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
81	C₂×C₇₉	C₂×C₄×C₈	1	1	yes	characteristic
82	C₂×C₇₉	C₄×M₁₆	1	1	yes	characteristic
83	C₂×C₇₉	C₂×C₂²⋊C₈	1	2	yes	—
84	C₂×C₇₉	#431	1	2	yes	—
85	D₇₉	—	2	4	no	—
86	C₄×C₂²⋊C₈	—	79	1	no	maximal, Sylow
87	C₇₉	C₄×C₂²⋊C₈	1	1	yes	characteristic, complemented, Sylow
88	C₂²×C₄²	—	79	1	no	—
89	C₂×C₂²⋊C₈	—	79	2	no	—
90	C₂×C₄×C₈	—	79	1	no	—
91	C₂×C₄×C₈	D₇₉	1	1	yes	characteristic, complemented
92	#336	—	79	2	no	—
93	C₂³×C₄	—	79	1	no	—
94	C₂³×C₄	—	79	2	no	—
95	C₂²×C₈	—	79	2	no	—
96	C₂²×C₈	C₂×D₇₉	1	2	yes	—
97	C₂×C₄²	—	79	1	no	—
98	C₂×C₄²	—	79	2	no	—
99	C₂×C₄²	—	158	2	no	—
100	C₂×C₄²	—	158	2	no	—
101	C₂×C₄²	C₂×D₇₉	1	1	yes	characteristic
102	C₂²⋊C₈	—	79	8	no	—
103	C₄×C₈	—	2	2	no	—
104	C₄×C₈	—	158	2	no	—
105	C₂⁴	—	79	1	no	—
106	C₂²×C₄	—	79	1	no	—
107	C₂²×C₄	—	79	2	no	—
108	C₂²×C₄	—	79	8	no	—
109	C₂²×C₄	—	79	4	no	—
110	C₂²×C₄	—	158	4	no	—
111	C₂²×C₄	—	158	4	no	—
112	C₂²×C₄	—	158	1	no	—
113	C₂²×C₄	—	158	1	no	—
114	C₂²×C₄	—	158	2	no	—
115	C₂²×C₄	C₄×D₇₉	1	2	yes	—
116	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
117	C₂×C₈	—	2	2	no	—
118	C₂×C₈	—	2	2	no	—
119	C₂×C₈	—	79	4	no	—
120	C₂×C₈	—	158	2	no	—
121	C₂×C₈	—	158	2	no	—
122	C₂×C₈	C₄×D₇₉	1	4	yes	complemented
123	C₄²	—	158	4	no	—
124	C₄²	—	158	1	no	—
125	C₄²	—	158	1	no	—
126	C₄²	D₃₁₆	1	2	yes	—
127	C₄²	C₂²⋊D₇₉	1	2	yes	—
128	C₂³	—	79	2	no	—
129	C₂³	—	79	4	no	—
130	C₂³	—	158	1	no	—
131	C₂³	—	158	1	no	—
132	C₂³	—	158	2	no	—
133	C₂³	C₂×C₄×D₇₉	1	1	yes	characteristic
134	C₂×C₄	—	79	2	no	—
135	C₂×C₄	—	79	4	no	—
136	C₂×C₄	—	158	1	no	—
137	C₂×C₄	—	158	2	no	—
138	C₂×C₄	—	158	1	no	—
139	C₂×C₄	—	158	2	no	—
140	C₂×C₄	—	158	16	no	—
141	C₂×C₄	—	158	4	no	—
142	C₂×C₄	—	158	4	no	—
143	C₂×C₄	(C₂×D₇₉)⋊C₄	1	4	yes	—
144	C₂×C₄	C₈×D₇₉	1	4	yes	—
145	C₂×C₄	#11929607	1	4	yes	—
146	C₂×C₄	C₂×C₄×D₇₉	1	2	yes	—
147	C₂×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
148	C₂×C₄	C₂×D₃₁₆	1	1	yes	characteristic
149	C₂×C₄	#11929624	1	2	yes	—
150	C₈	—	2	4	no	—
151	C₈	—	158	4	no	—
152	C₂²	—	79	4	no	—
153	C₂²	—	158	2	no	—
154	C₂²	—	158	2	no	—
155	C₂²	—	158	4	no	—
156	C₂²	—	158	4	no	—
157	C₂²	C₄²×D₇₉	1	1	yes	characteristic
158	C₂²	C₂×(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
159	C₂²	#14579118	1	1	yes	characteristic
160	C₂²	C₂×C₈×D₇₉	1	2	yes	—
161	C₂²	C₂×#11929607	1	2	yes	—
162	C₄	—	158	2	no	—
163	C₄	—	158	4	no	—
164	C₄	(C₂×D₇₉)⋊C₈	1	8	yes	direct product factor
165	C₄	C₄×C₂²⋊D₇₉	1	2	yes	—
166	C₄	C₄×D₃₁₆	1	2	yes	—
167	C₂	—	158	4	no	—
168	C₂	C₄×(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
169	C₂	C₄×C₈×D₇₉	1	1	yes	characteristic
170	C₂	C₄×#11929607	1	1	yes	characteristic
171	C₂	C₂×(C₂×D₇₉)⋊C₈	1	2	yes	—
172	C₂	#19098614	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄²×D₇₉

C₂

yes

maximal, characteristic

C₂×(C₂×D₇₉)⋊C₈

C₂

yes

maximal

C₂×C₄×C₇₉⋊C₈

C₂

yes

maximal, characteristic, complemented

#19098317

C₂

yes

maximal, complemented

C₂×C₄×C₈×C₇₉

C₂

yes

maximal, characteristic, complemented

C₂²×C₄×D₇₉

C₄

yes

—

C₂²×C₄×D₇₉

C₂²

yes

characteristic

C₂²×C₇₉⋊C₈

C₂²

yes

—

C₂×C₄×Dic₇₉

C₄

yes

—

C₂×C₄×Dic₇₉

C₂²

yes

characteristic

C₄²×D₇₉

—

C₄²×D₇₉

—

(C₂×D₇₉)⋊C₈

C₄

yes

direct product factor

C₄×C₇₉⋊C₈

—

C₂²×C₈×C₇₉

C₂²

yes

—

C₂×C₄²×C₇₉

C₂²

yes

characteristic

C₄×C₈×C₇₉

—

C₂³×D₇₉

C₂×C₄

yes

characteristic

C₂²×Dic₇₉

C₂×C₄

yes

characteristic

C₂²×Dic₇₉

C₂×C₄

yes

—

C₂×C₄×D₇₉

—

C₂×C₄×D₇₉

—

C₂×C₄×D₇₉

—

C₂×C₄×D₇₉

—

C₂×C₄×D₇₉

—

C₂×C₄×D₇₉

C₈

yes

complemented

C₂×C₄×D₇₉

C₂×C₄

yes

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

C₂×C₄

yes

complemented

C₄×Dic₇₉

—

C₄×Dic₇₉

—

C₄×Dic₇₉

—

C₂²×C₄×C₇₉

C₂×C₄

yes

—

C₂²×C₄×C₇₉

C₂³

yes

characteristic

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

C₂×C₄

yes

complemented

C₄²×C₇₉

D₄

yes

—

C₄²×C₇₉

D₄

yes

—

C₂³×C₇₉

C₂²×C₄

yes

characteristic

C₂²×D₇₉

—

C₂²×D₇₉

—

C₂²×D₇₉

—

C₂²×D₇₉

C₄²

yes

—

C₂²×D₇₉

C₂×C₈

yes

—

C₂×C₄×C₇₉

C₂²⋊C₄

yes

—

C₂×C₄×C₇₉

C₂×C₈

yes

—

C₂×C₄×C₇₉

M₁₆

yes

—

C₂×C₄×C₇₉

C₂²×C₄

yes

—

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

#41

yes

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

C₄²

yes

—

C₂×Dic₇₉

C₂×C₈

yes

—

C₄×D₇₉

—

C₄×D₇₉

—

C₄×D₇₉

—

C₈×C₇₉

—

C₇₉⋊C₈

—

C₂²×C₇₉

C₂×C₄²

yes

characteristic

C₂²×C₇₉

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₇₉

#117

yes

characteristic

C₂²×C₇₉

C₂²×C₈

yes

—

C₂²×C₇₉

C₂×M₁₆

yes

—

C₂×D₇₉

—

C₂×D₇₉

—

C₂×D₇₉

—

C₂×D₇₉

—

C₂×D₇₉

C₄×C₈

yes

complemented

C₄×C₇₉

C₂²⋊C₈

yes

complemented

C₄×C₇₉

C₄×D₄

yes

—

C₄×C₇₉

C₄×D₄

yes

—

Dic₇₉

—

Dic₇₉

—

C₂×C₇₉

C₄×C₂²⋊C₄

yes

characteristic

C₂×C₇₉

C₂×C₄×C₈

yes

characteristic

C₂×C₇₉

C₄×M₁₆

yes

characteristic

C₂×C₇₉

C₂×C₂²⋊C₈

yes

—

C₂×C₇₉

#431

yes

—

D₇₉

—

C₄×C₂²⋊C₈

—

maximal, Sylow

C₇₉

C₄×C₂²⋊C₈

yes

characteristic, complemented, Sylow

C₂²×C₄²

—

C₂×C₂²⋊C₈

—

C₂×C₄×C₈

—

C₂×C₄×C₈

D₇₉

yes

characteristic, complemented

#336

—

C₂³×C₄

—

C₂³×C₄

—

C₂²×C₈

—

C₂²×C₈

C₂×D₇₉

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

158

—

100

C₂×C₄²

—

158

—

101

C₂×C₄²

C₂×D₇₉

yes

characteristic

102

C₂²⋊C₈

—

103

C₄×C₈

—

104

C₄×C₈

—

158

—

105

C₂⁴

—

106

C₂²×C₄

—

107

C₂²×C₄

—

108

C₂²×C₄

—

109

C₂²×C₄

—

110

C₂²×C₄

—

158

—

111

C₂²×C₄

—

158

—

112

C₂²×C₄

—

158

—

113

C₂²×C₄

—

158

—

114

C₂²×C₄

—

158

—

115

C₂²×C₄

C₄×D₇₉

yes

—

116

C₂²×C₄

C₂²×D₇₉

yes

characteristic

117

C₂×C₈

—

118

C₂×C₈

—

119

C₂×C₈

—

120

C₂×C₈

—

158

—

121

C₂×C₈

—

158

—

122

C₂×C₈

C₄×D₇₉

yes

complemented

123

C₄²

—

158

—

124

C₄²

—

158

—

125

C₄²

—

158

—

126

C₄²

D₃₁₆

yes

—

127

C₄²

C₂²⋊D₇₉

yes

—

128

C₂³

—

129

C₂³

—

130

C₂³

—

158

—

131

C₂³

—

158

—

132

C₂³

—

158

—

133

C₂³

C₂×C₄×D₇₉

yes

characteristic

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

—

158

—

137

C₂×C₄

—

158

—

138

C₂×C₄

—

158

—

139

C₂×C₄

—

158

—

140

C₂×C₄

—

158

—

141

C₂×C₄

—

158

—

142

C₂×C₄

—

158

—

143

C₂×C₄

(C₂×D₇₉)⋊C₄

yes

—

144

C₂×C₄

C₈×D₇₉

yes

—

145

C₂×C₄

#11929607

yes

—

146

C₂×C₄

C₂×C₄×D₇₉

yes

—

147

C₂×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

148

C₂×C₄

C₂×D₃₁₆

yes

characteristic

149

C₂×C₄

#11929624

yes

—

150

C₈

—

151

C₈

—

158

—

152

C₂²

—

153

C₂²

—

158

—

154

C₂²

—

158

—

155

C₂²

—

158

—

156

C₂²

—

158

—

157

C₂²

C₄²×D₇₉

yes

characteristic

158

C₂²

C₂×(C₂×D₇₉)⋊C₄

yes

characteristic

159

C₂²

#14579118

yes

characteristic

160

C₂²

C₂×C₈×D₇₉

yes

—

161

C₂²

C₂×#11929607

yes

—

162

C₄

—

158

—

163

C₄

—

158

—

164

C₄

(C₂×D₇₉)⋊C₈

yes

direct product factor

165

C₄

C₄×C₂²⋊D₇₉

yes

—

166

C₄

C₄×D₃₁₆

yes

—

167

C₂

—

158

—

168

C₂

C₄×(C₂×D₇₉)⋊C₄

yes

characteristic

169

C₂

C₄×C₈×D₇₉

yes

characteristic

170

C₂

C₄×#11929607

yes

characteristic

171

C₂

C₂×(C₂×D₇₉)⋊C₈

yes

—

172

C₂

#19098614

yes

—

	subgroup	G/H
center	C₂×C₄²	C₂×D₇₉
commutator	C₂×C₇₉	C₂×C₄×C₈
Frattini	C₂²×C₄	C₂²×D₇₉
Fitting	C₂×C₄×C₈×C₇₉	C₂
socle	C₂³×C₇₉	C₂²×C₄
prime radical	C₂³×D₇₉	C₂×C₄
cosocle	C₂²×C₄×C₇₉	C₂³
hypercenter	C₂×C₄×C₈	D₇₉
hypocenter	C₇₉	C₄×C₂²⋊C₈
LCS	G ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄² ◁ C₂×C₄×C₈

subgroup

G/H

center

C₂×C₄²

C₂×D₇₉

commutator

C₂×C₇₉

C₂×C₄×C₈

Frattini

C₂²×C₄

C₂²×D₇₉

Fitting

C₂×C₄×C₈×C₇₉

C₂

socle

C₂³×C₇₉

C₂²×C₄

prime radical

C₂³×D₇₉

C₂×C₄

cosocle

C₂²×C₄×C₇₉

C₂³

hypercenter

C₂×C₄×C₈

D₇₉

hypocenter

C₇₉

C₄×C₂²⋊C₈

LCS

G ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂×C₄² ◁ C₂×C₄×C₈

N	H ≅ G/N	type
3. C₂×C₄×C₇₉⋊C₈	C₂	semidirect
4. #19098317	C₂	semidirect
5. C₂×C₄×C₈×C₇₉	C₂	semidirect
13. (C₂×D₇₉)⋊C₈	C₄	direct (N × H)
26. C₂×C₄×D₇₉	C₈	semidirect
30. C₂×C₇₉⋊C₈	C₂×C₄	semidirect
38. C₂×C₈×C₇₉	C₂×C₄	semidirect
74. C₂×D₇₉	C₄×C₈	semidirect
75. C₄×C₇₉	C₂²⋊C₈	semidirect
87. C₇₉	C₄×C₂²⋊C₈	semidirect
91. C₂×C₄×C₈	D₇₉	semidirect
122. C₂×C₈	C₄×D₇₉	semidirect
164. C₄	(C₂×D₇₉)⋊C₈	direct (N × H)

H ≅ G/N

type

3. C₂×C₄×C₇₉⋊C₈

C₂

semidirect

4. #19098317

C₂

semidirect

5. C₂×C₄×C₈×C₇₉

C₂

semidirect

13. (C₂×D₇₉)⋊C₈

C₄

direct (N × H)

26. C₂×C₄×D₇₉

C₈

semidirect

30. C₂×C₇₉⋊C₈

C₂×C₄

semidirect

38. C₂×C₈×C₇₉

C₂×C₄

semidirect

74. C₂×D₇₉

C₄×C₈

semidirect

75. C₄×C₇₉

C₂²⋊C₈

semidirect

87. C₇₉

C₄×C₂²⋊C₈

semidirect

91. C₂×C₄×C₈

D₇₉

semidirect

122. C₂×C₈

C₄×D₇₉

semidirect

164. C₄

(C₂×D₇₉)⋊C₈

direct (N × H)

Subgroups — C₄×(C₂×D₇₉)⋊C₈ #23763159

Conjugacy classes of subgroups

Complements

Subgroups — C4×(C2×D79)⋊C8 #23763159

Conjugacy classes of subgroups

Complements

Subgroups — C₄×(C₂×D₇₉)⋊C₈ #23763159