Group #23763542 — subgroups

Subgroups — #23763542

Order 10112.

240 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 105 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	C₄²×Dic₇₉	C₂	1	1	yes	maximal, characteristic
2	#19098318	C₂	1	1	yes	maximal, characteristic
3	#19098317	C₂	1	2	yes	maximal
4	#19098317	C₂	1	2	yes	maximal
5	#336×C₇₉	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₇₉⋊C₈	C₂²	1	2	yes	—
7	C₂×C₄×Dic₇₉	C₄	1	1	yes	characteristic
8	C₂×C₄×Dic₇₉	C₄	1	1	yes	characteristic
9	C₂×C₄×Dic₇₉	C₄	1	1	yes	characteristic
10	C₂×C₄×Dic₇₉	C₄	1	1	yes	characteristic
11	C₂×C₄×Dic₇₉	C₂²	1	1	yes	characteristic
12	C₂×C₄×Dic₇₉	C₂²	1	1	yes	characteristic
13	C₂²×C₈×C₇₉	C₂²	1	2	yes	—
14	C₂×C₄²×C₇₉	C₂²	1	1	yes	characteristic
15	C₂²×Dic₇₉	C₂×C₄	1	1	yes	characteristic
16	C₂²×Dic₇₉	C₂×C₄	1	1	yes	characteristic
17	C₂²×Dic₇₉	C₂×C₄	1	1	yes	characteristic
18	C₂²×Dic₇₉	C₂×C₄	1	1	yes	characteristic
19	C₂×C₇₉⋊C₈	—	2	2	no	—
20	C₂×C₇₉⋊C₈	—	2	2	no	—
21	C₂×C₇₉⋊C₈	—	2	2	no	—
22	C₄×Dic₇₉	—	2	2	no	—
23	C₄×Dic₇₉	—	2	2	no	—
24	C₄×Dic₇₉	—	2	2	no	—
25	C₄×Dic₇₉	—	2	1	no	—
26	C₄×Dic₇₉	—	2	2	no	—
27	C₄×Dic₇₉	—	2	1	no	—
28	C₄×Dic₇₉	C₈	1	4	yes	complemented
29	C₂²×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
31	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
32	C₂×C₈×C₇₉	—	2	2	no	—
33	C₂×C₈×C₇₉	—	2	2	no	—
34	C₂×C₈×C₇₉	—	2	2	no	—
35	C₄²×C₇₉	—	2	2	no	—
36	C₂³×C₇₉	C₂²×C₄	1	1	yes	characteristic
37	C₂×C₄×C₇₉	—	2	1	no	—
38	C₂×C₄×C₇₉	—	2	1	no	—
39	C₂×C₄×C₇₉	—	2	1	no	—
40	C₂×C₄×C₇₉	—	2	1	no	—
41	C₂×C₄×C₇₉	C₂×C₈	1	2	yes	—
42	C₂×C₄×C₇₉	M₁₆	1	2	yes	—
43	C₂×C₄×C₇₉	#41	1	1	yes	characteristic
44	C₂×C₄×C₇₉	#41	1	2	yes	—
45	C₂×C₄×C₇₉	#41	1	2	yes	—
46	C₂×C₄×C₇₉	#41	1	1	yes	characteristic
47	C₂×Dic₇₉	—	2	1	no	—
48	C₂×Dic₇₉	—	2	1	no	—
49	C₂×Dic₇₉	—	2	1	no	—
50	C₂×Dic₇₉	—	2	1	no	—
51	C₂×Dic₇₉	—	2	1	no	—
52	C₂×Dic₇₉	—	2	1	no	—
53	C₂×Dic₇₉	—	2	1	no	—
54	C₂×Dic₇₉	—	2	1	no	—
55	C₂×Dic₇₉	C₂×C₈	1	2	yes	—
56	C₂×Dic₇₉	C₂×C₈	1	2	yes	—
57	C₂×Dic₇₉	M₁₆	1	2	yes	—
58	C₂×Dic₇₉	M₁₆	1	2	yes	—
59	C₈×C₇₉	—	4	2	no	—
60	C₇₉⋊C₈	—	4	2	no	—
61	C₂²×C₇₉	#117	1	1	yes	characteristic
62	C₂²×C₇₉	#117	1	1	yes	characteristic
63	C₂²×C₇₉	#117	1	1	yes	characteristic
64	C₂²×C₇₉	C₂²×C₈	1	1	yes	characteristic
65	C₂²×C₇₉	C₂×M₁₆	1	1	yes	characteristic
66	C₂²×C₇₉	C₂×M₁₆	1	1	yes	characteristic
67	C₂²×C₇₉	C₂×M₁₆	1	1	yes	characteristic
68	C₄×C₇₉	—	2	2	no	—
69	C₄×C₇₉	—	2	2	no	—
70	C₄×C₇₉	#126	1	2	yes	—
71	C₄×C₇₉	#126	1	2	yes	—
72	Dic₇₉	—	2	2	no	—
73	Dic₇₉	—	2	2	no	—
74	Dic₇₉	—	2	2	no	—
75	Dic₇₉	—	2	2	no	—
76	C₂×C₇₉	#383	1	1	yes	characteristic
77	C₂×C₇₉	#431	1	1	yes	characteristic
78	C₂×C₇₉	#431	1	1	yes	characteristic
79	C₂×C₇₉	#431	1	1	yes	characteristic
80	C₂×C₇₉	#432	1	1	yes	characteristic
81	C₂×C₇₉	#432	1	1	yes	characteristic
82	C₂×C₇₉	#432	1	1	yes	characteristic
83	#1839	—	79	1	no	maximal, Sylow
84	C₇₉	#1839	1	1	yes	characteristic, complemented, Sylow
85	C₄³	—	79	1	no	—
86	#336	—	79	2	no	—
87	#336	—	79	2	no	—
88	#336	—	79	1	no	—
89	#336	D₇₉	1	1	yes	characteristic
90	C₂²×C₈	—	79	2	no	—
91	C₂²×C₈	C₂×D₇₉	1	2	yes	—
92	C₂×C₄²	—	79	1	no	—
93	C₂×C₄²	—	79	1	no	—
94	C₂×C₄²	—	79	1	no	—
95	C₂×C₄²	—	79	1	no	—
96	C₂×C₄²	—	79	1	no	—
97	C₂×C₄²	—	79	1	no	—
98	C₂×C₄²	C₂×D₇₉	1	1	yes	characteristic
99	C₂²×C₄	—	79	1	no	—
100	C₂²×C₄	—	79	1	no	—
101	C₂²×C₄	—	79	1	no	—
102	C₂²×C₄	—	79	1	no	—
103	C₂²×C₄	C₄×D₇₉	1	1	yes	characteristic
104	C₂²×C₄	C₄×D₇₉	1	1	yes	characteristic
105	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
106	C₂×C₈	—	2	2	no	—
107	C₂×C₈	—	2	2	no	—
108	C₂×C₈	—	2	2	no	—
109	C₂×C₈	—	158	2	no	—
110	C₂×C₈	—	158	2	no	—
111	C₂×C₈	—	158	2	no	—
112	C₄²	—	2	2	no	—
113	C₄²	—	79	4	no	—
114	C₄²	—	158	2	no	—
115	C₄²	—	158	2	no	—
116	C₄²	—	158	2	no	—
117	C₄²	—	158	1	no	—
118	C₄²	—	158	2	no	—
119	C₄²	—	158	1	no	—
120	C₂³	C₂×C₄×D₇₉	1	1	yes	characteristic
121	C₂×C₄	—	2	1	no	—
122	C₂×C₄	—	2	1	no	—
123	C₂×C₄	—	2	1	no	—
124	C₂×C₄	—	2	1	no	—
125	C₂×C₄	—	79	2	no	—
126	C₂×C₄	—	79	2	no	—
127	C₂×C₄	—	79	2	no	—
128	C₂×C₄	—	79	2	no	—
129	C₂×C₄	—	158	1	no	—
130	C₂×C₄	—	158	1	no	—
131	C₂×C₄	—	158	1	no	—
132	C₂×C₄	—	158	1	no	—
133	C₂×C₄	—	158	1	no	—
134	C₂×C₄	—	158	1	no	—
135	C₂×C₄	—	158	1	no	—
136	C₂×C₄	—	158	1	no	—
137	C₂×C₄	C₈×D₇₉	1	2	yes	—
138	C₂×C₄	#11929607	1	2	yes	—
139	C₂×C₄	#11929623	1	1	yes	characteristic
140	C₂×C₄	#11929623	1	2	yes	—
141	C₂×C₄	#11929624	1	2	yes	—
142	C₂×C₄	#11929625	1	1	yes	characteristic
143	C₈	—	4	2	no	—
144	C₈	—	316	2	no	—
145	C₂²	#14579117	1	1	yes	characteristic
146	C₂²	#14579118	1	1	yes	characteristic
147	C₂²	#14579119	1	1	yes	characteristic
148	C₂²	C₂×C₈×D₇₉	1	1	yes	characteristic
149	C₂²	M₁₆×D₇₉	1	1	yes	characteristic
150	C₂²	M₁₆×D₇₉	1	1	yes	characteristic
151	C₂²	C₂×#11929607	1	1	yes	characteristic
152	C₄	—	2	2	no	—
153	C₄	—	2	2	no	—
154	C₄	—	158	2	no	—
155	C₄	—	158	2	no	—
156	C₄	—	158	2	no	—
157	C₄	—	158	2	no	—
158	C₄	#14579154	1	2	yes	—
159	C₄	#14579156	1	2	yes	—
160	C₂	#19098430	1	1	yes	characteristic
161	C₂	#19098613	1	1	yes	characteristic
162	C₂	#19098614	1	1	yes	characteristic
163	C₂	#19098615	1	1	yes	characteristic
164	C₂	#19098617	1	1	yes	characteristic
165	C₂	#19098618	1	1	yes	characteristic
166	C₂	#19098619	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄²×Dic₇₉

C₂

yes

maximal, characteristic

#19098318

C₂

yes

maximal, characteristic

#19098317

C₂

yes

maximal

#19098317

C₂

yes

maximal

#336×C₇₉

C₂

yes

maximal, characteristic

C₂²×C₇₉⋊C₈

C₂²

yes

—

C₂×C₄×Dic₇₉

C₄

yes

characteristic

C₂×C₄×Dic₇₉

C₄

yes

characteristic

C₂×C₄×Dic₇₉

C₄

yes

characteristic

C₂×C₄×Dic₇₉

C₄

yes

characteristic

C₂×C₄×Dic₇₉

C₂²

yes

characteristic

C₂×C₄×Dic₇₉

C₂²

yes

characteristic

C₂²×C₈×C₇₉

C₂²

yes

—

C₂×C₄²×C₇₉

C₂²

yes

characteristic

C₂²×Dic₇₉

C₂×C₄

yes

characteristic

C₂²×Dic₇₉

C₂×C₄

yes

characteristic

C₂²×Dic₇₉

C₂×C₄

yes

characteristic

C₂²×Dic₇₉

C₂×C₄

yes

characteristic

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₄×Dic₇₉

—

C₄×Dic₇₉

—

C₄×Dic₇₉

—

C₄×Dic₇₉

—

C₄×Dic₇₉

—

C₄×Dic₇₉

—

C₄×Dic₇₉

C₈

yes

complemented

C₂²×C₄×C₇₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₇₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₇₉

C₂³

yes

characteristic

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₄²×C₇₉

—

C₂³×C₇₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂×C₈

yes

—

C₂×C₄×C₇₉

M₁₆

yes

—

C₂×C₄×C₇₉

#41

yes

characteristic

C₂×C₄×C₇₉

#41

yes

—

C₂×C₄×C₇₉

#41

yes

—

C₂×C₄×C₇₉

#41

yes

characteristic

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

C₂×C₈

yes

—

C₂×Dic₇₉

C₂×C₈

yes

—

C₂×Dic₇₉

M₁₆

yes

—

C₂×Dic₇₉

M₁₆

yes

—

C₈×C₇₉

—

C₇₉⋊C₈

—

C₂²×C₇₉

yes

C₂²×C₇₉

yes

C₂²×C₇₉

yes

C₂²×C₇₉

C₂²×C₈

yes

characteristic

C₂²×C₇₉

C₂×M₁₆

yes

characteristic

C₂²×C₇₉

C₂×M₁₆

yes

characteristic

C₂²×C₇₉

C₂×M₁₆

yes

characteristic

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

#126

yes

—

C₄×C₇₉

#126

yes

—

Dic₇₉

—

Dic₇₉

—

Dic₇₉

—

Dic₇₉

—

C₂×C₇₉

yes

C₂×C₇₉

yes

C₂×C₇₉

yes

C₂×C₇₉

yes

C₂×C₇₉

yes

C₂×C₇₉

yes

C₂×C₇₉

yes

—

C₇₉

yes

characteristic, complemented, Sylow

C₄³

—

—

—

—

D₇₉

yes

characteristic

C₂²×C₈

—

C₂²×C₈

C₂×D₇₉

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₇₉

yes

characteristic

C₂²×C₄

—

100

C₂²×C₄

—

101

C₂²×C₄

—

102

C₂²×C₄

—

103

C₂²×C₄

C₄×D₇₉

yes

characteristic

104

C₂²×C₄

C₄×D₇₉

yes

characteristic

105

C₂²×C₄

C₂²×D₇₉

yes

characteristic

106

C₂×C₈

—

107

C₂×C₈

—

108

C₂×C₈

—

109

C₂×C₈

—

158

—

110

C₂×C₈

—

158

—

111

C₂×C₈

—

158

—

112

C₄²

—

113

C₄²

—

114

C₄²

—

158

—

115

C₄²

—

158

—

116

C₄²

—

158

—

117

C₄²

—

158

—

118

C₄²

—

158

—

119

C₄²

—

158

—

120

C₂³

C₂×C₄×D₇₉

yes

characteristic

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

158

—

130

C₂×C₄

—

158

—

131

C₂×C₄

—

158

—

132

C₂×C₄

—

158

—

133

C₂×C₄

—

158

—

134

C₂×C₄

—

158

—

135

C₂×C₄

—

158

—

136

C₂×C₄

—

158

—

137

C₂×C₄

C₈×D₇₉

yes

—

138

C₂×C₄

#11929607

yes

—

139

C₂×C₄

#11929623

yes

characteristic

140

C₂×C₄

#11929623

yes

—

141

C₂×C₄

#11929624

yes

—

142

C₂×C₄

#11929625

yes

characteristic

143

C₈

—

144

C₈

—

316

—

145

C₂²

#14579117

yes

characteristic

146

C₂²

#14579118

yes

characteristic

147

C₂²

#14579119

yes

characteristic

148

C₂²

C₂×C₈×D₇₉

yes

characteristic

149

C₂²

M₁₆×D₇₉

yes

characteristic

150

C₂²

M₁₆×D₇₉

yes

characteristic

151

C₂²

C₂×#11929607

yes

characteristic

152

C₄

—

153

C₄

—

154

C₄

—

158

—

155

C₄

—

158

—

156

C₄

—

158

—

157

C₄

—

158

—

158

C₄

#14579154

yes

—

159

C₄

#14579156

yes

—

160

C₂

#19098430

yes

characteristic

161

C₂

#19098613

yes

characteristic

162

C₂

#19098614

yes

characteristic

163

C₂

#19098615

yes

characteristic

164

C₂

#19098617

yes

characteristic

165

C₂

#19098618

yes

characteristic

166

C₂

#19098619

yes

characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₇₉
commutator	C₂²×C₇₉	C₂²×C₈
Fitting	#336×C₇₉	C₂
socle, prime radical	C₂³×C₇₉	C₂²×C₄
cosocle	C₂²×C₄×C₇₉	C₂³
hypercenter	#336	D₇₉
hypocenter	C₇₉	#1839
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂²×C₄ ◁ #336

subgroup

G/H

center, Frattini

C₂²×C₄

C₂²×D₇₉

commutator

C₂²×C₇₉

C₂²×C₈

Fitting

#336×C₇₉

C₂

socle, prime radical

C₂³×C₇₉

C₂²×C₄

cosocle

C₂²×C₄×C₇₉

C₂³

D₇₉

C₇₉

G ▷ C₂²×C₇₉ ▷ C₇₉

C₁ ◁ C₂²×C₄ ◁ #336

N	H ≅ G/N	type
28. C₄×Dic₇₉	C₈	semidirect
84. C₇₉	#1839	semidirect

H ≅ G/N

type

28. C₄×Dic₇₉

C₈

semidirect

84. C₇₉

#1839

semidirect

Subgroups — #23763542

Conjugacy classes of subgroups

Complements