Group #16790234 — subgroups

Subgroups — #16790234

Order 3328.

274 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 100 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	#13130777	C₂	1	1	yes	maximal, characteristic
2	#13130776	C₂	1	1	yes	maximal, characteristic
3	#13129896	C₂	1	4	yes	maximal
4	D₁₃×#346	C₂	1	1	yes	maximal, characteristic
5	C₂×#88104	—	2	1	no	—
6	C₂×#88104	C₂²	1	2	yes	—
7	C₂×#88104	C₂²	1	2	yes	—
8	C₂×#88103	—	2	1	no	—
9	#11719053	—	2	1	no	—
10	#11719052	—	2	1	no	—
11	C₂×C₁₆×D₁₃	C₂²	1	2	yes	—
12	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
13	C₁₃×#346	C₄	1	1	yes	characteristic
14	#11718094	C₄	1	2	yes	—
15	#11718053	C₄	1	1	yes	characteristic
16	C₂×#6118	—	2	2	no	—
17	C₂×#6118	—	2	2	no	—
18	C₂×C₈×D₁₃	D₄	1	1	yes	characteristic
19	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
20	C₄²×D₁₃	D₄	1	1	yes	characteristic
21	#88112	—	4	2	no	—
22	C₄⋊#1057	—	4	2	no	—
23	#88104	—	2	4	no	—
24	#88104	—	2	4	no	—
25	#88104	—	4	2	no	—
26	#88103	—	4	2	no	—
27	C₂×C₁₃×C₁₆	C₂×C₄	1	2	yes	—
28	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
29	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
30	C₈×Dic₁₃	Q₈	1	1	yes	characteristic
31	C₂×#6090	C₂×C₄	1	2	yes	—
32	C₄×#1055	Q₈	1	1	yes	characteristic
33	C₁₆×D₁₃	—	2	2	no	—
34	C₁₆×D₁₃	—	2	2	no	—
35	#12892	—	13	1	no	maximal, Sylow
36	C₂×C₄×D₁₃	Q₁₆	1	2	yes	—
37	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
38	C₂×#1057	—	4	2	no	—
39	C₂×#1057	—	4	2	no	—
40	#6118	—	4	2	no	—
41	#6118	—	4	2	no	—
42	#6118	—	4	2	no	—
43	#6118	—	4	2	no	—
44	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
45	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
46	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
47	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
48	C₄×Dic₁₃	D₈	1	2	yes	—
49	C₂×#1055	C₄⋊C₄	1	1	yes	characteristic
50	C₂×#1055	C₂×Q₈	1	1	yes	characteristic
51	C₈×D₁₃	SD₁₆	1	2	yes	—
52	C₈×D₁₃	SD₁₆	1	2	yes	—
53	C₈×D₁₃	#41	1	2	yes	—
54	C₈×D₁₃	#41	1	2	yes	—
55	C₁₃×C₁₆	—	2	2	no	—
56	#6090	—	2	2	no	—
57	C₂×#346	—	13	1	no	—
58	#1848	—	13	1	no	—
59	#1848	—	13	1	no	—
60	#1381	—	13	4	no	—
61	C₂²×D₁₃	C₂×Q₁₆	1	1	yes	characteristic
62	C₂×C₄×C₁₃	#107	1	2	yes	—
63	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
64	C₂×Dic₁₃	#107	1	2	yes	—
65	C₂×Dic₁₃	C₂×D₈	1	1	yes	characteristic
66	C₄×D₁₃	—	4	2	no	—
67	C₄×D₁₃	#124	1	1	yes	characteristic
68	C₄×D₁₃	#124	1	1	yes	characteristic
69	C₄×D₁₃	C₂×SD₁₆	1	1	yes	characteristic
70	C₄×D₁₃	C₂×SD₁₆	1	1	yes	characteristic
71	#1057	—	8	2	no	—
72	#1057	—	8	2	no	—
73	C₈×C₁₃	#106	1	2	yes	—
74	C₈×C₁₃	#117	1	2	yes	—
75	#1055	#106	1	2	yes	—
76	#1055	#125	1	2	yes	—
77	C₂²×C₁₆	—	13	2	no	—
78	C₂×#108	—	13	2	no	—
79	C₂×#108	—	13	2	no	—
80	C₂×#108	—	26	1	no	—
81	C₂×#108	—	26	1	no	—
82	#423	—	26	1	no	—
83	#423	—	26	1	no	—
84	C₂×C₄×C₈	—	13	1	no	—
85	#346	—	13	2	no	—
86	#346	—	13	1	no	—
87	#346	#261	1	1	yes	characteristic
88	C₂²×C₁₃	C₂×#107	1	1	yes	characteristic
89	C₂×D₁₃	—	2	2	no	—
90	C₂×D₁₃	#487	1	1	yes	characteristic
91	C₂×D₁₃	#487	1	1	yes	characteristic
92	C₄×C₁₃	—	2	2	no	—
93	C₄×C₁₃	#382	1	1	yes	characteristic
94	C₄×C₁₃	C₂×#106	1	1	yes	characteristic
95	Dic₁₃	—	2	2	no	—
96	Dic₁₃	#486	1	1	yes	characteristic
97	Dic₁₃	#486	1	1	yes	characteristic
98	C₂×M₁₆	—	26	2	no	—
99	C₂×M₁₆	—	26	2	no	—
100	C₂²×C₈	—	13	1	no	—
101	C₂²×C₈	—	13	1	no	—
102	C₂×C₄²	—	13	1	no	—
103	C₂×C₁₆	—	13	2	no	—
104	C₂×C₁₆	—	26	2	no	—
105	C₂×C₁₆	—	26	2	no	—
106	C₂×C₁₆	C₂×#261	1	2	yes	—
107	#108	—	26	4	no	—
108	#108	—	26	4	no	—
109	#108	—	52	2	no	—
110	#108	—	52	2	no	—
111	C₄⋊C₈	—	52	2	no	—
112	C₄⋊C₈	—	52	2	no	—
113	C₄×C₈	—	13	1	no	—
114	C₄×C₈	—	13	1	no	—
115	C₄×C₈	—	13	1	no	—
116	C₄×C₈	C₂×#261	1	1	yes	characteristic
117	C₂×C₁₃	#1834	1	1	yes	characteristic
118	C₂×C₁₃	#2161	1	2	yes	—
119	D₁₃	—	2	1	no	—
120	D₁₃	—	2	1	no	—
121	C₂²×C₄	—	13	1	no	—
122	C₂²×C₄	—	13	2	no	—
123	M₁₆	—	52	2	no	—
124	M₁₆	—	52	2	no	—
125	M₁₆	—	52	2	no	—
126	M₁₆	—	52	2	no	—
127	C₂×C₈	—	13	1	no	—
128	C₂×C₈	—	13	1	no	—
129	C₂×C₈	—	13	2	no	—
130	C₂×C₈	—	13	2	no	—
131	C₂×C₈	—	13	2	no	—
132	C₂×C₈	—	13	2	no	—
133	C₂×C₈	—	52	2	no	—
134	C₂×C₈	—	52	2	no	—
135	C₂×C₈	C₄⋊#261	1	1	yes	characteristic
136	C₂×C₈	C₂²×#261	1	1	yes	characteristic
137	C₄²	—	13	2	no	—
138	C₄²	—	13	1	no	—
139	C₄²	C₄⋊#261	1	1	yes	characteristic
140	C₁₆	—	2	2	no	—
141	C₁₆	—	26	2	no	—
142	C₁₃	#12892	1	1	yes	characteristic, complemented, Sylow
143	C₂³	—	13	1	no	—
144	C₂×C₄	—	13	1	no	—
145	C₂×C₄	—	13	1	no	—
146	C₂×C₄	—	13	1	no	—
147	C₂×C₄	—	13	1	no	—
148	C₂×C₄	—	13	1	no	—
149	C₂×C₄	—	13	2	no	—
150	C₂×C₄	—	52	2	no	—
151	C₂×C₄	#88102	1	2	yes	—
152	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
153	C₈	—	13	2	no	—
154	C₈	—	13	2	no	—
155	C₈	—	104	2	no	—
156	C₈	—	104	2	no	—
157	C₈	#88101	1	2	yes	—
158	C₈	#88237	1	2	yes	—
159	C₂²	—	13	1	no	—
160	C₂²	—	13	1	no	—
161	C₂²	—	26	2	no	—
162	C₂²	C₂×#88102	1	1	yes	characteristic
163	C₄	—	2	2	no	—
164	C₄	—	13	1	no	—
165	C₄	—	13	1	no	—
166	C₄	—	26	2	no	—
167	C₄	#11719060	1	1	yes	characteristic
168	C₄	C₂×#88101	1	1	yes	characteristic
169	C₂	—	26	1	no	—
170	C₂	—	26	1	no	—
171	C₂	#13130757	1	1	yes	characteristic
172	C₂	#13131192	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#13130777

C₂

yes

maximal, characteristic

#13130776

C₂

yes

maximal, characteristic

#13129896

C₂

yes

maximal

D₁₃×#346

C₂

yes

maximal, characteristic

C₂×#88104

—

C₂×#88104

C₂²

yes

—

C₂×#88104

C₂²

yes

—

C₂×#88103

—

#11719053

—

#11719052

—

C₂×C₁₆×D₁₃

C₂²

yes

—

C₄×C₈×D₁₃

C₂²

yes

characteristic

C₁₃×#346

C₄

yes

characteristic

#11718094

C₄

yes

—

#11718053

C₄

yes

characteristic

C₂×#6118

—

C₂×#6118

—

C₂×C₈×D₁₃

D₄

yes

characteristic

C₂×C₈×D₁₃

C₂³

yes

characteristic

C₄²×D₁₃

D₄

yes

—

—

—

—

—

—

C₂×C₁₃×C₁₆

C₂×C₄

yes

—

C₄×C₈×C₁₃

C₂×C₄

yes

characteristic

C₈×Dic₁₃

C₂×C₄

yes

characteristic

C₈×Dic₁₃

Q₈

yes

characteristic

C₂×#6090

C₂×C₄

yes

—

C₄×#1055

Q₈

yes

characteristic

C₁₆×D₁₃

—

C₁₆×D₁₃

—

#12892

—

maximal, Sylow

C₂×C₄×D₁₃

Q₁₆

yes

—

C₂×C₄×D₁₃

C₂×D₄

yes

—

—

—

—

—

—

C₂×C₈×C₁₃

C₄⋊C₄

yes

characteristic

C₂×C₈×C₁₃

C₂²×C₄

yes

characteristic

C₄²×C₁₃

C₄⋊C₄

yes

characteristic

C₄×Dic₁₃

C₄⋊C₄

yes

characteristic

C₄×Dic₁₃

D₈

yes

—

C₂×#1055

C₄⋊C₄

yes

characteristic

C₂×#1055

C₂×Q₈

yes

characteristic

C₈×D₁₃

SD₁₆

yes

—

C₈×D₁₃

SD₁₆

yes

—

C₈×D₁₃

#41

yes

—

C₈×D₁₃

#41

yes

—

C₁₃×C₁₆

—

—

—

—

—

—

C₂²×D₁₃

C₂×Q₁₆

yes

characteristic

C₂×C₄×C₁₃

#107

yes

—

C₂×C₄×C₁₃

C₂×C₄⋊C₄

yes

characteristic

C₂×Dic₁₃

#107

yes

—

C₂×Dic₁₃

C₂×D₈

yes

characteristic

C₄×D₁₃

—

C₄×D₁₃

yes

C₄×D₁₃

yes

C₄×D₁₃

C₂×SD₁₆

yes

characteristic

C₄×D₁₃

C₂×SD₁₆

yes

characteristic

#1057

—

#1057

—

C₈×C₁₃

#106

yes

—

C₈×C₁₃

#117

yes

—

#1055

#106

yes

—

#1055

#125

yes

—

C₂²×C₁₆

—

—

—

—

—

—

—

C₂×C₄×C₈

—

—

—

yes

C₂²×C₁₃

yes

C₂×D₁₃

—

C₂×D₁₃

yes

C₂×D₁₃

yes

C₄×C₁₃

—

C₄×C₁₃

yes

C₄×C₁₃

yes

Dic₁₃

—

Dic₁₃

yes

Dic₁₃

yes

C₂×M₁₆

—

C₂×M₁₆

—

100

C₂²×C₈

—

101

C₂²×C₈

—

102

C₂×C₄²

—

103

C₂×C₁₆

—

104

C₂×C₁₆

—

105

C₂×C₁₆

—

106

C₂×C₁₆

C₂×#261

yes

—

107

#108

—

108

#108

—

109

#108

—

110

#108

—

111

C₄⋊C₈

—

112

C₄⋊C₈

—

113

C₄×C₈

—

114

C₄×C₈

—

115

C₄×C₈

—

116

C₄×C₈

C₂×#261

yes

characteristic

117

C₂×C₁₃

#1834

yes

characteristic

118

C₂×C₁₃

#2161

yes

—

119

D₁₃

—

120

D₁₃

—

121

C₂²×C₄

—

122

C₂²×C₄

—

123

M₁₆

—

124

M₁₆

—

125

M₁₆

—

126

M₁₆

—

127

C₂×C₈

—

128

C₂×C₈

—

129

C₂×C₈

—

130

C₂×C₈

—

131

C₂×C₈

—

132

C₂×C₈

—

133

C₂×C₈

—

134

C₂×C₈

—

135

C₂×C₈

C₄⋊#261

yes

characteristic

136

C₂×C₈

C₂²×#261

yes

characteristic

137

C₄²

—

138

C₄²

—

139

C₄²

C₄⋊#261

yes

characteristic

140

C₁₆

—

141

C₁₆

—

142

C₁₃

#12892

yes

characteristic, complemented, Sylow

143

C₂³

—

144

C₂×C₄

—

145

C₂×C₄

—

146

C₂×C₄

—

147

C₂×C₄

—

148

C₂×C₄

—

149

C₂×C₄

—

150

C₂×C₄

—

151

C₂×C₄

#88102

yes

—

152

C₂×C₄

C₂×C₄⋊#261

yes

characteristic

153

C₈

—

154

C₈

—

155

C₈

—

104

—

156

C₈

—

104

—

157

C₈

#88101

yes

—

158

C₈

#88237

yes

—

159

C₂²

—

160

C₂²

—

161

C₂²

—

162

C₂²

C₂×#88102

yes

characteristic

163

C₄

—

164

C₄

—

165

C₄

—

166

C₄

—

167

C₄

#11719060

yes

characteristic

168

C₄

C₂×#88101

yes

characteristic

169

C₂

—

170

C₂

—

171

C₂

#13130757

yes

characteristic

172

C₂

#13131192

yes

—

	subgroup	G/H
center	C₂²	C₂×#88102
commutator	C₂×C₈×C₁₃	C₂²×C₄
Frattini	C₂×C₈	C₂²×#261
Fitting	C₁₃×#346	C₄
socle	C₂²×C₁₃	C₂×#107
prime radical	C₂²×D₁₃	C₂×Q₁₆
cosocle	C₂×C₈×D₁₃	C₂³
hypercenter	#346	#261
hypocenter	C₁₃	#12892
LCS	G ▷ C₂×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #346

subgroup

G/H

center

C₂²

C₂×#88102

commutator

C₂×C₈×C₁₃

C₂²×C₄

Frattini

C₂×C₈

C₂²×#261

Fitting

C₁₃×#346

C₄

socle

C₂²×C₁₃

C₂×#107

prime radical

C₂²×D₁₃

C₂×Q₁₆

cosocle

C₂×C₈×D₁₃

C₂³

C₁₃

G ▷ C₂×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #346

N	H ≅ G/N	type
142. C₁₃	#12892	semidirect

H ≅ G/N

type

142. C₁₃

#12892

semidirect

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

subgroup	index
#13130777	2
#13130776	2
#13129896	2
D₁₃×#346	2
#12892	13

subgroup

index

D₁₃×#346

Subgroups — #16790234

Conjugacy classes of subgroups

Complements

Maximal subgroups