Group #16807384 — subgroups

Subgroups — #16807384

Order 3328.

444 conjugacy classes of subgroups; only the 210 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 210 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	#13131253	C₂	1	8	yes	maximal, complemented
2	#13131202	C₂	1	4	yes	maximal
3	#13131197	C₂	1	2	yes	maximal
4	#13123766	C₂	1	1	yes	maximal, characteristic
5	#11719175	C₄	1	1	yes	characteristic
6	C₁₃×#423	C₄	1	1	yes	characteristic
7	#11718783	C₂²	1	2	yes	—
8	#11718780	C₄	1	2	yes	—
9	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
10	#11718492	C₄	1	4	yes	—
11	#11718491	C₂²	1	4	yes	—
12	C₂²⋊#6092	C₂²	1	4	yes	—
13	#11718260	C₂²	1	8	yes	—
14	#11718258	C₂²	1	4	yes	—
15	#11718257	C₂²	1	4	yes	—
16	#11718231	C₂²	1	4	yes	—
17	C₄⋊#6092	C₂²	1	4	yes	—
18	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
19	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
20	#88180	C₂×C₄	1	2	yes	—
21	#88178	C₈	1	4	yes	—
22	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
23	C₂²×#1055	C₂³	1	1	yes	characteristic
24	#88124	C₈	1	2	yes	—
25	#88123	C₈	1	2	yes	—
26	C₄×Dic₂₆	C₂×C₄	1	4	yes	—
27	C₂×#6092	C₂³	1	8	yes	—
28	C₁₃×C₄⋊C₈	C₂×C₄	1	4	yes	—
29	#88055	C₂×C₄	1	4	yes	—
30	#88054	C₂×C₄	1	8	yes	—
31	C₈×Dic₁₃	C₂³	1	4	yes	—
32	C₄×#1055	C₂×C₄	1	2	yes	—
33	C₄×#1055	C₂³	1	2	yes	—
34	#33501	—	13	1	no	maximal, Sylow
35	C₂²×C₄×C₁₃	C₂×C₈	1	2	yes	—
36	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
37	C₂×Dic₂₆	C₂×C₈	1	4	yes	—
38	C₁₃×M₁₆	—	4	2	no	—
39	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
40	C₄²×C₁₃	C₂×C₈	1	1	yes	characteristic
41	C₄²×C₁₃	C₂×C₈	1	1	yes	characteristic
42	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
43	C₂²⋊Dic₁₃	C₂×C₈	1	4	yes	—
44	C₄⋊Dic₁₃	C₂×C₈	1	4	yes	—
45	C₄⋊Dic₁₃	C₂×C₈	1	4	yes	—
46	#6101	C₂×C₈	1	8	yes	—
47	C₄×Dic₁₃	C₂²×C₄	1	4	yes	—
48	C₂×#1055	—	2	2	no	—
49	C₂×#1055	—	4	1	no	—
50	C₂×#1055	C₂²×C₄	1	2	yes	—
51	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
52	C₂×#1055	C₂⁴	1	1	yes	characteristic
53	#6092	—	2	8	no	—
54	#2960	—	13	1	no	—
55	#2183	—	13	8	no	—
56	#2164	—	13	4	no	—
57	#2163	—	13	2	no	—
58	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
59	C₂×C₄×C₁₃	—	2	1	no	—
60	C₂×C₄×C₁₃	—	2	1	no	—
61	C₂×C₄×C₁₃	—	4	2	no	—
62	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
63	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
64	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
65	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
66	C₂×Dic₁₃	C₂²×C₈	1	8	yes	—
67	Dic₂₆	—	4	4	no	—
68	C₈×C₁₃	—	2	4	no	—
69	#1055	—	2	1	no	—
70	#1055	—	2	2	no	—
71	#1055	2₋¹⁺⁴	1	2	yes	—
72	#533	—	13	1	no	—
73	#446	—	13	4	no	—
74	C₈×Q₈	—	13	4	no	—
75	#424	—	13	2	no	—
76	#423	#261	1	1	yes	characteristic
77	#405	—	13	2	no	—
78	C₂×C₄×C₈	—	13	1	no	—
79	C₄⋊C₁₆	—	13	4	no	—
80	C₄⋊C₁₆	—	13	8	no	—
81	C₂²⋊C₁₆	—	13	4	no	—
82	#346	—	13	4	no	—
83	#346	—	13	4	no	—
84	C₄×C₁₆	—	13	4	no	—
85	C₂²×C₁₃	—	2	2	no	—
86	C₂²×C₁₃	—	2	1	no	—
87	C₂²×C₁₃	C₂³×C₈	1	1	yes	characteristic
88	C₄×C₁₃	—	2	2	no	—
89	C₄×C₁₃	—	2	2	no	—
90	C₄×C₁₃	—	2	1	no	—
91	C₄×C₁₃	#519	1	1	yes	characteristic
92	C₄×C₁₃	#568	1	1	yes	characteristic
93	Dic₁₃	—	2	8	no	—
94	C₂×M₁₆	C₂×#261	1	2	yes	—
95	C₂²×C₈	—	13	1	no	—
96	C₂²×C₈	—	13	1	no	—
97	C₄⋊Q₈	—	13	2	no	—
98	#125	—	13	2	no	—
99	C₂²⋊Q₈	—	13	4	no	—
100	C₄×Q₈	—	13	4	no	—
101	#117	—	13	2	no	—
102	C₂×C₄²	C₂×#261	1	1	yes	characteristic
103	C₂×C₁₆	—	13	8	no	—
104	C₄⋊C₈	—	13	8	no	—
105	C₄⋊C₈	C₂×#261	1	4	yes	—
106	#97	—	13	4	no	—
107	C₄×C₈	—	13	4	no	—
108	C₄×C₈	—	13	2	no	—
109	C₄×C₈	—	13	2	no	—
110	C₂×C₁₃	—	4	1	no	—
111	C₂×C₁₃	#2982	1	1	yes	characteristic
112	C₂×C₁₃	#3407	1	2	yes	—
113	C₂×Q₈	—	13	4	no	—
114	C₂²×C₄	D₁₃⋊C₈	1	2	yes	—
115	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
116	M₁₆	—	4	2	no	—
117	C₂×C₈	—	13	1	no	—
118	C₂×C₈	—	13	1	no	—
119	C₂×C₈	—	13	2	no	—
120	C₂×C₈	—	26	2	no	—
121	C₂×C₈	—	52	1	no	—
122	C₂×C₈	C₂²×#261	1	4	yes	—
123	C₄⋊C₄	—	13	4	no	—
124	C₄⋊C₄	—	13	8	no	—
125	C₄⋊C₄	—	13	4	no	—
126	C₂²⋊C₄	—	13	4	no	—
127	C₄²	—	13	4	no	—
128	C₄²	D₁₃⋊C₈	1	1	yes	characteristic
129	C₄²	D₁₃⋊C₈	1	1	yes	characteristic
130	C₄²	C₂²×#261	1	2	yes	—
131	C₁₆	—	26	8	no	—
132	C₁₃	#33501	1	1	yes	characteristic, complemented, Sylow
133	C₂³	C₂×D₁₃⋊C₈	1	1	yes	characteristic
134	Q₈	—	52	4	no	—
135	C₂×C₄	—	2	1	no	—
136	C₂×C₄	—	2	1	no	—
137	C₂×C₄	—	4	2	no	—
138	C₂×C₄	—	13	8	no	—
139	C₂×C₄	C₂×D₁₃⋊C₈	1	1	yes	characteristic
140	C₂×C₄	C₂×D₁₃⋊C₈	1	2	yes	—
141	C₂×C₄	C₂×D₁₃⋊C₈	1	2	yes	—
142	C₂×C₄	C₂³×#261	1	1	yes	characteristic
143	C₈	—	2	4	no	—
144	C₈	—	13	2	no	—
145	C₈	—	26	2	no	—
146	C₈	—	26	1	no	—
147	C₂²	—	2	2	no	—
148	C₂²	—	2	1	no	—
149	C₂²	C₂²×D₁₃⋊C₈	1	1	yes	characteristic
150	C₄	—	2	2	no	—
151	C₄	—	2	2	no	—
152	C₄	—	2	1	no	—
153	C₄	—	26	8	no	—
154	C₄	#11719621	1	1	yes	characteristic
155	C₄	#11719627	1	1	yes	characteristic
156	C₂	—	4	1	no	—
157	C₂	#13131731	1	1	yes	characteristic
158	C₂	#13131805	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#13131253

C₂

yes

maximal, complemented

#13131202

C₂

yes

maximal

#13131197

C₂

yes

maximal

#13123766

C₂

yes

maximal, characteristic

#11719175

C₄

yes

characteristic

C₁₃×#423

C₄

yes

characteristic

#11718783

C₂²

yes

—

#11718780

C₄

yes

—

C₂×C₄×#1055

C₂²

yes

characteristic

#11718492

C₄

yes

—

#11718491

C₂²

yes

—

C₂²⋊#6092

C₂²

yes

—

#11718260

C₂²

yes

—

#11718258

C₂²

yes

—

#11718257

C₂²

yes

—

#11718231

C₂²

yes

—

C₄⋊#6092

C₂²

yes

—

C₂×C₁₃×M₁₆

C₂×C₄

yes

—

C₂×C₄²×C₁₃

C₂×C₄

yes

characteristic

#88180

C₂×C₄

yes

—

#88178

C₈

yes

—

C₂²×#1055

C₂×C₄

yes

characteristic

C₂²×#1055

C₂³

yes

characteristic

#88124

C₈

yes

—

#88123

C₈

yes

—

C₄×Dic₂₆

C₂×C₄

yes

—

C₂×#6092

C₂³

yes

—

C₁₃×C₄⋊C₈

C₂×C₄

yes

—

#88055

C₂×C₄

yes

—

#88054

C₂×C₄

yes

—

C₈×Dic₁₃

C₂³

yes

—

C₄×#1055

C₂×C₄

yes

—

C₄×#1055

C₂³

yes

—

#33501

—

maximal, Sylow

C₂²×C₄×C₁₃

C₂×C₈

yes

—

C₂²×C₄×C₁₃

C₂²×C₄

yes

characteristic

C₂×Dic₂₆

C₂×C₈

yes

—

C₁₃×M₁₆

—

C₂×C₈×C₁₃

C₂²×C₄

yes

—

C₄²×C₁₃

C₂×C₈

yes

characteristic

C₄²×C₁₃

C₂×C₈

yes

characteristic

C₄²×C₁₃

C₂²×C₄

yes

—

C₂²⋊Dic₁₃

C₂×C₈

yes

—

C₄⋊Dic₁₃

C₂×C₈

yes

—

C₄⋊Dic₁₃

C₂×C₈

yes

—

#6101

C₂×C₈

yes

—

C₄×Dic₁₃

C₂²×C₄

yes

—

C₂×#1055

—

C₂×#1055

—

C₂×#1055

C₂²×C₄

yes

—

C₂×#1055

C₂²×C₄

yes

characteristic

C₂×#1055

C₂⁴

yes

—

—

—

—

—

C₂³×C₁₃

C₂²×C₈

yes

characteristic

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₂²×C₈

yes

—

C₂×C₄×C₁₃

C₂²×C₈

yes

characteristic

C₂×C₄×C₁₃

C₂²×C₈

yes

—

C₂×C₄×C₁₃

C₂³×C₄

yes

characteristic

C₂×Dic₁₃

C₂²×C₈

yes

—

Dic₂₆

—

C₈×C₁₃

—

#1055

—

#1055

—

#1055

2₋¹⁺⁴

yes

—

#533

—

#446

—

C₈×Q₈

—

—

yes

—

C₂×C₄×C₈

—

C₄⋊C₁₆

—

C₄⋊C₁₆

—

C₂²⋊C₁₆

—

#346

—

#346

—

C₄×C₁₆

—

C₂²×C₁₃

—

C₂²×C₁₃

—

C₂²×C₁₃

C₂³×C₈

yes

characteristic

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

yes

C₄×C₁₃

yes

Dic₁₃

—

C₂×M₁₆

C₂×#261

yes

—

C₂²×C₈

—

C₂²×C₈

—

C₄⋊Q₈

—

#125

—

C₂²⋊Q₈

—

100

C₄×Q₈

—

101

#117

—

102

C₂×C₄²

C₂×#261

yes

characteristic

103

C₂×C₁₆

—

104

C₄⋊C₈

—

105

C₄⋊C₈

C₂×#261

yes

—

106

#97

—

107

C₄×C₈

—

108

C₄×C₈

—

109

C₄×C₈

—

110

C₂×C₁₃

—

111

C₂×C₁₃

#2982

yes

characteristic

112

C₂×C₁₃

#3407

yes

—

113

C₂×Q₈

—

114

C₂²×C₄

D₁₃⋊C₈

yes

—

115

C₂²×C₄

C₂²×#261

yes

characteristic

116

M₁₆

—

117

C₂×C₈

—

118

C₂×C₈

—

119

C₂×C₈

—

120

C₂×C₈

—

121

C₂×C₈

—

122

C₂×C₈

C₂²×#261

yes

—

123

C₄⋊C₄

—

124

C₄⋊C₄

—

125

C₄⋊C₄

—

126

C₂²⋊C₄

—

127

C₄²

—

128

C₄²

D₁₃⋊C₈

yes

characteristic

129

C₄²

D₁₃⋊C₈

yes

characteristic

130

C₄²

C₂²×#261

yes

—

131

C₁₆

—

132

C₁₃

#33501

yes

characteristic, complemented, Sylow

133

C₂³

C₂×D₁₃⋊C₈

yes

characteristic

134

Q₈

—

135

C₂×C₄

—

136

C₂×C₄

—

137

C₂×C₄

—

138

C₂×C₄

—

139

C₂×C₄

C₂×D₁₃⋊C₈

yes

characteristic

140

C₂×C₄

C₂×D₁₃⋊C₈

yes

—

141

C₂×C₄

C₂×D₁₃⋊C₈

yes

—

142

C₂×C₄

C₂³×#261

yes

characteristic

143

C₈

—

144

C₈

—

145

C₈

—

146

C₈

—

147

C₂²

—

148

C₂²

—

149

C₂²

C₂²×D₁₃⋊C₈

yes

characteristic

150

C₄

—

151

C₄

—

152

C₄

—

153

C₄

—

154

C₄

#11719621

yes

characteristic

155

C₄

#11719627

yes

characteristic

156

C₂

—

157

C₂

#13131731

yes

characteristic

158

C₂

#13131805

yes

—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×#261
commutator, socle	C₂²×C₁₃	C₂³×C₈
Fitting	C₁₃×#423	C₄
prime radical	C₂³×C₁₃	C₂²×C₈
cosocle	C₂×#1055	C₂⁴
hypercenter	#423	#261
hypocenter	C₁₃	#33501
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ #423

subgroup

G/H

center, Frattini

C₂×C₄

C₂³×#261

commutator, socle

C₂²×C₁₃

C₂³×C₈

Fitting

C₁₃×#423

C₄

prime radical

C₂³×C₁₃

C₂²×C₈

C₂⁴

C₁₃

G ▷ C₂²×C₁₃ ▷ C₁₃

C₁ ◁ C₂×C₄ ◁ #423

N	H ≅ G/N	type
1. #13131253	C₂	semidirect
132. C₁₃	#33501	semidirect

H ≅ G/N

type

1. #13131253

C₂

semidirect

132. C₁₃

#33501

semidirect

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

subgroup	index
#13131253	2
#13131202	2
#13131197	2
#13123766	2
#33501	13

subgroup

index

Subgroups — #16807384

Conjugacy classes of subgroups

Complements

Maximal subgroups