Group #16790232 — subgroups

Subgroups — #16790232

Order 3328.

282 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 108 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	2	yes	maximal
2	#13129896	C₂	1	4	yes	maximal
3	C₄×C₁₆×D₁₃	C₂	1	1	yes	maximal, characteristic
4	C₂×#88104	—	2	2	no	—
5	C₂×#88104	C₂²	1	4	yes	—
6	#11719052	—	2	2	no	—
7	C₂×C₁₆×D₁₃	C₂²	1	2	yes	—
8	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
9	C₄×C₁₃×C₁₆	C₄	1	1	yes	characteristic
10	C₁₆×Dic₁₃	C₄	1	2	yes	—
11	C₄×#6090	C₄	1	1	yes	characteristic
12	C₂×#6118	—	2	4	no	—
13	C₂×C₈×D₁₃	D₄	1	1	yes	characteristic
14	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
15	C₄²×D₁₃	D₄	1	1	yes	characteristic
16	C₄⋊#1057	—	4	2	no	—
17	C₄⋊#1057	—	4	2	no	—
18	#88104	—	2	8	no	—
19	#88104	—	4	4	no	—
20	C₂×C₁₃×C₁₆	C₂×C₄	1	2	yes	—
21	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
22	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
23	C₈×Dic₁₃	Q₈	1	1	yes	characteristic
24	C₂×#6090	C₂×C₄	1	2	yes	—
25	C₄×#1055	Q₈	1	1	yes	characteristic
26	C₁₆×D₁₃	—	2	4	no	—
27	#12891	—	13	1	no	maximal, Sylow
28	C₂×C₄×D₁₃	Q₁₆	1	1	yes	characteristic
29	C₂×C₄×D₁₃	Q₁₆	1	1	yes	characteristic
30	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
31	C₂×#1057	—	4	4	no	—
32	#6118	—	4	4	no	—
33	#6118	—	4	4	no	—
34	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
35	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
36	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
37	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
38	C₄×Dic₁₃	D₈	1	1	yes	characteristic
39	C₄×Dic₁₃	D₈	1	1	yes	characteristic
40	C₂×#1055	C₄⋊C₄	1	1	yes	characteristic
41	C₂×#1055	C₂×Q₈	1	1	yes	characteristic
42	C₈×D₁₃	SD₁₆	1	4	yes	—
43	C₈×D₁₃	#41	1	4	yes	—
44	C₁₃×C₁₆	—	2	2	no	—
45	#6090	—	2	2	no	—
46	C₂×C₄×C₁₆	—	13	1	no	—
47	#1848	—	13	2	no	—
48	#1381	—	13	4	no	—
49	C₂²×D₁₃	C₂×Q₁₆	1	1	yes	characteristic
50	C₂×C₄×C₁₃	#107	1	1	yes	characteristic
51	C₂×C₄×C₁₃	#107	1	1	yes	characteristic
52	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
53	C₂×Dic₁₃	#107	1	1	yes	characteristic
54	C₂×Dic₁₃	#107	1	1	yes	characteristic
55	C₂×Dic₁₃	C₂×D₈	1	1	yes	characteristic
56	C₄×D₁₃	—	2	2	no	—
57	C₄×D₁₃	—	2	2	no	—
58	C₄×D₁₃	#124	1	2	yes	—
59	C₄×D₁₃	C₂×SD₁₆	1	2	yes	—
60	#1057	—	8	4	no	—
61	C₈×C₁₃	#106	1	2	yes	—
62	C₈×C₁₃	#117	1	2	yes	—
63	#1055	#106	1	2	yes	—
64	#1055	#125	1	2	yes	—
65	C₂²×C₁₆	—	13	2	no	—
66	C₂×#108	—	13	4	no	—
67	C₂×#108	—	26	2	no	—
68	#423	—	26	2	no	—
69	C₂×C₄×C₈	—	13	1	no	—
70	C₄×C₁₆	—	13	2	no	—
71	C₄×C₁₆	—	13	1	no	—
72	C₄×C₁₆	#261	1	1	yes	characteristic
73	C₂²×C₁₃	C₂×#107	1	1	yes	characteristic
74	C₂×D₁₃	—	2	1	no	—
75	C₂×D₁₃	—	2	1	no	—
76	C₂×D₁₃	#487	1	2	yes	—
77	C₄×C₁₃	#368	1	2	yes	—
78	C₄×C₁₃	#368	1	2	yes	—
79	C₄×C₁₃	#382	1	1	yes	characteristic
80	C₄×C₁₃	C₂×#106	1	1	yes	characteristic
81	Dic₁₃	—	2	1	no	—
82	Dic₁₃	—	2	1	no	—
83	Dic₁₃	#486	1	2	yes	—
84	C₂×M₁₆	—	26	4	no	—
85	C₂²×C₈	—	13	1	no	—
86	C₂²×C₈	—	13	1	no	—
87	C₂×C₄²	—	13	1	no	—
88	C₂×C₁₆	—	13	2	no	—
89	C₂×C₁₆	—	26	4	no	—
90	C₂×C₁₆	C₂×#261	1	2	yes	—
91	#108	—	26	8	no	—
92	#108	—	52	4	no	—
93	C₄⋊C₈	—	52	2	no	—
94	C₄⋊C₈	—	52	2	no	—
95	C₄×C₈	—	13	1	no	—
96	C₄×C₈	—	13	1	no	—
97	C₄×C₈	—	13	1	no	—
98	C₄×C₈	C₂×#261	1	1	yes	characteristic
99	C₂×C₁₃	#1834	1	1	yes	characteristic
100	C₂×C₁₃	C₂×#368	1	1	yes	characteristic
101	C₂×C₁₃	C₂×#368	1	1	yes	characteristic
102	D₁₃	—	2	2	no	—
103	C₂²×C₄	—	13	1	no	—
104	C₂²×C₄	—	13	1	no	—
105	C₂²×C₄	—	13	1	no	—
106	M₁₆	—	52	4	no	—
107	M₁₆	—	52	4	no	—
108	C₂×C₈	—	13	1	no	—
109	C₂×C₈	—	13	1	no	—
110	C₂×C₈	—	13	4	no	—
111	C₂×C₈	—	13	4	no	—
112	C₂×C₈	—	52	4	no	—
113	C₂×C₈	C₄⋊#261	1	1	yes	characteristic
114	C₂×C₈	C₂²×#261	1	1	yes	characteristic
115	C₄²	—	13	1	no	—
116	C₄²	—	13	1	no	—
117	C₄²	—	13	1	no	—
118	C₄²	C₄⋊#261	1	1	yes	characteristic
119	C₁₆	—	2	2	no	—
120	C₁₆	—	26	2	no	—
121	C₁₃	#12891	1	1	yes	characteristic, complemented, Sylow
122	C₂³	—	13	1	no	—
123	C₂×C₄	—	13	1	no	—
124	C₂×C₄	—	13	2	no	—
125	C₂×C₄	—	13	2	no	—
126	C₂×C₄	—	13	1	no	—
127	C₂×C₄	—	13	1	no	—
128	C₂×C₄	—	26	2	no	—
129	C₂×C₄	—	26	2	no	—
130	C₂×C₄	#88102	1	1	yes	characteristic
131	C₂×C₄	#88102	1	1	yes	characteristic
132	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
133	C₈	—	13	2	no	—
134	C₈	—	13	2	no	—
135	C₈	—	104	4	no	—
136	C₈	#88101	1	2	yes	—
137	C₈	#88237	1	2	yes	—
138	C₂²	—	13	2	no	—
139	C₂²	—	26	1	no	—
140	C₂²	—	26	1	no	—
141	C₂²	C₂×#88102	1	1	yes	characteristic
142	C₄	—	13	2	no	—
143	C₄	—	26	1	no	—
144	C₄	—	26	1	no	—
145	C₄	#11718223	1	2	yes	—
146	C₄	#11718224	1	2	yes	—
147	C₄	#11719060	1	1	yes	characteristic
148	C₄	C₂×#88101	1	1	yes	characteristic
149	C₂	—	26	2	no	—
150	C₂	#13130757	1	1	yes	characteristic
151	C₂	C₂×#11718223	1	1	yes	characteristic
152	C₂	C₂×#11718224	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#13130777

C₂

yes

maximal

#13129896

C₂

yes

maximal

C₄×C₁₆×D₁₃

C₂

yes

maximal, characteristic

C₂×#88104

—

C₂×#88104

C₂²

yes

—

#11719052

—

C₂×C₁₆×D₁₃

C₂²

yes

—

C₄×C₈×D₁₃

C₂²

yes

characteristic

C₄×C₁₃×C₁₆

C₄

yes

characteristic

C₁₆×Dic₁₃

C₄

yes

—

C₄×#6090

C₄

yes

characteristic

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

—

#12891

—

maximal, Sylow

C₂×C₄×D₁₃

Q₁₆

yes

characteristic

C₂×C₄×D₁₃

Q₁₆

yes

characteristic

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

characteristic

C₄×Dic₁₃

D₈

yes

characteristic

C₂×#1055

C₄⋊C₄

yes

characteristic

C₂×#1055

C₂×Q₈

yes

characteristic

C₈×D₁₃

SD₁₆

yes

—

C₈×D₁₃

#41

yes

—

C₁₃×C₁₆

—

#6090

—

C₂×C₄×C₁₆

—

#1848

—

#1381

—

C₂²×D₁₃

C₂×Q₁₆

yes

C₂×C₄×C₁₃

yes

C₂×C₄×C₁₃

yes

C₂×C₄×C₁₃

C₂×C₄⋊C₄

yes

C₂×Dic₁₃

yes

C₂×Dic₁₃

yes

C₂×Dic₁₃

C₂×D₈

yes

characteristic

C₄×D₁₃

—

C₄×D₁₃

—

C₄×D₁₃

#124

yes

—

C₄×D₁₃

C₂×SD₁₆

yes

—

#1057

—

C₈×C₁₃

#106

yes

—

C₈×C₁₃

#117

yes

—

#1055

#106

yes

—

#1055

#125

yes

—

C₂²×C₁₆

—

C₂×#108

—

C₂×#108

—

#423

—

C₂×C₄×C₈

—

C₄×C₁₆

—

C₄×C₁₆

—

C₄×C₁₆

yes

C₂²×C₁₃

yes

C₂×D₁₃

—

C₂×D₁₃

—

C₂×D₁₃

#487

yes

—

C₄×C₁₃

#368

yes

—

C₄×C₁₃

#368

yes

—

C₄×C₁₃

yes

C₄×C₁₃

yes

Dic₁₃

—

Dic₁₃

—

Dic₁₃

#486

yes

—

C₂×M₁₆

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

C₂×#261

yes

—

#108

—

#108

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

yes

C₂×C₁₃

yes

100

C₂×C₁₃

C₂×#368

yes

characteristic

101

C₂×C₁₃

C₂×#368

yes

characteristic

102

D₁₃

—

103

C₂²×C₄

—

104

C₂²×C₄

—

105

C₂²×C₄

—

106

M₁₆

—

107

M₁₆

—

108

C₂×C₈

—

109

C₂×C₈

—

110

C₂×C₈

—

111

C₂×C₈

—

112

C₂×C₈

—

113

C₂×C₈

C₄⋊#261

yes

characteristic

114

C₂×C₈

C₂²×#261

yes

characteristic

115

C₄²

—

116

C₄²

—

117

C₄²

—

118

C₄²

C₄⋊#261

yes

characteristic

119

C₁₆

—

120

C₁₆

—

121

C₁₃

#12891

yes

characteristic, complemented, Sylow

122

C₂³

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

#88102

yes

characteristic

131

C₂×C₄

#88102

yes

characteristic

132

C₂×C₄

C₂×C₄⋊#261

yes

characteristic

133

C₈

—

134

C₈

—

135

C₈

—

104

—

136

C₈

#88101

yes

—

137

C₈

#88237

yes

—

138

C₂²

—

139

C₂²

—

140

C₂²

—

141

C₂²

C₂×#88102

yes

characteristic

142

C₄

—

143

C₄

—

144

C₄

—

145

C₄

#11718223

yes

—

146

C₄

#11718224

yes

—

147

C₄

#11719060

yes

characteristic

148

C₄

C₂×#88101

yes

characteristic

149

C₂

—

150

C₂

#13130757

yes

characteristic

151

C₂

C₂×#11718223

yes

characteristic

152

C₂

C₂×#11718224

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×#88102
commutator	C₂×C₈×C₁₃	C₂²×C₄
Frattini	C₂×C₈	C₂²×#261
Fitting	C₄×C₁₃×C₁₆	C₄
socle	C₂²×C₁₃	C₂×#107
prime radical	C₂²×D₁₃	C₂×Q₁₆
cosocle	C₂×C₈×D₁₃	C₂³
hypercenter	C₄×C₁₆	#261
hypocenter	C₁₃	#12891
LCS	G ▷ C₂×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆

subgroup

G/H

center

C₂²

C₂×#88102

commutator

C₂×C₈×C₁₃

C₂²×C₄

Frattini

C₂×C₈

C₂²×#261

Fitting

C₄×C₁₃×C₁₆

C₄

socle

C₂²×C₁₃

C₂×#107

prime radical

C₂²×D₁₃

C₂×Q₁₆

cosocle

C₂×C₈×D₁₃

C₂³

C₄×C₁₆

C₁₃

G ▷ C₂×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆

N	H ≅ G/N	type
121. C₁₃	#12891	semidirect

H ≅ G/N

type

121. C₁₃

#12891

semidirect

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

subgroup	index
#13130777	2
#13129896	2
C₄×C₁₆×D₁₃	2
#12891	13

subgroup

index

#13130777

#13129896

C₄×C₁₆×D₁₃

#12891

Subgroups — #16790232

Conjugacy classes of subgroups

Complements

Maximal subgroups