Group #16789281 — subgroups

Subgroups — #16789281

Order 3328.

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

normal subgroups only

This group has 258 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	#13131059	C₂	1	1	yes	maximal, characteristic
2	#13131047	C₂	1	1	yes	maximal, characteristic
3	#13129891	C₂	1	2	yes	maximal
4	#13129887	C₂	1	2	yes	maximal
5	#13114592	C₂	1	1	yes	maximal, characteristic
6	C₂×#88106	C₂²	1	2	yes	—
7	C₂×#88106	C₂²	1	1	yes	characteristic
8	C₂²×#6092	C₂²	1	1	yes	characteristic
9	#11718783	C₂²	1	2	yes	—
10	#11718783	C₂²	1	1	yes	characteristic
11	#11718262	C₄	1	4	yes	complemented
12	#11718258	C₄	1	2	yes	complemented
13	#11718257	C₄	1	2	yes	complemented
14	C₁₃×#338	C₄	1	1	yes	characteristic
15	#11718149	C₄	1	2	yes	—
16	#11718149	C₄	1	1	yes	characteristic
17	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
18	C₂×C₁₃×M₁₆	C₂×C₄	1	1	yes	characteristic
19	#88180	C₂×C₄	1	2	yes	—
20	#88180	C₂×C₄	1	1	yes	characteristic
21	C₂²×#1055	C₂³	1	1	yes	characteristic
22	#88106	—	2	2	no	—
23	#88106	—	2	2	no	—
24	#88106	C₂×C₄	1	4	yes	—
25	C₂×#6092	—	2	2	no	—
26	C₂×#6092	—	2	2	no	—
27	C₂×#6092	C₂×C₄	1	1	yes	characteristic
28	C₂×#6092	C₂×C₄	1	2	yes	—
29	C₂×#6092	C₂×C₄	1	1	yes	characteristic
30	#88055	—	2	2	no	—
31	#88055	C₂×C₄	1	2	yes	—
32	C₈×Dic₁₃	—	2	2	no	—
33	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
34	#12597	—	13	1	no	maximal, Sylow
35	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
36	C₁₃×M₁₆	—	2	2	no	—
37	C₁₃×M₁₆	—	2	2	no	—
38	C₁₃×M₁₆	—	2	2	no	—
39	C₂×C₈×C₁₃	—	2	2	no	—
40	C₂×C₈×C₁₃	C₄²	1	2	yes	—
41	C₂²⋊Dic₁₃	—	2	1	no	—
42	C₂²⋊Dic₁₃	—	2	2	no	—
43	C₄⋊Dic₁₃	—	2	1	no	—
44	C₄⋊Dic₁₃	—	2	2	no	—
45	C₄×Dic₁₃	—	2	2	no	—
46	C₄×Dic₁₃	C₄²	1	2	yes	—
47	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
48	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
49	C₂×#1055	#41	1	2	yes	—
50	C₂×#1055	#41	1	2	yes	—
51	#6092	—	2	1	no	—
52	#6092	—	2	1	no	—
53	#6092	—	2	4	no	—
54	#6092	—	2	2	no	—
55	#2110	—	13	1	no	—
56	#2108	—	13	1	no	—
57	#1747	—	13	1	no	—
58	#1379	—	13	2	no	—
59	#1378	—	13	2	no	—
60	C₂³×C₁₃	#131	1	1	yes	characteristic
61	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
62	C₂×C₄×C₁₃	#117	1	2	yes	—
63	C₂×C₄×C₁₃	#131	1	2	yes	—
64	C₂×C₄×C₁₃	#131	1	1	yes	characteristic
65	C₂×Dic₁₃	—	2	2	no	—
66	C₂×Dic₁₃	—	4	2	no	—
67	C₈×C₁₃	—	2	2	no	—
68	C₈×C₁₃	—	4	2	no	—
69	#1055	#117	1	1	yes	characteristic
70	#1055	#117	1	2	yes	—
71	#1055	#117	1	1	yes	characteristic
72	C₂×M₃₂	—	13	1	no	—
73	C₂×M₃₂	—	13	2	no	—
74	C₂²×C₁₆	—	13	1	no	—
75	#405	—	13	1	no	—
76	#405	—	13	2	no	—
77	#347	—	13	4	no	—
78	#346	—	13	2	no	—
79	C₄×C₁₆	—	13	2	no	—
80	#338	#261	1	1	yes	characteristic
81	H(3,ℤ/4)	—	13	2	no	—
82	H(3,ℤ/4)	—	13	1	no	—
83	C₂²×C₁₃	—	4	1	no	—
84	C₂²×C₁₃	#405	1	1	yes	characteristic
85	C₂²×C₁₃	#433	1	2	yes	—
86	C₄×C₁₃	#376	1	1	yes	characteristic
87	C₄×C₁₃	#405	1	1	yes	characteristic
88	C₄×C₁₃	#433	1	2	yes	—
89	Dic₁₃	—	4	2	no	—
90	Dic₁₃	—	8	2	no	—
91	C₂×M₁₆	C₂×#261	1	2	yes	—
92	C₂×M₁₆	C₂×#261	1	1	yes	characteristic
93	C₂²×C₈	—	13	1	no	—
94	#117	—	13	1	no	—
95	#117	—	13	2	no	—
96	M₃₂	—	13	4	no	—
97	M₃₂	—	26	2	no	—
98	M₃₂	—	26	2	no	—
99	C₂×C₁₆	—	13	1	no	—
100	C₂×C₁₆	—	13	2	no	—
101	C₂×C₁₆	—	13	1	no	—
102	C₂×C₁₆	—	26	2	no	—
103	C₂×C₁₆	—	26	2	no	—
104	#97	—	13	2	no	—
105	#97	—	26	2	no	—
106	C₄×C₈	—	13	2	no	—
107	C₄×C₈	—	26	2	no	—
108	C₂×C₁₃	—	2	1	no	—
109	C₂×C₁₃	—	2	2	no	—
110	C₂×C₁₃	#1746	1	1	yes	characteristic
111	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
112	M₁₆	—	2	2	no	—
113	M₁₆	—	2	2	no	—
114	M₁₆	—	2	2	no	—
115	C₂×C₈	—	2	2	no	—
116	C₂×C₈	—	13	1	no	—
117	C₂×C₈	—	13	1	no	—
118	C₂×C₈	—	13	2	no	—
119	C₂×C₈	—	13	2	no	—
120	C₂×C₈	C₄×#261	1	2	yes	—
121	C₄⋊C₄	—	26	1	no	—
122	C₄⋊C₄	—	26	2	no	—
123	C₂²⋊C₄	—	26	1	no	—
124	C₂²⋊C₄	—	26	2	no	—
125	C₄²	—	13	2	no	—
126	C₄²	—	26	2	no	—
127	C₁₆	—	26	1	no	—
128	C₁₆	—	26	1	no	—
129	C₁₆	—	26	2	no	—
130	C₁₆	—	26	4	no	—
131	C₁₃	#12597	1	1	yes	characteristic, complemented, Sylow
132	C₂³	#88240	1	1	yes	characteristic
133	C₂×C₄	—	26	2	no	—
134	C₂×C₄	—	52	2	no	—
135	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
136	C₂×C₄	#88237	1	2	yes	—
137	C₂×C₄	#88238	1	2	yes	—
138	C₂×C₄	#88238	1	1	yes	characteristic
139	C₈	—	2	2	no	—
140	C₈	—	4	2	no	—
141	C₈	—	13	1	no	—
142	C₈	—	13	1	no	—
143	C₈	—	13	2	no	—
144	C₂²	—	4	1	no	—
145	C₂²	#11719072	1	1	yes	characteristic
146	C₂²	#11719077	1	2	yes	—
147	C₄	—	52	2	no	—
148	C₄	—	104	2	no	—
149	C₄	#11719057	1	1	yes	characteristic
150	C₄	#11719062	1	1	yes	characteristic
151	C₄	#11719068	1	2	yes	—
152	C₂	—	2	1	no	—
153	C₂	—	2	2	no	—
154	C₂	#13130555	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#13131059

C₂

yes

maximal, characteristic

#13131047

C₂

yes

maximal, characteristic

#13129891

C₂

yes

maximal

#13129887

C₂

yes

maximal

#13114592

C₂

yes

maximal, characteristic

C₂×#88106

C₂²

yes

—

C₂×#88106

C₂²

yes

characteristic

C₂²×#6092

C₂²

yes

characteristic

#11718783

C₂²

yes

—

#11718783

C₂²

yes

characteristic

#11718262

C₄

yes

complemented

#11718258

C₄

yes

complemented

#11718257

C₄

yes

complemented

C₁₃×#338

C₄

yes

characteristic

#11718149

C₄

yes

—

#11718149

C₄

yes

characteristic

C₂×C₁₃×M₁₆

C₂×C₄

yes

—

C₂×C₁₃×M₁₆

C₂×C₄

yes

characteristic

#88180

C₂×C₄

yes

—

#88180

C₂×C₄

yes

characteristic

C₂²×#1055

C₂³

yes

—

—

C₂×C₄

yes

—

C₂×#6092

—

C₂×#6092

—

C₂×#6092

C₂×C₄

yes

characteristic

C₂×#6092

C₂×C₄

yes

—

C₂×#6092

C₂×C₄

yes

characteristic

#88055

—

#88055

C₂×C₄

yes

—

C₈×Dic₁₃

—

C₈×Dic₁₃

C₂×C₄

yes

—

#12597

—

maximal, Sylow

C₂²×C₄×C₁₃

C₂²×C₄

yes

characteristic

C₁₃×M₁₆

—

C₁₃×M₁₆

—

C₁₃×M₁₆

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

C₄²

yes

—

C₂²⋊Dic₁₃

—

C₂²⋊Dic₁₃

—

C₄⋊Dic₁₃

—

C₄⋊Dic₁₃

—

C₄×Dic₁₃

—

C₄×Dic₁₃

C₄²

yes

—

C₂×#1055

C₂²×C₄

yes

characteristic

C₂×#1055

C₂²×C₄

yes

characteristic

C₂×#1055

#41

yes

—

C₂×#1055

#41

yes

—

—

—

—

—

—

—

—

—

—

C₂³×C₁₃

#131

yes

characteristic

C₂×C₄×C₁₃

C₂×C₄²

yes

characteristic

C₂×C₄×C₁₃

#117

yes

—

C₂×C₄×C₁₃

#131

yes

—

C₂×C₄×C₁₃

#131

yes

characteristic

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₈×C₁₃

—

C₈×C₁₃

—

yes

yes

—

#1055

#117

yes

characteristic

C₂×M₃₂

—

C₂×M₃₂

—

C₂²×C₁₆

—

—

—

—

—

C₄×C₁₆

—

yes

—

—

C₂²×C₁₃

—

C₂²×C₁₃

#405

yes

characteristic

C₂²×C₁₃

#433

yes

—

C₄×C₁₃

yes

C₄×C₁₃

yes

C₄×C₁₃

yes

—

Dic₁₃

—

Dic₁₃

—

C₂×M₁₆

C₂×#261

yes

—

C₂×M₁₆

C₂×#261

yes

characteristic

C₂²×C₈

—

#117

—

#117

—

M₃₂

—

M₃₂

—

M₃₂

—

C₂×C₁₆

—

100

C₂×C₁₆

—

101

C₂×C₁₆

—

102

C₂×C₁₆

—

103

C₂×C₁₆

—

104

#97

—

105

#97

—

106

C₄×C₈

—

107

C₄×C₈

—

108

C₂×C₁₃

—

109

C₂×C₁₃

—

110

C₂×C₁₃

#1746

yes

characteristic

111

C₂²×C₄

C₂²×#261

yes

characteristic

112

M₁₆

—

113

M₁₆

—

114

M₁₆

—

115

C₂×C₈

—

116

C₂×C₈

—

117

C₂×C₈

—

118

C₂×C₈

—

119

C₂×C₈

—

120

C₂×C₈

C₄×#261

yes

—

121

C₄⋊C₄

—

122

C₄⋊C₄

—

123

C₂²⋊C₄

—

124

C₂²⋊C₄

—

125

C₄²

—

126

C₄²

—

127

C₁₆

—

128

C₁₆

—

129

C₁₆

—

130

C₁₆

—

131

C₁₃

#12597

yes

characteristic, complemented, Sylow

132

C₂³

#88240

yes

characteristic

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

C₂×C₄×#261

yes

characteristic

136

C₂×C₄

#88237

yes

—

137

C₂×C₄

#88238

yes

—

138

C₂×C₄

#88238

yes

characteristic

139

C₈

—

140

C₈

—

141

C₈

—

142

C₈

—

143

C₈

—

144

C₂²

—

145

C₂²

#11719072

yes

characteristic

146

C₂²

#11719077

yes

—

147

C₄

—

148

C₄

—

104

—

149

C₄

#11719057

yes

characteristic

150

C₄

#11719062

yes

characteristic

151

C₄

#11719068

yes

—

152

C₂

—

153

C₂

—

154

C₂

#13130555

yes

characteristic

	subgroup	G/H
center	C₄	#11719057
commutator	C₂×C₄×C₁₃	C₂×C₄²
Frattini	C₂²×C₄	C₂²×#261
Fitting	C₁₃×#338	C₄
socle	C₂×C₁₃	#1746
prime radical	C₂³×C₁₃	#131
cosocle	C₂²×#1055	C₂³
hypercenter	#338	#261
hypocenter	C₁₃	#12597
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄ ◁ C₂×M₁₆ ◁ #338

subgroup

G/H

center

C₄

#11719057

commutator

C₂×C₄×C₁₃

C₂×C₄²

Frattini

C₂²×C₄

C₂²×#261

Fitting

C₁₃×#338

C₄

C₂×C₁₃

C₂³×C₁₃

C₂²×#1055

C₂³

C₁₃

G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₄ ◁ C₂×M₁₆ ◁ #338

N	H ≅ G/N	type
11. #11718262	C₄	semidirect
12. #11718258	C₄	semidirect
13. #11718257	C₄	semidirect
131. C₁₃	#12597	semidirect

H ≅ G/N

type

11. #11718262

C₄

semidirect

12. #11718258

C₄

semidirect

13. #11718257

C₄

semidirect

131. C₁₃

#12597

semidirect

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

subgroup	index
#13131059	2
#13131047	2
#13129891	2
#13129887	2
#13114592	2
#12597	13

subgroup

index

Subgroups — #16789281

Conjugacy classes of subgroups

Complements

Maximal subgroups