Group #16786587 — subgroups

Subgroups — #16786587

Order 3328.

330 conjugacy classes of subgroups; only the 172 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 172 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	C₄×D₁₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic
2	#13130040	C₂	1	1	yes	maximal, characteristic
3	#13129747	C₂	1	2	yes	maximal, complemented
4	C₁₆×#1057	C₂	1	2	yes	maximal, complemented
5	#13116429	C₂	1	1	yes	maximal, characteristic
6	C₂×D₁₃⋊C₁₆	C₄	1	2	yes	—
7	#11719049	C₄	1	2	yes	—
8	C₂×#88038	C₄	1	2	yes	—
9	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
10	#11718257	C₂²	1	1	yes	characteristic
11	#11718257	C₂²	1	1	yes	characteristic
12	#11718251	C₄	1	2	yes	—
13	C₈×#1057	C₂²	1	2	yes	—
14	C₄×#6092	C₄	1	2	yes	—
15	C₁₃×#346	C₄	1	1	yes	characteristic
16	C₁₆×Dic₁₃	C₂²	1	2	yes	—
17	#11718053	C₄	1	1	yes	characteristic
18	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
19	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
20	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
21	#88112	C₈	1	4	yes	—
22	#88111	C₈	1	4	yes	—
23	C₄×#1057	C₂×C₄	1	4	yes	—
24	C₂×#6092	C₂×C₄	1	2	yes	—
25	C₂×#6092	C₂×C₄	1	2	yes	—
26	D₁₃⋊C₁₆	C₈	1	8	yes	complemented
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	C₂³	1	1	yes	characteristic
31	C₂×#6090	C₂×C₄	1	2	yes	—
32	C₄×#1055	C₂×C₄	1	1	yes	characteristic
33	#88038	C₈	1	8	yes	complemented
34	#11399	—	13	1	no	maximal, Sylow
35	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
36	C₂×C₄×D₁₃	C₂×C₈	1	2	yes	—
37	C₂×#1057	C₂×C₈	1	8	yes	—
38	C₂×C₈×C₁₃	C₄²	1	1	yes	characteristic
39	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
40	C₄²×C₁₃	C₄²	1	1	yes	characteristic
41	C₄×Dic₁₃	C₂×C₈	1	2	yes	—
42	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
43	C₂×#1055	C₄²	1	1	yes	characteristic
44	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
45	C₈×D₁₃	C₂×C₈	1	4	yes	—
46	C₈×D₁₃	C₂×C₈	1	4	yes	—
47	#6092	C₂×C₈	1	4	yes	—
48	#6092	C₂×C₈	1	4	yes	—
49	C₁₃×C₁₆	C₂×C₈	1	4	yes	—
50	#6090	C₂×C₈	1	4	yes	—
51	C₄×M₃₂	—	13	1	no	—
52	C₂×C₄×C₁₆	—	13	1	no	—
53	#1450	—	13	1	no	—
54	#1311	—	13	2	no	—
55	C₈×C₁₆	—	13	2	no	—
56	C₂²×D₁₃	C₄×C₈	1	1	yes	characteristic
57	C₂×C₄×C₁₃	C₄×C₈	1	2	yes	—
58	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
59	C₂×Dic₁₃	C₄×C₈	1	1	yes	characteristic
60	C₂×Dic₁₃	C₂²×C₈	1	2	yes	—
61	C₄×D₁₃	—	2	4	no	—
62	C₄×D₁₃	C₄×C₈	1	2	yes	—
63	C₄×D₁₃	C₄×C₈	1	2	yes	—
64	#1057	—	2	8	no	—
65	C₈×C₁₃	C₄×C₈	1	2	yes	—
66	C₈×C₁₃	C₂²×C₈	1	2	yes	—
67	#1055	C₄×C₈	1	2	yes	—
68	#1055	C₂²×C₈	1	2	yes	—
69	C₂×M₃₂	—	13	2	no	—
70	C₂²×C₁₆	—	13	2	no	—
71	#431	—	13	2	no	—
72	C₂×C₄×C₈	—	13	1	no	—
73	#346	—	13	1	no	—
74	#346	#261	1	1	yes	characteristic
75	C₄×C₁₆	—	13	1	no	—
76	C₄×C₁₆	—	13	1	no	—
77	C₄×C₁₆	—	13	2	no	—
78	C₄×C₁₆	—	13	2	no	—
79	#322	—	13	2	no	—
80	C₈²	—	13	2	no	—
81	C₂²×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
82	C₂×D₁₃	—	2	2	no	—
83	C₂×D₁₃	C₈²	1	2	yes	—
84	C₄×C₁₃	—	2	2	no	—
85	C₄×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
86	C₄×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
87	Dic₁₃	C₈²	1	2	yes	—
88	Dic₁₃	#504	1	4	yes	—
89	C₂²×C₈	—	13	1	no	—
90	C₂²×C₈	—	13	1	no	—
91	C₂×C₄²	—	13	1	no	—
92	M₃₂	—	13	8	no	—
93	C₂×C₁₆	—	13	8	no	—
94	C₂×C₁₆	—	13	2	no	—
95	C₂×C₁₆	—	13	2	no	—
96	C₂×C₁₆	—	13	2	no	—
97	C₂×C₁₆	C₂×#261	1	2	yes	—
98	C₄⋊C₈	—	13	4	no	—
99	C₂²⋊C₈	—	13	4	no	—
100	C₄×C₈	—	13	4	no	—
101	C₄×C₈	—	13	1	no	—
102	C₄×C₈	—	13	1	no	—
103	C₄×C₈	—	13	1	no	—
104	C₄×C₈	C₂×#261	1	1	yes	characteristic
105	C₂×C₁₃	C₂×C₈²	1	1	yes	characteristic
106	C₂×C₁₃	#2108	1	2	yes	—
107	D₁₃	—	2	2	no	—
108	C₂²×C₄	—	13	1	no	—
109	C₂²×C₄	—	13	2	no	—
110	C₂×C₈	—	13	1	no	—
111	C₂×C₈	—	13	1	no	—
112	C₂×C₈	—	13	4	no	—
113	C₂×C₈	—	13	4	no	—
114	C₂×C₈	—	13	8	no	—
115	C₂×C₈	C₄×#261	1	1	yes	characteristic
116	C₂×C₈	C₂²×#261	1	1	yes	characteristic
117	C₄²	—	13	2	no	—
118	C₄²	—	13	1	no	—
119	C₄²	C₄×#261	1	1	yes	characteristic
120	C₁₆	—	13	4	no	—
121	C₁₆	—	13	4	no	—
122	C₁₆	—	13	4	no	—
123	C₁₆	D₁₃⋊C₈	1	4	yes	—
124	C₁₃	#11399	1	1	yes	characteristic, complemented, Sylow
125	C₂³	—	13	1	no	—
126	C₂×C₄	—	13	2	no	—
127	C₂×C₄	—	13	1	no	—
128	C₂×C₄	—	13	2	no	—
129	C₂×C₄	—	13	2	no	—
130	C₂×C₄	—	26	4	no	—
131	C₂×C₄	C₈×#261	1	2	yes	—
132	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
133	C₈	—	13	2	no	—
134	C₈	—	13	2	no	—
135	C₈	—	26	8	no	—
136	C₈	C₈×#261	1	2	yes	—
137	C₈	C₂×D₁₃⋊C₈	1	2	yes	—
138	C₂²	—	13	2	no	—
139	C₂²	—	26	2	no	—
140	C₂²	C₂×C₈×#261	1	1	yes	characteristic
141	C₄	—	2	2	no	—
142	C₄	—	13	4	no	—
143	C₄	—	13	2	no	—
144	C₄	C₄×D₁₃⋊C₈	1	1	yes	characteristic
145	C₄	C₂×C₈×#261	1	1	yes	characteristic
146	C₂	—	26	2	no	—
147	C₂	C₈×D₁₃⋊C₈	1	1	yes	characteristic
148	C₂	#13131048	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×D₁₃⋊C₁₆

C₂

yes

maximal, characteristic

#13130040

C₂

yes

maximal, characteristic

#13129747

C₂

yes

maximal, complemented

C₁₆×#1057

C₂

yes

maximal, complemented

#13116429

C₂

yes

maximal, characteristic

C₂×D₁₃⋊C₁₆

C₄

yes

—

#11719049

C₄

yes

—

C₂×#88038

C₄

yes

—

C₄×C₈×D₁₃

C₂²

yes

characteristic

#11718257

C₂²

yes

characteristic

#11718257

C₂²

yes

characteristic

#11718251

C₄

yes

—

C₈×#1057

C₂²

yes

—

C₄×#6092

C₄

yes

—

C₁₃×#346

C₄

yes

characteristic

C₁₆×Dic₁₃

C₂²

yes

—

#11718053

C₄

yes

characteristic

C₂×C₈×D₁₃

C₂×C₄

yes

characteristic

C₂×C₈×D₁₃

C₂×C₄

yes

characteristic

C₄²×D₁₃

C₂×C₄

yes

characteristic

#88112

C₈

yes

—

#88111

C₈

yes

—

C₄×#1057

C₂×C₄

yes

—

C₂×#6092

C₂×C₄

yes

—

C₂×#6092

C₂×C₄

yes

—

D₁₃⋊C₁₆

C₈

yes

complemented

C₂×C₁₃×C₁₆

C₂×C₄

yes

—

C₄×C₈×C₁₃

C₂×C₄

yes

characteristic

C₈×Dic₁₃

C₂×C₄

yes

characteristic

C₈×Dic₁₃

C₂³

yes

characteristic

C₂×#6090

C₂×C₄

yes

—

C₄×#1055

C₂×C₄

yes

characteristic

#88038

C₈

yes

complemented

#11399

—

maximal, Sylow

C₂×C₄×D₁₃

C₄²

yes

characteristic

C₂×C₄×D₁₃

C₂×C₈

yes

—

C₂×#1057

C₂×C₈

yes

—

C₂×C₈×C₁₃

C₄²

yes

characteristic

C₂×C₈×C₁₃

C₂²×C₄

yes

characteristic

C₄²×C₁₃

C₄²

yes

characteristic

C₄×Dic₁₃

C₂×C₈

yes

—

C₄×Dic₁₃

C₂²×C₄

yes

characteristic

C₂×#1055

C₄²

yes

characteristic

C₂×#1055

C₂²×C₄

yes

characteristic

C₈×D₁₃

C₂×C₈

yes

—

C₈×D₁₃

C₂×C₈

yes

—

#6092

C₂×C₈

yes

—

#6092

C₂×C₈

yes

—

C₁₃×C₁₆

C₂×C₈

yes

—

#6090

C₂×C₈

yes

—

C₄×M₃₂

—

C₂×C₄×C₁₆

—

#1450

—

#1311

—

C₈×C₁₆

—

C₂²×D₁₃

C₄×C₈

yes

characteristic

C₂×C₄×C₁₃

C₄×C₈

yes

—

C₂×C₄×C₁₃

C₂×C₄²

yes

characteristic

C₂×Dic₁₃

C₄×C₈

yes

characteristic

C₂×Dic₁₃

C₂²×C₈

yes

—

C₄×D₁₃

—

C₄×D₁₃

C₄×C₈

yes

—

C₄×D₁₃

C₄×C₈

yes

—

#1057

—

C₈×C₁₃

C₄×C₈

yes

—

C₈×C₁₃

C₂²×C₈

yes

—

#1055

C₄×C₈

yes

—

#1055

C₂²×C₈

yes

—

C₂×M₃₂

—

C₂²×C₁₆

—

#431

—

C₂×C₄×C₈

—

—

yes

C₄×C₁₆

—

C₄×C₁₆

—

C₄×C₁₆

—

C₄×C₁₆

—

#322

—

C₈²

—

C₂²×C₁₃

C₂×C₄×C₈

yes

characteristic

C₂×D₁₃

—

C₂×D₁₃

C₈²

yes

—

C₄×C₁₃

—

C₄×C₁₃

C₂×C₄×C₈

yes

characteristic

C₄×C₁₃

C₂×C₄×C₈

yes

characteristic

Dic₁₃

C₈²

yes

—

Dic₁₃

#504

yes

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

C₂×#261

yes

—

C₄⋊C₈

—

C₂²⋊C₈

—

100

C₄×C₈

—

101

C₄×C₈

—

102

C₄×C₈

—

103

C₄×C₈

—

104

C₄×C₈

C₂×#261

yes

characteristic

105

C₂×C₁₃

C₂×C₈²

yes

characteristic

106

C₂×C₁₃

#2108

yes

—

107

D₁₃

—

108

C₂²×C₄

—

109

C₂²×C₄

—

110

C₂×C₈

—

111

C₂×C₈

—

112

C₂×C₈

—

113

C₂×C₈

—

114

C₂×C₈

—

115

C₂×C₈

C₄×#261

yes

characteristic

116

C₂×C₈

C₂²×#261

yes

characteristic

117

C₄²

—

118

C₄²

—

119

C₄²

C₄×#261

yes

characteristic

120

C₁₆

—

121

C₁₆

—

122

C₁₆

—

123

C₁₆

D₁₃⋊C₈

yes

—

124

C₁₃

#11399

yes

characteristic, complemented, Sylow

125

C₂³

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

C₈×#261

yes

—

132

C₂×C₄

C₂×C₄×#261

yes

characteristic

133

C₈

—

134

C₈

—

135

C₈

—

136

C₈

C₈×#261

yes

—

137

C₈

C₂×D₁₃⋊C₈

yes

—

138

C₂²

—

139

C₂²

—

140

C₂²

C₂×C₈×#261

yes

characteristic

141

C₄

—

142

C₄

—

143

C₄

—

144

C₄

C₄×D₁₃⋊C₈

yes

characteristic

145

C₄

C₂×C₈×#261

yes

characteristic

146

C₂

—

147

C₂

C₈×D₁₃⋊C₈

yes

characteristic

148

C₂

#13131048

yes

—

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×#261
commutator	C₂×C₁₃	C₂×C₈²
Fitting	C₁₃×#346	C₄
socle	C₂²×C₁₃	C₂×C₄×C₈
prime radical	C₂²×D₁₃	C₄×C₈
cosocle	C₈×Dic₁₃	C₂³
hypercenter	#346	#261
hypocenter	C₁₃	#11399
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₈ ◁ #346

subgroup

G/H

center, Frattini

C₂×C₈

C₂²×#261

commutator

C₂×C₁₃

C₂×C₈²

Fitting

C₁₃×#346

C₄

socle

C₂²×C₁₃

C₂×C₄×C₈

prime radical

C₂²×D₁₃

C₄×C₈

cosocle

C₈×Dic₁₃

C₂³

C₁₃

G ▷ C₂×C₁₃ ▷ C₁₃

C₁ ◁ C₂×C₈ ◁ #346

N	H ≅ G/N	type
3. #13129747	C₂	semidirect
4. C₁₆×#1057	C₂	semidirect
26. D₁₃⋊C₁₆	C₈	semidirect
33. #88038	C₈	semidirect
124. C₁₃	#11399	semidirect

H ≅ G/N

type

3. #13129747

C₂

semidirect

4. C₁₆×#1057

C₂

semidirect

26. D₁₃⋊C₁₆

C₈

semidirect

33. #88038

C₈

semidirect

124. C₁₃

#11399

semidirect

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

subgroup	index
C₄×D₁₃⋊C₁₆	2
#13130040	2
#13129747	2
C₁₆×#1057	2
#13116429	2
#11399	13

subgroup

index

C₄×D₁₃⋊C₁₆

C₁₆×#1057

Subgroups — #16786587

Conjugacy classes of subgroups

Complements

Maximal subgroups