Group #16791413 — subgroups

Subgroups — #16791413

Order 3328.

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

normal subgroups only

This group has 206 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	C₂×#11718214	C₂	1	1	yes	maximal, characteristic
2	C₂×D₁₃⋊C₃₂	C₂	1	1	yes	maximal, characteristic
3	#13129994	C₂	1	2	yes	maximal, complemented
4	C₄⋊#88036	C₂	1	2	yes	maximal, complemented
5	#13116434	C₂	1	1	yes	maximal, characteristic
6	C₂×#88038	C₄	1	1	yes	characteristic
7	C₂×C₁₆×D₁₃	C₂²	1	1	yes	characteristic
8	#11718350	C₄	1	1	yes	characteristic
9	C₂×#88036	C₂²	1	2	yes	—
10	C₂×#88036	C₂²	1	2	yes	—
11	#11718214	—	2	2	no	—
12	D₁₃⋊C₃₂	—	2	2	no	—
13	C₁₃×#346	C₄	1	1	yes	characteristic
14	#11718094	C₄	1	1	yes	characteristic
15	C₁₆×Dic₁₃	C₂²	1	1	yes	characteristic
16	C₄×#6090	C₂²	1	1	yes	characteristic
17	C₂×#6094	C₈	1	1	yes	characteristic
18	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
19	#88126	C₈	1	1	yes	characteristic
20	C₂×C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
21	C₂×C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
22	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
23	#88055	C₈	1	1	yes	characteristic
24	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
25	C₂×#6090	C₂×C₄	1	1	yes	characteristic
26	C₂×#6090	C₂³	1	1	yes	characteristic
27	#88043	C₈	1	1	yes	characteristic
28	#88038	—	2	2	no	—
29	C₁₆×D₁₃	D₄	1	2	yes	—
30	C₁₆×D₁₃	Q₈	1	2	yes	—
31	#88036	—	2	2	no	—
32	#88036	—	2	2	no	—
33	#13628	—	13	1	no	maximal, Sylow
34	C₂×C₄×D₁₃	C₂×C₈	1	1	yes	characteristic
35	C₂×C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
36	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
37	C₄²×C₁₃	C₂×C₈	1	1	yes	characteristic
38	#6103	C₁₆	1	2	yes	—
39	#6101	C₁₆	1	2	yes	—
40	C₄×Dic₁₃	C₂×C₈	1	1	yes	characteristic
41	C₂×#1055	C₂×C₈	1	1	yes	characteristic
42	C₂×#1055	C₂×C₈	1	1	yes	characteristic
43	#6094	—	2	2	no	—
44	C₈×D₁₃	C₄⋊C₄	1	2	yes	—
45	C₈×D₁₃	M₁₆	1	2	yes	—
46	C₁₃×C₁₆	—	2	1	no	—
47	C₁₃×C₁₆	C₄⋊C₄	1	2	yes	—
48	#6090	—	2	1	no	—
49	#6090	C₂×D₄	1	1	yes	characteristic
50	#6090	C₂×Q₈	1	1	yes	characteristic
51	C₂×M₆₄	—	13	1	no	—
52	C₂²×C₃₂	—	13	1	no	—
53	#2108	—	13	1	no	—
54	C₄⋊C₃₂	—	13	2	no	—
55	C₄⋊C₃₂	—	13	2	no	—
56	C₂²×D₁₃	C₂×C₁₆	1	1	yes	characteristic
57	C₂×C₄×C₁₃	C₂×C₁₆	1	2	yes	—
58	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
59	C₂×Dic₁₃	C₂×C₁₆	1	2	yes	—
60	C₂×Dic₁₃	C₂×C₁₆	1	1	yes	characteristic
61	C₄×D₁₃	C₄⋊C₈	1	2	yes	—
62	C₄×D₁₃	M₃₂	1	2	yes	—
63	C₈×C₁₃	—	2	1	no	—
64	C₈×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
65	C₈×C₁₃	C₂×M₁₆	1	1	yes	characteristic
66	#1055	—	2	1	no	—
67	#1055	C₄⋊C₈	1	2	yes	—
68	C₂×M₃₂	—	13	1	no	—
69	C₂²×C₁₆	—	13	1	no	—
70	#405	—	13	1	no	—
71	M₆₄	—	26	2	no	—
72	C₂×C₃₂	—	13	2	no	—
73	C₂×C₃₂	—	13	2	no	—
74	C₂×C₃₂	—	26	2	no	—
75	#346	—	13	1	no	—
76	#346	#261	1	1	yes	characteristic
77	C₄×C₁₆	—	13	1	no	—
78	C₄×C₁₆	—	13	1	no	—
79	C₂²×C₁₃	C₂²×C₁₆	1	1	yes	characteristic
80	C₂×D₁₃	—	2	2	no	—
81	C₂×D₁₃	C₄⋊C₁₆	1	2	yes	—
82	C₄×C₁₃	—	2	2	no	—
83	C₄×C₁₃	C₂×C₄⋊C₈	1	1	yes	characteristic
84	C₄×C₁₃	C₂×M₃₂	1	1	yes	characteristic
85	Dic₁₃	—	2	2	no	—
86	Dic₁₃	C₄⋊C₁₆	1	2	yes	—
87	C₂×M₁₆	—	13	1	no	—
88	C₂²×C₈	—	13	1	no	—
89	#117	—	13	1	no	—
90	M₃₂	—	26	2	no	—
91	C₂×C₁₆	—	13	1	no	—
92	C₂×C₁₆	—	13	2	no	—
93	C₂×C₁₆	—	13	2	no	—
94	C₂×C₁₆	—	13	1	no	—
95	C₂×C₁₆	C₂×#261	1	1	yes	characteristic
96	C₂×C₁₆	C₂×#261	1	1	yes	characteristic
97	#97	—	13	1	no	—
98	#97	—	13	1	no	—
99	C₄×C₈	—	13	1	no	—
100	C₄×C₈	C₂×#261	1	1	yes	characteristic
101	C₃₂	—	26	2	no	—
102	C₃₂	—	26	2	no	—
103	C₂×C₁₃	C₂×C₄⋊C₁₆	1	1	yes	characteristic
104	C₂×C₁₃	#2258	1	2	yes	—
105	D₁₃	—	2	2	no	—
106	C₂²×C₄	—	13	1	no	—
107	M₁₆	—	26	2	no	—
108	C₂×C₈	—	13	1	no	—
109	C₂×C₈	—	13	2	no	—
110	C₂×C₈	—	13	2	no	—
111	C₂×C₈	—	13	1	no	—
112	C₂×C₈	D₁₃⋊C₈	1	1	yes	characteristic
113	C₂×C₈	C₂²×#261	1	1	yes	characteristic
114	C₄⋊C₄	—	13	2	no	—
115	C₂²⋊C₄	—	13	2	no	—
116	C₄²	—	13	1	no	—
117	C₄²	D₁₃⋊C₈	1	1	yes	characteristic
118	C₁₆	—	2	1	no	—
119	C₁₆	—	13	1	no	—
120	C₁₆	—	13	1	no	—
121	C₁₆	—	26	1	no	—
122	C₁₆	C₄⋊#261	1	2	yes	—
123	C₁₃	#13628	1	1	yes	characteristic, complemented, Sylow
124	C₂³	—	13	1	no	—
125	C₂×C₄	—	13	1	no	—
126	C₂×C₄	—	13	2	no	—
127	C₂×C₄	—	13	2	no	—
128	C₂×C₄	—	13	2	no	—
129	C₂×C₄	D₁₃⋊C₁₆	1	2	yes	—
130	C₂×C₄	C₂×D₁₃⋊C₈	1	1	yes	characteristic
131	C₈	—	2	1	no	—
132	C₈	—	13	2	no	—
133	C₈	—	26	1	no	—
134	C₈	D₁₃⋊M₁₆	1	1	yes	characteristic
135	C₈	C₂×C₄⋊#261	1	1	yes	characteristic
136	C₂²	—	13	2	no	—
137	C₂²	—	26	2	no	—
138	C₂²	C₂×D₁₃⋊C₁₆	1	1	yes	characteristic
139	C₄	—	2	2	no	—
140	C₄	—	13	2	no	—
141	C₄	—	26	2	no	—
142	C₄	D₁₃⋊(C₄⋊C₈)	1	1	yes	characteristic
143	C₄	D₁₃⋊M₃₂	1	1	yes	characteristic
144	C₂	—	26	2	no	—
145	C₂	D₁₃⋊(C₄⋊C₁₆)	1	1	yes	characteristic
146	C₂	#13131260	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11718214

C₂

yes

maximal, characteristic

C₂×D₁₃⋊C₃₂

C₂

yes

maximal, characteristic

#13129994

C₂

yes

maximal, complemented

C₄⋊#88036

C₂

yes

maximal, complemented

#13116434

C₂

yes

maximal, characteristic

C₂×#88038

C₄

yes

characteristic

C₂×C₁₆×D₁₃

C₂²

yes

characteristic

#11718350

C₄

yes

characteristic

C₂×#88036

C₂²

yes

—

C₂×#88036

C₂²

yes

—

#11718214

—

D₁₃⋊C₃₂

—

C₁₃×#346

C₄

yes

characteristic

#11718094

C₄

yes

characteristic

C₁₆×Dic₁₃

C₂²

yes

characteristic

C₄×#6090

C₂²

yes

characteristic

C₂×#6094

C₈

yes

characteristic

C₂×C₈×D₁₃

C₂×C₄

yes

characteristic

#88126

C₈

yes

characteristic

C₂×C₁₃×C₁₆

C₂×C₄

yes

characteristic

C₂×C₁₃×C₁₆

C₂×C₄

yes

characteristic

C₄×C₈×C₁₃

C₂×C₄

yes

characteristic

#88055

C₈

yes

characteristic

C₈×Dic₁₃

C₂×C₄

yes

characteristic

C₂×#6090

C₂×C₄

yes

characteristic

C₂×#6090

C₂³

yes

characteristic

#88043

C₈

yes

characteristic

#88038

—

C₁₆×D₁₃

D₄

yes

—

C₁₆×D₁₃

Q₈

yes

—

—

—

—

C₂×C₄×D₁₃

C₂×C₈

yes

characteristic

C₂×C₈×C₁₃

C₂×C₈

yes

characteristic

C₂×C₈×C₁₃

C₂²×C₄

yes

characteristic

C₄²×C₁₃

C₂×C₈

yes

characteristic

#6103

C₁₆

yes

—

#6101

C₁₆

yes

—

C₄×Dic₁₃

C₂×C₈

yes

characteristic

C₂×#1055

C₂×C₈

yes

characteristic

C₂×#1055

C₂×C₈

yes

characteristic

#6094

—

C₈×D₁₃

C₄⋊C₄

yes

—

C₈×D₁₃

M₁₆

yes

—

C₁₃×C₁₆

—

C₁₃×C₁₆

C₄⋊C₄

yes

—

#6090

—

#6090

C₂×D₄

yes

characteristic

#6090

C₂×Q₈

yes

characteristic

C₂×M₆₄

—

C₂²×C₃₂

—

#2108

—

C₄⋊C₃₂

—

C₄⋊C₃₂

—

C₂²×D₁₃

C₂×C₁₆

yes

characteristic

C₂×C₄×C₁₃

C₂×C₁₆

yes

—

C₂×C₄×C₁₃

C₂²×C₈

yes

characteristic

C₂×Dic₁₃

C₂×C₁₆

yes

—

C₂×Dic₁₃

C₂×C₁₆

yes

characteristic

C₄×D₁₃

C₄⋊C₈

yes

—

C₄×D₁₃

M₃₂

yes

—

C₈×C₁₃

—

C₈×C₁₃

C₂×C₄⋊C₄

yes

characteristic

C₈×C₁₃

C₂×M₁₆

yes

characteristic

#1055

—

#1055

C₄⋊C₈

yes

—

C₂×M₃₂

—

C₂²×C₁₆

—

#405

—

M₆₄

—

C₂×C₃₂

—

C₂×C₃₂

—

C₂×C₃₂

—

—

yes

C₄×C₁₆

—

C₄×C₁₆

—

C₂²×C₁₃

C₂²×C₁₆

yes

characteristic

C₂×D₁₃

—

C₂×D₁₃

C₄⋊C₁₆

yes

—

C₄×C₁₃

—

C₄×C₁₃

C₂×C₄⋊C₈

yes

characteristic

C₄×C₁₃

C₂×M₃₂

yes

characteristic

Dic₁₃

—

Dic₁₃

C₄⋊C₁₆

yes

—

C₂×M₁₆

—

C₂²×C₈

—

#117

—

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

yes

C₂×C₁₆

yes

—

—

C₄×C₈

—

100

C₄×C₈

C₂×#261

yes

characteristic

101

C₃₂

—

102

C₃₂

—

103

C₂×C₁₃

C₂×C₄⋊C₁₆

yes

characteristic

104

C₂×C₁₃

#2258

yes

—

105

D₁₃

—

106

C₂²×C₄

—

107

M₁₆

—

108

C₂×C₈

—

109

C₂×C₈

—

110

C₂×C₈

—

111

C₂×C₈

—

112

C₂×C₈

D₁₃⋊C₈

yes

characteristic

113

C₂×C₈

C₂²×#261

yes

characteristic

114

C₄⋊C₄

—

115

C₂²⋊C₄

—

116

C₄²

—

117

C₄²

D₁₃⋊C₈

yes

characteristic

118

C₁₆

—

119

C₁₆

—

120

C₁₆

—

121

C₁₆

—

122

C₁₆

C₄⋊#261

yes

—

123

C₁₃

#13628

yes

characteristic, complemented, Sylow

124

C₂³

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

D₁₃⋊C₁₆

yes

—

130

C₂×C₄

C₂×D₁₃⋊C₈

yes

characteristic

131

C₈

—

132

C₈

—

133

C₈

—

134

C₈

D₁₃⋊M₁₆

yes

characteristic

135

C₈

C₂×C₄⋊#261

yes

characteristic

136

C₂²

—

137

C₂²

—

138

C₂²

C₂×D₁₃⋊C₁₆

yes

characteristic

139

C₄

—

140

C₄

—

141

C₄

—

142

C₄

D₁₃⋊(C₄⋊C₈)

yes

characteristic

143

C₄

D₁₃⋊M₃₂

yes

characteristic

144

C₂

—

145

C₂

D₁₃⋊(C₄⋊C₁₆)

yes

characteristic

146

C₂

#13131260

yes

—

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×#261
commutator, socle	C₂²×C₁₃	C₂²×C₁₆
Fitting	C₁₃×#346	C₄
prime radical	C₂²×D₁₃	C₂×C₁₆
cosocle	C₂×#6090	C₂³
hypercenter	#346	#261
hypocenter	C₁₃	#13628
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₈ ◁ #346

subgroup

G/H

center, Frattini

C₂×C₈

C₂²×#261

commutator, socle

C₂²×C₁₃

C₂²×C₁₆

Fitting

C₁₃×#346

C₄

prime radical

C₂²×D₁₃

C₂×C₁₆

C₂³

C₁₃

G ▷ C₂²×C₁₃ ▷ C₁₃

C₁ ◁ C₂×C₈ ◁ #346

N	H ≅ G/N	type
3. #13129994	C₂	semidirect
4. C₄⋊#88036	C₂	semidirect
123. C₁₃	#13628	semidirect

H ≅ G/N

type

3. #13129994

C₂

semidirect

4. C₄⋊#88036

C₂

semidirect

123. C₁₃

#13628

semidirect

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

subgroup	index
C₂×#11718214	2
C₂×D₁₃⋊C₃₂	2
#13129994	2
C₄⋊#88036	2
#13116434	2
#13628	13

subgroup

index

C₂×D₁₃⋊C₃₂

Subgroups — #16791413

Conjugacy classes of subgroups

Complements

Maximal subgroups