Group #16791445 — subgroups

Subgroups — #16791445

Order 3328.

180 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 180 conjugacy classes of subgroups — too many to draw. Only its 84 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⋊#88036	C₂	1	2	yes	maximal, complemented
2	#13129950	C₂	1	2	yes	maximal
3	#13129944	C₂	1	1	yes	maximal, characteristic, complemented
4	#13129941	C₂	1	1	yes	maximal, characteristic, 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	C₁₃×#346	C₄	1	1	yes	characteristic
12	#11718094	C₄	1	1	yes	characteristic
13	C₁₆×Dic₁₃	C₂²	1	1	yes	characteristic
14	C₄×#6090	C₂²	1	1	yes	characteristic
15	C₂×#6094	C₈	1	1	yes	characteristic
16	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
17	#88126	C₈	1	1	yes	characteristic
18	C₂×C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
19	C₂×C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
20	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
21	#88055	C₈	1	1	yes	characteristic
22	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
23	C₂×#6090	C₂×C₄	1	1	yes	characteristic
24	C₂×#6090	C₂³	1	1	yes	characteristic
25	#88043	C₈	1	1	yes	characteristic
26	#88038	—	2	2	no	—
27	C₁₆×D₁₃	—	2	2	no	—
28	#88036	—	2	2	no	—
29	#88036	—	2	2	no	—
30	#13641	—	13	1	no	maximal, Sylow
31	C₂×C₄×D₁₃	C₂×C₈	1	1	yes	characteristic
32	C₂×C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
33	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
34	C₄²×C₁₃	C₂×C₈	1	1	yes	characteristic
35	#6103	C₁₆	1	2	yes	—
36	#6101	C₁₆	1	2	yes	—
37	C₄×Dic₁₃	C₂×C₈	1	1	yes	characteristic
38	C₂×#1055	C₂×C₈	1	1	yes	characteristic
39	C₂×#1055	C₂×C₈	1	1	yes	characteristic
40	#6094	—	2	2	no	—
41	C₈×D₁₃	—	2	1	no	—
42	C₈×D₁₃	—	2	1	no	—
43	C₁₃×C₁₆	—	2	1	no	—
44	C₁₃×C₁₆	M₁₆	1	2	yes	—
45	#6090	—	2	1	no	—
46	#6090	#41	1	2	yes	—
47	#2108	—	13	1	no	—
48	C₄⋊C₃₂	—	13	2	no	—
49	C₂²⋊C₃₂	—	13	2	no	—
50	#1397	—	13	1	no	—
51	C₄×C₃₂	—	13	1	no	—
52	C₂²×D₁₃	C₂×C₁₆	1	1	yes	characteristic
53	C₂×C₄×C₁₃	C₂×C₁₆	1	2	yes	—
54	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
55	C₂×Dic₁₃	C₂×C₁₆	1	2	yes	—
56	C₂×Dic₁₃	C₂×C₁₆	1	1	yes	characteristic
57	C₄×D₁₃	—	2	1	no	—
58	C₄×D₁₃	—	2	1	no	—
59	C₈×C₁₃	—	2	1	no	—
60	C₈×C₁₃	#117	1	1	yes	characteristic
61	C₈×C₁₃	C₂×M₁₆	1	1	yes	characteristic
62	#1055	—	2	1	no	—
63	#1055	M₃₂	1	2	yes	—
64	C₂×M₃₂	—	13	1	no	—
65	C₂²×C₁₆	—	13	1	no	—
66	#405	—	13	1	no	—
67	C₂×C₃₂	—	13	2	no	—
68	C₂×C₃₂	—	13	2	no	—
69	#346	—	13	1	no	—
70	#346	#261	1	1	yes	characteristic
71	C₄×C₁₆	—	13	1	no	—
72	C₄×C₁₆	—	13	1	no	—
73	C₂²×C₁₃	C₂²×C₁₆	1	1	yes	characteristic
74	C₂×D₁₃	—	2	1	no	—
75	C₂×D₁₃	—	2	2	no	—
76	C₄×C₁₃	—	2	2	no	—
77	C₄×C₁₃	#431	1	1	yes	characteristic
78	C₄×C₁₃	C₂×M₃₂	1	1	yes	characteristic
79	Dic₁₃	—	2	1	no	—
80	Dic₁₃	—	2	2	no	—
81	C₂×M₁₆	—	13	1	no	—
82	C₂²×C₈	—	13	1	no	—
83	#117	—	13	1	no	—
84	M₃₂	—	26	2	no	—
85	C₂×C₁₆	—	13	1	no	—
86	C₂×C₁₆	—	13	1	no	—
87	C₂×C₁₆	—	26	2	no	—
88	C₂×C₁₆	C₂×#261	1	1	yes	characteristic
89	C₂×C₁₆	C₂×#261	1	1	yes	characteristic
90	#97	—	13	1	no	—
91	#97	—	13	1	no	—
92	C₄×C₈	—	13	1	no	—
93	C₄×C₈	C₂×#261	1	1	yes	characteristic
94	C₃₂	—	26	2	no	—
95	C₃₂	—	26	2	no	—
96	C₂×C₁₃	#2162	1	1	yes	characteristic
97	C₂×C₁₃	#2258	1	2	yes	—
98	D₁₃	—	4	1	no	—
99	C₂²×C₄	—	13	1	no	—
100	M₁₆	—	26	2	no	—
101	C₂×C₈	—	13	1	no	—
102	C₂×C₈	—	13	1	no	—
103	C₂×C₈	—	26	1	no	—
104	C₂×C₈	—	26	1	no	—
105	C₂×C₈	D₁₃⋊C₈	1	1	yes	characteristic
106	C₂×C₈	C₂²×#261	1	1	yes	characteristic
107	C₄⋊C₄	—	13	2	no	—
108	C₂²⋊C₄	—	13	2	no	—
109	C₄²	—	13	1	no	—
110	C₄²	D₁₃⋊C₈	1	1	yes	characteristic
111	C₁₆	—	2	1	no	—
112	C₁₆	—	13	2	no	—
113	C₁₆	—	26	1	no	—
114	C₁₆	#6118	1	2	yes	—
115	C₁₃	#13641	1	1	yes	characteristic, complemented, Sylow
116	C₂³	—	13	1	no	—
117	C₂×C₄	—	13	2	no	—
118	C₂×C₄	—	13	1	no	—
119	C₂×C₄	—	26	1	no	—
120	C₂×C₄	—	26	1	no	—
121	C₂×C₄	D₁₃⋊C₁₆	1	2	yes	—
122	C₂×C₄	C₂×D₁₃⋊C₈	1	1	yes	characteristic
123	C₈	—	2	1	no	—
124	C₈	—	13	2	no	—
125	C₈	—	26	1	no	—
126	C₈	C₂×#6118	1	1	yes	characteristic
127	C₈	#88237	1	1	yes	characteristic
128	C₂²	—	26	1	no	—
129	C₂²	—	26	2	no	—
130	C₂²	C₂×D₁₃⋊C₁₆	1	1	yes	characteristic
131	C₄	—	2	2	no	—
132	C₄	—	26	1	no	—
133	C₄	—	26	2	no	—
134	C₄	#11719051	1	1	yes	characteristic
135	C₄	D₁₃⋊M₃₂	1	1	yes	characteristic
136	C₂	—	52	1	no	—
137	C₂	#13131196	1	1	yes	characteristic
138	C₂	#13131260	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₄⋊#88036

C₂

yes

maximal, complemented

#13129950

C₂

yes

maximal

#13129944

C₂

yes

maximal, characteristic, complemented

#13129941

C₂

yes

maximal, characteristic, 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

—

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

—

—

—

—

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

—

C₈×D₁₃

—

C₁₃×C₁₆

—

C₁₃×C₁₆

M₁₆

yes

—

#6090

—

#6090

#41

yes

—

#2108

—

C₄⋊C₃₂

—

C₂²⋊C₃₂

—

#1397

—

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×D₁₃

—

C₈×C₁₃

—

C₈×C₁₃

#117

yes

characteristic

C₈×C₁₃

C₂×M₁₆

yes

characteristic

#1055

—

#1055

M₃₂

yes

—

C₂×M₃₂

—

C₂²×C₁₆

—

#405

—

C₂×C₃₂

—

C₂×C₃₂

—

—

yes

C₄×C₁₆

—

C₄×C₁₆

—

C₂²×C₁₃

C₂²×C₁₆

yes

characteristic

C₂×D₁₃

—

C₂×D₁₃

—

C₄×C₁₃

—

C₄×C₁₃

#431

yes

characteristic

C₄×C₁₃

C₂×M₃₂

yes

characteristic

Dic₁₃

—

Dic₁₃

—

C₂×M₁₆

—

C₂²×C₈

—

#117

—

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

yes

C₂×C₁₆

yes

—

—

C₄×C₈

—

C₄×C₈

C₂×#261

yes

characteristic

C₃₂

—

C₃₂

—

C₂×C₁₃

#2162

yes

characteristic

C₂×C₁₃

#2258

yes

—

D₁₃

—

C₂²×C₄

—

100

M₁₆

—

101

C₂×C₈

—

102

C₂×C₈

—

103

C₂×C₈

—

104

C₂×C₈

—

105

C₂×C₈

D₁₃⋊C₈

yes

characteristic

106

C₂×C₈

C₂²×#261

yes

characteristic

107

C₄⋊C₄

—

108

C₂²⋊C₄

—

109

C₄²

—

110

C₄²

D₁₃⋊C₈

yes

characteristic

111

C₁₆

—

112

C₁₆

—

113

C₁₆

—

114

C₁₆

#6118

yes

—

115

C₁₃

#13641

yes

characteristic, complemented, Sylow

116

C₂³

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

D₁₃⋊C₁₆

yes

—

122

C₂×C₄

C₂×D₁₃⋊C₈

yes

characteristic

123

C₈

—

124

C₈

—

125

C₈

—

126

C₈

C₂×#6118

yes

characteristic

127

C₈

#88237

yes

characteristic

128

C₂²

—

129

C₂²

—

130

C₂²

C₂×D₁₃⋊C₁₆

yes

characteristic

131

C₄

—

132

C₄

—

133

C₄

—

134

C₄

#11719051

yes

characteristic

135

C₄

D₁₃⋊M₃₂

yes

characteristic

136

C₂

—

137

C₂

#13131196

yes

characteristic

138

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	#13641
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
1. C₄⋊#88036	C₂	semidirect
3. #13129944	C₂	semidirect
4. #13129941	C₂	semidirect
115. C₁₃	#13641	semidirect

H ≅ G/N

type

1. C₄⋊#88036

C₂

semidirect

3. #13129944

C₂

semidirect

4. #13129941

C₂

semidirect

115. C₁₃

#13641

semidirect

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

subgroup	index
C₄⋊#88036	2
#13129950	2
#13129944	2
#13129941	2
#13116434	2
#13641	13

subgroup

index

Subgroups — #16791445

Conjugacy classes of subgroups

Complements

Maximal subgroups