Group #16791469 — subgroups

Subgroups — #16791469

Order 3328.

184 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 76 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	#13131260	C₂	1	2	yes	maximal, complemented
2	#13129995	C₂	1	1	yes	maximal, characteristic, complemented
3	#13129954	C₂	1	2	yes	maximal, complemented
4	#13129943	C₂	1	1	yes	maximal, characteristic, complemented
5	#13116672	C₂	1	1	yes	maximal, characteristic
6	#11718568	C₂²	1	2	yes	—
7	#11718361	C₄	1	1	yes	characteristic
8	#11718249	C₂²	1	2	yes	—
9	C₂×#88036	C₂²	1	1	yes	characteristic
10	C₂×#88036	C₂²	1	1	yes	characteristic
11	#11718214	—	2	2	no	—
12	D₁₃⋊C₃₂	—	2	2	no	—
13	C₁₃×#364	C₄	1	1	yes	characteristic
14	#11718107	C₄	1	2	yes	—
15	C₄×#6090	C₂²	1	1	yes	characteristic
16	#88158	C₈	1	1	yes	characteristic
17	#88155	C₂×C₄	1	2	yes	—
18	C₁₃×M₃₂	C₂×C₄	1	2	yes	—
19	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
20	#88059	C₈	1	1	yes	characteristic
21	C₂×#6090	C₂×C₄	1	1	yes	characteristic
22	C₂×#6090	C₂³	1	1	yes	characteristic
23	#88045	C₈	1	2	yes	—
24	#88038	—	2	2	no	—
25	C₁₆×D₁₃	—	2	2	no	—
26	#88036	—	2	2	no	—
27	#88036	—	2	1	no	—
28	#88036	D₄	1	2	yes	—
29	#13648	—	13	1	no	maximal, Sylow
30	#6127	C₂×C₈	1	2	yes	—
31	C₂×C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
32	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
33	C₄²×C₁₃	C₂×C₈	1	1	yes	characteristic
34	#6099	C₂×C₈	1	2	yes	—
35	Dic₅₂	C₁₆	1	1	yes	characteristic
36	D₁₀₄	C₁₆	1	1	yes	characteristic
37	#6095	C₁₆	1	2	yes	—
38	#6094	—	2	2	no	—
39	C₈×D₁₃	—	2	2	no	—
40	C₁₃×C₁₆	—	2	2	no	—
41	#6090	—	2	1	no	—
42	#6090	C₂×D₄	1	1	yes	characteristic
43	#6090	#41	1	1	yes	characteristic
44	#2258	—	13	2	no	—
45	#2170	—	13	1	no	—
46	#1422	—	13	1	no	—
47	#1401	—	13	2	no	—
48	#1397	—	13	1	no	—
49	C₂×C₄×C₁₃	—	2	1	no	—
50	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
51	C₂²⋊D₁₃	—	2	2	no	—
52	D₅₂	C₂×C₁₆	1	2	yes	—
53	C₄×D₁₃	—	2	2	no	—
54	Dic₂₆	C₂×C₁₆	1	2	yes	—
55	C₈×C₁₃	C₂×C₁₆	1	1	yes	characteristic
56	C₈×C₁₃	C₂×C₁₆	1	1	yes	characteristic
57	C₈×C₁₃	C₄×D₄	1	1	yes	characteristic
58	C₈×C₁₃	#131	1	1	yes	characteristic
59	#1055	—	2	2	no	—
60	#504	—	13	2	no	—
61	#443	—	13	1	no	—
62	M₆₄	—	13	2	no	—
63	M₆₄	—	26	2	no	—
64	C₂×C₃₂	—	13	1	no	—
65	C₂×C₃₂	—	13	1	no	—
66	C₂×C₃₂	—	26	2	no	—
67	#364	#261	1	1	yes	characteristic
68	#350	—	13	2	no	—
69	C₄×C₁₆	—	13	1	no	—
70	C₂²×C₁₃	#504	1	1	yes	characteristic
71	C₂×D₁₃	—	2	2	no	—
72	C₄×C₁₃	—	4	1	no	—
73	C₄×C₁₃	C₈×D₄	1	1	yes	characteristic
74	C₄×C₁₃	C₂²×C₁₆	1	1	yes	characteristic
75	Dic₁₃	—	2	2	no	—
76	#135	—	13	1	no	—
77	#131	—	13	2	no	—
78	M₃₂	—	26	2	no	—
79	M₃₂	C₂×#261	1	2	yes	—
80	C₂×C₁₆	—	13	1	no	—
81	C₂×C₁₆	—	13	1	no	—
82	C₂×C₁₆	—	26	2	no	—
83	#108	—	13	1	no	—
84	#104	—	13	2	no	—
85	C₄×C₈	C₂×#261	1	1	yes	characteristic
86	C₃₂	—	13	2	no	—
87	C₃₂	—	26	1	no	—
88	C₃₂	—	26	2	no	—
89	C₂×C₁₃	—	2	1	no	—
90	C₂×C₁₃	D₄×C₁₆	1	1	yes	characteristic
91	D₁₃	—	4	2	no	—
92	#41	—	13	2	no	—
93	Q₁₆	—	13	1	no	—
94	SD₁₆	—	13	2	no	—
95	D₈	—	13	1	no	—
96	M₁₆	—	13	2	no	—
97	M₁₆	—	26	2	no	—
98	C₂×C₈	—	26	2	no	—
99	C₂×C₈	D₁₃⋊C₈	1	1	yes	characteristic
100	C₂×C₈	C₂²×#261	1	1	yes	characteristic
101	C₄²	D₁₃⋊C₈	1	1	yes	characteristic
102	C₁₆	—	2	2	no	—
103	C₁₆	—	13	1	no	—
104	C₁₆	—	13	1	no	—
105	C₁₆	—	26	1	no	—
106	C₁₃	#13648	1	1	yes	characteristic, complemented, Sylow
107	Q₈	—	13	2	no	—
108	D₄	—	13	2	no	—
109	D₄	—	26	2	no	—
110	C₂×C₄	—	2	1	no	—
111	C₂×C₄	—	26	2	no	—
112	C₂×C₄	C₂×D₁₃⋊C₈	1	1	yes	characteristic
113	C₈	—	26	2	no	—
114	C₈	D₁₃⋊C₁₆	1	1	yes	characteristic
115	C₈	D₁₃⋊C₁₆	1	1	yes	characteristic
116	C₈	D₄×#261	1	1	yes	characteristic
117	C₈	#88240	1	1	yes	characteristic
118	C₂²	—	26	2	no	—
119	C₂²	#11719096	1	1	yes	characteristic
120	C₄	—	4	1	no	—
121	C₄	—	26	2	no	—
122	C₄	#11719073	1	1	yes	characteristic
123	C₄	C₂×D₁₃⋊C₁₆	1	1	yes	characteristic
124	C₂	—	2	1	no	—
125	C₂	—	52	2	no	—
126	C₂	#13131215	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#13131260

C₂

yes

maximal, complemented

#13129995

C₂

yes

maximal, characteristic, complemented

#13129954

C₂

yes

maximal, complemented

#13129943

C₂

yes

maximal, characteristic, complemented

#13116672

C₂

yes

maximal, characteristic

#11718568

C₂²

yes

—

#11718361

C₄

yes

characteristic

#11718249

C₂²

yes

—

C₂×#88036

C₂²

yes

characteristic

C₂×#88036

C₂²

yes

characteristic

#11718214

—

D₁₃⋊C₃₂

—

C₁₃×#364

C₄

yes

characteristic

#11718107

C₄

yes

—

C₄×#6090

C₂²

yes

characteristic

#88158

C₈

yes

characteristic

#88155

C₂×C₄

yes

—

C₁₃×M₃₂

C₂×C₄

yes

—

C₄×C₈×C₁₃

C₂×C₄

yes

characteristic

#88059

C₈

yes

characteristic

C₂×#6090

C₂×C₄

yes

characteristic

C₂×#6090

C₂³

yes

characteristic

#88045

C₈

yes

—

#88038

—

C₁₆×D₁₃

—

#88036

—

#88036

—

#88036

D₄

yes

—

#13648

—

maximal, Sylow

#6127

C₂×C₈

yes

—

C₂×C₈×C₁₃

C₂×C₈

yes

characteristic

C₂×C₈×C₁₃

C₂²×C₄

yes

characteristic

C₄²×C₁₃

C₂×C₈

yes

characteristic

#6099

C₂×C₈

yes

—

Dic₅₂

C₁₆

yes

characteristic

D₁₀₄

C₁₆

yes

characteristic

#6095

C₁₆

yes

—

#6094

—

C₈×D₁₃

—

C₁₃×C₁₆

—

#6090

—

#6090

C₂×D₄

yes

yes

—

—

—

—

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₂²×C₈

yes

characteristic

C₂²⋊D₁₃

—

D₅₂

C₂×C₁₆

yes

—

C₄×D₁₃

—

Dic₂₆

C₂×C₁₆

yes

—

C₈×C₁₃

C₂×C₁₆

yes

characteristic

C₈×C₁₃

C₂×C₁₆

yes

characteristic

C₈×C₁₃

C₄×D₄

yes

C₈×C₁₃

yes

—

—

—

M₆₄

—

M₆₄

—

C₂×C₃₂

—

C₂×C₃₂

—

C₂×C₃₂

—

yes

—

C₄×C₁₆

—

C₂²×C₁₃

#504

yes

characteristic

C₂×D₁₃

—

C₄×C₁₃

—

C₄×C₁₃

C₈×D₄

yes

characteristic

C₄×C₁₃

C₂²×C₁₆

yes

characteristic

Dic₁₃

—

#135

—

#131

—

M₃₂

—

M₃₂

C₂×#261

yes

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

#108

—

#104

—

C₄×C₈

C₂×#261

yes

characteristic

C₃₂

—

C₃₂

—

C₃₂

—

C₂×C₁₃

—

C₂×C₁₃

D₄×C₁₆

yes

characteristic

D₁₃

—

#41

—

Q₁₆

—

SD₁₆

—

D₈

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

D₁₃⋊C₈

yes

characteristic

100

C₂×C₈

C₂²×#261

yes

characteristic

101

C₄²

D₁₃⋊C₈

yes

characteristic

102

C₁₆

—

103

C₁₆

—

104

C₁₆

—

105

C₁₆

—

106

C₁₃

#13648

yes

characteristic, complemented, Sylow

107

Q₈

—

108

D₄

—

109

D₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

C₂×D₁₃⋊C₈

yes

characteristic

113

C₈

—

114

C₈

D₁₃⋊C₁₆

yes

characteristic

115

C₈

D₁₃⋊C₁₆

yes

characteristic

116

C₈

D₄×#261

yes

characteristic

117

C₈

#88240

yes

characteristic

118

C₂²

—

119

C₂²

#11719096

yes

characteristic

120

C₄

—

121

C₄

—

122

C₄

#11719073

yes

characteristic

123

C₄

C₂×D₁₃⋊C₁₆

yes

characteristic

124

C₂

—

125

C₂

—

126

C₂

#13131215

yes

characteristic

	subgroup	G/H
center	C₈	D₄×#261
commutator	C₄×C₁₃	C₂²×C₁₆
Frattini	C₂×C₈	C₂²×#261
Fitting	C₁₃×#364	C₄
socle	C₂×C₁₃	D₄×C₁₆
prime radical	#88158	C₈
cosocle	C₂×#6090	C₂³
hypercenter	#364	#261
hypocenter	C₁₃	#13648
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ #364

subgroup

G/H

center

C₈

D₄×#261

commutator

C₄×C₁₃

C₂²×C₁₆

Frattini

C₂×C₈

C₂²×#261

Fitting

C₁₃×#364

C₄

socle

C₂×C₁₃

D₄×C₁₆

C₈

C₂³

C₁₃

G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₈ ◁ C₂×C₈ ◁ #364

N	H ≅ G/N	type
1. #13131260	C₂	semidirect
2. #13129995	C₂	semidirect
3. #13129954	C₂	semidirect
4. #13129943	C₂	semidirect
106. C₁₃	#13648	semidirect

H ≅ G/N

type

1. #13131260

C₂

semidirect

2. #13129995

C₂

semidirect

3. #13129954

C₂

semidirect

4. #13129943

C₂

semidirect

106. C₁₃

#13648

semidirect

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

subgroup	index
#13131260	2
#13129995	2
#13129954	2
#13129943	2
#13116672	2
#13648	13

subgroup

index

Subgroups — #16791469

Conjugacy classes of subgroups

Complements

Maximal subgroups