Group #15783489 — subgroups

Subgroups — #15783489

Order 3328.

184 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 83 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	#13117129	C₂	1	2	yes	maximal, complemented
2	#13116674	C₂	1	1	yes	maximal, characteristic
3	#13113034	C₂	1	1	yes	maximal, characteristic, complemented
4	#13112977	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1397	C₂	1	1	yes	maximal, characteristic, complemented
6	#11718562	C₂²	1	2	yes	—
7	#11718361	C₄	1	1	yes	characteristic
8	C₂×C₁₃×C₃₂	C₂²	1	1	yes	characteristic
9	C₂×C₁₃×C₃₂	C₂²	1	1	yes	characteristic
10	C₄×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
11	#11718100	C₄	1	2	yes	—
12	#11718091	C₂²	1	2	yes	—
13	#11718055	C₄	1	1	yes	characteristic
14	#11718039	—	2	2	no	—
15	D₁₃×C₃₂	—	2	2	no	—
16	#88158	C₈	1	1	yes	characteristic
17	#88155	C₂×C₄	1	2	yes	—
18	C₂×C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
19	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
20	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
21	#88059	C₈	1	1	yes	characteristic
22	#88052	C₂×C₄	1	2	yes	—
23	#88045	C₈	1	2	yes	—
24	#88038	—	2	2	no	—
25	C₁₆×D₁₃	—	2	2	no	—
26	C₁₃×C₃₂	—	2	1	no	—
27	C₁₃×C₃₂	D₄	1	2	yes	—
28	#88034	—	2	2	no	—
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	1	no	—
41	C₁₃×C₁₆	C₂×D₄	1	1	yes	characteristic
42	C₁₃×C₁₆	#41	1	1	yes	characteristic
43	#6090	—	2	2	no	—
44	#2258	—	13	2	no	—
45	#2170	—	13	1	no	—
46	#1422	—	13	1	no	—
47	#1401	—	13	2	no	—
48	#1397	D₁₃	1	1	yes	characteristic, complemented
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	—	26	2	no	—
65	C₂×C₃₂	C₂×D₁₃	1	1	yes	characteristic
66	C₂×C₃₂	C₂×D₁₃	1	1	yes	characteristic
67	#364	—	13	1	no	—
68	#350	—	13	2	no	—
69	C₄×C₁₆	C₂×D₁₃	1	1	yes	characteristic
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	—	13	2	no	—
79	M₃₂	—	26	2	no	—
80	C₂×C₁₆	—	26	2	no	—
81	C₂×C₁₆	C₄×D₁₃	1	1	yes	characteristic
82	C₂×C₁₆	C₂²×D₁₃	1	1	yes	characteristic
83	#108	—	13	1	no	—
84	#104	—	13	2	no	—
85	C₄×C₈	C₄×D₁₃	1	1	yes	characteristic
86	C₃₂	—	2	1	no	—
87	C₃₂	—	26	2	no	—
88	C₃₂	D₅₂	1	2	yes	—
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	C₈×D₁₃	1	1	yes	characteristic
100	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
101	C₄²	C₈×D₁₃	1	1	yes	characteristic
102	C₁₆	—	2	1	no	—
103	C₁₆	—	26	2	no	—
104	C₁₆	C₂×D₅₂	1	1	yes	characteristic
105	C₁₆	#6127	1	1	yes	characteristic
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×C₈×D₁₃	1	1	yes	characteristic
113	C₈	—	26	2	no	—
114	C₈	C₁₆×D₁₃	1	1	yes	characteristic
115	C₈	C₁₆×D₁₃	1	1	yes	characteristic
116	C₈	C₄×D₅₂	1	1	yes	characteristic
117	C₈	#88155	1	1	yes	characteristic
118	C₂²	—	26	2	no	—
119	C₂²	#11718562	1	1	yes	characteristic
120	C₄	—	4	1	no	—
121	C₄	—	26	2	no	—
122	C₄	C₈×D₅₂	1	1	yes	characteristic
123	C₄	C₂×C₁₆×D₁₃	1	1	yes	characteristic
124	C₂	—	2	1	no	—
125	C₂	—	52	2	no	—
126	C₂	C₁₆×D₅₂	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#13117129

C₂

yes

maximal, complemented

#13116674

C₂

yes

maximal, characteristic

#13113034

C₂

yes

maximal, characteristic, complemented

#13112977

C₂

yes

maximal, complemented

C₁₃×#1397

C₂

yes

maximal, characteristic, complemented

#11718562

C₂²

yes

—

#11718361

C₄

yes

characteristic

C₂×C₁₃×C₃₂

C₂²

yes

characteristic

C₂×C₁₃×C₃₂

C₂²

yes

characteristic

C₄×C₁₃×C₁₆

C₂²

yes

characteristic

#11718100

C₄

yes

—

#11718091

C₂²

yes

—

#11718055

C₄

yes

characteristic

#11718039

—

D₁₃×C₃₂

—

#88158

C₈

yes

characteristic

#88155

C₂×C₄

yes

—

C₂×C₁₃×C₁₆

C₂×C₄

yes

characteristic

C₂×C₁₃×C₁₆

C₂³

yes

characteristic

C₄×C₈×C₁₃

C₂×C₄

yes

characteristic

#88059

C₈

yes

characteristic

#88052

C₂×C₄

yes

—

#88045

C₈

yes

—

#88038

—

C₁₆×D₁₃

—

C₁₃×C₃₂

—

C₁₃×C₃₂

D₄

yes

—

—

—

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

—

C₁₃×C₁₆

C₂×D₄

yes

C₁₃×C₁₆

yes

—

—

—

—

—

D₁₃

yes

characteristic, complemented

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×D₁₃

yes

characteristic

C₂×C₃₂

C₂×D₁₃

yes

characteristic

#364

—

#350

—

C₄×C₁₆

C₂×D₁₃

yes

characteristic

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×C₁₆

—

C₂×C₁₆

C₄×D₁₃

yes

characteristic

C₂×C₁₆

C₂²×D₁₃

yes

characteristic

#108

—

#104

—

C₄×C₈

C₄×D₁₃

yes

characteristic

C₃₂

—

C₃₂

—

C₃₂

D₅₂

yes

—

C₂×C₁₃

—

C₂×C₁₃

D₄×C₁₆

yes

characteristic

D₁₃

—

#41

—

Q₁₆

—

SD₁₆

—

D₈

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

C₈×D₁₃

yes

characteristic

100

C₂×C₈

C₂×C₄×D₁₃

yes

characteristic

101

C₄²

C₈×D₁₃

yes

characteristic

102

C₁₆

—

103

C₁₆

—

104

C₁₆

C₂×D₅₂

yes

characteristic

105

C₁₆

#6127

yes

characteristic

106

C₁₃

#13648

yes

characteristic, complemented, Sylow

107

Q₈

—

108

D₄

—

109

D₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

C₂×C₈×D₁₃

yes

characteristic

113

C₈

—

114

C₈

C₁₆×D₁₃

yes

characteristic

115

C₈

C₁₆×D₁₃

yes

characteristic

116

C₈

C₄×D₅₂

yes

characteristic

117

C₈

#88155

yes

characteristic

118

C₂²

—

119

C₂²

#11718562

yes

characteristic

120

C₄

—

121

C₄

—

122

C₄

C₈×D₅₂

yes

characteristic

123

C₄

C₂×C₁₆×D₁₃

yes

characteristic

124

C₂

—

125

C₂

—

126

C₂

C₁₆×D₅₂

yes

characteristic

	subgroup	G/H
center	C₁₆	C₂×D₅₂
commutator	C₄×C₁₃	C₂²×C₁₆
Frattini	C₂×C₁₆	C₂²×D₁₃
Fitting	C₁₃×#1397	C₂
socle	C₂×C₁₃	D₄×C₁₆
prime radical	#88158	C₈
cosocle	C₂×C₁₃×C₁₆	C₂³
hypercenter	#1397	D₁₃
hypocenter	C₁₃	#13648
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₁₆ ◁ C₂×C₃₂ ◁ #1397

subgroup

G/H

center

C₁₆

C₂×D₅₂

commutator

C₄×C₁₃

C₂²×C₁₆

Frattini

C₂×C₁₆

C₂²×D₁₃

Fitting

C₁₃×#1397

C₂

socle

C₂×C₁₃

D₄×C₁₆

prime radical

#88158

C₈

cosocle

C₂×C₁₃×C₁₆

C₂³

D₁₃

C₁₃

G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₁₆ ◁ C₂×C₃₂ ◁ #1397

N	H ≅ G/N	type
1. #13117129	C₂	semidirect
3. #13113034	C₂	semidirect
4. #13112977	C₂	semidirect
5. C₁₃×#1397	C₂	semidirect
48. #1397	D₁₃	semidirect
106. C₁₃	#13648	semidirect

H ≅ G/N

type

1. #13117129

C₂

semidirect

3. #13113034

C₂

semidirect

4. #13112977

C₂

semidirect

5. C₁₃×#1397

C₂

semidirect

48. #1397

D₁₃

semidirect

106. C₁₃

#13648

semidirect

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

subgroup	index
#13117129	2
#13116674	2
#13113034	2
#13112977	2
C₁₃×#1397	2
#13648	13

subgroup

index

C₁₃×#1397

Subgroups — #15783489

Conjugacy classes of subgroups

Complements

Maximal subgroups