Group #15749795 — subgroups

Subgroups — #15749795

Order 3328.

214 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 119 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	#13113584	C₂	1	2	yes	maximal
2	C₂×C₁₃×#346	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₁₃×C₁₆	C₄	1	2	yes	—
4	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
5	#11718586	—	2	2	no	—
6	C₁₃×#346	—	2	2	no	—
7	#11718050	—	2	2	no	—
8	#11718049	C₄	1	4	yes	—
9	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
10	C₂²×C₈×C₁₃	Q₈	1	1	yes	characteristic
11	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
12	C₂×C₁₃×C₁₆	—	2	2	no	—
13	C₂×C₁₃×C₁₆	—	2	2	no	—
14	C₂×C₁₃×C₁₆	C₈	1	4	yes	complemented
15	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
16	C₄×C₈×C₁₃	D₄	1	2	yes	—
17	C₂²⋊#1055	—	4	2	no	—
18	C₄⋊#1055	—	2	4	no	—
19	C₄×#1055	—	4	2	no	—
20	#7157	—	13	1	no	maximal, Sylow
21	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
22	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
23	C₂²×C₄×C₁₃	Q₁₆	1	1	yes	characteristic
24	C₂×C₈×C₁₃	—	2	2	no	—
25	C₂×C₈×C₁₃	C₄²	1	1	yes	characteristic
26	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
28	C₂×C₈×C₁₃	C₂×C₈	1	2	yes	—
29	C₂×C₈×C₁₃	M₁₆	1	2	yes	—
30	C₄²×C₁₃	C₂²⋊C₄	1	2	yes	—
31	C₄²×C₁₃	SD₁₆	1	2	yes	—
32	C₂×#1055	—	4	4	no	—
33	C₁₃×C₁₆	—	2	4	no	—
34	C₂×#346	D₁₃	1	1	yes	characteristic
35	#1564	—	13	2	no	—
36	C₂³×C₁₃	#107	1	1	yes	characteristic
37	C₂×C₄×C₁₃	—	4	1	no	—
38	C₂×C₄×C₁₃	—	4	1	no	—
39	C₂×C₄×C₁₃	#95	1	1	yes	characteristic
40	C₂×C₄×C₁₃	#102	1	2	yes	—
41	C₂×C₄×C₁₃	#103	1	2	yes	—
42	C₂×C₄×C₁₃	C₄⋊C₈	1	2	yes	—
43	C₂×C₄×C₁₃	#106	1	1	yes	characteristic
44	C₂×C₄×C₁₃	#108	1	2	yes	—
45	C₈×C₁₃	—	2	2	no	—
46	C₈×C₁₃	C₄×C₈	1	1	yes	characteristic
47	C₈×C₁₃	#97	1	1	yes	characteristic
48	C₈×C₁₃	C₂²⋊C₈	1	2	yes	—
49	#1055	—	8	4	no	—
50	C₂²×C₁₆	Dic₁₃	1	2	yes	—
51	#431	—	26	2	no	—
52	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
53	#346	—	2	2	no	—
54	#335	—	26	2	no	—
55	#334	—	13	4	no	—
56	C₂²×C₁₃	—	2	1	no	—
57	C₂²×C₁₃	—	2	1	no	—
58	C₂²×C₁₃	#335	1	2	yes	—
59	C₂²×C₁₃	#340	1	1	yes	characteristic
60	C₄×C₁₃	—	2	2	no	—
61	C₄×C₁₃	—	2	2	no	—
62	C₄×C₁₃	#334	1	2	yes	—
63	C₄×C₁₃	#336	1	1	yes	characteristic
64	C₄×C₁₃	#341	1	1	yes	characteristic
65	C₂²×C₈	Dic₂₆	1	1	yes	characteristic
66	C₂²×C₈	C₂×Dic₁₃	1	1	yes	characteristic
67	C₂×C₄²	D₅₂	1	1	yes	characteristic
68	C₂×C₁₆	—	2	2	no	—
69	C₂×C₁₆	—	2	2	no	—
70	C₂×C₁₆	#1055	1	4	yes	complemented
71	C₄⋊C₈	—	26	4	no	—
72	C₂²⋊C₈	—	52	2	no	—
73	C₄×C₈	—	52	2	no	—
74	C₄×C₈	C₄×D₁₃	1	2	yes	—
75	C₄×C₈	C₂²⋊D₁₃	1	2	yes	—
76	C₂×C₁₃	—	2	2	no	—
77	C₂×C₁₃	#1277	1	1	yes	characteristic
78	C₂×C₁₃	#1384	1	1	yes	characteristic
79	C₂×C₁₃	#1385	1	1	yes	characteristic
80	C₂²×C₄	D₁₀₄	1	1	yes	characteristic
81	C₂²×C₄	Dic₅₂	1	1	yes	characteristic
82	C₂²×C₄	C₄⋊Dic₁₃	1	1	yes	characteristic
83	C₂×C₈	—	2	2	no	—
84	C₂×C₈	—	52	4	no	—
85	C₂×C₈	C₂×#1055	1	2	yes	—
86	C₂×C₈	#6099	1	2	yes	—
87	C₂×C₈	C₄×Dic₁₃	1	1	yes	characteristic
88	C₂×C₈	#6101	1	2	yes	—
89	C₂×C₈	C₂²⋊Dic₁₃	1	1	yes	characteristic
90	C₄²	#6095	1	2	yes	—
91	C₄²	#6103	1	2	yes	—
92	C₁₆	—	2	4	no	—
93	C₁₃	#7157	1	1	yes	characteristic, complemented, Sylow
94	C₂³	#88058	1	1	yes	characteristic
95	C₂×C₄	—	4	1	no	—
96	C₂×C₄	—	4	1	no	—
97	C₂×C₄	C₄⋊#1055	1	2	yes	—
98	C₂×C₄	#88056	1	2	yes	—
99	C₂×C₄	#88057	1	1	yes	characteristic
100	C₂×C₄	#88059	1	2	yes	—
101	C₂×C₄	#88061	1	2	yes	—
102	C₂×C₄	#88071	1	1	yes	characteristic
103	C₈	—	2	2	no	—
104	C₈	—	104	4	no	—
105	C₈	C₄×#1055	1	1	yes	characteristic
106	C₈	#88043	1	1	yes	characteristic
107	C₈	C₂²⋊#1055	1	2	yes	—
108	C₂²	—	2	1	no	—
109	C₂²	—	2	1	no	—
110	C₂²	#11718050	1	2	yes	—
111	C₂²	#11718143	1	1	yes	characteristic
112	C₄	—	2	2	no	—
113	C₄	—	2	2	no	—
114	C₄	#11718049	1	2	yes	—
115	C₄	#11718116	1	1	yes	characteristic
116	C₄	#11718144	1	1	yes	characteristic
117	C₂	—	2	2	no	—
118	C₂	#13112671	1	1	yes	characteristic
119	C₂	#13112938	1	1	yes	characteristic
120	C₂	#13112940	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#13113584

C₂

yes

maximal

C₂×C₁₃×#346

C₂

yes

maximal, characteristic

C₂²×C₁₃×C₁₆

C₄

yes

—

C₂×C₄×C₈×C₁₃

C₂²

yes

characteristic

#11718586

—

C₁₃×#346

—

#11718050

—

#11718049

C₄

yes

—

C₂²×C₈×C₁₃

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₃

Q₈

yes

characteristic

C₂×C₄²×C₁₃

D₄

yes

characteristic

C₂×C₁₃×C₁₆

—

C₂×C₁₃×C₁₆

—

C₂×C₁₃×C₁₆

C₈

yes

complemented

C₄×C₈×C₁₃

C₂×C₄

yes

—

C₄×C₈×C₁₃

D₄

yes

—

C₂²⋊#1055

—

—

—

—

C₂²×C₄×C₁₃

C₄⋊C₄

yes

characteristic

C₂²×C₄×C₁₃

D₈

yes

characteristic

C₂²×C₄×C₁₃

Q₁₆

yes

characteristic

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

C₄²

yes

characteristic

C₂×C₈×C₁₃

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₃

C₄⋊C₄

yes

—

C₂×C₈×C₁₃

C₂×C₈

yes

—

C₂×C₈×C₁₃

M₁₆

yes

—

C₄²×C₁₃

C₂²⋊C₄

yes

—

C₄²×C₁₃

SD₁₆

yes

—

C₂×#1055

—

C₁₃×C₁₆

—

C₂×#346

D₁₃

yes

characteristic

#1564

—

C₂³×C₁₃

#107

yes

characteristic

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

#95

yes

characteristic

C₂×C₄×C₁₃

#102

yes

—

C₂×C₄×C₁₃

#103

yes

—

C₂×C₄×C₁₃

C₄⋊C₈

yes

—

C₂×C₄×C₁₃

#106

yes

characteristic

C₂×C₄×C₁₃

#108

yes

—

C₈×C₁₃

—

C₈×C₁₃

C₄×C₈

yes

characteristic

C₈×C₁₃

#97

yes

characteristic

C₈×C₁₃

C₂²⋊C₈

yes

—

#1055

—

C₂²×C₁₆

Dic₁₃

yes

—

#431

—

C₂×C₄×C₈

C₂×D₁₃

yes

—

—

—

C₂²×C₁₃

—

C₂²×C₁₃

—

C₂²×C₁₃

#335

yes

—

C₂²×C₁₃

#340

yes

characteristic

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

#334

yes

—

C₄×C₁₃

yes

C₄×C₁₃

yes

C₂²×C₈

Dic₂₆

yes

characteristic

C₂²×C₈

C₂×Dic₁₃

yes

characteristic

C₂×C₄²

D₅₂

yes

characteristic

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

#1055

yes

complemented

C₄⋊C₈

—

C₂²⋊C₈

—

C₄×C₈

—

C₄×C₈

C₄×D₁₃

yes

—

C₄×C₈

C₂²⋊D₁₃

yes

—

C₂×C₁₃

—

C₂×C₁₃

yes

C₂×C₁₃

yes

C₂×C₁₃

yes

C₂²×C₄

D₁₀₄

yes

characteristic

C₂²×C₄

Dic₅₂

yes

characteristic

C₂²×C₄

C₄⋊Dic₁₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×#1055

yes

—

C₂×C₈

#6099

yes

—

C₂×C₈

C₄×Dic₁₃

yes

characteristic

C₂×C₈

#6101

yes

—

C₂×C₈

C₂²⋊Dic₁₃

yes

characteristic

C₄²

#6095

yes

—

C₄²

#6103

yes

—

C₁₆

—

C₁₃

#7157

yes

characteristic, complemented, Sylow

C₂³

#88058

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₄⋊#1055

yes

—

C₂×C₄

#88056

yes

—

C₂×C₄

#88057

yes

characteristic

100

C₂×C₄

#88059

yes

—

101

C₂×C₄

#88061

yes

—

102

C₂×C₄

#88071

yes

characteristic

103

C₈

—

104

C₈

—

104

—

105

C₈

C₄×#1055

yes

characteristic

106

C₈

#88043

yes

characteristic

107

C₈

C₂²⋊#1055

yes

—

108

C₂²

—

109

C₂²

—

110

C₂²

#11718050

yes

—

111

C₂²

#11718143

yes

characteristic

112

C₄

—

113

C₄

—

114

C₄

#11718049

yes

—

115

C₄

#11718116

yes

characteristic

116

C₄

#11718144

yes

characteristic

117

C₂

—

118

C₂

#13112671

yes

characteristic

119

C₂

#13112938

yes

characteristic

120

C₂

#13112940

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#88057
commutator	C₈×C₁₃	C₄×C₈
Frattini	C₂×C₄×C₈	C₂×D₁₃
Fitting	C₂×C₁₃×#346	C₂
socle	C₂²×C₁₃	#340
prime radical	C₂³×C₁₃	#107
cosocle	C₂×C₄×C₈×C₁₃	C₂²
hypercenter	C₂×#346	D₁₃
hypocenter	C₁₃	#7157
LCS	G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×#346

subgroup

G/H

center

C₂×C₄

#88057

commutator

C₈×C₁₃

C₄×C₈

Frattini

C₂×C₄×C₈

C₂×D₁₃

Fitting

C₂×C₁₃×#346

C₂

C₂²×C₁₃

C₂³×C₁₃

C₂×C₄×C₈×C₁₃

C₂²

D₁₃

C₁₃

G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×#346

N	H ≅ G/N	type
14. C₂×C₁₃×C₁₆	C₈	semidirect
70. C₂×C₁₆	#1055	semidirect
93. C₁₃	#7157	semidirect

H ≅ G/N

type

14. C₂×C₁₃×C₁₆

C₈

semidirect

70. C₂×C₁₆

#1055

semidirect

93. C₁₃

#7157

semidirect

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

subgroup	index
#13113584	2
C₂×C₁₃×#346	2
#7157	13

subgroup

index

#13113584

C₂×C₁₃×#346

#7157

Subgroups — #15749795

Conjugacy classes of subgroups

Complements

Maximal subgroups