Group #13112686 — subgroups

Subgroups — #13112686

Order 1664.

160 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 81 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×C₁₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
2	#11718586	C₂	1	1	yes	maximal, characteristic
3	C₄×#6099	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₈×C₁₃	C₄	1	2	yes	—
5	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
6	C₂×#6099	C₄	1	2	yes	—
7	C₁₃×C₄⋊C₈	—	2	1	no	—
8	C₁₃×C₄⋊C₈	—	2	1	no	—
9	C₂²⋊#1055	C₄	1	2	yes	—
10	C₄⋊#1055	—	2	1	no	—
11	#88043	—	2	1	no	—
12	C₄×#1055	—	2	1	no	—
13	C₄×#1055	—	2	1	no	—
14	C₂²×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
16	C₂²×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
17	C₂×C₈×C₁₃	—	2	2	no	—
18	C₂×C₈×C₁₃	—	4	2	no	—
19	C₄²×C₁₃	D₄	1	1	yes	characteristic
20	C₄²×C₁₃	D₄	1	1	yes	characteristic
21	C₄²×C₁₃	D₄	1	1	yes	characteristic
22	C₄²×C₁₃	Q₈	1	1	yes	characteristic
23	#6099	—	2	2	no	—
24	#6099	C₈	1	4	yes	complemented
25	C₂×#1055	—	2	2	no	—
26	C₂×#1055	—	2	2	no	—
27	#1283	—	13	1	no	maximal, Sylow
28	C₂³×C₁₃	C₄²	1	1	yes	characteristic
29	C₂×C₄×C₁₃	—	2	1	no	—
30	C₂×C₄×C₁₃	—	2	1	no	—
31	C₂×C₄×C₁₃	—	4	1	no	—
32	C₂×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
33	C₂×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
34	C₂×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
35	C₂×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
36	C₂×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
37	C₂×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
38	C₂×C₄×C₁₃	C₂×C₈	1	2	yes	—
39	C₂×C₄×C₁₃	M₁₆	1	2	yes	—
40	C₈×C₁₃	—	4	2	no	—
41	#1055	—	2	4	no	—
42	#1055	—	4	2	no	—
43	#431	—	13	1	no	—
44	C₂×C₄⋊C₈	D₁₃	1	1	yes	characteristic
45	C₄×M₁₆	—	13	1	no	—
46	C₂²×C₁₃	—	2	1	no	—
47	C₂²×C₁₃	—	2	1	no	—
48	C₂²×C₁₃	#95	1	1	yes	characteristic
49	C₂²×C₁₃	C₄×C₈	1	1	yes	characteristic
50	C₂²×C₁₃	#97	1	1	yes	characteristic
51	C₄×C₁₃	—	2	1	no	—
52	C₄×C₁₃	—	2	1	no	—
53	C₄×C₁₃	—	2	1	no	—
54	C₄×C₁₃	C₂²⋊C₈	1	2	yes	—
55	C₄×C₁₃	#100	1	1	yes	characteristic
56	C₄×C₁₃	#101	1	1	yes	characteristic
57	C₄×C₁₃	C₄⋊C₈	1	2	yes	—
58	C₂×M₁₆	—	13	2	no	—
59	C₂²×C₈	Dic₁₃	1	2	yes	—
60	C₂×C₄²	C₂×D₁₃	1	1	yes	characteristic
61	C₄⋊C₈	—	2	1	no	—
62	C₄⋊C₈	—	2	1	no	—
63	C₄⋊C₈	—	26	1	no	—
64	C₂²⋊C₈	—	13	2	no	—
65	#97	—	26	1	no	—
66	C₄×C₈	—	26	1	no	—
67	C₄×C₈	—	26	1	no	—
68	C₂×C₁₃	—	2	1	no	—
69	C₂×C₁₃	—	2	1	no	—
70	C₂×C₁₃	#336	1	1	yes	characteristic
71	C₂×C₁₃	#343	1	1	yes	characteristic
72	C₂×C₁₃	#344	1	1	yes	characteristic
73	C₂²×C₄	C₄×D₁₃	1	1	yes	characteristic
74	C₂²×C₄	C₄×D₁₃	1	1	yes	characteristic
75	C₂²×C₄	C₂×Dic₁₃	1	1	yes	characteristic
76	M₁₆	—	13	4	no	—
77	M₁₆	—	26	2	no	—
78	C₂×C₈	—	2	2	no	—
79	C₂×C₈	—	4	2	no	—
80	C₂×C₈	—	26	2	no	—
81	C₂×C₈	—	26	2	no	—
82	C₄²	Dic₂₆	1	1	yes	characteristic
83	C₄²	D₅₂	1	1	yes	characteristic
84	C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
85	C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
86	C₁₃	#1283	1	1	yes	characteristic, complemented, Sylow
87	C₂³	C₄×Dic₁₃	1	1	yes	characteristic
88	C₂×C₄	—	2	1	no	—
89	C₂×C₄	—	2	1	no	—
90	C₂×C₄	—	4	1	no	—
91	C₂×C₄	C₈×D₁₃	1	2	yes	—
92	C₂×C₄	#6094	1	2	yes	—
93	C₂×C₄	#6101	1	1	yes	characteristic
94	C₂×C₄	#6101	1	1	yes	characteristic
95	C₂×C₄	C₄⋊Dic₁₃	1	1	yes	characteristic
96	C₂×C₄	#6103	1	1	yes	characteristic
97	C₂×C₄	#6103	1	1	yes	characteristic
98	C₂×C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
99	C₈	—	4	2	no	—
100	C₈	—	26	4	no	—
101	C₈	—	52	2	no	—
102	C₂²	—	2	1	no	—
103	C₂²	—	2	1	no	—
104	C₂²	C₈×Dic₁₃	1	1	yes	characteristic
105	C₂²	#88055	1	1	yes	characteristic
106	C₂²	#88071	1	1	yes	characteristic
107	C₄	—	2	1	no	—
108	C₄	—	2	1	no	—
109	C₄	—	2	1	no	—
110	C₄	#88054	1	2	yes	—
111	C₄	#88060	1	2	yes	—
112	C₄	#88073	1	1	yes	characteristic
113	C₄	#88076	1	1	yes	characteristic
114	C₂	—	2	1	no	—
115	C₂	—	2	1	no	—
116	C₂	#11718122	1	1	yes	characteristic
117	C₂	#11718142	1	1	yes	characteristic
118	C₂	#11718148	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₁₃×C₄⋊C₈

C₂

yes

maximal, characteristic

#11718586

C₂

yes

maximal, characteristic

C₄×#6099

C₂

yes

maximal, characteristic

C₂²×C₈×C₁₃

C₄

yes

—

C₂×C₄²×C₁₃

C₂²

yes

characteristic

C₂×#6099

C₄

yes

—

C₁₃×C₄⋊C₈

—

C₁₃×C₄⋊C₈

—

C₂²⋊#1055

C₄

yes

—

—

—

—

—

C₂²×C₄×C₁₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₃

C₂×C₄

yes

characteristic

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₄²×C₁₃

D₄

yes

characteristic

C₄²×C₁₃

D₄

yes

characteristic

C₄²×C₁₃

D₄

yes

characteristic

C₄²×C₁₃

Q₈

yes

characteristic

#6099

—

#6099

C₈

yes

—

—

—

C₂³×C₁₃

C₄²

yes

characteristic

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₃

C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₃

C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₃

C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₃

C₂×C₈

yes

—

C₂×C₄×C₁₃

M₁₆

yes

—

C₈×C₁₃

—

#1055

—

#1055

—

#431

—

C₂×C₄⋊C₈

D₁₃

yes

characteristic

C₄×M₁₆

—

C₂²×C₁₃

—

C₂²×C₁₃

—

C₂²×C₁₃

#95

yes

characteristic

C₂²×C₁₃

C₄×C₈

yes

characteristic

C₂²×C₁₃

#97

yes

characteristic

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

C₂²⋊C₈

yes

—

C₄×C₁₃

yes

C₄×C₁₃

yes

C₄×C₁₃

C₄⋊C₈

yes

—

C₂×M₁₆

—

C₂²×C₈

Dic₁₃

yes

—

C₂×C₄²

C₂×D₁₃

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₂²⋊C₈

—

#97

—

C₄×C₈

—

C₄×C₈

—

C₂×C₁₃

—

C₂×C₁₃

—

C₂×C₁₃

yes

C₂×C₁₃

yes

C₂×C₁₃

yes

C₂²×C₄

C₄×D₁₃

yes

characteristic

C₂²×C₄

C₄×D₁₃

yes

characteristic

C₂²×C₄

C₂×Dic₁₃

yes

characteristic

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄²

Dic₂₆

yes

characteristic

C₄²

D₅₂

yes

characteristic

C₄²

C₂²⋊D₁₃

yes

characteristic

C₄²

C₂²⋊D₁₃

yes

characteristic

C₁₃

#1283

yes

characteristic, complemented, Sylow

C₂³

C₄×Dic₁₃

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₈×D₁₃

yes

—

C₂×C₄

#6094

yes

—

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

C₄⋊Dic₁₃

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

C₂²⋊Dic₁₃

yes

characteristic

C₈

—

100

C₈

—

101

C₈

—

102

C₂²

—

103

C₂²

—

104

C₂²

C₈×Dic₁₃

yes

characteristic

105

C₂²

#88055

yes

characteristic

106

C₂²

#88071

yes

characteristic

107

C₄

—

108

C₄

—

109

C₄

—

110

C₄

#88054

yes

—

111

C₄

#88060

yes

—

112

C₄

#88073

yes

characteristic

113

C₄

#88076

yes

characteristic

114

C₂

—

115

C₂

—

116

C₂

#11718122

yes

characteristic

117

C₂

#11718142

yes

characteristic

118

C₂

#11718148

yes

characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊Dic₁₃
commutator	C₂²×C₁₃	C₄×C₈
Frattini	C₂×C₄²	C₂×D₁₃
Fitting	C₂×C₁₃×C₄⋊C₈	C₂
socle	C₂²×C₁₃	#95
prime radical	C₂³×C₁₃	C₄²
cosocle	C₂×C₄²×C₁₃	C₂²
hypercenter	C₂×C₄⋊C₈	D₁₃
hypocenter	C₁₃	#1283
LCS	G ▷ C₂²×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄⋊C₈

subgroup

G/H

center

C₂×C₄

C₂²⋊Dic₁₃

commutator

C₂²×C₁₃

C₄×C₈

Frattini

C₂×C₄²

C₂×D₁₃

Fitting

C₂×C₁₃×C₄⋊C₈

C₂

socle

C₂²×C₁₃

#95

prime radical

C₂³×C₁₃

C₄²

cosocle

C₂×C₄²×C₁₃

C₂²

hypercenter

C₂×C₄⋊C₈

D₁₃

hypocenter

C₁₃

#1283

LCS

G ▷ C₂²×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄⋊C₈

N	H ≅ G/N	type
24. #6099	C₈	semidirect
86. C₁₃	#1283	semidirect

H ≅ G/N

type

24. #6099

C₈

semidirect

86. C₁₃

#1283

semidirect

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

subgroup	index
C₂×C₁₃×C₄⋊C₈	2
#11718586	2
C₄×#6099	2
#1283	13

subgroup

index

C₂×C₁₃×C₄⋊C₈

#11718586

C₄×#6099

#1283

Subgroups — #13112686

Conjugacy classes of subgroups

Complements

Maximal subgroups