Group #13116101 — subgroups

Subgroups — #13116101

Order 1664.

256 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 71 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	C₂²×C₁₃×Q₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂×#88076	C₂	1	2	yes	maximal
3	#11718886	C₂	1	2	yes	maximal
4	#11718763	C₂	1	1	yes	maximal, characteristic
5	#11718144	C₂	1	1	yes	maximal, characteristic
6	C₂²×Q₈×C₁₃	C₂²	1	2	yes	—
7	C₂×C₁₃×Q₁₆	—	2	4	no	—
8	C₂×C₁₃×Q₁₆	—	2	2	no	—
9	C₂²×C₈×C₁₃	C₂²	1	1	yes	characteristic
10	#88180	C₂²	1	1	yes	characteristic
11	C₂×#6099	C₂²	1	2	yes	—
12	C₂×#6099	C₂²	1	1	yes	characteristic
13	#88076	—	2	4	no	—
14	#88075	—	2	4	no	—
15	#88054	—	2	2	no	—
16	C₂×Q₈×C₁₃	—	2	2	no	—
17	C₂×Q₈×C₁₃	—	2	2	no	—
18	C₂×Q₈×C₁₃	—	2	2	no	—
19	C₂×Q₈×C₁₃	—	2	2	no	—
20	C₂×Q₈×C₁₃	—	2	2	no	—
21	C₂×Q₈×C₁₃	D₄	1	4	yes	—
22	C₂²×C₄×C₁₃	—	2	2	no	—
23	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
24	C₁₃×Q₁₆	—	2	8	no	—
25	C₂×C₈×C₁₃	—	2	2	no	—
26	C₂×C₈×C₁₃	D₄	1	2	yes	—
27	C₂²⋊Dic₁₃	—	2	1	no	—
28	C₄⋊Dic₁₃	D₄	1	2	yes	—
29	C₄×Dic₁₃	—	2	1	no	—
30	#6099	—	2	2	no	—
31	#6099	—	2	2	no	—
32	#6099	—	2	2	no	—
33	C₂×#1055	—	2	2	no	—
34	C₂×#1055	—	2	1	no	—
35	#2047	—	13	1	no	maximal, Sylow
36	C₂³×C₁₃	#41	1	1	yes	characteristic
37	Q₈×C₁₃	—	2	4	no	—
38	Q₈×C₁₃	—	2	4	no	—
39	Q₈×C₁₃	—	4	2	no	—
40	Q₈×C₁₃	—	4	2	no	—
41	C₂×C₄×C₁₃	—	2	4	no	—
42	C₂×C₄×C₁₃	—	4	2	no	—
43	C₂×C₄×C₁₃	—	4	2	no	—
44	C₂×C₄×C₁₃	C₂×D₄	1	2	yes	—
45	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
46	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
47	C₂×C₄×C₁₃	#41	1	2	yes	—
48	C₂×Dic₁₃	—	2	2	no	—
49	C₈×C₁₃	—	2	2	no	—
50	#1055	—	4	1	no	—
51	#1055	—	4	2	no	—
52	C₂²×Q₁₆	D₁₃	1	1	yes	characteristic
53	#424	—	13	1	no	—
54	#419	—	13	2	no	—
55	C₂×#101	—	13	2	no	—
56	#341	—	13	1	no	—
57	C₂²×C₁₃	—	2	2	no	—
58	C₂²×C₁₃	#121	1	1	yes	characteristic
59	C₂²×C₁₃	#123	1	2	yes	—
60	C₄×C₁₃	—	4	4	no	—
61	C₄×C₁₃	#120	1	1	yes	characteristic
62	C₄×C₁₃	#121	1	2	yes	—
63	C₄×C₁₃	#124	1	1	yes	characteristic
64	Dic₁₃	—	4	2	no	—
65	C₂²×Q₈	C₂×D₁₃	1	2	yes	—
66	C₂×Q₁₆	—	2	4	no	—
67	C₂×Q₁₆	—	2	2	no	—
68	C₂×M₁₆	—	13	2	no	—
69	C₂×M₁₆	—	13	1	no	—
70	C₂²×C₈	C₂×D₁₃	1	1	yes	characteristic
71	#117	—	13	1	no	—
72	C₄⋊C₈	—	26	2	no	—
73	#103	—	26	4	no	—
74	#101	—	26	4	no	—
75	C₂×C₁₃	—	2	2	no	—
76	C₂×C₁₃	#394	1	1	yes	characteristic
77	C₂×C₁₃	#473	1	2	yes	—
78	C₂×Q₈	—	2	2	no	—
79	C₂×Q₈	—	2	2	no	—
80	C₂×Q₈	—	2	2	no	—
81	C₂×Q₈	—	2	2	no	—
82	C₂×Q₈	—	2	2	no	—
83	C₂×Q₈	C₂²⋊D₁₃	1	4	yes	—
84	C₂²×C₄	—	2	2	no	—
85	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
86	Q₁₆	—	2	8	no	—
87	M₁₆	—	26	2	no	—
88	M₁₆	—	26	2	no	—
89	M₁₆	—	26	2	no	—
90	C₂×C₈	—	2	2	no	—
91	C₂×C₈	—	26	2	no	—
92	C₂×C₈	—	26	1	no	—
93	C₂×C₈	C₂²⋊D₁₃	1	2	yes	—
94	C₄⋊C₄	—	13	2	no	—
95	C₂²⋊C₄	—	26	1	no	—
96	C₄²	—	26	1	no	—
97	C₁₃	#2047	1	1	yes	characteristic, complemented, Sylow
98	C₂³	#6129	1	1	yes	characteristic
99	Q₈	—	2	4	no	—
100	Q₈	—	2	4	no	—
101	Q₈	—	4	2	no	—
102	Q₈	—	4	2	no	—
103	C₂×C₄	—	2	4	no	—
104	C₂×C₄	—	4	2	no	—
105	C₂×C₄	—	4	2	no	—
106	C₂×C₄	—	26	2	no	—
107	C₂×C₄	D₄×D₁₃	1	1	yes	characteristic
108	C₂×C₄	#6129	1	2	yes	—
109	C₂×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
110	C₂×C₄	C₂×C₂²⋊D₁₃	1	2	yes	—
111	C₈	—	2	2	no	—
112	C₈	—	52	2	no	—
113	C₈	—	52	1	no	—
114	C₂²	—	2	2	no	—
115	C₂²	#88189	1	2	yes	—
116	C₂²	#88192	1	1	yes	characteristic
117	C₄	—	4	4	no	—
118	C₄	—	52	2	no	—
119	C₄	#88190	1	1	yes	characteristic
120	C₄	#88193	1	2	yes	—
121	C₄	#88207	1	1	yes	characteristic
122	C₂	—	2	2	no	—
123	C₂	#11718853	1	2	yes	—
124	C₂	#11718883	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×C₁₃×Q₁₆

C₂

yes

maximal, characteristic

C₂×#88076

C₂

yes

maximal

#11718886

C₂

yes

maximal

#11718763

C₂

yes

maximal, characteristic

#11718144

C₂

yes

maximal, characteristic

C₂²×Q₈×C₁₃

C₂²

yes

—

C₂×C₁₃×Q₁₆

—

C₂×C₁₃×Q₁₆

—

C₂²×C₈×C₁₃

C₂²

yes

characteristic

#88180

C₂²

yes

characteristic

C₂×#6099

C₂²

yes

—

C₂×#6099

C₂²

yes

—

—

—

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

D₄

yes

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

C₂³

yes

characteristic

C₁₃×Q₁₆

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

D₄

yes

—

C₂²⋊Dic₁₃

—

C₄⋊Dic₁₃

D₄

yes

—

C₄×Dic₁₃

—

—

—

—

—

—

—

C₂³×C₁₃

yes

Q₈×C₁₃

—

Q₈×C₁₃

—

Q₈×C₁₃

—

Q₈×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₂×D₄

yes

—

C₂×C₄×C₁₃

C₂×D₄

yes

characteristic

C₂×C₄×C₁₃

C₂×D₄

yes

characteristic

C₂×C₄×C₁₃

#41

yes

—

C₂×Dic₁₃

—

C₈×C₁₃

—

#1055

—

#1055

—

C₂²×Q₁₆

D₁₃

yes

—

—

—

—

C₂²×C₁₃

—

C₂²×C₁₃

#121

yes

characteristic

C₂²×C₁₃

#123

yes

—

C₄×C₁₃

—

C₄×C₁₃

#120

yes

characteristic

C₄×C₁₃

#121

yes

—

C₄×C₁₃

#124

yes

characteristic

Dic₁₃

—

C₂²×Q₈

C₂×D₁₃

yes

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

C₂×D₁₃

yes

characteristic

#117

—

C₄⋊C₈

—

#103

—

#101

—

C₂×C₁₃

—

C₂×C₁₃

#394

yes

characteristic

C₂×C₁₃

#473

yes

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

C₂²⋊D₁₃

yes

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₁₃

yes

characteristic

Q₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂²⋊D₁₃

yes

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₁₃

#2047

yes

characteristic, complemented, Sylow

C₂³

#6129

yes

characteristic

Q₈

—

100

Q₈

—

101

Q₈

—

102

Q₈

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

D₄×D₁₃

yes

characteristic

108

C₂×C₄

#6129

yes

—

109

C₂×C₄

C₂×C₂²⋊D₁₃

yes

characteristic

110

C₂×C₄

C₂×C₂²⋊D₁₃

yes

—

111

C₈

—

112

C₈

—

113

C₈

—

114

C₂²

—

115

C₂²

#88189

yes

—

116

C₂²

#88192

yes

characteristic

117

C₄

—

118

C₄

—

119

C₄

#88190

yes

characteristic

120

C₄

#88193

yes

—

121

C₄

#88207

yes

characteristic

122

C₂

—

123

C₂

#11718853

yes

—

124

C₂

#11718883

yes

characteristic

	subgroup	G/H
center	C₂²	#88192
commutator, cosocle	C₂²×C₄×C₁₃	C₂³
Frattini	C₂²×C₄	C₂²×D₁₃
Fitting	C₂²×C₁₃×Q₁₆	C₂
socle	C₂²×C₁₃	#121
prime radical	C₂³×C₁₃	#41
hypercenter	C₂²×Q₁₆	D₁₃
hypocenter	C₁₃	#2047
LCS	G ▷ C₂²×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×Q₁₆

subgroup

G/H

center

C₂²

#88192

commutator, cosocle

C₂²×C₄×C₁₃

C₂³

Frattini

C₂²×C₄

C₂²×D₁₃

Fitting

C₂²×C₁₃×Q₁₆

C₂

C₂²×C₁₃

C₂³×C₁₃

C₂²×Q₁₆

D₁₃

hypocenter

C₁₃

#2047

LCS

G ▷ C₂²×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×Q₁₆

N	H ≅ G/N	type
97. C₁₃	#2047	semidirect

H ≅ G/N

type

97. C₁₃

#2047

semidirect

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

subgroup	index
C₂²×C₁₃×Q₁₆	2
C₂×#88076	2
#11718886	2
#11718763	2
#11718144	2
#2047	13

subgroup

index

C₂²×C₁₃×Q₁₆

Subgroups — #13116101

Conjugacy classes of subgroups

Complements

Maximal subgroups