Group #13116885 — subgroups

Subgroups — #13116885

Order 1664.

154 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 49 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	#11718842	C₂	1	1	yes	maximal, characteristic
2	C₂×#88069	C₂	1	1	yes	maximal, characteristic
3	C₂×Dic₁₀₄	C₂	1	1	yes	maximal, characteristic
4	#11718534	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#358	C₂	1	1	yes	maximal, characteristic
6	#11718093	C₂	1	1	yes	maximal, characteristic
7	#11718084	C₂	1	1	yes	maximal, characteristic
8	C₂×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
9	#88198	—	2	1	no	—
10	C₂×#6107	—	2	1	no	—
11	C₂×Dic₅₂	C₂²	1	1	yes	characteristic
12	C₂×Dic₅₂	C₂²	1	1	yes	characteristic
13	#88141	—	2	1	no	—
14	C₂×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
15	C₁₃×#107	C₂²	1	1	yes	characteristic
16	#88069	—	2	2	no	—
17	C₈×Dic₁₃	C₂²	1	1	yes	characteristic
18	C₂×#6090	C₂²	1	1	yes	characteristic
19	#88050	—	2	1	no	—
20	Dic₁₀₄	—	2	2	no	—
21	C₂×Q₈×C₁₃	—	2	1	no	—
22	C₂×Dic₂₆	—	2	1	no	—
23	C₂×Dic₂₆	—	2	1	no	—
24	C₁₃×Q₁₆	—	2	1	no	—
25	C₁₃×Q₁₆	—	2	1	no	—
26	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
27	C₁₃×C₄⋊C₄	—	2	1	no	—
28	#6107	—	4	2	no	—
29	#6101	—	4	1	no	—
30	#6101	—	4	1	no	—
31	#6101	—	4	1	no	—
32	C₄×Dic₁₃	—	4	1	no	—
33	C₄×Dic₁₃	D₄	1	1	yes	characteristic
34	C₂×#1055	D₄	1	1	yes	characteristic
35	Dic₅₂	—	2	1	no	—
36	Dic₅₂	—	2	1	no	—
37	Dic₅₂	—	2	1	no	—
38	Dic₅₂	D₄	1	2	yes	—
39	C₁₃×C₁₆	—	2	1	no	—
40	#6090	—	2	1	no	—
41	#2209	—	13	1	no	maximal, Sylow
42	Q₈×C₁₃	—	4	1	no	—
43	Q₈×C₁₃	—	4	1	no	—
44	C₂×C₄×C₁₃	—	4	1	no	—
45	C₂×C₄×C₁₃	—	4	1	no	—
46	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
47	C₂×Dic₁₃	—	4	1	no	—
48	C₂×Dic₁₃	—	4	1	no	—
49	C₂×Dic₁₃	D₈	1	1	yes	characteristic
50	C₂×Dic₁₃	D₈	1	1	yes	characteristic
51	Dic₂₆	—	2	2	no	—
52	Dic₂₆	—	4	1	no	—
53	Dic₂₆	—	4	1	no	—
54	Dic₂₆	—	4	1	no	—
55	C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
56	C₈×C₁₃	#41	1	1	yes	characteristic
57	#1055	—	2	1	no	—
58	C₂×Q₃₂	—	13	1	no	—
59	C₂×Q₃₂	—	13	1	no	—
60	#494	—	13	1	no	—
61	C₄×Q₁₆	—	13	1	no	—
62	C₄⋊C₁₆	—	13	1	no	—
63	#358	—	13	1	no	—
64	#358	D₁₃	1	1	yes	characteristic
65	C₂²×C₁₃	C₂×D₈	1	1	yes	characteristic
66	C₄×C₁₃	—	8	1	no	—
67	C₄×C₁₃	—	8	1	no	—
68	C₄×C₁₃	#121	1	1	yes	characteristic
69	C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
70	Dic₁₃	—	2	1	no	—
71	Dic₁₃	—	4	2	no	—
72	Dic₁₃	—	8	1	no	—
73	Dic₁₃	Q₃₂	1	2	yes	complemented
74	C₂×Q₁₆	—	13	1	no	—
75	C₂×Q₁₆	—	13	1	no	—
76	C₂×Q₁₆	—	26	1	no	—
77	C₂×Q₁₆	C₂×D₁₃	1	1	yes	characteristic
78	C₄⋊Q₈	—	26	1	no	—
79	C₄×Q₈	—	26	1	no	—
80	Q₃₂	—	26	2	no	—
81	Q₃₂	—	26	2	no	—
82	C₂×C₁₆	—	13	1	no	—
83	C₂×C₁₆	C₂×D₁₃	1	1	yes	characteristic
84	#107	C₂×D₁₃	1	1	yes	characteristic
85	#103	—	26	1	no	—
86	C₄×C₈	—	13	1	no	—
87	C₂×C₁₃	#459	1	1	yes	characteristic
88	C₂×C₁₃	C₂×Q₃₂	1	1	yes	characteristic
89	C₂×C₁₃	#510	1	1	yes	characteristic
90	C₂×Q₈	—	2	1	no	—
91	C₂×Q₈	—	26	1	no	—
92	C₂×Q₈	—	26	1	no	—
93	Q₁₆	—	2	1	no	—
94	Q₁₆	—	2	1	no	—
95	Q₁₆	—	13	2	no	—
96	Q₁₆	—	26	1	no	—
97	Q₁₆	—	26	1	no	—
98	Q₁₆	—	26	1	no	—
99	Q₁₆	—	52	2	no	—
100	C₂×C₈	—	13	1	no	—
101	C₂×C₈	C₂²×D₁₃	1	1	yes	characteristic
102	C₄⋊C₄	—	2	1	no	—
103	C₄⋊C₄	—	52	1	no	—
104	C₄⋊C₄	—	52	1	no	—
105	C₄⋊C₄	—	52	1	no	—
106	C₄²	—	13	1	no	—
107	C₄²	—	52	1	no	—
108	C₁₆	—	2	1	no	—
109	C₁₆	—	26	1	no	—
110	C₁₃	#2209	1	1	yes	characteristic, complemented, Sylow
111	Q₈	—	4	1	no	—
112	Q₈	—	4	1	no	—
113	Q₈	—	26	2	no	—
114	Q₈	—	52	1	no	—
115	Q₈	—	52	1	no	—
116	Q₈	—	52	1	no	—
117	C₂×C₄	—	4	1	no	—
118	C₂×C₄	—	4	1	no	—
119	C₂×C₄	—	13	1	no	—
120	C₂×C₄	—	13	1	no	—
121	C₂×C₄	—	52	1	no	—
122	C₂×C₄	—	52	1	no	—
123	C₂×C₄	D₄×D₁₃	1	1	yes	characteristic
124	C₈	—	26	1	no	—
125	C₈	#6127	1	1	yes	characteristic
126	C₈	D₄×D₁₃	1	1	yes	characteristic
127	C₂²	D₈×D₁₃	1	1	yes	characteristic
128	C₄	—	8	1	no	—
129	C₄	—	8	1	no	—
130	C₄	—	13	2	no	—
131	C₄	—	26	1	no	—
132	C₄	—	52	2	no	—
133	C₄	—	104	1	no	—
134	C₄	#88138	1	1	yes	characteristic
135	C₄	#88168	1	1	yes	characteristic
136	C₂	#11718447	1	1	yes	characteristic
137	C₂	#11718576	1	1	yes	characteristic
138	C₂	D₁₃×Q₃₂	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11718842

C₂

yes

maximal, characteristic

C₂×#88069

C₂

yes

maximal, characteristic

C₂×Dic₁₀₄

C₂

yes

maximal, characteristic

#11718534

C₂

yes

maximal, characteristic

C₁₃×#358

C₂

yes

maximal, characteristic

#11718093

C₂

yes

maximal, characteristic

#11718084

C₂

yes

maximal, characteristic

C₂×C₁₃×Q₁₆

C₂²

yes

characteristic

#88198

—

C₂×#6107

—

C₂×Dic₅₂

C₂²

yes

characteristic

C₂×Dic₅₂

C₂²

yes

characteristic

#88141

—

C₂×C₁₃×C₁₆

C₂²

yes

characteristic

C₁₃×#107

C₂²

yes

characteristic

#88069

—

C₈×Dic₁₃

C₂²

yes

characteristic

C₂×#6090

C₂²

yes

characteristic

#88050

—

Dic₁₀₄

—

C₂×Q₈×C₁₃

—

C₂×Dic₂₆

—

C₂×Dic₂₆

—

C₁₃×Q₁₆

—

C₁₃×Q₁₆

—

C₂×C₈×C₁₃

C₂³

yes

characteristic

C₁₃×C₄⋊C₄

—

—

—

—

—

C₄×Dic₁₃

—

C₄×Dic₁₃

D₄

yes

characteristic

C₂×#1055

D₄

yes

characteristic

Dic₅₂

—

Dic₅₂

—

Dic₅₂

—

Dic₅₂

D₄

yes

—

C₁₃×C₁₆

—

#6090

—

#2209

—

maximal, Sylow

Q₈×C₁₃

—

Q₈×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₂×D₄

yes

characteristic

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

D₈

yes

characteristic

C₂×Dic₁₃

D₈

yes

characteristic

Dic₂₆

—

Dic₂₆

—

Dic₂₆

—

Dic₂₆

—

C₈×C₁₃

C₂×D₄

yes

C₈×C₁₃

yes

—

C₂×Q₃₂

—

C₂×Q₃₂

—

#494

—

C₄×Q₁₆

—

C₄⋊C₁₆

—

#358

—

#358

D₁₃

yes

characteristic

C₂²×C₁₃

C₂×D₈

yes

characteristic

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

yes

C₄×C₁₃

yes

Dic₁₃

—

Dic₁₃

—

Dic₁₃

—

Dic₁₃

Q₃₂

yes

complemented

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×Q₁₆

C₂×D₁₃

yes

characteristic

C₄⋊Q₈

—

C₄×Q₈

—

Q₃₂

—

Q₃₂

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₁₃

yes

characteristic

#107

C₂×D₁₃

yes

characteristic

#103

—

C₄×C₈

—

C₂×C₁₃

#459

yes

characteristic

C₂×C₁₃

C₂×Q₃₂

yes

characteristic

C₂×C₁₃

#510

yes

characteristic

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

100

C₂×C₈

—

101

C₂×C₈

C₂²×D₁₃

yes

characteristic

102

C₄⋊C₄

—

103

C₄⋊C₄

—

104

C₄⋊C₄

—

105

C₄⋊C₄

—

106

C₄²

—

107

C₄²

—

108

C₁₆

—

109

C₁₆

—

110

C₁₃

#2209

yes

characteristic, complemented, Sylow

111

Q₈

—

112

Q₈

—

113

Q₈

—

114

Q₈

—

115

Q₈

—

116

Q₈

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

D₄×D₁₃

yes

characteristic

124

C₈

—

125

C₈

#6127

yes

characteristic

126

C₈

D₄×D₁₃

yes

characteristic

127

C₂²

D₈×D₁₃

yes

characteristic

128

C₄

—

129

C₄

—

130

C₄

—

131

C₄

—

132

C₄

—

133

C₄

—

104

—

134

C₄

#88138

yes

characteristic

135

C₄

#88168

yes

characteristic

136

C₂

#11718447

yes

characteristic

137

C₂

#11718576

yes

characteristic

138

C₂

D₁₃×Q₃₂

yes

characteristic

	subgroup	G/H
center	C₂²	D₈×D₁₃
commutator, cosocle	C₂×C₈×C₁₃	C₂³
Frattini	C₂×C₈	C₂²×D₁₃
Fitting	C₁₃×#358	C₂
socle, prime radical	C₂²×C₁₃	C₂×D₈
hypercenter	#358	D₁₃
hypocenter	C₁₃	#2209
LCS	G ▷ C₂×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #358

subgroup

G/H

center

C₂²

D₈×D₁₃

commutator, cosocle

C₂×C₈×C₁₃

C₂³

Frattini

C₂×C₈

C₂²×D₁₃

Fitting

C₁₃×#358

C₂

socle, prime radical

C₂²×C₁₃

C₂×D₈

D₁₃

C₁₃

G ▷ C₂×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #358

N	H ≅ G/N	type
73. Dic₁₃	Q₃₂	semidirect
110. C₁₃	#2209	semidirect

H ≅ G/N

type

73. Dic₁₃

Q₃₂

semidirect

110. C₁₃

#2209

semidirect

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

subgroup	index
#11718842	2
C₂×#88069	2
C₂×Dic₁₀₄	2
#11718534	2
C₁₃×#358	2
#11718093	2
#11718084	2
#2209	13

subgroup

index

C₂×Dic₁₀₄

C₁₃×#358

Subgroups — #13116885

Conjugacy classes of subgroups

Complements

Maximal subgroups