Group #13116308 — subgroups

Subgroups — #13116308

Order 1664.

230 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 91 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	C₁₃×#384	C₂	1	1	yes	maximal, characteristic
2	C₂×#88047	C₂	1	2	yes	maximal
3	#11718589	C₂	1	1	yes	maximal, characteristic
4	#11718121	C₂	1	2	yes	maximal
5	#11718116	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
7	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
8	C₂×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
9	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic
12	C₂×#6101	—	2	1	no	—
13	C₂²×#1055	C₂²	1	2	yes	—
14	#88071	—	2	1	no	—
15	#88047	—	2	4	no	—
16	C₂²×C₄×C₁₃	—	2	2	no	—
17	C₂²×C₄×C₁₃	D₄	1	1	yes	characteristic
18	C₂²×C₄×C₁₃	D₄	1	1	yes	characteristic
19	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
20	C₂²×Dic₁₃	—	2	1	no	—
21	C₂²×Dic₁₃	—	2	1	no	—
22	C₁₃×C₄⋊C₄	—	2	2	no	—
23	C₁₃×C₄⋊C₄	—	2	2	no	—
24	C₁₃×C₄⋊C₄	—	4	2	no	—
25	C₁₃×C₄⋊C₄	—	4	2	no	—
26	C₄²×C₁₃	—	2	2	no	—
27	C₄⋊Dic₁₃	—	2	1	no	—
28	C₄⋊Dic₁₃	—	2	2	no	—
29	C₄⋊Dic₁₃	D₄	1	2	yes	—
30	#6101	—	4	2	no	—
31	C₂×#1055	—	2	2	no	—
32	C₂×#1055	—	2	2	no	—
33	C₂×#1055	Q₈	1	4	yes	—
34	#2083	—	13	1	no	maximal, Sylow
35	C₂³×C₁₃	C₂×D₄	1	1	yes	characteristic
36	C₂×C₄×C₁₃	—	2	1	no	—
37	C₂×C₄×C₁₃	—	2	1	no	—
38	C₂×C₄×C₁₃	—	2	1	no	—
39	C₂×C₄×C₁₃	—	2	1	no	—
40	C₂×C₄×C₁₃	—	4	2	no	—
41	C₂×C₄×C₁₃	—	4	2	no	—
42	C₂×C₄×C₁₃	—	4	2	no	—
43	C₂×C₄×C₁₃	D₈	1	2	yes	—
44	C₂×C₄×C₁₃	Q₁₆	1	2	yes	—
45	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
46	C₂×C₄×C₁₃	C₂×Q₈	1	2	yes	—
47	C₂×C₄×C₁₃	#41	1	2	yes	—
48	C₂×C₄×C₁₃	#41	1	1	yes	characteristic
49	C₂×Dic₁₃	—	2	2	no	—
50	C₂×Dic₁₃	—	4	1	no	—
51	C₂×Dic₁₃	—	4	1	no	—
52	C₂×Dic₁₃	—	4	1	no	—
53	C₂×Dic₁₃	—	4	1	no	—
54	C₂×Dic₁₃	—	4	1	no	—
55	#1055	—	2	4	no	—
56	C₂×#107	—	13	2	no	—
57	#389	—	13	1	no	—
58	#384	D₁₃	1	1	yes	characteristic
59	#340	—	13	2	no	—
60	#336	—	13	1	no	—
61	C₂²×C₁₃	#121	1	1	yes	characteristic
62	C₂²×C₁₃	#123	1	1	yes	characteristic
63	C₂²×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
64	C₂²×C₁₃	C₂×D₈	1	1	yes	characteristic
65	C₂²×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
66	C₂²×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
67	C₂²×C₁₃	#137	1	1	yes	characteristic
68	C₄×C₁₃	—	2	2	no	—
69	C₄×C₁₃	—	2	2	no	—
70	C₄×C₁₃	—	8	2	no	—
71	C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
72	C₄×C₁₃	#125	1	2	yes	—
73	Dic₁₃	—	4	2	no	—
74	Dic₁₃	—	8	1	no	—
75	C₂²×C₈	—	13	2	no	—
76	C₂×C₄⋊C₄	—	2	1	no	—
77	C₂×C₄⋊C₄	—	2	1	no	—
78	C₂×C₄⋊C₄	—	13	1	no	—
79	C₂×C₄⋊C₄	—	13	1	no	—
80	C₂×C₄⋊C₄	—	26	1	no	—
81	C₂×C₄⋊C₄	C₂×D₁₃	1	2	yes	—
82	C₂×C₄²	C₂×D₁₃	1	1	yes	characteristic
83	#107	—	26	4	no	—
84	#95	—	26	1	no	—
85	C₂×C₁₃	#398	1	1	yes	characteristic
86	C₂×C₁₃	#459	1	1	yes	characteristic
87	C₂×C₁₃	#462	1	1	yes	characteristic
88	C₂×C₁₃	#480	1	1	yes	characteristic
89	C₂×C₁₃	#484	1	1	yes	characteristic
90	C₂×C₁₃	#500	1	1	yes	characteristic
91	C₂×C₁₃	#501	1	1	yes	characteristic
92	C₂²×C₄	—	2	2	no	—
93	C₂²×C₄	—	26	1	no	—
94	C₂²×C₄	—	26	1	no	—
95	C₂²×C₄	C₂²⋊D₁₃	1	1	yes	characteristic
96	C₂²×C₄	C₂²⋊D₁₃	1	1	yes	characteristic
97	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
98	C₂×C₈	—	13	4	no	—
99	C₂×C₈	—	26	2	no	—
100	C₂×C₈	—	26	2	no	—
101	C₄⋊C₄	—	2	2	no	—
102	C₄⋊C₄	—	2	2	no	—
103	C₄⋊C₄	—	4	2	no	—
104	C₄⋊C₄	—	4	2	no	—
105	C₄⋊C₄	—	13	2	no	—
106	C₄⋊C₄	—	26	1	no	—
107	C₄⋊C₄	—	26	2	no	—
108	C₄⋊C₄	—	52	2	no	—
109	C₄²	—	2	2	no	—
110	C₁₃	#2083	1	1	yes	characteristic, complemented, Sylow
111	C₂³	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
112	C₂×C₄	—	2	1	no	—
113	C₂×C₄	—	2	1	no	—
114	C₂×C₄	—	2	1	no	—
115	C₂×C₄	—	2	1	no	—
116	C₂×C₄	—	4	2	no	—
117	C₂×C₄	—	4	2	no	—
118	C₂×C₄	—	4	2	no	—
119	C₂×C₄	—	26	2	no	—
120	C₂×C₄	—	52	1	no	—
121	C₂×C₄	—	52	1	no	—
122	C₂×C₄	—	52	1	no	—
123	C₂×C₄	—	52	1	no	—
124	C₂×C₄	—	52	1	no	—
125	C₂×C₄	#6104	1	2	yes	—
126	C₂×C₄	#6107	1	2	yes	—
127	C₂×C₄	#6127	1	2	yes	—
128	C₂×C₄	D₄×D₁₃	1	1	yes	characteristic
129	C₂×C₄	#6129	1	1	yes	characteristic
130	C₂×C₄	Q₈×D₁₃	1	2	yes	—
131	C₈	—	26	4	no	—
132	C₂²	#88183	1	1	yes	characteristic
133	C₂²	C₂×#6104	1	1	yes	characteristic
134	C₂²	#88186	1	1	yes	characteristic
135	C₂²	#88192	1	1	yes	characteristic
136	C₂²	#88196	1	1	yes	characteristic
137	C₂²	C₂×#6107	1	1	yes	characteristic
138	C₂²	#88198	1	1	yes	characteristic
139	C₄	—	2	2	no	—
140	C₄	—	2	2	no	—
141	C₄	—	8	2	no	—
142	C₄	—	52	2	no	—
143	C₄	—	104	1	no	—
144	C₄	#88143	1	2	yes	—
145	C₄	#88150	1	2	yes	—
146	C₂	#11718628	1	1	yes	characteristic
147	C₂	#11718631	1	1	yes	characteristic
148	C₂	#11718641	1	1	yes	characteristic
149	C₂	#11718733	1	1	yes	characteristic
150	C₂	#11718739	1	1	yes	characteristic
151	C₂	#11718741	1	1	yes	characteristic
152	C₂	#11718751	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₃×#384

C₂

yes

maximal, characteristic

C₂×#88047

C₂

yes

maximal

#11718589

C₂

yes

maximal, characteristic

#11718121

C₂

yes

maximal

#11718116

C₂

yes

maximal, characteristic

C₂×C₁₃×C₄⋊C₄

—

C₂×C₁₃×C₄⋊C₄

—

C₂×C₁₃×C₄⋊C₄

C₂²

yes

—

C₂×C₄²×C₁₃

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₃

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₃

C₂²

yes

characteristic

C₂×#6101

—

C₂²×#1055

C₂²

yes

—

#88071

—

#88047

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

D₄

yes

characteristic

C₂²×C₄×C₁₃

D₄

yes

characteristic

C₂²×C₄×C₁₃

C₂³

yes

characteristic

C₂²×Dic₁₃

—

C₂²×Dic₁₃

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₄²×C₁₃

—

C₄⋊Dic₁₃

—

C₄⋊Dic₁₃

—

C₄⋊Dic₁₃

D₄

yes

—

—

—

—

Q₈

yes

—

#2083

—

maximal, Sylow

C₂³×C₁₃

C₂×D₄

yes

characteristic

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

D₈

yes

—

C₂×C₄×C₁₃

Q₁₆

yes

—

C₂×C₄×C₁₃

C₂×D₄

yes

characteristic

C₂×C₄×C₁₃

C₂×Q₈

yes

—

C₂×C₄×C₁₃

#41

yes

—

C₂×C₄×C₁₃

#41

yes

characteristic

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

—

—

—

D₁₃

yes

characteristic

#340

—

#336

—

C₂²×C₁₃

yes

C₂²×C₁₃

yes

C₂²×C₁₃

C₄⋊Q₈

yes

characteristic

C₂²×C₁₃

C₂×D₈

yes

characteristic

C₂²×C₁₃

C₂×Q₁₆

yes

C₂²×C₁₃

yes

C₂²×C₁₃

yes

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

C₂²⋊Q₈

yes

—

C₄×C₁₃

#125

yes

—

Dic₁₃

—

Dic₁₃

—

C₂²×C₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₁₃

yes

—

C₂×C₄²

C₂×D₁₃

yes

characteristic

#107

—

#95

—

C₂×C₁₃

yes

C₂×C₁₃

yes

C₂×C₁₃

yes

C₂×C₁₃

yes

C₂×C₁₃

yes

C₂×C₁₃

yes

C₂×C₁₃

yes

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²⋊D₁₃

yes

characteristic

C₂²×C₄

C₂²⋊D₁₃

yes

characteristic

C₂²×C₄

C₂²×D₁₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

100

C₂×C₈

—

101

C₄⋊C₄

—

102

C₄⋊C₄

—

103

C₄⋊C₄

—

104

C₄⋊C₄

—

105

C₄⋊C₄

—

106

C₄⋊C₄

—

107

C₄⋊C₄

—

108

C₄⋊C₄

—

109

C₄²

—

110

C₁₃

#2083

yes

characteristic, complemented, Sylow

111

C₂³

C₂×C₂²⋊D₁₃

yes

characteristic

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

#6104

yes

—

126

C₂×C₄

#6107

yes

—

127

C₂×C₄

#6127

yes

—

128

C₂×C₄

D₄×D₁₃

yes

characteristic

129

C₂×C₄

#6129

yes

characteristic

130

C₂×C₄

Q₈×D₁₃

yes

—

131

C₈

—

132

C₂²

#88183

yes

characteristic

133

C₂²

C₂×#6104

yes

characteristic

134

C₂²

#88186

yes

characteristic

135

C₂²

#88192

yes

characteristic

136

C₂²

#88196

yes

characteristic

137

C₂²

C₂×#6107

yes

characteristic

138

C₂²

#88198

yes

characteristic

139

C₄

—

140

C₄

—

141

C₄

—

142

C₄

—

143

C₄

—

104

—

144

C₄

#88143

yes

—

145

C₄

#88150

yes

—

146

C₂

#11718628

yes

characteristic

147

C₂

#11718631

yes

characteristic

148

C₂

#11718641

yes

characteristic

149

C₂

#11718733

yes

characteristic

150

C₂

#11718739

yes

characteristic

151

C₂

#11718741

yes

characteristic

152

C₂

#11718751

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₁₃
commutator, cosocle	C₂²×C₄×C₁₃	C₂³
Frattini	C₂²×C₄	C₂²×D₁₃
Fitting	C₁₃×#384	C₂
socle, prime radical	C₂³×C₁₃	C₂×D₄
hypercenter	#384	D₁₃
hypocenter	C₁₃	#2083
LCS	G ▷ C₂²×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #384

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₁₃

commutator, cosocle

C₂²×C₄×C₁₃

C₂³

Frattini

C₂²×C₄

C₂²×D₁₃

Fitting

C₁₃×#384

C₂

socle, prime radical

C₂³×C₁₃

C₂×D₄

D₁₃

C₁₃

G ▷ C₂²×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #384

N	H ≅ G/N	type
110. C₁₃	#2083	semidirect

H ≅ G/N

type

110. C₁₃

#2083

semidirect

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

subgroup	index
C₁₃×#384	2
C₂×#88047	2
#11718589	2
#11718121	2
#11718116	2
#2083	13

subgroup

index

C₁₃×#384

Subgroups — #13116308

Conjugacy classes of subgroups

Complements

Maximal subgroups