Group #13114345 — subgroups

Subgroups — #13114345

Order 1664.

146 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 146 conjugacy classes of subgroups — too many to draw. Only its 51 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	#11718752	C₂	1	1	yes	maximal, characteristic
2	#11718740	C₂	1	1	yes	maximal, characteristic
3	#11718510	C₂	1	1	yes	maximal, characteristic
4	#11718492	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#333	C₂	1	1	yes	maximal, characteristic
6	#11718078	C₂	1	1	yes	maximal, characteristic
7	#11718071	C₂	1	1	yes	maximal, characteristic
8	C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
9	C₂×Dic₅₂	—	2	1	no	—
10	#88123	C₂²	1	1	yes	characteristic
11	C₄×Dic₂₆	C₂²	1	1	yes	characteristic
12	C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
13	C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
14	#88056	—	2	1	no	—
15	#88055	—	2	1	no	—
16	#88054	—	2	1	no	—
17	#88050	—	2	1	no	—
18	#88048	—	2	1	no	—
19	#88048	—	2	1	no	—
20	#88047	—	2	1	no	—
21	C₄⋊#1055	C₂²	1	1	yes	characteristic
22	C₄×#1055	C₂²	1	1	yes	characteristic
23	C₂×Q₈×C₁₃	—	2	1	no	—
24	C₂×Dic₂₆	—	2	1	no	—
25	C₂×Dic₂₆	D₄	1	1	yes	characteristic
26	C₂×C₈×C₁₃	—	2	1	no	—
27	C₂×C₈×C₁₃	—	2	1	no	—
28	C₁₃×C₄⋊C₄	—	2	1	no	—
29	C₁₃×C₄⋊C₄	—	2	1	no	—
30	C₄²×C₁₃	C₂³	1	1	yes	characteristic
31	C₄⋊Dic₁₃	—	2	1	no	—
32	C₄⋊Dic₁₃	—	2	1	no	—
33	C₄⋊Dic₁₃	D₄	1	1	yes	characteristic
34	#6101	—	2	1	no	—
35	C₄×Dic₁₃	—	2	1	no	—
36	C₂×#1055	—	2	1	no	—
37	C₂×#1055	D₄	1	1	yes	characteristic
38	C₂×#1055	D₄	1	1	yes	characteristic
39	Dic₅₂	—	4	2	no	—
40	#1692	—	13	1	no	maximal, Sylow
41	Q₈×C₁₃	—	8	1	no	—
42	C₂×C₄×C₁₃	—	4	1	no	—
43	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
44	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
45	C₂×C₄×C₁₃	#41	1	1	yes	characteristic
46	C₂×Dic₁₃	—	2	1	no	—
47	C₂×Dic₁₃	—	2	1	no	—
48	C₂×Dic₁₃	—	4	1	no	—
49	Dic₂₆	—	2	1	no	—
50	Dic₂₆	—	2	1	no	—
51	Dic₂₆	—	4	1	no	—
52	Dic₂₆	—	4	1	no	—
53	C₈×C₁₃	—	4	1	no	—
54	C₈×C₁₃	—	4	1	no	—
55	#1055	—	2	1	no	—
56	#1055	—	4	1	no	—
57	#1055	Q₁₆	1	2	yes	complemented
58	#498	—	13	1	no	—
59	#477	—	13	1	no	—
60	#462	—	13	1	no	—
61	#446	—	13	1	no	—
62	#335	—	13	1	no	—
63	#333	D₁₃	1	1	yes	characteristic
64	#332	—	13	1	no	—
65	C₂²×C₁₃	#121	1	1	yes	characteristic
66	C₄×C₁₃	—	2	1	no	—
67	C₄×C₁₃	—	8	1	no	—
68	C₄×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
69	C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
70	C₄×C₁₃	#137	1	1	yes	characteristic
71	C₄×C₁₃	#137	1	1	yes	characteristic
72	Dic₁₃	—	4	1	no	—
73	Dic₁₃	—	4	1	no	—
74	Dic₁₃	—	8	1	no	—
75	C₂×Q₁₆	—	26	1	no	—
76	C₄⋊Q₈	—	13	1	no	—
77	C₄⋊Q₈	C₂×D₁₃	1	1	yes	characteristic
78	C₄×Q₈	—	13	1	no	—
79	#107	—	26	1	no	—
80	#106	—	26	1	no	—
81	#106	—	26	1	no	—
82	C₄⋊C₈	—	13	1	no	—
83	C₄⋊C₈	—	26	1	no	—
84	C₄⋊C₈	C₂×D₁₃	1	1	yes	characteristic
85	C₄⋊C₈	C₂×D₁₃	1	1	yes	characteristic
86	#103	—	26	1	no	—
87	#103	—	26	1	no	—
88	#97	—	26	1	no	—
89	C₄×C₈	—	13	1	no	—
90	C₂×C₁₃	#462	1	1	yes	characteristic
91	C₂×C₁₃	#468	1	1	yes	characteristic
92	C₂×C₁₃	#471	1	1	yes	characteristic
93	C₂×Q₈	—	2	1	no	—
94	C₂×Q₈	—	13	1	no	—
95	C₂×Q₈	—	26	1	no	—
96	Q₁₆	—	52	2	no	—
97	C₂×C₈	—	2	1	no	—
98	C₂×C₈	—	2	1	no	—
99	C₂×C₈	—	13	1	no	—
100	C₂×C₈	—	13	1	no	—
101	C₂×C₈	—	26	1	no	—
102	C₄⋊C₄	—	2	1	no	—
103	C₄⋊C₄	—	2	1	no	—
104	C₄⋊C₄	—	13	1	no	—
105	C₄⋊C₄	—	26	1	no	—
106	C₄⋊C₄	—	26	1	no	—
107	C₄⋊C₄	—	26	1	no	—
108	C₄²	—	26	1	no	—
109	C₄²	C₂²×D₁₃	1	1	yes	characteristic
110	C₁₃	#1692	1	1	yes	characteristic, complemented, Sylow
111	Q₈	—	8	1	no	—
112	Q₈	—	26	1	no	—
113	Q₈	—	26	1	no	—
114	Q₈	—	52	1	no	—
115	Q₈	—	52	1	no	—
116	C₂×C₄	—	4	1	no	—
117	C₂×C₄	—	26	1	no	—
118	C₂×C₄	—	26	1	no	—
119	C₂×C₄	—	52	1	no	—
120	C₂×C₄	#6127	1	1	yes	characteristic
121	C₂×C₄	D₄×D₁₃	1	1	yes	characteristic
122	C₂×C₄	D₄×D₁₃	1	1	yes	characteristic
123	C₈	—	4	1	no	—
124	C₈	—	4	1	no	—
125	C₈	—	13	2	no	—
126	C₈	—	26	1	no	—
127	C₈	—	52	1	no	—
128	C₂²	#88138	1	1	yes	characteristic
129	C₄	—	2	1	no	—
130	C₄	—	8	1	no	—
131	C₄	—	52	1	no	—
132	C₄	—	52	1	no	—
133	C₄	—	104	1	no	—
134	C₄	#88168	1	1	yes	characteristic
135	C₄	#88169	1	1	yes	characteristic
136	C₄	Q₁₆×D₁₃	1	1	yes	characteristic
137	C₄	#88172	1	1	yes	characteristic
138	C₂	#11718409	1	1	yes	characteristic
139	C₂	#11718454	1	1	yes	characteristic
140	C₂	#11718473	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11718752

C₂

yes

maximal, characteristic

#11718740

C₂

yes

maximal, characteristic

#11718510

C₂

yes

maximal, characteristic

#11718492

C₂

yes

maximal, characteristic

C₁₃×#333

C₂

yes

maximal, characteristic

#11718078

C₂

yes

maximal, characteristic

#11718071

C₂

yes

maximal, characteristic

C₁₃×C₄⋊Q₈

C₂²

yes

characteristic

C₂×Dic₅₂

—

#88123

C₂²

yes

characteristic

C₄×Dic₂₆

C₂²

yes

characteristic

C₁₃×C₄⋊C₈

C₂²

yes

characteristic

C₁₃×C₄⋊C₈

C₂²

yes

—

—

—

—

—

—

—

C₂²

yes

characteristic

C₄×#1055

C₂²

yes

characteristic

C₂×Q₈×C₁₃

—

C₂×Dic₂₆

—

C₂×Dic₂₆

D₄

yes

characteristic

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₄²×C₁₃

C₂³

yes

characteristic

C₄⋊Dic₁₃

—

C₄⋊Dic₁₃

—

C₄⋊Dic₁₃

D₄

yes

characteristic

#6101

—

C₄×Dic₁₃

—

C₂×#1055

—

C₂×#1055

D₄

yes

characteristic

C₂×#1055

D₄

yes

characteristic

Dic₅₂

—

#1692

—

maximal, Sylow

Q₈×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₂×D₄

yes

characteristic

C₂×C₄×C₁₃

C₂×D₄

yes

characteristic

C₂×C₄×C₁₃

#41

yes

characteristic

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

Dic₂₆

—

Dic₂₆

—

Dic₂₆

—

Dic₂₆

—

C₈×C₁₃

—

C₈×C₁₃

—

#1055

—

#1055

—

#1055

Q₁₆

yes

—

—

—

—

—

D₁₃

yes

characteristic

#332

—

C₂²×C₁₃

#121

yes

characteristic

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

C₂×Q₁₆

yes

C₄×C₁₃

yes

C₄×C₁₃

yes

C₄×C₁₃

yes

Dic₁₃

—

Dic₁₃

—

Dic₁₃

—

C₂×Q₁₆

—

C₄⋊Q₈

—

C₄⋊Q₈

C₂×D₁₃

yes

characteristic

C₄×Q₈

—

#107

—

#106

—

#106

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

C₂×D₁₃

yes

characteristic

C₄⋊C₈

C₂×D₁₃

yes

—

—

—

C₄×C₈

—

C₂×C₁₃

yes

C₂×C₁₃

yes

C₂×C₁₃

yes

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

Q₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

100

C₂×C₈

—

101

C₂×C₈

—

102

C₄⋊C₄

—

103

C₄⋊C₄

—

104

C₄⋊C₄

—

105

C₄⋊C₄

—

106

C₄⋊C₄

—

107

C₄⋊C₄

—

108

C₄²

—

109

C₄²

C₂²×D₁₃

yes

characteristic

110

C₁₃

#1692

yes

characteristic, complemented, Sylow

111

Q₈

—

112

Q₈

—

113

Q₈

—

114

Q₈

—

115

Q₈

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

#6127

yes

characteristic

121

C₂×C₄

D₄×D₁₃

yes

characteristic

122

C₂×C₄

D₄×D₁₃

yes

characteristic

123

C₈

—

124

C₈

—

125

C₈

—

126

C₈

—

127

C₈

—

128

C₂²

#88138

yes

characteristic

129

C₄

—

130

C₄

—

131

C₄

—

132

C₄

—

133

C₄

—

104

—

134

C₄

#88168

yes

characteristic

135

C₄

#88169

yes

characteristic

136

C₄

Q₁₆×D₁₃

yes

characteristic

137

C₄

#88172

yes

characteristic

138

C₂

#11718409

yes

characteristic

139

C₂

#11718454

yes

characteristic

140

C₂

#11718473

yes

characteristic

	subgroup	G/H
center	C₂²	#88138
commutator, cosocle	C₄²×C₁₃	C₂³
Frattini	C₄²	C₂²×D₁₃
Fitting	C₁₃×#333	C₂
socle, prime radical	C₂²×C₁₃	#121
hypercenter	#333	D₁₃
hypocenter	C₁₃	#1692
LCS	G ▷ C₄²×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #333

subgroup

G/H

center

C₂²

#88138

commutator, cosocle

C₄²×C₁₃

C₂³

Frattini

C₄²

C₂²×D₁₃

Fitting

C₁₃×#333

C₂

C₂²×C₁₃

D₁₃

C₁₃

G ▷ C₄²×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #333

N	H ≅ G/N	type
57. #1055	Q₁₆	semidirect
110. C₁₃	#1692	semidirect

H ≅ G/N

type

57. #1055

Q₁₆

semidirect

110. C₁₃

#1692

semidirect

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

subgroup	index
#11718752	2
#11718740	2
#11718510	2
#11718492	2
C₁₃×#333	2
#11718078	2
#11718071	2
#1692	13

subgroup

index

C₁₃×#333

Subgroups — #13114345

Conjugacy classes of subgroups

Complements

Maximal subgroups