Group #13114952 — subgroups

Subgroups — #13114952

Order 1664.

260 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 129 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	C₄²×Dic₁₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄⋊#1055	C₂	1	1	yes	maximal, characteristic
4	#11718142	C₂	1	4	yes	maximal
5	C₂²×C₈×C₁₃	C₂²	1	2	yes	—
6	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
7	C₂×C₄×Dic₁₃	C₄	1	1	yes	characteristic
8	C₂×C₄×Dic₁₃	C₄	1	2	yes	—
9	C₂×C₄×Dic₁₃	C₄	1	1	yes	characteristic
10	C₂×C₄×Dic₁₃	C₂²	1	2	yes	—
11	C₂²×#1055	C₂²	1	2	yes	—
12	C₁₃×C₄⋊C₈	—	2	2	no	—
13	C₄⋊#1055	—	2	2	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	C₂³	1	1	yes	characteristic
17	C₂²×Dic₁₃	C₂×C₄	1	2	yes	—
18	C₂²×Dic₁₃	C₂×C₄	1	2	yes	—
19	C₂×C₈×C₁₃	—	2	2	no	—
20	C₂×C₈×C₁₃	—	2	4	no	—
21	C₄²×C₁₃	D₄	1	2	yes	—
22	C₄²×C₁₃	Q₈	1	2	yes	—
23	C₄×Dic₁₃	—	2	2	no	—
24	C₄×Dic₁₃	—	2	2	no	—
25	C₄×Dic₁₃	—	2	2	no	—
26	C₄×Dic₁₃	—	2	4	no	—
27	C₄×Dic₁₃	C₈	1	4	yes	complemented
28	C₂×#1055	—	2	2	no	—
29	C₂×#1055	—	2	4	no	—
30	#1831	—	13	1	no	maximal, Sylow
31	C₂³×C₁₃	C₂²×C₄	1	1	yes	characteristic
32	C₂×C₄×C₁₃	—	2	2	no	—
33	C₂×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
34	C₂×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
35	C₂×C₄×C₁₃	C₂×C₈	1	2	yes	—
36	C₂×C₄×C₁₃	M₁₆	1	2	yes	—
37	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
38	C₂×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
39	C₂×C₄×C₁₃	#41	1	2	yes	—
40	C₂×C₄×C₁₃	#41	1	2	yes	—
41	C₂×Dic₁₃	—	2	2	no	—
42	C₂×Dic₁₃	—	2	2	no	—
43	C₂×Dic₁₃	—	2	2	no	—
44	C₂×Dic₁₃	—	2	2	no	—
45	C₂×Dic₁₃	C₂×C₈	1	4	yes	—
46	C₂×Dic₁₃	M₁₆	1	4	yes	—
47	C₈×C₁₃	—	4	2	no	—
48	#1055	—	4	2	no	—
49	C₂×C₄⋊C₈	—	13	1	no	—
50	C₂×C₄⋊C₈	D₁₃	1	1	yes	characteristic
51	C₄³	—	13	1	no	—
52	#336	—	13	4	no	—
53	C₂²×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
54	C₂²×C₁₃	#117	1	2	yes	—
55	C₂²×C₁₃	C₂²×C₈	1	1	yes	characteristic
56	C₂²×C₁₃	C₂×M₁₆	1	1	yes	characteristic
57	C₂²×C₁₃	C₂×M₁₆	1	2	yes	—
58	C₄×C₁₃	—	2	2	no	—
59	C₄×C₁₃	C₄⋊C₈	1	4	yes	—
60	C₄×C₁₃	#124	1	1	yes	characteristic
61	C₄×C₁₃	#124	1	1	yes	characteristic
62	C₄×C₁₃	#125	1	2	yes	—
63	Dic₁₃	—	2	4	no	—
64	Dic₁₃	—	2	4	no	—
65	C₂²×C₈	—	13	2	no	—
66	C₂²×C₈	C₂×D₁₃	1	2	yes	—
67	C₂×C₄²	—	13	1	no	—
68	C₂×C₄²	—	13	2	no	—
69	C₂×C₄²	—	13	1	no	—
70	C₂×C₄²	—	13	2	no	—
71	C₂×C₄²	C₂×D₁₃	1	1	yes	characteristic
72	C₄⋊C₈	—	2	2	no	—
73	C₄⋊C₈	—	26	2	no	—
74	C₂×C₁₃	#382	1	1	yes	characteristic
75	C₂×C₁₃	C₂×C₄⋊C₈	1	1	yes	characteristic
76	C₂×C₁₃	#423	1	1	yes	characteristic
77	C₂×C₁₃	#431	1	2	yes	—
78	C₂×C₁₃	#432	1	2	yes	—
79	C₂²×C₄	—	13	2	no	—
80	C₂²×C₄	—	13	2	no	—
81	C₂²×C₄	C₄×D₁₃	1	1	yes	characteristic
82	C₂²×C₄	C₄×D₁₃	1	1	yes	characteristic
83	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
84	C₂×C₈	—	2	4	no	—
85	C₂×C₈	—	2	2	no	—
86	C₂×C₈	—	26	4	no	—
87	C₂×C₈	—	26	2	no	—
88	C₄²	—	13	4	no	—
89	C₄²	—	26	4	no	—
90	C₄²	—	26	2	no	—
91	C₄²	—	26	2	no	—
92	C₄²	—	26	2	no	—
93	C₄²	Dic₂₆	1	2	yes	—
94	C₄²	C₂²⋊D₁₃	1	2	yes	—
95	C₁₃	#1831	1	1	yes	characteristic, complemented, Sylow
96	C₂³	C₂×C₄×D₁₃	1	1	yes	characteristic
97	C₂×C₄	—	2	2	no	—
98	C₂×C₄	—	13	4	no	—
99	C₂×C₄	—	13	4	no	—
100	C₂×C₄	—	26	2	no	—
101	C₂×C₄	—	26	2	no	—
102	C₂×C₄	—	26	2	no	—
103	C₂×C₄	—	26	2	no	—
104	C₂×C₄	C₈×D₁₃	1	2	yes	—
105	C₂×C₄	#6094	1	2	yes	—
106	C₂×C₄	#6101	1	2	yes	—
107	C₂×C₄	#6101	1	2	yes	—
108	C₂×C₄	C₂×Dic₂₆	1	1	yes	characteristic
109	C₂×C₄	#6129	1	2	yes	—
110	C₂×C₄	#6131	1	2	yes	—
111	C₂×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
112	C₈	—	4	2	no	—
113	C₈	—	52	2	no	—
114	C₂²	#88146	1	2	yes	—
115	C₂²	C₂×C₈×D₁₃	1	1	yes	characteristic
116	C₂²	C₂×#6094	1	1	yes	characteristic
117	C₂²	M₁₆×D₁₃	1	2	yes	—
118	C₂²	C₂×#6101	1	1	yes	characteristic
119	C₄	—	2	2	no	—
120	C₄	—	26	4	no	—
121	C₄	—	26	4	no	—
122	C₄	#88054	1	4	yes	—
123	C₄	#88144	1	2	yes	—
124	C₄	#88190	1	1	yes	characteristic
125	C₄	#88201	1	1	yes	characteristic
126	C₂	#11718494	1	2	yes	—
127	C₂	#11718496	1	2	yes	—
128	C₂	#11718638	1	1	yes	characteristic
129	C₂	C₂×#88054	1	1	yes	characteristic
130	C₂	#11718779	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₁₃×C₄⋊C₈

C₂

yes

maximal, characteristic

C₄²×Dic₁₃

C₂

yes

maximal, characteristic

C₂×C₄⋊#1055

C₂

yes

maximal, characteristic

#11718142

C₂

yes

maximal

C₂²×C₈×C₁₃

C₂²

yes

—

C₂×C₄²×C₁₃

C₂²

yes

characteristic

C₂×C₄×Dic₁₃

C₄

yes

characteristic

C₂×C₄×Dic₁₃

C₄

yes

—

C₂×C₄×Dic₁₃

C₄

yes

characteristic

C₂×C₄×Dic₁₃

C₂²

yes

—

C₂²×#1055

C₂²

yes

—

C₁₃×C₄⋊C₈

—

C₄⋊#1055

—

C₂²×C₄×C₁₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₃

C₂³

yes

characteristic

C₂²×Dic₁₃

C₂×C₄

yes

—

C₂²×Dic₁₃

C₂×C₄

yes

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₄²×C₁₃

D₄

yes

—

C₄²×C₁₃

Q₈

yes

—

C₄×Dic₁₃

—

C₄×Dic₁₃

—

C₄×Dic₁₃

—

C₄×Dic₁₃

—

C₄×Dic₁₃

C₈

yes

—

—

—

C₂³×C₁₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₄⋊C₄

yes

—

C₂×C₄×C₁₃

C₄⋊C₄

yes

—

C₂×C₄×C₁₃

C₂×C₈

yes

—

C₂×C₄×C₁₃

M₁₆

yes

—

C₂×C₄×C₁₃

C₂×D₄

yes

characteristic

C₂×C₄×C₁₃

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₃

#41

yes

—

C₂×C₄×C₁₃

#41

yes

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

C₂×C₈

yes

—

C₂×Dic₁₃

M₁₆

yes

—

C₈×C₁₃

—

#1055

—

C₂×C₄⋊C₈

—

C₂×C₄⋊C₈

D₁₃

yes

characteristic

C₄³

—

#336

—

C₂²×C₁₃

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₁₃

#117

yes

—

C₂²×C₁₃

C₂²×C₈

yes

characteristic

C₂²×C₁₃

C₂×M₁₆

yes

characteristic

C₂²×C₁₃

C₂×M₁₆

yes

—

C₄×C₁₃

—

C₄×C₁₃

C₄⋊C₈

yes

—

C₄×C₁₃

yes

C₄×C₁₃

yes

C₄×C₁₃

yes

—

Dic₁₃

—

Dic₁₃

—

C₂²×C₈

—

C₂²×C₈

C₂×D₁₃

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₁₃

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

C₂×C₁₃

#382

yes

characteristic

C₂×C₁₃

C₂×C₄⋊C₈

yes

C₂×C₁₃

yes

C₂×C₁₃

yes

—

C₂×C₁₃

#432

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₄×D₁₃

yes

characteristic

C₂²×C₄

C₄×D₁₃

yes

characteristic

C₂²×C₄

C₂²×D₁₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₄²

Dic₂₆

yes

—

C₄²

C₂²⋊D₁₃

yes

—

C₁₃

#1831

yes

characteristic, complemented, Sylow

C₂³

C₂×C₄×D₁₃

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

C₈×D₁₃

yes

—

105

C₂×C₄

#6094

yes

—

106

C₂×C₄

#6101

yes

—

107

C₂×C₄

#6101

yes

—

108

C₂×C₄

C₂×Dic₂₆

yes

characteristic

109

C₂×C₄

#6129

yes

—

110

C₂×C₄

#6131

yes

—

111

C₂×C₄

C₂×C₂²⋊D₁₃

yes

characteristic

112

C₈

—

113

C₈

—

114

C₂²

#88146

yes

—

115

C₂²

C₂×C₈×D₁₃

yes

characteristic

116

C₂²

C₂×#6094

yes

characteristic

117

C₂²

M₁₆×D₁₃

yes

—

118

C₂²

C₂×#6101

yes

characteristic

119

C₄

—

120

C₄

—

121

C₄

—

122

C₄

#88054

yes

—

123

C₄

#88144

yes

—

124

C₄

#88190

yes

characteristic

125

C₄

#88201

yes

characteristic

126

C₂

#11718494

yes

—

127

C₂

#11718496

yes

—

128

C₂

#11718638

yes

characteristic

129

C₂

C₂×#88054

yes

characteristic

130

C₂

#11718779

yes

characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₁₃
commutator	C₂²×C₁₃	C₂²×C₈
Fitting	C₂×C₁₃×C₄⋊C₈	C₂
socle, prime radical	C₂³×C₁₃	C₂²×C₄
cosocle	C₂²×C₄×C₁₃	C₂³
hypercenter	C₂×C₄⋊C₈	D₁₃
hypocenter	C₁₃	#1831
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₈

subgroup

G/H

center, Frattini

C₂²×C₄

C₂²×D₁₃

commutator

C₂²×C₁₃

C₂²×C₈

Fitting

C₂×C₁₃×C₄⋊C₈

C₂

socle, prime radical

C₂³×C₁₃

C₂²×C₄

cosocle

C₂²×C₄×C₁₃

C₂³

hypercenter

C₂×C₄⋊C₈

D₁₃

C₁₃

G ▷ C₂²×C₁₃ ▷ C₁₃

C₁ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₈

N	H ≅ G/N	type
27. C₄×Dic₁₃	C₈	semidirect
95. C₁₃	#1831	semidirect

H ≅ G/N

type

27. C₄×Dic₁₃

C₈

semidirect

95. C₁₃

#1831

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
C₄²×Dic₁₃	2
C₂×C₄⋊#1055	2
#11718142	2
#1831	13

subgroup

index

C₂×C₁₃×C₄⋊C₈

C₄²×Dic₁₃

C₂×C₄⋊#1055

#11718142

#1831

Subgroups — #13114952

Conjugacy classes of subgroups

Complements

Maximal subgroups