Group #13116450 — subgroups

Subgroups — #13116450

Order 1664.

228 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 109 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×#131	C₂	1	1	yes	maximal, characteristic
2	C₂×#88052	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#6090	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²⋊#6090	C₂	1	4	yes	maximal, complemented
5	C₂×C₁₃×#41	C₄	1	1	yes	characteristic
6	C₁₃×#131	—	2	2	no	—
7	C₁₃×#131	—	2	2	no	—
8	C₂×C₁₃×M₁₆	C₄	1	1	yes	characteristic
9	C₂×C₁₃×M₁₆	C₄	1	2	yes	—
10	C₂²×C₈×C₁₃	C₂²	1	2	yes	—
11	C₂²×C₈×C₁₃	C₂²	1	1	yes	characteristic
12	#88052	—	2	2	no	—
13	C₂×#6090	—	2	2	no	—
14	C₂×#6090	C₂²	1	2	yes	—
15	C₂×#6090	C₂²	1	2	yes	—
16	C₁₃×#41	—	2	2	no	—
17	C₁₃×#41	—	2	2	no	—
18	C₂×Q₈×C₁₃	C₈	1	1	yes	characteristic
19	C₂×D₄×C₁₃	C₈	1	2	yes	—
20	C₂×D₄×C₁₃	C₈	1	1	yes	characteristic
21	C₂²×C₄×C₁₃	C₂×C₄	1	2	yes	—
22	C₂²×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
23	C₁₃×M₁₆	—	2	2	no	—
24	C₁₃×M₁₆	—	2	4	no	—
25	C₂×C₈×C₁₃	—	2	2	no	—
26	C₂×C₈×C₁₃	—	2	2	no	—
27	C₂×C₈×C₁₃	C₂×C₄	1	2	yes	—
28	C₂×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
29	C₂×C₈×C₁₃	D₄	1	2	yes	—
30	C₂×C₈×C₁₃	D₄	1	2	yes	—
31	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
32	#6090	—	2	2	no	—
33	#6090	—	2	2	no	—
34	#2113	—	13	1	no	maximal, Sylow
35	C₂³×C₁₃	C₂×C₈	1	2	yes	—
36	C₂³×C₁₃	C₂×C₈	1	1	yes	characteristic
37	Q₈×C₁₃	—	2	2	no	—
38	D₄×C₁₃	—	2	4	no	—
39	D₄×C₁₃	—	2	2	no	—
40	C₂×C₄×C₁₃	—	2	2	no	—
41	C₂×C₄×C₁₃	—	2	2	no	—
42	C₂×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
43	C₂×C₄×C₁₃	C₂×C₈	1	2	yes	—
44	C₂×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
45	C₂×C₄×C₁₃	M₁₆	1	2	yes	—
46	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
47	C₈×C₁₃	—	2	2	no	—
48	C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
49	C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
50	C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
51	C₂×#131	D₁₃	1	1	yes	characteristic
52	C₂×M₃₂	—	13	1	no	—
53	C₂²×C₁₆	—	13	1	no	—
54	C₂²⋊C₁₆	—	13	4	no	—
55	C₂²×C₁₃	—	2	2	no	—
56	C₂²×C₁₃	—	2	2	no	—
57	C₂²×C₁₃	—	2	4	no	—
58	C₂²×C₁₃	C₂²⋊C₈	1	2	yes	—
59	C₂²×C₁₃	C₂²×C₈	1	1	yes	characteristic
60	C₄×C₁₃	—	2	2	no	—
61	C₄×C₁₃	C₂²⋊C₈	1	2	yes	—
62	C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
63	C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
64	C₂×#41	Dic₁₃	1	1	yes	characteristic
65	#131	—	2	2	no	—
66	#131	—	2	2	no	—
67	C₂×M₁₆	Dic₁₃	1	1	yes	characteristic
68	C₂×M₁₆	Dic₁₃	1	2	yes	—
69	C₂²×C₈	C₂×D₁₃	1	2	yes	—
70	C₂²×C₈	C₂×D₁₃	1	1	yes	characteristic
71	M₃₂	—	26	2	no	—
72	C₂×C₁₆	—	13	2	no	—
73	C₂×C₁₆	—	13	2	no	—
74	C₂×C₁₆	—	26	2	no	—
75	C₂×C₁₃	—	2	2	no	—
76	C₂×C₁₃	—	4	2	no	—
77	C₂×C₁₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
78	C₂×C₁₃	#504	1	2	yes	—
79	#41	—	2	2	no	—
80	#41	—	2	2	no	—
81	C₂×Q₈	#1055	1	1	yes	characteristic
82	C₂×D₄	#1055	1	2	yes	—
83	C₂×D₄	#1055	1	1	yes	characteristic
84	C₂²×C₄	C₂×Dic₁₃	1	2	yes	—
85	C₂²×C₄	C₂×Dic₁₃	1	1	yes	characteristic
86	M₁₆	—	2	2	no	—
87	M₁₆	—	2	4	no	—
88	C₂×C₈	—	2	2	no	—
89	C₂×C₈	—	2	2	no	—
90	C₂×C₈	C₂×Dic₁₃	1	2	yes	—
91	C₂×C₈	C₂×Dic₁₃	1	1	yes	characteristic
92	C₂×C₈	C₂²⋊D₁₃	1	2	yes	—
93	C₂×C₈	C₂²⋊D₁₃	1	2	yes	—
94	C₂×C₈	C₂²×D₁₃	1	1	yes	characteristic
95	C₁₆	—	26	2	no	—
96	C₁₆	—	26	2	no	—
97	C₁₃	#2113	1	1	yes	characteristic, complemented, Sylow
98	C₂³	C₂×#1055	1	2	yes	—
99	C₂³	C₂×#1055	1	1	yes	characteristic
100	Q₈	—	2	2	no	—
101	D₄	—	2	4	no	—
102	D₄	—	2	2	no	—
103	C₂×C₄	—	2	2	no	—
104	C₂×C₄	—	2	2	no	—
105	C₂×C₄	C₂×#1055	1	2	yes	—
106	C₂×C₄	C₂×#1055	1	1	yes	characteristic
107	C₂×C₄	#6099	1	2	yes	—
108	C₂×C₄	C₂²⋊Dic₁₃	1	2	yes	—
109	C₂×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
110	C₈	—	2	2	no	—
111	C₈	C₂²⋊Dic₁₃	1	2	yes	—
112	C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
113	C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
114	C₂²	—	2	2	no	—
115	C₂²	—	2	4	no	—
116	C₂²	—	2	2	no	—
117	C₂²	C₂²⋊#1055	1	2	yes	—
118	C₂²	C₂²×#1055	1	1	yes	characteristic
119	C₄	—	2	2	no	—
120	C₄	C₂²⋊#1055	1	2	yes	—
121	C₄	C₂×#6099	1	1	yes	characteristic
122	C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
123	C₂	—	2	2	no	—
124	C₂	—	4	2	no	—
125	C₂	#11718801	1	2	yes	—
126	C₂	C₂×C₂²⋊#1055	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₁₃×#131

C₂

yes

maximal, characteristic

C₂×#88052

C₂

yes

maximal, characteristic, complemented

C₂²×#6090

C₂

yes

maximal, characteristic, complemented

C₂²⋊#6090

C₂

yes

maximal, complemented

C₂×C₁₃×#41

C₄

yes

characteristic

C₁₃×#131

—

C₁₃×#131

—

C₂×C₁₃×M₁₆

C₄

yes

characteristic

C₂×C₁₃×M₁₆

C₄

yes

—

C₂²×C₈×C₁₃

C₂²

yes

—

C₂²×C₈×C₁₃

C₂²

yes

—

—

C₂²

yes

—

C₂×#6090

C₂²

yes

—

C₁₃×#41

—

C₁₃×#41

—

C₂×Q₈×C₁₃

C₈

yes

characteristic

C₂×D₄×C₁₃

C₈

yes

—

C₂×D₄×C₁₃

C₈

yes

characteristic

C₂²×C₄×C₁₃

C₂×C₄

yes

—

C₂²×C₄×C₁₃

C₂×C₄

yes

characteristic

C₁₃×M₁₆

—

C₁₃×M₁₆

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

C₂×C₄

yes

—

C₂×C₈×C₁₃

C₂×C₄

yes

characteristic

C₂×C₈×C₁₃

D₄

yes

—

C₂×C₈×C₁₃

D₄

yes

—

C₂×C₈×C₁₃

C₂³

yes

—

—

—

C₂³×C₁₃

C₂×C₈

yes

—

C₂³×C₁₃

C₂×C₈

yes

characteristic

Q₈×C₁₃

—

D₄×C₁₃

—

D₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₂²⋊C₄

yes

—

C₂×C₄×C₁₃

C₂×C₈

yes

—

C₂×C₄×C₁₃

C₂×C₈

yes

characteristic

C₂×C₄×C₁₃

M₁₆

yes

—

C₂×C₄×C₁₃

C₂²×C₄

yes

characteristic

C₈×C₁₃

—

C₈×C₁₃

C₂²⋊C₄

yes

—

C₈×C₁₃

C₂×D₄

yes

characteristic

C₈×C₁₃

C₂×D₄

yes

characteristic

C₂×#131

D₁₃

yes

characteristic

C₂×M₃₂

—

C₂²×C₁₆

—

C₂²⋊C₁₆

—

C₂²×C₁₃

—

C₂²×C₁₃

—

C₂²×C₁₃

—

C₂²×C₁₃

C₂²⋊C₈

yes

—

C₂²×C₁₃

C₂²×C₈

yes

characteristic

C₄×C₁₃

—

C₄×C₁₃

C₂²⋊C₈

yes

—

C₄×C₁₃

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₁₃

C₂×M₁₆

yes

characteristic

C₂×#41

Dic₁₃

yes

characteristic

#131

—

#131

—

C₂×M₁₆

Dic₁₃

yes

characteristic

C₂×M₁₆

Dic₁₃

yes

—

C₂²×C₈

C₂×D₁₃

yes

—

C₂²×C₈

C₂×D₁₃

yes

characteristic

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₃

—

C₂×C₁₃

—

C₂×C₁₃

C₂×C₂²⋊C₈

yes

characteristic

C₂×C₁₃

#504

yes

—

#41

—

#41

—

C₂×Q₈

#1055

yes

characteristic

C₂×D₄

#1055

yes

—

C₂×D₄

#1055

yes

characteristic

C₂²×C₄

C₂×Dic₁₃

yes

—

C₂²×C₄

C₂×Dic₁₃

yes

characteristic

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×Dic₁₃

yes

—

C₂×C₈

C₂×Dic₁₃

yes

characteristic

C₂×C₈

C₂²⋊D₁₃

yes

—

C₂×C₈

C₂²⋊D₁₃

yes

—

C₂×C₈

C₂²×D₁₃

yes

characteristic

C₁₆

—

C₁₆

—

C₁₃

#2113

yes

characteristic, complemented, Sylow

C₂³

C₂×#1055

yes

—

C₂³

C₂×#1055

yes

characteristic

100

Q₈

—

101

D₄

—

102

D₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

C₂×#1055

yes

—

106

C₂×C₄

C₂×#1055

yes

characteristic

107

C₂×C₄

#6099

yes

—

108

C₂×C₄

C₂²⋊Dic₁₃

yes

—

109

C₂×C₄

C₂²×Dic₁₃

yes

characteristic

110

C₈

—

111

C₈

C₂²⋊Dic₁₃

yes

—

112

C₈

C₂×C₂²⋊D₁₃

yes

characteristic

113

C₈

C₂×C₂²⋊D₁₃

yes

characteristic

114

C₂²

—

115

C₂²

—

116

C₂²

—

117

C₂²

C₂²⋊#1055

yes

—

118

C₂²

C₂²×#1055

yes

characteristic

119

C₄

—

120

C₄

C₂²⋊#1055

yes

—

121

C₄

C₂×#6099

yes

characteristic

122

C₄

C₂×C₂²⋊Dic₁₃

yes

characteristic

123

C₂

—

124

C₂

—

125

C₂

#11718801

yes

—

126

C₂

C₂×C₂²⋊#1055

yes

characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×D₁₃
commutator, socle	C₂²×C₁₃	C₂²×C₈
Fitting	C₂×C₁₃×#131	C₂
prime radical	C₂×C₁₃×#41	C₄
cosocle	C₂×C₈×C₁₃	C₂³
hypercenter	C₂×#131	D₁₃
hypocenter	C₁₃	#2113
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂×#131

subgroup

G/H

center, Frattini

C₂×C₈

C₂²×D₁₃

commutator, socle

C₂²×C₁₃

C₂²×C₈

Fitting

C₂×C₁₃×#131

C₂

prime radical

C₂×C₁₃×#41

C₄

cosocle

C₂×C₈×C₁₃

C₂³

D₁₃

C₁₃

G ▷ C₂²×C₁₃ ▷ C₁₃

C₁ ◁ C₂×C₈ ◁ C₂×#131

N	H ≅ G/N	type
2. C₂×#88052	C₂	semidirect
3. C₂²×#6090	C₂	semidirect
4. C₂²⋊#6090	C₂	semidirect
97. C₁₃	#2113	semidirect

H ≅ G/N

type

2. C₂×#88052

C₂

semidirect

3. C₂²×#6090

C₂

semidirect

4. C₂²⋊#6090

C₂

semidirect

97. C₁₃

#2113

semidirect

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

subgroup	index
C₂×C₁₃×#131	2
C₂×#88052	2
C₂²×#6090	2
C₂²⋊#6090	2
#2113	13

subgroup

index

C₂×C₁₃×#131

C₂×#88052

C₂²×#6090

C₂²⋊#6090

#2113

Subgroups — #13116450

Conjugacy classes of subgroups

Complements

Maximal subgroups