Group #13116282 — subgroups

Subgroups — #13116282

Order 1664.

198 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 63 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×#106	C₂	1	1	yes	maximal, characteristic, complemented
2	#11718771	C₂	1	1	yes	maximal, characteristic
3	#11718627	C₂	1	2	yes	maximal
4	#11718144	C₂	1	1	yes	maximal, characteristic, complemented
5	#11718122	C₂	1	2	yes	maximal, complemented
6	C₂×#6127	C₂²	1	1	yes	characteristic
7	C₂²×C₈×C₁₃	C₂²	1	1	yes	characteristic
8	C₂×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
9	C₂×#6099	C₂²	1	2	yes	—
10	C₂×#6099	C₂²	1	1	yes	characteristic
11	C₁₃×#106	—	2	2	no	—
12	#88060	—	2	2	no	—
13	#88050	—	2	2	no	—
14	#88049	—	2	2	no	—
15	C₂²×C₄×C₁₃	—	2	2	no	—
16	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
17	C₂×C₂²⋊D₁₃	—	2	1	no	—
18	#6127	—	2	2	no	—
19	#6127	—	2	2	no	—
20	C₂×D₅₂	D₄	1	1	yes	characteristic
21	C₂×C₄×D₁₃	—	2	1	no	—
22	C₂×Dic₂₆	D₄	1	1	yes	characteristic
23	C₂×C₈×C₁₃	—	2	2	no	—
24	C₂×C₈×C₁₃	D₄	1	2	yes	—
25	C₁₃×C₄⋊C₄	—	2	2	no	—
26	C₁₃×C₄⋊C₄	—	2	2	no	—
27	#6099	—	2	2	no	—
28	#6099	—	2	2	no	—
29	#6099	—	2	2	no	—
30	C₂×#1055	—	2	2	no	—
31	C₂×#1055	—	2	1	no	—
32	#2079	—	13	1	no	maximal, Sylow
33	C₂³×C₁₃	#41	1	1	yes	characteristic
34	C₂²×D₁₃	—	2	1	no	—
35	C₂×C₄×C₁₃	—	4	2	no	—
36	C₂×C₄×C₁₃	—	8	2	no	—
37	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
38	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
39	C₂×C₄×C₁₃	#41	1	2	yes	—
40	C₂×C₄×C₁₃	#41	1	2	yes	—
41	C₂²⋊D₁₃	—	4	2	no	—
42	C₂×Dic₁₃	—	2	1	no	—
43	D₅₂	—	2	2	no	—
44	C₄×D₁₃	—	4	1	no	—
45	C₄×D₁₃	—	4	1	no	—
46	Dic₂₆	—	2	2	no	—
47	C₈×C₁₃	—	2	2	no	—
48	#1055	—	4	2	no	—
49	#1055	—	4	1	no	—
50	C₂×#106	D₁₃	1	1	yes	characteristic, complemented
51	#417	—	13	2	no	—
52	#408	—	13	1	no	—
53	#343	—	13	2	no	—
54	#341	—	13	1	no	—
55	C₂²×C₁₃	—	2	2	no	—
56	C₂²×C₁₃	#121	1	1	yes	characteristic
57	C₂²×C₁₃	#126	1	2	yes	—
58	C₂×D₁₃	—	4	1	no	—
59	C₂×D₁₃	—	4	2	no	—
60	C₄×C₁₃	—	8	2	no	—
61	C₄×C₁₃	#123	1	2	yes	—
62	C₄×C₁₃	#123	1	1	yes	characteristic
63	C₄×C₁₃	#124	1	1	yes	characteristic
64	Dic₁₃	—	4	1	no	—
65	C₂×#41	—	13	1	no	—
66	C₂×M₁₆	—	13	2	no	—
67	C₂×M₁₆	—	13	1	no	—
68	C₂²×C₈	C₂×D₁₃	1	1	yes	characteristic
69	C₂×C₄⋊C₄	C₂×D₁₃	1	2	yes	—
70	#106	—	2	2	no	—
71	#103	—	26	2	no	—
72	#102	—	26	2	no	—
73	C₂²⋊C₈	—	26	2	no	—
74	C₂×C₁₃	—	2	2	no	—
75	C₂×C₁₃	#397	1	1	yes	characteristic
76	C₂×C₁₃	#471	1	2	yes	—
77	D₁₃	—	8	1	no	—
78	#41	—	26	2	no	—
79	#41	—	26	2	no	—
80	C₂×Q₈	—	13	1	no	—
81	C₂×D₄	—	13	1	no	—
82	C₂×D₄	—	26	1	no	—
83	C₂²×C₄	—	2	2	no	—
84	C₂²×C₄	—	26	1	no	—
85	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
86	M₁₆	—	26	2	no	—
87	M₁₆	—	26	2	no	—
88	M₁₆	—	26	2	no	—
89	C₂×C₈	—	2	2	no	—
90	C₂×C₈	—	26	2	no	—
91	C₂×C₈	—	26	1	no	—
92	C₂×C₈	C₂²⋊D₁₃	1	2	yes	—
93	C₄⋊C₄	—	2	2	no	—
94	C₄⋊C₄	—	2	2	no	—
95	C₁₃	#2079	1	1	yes	characteristic, complemented, Sylow
96	C₂³	—	26	1	no	—
97	C₂³	#6129	1	1	yes	characteristic
98	Q₈	—	26	2	no	—
99	D₄	—	26	2	no	—
100	D₄	—	52	2	no	—
101	C₂×C₄	—	4	2	no	—
102	C₂×C₄	—	8	2	no	—
103	C₂×C₄	—	26	1	no	—
104	C₂×C₄	—	52	1	no	—
105	C₂×C₄	—	52	1	no	—
106	C₂×C₄	#6127	1	2	yes	—
107	C₂×C₄	D₄×D₁₃	1	1	yes	characteristic
108	C₂×C₄	#6131	1	2	yes	—
109	C₂×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
110	C₈	—	2	2	no	—
111	C₈	—	52	2	no	—
112	C₈	—	52	1	no	—
113	C₂²	—	2	2	no	—
114	C₂²	—	52	2	no	—
115	C₂²	—	52	1	no	—
116	C₂²	#88152	1	2	yes	—
117	C₂²	#88192	1	1	yes	characteristic
118	C₄	—	8	2	no	—
119	C₄	—	52	1	no	—
120	C₄	#88148	1	2	yes	—
121	C₄	#88183	1	1	yes	characteristic
122	C₄	#88201	1	1	yes	characteristic
123	C₂	—	2	2	no	—
124	C₂	—	104	1	no	—
125	C₂	#11718654	1	1	yes	characteristic
126	C₂	#11718838	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₁₃×#106

C₂

yes

maximal, characteristic, complemented

#11718771

C₂

yes

maximal, characteristic

#11718627

C₂

yes

maximal

#11718144

C₂

yes

maximal, characteristic, complemented

#11718122

C₂

yes

maximal, complemented

C₂×#6127

C₂²

yes

characteristic

C₂²×C₈×C₁₃

C₂²

yes

characteristic

C₂×C₁₃×C₄⋊C₄

C₂²

yes

—

C₂×#6099

C₂²

yes

—

C₂×#6099

C₂²

yes

characteristic

C₁₃×#106

—

#88060

—

#88050

—

#88049

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

C₂³

yes

characteristic

C₂×C₂²⋊D₁₃

—

#6127

—

#6127

—

C₂×D₅₂

D₄

yes

characteristic

C₂×C₄×D₁₃

—

C₂×Dic₂₆

D₄

yes

characteristic

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

D₄

yes

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

—

—

—

—

—

—

C₂³×C₁₃

yes

C₂²×D₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₂×D₄

yes

characteristic

C₂×C₄×C₁₃

C₂×D₄

yes

characteristic

C₂×C₄×C₁₃

#41

yes

—

C₂×C₄×C₁₃

#41

yes

—

C₂²⋊D₁₃

—

C₂×Dic₁₃

—

D₅₂

—

C₄×D₁₃

—

C₄×D₁₃

—

Dic₂₆

—

C₈×C₁₃

—

#1055

—

#1055

—

C₂×#106

D₁₃

yes

characteristic, complemented

—

—

—

—

C₂²×C₁₃

—

C₂²×C₁₃

#121

yes

characteristic

C₂²×C₁₃

#126

yes

—

C₂×D₁₃

—

C₂×D₁₃

—

C₄×C₁₃

—

C₄×C₁₃

#123

yes

—

C₄×C₁₃

yes

C₄×C₁₃

yes

Dic₁₃

—

C₂×#41

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

C₂×D₁₃

yes

characteristic

C₂×C₄⋊C₄

C₂×D₁₃

yes

—

#106

—

#103

—

#102

—

C₂²⋊C₈

—

C₂×C₁₃

—

C₂×C₁₃

#397

yes

characteristic

C₂×C₁₃

#471

yes

—

D₁₃

—

#41

—

#41

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₁₃

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂²⋊D₁₃

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₁₃

#2079

yes

characteristic, complemented, Sylow

C₂³

—

C₂³

#6129

yes

characteristic

Q₈

—

D₄

—

100

D₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

#6127

yes

—

107

C₂×C₄

D₄×D₁₃

yes

characteristic

108

C₂×C₄

#6131

yes

—

109

C₂×C₄

C₂×C₂²⋊D₁₃

yes

characteristic

110

C₈

—

111

C₈

—

112

C₈

—

113

C₂²

—

114

C₂²

—

115

C₂²

—

116

C₂²

#88152

yes

—

117

C₂²

#88192

yes

characteristic

118

C₄

—

119

C₄

—

120

C₄

#88148

yes

—

121

C₄

#88183

yes

characteristic

122

C₄

#88201

yes

characteristic

123

C₂

—

124

C₂

—

104

—

125

C₂

#11718654

yes

characteristic

126

C₂

#11718838

yes

—

	subgroup	G/H
center	C₂²	#88192
commutator, cosocle	C₂²×C₄×C₁₃	C₂³
Frattini	C₂²×C₄	C₂²×D₁₃
Fitting	C₂×C₁₃×#106	C₂
socle	C₂²×C₁₃	#121
prime radical	C₂×#6127	C₂²
hypercenter	C₂×#106	D₁₃
hypocenter	C₁₃	#2079
LCS	G ▷ C₂²×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#106

subgroup

G/H

center

C₂²

#88192

commutator, cosocle

C₂²×C₄×C₁₃

C₂³

Frattini

C₂²×C₄

C₂²×D₁₃

Fitting

C₂×C₁₃×#106

C₂

C₂²×C₁₃

C₂²

D₁₃

C₁₃

G ▷ C₂²×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#106

N	H ≅ G/N	type
1. C₂×C₁₃×#106	C₂	semidirect
4. #11718144	C₂	semidirect
5. #11718122	C₂	semidirect
50. C₂×#106	D₁₃	semidirect
95. C₁₃	#2079	semidirect

H ≅ G/N

type

1. C₂×C₁₃×#106

C₂

semidirect

4. #11718144

C₂

semidirect

5. #11718122

C₂

semidirect

50. C₂×#106

D₁₃

semidirect

95. C₁₃

#2079

semidirect

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

subgroup	index
C₂×C₁₃×#106	2
#11718771	2
#11718627	2
#11718144	2
#11718122	2
#2079	13

subgroup

index

C₂×C₁₃×#106

Subgroups — #13116282

Conjugacy classes of subgroups

Complements

Maximal subgroups