Group #13116373 — subgroups

Subgroups — #13116373

Order 1664.

254 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 254 conjugacy classes of subgroups — too many to draw. Only its 95 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×#88058	C₂	1	2	yes	maximal
2	C₂×#88056	C₂	1	2	yes	maximal
3	#11718596	C₂	1	1	yes	maximal, characteristic
4	#11718590	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#336	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₂₆	C₂²	1	1	yes	characteristic
7	C₂²×C₈×C₁₃	C₂²	1	2	yes	—
8	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊Dic₁₃	—	2	2	no	—
10	C₂×C₄⋊Dic₁₃	C₂²	1	2	yes	—
11	C₂×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic
12	#88071	—	2	2	no	—
13	#88058	—	2	4	no	—
14	#88056	—	2	4	no	—
15	C₂²×C₄×C₁₃	D₄	1	2	yes	—
16	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
17	C₂²×Dic₁₃	—	2	1	no	—
18	C₂²×Dic₁₃	—	2	1	no	—
19	C₂²×Dic₁₃	—	2	2	no	—
20	C₂×Dic₂₆	—	2	2	no	—
21	C₂×Dic₂₆	—	2	2	no	—
22	C₂×Dic₂₆	—	2	1	no	—
23	C₂×Dic₂₆	Q₈	1	2	yes	—
24	C₂×C₈×C₁₃	—	2	2	no	—
25	C₂×C₈×C₁₃	—	2	2	no	—
26	C₂×C₈×C₁₃	D₄	1	4	yes	—
27	C₄²×C₁₃	—	2	2	no	—
28	C₄⋊Dic₁₃	—	2	2	no	—
29	C₄⋊Dic₁₃	—	2	2	no	—
30	C₄⋊Dic₁₃	—	2	2	no	—
31	C₄⋊Dic₁₃	—	4	4	no	—
32	#2095	—	13	1	no	maximal, Sylow
33	C₂³×C₁₃	C₂×D₄	1	1	yes	characteristic
34	C₂×C₄×C₁₃	—	2	2	no	—
35	C₂×C₄×C₁₃	—	2	2	no	—
36	C₂×C₄×C₁₃	Q₁₆	1	4	yes	—
37	C₂×C₄×C₁₃	C₂×D₄	1	2	yes	—
38	C₂×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
39	C₂×C₄×C₁₃	#41	1	2	yes	—
40	C₂×C₄×C₁₃	#41	1	1	yes	characteristic
41	C₂×Dic₁₃	—	2	2	no	—
42	C₂×Dic₁₃	—	4	1	no	—
43	C₂×Dic₁₃	—	4	1	no	—
44	C₂×Dic₁₃	—	4	2	no	—
45	C₂×Dic₁₃	—	4	1	no	—
46	C₂×Dic₁₃	—	4	4	no	—
47	C₂×Dic₁₃	—	4	2	no	—
48	Dic₂₆	—	2	4	no	—
49	Dic₂₆	—	4	2	no	—
50	C₈×C₁₃	—	2	4	no	—
51	C₂×#107	—	13	2	no	—
52	C₂×#103	—	13	2	no	—
53	#391	—	13	1	no	—
54	#384	—	13	1	no	—
55	#336	D₁₃	1	1	yes	characteristic
56	C₂²×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
57	C₂²×C₁₃	#123	1	1	yes	characteristic
58	C₂²×C₁₃	#127	1	1	yes	characteristic
59	C₂²×C₁₃	C₂×Q₁₆	1	2	yes	—
60	C₂²×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
61	C₄×C₁₃	—	2	4	no	—
62	C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
63	C₄×C₁₃	#123	1	2	yes	—
64	Dic₁₃	—	4	2	no	—
65	Dic₁₃	—	8	2	no	—
66	Dic₁₃	—	8	1	no	—
67	C₂²×Q₈	—	13	1	no	—
68	C₂²×C₈	C₂×D₁₃	1	2	yes	—
69	C₂×C₄⋊C₄	—	13	2	no	—
70	C₂×C₄⋊C₄	—	13	1	no	—
71	C₂×C₄⋊C₄	—	26	2	no	—
72	C₂×C₄²	C₂×D₁₃	1	1	yes	characteristic
73	#107	—	26	4	no	—
74	#103	—	26	4	no	—
75	#95	—	26	2	no	—
76	C₂×C₁₃	#399	1	1	yes	characteristic
77	C₂×C₁₃	#477	1	2	yes	—
78	C₂×C₁₃	#484	1	2	yes	—
79	C₂×C₁₃	#494	1	1	yes	characteristic
80	C₂×C₁₃	#496	1	1	yes	characteristic
81	C₂×Q₈	—	13	2	no	—
82	C₂×Q₈	—	26	1	no	—
83	C₂×Q₈	—	26	2	no	—
84	C₂×Q₈	—	26	2	no	—
85	C₂²×C₄	—	26	1	no	—
86	C₂²×C₄	—	26	1	no	—
87	C₂²×C₄	—	26	2	no	—
88	C₂²×C₄	D₅₂	1	2	yes	—
89	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
90	C₂×C₈	—	2	2	no	—
91	C₂×C₈	—	2	2	no	—
92	C₂×C₈	D₅₂	1	4	yes	—
93	C₄⋊C₄	—	26	2	no	—
94	C₄⋊C₄	—	26	2	no	—
95	C₄⋊C₄	—	26	2	no	—
96	C₄⋊C₄	—	52	4	no	—
97	C₄²	—	2	2	no	—
98	C₁₃	#2095	1	1	yes	characteristic, complemented, Sylow
99	C₂³	C₂×D₅₂	1	1	yes	characteristic
100	Q₈	—	26	4	no	—
101	Q₈	—	52	2	no	—
102	C₂×C₄	—	2	2	no	—
103	C₂×C₄	—	2	2	no	—
104	C₂×C₄	—	26	2	no	—
105	C₂×C₄	—	52	1	no	—
106	C₂×C₄	—	52	1	no	—
107	C₂×C₄	—	52	2	no	—
108	C₂×C₄	—	52	1	no	—
109	C₂×C₄	—	52	4	no	—
110	C₂×C₄	—	52	2	no	—
111	C₂×C₄	Dic₅₂	1	4	yes	—
112	C₂×C₄	C₂×D₅₂	1	2	yes	—
113	C₂×C₄	#6129	1	1	yes	characteristic
114	C₂×C₄	#6129	1	2	yes	—
115	C₂×C₄	Q₈×D₁₃	1	1	yes	characteristic
116	C₈	—	2	4	no	—
117	C₂²	#88128	1	1	yes	characteristic
118	C₂²	#88140	1	1	yes	characteristic
119	C₂²	#88151	1	1	yes	characteristic
120	C₂²	C₂×Dic₅₂	1	2	yes	—
121	C₂²	#88162	1	2	yes	—
122	C₄	—	2	4	no	—
123	C₄	—	52	2	no	—
124	C₄	—	104	2	no	—
125	C₄	—	104	1	no	—
126	C₄	#88140	1	2	yes	—
127	C₄	#88151	1	2	yes	—
128	C₂	#11718338	1	1	yes	characteristic
129	C₂	#11718360	1	1	yes	characteristic
130	C₂	#11718373	1	1	yes	characteristic
131	C₂	#11718383	1	2	yes	—
132	C₂	#11718511	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#88058

C₂

yes

maximal

C₂×#88056

C₂

yes

maximal

#11718596

C₂

yes

maximal, characteristic

#11718590

C₂

yes

maximal, characteristic

C₁₃×#336

C₂

yes

maximal, characteristic

C₂²×Dic₂₆

C₂²

yes

characteristic

C₂²×C₈×C₁₃

C₂²

yes

—

C₂×C₄²×C₁₃

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₃

—

C₂×C₄⋊Dic₁₃

C₂²

yes

—

C₂×C₄⋊Dic₁₃

C₂²

yes

—

—

—

C₂²×C₄×C₁₃

D₄

yes

—

C₂²×C₄×C₁₃

C₂³

yes

characteristic

C₂²×Dic₁₃

—

C₂²×Dic₁₃

—

C₂²×Dic₁₃

—

C₂×Dic₂₆

—

C₂×Dic₂₆

—

C₂×Dic₂₆

—

C₂×Dic₂₆

Q₈

yes

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

D₄

yes

—

C₄²×C₁₃

—

C₄⋊Dic₁₃

—

C₄⋊Dic₁₃

—

C₄⋊Dic₁₃

—

C₄⋊Dic₁₃

—

#2095

—

maximal, Sylow

C₂³×C₁₃

C₂×D₄

yes

characteristic

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

Q₁₆

yes

—

C₂×C₄×C₁₃

C₂×D₄

yes

—

C₂×C₄×C₁₃

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₃

#41

yes

—

C₂×C₄×C₁₃

#41

yes

characteristic

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

Dic₂₆

—

Dic₂₆

—

C₈×C₁₃

—

—

—

—

—

D₁₃

yes

characteristic

C₂²×C₁₃

C₂²⋊Q₈

yes

C₂²×C₁₃

yes

C₂²×C₁₃

yes

C₂²×C₁₃

C₂×Q₁₆

yes

—

C₂²×C₁₃

AGL(1,ℤ/8)

yes

—

C₄×C₁₃

—

C₄×C₁₃

C₂²⋊Q₈

yes

—

C₄×C₁₃

#123

yes

—

Dic₁₃

—

Dic₁₃

—

Dic₁₃

—

C₂²×Q₈

—

C₂²×C₈

C₂×D₁₃

yes

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂×D₁₃

yes

—

—

—

C₂×C₁₃

#399

yes

characteristic

C₂×C₁₃

#477

yes

—

C₂×C₁₃

#484

yes

—

C₂×C₁₃

yes

C₂×C₁₃

yes

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

D₅₂

yes

—

C₂²×C₄

C₂²×D₁₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

D₅₂

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₁₃

#2095

yes

characteristic, complemented, Sylow

C₂³

C₂×D₅₂

yes

characteristic

100

Q₈

—

101

Q₈

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

Dic₅₂

yes

—

112

C₂×C₄

C₂×D₅₂

yes

—

113

C₂×C₄

#6129

yes

characteristic

114

C₂×C₄

#6129

yes

—

115

C₂×C₄

Q₈×D₁₃

yes

characteristic

116

C₈

—

117

C₂²

#88128

yes

characteristic

118

C₂²

#88140

yes

characteristic

119

C₂²

#88151

yes

characteristic

120

C₂²

C₂×Dic₅₂

yes

—

121

C₂²

#88162

yes

—

122

C₄

—

123

C₄

—

124

C₄

—

104

—

125

C₄

—

104

—

126

C₄

#88140

yes

—

127

C₄

#88151

yes

—

128

C₂

#11718338

yes

characteristic

129

C₂

#11718360

yes

characteristic

130

C₂

#11718373

yes

characteristic

131

C₂

#11718383

yes

—

132

C₂

#11718511

yes

—

	subgroup	G/H
center	C₂³	C₂×D₅₂
commutator, cosocle	C₂²×C₄×C₁₃	C₂³
Frattini	C₂²×C₄	C₂²×D₁₃
Fitting	C₁₃×#336	C₂
socle, prime radical	C₂³×C₁₃	C₂×D₄
hypercenter	#336	D₁₃
hypocenter	C₁₃	#2095
LCS	G ▷ C₂²×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #336

subgroup

G/H

center

C₂³

C₂×D₅₂

commutator, cosocle

C₂²×C₄×C₁₃

C₂³

Frattini

C₂²×C₄

C₂²×D₁₃

Fitting

C₁₃×#336

C₂

socle, prime radical

C₂³×C₁₃

C₂×D₄

D₁₃

C₁₃

G ▷ C₂²×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #336

N	H ≅ G/N	type
98. C₁₃	#2095	semidirect

H ≅ G/N

type

98. C₁₃

#2095

semidirect

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

subgroup	index
C₂×#88058	2
C₂×#88056	2
#11718596	2
#11718590	2
C₁₃×#336	2
#2095	13

subgroup

index

C₁₃×#336

Subgroups — #13116373

Conjugacy classes of subgroups

Complements

Maximal subgroups