Group #13131253 — subgroups

Subgroups — #13131253

Order 1664.

126 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 126 conjugacy classes of subgroups — too many to draw. Only its 64 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	#11718491	C₂	1	1	yes	maximal, characteristic
2	#11718260	C₂	1	1	yes	maximal, characteristic
3	#11718260	C₂	1	1	yes	maximal, characteristic
4	#11718258	C₂	1	1	yes	maximal, characteristic
5	#11718257	C₂	1	1	yes	maximal, characteristic
6	#11718231	C₂	1	1	yes	maximal, characteristic
7	C₄⋊#6092	C₂	1	1	yes	maximal, characteristic
8	C₄×Dic₂₆	C₄	1	1	yes	characteristic
9	C₂×#6092	C₂²	1	1	yes	characteristic
10	C₂×#6092	C₂²	1	1	yes	characteristic
11	C₂×#6092	C₂²	1	1	yes	characteristic
12	C₂×#6092	C₂²	1	1	yes	characteristic
13	C₁₃×C₄⋊C₈	C₄	1	1	yes	characteristic
14	#88054	C₄	1	1	yes	characteristic
15	#88054	C₄	1	1	yes	characteristic
16	C₈×Dic₁₃	C₂²	1	1	yes	characteristic
17	C₈×Dic₁₃	C₂²	1	1	yes	characteristic
18	C₄×#1055	C₂²	1	1	yes	characteristic
19	C₂×Dic₂₆	C₈	1	1	yes	characteristic
20	C₂×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
21	C₂×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
22	C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
23	C₄⋊Dic₁₃	C₈	1	1	yes	characteristic
24	#6101	C₈	1	1	yes	characteristic
25	#6101	C₈	1	1	yes	characteristic
26	C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
27	C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
28	C₂×#1055	C₂×C₄	1	1	yes	characteristic
29	C₂×#1055	C₂³	1	1	yes	characteristic
30	#6092	—	2	1	no	—
31	#6092	—	2	1	no	—
32	#6092	—	2	1	no	—
33	#6092	Q₈	1	2	yes	complemented
34	#2183	—	13	1	no	maximal, Sylow
35	C₂×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
36	C₂×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
37	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
38	C₂×Dic₁₃	C₂×C₈	1	1	yes	characteristic
39	C₂×Dic₁₃	C₂×C₈	1	1	yes	characteristic
40	C₂×Dic₁₃	C₂×C₈	1	1	yes	characteristic
41	C₂×Dic₁₃	C₂×C₈	1	1	yes	characteristic
42	Dic₂₆	—	2	2	no	—
43	C₈×C₁₃	—	2	1	no	—
44	C₈×C₁₃	—	2	1	no	—
45	#1055	—	2	1	no	—
46	#1055	C₂×Q₈	1	1	yes	characteristic
47	#1055	#41	1	1	yes	characteristic
48	C₈×Q₈	—	13	1	no	—
49	C₄⋊C₁₆	—	13	1	no	—
50	C₄⋊C₁₆	—	13	1	no	—
51	C₄⋊C₁₆	—	13	1	no	—
52	#346	—	13	1	no	—
53	#346	—	13	1	no	—
54	C₄×C₁₆	—	13	1	no	—
55	C₂²×C₁₃	C₂²×C₈	1	1	yes	characteristic
56	C₄×C₁₃	—	2	1	no	—
57	C₄×C₁₃	—	2	1	no	—
58	C₄×C₁₃	C₄×Q₈	1	1	yes	characteristic
59	C₄×C₁₃	#131	1	1	yes	characteristic
60	Dic₁₃	—	2	1	no	—
61	Dic₁₃	—	2	1	no	—
62	Dic₁₃	—	2	1	no	—
63	Dic₁₃	M₃₂	1	2	yes	—
64	C₄×Q₈	—	13	1	no	—
65	C₂×C₁₆	—	13	1	no	—
66	C₂×C₁₆	—	13	1	no	—
67	C₂×C₁₆	—	13	1	no	—
68	C₂×C₁₆	—	13	1	no	—
69	C₄⋊C₈	—	13	1	no	—
70	C₄⋊C₈	—	13	1	no	—
71	C₄⋊C₈	#261	1	1	yes	characteristic
72	C₄×C₈	—	13	1	no	—
73	C₄×C₈	—	13	1	no	—
74	C₄×C₈	—	13	1	no	—
75	C₂×C₁₃	C₈×Q₈	1	1	yes	characteristic
76	C₂×C₁₃	C₂×M₃₂	1	1	yes	characteristic
77	C₂×C₁₃	#504	1	1	yes	characteristic
78	C₂×Q₈	—	13	1	no	—
79	C₂×C₈	—	13	1	no	—
80	C₂×C₈	—	13	1	no	—
81	C₂×C₈	C₂×#261	1	1	yes	characteristic
82	C₂×C₈	C₂×#261	1	1	yes	characteristic
83	C₄⋊C₄	—	13	1	no	—
84	C₄⋊C₄	—	13	1	no	—
85	C₄⋊C₄	—	13	1	no	—
86	C₄²	—	13	1	no	—
87	C₄²	—	13	1	no	—
88	C₄²	C₂×#261	1	1	yes	characteristic
89	C₁₆	—	13	2	no	—
90	C₁₆	—	26	1	no	—
91	C₁₆	—	26	1	no	—
92	C₁₆	—	26	1	no	—
93	C₁₃	#2183	1	1	yes	characteristic, complemented, Sylow
94	Q₈	—	26	2	no	—
95	C₂×C₄	—	13	1	no	—
96	C₂×C₄	—	13	1	no	—
97	C₂×C₄	—	13	1	no	—
98	C₂×C₄	—	13	1	no	—
99	C₂×C₄	D₁₃⋊C₈	1	1	yes	characteristic
100	C₂×C₄	D₁₃⋊C₈	1	1	yes	characteristic
101	C₂×C₄	C₂²×#261	1	1	yes	characteristic
102	C₈	—	2	1	no	—
103	C₈	—	2	1	no	—
104	C₈	—	13	1	no	—
105	C₈	—	13	1	no	—
106	C₈	—	26	1	no	—
107	C₂²	C₂×D₁₃⋊C₈	1	1	yes	characteristic
108	C₄	—	2	1	no	—
109	C₄	—	2	1	no	—
110	C₄	—	13	2	no	—
111	C₄	—	26	1	no	—
112	C₄	—	26	1	no	—
113	C₄	—	26	1	no	—
114	C₄	#88238	1	1	yes	characteristic
115	C₄	Q₈×#261	1	1	yes	characteristic
116	C₂	#11719074	1	1	yes	characteristic
117	C₂	D₁₃⋊M₃₂	1	1	yes	characteristic
118	C₂	#11719096	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11718491

C₂

yes

maximal, characteristic

#11718260

C₂

yes

maximal, characteristic

#11718260

C₂

yes

maximal, characteristic

#11718258

C₂

yes

maximal, characteristic

#11718257

C₂

yes

maximal, characteristic

#11718231

C₂

yes

maximal, characteristic

C₄⋊#6092

C₂

yes

maximal, characteristic

C₄×Dic₂₆

C₄

yes

characteristic

C₂×#6092

C₂²

yes

characteristic

C₂×#6092

C₂²

yes

characteristic

C₂×#6092

C₂²

yes

characteristic

C₂×#6092

C₂²

yes

characteristic

C₁₃×C₄⋊C₈

C₄

yes

characteristic

#88054

C₄

yes

characteristic

#88054

C₄

yes

characteristic

C₈×Dic₁₃

C₂²

yes

characteristic

C₈×Dic₁₃

C₂²

yes

characteristic

C₄×#1055

C₂²

yes

characteristic

C₂×Dic₂₆

C₈

yes

characteristic

C₂×C₈×C₁₃

C₂×C₄

yes

characteristic

C₂×C₈×C₁₃

C₂×C₄

yes

characteristic

C₄²×C₁₃

C₂×C₄

yes

characteristic

C₄⋊Dic₁₃

C₈

yes

characteristic

#6101

C₈

yes

characteristic

#6101

C₈

yes

characteristic

C₄×Dic₁₃

C₂×C₄

yes

characteristic

C₄×Dic₁₃

C₂×C₄

yes

characteristic

C₂×#1055

C₂×C₄

yes

characteristic

C₂×#1055

C₂³

yes

—

—

—

Q₈

yes

complemented

#2183

—

maximal, Sylow

C₂×C₄×C₁₃

C₂×C₈

yes

characteristic

C₂×C₄×C₁₃

C₂×C₈

yes

characteristic

C₂×C₄×C₁₃

C₂²×C₄

yes

characteristic

C₂×Dic₁₃

C₂×C₈

yes

characteristic

C₂×Dic₁₃

C₂×C₈

yes

characteristic

C₂×Dic₁₃

C₂×C₈

yes

characteristic

C₂×Dic₁₃

C₂×C₈

yes

characteristic

Dic₂₆

—

C₈×C₁₃

—

C₈×C₁₃

—

#1055

—

#1055

C₂×Q₈

yes

yes

C₈×Q₈

—

C₄⋊C₁₆

—

C₄⋊C₁₆

—

C₄⋊C₁₆

—

#346

—

#346

—

C₄×C₁₆

—

C₂²×C₁₃

C₂²×C₈

yes

characteristic

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

C₄×Q₈

yes

characteristic

C₄×C₁₃

#131

yes

characteristic

Dic₁₃

—

Dic₁₃

—

Dic₁₃

—

Dic₁₃

M₃₂

yes

—

C₄×Q₈

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

#261

yes

characteristic

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₂×C₁₃

C₈×Q₈

yes

characteristic

C₂×C₁₃

C₂×M₃₂

yes

characteristic

C₂×C₁₃

#504

yes

characteristic

C₂×Q₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

yes

C₂×C₈

yes

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

—

C₄²

C₂×#261

yes

characteristic

C₁₆

—

C₁₆

—

C₁₆

—

C₁₆

—

C₁₃

#2183

yes

characteristic, complemented, Sylow

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

D₁₃⋊C₈

yes

characteristic

100

C₂×C₄

D₁₃⋊C₈

yes

characteristic

101

C₂×C₄

C₂²×#261

yes

characteristic

102

C₈

—

103

C₈

—

104

C₈

—

105

C₈

—

106

C₈

—

107

C₂²

C₂×D₁₃⋊C₈

yes

characteristic

108

C₄

—

109

C₄

—

110

C₄

—

111

C₄

—

112

C₄

—

113

C₄

—

114

C₄

#88238

yes

characteristic

115

C₄

Q₈×#261

yes

characteristic

116

C₂

#11719074

yes

characteristic

117

C₂

D₁₃⋊M₃₂

yes

characteristic

118

C₂

#11719096

yes

characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#261
commutator, socle, prime radical	C₂²×C₁₃	C₂²×C₈
Fitting	C₁₃×C₄⋊C₈	C₄
cosocle	C₂×#1055	C₂³
hypercenter	C₄⋊C₈	#261
hypocenter	C₁₃	#2183
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄⋊C₈

subgroup

G/H

center, Frattini

C₂×C₄

C₂²×#261

commutator, socle, prime radical

C₂²×C₁₃

C₂²×C₈

Fitting

C₁₃×C₄⋊C₈

C₄

C₂³

C₄⋊C₈

C₁₃

G ▷ C₂²×C₁₃ ▷ C₁₃

C₁ ◁ C₂×C₄ ◁ C₄⋊C₈

N	H ≅ G/N	type
33. #6092	Q₈	semidirect
93. C₁₃	#2183	semidirect

H ≅ G/N

type

33. #6092

Q₈

semidirect

93. C₁₃

#2183

semidirect

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

subgroup	index
#11718491	2
#11718260	2
#11718258	2
#11718257	2
#11718231	2
C₄⋊#6092	2
#2183	13

subgroup

index

Subgroups — #13131253

Conjugacy classes of subgroups

Complements

Maximal subgroups