Group #13114954 — subgroups

Subgroups — #13114954

Order 1664.

216 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 93 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×#88054	C₂	1	2	yes	maximal
2	#11718593	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#336	C₂	1	1	yes	maximal, characteristic
4	#11718142	C₂	1	2	yes	maximal
5	#11718116	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₈×C₁₃	C₂²	1	2	yes	—
7	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
8	C₂×C₄×Dic₁₃	C₂²	1	1	yes	characteristic
9	C₂×C₄×Dic₁₃	C₂²	1	1	yes	characteristic
10	C₂²×#1055	C₂²	1	2	yes	—
11	#88071	C₄	1	2	yes	—
12	#88071	C₄	1	2	yes	—
13	#88054	—	2	4	no	—
14	C₂²×C₄×C₁₃	C₂×C₄	1	2	yes	—
15	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
16	C₂²×Dic₁₃	C₂×C₄	1	1	yes	characteristic
17	C₂²×Dic₁₃	C₂×C₄	1	1	yes	characteristic
18	C₂²×Dic₁₃	C₂×C₄	1	2	yes	—
19	C₂×C₈×C₁₃	—	2	2	no	—
20	C₂×C₈×C₁₃	—	2	2	no	—
21	C₂×C₈×C₁₃	—	2	2	no	—
22	C₄²×C₁₃	—	2	2	no	—
23	C₄×Dic₁₃	—	2	2	no	—
24	C₄×Dic₁₃	D₄	1	2	yes	—
25	C₄×Dic₁₃	Q₈	1	2	yes	—
26	C₂×#1055	—	2	2	no	—
27	C₂×#1055	—	2	2	no	—
28	C₂×#1055	—	2	2	no	—
29	#1832	—	13	1	no	maximal, Sylow
30	C₂³×C₁₃	C₂²×C₄	1	1	yes	characteristic
31	C₂×C₄×C₁₃	—	2	2	no	—
32	C₂×C₄×C₁₃	—	2	2	no	—
33	C₂×C₄×C₁₃	—	2	2	no	—
34	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
35	C₂×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
36	C₂×C₄×C₁₃	#41	1	2	yes	—
37	C₂×C₄×C₁₃	#41	1	2	yes	—
38	C₂×Dic₁₃	—	2	2	no	—
39	C₂×Dic₁₃	—	2	2	no	—
40	C₂×Dic₁₃	—	2	1	no	—
41	C₂×Dic₁₃	—	2	1	no	—
42	C₂×Dic₁₃	—	2	2	no	—
43	C₂×Dic₁₃	—	2	2	no	—
44	C₂×Dic₁₃	C₄⋊C₄	1	4	yes	—
45	C₈×C₁₃	—	4	2	no	—
46	#1055	—	4	2	no	—
47	C₂×C₄⋊C₈	—	13	2	no	—
48	#376	—	13	1	no	—
49	#336	—	13	2	no	—
50	#336	—	13	1	no	—
51	#336	D₁₃	1	1	yes	characteristic
52	C₂²×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
53	C₂²×C₁₃	#117	1	1	yes	characteristic
54	C₂²×C₁₃	#117	1	1	yes	characteristic
55	C₂²×C₁₃	#131	1	2	yes	—
56	C₂²×C₁₃	#131	1	2	yes	—
57	C₄×C₁₃	—	4	2	no	—
58	C₄×C₁₃	#124	1	2	yes	—
59	C₄×C₁₃	#125	1	2	yes	—
60	Dic₁₃	—	2	4	no	—
61	Dic₁₃	—	4	1	no	—
62	Dic₁₃	—	4	1	no	—
63	C₂²×C₈	—	13	2	no	—
64	C₂²×C₈	C₂×D₁₃	1	2	yes	—
65	C₂×C₄²	—	13	1	no	—
66	C₂×C₄²	—	13	1	no	—
67	C₂×C₄²	C₂×D₁₃	1	1	yes	characteristic
68	C₄⋊C₈	—	26	4	no	—
69	#95	—	13	2	no	—
70	#95	—	13	2	no	—
71	C₂×C₁₃	#382	1	1	yes	characteristic
72	C₂×C₁₃	#424	1	2	yes	—
73	C₂×C₁₃	#433	1	1	yes	characteristic
74	C₂×C₁₃	#433	1	1	yes	characteristic
75	C₂×C₁₃	#433	1	2	yes	—
76	C₂²×C₄	—	13	2	no	—
77	C₂²×C₄	—	13	1	no	—
78	C₂²×C₄	—	13	1	no	—
79	C₂²×C₄	C₄×D₁₃	1	2	yes	—
80	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
81	C₂×C₈	—	2	2	no	—
82	C₂×C₈	—	2	2	no	—
83	C₂×C₈	—	2	2	no	—
84	C₂×C₈	—	26	2	no	—
85	C₂×C₈	—	26	2	no	—
86	C₂×C₈	—	26	2	no	—
87	C₄²	—	2	2	no	—
88	C₄²	—	13	2	no	—
89	C₄²	—	13	2	no	—
90	C₄²	—	26	2	no	—
91	C₁₃	#1832	1	1	yes	characteristic, complemented, Sylow
92	C₂³	C₂×C₄×D₁₃	1	1	yes	characteristic
93	C₂×C₄	—	2	2	no	—
94	C₂×C₄	—	2	2	no	—
95	C₂×C₄	—	2	2	no	—
96	C₂×C₄	—	13	4	no	—
97	C₂×C₄	—	26	2	no	—
98	C₂×C₄	—	26	2	no	—
99	C₂×C₄	—	26	1	no	—
100	C₂×C₄	—	26	1	no	—
101	C₂×C₄	—	26	2	no	—
102	C₂×C₄	—	26	2	no	—
103	C₂×C₄	#6127	1	2	yes	—
104	C₂×C₄	D₄×D₁₃	1	1	yes	characteristic
105	C₂×C₄	#6129	1	2	yes	—
106	C₂×C₄	Q₈×D₁₃	1	1	yes	characteristic
107	C₈	—	4	2	no	—
108	C₈	—	52	2	no	—
109	C₂²	#88126	1	1	yes	characteristic
110	C₂²	#88131	1	1	yes	characteristic
111	C₂²	C₄⋊C₄×D₁₃	1	1	yes	characteristic
112	C₂²	#88155	1	2	yes	—
113	C₂²	#88161	1	2	yes	—
114	C₄	—	4	2	no	—
115	C₄	—	26	4	no	—
116	C₄	—	52	1	no	—
117	C₄	—	52	1	no	—
118	C₄	#88139	1	2	yes	—
119	C₄	#88143	1	2	yes	—
120	C₂	#11718311	1	1	yes	characteristic
121	C₂	#11718351	1	1	yes	characteristic
122	C₂	#11718370	1	1	yes	characteristic
123	C₂	#11718381	1	2	yes	—
124	C₂	#11718500	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#88054

C₂

yes

maximal

#11718593

C₂

yes

maximal, characteristic

C₁₃×#336

C₂

yes

maximal, characteristic

#11718142

C₂

yes

maximal

#11718116

C₂

yes

maximal, characteristic

C₂²×C₈×C₁₃

C₂²

yes

—

C₂×C₄²×C₁₃

C₂²

yes

characteristic

C₂×C₄×Dic₁₃

C₂²

yes

characteristic

C₂×C₄×Dic₁₃

C₂²

yes

characteristic

C₂²×#1055

C₂²

yes

—

#88071

C₄

yes

—

#88071

C₄

yes

—

#88054

—

C₂²×C₄×C₁₃

C₂×C₄

yes

—

C₂²×C₄×C₁₃

C₂³

yes

characteristic

C₂²×Dic₁₃

C₂×C₄

yes

characteristic

C₂²×Dic₁₃

C₂×C₄

yes

characteristic

C₂²×Dic₁₃

C₂×C₄

yes

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₄²×C₁₃

—

C₄×Dic₁₃

—

C₄×Dic₁₃

D₄

yes

—

C₄×Dic₁₃

Q₈

yes

—

—

—

—

—

C₂³×C₁₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

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×Dic₁₃

—

C₂×Dic₁₃

C₄⋊C₄

yes

—

C₈×C₁₃

—

#1055

—

C₂×C₄⋊C₈

—

—

—

—

D₁₃

yes

characteristic

C₂²×C₁₃

C₂×C₄⋊C₄

yes

C₂²×C₁₃

yes

C₂²×C₁₃

yes

C₂²×C₁₃

yes

—

C₂²×C₁₃

#131

yes

—

C₄×C₁₃

—

C₄×C₁₃

#124

yes

—

C₄×C₁₃

#125

yes

—

Dic₁₃

—

Dic₁₃

—

Dic₁₃

—

C₂²×C₈

—

C₂²×C₈

C₂×D₁₃

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₁₃

yes

characteristic

C₄⋊C₈

—

#95

—

#95

—

C₂×C₁₃

#382

yes

characteristic

C₂×C₁₃

#424

yes

—

C₂×C₁₃

yes

C₂×C₁₃

yes

C₂×C₁₃

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₄×D₁₃

yes

—

C₂²×C₄

C₂²×D₁₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₁₃

#1832

yes

characteristic, complemented, Sylow

C₂³

C₂×C₄×D₁₃

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

#6127

yes

—

104

C₂×C₄

D₄×D₁₃

yes

characteristic

105

C₂×C₄

#6129

yes

—

106

C₂×C₄

Q₈×D₁₃

yes

characteristic

107

C₈

—

108

C₈

—

109

C₂²

#88126

yes

characteristic

110

C₂²

#88131

yes

characteristic

111

C₂²

C₄⋊C₄×D₁₃

yes

characteristic

112

C₂²

#88155

yes

—

113

C₂²

#88161

yes

—

114

C₄

—

115

C₄

—

116

C₄

—

117

C₄

—

118

C₄

#88139

yes

—

119

C₄

#88143

yes

—

120

C₂

#11718311

yes

characteristic

121

C₂

#11718351

yes

characteristic

122

C₂

#11718370

yes

characteristic

123

C₂

#11718381

yes

—

124

C₂

#11718500

yes

—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₁₃
commutator, socle, prime radical	C₂³×C₁₃	C₂²×C₄
Fitting	C₁₃×#336	C₂
cosocle	C₂²×C₄×C₁₃	C₂³
hypercenter	#336	D₁₃
hypocenter	C₁₃	#1832
LCS	G ▷ C₂³×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ #336

subgroup

G/H

center, Frattini

C₂²×C₄

C₂²×D₁₃

commutator, socle, prime radical

C₂³×C₁₃

C₂²×C₄

Fitting

C₁₃×#336

C₂

cosocle

C₂²×C₄×C₁₃

C₂³

D₁₃

C₁₃

G ▷ C₂³×C₁₃ ▷ C₁₃

C₁ ◁ C₂²×C₄ ◁ #336

N	H ≅ G/N	type
91. C₁₃	#1832	semidirect

H ≅ G/N

type

91. C₁₃

#1832

semidirect

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

subgroup	index
C₂×#88054	2
#11718593	2
C₁₃×#336	2
#11718142	2
#11718116	2
#1832	13

subgroup

index

C₁₃×#336

Subgroups — #13114954

Conjugacy classes of subgroups

Complements

Maximal subgroups