Group #13116447 — subgroups

Subgroups — #13116447

Order 1664.

260 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 117 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	C₂³×C₈×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#88052	C₂	1	2	yes	maximal, complemented
3	C₂²⋊#6090	C₂	1	4	yes	maximal, complemented
4	C₂³×C₄×C₁₃	C₄	1	1	yes	characteristic
5	C₂²×C₈×C₁₃	—	2	4	no	—
6	C₂²×C₈×C₁₃	C₄	1	1	yes	characteristic
7	C₂²×C₈×C₁₃	C₄	1	2	yes	—
8	C₂²×C₈×C₁₃	C₂²	1	2	yes	—
9	C₂²×C₈×C₁₃	C₂²	1	1	yes	characteristic
10	#88052	—	2	4	no	—
11	C₂×#6090	C₂²	1	4	yes	complemented
12	C₂⁴×C₁₃	C₈	1	1	yes	characteristic
13	C₂²×C₄×C₁₃	—	2	2	no	—
14	C₂²×C₄×C₁₃	—	2	2	no	—
15	C₂²×C₄×C₁₃	C₈	1	1	yes	characteristic
16	C₂²×C₄×C₁₃	C₈	1	2	yes	—
17	C₂²×C₄×C₁₃	C₂×C₄	1	2	yes	—
18	C₂²×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
19	C₂×C₈×C₁₃	—	2	2	no	—
20	C₂×C₈×C₁₃	—	2	4	no	—
21	C₂×C₈×C₁₃	—	2	4	no	—
22	C₂×C₈×C₁₃	C₂×C₄	1	2	yes	—
23	C₂×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
24	C₂×C₈×C₁₃	D₄	1	4	yes	—
25	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
26	#6090	—	2	4	no	—
27	#2112	—	13	1	no	maximal, Sylow
28	C₂³×C₁₃	—	2	2	no	—
29	C₂³×C₁₃	—	2	4	no	—
30	C₂³×C₁₃	C₂×C₈	1	1	yes	characteristic
31	C₂³×C₁₃	C₂×C₈	1	2	yes	—
32	C₂×C₄×C₁₃	—	2	2	no	—
33	C₂×C₄×C₁₃	—	2	4	no	—
34	C₂×C₄×C₁₃	—	2	2	no	—
35	C₂×C₄×C₁₃	—	2	2	no	—
36	C₂×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
37	C₂×C₄×C₁₃	C₂×C₈	1	2	yes	—
38	C₂×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
39	C₂×C₄×C₁₃	M₁₆	1	2	yes	—
40	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
41	C₈×C₁₃	—	2	2	no	—
42	C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
43	C₈×C₁₃	C₂×D₄	1	2	yes	—
44	C₂³×C₈	D₁₃	1	1	yes	characteristic
45	C₂×M₃₂	—	13	2	no	—
46	C₂²⋊C₁₆	—	13	4	no	—
47	C₂²×C₁₃	—	2	8	no	—
48	C₂²×C₁₃	—	2	2	no	—
49	C₂²×C₁₃	—	2	2	no	—
50	C₂²×C₁₃	—	2	2	no	—
51	C₂²×C₁₃	C₂²⋊C₈	1	2	yes	—
52	C₂²×C₁₃	M₃₂	1	4	yes	complemented
53	C₂²×C₁₃	C₂²×C₈	1	1	yes	characteristic
54	C₄×C₁₃	—	2	2	no	—
55	C₄×C₁₃	C₂²⋊C₈	1	2	yes	—
56	C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
57	C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
58	C₂³×C₄	Dic₁₃	1	1	yes	characteristic
59	C₂²×C₈	—	2	4	no	—
60	C₂²×C₈	Dic₁₃	1	1	yes	characteristic
61	C₂²×C₈	Dic₁₃	1	2	yes	—
62	C₂²×C₈	C₂×D₁₃	1	2	yes	—
63	C₂²×C₈	C₂×D₁₃	1	1	yes	characteristic
64	M₃₂	—	26	4	no	—
65	C₂×C₁₆	—	13	4	no	—
66	C₂×C₁₃	—	2	2	no	—
67	C₂×C₁₃	—	2	4	no	—
68	C₂×C₁₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
69	C₂×C₁₃	C₂×M₃₂	1	2	yes	—
70	C₂⁴	#1055	1	1	yes	characteristic
71	C₂²×C₄	—	2	2	no	—
72	C₂²×C₄	—	2	2	no	—
73	C₂²×C₄	#1055	1	1	yes	characteristic
74	C₂²×C₄	#1055	1	2	yes	—
75	C₂²×C₄	C₂×Dic₁₃	1	2	yes	—
76	C₂²×C₄	C₂×Dic₁₃	1	1	yes	characteristic
77	C₂×C₈	—	2	2	no	—
78	C₂×C₈	—	2	4	no	—
79	C₂×C₈	—	2	4	no	—
80	C₂×C₈	C₂×Dic₁₃	1	2	yes	—
81	C₂×C₈	C₂×Dic₁₃	1	1	yes	characteristic
82	C₂×C₈	C₂²⋊D₁₃	1	4	yes	—
83	C₂×C₈	C₂²×D₁₃	1	1	yes	characteristic
84	C₁₆	—	26	4	no	—
85	C₁₃	#2112	1	1	yes	characteristic, complemented, Sylow
86	C₂³	—	2	2	no	—
87	C₂³	—	2	4	no	—
88	C₂³	C₂×#1055	1	1	yes	characteristic
89	C₂³	C₂×#1055	1	2	yes	—
90	C₂×C₄	—	2	2	no	—
91	C₂×C₄	—	2	4	no	—
92	C₂×C₄	—	2	2	no	—
93	C₂×C₄	—	2	2	no	—
94	C₂×C₄	C₂×#1055	1	2	yes	—
95	C₂×C₄	C₂×#1055	1	1	yes	characteristic
96	C₂×C₄	#6099	1	2	yes	—
97	C₂×C₄	C₂²⋊Dic₁₃	1	2	yes	—
98	C₂×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
99	C₈	—	2	2	no	—
100	C₈	C₂²⋊Dic₁₃	1	2	yes	—
101	C₈	C₂×C₂²⋊D₁₃	1	2	yes	—
102	C₂²	—	2	8	no	—
103	C₂²	—	2	2	no	—
104	C₂²	—	2	2	no	—
105	C₂²	—	2	2	no	—
106	C₂²	#88052	1	4	yes	complemented
107	C₂²	C₂²⋊#1055	1	2	yes	—
108	C₂²	C₂²×#1055	1	1	yes	characteristic
109	C₄	—	2	2	no	—
110	C₄	C₂²⋊#1055	1	2	yes	—
111	C₄	C₂×#6099	1	1	yes	characteristic
112	C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
113	C₂	—	2	2	no	—
114	C₂	—	2	4	no	—
115	C₂	C₂×#88052	1	2	yes	—
116	C₂	C₂×C₂²⋊#1055	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂³×C₈×C₁₃

C₂

yes

maximal, characteristic

C₂×#88052

C₂

yes

maximal, complemented

C₂²⋊#6090

C₂

yes

maximal, complemented

C₂³×C₄×C₁₃

C₄

yes

characteristic

C₂²×C₈×C₁₃

—

C₂²×C₈×C₁₃

C₄

yes

characteristic

C₂²×C₈×C₁₃

C₄

yes

—

C₂²×C₈×C₁₃

C₂²

yes

—

C₂²×C₈×C₁₃

C₂²

yes

characteristic

#88052

—

C₂×#6090

C₂²

yes

complemented

C₂⁴×C₁₃

C₈

yes

characteristic

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

C₈

yes

characteristic

C₂²×C₄×C₁₃

C₈

yes

—

C₂²×C₄×C₁₃

C₂×C₄

yes

—

C₂²×C₄×C₁₃

C₂×C₄

yes

characteristic

C₂×C₈×C₁₃

—

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

C₂³

yes

—

—

C₂³×C₁₃

—

C₂³×C₁₃

—

C₂³×C₁₃

C₂×C₈

yes

characteristic

C₂³×C₁₃

C₂×C₈

yes

—

C₂×C₄×C₁₃

—

C₂×C₄×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

—

C₂³×C₈

D₁₃

yes

characteristic

C₂×M₃₂

—

C₂²⋊C₁₆

—

C₂²×C₁₃

—

C₂²×C₁₃

—

C₂²×C₁₃

—

C₂²×C₁₃

—

C₂²×C₁₃

C₂²⋊C₈

yes

—

C₂²×C₁₃

M₃₂

yes

complemented

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

C₂³×C₄

Dic₁₃

yes

characteristic

C₂²×C₈

—

C₂²×C₈

Dic₁₃

yes

characteristic

C₂²×C₈

Dic₁₃

yes

—

C₂²×C₈

C₂×D₁₃

yes

—

C₂²×C₈

C₂×D₁₃

yes

characteristic

M₃₂

—

C₂×C₁₆

—

C₂×C₁₃

—

C₂×C₁₃

—

C₂×C₁₃

C₂×C₂²⋊C₈

yes

characteristic

C₂×C₁₃

C₂×M₃₂

yes

—

C₂⁴

#1055

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

#1055

yes

characteristic

C₂²×C₄

#1055

yes

—

C₂²×C₄

C₂×Dic₁₃

yes

—

C₂²×C₄

C₂×Dic₁₃

yes

characteristic

C₂×C₈

—

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

characteristic

C₁₆

—

C₁₃

#2112

yes

characteristic, complemented, Sylow

C₂³

—

C₂³

—

C₂³

C₂×#1055

yes

characteristic

C₂³

C₂×#1055

yes

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×#1055

yes

—

C₂×C₄

C₂×#1055

yes

characteristic

C₂×C₄

#6099

yes

—

C₂×C₄

C₂²⋊Dic₁₃

yes

—

C₂×C₄

C₂²×Dic₁₃

yes

characteristic

C₈

—

100

C₈

C₂²⋊Dic₁₃

yes

—

101

C₈

C₂×C₂²⋊D₁₃

yes

—

102

C₂²

—

103

C₂²

—

104

C₂²

—

105

C₂²

—

106

C₂²

#88052

yes

complemented

107

C₂²

C₂²⋊#1055

yes

—

108

C₂²

C₂²×#1055

yes

characteristic

109

C₄

—

110

C₄

C₂²⋊#1055

yes

—

111

C₄

C₂×#6099

yes

characteristic

112

C₄

C₂×C₂²⋊Dic₁₃

yes

characteristic

113

C₂

—

114

C₂

—

115

C₂

C₂×#88052

yes

—

116

C₂

C₂×C₂²⋊#1055

yes

characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×D₁₃
commutator, socle	C₂²×C₁₃	C₂²×C₈
Fitting	C₂³×C₈×C₁₃	C₂
prime radical	C₂⁴×C₁₃	C₈
cosocle	C₂×C₈×C₁₃	C₂³
hypercenter	C₂³×C₈	D₁₃
hypocenter	C₁₃	#2112
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂³×C₈

subgroup

G/H

center, Frattini

C₂×C₈

C₂²×D₁₃

commutator, socle

C₂²×C₁₃

C₂²×C₈

Fitting

C₂³×C₈×C₁₃

C₂

prime radical

C₂⁴×C₁₃

C₈

cosocle

C₂×C₈×C₁₃

C₂³

hypercenter

C₂³×C₈

D₁₃

C₁₃

G ▷ C₂²×C₁₃ ▷ C₁₃

C₁ ◁ C₂×C₈ ◁ C₂³×C₈

N	H ≅ G/N	type
2. C₂×#88052	C₂	semidirect
3. C₂²⋊#6090	C₂	semidirect
11. C₂×#6090	C₂²	semidirect
52. C₂²×C₁₃	M₃₂	semidirect
85. C₁₃	#2112	semidirect
106. C₂²	#88052	semidirect

H ≅ G/N

type

2. C₂×#88052

C₂

semidirect

3. C₂²⋊#6090

C₂

semidirect

11. C₂×#6090

C₂²

semidirect

52. C₂²×C₁₃

M₃₂

semidirect

85. C₁₃

#2112

semidirect

106. C₂²

#88052

semidirect

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

subgroup	index
C₂³×C₈×C₁₃	2
C₂×#88052	2
C₂²⋊#6090	2
#2112	13

subgroup

index

C₂³×C₈×C₁₃

C₂×#88052

C₂²⋊#6090

#2112

Subgroups — #13116447

Conjugacy classes of subgroups

Complements

Maximal subgroups