Group #13114737 — subgroups

Subgroups — #13114737

Order 1664.

228 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 109 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×#88062	C₂	1	2	yes	maximal
2	M₁₆×Dic₁₃	C₂	1	2	yes	maximal
3	C₂×C₈×Dic₁₃	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#341	C₂	1	1	yes	maximal, characteristic
5	#11718144	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₃×M₁₆	C₂²	1	2	yes	—
7	C₂²×C₈×C₁₃	C₂²	1	1	yes	characteristic
8	C₂×C₄×Dic₁₃	C₂²	1	1	yes	characteristic
9	C₂×#6099	C₂²	1	2	yes	—
10	C₂²×#1055	C₂²	1	1	yes	characteristic
11	#88062	C₄	1	8	yes	complemented
12	#88055	—	2	2	no	—
13	C₈×Dic₁₃	—	2	2	no	—
14	C₈×Dic₁₃	C₄	1	4	yes	—
15	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
16	C₂²×Dic₁₃	Q₈	1	2	yes	—
17	C₁₃×M₁₆	—	2	2	no	—
18	C₁₃×M₁₆	C₂×C₄	1	4	yes	—
19	C₂×C₈×C₁₃	—	2	2	no	—
20	C₂×C₈×C₁₃	—	2	2	no	—
21	C₂×C₈×C₁₃	C₂×C₄	1	2	yes	—
22	C₄×Dic₁₃	C₂×C₄	1	2	yes	—
23	C₄×Dic₁₃	D₄	1	1	yes	characteristic
24	C₄×Dic₁₃	D₄	1	1	yes	characteristic
25	#6099	—	2	2	no	—
26	#6099	C₂×C₄	1	4	yes	—
27	C₂×#1055	—	2	2	no	—
28	C₂×#1055	C₂×C₄	1	2	yes	—
29	C₂×#1055	C₂×C₄	1	4	yes	—
30	C₄×#108	—	13	1	no	maximal, Sylow
31	C₂³×C₁₃	C₂×Q₈	1	1	yes	characteristic
32	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
33	C₂×C₄×C₁₃	C₂²×C₄	1	2	yes	—
34	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
35	C₂×C₄×C₁₃	#41	1	2	yes	—
36	C₂×Dic₁₃	—	2	4	no	—
37	C₂×Dic₁₃	C₄⋊C₄	1	2	yes	—
38	C₂×Dic₁₃	C₄⋊C₄	1	2	yes	—
39	C₈×C₁₃	—	2	2	no	—
40	C₈×C₁₃	—	2	4	no	—
41	#1055	—	2	4	no	—
42	#1055	C₄²	1	4	yes	—
43	C₂×#108	—	13	2	no	—
44	C₄×M₁₆	—	13	2	no	—
45	C₂×C₄×C₈	—	13	1	no	—
46	#341	—	13	1	no	—
47	#341	D₁₃	1	1	yes	characteristic
48	C₂²×C₁₃	—	2	2	no	—
49	C₂²×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
50	C₂²×C₁₃	C₄×Q₈	1	2	yes	—
51	C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
52	C₄×C₁₃	#117	1	1	yes	characteristic
53	C₄×C₁₃	C₄×D₄	1	2	yes	—
54	Dic₁₃	—	2	2	no	—
55	Dic₁₃	#108	1	4	yes	complemented
56	C₂×M₁₆	—	13	2	no	—
57	C₂×M₁₆	C₂×D₁₃	1	2	yes	—
58	C₂²×C₈	—	13	1	no	—
59	C₂²×C₈	C₂×D₁₃	1	1	yes	characteristic
60	C₂×C₄²	—	13	1	no	—
61	#108	—	13	8	no	—
62	#97	—	26	2	no	—
63	C₄×C₈	—	13	4	no	—
64	C₄×C₈	—	26	2	no	—
65	C₂×C₁₃	—	2	2	no	—
66	C₂×C₁₃	C₄×C₄⋊C₄	1	1	yes	characteristic
67	C₂×C₁₃	C₂×#108	1	2	yes	—
68	C₂²×C₄	—	13	2	no	—
69	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
70	M₁₆	—	2	2	no	—
71	M₁₆	—	13	4	no	—
72	M₁₆	—	26	2	no	—
73	M₁₆	C₄×D₁₃	1	4	yes	—
74	C₂×C₈	—	2	2	no	—
75	C₂×C₈	—	2	2	no	—
76	C₂×C₈	—	13	2	no	—
77	C₂×C₈	—	13	4	no	—
78	C₂×C₈	—	26	2	no	—
79	C₂×C₈	C₄×D₁₃	1	2	yes	—
80	C₄²	—	13	2	no	—
81	C₄²	—	13	1	no	—
82	C₄²	—	13	1	no	—
83	C₁₃	C₄×#108	1	1	yes	characteristic, complemented, Sylow
84	C₂³	Q₈×D₁₃	1	1	yes	characteristic
85	C₂×C₄	—	13	2	no	—
86	C₂×C₄	—	13	2	no	—
87	C₂×C₄	—	26	4	no	—
88	C₂×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
89	C₂×C₄	C₂×C₄×D₁₃	1	2	yes	—
90	C₂×C₄	D₄×D₁₃	1	1	yes	characteristic
91	C₂×C₄	#6129	1	2	yes	—
92	C₈	—	2	2	no	—
93	C₈	—	2	4	no	—
94	C₈	—	13	4	no	—
95	C₈	—	26	4	no	—
96	C₂²	—	2	2	no	—
97	C₂²	#88141	1	2	yes	—
98	C₂²	C₄⋊C₄×D₁₃	1	1	yes	characteristic
99	C₄	—	13	4	no	—
100	C₄	—	26	2	no	—
101	C₄	C₄²×D₁₃	1	1	yes	characteristic
102	C₄	#88131	1	1	yes	characteristic
103	C₄	#88135	1	2	yes	—
104	C₂	—	2	2	no	—
105	C₂	#11718310	1	1	yes	characteristic
106	C₂	D₁₃×#108	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#88062

C₂

yes

maximal

M₁₆×Dic₁₃

C₂

yes

maximal

C₂×C₈×Dic₁₃

C₂

yes

maximal, characteristic

C₁₃×#341

C₂

yes

maximal, characteristic

#11718144

C₂

yes

maximal, characteristic

C₂×C₁₃×M₁₆

C₂²

yes

—

C₂²×C₈×C₁₃

C₂²

yes

characteristic

C₂×C₄×Dic₁₃

C₂²

yes

characteristic

C₂×#6099

C₂²

yes

—

C₂²×#1055

C₂²

yes

characteristic

#88062

C₄

yes

complemented

#88055

—

C₈×Dic₁₃

—

C₈×Dic₁₃

C₄

yes

—

C₂²×C₄×C₁₃

C₂³

yes

characteristic

C₂²×Dic₁₃

Q₈

yes

—

C₁₃×M₁₆

—

C₁₃×M₁₆

C₂×C₄

yes

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

C₂×C₄

yes

—

C₄×Dic₁₃

C₂×C₄

yes

—

C₄×Dic₁₃

D₄

yes

characteristic

C₄×Dic₁₃

D₄

yes

characteristic

#6099

—

#6099

C₂×C₄

yes

—

C₂×#1055

—

C₂×#1055

C₂×C₄

yes

—

C₂×#1055

C₂×C₄

yes

—

C₄×#108

—

maximal, Sylow

C₂³×C₁₃

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₃

C₂²×C₄

yes

—

C₂×C₄×C₁₃

C₂×D₄

yes

characteristic

C₂×C₄×C₁₃

#41

yes

—

C₂×Dic₁₃

—

C₂×Dic₁₃

C₄⋊C₄

yes

—

C₂×Dic₁₃

C₄⋊C₄

yes

—

C₈×C₁₃

—

C₈×C₁₃

—

#1055

—

#1055

C₄²

yes

—

C₂×#108

—

C₄×M₁₆

—

C₂×C₄×C₈

—

#341

—

#341

D₁₃

yes

characteristic

C₂²×C₁₃

—

C₂²×C₁₃

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₁₃

C₄×Q₈

yes

—

C₄×C₁₃

C₂×C₄²

yes

characteristic

C₄×C₁₃

#117

yes

characteristic

C₄×C₁₃

C₄×D₄

yes

—

Dic₁₃

—

Dic₁₃

#108

yes

complemented

C₂×M₁₆

—

C₂×M₁₆

C₂×D₁₃

yes

—

C₂²×C₈

—

C₂²×C₈

C₂×D₁₃

yes

characteristic

C₂×C₄²

—

#108

—

#97

—

C₄×C₈

—

C₄×C₈

—

C₂×C₁₃

—

C₂×C₁₃

C₄×C₄⋊C₄

yes

characteristic

C₂×C₁₃

C₂×#108

yes

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₁₃

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

C₄×D₁₃

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₁₃

yes

—

C₄²

—

C₄²

—

C₄²

—

C₁₃

C₄×#108

yes

characteristic, complemented, Sylow

C₂³

Q₈×D₁₃

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×C₄×D₁₃

yes

characteristic

C₂×C₄

C₂×C₄×D₁₃

yes

—

C₂×C₄

D₄×D₁₃

yes

characteristic

C₂×C₄

#6129

yes

—

C₈

—

C₈

—

C₈

—

C₈

—

C₂²

—

C₂²

#88141

yes

—

C₂²

C₄⋊C₄×D₁₃

yes

characteristic

C₄

—

100

C₄

—

101

C₄

C₄²×D₁₃

yes

characteristic

102

C₄

#88131

yes

characteristic

103

C₄

#88135

yes

—

104

C₂

—

105

C₂

#11718310

yes

characteristic

106

C₂

D₁₃×#108

yes

—

	subgroup	G/H
center	C₂×C₄	D₄×D₁₃
commutator	C₄×C₁₃	C₂×C₄²
Frattini	C₂²×C₄	C₂²×D₁₃
Fitting	C₁₃×#341	C₂
socle	C₂²×C₁₃	C₂×C₄⋊C₄
prime radical	C₂³×C₁₃	C₂×Q₈
cosocle	C₂²×C₄×C₁₃	C₂³
hypercenter	#341	D₁₃
hypocenter	C₁₃	C₄×#108
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #341

subgroup

G/H

center

C₂×C₄

D₄×D₁₃

commutator

C₄×C₁₃

C₂×C₄²

Frattini

C₂²×C₄

C₂²×D₁₃

Fitting

C₁₃×#341

C₂

socle

C₂²×C₁₃

C₂×C₄⋊C₄

prime radical

C₂³×C₁₃

C₂×Q₈

cosocle

C₂²×C₄×C₁₃

C₂³

D₁₃

C₁₃

G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #341

N	H ≅ G/N	type
11. #88062	C₄	semidirect
55. Dic₁₃	#108	semidirect
83. C₁₃	C₄×#108	semidirect

H ≅ G/N

type

11. #88062

C₄

semidirect

55. Dic₁₃

#108

semidirect

83. C₁₃

C₄×#108

semidirect

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

subgroup	index
C₂×#88062	2
M₁₆×Dic₁₃	2
C₂×C₈×Dic₁₃	2
C₁₃×#341	2
#11718144	2
C₄×#108	13

subgroup

index

C₂×#88062

M₁₆×Dic₁₃

C₂×C₈×Dic₁₃

C₁₃×#341

#11718144

C₄×#108

Subgroups — #13114737

Conjugacy classes of subgroups

Complements

Maximal subgroups