Group #13113974 — subgroups

Subgroups — #13113974

Order 1664.

206 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 57 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	#11719427	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#494	C₂	1	1	yes	maximal, characteristic
3	#11718752	C₂	1	2	yes	maximal
4	#11718138	C₂	1	1	yes	maximal, characteristic
5	#11718048	C₂	1	2	yes	maximal
6	C₂×C₁₃×Q₁₆	—	2	2	no	—
7	C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
8	C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
9	#88198	—	2	2	no	—
10	#88142	—	2	2	no	—
11	#88141	—	2	2	no	—
12	C₄×Dic₂₆	C₂²	1	2	yes	—
13	C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
14	#88050	—	2	2	no	—
15	#88047	—	2	2	no	—
16	C₄⋊#1055	C₂²	1	2	yes	—
17	C₂×Q₈×C₁₃	—	2	1	no	—
18	C₂×Q₈×C₁₃	D₄	1	2	yes	—
19	C₂×Dic₂₆	—	2	2	no	—
20	C₂×Dic₂₆	D₄	1	2	yes	—
21	C₁₃×Q₁₆	—	4	4	no	—
22	C₂×C₈×C₁₃	—	2	1	no	—
23	C₁₃×C₄⋊C₄	—	2	2	no	—
24	C₁₃×C₄⋊C₄	—	2	2	no	—
25	C₄²×C₁₃	C₂³	1	1	yes	characteristic
26	C₄⋊Dic₁₃	D₄	1	2	yes	—
27	#6101	—	2	4	no	—
28	#6101	—	2	2	no	—
29	C₄×Dic₁₃	—	2	2	no	—
30	C₄×Dic₁₃	—	2	2	no	—
31	C₂×#1055	—	2	2	no	—
32	#1633	—	13	1	no	maximal, Sylow
33	Q₈×C₁₃	—	4	2	no	—
34	Q₈×C₁₃	—	4	2	no	—
35	C₂×C₄×C₁₃	—	2	2	no	—
36	C₂×C₄×C₁₃	—	4	1	no	—
37	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
38	C₂×C₄×C₁₃	C₂×D₄	1	2	yes	—
39	C₂×Dic₁₃	—	2	2	no	—
40	C₂×Dic₁₃	—	2	2	no	—
41	Dic₂₆	—	2	2	no	—
42	Dic₂₆	—	8	2	no	—
43	Dic₂₆	Q₁₆	1	4	yes	complemented
44	C₈×C₁₃	—	2	2	no	—
45	#1055	—	4	2	no	—
46	Q₈²	—	13	1	no	—
47	#494	D₁₃	1	1	yes	characteristic
48	#477	—	13	2	no	—
49	#333	—	13	1	no	—
50	Q₈⋊C₈	—	13	2	no	—
51	C₂²×C₁₃	#120	1	1	yes	characteristic
52	C₄×C₁₃	—	2	1	no	—
53	C₄×C₁₃	—	4	2	no	—
54	C₄×C₁₃	—	8	1	no	—
55	C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
56	C₄×C₁₃	#137	1	2	yes	—
57	Dic₁₃	—	2	4	no	—
58	Dic₁₃	—	4	2	no	—
59	C₂×Q₁₆	—	2	2	no	—
60	C₄⋊Q₈	—	26	2	no	—
61	C₄⋊Q₈	—	26	2	no	—
62	C₄⋊Q₈	C₂×D₁₃	1	1	yes	characteristic
63	C₄⋊Q₈	C₂×D₁₃	1	1	yes	characteristic
64	C₄×Q₈	—	13	2	no	—
65	C₄×Q₈	—	26	2	no	—
66	#107	—	26	2	no	—
67	C₄⋊C₈	—	13	2	no	—
68	#103	—	26	2	no	—
69	C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
70	C₂×C₁₃	#451	1	2	yes	—
71	C₂×C₁₃	#453	1	1	yes	characteristic
72	C₂×Q₈	—	2	1	no	—
73	C₂×Q₈	—	13	2	no	—
74	C₂×Q₈	—	26	2	no	—
75	C₂×Q₈	C₂²⋊D₁₃	1	2	yes	—
76	Q₁₆	—	4	4	no	—
77	C₂×C₈	—	2	1	no	—
78	C₂×C₈	—	26	2	no	—
79	C₄⋊C₄	—	2	2	no	—
80	C₄⋊C₄	—	2	2	no	—
81	C₄⋊C₄	—	13	2	no	—
82	C₄⋊C₄	—	26	4	no	—
83	C₄⋊C₄	—	26	2	no	—
84	C₄²	—	26	2	no	—
85	C₄²	—	26	2	no	—
86	C₄²	C₂²×D₁₃	1	1	yes	characteristic
87	C₁₃	#1633	1	1	yes	characteristic, complemented, Sylow
88	Q₈	—	4	2	no	—
89	Q₈	—	4	2	no	—
90	Q₈	—	13	4	no	—
91	Q₈	—	26	2	no	—
92	Q₈	—	104	2	no	—
93	C₂×C₄	—	2	2	no	—
94	C₂×C₄	—	4	1	no	—
95	C₂×C₄	—	26	2	no	—
96	C₂×C₄	—	26	2	no	—
97	C₂×C₄	D₄×D₁₃	1	2	yes	—
98	C₂×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
99	C₈	—	2	2	no	—
100	C₈	—	52	2	no	—
101	C₂²	#88191	1	1	yes	characteristic
102	C₄	—	2	1	no	—
103	C₄	—	4	2	no	—
104	C₄	—	8	1	no	—
105	C₄	—	26	4	no	—
106	C₄	—	52	2	no	—
107	C₄	Q₁₆×D₁₃	1	2	yes	—
108	C₄	#88172	1	2	yes	—
109	C₂	#11718738	1	1	yes	characteristic
110	C₂	#11718847	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#11719427

C₂

yes

maximal, characteristic

C₁₃×#494

C₂

yes

maximal, characteristic

#11718752

C₂

yes

maximal

#11718138

C₂

yes

maximal, characteristic

#11718048

C₂

yes

maximal

C₂×C₁₃×Q₁₆

—

C₁₃×C₄⋊Q₈

C₂²

yes

characteristic

C₁₃×C₄⋊Q₈

C₂²

yes

—

—

—

C₄×Dic₂₆

C₂²

yes

—

C₄×C₈×C₁₃

C₂²

yes

—

—

C₂²

yes

—

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

D₄

yes

—

C₂×Dic₂₆

—

C₂×Dic₂₆

D₄

yes

—

C₁₃×Q₁₆

—

C₂×C₈×C₁₃

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₄²×C₁₃

C₂³

yes

characteristic

C₄⋊Dic₁₃

D₄

yes

—

#6101

—

#6101

—

C₄×Dic₁₃

—

C₄×Dic₁₃

—

C₂×#1055

—

#1633

—

maximal, Sylow

Q₈×C₁₃

—

Q₈×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₂×D₄

yes

characteristic

C₂×C₄×C₁₃

C₂×D₄

yes

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

Dic₂₆

—

Dic₂₆

—

Dic₂₆

Q₁₆

yes

complemented

C₈×C₁₃

—

#1055

—

Q₈²

—

#494

D₁₃

yes

characteristic

#477

—

#333

—

Q₈⋊C₈

—

C₂²×C₁₃

#120

yes

characteristic

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

C₂×Q₁₆

yes

—

C₄×C₁₃

#137

yes

—

Dic₁₃

—

Dic₁₃

—

C₂×Q₁₆

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

C₂×D₁₃

yes

characteristic

C₄⋊Q₈

C₂×D₁₃

yes

characteristic

C₄×Q₈

—

C₄×Q₈

—

#107

—

C₄⋊C₈

—

#103

—

C₄×C₈

C₂×D₁₃

yes

characteristic

C₂×C₁₃

#451

yes

—

C₂×C₁₃

#453

yes

characteristic

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

C₂²⋊D₁₃

yes

—

Q₁₆

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

—

C₄²

C₂²×D₁₃

yes

characteristic

C₁₃

#1633

yes

characteristic, complemented, Sylow

Q₈

—

Q₈

—

Q₈

—

Q₈

—

Q₈

—

104

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

D₄×D₁₃

yes

—

C₂×C₄

C₂×C₂²⋊D₁₃

yes

characteristic

C₈

—

100

C₈

—

101

C₂²

#88191

yes

characteristic

102

C₄

—

103

C₄

—

104

C₄

—

105

C₄

—

106

C₄

—

107

C₄

Q₁₆×D₁₃

yes

—

108

C₄

#88172

yes

—

109

C₂

#11718738

yes

characteristic

110

C₂

#11718847

yes

—

	subgroup	G/H
center	C₂²	#88191
commutator, cosocle	C₄²×C₁₃	C₂³
Frattini	C₄²	C₂²×D₁₃
Fitting	C₁₃×#494	C₂
socle, prime radical	C₂²×C₁₃	#120
hypercenter	#494	D₁₃
hypocenter	C₁₃	#1633
LCS	G ▷ C₄²×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #494

subgroup

G/H

center

C₂²

#88191

commutator, cosocle

C₄²×C₁₃

C₂³

Frattini

C₄²

C₂²×D₁₃

Fitting

C₁₃×#494

C₂

C₂²×C₁₃

D₁₃

C₁₃

G ▷ C₄²×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #494

N	H ≅ G/N	type
43. Dic₂₆	Q₁₆	semidirect
87. C₁₃	#1633	semidirect

H ≅ G/N

type

43. Dic₂₆

Q₁₆

semidirect

87. C₁₃

#1633

semidirect

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

subgroup	index
#11719427	2
C₁₃×#494	2
#11718752	2
#11718138	2
#11718048	2
#1633	13

subgroup

index

C₁₃×#494

Subgroups — #13113974

Conjugacy classes of subgroups

Complements

Maximal subgroups