Group #15750556 — subgroups

Subgroups — #15750556

Order 3328.

132 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 132 conjugacy classes of subgroups — too many to draw. Only its 53 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	#13117089	C₂	1	1	yes	maximal, characteristic
2	#13112908	C₂	1	1	yes	maximal, characteristic
3	C₁₃×C₄⋊C₃₂	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₁₀₄	—	2	1	no	—
5	C₂×Dic₁₀₄	C₄	1	2	yes	—
6	#11718360	—	2	1	no	—
7	C₂×C₁₃×C₃₂	—	2	1	no	—
8	C₄×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
9	#11718050	—	2	1	no	—
10	C₂×Dic₅₂	—	2	2	no	—
11	C₂×Dic₅₂	—	4	1	no	—
12	#88123	—	4	1	no	—
13	C₂×C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
14	C₂×C₁₃×C₁₆	D₄	1	1	yes	characteristic
15	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
16	C₄⋊#1055	—	4	1	no	—
17	Dic₁₀₄	—	4	2	no	—
18	Dic₁₀₄	—	4	1	no	—
19	Dic₁₀₄	—	4	1	no	—
20	C₁₃×C₃₂	—	4	1	no	—
21	#7445	—	13	1	no	maximal, Sylow
22	C₂×Dic₂₆	—	4	2	no	—
23	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
24	C₂×C₈×C₁₃	SD₁₆	1	1	yes	characteristic
25	C₄²×C₁₃	D₈	1	1	yes	characteristic
26	C₄⋊Dic₁₃	—	8	1	no	—
27	C₄⋊Dic₁₃	—	8	1	no	—
28	C₂×#1055	—	8	1	no	—
29	Dic₅₂	—	4	2	no	—
30	Dic₅₂	—	4	2	no	—
31	Dic₅₂	—	8	2	no	—
32	C₁₃×C₁₆	—	2	1	no	—
33	C₁₃×C₁₆	D₈	1	1	yes	characteristic
34	C₁₃×C₁₆	SD₁₆	1	1	yes	characteristic
35	#2247	—	13	1	no	—
36	C₄⋊C₃₂	D₁₃	1	1	yes	characteristic
37	#1371	—	13	1	no	—
38	C₂×C₄×C₁₃	#102	1	1	yes	characteristic
39	C₂×C₄×C₁₃	D₁₆	1	1	yes	characteristic
40	C₂×C₄×C₁₃	SD₃₂	1	1	yes	characteristic
41	C₂×Dic₁₃	—	8	2	no	—
42	Dic₂₆	—	8	2	no	—
43	Dic₂₆	—	8	2	no	—
44	C₈×C₁₃	—	2	1	no	—
45	C₈×C₁₃	#100	1	1	yes	characteristic
46	C₈×C₁₃	#102	1	1	yes	characteristic
47	#1055	—	16	1	no	—
48	C₂×Q₃₂	—	13	2	no	—
49	C₂×Q₃₂	—	26	1	no	—
50	#494	—	26	1	no	—
51	C₂×C₃₂	—	2	1	no	—
52	C₄×C₁₆	C₂×D₁₃	1	1	yes	characteristic
53	#335	—	26	1	no	—
54	C₂²×C₁₃	#357	1	1	yes	characteristic
55	C₄×C₁₃	—	2	1	no	—
56	C₄×C₁₃	#331	1	1	yes	characteristic
57	C₄×C₁₃	#361	1	1	yes	characteristic
58	C₄×C₁₃	SD₆₄	1	1	yes	characteristic
59	C₄×C₁₃	Q₆₄	1	1	yes	characteristic
60	Dic₁₃	—	16	2	no	—
61	C₂×Q₁₆	—	26	2	no	—
62	C₂×Q₁₆	—	52	1	no	—
63	C₄⋊Q₈	—	52	1	no	—
64	Q₃₂	—	52	2	no	—
65	Q₃₂	—	52	1	no	—
66	Q₃₂	—	52	1	no	—
67	C₂×C₁₆	C₄×D₁₃	1	1	yes	characteristic
68	C₂×C₁₆	C₂²⋊D₁₃	1	1	yes	characteristic
69	C₄⋊C₈	—	52	1	no	—
70	C₄×C₈	D₅₂	1	1	yes	characteristic
71	C₃₂	—	4	1	no	—
72	C₂×C₁₃	#1361	1	1	yes	characteristic
73	C₂×C₁₃	#1416	1	1	yes	characteristic
74	C₂×C₁₃	#1420	1	1	yes	characteristic
75	C₂×Q₈	—	52	2	no	—
76	Q₁₆	—	52	2	no	—
77	Q₁₆	—	52	2	no	—
78	Q₁₆	—	104	2	no	—
79	C₂×C₈	—	104	1	no	—
80	C₂×C₈	#6095	1	1	yes	characteristic
81	C₂×C₈	#6103	1	1	yes	characteristic
82	C₄⋊C₄	—	104	1	no	—
83	C₄⋊C₄	—	104	1	no	—
84	C₄²	D₁₀₄	1	1	yes	characteristic
85	C₁₆	—	2	1	no	—
86	C₁₆	#6104	1	1	yes	characteristic
87	C₁₆	#6106	1	1	yes	characteristic
88	C₁₃	#7445	1	1	yes	characteristic, complemented, Sylow
89	Q₈	—	104	2	no	—
90	Q₈	—	104	2	no	—
91	C₂×C₄	—	104	2	no	—
92	C₂×C₄	D₂₀₈	1	1	yes	characteristic
93	C₂×C₄	#88040	1	1	yes	characteristic
94	C₂×C₄	#88061	1	1	yes	characteristic
95	C₈	—	2	1	no	—
96	C₈	—	208	1	no	—
97	C₈	#88049	1	1	yes	characteristic
98	C₈	#88063	1	1	yes	characteristic
99	C₂²	#11718101	1	1	yes	characteristic
100	C₄	—	2	1	no	—
101	C₄	—	208	2	no	—
102	C₄	#11718041	1	1	yes	characteristic
103	C₄	Dic₂₀₈	1	1	yes	characteristic
104	C₄	#11718077	1	1	yes	characteristic
105	C₄	#11718108	1	1	yes	characteristic
106	C₂	#13112883	1	1	yes	characteristic
107	C₂	#13113018	1	1	yes	characteristic
108	C₂	#13113030	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#13117089

C₂

yes

maximal, characteristic

#13112908

C₂

yes

maximal, characteristic

C₁₃×C₄⋊C₃₂

C₂

yes

maximal, characteristic

C₂×Dic₁₀₄

—

C₂×Dic₁₀₄

C₄

yes

—

#11718360

—

C₂×C₁₃×C₃₂

—

C₄×C₁₃×C₁₆

C₂²

yes

characteristic

#11718050

—

C₂×Dic₅₂

—

C₂×Dic₅₂

—

#88123

—

C₂×C₁₃×C₁₆

C₂×C₄

yes

characteristic

C₂×C₁₃×C₁₆

D₄

yes

characteristic

C₄×C₈×C₁₃

D₄

yes

characteristic

C₄⋊#1055

—

Dic₁₀₄

—

Dic₁₀₄

—

Dic₁₀₄

—

C₁₃×C₃₂

—

#7445

—

maximal, Sylow

C₂×Dic₂₆

—

C₂×C₈×C₁₃

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₃

SD₁₆

yes

characteristic

C₄²×C₁₃

D₈

yes

characteristic

C₄⋊Dic₁₃

—

C₄⋊Dic₁₃

—

C₂×#1055

—

Dic₅₂

—

Dic₅₂

—

Dic₅₂

—

C₁₃×C₁₆

—

C₁₃×C₁₆

D₈

yes

characteristic

C₁₃×C₁₆

SD₁₆

yes

characteristic

#2247

—

C₄⋊C₃₂

D₁₃

yes

characteristic

#1371

—

C₂×C₄×C₁₃

#102

yes

characteristic

C₂×C₄×C₁₃

D₁₆

yes

characteristic

C₂×C₄×C₁₃

SD₃₂

yes

characteristic

C₂×Dic₁₃

—

Dic₂₆

—

Dic₂₆

—

C₈×C₁₃

—

C₈×C₁₃

yes

C₈×C₁₃

yes

—

C₂×Q₃₂

—

C₂×Q₃₂

—

#494

—

C₂×C₃₂

—

C₄×C₁₆

C₂×D₁₃

yes

characteristic

#335

—

C₂²×C₁₃

#357

yes

characteristic

C₄×C₁₃

—

C₄×C₁₃

yes

C₄×C₁₃

yes

C₄×C₁₃

SD₆₄

yes

characteristic

C₄×C₁₃

Q₆₄

yes

characteristic

Dic₁₃

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₄⋊Q₈

—

Q₃₂

—

Q₃₂

—

Q₃₂

—

C₂×C₁₆

C₄×D₁₃

yes

characteristic

C₂×C₁₆

C₂²⋊D₁₃

yes

characteristic

C₄⋊C₈

—

C₄×C₈

D₅₂

yes

characteristic

C₃₂

—

C₂×C₁₃

yes

C₂×C₁₃

yes

C₂×C₁₃

yes

C₂×Q₈

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

104

—

C₂×C₈

—

104

—

C₂×C₈

yes

C₂×C₈

yes

C₄⋊C₄

—

104

—

C₄⋊C₄

—

104

—

C₄²

D₁₀₄

yes

characteristic

C₁₆

—

C₁₆

yes

C₁₆

yes

C₁₃

yes

characteristic, complemented, Sylow

Q₈

—

104

—

Q₈

—

104

—

C₂×C₄

—

104

—

C₂×C₄

D₂₀₈

yes

C₂×C₄

yes

C₂×C₄

yes

C₈

—

C₈

—

208

—

C₈

yes

C₈

yes

C₂²

yes

100

C₄

—

101

C₄

—

208

—

102

C₄

#11718041

yes

characteristic

103

C₄

Dic₂₀₈

yes

characteristic

104

C₄

#11718077

yes

characteristic

105

C₄

#11718108

yes

characteristic

106

C₂

#13112883

yes

characteristic

107

C₂

#13113018

yes

characteristic

108

C₂

#13113030

yes

characteristic

	subgroup	G/H
center	C₂²	#11718101
commutator	C₂×C₁₃×C₁₆	C₂×C₄
Frattini	C₄×C₁₆	C₂×D₁₃
Fitting	C₁₃×C₄⋊C₃₂	C₂
socle, prime radical	C₂²×C₁₃	#357
cosocle	C₄×C₁₃×C₁₆	C₂²
hypercenter	C₄⋊C₃₂	D₁₃
hypocenter	C₁₃	#7445
LCS	G ▷ C₂×C₁₃×C₁₆ ▷ C₂×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ C₄⋊C₃₂

subgroup

G/H

center

C₂²

#11718101

commutator

C₂×C₁₃×C₁₆

C₂×C₄

Frattini

C₄×C₁₆

C₂×D₁₃

Fitting

C₁₃×C₄⋊C₃₂

C₂

socle, prime radical

C₂²×C₁₃

#357

cosocle

C₄×C₁₃×C₁₆

C₂²

hypercenter

C₄⋊C₃₂

D₁₃

hypocenter

C₁₃

#7445

LCS

G ▷ C₂×C₁₃×C₁₆ ▷ C₂×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ C₄⋊C₃₂

N	H ≅ G/N	type
88. C₁₃	#7445	semidirect

H ≅ G/N

type

88. C₁₃

#7445

semidirect

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

subgroup	index
#13117089	2
#13112908	2
C₁₃×C₄⋊C₃₂	2
#7445	13

subgroup

index

#13117089

#13112908

C₁₃×C₄⋊C₃₂

#7445

Subgroups — #15750556

Conjugacy classes of subgroups

Complements

Maximal subgroups