Group #14544347 — subgroups

Subgroups — #14544347

Order 2176.

168 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 168 conjugacy classes of subgroups — too many to draw. Only its 66 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	#11763831	C₂	1	2	yes	maximal
2	#11763673	C₂	1	2	yes	maximal, complemented
3	#11763671	C₂	1	2	yes	maximal, complemented
4	C₄×C₈×D₁₇	C₂	1	1	yes	maximal, characteristic
5	C₂×C₈×D₁₇	C₄	1	1	yes	characteristic
6	C₂×C₈×D₁₇	C₄	1	1	yes	characteristic
7	C₄²×D₁₇	C₂²	1	1	yes	characteristic
8	#10587543	—	2	2	no	—
9	#10587542	—	2	2	no	—
10	C₄⋊#3624	C₂²	1	4	yes	—
11	C₄×C₈×C₁₇	C₄	1	1	yes	characteristic
12	C₈×Dic₁₇	C₂²	1	1	yes	characteristic
13	C₈×Dic₁₇	C₂²	1	1	yes	characteristic
14	C₄×#3622	C₄	1	1	yes	characteristic
15	C₂×C₄×D₁₇	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄×D₁₇	D₄	1	1	yes	characteristic
17	C₂×C₄×D₁₇	Q₈	1	1	yes	characteristic
18	C₂×#3624	—	2	4	no	—
19	C₂×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
20	C₂×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
21	C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
22	C₄×Dic₁₇	D₄	1	1	yes	characteristic
23	C₄×Dic₁₇	Q₈	1	1	yes	characteristic
24	C₄×Dic₁₇	C₂³	1	1	yes	characteristic
25	C₂×#3622	C₂×C₄	1	1	yes	characteristic
26	C₂×#3622	C₂×C₄	1	1	yes	characteristic
27	C₈×D₁₇	—	2	2	no	—
28	C₈×D₁₇	—	2	2	no	—
29	C₂²×D₁₇	C₄⋊C₄	1	1	yes	characteristic
30	C₂×C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
31	C₂×C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
32	C₂×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
33	C₂×Dic₁₇	C₄⋊C₄	1	1	yes	characteristic
34	C₂×Dic₁₇	C₂×D₄	1	1	yes	characteristic
35	C₂×Dic₁₇	C₂×Q₈	1	1	yes	characteristic
36	C₄×D₁₇	—	2	2	no	—
37	C₄×D₁₇	—	2	1	no	—
38	C₄×D₁₇	—	2	1	no	—
39	C₄×D₁₇	—	2	2	no	—
40	#3624	—	4	4	no	—
41	C₈×C₁₇	—	2	1	no	—
42	C₈×C₁₇	—	2	1	no	—
43	#3622	M₁₆	1	2	yes	—
44	#3622	M₁₆	1	2	yes	—
45	#1568	—	17	1	no	maximal, Sylow
46	C₂²×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
47	C₂×D₁₇	—	2	1	no	—
48	C₂×D₁₇	—	2	1	no	—
49	C₂×D₁₇	#108	1	2	yes	—
50	C₄×C₁₇	—	2	1	no	—
51	C₄×C₁₇	—	2	1	no	—
52	C₄×C₁₇	C₂×M₁₆	1	1	yes	characteristic
53	C₄×C₁₇	C₂×M₁₆	1	1	yes	characteristic
54	Dic₁₇	—	2	1	no	—
55	Dic₁₇	—	2	1	no	—
56	Dic₁₇	#135	1	2	yes	—
57	#432	—	17	2	no	—
58	C₂×C₄×C₈	—	17	1	no	—
59	#335	—	17	2	no	—
60	#334	—	17	2	no	—
61	C₂×C₁₇	#423	1	1	yes	characteristic
62	C₂×C₁₇	#427	1	1	yes	characteristic
63	C₂×C₁₇	C₂×#108	1	1	yes	characteristic
64	D₁₇	—	2	2	no	—
65	C₂²×C₈	—	17	1	no	—
66	C₂²×C₈	—	17	1	no	—
67	C₂×C₄²	—	17	1	no	—
68	C₄⋊C₈	—	17	4	no	—
69	C₂²⋊C₈	—	34	2	no	—
70	#97	—	34	2	no	—
71	C₄×C₈	—	17	1	no	—
72	C₄×C₈	—	17	1	no	—
73	C₄×C₈	—	17	1	no	—
74	C₄×C₈	#595	1	1	yes	characteristic
75	C₁₇	#1568	1	1	yes	characteristic, complemented, Sylow
76	C₂²×C₄	—	17	1	no	—
77	C₂²×C₄	—	17	1	no	—
78	C₂²×C₄	—	17	1	no	—
79	C₂×C₈	—	17	1	no	—
80	C₂×C₈	—	17	1	no	—
81	C₂×C₈	—	34	2	no	—
82	C₂×C₈	—	34	2	no	—
83	C₂×C₈	—	34	4	no	—
84	C₂×C₈	C₂×#595	1	1	yes	characteristic
85	C₂×C₈	C₂×#595	1	1	yes	characteristic
86	C₄²	—	17	1	no	—
87	C₄²	—	17	1	no	—
88	C₄²	—	17	1	no	—
89	C₄²	C₂×#595	1	1	yes	characteristic
90	C₂³	—	17	1	no	—
91	C₂×C₄	—	17	1	no	—
92	C₂×C₄	—	17	1	no	—
93	C₂×C₄	—	17	1	no	—
94	C₂×C₄	—	34	2	no	—
95	C₂×C₄	—	34	2	no	—
96	C₂×C₄	—	34	1	no	—
97	C₂×C₄	—	34	1	no	—
98	C₂×C₄	C₄⋊#595	1	1	yes	characteristic
99	C₂×C₄	C₄⋊#595	1	1	yes	characteristic
100	C₂×C₄	C₂²×#595	1	1	yes	characteristic
101	C₈	—	2	1	no	—
102	C₈	—	2	1	no	—
103	C₈	—	17	2	no	—
104	C₈	—	17	2	no	—
105	C₈	—	68	4	no	—
106	C₂²	—	17	2	no	—
107	C₂²	—	34	1	no	—
108	C₂²	—	34	1	no	—
109	C₂²	C₂×C₄⋊#595	1	1	yes	characteristic
110	C₄	—	2	1	no	—
111	C₄	—	2	1	no	—
112	C₄	—	17	2	no	—
113	C₄	—	34	1	no	—
114	C₄	—	34	1	no	—
115	C₄	D₁₇⋊M₁₆	1	1	yes	characteristic
116	C₄	D₁₇⋊M₁₆	1	1	yes	characteristic
117	C₂	—	34	2	no	—
118	C₂	#11763814	1	1	yes	characteristic
119	C₂	#11763819	1	1	yes	characteristic
120	C₂	D₁₇⋊#108	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11763831

C₂

yes

maximal

#11763673

C₂

yes

maximal, complemented

#11763671

C₂

yes

maximal, complemented

C₄×C₈×D₁₇

C₂

yes

maximal, characteristic

C₂×C₈×D₁₇

C₄

yes

characteristic

C₂×C₈×D₁₇

C₄

yes

characteristic

C₄²×D₁₇

C₂²

yes

—

—

C₂²

yes

—

C₄×C₈×C₁₇

C₄

yes

characteristic

C₈×Dic₁₇

C₂²

yes

characteristic

C₈×Dic₁₇

C₂²

yes

characteristic

C₄×#3622

C₄

yes

characteristic

C₂×C₄×D₁₇

C₂×C₄

yes

characteristic

C₂×C₄×D₁₇

D₄

yes

characteristic

C₂×C₄×D₁₇

Q₈

yes

characteristic

C₂×#3624

—

C₂×C₈×C₁₇

C₂×C₄

yes

characteristic

C₂×C₈×C₁₇

C₂×C₄

yes

characteristic

C₄²×C₁₇

C₂×C₄

yes

characteristic

C₄×Dic₁₇

D₄

yes

characteristic

C₄×Dic₁₇

Q₈

yes

characteristic

C₄×Dic₁₇

C₂³

yes

characteristic

C₂×#3622

C₂×C₄

yes

characteristic

C₂×#3622

C₂×C₄

yes

characteristic

C₈×D₁₇

—

C₈×D₁₇

—

C₂²×D₁₇

C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₇

C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₇

C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₇

C₂²×C₄

yes

characteristic

C₂×Dic₁₇

C₄⋊C₄

yes

characteristic

C₂×Dic₁₇

C₂×D₄

yes

characteristic

C₂×Dic₁₇

C₂×Q₈

yes

characteristic

C₄×D₁₇

—

C₄×D₁₇

—

C₄×D₁₇

—

C₄×D₁₇

—

#3624

—

C₈×C₁₇

—

C₈×C₁₇

—

#3622

M₁₆

yes

—

#3622

M₁₆

yes

—

#1568

—

maximal, Sylow

C₂²×C₁₇

C₂×C₄⋊C₄

yes

characteristic

C₂×D₁₇

—

C₂×D₁₇

—

C₂×D₁₇

#108

yes

—

C₄×C₁₇

—

C₄×C₁₇

—

C₄×C₁₇

C₂×M₁₆

yes

characteristic

C₄×C₁₇

C₂×M₁₆

yes

characteristic

Dic₁₇

—

Dic₁₇

—

Dic₁₇

#135

yes

—

#432

—

C₂×C₄×C₈

—

#335

—

#334

—

C₂×C₁₇

yes

C₂×C₁₇

yes

C₂×C₁₇

yes

D₁₇

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

C₄⋊C₈

—

C₂²⋊C₈

—

#97

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

#595

yes

characteristic

C₁₇

#1568

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

yes

C₂×C₈

yes

C₄²

—

C₄²

—

C₄²

—

C₄²

C₂×#595

yes

characteristic

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

yes

C₂×C₄

yes

100

C₂×C₄

C₂²×#595

yes

characteristic

101

C₈

—

102

C₈

—

103

C₈

—

104

C₈

—

105

C₈

—

106

C₂²

—

107

C₂²

—

108

C₂²

—

109

C₂²

C₂×C₄⋊#595

yes

characteristic

110

C₄

—

111

C₄

—

112

C₄

—

113

C₄

—

114

C₄

—

115

C₄

D₁₇⋊M₁₆

yes

characteristic

116

C₄

D₁₇⋊M₁₆

yes

characteristic

117

C₂

—

118

C₂

#11763814

yes

characteristic

119

C₂

#11763819

yes

characteristic

120

C₂

D₁₇⋊#108

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×C₄⋊#595
commutator	C₂×C₄×C₁₇	C₂²×C₄
Frattini	C₂×C₄	C₂²×#595
Fitting	C₄×C₈×C₁₇	C₄
socle	C₂²×C₁₇	C₂×C₄⋊C₄
prime radical	C₂²×D₁₇	C₄⋊C₄
cosocle	C₄×Dic₁₇	C₂³
hypercenter	C₄×C₈	#595
hypocenter	C₁₇	#1568
LCS	G ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈

subgroup

G/H

center

C₂²

C₂×C₄⋊#595

commutator

C₂×C₄×C₁₇

C₂²×C₄

Frattini

C₂×C₄

C₂²×#595

Fitting

C₄×C₈×C₁₇

C₄

socle

C₂²×C₁₇

C₂×C₄⋊C₄

prime radical

C₂²×D₁₇

C₄⋊C₄

cosocle

C₄×Dic₁₇

C₂³

C₄×C₈

C₁₇

G ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈

N	H ≅ G/N	type
2. #11763673	C₂	semidirect
3. #11763671	C₂	semidirect
75. C₁₇	#1568	semidirect

H ≅ G/N

type

2. #11763673

C₂

semidirect

3. #11763671

C₂

semidirect

75. C₁₇

#1568

semidirect

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

subgroup	index
#11763831	2
#11763673	2
#11763671	2
C₄×C₈×D₁₇	2
#1568	17

subgroup

index

C₄×C₈×D₁₇

Subgroups — #14544347

Conjugacy classes of subgroups

Complements

Maximal subgroups