Group #14528957 — subgroups

Subgroups — #14528957

Order 2176.

212 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 101 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×#10587490	C₂	1	1	yes	maximal, characteristic
2	C₂×#10587493	C₂	1	2	yes	maximal
3	#11762832	C₂	1	2	yes	maximal
4	C₂×#10587486	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₇×#108	C₂	1	1	yes	maximal, characteristic
6	C₂×M₁₆×C₁₇	C₂²	1	2	yes	—
7	C₂²×C₈×C₁₇	C₂²	1	1	yes	characteristic
8	C₂×C₄×Dic₁₇	C₂²	1	1	yes	characteristic
9	C₂×#63223	C₂²	1	2	yes	—
10	C₂²×#3622	C₂²	1	1	yes	characteristic
11	C₁₇×#108	—	2	2	no	—
12	#10587493	—	2	4	no	—
13	#10587490	—	2	2	no	—
14	#10587486	C₄	1	4	yes	—
15	#10587485	—	2	4	no	—
16	C₂²×C₄×C₁₇	C₂³	1	1	yes	characteristic
17	C₂²×Dic₁₇	Q₈	1	2	yes	—
18	M₁₆×C₁₇	—	2	2	no	—
19	M₁₆×C₁₇	—	2	2	no	—
20	C₂×C₈×C₁₇	—	2	2	no	—
21	C₂×C₈×C₁₇	C₂×C₄	1	2	yes	—
22	C₂×C₈×C₁₇	D₄	1	2	yes	—
23	C₂×C₈×C₁₇	Q₈	1	2	yes	—
24	C₄×Dic₁₇	C₂×C₄	1	2	yes	—
25	C₄×Dic₁₇	D₄	1	2	yes	—
26	#63223	—	2	2	no	—
27	#63223	—	2	2	no	—
28	C₂×#3622	—	2	2	no	—
29	C₂×#3622	C₂×C₄	1	2	yes	—
30	C₂×#3622	D₄	1	2	yes	—
31	C₂×#3622	Q₈	1	2	yes	—
32	C₂³×C₁₇	C₂×Q₈	1	1	yes	characteristic
33	C₂×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
34	C₂×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
35	C₂×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
36	C₂×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
37	C₂×C₄×C₁₇	C₂×Q₈	1	1	yes	characteristic
38	C₂×C₄×C₁₇	C₂×Q₈	1	1	yes	characteristic
39	C₂×Dic₁₇	—	4	2	no	—
40	C₂×Dic₁₇	C₄⋊C₄	1	4	yes	—
41	C₈×C₁₇	—	4	2	no	—
42	C₈×C₁₇	C₄⋊C₄	1	4	yes	—
43	#3622	—	4	2	no	—
44	#3622	C₄⋊C₄	1	4	yes	—
45	#1849	—	17	1	no	maximal, Sylow
46	C₂²×C₁₇	—	2	2	no	—
47	C₂²×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
48	C₂²×C₁₇	C₄⋊Q₈	1	1	yes	characteristic
49	C₂²×C₁₇	C₄⋊Q₈	1	1	yes	characteristic
50	C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
51	C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
52	C₄×C₁₇	#127	1	1	yes	characteristic
53	C₄×C₁₇	C₄⋊Q₈	1	1	yes	characteristic
54	Dic₁₇	—	2	4	no	—
55	C₂×#108	—	17	2	no	—
56	C₂×#108	—	17	1	no	—
57	C₂×#108	D₁₇	1	1	yes	characteristic
58	#423	—	17	2	no	—
59	C₂×#97	—	17	1	no	—
60	C₂×C₁₇	—	2	1	no	—
61	C₂×C₁₇	—	2	1	no	—
62	C₂×C₁₇	#384	1	1	yes	characteristic
63	C₂×C₁₇	#430	1	2	yes	—
64	C₂×M₁₆	—	17	2	no	—
65	C₂×M₁₆	C₂×D₁₇	1	2	yes	—
66	C₂²×C₈	—	17	1	no	—
67	C₂²×C₈	C₂×D₁₇	1	1	yes	characteristic
68	C₂×C₄²	—	17	1	no	—
69	#108	—	2	2	no	—
70	#108	—	34	4	no	—
71	#108	—	34	2	no	—
72	C₄⋊C₈	—	34	4	no	—
73	#97	—	17	4	no	—
74	C₁₇	#1849	1	1	yes	characteristic, complemented, Sylow
75	C₂²×C₄	—	17	2	no	—
76	C₂²×C₄	C₂²×D₁₇	1	1	yes	characteristic
77	M₁₆	—	2	2	no	—
78	M₁₆	—	2	2	no	—
79	M₁₆	—	34	2	no	—
80	M₁₆	—	34	2	no	—
81	C₂×C₈	—	2	2	no	—
82	C₂×C₈	—	17	2	no	—
83	C₂×C₈	—	17	2	no	—
84	C₂×C₈	—	17	2	no	—
85	C₂×C₈	—	34	2	no	—
86	C₂×C₈	Dic₃₄	1	2	yes	—
87	C₂×C₈	C₄×D₁₇	1	2	yes	—
88	C₂×C₈	C₂²⋊D₁₇	1	2	yes	—
89	C₄²	—	17	2	no	—
90	C₄²	—	17	2	no	—
91	C₂³	Q₈×D₁₇	1	1	yes	characteristic
92	C₂×C₄	—	17	4	no	—
93	C₂×C₄	—	68	2	no	—
94	C₂×C₄	C₂×Dic₃₄	1	1	yes	characteristic
95	C₂×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
96	C₂×C₄	D₄×D₁₇	1	1	yes	characteristic
97	C₂×C₄	D₄×D₁₇	1	1	yes	characteristic
98	C₂×C₄	Q₈×D₁₇	1	1	yes	characteristic
99	C₂×C₄	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
100	C₈	—	4	2	no	—
101	C₈	—	17	4	no	—
102	C₈	—	68	2	no	—
103	C₈	#63225	1	4	yes	—
104	C₂²	—	2	2	no	—
105	C₂²	#10587574	1	1	yes	characteristic
106	C₂²	C₄⋊C₄×D₁₇	1	1	yes	characteristic
107	C₂²	#10587630	1	1	yes	characteristic
108	C₄	—	34	4	no	—
109	C₄	#10587574	1	1	yes	characteristic
110	C₄	C₄⋊C₄×D₁₇	1	1	yes	characteristic
111	C₄	C₂×#63225	1	1	yes	characteristic
112	C₄	#10587626	1	1	yes	characteristic
113	C₂	—	2	1	no	—
114	C₂	—	2	1	no	—
115	C₂	#11762678	1	1	yes	characteristic
116	C₂	#11762856	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10587490

C₂

yes

maximal, characteristic

C₂×#10587493

C₂

yes

maximal

#11762832

C₂

yes

maximal

C₂×#10587486

C₂

yes

maximal, characteristic

C₂×C₁₇×#108

C₂

yes

maximal, characteristic

C₂×M₁₆×C₁₇

C₂²

yes

—

C₂²×C₈×C₁₇

C₂²

yes

characteristic

C₂×C₄×Dic₁₇

C₂²

yes

characteristic

C₂×#63223

C₂²

yes

—

C₂²×#3622

C₂²

yes

characteristic

C₁₇×#108

—

#10587493

—

#10587490

—

#10587486

C₄

yes

—

#10587485

—

C₂²×C₄×C₁₇

C₂³

yes

characteristic

C₂²×Dic₁₇

Q₈

yes

—

M₁₆×C₁₇

—

M₁₆×C₁₇

—

C₂×C₈×C₁₇

—

C₂×C₈×C₁₇

C₂×C₄

yes

—

C₂×C₈×C₁₇

D₄

yes

—

C₂×C₈×C₁₇

Q₈

yes

—

C₄×Dic₁₇

C₂×C₄

yes

—

C₄×Dic₁₇

D₄

yes

—

—

—

—

C₂×C₄

yes

—

C₂×#3622

D₄

yes

—

C₂×#3622

Q₈

yes

—

C₂³×C₁₇

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₇

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₇

C₂×D₄

yes

characteristic

C₂×C₄×C₁₇

C₂×D₄

yes

characteristic

C₂×C₄×C₁₇

C₂×D₄

yes

characteristic

C₂×C₄×C₁₇

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₇

C₂×Q₈

yes

characteristic

C₂×Dic₁₇

—

C₂×Dic₁₇

C₄⋊C₄

yes

—

C₈×C₁₇

—

C₈×C₁₇

C₄⋊C₄

yes

—

#3622

—

#3622

C₄⋊C₄

yes

—

#1849

—

maximal, Sylow

C₂²×C₁₇

—

C₂²×C₁₇

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₁₇

C₄⋊Q₈

yes

characteristic

C₂²×C₁₇

C₄⋊Q₈

yes

characteristic

C₄×C₁₇

C₂×C₄⋊C₄

yes

characteristic

C₄×C₁₇

C₂×C₄⋊C₄

yes

characteristic

C₄×C₁₇

#127

yes

characteristic

C₄×C₁₇

C₄⋊Q₈

yes

characteristic

Dic₁₇

—

C₂×#108

—

C₂×#108

—

C₂×#108

D₁₇

yes

characteristic

#423

—

C₂×#97

—

C₂×C₁₇

—

C₂×C₁₇

—

C₂×C₁₇

#384

yes

characteristic

C₂×C₁₇

#430

yes

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₁₇

yes

—

C₂²×C₈

—

C₂²×C₈

C₂×D₁₇

yes

characteristic

C₂×C₄²

—

#108

—

#108

—

#108

—

C₄⋊C₈

—

#97

—

C₁₇

#1849

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

C₂²×D₁₇

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

Dic₃₄

yes

—

C₂×C₈

C₄×D₁₇

yes

—

C₂×C₈

C₂²⋊D₁₇

yes

—

C₄²

—

C₄²

—

C₂³

Q₈×D₁₇

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×Dic₃₄

yes

characteristic

C₂×C₄

C₂×C₄×D₁₇

yes

characteristic

C₂×C₄

D₄×D₁₇

yes

characteristic

C₂×C₄

D₄×D₁₇

yes

characteristic

C₂×C₄

Q₈×D₁₇

yes

characteristic

C₂×C₄

C₂×C₂²⋊D₁₇

yes

characteristic

100

C₈

—

101

C₈

—

102

C₈

—

103

C₈

#63225

yes

—

104

C₂²

—

105

C₂²

#10587574

yes

characteristic

106

C₂²

C₄⋊C₄×D₁₇

yes

characteristic

107

C₂²

#10587630

yes

characteristic

108

C₄

—

109

C₄

#10587574

yes

characteristic

110

C₄

C₄⋊C₄×D₁₇

yes

characteristic

111

C₄

C₂×#63225

yes

characteristic

112

C₄

#10587626

yes

characteristic

113

C₂

—

114

C₂

—

115

C₂

#11762678

yes

characteristic

116

C₂

#11762856

yes

—

	subgroup	G/H
center	C₂×C₄	D₄×D₁₇
commutator	C₂×C₄×C₁₇	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₇
Fitting	C₂×C₁₇×#108	C₂
socle	C₂²×C₁₇	C₂×C₄⋊C₄
prime radical	C₂³×C₁₇	C₂×Q₈
cosocle	C₂²×C₄×C₁₇	C₂³
hypercenter	C₂×#108	D₁₇
hypocenter	C₁₇	#1849
LCS	G ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×#108

subgroup

G/H

center

C₂×C₄

D₄×D₁₇

commutator

C₂×C₄×C₁₇

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₇

Fitting

C₂×C₁₇×#108

C₂

socle

C₂²×C₁₇

C₂×C₄⋊C₄

prime radical

C₂³×C₁₇

C₂×Q₈

cosocle

C₂²×C₄×C₁₇

C₂³

D₁₇

C₁₇

G ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×#108

N	H ≅ G/N	type
74. C₁₇	#1849	semidirect

H ≅ G/N

type

74. C₁₇

#1849

semidirect

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

subgroup	index
C₂×#10587490	2
C₂×#10587493	2
#11762832	2
C₂×#10587486	2
C₂×C₁₇×#108	2
#1849	17

subgroup

index

C₂×C₁₇×#108

Subgroups — #14528957

Conjugacy classes of subgroups

Complements

Maximal subgroups