Group #14528902 — subgroups

Subgroups — #14528902

Order 2176.

216 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 93 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×#10587485	C₂	1	2	yes	maximal
2	#11762655	C₂	1	1	yes	maximal, characteristic
3	#11762564	C₂	1	1	yes	maximal, characteristic
4	#11762563	C₂	1	2	yes	maximal
5	C₁₇×#336	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₈×C₁₇	C₂²	1	2	yes	—
7	C₂×C₄²×C₁₇	C₂²	1	1	yes	characteristic
8	C₂×C₄×Dic₁₇	C₂²	1	1	yes	characteristic
9	C₂×C₄×Dic₁₇	C₂²	1	1	yes	characteristic
10	C₂²×#3622	C₂²	1	2	yes	—
11	#10587502	C₄	1	2	yes	—
12	#10587502	C₄	1	2	yes	—
13	#10587485	—	2	4	no	—
14	C₂²×C₄×C₁₇	C₂×C₄	1	2	yes	—
15	C₂²×C₄×C₁₇	C₂³	1	1	yes	characteristic
16	C₂²×Dic₁₇	C₂×C₄	1	1	yes	characteristic
17	C₂²×Dic₁₇	C₂×C₄	1	1	yes	characteristic
18	C₂²×Dic₁₇	C₂×C₄	1	2	yes	—
19	C₂×C₈×C₁₇	—	2	2	no	—
20	C₂×C₈×C₁₇	—	2	2	no	—
21	C₂×C₈×C₁₇	—	2	2	no	—
22	C₄²×C₁₇	—	2	2	no	—
23	C₄×Dic₁₇	—	2	2	no	—
24	C₄×Dic₁₇	D₄	1	2	yes	—
25	C₄×Dic₁₇	Q₈	1	2	yes	—
26	C₂×#3622	—	2	2	no	—
27	C₂×#3622	—	2	2	no	—
28	C₂×#3622	—	2	2	no	—
29	C₂³×C₁₇	C₂²×C₄	1	1	yes	characteristic
30	C₂×C₄×C₁₇	—	2	2	no	—
31	C₂×C₄×C₁₇	—	2	2	no	—
32	C₂×C₄×C₁₇	—	2	2	no	—
33	C₂×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
34	C₂×C₄×C₁₇	C₂×Q₈	1	1	yes	characteristic
35	C₂×C₄×C₁₇	#41	1	2	yes	—
36	C₂×C₄×C₁₇	#41	1	2	yes	—
37	C₂×Dic₁₇	—	2	2	no	—
38	C₂×Dic₁₇	—	2	2	no	—
39	C₂×Dic₁₇	—	2	1	no	—
40	C₂×Dic₁₇	—	2	1	no	—
41	C₂×Dic₁₇	—	2	2	no	—
42	C₂×Dic₁₇	—	2	2	no	—
43	C₂×Dic₁₇	C₄⋊C₄	1	4	yes	—
44	C₈×C₁₇	—	4	2	no	—
45	#3622	—	4	2	no	—
46	#1832	—	17	1	no	maximal, Sylow
47	C₂²×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
48	C₂²×C₁₇	#117	1	1	yes	characteristic
49	C₂²×C₁₇	#117	1	1	yes	characteristic
50	C₂²×C₁₇	#131	1	2	yes	—
51	C₂²×C₁₇	#131	1	2	yes	—
52	C₄×C₁₇	—	4	2	no	—
53	C₄×C₁₇	#124	1	2	yes	—
54	C₄×C₁₇	#125	1	2	yes	—
55	Dic₁₇	—	2	4	no	—
56	Dic₁₇	—	4	1	no	—
57	Dic₁₇	—	4	1	no	—
58	C₂×C₄⋊C₈	—	17	2	no	—
59	#376	—	17	1	no	—
60	#336	—	17	2	no	—
61	#336	—	17	1	no	—
62	#336	D₁₇	1	1	yes	characteristic
63	C₂×C₁₇	#382	1	1	yes	characteristic
64	C₂×C₁₇	#424	1	2	yes	—
65	C₂×C₁₇	#433	1	2	yes	—
66	C₂×C₁₇	#433	1	1	yes	characteristic
67	C₂×C₁₇	#433	1	1	yes	characteristic
68	C₂²×C₈	—	17	2	no	—
69	C₂²×C₈	C₂×D₁₇	1	2	yes	—
70	C₂×C₄²	—	17	1	no	—
71	C₂×C₄²	—	17	1	no	—
72	C₂×C₄²	C₂×D₁₇	1	1	yes	characteristic
73	C₄⋊C₈	—	34	4	no	—
74	#95	—	17	2	no	—
75	#95	—	17	2	no	—
76	C₁₇	#1832	1	1	yes	characteristic, complemented, Sylow
77	C₂²×C₄	—	17	2	no	—
78	C₂²×C₄	—	17	1	no	—
79	C₂²×C₄	—	17	1	no	—
80	C₂²×C₄	C₄×D₁₇	1	2	yes	—
81	C₂²×C₄	C₂²×D₁₇	1	1	yes	characteristic
82	C₂×C₈	—	2	2	no	—
83	C₂×C₈	—	2	2	no	—
84	C₂×C₈	—	2	2	no	—
85	C₂×C₈	—	34	2	no	—
86	C₂×C₈	—	34	2	no	—
87	C₂×C₈	—	34	2	no	—
88	C₄²	—	2	2	no	—
89	C₄²	—	17	2	no	—
90	C₄²	—	17	2	no	—
91	C₄²	—	34	2	no	—
92	C₂³	C₂×C₄×D₁₇	1	1	yes	characteristic
93	C₂×C₄	—	2	2	no	—
94	C₂×C₄	—	2	2	no	—
95	C₂×C₄	—	2	2	no	—
96	C₂×C₄	—	17	4	no	—
97	C₂×C₄	—	34	2	no	—
98	C₂×C₄	—	34	2	no	—
99	C₂×C₄	—	34	1	no	—
100	C₂×C₄	—	34	1	no	—
101	C₂×C₄	—	34	2	no	—
102	C₂×C₄	—	34	2	no	—
103	C₂×C₄	#63252	1	2	yes	—
104	C₂×C₄	D₄×D₁₇	1	1	yes	characteristic
105	C₂×C₄	#63254	1	2	yes	—
106	C₂×C₄	Q₈×D₁₇	1	1	yes	characteristic
107	C₈	—	4	2	no	—
108	C₈	—	68	2	no	—
109	C₂²	#10587558	1	1	yes	characteristic
110	C₂²	#10587563	1	1	yes	characteristic
111	C₂²	C₄⋊C₄×D₁₇	1	1	yes	characteristic
112	C₂²	#10587587	1	2	yes	—
113	C₂²	#10587593	1	2	yes	—
114	C₄	—	4	2	no	—
115	C₄	—	34	4	no	—
116	C₄	—	68	1	no	—
117	C₄	—	68	1	no	—
118	C₄	#10587571	1	2	yes	—
119	C₄	#10587575	1	2	yes	—
120	C₂	#11762673	1	1	yes	characteristic
121	C₂	#11762834	1	2	yes	—
122	C₂	#11762867	1	2	yes	—
123	C₂	#11762868	1	1	yes	characteristic
124	C₂	#11762871	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10587485

C₂

yes

maximal

#11762655

C₂

yes

maximal, characteristic

#11762564

C₂

yes

maximal, characteristic

#11762563

C₂

yes

maximal

C₁₇×#336

C₂

yes

maximal, characteristic

C₂²×C₈×C₁₇

C₂²

yes

—

C₂×C₄²×C₁₇

C₂²

yes

characteristic

C₂×C₄×Dic₁₇

C₂²

yes

characteristic

C₂×C₄×Dic₁₇

C₂²

yes

characteristic

C₂²×#3622

C₂²

yes

—

#10587502

C₄

yes

—

#10587502

C₄

yes

—

#10587485

—

C₂²×C₄×C₁₇

C₂×C₄

yes

—

C₂²×C₄×C₁₇

C₂³

yes

characteristic

C₂²×Dic₁₇

C₂×C₄

yes

characteristic

C₂²×Dic₁₇

C₂×C₄

yes

characteristic

C₂²×Dic₁₇

C₂×C₄

yes

—

C₂×C₈×C₁₇

—

C₂×C₈×C₁₇

—

C₂×C₈×C₁₇

—

C₄²×C₁₇

—

C₄×Dic₁₇

—

C₄×Dic₁₇

D₄

yes

—

C₄×Dic₁₇

Q₈

yes

—

C₂×#3622

—

C₂×#3622

—

C₂×#3622

—

C₂³×C₁₇

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

C₂×D₄

yes

characteristic

C₂×C₄×C₁₇

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₇

#41

yes

—

C₂×C₄×C₁₇

#41

yes

—

C₂×Dic₁₇

—

C₂×Dic₁₇

—

C₂×Dic₁₇

—

C₂×Dic₁₇

—

C₂×Dic₁₇

—

C₂×Dic₁₇

—

C₂×Dic₁₇

C₄⋊C₄

yes

—

C₈×C₁₇

—

#3622

—

#1832

—

maximal, Sylow

C₂²×C₁₇

C₂×C₄⋊C₄

yes

C₂²×C₁₇

yes

C₂²×C₁₇

yes

C₂²×C₁₇

yes

—

C₂²×C₁₇

#131

yes

—

C₄×C₁₇

—

C₄×C₁₇

#124

yes

—

C₄×C₁₇

#125

yes

—

Dic₁₇

—

Dic₁₇

—

Dic₁₇

—

C₂×C₄⋊C₈

—

—

—

—

D₁₇

yes

C₂×C₁₇

yes

C₂×C₁₇

yes

—

C₂×C₁₇

#433

yes

—

C₂×C₁₇

yes

C₂×C₁₇

yes

C₂²×C₈

—

C₂²×C₈

C₂×D₁₇

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₁₇

yes

characteristic

C₄⋊C₈

—

#95

—

#95

—

C₁₇

#1832

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₄×D₁₇

yes

—

C₂²×C₄

C₂²×D₁₇

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₂³

C₂×C₄×D₁₇

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

#63252

yes

—

104

C₂×C₄

D₄×D₁₇

yes

characteristic

105

C₂×C₄

#63254

yes

—

106

C₂×C₄

Q₈×D₁₇

yes

characteristic

107

C₈

—

108

C₈

—

109

C₂²

#10587558

yes

characteristic

110

C₂²

#10587563

yes

characteristic

111

C₂²

C₄⋊C₄×D₁₇

yes

characteristic

112

C₂²

#10587587

yes

—

113

C₂²

#10587593

yes

—

114

C₄

—

115

C₄

—

116

C₄

—

117

C₄

—

118

C₄

#10587571

yes

—

119

C₄

#10587575

yes

—

120

C₂

#11762673

yes

characteristic

121

C₂

#11762834

yes

—

122

C₂

#11762867

yes

—

123

C₂

#11762868

yes

characteristic

124

C₂

#11762871

yes

characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₁₇
commutator, socle, prime radical	C₂³×C₁₇	C₂²×C₄
Fitting	C₁₇×#336	C₂
cosocle	C₂²×C₄×C₁₇	C₂³
hypercenter	#336	D₁₇
hypocenter	C₁₇	#1832
LCS	G ▷ C₂³×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂²×C₄ ◁ #336

subgroup

G/H

center, Frattini

C₂²×C₄

C₂²×D₁₇

commutator, socle, prime radical

C₂³×C₁₇

C₂²×C₄

Fitting

C₁₇×#336

C₂

cosocle

C₂²×C₄×C₁₇

C₂³

D₁₇

C₁₇

G ▷ C₂³×C₁₇ ▷ C₁₇

C₁ ◁ C₂²×C₄ ◁ #336

N	H ≅ G/N	type
76. C₁₇	#1832	semidirect

H ≅ G/N

type

76. C₁₇

#1832

semidirect

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

subgroup	index
C₂×#10587485	2
#11762655	2
#11762564	2
#11762563	2
C₁₇×#336	2
#1832	17

subgroup

index

C₁₇×#336

Subgroups — #14528902

Conjugacy classes of subgroups

Complements

Maximal subgroups