Group #14528638 — subgroups

Subgroups — #14528638

Order 2176.

292 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 141 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	C₂×#10587474	C₂	1	1	yes	maximal, characteristic
3	C₄²×Dic₁₇	C₂	1	1	yes	maximal, characteristic
4	#11762563	C₂	1	2	yes	maximal
5	C₂×C₁₇×#97	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	C₄	1	2	yes	—
9	C₂×C₄×Dic₁₇	C₄	1	2	yes	—
10	C₂×C₄×Dic₁₇	C₂²	1	1	yes	characteristic
11	C₂×C₄×Dic₁₇	C₂²	1	1	yes	characteristic
12	C₂²×#3622	C₂²	1	2	yes	—
13	C₁₇×#97	—	2	2	no	—
14	#10587485	C₄	1	8	yes	complemented
15	#10587474	—	2	2	no	—
16	C₂²×C₄×C₁₇	C₂×C₄	1	2	yes	—
17	C₂²×C₄×C₁₇	C₂³	1	1	yes	characteristic
18	C₂²×Dic₁₇	C₂×C₄	1	1	yes	characteristic
19	C₂²×Dic₁₇	C₂×C₄	1	2	yes	—
20	C₂²×Dic₁₇	C₂×C₄	1	1	yes	characteristic
21	C₂×C₈×C₁₇	—	2	2	no	—
22	C₂×C₈×C₁₇	—	2	2	no	—
23	C₂×C₈×C₁₇	C₂×C₄	1	4	yes	—
24	C₄²×C₁₇	D₄	1	2	yes	—
25	C₄²×C₁₇	Q₈	1	2	yes	—
26	C₄×Dic₁₇	—	2	2	no	—
27	C₄×Dic₁₇	—	2	4	no	—
28	C₄×Dic₁₇	—	2	4	no	—
29	C₄×Dic₁₇	C₂×C₄	1	4	yes	—
30	C₂×#3622	—	2	2	no	—
31	C₂×#3622	—	2	2	no	—
32	C₂×#3622	C₂×C₄	1	4	yes	—
33	C₂³×C₁₇	C₂²×C₄	1	1	yes	characteristic
34	C₂×C₄×C₁₇	—	2	2	no	—
35	C₂×C₄×C₁₇	—	2	2	no	—
36	C₂×C₄×C₁₇	C₄⋊C₄	1	4	yes	—
37	C₂×C₄×C₁₇	C₂²×C₄	1	2	yes	—
38	C₂×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
39	C₂×C₄×C₁₇	C₂×Q₈	1	1	yes	characteristic
40	C₂×C₄×C₁₇	#41	1	2	yes	—
41	C₂×Dic₁₇	—	2	2	no	—
42	C₂×Dic₁₇	—	2	2	no	—
43	C₂×Dic₁₇	—	2	2	no	—
44	C₂×Dic₁₇	C₄²	1	2	yes	—
45	C₂×Dic₁₇	C₄²	1	2	yes	—
46	C₂×Dic₁₇	M₁₆	1	4	yes	—
47	C₂×Dic₁₇	M₁₆	1	4	yes	—
48	C₈×C₁₇	—	2	4	no	—
49	#3622	—	2	4	no	—
50	#1767	—	17	1	no	maximal, Sylow
51	C₂²×C₁₇	C₂×C₄²	1	1	yes	characteristic
52	C₂²×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
53	C₂²×C₁₇	#117	1	1	yes	characteristic
54	C₂²×C₁₇	C₂×M₁₆	1	2	yes	—
55	C₂²×C₁₇	C₂×M₁₆	1	2	yes	—
56	C₄×C₁₇	—	2	4	no	—
57	C₄×C₁₇	C₄×D₄	1	2	yes	—
58	C₄×C₁₇	C₄×Q₈	1	2	yes	—
59	Dic₁₇	—	2	2	no	—
60	Dic₁₇	—	2	4	no	—
61	Dic₁₇	#97	1	4	yes	complemented
62	C₂×C₄⋊C₈	—	17	2	no	—
63	C₂×#97	—	17	1	no	—
64	C₂×#97	D₁₇	1	1	yes	characteristic
65	C₄³	—	17	1	no	—
66	#336	—	17	2	no	—
67	C₂×C₁₇	C₄×C₄⋊C₄	1	1	yes	characteristic
68	C₂×C₁₇	C₂×#97	1	1	yes	characteristic
69	C₂×C₁₇	C₄×M₁₆	1	1	yes	characteristic
70	C₂×C₁₇	#423	1	2	yes	—
71	C₂×C₁₇	#432	1	2	yes	—
72	C₂²×C₈	—	17	2	no	—
73	C₂²×C₈	C₂×D₁₇	1	2	yes	—
74	C₂×C₄²	—	17	1	no	—
75	C₂×C₄²	—	17	2	no	—
76	C₂×C₄²	—	17	2	no	—
77	C₂×C₄²	—	17	1	no	—
78	C₂×C₄²	C₂×D₁₇	1	1	yes	characteristic
79	C₄⋊C₈	—	17	8	no	—
80	#97	—	2	2	no	—
81	#97	—	34	2	no	—
82	C₁₇	#1767	1	1	yes	characteristic, complemented, Sylow
83	C₂²×C₄	—	17	1	no	—
84	C₂²×C₄	—	17	1	no	—
85	C₂²×C₄	—	17	2	no	—
86	C₂²×C₄	C₄×D₁₇	1	2	yes	—
87	C₂²×C₄	C₂²×D₁₇	1	1	yes	characteristic
88	C₂×C₈	—	2	2	no	—
89	C₂×C₈	—	2	2	no	—
90	C₂×C₈	—	17	4	no	—
91	C₂×C₈	—	34	2	no	—
92	C₂×C₈	—	34	2	no	—
93	C₂×C₈	C₄×D₁₇	1	4	yes	—
94	C₄²	—	17	4	no	—
95	C₄²	—	34	4	no	—
96	C₄²	—	34	4	no	—
97	C₄²	—	34	2	no	—
98	C₄²	Dic₃₄	1	2	yes	—
99	C₄²	C₂²⋊D₁₇	1	2	yes	—
100	C₂³	C₂×C₄×D₁₇	1	1	yes	characteristic
101	C₂×C₄	—	2	2	no	—
102	C₂×C₄	—	2	2	no	—
103	C₂×C₄	—	17	2	no	—
104	C₂×C₄	—	17	4	no	—
105	C₂×C₄	—	17	2	no	—
106	C₂×C₄	—	17	4	no	—
107	C₂×C₄	—	34	2	no	—
108	C₂×C₄	—	34	2	no	—
109	C₂×C₄	—	34	2	no	—
110	C₂×C₄	#63225	1	4	yes	—
111	C₂×C₄	C₂×Dic₃₄	1	1	yes	characteristic
112	C₂×C₄	C₂×C₄×D₁₇	1	2	yes	—
113	C₂×C₄	#63252	1	2	yes	—
114	C₂×C₄	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
115	C₈	—	2	4	no	—
116	C₈	—	34	4	no	—
117	C₂²	C₄²×D₁₇	1	1	yes	characteristic
118	C₂²	#10587558	1	1	yes	characteristic
119	C₂²	M₁₆×D₁₇	1	2	yes	—
120	C₂²	M₁₆×D₁₇	1	2	yes	—
121	C₂²	C₂×#63225	1	1	yes	characteristic
122	C₄	—	2	4	no	—
123	C₄	—	17	4	no	—
124	C₄	—	34	2	no	—
125	C₄	—	34	4	no	—
126	C₄	C₄×Dic₃₄	1	2	yes	—
127	C₄	C₄×C₂²⋊D₁₇	1	2	yes	—
128	C₂	C₄×#63225	1	1	yes	characteristic
129	C₂	#97×D₁₇	1	1	yes	characteristic
130	C₂	#11762761	1	1	yes	characteristic
131	C₂	#11762832	1	2	yes	—
132	C₂	#11762864	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10587485

C₂

yes

maximal

C₂×#10587474

C₂

yes

maximal, characteristic

C₄²×Dic₁₇

C₂

yes

maximal, characteristic

#11762563

C₂

yes

maximal

C₂×C₁₇×#97

C₂

yes

maximal, characteristic

C₂²×C₈×C₁₇

C₂²

yes

—

C₂×C₄²×C₁₇

C₂²

yes

characteristic

C₂×C₄×Dic₁₇

C₄

yes

—

C₂×C₄×Dic₁₇

C₄

yes

—

C₂×C₄×Dic₁₇

C₂²

yes

characteristic

C₂×C₄×Dic₁₇

C₂²

yes

characteristic

C₂²×#3622

C₂²

yes

—

C₁₇×#97

—

#10587485

C₄

yes

complemented

#10587474

—

C₂²×C₄×C₁₇

C₂×C₄

yes

—

C₂²×C₄×C₁₇

C₂³

yes

characteristic

C₂²×Dic₁₇

C₂×C₄

yes

characteristic

C₂²×Dic₁₇

C₂×C₄

yes

—

C₂²×Dic₁₇

C₂×C₄

yes

characteristic

C₂×C₈×C₁₇

—

C₂×C₈×C₁₇

—

C₂×C₈×C₁₇

C₂×C₄

yes

—

C₄²×C₁₇

D₄

yes

—

C₄²×C₁₇

Q₈

yes

—

C₄×Dic₁₇

—

C₄×Dic₁₇

—

C₄×Dic₁₇

—

C₄×Dic₁₇

C₂×C₄

yes

—

C₂×#3622

—

C₂×#3622

—

C₂×#3622

C₂×C₄

yes

—

C₂³×C₁₇

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

C₄⋊C₄

yes

—

C₂×C₄×C₁₇

C₂²×C₄

yes

—

C₂×C₄×C₁₇

C₂×D₄

yes

characteristic

C₂×C₄×C₁₇

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₇

#41

yes

—

C₂×Dic₁₇

—

C₂×Dic₁₇

—

C₂×Dic₁₇

—

C₂×Dic₁₇

C₄²

yes

—

C₂×Dic₁₇

C₄²

yes

—

C₂×Dic₁₇

M₁₆

yes

—

C₂×Dic₁₇

M₁₆

yes

—

C₈×C₁₇

—

#3622

—

#1767

—

maximal, Sylow

C₂²×C₁₇

C₂×C₄²

yes

characteristic

C₂²×C₁₇

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₁₇

#117

yes

characteristic

C₂²×C₁₇

C₂×M₁₆

yes

—

C₂²×C₁₇

C₂×M₁₆

yes

—

C₄×C₁₇

—

C₄×C₁₇

C₄×D₄

yes

—

C₄×C₁₇

C₄×Q₈

yes

—

Dic₁₇

—

Dic₁₇

—

Dic₁₇

#97

yes

complemented

C₂×C₄⋊C₈

—

C₂×#97

—

C₂×#97

D₁₇

yes

characteristic

C₄³

—

#336

—

C₂×C₁₇

C₄×C₄⋊C₄

yes

characteristic

C₂×C₁₇

C₂×#97

yes

characteristic

C₂×C₁₇

C₄×M₁₆

yes

characteristic

C₂×C₁₇

#423

yes

—

C₂×C₁₇

#432

yes

—

C₂²×C₈

—

C₂²×C₈

C₂×D₁₇

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₁₇

yes

characteristic

C₄⋊C₈

—

#97

—

#97

—

C₁₇

#1767

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

C₄×D₁₇

yes

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₄²

Dic₃₄

yes

—

C₄²

C₂²⋊D₁₇

yes

—

100

C₂³

C₂×C₄×D₁₇

yes

characteristic

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

#63225

yes

—

111

C₂×C₄

C₂×Dic₃₄

yes

characteristic

112

C₂×C₄

C₂×C₄×D₁₇

yes

—

113

C₂×C₄

#63252

yes

—

114

C₂×C₄

C₂×C₂²⋊D₁₇

yes

characteristic

115

C₈

—

116

C₈

—

117

C₂²

C₄²×D₁₇

yes

characteristic

118

C₂²

#10587558

yes

characteristic

119

C₂²

M₁₆×D₁₇

yes

—

120

C₂²

M₁₆×D₁₇

yes

—

121

C₂²

C₂×#63225

yes

characteristic

122

C₄

—

123

C₄

—

124

C₄

—

125

C₄

—

126

C₄

C₄×Dic₃₄

yes

—

127

C₄

C₄×C₂²⋊D₁₇

yes

—

128

C₂

C₄×#63225

yes

characteristic

129

C₂

#97×D₁₇

yes

characteristic

130

C₂

#11762761

yes

characteristic

131

C₂

#11762832

yes

—

132

C₂

#11762864

yes

—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₁₇
commutator	C₂²×C₁₇	C₂×C₄²
Fitting	C₂×C₁₇×#97	C₂
socle, prime radical	C₂³×C₁₇	C₂²×C₄
cosocle	C₂²×C₄×C₁₇	C₂³
hypercenter	C₂×#97	D₁₇
hypocenter	C₁₇	#1767
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#97

subgroup

G/H

center, Frattini

C₂²×C₄

C₂²×D₁₇

commutator

C₂²×C₁₇

C₂×C₄²

Fitting

C₂×C₁₇×#97

C₂

socle, prime radical

C₂³×C₁₇

C₂²×C₄

cosocle

C₂²×C₄×C₁₇

C₂³

hypercenter

C₂×#97

D₁₇

C₁₇

G ▷ C₂²×C₁₇ ▷ C₁₇

C₁ ◁ C₂²×C₄ ◁ C₂×#97

N	H ≅ G/N	type
14. #10587485	C₄	semidirect
61. Dic₁₇	#97	semidirect
82. C₁₇	#1767	semidirect

H ≅ G/N

type

14. #10587485

C₄

semidirect

61. Dic₁₇

#97

semidirect

82. C₁₇

#1767

semidirect

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

subgroup	index
C₂×#10587485	2
C₂×#10587474	2
C₄²×Dic₁₇	2
#11762563	2
C₂×C₁₇×#97	2
#1767	17

subgroup

index

C₄²×Dic₁₇

C₂×C₁₇×#97

Subgroups — #14528638

Conjugacy classes of subgroups

Complements

Maximal subgroups