Group #17982790 — subgroups

Subgroups — #17982790

Order 4352.

170 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 67 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	#14545884	C₂	1	2	yes	maximal, complemented
2	#14545878	C₂	1	2	yes	maximal
3	#14545873	C₂	1	2	yes	maximal, complemented
4	#14544990	C₂	1	1	yes	maximal, characteristic
5	#11763917	C₂²	1	4	yes	—
6	C₂×#10587538	C₄	1	1	yes	characteristic
7	C₂×#10587538	C₂²	1	1	yes	characteristic
8	#11763698	C₄	1	1	yes	characteristic
9	#11763698	C₂²	1	1	yes	characteristic
10	#11763695	C₄	1	1	yes	characteristic
11	#11763695	C₂²	1	1	yes	characteristic
12	C₂×C₈×Dic₁₇	C₄	1	1	yes	characteristic
13	C₂²×C₈×C₁₇	C₈	1	1	yes	characteristic
14	C₂×C₄×Dic₁₇	C₈	1	1	yes	characteristic
15	C₂²×#3622	C₂×C₄	1	1	yes	characteristic
16	#10587538	—	2	2	no	—
17	#10587538	—	2	2	no	—
18	C₂×#63216	C₂×C₄	1	1	yes	characteristic
19	C₂×#63216	C₂×C₄	1	1	yes	characteristic
20	C₂×#63216	C₂×C₄	1	1	yes	characteristic
21	C₂×#63216	C₂³	1	1	yes	characteristic
22	#10587528	—	2	4	no	—
23	C₈×Dic₁₇	C₈	1	1	yes	characteristic
24	C₈×Dic₁₇	C₈	1	1	yes	characteristic
25	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
26	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
27	C₂²×C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
28	C₂²×Dic₁₇	—	2	1	no	—
29	C₂×C₈×C₁₇	—	2	2	no	—
30	C₂×C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
31	C₂×C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
32	C₄×Dic₁₇	—	2	1	no	—
33	C₄×Dic₁₇	C₂×C₈	1	1	yes	characteristic
34	C₄×Dic₁₇	C₂×C₈	1	1	yes	characteristic
35	C₂×#3622	—	2	1	no	—
36	C₂×#3622	—	2	1	no	—
37	C₂×#3622	C₂×C₈	1	1	yes	characteristic
38	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
39	#63216	—	2	1	no	—
40	#63216	—	2	1	no	—
41	#63216	M₁₆	1	2	yes	—
42	#63216	#41	1	2	yes	—
43	#13642	—	17	1	no	maximal, Sylow
44	C₂³×C₁₇	M₃₂	1	1	yes	characteristic
45	C₂×C₄×C₁₇	—	2	1	no	—
46	C₂×C₄×C₁₇	—	2	1	no	—
47	C₂×C₄×C₁₇	M₃₂	1	1	yes	characteristic
48	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
49	C₂×Dic₁₇	—	2	1	no	—
50	C₂×Dic₁₇	—	2	1	no	—
51	C₂×Dic₁₇	—	4	2	no	—
52	C₈×C₁₇	—	2	1	no	—
53	C₈×C₁₇	M₃₂	1	2	yes	—
54	#3622	—	2	1	no	—
55	#3622	#117	1	1	yes	characteristic
56	#3622	C₂×M₁₆	1	1	yes	characteristic
57	C₄×M₃₂	—	17	1	no	—
58	#1422	—	17	2	no	—
59	#1400	—	17	2	no	—
60	#1398	—	17	2	no	—
61	C₂²×C₁₇	—	2	1	no	—
62	C₂²×C₁₇	—	4	1	no	—
63	C₂²×C₁₇	C₂×M₃₂	1	1	yes	characteristic
64	C₄×C₁₇	—	2	1	no	—
65	C₄×C₁₇	#431	1	1	yes	characteristic
66	C₄×C₁₇	C₂×M₃₂	1	1	yes	characteristic
67	Dic₁₇	—	2	2	no	—
68	Dic₁₇	—	4	1	no	—
69	C₂×M₃₂	—	17	1	no	—
70	C₂×M₃₂	—	17	1	no	—
71	C₂×C₄×C₈	—	17	1	no	—
72	M₆₄	—	17	4	no	—
73	#346	—	17	1	no	—
74	#346	—	17	1	no	—
75	C₄×C₁₆	—	17	1	no	—
76	C₄×C₁₆	—	17	1	no	—
77	C₂×C₁₇	—	2	1	no	—
78	C₂×C₁₇	—	4	1	no	—
79	C₂×C₁₇	#2163	1	1	yes	characteristic
80	C₂²×C₈	—	17	1	no	—
81	C₂²×C₈	#3633	1	1	yes	characteristic
82	C₂×C₄²	—	17	1	no	—
83	M₃₂	—	34	2	no	—
84	M₃₂	—	34	2	no	—
85	C₂×C₁₆	—	17	1	no	—
86	C₂×C₁₆	—	17	1	no	—
87	C₂×C₁₆	—	17	1	no	—
88	C₂×C₁₆	—	17	1	no	—
89	C₄×C₈	—	17	1	no	—
90	C₄×C₈	—	17	1	no	—
91	C₄×C₈	—	17	1	no	—
92	C₄×C₈	—	17	1	no	—
93	C₃₂	—	34	4	no	—
94	C₁₇	#13642	1	1	yes	characteristic, complemented, Sylow
95	C₂²×C₄	—	34	1	no	—
96	C₂²×C₄	C₂×#3633	1	1	yes	characteristic
97	C₂×C₈	—	2	2	no	—
98	C₂×C₈	—	17	1	no	—
99	C₂×C₈	—	17	1	no	—
100	C₂×C₈	—	34	1	no	—
101	C₂×C₈	—	34	1	no	—
102	C₂×C₈	C₂×#3633	1	1	yes	characteristic
103	C₂×C₈	C₂×#3633	1	1	yes	characteristic
104	C₄²	—	17	1	no	—
105	C₄²	—	17	1	no	—
106	C₄²	—	34	1	no	—
107	C₁₆	—	17	2	no	—
108	C₁₆	—	17	2	no	—
109	C₁₆	—	34	1	no	—
110	C₁₆	—	34	1	no	—
111	C₂³	#10587666	1	1	yes	characteristic
112	C₂×C₄	—	2	1	no	—
113	C₂×C₄	—	2	1	no	—
114	C₂×C₄	—	34	1	no	—
115	C₂×C₄	—	34	1	no	—
116	C₂×C₄	—	68	2	no	—
117	C₂×C₄	#10587666	1	1	yes	characteristic
118	C₂×C₄	C₂²×#3633	1	1	yes	characteristic
119	C₈	—	2	1	no	—
120	C₈	—	17	1	no	—
121	C₈	—	17	1	no	—
122	C₈	—	34	1	no	—
123	C₈	#10587670	1	2	yes	—
124	C₂²	—	2	1	no	—
125	C₂²	—	4	1	no	—
126	C₂²	C₂×#10587666	1	1	yes	characteristic
127	C₄	—	2	1	no	—
128	C₄	—	34	2	no	—
129	C₄	—	68	1	no	—
130	C₄	#11763922	1	1	yes	characteristic
131	C₄	C₂×#10587670	1	1	yes	characteristic
132	C₂	—	2	1	no	—
133	C₂	—	4	1	no	—
134	C₂	#14545986	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14545884

C₂

yes

maximal, complemented

#14545878

C₂

yes

maximal

#14545873

C₂

yes

maximal, complemented

#14544990

C₂

yes

maximal, characteristic

#11763917

C₂²

yes

—

C₂×#10587538

C₄

yes

characteristic

C₂×#10587538

C₂²

yes

characteristic

#11763698

C₄

yes

characteristic

#11763698

C₂²

yes

characteristic

#11763695

C₄

yes

characteristic

#11763695

C₂²

yes

characteristic

C₂×C₈×Dic₁₇

C₄

yes

characteristic

C₂²×C₈×C₁₇

C₈

yes

characteristic

C₂×C₄×Dic₁₇

C₈

yes

characteristic

C₂²×#3622

C₂×C₄

yes

—

—

C₂×C₄

yes

characteristic

C₂×#63216

C₂×C₄

yes

characteristic

C₂×#63216

C₂×C₄

yes

characteristic

C₂×#63216

C₂³

yes

characteristic

#10587528

—

C₈×Dic₁₇

C₈

yes

characteristic

C₈×Dic₁₇

C₈

yes

characteristic

C₈×Dic₁₇

C₂×C₄

yes

characteristic

C₈×Dic₁₇

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₇

C₂×C₈

yes

characteristic

C₂²×Dic₁₇

—

C₂×C₈×C₁₇

—

C₂×C₈×C₁₇

C₂×C₈

yes

characteristic

C₂×C₈×C₁₇

C₂×C₈

yes

characteristic

C₄×Dic₁₇

—

C₄×Dic₁₇

C₂×C₈

yes

characteristic

C₄×Dic₁₇

C₂×C₈

yes

—

—

C₂×C₈

yes

characteristic

C₂×#3622

C₂²×C₄

yes

—

—

M₁₆

yes

—

#63216

#41

yes

—

#13642

—

maximal, Sylow

C₂³×C₁₇

M₃₂

yes

characteristic

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

M₃₂

yes

characteristic

C₂×C₄×C₁₇

C₂²×C₈

yes

characteristic

C₂×Dic₁₇

—

C₂×Dic₁₇

—

C₂×Dic₁₇

—

C₈×C₁₇

—

C₈×C₁₇

M₃₂

yes

—

—

yes

C₂×M₁₆

yes

characteristic

C₄×M₃₂

—

#1422

—

#1400

—

#1398

—

C₂²×C₁₇

—

C₂²×C₁₇

—

C₂²×C₁₇

C₂×M₃₂

yes

characteristic

C₄×C₁₇

—

C₄×C₁₇

#431

yes

characteristic

C₄×C₁₇

C₂×M₃₂

yes

characteristic

Dic₁₇

—

Dic₁₇

—

C₂×M₃₂

—

C₂×M₃₂

—

C₂×C₄×C₈

—

M₆₄

—

#346

—

#346

—

C₄×C₁₆

—

C₄×C₁₆

—

C₂×C₁₇

—

C₂×C₁₇

—

C₂×C₁₇

#2163

yes

characteristic

C₂²×C₈

—

C₂²×C₈

#3633

yes

characteristic

C₂×C₄²

—

M₃₂

—

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₃₂

—

C₁₇

#13642

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

C₂×#3633

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

100

C₂×C₈

—

101

C₂×C₈

—

102

C₂×C₈

C₂×#3633

yes

characteristic

103

C₂×C₈

C₂×#3633

yes

characteristic

104

C₄²

—

105

C₄²

—

106

C₄²

—

107

C₁₆

—

108

C₁₆

—

109

C₁₆

—

110

C₁₆

—

111

C₂³

#10587666

yes

characteristic

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

#10587666

yes

characteristic

118

C₂×C₄

C₂²×#3633

yes

characteristic

119

C₈

—

120

C₈

—

121

C₈

—

122

C₈

—

123

C₈

#10587670

yes

—

124

C₂²

—

125

C₂²

—

126

C₂²

C₂×#10587666

yes

characteristic

127

C₄

—

128

C₄

—

129

C₄

—

130

C₄

#11763922

yes

characteristic

131

C₄

C₂×#10587670

yes

characteristic

132

C₂

—

133

C₂

—

134

C₂

#14545986

yes

characteristic

	subgroup	G/H
center	C₄	#11763922
commutator	C₂×C₄×C₁₇	C₂²×C₈
Frattini	C₂×C₄	C₂²×#3633
Fitting	C₂²×C₈×C₁₇	C₈
socle	C₂×C₁₇	#2163
prime radical	C₂³×C₁₇	M₃₂
cosocle	C₂×#63216	C₂³
hypercenter	C₂²×C₈	#3633
hypocenter	C₁₇	#13642
LCS	G ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ C₂²×C₈

subgroup

G/H

center

C₄

#11763922

commutator

C₂×C₄×C₁₇

C₂²×C₈

Frattini

C₂×C₄

C₂²×#3633

Fitting

C₂²×C₈×C₁₇

C₈

socle

C₂×C₁₇

#2163

prime radical

C₂³×C₁₇

M₃₂

C₂³

C₂²×C₈

C₁₇

G ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇

UCS

C₁ ◁ C₄ ◁ C₂×C₈ ◁ C₂²×C₈

N	H ≅ G/N	type
1. #14545884	C₂	semidirect
3. #14545873	C₂	semidirect
94. C₁₇	#13642	semidirect

H ≅ G/N

type

1. #14545884

C₂

semidirect

3. #14545873

C₂

semidirect

94. C₁₇

#13642

semidirect

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

subgroup	index
#14545884	2
#14545878	2
#14545873	2
#14544990	2
#13642	17

subgroup

index

Subgroups — #17982790

Conjugacy classes of subgroups

Complements

Maximal subgroups