Group #17958058 — subgroups

Subgroups — #17958058

Order 4352.

306 conjugacy classes of subgroups; only the 152 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 152 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	#14545143	C₂	1	2	yes	maximal
2	#14543699	C₂	1	2	yes	maximal, complemented
3	C₈×#63216	C₂	1	2	yes	maximal, complemented
4	C₈²×D₁₇	C₂	1	1	yes	maximal, characteristic
5	#11763730	C₄	1	4	yes	—
6	#11763704	C₄	1	4	yes	—
7	C₄×#63216	C₂²	1	4	yes	—
8	C₄×C₈×D₁₇	C₄	1	1	yes	characteristic
9	C₄×C₈×D₁₇	C₄	1	1	yes	characteristic
10	C₄×C₈×D₁₇	C₂²	1	1	yes	characteristic
11	C₈×#3622	C₄	1	1	yes	characteristic
12	C₈×#3622	C₂²	1	1	yes	characteristic
13	C₈×#3622	C₂²	1	1	yes	characteristic
14	C₈²×C₁₇	C₄	1	1	yes	characteristic
15	C₂×C₈×D₁₇	C₈	1	2	yes	—
16	C₂×C₈×D₁₇	C₈	1	2	yes	—
17	C₂×C₈×D₁₇	C₂×C₄	1	2	yes	—
18	C₄²×D₁₇	C₂×C₄	1	1	yes	characteristic
19	C₂×#63216	C₂×C₄	1	8	yes	—
20	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
21	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
22	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
23	C₈×Dic₁₇	C₈	1	2	yes	—
24	C₈×Dic₁₇	C₈	1	2	yes	—
25	C₈×Dic₁₇	C₂×C₄	1	2	yes	—
26	C₄×#3622	C₂×C₄	1	1	yes	characteristic
27	C₄×#3622	C₂×C₄	1	1	yes	characteristic
28	C₄×#3622	C₂³	1	1	yes	characteristic
29	C₂×C₄×D₁₇	C₄²	1	1	yes	characteristic
30	C₂×C₄×D₁₇	C₂×C₈	1	1	yes	characteristic
31	C₂×C₄×D₁₇	C₂×C₈	1	1	yes	characteristic
32	C₂×C₈×C₁₇	C₄²	1	2	yes	—
33	C₂×C₈×C₁₇	C₂×C₈	1	2	yes	—
34	C₂×C₈×C₁₇	C₂×C₈	1	2	yes	—
35	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
36	C₄×Dic₁₇	C₄²	1	1	yes	characteristic
37	C₄×Dic₁₇	C₂×C₈	1	1	yes	characteristic
38	C₄×Dic₁₇	C₂×C₈	1	1	yes	characteristic
39	C₂×#3622	C₂×C₈	1	2	yes	—
40	C₂×#3622	C₂×C₈	1	2	yes	—
41	C₂×#3622	C₂²×C₄	1	2	yes	—
42	C₈×D₁₇	—	2	4	no	—
43	C₈×D₁₇	—	2	4	no	—
44	C₈×D₁₇	C₁₆	1	8	yes	complemented
45	#63216	—	2	8	no	—
46	#11410	—	17	1	no	maximal, Sylow
47	C₂²×D₁₇	C₄×C₈	1	1	yes	characteristic
48	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
49	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
50	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
51	C₂×Dic₁₇	C₄×C₈	1	1	yes	characteristic
52	C₂×Dic₁₇	C₄×C₈	1	1	yes	characteristic
53	C₂×Dic₁₇	C₄×C₈	1	1	yes	characteristic
54	C₄×D₁₇	—	2	2	no	—
55	C₄×D₁₇	—	2	2	no	—
56	C₄×D₁₇	C₂×C₁₆	1	4	yes	—
57	C₈×C₁₇	—	2	2	no	—
58	C₈×C₁₇	—	2	2	no	—
59	C₈×C₁₇	C₂×C₁₆	1	4	yes	—
60	#3622	C₂×C₁₆	1	4	yes	—
61	#3622	M₃₂	1	4	yes	—
62	#3622	#131	1	4	yes	—
63	#2162	—	17	2	no	—
64	C₂×C₈²	—	17	1	no	—
65	#1312	—	17	2	no	—
66	C₈×C₁₆	—	17	2	no	—
67	C₂²×C₁₇	C₂×C₄×C₈	1	1	yes	characteristic
68	C₂×D₁₇	—	2	1	no	—
69	C₂×D₁₇	—	2	1	no	—
70	C₂×D₁₇	C₄×C₁₆	1	2	yes	—
71	C₄×C₁₇	#405	1	2	yes	—
72	C₄×C₁₇	C₂²×C₁₆	1	2	yes	—
73	C₄×C₁₇	C₂×M₃₂	1	2	yes	—
74	Dic₁₇	—	2	1	no	—
75	Dic₁₇	—	2	1	no	—
76	Dic₁₇	C₄×C₁₆	1	2	yes	—
77	C₂×C₄×C₈	—	17	1	no	—
78	C₂×C₄×C₈	—	17	1	no	—
79	C₂×C₄×C₈	—	17	1	no	—
80	C₄⋊C₁₆	—	17	4	no	—
81	C₂²⋊C₁₆	—	17	4	no	—
82	C₄×C₁₆	—	17	4	no	—
83	C₈²	—	17	1	no	—
84	C₈²	—	17	1	no	—
85	C₈²	—	17	1	no	—
86	C₈²	#595	1	1	yes	characteristic
87	C₂×C₁₇	#1450	1	1	yes	characteristic
88	C₂×C₁₇	C₂×C₄×C₁₆	1	1	yes	characteristic
89	C₂×C₁₇	C₄×M₃₂	1	1	yes	characteristic
90	D₁₇	—	2	2	no	—
91	C₂²×C₈	—	17	2	no	—
92	C₂²×C₈	—	17	2	no	—
93	C₂²×C₈	—	17	2	no	—
94	C₂×C₄²	—	17	1	no	—
95	C₂×C₁₆	—	17	8	no	—
96	C₄×C₈	—	17	2	no	—
97	C₄×C₈	—	17	2	no	—
98	C₄×C₈	—	17	2	no	—
99	C₄×C₈	—	17	1	no	—
100	C₄×C₈	—	17	1	no	—
101	C₄×C₈	—	17	1	no	—
102	C₄×C₈	C₂×#595	1	1	yes	characteristic
103	C₄×C₈	C₂×#595	1	1	yes	characteristic
104	C₄×C₈	C₂×#595	1	1	yes	characteristic
105	C₁₇	#11410	1	1	yes	characteristic, complemented, Sylow
106	C₂²×C₄	—	17	1	no	—
107	C₂²×C₄	—	17	1	no	—
108	C₂²×C₄	—	17	1	no	—
109	C₂×C₈	—	17	2	no	—
110	C₂×C₈	—	17	2	no	—
111	C₂×C₈	—	17	2	no	—
112	C₂×C₈	—	17	8	no	—
113	C₂×C₈	—	34	4	no	—
114	C₂×C₈	—	34	4	no	—
115	C₂×C₈	#63242	1	2	yes	—
116	C₂×C₈	#63242	1	2	yes	—
117	C₂×C₈	C₄×#595	1	2	yes	—
118	C₄²	—	17	1	no	—
119	C₄²	—	17	1	no	—
120	C₄²	—	17	1	no	—
121	C₄²	C₂²×#595	1	1	yes	characteristic
122	C₁₆	—	34	8	no	—
123	C₂³	—	17	1	no	—
124	C₂×C₄	—	17	1	no	—
125	C₂×C₄	—	17	4	no	—
126	C₂×C₄	—	17	1	no	—
127	C₂×C₄	—	17	1	no	—
128	C₂×C₄	—	34	2	no	—
129	C₂×C₄	—	34	2	no	—
130	C₂×C₄	C₂×#63242	1	1	yes	characteristic
131	C₂×C₄	C₂×#63242	1	1	yes	characteristic
132	C₂×C₄	C₂×C₄×#595	1	1	yes	characteristic
133	C₈	—	2	2	no	—
134	C₈	—	2	2	no	—
135	C₈	—	17	4	no	—
136	C₈	—	17	4	no	—
137	C₈	—	17	4	no	—
138	C₈	#10587529	1	4	yes	—
139	C₂²	—	17	2	no	—
140	C₂²	—	34	1	no	—
141	C₂²	—	34	1	no	—
142	C₂²	C₄×#63242	1	1	yes	characteristic
143	C₄	—	17	2	no	—
144	C₄	—	34	1	no	—
145	C₄	—	34	1	no	—
146	C₄	#11763772	1	2	yes	—
147	C₄	C₂×#10587529	1	2	yes	—
148	C₄	#11763865	1	2	yes	—
149	C₂	—	34	2	no	—
150	C₂	#14543988	1	1	yes	characteristic
151	C₂	C₄×#10587529	1	1	yes	characteristic
152	C₂	#14544991	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14545143

C₂

yes

maximal

#14543699

C₂

yes

maximal, complemented

C₈×#63216

C₂

yes

maximal, complemented

C₈²×D₁₇

C₂

yes

maximal, characteristic

#11763730

C₄

yes

—

#11763704

C₄

yes

—

C₄×#63216

C₂²

yes

—

C₄×C₈×D₁₇

C₄

yes

characteristic

C₄×C₈×D₁₇

C₄

yes

characteristic

C₄×C₈×D₁₇

C₂²

yes

characteristic

C₈×#3622

C₄

yes

characteristic

C₈×#3622

C₂²

yes

characteristic

C₈×#3622

C₂²

yes

characteristic

C₈²×C₁₇

C₄

yes

characteristic

C₂×C₈×D₁₇

C₈

yes

—

C₂×C₈×D₁₇

C₈

yes

—

C₂×C₈×D₁₇

C₂×C₄

yes

—

C₄²×D₁₇

C₂×C₄

yes

characteristic

C₂×#63216

C₂×C₄

yes

—

C₄×C₈×C₁₇

C₂×C₄

yes

characteristic

C₄×C₈×C₁₇

C₂×C₄

yes

characteristic

C₄×C₈×C₁₇

C₂×C₄

yes

characteristic

C₈×Dic₁₇

C₈

yes

—

C₈×Dic₁₇

C₈

yes

—

C₈×Dic₁₇

C₂×C₄

yes

—

C₄×#3622

C₂×C₄

yes

characteristic

C₄×#3622

C₂×C₄

yes

characteristic

C₄×#3622

C₂³

yes

characteristic

C₂×C₄×D₁₇

C₄²

yes

characteristic

C₂×C₄×D₁₇

C₂×C₈

yes

characteristic

C₂×C₄×D₁₇

C₂×C₈

yes

characteristic

C₂×C₈×C₁₇

C₄²

yes

—

C₂×C₈×C₁₇

C₂×C₈

yes

—

C₂×C₈×C₁₇

C₂×C₈

yes

—

C₄²×C₁₇

C₂²×C₄

yes

characteristic

C₄×Dic₁₇

C₄²

yes

characteristic

C₄×Dic₁₇

C₂×C₈

yes

characteristic

C₄×Dic₁₇

C₂×C₈

yes

characteristic

C₂×#3622

C₂×C₈

yes

—

C₂×#3622

C₂×C₈

yes

—

C₂×#3622

C₂²×C₄

yes

—

C₈×D₁₇

—

C₈×D₁₇

—

C₈×D₁₇

C₁₆

yes

—

—

C₂²×D₁₇

C₄×C₈

yes

characteristic

C₂×C₄×C₁₇

C₂×C₄²

yes

characteristic

C₂×C₄×C₁₇

C₂²×C₈

yes

characteristic

C₂×C₄×C₁₇

C₂²×C₈

yes

characteristic

C₂×Dic₁₇

C₄×C₈

yes

characteristic

C₂×Dic₁₇

C₄×C₈

yes

characteristic

C₂×Dic₁₇

C₄×C₈

yes

characteristic

C₄×D₁₇

—

C₄×D₁₇

—

C₄×D₁₇

C₂×C₁₆

yes

—

C₈×C₁₇

—

C₈×C₁₇

—

C₈×C₁₇

C₂×C₁₆

yes

—

#3622

C₂×C₁₆

yes

—

#3622

M₃₂

yes

—

#3622

#131

yes

—

#2162

—

C₂×C₈²

—

#1312

—

C₈×C₁₆

—

C₂²×C₁₇

C₂×C₄×C₈

yes

characteristic

C₂×D₁₇

—

C₂×D₁₇

—

C₂×D₁₇

C₄×C₁₆

yes

—

C₄×C₁₇

#405

yes

—

C₄×C₁₇

C₂²×C₁₆

yes

—

C₄×C₁₇

C₂×M₃₂

yes

—

Dic₁₇

—

Dic₁₇

—

Dic₁₇

C₄×C₁₆

yes

—

C₂×C₄×C₈

—

C₂×C₄×C₈

—

C₂×C₄×C₈

—

C₄⋊C₁₆

—

C₂²⋊C₁₆

—

C₄×C₁₆

—

C₈²

—

C₈²

—

C₈²

—

C₈²

yes

C₂×C₁₇

yes

C₂×C₁₇

C₂×C₄×C₁₆

yes

characteristic

C₂×C₁₇

C₄×M₃₂

yes

characteristic

D₁₇

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

C₂×C₁₆

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

100

C₄×C₈

—

101

C₄×C₈

—

102

C₄×C₈

C₂×#595

yes

characteristic

103

C₄×C₈

C₂×#595

yes

characteristic

104

C₄×C₈

C₂×#595

yes

characteristic

105

C₁₇

#11410

yes

characteristic, complemented, Sylow

106

C₂²×C₄

—

107

C₂²×C₄

—

108

C₂²×C₄

—

109

C₂×C₈

—

110

C₂×C₈

—

111

C₂×C₈

—

112

C₂×C₈

—

113

C₂×C₈

—

114

C₂×C₈

—

115

C₂×C₈

#63242

yes

—

116

C₂×C₈

#63242

yes

—

117

C₂×C₈

C₄×#595

yes

—

118

C₄²

—

119

C₄²

—

120

C₄²

—

121

C₄²

C₂²×#595

yes

characteristic

122

C₁₆

—

123

C₂³

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

C₂×#63242

yes

characteristic

131

C₂×C₄

C₂×#63242

yes

characteristic

132

C₂×C₄

C₂×C₄×#595

yes

characteristic

133

C₈

—

134

C₈

—

135

C₈

—

136

C₈

—

137

C₈

—

138

C₈

#10587529

yes

—

139

C₂²

—

140

C₂²

—

141

C₂²

—

142

C₂²

C₄×#63242

yes

characteristic

143

C₄

—

144

C₄

—

145

C₄

—

146

C₄

#11763772

yes

—

147

C₄

C₂×#10587529

yes

—

148

C₄

#11763865

yes

—

149

C₂

—

150

C₂

#14543988

yes

characteristic

151

C₂

C₄×#10587529

yes

characteristic

152

C₂

#14544991

yes

characteristic

	subgroup	G/H
center	C₄×C₈	C₂×#595
commutator	C₂×C₁₇	C₂×C₄×C₁₆
Frattini	C₄²	C₂²×#595
Fitting	C₈²×C₁₇	C₄
socle	C₂²×C₁₇	C₂×C₄×C₈
prime radical	C₂²×D₁₇	C₄×C₈
cosocle	C₄×#3622	C₂³
hypercenter	C₈²	#595
hypocenter	C₁₇	#11410
LCS	G ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₄×C₈ ◁ C₈²

subgroup

G/H

center

C₄×C₈

C₂×#595

commutator

C₂×C₁₇

C₂×C₄×C₁₆

Frattini

C₄²

C₂²×#595

Fitting

C₈²×C₁₇

C₄

socle

C₂²×C₁₇

C₂×C₄×C₈

prime radical

C₂²×D₁₇

C₄×C₈

C₂³

C₈²

C₁₇

G ▷ C₂×C₁₇ ▷ C₁₇

C₁ ◁ C₄×C₈ ◁ C₈²

N	H ≅ G/N	type
2. #14543699	C₂	semidirect
3. C₈×#63216	C₂	semidirect
44. C₈×D₁₇	C₁₆	semidirect
105. C₁₇	#11410	semidirect

H ≅ G/N

type

2. #14543699

C₂

semidirect

3. C₈×#63216

C₂

semidirect

44. C₈×D₁₇

C₁₆

semidirect

105. C₁₇

#11410

semidirect

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

subgroup	index
#14545143	2
#14543699	2
C₈×#63216	2
C₈²×D₁₇	2
#11410	17

subgroup

index

C₈²×D₁₇

Subgroups — #17958058

Conjugacy classes of subgroups

Complements

Maximal subgroups