Group #17960654 — subgroups

Subgroups — #17960654

Order 4352.

390 conjugacy classes of subgroups; only the 148 normal subgroups are shown.

normal subgroups only

This group has 390 conjugacy classes of subgroups — too many to draw. Only its 148 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	#14544985	C₂	1	1	yes	maximal, characteristic
2	C₄×C₈×#595	C₂	1	1	yes	maximal, characteristic
3	#14543821	C₂	1	4	yes	maximal
4	D₁₇×#346	C₂	1	1	yes	maximal, characteristic
5	C₂×#10587529	C₂²	1	2	yes	—
6	C₄×#63242	C₄	1	1	yes	characteristic
7	C₂×C₈×#595	C₄	1	2	yes	—
8	C₂×C₈×#595	C₂²	1	2	yes	—
9	C₄²×#595	C₄	1	1	yes	characteristic
10	#11763698	C₄	1	2	yes	complemented
11	#11763697	C₄	1	2	yes	complemented
12	C₂×C₁₆×D₁₇	C₂²	1	2	yes	—
13	C₄×C₈×D₁₇	C₂²	1	1	yes	characteristic
14	#11762585	C₄	1	1	yes	characteristic, complemented
15	#11762584	C₄	1	2	yes	complemented
16	C₁₇×#346	C₄	1	1	yes	characteristic, complemented
17	C₂×C₄×#595	C₈	1	4	yes	—
18	C₂×C₄×#595	C₂×C₄	1	2	yes	—
19	C₂×#63242	C₂×C₄	1	2	yes	—
20	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
21	C₂×C₈×D₁₇	C₂³	1	1	yes	characteristic
22	C₄²×D₁₇	C₂×C₄	1	1	yes	characteristic
23	C₄×#3624	C₈	1	4	yes	—
24	C₂×#63216	C₂×C₄	1	4	yes	—
25	C₈×#595	—	2	4	no	—
26	C₈×#595	—	2	4	no	—
27	#10587529	—	2	4	no	—
28	C₂×C₁₆×C₁₇	C₂×C₄	1	2	yes	—
29	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
30	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
31	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
32	C₂×#63214	C₂×C₄	1	2	yes	—
33	C₄×#3622	C₂×C₄	1	1	yes	characteristic
34	C₁₆×D₁₇	—	2	4	no	—
35	C₂²×#595	C₂×C₈	1	4	yes	—
36	C₂×C₄×D₁₇	C₂×C₈	1	2	yes	—
37	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
38	C₂×#3624	C₂×C₈	1	4	yes	—
39	C₄×#595	—	2	8	no	—
40	C₄×#595	—	2	2	no	—
41	C₄×#595	—	2	2	no	—
42	#63242	—	2	2	no	—
43	#63242	—	2	2	no	—
44	C₂×C₈×C₁₇	C₄²	1	1	yes	characteristic
45	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
46	C₄²×C₁₇	C₄²	1	1	yes	characteristic
47	C₄×Dic₁₇	C₄²	1	1	yes	characteristic
48	C₄×Dic₁₇	C₂×C₈	1	2	yes	—
49	C₂×#3622	C₄²	1	1	yes	characteristic
50	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
51	C₈×D₁₇	M₁₆	1	4	yes	—
52	C₈×D₁₇	#41	1	4	yes	—
53	#63216	—	2	4	no	—
54	C₁₆×C₁₇	—	2	2	no	—
55	#63214	—	2	2	no	—
56	#12591	—	17	1	no	maximal, Sylow
57	C₂²×D₁₇	C₂²×C₈	1	1	yes	characteristic
58	C₂×#595	—	2	4	no	—
59	C₂×#595	—	2	4	no	—
60	C₂×#595	M₃₂	1	8	yes	—
61	C₂×C₄×C₁₇	C₄×C₈	1	2	yes	—
62	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
63	C₂×Dic₁₇	C₄×C₈	1	2	yes	—
64	C₂×Dic₁₇	C₂²×C₈	1	1	yes	characteristic
65	C₄×D₁₇	—	2	4	no	—
66	C₄×D₁₇	#117	1	2	yes	—
67	C₄×D₁₇	C₂×M₁₆	1	2	yes	—
68	#3624	—	2	4	no	—
69	C₈×C₁₇	#97	1	2	yes	—
70	C₈×C₁₇	#117	1	2	yes	—
71	#3622	#97	1	2	yes	—
72	#3622	#117	1	2	yes	—
73	C₂×#346	—	17	1	no	—
74	C₂×#346	—	17	1	no	—
75	C₄²×C₈	—	17	1	no	—
76	#1374	—	17	4	no	—
77	C₂²×C₁₇	C₂×C₄×C₈	1	1	yes	characteristic
78	C₂×D₁₇	#431	1	2	yes	—
79	C₂×D₁₇	C₂×M₃₂	1	4	yes	—
80	#595	—	2	8	no	—
81	C₄×C₁₇	—	2	2	no	—
82	C₄×C₁₇	#376	1	1	yes	characteristic
83	C₄×C₁₇	C₂×#97	1	1	yes	characteristic
84	Dic₁₇	—	2	2	no	—
85	Dic₁₇	#431	1	2	yes	—
86	C₂²×C₁₆	—	17	2	no	—
87	C₂²×C₁₆	—	17	2	no	—
88	C₂×C₄×C₈	—	17	1	no	—
89	C₂×C₄×C₈	—	17	1	no	—
90	C₂×C₄×C₈	—	17	2	no	—
91	C₂×C₄×C₈	—	17	2	no	—
92	C₄³	—	17	1	no	—
93	#346	—	17	2	no	—
94	#346	—	17	2	no	—
95	#346	—	17	2	no	—
96	#346	—	17	1	no	—
97	#346	#595	1	1	yes	characteristic, complemented
98	C₂×C₁₇	#1744	1	1	yes	characteristic
99	C₂×C₁₇	C₄×M₃₂	1	2	yes	—
100	D₁₇	#2163	1	4	yes	—
101	C₂²×C₈	—	17	1	no	—
102	C₂²×C₈	—	17	1	no	—
103	C₂²×C₈	—	17	2	no	—
104	C₂×C₄²	—	17	1	no	—
105	C₂×C₄²	—	17	4	no	—
106	C₂×C₄²	—	17	2	no	—
107	C₂×C₁₆	—	17	4	no	—
108	C₂×C₁₆	—	17	2	no	—
109	C₂×C₁₆	—	34	4	no	—
110	C₂×C₁₆	—	34	4	no	—
111	C₂×C₁₆	C₂×#595	1	2	yes	—
112	C₄×C₈	—	17	4	no	—
113	C₄×C₈	—	17	1	no	—
114	C₄×C₈	—	17	1	no	—
115	C₄×C₈	—	17	1	no	—
116	C₄×C₈	—	34	4	no	—
117	C₄×C₈	—	34	4	no	—
118	C₄×C₈	C₂×#595	1	1	yes	characteristic
119	C₁₇	#12591	1	1	yes	characteristic, complemented, Sylow
120	C₂²×C₄	—	17	1	no	—
121	C₂²×C₄	—	17	4	no	—
122	C₂²×C₄	—	17	2	no	—
123	C₂×C₈	—	17	1	no	—
124	C₂×C₈	—	17	1	no	—
125	C₂×C₈	—	17	4	no	—
126	C₂×C₈	—	17	4	no	—
127	C₂×C₈	—	17	4	no	—
128	C₂×C₈	—	34	2	no	—
129	C₂×C₈	—	34	2	no	—
130	C₂×C₈	C₄×#595	1	1	yes	characteristic
131	C₂×C₈	C₂²×#595	1	1	yes	characteristic
132	C₄²	—	17	1	no	—
133	C₄²	—	17	2	no	—
134	C₄²	—	34	2	no	—
135	C₄²	—	34	2	no	—
136	C₄²	—	34	8	no	—
137	C₄²	C₄×#595	1	1	yes	characteristic
138	C₁₆	—	2	2	no	—
139	C₁₆	—	34	4	no	—
140	C₁₆	—	34	2	no	—
141	C₂³	—	17	1	no	—
142	C₂×C₄	—	17	1	no	—
143	C₂×C₄	—	17	2	no	—
144	C₂×C₄	—	17	2	no	—
145	C₂×C₄	—	17	8	no	—
146	C₂×C₄	—	17	2	no	—
147	C₂×C₄	—	34	4	no	—
148	C₂×C₄	—	34	4	no	—
149	C₂×C₄	—	34	4	no	—
150	C₂×C₄	C₈×#595	1	2	yes	—
151	C₂×C₄	C₂×C₄×#595	1	1	yes	characteristic
152	C₈	—	17	2	no	—
153	C₈	—	17	2	no	—
154	C₈	—	34	4	no	—
155	C₈	#10587532	1	2	yes	—
156	C₈	#10587677	1	2	yes	—
157	C₂²	—	17	4	no	—
158	C₂²	—	17	2	no	—
159	C₂²	C₂×C₈×#595	1	1	yes	characteristic
160	C₄	—	2	2	no	—
161	C₄	—	17	2	no	—
162	C₄	—	34	8	no	—
163	C₄	—	34	2	no	—
164	C₄	#11763745	1	1	yes	characteristic
165	C₄	C₂×#10587532	1	1	yes	characteristic
166	C₂	—	17	4	no	—
167	C₂	#14544497	1	1	yes	characteristic
168	C₂	M₃₂×#595	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14544985

C₂

yes

maximal, characteristic

C₄×C₈×#595

C₂

yes

maximal, characteristic

#14543821

C₂

yes

maximal

D₁₇×#346

C₂

yes

maximal, characteristic

C₂×#10587529

C₂²

yes

—

C₄×#63242

C₄

yes

characteristic

C₂×C₈×#595

C₄

yes

—

C₂×C₈×#595

C₂²

yes

—

C₄²×#595

C₄

yes

characteristic

#11763698

C₄

yes

complemented

#11763697

C₄

yes

complemented

C₂×C₁₆×D₁₇

C₂²

yes

—

C₄×C₈×D₁₇

C₂²

yes

characteristic

#11762585

C₄

yes

characteristic, complemented

#11762584

C₄

yes

complemented

C₁₇×#346

C₄

yes

characteristic, complemented

C₂×C₄×#595

C₈

yes

—

C₂×C₄×#595

C₂×C₄

yes

—

C₂×#63242

C₂×C₄

yes

—

C₂×C₈×D₁₇

C₂×C₄

yes

characteristic

C₂×C₈×D₁₇

C₂³

yes

characteristic

C₄²×D₁₇

C₂×C₄

yes

characteristic

C₄×#3624

C₈

yes

—

C₂×#63216

C₂×C₄

yes

—

C₈×#595

—

C₈×#595

—

#10587529

—

C₂×C₁₆×C₁₇

C₂×C₄

yes

—

C₄×C₈×C₁₇

C₂×C₄

yes

characteristic

C₈×Dic₁₇

C₂×C₄

yes

characteristic

C₈×Dic₁₇

C₂×C₄

yes

characteristic

C₂×#63214

C₂×C₄

yes

—

C₄×#3622

C₂×C₄

yes

characteristic

C₁₆×D₁₇

—

C₂²×#595

C₂×C₈

yes

—

C₂×C₄×D₁₇

C₂×C₈

yes

—

C₂×C₄×D₁₇

C₂²×C₄

yes

characteristic

C₂×#3624

C₂×C₈

yes

—

—

—

—

—

—

C₂×C₈×C₁₇

C₄²

yes

characteristic

C₂×C₈×C₁₇

C₂²×C₄

yes

characteristic

C₄²×C₁₇

C₄²

yes

characteristic

C₄×Dic₁₇

C₄²

yes

characteristic

C₄×Dic₁₇

C₂×C₈

yes

—

C₂×#3622

C₄²

yes

characteristic

C₂×#3622

C₂²×C₄

yes

characteristic

C₈×D₁₇

M₁₆

yes

—

C₈×D₁₇

#41

yes

—

#63216

—

C₁₆×C₁₇

—

#63214

—

#12591

—

maximal, Sylow

C₂²×D₁₇

C₂²×C₈

yes

—

—

M₃₂

yes

—

C₂×C₄×C₁₇

C₄×C₈

yes

—

C₂×C₄×C₁₇

C₂×C₄²

yes

characteristic

C₂×Dic₁₇

C₄×C₈

yes

—

C₂×Dic₁₇

C₂²×C₈

yes

characteristic

C₄×D₁₇

—

C₄×D₁₇

#117

yes

—

C₄×D₁₇

C₂×M₁₆

yes

—

#3624

—

C₈×C₁₇

#97

yes

—

C₈×C₁₇

#117

yes

—

#3622

#97

yes

—

#3622

#117

yes

—

C₂×#346

—

C₂×#346

—

C₄²×C₈

—

#1374

—

C₂²×C₁₇

C₂×C₄×C₈

yes

characteristic

C₂×D₁₇

#431

yes

—

C₂×D₁₇

C₂×M₃₂

yes

—

#595

—

C₄×C₁₇

—

C₄×C₁₇

#376

yes

characteristic

C₄×C₁₇

C₂×#97

yes

characteristic

Dic₁₇

—

Dic₁₇

#431

yes

—

C₂²×C₁₆

—

C₂²×C₁₆

—

C₂×C₄×C₈

—

C₂×C₄×C₈

—

C₂×C₄×C₈

—

C₂×C₄×C₈

—

C₄³

—

—

—

—

—

yes

characteristic, complemented

C₂×C₁₇

#1744

yes

characteristic

C₂×C₁₇

C₄×M₃₂

yes

—

100

D₁₇

#2163

yes

—

101

C₂²×C₈

—

102

C₂²×C₈

—

103

C₂²×C₈

—

104

C₂×C₄²

—

105

C₂×C₄²

—

106

C₂×C₄²

—

107

C₂×C₁₆

—

108

C₂×C₁₆

—

109

C₂×C₁₆

—

110

C₂×C₁₆

—

111

C₂×C₁₆

C₂×#595

yes

—

112

C₄×C₈

—

113

C₄×C₈

—

114

C₄×C₈

—

115

C₄×C₈

—

116

C₄×C₈

—

117

C₄×C₈

—

118

C₄×C₈

C₂×#595

yes

characteristic

119

C₁₇

#12591

yes

characteristic, complemented, Sylow

120

C₂²×C₄

—

121

C₂²×C₄

—

122

C₂²×C₄

—

123

C₂×C₈

—

124

C₂×C₈

—

125

C₂×C₈

—

126

C₂×C₈

—

127

C₂×C₈

—

128

C₂×C₈

—

129

C₂×C₈

—

130

C₂×C₈

C₄×#595

yes

characteristic

131

C₂×C₈

C₂²×#595

yes

characteristic

132

C₄²

—

133

C₄²

—

134

C₄²

—

135

C₄²

—

136

C₄²

—

137

C₄²

C₄×#595

yes

characteristic

138

C₁₆

—

139

C₁₆

—

140

C₁₆

—

141

C₂³

—

142

C₂×C₄

—

143

C₂×C₄

—

144

C₂×C₄

—

145

C₂×C₄

—

146

C₂×C₄

—

147

C₂×C₄

—

148

C₂×C₄

—

149

C₂×C₄

—

150

C₂×C₄

C₈×#595

yes

—

151

C₂×C₄

C₂×C₄×#595

yes

characteristic

152

C₈

—

153

C₈

—

154

C₈

—

155

C₈

#10587532

yes

—

156

C₈

#10587677

yes

—

157

C₂²

—

158

C₂²

—

159

C₂²

C₂×C₈×#595

yes

characteristic

160

C₄

—

161

C₄

—

162

C₄

—

163

C₄

—

164

C₄

#11763745

yes

characteristic

165

C₄

C₂×#10587532

yes

characteristic

166

C₂

—

167

C₂

#14544497

yes

characteristic

168

C₂

M₃₂×#595

yes

—

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×#595
commutator, socle	C₂²×C₁₇	C₂×C₄×C₈
Fitting	C₁₇×#346	C₄
prime radical	C₂²×D₁₇	C₂²×C₈
cosocle	C₂×C₈×D₁₇	C₂³
hypercenter	#346	#595
hypocenter	C₁₇	#12591
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₈ ◁ #346

subgroup

G/H

center, Frattini

C₂×C₈

C₂²×#595

commutator, socle

C₂²×C₁₇

C₂×C₄×C₈

Fitting

C₁₇×#346

C₄

prime radical

C₂²×D₁₇

C₂²×C₈

cosocle

C₂×C₈×D₁₇

C₂³

C₁₇

G ▷ C₂²×C₁₇ ▷ C₁₇

C₁ ◁ C₂×C₈ ◁ #346

N	H ≅ G/N	type
10. #11763698	C₄	semidirect
11. #11763697	C₄	semidirect
14. #11762585	C₄	semidirect
15. #11762584	C₄	semidirect
16. C₁₇×#346	C₄	semidirect
97. #346	#595	semidirect
119. C₁₇	#12591	semidirect

H ≅ G/N

type

10. #11763698

C₄

semidirect

11. #11763697

C₄

semidirect

14. #11762585

C₄

semidirect

15. #11762584

C₄

semidirect

16. C₁₇×#346

C₄

semidirect

97. #346

#595

semidirect

119. C₁₇

#12591

semidirect

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

subgroup	index
#14544985	2
C₄×C₈×#595	2
#14543821	2
D₁₇×#346	2
#12591	17

subgroup

index

#14544985

C₄×C₈×#595

#14543821

D₁₇×#346

#12591

Subgroups — #17960654

Conjugacy classes of subgroups

Complements

Maximal subgroups