Group #17948563 — subgroups

Subgroups — #17948563

Order 4352.

200 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 92 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×#11763731	C₂	1	1	yes	maximal, characteristic
2	C₂×#11763731	C₂	1	1	yes	maximal, characteristic
3	M₃₂×Dic₁₇	C₂	1	1	yes	maximal, characteristic
4	C₂×#10587538	—	2	1	no	—
5	C₂×#10587538	—	2	1	no	—
6	#11763731	—	2	1	no	—
7	#11763731	—	2	1	no	—
8	#11763731	C₄	1	2	yes	—
9	#11763731	C₄	1	2	yes	—
10	C₂×#10587483	C₄	1	1	yes	characteristic
11	C₂×C₈×Dic₁₇	C₂²	1	1	yes	characteristic
12	#11762584	—	2	1	no	—
13	C₁₆×Dic₁₇	—	2	1	no	—
14	C₂×C₁₇×M₃₂	C₄	1	1	yes	characteristic
15	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄×Dic₁₇	Q₈	1	1	yes	characteristic
17	C₂²×#3622	D₄	1	1	yes	characteristic
18	#10587538	—	2	2	no	—
19	#10587538	—	2	2	no	—
20	#10587538	—	4	1	no	—
21	#10587538	—	4	1	no	—
22	C₂×#63216	—	4	1	no	—
23	C₂×#63216	—	4	1	no	—
24	C₁₇×M₃₂	—	2	1	no	—
25	C₁₇×M₃₂	C₈	1	2	yes	—
26	C₂×C₁₆×C₁₇	—	2	1	no	—
27	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
28	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
29	C₈×Dic₁₇	D₄	1	1	yes	characteristic
30	C₈×Dic₁₇	D₄	1	1	yes	characteristic
31	#10587483	—	2	1	no	—
32	#10587483	C₈	1	2	yes	—
33	C₂×#63214	—	2	1	no	—
34	C₂²×C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
35	C₂²×Dic₁₇	—	2	1	no	—
36	C₂×C₈×C₁₇	C₄²	1	1	yes	characteristic
37	C₂×C₈×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
38	C₂×C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
39	C₂×C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
40	C₂×C₈×C₁₇	M₁₆	1	1	yes	characteristic
41	C₂×C₈×C₁₇	M₁₆	1	1	yes	characteristic
42	C₄×Dic₁₇	—	2	1	no	—
43	C₄×Dic₁₇	C₄⋊C₄	1	1	yes	characteristic
44	C₄×Dic₁₇	C₄⋊C₄	1	1	yes	characteristic
45	C₂×#3622	C₂²⋊C₄	1	1	yes	characteristic
46	C₂×#3622	C₂²⋊C₄	1	1	yes	characteristic
47	C₂×#3622	D₈	1	1	yes	characteristic
48	C₂×#3622	SD₁₆	1	1	yes	characteristic
49	C₂×#3622	SD₁₆	1	1	yes	characteristic
50	C₂×#3622	Q₁₆	1	1	yes	characteristic
51	#63216	—	4	2	no	—
52	#63216	—	4	2	no	—
53	C₁₆×C₁₇	—	2	2	no	—
54	#63214	—	2	2	no	—
55	#7162	—	17	1	no	maximal, Sylow
56	C₂³×C₁₇	#108	1	1	yes	characteristic
57	C₂×C₄×C₁₇	#95	1	1	yes	characteristic
58	C₂×C₄×C₁₇	C₄⋊C₈	1	1	yes	characteristic
59	C₂×C₄×C₁₇	C₄⋊C₈	1	1	yes	characteristic
60	C₂×C₄×C₁₇	#106	1	1	yes	characteristic
61	C₂×C₄×C₁₇	#107	1	1	yes	characteristic
62	C₂×C₄×C₁₇	#108	1	1	yes	characteristic
63	C₂×Dic₁₇	—	2	1	no	—
64	C₂×Dic₁₇	—	2	1	no	—
65	C₂×Dic₁₇	—	4	2	no	—
66	C₈×C₁₇	C₄×C₈	1	1	yes	characteristic
67	C₈×C₁₇	#97	1	1	yes	characteristic
68	C₈×C₁₇	C₂²⋊C₈	1	1	yes	characteristic
69	C₈×C₁₇	C₂²⋊C₈	1	1	yes	characteristic
70	#3622	#102	1	1	yes	characteristic
71	#3622	#102	1	1	yes	characteristic
72	#3622	#103	1	1	yes	characteristic
73	#3622	#103	1	1	yes	characteristic
74	C₂×#364	—	17	1	no	—
75	C₂×#364	—	17	1	no	—
76	C₄×M₃₂	—	17	1	no	—
77	C₂²×C₁₇	—	4	1	no	—
78	C₂²×C₁₇	#334	1	1	yes	characteristic
79	C₂²×C₁₇	#335	1	1	yes	characteristic
80	C₂²×C₁₇	#341	1	1	yes	characteristic
81	C₄×C₁₇	#334	1	1	yes	characteristic
82	C₄×C₁₇	#335	1	1	yes	characteristic
83	C₄×C₁₇	#336	1	1	yes	characteristic
84	C₄×C₁₇	#340	1	1	yes	characteristic
85	Dic₁₇	—	2	2	no	—
86	Dic₁₇	—	4	1	no	—
87	C₂×M₃₂	—	17	1	no	—
88	C₂×M₃₂	—	34	1	no	—
89	C₂×M₃₂	—	34	1	no	—
90	C₂×M₃₂	#595	1	1	yes	characteristic
91	C₂×C₄×C₈	—	17	1	no	—
92	#364	—	17	2	no	—
93	#364	—	17	2	no	—
94	#364	—	34	1	no	—
95	#364	—	34	1	no	—
96	#346	—	34	1	no	—
97	C₄×C₁₆	—	34	1	no	—
98	C₂×C₁₇	—	2	1	no	—
99	C₂×C₁₇	—	2	1	no	—
100	C₂×C₁₇	—	2	1	no	—
101	C₂×C₁₇	#1277	1	1	yes	characteristic
102	C₂²×C₈	—	17	1	no	—
103	C₂²×C₈	C₂×#595	1	1	yes	characteristic
104	C₂×C₄²	—	17	1	no	—
105	M₃₂	—	2	1	no	—
106	M₃₂	—	17	2	no	—
107	M₃₂	—	34	1	no	—
108	M₃₂	—	34	2	no	—
109	M₃₂	—	34	2	no	—
110	M₃₂	—	68	1	no	—
111	M₃₂	—	68	1	no	—
112	M₃₂	#3624	1	2	yes	—
113	C₂×C₁₆	—	2	1	no	—
114	C₂×C₁₆	—	34	1	no	—
115	C₂×C₁₆	—	68	1	no	—
116	C₂×C₁₆	—	68	1	no	—
117	C₄×C₈	—	17	1	no	—
118	C₄×C₈	—	17	1	no	—
119	C₄×C₈	—	17	1	no	—
120	C₄×C₈	—	17	1	no	—
121	C₁₇	#7162	1	1	yes	characteristic, complemented, Sylow
122	C₂²×C₄	—	34	1	no	—
123	C₂²×C₄	C₄⋊#595	1	1	yes	characteristic
124	C₂×C₈	—	17	1	no	—
125	C₂×C₈	—	17	1	no	—
126	C₂×C₈	—	17	1	no	—
127	C₂×C₈	—	17	1	no	—
128	C₂×C₈	—	17	1	no	—
129	C₂×C₈	—	17	1	no	—
130	C₂×C₈	#63242	1	1	yes	characteristic
131	C₂×C₈	#63243	1	1	yes	characteristic
132	C₂×C₈	C₄×#595	1	1	yes	characteristic
133	C₂×C₈	C₂×#3624	1	1	yes	characteristic
134	C₂×C₈	#63247	1	1	yes	characteristic
135	C₂×C₈	C₂²⋊#595	1	1	yes	characteristic
136	C₄²	—	17	1	no	—
137	C₄²	—	17	1	no	—
138	C₄²	—	34	1	no	—
139	C₁₆	—	2	2	no	—
140	C₁₆	—	34	2	no	—
141	C₁₆	—	68	2	no	—
142	C₁₆	—	68	2	no	—
143	C₂³	#10587535	1	1	yes	characteristic
144	C₂×C₄	—	34	1	no	—
145	C₂×C₄	—	34	1	no	—
146	C₂×C₄	—	68	2	no	—
147	C₂×C₄	#10587533	1	1	yes	characteristic
148	C₂×C₄	#10587534	1	1	yes	characteristic
149	C₂×C₄	#10587536	1	1	yes	characteristic
150	C₂×C₄	C₄⋊#3624	1	1	yes	characteristic
151	C₂×C₄	#10587544	1	1	yes	characteristic
152	C₂×C₄	(C₂×#595)⋊C₄	1	1	yes	characteristic
153	C₈	—	17	1	no	—
154	C₈	—	17	1	no	—
155	C₈	—	17	1	no	—
156	C₈	—	17	1	no	—
157	C₈	C₄×#3624	1	1	yes	characteristic
158	C₈	#10587542	1	1	yes	characteristic
159	C₈	#10587543	1	1	yes	characteristic
160	C₈	C₂²⋊#3624	1	1	yes	characteristic
161	C₂²	—	4	1	no	—
162	C₂²	#11763670	1	1	yes	characteristic
163	C₂²	#11763673	1	1	yes	characteristic
164	C₂²	#11763685	1	1	yes	characteristic
165	C₄	—	34	2	no	—
166	C₄	—	68	1	no	—
167	C₄	#11763671	1	1	yes	characteristic
168	C₄	#11763672	1	1	yes	characteristic
169	C₄	#11763675	1	1	yes	characteristic
170	C₄	#11763683	1	1	yes	characteristic
171	C₂	—	2	1	no	—
172	C₂	—	2	1	no	—
173	C₂	—	2	1	no	—
174	C₂	#14543614	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11763731

C₂

yes

maximal, characteristic

C₂×#11763731

C₂

yes

maximal, characteristic

M₃₂×Dic₁₇

C₂

yes

maximal, characteristic

—

—

—

—

C₄

yes

—

#11763731

C₄

yes

—

C₂×#10587483

C₄

yes

characteristic

C₂×C₈×Dic₁₇

C₂²

yes

characteristic

#11762584

—

C₁₆×Dic₁₇

—

C₂×C₁₇×M₃₂

C₄

yes

characteristic

C₂²×C₈×C₁₇

C₂×C₄

yes

characteristic

C₂×C₄×Dic₁₇

Q₈

yes

characteristic

C₂²×#3622

D₄

yes

—

—

—

—

—

—

C₁₇×M₃₂

—

C₁₇×M₃₂

C₈

yes

—

C₂×C₁₆×C₁₇

—

C₈×Dic₁₇

C₂×C₄

yes

characteristic

C₈×Dic₁₇

C₂×C₄

yes

characteristic

C₈×Dic₁₇

D₄

yes

characteristic

C₈×Dic₁₇

D₄

yes

characteristic

#10587483

—

#10587483

C₈

yes

—

C₂×#63214

—

C₂²×C₄×C₁₇

C₄⋊C₄

yes

characteristic

C₂²×Dic₁₇

—

C₂×C₈×C₁₇

C₄²

yes

characteristic

C₂×C₈×C₁₇

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₇

C₂×C₈

yes

characteristic

C₂×C₈×C₁₇

C₂×C₈

yes

characteristic

C₂×C₈×C₁₇

M₁₆

yes

characteristic

C₂×C₈×C₁₇

M₁₆

yes

characteristic

C₄×Dic₁₇

—

C₄×Dic₁₇

C₄⋊C₄

yes

characteristic

C₄×Dic₁₇

C₄⋊C₄

yes

characteristic

C₂×#3622

C₂²⋊C₄

yes

characteristic

C₂×#3622

C₂²⋊C₄

yes

characteristic

C₂×#3622

D₈

yes

characteristic

C₂×#3622

SD₁₆

yes

characteristic

C₂×#3622

SD₁₆

yes

characteristic

C₂×#3622

Q₁₆

yes

characteristic

#63216

—

#63216

—

C₁₆×C₁₇

—

—

—

C₂³×C₁₇

yes

C₂×C₄×C₁₇

yes

C₂×C₄×C₁₇

C₄⋊C₈

yes

characteristic

C₂×C₄×C₁₇

C₄⋊C₈

yes

C₂×C₄×C₁₇

yes

C₂×C₄×C₁₇

yes

C₂×C₄×C₁₇

yes

C₂×Dic₁₇

—

C₂×Dic₁₇

—

C₂×Dic₁₇

—

C₈×C₁₇

C₄×C₈

yes

characteristic

C₈×C₁₇

#97

yes

characteristic

C₈×C₁₇

C₂²⋊C₈

yes

characteristic

C₈×C₁₇

C₂²⋊C₈

yes

yes

yes

yes

yes

—

—

C₄×M₃₂

—

C₂²×C₁₇

—

C₂²×C₁₇

yes

C₂²×C₁₇

yes

C₂²×C₁₇

yes

C₄×C₁₇

yes

C₄×C₁₇

yes

C₄×C₁₇

yes

C₄×C₁₇

yes

Dic₁₇

—

Dic₁₇

—

C₂×M₃₂

—

C₂×M₃₂

—

C₂×M₃₂

—

C₂×M₃₂

#595

yes

characteristic

C₂×C₄×C₈

—

—

—

—

—

—

C₄×C₁₆

—

C₂×C₁₇

—

C₂×C₁₇

—

100

C₂×C₁₇

—

101

C₂×C₁₇

#1277

yes

characteristic

102

C₂²×C₈

—

103

C₂²×C₈

C₂×#595

yes

characteristic

104

C₂×C₄²

—

105

M₃₂

—

106

M₃₂

—

107

M₃₂

—

108

M₃₂

—

109

M₃₂

—

110

M₃₂

—

111

M₃₂

—

112

M₃₂

#3624

yes

—

113

C₂×C₁₆

—

114

C₂×C₁₆

—

115

C₂×C₁₆

—

116

C₂×C₁₆

—

117

C₄×C₈

—

118

C₄×C₈

—

119

C₄×C₈

—

120

C₄×C₈

—

121

C₁₇

#7162

yes

characteristic, complemented, Sylow

122

C₂²×C₄

—

123

C₂²×C₄

C₄⋊#595

yes

characteristic

124

C₂×C₈

—

125

C₂×C₈

—

126

C₂×C₈

—

127

C₂×C₈

—

128

C₂×C₈

—

129

C₂×C₈

—

130

C₂×C₈

#63242

yes

characteristic

131

C₂×C₈

#63243

yes

characteristic

132

C₂×C₈

C₄×#595

yes

characteristic

133

C₂×C₈

C₂×#3624

yes

characteristic

134

C₂×C₈

#63247

yes

characteristic

135

C₂×C₈

C₂²⋊#595

yes

characteristic

136

C₄²

—

137

C₄²

—

138

C₄²

—

139

C₁₆

—

140

C₁₆

—

141

C₁₆

—

142

C₁₆

—

143

C₂³

#10587535

yes

characteristic

144

C₂×C₄

—

145

C₂×C₄

—

146

C₂×C₄

—

147

C₂×C₄

#10587533

yes

characteristic

148

C₂×C₄

#10587534

yes

characteristic

149

C₂×C₄

#10587536

yes

characteristic

150

C₂×C₄

C₄⋊#3624

yes

characteristic

151

C₂×C₄

#10587544

yes

characteristic

152

C₂×C₄

(C₂×#595)⋊C₄

yes

characteristic

153

C₈

—

154

C₈

—

155

C₈

—

156

C₈

—

157

C₈

C₄×#3624

yes

characteristic

158

C₈

#10587542

yes

characteristic

159

C₈

#10587543

yes

characteristic

160

C₈

C₂²⋊#3624

yes

characteristic

161

C₂²

—

162

C₂²

#11763670

yes

characteristic

163

C₂²

#11763673

yes

characteristic

164

C₂²

#11763685

yes

characteristic

165

C₄

—

166

C₄

—

167

C₄

#11763671

yes

characteristic

168

C₄

#11763672

yes

characteristic

169

C₄

#11763675

yes

characteristic

170

C₄

#11763683

yes

characteristic

171

C₂

—

172

C₂

—

173

C₂

—

174

C₂

#14543614

yes

characteristic

	subgroup	G/H
center	C₄	#11763683
commutator	C₈×C₁₇	C₄×C₈
Frattini	C₂²×C₈	C₂×#595
Fitting	C₂×C₁₇×M₃₂	C₄
socle	C₂×C₁₇	#1277
prime radical	C₂³×C₁₇	#108
cosocle	C₂×C₈×Dic₁₇	C₂²
hypercenter	C₂×M₃₂	#595
hypocenter	C₁₇	#7162
LCS	G ▷ C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×M₃₂

subgroup

G/H

center

C₄

#11763683

commutator

C₈×C₁₇

C₄×C₈

Frattini

C₂²×C₈

C₂×#595

Fitting

C₂×C₁₇×M₃₂

C₄

C₂×C₁₇

C₂³×C₁₇

C₂×C₈×Dic₁₇

C₂²

C₂×M₃₂

C₁₇

G ▷ C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×M₃₂

N	H ≅ G/N	type
121. C₁₇	#7162	semidirect

H ≅ G/N

type

121. C₁₇

#7162

semidirect

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

subgroup	index
C₂×#11763731	2
M₃₂×Dic₁₇	2
#7162	17

subgroup

index

C₂×#11763731

M₃₂×Dic₁₇

#7162

Subgroups — #17948563

Conjugacy classes of subgroups

Complements

Maximal subgroups