Group #16933788 — subgroups

Subgroups — #16933788

Order 4352.

478 conjugacy classes of subgroups; only the 159 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 159 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	#14528956	C₂	1	1	yes	maximal, characteristic
2	#14527456	C₂	1	4	yes	maximal
3	#14527067	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₇×#494	C₂	1	1	yes	maximal, characteristic
5	#11762862	C₂²	1	2	yes	—
6	C₂×#10587490	—	2	2	no	—
7	#11762833	C₂²	1	2	yes	—
8	#11762555	—	2	8	no	—
9	#11762530	—	2	1	no	—
10	C₈×#3622	—	2	1	no	—
11	C₂²×Q₁₆×C₁₇	—	2	2	no	—
12	C₂×C₁₇×C₄⋊Q₈	C₂²	1	2	yes	—
13	C₁₇×#494	—	2	1	no	—
14	C₁₇×#494	—	2	1	no	—
15	C₁₇×#494	C₄	1	4	yes	—
16	C₂×C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
17	C₂²×Q₈×C₁₇	—	2	2	no	—
18	C₂×Q₁₆×C₁₇	—	2	4	no	—
19	C₂×Q₁₆×C₁₇	—	2	4	no	—
20	C₂×Q₁₆×C₁₇	—	4	4	no	—
21	C₂×Q₁₆×C₁₇	—	4	4	no	—
22	C₂²×C₈×C₁₇	D₄	1	2	yes	—
23	C₁₇×C₄⋊Q₈	—	2	4	no	—
24	C₁₇×C₄⋊Q₈	—	2	2	no	—
25	C₁₇×C₄⋊Q₈	C₂×C₄	1	4	yes	—
26	C₂×C₄⋊C₄×C₁₇	—	2	4	no	—
27	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
28	C₂×#63223	—	2	2	no	—
29	C₄×C₈×C₁₇	C₂×C₄	1	2	yes	—
30	C₄×C₈×C₁₇	D₄	1	1	yes	characteristic
31	C₄×C₈×C₁₇	D₄	1	1	yes	characteristic
32	C₂²⋊#3622	—	2	2	no	—
33	#10587490	—	4	4	no	—
34	C₄⋊#3622	—	2	4	no	—
35	C₄⋊#3622	D₄	1	4	yes	—
36	C₄×#3622	—	2	2	no	—
37	C₂×Q₈×C₁₇	—	2	4	no	—
38	C₂×Q₈×C₁₇	—	4	2	no	—
39	C₂×Q₈×C₁₇	—	4	4	no	—
40	C₂×Q₈×C₁₇	—	4	4	no	—
41	C₂²×C₄×C₁₇	—	4	2	no	—
42	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
43	C₂²×C₄×C₁₇	#41	1	2	yes	—
44	Q₁₆×C₁₇	—	4	8	no	—
45	Q₁₆×C₁₇	—	4	8	no	—
46	C₂×C₈×C₁₇	C₂²⋊C₄	1	2	yes	—
47	C₂×C₈×C₁₇	C₂²⋊C₄	1	2	yes	—
48	C₂×C₈×C₁₇	D₈	1	4	yes	—
49	C₂×C₈×C₁₇	SD₁₆	1	4	yes	—
50	C₄⋊C₄×C₁₇	—	2	8	no	—
51	C₄⋊C₄×C₁₇	—	4	4	no	—
52	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
53	C₄²×C₁₇	C₂×D₄	1	2	yes	—
54	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
55	#63223	—	4	4	no	—
56	C₂×#3622	—	2	4	no	—
57	C₂×#3622	—	4	2	no	—
58	#9772	—	17	1	no	maximal, Sylow
59	C₂³×C₁₇	#124	1	1	yes	characteristic
60	Q₈×C₁₇	—	4	8	no	—
61	Q₈×C₁₇	—	8	2	no	—
62	Q₈×C₁₇	—	8	2	no	—
63	C₂×C₄×C₁₇	—	2	4	no	—
64	C₂×C₄×C₁₇	—	4	4	no	—
65	C₂×C₄×C₁₇	—	8	4	no	—
66	C₂×C₄×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
67	C₂×C₄×C₁₇	C₄×D₄	1	2	yes	—
68	C₂×C₄×C₁₇	#121	1	2	yes	—
69	C₂×C₄×C₁₇	#127	1	1	yes	characteristic
70	C₂×C₄×C₁₇	C₂×D₈	1	2	yes	—
71	C₂×C₄×C₁₇	C₂×SD₁₆	1	2	yes	—
72	C₈×C₁₇	#102	1	4	yes	—
73	C₈×C₁₇	#102	1	4	yes	—
74	#3622	—	4	4	no	—
75	#3622	—	8	2	no	—
76	C₂×#494	D₁₇	1	1	yes	characteristic
77	#1848	—	17	1	no	—
78	#1546	—	17	4	no	—
79	#1450	—	17	1	no	—
80	C₂²×C₁₇	—	2	2	no	—
81	C₂²×C₁₇	#390	1	1	yes	characteristic
82	C₂²×C₁₇	#486	1	2	yes	—
83	C₄×C₁₇	—	2	2	no	—
84	C₄×C₁₇	—	8	4	no	—
85	C₄×C₁₇	C₂×#102	1	2	yes	—
86	C₄×C₁₇	#473	1	4	yes	—
87	C₄×C₁₇	#492	1	1	yes	characteristic
88	C₄×C₁₇	#493	1	1	yes	characteristic
89	C₂²×Q₁₆	—	2	2	no	—
90	C₂×C₄⋊Q₈	C₂×D₁₇	1	2	yes	—
91	#494	—	2	1	no	—
92	#494	—	2	1	no	—
93	#494	Dic₁₇	1	4	yes	—
94	#431	—	17	2	no	—
95	C₂×#108	—	34	2	no	—
96	#423	—	17	2	no	—
97	C₂×C₄×C₈	C₂×D₁₇	1	1	yes	characteristic
98	#332	—	34	8	no	—
99	#322	—	34	1	no	—
100	C₈²	—	34	1	no	—
101	C₂×C₁₇	—	2	2	no	—
102	C₂×C₁₇	#1957	1	1	yes	characteristic
103	C₂×C₁₇	#1979	1	2	yes	—
104	C₂²×Q₈	—	2	2	no	—
105	C₂×Q₁₆	—	2	4	no	—
106	C₂×Q₁₆	—	2	4	no	—
107	C₂×Q₁₆	—	4	4	no	—
108	C₂×Q₁₆	—	4	4	no	—
109	C₂×M₁₆	—	34	2	no	—
110	C₂²×C₈	C₂²⋊D₁₇	1	2	yes	—
111	C₄⋊Q₈	—	2	4	no	—
112	C₄⋊Q₈	—	2	2	no	—
113	C₄⋊Q₈	C₂×Dic₁₇	1	4	yes	—
114	C₂×C₄⋊C₄	—	2	4	no	—
115	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
116	#108	—	68	4	no	—
117	C₄⋊C₈	—	17	4	no	—
118	C₄⋊C₈	—	34	4	no	—
119	C₂²⋊C₈	—	34	2	no	—
120	C₄×C₈	—	34	2	no	—
121	C₄×C₈	C₂×Dic₁₇	1	2	yes	—
122	C₄×C₈	C₂²⋊D₁₇	1	1	yes	characteristic
123	C₄×C₈	C₂²⋊D₁₇	1	1	yes	characteristic
124	C₁₇	#9772	1	1	yes	characteristic, complemented, Sylow
125	C₂×Q₈	—	2	4	no	—
126	C₂×Q₈	—	4	2	no	—
127	C₂×Q₈	—	4	4	no	—
128	C₂×Q₈	—	4	4	no	—
129	C₂²×C₄	—	4	2	no	—
130	C₂²×C₄	#63254	1	2	yes	—
131	C₂²×C₄	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
132	Q₁₆	—	4	8	no	—
133	Q₁₆	—	4	8	no	—
134	M₁₆	—	68	4	no	—
135	C₂×C₈	—	34	4	no	—
136	C₂×C₈	—	68	2	no	—
137	C₂×C₈	#63228	1	4	yes	—
138	C₂×C₈	#63229	1	4	yes	—
139	C₂×C₈	C₂²⋊Dic₁₇	1	2	yes	—
140	C₂×C₈	C₂²⋊Dic₁₇	1	2	yes	—
141	C₄⋊C₄	—	2	8	no	—
142	C₄⋊C₄	—	4	4	no	—
143	C₄²	D₄×D₁₇	1	2	yes	—
144	C₄²	C₂²×Dic₁₇	1	1	yes	characteristic
145	C₄²	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
146	C₂³	#10587622	1	1	yes	characteristic
147	Q₈	—	4	8	no	—
148	Q₈	—	8	2	no	—
149	Q₈	—	8	2	no	—
150	C₂×C₄	—	2	4	no	—
151	C₂×C₄	—	4	4	no	—
152	C₂×C₄	—	8	4	no	—
153	C₂×C₄	C₂×#63228	1	2	yes	—
154	C₂×C₄	C₂×#63229	1	2	yes	—
155	C₂×C₄	D₄×Dic₁₇	1	2	yes	—
156	C₂×C₄	#10587624	1	2	yes	—
157	C₂×C₄	#10587626	1	1	yes	characteristic
158	C₂×C₄	C₂×C₂²⋊Dic₁₇	1	1	yes	characteristic
159	C₈	—	68	4	no	—
160	C₈	—	136	2	no	—
161	C₈	#10587503	1	4	yes	—
162	C₈	#10587503	1	4	yes	—
163	C₂²	—	2	2	no	—
164	C₂²	#11762712	1	1	yes	characteristic
165	C₂²	#11763155	1	2	yes	—
166	C₄	—	2	2	no	—
167	C₄	—	8	4	no	—
168	C₄	C₂×#10587503	1	2	yes	—
169	C₄	#11763081	1	4	yes	—
170	C₄	#11763181	1	1	yes	characteristic
171	C₄	#11763185	1	1	yes	characteristic
172	C₂	—	2	2	no	—
173	C₂	#14529591	1	1	yes	characteristic
174	C₂	#14529700	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14528956

C₂

yes

maximal, characteristic

#14527456

C₂

yes

maximal

#14527067

C₂

yes

maximal, characteristic

C₂×C₁₇×#494

C₂

yes

maximal, characteristic

#11762862

C₂²

yes

—

C₂×#10587490

—

#11762833

C₂²

yes

—

#11762555

—

#11762530

—

C₈×#3622

—

C₂²×Q₁₆×C₁₇

—

C₂×C₁₇×C₄⋊Q₈

C₂²

yes

—

C₁₇×#494

—

C₁₇×#494

—

C₁₇×#494

C₄

yes

—

C₂×C₄×C₈×C₁₇

C₂²

yes

characteristic

C₂²×Q₈×C₁₇

—

C₂×Q₁₆×C₁₇

—

C₂×Q₁₆×C₁₇

—

C₂×Q₁₆×C₁₇

—

C₂×Q₁₆×C₁₇

—

C₂²×C₈×C₁₇

D₄

yes

—

C₁₇×C₄⋊Q₈

—

C₁₇×C₄⋊Q₈

—

C₁₇×C₄⋊Q₈

C₂×C₄

yes

—

C₂×C₄⋊C₄×C₁₇

—

C₂×C₄²×C₁₇

C₂³

yes

characteristic

C₂×#63223

—

C₄×C₈×C₁₇

C₂×C₄

yes

—

C₄×C₈×C₁₇

D₄

yes

characteristic

C₄×C₈×C₁₇

D₄

yes

characteristic

C₂²⋊#3622

—

#10587490

—

C₄⋊#3622

—

C₄⋊#3622

D₄

yes

—

C₄×#3622

—

C₂×Q₈×C₁₇

—

C₂×Q₈×C₁₇

—

C₂×Q₈×C₁₇

—

C₂×Q₈×C₁₇

—

C₂²×C₄×C₁₇

—

C₂²×C₄×C₁₇

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₇

#41

yes

—

Q₁₆×C₁₇

—

Q₁₆×C₁₇

—

C₂×C₈×C₁₇

C₂²⋊C₄

yes

—

C₂×C₈×C₁₇

C₂²⋊C₄

yes

—

C₂×C₈×C₁₇

D₈

yes

—

C₂×C₈×C₁₇

SD₁₆

yes

—

C₄⋊C₄×C₁₇

—

C₄⋊C₄×C₁₇

—

C₄²×C₁₇

C₂²×C₄

yes

characteristic

C₄²×C₁₇

C₂×D₄

yes

—

C₄²×C₁₇

C₂×D₄

yes

—

—

—

—

C₂³×C₁₇

yes

Q₈×C₁₇

—

Q₈×C₁₇

—

Q₈×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₇

C₄×D₄

yes

—

C₂×C₄×C₁₇

#121

yes

—

C₂×C₄×C₁₇

#127

yes

characteristic

C₂×C₄×C₁₇

C₂×D₈

yes

—

C₂×C₄×C₁₇

C₂×SD₁₆

yes

—

C₈×C₁₇

#102

yes

—

C₈×C₁₇

#102

yes

—

#3622

—

#3622

—

C₂×#494

D₁₇

yes

—

—

—

C₂²×C₁₇

—

C₂²×C₁₇

#390

yes

characteristic

C₂²×C₁₇

#486

yes

—

C₄×C₁₇

—

C₄×C₁₇

—

C₄×C₁₇

C₂×#102

yes

—

C₄×C₁₇

#473

yes

—

C₄×C₁₇

yes

C₄×C₁₇

yes

C₂²×Q₁₆

—

C₂×C₄⋊Q₈

C₂×D₁₇

yes

—

#494

—

#494

—

#494

Dic₁₇

yes

—

#431

—

C₂×#108

—

#423

—

C₂×C₄×C₈

C₂×D₁₇

yes

characteristic

#332

—

#322

—

100

C₈²

—

101

C₂×C₁₇

—

102

C₂×C₁₇

#1957

yes

characteristic

103

C₂×C₁₇

#1979

yes

—

104

C₂²×Q₈

—

105

C₂×Q₁₆

—

106

C₂×Q₁₆

—

107

C₂×Q₁₆

—

108

C₂×Q₁₆

—

109

C₂×M₁₆

—

110

C₂²×C₈

C₂²⋊D₁₇

yes

—

111

C₄⋊Q₈

—

112

C₄⋊Q₈

—

113

C₄⋊Q₈

C₂×Dic₁₇

yes

—

114

C₂×C₄⋊C₄

—

115

C₂×C₄²

C₂²×D₁₇

yes

characteristic

116

#108

—

117

C₄⋊C₈

—

118

C₄⋊C₈

—

119

C₂²⋊C₈

—

120

C₄×C₈

—

121

C₄×C₈

C₂×Dic₁₇

yes

—

122

C₄×C₈

C₂²⋊D₁₇

yes

characteristic

123

C₄×C₈

C₂²⋊D₁₇

yes

characteristic

124

C₁₇

#9772

yes

characteristic, complemented, Sylow

125

C₂×Q₈

—

126

C₂×Q₈

—

127

C₂×Q₈

—

128

C₂×Q₈

—

129

C₂²×C₄

—

130

C₂²×C₄

#63254

yes

—

131

C₂²×C₄

C₂×C₂²⋊D₁₇

yes

characteristic

132

Q₁₆

—

133

Q₁₆

—

134

M₁₆

—

135

C₂×C₈

—

136

C₂×C₈

—

137

C₂×C₈

#63228

yes

—

138

C₂×C₈

#63229

yes

—

139

C₂×C₈

C₂²⋊Dic₁₇

yes

—

140

C₂×C₈

C₂²⋊Dic₁₇

yes

—

141

C₄⋊C₄

—

142

C₄⋊C₄

—

143

C₄²

D₄×D₁₇

yes

—

144

C₄²

C₂²×Dic₁₇

yes

characteristic

145

C₄²

C₂×C₂²⋊D₁₇

yes

characteristic

146

C₂³

#10587622

yes

characteristic

147

Q₈

—

148

Q₈

—

149

Q₈

—

150

C₂×C₄

—

151

C₂×C₄

—

152

C₂×C₄

—

153

C₂×C₄

C₂×#63228

yes

—

154

C₂×C₄

C₂×#63229

yes

—

155

C₂×C₄

D₄×Dic₁₇

yes

—

156

C₂×C₄

#10587624

yes

—

157

C₂×C₄

#10587626

yes

characteristic

158

C₂×C₄

C₂×C₂²⋊Dic₁₇

yes

characteristic

159

C₈

—

160

C₈

—

136

—

161

C₈

#10587503

yes

—

162

C₈

#10587503

yes

—

163

C₂²

—

164

C₂²

#11762712

yes

characteristic

165

C₂²

#11763155

yes

—

166

C₄

—

167

C₄

—

168

C₄

C₂×#10587503

yes

—

169

C₄

#11763081

yes

—

170

C₄

#11763181

yes

characteristic

171

C₄

#11763185

yes

characteristic

172

C₂

—

173

C₂

#14529591

yes

characteristic

174

C₂

#14529700

yes

—

	subgroup	G/H
center	C₂²	#11762712
commutator	C₄²×C₁₇	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₇
Fitting	C₂×C₁₇×#494	C₂
socle	C₂²×C₁₇	#390
prime radical	C₂³×C₁₇	#124
cosocle	C₂×C₄²×C₁₇	C₂³
hypercenter	C₂×#494	D₁₇
hypocenter	C₁₇	#9772
LCS	G ▷ C₄²×C₁₇ ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×#494

subgroup

G/H

center

C₂²

#11762712

commutator

C₄²×C₁₇

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₇

Fitting

C₂×C₁₇×#494

C₂

C₂²×C₁₇

C₂³×C₁₇

C₂×C₄²×C₁₇

C₂³

D₁₇

C₁₇

G ▷ C₄²×C₁₇ ▷ C₂²×C₁₇ ▷ C₁₇

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×#494

N	H ≅ G/N	type
124. C₁₇	#9772	semidirect

H ≅ G/N

type

124. C₁₇

#9772

semidirect

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

subgroup	index
#14528956	2
#14527456	2
#14527067	2
C₂×C₁₇×#494	2
#9772	17

subgroup

index

C₂×C₁₇×#494

Subgroups — #16933788

Conjugacy classes of subgroups

Complements

Maximal subgroups