Group #13179669 — subgroups

Subgroups — #13179669

Order 1728.

2968 conjugacy classes of subgroups; only the 723 normal subgroups are shown.

normal subgroups only

This group has 2968 conjugacy classes of subgroups — too many to draw. Only its 723 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	C₃³×C₄×D₄	C₂	1	1	yes	maximal, characteristic
2	#11723977	C₂	1	2	yes	maximal
3	#11723967	C₂	1	2	yes	maximal, complemented
4	#11723965	C₂	1	2	yes	maximal, complemented
5	#11723928	C₂	1	2	yes	maximal, complemented
6	#11723920	C₂	1	4	yes	maximal, complemented
7	#11723910	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×#6308	C₂	1	1	yes	maximal, characteristic, complemented
9	#10596013	—	3	13	no	maximal
10	C₂×C₃³×D₄	C₂²	1	1	yes	characteristic
11	C₂²×C₃³×C₄	C₂²	1	2	yes	—
12	C₂×#6308	C₂²	1	1	yes	characteristic
13	C₂×#6308	C₂²	1	2	yes	—
14	C₃³×C₄⋊C₄	C₂²	1	1	yes	characteristic
15	C₃³×C₂²⋊C₄	C₂²	1	2	yes	—
16	C₃³×C₄²	C₂²	1	1	yes	characteristic
17	#88864	C₂²	1	4	yes	—
18	#88864	C₂²	1	4	yes	—
19	C₄⋊(C₃⋊(C₃⋊Dic₃))	C₂²	1	1	yes	characteristic
20	C₄⋊(C₃⋊(C₃⋊Dic₃))	C₂²	1	2	yes	—
21	C₄⋊(C₃⋊(C₃⋊Dic₃))	C₂²	1	2	yes	—
22	#88857	C₂²	1	2	yes	—
23	#88857	C₂²	1	4	yes	—
24	C₄×C₃⋊(C₃⋊Dic₃)	C₂²	1	2	yes	—
25	C₄×C₃⋊(C₃⋊Dic₃)	C₂²	1	4	yes	—
26	C₃²×C₄×D₄	D₃	1	13	yes	—
27	#64145	—	3	26	no	—
28	#64135	—	3	26	no	—
29	#64133	—	3	26	no	—
30	#64096	—	3	26	no	—
31	#64088	—	3	52	no	—
32	#64078	—	3	13	no	—
33	C₄×#634	—	3	13	no	—
34	C₂³×C₃³	C₂³	1	2	yes	—
35	C₃³×D₄	—	2	2	no	—
36	C₂×C₃³×C₄	—	2	4	no	—
37	C₂×C₃³×C₄	C₂³	1	2	yes	—
38	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
39	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
40	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
41	C₂×C₃⋊(C₃⋊Dic₃)	C₂³	1	2	yes	—
42	C₂×C₃⋊(C₃⋊Dic₃)	C₂³	1	2	yes	—
43	C₂×C₃⋊(C₃⋊Dic₃)	C₂³	1	4	yes	—
44	#6308	—	2	4	no	—
45	#6308	—	2	2	no	—
46	#5542	—	9	13	no	—
47	C₂×C₃²×D₄	C₂×D₃	1	13	yes	—
48	C₂²×C₃²×C₄	C₂×D₃	1	26	yes	—
49	C₂×#634	—	3	13	no	—
50	C₂×#634	—	3	26	no	—
51	C₃²×C₄⋊C₄	C₂×D₃	1	13	yes	—
52	C₃²×C₂²⋊C₄	C₂×D₃	1	26	yes	—
53	C₃²×C₄²	C₂×D₃	1	13	yes	—
54	#3757	—	3	52	no	—
55	#3757	—	3	52	no	—
56	C₄⋊(C₃⋊Dic₃)	—	3	13	no	—
57	C₄⋊(C₃⋊Dic₃)	—	3	26	no	—
58	C₄⋊(C₃⋊Dic₃)	—	3	26	no	—
59	#3750	—	3	26	no	—
60	#3750	—	3	52	no	—
61	C₄×C₃⋊Dic₃	—	3	26	no	—
62	C₄×C₃⋊Dic₃	—	3	52	no	—
63	C₂²×C₃³	—	2	2	no	—
64	C₂²×C₃³	—	2	2	no	—
65	C₂²×C₃³	—	2	2	no	—
66	C₂²×C₃³	C₂⁴	1	1	yes	characteristic
67	C₃³×C₄	—	2	2	no	—
68	C₃³×C₄	—	2	1	no	—
69	C₃³×C₄	#41	1	2	yes	—
70	C₃³×C₄	#41	1	2	yes	—
71	C₃⋊(C₃⋊Dic₃)	—	2	4	no	—
72	C₃⋊(C₃⋊Dic₃)	—	2	2	no	—
73	C₃⋊(C₃⋊Dic₃)	—	2	2	no	—
74	C₃×C₄×D₄	C₃⋊D₃	1	13	yes	—
75	#936	—	9	26	no	—
76	#926	—	9	26	no	—
77	#924	—	9	26	no	—
78	#887	—	9	26	no	—
79	#879	—	9	52	no	—
80	#869	—	9	13	no	—
81	C₄×Dic₆	—	9	13	no	—
82	C₂³×C₃²	C₂²×D₃	1	26	yes	—
83	C₃²×D₄	—	2	26	no	—
84	C₂×C₃²×C₄	—	2	52	no	—
85	C₂×C₃²×C₄	C₂²×D₃	1	26	yes	—
86	C₂×C₃²×C₄	C₂²×D₃	1	13	yes	—
87	C₂×C₃²×C₄	C₂²×D₃	1	13	yes	—
88	C₂×C₃²×C₄	C₂²×D₃	1	13	yes	—
89	C₂×C₃⋊Dic₃	—	3	26	no	—
90	C₂×C₃⋊Dic₃	—	3	26	no	—
91	C₂×C₃⋊Dic₃	—	3	52	no	—
92	#634	—	6	52	no	—
93	#634	—	6	26	no	—
94	#556	—	27	1	no	Sylow
95	C₂×C₃³	—	4	2	no	—
96	C₂×C₃³	C₂×#41	1	1	yes	characteristic
97	C₂×C₃³	C₂×#41	1	1	yes	characteristic
98	C₂×C₃³	2₋¹⁺⁴	1	1	yes	characteristic
99	C₂×C₃×D₄	C₂×C₃⋊D₃	1	13	yes	—
100	C₂²×C₃×C₄	C₂×C₃⋊D₃	1	26	yes	—
101	C₂×Dic₆	—	9	13	no	—
102	C₂×Dic₆	—	9	26	no	—
103	C₃×C₄⋊C₄	C₂×C₃⋊D₃	1	13	yes	—
104	C₃×C₂²⋊C₄	C₂×C₃⋊D₃	1	26	yes	—
105	C₃×C₄²	C₂×C₃⋊D₃	1	13	yes	—
106	#217	—	9	52	no	—
107	#217	—	9	52	no	—
108	C₄⋊Dic₃	—	9	13	no	—
109	C₄⋊Dic₃	—	9	26	no	—
110	C₄⋊Dic₃	—	9	26	no	—
111	Dic₃⋊C₄	—	9	26	no	—
112	Dic₃⋊C₄	—	9	52	no	—
113	C₄×Dic₃	—	9	26	no	—
114	C₄×Dic₃	—	9	52	no	—
115	C₂²×C₃²	—	2	26	no	—
116	C₂²×C₃²	—	2	26	no	—
117	C₂²×C₃²	—	2	26	no	—
118	C₂²×C₃²	C₂³×D₃	1	13	yes	—
119	C₃²×C₄	—	2	26	no	—
120	C₃²×C₄	—	2	13	no	—
121	C₃²×C₄	#235	1	26	yes	—
122	C₃²×C₄	#237	1	26	yes	—
123	C₃⋊Dic₃	—	6	52	no	—
124	C₃⋊Dic₃	—	6	26	no	—
125	C₃⋊Dic₃	—	6	26	no	—
126	C₄⋊Q₈	—	27	1	no	—
127	#126	—	27	4	no	—
128	#124	—	27	2	no	—
129	C₂²⋊Q₈	—	27	2	no	—
130	C₄×Q₈	—	27	2	no	—
131	C₄×Q₈	—	27	1	no	—
132	C₄×D₄	C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
133	#117	—	27	2	no	—
134	C₃³	#556	1	1	yes	characteristic, complemented, Sylow
135	C₂³×C₃	C₂²×C₃⋊D₃	1	26	yes	—
136	C₃×D₄	—	2	26	no	—
137	C₂×C₃×C₄	—	2	52	no	—
138	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	26	yes	—
139	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	13	yes	—
140	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	13	yes	—
141	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	13	yes	—
142	C₂×Dic₃	—	9	26	no	—
143	C₂×Dic₃	—	9	26	no	—
144	C₂×Dic₃	—	9	52	no	—
145	Dic₆	—	18	52	no	—
146	Dic₆	—	18	26	no	—
147	C₂×C₃²	—	4	26	no	—
148	C₂×C₃²	C₂×#235	1	13	yes	—
149	C₂×C₃²	C₂×#237	1	13	yes	—
150	C₂×C₃²	#1010	1	13	yes	—
151	C₂×Q₈	—	27	1	no	—
152	C₂×Q₈	—	27	2	no	—
153	C₂×D₄	C₂×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
154	C₂²×C₄	C₂×C₃⋊(C₃⋊D₃)	1	2	yes	—
155	C₄⋊C₄	—	27	1	no	—
156	C₄⋊C₄	—	27	2	no	—
157	C₄⋊C₄	—	27	4	no	—
158	C₄⋊C₄	—	27	2	no	—
159	C₄⋊C₄	—	27	2	no	—
160	C₄⋊C₄	C₂×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
161	C₂²⋊C₄	—	27	4	no	—
162	C₂²⋊C₄	—	27	4	no	—
163	C₂²⋊C₄	C₂×C₃⋊(C₃⋊D₃)	1	2	yes	—
164	C₄²	—	27	4	no	—
165	C₄²	—	27	2	no	—
166	C₄²	C₂×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
167	C₂²×C₃	—	2	26	no	—
168	C₂²×C₃	—	2	26	no	—
169	C₂²×C₃	—	2	26	no	—
170	C₂²×C₃	C₂³×C₃⋊D₃	1	13	yes	—
171	C₃×C₄	—	2	26	no	—
172	C₃×C₄	—	2	13	no	—
173	C₃×C₄	#3828	1	26	yes	—
174	C₃×C₄	#3830	1	26	yes	—
175	Dic₃	—	18	52	no	—
176	Dic₃	—	18	26	no	—
177	Dic₃	—	18	26	no	—
178	C₃²	#5542	1	13	yes	complemented
179	C₂³	C₂²×C₃⋊(C₃⋊D₃)	1	2	yes	—
180	Q₈	—	54	4	no	—
181	Q₈	—	54	2	no	—
182	D₄	—	2	2	no	—
183	C₂×C₄	—	2	4	no	—
184	C₂×C₄	—	27	2	no	—
185	C₂×C₄	—	27	4	no	—
186	C₂×C₄	—	27	2	no	—
187	C₂×C₄	C₂²×C₃⋊(C₃⋊D₃)	1	2	yes	—
188	C₂×C₄	C₂²×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
189	C₂×C₄	C₂²×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
190	C₂×C₄	C₂²×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
191	C₂×C₃	—	4	26	no	—
192	C₂×C₃	C₂×#3828	1	13	yes	—
193	C₂×C₃	C₂×#3830	1	13	yes	—
194	C₂×C₃	#64367	1	13	yes	—
195	C₂²	—	2	2	no	—
196	C₂²	—	2	2	no	—
197	C₂²	—	2	2	no	—
198	C₂²	C₂³×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
199	C₄	—	2	2	no	—
200	C₄	—	2	1	no	—
201	C₄	—	54	4	no	—
202	C₄	—	54	2	no	—
203	C₄	—	54	2	no	—
204	C₄	#89076	1	2	yes	—
205	C₄	#89078	1	2	yes	—
206	C₃	#10596013	1	13	yes	complemented
207	C₂	—	4	2	no	—
208	C₂	C₂×#89076	1	1	yes	characteristic
209	C₂	C₂×#89078	1	1	yes	characteristic
210	C₂	#11724685	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₃³×C₄×D₄

C₂

yes

maximal, characteristic

#11723977

C₂

yes

maximal

#11723967

C₂

yes

maximal, complemented

#11723965

C₂

yes

maximal, complemented

#11723928

C₂

yes

maximal, complemented

#11723920

C₂

yes

maximal, complemented

#11723910

C₂

yes

maximal, characteristic, complemented

C₄×#6308

C₂

yes

maximal, characteristic, complemented

#10596013

—

maximal

C₂×C₃³×D₄

C₂²

yes

characteristic

C₂²×C₃³×C₄

C₂²

yes

—

C₂×#6308

C₂²

yes

characteristic

C₂×#6308

C₂²

yes

—

C₃³×C₄⋊C₄

C₂²

yes

characteristic

C₃³×C₂²⋊C₄

C₂²

yes

—

C₃³×C₄²

C₂²

yes

characteristic

#88864

C₂²

yes

—

#88864

C₂²

yes

—

C₄⋊(C₃⋊(C₃⋊Dic₃))

C₂²

yes

characteristic

C₄⋊(C₃⋊(C₃⋊Dic₃))

C₂²

yes

—

C₄⋊(C₃⋊(C₃⋊Dic₃))

C₂²

yes

—

#88857

C₂²

yes

—

#88857

C₂²

yes

—

C₄×C₃⋊(C₃⋊Dic₃)

C₂²

yes

—

C₄×C₃⋊(C₃⋊Dic₃)

C₂²

yes

—

C₃²×C₄×D₄

D₃

yes

—

—

—

—

—

—

—

—

C₂³×C₃³

C₂³

yes

—

C₃³×D₄

—

C₂×C₃³×C₄

—

C₂×C₃³×C₄

C₂³

yes

—

C₂×C₃³×C₄

C₂³

yes

characteristic

C₂×C₃³×C₄

C₂³

yes

characteristic

C₂×C₃³×C₄

C₂³

yes

characteristic

C₂×C₃⋊(C₃⋊Dic₃)

C₂³

yes

—

C₂×C₃⋊(C₃⋊Dic₃)

C₂³

yes

—

C₂×C₃⋊(C₃⋊Dic₃)

C₂³

yes

—

#6308

—

#6308

—

#5542

—

C₂×C₃²×D₄

C₂×D₃

yes

—

C₂²×C₃²×C₄

C₂×D₃

yes

—

C₂×#634

—

C₂×#634

—

C₃²×C₄⋊C₄

C₂×D₃

yes

—

C₃²×C₂²⋊C₄

C₂×D₃

yes

—

C₃²×C₄²

C₂×D₃

yes

—

#3757

—

#3757

—

C₄⋊(C₃⋊Dic₃)

—

C₄⋊(C₃⋊Dic₃)

—

C₄⋊(C₃⋊Dic₃)

—

#3750

—

#3750

—

C₄×C₃⋊Dic₃

—

C₄×C₃⋊Dic₃

—

C₂²×C₃³

—

C₂²×C₃³

—

C₂²×C₃³

—

C₂²×C₃³

C₂⁴

yes

characteristic

C₃³×C₄

—

C₃³×C₄

—

C₃³×C₄

#41

yes

—

C₃³×C₄

#41

yes

—

C₃⋊(C₃⋊Dic₃)

—

C₃⋊(C₃⋊Dic₃)

—

C₃⋊(C₃⋊Dic₃)

—

C₃×C₄×D₄

C₃⋊D₃

yes

—

—

—

—

—

—

—

C₄×Dic₆

—

C₂³×C₃²

C₂²×D₃

yes

—

C₃²×D₄

—

C₂×C₃²×C₄

—

C₂×C₃²×C₄

C₂²×D₃

yes

—

C₂×C₃²×C₄

C₂²×D₃

yes

—

C₂×C₃²×C₄

C₂²×D₃

yes

—

C₂×C₃²×C₄

C₂²×D₃

yes

—

C₂×C₃⋊Dic₃

—

C₂×C₃⋊Dic₃

—

C₂×C₃⋊Dic₃

—

—

—

—

C₂×C₃³

—

C₂×C₃³

C₂×#41

yes

characteristic

C₂×C₃³

C₂×#41

yes

characteristic

C₂×C₃³

2₋¹⁺⁴

yes

characteristic

C₂×C₃×D₄

C₂×C₃⋊D₃

yes

—

100

C₂²×C₃×C₄

C₂×C₃⋊D₃

yes

—

101

C₂×Dic₆

—

102

C₂×Dic₆

—

103

C₃×C₄⋊C₄

C₂×C₃⋊D₃

yes

—

104

C₃×C₂²⋊C₄

C₂×C₃⋊D₃

yes

—

105

C₃×C₄²

C₂×C₃⋊D₃

yes

—

106

#217

—

107

#217

—

108

C₄⋊Dic₃

—

109

C₄⋊Dic₃

—

110

C₄⋊Dic₃

—

111

Dic₃⋊C₄

—

112

Dic₃⋊C₄

—

113

C₄×Dic₃

—

114

C₄×Dic₃

—

115

C₂²×C₃²

—

116

C₂²×C₃²

—

117

C₂²×C₃²

—

118

C₂²×C₃²

C₂³×D₃

yes

—

119

C₃²×C₄

—

120

C₃²×C₄

—

121

C₃²×C₄

#235

yes

—

122

C₃²×C₄

#237

yes

—

123

C₃⋊Dic₃

—

124

C₃⋊Dic₃

—

125

C₃⋊Dic₃

—

126

C₄⋊Q₈

—

127

#126

—

128

#124

—

129

C₂²⋊Q₈

—

130

C₄×Q₈

—

131

C₄×Q₈

—

132

C₄×D₄

C₃⋊(C₃⋊D₃)

yes

characteristic

133

#117

—

134

C₃³

#556

yes

characteristic, complemented, Sylow

135

C₂³×C₃

C₂²×C₃⋊D₃

yes

—

136

C₃×D₄

—

137

C₂×C₃×C₄

—

138

C₂×C₃×C₄

C₂²×C₃⋊D₃

yes

—

139

C₂×C₃×C₄

C₂²×C₃⋊D₃

yes

—

140

C₂×C₃×C₄

C₂²×C₃⋊D₃

yes

—

141

C₂×C₃×C₄

C₂²×C₃⋊D₃

yes

—

142

C₂×Dic₃

—

143

C₂×Dic₃

—

144

C₂×Dic₃

—

145

Dic₆

—

146

Dic₆

—

147

C₂×C₃²

—

148

C₂×C₃²

C₂×#235

yes

—

149

C₂×C₃²

C₂×#237

yes

—

150

C₂×C₃²

#1010

yes

—

151

C₂×Q₈

—

152

C₂×Q₈

—

153

C₂×D₄

C₂×C₃⋊(C₃⋊D₃)

yes

characteristic

154

C₂²×C₄

C₂×C₃⋊(C₃⋊D₃)

yes

—

155

C₄⋊C₄

—

156

C₄⋊C₄

—

157

C₄⋊C₄

—

158

C₄⋊C₄

—

159

C₄⋊C₄

—

160

C₄⋊C₄

C₂×C₃⋊(C₃⋊D₃)

yes

characteristic

161

C₂²⋊C₄

—

162

C₂²⋊C₄

—

163

C₂²⋊C₄

C₂×C₃⋊(C₃⋊D₃)

yes

—

164

C₄²

—

165

C₄²

—

166

C₄²

C₂×C₃⋊(C₃⋊D₃)

yes

characteristic

167

C₂²×C₃

—

168

C₂²×C₃

—

169

C₂²×C₃

—

170

C₂²×C₃

C₂³×C₃⋊D₃

yes

—

171

C₃×C₄

—

172

C₃×C₄

—

173

C₃×C₄

#3828

yes

—

174

C₃×C₄

#3830

yes

—

175

Dic₃

—

176

Dic₃

—

177

Dic₃

—

178

C₃²

#5542

yes

complemented

179

C₂³

C₂²×C₃⋊(C₃⋊D₃)

yes

—

180

Q₈

—

181

Q₈

—

182

D₄

—

183

C₂×C₄

—

184

C₂×C₄

—

185

C₂×C₄

—

186

C₂×C₄

—

187

C₂×C₄

C₂²×C₃⋊(C₃⋊D₃)

yes

—

188

C₂×C₄

C₂²×C₃⋊(C₃⋊D₃)

yes

characteristic

189

C₂×C₄

C₂²×C₃⋊(C₃⋊D₃)

yes

characteristic

190

C₂×C₄

C₂²×C₃⋊(C₃⋊D₃)

yes

characteristic

191

C₂×C₃

—

192

C₂×C₃

C₂×#3828

yes

—

193

C₂×C₃

C₂×#3830

yes

—

194

C₂×C₃

#64367

yes

—

195

C₂²

—

196

C₂²

—

197

C₂²

—

198

C₂²

C₂³×C₃⋊(C₃⋊D₃)

yes

characteristic

199

C₄

—

200

C₄

—

201

C₄

—

202

C₄

—

203

C₄

—

204

C₄

#89076

yes

—

205

C₄

#89078

yes

—

206

C₃

#10596013

yes

complemented

207

C₂

—

208

C₂

C₂×#89076

yes

characteristic

209

C₂

C₂×#89078

yes

characteristic

210

C₂

#11724685

yes

characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂³×C₃⋊(C₃⋊D₃)
commutator, socle, cosocle	C₂²×C₃³	C₂⁴
Fitting	C₃³×C₄×D₄	C₂
prime radical	C₂×C₃³×D₄	C₂²
hypercenter	C₄×D₄	C₃⋊(C₃⋊D₃)
hypocenter	C₃³	#556
LCS	G ▷ C₂²×C₃³ ▷ C₃³
UCS	C₁ ◁ C₂² ◁ C₄×D₄

subgroup

G/H

center, Frattini

C₂²

C₂³×C₃⋊(C₃⋊D₃)

commutator, socle, cosocle

C₂²×C₃³

C₂⁴

Fitting

C₃³×C₄×D₄

C₂

prime radical

C₂×C₃³×D₄

C₂²

hypercenter

C₄×D₄

C₃⋊(C₃⋊D₃)

C₃³

G ▷ C₂²×C₃³ ▷ C₃³

C₁ ◁ C₂² ◁ C₄×D₄

N	H ≅ G/N	type
3. #11723967	C₂	semidirect
4. #11723965	C₂	semidirect
5. #11723928	C₂	semidirect
6. #11723920	C₂	semidirect
7. #11723910	C₂	semidirect
8. C₄×#6308	C₂	semidirect
134. C₃³	#556	semidirect
178. C₃²	#5542	semidirect
206. C₃	#10596013	semidirect

H ≅ G/N

type

3. #11723967

C₂

semidirect

4. #11723965

C₂

semidirect

5. #11723928

C₂

semidirect

6. #11723920

C₂

semidirect

7. #11723910

C₂

semidirect

8. C₄×#6308

C₂

semidirect

134. C₃³

#556

semidirect

178. C₃²

#5542

semidirect

206. C₃

#10596013

semidirect

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

subgroup	index
C₃³×C₄×D₄	2
#11723977	2
#11723967	2
#11723965	2
#11723928	2
#11723920	2
#11723910	2
C₄×#6308	2
#10596013	3

subgroup

index

C₃³×C₄×D₄

Subgroups — #13179669

Conjugacy classes of subgroups

Complements

Maximal subgroups