Finite Group Databasebeta

← #17043781

Subgroups — #17043781

Order 4352.

990 conjugacy classes of subgroups; only the 315 normal subgroups are shown.

normal subgroups only

This group has 990 conjugacy classes of subgroups — too many to draw. Only its 315 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14531387C212yesmaximal
2#14529770C218yesmaximal
3#14528861C214yesmaximal
4C2×C17×#544C211yesmaximal, characteristic
5#11762695—28no—
6#11762672C2214yes—
7#11762669C2214yes—
8C4×C22⋊Dic17C2214yes—
9#11762576C22116yes—
10C17×#544—28no—
11C2×C17×C4⋊Q8C414yescomplemented
12C2×C17×#125C414yescomplemented
13C2×C17×C22⋊Q8C2214yes—
14C2×C17×#117C2212yes—
15C22×C4⋊C4×C17C2211yescharacteristic
16C22×Q8×C17C2×C414yes—
17C23×C4×C17C2311yescharacteristic
18C23×C4×C17C2312yes—
19C17×C4⋊Q8—216no—
20C17×#125—216no—
21C17×C22⋊Q8—28no—
22C17×C22⋊Q8—28no—
23C17×#117—28no—
24C2×C4⋊C4×C17C2×C412yes—
25C2×C4⋊C4×C17C2×C412yes—
26C2×C4⋊C4×C17C2×C414yes—
27C2×C4⋊C4×C17C2×C418yes—
28C2×C4⋊C4×C17C2×C414yes—
29C2×C4⋊C4×C17D418yes—
30C2×C22⋊C4×C17C2314yes—
31C2×C42×C17C2×C414yes—
32C2×C22⋊Dic17C2318yes—
33C2×C4⋊Dic17—24no—
34C2×C4×Dic17—24no—
35#10587502—24no—
36#10587502—24no—
37#10587502—28no—
38C24×C17C2411yescharacteristic
39C2×Q8×C17—28no—
40C2×Q8×C17—84no—
41C22×C4×C17—24no—
42C22×C4×C17—82no—
43C22×C4×C17C22×C412yes—
44C22×C4×C17C22×C414yes—
45C22×C4×C17C22×C414yes—
46C22×C4×C17C22×C414yes—
47C22×C4×C17C2×D414yes—
48C22×C4×C17C2×D414yes—
49C22×C4×C17C2×D414yes—
50C22×Dic17—28no—
51C4⋊C4×C17—28no—
52C4⋊C4×C17—216no—
53C4⋊C4×C17—24no—
54C4⋊C4×C17—24no—
55C4⋊C4×C17C22⋊C4116yes—
56C22⋊C4×C17—28no—
57C42×C17—28no—
58C22⋊Dic17—216no—
59C4⋊Dic17—84no—
60C4×Dic17—84no—
61#21828—171nomaximal, Sylow
62C23×C17—41no—
63C23×C17—41no—
64C23×C17C23×C411yescharacteristic
65C23×C17C22×D412yes—
66C23×C172−1+414yes—
67Q8×C17—88no—
68C2×C4×C17—24no—
69C2×C4×C17—28no—
70C2×C4×C17—24no—
71C2×C4×C17—24no—
72C2×C4×C17—44no—
73C2×C4×C17—44no—
74C2×C4×C17—44no—
75C2×C4×C17—44no—
76C2×C4×C17—44no—
77C2×C4×C17C2×C22⋊C414yes—
78C2×C4×C17C2×C22⋊C418yes—
79C2×Dic17—48no—
80C2×Dic17—48no—
81C2×Dic17—48no—
82C2×#544D1711yescharacteristic
83#2313—172no—
84#1996—178no—
85#1820—174no—
86C22×C17—22no—
87C22×C17—21no—
88C22×C17—22no—
89C22×C17—21no—
90C22×C17—44no—
91C22×C17C22×C22⋊C411yescharacteristic
92C22×C17#51912yes—
93C22×C17#53614yes—
94C4×C17—24no—
95C4×C17—28no—
96C4×C17—44no—
97C4×C17—44no—
98Dic17—88no—
99#544—28no—
100C2×C4⋊Q8Dic1714yescomplemented
101C2×#125Dic1714yescomplemented
102C2×C22⋊Q8C2×D1714yes—
103C2×#117C2×D1712yes—
104C22×C4⋊C4C2×D1711yescharacteristic
105#387—348no—
106#381—174no—
107#380—174no—
108C4×C22⋊C4—174no—
109#342—1716no—
110C2×C17—24no—
111C2×C17—22no—
112C2×C17#231011yescharacteristic
113C2×C17#288311yescharacteristic
114C2×C17#288411yescharacteristic
115C22×Q8C2×Dic1714yes—
116C23×C4C22×D1711yescharacteristic
117C23×C4C22×D1712yes—
118C4⋊Q8—216no—
119#125—216no—
120C22⋊Q8—28no—
121C22⋊Q8—28no—
122#117—28no—
123C2×C4⋊C4—344no—
124C2×C4⋊C4C2×Dic1712yes—
125C2×C4⋊C4C2×Dic1712yes—
126C2×C4⋊C4C2×Dic1714yes—
127C2×C4⋊C4C2×Dic1718yes—
128C2×C4⋊C4C2×Dic1714yes—
129C2×C4⋊C4C22⋊D1718yes—
130C2×C22⋊C4—178no—
131C2×C22⋊C4C22×D1714yes—
132C2×C42—344no—
133C2×C42C2×Dic1714yes—
134#95—344no—
135#95—344no—
136#95—348no—
137C17#2182811yescharacteristic, complemented, Sylow
138C24C23×D1711yescharacteristic
139C2×Q8—28no—
140C2×Q8—84no—
141C22×C4—24no—
142C22×C4—82no—
143C22×C4—348no—
144C22×C4C22×Dic1712yes—
145C22×C4C22×Dic1714yes—
146C22×C4C22×Dic1714yes—
147C22×C4C22×Dic1714yes—
148C22×C4C2×C22⋊D1714yes—
149C22×C4C2×C22⋊D1714yes—
150C22×C4C2×C22⋊D1714yes—
151C4⋊C4—24no—
152C4⋊C4—24no—
153C4⋊C4—28no—
154C4⋊C4—216no—
155C4⋊C4—1364no—
156C4⋊C4C22⋊Dic17116yes—
157C22⋊C4—28no—
158C22⋊C4—3416no—
159C42—28no—
160C42—1364no—
161C23—41no—
162C23—41no—
163C23#1058769414yes—
164C23C23×Dic1711yescharacteristic
165C23C22×C22⋊D1712yes—
166Q8—88no—
167C2×C4—24no—
168C2×C4—28no—
169C2×C4—24no—
170C2×C4—24no—
171C2×C4—44no—
172C2×C4—44no—
173C2×C4—44no—
174C2×C4—44no—
175C2×C4—44no—
176C2×C4—688no—
177C2×C4—688no—
178C2×C4—688no—
179C2×C4C2×C22⋊Dic1714yes—
180C2×C4C2×C22⋊Dic1718yes—
181C22—21no—
182C22—22no—
183C22—21no—
184C22—22no—
185C22—44no—
186C22C22×C22⋊Dic1711yescharacteristic
187C22#1176328712yes—
188C22#1176338314yes—
189C4—28no—
190C4—24no—
191C4—44no—
192C4—44no—
193C4—1368no—
194C2—24no—
195C2—22no—
196C2#1453137011yescharacteristic
197C2#1453724511yescharacteristic
198C2#1453724811yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic17
commutatorC23×C17C23×C4
FrattiniC24C23×D17
FittingC2×C17×#544C2
socleC22×C17C22×C22⋊C4
prime radical, cosocleC24×C17C24
hypercenterC2×#544D17
hypocenterC17#21828
LCSG ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4⋊C4 ◁ C2×#544

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
11. C2×C17×C4⋊Q8C4semidirect
12. C2×C17×#125C4semidirect
100. C2×C4⋊Q8Dic17semidirect
101. C2×#125Dic17semidirect
137. C17#21828semidirect

Maximal subgroups

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

subgroupindex
#145313872
#145297702
#145288612
C2×C17×#5442
#2182817