Finite Group Databasebeta

← #17958425

Subgroups — #17958425

Order 4352.

490 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 84 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#14544032C212yesmaximal
2#14543725C214yesmaximal, complemented
3C2×#11762674C211yesmaximal, characteristic
4#11763779—22no—
5#11763654—22no—
6#11763654C2214yes—
7C22×C4⋊Dic17C2211yescharacteristic
8C22×C4×Dic17C411yescharacteristic
9#11762674—22no—
10#11762674C412yes—
11#11762674C2212yes—
12C2×#10587502—22no—
13C22×C4⋊C4×C17C411yescharacteristic
14C23×C4×C17—21no—
15C23×C4×C17C2×C411yescharacteristic
16C23×Dic17—21no—
17C23×Dic17D412yes—
18C2×#63247—42no—
19C2×C4⋊C4×C17—21no—
20C2×C4⋊C4×C17—41no—
21C2×C4⋊C4×C17—41no—
22C2×C4⋊C4×C17C2×C412yes—
23C2×C4⋊Dic17—41no—
24C2×C4⋊Dic17—41no—
25C2×C4⋊Dic17C2×C411yescharacteristic
26C2×C4⋊Dic17D412yes—
27C2×C4⋊Dic17C2311yescharacteristic
28C2×C4×Dic17—24no—
29C2×C4×Dic17—21no—
30C2×C4×Dic17C2×C412yes—
31C22⋊#3624—24no—
32C22⋊#3624—42no—
33#10587502—24no—
34#10587502—24no—
35C24×C17C22⋊C411yescharacteristic
36C22×C4×C17—21no—
37C22×C4×C17—21no—
38C22×C4×C17—22no—
39C22×C4×C17—22no—
40C22×C4×C17—22no—
41C22×C4×C17—44no—
42C22×C4×C17—41no—
43C22×C4×C17—41no—
44C22×C4×C17C22⋊C411yescharacteristic
45C22×C4×C17C22×C411yescharacteristic
46C22×Dic17—24no—
47C22×Dic17—22no—
48C22×Dic17—22no—
49C22×Dic17—22no—
50C22×Dic17—42no—
51C22×Dic17—42no—
52C22×Dic17—44no—
53C22×Dic17C22⋊C412yes—
54C22×Dic17C2×D412yes—
55#63247—84no—
56C2×#3624—44no—
57C4⋊C4×C17—42no—
58C4⋊C4×C17—42no—
59C4⋊Dic17—41no—
60C4⋊Dic17—42no—
61C4⋊Dic17—41no—
62C4×Dic17—24no—
63C4×Dic17—22no—
64C4×Dic17M1614yescomplemented
65#11511—171nomaximal, Sylow
66C23×C17—22no—
67C23×C17—22no—
68C23×C17—21no—
69C23×C17—21no—
70C23×C17#9911yescharacteristic
71C23×C17#9911yescharacteristic
72C23×C17C2×C22⋊C411yescharacteristic
73C2×C4×C17—24no—
74C2×C4×C17—24no—
75C2×C4×C17—21no—
76C2×C4×C17—21no—
77C2×C4×C17—21no—
78C2×C4×C17—21no—
79C2×C4×C17—44no—
80C2×C4×C17—42no—
81C2×C4×C17—82no—
82C2×C4×C17—82no—
83C2×C4×C17#10112yes—
84C2×C4×C17C2×M1612yes—
85C2×Dic17—24no—
86C2×Dic17—22no—
87C2×Dic17—22no—
88C2×Dic17—48no—
89C2×Dic17—42no—
90C2×Dic17—42no—
91C2×Dic17—44no—
92C2×Dic17—42no—
93C2×Dic17—42no—
94C2×Dic17—82no—
95#3624—84no—
96C2×#382—171no—
97#1463—172no—
98#1324—174no—
99C22×C17—24no—
100C22×C17—24no—
101C22×C17—21no—
102C22×C17—21no—
103C22×C17—21no—
104C22×C17—21no—
105C22×C17—21no—
106C22×C17—21no—
107C22×C17#35412yes—
108C22×C17#35512yes—
109C22×C17#40711yescharacteristic
110C22×C17C2×#9911yescharacteristic
111C22×C17C2×#10111yescharacteristic
112C4×C17—22no—
113C4×C17—22no—
114C4×C17—82no—
115Dic17—44no—
116Dic17—42no—
117Dic17—42no—
118C22×C4⋊C4—171no—
119C22×C4⋊C4#59511yescharacteristic
120C22×C42—171no—
121#407—342no—
122#382—172no—
123#382—172no—
124#382—342no—
125C2×#95—342no—
126#324—174no—
127#324—342no—
128C2×C17—21no—
129C2×C17—22no—
130C2×C17—22no—
131C2×C17—21no—
132C2×C17#146311yescharacteristic
133C2×C17C2×#35411yescharacteristic
134C2×C17C2×#35511yescharacteristic
135C23×C4—21no—
136C23×C4—172no—
137C23×C4—341no—
138C23×C4C2×#59511yescharacteristic
139C2×M16—682no—
140C2×C4⋊C4—21no—
141C2×C4⋊C4—41no—
142C2×C4⋊C4—41no—
143C2×C4⋊C4—172no—
144C2×C4⋊C4—171no—
145C2×C4⋊C4—171no—
146C2×C4⋊C4—681no—
147C2×C4⋊C4—681no—
148C2×C4⋊C4C2×#59512yes—
149C2×C42—172no—
150C2×C42—344no—
151C2×C42—341no—
152C22⋊C8—344no—
153C22⋊C8—682no—
154#95—344no—
155#95—344no—
156C17#1151111yescharacteristic, complemented, Sylow
157C24C22⋊#59511yescharacteristic
158C22×C4—21no—
159C22×C4—21no—
160C22×C4—22no—
161C22×C4—22no—
162C22×C4—22no—
163C22×C4—44no—
164C22×C4—41no—
165C22×C4—41no—
166C22×C4—172no—
167C22×C4—172no—
168C22×C4—344no—
169C22×C4—342no—
170C22×C4—342no—
171C22×C4—342no—
172C22×C4—682no—
173C22×C4—682no—
174C22×C4—684no—
175C22×C4C22⋊#59511yescharacteristic
176C22×C4C22×#59511yescharacteristic
177M16—1364no—
178C2×C8—684no—
179C4⋊C4—42no—
180C4⋊C4—42no—
181C4⋊C4—682no—
182C4⋊C4—681no—
183C4⋊C4—681no—
184C42—174no—
185C42—344no—
186C42—342no—
187C23—22no—
188C23—22no—
189C23—21no—
190C23—21no—
191C23#1058755111yescharacteristic
192C23#1058755111yescharacteristic
193C23C2×C22⋊#59511yescharacteristic
194C2×C4—24no—
195C2×C4—24no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—44no—
201C2×C4—42no—
202C2×C4—82no—
203C2×C4—82no—
204C2×C4—344no—
205C2×C4—342no—
206C2×C4—342no—
207C2×C4—688no—
208C2×C4—682no—
209C2×C4—682no—
210C2×C4—684no—
211C2×C4—682no—
212C2×C4—682no—
213C2×C4—1362no—
214C2×C4#1058754512yes—
215C2×C4D17⋊M1612yes—
216C8—1364no—
217C22—24no—
218C22—24no—
219C22—21no—
220C22—21no—
221C22—21no—
222C22—21no—
223C22—21no—
224C22—21no—
225C22#1176371512yes—
226C22#1176371712yes—
227C22#1176378111yescharacteristic
228C22C2×#1058755111yescharacteristic
229C22C2×#1058754511yescharacteristic
230C4—22no—
231C4—22no—
232C4—82no—
233C4—684no—
234C4—682no—
235C4—682no—
236C2—21no—
237C2—22no—
238C2—22no—
239C2—21no—
240C2#1454403411yescharacteristic
241C2C2×#1176371511yescharacteristic
242C2C2×#1176371711yescharacteristic
subgroupG/H
centerC22C2×#10587551
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC22×C4⋊C4×C17C4
socleC22×C17C2×#99
prime radicalC24×C17C22⋊C4
cosocleC2×C4⋊Dic17C23
hypercenterC22×C4⋊C4#595
hypocenterC17#11511
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C24 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #14543725C2semidirect
64. C4×Dic17M16semidirect
156. C17#11511semidirect

Maximal subgroups

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

subgroupindex
#145440322
#145437252
C2×#117626742
#1151117