Finite Group Databasebeta

← #17958388

Subgroups — #17958388

Order 4352.

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

normal subgroups only

This group has 706 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#14544029C212yesmaximal
2#14543711C214yesmaximal, complemented
3C2×#11762670C211yesmaximal, characteristic
4#11763779—22no—
5#11763652—22no—
6#11763652C2214yes—
7C24×Dic17C411yescharacteristic
8C22×C22⋊Dic17C2211yescharacteristic
9#11762670—22no—
10#11762670C412yes—
11#11762670C2212yes—
12C2×#10587502—22no—
13C22×C22⋊C4×C17C411yescharacteristic
14C25×C17C2×C411yescharacteristic
15C23×C4×C17—21no—
16C23×Dic17—21no—
17C23×Dic17—21no—
18C23×Dic17—24no—
19C23×Dic17—42no—
20C23×Dic17—42no—
21C23×Dic17C2×C412yes—
22C23×Dic17D412yes—
23C2×#63247—42no—
24C2×C22⋊C4×C17—21no—
25C2×C22⋊C4×C17—42no—
26C2×C22⋊C4×C17C2×C412yes—
27C2×C22⋊Dic17—42no—
28C2×C22⋊Dic17C2×C411yescharacteristic
29C2×C22⋊Dic17D412yes—
30C2×C22⋊Dic17C2311yescharacteristic
31C22⋊#3624—24no—
32C22⋊#3624—42no—
33#10587502—24no—
34#10587502—24no—
35C24×C17—22no—
36C24×C17—22no—
37C24×C17—22no—
38C24×C17—44no—
39C24×C17C22⋊C411yescharacteristic
40C24×C17C22⋊C411yescharacteristic
41C24×C17C22×C411yescharacteristic
42C22×C4×C17—22no—
43C22×C4×C17—44no—
44C22×C4×C17—42no—
45C22×Dic17—24no—
46C22×Dic17—24no—
47C22×Dic17—22no—
48C22×Dic17—22no—
49C22×Dic17—22no—
50C22×Dic17—22no—
51C22×Dic17—416no—
52C22×Dic17—42no—
53C22×Dic17—42no—
54C22×Dic17—42no—
55C22×Dic17—42no—
56C22×Dic17—42no—
57C22×Dic17—42no—
58C22×Dic17—44no—
59C22×Dic17C22⋊C412yes—
60C22×Dic17M1614yescomplemented
61C22×Dic17C2×D412yes—
62#63247—84no—
63C2×#3624—44no—
64C22⋊C4×C17—42no—
65C22⋊C4×C17—42no—
66C22⋊Dic17—41no—
67C22⋊Dic17—42no—
68C22⋊Dic17—41no—
69#11500—171nomaximal, Sylow
70C23×C17—24no—
71C23×C17—21no—
72C23×C17—21no—
73C23×C17—28no—
74C23×C17—21no—
75C23×C17—21no—
76C23×C17—21no—
77C23×C17—21no—
78C23×C17—42no—
79C23×C17—42no—
80C23×C17—48no—
81C23×C17—48no—
82C23×C17—44no—
83C23×C17—44no—
84C23×C17#9912yes—
85C23×C17#10012yes—
86C23×C17C2×C22⋊C411yescharacteristic
87C23×C17C2×M1612yes—
88C2×C4×C17—44no—
89C2×C4×C17—42no—
90C2×C4×C17—84no—
91C2×Dic17—24no—
92C2×Dic17—22no—
93C2×Dic17—22no—
94C2×Dic17—48no—
95C2×Dic17—48no—
96C2×Dic17—44no—
97C2×Dic17—44no—
98C2×Dic17—42no—
99C2×Dic17—42no—
100C2×Dic17—44no—
101C2×Dic17—42no—
102C2×Dic17—42no—
103C2×Dic17—82no—
104#3624—84no—
105C2×#381—171no—
106#1462—172no—
107#1317—174no—
108C22×C17—24no—
109C22×C17—24no—
110C22×C17—22no—
111C22×C17—22no—
112C22×C17—22no—
113C22×C17—22no—
114C22×C17—22no—
115C22×C17—42no—
116C22×C17—42no—
117C22×C17—42no—
118C22×C17—416no—
119C22×C17—42no—
120C22×C17—42no—
121C22×C17—42no—
122C22×C17#35214yes—
123C22×C17#40711yescharacteristic
124C22×C17C2×#9911yescharacteristic
125C22×C17C2×#10011yescharacteristic
126C4×C17—82no—
127Dic17—42no—
128Dic17—42no—
129Dic17—44no—
130C24×C4—171no—
131C22×C22⋊C4—171no—
132C22×C22⋊C4#59511yescharacteristic
133#407—342no—
134#381—172no—
135#381—172no—
136#381—342no—
137C2×#95—342no—
138#323—174no—
139#323—342no—
140C2×C17—21no—
141C2×C17—24no—
142C2×C17—21no—
143C2×C17—42no—
144C2×C17—42no—
145C2×C17#146211yescharacteristic
146C2×C17C2×#35212yes—
147C25C2×#59511yescharacteristic
148C23×C4—21no—
149C23×C4—172no—
150C23×C4—172no—
151C23×C4—344no—
152C23×C4—341no—
153C23×C4—341no—
154C23×C4—682no—
155C23×C4—682no—
156C2×M16—682no—
157C2×C22⋊C4—21no—
158C2×C22⋊C4—42no—
159C2×C22⋊C4—172no—
160C2×C22⋊C4—171no—
161C2×C22⋊C4—171no—
162C2×C22⋊C4—682no—
163C2×C22⋊C4C2×#59512yes—
164C22⋊C8—344no—
165C22⋊C8—682no—
166#95—344no—
167#95—344no—
168C17#1150011yescharacteristic, complemented, Sylow
169C24—22no—
170C24—22no—
171C24—22no—
172C24—44no—
173C24C22⋊#59511yescharacteristic
174C24C22⋊#59511yescharacteristic
175C24C22×#59511yescharacteristic
176C22×C4—22no—
177C22×C4—42no—
178C22×C4—44no—
179C22×C4—174no—
180C22×C4—172no—
181C22×C4—172no—
182C22×C4—344no—
183C22×C4—344no—
184C22×C4—342no—
185C22×C4—342no—
186C22×C4—342no—
187C22×C4—342no—
188C22×C4—6816no—
189C22×C4—682no—
190C22×C4—682no—
191C22×C4—682no—
192C22×C4—682no—
193C22×C4—682no—
194C22×C4—682no—
195C22×C4—684no—
196M16—1364no—
197C2×C8—684no—
198C22⋊C4—42no—
199C22⋊C4—42no—
200C22⋊C4—681no—
201C22⋊C4—682no—
202C22⋊C4—681no—
203C23—24no—
204C23—21no—
205C23—21no—
206C23—28no—
207C23—21no—
208C23—21no—
209C23—21no—
210C23—21no—
211C23—42no—
212C23—42no—
213C23—48no—
214C23—48no—
215C23—44no—
216C23—44no—
217C23#1058753912yes—
218C23#1058755312yes—
219C23D17⋊M1612yes—
220C23C2×C22⋊#59511yescharacteristic
221C2×C4—44no—
222C2×C4—42no—
223C2×C4—84no—
224C2×C4—344no—
225C2×C4—342no—
226C2×C4—342no—
227C2×C4—688no—
228C2×C4—684no—
229C2×C4—688no—
230C2×C4—684no—
231C2×C4—682no—
232C2×C4—682no—
233C2×C4—684no—
234C2×C4—682no—
235C2×C4—682no—
236C2×C4—1362no—
237C8—1364no—
238C22—24no—
239C22—24no—
240C22—22no—
241C22—22no—
242C22—22no—
243C22—22no—
244C22—22no—
245C22—42no—
246C22—42no—
247C22—42no—
248C22—416no—
249C22—42no—
250C22—42no—
251C22—42no—
252C22#1176371214yes—
253C22#1176378111yescharacteristic
254C22C2×#1058753911yescharacteristic
255C22C2×#1058755311yescharacteristic
256C4—82no—
257C4—682no—
258C4—682no—
259C4—684no—
260C2—21no—
261C2—24no—
262C2—21no—
263C2—42no—
264C2—42no—
265C2#1454403111yescharacteristic
266C2C2×#1176371212yes—
subgroupG/H
centerC22C2×#10587539
commutatorC24×C17C22×C4
FrattiniC24C22×#595
FittingC22×C22⋊C4×C17C4
socleC22×C17C2×#99
prime radicalC25×C17C2×C4
cosocleC2×C22⋊Dic17C23
hypercenterC22×C22⋊C4#595
hypocenterC17#11500
LCSG ▷ C24×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C24 ◁ C25 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #14543711C2semidirect
60. C22×Dic17M16semidirect
168. C17#11500semidirect

Maximal subgroups

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

subgroupindex
#145440292
#145437112
C2×#117626702
#1150017