Finite Group Databasebeta

← #17958405

Subgroups — #17958405

Order 4352.

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

normal subgroups only

This group has 814 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, complemented
2#14543713C214yesmaximal, complemented
3C2×#11762711C211yesmaximal, characteristic
4#11763779—22no—
5#11763654—22no—
6#11763654C2214yescomplemented
7C23×D68C411yescharacteristic
8C22×C4⋊Dic17C2211yescharacteristic
9C22×#63227—22no—
10#11762711—22no—
11#11762711C412yes—
12#11762711C2212yes—
13C22×C42×C17C411yescharacteristic
14C24×D17—21no—
15C23×C4×C17—21no—
16C23×C4×C17C2×C411yescharacteristic
17C23×Dic17D412yes—
18C22×D68—21no—
19C22×D68—24no—
20C22×D68—41no—
21C22×D68—41no—
22C22×D68—42no—
23C22×D68C2×C412yes—
24C2×#63247—42no—
25C2×C42×C17—21no—
26C2×C42×C17—42no—
27C2×C42×C17C2×C412yes—
28C2×#63227—24no—
29C2×#63227—24no—
30C2×#63227—48no—
31C2×C4⋊Dic17—41no—
32C2×C4⋊Dic17—41no—
33C2×C4⋊Dic17C2×C411yescharacteristic
34C2×C4⋊Dic17D412yes—
35C2×C4⋊Dic17C2311yescharacteristic
36C22⋊#3624—24no—
37C22⋊#3624—42no—
38C24×C17C22⋊C411yescharacteristic
39C23×D17—24no—
40C23×D17—22no—
41C23×D17—42no—
42C23×D17—44no—
43C23×D17—44no—
44C23×D17—41no—
45C23×D17—41no—
46C22×C4×C17—21no—
47C22×C4×C17—21no—
48C22×C4×C17—22no—
49C22×C4×C17—22no—
50C22×C4×C17—24no—
51C22×C4×C17—22no—
52C22×C4×C17—42no—
53C22×C4×C17—42no—
54C22×C4×C17C22⋊C411yescharacteristic
55C22×C4×C17C22×C411yescharacteristic
56C22×Dic17—22no—
57C22×Dic17—22no—
58C22×Dic17—44no—
59C22×Dic17C22⋊C412yes—
60C22×Dic17C2×D412yes—
61C2×D68—24no—
62C2×D68—22no—
63C2×D68—42no—
64C2×D68—42no—
65C2×D68—48no—
66C2×D68—48no—
67C2×D68—42no—
68C2×D68—42no—
69C2×D68M1614yescomplemented
70#63247—84no—
71C2×#3624—44no—
72C42×C17—42no—
73C42×C17—42no—
74#63227—48no—
75#63227—48no—
76C4⋊Dic17—41no—
77C4⋊Dic17—42no—
78C4⋊Dic17—41no—
79#11505—171nomaximal, Sylow
80C23×C17—22no—
81C23×C17—22no—
82C23×C17—21no—
83C23×C17—21no—
84C23×C17#9911yescharacteristic
85C23×C17#9911yescharacteristic
86C23×C17C2×C22⋊C411yescharacteristic
87C22×D17—24no—
88C22×D17—44no—
89C22×D17—44no—
90C22×D17—416no—
91C22×D17—44no—
92C22×D17—44no—
93C22×D17—42no—
94C22×D17—42no—
95C22×D17—88no—
96C22×D17—82no—
97C22×D17—82no—
98C22×D17—82no—
99C22×D17—82no—
100C2×C4×C17—24no—
101C2×C4×C17—24no—
102C2×C4×C17—21no—
103C2×C4×C17—21no—
104C2×C4×C17—21no—
105C2×C4×C17—21no—
106C2×C4×C17—24no—
107C2×C4×C17—48no—
108C2×C4×C17—42no—
109C2×C4×C17—42no—
110C2×C4×C17#10012yes—
111C2×C4×C17C2×M1612yes—
112C2×Dic17—22no—
113C2×Dic17—22no—
114C2×Dic17—44no—
115C2×Dic17—42no—
116C2×Dic17—42no—
117C2×Dic17—82no—
118D68—44no—
119D68—48no—
120D68—44no—
121#3624—84no—
122C2×#390—171no—
123#1463—172no—
124#1318—174no—
125C22×C17—24no—
126C22×C17—24no—
127C22×C17—21no—
128C22×C17—21no—
129C22×C17—21no—
130C22×C17—21no—
131C22×C17—21no—
132C22×C17—21no—
133C22×C17#35312yes—
134C22×C17#35512yes—
135C22×C17#40711yescharacteristic
136C22×C17C2×#9911yescharacteristic
137C22×C17C2×#10011yescharacteristic
138C2×D17—48no—
139C2×D17—44no—
140C2×D17—84no—
141C2×D17—88no—
142C2×D17—88no—
143C2×D17—82no—
144C2×D17—82no—
145C4×C17—22no—
146C4×C17—22no—
147C4×C17—44no—
148Dic17—42no—
149Dic17—42no—
150C23×D4—171no—
151C22×C4⋊C4—171no—
152C22×C22⋊C4—342no—
153C22×C42#59511yescharacteristic
154#407—342no—
155#390—172no—
156#390—172no—
157#390—342no—
158#324—174no—
159#324—342no—
160C2×C17—21no—
161C2×C17—21no—
162C2×C17—22no—
163C2×C17—22no—
164C2×C17#146211yescharacteristic
165C2×C17C2×#35311yescharacteristic
166C2×C17C2×#35511yescharacteristic
167D17—84no—
168C25—341no—
169C22×D4—172no—
170C22×D4—344no—
171C22×D4—341no—
172C22×D4—681no—
173C22×D4—681no—
174C22×D4—682no—
175C23×C4—21no—
176C23×C4—172no—
177C23×C4C2×#59511yescharacteristic
178C2×M16—682no—
179C2×C4⋊C4—172no—
180C2×C4⋊C4—171no—
181C2×C4⋊C4—171no—
182C2×C4⋊C4—681no—
183C2×C4⋊C4—681no—
184C2×C22⋊C4—344no—
185C2×C22⋊C4—344no—
186C2×C22⋊C4—688no—
187C2×C42—21no—
188C2×C42—42no—
189C2×C42C2×#59512yes—
190C22⋊C8—344no—
191C22⋊C8—682no—
192C17#1150511yescharacteristic, complemented, Sylow
193C24—344no—
194C24—342no—
195C24—684no—
196C24—682no—
197C24—684no—
198C24—681no—
199C24—681no—
200C24C22⋊#59511yescharacteristic
201C2×D4—174no—
202C2×D4—344no—
203C2×D4—342no—
204C2×D4—682no—
205C2×D4—682no—
206C2×D4—688no—
207C2×D4—688no—
208C2×D4—682no—
209C2×D4—682no—
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—22no—
213C22×C4—22no—
214C22×C4—24no—
215C22×C4—22no—
216C22×C4—42no—
217C22×C4—42no—
218C22×C4—172no—
219C22×C4—172no—
220C22×C4—342no—
221C22×C4—342no—
222C22×C4—684no—
223C22×C4C22⋊#59511yescharacteristic
224C22×C4C22×#59511yescharacteristic
225M16—1364no—
226C2×C8—684no—
227C4⋊C4—682no—
228C4⋊C4—681no—
229C4⋊C4—681no—
230C22⋊C4—688no—
231C22⋊C4—688no—
232C42—42no—
233C42—42no—
234C23—22no—
235C23—22no—
236C23—21no—
237C23—21no—
238C23—344no—
239C23—684no—
240C23—684no—
241C23—684no—
242C23—6816no—
243C23—684no—
244C23—682no—
245C23—682no—
246C23—1368no—
247C23—1362no—
248C23—1362no—
249C23—1362no—
250C23—1362no—
251C23#1058753911yescharacteristic
252C23#1058753911yescharacteristic
253C23C2×C22⋊#59511yescharacteristic
254D4—684no—
255D4—684no—
256D4—688no—
257C2×C4—24no—
258C2×C4—24no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—24no—
264C2×C4—48no—
265C2×C4—42no—
266C2×C4—42no—
267C2×C4—342no—
268C2×C4—342no—
269C2×C4—684no—
270C2×C4—682no—
271C2×C4—682no—
272C2×C4—1362no—
273C2×C4#1058755312yes—
274C2×C4D17⋊M1612yes—
275C8—1364no—
276C22—24no—
277C22—24no—
278C22—21no—
279C22—21no—
280C22—21no—
281C22—21no—
282C22—21no—
283C22—21no—
284C22—688no—
285C22—684no—
286C22—1364no—
287C22—1368no—
288C22—1368no—
289C22—1362no—
290C22—1362no—
291C22#1176371412yes—
292C22#1176371812yes—
293C22#1176378111yescharacteristic
294C22C2×#1058753911yescharacteristic
295C22C2×#1058755311yescharacteristic
296C4—22no—
297C4—22no—
298C4—44no—
299C4—682no—
300C4—682no—
301C2—21no—
302C2—21no—
303C2—22no—
304C2—22no—
305C2—1364no—
306C2#1454403111yescharacteristic
307C2C2×#1176371411yescharacteristic
308C2C2×#1176371811yescharacteristic
subgroupG/H
centerC22C2×#10587539
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC22×C42×C17C4
socleC22×C17C2×#99
prime radicalC23×D68C4
cosocleC2×C4⋊Dic17C23
hypercenterC22×C42#595
hypocenterC17#11505
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C24 ◁ C23×C4 ◁ C22×C42

Complements

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

NH ≅ G/Ntype
1. #14544032C2semidirect
2. #14543713C2semidirect
6. #11763654C22semidirect
69. C2×D68M16semidirect
192. C17#11505semidirect

Maximal subgroups

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

subgroupindex
#145440322
#145437132
C2×#117627112
#1150517