Finite Group Databasebeta

← #17951254

Subgroups — #17951254

Order 4352.

954 conjugacy classes of subgroups; only the 148 normal subgroups are shown.

normal subgroups only

This group has 954 conjugacy classes of subgroups — too many to draw. Only its 148 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#14545228C212yesmaximal
2#14543664C214yesmaximal, complemented
3D17×#407C211yesmaximal, characteristic
4C2×#10587677—22no—
5#11763752C414yescomplemented
6#11763751—22no—
7#11763751C414yescomplemented
8#11763750—22no—
9C4×C22⋊#595—22no—
10C4×C22⋊#595C2214yes—
11C23×C4×D17C2211yescharacteristic
12C2×M16×D17C412yescomplemented
13#11762773C411yescharacteristic, complemented
14#11762772C2212yes—
15#11762771—22no—
16C22⋊C8×D17—22no—
17C17×#407C411yescharacteristic, complemented
18C24×D17D411yescharacteristic
19C23×C4×C17C2×C411yescharacteristic
20C23×Dic17Q811yescharacteristic
21C22×C4×D17—44no—
22C22×C4×D17C2×C411yescharacteristic
23C22×C4×D17C2×C412yes—
24C22×C4×D17C2×C412yes—
25C22×C4×D17D412yes—
26C22×C4×D17D411yescharacteristic
27C22×C4×D17D412yes—
28C22×C4×D17Q811yescharacteristic
29C22×C4×D17C2311yescharacteristic
30C2×C22⋊#595—24no—
31C2×C22⋊#595—24no—
32C2×C22⋊#595—24no—
33#10587677—48no—
34C2×C4⋊#595—24no—
35C2×C4×#595—24no—
36C2×M16×C17C2×C412yes—
37C2×#63223C2×C412yes—
38M16×D17—44no—
39C2×#63218—22no—
40C2×C8×D17—22no—
41(C2×#595)⋊C4—24no—
42(C2×#595)⋊C4C2×C418yes—
43C17×C22⋊C8—22no—
44C22⋊#3622—22no—
45#10587491—24no—
46C24×C17C4⋊C411yescharacteristic
47C23×D17—42no—
48C23×D17—44no—
49C23×D17C22⋊C412yes—
50C23×D17C22⋊C412yes—
51C23×D17C4⋊C411yescharacteristic
52C23×D17C2×D411yescharacteristic
53C22×#595—28no—
54C22×C4×C17—42no—
55C22×C4×C17C4212yes—
56C22×C4×C17C22⋊C412yes—
57C22×C4×C17C4⋊C411yescharacteristic
58C22×C4×C17C22×C411yescharacteristic
59C22×Dic17—42no—
60C22×Dic17C4⋊C411yescharacteristic
61C22×Dic17C4⋊C412yes—
62C22×Dic17C4⋊C412yes—
63C22×Dic17C2×Q811yescharacteristic
64C2×C4×D17—28no—
65C2×C4×D17—24no—
66C2×C4×D17—44no—
67C2×C4×D17—42no—
68C2×C4×D17—44no—
69C2×C4×D17—42no—
70C2×C4×D17—44no—
71C2×C4×D17—42no—
72C2×C4×D17C4211yescharacteristic
73C2×C4×D17C4211yescharacteristic
74C2×C4×D17C22⋊C412yes—
75C2×C4×D17C22⋊C411yescharacteristic
76C2×C4×D17C22⋊C412yes—
77C2×C4×D17C22⋊C411yescharacteristic
78C2×C4×D17C4⋊C412yes—
79C2×C4×D17C4⋊C412yes—
80C2×C4×D17C22×C412yes—
81C2×C4×D17C2×D412yes—
82C22⋊#595—48no—
83C22⋊#595—48no—
84C22⋊#595—48no—
85C4⋊#595—48no—
86C4×#595—48no—
87M16×C17—42no—
88C2×C8×C17—22no—
89#63223—42no—
90C2×#3622—22no—
91#63218—44no—
92C8×D17—44no—
93#8049—171nomaximal, Sylow
94C23×C17—41no—
95C23×C17—42no—
96C23×C17#9512yes—
97C23×C17C2×C4⋊C411yescharacteristic
98C22×D17—24no—
99C22×D17—22no—
100C22×D17—24no—
101C22×D17—24no—
102C22×D17—24no—
103C22×D17—42no—
104C22×D17—41no—
105C22×D17—42no—
106C22×D17—42no—
107C22×D17—42no—
108C22×D17—416no—
109C22×D17#9511yescharacteristic
110C22×D17#9511yescharacteristic
111C22×D17C2×C22⋊C412yes—
112C2×#595—48no—
113C2×#595—48no—
114C2×#595—48no—
115C2×C4×C17—22no—
116C2×C4×C17—24no—
117C2×C4×C17—42no—
118C2×C4×C17—41no—
119C2×C4×C17#9512yes—
120C2×C4×C17C2×C4211yescharacteristic
121C2×C4×C17C2×C22⋊C411yescharacteristic
122C2×Dic17—22no—
123C2×Dic17—24no—
124C2×Dic17—42no—
125C2×Dic17—41no—
126C2×Dic17#9511yescharacteristic
127C2×Dic17#9511yescharacteristic
128C2×Dic17C2×C4⋊C412yes—
129C4×D17—22no—
130C4×D17—24no—
131C4×D17—24no—
132C4×D17—22no—
133C4×D17—24no—
134C4×D17—22no—
135C4×D17—42no—
136C4×D17—42no—
137C4×D17—42no—
138C4×D17#9914yes—
139C8×C17—42no—
140#3622—42no—
141C2×#407—171no—
142#2280—172no—
143#1297—174no—
144C22×C17—22no—
145C22×C17—22no—
146C22×C17—22no—
147C22×C17—22no—
148C22×C17—21no—
149C22×C17—44no—
150C22×C17C2×#9511yescharacteristic
151C2×D17—22no—
152C2×D17—22no—
153C2×D17—22no—
154C2×D17—22no—
155C2×D17—21no—
156C2×D17—44no—
157C2×D17—48no—
158C2×D17—48no—
159C2×D17—44no—
160C2×D17#34212yes—
161C2×D17#42114yes—
162#595—88no—
163C4×C17—22no—
164C4×C17—21no—
165C4×C17C2×#9912yes—
166Dic17—21no—
167Dic17—22no—
168Dic17#34212yes—
169C24×C4—171no—
170C22×M16—172no—
171C2×#117—342no—
172#407—171no—
173#407—172no—
174#407—342no—
175#407#59511yescharacteristic, complemented
176C2×C22⋊C8—342no—
177#381—174no—
178#380—174no—
179#380—342no—
180#379—342no—
181C4×C22⋊C4—174no—
182C4×C22⋊C4—342no—
183C2×C17—42no—
184C2×C17—41no—
185C2×C17#173312yes—
186C2×C17C2×#34211yescharacteristic
187D17—24no—
188D17—22no—
189D17—41no—
190C25—171no—
191C23×C4—171no—
192C23×C4—172no—
193C23×C4—171no—
194C23×C4—172no—
195C23×C4—172no—
196C23×C4—171no—
197C23×C4—171no—
198C23×C4—172no—
199C23×C4—171no—
200C23×C4—684no—
201C23×C4C2×#59511yescharacteristic
202C2×M16—172no—
203C2×M16—342no—
204C2×M16—684no—
205C2×M16C2×#59512yes—
206C22×C8—342no—
207#117—688no—
208C2×C4⋊C4—344no—
209C2×C22⋊C4—344no—
210C2×C22⋊C4—344no—
211C2×C22⋊C4—344no—
212C2×C42—344no—
213C22⋊C8—22no—
214C22⋊C8—344no—
215C22⋊C8—342no—
216#95—178no—
217#95—344no—
218C17#804911yescharacteristic, complemented, Sylow
219C24—171no—
220C24—172no—
221C24—171no—
222C24—172no—
223C24—682no—
224C24—684no—
225C24C4⋊#59511yescharacteristic
226C22×C4—42no—
227C22×C4—171no—
228C22×C4—171no—
229C22×C4—172no—
230C22×C4—171no—
231C22×C4—172no—
232C22×C4—171no—
233C22×C4—171no—
234C22×C4—171no—
235C22×C4—172no—
236C22×C4—172no—
237C22×C4—172no—
238C22×C4—172no—
239C22×C4—172no—
240C22×C4—172no—
241C22×C4—348no—
242C22×C4—344no—
243C22×C4—348no—
244C22×C4—682no—
245C22×C4—684no—
246C22×C4—684no—
247C22×C4—682no—
248C22×C4—684no—
249C22×C4—682no—
250C22×C4—682no—
251C22×C4C4×#59512yes—
252C22×C4C4⋊#59511yescharacteristic
253C22×C4C22⋊#59512yes—
254C22×C4C22×#59511yescharacteristic
255M16—42no—
256M16—684no—
257M16—682no—
258C2×C8—22no—
259C2×C8—342no—
260C2×C8—684no—
261C4⋊C4—688no—
262C22⋊C4—688no—
263C22⋊C4—688no—
264C22⋊C4—688no—
265C42—688no—
266C23—41no—
267C23—42no—
268C23—172no—
269C23—171no—
270C23—171no—
271C23—344no—
272C23—344no—
273C23—344no—
274C23—342no—
275C23—344no—
276C23—681no—
277C23—682no—
278C23—682no—
279C23—682no—
280C23—682no—
281C23—6816no—
282C23(C2×#595)⋊C412yes—
283C23C2×C4⋊#59511yescharacteristic
284C2×C4—22no—
285C2×C4—24no—
286C2×C4—42no—
287C2×C4—41no—
288C2×C4—171no—
289C2×C4—174no—
290C2×C4—171no—
291C2×C4—172no—
292C2×C4—344no—
293C2×C4—342no—
294C2×C4—342no—
295C2×C4—344no—
296C2×C4—342no—
297C2×C4—344no—
298C2×C4—344no—
299C2×C4—342no—
300C2×C4—682no—
301C2×C4—682no—
302C2×C4—682no—
303C2×C4—681no—
304C2×C4—682no—
305C2×C4—688no—
306C2×C4—688no—
307C2×C4—688no—
308C2×C4(C2×#595)⋊C412yes—
309C2×C4C2×C4×#59511yescharacteristic
310C2×C4C2×C22⋊#59511yescharacteristic
311C8—42no—
312C8—682no—
313C22—22no—
314C22—22no—
315C22—22no—
316C22—21no—
317C22—22no—
318C22—44no—
319C22—174no—
320C22—172no—
321C22—342no—
322C22—342no—
323C22—342no—
324C22—342no—
325C22—341no—
326C22—684no—
327C22—688no—
328C22—688no—
329C22—684no—
330C22C2×(C2×#595)⋊C411yescharacteristic
331C4—21no—
332C4—22no—
333C4—172no—
334C4—341no—
335C4—342no—
336C4—1368no—
337C4D17⋊#9912yes—
338C2—41no—
339C2—42no—
340C2—344no—
341C2—342no—
342C2—681no—
343C2#1454446612yes—
344C2#1454448111yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#595
commutatorC2×C4×C17C2×C42
FrattiniC22×C4C22×#595
FittingC17×#407C4
socleC22×C17C2×#95
prime radicalC24×D17D4
cosocleC22×C4×D17C23
hypercenter#407#595
hypocenterC17#8049
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
2. #14543664C2semidirect
5. #11763752C4semidirect
7. #11763751C4semidirect
12. C2×M16×D17C4semidirect
13. #11762773C4semidirect
17. C17×#407C4semidirect
175. #407#595semidirect
218. C17#8049semidirect

Maximal subgroups

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

subgroupindex
#145452282
#145436642
D17×#4072
#804917