Finite Group Databasebeta

← #17959788

Subgroups — #17959788

Order 4352.

508 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 508 conjugacy classes of subgroups — too many to draw. Only its 80 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#14544645C211yesmaximal, characteristic
2#14544021C211yesmaximal, characteristic
3#14543781C214yesmaximal, complemented
4#14533738C211yesmaximal, characteristic
5C2×#10587539—21no—
6#11763777—21no—
7#11763751—21no—
8#11763687C2212yes—
9#11763654—21no—
10#11763653C2212yes—
11C2×#10587632—21no—
12C2×#10587632—21no—
13C2×C4×D68C2211yescharacteristic
14#11762744C412yescomplemented
15#11762744C2212yes—
16#11762710—21no—
17#11762678—21no—
18C4×C4⋊Dic17C411yescharacteristic, complemented
19C2×C17×C4⋊Q8C411yescharacteristic, complemented
20C22×Q8×C17—21no—
21C22×D68D411yescharacteristic
22C22×C4×D17D411yescharacteristic
23C22×C4×D17D411yescharacteristic
24C2×C22⋊#595—22no—
25C2×C4⋊#595—41no—
26C2×#63242—41no—
27C17×C4⋊Q8—41no—
28C17×C4⋊Q8—41no—
29C2×C4⋊C4×C17—21no—
30C2×C4⋊C4×C17C2×C412yes—
31C2×C42×C17C2×C411yescharacteristic
32#10587632—44no—
33#10587632—44no—
34C2×#63227—22no—
35C2×#63227—22no—
36C2×#63227C2×C411yescharacteristic
37C2×#63227C2311yescharacteristic
38C2×C4⋊Dic17—21no—
39C2×C4⋊Dic17D411yescharacteristic
40C2×#63225—22no—
41C2×#63225—22no—
42C2×C4×Dic17—21no—
43C4×D68—41no—
44C4×D68—41no—
45C22⋊#3624—22no—
46(C2×#595)⋊C4—41no—
47#10587543—41no—
48#10587539—42no—
49#10587502C2×C412yes—
50C23×D17C22⋊C411yescharacteristic
51C23×D17C2×D411yescharacteristic
52C22×#595—42no—
53C2×Q8×C17—42no—
54C2×Q8×C17—42no—
55C2×Q8×C17—41no—
56C2×Q8×C17—41no—
57C22×C4×C17—22no—
58C22×C4×C17C22⋊C411yescharacteristic
59C22×C4×C17C22⋊C411yescharacteristic
60C22×C4×C17C22×C411yescharacteristic
61C22×Dic17—22no—
62C22×Dic17C22⋊C411yescharacteristic
63C22×Dic17C2×D411yescharacteristic
64C2×D68—41no—
65C2×D68—41no—
66C2×D68SD1612yes—
67C2×D68Q1612yes—
68C2×C4×D17—21no—
69C2×C4×D17—21no—
70C2×C4×D17—21no—
71C2×C4×D17—21no—
72C2×C4×D17—42no—
73C2×C4×D17—42no—
74C22⋊#595—42no—
75C22⋊#595—42no—
76C2×#3624—42no—
77C4⋊#595—82no—
78#63242—82no—
79C4⋊C4×C17—42no—
80C4⋊C4×C17—42no—
81C42×C17—21no—
82C42×C17—21no—
83#63227—41no—
84#63227—41no—
85#63227—44no—
86#63227—44no—
87C4⋊Dic17—24no—
88C4⋊Dic17—41no—
89#63225—44no—
90#63225—44no—
91C4×Dic17—42no—
92#11901—171nomaximal, Sylow
93C23×C17C2×C22⋊C411yescharacteristic
94C22×D17—21no—
95C22×D17—21no—
96C22×D17—21no—
97C22×D17—21no—
98C22×D17—41no—
99C22×D17—41no—
100C22×D17—41no—
101C22×D17—41no—
102C22×D17#10312yes—
103C22×D17C2×SD1611yescharacteristic
104C22×D17C2×Q1611yescharacteristic
105C2×#595—82no—
106C2×#595—82no—
107C2×#595—82no—
108Q8×C17—82no—
109Q8×C17—82no—
110C2×C4×C17—21no—
111C2×C4×C17—21no—
112C2×C4×C17—22no—
113C2×C4×C17—21no—
114C2×C4×C17—41no—
115C2×C4×C17—42no—
116C2×C4×C17—42no—
117C2×C4×C17—42no—
118C2×C4×C17#9911yescharacteristic
119C2×C4×C17#9911yescharacteristic
120C2×C4×C17#10312yes—
121C2×Dic17—24no—
122C2×Dic17—21no—
123C2×Dic17—21no—
124C2×Dic17—42no—
125C2×Dic17—42no—
126C2×Dic17—41no—
127C2×Dic17—41no—
128D68—42no—
129D68—42no—
130C4×D17—42no—
131C4×D17—42no—
132C4×D17—81no—
133C4×D17—81no—
134#3624—82no—
135#2542—171no—
136#1799—171no—
137#1459—171no—
138#1352—174no—
139C22×C17—21no—
140C22×C17—21no—
141C22×C17C2×#9911yescharacteristic
142C22×C17C2×#10311yescharacteristic
143C22×C17#42111yescharacteristic
144C2×D17—21no—
145C2×D17—22no—
146C2×D17—21no—
147C2×D17—41no—
148C2×D17—41no—
149C2×D17—41no—
150C2×D17—41no—
151C2×D17—42no—
152C2×D17—41no—
153C2×D17—41no—
154C2×D17—81no—
155C2×D17—81no—
156#595—162no—
157C4×C17—21no—
158C4×C17—22no—
159C4×C17—41no—
160C4×C17—82no—
161C4×C17#35312yes—
162Dic17—44no—
163Dic17—41no—
164Dic17—41no—
165C2×C4⋊Q8#59511yescharacteristic, complemented
166C2×C22⋊Q8—341no—
167C2×C22⋊Q8—341no—
168C2×C4×D4—171no—
169C2×#99—341no—
170C2×C22⋊C8—341no—
171#399—172no—
172#399—172no—
173#390—341no—
174#384—341no—
175#380—341no—
176C4×C4⋊C4—171no—
177#342—172no—
178#324—341no—
179#323—172no—
180C2×C17—21no—
181C2×C17—21no—
182C2×C17#152011yescharacteristic
183C2×C17#212311yescharacteristic
184C2×C17C2×#35311yescharacteristic
185D17—41no—
186D17—42no—
187D17—41no—
188C22×Q8—21no—
189C22×D4—171no—
190C23×C4—171no—
191C23×C4—171no—
192C22×C8—681no—
193C4⋊Q8—41no—
194C4⋊Q8—41no—
195C22⋊Q8—684no—
196C22⋊Q8—684no—
197C4×D4—681no—
198C4×D4—681no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—171no—
201C2×C4⋊C4—341no—
202C2×C4⋊C4—342no—
203C2×C4⋊C4—342no—
204C2×C4⋊C4—681no—
205C2×C4⋊C4C2×#59512yes—
206C2×C22⋊C4—171no—
207C2×C22⋊C4—171no—
208C2×C22⋊C4—342no—
209C2×C22⋊C4—342no—
210C2×C22⋊C4—342no—
211C2×C42—341no—
212C2×C42C2×#59511yescharacteristic
213#99—682no—
214C22⋊C8—342no—
215C22⋊C8—681no—
216#95—172no—
217#95—681no—
218C17#1190111yescharacteristic, complemented, Sylow
219C24—171no—
220C24—171no—
221C2×Q8—42no—
222C2×Q8—42no—
223C2×Q8—41no—
224C2×Q8—41no—
225C2×D4—172no—
226C2×D4—172no—
227C2×D4—681no—
228C2×D4—681no—
229C22×C4—22no—
230C22×C4—171no—
231C22×C4—171no—
232C22×C4—342no—
233C22×C4—341no—
234C22×C4—341no—
235C22×C4—341no—
236C22×C4—341no—
237C22×C4—682no—
238C22×C4—682no—
239C22×C4—682no—
240C22×C4C22⋊#59511yescharacteristic
241C22×C4C22⋊#59511yescharacteristic
242C22×C4C22×#59511yescharacteristic
243C2×C8—682no—
244C2×C8—1362no—
245C4⋊C4—42no—
246C4⋊C4—42no—
247C4⋊C4—344no—
248C4⋊C4—681no—
249C4⋊C4—684no—
250C4⋊C4—684no—
251C4⋊C4—1362no—
252C22⋊C4—681no—
253C22⋊C4—681no—
254C22⋊C4—684no—
255C22⋊C4—684no—
256C22⋊C4—682no—
257C22⋊C4—682no—
258C42—21no—
259C42—21no—
260C42—682no—
261C23—171no—
262C23—172no—
263C23—171no—
264C23—341no—
265C23—341no—
266C23—341no—
267C23—341no—
268C23—681no—
269C23—681no—
270C23—681no—
271C23—681no—
272C23C2×C22⋊#59511yescharacteristic
273Q8—82no—
274Q8—82no—
275D4—682no—
276D4—682no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—22no—
280C2×C4—21no—
281C2×C4—41no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—344no—
286C2×C4—341no—
287C2×C4—341no—
288C2×C4—682no—
289C2×C4—682no—
290C2×C4—682no—
291C2×C4—682no—
292C2×C4—681no—
293C2×C4—681no—
294C2×C4—1361no—
295C2×C4—1361no—
296C2×C4—1362no—
297C2×C4—1362no—
298C2×C4—1362no—
299C2×C4#1058754912yes—
300C2×C4#1058755111yescharacteristic
301C2×C4#1058755111yescharacteristic
302C8—1362no—
303C22—21no—
304C22—21no—
305C22—341no—
306C22—342no—
307C22—341no—
308C22—681no—
309C22—682no—
310C22—681no—
311C22—681no—
312C22—681no—
313C22—681no—
314C22—681no—
315C22—1361no—
316C22—1361no—
317C22C2×#1058755111yescharacteristic
318C22C2×#1058754911yescharacteristic
319C22#1176380811yescharacteristic
320C4—22no—
321C4—21no—
322C4—41no—
323C4—82no—
324C4—2722no—
325C4—684no—
326C4—681no—
327C4—681no—
328C4#1176371312yes—
329C2—21no—
330C2—21no—
331C2—681no—
332C2—681no—
333C2—682no—
334C2#1454422411yescharacteristic
335C2#1454504611yescharacteristic
336C2C2×#1176371311yescharacteristic
subgroupG/H
centerC22C2×#10587551
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC2×C17×C4⋊Q8C4
socleC22×C17C2×#99
prime radicalC22×D68D4
cosocleC2×#63227C23
hypercenterC2×C4⋊Q8#595
hypocenterC17#11901
LCSG ▷ C22×C4×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
3. #14543781C2semidirect
14. #11762744C4semidirect
18. C4×C4⋊Dic17C4semidirect
19. C2×C17×C4⋊Q8C4semidirect
165. C2×C4⋊Q8#595semidirect
218. C17#11901semidirect

Maximal subgroups

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

subgroupindex
#145446452
#145440212
#145437812
#145337382
#1190117