Finite Group Databasebeta

← #16944950

Subgroups — #16944950

Order 4352.

462 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 91 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
1C4×#10587505C211yesmaximal, characteristic
2#14527125C211yesmaximal, characteristic
3#14526808C212yesmaximal, complemented
4#14526805C212yesmaximal, complemented
5C17×#2564C211yesmaximal, characteristic
6#11762866—21no—
7C2×#10587505—21no—
8C4×C22⋊Dic17—21no—
9#11762576C2212yes—
10#11762533—21no—
11#11762533C2212yes—
12C2×C17×C22⋊Q8C411yescharacteristic, complemented
13C2×C4×D4×C17C2211yescharacteristic
14C17×#400C411yescharacteristic, complemented
15C17×#399C2211yescharacteristic
16C17×#395C411yescharacteristic, complemented
17C17×#393C2211yescharacteristic
18C17×#387—21no—
19C17×#386—21no—
20C17×#385—21no—
21C17×#380—21no—
22C2×C17×#95C411yescharacteristic, complemented
23C22×Q8×C17C2×C411yescharacteristic
24C22×D4×C17D411yescharacteristic
25C23×C4×C17—21no—
26C23×C4×C17C2×C411yescharacteristic
27C23×C4×C17D411yescharacteristic
28C17×C22⋊Q8—41no—
29C17×C22⋊Q8—41no—
30C4×D4×C17—41no—
31C4×D4×C17—41no—
32C2×C4⋊C4×C17—21no—
33C2×C4⋊C4×C17—21no—
34C2×C4⋊C4×C17—21no—
35C2×C4⋊C4×C17C2×C411yescharacteristic
36C2×C4⋊C4×C17C2×C411yescharacteristic
37C2×C22⋊C4×C17—21no—
38C2×C22⋊C4×C17—21no—
39C2×C22⋊C4×C17—21no—
40C2×C22⋊C4×C17D411yescharacteristic
41C2×C22⋊C4×C17C2311yescharacteristic
42C2×C42×C17D411yescharacteristic
43C2×C22⋊Dic17—22no—
44C2×C4×Dic17—41no—
45C17×#95—21no—
46C17×#95—21no—
47C17×#95—21no—
48C17×#95—21no—
49C17×#95—21no—
50C17×#95C2×C411yescharacteristic
51C17×#95C2×C411yescharacteristic
52#10587505—24no—
53#10587502—41no—
54C22⋊#3622—22no—
55C4⋊#3622—41no—
56#10587474—41no—
57C24×C17C22⋊C411yescharacteristic
58C24×C17C2×D411yescharacteristic
59C2×Q8×C17—41no—
60C2×Q8×C17—81no—
61C2×D4×C17—22no—
62C2×D4×C17—22no—
63C2×D4×C17—41no—
64C22×C4×C17—21no—
65C22×C4×C17—21no—
66C22×C4×C17—21no—
67C22×C4×C17—21no—
68C22×C4×C17—21no—
69C22×C4×C17—21no—
70C22×C4×C17—21no—
71C22×C4×C17—21no—
72C22×C4×C17—42no—
73C22×C4×C17—42no—
74C22×C4×C17—81no—
75C22×C4×C17—81no—
76C22×C4×C17—81no—
77C22×C4×C17C22⋊C411yescharacteristic
78C22×C4×C17C22⋊C411yescharacteristic
79C22×C4×C17C22⋊C411yescharacteristic
80C22×C4×C17C22×C411yescharacteristic
81C22×C4×C17C2×D411yescharacteristic
82C22×Dic17—42no—
83C4⋊C4×C17—41no—
84C4⋊C4×C17—41no—
85C4⋊C4×C17—42no—
86C4⋊C4×C17—41no—
87C4⋊C4×C17—41no—
88C4⋊C4×C17—81no—
89C22⋊C4×C17—41no—
90C22⋊C4×C17—41no—
91C22⋊C4×C17—42no—
92C22⋊C4×C17—42no—
93C22⋊C4×C17—81no—
94C42×C17—21no—
95C42×C17—21no—
96C22⋊Dic17—24no—
97C22⋊Dic17—42no—
98C4×Dic17—82no—
99C2×#3622—42no—
100#11789—171nomaximal, Sylow
101C23×C17—21no—
102C23×C17—21no—
103C23×C17—21no—
104C23×C17—21no—
105C23×C17—41no—
106C23×C17—41no—
107C23×C17—41no—
108C23×C17—41no—
109C23×C17#10412yes—
110C23×C17C2×C22⋊C411yescharacteristic
111C23×C17#13712yes—
112Q8×C17—82no—
113D4×C17—44no—
114C2×C4×C17—22no—
115C2×C4×C17—21no—
116C2×C4×C17—21no—
117C2×C4×C17—21no—
118C2×C4×C17—21no—
119C2×C4×C17—21no—
120C2×C4×C17—21no—
121C2×C4×C17—41no—
122C2×C4×C17—42no—
123C2×C4×C17—41no—
124C2×C4×C17—41no—
125C2×C4×C17—41no—
126C2×C4×C17—41no—
127C2×C4×C17—41no—
128C2×C4×C17—41no—
129C2×C4×C17—41no—
130C2×C4×C17—41no—
131C2×C4×C17—41no—
132C2×C4×C17—41no—
133C2×C4×C17—41no—
134C2×C4×C17—41no—
135C2×C4×C17—41no—
136C2×C4×C17—41no—
137C2×C4×C17—81no—
138C2×C4×C17—81no—
139C2×C4×C17—81no—
140C2×C4×C17—84no—
141C2×C4×C17#9911yescharacteristic
142C2×C4×C17#9911yescharacteristic
143C2×Dic17—44no—
144C2×Dic17—82no—
145C2×Dic17—82no—
146#3622—82no—
147#2564D1711yescharacteristic
148C4×#99—171no—
149#1466—171no—
150#1352—172no—
151#1351—172no—
152C22×C17—21no—
153C22×C17—21no—
154C22×C17—22no—
155C22×C17—22no—
156C22×C17—42no—
157C22×C17—42no—
158C22×C17—42no—
159C22×C17—41no—
160C22×C17—41no—
161C22×C17—41no—
162C22×C17—41no—
163C22×C17—81no—
164C22×C17C2×#9911yescharacteristic
165C22×C17#41911yescharacteristic
166C22×C17C2×#10411yescharacteristic
167C4×C17—21no—
168C4×C17—21no—
169C4×C17—42no—
170C4×C17—41no—
171C4×C17—41no—
172C4×C17—41no—
173C4×C17—41no—
174C4×C17—81no—
175C4×C17—81no—
176C4×C17—81no—
177Dic17—84no—
178C2×C22⋊Q8Dic1711yescharacteristic, complemented
179C2×C4×D4C2×D1711yescharacteristic
180#432—341no—
181C2×#99—341no—
182#400Dic1711yescharacteristic, complemented
183#399C2×D1711yescharacteristic
184#395Dic1711yescharacteristic, complemented
185#393C2×D1711yescharacteristic
186#387—21no—
187#386—21no—
188#385—21no—
189#380—21no—
190C4×C22⋊C4—341no—
191C2×#95Dic1711yescharacteristic, complemented
192#342—172no—
193#323—172no—
194#323—341no—
195C2×C17—21no—
196C2×C17—21no—
197C2×C17—42no—
198C2×C17—42no—
199C2×C17#150811yescharacteristic
200C2×C17#212111yescharacteristic
201C2×C17#212611yescharacteristic
202C22×Q8C2×Dic1711yescharacteristic
203C22×D4C22⋊D1711yescharacteristic
204C23×C4—21no—
205C23×C4C2×Dic1711yescharacteristic
206C23×C4C22⋊D1711yescharacteristic
207C22⋊Q8—41no—
208C22⋊Q8—41no—
209C4×D4—41no—
210C4×D4—41no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4C2×Dic1711yescharacteristic
215C2×C4⋊C4C2×Dic1711yescharacteristic
216C2×C22⋊C4—21no—
217C2×C22⋊C4—21no—
218C2×C22⋊C4—21no—
219C2×C22⋊C4—342no—
220C2×C22⋊C4C22⋊D1711yescharacteristic
221C2×C22⋊C4C22×D1711yescharacteristic
222C2×C42—681no—
223C2×C42C22⋊D1711yescharacteristic
224C4⋊C8—681no—
225#99—344no—
226C22⋊C8—342no—
227#97—681no—
228#95—21no—
229#95—21no—
230#95—21no—
231#95—21no—
232#95—21no—
233#95—681no—
234#95C2×Dic1711yescharacteristic
235#95C2×Dic1711yescharacteristic
236C17#1178911yescharacteristic, complemented, Sylow
237C24C22⋊Dic1711yescharacteristic
238C24C2×C22⋊D1711yescharacteristic
239C2×Q8—41no—
240C2×Q8—81no—
241C2×D4—22no—
242C2×D4—22no—
243C2×D4—41no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—42no—
253C22×C4—42no—
254C22×C4—81no—
255C22×C4—81no—
256C22×C4—81no—
257C22×C4—682no—
258C22×C4C22⋊Dic1711yescharacteristic
259C22×C4C22⋊Dic1711yescharacteristic
260C22×C4C22⋊Dic1711yescharacteristic
261C22×C4C22×Dic1711yescharacteristic
262C22×C4C2×C22⋊D1711yescharacteristic
263C2×C8—682no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—42no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—81no—
270C22⋊C4—41no—
271C22⋊C4—41no—
272C22⋊C4—42no—
273C22⋊C4—42no—
274C22⋊C4—81no—
275C22⋊C4—344no—
276C22⋊C4—682no—
277C42—21no—
278C42—21no—
279C42—1362no—
280C23—21no—
281C23—21no—
282C23—21no—
283C23—21no—
284C23—41no—
285C23—41no—
286C23—41no—
287C23—41no—
288C23#1058750812yes—
289C23#1058762812yes—
290C23C2×C22⋊Dic1711yescharacteristic
291Q8—82no—
292D4—44no—
293C2×C4—22no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—41no—
301C2×C4—42no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—81no—
317C2×C4—81no—
318C2×C4—81no—
319C2×C4—84no—
320C2×C4—684no—
321C2×C4—1362no—
322C2×C4—1362no—
323C2×C4#1058750511yescharacteristic
324C2×C4#1058750511yescharacteristic
325C8—1362no—
326C22—21no—
327C22—21no—
328C22—22no—
329C22—22no—
330C22—42no—
331C22—42no—
332C22—42no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—81no—
338C22C2×#1058750511yescharacteristic
339C22#1176281811yescharacteristic
340C22C2×#1058750811yescharacteristic
341C4—21no—
342C4—21no—
343C4—42no—
344C4—41no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—81no—
349C4—81no—
350C4—81no—
351C4—1364no—
352C2—21no—
353C2—21no—
354C2—42no—
355C2—42no—
356C2#1452730411yescharacteristic
357C2#1453043011yescharacteristic
358C2#1453044911yescharacteristic
subgroupG/H
centerC22C2×#10587505
commutatorC22×C4×C17C22×C4
FrattiniC2×C22⋊C4C22×D17
FittingC17×#2564C2
socleC22×C17C2×#99
prime radicalC22×D4×C17D4
cosocleC2×C22⋊C4×C17C23
hypercenter#2564D17
hypocenterC17#11789
LCSG ▷ C22×C4×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2564

Complements

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

NH ≅ G/Ntype
3. #14526808C2semidirect
4. #14526805C2semidirect
12. C2×C17×C22⋊Q8C4semidirect
14. C17×#400C4semidirect
16. C17×#395C4semidirect
22. C2×C17×#95C4semidirect
178. C2×C22⋊Q8Dic17semidirect
182. #400Dic17semidirect
184. #395Dic17semidirect
191. C2×#95Dic17semidirect
236. C17#11789semidirect

Maximal subgroups

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

subgroupindex
C4×#105875052
#145271252
#145268082
#145268052
C17×#25642
#1178917