Finite Group Databasebeta

← C22×#11763772 #17979408

Subgroups — C22×#11763772 #17979408

Order 4352.

3518 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D17⋊M16C211yesmaximal, characteristic
2C22×#10587677C211yesmaximal, characteristic
3C2×#11763772C2124yesmaximal, direct product factor
4C22×#10587532C212yesmaximal, complemented
5C22×C8×#595C212yesmaximal, complemented
6C23×C8×D17C211yesmaximal, characteristic
7C22×#63243C412yescomplemented
8C2×D17⋊M16C4112yescomplemented
9C2×D17⋊M16C22112yes—
10C22×#63247C412yescomplemented
11C22×#63242C2212yes—
12C2×#10587677C4112yes—
13C2×#10587677C22112yes—
14C22×C4⋊#595C412yes—
15C22×C22⋊#595C412yes—
16C22×C4×#595C2212yes—
17#11763772C22164yesdirect product factor
18C2×#10587532C22124yescomplemented
19C2×C8×#595C22124yescomplemented
20C23×C4×D17C2211yescharacteristic
21C23×#3622C411yescharacteristic, complemented
22C22×C8×D17C411yescharacteristic, complemented
23C22×C8×D17C411yescharacteristic, complemented
24C22×C8×D17C4112yescomplemented
25C22×C8×D17C2211yescharacteristic
26C22×C8×D17C2211yescharacteristic
27C22×C8×D17C22112yes—
28C23×C8×C17C411yescharacteristic, complemented
29C24×D17C2×C411yescharacteristic
30C23×#595C2×C414yes—
31C23×C4×C17C2×C411yescharacteristic
32C23×Dic17C2×C411yescharacteristic
33C22×C4×D17C2×C411yescharacteristic
34C22×C4×D17C2×C416yes—
35C22×C4×D17C2×C416yes—
36C22×C4×D17C2×C411yescharacteristic
37C22×C4×D17C2×C416yes—
38C22×C4×D17C2×C411yescharacteristic
39C22×C4×D17C2311yescharacteristic
40C22×C4×D17C2316yes—
41C2×C22⋊#595C2×C4124yes—
42C2×#63247C2×C4124yescomplemented
43C22×#3624C2×C414yes—
44#10587677C2×C4148yes—
45#10587677C23116yes—
46C2×C4⋊#595C2×C4124yes—
47C2×C4×#595C2×C4112yes—
48C2×C4×#595C23112yes—
49D17⋊M16C2×C4148yescomplemented
50D17⋊M16C23116yes—
51C2×#63243C2×C4124yescomplemented
52C2×#63242C2×C4112yes—
53C2×#63242C23112yes—
54C22×C8×C17C2×C411yescharacteristic
55C22×C8×C17C2×C411yescharacteristic
56C22×C8×C17C2×C4112yescomplemented
57C22×#3622C2×C411yescharacteristic
58C22×#3622C2×C411yescharacteristic
59C22×#3622C2×C4112yescomplemented
60C2×C8×D17C2×C416yes—
61C2×C8×D17C2×C416yes—
62C2×C8×D17C2×C4112yescomplemented
63C2×C8×D17C2×C4112yescomplemented
64C2×C8×D17C2×C4148yescomplemented
65C2×C8×D17C2316yes—
66C2×C8×D17C2316yes—
67C2×C8×D17C23116yes—
68#10587532C23132yescomplemented
69C8×#595C23132yescomplemented
70C24×C17C4211yescharacteristic
71C23×D17—28no—
72C23×D17C4211yescharacteristic
73C23×D17C4216yes—
74C23×D17C22×C416yes—
75C23×D17C22×C411yescharacteristic
76C22×#595—216no—
77C22×#595C22×C4124yes—
78C22×C4×C17C4216yes—
79C22×C4×C17C4211yescharacteristic
80C22×C4×C17C22×C411yescharacteristic
81C22×C4×C17C22×C416yes—
82C22×Dic17C4216yes—
83C22×Dic17C4211yescharacteristic
84C22×Dic17C22×C411yescharacteristic
85C22×Dic17C22×C416yes—
86C2×C4×D17C42124yes—
87C2×C4×D17C4216yes—
88C2×C4×D17C4216yes—
89C2×C4×D17C4216yes—
90C2×C4×D17C22×C413yes—
91C2×C4×D17C22×C416yes—
92C2×C4×D17C22×C4112yes—
93C2×C4×D17C22×C413yes—
94C2×C4×D17C22×C4112yes—
95C2×C4×D17C22×C416yes—
96C2×C4×D17C22×C413yes—
97C2×C4×D17C22×C416yes—
98C2×C4×D17C22×C4112yes—
99C2×C4×D17C2413yes—
100C2×C4×D17C2414yes—
101C22⋊#595C22×C4132yes—
102#63247C22×C4132yescomplemented
103C2×#3624C22×C4124yes—
104C4⋊#595C22×C4132yes—
105C4×#595C22×C4124yes—
106C4×#595C2418yes—
107#63243C22×C4132yescomplemented
108#63242C22×C4124yes—
109#63242C2418yes—
110C2×C8×C17C22×C416yes—
111C2×C8×C17C22×C416yes—
112C2×C8×C17C22×C4116yescomplemented
113C2×#3622C22×C416yes—
114C2×#3622C22×C416yes—
115C2×#3622C22×C4116yescomplemented
116C8×D17C22×C4112yes—
117C8×D17C22×C4112yes—
118C8×D17C22×C4116yescomplemented
119C8×D17C22×C4116yescomplemented
120C8×D17C2414yes—
121C8×D17C2414yes—
122C22×#405—171nomaximal, Sylow
123C23×C17—24no—
124C23×C17C2×C4216yes—
125C23×C17C2×C4211yescharacteristic
126C22×D17—24no—
127C22×D17—224no—
128C22×D17—224no—
129C22×D17C2×C4216yes—
130C22×D17C2×C42112yes—
131C22×D17C2×C4213yes—
132C22×D17#13118yes—
133C22×D17C23×C414yes—
134C22×D17C23×C413yes—
135C2×#595—248no—
136C2×#595C23×C4116yes—
137C2×C4×C17C2×C42112yes—
138C2×C4×C17C2×C4213yes—
139C2×C4×C17C2×C4216yes—
140C2×C4×C17C23×C413yes—
141C2×C4×C17C23×C414yes—
142C2×Dic17C2×C42112yes—
143C2×Dic17C2×C4213yes—
144C2×Dic17C2×C4216yes—
145C2×Dic17C23×C413yes—
146C2×Dic17C23×C414yes—
147C4×D17C2×C42112yes—
148C4×D17C2×C42112yes—
149C4×D17C2×C4216yes—
150C4×D17C2×C42112yes—
151C4×D17C23×C413yes—
152C4×D17C23×C414yes—
153C4×D17C23×C413yes—
154C4×D17C23×C414yes—
155C4×D17C23×C413yes—
156C4×D17C23×C414yes—
157C4×D17C2511yescharacteristic
158#3624C23×C4116yes—
159C8×C17C23×C414yes—
160C8×C17C23×C414yes—
161#3622C23×C414yes—
162#3622C23×C414yes—
163C23×M16—171no—
164C24×C8—171no—
165C22×#117—171no—
166C2×#405—1724no—
167C22×#97—172no—
168C22×C4×C8—172no—
169C22×C17—212no—
170C22×C17#40514yescomplemented
171C22×C17C22×C4214yes—
172C22×C17C22×C4213yes—
173C2×D17—212no—
174C2×D17—224no—
175C2×D17—28no—
176C2×D17#405112yescomplemented
177C2×D17C22×C4214yes—
178C2×D17C22×C4213yes—
179C2×D17C2×#131112yes—
180C2×D17C24×C411yescharacteristic
181#595—216no—
182C4×C17C22×C4213yes—
183C4×C17C22×C4214yes—
184C4×C17C24×C411yescharacteristic
185Dic17C22×C4213yes—
186Dic17C22×C4214yes—
187Dic17C24×C411yescharacteristic
188C24×C4—171no—
189C22×M16—1712no—
190C22×M16—172no—
191C22×M16—1712no—
192C22×M16—172no—
193C23×C8—172no—
194C23×C8—171no—
195C23×C8—171no—
196C23×C8—171no—
197C23×C8—171no—
198C23×C8—171no—
199C23×C8—1712no—
200C23×C8—1712no—
201C23×C8#59511yescharacteristic, complemented
202C2×#117—1712no—
203C2×#117—1712no—
204C22×C4⋊C4—172no—
205C22×C22⋊C4—172no—
206C22×C42—172no—
207#405—1764no—
208C2×#97—1724no—
209C2×C4×C8—1724no—
210C2×C17—24no—
211C2×C17C2×#40516yescomplemented
212C2×C17C23×C4211yescharacteristic
213D17—24no—
214D17C2×#40516yescomplemented
215D17C22×#13112yes—
216C25—171no—
217C23×C4—171no—
218C23×C4—171no—
219C23×C4—176no—
220C23×C4—171no—
221C23×C4—176no—
222C23×C4—176no—
223C23×C4—171no—
224C23×C4—176no—
225C23×C4—171no—
226C23×C4—174no—
227C23×C4C2×#59511yescharacteristic
228C2×M16—1724no—
229C2×M16—1748no—
230C2×M16—1716no—
231C2×M16—1724no—
232C22×C8—1712no—
233C22×C8—1712no—
234C22×C8—174no—
235C22×C8—171no—
236C22×C8—171no—
237C22×C8—1712no—
238C22×C8—176no—
239C22×C8—176no—
240C22×C8—176no—
241C22×C8—176no—
242C22×C8—1712no—
243C22×C8—1712no—
244C22×C8—1716no—
245C22×C8—1748no—
246C22×C8C2×#59511yescharacteristic
247C22×C8C2×#59511yescharacteristic
248C22×C8C2×#595112yescomplemented
249#117—1748no—
250#117—1716no—
251C2×C4⋊C4—1724no—
252C2×C22⋊C4—1724no—
253C2×C42—1712no—
254C2×C42—1712no—
255#97—1732no—
256C4×C8—1732no—
257C17C22×#40511yescharacteristic, complemented, Sylow
258C24—171no—
259C24—176no—
260C24—171no—
261C24—176no—
262C24—348no—
263C24C4×#59511yescharacteristic
264C22×C4—176no—
265C22×C4—171no—
266C22×C4—171no—
267C22×C4—176no—
268C22×C4—176no—
269C22×C4—1724no—
270C22×C4—176no—
271C22×C4—176no—
272C22×C4—173no—
273C22×C4—176no—
274C22×C4—1712no—
275C22×C4—173no—
276C22×C4—176no—
277C22×C4—1712no—
278C22×C4—173no—
279C22×C4—176no—
280C22×C4—1712no—
281C22×C4—173no—
282C22×C4—174no—
283C22×C4—1724no—
284C22×C4—3416no—
285C22×C4C4×#59516yes—
286C22×C4C4×#59511yescharacteristic
287C22×C4C22×#59511yescharacteristic
288C22×C4C22×#59516yes—
289M16—1732no—
290M16—1732no—
291C2×C8—1724no—
292C2×C8—178no—
293C2×C8—1724no—
294C2×C8—176no—
295C2×C8—176no—
296C2×C8—1716no—
297C2×C8—174no—
298C2×C8—174no—
299C2×C8—1712no—
300C2×C8—1712no—
301C2×C8—1716no—
302C2×C8—1716no—
303C2×C8C22×#59516yes—
304C2×C8C22×#59516yes—
305C2×C8C22×#595116yescomplemented
306C4⋊C4—1732no—
307C22⋊C4—1732no—
308C42—1724no—
309C42—178no—
310C23—24no—
311C23—178no—
312C23—173no—
313C23—173no—
314C23—174no—
315C23—1712no—
316C23—176no—
317C23—3424no—
318C23—3424no—
319C23—344no—
320C23C2×C4×#59516yes—
321C23C2×C4×#59511yescharacteristic
322C2×C4—173no—
323C2×C4—174no—
324C2×C4—1712no—
325C2×C4—173no—
326C2×C4—176no—
327C2×C4—173no—
328C2×C4—174no—
329C2×C4—173no—
330C2×C4—174no—
331C2×C4—176no—
332C2×C4—1712no—
333C2×C4—1712no—
334C2×C4—1712no—
335C2×C4—171no—
336C2×C4—173no—
337C2×C4—174no—
338C2×C4—1716no—
339C2×C4—3448no—
340C2×C4C2×C4×#595112yes—
341C2×C4C2×C4×#59513yes—
342C2×C4C2×C4×#59516yes—
343C2×C4C23×#59513yes—
344C2×C4C23×#59514yes—
345C8—1716no—
346C8—174no—
347C8—174no—
348C8C23×#59514yes—
349C8C23×#59514yes—
350C22—212no—
351C22—171no—
352C22—173no—
353C22—1712no—
354C22—1712no—
355C22—174no—
356C22—348no—
357C22—3424no—
358C22—3412no—
359C22#1176377214yesdirect product factor
360C22C22×C4×#59514yes—
361C22C22×C4×#59513yes—
362C4—171no—
363C4—173no—
364C4—174no—
365C4—3416no—
366C4C22×C4×#59513yes—
367C4C22×C4×#59514yes—
368C4C24×#59511yescharacteristic
369C2—24no—
370C2—172no—
371C2—176no—
372C2—344no—
373C2C2×#1176377216yesdirect product factor
374C2C23×C4×#59511yescharacteristic
subgroupG/H
centerC22×C8C2×#595
commutatorC2×C17C23×C42
FrattiniC4C24×#595
FittingC23×C8×C17C4
socleC23×C17C2×C42
prime radicalC24×D17C2×C4
cosocleC4×D17C25
hypercenterC23×C8#595
hypocenterC17C22×#405
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C8 ◁ C23×C8

Complements

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

NH ≅ G/Ntype
3. C2×#11763772C2direct (N × H)
4. C22×#10587532C2semidirect
5. C22×C8×#595C2semidirect
7. C22×#63243C4semidirect
8. C2×D17⋊M16C4semidirect
10. C22×#63247C4semidirect
17. #11763772C22direct (N × H)
18. C2×#10587532C22semidirect
19. C2×C8×#595C22semidirect
21. C23×#3622C4semidirect
22. C22×C8×D17C4semidirect
23. C22×C8×D17C4semidirect
24. C22×C8×D17C4semidirect
28. C23×C8×C17C4semidirect
42. C2×#63247C2×C4semidirect
49. D17⋊M16C2×C4semidirect
51. C2×#63243C2×C4semidirect
56. C22×C8×C17C2×C4semidirect
59. C22×#3622C2×C4semidirect
62. C2×C8×D17C2×C4semidirect
63. C2×C8×D17C2×C4semidirect
64. C2×C8×D17C2×C4semidirect
68. #10587532C23semidirect
69. C8×#595C23semidirect
102. #63247C22×C4semidirect
107. #63243C22×C4semidirect
112. C2×C8×C17C22×C4semidirect
115. C2×#3622C22×C4semidirect
118. C8×D17C22×C4semidirect
119. C8×D17C22×C4semidirect
170. C22×C17#405semidirect
176. C2×D17#405semidirect
201. C23×C8#595semidirect
211. C2×C17C2×#405semidirect
214. D17C2×#405semidirect
248. C22×C8C2×#595semidirect
257. C17C22×#405semidirect
305. C2×C8C22×#595semidirect
359. C22#11763772direct (N × H)
373. C2C2×#11763772direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D17⋊M162
C22×#105876772
C2×#117637722
C22×#105875322
C22×C8×#5952
C23×C8×D172
C22×#40517