Finite Group Databasebeta

← C2×#14545375 #17979455

Subgroups — C2×#14545375 #17979455

Order 4352.

5206 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587680C212yesmaximal, complemented
2#14545375C2116yesmaximal, direct product factor
3C2×#11763783C216yesmaximal, complemented
4C2×#11763780C213yesmaximal, complemented
5C2×#11763777C213yesmaximal, complemented
6C22×#41×D17C211yesmaximal, characteristic
7C2×#10587680—216no—
8C2×#10587680C22116yescomplemented
9C22×#63243C2216yescomplemented
10C22×#63242C2216yescomplemented
11#11763783C22148yescomplemented
12#11763780C22124yescomplemented
13C2×#10587543C2211yescharacteristic
14C2×#10587543C2213yes—
15#11763777C22124yescomplemented
16C2×C22⋊#3624C2216yescomplemented
17C2×C22⋊#3624C2216yescomplemented
18C22×#63256C2211yescharacteristic
19C22×#63252C413yes—
20C22×#63254C2213yes—
21C2×#41×D17—216no—
22C2×#41×D17C418yes—
23C2×#41×D17C2218yes—
24C22×Q8×D17C411yescharacteristic
25C22×D4×D17C413yes—
26C23×C4×D17C2213yes—
27C22×#41×C17C411yescharacteristic
28C24×D17C2×C413yes—
29C2×#41×C17—28no—
30C2×#41×C17C2×C418yes—
31C22×Q8×C17C2×C411yescharacteristic
32C22×D4×C17C2×C413yes—
33C23×C4×C17C2×C413yes—
34C22×C22⋊D17C2×C416yes—
35C23×Dic17C2313yes—
36#41×D17—264no—
37#41×D17—264no—
38C2×#63256C2×C414yes—
39C2×#63256D4116yes—
40C2×#63256C2314yes—
41C2×Q8×D17—28no—
42C2×Q8×D17C2×C418yes—
43C2×#63254—224no—
44C2×#63254C2×C4112yes—
45C2×#63254C23112yes—
46C2×D4×D17—224no—
47C2×D4×D17C2×C4124yes—
48C2×#63252—224no—
49C2×#63252C2×C4124yes—
50C22×D68C2×C413yes—
51C22×C4×D17—224no—
52C22×C4×D17C2×C413yes—
53C22×C4×D17C2×C4112yes—
54C22×C4×D17C2×C413yes—
55C22×C4×D17C23112yes—
56C22×C4×D17C2311yescharacteristic
57C22×C4×D17C2313yes—
58C22×Dic34C2×C413yes—
59C22×#3624C2312yes—
60C22×#3624C2316yes—
61#10587680—264no—
62C2×#63243—224no—
63C2×#63243C23124yescomplemented
64C2×#63242—224no—
65C2×#63242C23124yescomplemented
66C22⋊#3624C23124yescomplemented
67C22⋊#3624C23124yescomplemented
68#10587543C2314yes—
69#10587543C23112yes—
70C24×C17C22×C413yes—
71C23×D17—212no—
72C23×D17—212no—
73C23×D17—46no—
74C23×D17C22×C4112yes—
75C23×D17C22×C413yes—
76C23×D17C22×C411yescharacteristic
77#41×C17—232no—
78C2×Q8×C17C22⋊C418yes—
79C2×Q8×C17C22×C414yes—
80C2×D4×C17—212no—
81C2×D4×C17C22×C4112yes—
82C22×C4×C17—212no—
83C22×C4×C17C22×C411yescharacteristic
84C22×C4×C17C22×C4112yes—
85C22×C4×C17C22×C413yes—
86C2×C22⋊D17—224no—
87C2×C22⋊D17C22×C4124yes—
88C22×Dic17—212no—
89C22×Dic17C22×C413yes—
90C22×Dic17C22×C416yes—
91C22×Dic17C2416yes—
92C22×Dic17C2411yescharacteristic
93#63256C22⋊C4132yes—
94#63256C2×D4132yes—
95Q8×D17—232no—
96#63254—248no—
97#63254—248no—
98D4×D17—296no—
99#63252—296no—
100C2×D68C22⋊C4124yes—
101C2×D68C22×C4112yes—
102C2×C4×D17—212no—
103C2×C4×D17—212no—
104C2×C4×D17—24no—
105C2×C4×D17—248no—
106C2×C4×D17—248no—
107C2×C4×D17C22×C412yes—
108C2×C4×D17C22×C4112yes—
109C2×C4×D17C22×C4112yes—
110C2×C4×D17C22×C416yes—
111C2×C4×D17C2×D4124yes—
112C2×C4×D17C2412yes—
113C2×C4×D17C2416yes—
114C2×Dic34—212no—
115C2×Dic34C22×C4112yes—
116C2×#3624—24no—
117C2×#3624—212no—
118C2×#3624C2414yes—
119C2×#3624C24112yes—
120#63243—248no—
121#63242—248no—
122C2×#2880—171nomaximal, Sylow
123C23×C17—26no—
124C23×C17—26no—
125C23×C17—26no—
126C23×C17C23×C416yes—
127C23×C17C23×C411yescharacteristic
128C22×D17—22no—
129C22×D17—26no—
130C22×D17—22no—
131C22×D17—26no—
132C22×D17—224no—
133C22×D17—224no—
134C22×D17—412no—
135C22×D17—448no—
136C22×D17C2×C22⋊C4112yes—
137C22×D17#13114yescomplemented
138C22×D17C23×C416yes—
139C22×D17C23×C412yes—
140Q8×C17C2×C22⋊C4116yes—
141D4×C17—224no—
142C2×C4×C17—22no—
143C2×C4×C17—224no—
144C2×C4×C17C2×C22⋊C4112yes—
145C2×C4×C17C23×C412yes—
146C2×C4×C17C23×C416yes—
147C22⋊D17—248no—
148C2×Dic17—26no—
149C2×Dic17—212no—
150C2×Dic17—212no—
151C2×Dic17C23×C416yes—
152C2×Dic17C23×C411yescharacteristic
153C2×Dic17C22×D414yes—
154C2×Dic17C2511yescharacteristic
155D68C2×C22⋊C4148yes—
156C4×D17—224no—
157C4×D17—224no—
158C4×D17—24no—
159C4×D17—24no—
160C4×D17C2×C22⋊C4124yes—
161C4×D17C22×D4124yes—
162Dic34—224no—
163#3624—24no—
164#3624—212no—
165C23×#41—171no—
166C22×#131—172no—
167#2880—1716no—
168C2×#408—176no—
169C2×#407—173no—
170C22×C22⋊C8—173no—
171C22×C17—26no—
172C22×C17—26no—
173C22×C17—26no—
174C22×C17—412no—
175C22×C17C22×C22⋊C412yes—
176C22×C17C2×#13112yes—
177C22×C17#56812yes—
178C22×C17C24×C411yescharacteristic
179C2×D17—28no—
180C2×D17—224no—
181C2×D17—22no—
182C2×D17—26no—
183C2×D17—22no—
184C2×D17—26no—
185C2×D17—448no—
186C2×D17C22×C22⋊C4112yes—
187C2×D17C2×#13114yescomplemented
188C4×C17—22no—
189C4×C17C22×C22⋊C4112yes—
190Dic17—26no—
191Dic17C22×C22⋊C412yes—
192Dic17C23×D412yes—
193C22×#41—178no—
194C22×#41—178no—
195C22×#41—171no—
196C22×#41—173no—
197C22×#41—173no—
198C22×#41—3416no—
199C22×#41#59511yescharacteristic
200C23×Q8—171no—
201C23×D4—173no—
202C24×C4—173no—
203C2×#131—1716no—
204C2×#131—3416no—
205C22×M16—176no—
206C23×C8—176no—
207#408—1748no—
208#407—1724no—
209C2×C22⋊C8—171no—
210C2×C22⋊C8—173no—
211C2×C22⋊C8—176no—
212C2×C22⋊C8—1724no—
213C2×C22⋊C8—176no—
214C2×C17—46no—
215C2×C17#288014yescomplemented
216C2×C17C23×C22⋊C411yescharacteristic
217C2×C17C22×#13111yescharacteristic
218C2×C17C2×#56811yescharacteristic
219D17—24no—
220D17—212no—
221C25—173no—
222C2×#41—28no—
223C2×#41—1716no—
224C2×#41—174no—
225C2×#41—174no—
226C2×#41—1712no—
227C2×#41—1712no—
228C2×#41—1724no—
229C2×#41—3424no—
230C2×#41—3424no—
231C2×#41—3464no—
232C2×#41—3464no—
233C2×#41C2×#59518yes—
234C22×Q8—178no—
235C22×Q8—173no—
236C22×Q8—348no—
237C22×Q8C2×#59511yescharacteristic
238C22×D4—176no—
239C22×D4—1724no—
240C22×D4—173no—
241C22×D4—3424no—
242C22×D4C2×#59513yes—
243C23×C4—173no—
244C23×C4—173no—
245C23×C4—173no—
246C23×C4—1712no—
247C23×C4—173no—
248C23×C4—171no—
249C23×C4—1712no—
250C23×C4—3424no—
251C23×C4C2×#59513yes—
252#131—3464no—
253C2×M16—1724no—
254C2×M16—3424no—
255C22×C8—1724no—
256C22×C8—172no—
257C22×C8—176no—
258C22×C8—3424no—
259C22⋊C8—174no—
260C22⋊C8—1712no—
261C22⋊C8—1724no—
262C22⋊C8—1724no—
263C17C2×#288011yescharacteristic, complemented, Sylow
264C24—171no—
265C24—173no—
266C24—1712no—
267C24—3412no—
268C24—3412no—
269C24—686no—
270C24C22×#59513yes—
271#41—232no—
272#41—1732no—
273#41—1732no—
274#41—3496no—
275#41—3448no—
276#41—3448no—
277C2×Q8—1712no—
278C2×Q8—3432no—
279C2×Q8—3412no—
280C2×Q8C22⋊#59518yes—
281C2×Q8C22×#59514yes—
282C2×D4—212no—
283C2×D4—1724no—
284C2×D4—1724no—
285C2×D4—1712no—
286C2×D4—3496no—
287C2×D4—3424no—
288C2×D4C22×#595112yes—
289C22×C4—212no—
290C22×C4—171no—
291C22×C4—1724no—
292C22×C4—176no—
293C22×C4—176no—
294C22×C4—176no—
295C22×C4—176no—
296C22×C4—173no—
297C22×C4—172no—
298C22×C4—1712no—
299C22×C4—1712no—
300C22×C4—172no—
301C22×C4—344no—
302C22×C4—3448no—
303C22×C4—3448no—
304C22×C4—3412no—
305C22×C4—3412no—
306C22×C4—3412no—
307C22×C4C22×#595112yes—
308C22×C4C22×#59511yescharacteristic
309C22×C4C22×#59513yes—
310M16—3448no—
311C2×C8—174no—
312C2×C8—1712no—
313C2×C8—3448no—
314C2×C8—344no—
315C2×C8—3412no—
316C23—26no—
317C23—26no—
318C23—26no—
319C23—1712no—
320C23—174no—
321C23—172no—
322C23—176no—
323C23—3424no—
324C23—3424no—
325C23—342no—
326C23—346no—
327C23—342no—
328C23—346no—
329C23—6812no—
330C23—6848no—
331C23C23×#59516yes—
332C23C23×#59511yescharacteristic
333Q8—3424no—
334Q8C2×C22⋊#595116yes—
335D4—224no—
336D4—1748no—
337D4—3448no—
338C2×C4—22no—
339C2×C4—224no—
340C2×C4—174no—
341C2×C4—171no—
342C2×C4—171no—
343C2×C4—1724no—
344C2×C4—1724no—
345C2×C4—176no—
346C2×C4—344no—
347C2×C4—344no—
348C2×C4—3424no—
349C2×C4—3412no—
350C2×C4—3412no—
351C2×C4—346no—
352C2×C4—3424no—
353C2×C4C2×C22⋊#595112yes—
354C2×C4C23×#59512yes—
355C2×C4C23×#59516yes—
356C8—344no—
357C8—3412no—
358C22—26no—
359C22—26no—
360C22—26no—
361C22—412no—
362C22—1712no—
363C22—174no—
364C22—342no—
365C22—346no—
366C22—342no—
367C22—346no—
368C22—348no—
369C22—3424no—
370C22—6848no—
371C22C22×C22⋊#59512yes—
372C22D17⋊#13112yes—
373C22#1176388812yes—
374C22C24×#59511yescharacteristic
375C4—22no—
376C4—172no—
377C4—172no—
378C4—346no—
379C4C22×C22⋊#595112yes—
380C2—46no—
381C2—344no—
382C2—3412no—
383C2#1454537514yesdirect product factor
384C2C23×C22⋊#59511yescharacteristic
385C2C2×D17⋊#13111yescharacteristic
386C2C2×#1176388811yescharacteristic
subgroupG/H
centerC23C23×#595
commutatorC22×C17C24×C4
FrattiniC22C24×#595
FittingC22×#41×C17C4
socleC23×C17C23×C4
prime radicalC22×#41×D17C2
cosocleC2×Dic17C25
hypercenterC22×#41#595
hypocenterC17C2×#2880
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
1. C22×#10587680C2semidirect
2. #14545375C2direct (N × H)
3. C2×#11763783C2semidirect
4. C2×#11763780C2semidirect
5. C2×#11763777C2semidirect
8. C2×#10587680C22semidirect
9. C22×#63243C22semidirect
10. C22×#63242C22semidirect
11. #11763783C22semidirect
12. #11763780C22semidirect
15. #11763777C22semidirect
16. C2×C22⋊#3624C22semidirect
17. C2×C22⋊#3624C22semidirect
63. C2×#63243C23semidirect
65. C2×#63242C23semidirect
66. C22⋊#3624C23semidirect
67. C22⋊#3624C23semidirect
137. C22×D17#131semidirect
187. C2×D17C2×#131semidirect
215. C2×C17#2880semidirect
263. C17C2×#2880semidirect
383. C2#14545375direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#105876802
#145453752
C2×#117637832
C2×#117637802
C2×#117637772
C22×#41×D172
C2×#288017