Finite Group Databasebeta

← C2×#14545373 #17979453

Subgroups — C2×#14545373 #17979453

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#14545373C2116yesmaximal, direct product factor
3C2×#11763784C216yesmaximal, complemented
4C2×#11763780C213yesmaximal, complemented
5C2×#11763777C213yesmaximal, complemented
6C23×#63256C211yesmaximal, characteristic
7C2×#10587680—216no—
8C2×#10587680C22116yescomplemented
9C22×#63243C2216yescomplemented
10C22×#63242C2216yescomplemented
11#11763784C22148yescomplemented
12#11763780C22124yescomplemented
13C2×#10587543C2216yescomplemented
14C2×#10587543C2216yescomplemented
15#11763777C22124yescomplemented
16C2×C22⋊#3624C2211yescharacteristic
17C2×C22⋊#3624C2213yes—
18C22×#63256—216no—
19C22×#63256C411yescharacteristic
20C22×#63256C418yes—
21C22×#63256C413yes—
22C22×#63256C2213yes—
23C22×#63256C2218yes—
24C22×#63256C2211yescharacteristic
25C23×D68C413yes—
26C23×C4×D17C2213yes—
27C23×Q8×C17C411yescharacteristic
28C24×D17C2×C413yes—
29C22×Q8×C17—28no—
30C22×Q8×C17C2×C418yes—
31C22×Q8×C17C2×C413yes—
32C22×Q8×C17C2×C411yescharacteristic
33C23×C4×C17C2×C413yes—
34C23×Dic17C2311yescharacteristic
35C2×#63256—28no—
36C2×#63256—264no—
37C2×#63256—264no—
38C2×#63256—224no—
39C2×#63256—224no—
40C2×#63256C2×C418yes—
41C2×#63256C2×C4124yes—
42C2×#63256C2×C4112yes—
43C2×#63256C2×C414yes—
44C2×#63256D4116yes—
45C2×#63256C23112yes—
46C2×#63256C2314yes—
47C22×D68—224no—
48C22×D68C2×C416yes—
49C22×D68C2×C413yes—
50C22×D68C2×C4124yes—
51C22×D68C2×C413yes—
52C22×C4×D17—224no—
53C22×C4×D17C2×C413yes—
54C22×C4×D17C2×C413yes—
55C22×C4×D17C2×C4112yes—
56C22×C4×D17C23112yes—
57C22×C4×D17C2313yes—
58C22×C4×D17C2313yes—
59C22×#3624C2312yes—
60C22×#3624C2316yes—
61#10587680—264no—
62C2×#63243—224no—
63C2×#63243C23124yescomplemented
64C2×#63242—224no—
65C2×#63242C23124yescomplemented
66C22⋊#3624C2314yes—
67C22⋊#3624C23112yes—
68#10587543C23124yescomplemented
69#10587543C23124yescomplemented
70C24×C17C22×C411yescharacteristic
71C23×D17—212no—
72C23×D17—212no—
73C23×D17—46no—
74C23×D17C22×C413yes—
75C23×D17C22×C4112yes—
76C23×D17C22×C413yes—
77C2×Q8×C17—232no—
78C2×Q8×C17—212no—
79C2×Q8×C17C22⋊C418yes—
80C2×Q8×C17C22×C4112yes—
81C2×Q8×C17C22×C414yes—
82C22×C4×C17—212no—
83C22×C4×C17C22×C4112yes—
84C22×C4×C17C22×C413yes—
85C22×C4×C17C22×C413yes—
86C22×Dic17—24no—
87C22×Dic17C22×C412yes—
88C22×Dic17C22×C411yescharacteristic
89C22×Dic17C2412yes—
90C22×Dic17C2411yescharacteristic
91#63256—232no—
92#63256—296no—
93#63256—248no—
94#63256—248no—
95#63256C22⋊C4132yes—
96#63256C2×D4132yes—
97C2×D68—224no—
98C2×D68—212no—
99C2×D68—296no—
100C2×D68C22⋊C4124yes—
101C2×D68C22×C4124yes—
102C2×D68C22×C4112yes—
103C2×D68C22×C4112yes—
104C2×C4×D17—212no—
105C2×C4×D17—212no—
106C2×C4×D17—212no—
107C2×C4×D17—248no—
108C2×C4×D17—248no—
109C2×C4×D17C22×C4112yes—
110C2×C4×D17C22×C4112yes—
111C2×C4×D17C22×C416yes—
112C2×C4×D17C22×C416yes—
113C2×C4×D17C2×D4124yes—
114C2×C4×D17C2416yes—
115C2×C4×D17C2416yes—
116C2×#3624—24no—
117C2×#3624—212no—
118C2×#3624C2414yes—
119C2×#3624C24112yes—
120#63243—248no—
121#63242—248no—
122C2×#2880—171nomaximal, Sylow
123C23×C17—22no—
124C23×C17—22no—
125C23×C17#13114yescomplemented
126C23×C17C23×C412yes—
127C23×C17C23×C411yescharacteristic
128C22×D17—26no—
129C22×D17—26no—
130C22×D17—26no—
131C22×D17—26no—
132C22×D17—224no—
133C22×D17—26no—
134C22×D17—224no—
135C22×D17—412no—
136C22×D17—448no—
137C22×D17C2×C22⋊C4112yes—
138C22×D17C23×C416yes—
139C22×D17C23×C416yes—
140Q8×C17—224no—
141Q8×C17C2×C22⋊C4116yes—
142C2×C4×C17—26no—
143C2×C4×C17—224no—
144C2×C4×C17C2×C22⋊C4112yes—
145C2×C4×C17C23×C416yes—
146C2×C4×C17C23×C416yes—
147C2×Dic17—22no—
148C2×Dic17—24no—
149C2×Dic17—24no—
150C2×Dic17C23×C412yes—
151C2×Dic17C23×C411yescharacteristic
152C2×Dic17C22×D414yes—
153C2×Dic17C2511yescharacteristic
154D68—248no—
155D68—224no—
156D68C2×C22⋊C4148yes—
157C4×D17—224no—
158C4×D17—224no—
159C4×D17—212no—
160C4×D17—212no—
161C4×D17C2×C22⋊C4124yes—
162C4×D17C22×D4124yes—
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—28no—
172C22×C17—22no—
173C22×C17—22no—
174C22×C17C22×C22⋊C412yes—
175C22×C17C2×#13112yes—
176C22×C17C2×#13114yescomplemented
177C22×C17#56812yes—
178C22×C17C24×C411yescharacteristic
179C2×D17—224no—
180C2×D17—26no—
181C2×D17—26no—
182C2×D17—26no—
183C2×D17—26no—
184C2×D17—26no—
185C2×D17—448no—
186C2×D17—412no—
187C2×D17C22×C22⋊C4112yes—
188C4×C17—26no—
189C4×C17C22×C22⋊C4112yes—
190Dic17—22no—
191Dic17C22×C22⋊C412yes—
192Dic17C23×D412yes—
193C22×#41—171no—
194C22×#41—173no—
195C22×#41—178no—
196C22×#41—173no—
197C22×#41—178no—
198C22×#41—171no—
199C22×#41—3416no—
200C23×Q8#59511yescharacteristic
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—24no—
215C2×C17#288014yescomplemented
216C2×C17C23×C22⋊C411yescharacteristic
217C2×C17C22×#13111yescharacteristic
218C2×C17C2×#56811yescharacteristic
219D17—212no—
220D17—46no—
221C25—173no—
222C2×#41—1716no—
223C2×#41—174no—
224C2×#41—174no—
225C2×#41—1712no—
226C2×#41—1724no—
227C2×#41—178no—
228C2×#41—1712no—
229C2×#41—3424no—
230C2×#41—3424no—
231C2×#41—3464no—
232C2×#41—3464no—
233C2×#41—348no—
234C22×Q8—28no—
235C22×Q8C2×#59518yes—
236C22×Q8C2×#59513yes—
237C22×Q8C2×#59511yescharacteristic
238C22×D4—173no—
239C22×D4—1724no—
240C22×D4—176no—
241C22×D4—173no—
242C22×D4—3424no—
243C23×C4—173no—
244C23×C4—171no—
245C23×C4—1712no—
246C23×C4—173no—
247C23×C4—173no—
248C23×C4—173no—
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—173no—
265C24—173no—
266C24—1712no—
267C24—3412no—
268C24—3412no—
269C24—686no—
270C24C22×#59511yescharacteristic
271#41—1732no—
272#41—1732no—
273#41—3448no—
274#41—3448no—
275#41—3496no—
276#41—3432no—
277C2×Q8—232no—
278C2×Q8—212no—
279C2×Q8C22⋊#59518yes—
280C2×Q8C22×#595112yes—
281C2×Q8C22×#59514yes—
282C2×D4—1724no—
283C2×D4—1712no—
284C2×D4—1724no—
285C2×D4—1712no—
286C2×D4—3496no—
287C2×D4—3424no—
288C2×D4—3412no—
289C22×C4—212no—
290C22×C4—171no—
291C22×C4—1724no—
292C22×C4—176no—
293C22×C4—176no—
294C22×C4—172no—
295C22×C4—172no—
296C22×C4—171no—
297C22×C4—176no—
298C22×C4—1712no—
299C22×C4—1712no—
300C22×C4—176no—
301C22×C4—3412no—
302C22×C4—3448no—
303C22×C4—3448no—
304C22×C4—3412no—
305C22×C4—344no—
306C22×C4—3412no—
307C22×C4C22×#595112yes—
308C22×C4C22×#59513yes—
309C22×C4C22×#59513yes—
310M16—3448no—
311C2×C8—174no—
312C2×C8—1712no—
313C2×C8—3448no—
314C2×C8—344no—
315C2×C8—3412no—
316C23—22no—
317C23—22no—
318C23—1712no—
319C23—176no—
320C23—176no—
321C23—3424no—
322C23—346no—
323C23—346no—
324C23—346no—
325C23—346no—
326C23—3424no—
327C23—346no—
328C23—6812no—
329C23—6848no—
330C23#1058768014yescomplemented
331C23C23×#59512yes—
332C23C23×#59511yescharacteristic
333Q8—224no—
334Q8C2×C22⋊#595116yes—
335D4—1748no—
336D4—3448no—
337D4—3424no—
338C2×C4—26no—
339C2×C4—224no—
340C2×C4—174no—
341C2×C4—171no—
342C2×C4—171no—
343C2×C4—1724no—
344C2×C4—1724no—
345C2×C4—172no—
346C2×C4—3412no—
347C2×C4—3412no—
348C2×C4—3424no—
349C2×C4—344no—
350C2×C4—344no—
351C2×C4—342no—
352C2×C4—3424no—
353C2×C4C2×C22⋊#595112yes—
354C2×C4C23×#59516yes—
355C2×C4C23×#59516yes—
356C8—344no—
357C8—3412no—
358C22—22no—
359C22—22no—
360C22—28no—
361C22—1712no—
362C22—346no—
363C22—346no—
364C22—3424no—
365C22—346no—
366C22—346no—
367C22—346no—
368C22—6848no—
369C22—6812no—
370C22C22×C22⋊#59512yes—
371C22C2×#1058768012yes—
372C22C2×#1058768014yescomplemented
373C22#1176388912yes—
374C22C24×#59511yescharacteristic
375C4—26no—
376C4—172no—
377C4—172no—
378C4—342no—
379C4C22×C22⋊#595112yes—
380C2—24no—
381C2—3412no—
382C2—686no—
383C2#1454537314yesdirect product factor
384C2C23×C22⋊#59511yescharacteristic
385C2C22×#1058768011yescharacteristic
386C2C2×#1176388911yescharacteristic
subgroupG/H
centerC23C23×#595
commutatorC22×C17C24×C4
FrattiniC22C24×#595
FittingC23×Q8×C17C4
socleC23×C17C23×C4
prime radicalC23×#63256C2
cosocleC2×Dic17C25
hypercenterC23×Q8#595
hypocenterC17C2×#2880
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×Q8

Complements

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

NH ≅ G/Ntype
1. C22×#10587680C2semidirect
2. #14545373C2direct (N × H)
3. C2×#11763784C2semidirect
4. C2×#11763780C2semidirect
5. C2×#11763777C2semidirect
8. C2×#10587680C22semidirect
9. C22×#63243C22semidirect
10. C22×#63242C22semidirect
11. #11763784C22semidirect
12. #11763780C22semidirect
13. C2×#10587543C22semidirect
14. C2×#10587543C22semidirect
15. #11763777C22semidirect
63. C2×#63243C23semidirect
65. C2×#63242C23semidirect
68. #10587543C23semidirect
69. #10587543C23semidirect
125. C23×C17#131semidirect
176. C22×C17C2×#131semidirect
215. C2×C17#2880semidirect
263. C17C2×#2880semidirect
330. C23#10587680semidirect
372. C22C2×#10587680semidirect
383. C2#14545373direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#105876802
#145453732
C2×#117637842
C2×#117637802
C2×#117637772
C23×#632562
C2×#288017