Finite Group Databasebeta

← C2×#14542406 #17941422

Subgroups — C2×#14542406 #17941422

Order 4352.

7706 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14542406C2132yesmaximal, direct product factor
2C2×#11763538C211yesmaximal, characteristic, complemented
3C2×#11763529C213yesmaximal, complemented
4C2×#11763498C216yesmaximal, complemented
5C2×Q8×D68C211yesmaximal, characteristic, complemented
6C2×#11763466C212yesmaximal, complemented
7C2×#11763464C213yesmaximal, complemented
8C2×#11763366C213yesmaximal, complemented
9C2×#11763341C216yesmaximal, complemented
10C2×C4×#63252C213yesmaximal, complemented
11C2×C4×Q8×D17C212yesmaximal, complemented
12C2×C4×#41×C17C211yesmaximal, characteristic, complemented
13C22×#63252C2213yes—
14C22×Q8×D17C2212yes—
15#11763538C22116yescomplemented
16#11763529C22148yescomplemented
17#11763498C22196yescomplemented
18Q8×D68C22116yescomplemented
19#11763466C22132yescomplemented
20#11763464C22148yescomplemented
21#11763366C22148yescomplemented
22C2×#10587555C2213yes—
23C2×#10587555C2213yes—
24#11763341C22196yescomplemented
25C2×#10587565C22112yes—
26C2×#10587556C2216yes—
27C2×#10587576C2216yes—
28C2×#10587622C2216yes—
29C2×#10587569C22112yes—
30C2×#10587583C2216yes—
31C2×#10587610C2216yes—
32C2×#10587610C2216yes—
33C2×#10587624C2216yes—
34C4×#63252C22148yescomplemented
35C2×Q8×Dic17C2212yes—
36C2×C4×Dic34C2213yes—
37C2×C4×Dic34C2216yes—
38C2×C4×Dic34C2213yes—
39C2×#10587573C2216yes—
40C4×Q8×D17C22132yescomplemented
41C2×C4×D68C2211yescharacteristic
42C2×C4×D68C2213yes—
43C2×C4×C22⋊D17C2216yes—
44C2×C4×C22⋊D17C2216yes—
45C2×#10587612C2213yes—
46C2×#10587612C2216yes—
47C2×#10587558C2216yes—
48C2×C4⋊C4×D17C2216yes—
49C2×C42×D17C2216yes—
50C22×#41×C17C2211yescharacteristic
51C4×#41×C17C22116yescomplemented
52C2×C4×Q8×C17C2211yescharacteristic
53C2×C4×Q8×C17C2211yescharacteristic
54C2×C4×D4×C17C2213yes—
55C2×C4×D4×C17C2213yes—
56C2×C17×#117C2213yes—
57C22×C42×C17C2213yes—
58C2×#41×C17—28no—
59C2×#41×C17C2318yes—
60C22×Q8×C17C2311yescharacteristic
61C22×D4×C17C2313yes—
62C23×C4×C17C2313yes—
63C23×C4×C17C2313yes—
64C23×C4×C17C2313yes—
65C22×C22⋊D17C2316yes—
66C2×Q8×D17—216no—
67C2×Q8×D17C23116yes—
68C2×#63252—224no—
69C2×#63252C23124yes—
70C22×D68C2311yescharacteristic
71C22×C4×D17C2312yes—
72C22×C4×D17C2316yes—
73C22×C4×D17C2316yes—
74C22×Dic34C2316yes—
75C22×Dic34C2313yes—
76C4×Q8×C17C2318yes—
77C4×Q8×C17C2318yes—
78C4×D4×C17C23124yes—
79C4×D4×C17C23124yes—
80C17×#117C23124yes—
81C2×C4⋊C4×C17C2313yes—
82C2×C4⋊C4×C17C2313yes—
83C2×C22⋊C4×C17C2316yes—
84C2×C42×C17C2311yescharacteristic
85C2×C42×C17C2313yes—
86C2×C42×C17C2313yes—
87C2×C42×C17C2313yes—
88C2×C42×C17C23124yes—
89C2×C22⋊Dic17C2316yes—
90C2×C22⋊Dic17C23112yes—
91Q8×Dic17C23116yes—
92#10587624C23148yes—
93#10587622C23148yes—
94C4×C22⋊D17C23148yes—
95C4×C22⋊D17C23148yes—
96C2×#63227C2312yes—
97C2×#63227C2316yes—
98#10587612C23124yes—
99#10587612C23148yes—
100C2×C4⋊Dic17C2316yes—
101C2×C4⋊Dic17C2311yescharacteristic
102C2×C4⋊Dic17C2313yes—
103C2×C4⋊Dic17C2316yes—
104C2×C4⋊Dic17C2316yes—
105#10587610C23148yes—
106#10587610C23148yes—
107C2×#63225C23112yes—
108C2×#63225C2316yes—
109C2×#63225C2316yes—
110C2×C4×Dic17C2316yes—
111C2×C4×Dic17C2316yes—
112C2×C4×Dic17C2316yes—
113#10587583C23148yes—
114C4⋊C4×D17C23148yes—
115#10587576C23148yes—
116#10587573C23148yes—
117#10587569C23196yes—
118#10587565C23196yes—
119C4×D68C23124yes—
120C4×D68C2318yes—
121#10587558C23148yes—
122C42×D17C23148yes—
123#10587556C23148yes—
124#10587555C23124yes—
125#10587555C23124yes—
126C4×Dic34C23148yes—
127C4×Dic34C23124yes—
128C4×Dic34C23124yes—
129C24×C17C2413yes—
130C23×D17C2412yes—
131#41×C17—232no—
132C2×Q8×C17#4118yescomplemented
133C2×Q8×C17C2414yes—
134C2×D4×C17—212no—
135C2×D4×C17C24112yes—
136C22×C4×C17—212no—
137C22×C4×C17—212no—
138C22×C4×C17—212no—
139C22×C4×C17C2413yes—
140C22×C4×C17C24112yes—
141C22×C4×C17C2411yescharacteristic
142C22×C4×C17C24112yes—
143C22×C4×C17C2413yes—
144C22×C4×C17C24112yes—
145C22×C4×C17C2411yescharacteristic
146C22×C4×C17C2413yes—
147C22×C4×C17C2411yescharacteristic
148C2×C22⋊D17—224no—
149C2×C22⋊D17C24124yes—
150C22×Dic17C2416yes—
151C22×Dic17C2416yes—
152C22×Dic17C2412yes—
153Q8×D17—264no—
154#63252—296no—
155C2×D68#4118yescomplemented
156C2×D68C2414yes—
157C2×C4×D17—224no—
158C2×C4×D17—224no—
159C2×C4×D17—28no—
160C2×C4×D17C24124yes—
161C2×C4×D17C24124yes—
162C2×C4×D17C2418yes—
163C2×Dic34—212no—
164C2×Dic34—224no—
165C2×Dic34C24112yes—
166C2×Dic34C24124yes—
167C4⋊C4×C17C24112yes—
168C4⋊C4×C17C24112yes—
169C22⋊C4×C17C24124yes—
170C42×C17C2414yes—
171C42×C17C24112yes—
172C42×C17C24112yes—
173C42×C17C24112yes—
174C22⋊Dic17C24124yes—
175C22⋊Dic17C24148yes—
176#63227C2418yes—
177#63227C24124yes—
178C4⋊Dic17C2414yes—
179C4⋊Dic17C24112yes—
180C4⋊Dic17C24124yes—
181C4⋊Dic17C24124yes—
182C4⋊Dic17C24124yes—
183#63225C24124yes—
184#63225C24148yes—
185#63225C24124yes—
186C4×Dic17C24124yes—
187C4×Dic17C24124yes—
188C4×Dic17C24124yes—
189C2×#3482—171nomaximal, Sylow
190C23×C17—26no—
191C23×C17—26no—
192C23×C17—26no—
193C23×C17C2516yes—
194C23×C17C2511yescharacteristic
195C22×D17—24no—
196C22×D17—24no—
197C22×D17C2×#4118yes—
198C22×D17C2514yes—
199Q8×C17C2×#41116yescomplemented
200D4×C17—224no—
201C2×C4×C17—26no—
202C2×C4×C17—22no—
203C2×C4×C17—26no—
204C2×C4×C17—224no—
205C2×C4×C17—224no—
206C2×C4×C17—224no—
207C2×C4×C17C2×#41112yes—
208C2×C4×C17C2×#4114yes—
209C2×C4×C172−1+414yes—
210C2×C4×C17C2512yes—
211C2×C4×C17C2516yes—
212C2×C4×C17C2516yes—
213C2×C4×C17C2512yes—
214C2×C4×C17C2516yes—
215C2×C4×C17C2512yes—
216C22⋊D17—248no—
217C2×Dic17—212no—
218C2×Dic17—212no—
219C2×Dic17—24no—
220C2×Dic17C25112yes—
221C2×Dic17C2514yes—
222C2×Dic17C25112yes—
223D68C2×#41116yescomplemented
224C4×D17—248no—
225C4×D17—248no—
226C4×D17—216no—
227Dic34—224no—
228Dic34—248no—
229#3482—1732no—
230C2×#557—171no—
231C2×#556—173no—
232C2×#552—176no—
233C2×D4×Q8—171no—
234C2×#548—172no—
235C2×#547—173no—
236C2×#533—173no—
237C2×#529—176no—
238C2×C4×#41—173no—
239C2×C4×#41D1711yescharacteristic, complemented
240C22×C4×Q8—172no—
241C22×C17—26no—
242C22×C17—26no—
243C22×C17—26no—
244C22×C17—412no—
245C22×C17C22×#4112yes—
246C22×C17C22×#4112yes—
247C22×C17C2×2−1+412yes—
248C22×C17C2611yescharacteristic
249C2×D17—24no—
250C2×D17—24no—
251C2×D17—216no—
252C2×D17C22×#4118yes—
253C4×C17—26no—
254C4×C17—22no—
255C4×C17—26no—
256C4×C17C22×#4114yes—
257C4×C17C22×#41112yes—
258C4×C17C2×2−1+414yes—
259Dic17—212no—
260Dic17—212no—
261Dic17—24no—
262C22×#41—173no—
263C22×#41C2×D1711yescharacteristic
264C23×Q8—172no—
265#557—1716no—
266#556—1748no—
267#552—1796no—
268D4×Q8—1716no—
269#548—1732no—
270#547—1748no—
271#533—1748no—
272C2×C4⋊Q8—173no—
273C2×C4⋊Q8—173no—
274#529—1796no—
275C2×#126—1712no—
276C2×#125—176no—
277C2×#125—176no—
278C2×#124—176no—
279C2×#123—1712no—
280C2×C22⋊Q8—176no—
281C2×C22⋊Q8—176no—
282C2×C22⋊Q8—176no—
283C2×#121—176no—
284C4×#41—1748no—
285C4×#41C2×D17116yescomplemented
286C2×C4×Q8—172no—
287C2×C4×Q8—1732no—
288C2×C4×Q8—176no—
289C2×C4×Q8—176no—
290C2×C4×Q8—173no—
291C2×C4×Q8—173no—
292C2×C4×Q8C2×D1711yescharacteristic
293C2×C4×Q8C2×D1711yescharacteristic
294C2×C4×D4—176no—
295C2×C4×D4—176no—
296C2×C4×D4—171no—
297C2×C4×D4—173no—
298C2×C4×D4C2×D1713yes—
299C2×C4×D4C2×D1713yes—
300C2×#117—173no—
301C2×#117—176no—
302C2×#117—176no—
303C2×#117C2×D1713yes—
304C22×C4⋊C4—176no—
305C22×C42—176no—
306C22×C42C2×D1713yes—
307C2×C17—46no—
308C2×C17#348214yescomplemented
309C2×C17C23×#4111yescharacteristic
310C2×C17C23×#4111yescharacteristic
311C2×C17C22×2−1+411yescharacteristic
312D17—28no—
313C2×#41—28no—
314C2×#41—1724no—
315C2×#41—3424no—
316C2×#41C22×D1718yes—
317C22×Q8—1716no—
318C22×Q8—176no—
319C22×Q8—173no—
320C22×Q8—3416no—
321C22×Q8C22×D1711yescharacteristic
322C22×D4—176no—
323C22×D4—171no—
324C22×D4C22×D1713yes—
325C23×C4—176no—
326C23×C4—176no—
327C23×C4—172no—
328C23×C4C22×D1713yes—
329C23×C4C22×D1713yes—
330C23×C4C22×D1713yes—
331C4⋊Q8—1724no—
332C4⋊Q8—1724no—
333#126—1796no—
334#125—1748no—
335#125—1748no—
336#124—1748no—
337#123—1796no—
338C22⋊Q8—1748no—
339C22⋊Q8—1748no—
340C22⋊Q8—1748no—
341#121—1748no—
342C4×Q8—1716no—
343C4×Q8—1748no—
344C4×Q8—1748no—
345C4×Q8—1724no—
346C4×Q8—1724no—
347C4×Q8C22×D1718yes—
348C4×Q8C22×D1718yes—
349C4×D4—1748no—
350C4×D4—1748no—
351C4×D4—178no—
352C4×D4—1724no—
353C4×D4C22×D17124yes—
354C4×D4C22×D17124yes—
355#117—1724no—
356#117—1748no—
357#117—1748no—
358#117C22×D17124yes—
359C2×C4⋊C4—176no—
360C2×C4⋊C4—1712no—
361C2×C4⋊C4—171no—
362C2×C4⋊C4—176no—
363C2×C4⋊C4—173no—
364C2×C4⋊C4—176no—
365C2×C4⋊C4—176no—
366C2×C4⋊C4—176no—
367C2×C4⋊C4—1748no—
368C2×C4⋊C4C22×D1713yes—
369C2×C4⋊C4C22×D1713yes—
370C2×C22⋊C4—176no—
371C2×C22⋊C4—1712no—
372C2×C22⋊C4—172no—
373C2×C22⋊C4—176no—
374C2×C22⋊C4C22×D1716yes—
375C2×C42—176no—
376C2×C42—176no—
377C2×C42—176no—
378C2×C42—1748no—
379C2×C42C22×D1713yes—
380C2×C42C22×D1713yes—
381C2×C42C22×D17124yes—
382C2×C42C22×D1711yescharacteristic
383C2×C42C22×D1713yes—
384C17C2×#348211yescharacteristic, complemented, Sylow
385C24—172no—
386C24C23×D1713yes—
387#41—232no—
388#41—3496no—
389C2×Q8—1724no—
390C2×Q8—1712no—
391C2×Q8—3464no—
392C2×Q8—3424no—
393C2×Q8—3412no—
394C2×Q8#6325218yescomplemented
395C2×Q8C23×D1714yes—
396C2×D4—212no—
397C2×D4—1724no—
398C2×D4—178no—
399C2×D4—174no—
400C2×D4—3424no—
401C2×D4C23×D17112yes—
402C22×C4—212no—
403C22×C4—212no—
404C22×C4—212no—
405C22×C4—172no—
406C22×C4—176no—
407C22×C4—176no—
408C22×C4—178no—
409C22×C4—1724no—
410C22×C4—1724no—
411C22×C4—3424no—
412C22×C4—3424no—
413C22×C4—348no—
414C22×C4C23×D1713yes—
415C22×C4C23×D1711yescharacteristic
416C22×C4C23×D1713yes—
417C22×C4C23×D17112yes—
418C22×C4C23×D17112yes—
419C22×C4C23×D17112yes—
420C22×C4C23×D1713yes—
421C22×C4C23×D1711yescharacteristic
422C22×C4C23×D1711yescharacteristic
423C4⋊C4—1724no—
424C4⋊C4—1748no—
425C4⋊C4—174no—
426C4⋊C4—1724no—
427C4⋊C4—1712no—
428C4⋊C4—1724no—
429C4⋊C4—1724no—
430C4⋊C4—1724no—
431C4⋊C4C23×D17112yes—
432C4⋊C4C23×D17112yes—
433C22⋊C4—1724no—
434C22⋊C4—1748no—
435C22⋊C4—178no—
436C22⋊C4—1724no—
437C22⋊C4C23×D17124yes—
438C42—1724no—
439C42—1724no—
440C42—1724no—
441C42C23×D17112yes—
442C42C23×D1714yes—
443C42C23×D17112yes—
444C42C23×D17112yes—
445C23—26no—
446C23—26no—
447C23—26no—
448C23—178no—
449C23—174no—
450C23—344no—
451C23—344no—
452C23C24×D1716yes—
453C23C24×D1711yescharacteristic
454Q8—3424no—
455Q8—3448no—
456Q8C2×#63252116yescomplemented
457D4—224no—
458D4—1716no—
459D4—3448no—
460C2×C4—26no—
461C2×C4—22no—
462C2×C4—26no—
463C2×C4—224no—
464C2×C4—224no—
465C2×C4—224no—
466C2×C4—174no—
467C2×C4—1712no—
468C2×C4—1712no—
469C2×C4—3448no—
470C2×C4—3412no—
471C2×C4—3412no—
472C2×C4—344no—
473C2×C4—3448no—
474C2×C4—3416no—
475C2×C4C2×#63252112yes—
476C2×C4#41×D1714yes—
477C2×C4#1058769714yes—
478C2×C4C24×D1716yes—
479C2×C4C24×D1712yes—
480C2×C4C24×D1716yes—
481C2×C4C24×D1712yes—
482C2×C4C24×D1716yes—
483C2×C4C24×D1712yes—
484C22—26no—
485C22—26no—
486C22—26no—
487C22—412no—
488C22—178no—
489C22—3416no—
490C22—344no—
491C22—344no—
492C22C2×#41×D1712yes—
493C22C22×#6325212yes—
494C22C2×#1058769712yes—
495C22C25×D1711yescharacteristic
496C4—26no—
497C4—22no—
498C4—26no—
499C4—3412no—
500C4—3412no—
501C4—344no—
502C4C2×#41×D1714yes—
503C4C22×#63252112yes—
504C4C2×#1058769714yes—
505C2—46no—
506C2—348no—
507C2#1454240614yesdirect product factor
508C2C22×#41×D1711yescharacteristic
509C2C23×#6325211yescharacteristic
510C2C22×#1058769711yescharacteristic
subgroupG/H
centerC22×C4C23×D17
commutator, cosocleC22×C17C26
FrattiniC22C25×D17
FittingC2×C4×#41×C17C2
socleC23×C17C25
hypercenterC2×C4×#41D17
hypocenterC17C2×#3482
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C2×C4×#41

Complements

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

NH ≅ G/Ntype
1. #14542406C2direct (N × H)
2. C2×#11763538C2semidirect
3. C2×#11763529C2semidirect
4. C2×#11763498C2semidirect
5. C2×Q8×D68C2semidirect
6. C2×#11763466C2semidirect
7. C2×#11763464C2semidirect
8. C2×#11763366C2semidirect
9. C2×#11763341C2semidirect
10. C2×C4×#63252C2semidirect
11. C2×C4×Q8×D17C2semidirect
12. C2×C4×#41×C17C2semidirect
15. #11763538C22semidirect
16. #11763529C22semidirect
17. #11763498C22semidirect
18. Q8×D68C22semidirect
19. #11763466C22semidirect
20. #11763464C22semidirect
21. #11763366C22semidirect
24. #11763341C22semidirect
34. C4×#63252C22semidirect
40. C4×Q8×D17C22semidirect
51. C4×#41×C17C22semidirect
132. C2×Q8×C17#41semidirect
155. C2×D68#41semidirect
199. Q8×C17C2×#41semidirect
223. D68C2×#41semidirect
239. C2×C4×#41D17semidirect
285. C4×#41C2×D17semidirect
308. C2×C17#3482semidirect
384. C17C2×#3482semidirect
394. C2×Q8#63252semidirect
456. Q8C2×#63252semidirect
507. C2#14542406direct (N × H)

Maximal subgroups

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

subgroupindex
#145424062
C2×#117635382
C2×#117635292
C2×#117634982
C2×Q8×D682
C2×#117634662
C2×#117634642
C2×#117633662
C2×#117633412
C2×C4×#632522
C2×C4×Q8×D172
C2×C4×#41×C172
C2×#348217