Finite Group Databasebeta

← C2×#14529014 #17035183

Subgroups — C2×#14529014 #17035183

Order 4352.

1478 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763289C211yesmaximal, characteristic
2C22×#10587496C211yesmaximal, characteristic
3C2×#11762808C211yesmaximal, characteristic
4C2×#11762674C211yesmaximal, characteristic, complemented
5#14529014C218yesmaximal, direct product factor
6C2×#11762577C211yesmaximal, characteristic, complemented
7C2×#11762568C211yesmaximal, characteristic, complemented
8C2×C17×#428C211yesmaximal, characteristic, complemented
9C22×#63252C2211yescharacteristic
10C22×#63223C2211yescharacteristic
11#11763289—22no—
12#11763289—22no—
13#11763289—22no—
14#11763289C2214yes—
15C2×C4×Dic34—21no—
16C2×C4×D68—21no—
17C2×#10587567—22no—
18C2×#10587578—21no—
19C22×C4⋊Dic17C2211yescharacteristic
20C2×C4⋊C4×D17—21no—
21C22×C4×Dic17C2211yescharacteristic
22C2×#10587496C418yescomplemented
23C2×#10587496C2214yes—
24#11762808—22no—
25#11762808C2214yes—
26C2×#10587481—21no—
27C2×#10587480—21no—
28#11762674—22no—
29#11762674C2214yescomplemented
30C2×#10587502—22no—
31#11762577C2214yescomplemented
32#11762568C2214yescomplemented
33C22×M16×C17C2211yescharacteristic
34C2×C17×#117C2211yescharacteristic
35C22×C4⋊C4×C17C2211yescharacteristic
36C17×#428—22no—
37C17×#428C2214yescomplemented
38C2×C17×#107—21no—
39C2×C17×#106—21no—
40C23×C4×C17—21no—
41C23×C4×C17C2311yescharacteristic
42C22×C22⋊D17—21no—
43C23×Dic17—21no—
44C23×Dic17D412yes—
45C2×#63252—21no—
46C2×#63252—21no—
47C2×#63252—22no—
48C2×#63252—22no—
49C2×#63252C2×C414yes—
50C2×#63252D412yes—
51C2×#63252Q814yes—
52C2×#63252C2312yes—
53C22×D68D411yescharacteristic
54C22×C4×D17—21no—
55C22×C4×D17—22no—
56C22×Dic34D411yescharacteristic
57C2×M16×C17—21no—
58C2×M16×C17—22no—
59C2×M16×C17C2×C414yescomplemented
60C2×M16×C17C2312yes—
61C22×C8×C17—21no—
62C17×#117—21no—
63C17×#117—21no—
64C17×#117D412yes—
65C17×#117C2312yes—
66C2×C4⋊C4×C17—21no—
67C2×C4⋊C4×C17—21no—
68C2×C4⋊C4×C17—21no—
69C2×C4⋊C4×C17—21no—
70C2×C4⋊C4×C17—21no—
71C2×C4⋊C4×C17D411yescharacteristic
72C2×C4⋊C4×C17D411yescharacteristic
73C2×C4⋊C4×C17C2312yes—
74C2×C22⋊C4×C17—21no—
75C2×C42×C17—21no—
76C2×#63227—22no—
77C2×C4⋊Dic17—21no—
78C2×C4⋊Dic17—21no—
79C2×C4⋊Dic17—21no—
80C2×C4⋊Dic17—21no—
81C2×C4⋊Dic17D412yes—
82C2×C4⋊Dic17C2312yes—
83C2×#63225—22no—
84C2×C4×Dic17—22no—
85C2×C4×Dic17—21no—
86C2×C4×Dic17—22no—
87C2×C4×Dic17C2×C414yescomplemented
88C2×C4×Dic17C2312yes—
89C2×#63223—21no—
90C2×#63223—22no—
91C2×#63223—22no—
92C2×#63223C2312yes—
93C22×#3622—21no—
94#10587578—24no—
95#10587578—24no—
96C4⋊C4×D17—24no—
97C4⋊C4×D17—24no—
98#10587567—28no—
99#10587567—28no—
100C4×D68—24no—
101C4×D68—24no—
102C4×Dic34—24no—
103C4×Dic34—24no—
104C17×#107—24no—
105C17×#106—24no—
106#10587502—28no—
107#10587496C2×C4116yescomplemented
108#10587481—24no—
109#10587480—24no—
110C24×C17C2×D411yescharacteristic
111C23×D17—21no—
112C22×C4×C17—21no—
113C22×C4×C17—21no—
114C22×C4×C17—22no—
115C22×C4×C17—44no—
116C22×C4×C17—41no—
117C22×C4×C17—41no—
118C22×C4×C17C22×C412yes—
119C22×C4×C17C2×D411yescharacteristic
120C22×C4×C17C2×D411yescharacteristic
121C22×C4×C17C2×D411yescharacteristic
122C22×C4×C17C2×D411yescharacteristic
123C22×C4×C17C2×D411yescharacteristic
124C22×C4×C17C2×Q812yes—
125C22×C4×C17#4112yes—
126C22×C4×C17#4112yes—
127C22×C4×C17C2411yescharacteristic
128C2×C22⋊D17—24no—
129C2×C22⋊D17—22no—
130C2×C22⋊D17—24no—
131C2×C22⋊D17—22no—
132C22×Dic17—21no—
133C22×Dic17—24no—
134C22×Dic17—22no—
135C22×Dic17—22no—
136C22×Dic17—22no—
137C22×Dic17—42no—
138C22×Dic17—42no—
139C22×Dic17—44no—
140C22×Dic17C2×D414yes—
141#63252—24no—
142#63252—24no—
143#63252—24no—
144#63252—24no—
145#63252—24no—
146#63252—22no—
147#63252—22no—
148#63252C4⋊C418yes—
149#63252C22×C414yes—
150#63252C2×Q814yes—
151C2×D68—21no—
152C2×D68—22no—
153C2×D68C4⋊C414yes—
154C2×D68C2×D412yes—
155C2×C4×D17—24no—
156C2×C4×D17—22no—
157C2×C4×D17—24no—
158C2×C4×D17—22no—
159C2×C4×D17—28no—
160C2×C4×D17—84no—
161C2×Dic34—21no—
162C2×Dic34—22no—
163C2×Dic34C4⋊C414yes—
164C2×Dic34C2×D412yes—
165M16×C17—24no—
166M16×C17—22no—
167M16×C17C22×C414yescomplemented
168C2×C8×C17—24no—
169C2×C8×C17—22no—
170C4⋊C4×C17—21no—
171C4⋊C4×C17—21no—
172C4⋊C4×C17—22no—
173C4⋊C4×C17—22no—
174C4⋊C4×C17—41no—
175C4⋊C4×C17—41no—
176C4⋊C4×C17C2×D412yes—
177C4⋊C4×C17C2×D412yes—
178C22⋊C4×C17—22no—
179C22⋊C4×C17—22no—
180C42×C17—22no—
181C42×C17—22no—
182#63227—28no—
183C4⋊Dic17—22no—
184C4⋊Dic17—22no—
185C4⋊Dic17—22no—
186C4⋊Dic17—22no—
187#63225—28no—
188C4×Dic17—28no—
189C4×Dic17—24no—
190C4×Dic17—22no—
191C4×Dic17C22×C414yescomplemented
192#63223—22no—
193#63223—22no—
194#63223—42no—
195C2×#3622—22no—
196C2×#3622—42no—
197C2×#1860—171nomaximal, Sylow
198C23×C17—22no—
199C23×C17—22no—
200C23×C17C4×D412yes—
201C23×C17#12011yescharacteristic
202C23×C17#12011yescharacteristic
203C23×C17C22⋊Q812yes—
204C23×C17C22×D411yescharacteristic
205C22×D17—22no—
206C22×D17—24no—
207C22×D17—42no—
208C22×D17—42no—
209C2×C4×C17—22no—
210C2×C4×C17—22no—
211C2×C4×C17—42no—
212C2×C4×C17—42no—
213C2×C4×C17—44no—
214C2×C4×C17—42no—
215C2×C4×C17—82no—
216C2×C4×C17—82no—
217C2×C4×C17C2×C4⋊C412yes—
218C2×C4×C17C2×C4⋊C412yes—
219C2×C4×C17C4×D412yes—
220C2×C4×C17C4×D412yes—
221C2×C4×C17C4×D412yes—
222C2×C4×C17#12011yescharacteristic
223C2×C4×C17#12011yescharacteristic
224C2×C4×C17C22⋊Q812yes—
225C2×C4×C17C22⋊Q812yes—
226C2×C4×C17C22⋊Q812yes—
227C2×C4×C17#12312yes—
228C2×C4×C17#12312yes—
229C2×C4×C17C23×C411yescharacteristic
230C2×C4×C17C22×D411yescharacteristic
231C2×C4×C17C22×D411yescharacteristic
232C2×C4×C17C22×Q811yescharacteristic
233C2×C4×C17C2×#4111yescharacteristic
234C2×C4×C17C2×#4111yescharacteristic
235C22⋊D17—24no—
236C22⋊D17—24no—
237C22⋊D17—28no—
238C2×Dic17—22no—
239C2×Dic17—24no—
240C2×Dic17—24no—
241C2×Dic17—24no—
242C2×Dic17—48no—
243C2×Dic17—42no—
244C2×Dic17—42no—
245C2×Dic17—44no—
246C2×Dic17—44no—
247C2×Dic17—82no—
248D68—22no—
249D68—24no—
250D68C2×C4⋊C414yes—
251C4×D17—24no—
252C4×D17—24no—
253C4×D17—28no—
254C4×D17—88no—
255Dic34—22no—
256Dic34—24no—
257Dic34C2×C4⋊C414yes—
258C8×C17—24no—
259#3622—42no—
260C2×#520—171no—
261C2×#428D1711yescharacteristic, complemented
262C22×#104—171no—
263C2×#417—171no—
264C2×#382—171no—
265#1860—178no—
266C2×#343—171no—
267C2×#339—171no—
268C22×C17—24no—
269C22×C17—24no—
270C22×C17—21no—
271C22×C17—21no—
272C22×C17—21no—
273C22×C17—21no—
274C22×C17#38512yes—
275C22×C17#38512yes—
276C22×C17#45412yes—
277C22×C17#45512yes—
278C22×C17C2×C4×D411yescharacteristic
279C22×C17C2×#12011yescharacteristic
280C22×C17C2×C22⋊Q811yescharacteristic
281C2×D17—24no—
282C2×D17—48no—
283C2×D17—42no—
284C2×D17—42no—
285C4×C17—42no—
286C4×C17—42no—
287C4×C17—82no—
288C4×C17#38512yes—
289C4×C17#38512yes—
290C4×C17C22×C4⋊C411yescharacteristic
291C4×C17C2×C4×D411yescharacteristic
292C4×C17C2×C22⋊Q811yescharacteristic
293C4×C17C2×#12311yescharacteristic
294Dic17—24no—
295Dic17—44no—
296Dic17—44no—
297C22×#41—171no—
298C22×M16—171no—
299C22×M16C2×D1711yescharacteristic
300#520—174no—
301#520—342no—
302#520—342no—
303#520—342no—
304C2×C4×Q8—341no—
305C2×C4×D4—341no—
306C2×C4×D4—342no—
307C2×#117—341no—
308C2×#117C2×D1711yescharacteristic
309C22×C4⋊C4—171no—
310C22×C4⋊C4—341no—
311C22×C4⋊C4C2×D1711yescharacteristic
312C22×C42—171no—
313#428—22no—
314#428C2×D1714yescomplemented
315C2×#107—21no—
316C2×#106—21no—
317C2×#104—178no—
318C2×#104—174no—
319#417—174no—
320#417—342no—
321C2×#103—341no—
322C2×#102—341no—
323#382—174no—
324#382—342no—
325C2×#95—342no—
326#343—174no—
327#339—174no—
328C2×C17—21no—
329C2×C17—21no—
330C2×C17—22no—
331C2×C17#186014yescomplemented
332C2×C17C2×#38511yescharacteristic
333C2×C17C2×#45511yescharacteristic
334C2×C17C2×#45411yescharacteristic
335D17—44no—
336C2×#41—174no—
337C2×#41—172no—
338C2×#41—174no—
339C2×#41—172no—
340C2×#41—342no—
341C2×#41—341no—
342C2×#41—342no—
343C2×#41—341no—
344C22×Q8—171no—
345C22×D4—171no—
346C22×D4—341no—
347C23×C4—21no—
348C23×C4—172no—
349C23×C4—342no—
350C23×C4—341no—
351C23×C4—341no—
352C23×C4C22×D1711yescharacteristic
353C2×M16—22no—
354C2×M16—21no—
355C2×M16—172no—
356C2×M16—341no—
357C2×M16—342no—
358C2×M16—342no—
359C2×M16C4×D1714yescomplemented
360C2×M16C22×D1712yes—
361C22×C8—21no—
362C22×C8—341no—
363C4×Q8—344no—
364C4×Q8—344no—
365C4×D4—344no—
366C4×D4—344no—
367C4×D4—348no—
368C4×D4—348no—
369#117—21no—
370#117—21no—
371#117—344no—
372#117—344no—
373#117C22⋊D1712yes—
374#117C22×D1712yes—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—172no—
381C2×C4⋊C4—172no—
382C2×C4⋊C4—344no—
383C2×C4⋊C4—342no—
384C2×C4⋊C4—341no—
385C2×C4⋊C4—341no—
386C2×C4⋊C4—341no—
387C2×C4⋊C4—341no—
388C2×C4⋊C4—344no—
389C2×C4⋊C4C22⋊D1711yescharacteristic
390C2×C4⋊C4C22⋊D1711yescharacteristic
391C2×C4⋊C4C22×D1712yes—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—342no—
394C2×C42—21no—
395C2×C42—174no—
396C2×C42—172no—
397C2×C42—342no—
398C2×C42—341no—
399C2×C42—342no—
400#107—24no—
401#106—24no—
402#104—1716no—
403#103—344no—
404#102—344no—
405#95—348no—
406C17C2×#186011yescharacteristic, complemented, Sylow
407C24—341no—
408C24D4×D1711yescharacteristic
409#41—174no—
410#41—174no—
411#41—178no—
412#41—342no—
413#41—342no—
414#41—344no—
415#41—344no—
416#41—344no—
417#41—344no—
418#41—344no—
419C2×Q8—172no—
420C2×Q8—174no—
421C2×Q8—342no—
422C2×Q8—341no—
423C2×D4—172no—
424C2×D4—174no—
425C2×D4—342no—
426C2×D4—344no—
427C2×D4—344no—
428C2×D4—342no—
429C2×D4—342no—
430C2×D4—341no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—22no—
434C22×C4—44no—
435C22×C4—41no—
436C22×C4—41no—
437C22×C4—174no—
438C22×C4—348no—
439C22×C4—341no—
440C22×C4—342no—
441C22×C4—344no—
442C22×C4—342no—
443C22×C4—344no—
444C22×C4—342no—
445C22×C4—344no—
446C22×C4—342no—
447C22×C4—342no—
448C22×C4—682no—
449C22×C4—682no—
450C22×C4—684no—
451C22×C4—1364no—
452C22×C4C2×C4×D1712yes—
453C22×C4#6325212yes—
454C22×C4D4×D1711yescharacteristic
455C22×C4D4×D1711yescharacteristic
456C22×C4D4×D1711yescharacteristic
457C22×C4Q8×D1712yes—
458C22×C4#6325612yes—
459C22×C4C2×C22⋊D1711yescharacteristic
460C22×C4C2×C22⋊D1711yescharacteristic
461C22×C4C23×D1711yescharacteristic
462M16—22no—
463M16—24no—
464M16—342no—
465M16—342no—
466M16—682no—
467M16C2×C4×D1714yescomplemented
468C2×C8—22no—
469C2×C8—24no—
470C2×C8—342no—
471C2×C8—682no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—22no—
475C4⋊C4—22no—
476C4⋊C4—41no—
477C4⋊C4—41no—
478C4⋊C4—348no—
479C4⋊C4—342no—
480C4⋊C4—342no—
481C4⋊C4—342no—
482C4⋊C4—342no—
483C4⋊C4C2×C22⋊D1712yes—
484C4⋊C4C2×C22⋊D1712yes—
485C22⋊C4—22no—
486C22⋊C4—22no—
487C22⋊C4—348no—
488C42—22no—
489C42—22no—
490C42—174no—
491C42—348no—
492C42—342no—
493C42—344no—
494C23—22no—
495C23—22no—
496C23—342no—
497C23—344no—
498C23—682no—
499C23—682no—
500C23#1058757912yes—
501C23#1058758212yes—
502C23#1058762311yescharacteristic
503C23#1058762311yescharacteristic
504C23C2×D4×D1711yescharacteristic
505Q8—174no—
506Q8—342no—
507Q8—344no—
508D4—174no—
509D4—344no—
510D4—344no—
511D4—348no—
512D4—342no—
513D4—344no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—44no—
519C2×C4—42no—
520C2×C4—82no—
521C2×C4—82no—
522C2×C4—342no—
523C2×C4—344no—
524C2×C4—344no—
525C2×C4—344no—
526C2×C4—348no—
527C2×C4—344no—
528C2×C4—344no—
529C2×C4—682no—
530C2×C4—682no—
531C2×C4—688no—
532C2×C4—684no—
533C2×C4—684no—
534C2×C4—1368no—
535C2×C4—1362no—
536C2×C4C4⋊C4×D1712yes—
537C2×C4C4⋊C4×D1712yes—
538C2×C4#1058757912yes—
539C2×C4#1058758012yes—
540C2×C4#1058758012yes—
541C2×C4#1058758212yes—
542C2×C4C4×C22⋊D1712yes—
543C2×C4C4×C22⋊D1712yes—
544C2×C4#1058762311yescharacteristic
545C2×C4#1058762311yescharacteristic
546C2×C4#1058763212yes—
547C2×C4#1058763212yes—
548C2×C4C22×C4×D1711yescharacteristic
549C2×C4C2×#6325211yescharacteristic
550C2×C4C2×D4×D1711yescharacteristic
551C2×C4C2×Q8×D1711yescharacteristic
552C2×C4C2×#6325611yescharacteristic
553C2×C4C22×C22⋊D1711yescharacteristic
554C8—24no—
555C8—682no—
556C22—21no—
557C22—21no—
558C22—21no—
559C22—21no—
560C22—24no—
561C22—24no—
562C22—344no—
563C22—682no—
564C22—682no—
565C22—688no—
566C22#1176268012yes—
567C22#1176268012yes—
568C22#1176298012yes—
569C22#1176298512yes—
570C22C2×#1058757911yescharacteristic
571C22C2×#1058762311yescharacteristic
572C22C2×#1058758211yescharacteristic
573C4—42no—
574C4—42no—
575C4—82no—
576C4—344no—
577C4—684no—
578C4—684no—
579C4#1176268012yes—
580C4#1176268012yes—
581C4C2×C4⋊C4×D1711yescharacteristic
582C4C2×C4×C22⋊D1711yescharacteristic
583C4C2×#1058763211yescharacteristic
584C4C2×#1058758011yescharacteristic
585C2—21no—
586C2—21no—
587C2—22no—
588C2—684no—
589C2#1452901414yesdirect product factor
590C2C2×#1176268011yescharacteristic
591C2C2×#1176298511yescharacteristic
592C2C2×#1176298011yescharacteristic
subgroupG/H
centerC23#10587623
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC2×C17×#428C2
socleC23×C17#120
prime radicalC22×#63252C22
cosocleC22×C4×C17C24
hypercenterC2×#428D17
hypocenterC17C2×#1860
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#428

Complements

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

NH ≅ G/Ntype
4. C2×#11762674C2semidirect
5. #14529014C2direct (N × H)
6. C2×#11762577C2semidirect
7. C2×#11762568C2semidirect
8. C2×C17×#428C2semidirect
22. C2×#10587496C4semidirect
29. #11762674C22semidirect
31. #11762577C22semidirect
32. #11762568C22semidirect
37. C17×#428C22semidirect
59. C2×M16×C17C2×C4semidirect
87. C2×C4×Dic17C2×C4semidirect
107. #10587496C2×C4semidirect
167. M16×C17C22×C4semidirect
191. C4×Dic17C22×C4semidirect
261. C2×#428D17semidirect
314. #428C2×D17semidirect
331. C2×C17#1860semidirect
359. C2×M16C4×D17semidirect
406. C17C2×#1860semidirect
467. M16C2×C4×D17semidirect
589. C2#14529014direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117632892
C22×#105874962
C2×#117628082
C2×#117626742
#145290142
C2×#117625772
C2×#117625682
C2×C17×#4282
C2×#186017