Finite Group Databasebeta

← C4×#11763032 #17040561

Subgroups — C4×#11763032 #17040561

Order 4352.

1016 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763032C211yesmaximal, characteristic
2C2×C4×Dic68C211yesmaximal, characteristic, complemented
3C2×C4×#63219C211yesmaximal, characteristic
4C4×#10587561C211yesmaximal, characteristic
5C42×Dic34C211yesmaximal, characteristic, complemented
6#14529714C211yesmaximal, characteristic
7#14529554C211yesmaximal, characteristic, complemented
8#14529419C211yesmaximal, characteristic, complemented
9#14529405C211yesmaximal, characteristic
10#14529138C211yesmaximal, characteristic
11#14529124C211yesmaximal, characteristic, complemented
12#14528800C211yesmaximal, characteristic, complemented
13C4×#10587487C211yesmaximal, characteristic, complemented
14C4×#10587492C211yesmaximal, characteristic
15C4×C17×C4⋊C8C211yesmaximal, characteristic, complemented
16C22×Dic68C2211yescharacteristic
17C22×#63219C2211yescharacteristic
18C2×#10587561C2211yescharacteristic
19C2×C4×Dic34C2211yescharacteristic
20C2×C4×Dic34C2211yescharacteristic
21C2×C4×Dic34C2211yescharacteristic
22C2×C4×Dic34C2211yescharacteristic
23C2×C4×D68C2211yescharacteristic
24#11763032C418yesdirect product factor
25C4×Dic68—24no—
26C4×#63219—24no—
27C2×#10587489C2211yescharacteristic
28C2×#10587488C2211yescharacteristic
29C2×#10587487C2211yescharacteristic
30C2×#10587487C2211yescharacteristic
31C2×#10587487C2211yescharacteristic
32C2×#10587487C2211yescharacteristic
33C2×#10587487C2211yescharacteristic
34C2×#10587492C2211yescharacteristic
35C2×#10587492C2211yescharacteristic
36C2×#10587492C2211yescharacteristic
37#11762715C2211yescharacteristic
38#11762711C2211yescharacteristic
39#11762700—21no—
40#11762700—21no—
41#11762675C2211yescharacteristic
42C4×#63225—21no—
43C4×#63225—21no—
44C4×#63225—21no—
45C4×C4⋊Dic17C2211yescharacteristic
46C4×C4⋊Dic17C2211yescharacteristic
47C4×C4⋊Dic17C2211yescharacteristic
48C4×#63227—21no—
49C4×#63227—21no—
50C42×Dic17—21no—
51#11762572C2211yescharacteristic
52#11762572C2211yescharacteristic
53#11762572C2211yescharacteristic
54#11762572C2211yescharacteristic
55C2×C17×C4⋊C8C2211yescharacteristic
56C2×C17×C4⋊C8C2211yescharacteristic
57C2×C4×C8×C17C2211yescharacteristic
58C2×C4×C8×C17C2211yescharacteristic
59C43×C17C2211yescharacteristic
60C17×#336C2211yescharacteristic
61C17×#336C2211yescharacteristic
62C22×D68C2311yescharacteristic
63C22×C4×D17—21no—
64C22×Dic34C2311yescharacteristic
65C22×Dic34C2311yescharacteristic
66C22×C8×C17C2311yescharacteristic
67C22×C8×C17C2311yescharacteristic
68C22×C8×C17C2311yescharacteristic
69C22×C8×C17C2311yescharacteristic
70C2×C42×C17D411yescharacteristic
71C2×C42×C17D411yescharacteristic
72C2×C42×C17D411yescharacteristic
73C2×C42×C17D411yescharacteristic
74C2×C42×C17C2311yescharacteristic
75C2×C42×C17C2311yescharacteristic
76C2×C42×C17C2311yescharacteristic
77C2×#63227—21no—
78C2×#63227—21no—
79C2×#63227—21no—
80C2×#63227—21no—
81C2×#63227—21no—
82C2×C4⋊Dic17C2311yescharacteristic
83C2×C4⋊Dic17C2311yescharacteristic
84C2×C4⋊Dic17C2311yescharacteristic
85C2×C4⋊Dic17C2311yescharacteristic
86C2×C4⋊Dic17C2311yescharacteristic
87C2×#63225—21no—
88C2×#63225—21no—
89C2×#63225—21no—
90C2×#63225—21no—
91C2×C4×Dic17—21no—
92C2×C4×Dic17—21no—
93C2×C4×Dic17—21no—
94C2×C4×Dic17—21no—
95C2×C4×Dic17—21no—
96C2×C4×Dic17—21no—
97C2×C4×Dic17—21no—
98C2×Dic68—22no—
99C2×Dic68—22no—
100C2×Dic68C2×C414yescomplemented
101C2×#63219—22no—
102C2×#63219—22no—
103C2×#63219C2×C414yes—
104#10587561—22no—
105#10587561C2×C414yes—
106C4×D68—22no—
107C4×D68—22no—
108C4×Dic34—22no—
109C4×Dic34—22no—
110C4×Dic34—22no—
111C4×Dic34—22no—
112C4×Dic34—22no—
113C4×Dic34—22no—
114C4×Dic34C2×C414yescomplemented
115C4×Dic34D414yes—
116C17×C4⋊C8—22no—
117C17×C4⋊C8C2×C414yescomplemented
118C4×C8×C17—22no—
119C4×C8×C17—22no—
120#10587502—21no—
121#10587502—21no—
122#10587502—21no—
123#10587502—21no—
124#10587502—21no—
125#10587502—21no—
126#10587502—21no—
127#10587492—22no—
128#10587492—22no—
129#10587492C2×C414yes—
130#10587489—22no—
131#10587488—22no—
132#10587487—22no—
133#10587487—22no—
134#10587487—22no—
135#10587487—22no—
136#10587487C2×C414yescomplemented
137C23×D17—21no—
138C22×C4×C17C2×D411yescharacteristic
139C22×C4×C17C2×D411yescharacteristic
140C22×C4×C17C2×D411yescharacteristic
141C22×C4×C17C2×D411yescharacteristic
142C22×C4×C17C2×D411yescharacteristic
143C22×C4×C17C2×D411yescharacteristic
144C22×C4×C17C2411yescharacteristic
145C22×Dic17—21no—
146C22×Dic17—21no—
147C22×Dic17—21no—
148C22×Dic17—21no—
149C22×Dic17—21no—
150C22×Dic17—21no—
151C22×Dic17—21no—
152C2×D68—21no—
153C2×D68—21no—
154C2×D68—21no—
155C2×D68—21no—
156C2×D68—21no—
157C2×D68C22×C412yes—
158C2×C4×D17—42no—
159C2×C4×D17—42no—
160C2×C4×D17—42no—
161C2×Dic34—21no—
162C2×Dic34—21no—
163C2×Dic34—21no—
164C2×Dic34—21no—
165C2×Dic34—21no—
166C2×Dic34—21no—
167C2×Dic34—21no—
168C2×Dic34—21no—
169C2×Dic34C22×C412yes—
170C2×Dic34C22×C412yes—
171C2×Dic34C2×D412yes—
172C2×Dic34#4112yes—
173C2×C8×C17—21no—
174C2×C8×C17—21no—
175C2×C8×C17—21no—
176C2×C8×C17—21no—
177C2×C8×C17—21no—
178C2×C8×C17—21no—
179C2×C8×C17—21no—
180C2×C8×C17—21no—
181C2×C8×C17—21no—
182C2×C8×C17—21no—
183C2×C8×C17C22×C412yes—
184C2×C8×C17C22×C412yes—
185C42×C17—22no—
186C42×C17—22no—
187C42×C17—22no—
188C42×C17—21no—
189C42×C17—21no—
190C42×C17—41no—
191C42×C17C22×C412yes—
192C42×C17C2×D412yes—
193C42×C17#4112yes—
194C42×C17#4112yes—
195#63227—24no—
196#63227—24no—
197#63227—42no—
198#63227—42no—
199#63227—42no—
200C4⋊Dic17—21no—
201C4⋊Dic17—21no—
202C4⋊Dic17—21no—
203C4⋊Dic17—21no—
204C4⋊Dic17—21no—
205C4⋊Dic17—21no—
206C4⋊Dic17—21no—
207C4⋊Dic17C22×C412yes—
208C4⋊Dic17C2×D412yes—
209C4⋊Dic17#4112yes—
210#63225—24no—
211#63225—24no—
212#63225—24no—
213#63225—42no—
214C4×Dic17—24no—
215C4×Dic17—24no—
216C4×Dic17—24no—
217C4×Dic17—42no—
218C4×Dic17—42no—
219C4×Dic17—42no—
220C4×Dic17—42no—
221Dic68—28no—
222#63219—28no—
223C4×#464—171nomaximal, Sylow
224C23×C17C22×D411yescharacteristic
225C22×D17—22no—
226C22×D17—41no—
227C22×D17—41no—
228C22×D17—41no—
229C22×D17—41no—
230C22×D17—41no—
231C22×D17—41no—
232C2×C4×C17—21no—
233C2×C4×C17—21no—
234C2×C4×C17—21no—
235C2×C4×C17—21no—
236C2×C4×C17—21no—
237C2×C4×C17—21no—
238C2×C4×C17—21no—
239C2×C4×C17—21no—
240C2×C4×C17—21no—
241C2×C4×C17—21no—
242C2×C4×C17—21no—
243C2×C4×C17C4×D412yes—
244C2×C4×C17C4×D412yes—
245C2×C4×C17#12112yes—
246C2×C4×C17#12112yes—
247C2×C4×C17#13512yes—
248C2×C4×C17#13512yes—
249C2×C4×C17#13712yes—
250C2×C4×C17C23×C411yescharacteristic
251C2×C4×C17C22×D411yescharacteristic
252C2×C4×C17C2×#4111yescharacteristic
253C2×C4×C17C2×#4111yescharacteristic
254C2×C4×C17C2×#4111yescharacteristic
255C2×C4×C17C2×#4111yescharacteristic
256C2×Dic17—22no—
257C2×Dic17—22no—
258C2×Dic17—22no—
259C2×Dic17—22no—
260C2×Dic17—22no—
261C2×Dic17—22no—
262C2×Dic17—22no—
263C2×Dic17—41no—
264C2×Dic17—41no—
265C2×Dic17—41no—
266C2×Dic17—41no—
267C2×Dic17—41no—
268C2×Dic17—41no—
269C2×Dic17—41no—
270C2×Dic17—41no—
271C2×Dic17—41no—
272C2×Dic17—41no—
273C2×Dic17—41no—
274C2×Dic17—41no—
275C2×Dic17—41no—
276C2×Dic17—41no—
277D68—22no—
278D68—22no—
279D68—41no—
280D68—41no—
281C4×D17—84no—
282Dic34—22no—
283Dic34—22no—
284Dic34—22no—
285Dic34—22no—
286Dic34—22no—
287Dic34—41no—
288Dic34—41no—
289Dic34C4×D414yes—
290C8×C17—22no—
291C8×C17—22no—
292C8×C17—41no—
293C8×C17—41no—
294C2×#464—171no—
295C2×C4×Q16—171no—
296C2×C4×SD16—171no—
297C4×#124—171no—
298C42×Q8—171no—
299#1983—171no—
300#1949—171no—
301#1927—171no—
302#1925—171no—
303#1880—171no—
304#1878—171no—
305#1805—171no—
306C4×C4⋊C8D1711yescharacteristic, complemented
307C4×#103—171no—
308C4×#102—171no—
309C22×C17C2×C4×D411yescharacteristic
310C22×C17C2×#12111yescharacteristic
311C22×C17#52511yescharacteristic
312C22×C17C2×#13511yescharacteristic
313C22×C17C2×#13511yescharacteristic
314C22×C17C2×#13711yescharacteristic
315C22×C17#57511yescharacteristic
316C2×D17—42no—
317C2×D17—42no—
318C2×D17—42no—
319C2×D17—81no—
320C2×D17—81no—
321C2×D17—81no—
322C2×D17—81no—
323C4×C17—22no—
324C4×C17—22no—
325C4×C17—22no—
326C4×C17—22no—
327C4×C17—41no—
328C4×C17#46414yescomplemented
329C4×C17C2×C4×D411yescharacteristic
330C4×C17C4×#4111yescharacteristic
331C4×C17#52911yescharacteristic
332C4×C17#53211yescharacteristic
333Dic17—24no—
334Dic17—42no—
335Dic17—42no—
336Dic17—42no—
337Dic17—42no—
338Dic17—81no—
339Dic17—81no—
340C22×Q16—171no—
341C22×SD16—171no—
342C2×#124—171no—
343C2×C4×Q8—171no—
344C2×C4×Q8—171no—
345C2×C4×Q8—171no—
346C2×C4×Q8—171no—
347C2×C4×D4—171no—
348#464—178no—
349C4×Q16—344no—
350C4×SD16—344no—
351C2×#107—171no—
352C2×#106—171no—
353C2×C4⋊C8C2×D1711yescharacteristic
354C2×C4⋊C8C2×D1711yescharacteristic
355C2×#103—171no—
356C2×#103—171no—
357C2×#103—171no—
358C2×#103—171no—
359C2×#103—171no—
360C2×#102—171no—
361C2×#102—171no—
362C2×#102—171no—
363C2×C4×C8C2×D1711yescharacteristic
364C2×C4×C8C2×D1711yescharacteristic
365#391—171no—
366#390—171no—
367#388—341no—
368#388—341no—
369#382—171no—
370C4×C4⋊C4—171no—
371C4×C4⋊C4—171no—
372C4×C4⋊C4—171no—
373C4×C4⋊C4—341no—
374C4×C4⋊C4—341no—
375C4×C4⋊C4—341no—
376C4×C22⋊C4—341no—
377C4×C22⋊C4—341no—
378C43—341no—
379C43C2×D1711yescharacteristic
380#340—171no—
381#340—171no—
382#340—171no—
383#340—171no—
384#336C2×D1711yescharacteristic
385#336C2×D1711yescharacteristic
386C2×C17C4×#12111yescharacteristic
387C2×C17C4×#13511yescharacteristic
388C2×C17C4×#13711yescharacteristic
389C2×C17C2×#46411yescharacteristic
390C2×C17#303511yescharacteristic
391C2×C17#310211yescharacteristic
392C2×C17#310811yescharacteristic
393D17—82no—
394C22×Q8—171no—
395C22×Q8—171no—
396C22×D4—171no—
397C23×C4—341no—
398C2×Q16—174no—
399C2×Q16—342no—
400C2×Q16—342no—
401C2×SD16—174no—
402C2×SD16—342no—
403C2×SD16—342no—
404C22×C8C22×D1711yescharacteristic
405C22×C8C22×D1711yescharacteristic
406C22×C8C22×D1711yescharacteristic
407C22×C8C22×D1711yescharacteristic
408#124—174no—
409#124—342no—
410C4×Q8—174no—
411C4×Q8—174no—
412C4×Q8—342no—
413C4×Q8—342no—
414C4×Q8—342no—
415C4×Q8—342no—
416C4×Q8—342no—
417C4×Q8—342no—
418C4×D4—342no—
419C4×D4—342no—
420C2×C4⋊C4—171no—
421C2×C4⋊C4—171no—
422C2×C4⋊C4—171no—
423C2×C4⋊C4—171no—
424C2×C4⋊C4—171no—
425C2×C4⋊C4—341no—
426C2×C4⋊C4—341no—
427C2×C4⋊C4—341no—
428C2×C4⋊C4—341no—
429C2×C22⋊C4—341no—
430C2×C22⋊C4—341no—
431C2×C22⋊C4—341no—
432C2×C22⋊C4—341no—
433C2×C22⋊C4—341no—
434C2×C42—341no—
435C2×C42—341no—
436C2×C42—341no—
437C2×C42—341no—
438C2×C42—341no—
439C2×C42—341no—
440C2×C42—341no—
441C2×C42D6811yescharacteristic
442C2×C42D6811yescharacteristic
443C2×C42D6811yescharacteristic
444C2×C42D6811yescharacteristic
445C2×C42C22×D1711yescharacteristic
446C2×C42C22×D1711yescharacteristic
447C2×C42C22×D1711yescharacteristic
448#107—342no—
449#106—342no—
450C4⋊C8—22no—
451C4⋊C8C4×D1714yescomplemented
452#103—174no—
453#103—342no—
454#103—342no—
455#103—342no—
456#103—342no—
457#102—174no—
458#102—342no—
459#102—342no—
460C4×C8—22no—
461C4×C8—22no—
462#95—341no—
463#95—341no—
464#95—341no—
465#95—341no—
466#95—341no—
467#95—341no—
468#95—341no—
469C17C4×#46411yescharacteristic, complemented, Sylow
470C24—341no—
471C2×Q8—172no—
472C2×Q8—172no—
473C2×Q8—172no—
474C2×Q8—172no—
475C2×Q8—341no—
476C2×Q8—341no—
477C2×Q8—341no—
478C2×Q8—341no—
479C2×Q8—341no—
480C2×Q8—341no—
481C2×Q8—341no—
482C2×Q8—341no—
483C2×D4—172no—
484C2×D4—341no—
485C2×D4—341no—
486C2×D4—341no—
487C2×D4—341no—
488C2×D4—341no—
489C22×C4—341no—
490C22×C4—341no—
491C22×C4—341no—
492C22×C4—341no—
493C22×C4—341no—
494C22×C4—341no—
495C22×C4—341no—
496C22×C4—682no—
497C22×C4—682no—
498C22×C4—682no—
499C22×C4C2×D6811yescharacteristic
500C22×C4C2×D6811yescharacteristic
501C22×C4C2×D6811yescharacteristic
502C22×C4C2×D6811yescharacteristic
503C22×C4C2×D6811yescharacteristic
504C22×C4C2×D6811yescharacteristic
505C22×C4C23×D1711yescharacteristic
506Q16—348no—
507SD16—348no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8C2×C4×D1712yes—
519C2×C8C2×C4×D1712yes—
520C4⋊C4—172no—
521C4⋊C4—172no—
522C4⋊C4—172no—
523C4⋊C4—344no—
524C4⋊C4—341no—
525C4⋊C4—341no—
526C4⋊C4—341no—
527C4⋊C4—344no—
528C4⋊C4—344no—
529C4⋊C4—341no—
530C4⋊C4—341no—
531C4⋊C4—341no—
532C4⋊C4—341no—
533C4⋊C4—682no—
534C22⋊C4—344no—
535C22⋊C4—344no—
536C22⋊C4—682no—
537C22⋊C4—682no—
538C22⋊C4—682no—
539C42—21no—
540C42—21no—
541C42—22no—
542C42—22no—
543C42—22no—
544C42—41no—
545C42—344no—
546C42—344no—
547C42—344no—
548C42—682no—
549C42—682no—
550C42—682no—
551C42—682no—
552C42C2×C4×D1712yes—
553C42#6325212yes—
554C42D4×D1712yes—
555C42#6325612yes—
556C23—342no—
557C23—681no—
558C23—681no—
559C23—681no—
560C23—681no—
561C23—681no—
562C23—681no—
563C23C22×D6811yescharacteristic
564Q8—174no—
565Q8—342no—
566Q8—342no—
567Q8—342no—
568Q8—342no—
569Q8—342no—
570Q8—681no—
571Q8—681no—
572D4—342no—
573D4—342no—
574D4—681no—
575D4—681no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—342no—
588C2×C4—342no—
589C2×C4—342no—
590C2×C4—342no—
591C2×C4—342no—
592C2×C4—342no—
593C2×C4—342no—
594C2×C4—681no—
595C2×C4—681no—
596C2×C4—681no—
597C2×C4—681no—
598C2×C4—681no—
599C2×C4—681no—
600C2×C4—681no—
601C2×C4—681no—
602C2×C4—681no—
603C2×C4—681no—
604C2×C4—681no—
605C2×C4—681no—
606C2×C4—681no—
607C2×C4—681no—
608C2×C4—1364no—
609C2×C4C4×D6812yes—
610C2×C4C4×D6812yes—
611C2×C4#1058758112yes—
612C2×C4#1058758112yes—
613C2×C4#1058759012yes—
614C2×C4#1058759012yes—
615C2×C4#1058759512yes—
616C2×C4C22×C4×D1711yescharacteristic
617C2×C4C2×#6325211yescharacteristic
618C2×C4C2×D4×D1711yescharacteristic
619C2×C4C2×#6325611yescharacteristic
620C2×C4#41×D1711yescharacteristic
621C2×C4#41×D1711yescharacteristic
622C8—22no—
623C8—22no—
624C8—41no—
625C8—41no—
626C22—682no—
627C22—682no—
628C22—682no—
629C22—1361no—
630C22—1361no—
631C22—1361no—
632C22—1361no—
633C22C2×C4×D6811yescharacteristic
634C22C2×#1058758111yescharacteristic
635C22#1176332111yescharacteristic
636C22C2×#1058759011yescharacteristic
637C22C2×#1058759011yescharacteristic
638C22C2×#1058759511yescharacteristic
639C22#1176360911yescharacteristic
640C4—22no—
641C4—22no—
642C4—22no—
643C4—22no—
644C4—41no—
645C4—344no—
646C4—682no—
647C4—682no—
648C4—682no—
649C4—682no—
650C4—1361no—
651C4—1361no—
652C4#1176303214yesdirect product factor
653C4C4×D4×D1711yescharacteristic
654C4C4×#6325611yescharacteristic
655C4#1176334611yescharacteristic
656C4#1176335611yescharacteristic
657C2—1362no—
658C2C4×#1058758111yescharacteristic
659C2C4×#1058759011yescharacteristic
660C2C4×#1058759511yescharacteristic
661C2C2×#1176303211yescharacteristic
662C2#1453824111yescharacteristic
663C2#1453880411yescharacteristic
664C2#1453886611yescharacteristic
subgroupG/H
centerC22×C4C2×D68
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC4×C17×C4⋊C8C2
socleC23×C17C22×D4
prime radicalC22×D68C23
cosocleC22×C4×C17C24
hypercenterC4×C4⋊C8D17
hypocenterC17C4×#464
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C43 ◁ C4×C4⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×C4×Dic68C2semidirect
5. C42×Dic34C2semidirect
7. #14529554C2semidirect
8. #14529419C2semidirect
11. #14529124C2semidirect
12. #14528800C2semidirect
13. C4×#10587487C2semidirect
15. C4×C17×C4⋊C8C2semidirect
24. #11763032C4direct (N × H)
100. C2×Dic68C2×C4semidirect
114. C4×Dic34C2×C4semidirect
117. C17×C4⋊C8C2×C4semidirect
136. #10587487C2×C4semidirect
306. C4×C4⋊C8D17semidirect
328. C4×C17#464semidirect
451. C4⋊C8C4×D17semidirect
469. C17C4×#464semidirect
652. C4#11763032direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117630322
C2×C4×Dic682
C2×C4×#632192
C4×#105875612
C42×Dic342
#145297142
#145295542
#145294192
#145294052
#145291382
#145291242
#145288002
C4×#105874872
C4×#105874922
C4×C17×C4⋊C82
C4×#46417