Finite Group Databasebeta

← C4×#11763065 #17040975

Subgroups — C4×#11763065 #17040975

Order 4352.

1002 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763065C211yesmaximal, characteristic
2C2×C4×#63231C211yesmaximal, characteristic, complemented
3C2×C4×#63223C211yesmaximal, characteristic
4C4×#10587610C211yesmaximal, characteristic
5#14529654C211yesmaximal, characteristic, complemented
6#14529524C211yesmaximal, characteristic, complemented
7#14529477C211yesmaximal, characteristic, complemented
8#14529473C211yesmaximal, characteristic, complemented
9#14529218C211yesmaximal, characteristic
10#14529215C211yesmaximal, characteristic
11#14528815C211yesmaximal, characteristic
12C4×#10587479C211yesmaximal, characteristic, complemented
13C4×#10587481C211yesmaximal, characteristic, complemented
14C4×#10587506C211yesmaximal, characteristic, complemented
15C4×C17×C22⋊Q8C211yesmaximal, characteristic
16C22×#63231C2211yescharacteristic
17C22×#63223C2211yescharacteristic
18C22×#63223C2211yescharacteristic
19C2×#10587610C2211yescharacteristic
20C2×C4×Dic34C2211yescharacteristic
21#11763065C418yesdirect product factor
22C4×#63231—24no—
23C2×#10587478C2211yescharacteristic
24C2×#10587479C2211yescharacteristic
25C2×#10587479C2211yescharacteristic
26C2×#10587506C2211yescharacteristic
27C2×#10587506C2211yescharacteristic
28C2×#10587506C2211yescharacteristic
29C2×#10587481C2211yescharacteristic
30C2×#10587481C2211yescharacteristic
31C2×#10587481C2211yescharacteristic
32C4×#63223—24no—
33C2×#10587474C2211yescharacteristic
34C2×#10587474C2211yescharacteristic
35C2×C4×#3622C2211yescharacteristic
36C2×C4×#3622C2211yescharacteristic
37#11762715C2211yescharacteristic
38#11762707C2211yescharacteristic
39#11762693—21no—
40#11762682—21no—
41#11762669C2211yescharacteristic
42C4×#63225—21no—
43C4×C4⋊Dic17C2211yescharacteristic
44C4×C22⋊Dic17—21no—
45#11762571C2211yescharacteristic
46#11762571C2211yescharacteristic
47#11762571C2211yescharacteristic
48#11762571C2211yescharacteristic
49#11762571C2211yescharacteristic
50#11762571C2211yescharacteristic
51C2×C17×C22⋊Q8C2211yescharacteristic
52C2×C4×Q8×C17C2211yescharacteristic
53C22×C42×C17C2211yescharacteristic
54C17×#391C2211yescharacteristic
55C17×#389C2211yescharacteristic
56C17×#387—21no—
57C17×#385—21no—
58C17×#380C2211yescharacteristic
59C4×C4⋊C4×C17—21no—
60C4×C4⋊C4×C17C2211yescharacteristic
61C4×C22⋊C4×C17—21no—
62C22×Q8×C17C2311yescharacteristic
63C23×C4×C17D411yescharacteristic
64C23×C4×C17D411yescharacteristic
65C23×C4×C17C2311yescharacteristic
66C22×Dic34C2311yescharacteristic
67C17×C22⋊Q8—22no—
68C17×C22⋊Q8C2×C414yes—
69C4×Q8×C17—22no—
70C4×Q8×C17—22no—
71C2×C4⋊C4×C17—21no—
72C2×C4⋊C4×C17—21no—
73C2×C4⋊C4×C17—21no—
74C2×C4⋊C4×C17C2311yescharacteristic
75C2×C4⋊C4×C17C2311yescharacteristic
76C2×C4⋊C4×C17C2311yescharacteristic
77C2×C22⋊C4×C17—21no—
78C2×C22⋊C4×C17—21no—
79C2×C42×C17—22no—
80C2×C42×C17—22no—
81C2×C42×C17—21no—
82C2×C42×C17—21no—
83C2×C42×C17D411yescharacteristic
84C2×C42×C17D411yescharacteristic
85C2×C42×C17C2311yescharacteristic
86C2×C42×C17C2311yescharacteristic
87C2×C22⋊Dic17—21no—
88C2×C22⋊Dic17—21no—
89C2×#63231—22no—
90C2×#63231—22no—
91C2×#63231C2×C414yescomplemented
92C2×C4⋊Dic17C2311yescharacteristic
93C2×C4⋊Dic17C2311yescharacteristic
94C2×C4⋊Dic17C2311yescharacteristic
95#10587610—22no—
96#10587610C2×C414yes—
97C2×#63225—21no—
98C2×#63225—21no—
99C2×#63225—21no—
100C2×C4×Dic17—21no—
101C2×C4×Dic17—21no—
102C2×#63223—22no—
103C2×#63223—22no—
104C2×#63223—22no—
105C2×#63223—22no—
106C2×#63223—22no—
107C2×#63223C2×C414yes—
108C22×#3622C2311yescharacteristic
109C22×#3622C2311yescharacteristic
110C22×#3622C2311yescharacteristic
111C22×#3622C2311yescharacteristic
112C4×Dic34—22no—
113C4×Dic34—22no—
114C17×#95—21no—
115C17×#95—21no—
116C17×#95—21no—
117C17×#95—21no—
118C17×#95—21no—
119#10587506—22no—
120#10587506—22no—
121#10587506C2×C414yescomplemented
122#10587502—21no—
123#10587502—21no—
124#10587502—21no—
125#10587502—21no—
126#10587502—21no—
127#10587481—22no—
128#10587481—22no—
129#10587481C2×C414yescomplemented
130#10587479—22no—
131#10587479C2×C414yescomplemented
132#10587478—22no—
133#10587474—22no—
134#10587474—22no—
135C4×#3622—22no—
136C4×#3622D414yes—
137C24×C17C2×D411yescharacteristic
138C2×Q8×C17—21no—
139C2×Q8×C17—21no—
140C2×Q8×C17—21no—
141C2×Q8×C17—21no—
142C2×Q8×C17—21no—
143C2×Q8×C17C22×C412yes—
144C22×C4×C17—21no—
145C22×C4×C17—21no—
146C22×C4×C17—21no—
147C22×C4×C17—21no—
148C22×C4×C17—21no—
149C22×C4×C17—21no—
150C22×C4×C17—22no—
151C22×C4×C17—22no—
152C22×C4×C17—22no—
153C22×C4×C17—22no—
154C22×C4×C17—21no—
155C22×C4×C17—21no—
156C22×C4×C17—41no—
157C22×C4×C17—41no—
158C22×C4×C17C22×C412yes—
159C22×C4×C17C2×D411yescharacteristic
160C22×C4×C17C2×D411yescharacteristic
161C22×C4×C17C2×D411yescharacteristic
162C22×C4×C17C2×D411yescharacteristic
163C22×C4×C17C2×D411yescharacteristic
164C22×C4×C17#4112yes—
165C22×C4×C17C2411yescharacteristic
166C22×Dic17—21no—
167C22×Dic17—21no—
168C22×Dic17—21no—
169C22×Dic17—21no—
170C2×Dic34—21no—
171C2×Dic34—21no—
172C2×Dic34—21no—
173C2×Dic34—21no—
174C2×Dic34—21no—
175C2×Dic34C22×C412yes—
176C4⋊C4×C17—24no—
177C4⋊C4×C17—21no—
178C4⋊C4×C17—21no—
179C4⋊C4×C17—21no—
180C4⋊C4×C17—21no—
181C4⋊C4×C17—21no—
182C4⋊C4×C17—42no—
183C4⋊C4×C17—42no—
184C4⋊C4×C17C22×C412yes—
185C22⋊C4×C17—24no—
186C22⋊C4×C17—42no—
187C42×C17—22no—
188C42×C17—22no—
189C42×C17—21no—
190C42×C17—21no—
191C42×C17—42no—
192C42×C17—42no—
193C42×C17C2×D412yes—
194C42×C17#4112yes—
195C22⋊Dic17—24no—
196C22⋊Dic17—42no—
197#63231—28no—
198C4⋊Dic17—21no—
199C4⋊Dic17—21no—
200C4⋊Dic17—21no—
201C4⋊Dic17—21no—
202C4⋊Dic17—21no—
203C4⋊Dic17C22×C412yes—
204#63225—24no—
205#63225—42no—
206#63225—42no—
207C4×Dic17—42no—
208C4×Dic17—42no—
209#63223—28no—
210#63223—28no—
211C2×#3622—21no—
212C2×#3622—21no—
213C2×#3622—21no—
214C2×#3622—21no—
215C2×#3622—21no—
216C2×#3622—21no—
217C2×#3622C22×C412yes—
218C2×#3622C22×C412yes—
219C2×#3622C2×D412yes—
220C2×#3622C2×D412yes—
221C2×#3622#4112yes—
222C2×#3622#4112yes—
223C4×#470—171nomaximal, Sylow
224C23×C17—21no—
225C23×C17—21no—
226C23×C17—21no—
227C23×C17—21no—
228C23×C17—21no—
229C23×C17—21no—
230C23×C17C4×D412yes—
231C23×C17C22×D411yescharacteristic
232Q8×C17—22no—
233Q8×C17—22no—
234Q8×C17—41no—
235Q8×C17—41no—
236C2×C4×C17—21no—
237C2×C4×C17—21no—
238C2×C4×C17—21no—
239C2×C4×C17—21no—
240C2×C4×C17—22no—
241C2×C4×C17—22no—
242C2×C4×C17—22no—
243C2×C4×C17—22no—
244C2×C4×C17—22no—
245C2×C4×C17—22no—
246C2×C4×C17—21no—
247C2×C4×C17—21no—
248C2×C4×C17—21no—
249C2×C4×C17—21no—
250C2×C4×C17—21no—
251C2×C4×C17—21no—
252C2×C4×C17—44no—
253C2×C4×C17—41no—
254C2×C4×C17—41no—
255C2×C4×C17—41no—
256C2×C4×C17—41no—
257C2×C4×C17—44no—
258C2×C4×C17—41no—
259C2×C4×C17—41no—
260C2×C4×C17—41no—
261C2×C4×C17—41no—
262C2×C4×C17—41no—
263C2×C4×C17—41no—
264C2×C4×C17C4×D412yes—
265C2×C4×C17#12112yes—
266C2×C4×C17#12112yes—
267C2×C4×C17#13712yes—
268C2×C4×C17#13712yes—
269C2×C4×C17C23×C411yescharacteristic
270C2×C4×C17C22×D411yescharacteristic
271C2×C4×C17C2×#4111yescharacteristic
272C2×C4×C17C2×#4111yescharacteristic
273C2×C4×C17C2×#4111yescharacteristic
274C2×C4×C17C2×#4111yescharacteristic
275C2×Dic17—22no—
276C2×Dic17—22no—
277C2×Dic17—41no—
278C2×Dic17—41no—
279C2×Dic17—41no—
280C2×Dic17—41no—
281C2×Dic17—41no—
282C2×Dic17—41no—
283C2×Dic17—41no—
284C2×Dic17—41no—
285C2×Dic17—41no—
286C2×Dic17—41no—
287Dic34—22no—
288Dic34—22no—
289Dic34—41no—
290Dic34—41no—
291#3622—22no—
292#3622—22no—
293#3622—22no—
294#3622C4×D414yes—
295C2×#470—171no—
296C2×C4×Q16—171no—
297C2×C4×M16—171no—
298C4×C22⋊Q8—171no—
299C4×C22⋊Q8D1711yescharacteristic
300#1971—171no—
301#1944—171no—
302#1935—171no—
303#1935—171no—
304#1894—171no—
305#1894—171no—
306#1809—171no—
307C4×#106—171no—
308C4×#103—171no—
309C4×#103—171no—
310C22×C17—22no—
311C22×C17—22no—
312C22×C17—22no—
313C22×C17—41no—
314C22×C17—41no—
315C22×C17—41no—
316C22×C17—41no—
317C22×C17C2×C4×D411yescharacteristic
318C22×C17C2×#12111yescharacteristic
319C22×C17#53211yescharacteristic
320C22×C17C2×#13711yescharacteristic
321C22×C17C2×#13711yescharacteristic
322C22×C17#57511yescharacteristic
323C22×C17#57511yescharacteristic
324C4×C17—22no—
325C4×C17—22no—
326C4×C17—42no—
327C4×C17—41no—
328C4×C17—41no—
329C4×C17—42no—
330C4×C17—81no—
331C4×C17—81no—
332C4×C17#47014yescomplemented
333C4×C17C2×C4×D411yescharacteristic
334C4×C17C4×#4111yescharacteristic
335C4×C17#52511yescharacteristic
336C4×C17#52911yescharacteristic
337Dic17—42no—
338Dic17—42no—
339Dic17—81no—
340Dic17—81no—
341C22×Q16—171no—
342C22×M16—171no—
343C22×M16—171no—
344C2×C22⋊Q8—171no—
345C2×C22⋊Q8C2×D1711yescharacteristic
346C2×C4×Q8—171no—
347C2×C4×Q8C2×D1711yescharacteristic
348C22×C42C2×D1711yescharacteristic
349#470—178no—
350C4×Q16—344no—
351C2×#107—171no—
352C2×#106—171no—
353C2×#106—171no—
354C2×#103—171no—
355C2×#103—171no—
356C2×#103—171no—
357C2×#103—171no—
358C2×#103—171no—
359C2×#103—171no—
360C4×M16—344no—
361C2×#97—171no—
362C2×#97—171no—
363C2×C4×C8—171no—
364C2×C4×C8—171no—
365#391—171no—
366#391C2×D1711yescharacteristic
367#389—171no—
368#389C2×D1711yescharacteristic
369#387—21no—
370#387—341no—
371#385—21no—
372#385—341no—
373#380—171no—
374#380C2×D1711yescharacteristic
375C4×C4⋊C4—21no—
376C4×C4⋊C4—171no—
377C4×C4⋊C4—341no—
378C4×C4⋊C4C2×D1711yescharacteristic
379C4×C22⋊C4—21no—
380C4×C22⋊C4—341no—
381#340—171no—
382#340—171no—
383#340—171no—
384#340—171no—
385#340—171no—
386#340—171no—
387C2×C17—42no—
388C2×C17C4×#12111yescharacteristic
389C2×C17C4×#13711yescharacteristic
390C2×C17C4×#13711yescharacteristic
391C2×C17C2×#47011yescharacteristic
392C2×C17#305411yescharacteristic
393C2×C17#317211yescharacteristic
394C2×C17#317211yescharacteristic
395C22×Q8—171no—
396C22×Q8C22×D1711yescharacteristic
397C23×C4C22⋊D1711yescharacteristic
398C23×C4C22⋊D1711yescharacteristic
399C23×C4C22×D1711yescharacteristic
400C2×Q16—174no—
401C2×Q16—342no—
402C2×Q16—342no—
403C2×M16—174no—
404C2×M16—342no—
405C2×M16—342no—
406C2×M16—342no—
407C2×M16—342no—
408C2×M16—342no—
409C22×C8—171no—
410C22×C8—171no—
411C22×C8—171no—
412C22×C8—171no—
413C22⋊Q8—22no—
414C22⋊Q8—174no—
415C22⋊Q8—342no—
416C22⋊Q8C4×D1714yes—
417C4×Q8—22no—
418C4×Q8—22no—
419C4×Q8—342no—
420C4×Q8—342no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—171no—
425C2×C4⋊C4—171no—
426C2×C4⋊C4—171no—
427C2×C4⋊C4—341no—
428C2×C4⋊C4—341no—
429C2×C4⋊C4—341no—
430C2×C4⋊C4C22×D1711yescharacteristic
431C2×C4⋊C4C22×D1711yescharacteristic
432C2×C4⋊C4C22×D1711yescharacteristic
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—341no—
436C2×C22⋊C4—341no—
437C2×C42—22no—
438C2×C42—22no—
439C2×C42—21no—
440C2×C42—21no—
441C2×C42—341no—
442C2×C42—341no—
443C2×C42C22⋊D1711yescharacteristic
444C2×C42C22⋊D1711yescharacteristic
445C2×C42C22×D1711yescharacteristic
446C2×C42C22×D1711yescharacteristic
447#107—342no—
448#106—174no—
449#106—342no—
450#103—174no—
451#103—174no—
452#103—342no—
453#103—342no—
454#103—342no—
455#103—342no—
456#97—342no—
457#97—342no—
458C4×C8—174no—
459C4×C8—342no—
460#95—21no—
461#95—21no—
462#95—21no—
463#95—21no—
464#95—21no—
465#95—341no—
466#95—341no—
467#95—341no—
468#95—341no—
469#95—341no—
470C17C4×#47011yescharacteristic, complemented, Sylow
471C24C2×C22⋊D1711yescharacteristic
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—172no—
478C2×Q8—341no—
479C2×Q8—341no—
480C2×Q8—341no—
481C2×Q8—341no—
482C2×Q8—341no—
483C2×Q8C2×C4×D1712yes—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—41no—
497C22×C4—41no—
498C22×C4—341no—
499C22×C4—341no—
500C22×C4—341no—
501C22×C4—341no—
502C22×C4C2×C4×D1712yes—
503C22×C4#6325212yes—
504C22×C4C2×C22⋊D1711yescharacteristic
505C22×C4C2×C22⋊D1711yescharacteristic
506C22×C4C2×C22⋊D1711yescharacteristic
507C22×C4C2×C22⋊D1711yescharacteristic
508C22×C4C2×C22⋊D1711yescharacteristic
509C22×C4C23×D1711yescharacteristic
510Q16—348no—
511M16—348no—
512M16—348no—
513C2×C8—172no—
514C2×C8—172no—
515C2×C8—172no—
516C2×C8—172no—
517C2×C8—172no—
518C2×C8—172no—
519C2×C8—341no—
520C2×C8—341no—
521C2×C8—341no—
522C2×C8—341no—
523C2×C8—341no—
524C2×C8—341no—
525C4⋊C4—21no—
526C4⋊C4—24no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—42no—
532C4⋊C4—42no—
533C4⋊C4—172no—
534C4⋊C4—341no—
535C4⋊C4—344no—
536C4⋊C4—341no—
537C4⋊C4—341no—
538C4⋊C4—341no—
539C4⋊C4—341no—
540C4⋊C4—682no—
541C4⋊C4—682no—
542C4⋊C4C2×C4×D1712yes—
543C22⋊C4—24no—
544C22⋊C4—42no—
545C22⋊C4—344no—
546C22⋊C4—682no—
547C42—21no—
548C42—21no—
549C42—22no—
550C42—22no—
551C42—42no—
552C42—42no—
553C42—682no—
554C42—682no—
555C42D4×D1712yes—
556C42#6325412yes—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23C4×C22⋊D1712yes—
564C23C22×C22⋊D1711yescharacteristic
565Q8—22no—
566Q8—22no—
567Q8—41no—
568Q8—41no—
569Q8—342no—
570Q8—342no—
571Q8—681no—
572Q8—681no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—44no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—44no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—342no—
602C2×C4—342no—
603C2×C4—681no—
604C2×C4—681no—
605C2×C4—681no—
606C2×C4—681no—
607C2×C4—681no—
608C2×C4—681no—
609C2×C4—681no—
610C2×C4—681no—
611C2×C4—681no—
612C2×C4—681no—
613C2×C4C4×C22⋊D1712yes—
614C2×C4#1058762512yes—
615C2×C4#1058762512yes—
616C2×C4#1058762812yes—
617C2×C4#1058763712yes—
618C2×C4C22×C4×D1711yescharacteristic
619C2×C4C2×#6325211yescharacteristic
620C2×C4C2×D4×D1711yescharacteristic
621C2×C4C2×#6325411yescharacteristic
622C2×C4#41×D1711yescharacteristic
623C2×C4#41×D1711yescharacteristic
624C8—174no—
625C8—342no—
626C8—342no—
627C8—342no—
628C22—22no—
629C22—22no—
630C22—22no—
631C22—41no—
632C22—41no—
633C22—41no—
634C22—41no—
635C22C2×C4×C22⋊D1711yescharacteristic
636C22C2×#1058762511yescharacteristic
637C22#1176335511yescharacteristic
638C22C2×#1058763711yescharacteristic
639C22C2×#1058762811yescharacteristic
640C22#1176360711yescharacteristic
641C22#1176360711yescharacteristic
642C4—22no—
643C4—22no—
644C4—42no—
645C4—41no—
646C4—41no—
647C4—42no—
648C4—81no—
649C4—81no—
650C4—682no—
651C4—682no—
652C4—1361no—
653C4—1361no—
654C4#1176306514yesdirect product factor
655C4C4×D4×D1711yescharacteristic
656C4C4×#6325411yescharacteristic
657C4#1176331811yescharacteristic
658C4#1176333911yescharacteristic
659C2—42no—
660C2C4×#1058762511yescharacteristic
661C2C4×#1058763711yescharacteristic
662C2C4×#1058762811yescharacteristic
663C2C2×#1176306511yescharacteristic
664C2#1453839011yescharacteristic
665C2#1453938411yescharacteristic
666C2#1453939111yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC4×C17×C22⋊Q8C2
socleC23×C17C22×D4
prime radicalC24×C17C2×D4
cosocleC22×C4×C17C24
hypercenterC4×C22⋊Q8D17
hypocenterC17C4×#470
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C4×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. C2×C4×#63231C2semidirect
5. #14529654C2semidirect
6. #14529524C2semidirect
7. #14529477C2semidirect
8. #14529473C2semidirect
12. C4×#10587479C2semidirect
13. C4×#10587481C2semidirect
14. C4×#10587506C2semidirect
21. #11763065C4direct (N × H)
91. C2×#63231C2×C4semidirect
121. #10587506C2×C4semidirect
129. #10587481C2×C4semidirect
131. #10587479C2×C4semidirect
332. C4×C17#470semidirect
470. C17C4×#470semidirect
654. C4#11763065direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117630652
C2×C4×#632312
C2×C4×#632232
C4×#105876102
#145296542
#145295242
#145294772
#145294732
#145292182
#145292152
#145288152
C4×#105874792
C4×#105874812
C4×#105875062
C4×C17×C22⋊Q82
C4×#47017