Finite Group Databasebeta

← #17075700

Subgroups — #17075700

Order 4352.

738 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763117C211yesmaximal, characteristic, complemented
2#14534614C211yesmaximal, characteristic
3#14531466C211yesmaximal, characteristic
4#14530217C211yesmaximal, characteristic
5#14530207C211yesmaximal, characteristic
6#14529988C211yesmaximal, characteristic
7#14529988C211yesmaximal, characteristic
8#14529739C211yesmaximal, characteristic, complemented
9#14529543C211yesmaximal, characteristic, complemented
10#14529522C211yesmaximal, characteristic, complemented
11#14529517C211yesmaximal, characteristic, complemented
12#14529474C211yesmaximal, characteristic, complemented
13#14529460C211yesmaximal, characteristic, complemented
14#14528790C211yesmaximal, characteristic, complemented
15C2×C17×#433C211yesmaximal, characteristic
16C2×#10587556C2211yescharacteristic
17C2×#10587610C2211yescharacteristic
18C2×C4×Dic34C2211yescharacteristic
19#11763117—24no—
20C2×#10587489C2211yescharacteristic
21C2×#10587489C2211yescharacteristic
22C2×#10587489C2211yescharacteristic
23C2×#10587488C2211yescharacteristic
24C2×#10587487C2211yescharacteristic
25C2×#10587487C2211yescharacteristic
26C2×#10587487C2211yescharacteristic
27C2×#10587487C2211yescharacteristic
28#11762742—21no—
29#11762742—21no—
30#11762732—21no—
31#11762732—21no—
32#11762715C2211yescharacteristic
33#11762707C2211yescharacteristic
34#11762707C2211yescharacteristic
35#11762707C2211yescharacteristic
36#11762704—21no—
37#11762703—21no—
38#11762697—21no—
39#11762690—21no—
40#11762679C2211yescharacteristic
41#11762669C2211yescharacteristic
42#11762669C2211yescharacteristic
43#11762669C2211yescharacteristic
44C4×C4⋊Dic17C2211yescharacteristic
45#11762572C2211yescharacteristic
46#11762572C2211yescharacteristic
47#11762572C2211yescharacteristic
48#11762572C2211yescharacteristic
49#11762572C2211yescharacteristic
50#11762572C2211yescharacteristic
51#11762572C2211yescharacteristic
52#11762572C2211yescharacteristic
53C2×C17×#117C2211yescharacteristic
54C17×#433—24no—
55C2×C17×C4⋊C8C2211yescharacteristic
56C2×C17×C4⋊C8C2211yescharacteristic
57C2×C17×C22⋊C8C2211yescharacteristic
58C2×C17×C22⋊C8C2211yescharacteristic
59C2×C17×#97C2211yescharacteristic
60C2×C4×C8×C17C2211yescharacteristic
61C23×C4×C17C2311yescharacteristic
62C22×Dic34C2311yescharacteristic
63C22×C8×C17C2311yescharacteristic
64C22×C8×C17C2311yescharacteristic
65C22×C8×C17C2311yescharacteristic
66C22×C8×C17C2311yescharacteristic
67C17×#117—22no—
68C17×#117—22no—
69C2×C4⋊C4×C17D411yescharacteristic
70C2×C4⋊C4×C17D411yescharacteristic
71C2×C22⋊C4×C17D411yescharacteristic
72C2×C22⋊C4×C17D411yescharacteristic
73C2×C42×C17C2311yescharacteristic
74C2×C42×C17C2311yescharacteristic
75C2×C22⋊Dic17—21no—
76C2×C22⋊Dic17—21no—
77C2×C22⋊Dic17—21no—
78C2×C22⋊Dic17—21no—
79C2×C4⋊Dic17—21no—
80C2×C4⋊Dic17—21no—
81C2×C4⋊Dic17C2311yescharacteristic
82C2×C4⋊Dic17C2311yescharacteristic
83C2×C4⋊Dic17C2311yescharacteristic
84C2×C4⋊Dic17C2311yescharacteristic
85C2×C4⋊Dic17C2311yescharacteristic
86C2×C4⋊Dic17C2311yescharacteristic
87C2×C4⋊Dic17C2311yescharacteristic
88#10587610—22no—
89#10587610—22no—
90C2×#63225—21no—
91C2×#63225—21no—
92C2×#63225—21no—
93C2×#63225—21no—
94C2×#63225—21no—
95C2×#63225—21no—
96C2×#63225—21no—
97C2×C4×Dic17—21no—
98C2×C4×Dic17—21no—
99#10587556—22no—
100#10587556—22no—
101C4×Dic34—22no—
102C4×Dic34—22no—
103C17×C4⋊C8—22no—
104C17×C4⋊C8D414yes—
105C17×C22⋊C8—22no—
106C17×C22⋊C8—22no—
107C17×#97—22no—
108C4×C8×C17—22no—
109#10587502—21no—
110#10587502—21no—
111#10587502—21no—
112#10587502—21no—
113#10587502—21no—
114#10587502—21no—
115#10587502—21no—
116#10587502—21no—
117#10587502—21no—
118#10587489—22no—
119#10587489—22no—
120#10587489—22no—
121#10587488—22no—
122#10587487—22no—
123#10587487—22no—
124#10587487—22no—
125#10587487—22no—
126C24×C17C2×D411yescharacteristic
127C22×C4×C17—21no—
128C22×C4×C17—21no—
129C22×C4×C17—21no—
130C22×C4×C17—21no—
131C22×C4×C17—21no—
132C22×C4×C17—21no—
133C22×C4×C17C2×D411yescharacteristic
134C22×C4×C17C2×D411yescharacteristic
135C22×C4×C17C2×D411yescharacteristic
136C22×C4×C17C2×D411yescharacteristic
137C22×C4×C17C2×D411yescharacteristic
138C22×C4×C17C2411yescharacteristic
139C22×Dic17—21no—
140C22×Dic17—21no—
141C22×Dic17—21no—
142C22×Dic17—21no—
143C22×Dic17—21no—
144C22×Dic17—21no—
145C22×Dic17—21no—
146C22×Dic17—21no—
147C2×Dic34—21no—
148C2×Dic34—21no—
149C2×Dic34—21no—
150C2×Dic34—21no—
151C2×Dic34—21no—
152C2×Dic34#4112yes—
153C2×C8×C17—21no—
154C2×C8×C17—21no—
155C2×C8×C17—21no—
156C2×C8×C17—21no—
157C2×C8×C17—21no—
158C2×C8×C17—21no—
159C2×C8×C17—21no—
160C2×C8×C17—21no—
161C2×C8×C17—21no—
162C2×C8×C17—21no—
163C2×C8×C17C2×D412yes—
164C2×C8×C17C2×D412yes—
165C4⋊C4×C17—22no—
166C4⋊C4×C17—22no—
167C22⋊C4×C17—22no—
168C22⋊C4×C17—22no—
169C42×C17—21no—
170C42×C17—21no—
171C42×C17C2×D412yes—
172C42×C17#4112yes—
173C22⋊Dic17—24no—
174C22⋊Dic17—81no—
175C22⋊Dic17—81no—
176C22⋊Dic17—81no—
177C4⋊Dic17—21no—
178C4⋊Dic17—21no—
179C4⋊Dic17—21no—
180C4⋊Dic17—21no—
181C4⋊Dic17—21no—
182C4⋊Dic17—21no—
183C4⋊Dic17—21no—
184C4⋊Dic17—21no—
185C4⋊Dic17—21no—
186C4⋊Dic17—21no—
187C4⋊Dic17—21no—
188C4⋊Dic17—21no—
189C4⋊Dic17—21no—
190C4⋊Dic17—81no—
191C4⋊Dic17—81no—
192C4⋊Dic17#4112yes—
193#63225—24no—
194#63225—42no—
195#63225—42no—
196#63225—42no—
197#63225—81no—
198#63225—81no—
199#63225—81no—
200C4×Dic17—42no—
201C4×Dic17—81no—
202#24715—171nomaximal, Sylow
203C23×C17—21no—
204C23×C17—21no—
205C23×C17—21no—
206C23×C17—21no—
207C23×C17—21no—
208C23×C17—21no—
209C23×C17—21no—
210C23×C17C22×D411yescharacteristic
211C2×C4×C17—21no—
212C2×C4×C17—21no—
213C2×C4×C17—21no—
214C2×C4×C17—21no—
215C2×C4×C17—21no—
216C2×C4×C17—21no—
217C2×C4×C17—21no—
218C2×C4×C17—21no—
219C2×C4×C17—21no—
220C2×C4×C17—21no—
221C2×C4×C17—21no—
222C2×C4×C17—21no—
223C2×C4×C17—21no—
224C2×C4×C17—41no—
225C2×C4×C17—41no—
226C2×C4×C17—41no—
227C2×C4×C17—41no—
228C2×C4×C17#12112yes—
229C2×C4×C17#12112yes—
230C2×C4×C17C22×D411yescharacteristic
231C2×C4×C17C2×#4111yescharacteristic
232C2×C4×C17C2×#4111yescharacteristic
233C2×C4×C17C2×#4111yescharacteristic
234C2×C4×C172−1+411yescharacteristic
235C2×C4×C172−1+411yescharacteristic
236C2×Dic17—22no—
237C2×Dic17—22no—
238C2×Dic17—41no—
239C2×Dic17—41no—
240C2×Dic17—41no—
241C2×Dic17—41no—
242C2×Dic17—41no—
243C2×Dic17—41no—
244C2×Dic17—41no—
245C2×Dic17—41no—
246C2×Dic17—41no—
247C2×Dic17—41no—
248C2×Dic17—41no—
249C2×Dic17—41no—
250C2×Dic17—41no—
251C2×Dic17—41no—
252C2×Dic17—41no—
253C2×Dic17—41no—
254C2×Dic17—41no—
255C2×Dic17—41no—
256C2×Dic17—41no—
257C2×Dic17—41no—
258C2×Dic17—41no—
259C2×Dic17—41no—
260Dic34—22no—
261Dic34—22no—
262Dic34—41no—
263Dic34—41no—
264C8×C17—22no—
265C8×C17—22no—
266C8×C17—41no—
267C8×C17—41no—
268C2×#479—171no—
269C2×#433D1711yescharacteristic
270#2629—171no—
271#2323—171no—
272#2077—171no—
273#2075—171no—
274#2036—171no—
275#2036—171no—
276#1989—171no—
277#1947—171no—
278#1943—171no—
279#1942—171no—
280#1935—171no—
281#1933—171no—
282#1803—171no—
283C22×C17—41no—
284C22×C17—41no—
285C22×C17—41no—
286C22×C17—41no—
287C22×C17—41no—
288C22×C17—41no—
289C22×C17—41no—
290C22×C17C2×#12111yescharacteristic
291C22×C17#52511yescharacteristic
292C22×C17#53611yescharacteristic
293C22×C17#57611yescharacteristic
294C22×C17#57711yescharacteristic
295C22×C17#57811yescharacteristic
296C22×C17#57811yescharacteristic
297C4×C17—22no—
298C4×C17—22no—
299C4×C17—41no—
300C4×C17—41no—
301C4×C17—41no—
302C4×C17#54711yescharacteristic
303C4×C17#54811yescharacteristic
304C4×C17#55211yescharacteristic
305C4×C17#55611yescharacteristic
306Dic17—42no—
307Dic17—42no—
308Dic17—81no—
309Dic17—81no—
310Dic17—81no—
311Dic17—81no—
312Dic17—81no—
313Dic17—81no—
314C2×#125—171no—
315C2×C22⋊Q8—171no—
316C2×C4×Q8—171no—
317C2×#117C2×D1711yescharacteristic
318#479—344no—
319#433—24no—
320C2×#107—171no—
321C2×#107—171no—
322C2×#107—171no—
323C2×#106—171no—
324C2×C4⋊C8C2×D1711yescharacteristic
325C2×C4⋊C8C2×D1711yescharacteristic
326C2×#103—171no—
327C2×#103—171no—
328C2×#103—171no—
329C2×#103—171no—
330C2×C22⋊C8C2×D1711yescharacteristic
331C2×C22⋊C8C2×D1711yescharacteristic
332C2×#97C2×D1711yescharacteristic
333C2×C4×C8C2×D1711yescharacteristic
334#398—341no—
335#398—341no—
336#396—341no—
337#396—341no—
338#391—171no—
339#389—171no—
340#389—171no—
341#389—171no—
342#389—341no—
343#388—341no—
344#388—341no—
345#387—341no—
346#384—171no—
347#380—171no—
348#380—171no—
349#380—171no—
350C4×C4⋊C4—171no—
351#340—171no—
352#340—171no—
353#340—171no—
354#340—171no—
355#340—171no—
356#340—171no—
357#340—171no—
358#340—171no—
359C2×C17—81no—
360C2×C17#241511yescharacteristic
361C2×C17#306111yescharacteristic
362C2×C17#306311yescharacteristic
363C2×C17#311911yescharacteristic
364C2×C17#312711yescharacteristic
365C2×C17#324211yescharacteristic
366C2×C17#324311yescharacteristic
367C22×Q8—171no—
368C23×C4C22×D1711yescharacteristic
369C22×C8C22×D1711yescharacteristic
370C22×C8C22×D1711yescharacteristic
371C22×C8C22×D1711yescharacteristic
372C22×C8C22×D1711yescharacteristic
373#125—342no—
374#125—342no—
375C22⋊Q8—342no—
376C22⋊Q8—342no—
377C4×Q8—342no—
378C4×Q8—342no—
379#117—22no—
380#117—22no—
381C2×C4⋊C4—171no—
382C2×C4⋊C4—171no—
383C2×C4⋊C4—171no—
384C2×C4⋊C4—171no—
385C2×C4⋊C4—171no—
386C2×C4⋊C4—171no—
387C2×C4⋊C4—171no—
388C2×C4⋊C4—341no—
389C2×C4⋊C4—341no—
390C2×C4⋊C4—341no—
391C2×C4⋊C4—341no—
392C2×C4⋊C4—341no—
393C2×C4⋊C4—341no—
394C2×C4⋊C4—341no—
395C2×C4⋊C4—341no—
396C2×C4⋊C4—341no—
397C2×C4⋊C4D6811yescharacteristic
398C2×C4⋊C4D6811yescharacteristic
399C2×C22⋊C4—341no—
400C2×C22⋊C4—341no—
401C2×C22⋊C4—341no—
402C2×C22⋊C4—341no—
403C2×C22⋊C4D6811yescharacteristic
404C2×C22⋊C4D6811yescharacteristic
405C2×C42—341no—
406C2×C42—341no—
407C2×C42C22×D1711yescharacteristic
408C2×C42C22×D1711yescharacteristic
409#107—342no—
410#107—342no—
411#107—342no—
412#106—342no—
413C4⋊C8—22no—
414C4⋊C8C22⋊D1714yes—
415#103—342no—
416#103—342no—
417#103—342no—
418#103—342no—
419C22⋊C8—22no—
420C22⋊C8—22no—
421#97—22no—
422C4×C8—22no—
423#95—341no—
424#95—341no—
425#95—341no—
426#95—341no—
427#95—341no—
428#95—341no—
429#95—341no—
430#95—341no—
431#95—341no—
432C17#2471511yescharacteristic, complemented, Sylow
433C24C2×D6811yescharacteristic
434C2×Q8—172no—
435C2×Q8—341no—
436C2×Q8—341no—
437C2×Q8—341no—
438C2×Q8—341no—
439C2×Q8—341no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—341no—
447C22×C4—341no—
448C22×C4—341no—
449C22×C4—341no—
450C22×C4—341no—
451C22×C4—341no—
452C22×C4—341no—
453C22×C4—341no—
454C22×C4C2×D6811yescharacteristic
455C22×C4C2×D6811yescharacteristic
456C22×C4C2×D6811yescharacteristic
457C22×C4C2×D6811yescharacteristic
458C22×C4C2×D6811yescharacteristic
459C22×C4C23×D1711yescharacteristic
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8C2×C22⋊D1712yes—
471C2×C8C2×C22⋊D1712yes—
472C4⋊C4—22no—
473C4⋊C4—22no—
474C4⋊C4—172no—
475C4⋊C4—344no—
476C4⋊C4—341no—
477C4⋊C4—341no—
478C4⋊C4—341no—
479C4⋊C4—341no—
480C4⋊C4—341no—
481C4⋊C4—341no—
482C4⋊C4—341no—
483C4⋊C4—341no—
484C4⋊C4—341no—
485C4⋊C4—341no—
486C4⋊C4—341no—
487C4⋊C4—341no—
488C4⋊C4—341no—
489C4⋊C4—682no—
490C4⋊C4—682no—
491C4⋊C4—682no—
492C4⋊C4—1361no—
493C4⋊C4—1361no—
494C4⋊C4—1361no—
495C4⋊C4—1361no—
496C4⋊C4—1361no—
497C22⋊C4—22no—
498C22⋊C4—22no—
499C22⋊C4—344no—
500C22⋊C4—1361no—
501C22⋊C4—1361no—
502C22⋊C4—1361no—
503C42—21no—
504C42—21no—
505C42—682no—
506C42—1361no—
507C42#6325212yes—
508C42C2×C22⋊D1712yes—
509C23—21no—
510C23—21no—
511C23—21no—
512C23—21no—
513C23—21no—
514C23—21no—
515C23—21no—
516C23C22×D6811yescharacteristic
517Q8—342no—
518Q8—342no—
519Q8—681no—
520Q8—681no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—342no—
539C2×C4—342no—
540C2×C4—681no—
541C2×C4—681no—
542C2×C4—681no—
543C2×C4—681no—
544C2×C4—681no—
545C2×C4—681no—
546C2×C4—681no—
547C2×C4—681no—
548C2×C4—681no—
549C2×C4—681no—
550C2×C4—681no—
551C2×C4—681no—
552C2×C4—681no—
553C2×C4—681no—
554C2×C4—681no—
555C2×C4—681no—
556C2×C4—681no—
557C2×C4—681no—
558C2×C4—681no—
559C2×C4—681no—
560C2×C4—681no—
561C2×C4—681no—
562C2×C4#1058761612yes—
563C2×C4#1058761612yes—
564C2×C4C2×#6325211yescharacteristic
565C2×C4#41×D1711yescharacteristic
566C2×C4#41×D1711yescharacteristic
567C2×C4#1058769711yescharacteristic
568C2×C4#1058769711yescharacteristic
569C2×C4C22×C22⋊D1711yescharacteristic
570C8—22no—
571C8—22no—
572C8—41no—
573C8—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22C2×#1058761611yescharacteristic
582C22#1176332111yescharacteristic
583C22#1176338511yescharacteristic
584C22#1176361411yescharacteristic
585C22#1176362111yescharacteristic
586C22#1176362611yescharacteristic
587C22#1176362611yescharacteristic
588C4—22no—
589C4—22no—
590C4—41no—
591C4—41no—
592C4—41no—
593C4—682no—
594C4—682no—
595C4—1361no—
596C4—1361no—
597C4—1361no—
598C4—1361no—
599C4—1361no—
600C4—1361no—
601C4#1176345811yescharacteristic
602C4#1176346611yescharacteristic
603C4#1176349811yescharacteristic
604C4#1176352711yescharacteristic
605C2—81no—
606C2#1453220711yescharacteristic
607C2#1453845411yescharacteristic
608C2#1453847511yescharacteristic
609C2#1453898511yescharacteristic
610C2#1453908511yescharacteristic
611C2#1454005411yescharacteristic
612C2#1454006911yescharacteristic
subgroupG/H
centerC23C22×D68
commutator, cosocleC22×C4×C17C24
FrattiniC22×C4C23×D17
FittingC2×C17×#433C2
socleC23×C17C22×D4
prime radicalC24×C17C2×D4
hypercenterC2×#433D17
hypocenterC17#24715
LCSG ▷ C22×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
1. C2×#11763117C2semidirect
8. #14529739C2semidirect
9. #14529543C2semidirect
10. #14529522C2semidirect
11. #14529517C2semidirect
12. #14529474C2semidirect
13. #14529460C2semidirect
14. #14528790C2semidirect
432. C17#24715semidirect

Maximal subgroups

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

subgroupindex
C2×#117631172
#145346142
#145314662
#145302172
#145302072
#145299882
#145297392
#145295432
#145295222
#145295172
#145294742
#145294602
#145287902
C2×C17×#4332
#2471517