Finite Group Databasebeta

← #17075655

Subgroups — #17075655

Order 4352.

802 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763090C211yesmaximal, characteristic, complemented
2#14534605C211yesmaximal, characteristic, complemented
3#14531477C211yesmaximal, characteristic
4#14530212C211yesmaximal, characteristic, complemented
5#14530207C211yesmaximal, characteristic, complemented
6#14529974C211yesmaximal, characteristic
7#14529967C211yesmaximal, characteristic
8#14529731C211yesmaximal, characteristic, complemented
9#14529554C211yesmaximal, characteristic, complemented
10#14529527C211yesmaximal, characteristic, complemented
11#14529517C211yesmaximal, characteristic, complemented
12#14529481C211yesmaximal, characteristic, complemented
13#14529467C211yesmaximal, characteristic, complemented
14#14528795C211yesmaximal, characteristic, complemented
15C2×C17×#433C211yesmaximal, characteristic, complemented
16C2×#10587555C2211yescharacteristic
17C2×#10587616C2211yescharacteristic
18C2×C4×D68C2211yescharacteristic
19#11763090—24no—
20C2×#10587489C2211yescharacteristic
21C2×#10587489C2211yescharacteristic
22C2×#10587489C2211yescharacteristic
23C2×#10587488C2211yescharacteristic
24C2×#10587492C2211yescharacteristic
25C2×#10587492C2211yescharacteristic
26C2×#10587492C2211yescharacteristic
27C2×#10587492C2211yescharacteristic
28#11762748—21no—
29#11762745—21no—
30#11762729—21no—
31#11762721—21no—
32#11762711C2211yescharacteristic
33#11762709—21no—
34#11762707C2211yescharacteristic
35#11762707C2211yescharacteristic
36#11762707C2211yescharacteristic
37#11762699—21no—
38#11762685—21no—
39#11762680—21no—
40#11762675C2211yescharacteristic
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×C22⋊D17—21no—
63C22×D68C2311yescharacteristic
64C22×C4×D17—21no—
65C22×Dic34—21no—
66C22×C8×C17C2311yescharacteristic
67C22×C8×C17C2311yescharacteristic
68C22×C8×C17C2311yescharacteristic
69C22×C8×C17C2311yescharacteristic
70C17×#117—22no—
71C17×#117—22no—
72C2×C4⋊C4×C17D411yescharacteristic
73C2×C4⋊C4×C17D411yescharacteristic
74C2×C22⋊C4×C17D411yescharacteristic
75C2×C22⋊C4×C17D411yescharacteristic
76C2×C42×C17C2311yescharacteristic
77C2×C42×C17C2311yescharacteristic
78C2×C22⋊Dic17—21no—
79C2×C22⋊Dic17—21no—
80C2×C22⋊Dic17—21no—
81#10587616—22no—
82#10587616—22no—
83C2×#63227—21no—
84C2×#63227—21no—
85C2×#63227—21no—
86C2×#63227—21no—
87C2×C4⋊Dic17—21no—
88C2×C4⋊Dic17C2311yescharacteristic
89C2×C4⋊Dic17C2311yescharacteristic
90C2×C4⋊Dic17C2311yescharacteristic
91C2×C4⋊Dic17C2311yescharacteristic
92C2×C4⋊Dic17C2311yescharacteristic
93C2×C4⋊Dic17C2311yescharacteristic
94C2×C4⋊Dic17C2311yescharacteristic
95C2×#63225—21no—
96C2×#63225—21no—
97C2×#63225—21no—
98C2×C4×Dic17—21no—
99C4×D68—22no—
100C4×D68—22no—
101#10587555—22no—
102#10587555—22no—
103C17×C4⋊C8—22no—
104C17×C4⋊C8D414yescomplemented
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#10587492—22no—
119#10587492—22no—
120#10587492—22no—
121#10587492—22no—
122#10587489—22no—
123#10587489—22no—
124#10587489—22no—
125#10587488—22no—
126C24×C17C2×D411yescharacteristic
127C23×D17—21no—
128C22×C4×C17—21no—
129C22×C4×C17—21no—
130C22×C4×C17—21no—
131C22×C4×C17—21no—
132C22×C4×C17—21no—
133C22×C4×C17—21no—
134C22×C4×C17C2×D411yescharacteristic
135C22×C4×C17C2×D411yescharacteristic
136C22×C4×C17C2×D411yescharacteristic
137C22×C4×C17C2×D411yescharacteristic
138C22×C4×C17C2×D411yescharacteristic
139C22×C4×C17C2411yescharacteristic
140C2×C22⋊D17—24no—
141C2×C22⋊D17—81no—
142C2×C22⋊D17—81no—
143C22×Dic17—21no—
144C22×Dic17—21no—
145C22×Dic17—21no—
146C22×Dic17—21no—
147C22×Dic17—21no—
148C22×Dic17—21no—
149C22×Dic17—21no—
150C2×D68—21no—
151C2×D68—21no—
152C2×D68—21no—
153C2×D68—21no—
154C2×D68—21no—
155C2×D68#4112yes—
156C2×C4×D17—42no—
157C2×C4×D17—81no—
158C2×C4×D17—81no—
159C2×Dic34—42no—
160C2×Dic34—81no—
161C2×Dic34—81no—
162C2×C8×C17—21no—
163C2×C8×C17—21no—
164C2×C8×C17—21no—
165C2×C8×C17—21no—
166C2×C8×C17—21no—
167C2×C8×C17—21no—
168C2×C8×C17—21no—
169C2×C8×C17—21no—
170C2×C8×C17—21no—
171C2×C8×C17—21no—
172C2×C8×C17C2×D412yes—
173C2×C8×C17C2×D412yes—
174C4⋊C4×C17—22no—
175C4⋊C4×C17—22no—
176C22⋊C4×C17—22no—
177C22⋊C4×C17—22no—
178C42×C17—21no—
179C42×C17—21no—
180C42×C17C2×D412yes—
181C42×C17#4112yes—
182C22⋊Dic17—81no—
183C22⋊Dic17—81no—
184C22⋊Dic17—81no—
185#63227—24no—
186#63227—42no—
187#63227—81no—
188#63227—81no—
189C4⋊Dic17—21no—
190C4⋊Dic17—21no—
191C4⋊Dic17—21no—
192C4⋊Dic17—21no—
193C4⋊Dic17—21no—
194C4⋊Dic17—21no—
195C4⋊Dic17—21no—
196C4⋊Dic17—21no—
197C4⋊Dic17—21no—
198C4⋊Dic17—21no—
199C4⋊Dic17—21no—
200C4⋊Dic17—21no—
201C4⋊Dic17—21no—
202C4⋊Dic17—42no—
203C4⋊Dic17#4112yes—
204#63225—81no—
205#63225—81no—
206#63225—81no—
207C4×Dic17—81no—
208#24712—171nomaximal, Sylow
209C23×C17—21no—
210C23×C17—21no—
211C23×C17—21no—
212C23×C17—21no—
213C23×C17—21no—
214C23×C17—21no—
215C23×C17—21no—
216C23×C17C22×D411yescharacteristic
217C22×D17—22no—
218C22×D17—41no—
219C22×D17—41no—
220C22×D17—41no—
221C22×D17—41no—
222C22×D17—41no—
223C22×D17—41no—
224C2×C4×C17—21no—
225C2×C4×C17—21no—
226C2×C4×C17—21no—
227C2×C4×C17—21no—
228C2×C4×C17—21no—
229C2×C4×C17—21no—
230C2×C4×C17—21no—
231C2×C4×C17—21no—
232C2×C4×C17—21no—
233C2×C4×C17—21no—
234C2×C4×C17—21no—
235C2×C4×C17—21no—
236C2×C4×C17—21no—
237C2×C4×C17—41no—
238C2×C4×C17—41no—
239C2×C4×C17—41no—
240C2×C4×C17—41no—
241C2×C4×C17#12112yes—
242C2×C4×C17#12112yes—
243C2×C4×C17C22×D411yescharacteristic
244C2×C4×C17C2×#4111yescharacteristic
245C2×C4×C17C2×#4111yescharacteristic
246C2×C4×C17C2×#4111yescharacteristic
247C2×C4×C172−1+411yescharacteristic
248C2×C4×C172−1+411yescharacteristic
249C22⋊D17—84no—
250C2×Dic17—22no—
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—
260C2×Dic17—41no—
261C2×Dic17—41no—
262C2×Dic17—41no—
263C2×Dic17—41no—
264C2×Dic17—41no—
265C2×Dic17—41no—
266C2×Dic17—41no—
267C2×Dic17—41no—
268C2×Dic17—41no—
269C2×Dic17—41no—
270C2×Dic17—41no—
271D68—22no—
272D68—22no—
273D68—41no—
274D68—41no—
275C4×D17—84no—
276Dic34—84no—
277C8×C17—22no—
278C8×C17—22no—
279C8×C17—41no—
280C8×C17—41no—
281C2×#474—171no—
282C2×#433D1711yescharacteristic, complemented
283#2628—171no—
284#2324—171no—
285#2076—171no—
286#2075—171no—
287#2034—171no—
288#2033—171no—
289#1987—171no—
290#1949—171no—
291#1944—171no—
292#1942—171no—
293#1936—171no—
294#1934—171no—
295#1804—171no—
296C22×C17—41no—
297C22×C17—41no—
298C22×C17—41no—
299C22×C17—41no—
300C22×C17—41no—
301C22×C17—41no—
302C22×C17—41no—
303C22×C17C2×#12111yescharacteristic
304C22×C17#52511yescharacteristic
305C22×C17#53611yescharacteristic
306C22×C17#57611yescharacteristic
307C22×C17#57611yescharacteristic
308C22×C17#57711yescharacteristic
309C22×C17#57811yescharacteristic
310C2×D17—42no—
311C2×D17—42no—
312C2×D17—42no—
313C2×D17—81no—
314C2×D17—81no—
315C2×D17—81no—
316C2×D17—81no—
317C4×C17—22no—
318C4×C17—22no—
319C4×C17—41no—
320C4×C17—41no—
321C4×C17—41no—
322C4×C17#54711yescharacteristic
323C4×C17#54811yescharacteristic
324C4×C17#55211yescharacteristic
325C4×C17#55611yescharacteristic
326Dic17—42no—
327Dic17—81no—
328Dic17—81no—
329Dic17—81no—
330Dic17—81no—
331Dic17—81no—
332Dic17—81no—
333C2×C4⋊Q8—171no—
334C2×#121—171no—
335C2×C4×D4—171no—
336C2×#117C2×D1711yescharacteristic
337#474—344no—
338#433—24no—
339C2×#107—171no—
340C2×#107—171no—
341C2×#107—171no—
342C2×#106—171no—
343C2×C4⋊C8C2×D1711yescharacteristic
344C2×C4⋊C8C2×D1711yescharacteristic
345C2×#102—171no—
346C2×#102—171no—
347C2×#102—171no—
348C2×#102—171no—
349C2×C22⋊C8C2×D1711yescharacteristic
350C2×C22⋊C8C2×D1711yescharacteristic
351C2×#97C2×D1711yescharacteristic
352C2×C4×C8C2×D1711yescharacteristic
353#400—341no—
354#399—341no—
355#395—341no—
356#393—341no—
357#390—171no—
358#390—341no—
359#389—171no—
360#389—171no—
361#389—171no—
362#388—341no—
363#386—341no—
364#385—341no—
365#382—171no—
366#380—171no—
367#380—171no—
368#380—171no—
369C4×C4⋊C4—171no—
370#340—171no—
371#340—171no—
372#340—171no—
373#340—171no—
374#340—171no—
375#340—171no—
376#340—171no—
377#340—171no—
378C2×C17—81no—
379C2×C17#241511yescharacteristic
380C2×C17#305811yescharacteristic
381C2×C17#306311yescharacteristic
382C2×C17#311811yescharacteristic
383C2×C17#312411yescharacteristic
384C2×C17#324111yescharacteristic
385C2×C17#324311yescharacteristic
386D17—82no—
387C22×Q8—341no—
388C22×D4—171no—
389C22×D4—341no—
390C23×C4—341no—
391C23×C4C22×D1711yescharacteristic
392C22×C8C22×D1711yescharacteristic
393C22×C8C22×D1711yescharacteristic
394C22×C8C22×D1711yescharacteristic
395C22×C8C22×D1711yescharacteristic
396C4⋊Q8—342no—
397C4⋊Q8—342no—
398#121—342no—
399#121—342no—
400C4×D4—342no—
401C4×D4—342no—
402#117—22no—
403#117—22no—
404C2×C4⋊C4—171no—
405C2×C4⋊C4—171no—
406C2×C4⋊C4—171no—
407C2×C4⋊C4—171no—
408C2×C4⋊C4—171no—
409C2×C4⋊C4—171no—
410C2×C4⋊C4—171no—
411C2×C4⋊C4—341no—
412C2×C4⋊C4—341no—
413C2×C4⋊C4—341no—
414C2×C4⋊C4—341no—
415C2×C4⋊C4D6811yescharacteristic
416C2×C4⋊C4D6811yescharacteristic
417C2×C22⋊C4—341no—
418C2×C22⋊C4—341no—
419C2×C22⋊C4—341no—
420C2×C22⋊C4—341no—
421C2×C22⋊C4—341no—
422C2×C22⋊C4—341no—
423C2×C22⋊C4—341no—
424C2×C22⋊C4D6811yescharacteristic
425C2×C22⋊C4D6811yescharacteristic
426C2×C42—341no—
427C2×C42C22×D1711yescharacteristic
428C2×C42C22×D1711yescharacteristic
429#107—342no—
430#107—342no—
431#107—342no—
432#106—342no—
433C4⋊C8—22no—
434C4⋊C8C22⋊D1714yescomplemented
435#102—342no—
436#102—342no—
437#102—342no—
438#102—342no—
439C22⋊C8—22no—
440C22⋊C8—22no—
441#97—22no—
442C4×C8—22no—
443#95—341no—
444#95—341no—
445#95—341no—
446#95—341no—
447#95—341no—
448#95—341no—
449#95—341no—
450#95—341no—
451#95—341no—
452C17#2471211yescharacteristic, complemented, Sylow
453C24—341no—
454C24C2×D6811yescharacteristic
455C2×Q8—682no—
456C2×Q8—1361no—
457C2×Q8—1361no—
458C2×D4—172no—
459C2×D4—344no—
460C2×D4—341no—
461C2×D4—341no—
462C2×D4—341no—
463C2×D4—341no—
464C2×D4—341no—
465C2×D4—1361no—
466C2×D4—1361no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—341no—
474C22×C4—341no—
475C22×C4—341no—
476C22×C4—341no—
477C22×C4—341no—
478C22×C4—341no—
479C22×C4—341no—
480C22×C4—682no—
481C22×C4—1361no—
482C22×C4—1361no—
483C22×C4C2×D6811yescharacteristic
484C22×C4C2×D6811yescharacteristic
485C22×C4C2×D6811yescharacteristic
486C22×C4C2×D6811yescharacteristic
487C22×C4C2×D6811yescharacteristic
488C22×C4C23×D1711yescharacteristic
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8C2×C22⋊D1712yes—
500C2×C8C2×C22⋊D1712yes—
501C4⋊C4—22no—
502C4⋊C4—22no—
503C4⋊C4—172no—
504C4⋊C4—341no—
505C4⋊C4—341no—
506C4⋊C4—341no—
507C4⋊C4—341no—
508C4⋊C4—341no—
509C4⋊C4—341no—
510C4⋊C4—341no—
511C4⋊C4—341no—
512C4⋊C4—341no—
513C4⋊C4—341no—
514C4⋊C4—341no—
515C4⋊C4—341no—
516C4⋊C4—341no—
517C4⋊C4—682no—
518C4⋊C4—1361no—
519C4⋊C4—1361no—
520C4⋊C4—1361no—
521C22⋊C4—22no—
522C22⋊C4—22no—
523C22⋊C4—344no—
524C22⋊C4—682no—
525C22⋊C4—1361no—
526C22⋊C4—1361no—
527C22⋊C4—1361no—
528C22⋊C4—1361no—
529C22⋊C4—1361no—
530C42—21no—
531C42—21no—
532C42—1361no—
533C42#6325212yes—
534C42C2×C22⋊D1712yes—
535C23—21no—
536C23—21no—
537C23—21no—
538C23—21no—
539C23—21no—
540C23—21no—
541C23—21no—
542C23—342no—
543C23—681no—
544C23—681no—
545C23—681no—
546C23—681no—
547C23—681no—
548C23—681no—
549C23C22×D6811yescharacteristic
550Q8—1364no—
551D4—342no—
552D4—342no—
553D4—681no—
554D4—681no—
555D4—1364no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—342no—
574C2×C4—681no—
575C2×C4—681no—
576C2×C4—681no—
577C2×C4—681no—
578C2×C4—681no—
579C2×C4—681no—
580C2×C4—681no—
581C2×C4—681no—
582C2×C4—681no—
583C2×C4—681no—
584C2×C4—681no—
585C2×C4—681no—
586C2×C4—681no—
587C2×C4—681no—
588C2×C4—681no—
589C2×C4—681no—
590C2×C4—681no—
591C2×C4—681no—
592C2×C4—681no—
593C2×C4—681no—
594C2×C4—1364no—
595C2×C4#1058761612yes—
596C2×C4#1058761612yes—
597C2×C4C2×#6325211yescharacteristic
598C2×C4#41×D1711yescharacteristic
599C2×C4#41×D1711yescharacteristic
600C2×C4#1058769711yescharacteristic
601C2×C4#1058769711yescharacteristic
602C2×C4C22×C22⋊D1711yescharacteristic
603C8—22no—
604C8—22no—
605C8—41no—
606C8—41no—
607C22—41no—
608C22—41no—
609C22—41no—
610C22—41no—
611C22—41no—
612C22—41no—
613C22—41no—
614C22—682no—
615C22—682no—
616C22—682no—
617C22—1361no—
618C22—1361no—
619C22—1361no—
620C22—1361no—
621C22C2×#1058761611yescharacteristic
622C22#1176332111yescharacteristic
623C22#1176338511yescharacteristic
624C22#1176361411yescharacteristic
625C22#1176361411yescharacteristic
626C22#1176362111yescharacteristic
627C22#1176362611yescharacteristic
628C4—22no—
629C4—22no—
630C4—41no—
631C4—41no—
632C4—41no—
633C4—682no—
634C4—1361no—
635C4—1361no—
636C4—1361no—
637C4—1361no—
638C4—1361no—
639C4—1361no—
640C4#1176345811yescharacteristic
641C4#1176346611yescharacteristic
642C4#1176349811yescharacteristic
643C4#1176352711yescharacteristic
644C2—81no—
645C2—1362no—
646C2#1453220711yescharacteristic
647C2#1453843211yescharacteristic
648C2#1453847511yescharacteristic
649C2#1453897011yescharacteristic
650C2#1453904811yescharacteristic
651C2#1454003911yescharacteristic
652C2#1454006911yescharacteristic
subgroupG/H
centerC23C22×D68
commutator, cosocleC22×C4×C17C24
FrattiniC22×C4C23×D17
FittingC2×C17×#433C2
socleC23×C17C22×D4
prime radicalC2×#10587616C22
hypercenterC2×#433D17
hypocenterC17#24712
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×#11763090C2semidirect
2. #14534605C2semidirect
4. #14530212C2semidirect
5. #14530207C2semidirect
8. #14529731C2semidirect
9. #14529554C2semidirect
10. #14529527C2semidirect
11. #14529517C2semidirect
12. #14529481C2semidirect
13. #14529467C2semidirect
14. #14528795C2semidirect
15. C2×C17×#433C2semidirect
104. C17×C4⋊C8D4semidirect
282. C2×#433D17semidirect
434. C4⋊C8C22⋊D17semidirect
452. C17#24712semidirect

Maximal subgroups

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

subgroupindex
C2×#117630902
#145346052
#145314772
#145302122
#145302072
#145299742
#145299672
#145297312
#145295542
#145295272
#145295172
#145294812
#145294672
#145287952
C2×C17×#4332
#2471217