Finite Group Databasebeta

← #17102996

Subgroups — #17102996

Order 4352.

712 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14531853C211yesmaximal, characteristic
2#14530188C211yesmaximal, characteristic
3#14530169C211yesmaximal, characteristic
4#14530025C211yesmaximal, characteristic
5#14530025C211yesmaximal, characteristic
6#14529459C211yesmaximal, characteristic, complemented
7#14529425C211yesmaximal, characteristic, complemented
8#14529359C211yesmaximal, characteristic, complemented
9#14529352C211yesmaximal, characteristic, complemented
10#14529343C211yesmaximal, characteristic, complemented
11#14529051C211yesmaximal, characteristic, complemented
12#14529044C211yesmaximal, characteristic
13#14528786C211yesmaximal, characteristic, complemented
14C4×#10587480C211yesmaximal, characteristic
15C17×#2507C211yesmaximal, characteristic, complemented
16C2×#10587561C2211yescharacteristic
17C2×C4×Dic34C2211yescharacteristic
18C2×C4×D68C2211yescharacteristic
19C2×#10587478C2211yescharacteristic
20C2×#10587479C2211yescharacteristic
21C2×C4⋊#3622C2211yescharacteristic
22C2×#10587481C2211yescharacteristic
23C2×#10587481C2211yescharacteristic
24C2×#10587481C2211yescharacteristic
25C2×#10587481C2211yescharacteristic
26C2×#10587480C2211yescharacteristic
27C2×#10587480C2211yescharacteristic
28C2×#10587480C2211yescharacteristic
29C2×#10587480C2211yescharacteristic
30C2×C4×#3622C2211yescharacteristic
31#11762715C2211yescharacteristic
32#11762711C2211yescharacteristic
33#11762699—21no—
34#11762698—21no—
35#11762680—21no—
36C4×C4⋊Dic17C2211yescharacteristic
37#11762656—21no—
38#11762571C2211yescharacteristic
39#11762571C2211yescharacteristic
40#11762571C2211yescharacteristic
41#11762571C2211yescharacteristic
42#11762571C2211yescharacteristic
43#11762571C2211yescharacteristic
44#11762564C2211yescharacteristic
45#11762564C2211yescharacteristic
46#11762564C2211yescharacteristic
47#11762564C2211yescharacteristic
48C17×#398—21no—
49C17×#398—21no—
50C17×#389—21no—
51C17×#389C2211yescharacteristic
52C17×#389C2211yescharacteristic
53C17×#389C2211yescharacteristic
54C17×#389C2211yescharacteristic
55C17×#387—21no—
56C17×#384C2211yescharacteristic
57C4×C4⋊C4×C17C2211yescharacteristic
58C4×C4⋊C4×C17C2211yescharacteristic
59C22×D68C2311yescharacteristic
60C22×C4×D17—21no—
61C22×Dic34C2311yescharacteristic
62C2×C4⋊C4×C17—21no—
63C2×C4⋊C4×C17—21no—
64C2×C4⋊C4×C17—21no—
65C2×C4⋊C4×C17—21no—
66C2×C4⋊C4×C17—21no—
67C2×C4⋊C4×C17—21no—
68C2×C4⋊C4×C17D411yescharacteristic
69C2×C4⋊C4×C17D411yescharacteristic
70C2×C4⋊C4×C17C2311yescharacteristic
71C2×C4⋊C4×C17C2311yescharacteristic
72C2×C4⋊C4×C17C2311yescharacteristic
73C2×C4⋊C4×C17C2311yescharacteristic
74C2×C42×C17—21no—
75C2×C42×C17C2311yescharacteristic
76C2×C42×C17C2311yescharacteristic
77C2×C42×C17C2311yescharacteristic
78C2×#63227—21no—
79C2×#63227—21no—
80C2×#63227—21no—
81C2×#63227—21no—
82C2×#63227—21no—
83C2×C4⋊Dic17C2311yescharacteristic
84C2×C4⋊Dic17C2311yescharacteristic
85C2×#63225—21no—
86C2×C4×Dic17—21no—
87C2×C4×Dic17—21no—
88C22×#3622C2311yescharacteristic
89C22×#3622C2311yescharacteristic
90C22×#3622C2311yescharacteristic
91C22×#3622C2311yescharacteristic
92#10587561—22no—
93#10587561—22no—
94C4×D68—22no—
95C4×D68—41no—
96C4×Dic34—22no—
97C4×Dic34—41no—
98C17×#95—21no—
99C17×#95—21no—
100C17×#95—21no—
101C17×#95—21no—
102C17×#95—21no—
103C17×#95D411yescharacteristic
104C17×#95D411yescharacteristic
105#10587502—21no—
106#10587502—21no—
107#10587502—21no—
108#10587481—22no—
109#10587481—22no—
110#10587481—22no—
111#10587481—41no—
112#10587480—22no—
113#10587480—22no—
114#10587480—22no—
115#10587480—41no—
116#10587479—22no—
117#10587478—22no—
118C4⋊#3622—41no—
119C4×#3622—41no—
120C23×D17—21no—
121C22×C4×C17—21no—
122C22×C4×C17—21no—
123C22×C4×C17—21no—
124C22×C4×C17—21no—
125C22×C4×C17C2×D411yescharacteristic
126C22×C4×C17C2×D411yescharacteristic
127C22×C4×C17C2×D411yescharacteristic
128C22×C4×C17C2×D411yescharacteristic
129C22×C4×C17C2×D411yescharacteristic
130C22×C4×C17C2×D411yescharacteristic
131C22×C4×C17C2411yescharacteristic
132C22×Dic17—21no—
133C22×Dic17—21no—
134C22×Dic17—21no—
135C2×D68—21no—
136C2×D68—21no—
137C2×D68—21no—
138C2×D68—21no—
139C2×D68—21no—
140C2×D68#4112yes—
141C2×C4×D17—42no—
142C2×C4×D17—42no—
143C2×C4×D17—81no—
144C2×Dic34—21no—
145C2×Dic34—21no—
146C2×Dic34—21no—
147C2×Dic34—21no—
148C2×Dic34—21no—
149C2×Dic34#4112yes—
150C4⋊C4×C17—22no—
151C4⋊C4×C17—22no—
152C4⋊C4×C17—21no—
153C4⋊C4×C17—21no—
154C4⋊C4×C17—21no—
155C4⋊C4×C17—21no—
156C4⋊C4×C17—21no—
157C4⋊C4×C17—21no—
158C4⋊C4×C17—21no—
159C4⋊C4×C17—42no—
160C4⋊C4×C17—81no—
161C4⋊C4×C17—81no—
162C4⋊C4×C17—81no—
163C4⋊C4×C17—81no—
164C4⋊C4×C17—81no—
165C4⋊C4×C17#4112yes—
166C42×C17—21no—
167C42×C17—21no—
168C42×C17—21no—
169C42×C17—21no—
170C42×C17—21no—
171C42×C17—21no—
172C42×C17—81no—
173#63227—24no—
174#63227—24no—
175#63227—42no—
176#63227—42no—
177#63227—81no—
178C4⋊Dic17—21no—
179C4⋊Dic17—21no—
180C4⋊Dic17—21no—
181C4⋊Dic17#4112yes—
182#63225—42no—
183C4×Dic17—42no—
184C4×Dic17—81no—
185C2×#3622—21no—
186C2×#3622—21no—
187C2×#3622—21no—
188C2×#3622—21no—
189C2×#3622—21no—
190C2×#3622—21no—
191C2×#3622—21no—
192C2×#3622—21no—
193C2×#3622—21no—
194C2×#3622—21no—
195C2×#3622—21no—
196C2×#3622—21no—
197#26763—171nomaximal, Sylow
198C23×C17C22×D411yescharacteristic
199C22×D17—22no—
200C22×D17—41no—
201C22×D17—41no—
202C22×D17—41no—
203C22×D17—41no—
204C22×D17—41no—
205C22×D17—41no—
206C2×C4×C17—21no—
207C2×C4×C17—21no—
208C2×C4×C17—21no—
209C2×C4×C17—21no—
210C2×C4×C17—21no—
211C2×C4×C17—21no—
212C2×C4×C17—21no—
213C2×C4×C17—21no—
214C2×C4×C17—22no—
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—41no—
224C2×C4×C17—41no—
225C2×C4×C17—41no—
226C2×C4×C17—41no—
227C2×C4×C17—41no—
228C2×C4×C17—41no—
229C2×C4×C17—41no—
230C2×C4×C17—41no—
231C2×C4×C17—41no—
232C2×C4×C17—41no—
233C2×C4×C17—41no—
234C2×C4×C17#13512yes—
235C2×C4×C17#13712yes—
236C2×C4×C17C2×#4111yescharacteristic
237C2×C4×C17C2×#4111yescharacteristic
238C2×C4×C17C2×#4111yescharacteristic
239C2×C4×C17C2×#4111yescharacteristic
240C2×C4×C17H(5,𝔽2)11yescharacteristic
241C2×C4×C172−1+411yescharacteristic
242C2×Dic17—22no—
243C2×Dic17—22no—
244C2×Dic17—41no—
245C2×Dic17—41no—
246C2×Dic17—41no—
247C2×Dic17—41no—
248C2×Dic17—41no—
249C2×Dic17—41no—
250C2×Dic17—41no—
251D68—22no—
252D68—22no—
253D68—41no—
254D68—41no—
255C4×D17—84no—
256Dic34—22no—
257Dic34—22no—
258Dic34—41no—
259Dic34—41no—
260#3622—41no—
261#3622—41no—
262#3622—41no—
263#3622—41no—
264#2507D1711yescharacteristic, complemented
265#2367—171no—
266#2071—171no—
267#2067—171no—
268#2042—171no—
269#2042—171no—
270#1933—171no—
271#1928—171no—
272#1919—171no—
273#1918—171no—
274#1916—171no—
275#1865—171no—
276#1864—171no—
277#1803—171no—
278C4×#102—171no—
279C22×C17#52511yescharacteristic
280C22×C17#54611yescharacteristic
281C22×C17#54811yescharacteristic
282C22×C17C2×#13511yescharacteristic
283C22×C17C2×#13711yescharacteristic
284C22×C17#57611yescharacteristic
285C22×C17#57711yescharacteristic
286C2×D17—42no—
287C2×D17—42no—
288C2×D17—42no—
289C2×D17—81no—
290C2×D17—81no—
291C2×D17—81no—
292C2×D17—81no—
293C4×C17—22no—
294C4×C17—22no—
295C4×C17—42no—
296C4×C17—41no—
297C4×C17—41no—
298C4×C17—41no—
299C4×C17—41no—
300C4×C17—81no—
301C4×C17—81no—
302C4×C17—81no—
303C4×C17#52911yescharacteristic
304C4×C17#53911yescharacteristic
305C4×C17#55211yescharacteristic
306C4×C17#55311yescharacteristic
307Dic17—42no—
308Dic17—42no—
309Dic17—81no—
310C2×#124—171no—
311C2×C4×Q8—171no—
312C2×C4×D4—171no—
313C2×#107—171no—
314C2×#106—171no—
315C2×C4⋊C8—171no—
316C2×#103—171no—
317C2×#103—171no—
318C2×#103—171no—
319C2×#103—171no—
320C2×#102—171no—
321C2×#102—171no—
322C2×#102—171no—
323C2×#102—171no—
324C2×C4×C8—171no—
325#398—21no—
326#398—21no—
327#391—171no—
328#390—171no—
329#389—21no—
330#389C2×D1711yescharacteristic
331#389C2×D1711yescharacteristic
332#389C2×D1711yescharacteristic
333#389C2×D1711yescharacteristic
334#388—341no—
335#388—341no—
336#387—21no—
337#385—341no—
338#384C2×D1711yescharacteristic
339C4×C4⋊C4—171no—
340C4×C4⋊C4C2×D1711yescharacteristic
341C4×C4⋊C4C2×D1711yescharacteristic
342C4×C22⋊C4—341no—
343#340—171no—
344#340—171no—
345#340—171no—
346#340—171no—
347#340—171no—
348#340—171no—
349#336—171no—
350#336—171no—
351#336—171no—
352#336—171no—
353C2×C17#246011yescharacteristic
354C2×C17#310711yescharacteristic
355C2×C17#311911yescharacteristic
356C2×C17#330111yescharacteristic
357C2×C17#331411yescharacteristic
358C2×C17#336111yescharacteristic
359C2×C17#336911yescharacteristic
360D17—82no—
361C22×Q8—171no—
362C22×D4—171no—
363C23×C4—341no—
364C22×C8—171no—
365C22×C8—171no—
366C22×C8—171no—
367C22×C8—171no—
368#124—342no—
369#124—342no—
370C4×Q8—342no—
371C4×Q8—681no—
372C4×D4—342no—
373C4×D4—681no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—171no—
381C2×C4⋊C4—171no—
382C2×C4⋊C4—341no—
383C2×C4⋊C4C22⋊D1711yescharacteristic
384C2×C4⋊C4C22⋊D1711yescharacteristic
385C2×C4⋊C4C22×D1711yescharacteristic
386C2×C4⋊C4C22×D1711yescharacteristic
387C2×C4⋊C4C22×D1711yescharacteristic
388C2×C4⋊C4C22×D1711yescharacteristic
389C2×C22⋊C4—341no—
390C2×C22⋊C4—341no—
391C2×C22⋊C4—341no—
392C2×C22⋊C4—341no—
393C2×C22⋊C4—341no—
394C2×C42—21no—
395C2×C42—341no—
396C2×C42—341no—
397C2×C42C22×D1711yescharacteristic
398C2×C42C22×D1711yescharacteristic
399C2×C42C22×D1711yescharacteristic
400#107—342no—
401#106—342no—
402C4⋊C8—681no—
403#103—342no—
404#103—342no—
405#103—342no—
406#103—681no—
407#102—342no—
408#102—342no—
409#102—342no—
410#102—681no—
411C4×C8—681no—
412#95—21no—
413#95—21no—
414#95—21no—
415#95—21no—
416#95—21no—
417#95—341no—
418#95—341no—
419#95—341no—
420#95C22⋊D1711yescharacteristic
421#95C22⋊D1711yescharacteristic
422C17#2676311yescharacteristic, complemented, Sylow
423C24—341no—
424C2×Q8—172no—
425C2×Q8—341no—
426C2×Q8—341no—
427C2×Q8—341no—
428C2×Q8—341no—
429C2×Q8—341no—
430C2×D4—172no—
431C2×D4—341no—
432C2×D4—341no—
433C2×D4—341no—
434C2×D4—341no—
435C2×D4—341no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—341no—
441C22×C4—341no—
442C22×C4—341no—
443C22×C4—682no—
444C22×C4—682no—
445C22×C4—1361no—
446C22×C4C2×C22⋊D1711yescharacteristic
447C22×C4C2×C22⋊D1711yescharacteristic
448C22×C4C2×C22⋊D1711yescharacteristic
449C22×C4C2×C22⋊D1711yescharacteristic
450C22×C4C2×C22⋊D1711yescharacteristic
451C22×C4C2×C22⋊D1711yescharacteristic
452C22×C4C23×D1711yescharacteristic
453C2×C8—341no—
454C2×C8—341no—
455C2×C8—341no—
456C2×C8—341no—
457C2×C8—341no—
458C2×C8—341no—
459C2×C8—341no—
460C2×C8—341no—
461C2×C8—341no—
462C2×C8—341no—
463C2×C8—341no—
464C2×C8—341no—
465C4⋊C4—21no—
466C4⋊C4—22no—
467C4⋊C4—22no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—42no—
475C4⋊C4—81no—
476C4⋊C4—81no—
477C4⋊C4—81no—
478C4⋊C4—81no—
479C4⋊C4—81no—
480C4⋊C4—172no—
481C4⋊C4—341no—
482C4⋊C4—341no—
483C4⋊C4—341no—
484C4⋊C4—682no—
485C4⋊C4#6325612yes—
486C22⋊C4—344no—
487C22⋊C4—344no—
488C22⋊C4—682no—
489C22⋊C4—682no—
490C22⋊C4—1361no—
491C42—21no—
492C42—21no—
493C42—21no—
494C42—21no—
495C42—21no—
496C42—21no—
497C42—81no—
498C42—682no—
499C42—1361no—
500C23—342no—
501C23—681no—
502C23—681no—
503C23—681no—
504C23—681no—
505C23—681no—
506C23—681no—
507C23C22×C22⋊D1711yescharacteristic
508Q8—342no—
509Q8—342no—
510Q8—681no—
511Q8—681no—
512D4—342no—
513D4—342no—
514D4—681no—
515D4—681no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—22no—
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—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—342no—
545C2×C4—342no—
546C2×C4—681no—
547C2×C4—681no—
548C2×C4—681no—
549C2×C4—681no—
550C2×C4—681no—
551C2×C4—681no—
552C2×C4—681no—
553C2×C4—1364no—
554C2×C4#1058762812yes—
555C2×C4#1058763612yes—
556C2×C4C2×#6325611yescharacteristic
557C2×C4#1058769411yescharacteristic
558C2×C4#41×D1711yescharacteristic
559C2×C4#41×D1711yescharacteristic
560C2×C4#41×D1711yescharacteristic
561C2×C4#1058769611yescharacteristic
562C8—681no—
563C8—681no—
564C8—681no—
565C8—681no—
566C22—682no—
567C22—682no—
568C22—682no—
569C22—1361no—
570C22—1361no—
571C22—1361no—
572C22—1361no—
573C22#1176331611yescharacteristic
574C22#1176344711yescharacteristic
575C22#1176347011yescharacteristic
576C22C2×#1058763611yescharacteristic
577C22C2×#1058762811yescharacteristic
578C22#1176361211yescharacteristic
579C22#1176362011yescharacteristic
580C4—22no—
581C4—22no—
582C4—41no—
583C4—41no—
584C4—42no—
585C4—41no—
586C4—41no—
587C4—81no—
588C4—81no—
589C4—81no—
590C4—682no—
591C4—682no—
592C4—1361no—
593C4#1176334411yescharacteristic
594C4#1176340711yescharacteristic
595C4#1176349111yescharacteristic
596C4#1176351211yescharacteristic
597C2—1362no—
598C2#1453273211yescharacteristic
599C2#1453884911yescharacteristic
600C2#1453897711yescharacteristic
601C2#1454068011yescharacteristic
602C2#1454085911yescharacteristic
603C2#1454144411yescharacteristic
604C2#1454152411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D17
commutator, cosocleC22×C4×C17C24
FrattiniC22×C4C23×D17
FittingC17×#2507C2
socleC23×C17C22×D4
prime radicalC22×D68C23
hypercenter#2507D17
hypocenterC17#26763
LCSG ▷ C22×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2507

Complements

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

NH ≅ G/Ntype
6. #14529459C2semidirect
7. #14529425C2semidirect
8. #14529359C2semidirect
9. #14529352C2semidirect
10. #14529343C2semidirect
11. #14529051C2semidirect
13. #14528786C2semidirect
15. C17×#2507C2semidirect
264. #2507D17semidirect
422. C17#26763semidirect

Maximal subgroups

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

subgroupindex
#145318532
#145301882
#145301692
#145300252
#145294592
#145294252
#145293592
#145293522
#145293432
#145290512
#145290442
#145287862
C4×#105874802
C17×#25072
#2676317