Finite Group Databasebeta

← #17004287

Subgroups — #17004287

Order 4352.

626 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14538796C211yesmaximal, characteristic
2#14537760C211yesmaximal, characteristic, complemented
3#14537740C211yesmaximal, characteristic, complemented
4#14527665C211yesmaximal, characteristic, complemented
5#14527658C211yesmaximal, characteristic, complemented
6#14527651C211yesmaximal, characteristic, complemented
7#14527644C211yesmaximal, characteristic, complemented
8#14527605C211yesmaximal, characteristic, complemented
9#14527600C211yesmaximal, characteristic, complemented
10#14527599C211yesmaximal, characteristic, complemented
11#14527593C211yesmaximal, characteristic, complemented
12#14527562C211yesmaximal, characteristic, complemented
13#14527219C211yesmaximal, characteristic, complemented
14#14527077C211yesmaximal, characteristic, complemented
15C17×#1482C211yesmaximal, characteristic, complemented
16C4×#63252C2211yescharacteristic
17#11763147C411yescharacteristic
18#11763130C411yescharacteristic
19#11763113C411yescharacteristic
20#11763106C411yescharacteristic
21#11763028C411yescharacteristic
22#11763021C411yescharacteristic
23#11762969C411yescharacteristic
24#11762952C411yescharacteristic
25#11762940C2211yescharacteristic
26Q8×#3622C2211yescharacteristic
27#11762933C2211yescharacteristic
28#11762933C2211yescharacteristic
29C4×#63231C2211yescharacteristic
30C4×#63230C2211yescharacteristic
31C4×#63229C2211yescharacteristic
32C4×#63228C2211yescharacteristic
33#11762887C2211yescharacteristic
34#11762881—21no—
35D4×#3622—21no—
36D4×#3622C2211yescharacteristic
37#11762874C2211yescharacteristic
38#11762874C2211yescharacteristic
39#11762872—21no—
40#11762872—21no—
41#11762870—21no—
42#11762866C2211yescharacteristic
43#11762862C2211yescharacteristic
44#11762860—21no—
45#11762765—21no—
46C2×C4×#3622C2211yescharacteristic
47C4×C8×D17—21no—
48#11762561C2211yescharacteristic
49#11762561C2211yescharacteristic
50#11762559C2211yescharacteristic
51#11762559C2211yescharacteristic
52#11762541C2211yescharacteristic
53#11762541C2211yescharacteristic
54#11762538C2211yescharacteristic
55#11762538C2211yescharacteristic
56#11762531C2211yescharacteristic
57#11762531C2211yescharacteristic
58#11762530C2211yescharacteristic
59#11762530C2211yescharacteristic
60C17×#529C2211yescharacteristic
61C17×#431C2211yescharacteristic
62C17×#431C2211yescharacteristic
63C17×Q8⋊C8C2211yescharacteristic
64C17×Q8⋊C8C2211yescharacteristic
65C17×D4⋊C8C2211yescharacteristic
66C17×D4⋊C8C2211yescharacteristic
67C2×#63252C2×C411yescharacteristic
68C17×#126—21no—
69C17×#125C2×C411yescharacteristic
70C17×#124C2×C411yescharacteristic
71C17×#123—21no—
72C17×C22⋊Q8C2×C411yescharacteristic
73C17×#121C2×C411yescharacteristic
74C4×Q8×C17C2311yescharacteristic
75C4×D4×C17—21no—
76C4×D4×C17C2311yescharacteristic
77C17×#117—21no—
78C2×C42×C17C2311yescharacteristic
79C2×#63231C2×C411yescharacteristic
80C2×#63230C2×C411yescharacteristic
81C2×#63229C2×C411yescharacteristic
82C2×#63228C2×C411yescharacteristic
83C4×C22⋊D17—21no—
84C4×C22⋊D17—21no—
85#10587612C2×C411yescharacteristic
86C2×#63223—21no—
87C22×#3622—21no—
88C22×#3622D411yescharacteristic
89C22×#3622D411yescharacteristic
90C2×C8×D17—21no—
91C2×C8×D17—21no—
92C4×D68C2×C411yescharacteristic
93C4×D68C2311yescharacteristic
94#10587558—21no—
95C42×D17—21no—
96C4×Dic34C2×C411yescharacteristic
97C4×Dic34C2311yescharacteristic
98C17×C4⋊C8—21no—
99C17×C4⋊C8C2311yescharacteristic
100C17×C4⋊C8C2311yescharacteristic
101C17×C22⋊C8—21no—
102C17×C22⋊C8—21no—
103C4×C8×C17—21no—
104C4×C8×C17C2311yescharacteristic
105C4×C8×C17C2311yescharacteristic
106#10587506C2×C411yescharacteristic
107#10587506C2×C411yescharacteristic
108#10587503C2×C411yescharacteristic
109#10587503C2×C411yescharacteristic
110C22⋊#3622—21no—
111C22⋊#3622—21no—
112C22⋊#3622—21no—
113C22⋊#3622C2×C411yescharacteristic
114C22⋊#3622C2×C411yescharacteristic
115#10587491—21no—
116#10587491—21no—
117#10587485—21no—
118#10587485—21no—
119C8×Dic17—21no—
120C8×Dic17—21no—
121#10587481C2×C411yescharacteristic
122#10587481C2×C411yescharacteristic
123#10587480C2×C411yescharacteristic
124#10587480C2×C411yescharacteristic
125#10587479C2×C411yescharacteristic
126#10587479C2×C411yescharacteristic
127#10587478C2×C411yescharacteristic
128#10587478C2×C411yescharacteristic
129C4⋊#3622—21no—
130C4⋊#3622—21no—
131C4⋊#3622C2×C411yescharacteristic
132C4⋊#3622C2×C411yescharacteristic
133C4⋊#3622C2311yescharacteristic
134C4⋊#3622C2311yescharacteristic
135#10587474—21no—
136#10587474—21no—
137C4×#3622—21no—
138C4×#3622D411yescharacteristic
139C4×#3622D411yescharacteristic
140C4×#3622C2311yescharacteristic
141C4×#3622C2311yescharacteristic
142C4×#3622C2311yescharacteristic
143C4×#3622C2311yescharacteristic
144C2×Q8×C17C22×C411yescharacteristic
145C2×D4×C17—21no—
146C2×D4×C17C22×C411yescharacteristic
147C22×C4×C17—21no—
148C22×C4×C17C22×C411yescharacteristic
149C22×C4×C17C2×D411yescharacteristic
150C22×C4×C17#4111yescharacteristic
151C2×C22⋊D17—21no—
152#63252—22no—
153#63252—22no—
154C2×D68C22×C411yescharacteristic
155C2×C4×D17—21no—
156C2×C4×D17—21no—
157C2×C4×D17—21no—
158C2×Dic34C22×C411yescharacteristic
159C2×C8×C17—21no—
160C2×C8×C17—21no—
161C2×C8×C17—21no—
162C2×C8×C17—21no—
163C4⋊C4×C17—21no—
164C4⋊C4×C17—21no—
165C4⋊C4×C17—21no—
166C4⋊C4×C17—21no—
167C4⋊C4×C17C22×C411yescharacteristic
168C4⋊C4×C17C22×C411yescharacteristic
169C22⋊C4×C17—21no—
170C22⋊C4×C17—21no—
171C22⋊C4×C17—21no—
172C22⋊C4×C17—21no—
173C22⋊C4×C17—21no—
174C42×C17—21no—
175C42×C17C22×C411yescharacteristic
176C42×C17C2×D411yescharacteristic
177C42×C17#4111yescharacteristic
178C42×C17C2411yescharacteristic
179C22⋊Dic17—21no—
180#63231—22no—
181#63230—22no—
182#63229—22no—
183#63228—22no—
184#63227—21no—
185#63227—21no—
186C4⋊Dic17C22×C411yescharacteristic
187C4⋊Dic17C22×C411yescharacteristic
188#63225—21no—
189#63225—21no—
190C4×Dic17—21no—
191C4×Dic17—21no—
192C4×Dic17—21no—
193#63223—42no—
194C2×#3622—21no—
195C2×#3622—21no—
196C2×#3622—41no—
197C2×#3622—41no—
198C2×#3622—42no—
199C2×#3622C22×C411yescharacteristic
200C2×#3622C22×C411yescharacteristic
201C2×#3622C22×C411yescharacteristic
202C2×#3622C22×C411yescharacteristic
203C2×#3622C2×D411yescharacteristic
204C2×#3622C2×D411yescharacteristic
205C2×#3622C2×D411yescharacteristic
206C2×#3622C2×D411yescharacteristic
207C8×D17—42no—
208C8×D17—42no—
209#17909—171nomaximal, Sylow
210C23×C17—21no—
211C23×C17C4×D411yescharacteristic
212C22×D17—21no—
213Q8×C17—21no—
214Q8×C17—21no—
215D4×C17—21no—
216D4×C17—21no—
217D4×C17—42no—
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—21no—
225C2×C4×C17—41no—
226C2×C4×C17—41no—
227C2×C4×C17—41no—
228C2×C4×C17C4×D411yescharacteristic
229C2×C4×C17C4×D411yescharacteristic
230C2×C4×C17C4×D411yescharacteristic
231C2×C4×C17C23×C411yescharacteristic
232C2×C4×C17C22×D411yescharacteristic
233C2×C4×C17C2×#4111yescharacteristic
234C22⋊D17—24no—
235C2×Dic17—21no—
236C2×Dic17—21no—
237C2×Dic17—21no—
238D68—21no—
239D68#13112yes—
240C4×D17—24no—
241C4×D17—42no—
242C4×D17—41no—
243C4×D17—41no—
244Dic34—21no—
245Dic34#13112yes—
246C8×C17—41no—
247C8×C17—41no—
248C8×C17—41no—
249C8×C17—41no—
250#3622—21no—
251#3622—21no—
252#3622—21no—
253#3622—21no—
254#3622—21no—
255#3622—21no—
256#3622—21no—
257#3622—21no—
258#3622—41no—
259#3622—41no—
260#3102—171no—
261#2966—171no—
262C8×#41—171no—
263#1588—171no—
264#1587—171no—
265#1586—171no—
266#1585—171no—
267#1580—171no—
268#1579—171no—
269SD16⋊C8—171no—
270SD16⋊C8—171no—
271#1572—171no—
272#1488—171no—
273#1482D1711yescharacteristic, complemented
274#1452—171no—
275C22×C17—21no—
276C22×C17—21no—
277C22×C17—21no—
278C22×C17—41no—
279C22×C17—41no—
280C22×C17—41no—
281C22×C17C2×C4×D411yescharacteristic
282C2×D17—22no—
283C2×D17—41no—
284C2×D17—41no—
285C4×C17—21no—
286C4×C17—21no—
287C4×C17—21no—
288C4×C17—21no—
289C4×C17—41no—
290C4×C17—41no—
291C4×C17—41no—
292C4×C17C2×#13111yescharacteristic
293C4×C17C2×#13111yescharacteristic
294C4×C17#57511yescharacteristic
295C4×C17#57511yescharacteristic
296Dic17—22no—
297Dic17—41no—
298Dic17—41no—
299#529C2×D1711yescharacteristic
300C4×#41—171no—
301#485—171no—
302#482—171no—
303#479—171no—
304#478—171no—
305#464—171no—
306#463—171no—
307#452—171no—
308#449—171no—
309#446—171no—
310C8×Q8—171no—
311C8×Q8—171no—
312C8×Q8—171no—
313C4×Q16—171no—
314C4×SD16—171no—
315C4×SD16—171no—
316C4×D8—171no—
317#436—171no—
318#435—341no—
319C8×D4—171no—
320C8×D4—171no—
321C8×D4—171no—
322C8×D4—341no—
323C8×D4—341no—
324C8×D4—341no—
325#433—341no—
326#432—171no—
327#431—171no—
328#431—341no—
329#431C2×D1711yescharacteristic
330#431C2×D1711yescharacteristic
331#405—341no—
332C2×C4×C8—171no—
333C2×C4×C8—341no—
334#335—171no—
335#335—171no—
336#334—171no—
337#334—171no—
338Q8⋊C8—171no—
339Q8⋊C8—171no—
340Q8⋊C8C2×D1711yescharacteristic
341Q8⋊C8C2×D1711yescharacteristic
342D4⋊C8—171no—
343D4⋊C8—171no—
344D4⋊C8C2×D1711yescharacteristic
345D4⋊C8C2×D1711yescharacteristic
346#322—171no—
347#322—171no—
348#322—171no—
349#322—171no—
350C2×C17—41no—
351C2×C17—81no—
352C2×C17#292911yescharacteristic
353C2×C17#294311yescharacteristic
354C2×C17#295511yescharacteristic
355D17—42no—
356C2×#41—171no—
357C2×Q16—171no—
358C2×SD16—171no—
359C2×SD16—171no—
360C2×D8—171no—
361C2×M16—341no—
362C22×C8—171no—
363C22×C8—171no—
364C22×C8—341no—
365C22×C8—341no—
366C22×C8—341no—
367#126—21no—
368#125C4×D1711yescharacteristic
369#124C4×D1711yescharacteristic
370#123—21no—
371C22⋊Q8C4×D1711yescharacteristic
372#121C4×D1711yescharacteristic
373C4×Q8—171no—
374C4×Q8—171no—
375C4×Q8C22×D1711yescharacteristic
376C4×D4—21no—
377C4×D4—171no—
378C4×D4—171no—
379C4×D4—341no—
380C4×D4—341no—
381C4×D4C22×D1711yescharacteristic
382#117—21no—
383#117—171no—
384#117—341no—
385C2×C42—341no—
386C2×C42C22×D1711yescharacteristic
387#107—171no—
388#107—171no—
389#106—171no—
390#106—171no—
391C4⋊C8—21no—
392C4⋊C8—171no—
393C4⋊C8—171no—
394C4⋊C8—171no—
395C4⋊C8—171no—
396C4⋊C8—341no—
397C4⋊C8—341no—
398C4⋊C8—341no—
399C4⋊C8—341no—
400C4⋊C8C22×D1711yescharacteristic
401C4⋊C8C22×D1711yescharacteristic
402#103—171no—
403#103—171no—
404#103—171no—
405#103—171no—
406#102—171no—
407#102—171no—
408#102—171no—
409#102—171no—
410C22⋊C8—21no—
411C22⋊C8—21no—
412C22⋊C8—171no—
413C22⋊C8—171no—
414C22⋊C8—341no—
415C22⋊C8—341no—
416C22⋊C8—341no—
417C22⋊C8—341no—
418C22⋊C8—341no—
419#97—341no—
420#97—341no—
421C4×C8—21no—
422C4×C8—171no—
423C4×C8—171no—
424C4×C8—171no—
425C4×C8—171no—
426C4×C8—171no—
427C4×C8—171no—
428C4×C8—341no—
429C4×C8—341no—
430C4×C8—341no—
431C4×C8C22×D1711yescharacteristic
432C4×C8C22×D1711yescharacteristic
433C17#1790911yescharacteristic, complemented, Sylow
434#41—342no—
435#41—342no—
436C2×Q8—171no—
437C2×Q8C2×C4×D1711yescharacteristic
438C2×D4—21no—
439C2×D4—171no—
440C2×D4—341no—
441C2×D4C2×C4×D1711yescharacteristic
442C22×C4—21no—
443C22×C4—341no—
444C22×C4—341no—
445C22×C4—341no—
446C22×C4C2×C4×D1711yescharacteristic
447C22×C4D4×D1711yescharacteristic
448C22×C4#6325411yescharacteristic
449Q16—342no—
450SD16—342no—
451SD16—342no—
452D8—342no—
453M16—682no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—171no—
459C2×C8—171no—
460C2×C8—171no—
461C2×C8—171no—
462C2×C8—171no—
463C2×C8—171no—
464C2×C8—171no—
465C2×C8—171no—
466C2×C8—341no—
467C2×C8—341no—
468C2×C8—682no—
469C2×C8—682no—
470C2×C8—681no—
471C2×C8—681no—
472C2×C8—682no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—171no—
478C4⋊C4—171no—
479C4⋊C4—341no—
480C4⋊C4—341no—
481C4⋊C4C2×C4×D1711yescharacteristic
482C4⋊C4C2×C4×D1711yescharacteristic
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—341no—
489C22⋊C4—341no—
490C22⋊C4—341no—
491C42—21no—
492C42—341no—
493C42—341no—
494C42—341no—
495C42C2×C4×D1711yescharacteristic
496C42D4×D1711yescharacteristic
497C42#6325411yescharacteristic
498C42C23×D1711yescharacteristic
499C23—21no—
500C23—341no—
501C23#1058756711yescharacteristic
502Q8—21no—
503Q8—21no—
504Q8—172no—
505Q8—341no—
506D4—21no—
507D4—21no—
508D4—42no—
509D4—172no—
510D4—344no—
511D4—341no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—344no—
523C2×C4—341no—
524C2×C4—341no—
525C2×C4—341no—
526C2×C4—682no—
527C2×C4—681no—
528C2×C4—681no—
529C2×C4#1058756711yescharacteristic
530C2×C4#1058756711yescharacteristic
531C2×C4#1058756711yescharacteristic
532C2×C4C22×C4×D1711yescharacteristic
533C2×C4C2×D4×D1711yescharacteristic
534C2×C4C2×#6325411yescharacteristic
535C8—41no—
536C8—41no—
537C8—41no—
538C8—41no—
539C8—341no—
540C8—341no—
541C8—341no—
542C8—341no—
543C8—341no—
544C8—341no—
545C8—341no—
546C8—341no—
547C8—681no—
548C8—681no—
549C22—21no—
550C22—21no—
551C22—21no—
552C22—41no—
553C22—41no—
554C22—41no—
555C22—342no—
556C22—681no—
557C22—681no—
558C22C2×#1058756711yescharacteristic
559C4—21no—
560C4—21no—
561C4—21no—
562C4—21no—
563C4—41no—
564C4—41no—
565C4—41no—
566C4—342no—
567C4—681no—
568C4—681no—
569C4#131×D1711yescharacteristic
570C4#131×D1711yescharacteristic
571C4#1176360611yescharacteristic
572C4#1176360611yescharacteristic
573C2—41no—
574C2—81no—
575C2—682no—
576C2#1453748111yescharacteristic
577C2#1453758011yescharacteristic
578C2#1453768311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D17
commutatorC2×C4×C17C23×C4
FrattiniC42C23×D17
FittingC17×#1482C2
socleC22×C17C2×C4×D4
prime radical#11762952C4
cosocleC42×C17C24
hypercenter#1482D17
hypocenterC17#17909
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1482

Complements

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

NH ≅ G/Ntype
2. #14537760C2semidirect
3. #14537740C2semidirect
4. #14527665C2semidirect
5. #14527658C2semidirect
6. #14527651C2semidirect
7. #14527644C2semidirect
8. #14527605C2semidirect
9. #14527600C2semidirect
10. #14527599C2semidirect
11. #14527593C2semidirect
12. #14527562C2semidirect
13. #14527219C2semidirect
14. #14527077C2semidirect
15. C17×#1482C2semidirect
273. #1482D17semidirect
433. C17#17909semidirect

Maximal subgroups

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

subgroupindex
#145387962
#145377602
#145377402
#145276652
#145276582
#145276512
#145276442
#145276052
#145276002
#145275992
#145275932
#145275622
#145272192
#145270772
C17×#14822
#1790917