Finite Group Databasebeta

← #17005143

Subgroups — #17005143

Order 4352.

606 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14539379C211yesmaximal, characteristic
2#14537935C211yesmaximal, characteristic, complemented
3#14537859C211yesmaximal, characteristic, complemented
4#14527664C211yesmaximal, characteristic, complemented
5#14527650C211yesmaximal, characteristic, complemented
6#14527650C211yesmaximal, characteristic, complemented
7#14527643C211yesmaximal, characteristic, complemented
8#14527629C211yesmaximal, characteristic, complemented
9#14527622C211yesmaximal, characteristic, complemented
10#14527615C211yesmaximal, characteristic, complemented
11#14527615C211yesmaximal, characteristic, complemented
12#14527551C211yesmaximal, characteristic, complemented
13#14527245C211yesmaximal, characteristic, complemented
14#14527236C211yesmaximal, characteristic, complemented
15C17×#1451C211yesmaximal, characteristic, complemented
16#11763359C2211yescharacteristic
17#11763343C2211yescharacteristic
18#11763218C411yescharacteristic
19#11763198C411yescharacteristic
20#11763174C411yescharacteristic
21#11763169C411yescharacteristic
22#11763062C411yescharacteristic
23#11763062C411yescharacteristic
24#11763055C411yescharacteristic
25#11763055C411yescharacteristic
26#11762939C2211yescharacteristic
27C8×Dic34C2211yescharacteristic
28C4×#63219C2211yescharacteristic
29C4×#63219C2211yescharacteristic
30C4×D136C2211yescharacteristic
31C4×D136C2211yescharacteristic
32#11762888C2211yescharacteristic
33#11762888C2211yescharacteristic
34#11762888C2211yescharacteristic
35#11762884—21no—
36#11762883—21no—
37#11762879—21no—
38#11762879—21no—
39C8×D68C2211yescharacteristic
40C8×D68C2211yescharacteristic
41C8×D68C2211yescharacteristic
42#11762869—21no—
43#11762866C2211yescharacteristic
44#11762834—21no—
45#11762833C2211yescharacteristic
46#11762774—21no—
47#11762774—21no—
48#11762562C2211yescharacteristic
49#11762562C2211yescharacteristic
50#11762560C2211yescharacteristic
51#11762560C2211yescharacteristic
52#11762541C2211yescharacteristic
53#11762541C2211yescharacteristic
54#11762538C2211yescharacteristic
55#11762538C2211yescharacteristic
56#11762538C2211yescharacteristic
57#11762538C2211yescharacteristic
58#11762538C2211yescharacteristic
59#11762538C2211yescharacteristic
60C17×#431C2211yescharacteristic
61C4×M16×C17C2211yescharacteristic
62C2×C4×C8×C17C2211yescharacteristic
63C17×#322C2211yescharacteristic
64C17×#322C2211yescharacteristic
65C17×#322C2211yescharacteristic
66C17×#322C2211yescharacteristic
67C2×#63252—21no—
68C2×M16×C17C2×C411yescharacteristic
69C2×M16×C17C2×C411yescharacteristic
70C22×C8×C17—21no—
71C2×C42×C17C2311yescharacteristic
72#10587616—21no—
73#10587616C2×C411yescharacteristic
74#10587616C2×C411yescharacteristic
75#10587616C2×C411yescharacteristic
76#10587615—21no—
77C4×C22⋊D17—21no—
78#10587610C2×C411yescharacteristic
79C2×#63223—21no—
80C2×D136C2×C411yescharacteristic
81C2×D136C2×C411yescharacteristic
82C2×#63219C2×C411yescharacteristic
83C2×#63219C2×C411yescharacteristic
84C2×#63218—21no—
85C2×#63218—21no—
86C2×#63218—21no—
87C2×C8×D17—21no—
88C2×C8×D17—21no—
89C2×C8×D17—21no—
90#10587562—21no—
91#10587561—21no—
92#10587561C2×C411yescharacteristic
93#10587560C2×C411yescharacteristic
94C4×D68—21no—
95C4×D68C2311yescharacteristic
96C4×D68C2311yescharacteristic
97C4×D68C2311yescharacteristic
98#10587558—21no—
99#10587556C2×C411yescharacteristic
100#10587555C2×C411yescharacteristic
101C4×Dic34C2311yescharacteristic
102C17×C4⋊C8D411yescharacteristic
103C17×C4⋊C8D411yescharacteristic
104C17×C22⋊C8D411yescharacteristic
105C17×C22⋊C8D411yescharacteristic
106C17×#97C2×C411yescharacteristic
107C17×#97C2×C411yescharacteristic
108C4×C8×C17—21no—
109C4×C8×C17C2311yescharacteristic
110C4×C8×C17C2311yescharacteristic
111C4×C8×C17C2311yescharacteristic
112C4×C8×C17C2311yescharacteristic
113C4×C8×C17C2311yescharacteristic
114C4×C8×C17C2311yescharacteristic
115C22⋊#3622—21no—
116#10587492C2×C411yescharacteristic
117#10587492C2×C411yescharacteristic
118#10587492C2×C411yescharacteristic
119#10587492C2×C411yescharacteristic
120#10587492C2×C411yescharacteristic
121#10587492C2×C411yescharacteristic
122#10587491—21no—
123#10587491—21no—
124#10587491—21no—
125#10587491—21no—
126#10587491—21no—
127#10587491—21no—
128#10587489C2×C411yescharacteristic
129#10587489C2×C411yescharacteristic
130#10587488C2×C411yescharacteristic
131#10587488C2×C411yescharacteristic
132#10587487C2×C411yescharacteristic
133#10587487C2×C411yescharacteristic
134#10587486—21no—
135#10587485—21no—
136#10587485—21no—
137C8×Dic17—21no—
138C4⋊#3622—21no—
139C4⋊#3622C2311yescharacteristic
140C4⋊#3622C2311yescharacteristic
141C4⋊#3622C2311yescharacteristic
142C4⋊#3622C2311yescharacteristic
143#10587474—21no—
144C22×C4×C17C22×C411yescharacteristic
145C22×C4×C17C2×D411yescharacteristic
146C22×C4×C17#4111yescharacteristic
147C2×C22⋊D17—21no—
148C2×C22⋊D17—21no—
149C2×C22⋊D17—21no—
150#63252—81no—
151#63252—81no—
152C2×D68—21no—
153C2×D68—21no—
154C2×D68C22×C411yescharacteristic
155C2×D68C22×C411yescharacteristic
156C2×D68C22×C411yescharacteristic
157C2×C4×D17—21no—
158C2×C4×D17—21no—
159C2×C4×D17—21no—
160C2×Dic34—21no—
161C2×Dic34C22×C411yescharacteristic
162M16×C17—41no—
163M16×C17—41no—
164C2×C8×C17—21no—
165C2×C8×C17—21no—
166C2×C8×C17—42no—
167C2×C8×C17C22×C411yescharacteristic
168C2×C8×C17C22×C411yescharacteristic
169C2×C8×C17C22×C411yescharacteristic
170C2×C8×C17C22×C411yescharacteristic
171C2×C8×C17C2×D411yescharacteristic
172C2×C8×C17C2×D411yescharacteristic
173C2×C8×C17C2×D411yescharacteristic
174C2×C8×C17C2×D411yescharacteristic
175C42×C17C22×C411yescharacteristic
176C42×C17C2×D411yescharacteristic
177C42×C17#4111yescharacteristic
178C42×C17C2411yescharacteristic
179C22⋊Dic17—21no—
180#63227—21no—
181#63227—21no—
182#63227—21no—
183#63227—21no—
184#63227—21no—
185#63227—21no—
186#63227—21no—
187#63227—21no—
188C4⋊Dic17—21no—
189C4⋊Dic17C22×C411yescharacteristic
190C4⋊Dic17C22×C411yescharacteristic
191C4⋊Dic17C22×C411yescharacteristic
192C4⋊Dic17C22×C411yescharacteristic
193#63225—21no—
194#63225—21no—
195#63225—21no—
196#63225—21no—
197C4×Dic17—21no—
198#63223—81no—
199C2×#3622—21no—
200C2×#3622—21no—
201C2×#3622—21no—
202C2×#3622—21no—
203D136—41no—
204D136—41no—
205#63219—41no—
206#63219—41no—
207#63218—81no—
208#63218—81no—
209#63218—81no—
210C8×D17—81no—
211C8×D17—81no—
212C8×D17—81no—
213#17987—171nomaximal, Sylow
214C23×C17C4×D411yescharacteristic
215C22×D17—21no—
216C22×D17—21no—
217C22×D17—21no—
218C2×C4×C17—21no—
219C2×C4×C17—21no—
220C2×C4×C17—21no—
221C2×C4×C17—21no—
222C2×C4×C17—41no—
223C2×C4×C17C4×D411yescharacteristic
224C2×C4×C17C4×D411yescharacteristic
225C2×C4×C17C4×D411yescharacteristic
226C2×C4×C17C23×C411yescharacteristic
227C2×C4×C17C22×D411yescharacteristic
228C2×C4×C17C2×#4111yescharacteristic
229C22⋊D17—81no—
230C22⋊D17—81no—
231C22⋊D17—81no—
232C2×Dic17—21no—
233C2×Dic17—21no—
234C2×Dic17—21no—
235C2×Dic17—21no—
236C2×Dic17—21no—
237D68—21no—
238D68—21no—
239D68—21no—
240D68—21no—
241D68—21no—
242D68—21no—
243D68—81no—
244D68—81no—
245C4×D17—41no—
246C4×D17—41no—
247C4×D17—41no—
248C4×D17—41no—
249C4×D17—41no—
250C4×D17—41no—
251Dic34—21no—
252Dic34—21no—
253Dic34—81no—
254C8×C17—22no—
255C8×C17—21no—
256C8×C17—21no—
257C8×C17—21no—
258C8×C17—21no—
259C8×C17—21no—
260C8×C17—21no—
261C8×C17—21no—
262C8×C17—21no—
263C8×C17—41no—
264#3622—41no—
265#3622—41no—
266#3622—41no—
267#3622—41no—
268#3171—171no—
269#2993—171no—
270#2981—171no—
271#1588—171no—
272#1586—171no—
273#1586—171no—
274#1585—171no—
275#1583—171no—
276#1582—171no—
277#1581—171no—
278#1581—171no—
279#1569—171no—
280#1494—171no—
281#1492—171no—
282#1451D1711yescharacteristic, complemented
283C22×C17—21no—
284C22×C17—21no—
285C22×C17—21no—
286C22×C17C2×C4×D411yescharacteristic
287C2×D17—41no—
288C2×D17—41no—
289C2×D17—41no—
290C2×D17—41no—
291C2×D17—41no—
292C2×D17—41no—
293C2×D17—41no—
294C2×D17—41no—
295C2×D17—41no—
296C4×C17—21no—
297C4×C17—21no—
298C4×C17—21no—
299C4×C17—21no—
300C4×C17#56811yescharacteristic
301C4×C17#56811yescharacteristic
302C4×C17#57611yescharacteristic
303C4×C17#57711yescharacteristic
304Dic17—41no—
305Dic17—41no—
306Dic17—41no—
307Dic17—41no—
308Dic17—41no—
309#532—171no—
310#529—171no—
311#501—171no—
312#496—171no—
313#490—171no—
314#489—171no—
315#469—171no—
316#469—171no—
317#468—171no—
318#468—171no—
319#446—171no—
320C8×Q8—171no—
321C4×SD16—171no—
322C4×SD16—171no—
323C4×D8—171no—
324C4×D8—171no—
325#436—171no—
326#436—171no—
327#436—171no—
328#436—341no—
329#435—341no—
330#435—341no—
331#435—341no—
332C8×D4—171no—
333C8×D4—171no—
334C8×D4—171no—
335#433—341no—
336#432—171no—
337#431C2×D1711yescharacteristic
338#424—341no—
339#423—171no—
340#408—341no—
341#408—341no—
342C4×M16C2×D1711yescharacteristic
343C2×C4×C8C2×D1711yescharacteristic
344#335—171no—
345#335—171no—
346#334—171no—
347#334—171no—
348Q8⋊C8—171no—
349Q8⋊C8—171no—
350D4⋊C8—171no—
351D4⋊C8—171no—
352D4⋊C8—171no—
353D4⋊C8—171no—
354D4⋊C8—171no—
355D4⋊C8—171no—
356#322C2×D1711yescharacteristic
357#322C2×D1711yescharacteristic
358#322C2×D1711yescharacteristic
359#322C2×D1711yescharacteristic
360C2×C17—41no—
361C2×C17#293211yescharacteristic
362C2×C17#294611yescharacteristic
363C2×C17#295611yescharacteristic
364D17—81no—
365D17—81no—
366D17—81no—
367C2×#41—341no—
368C2×SD16—171no—
369C2×SD16—171no—
370C2×D8—171no—
371C2×D8—171no—
372C2×M16—341no—
373C2×M16—341no—
374C2×M16—341no—
375C2×M16—341no—
376C2×M16C4×D1711yescharacteristic
377C2×M16C4×D1711yescharacteristic
378C22×C8—21no—
379C22×C8—341no—
380C22×C8—341no—
381C22×C8—341no—
382C4⋊Q8—171no—
383#127—171no—
384#126—341no—
385#125—171no—
386#124—171no—
387#124—341no—
388#123—341no—
389C22⋊Q8—171no—
390#121—171no—
391#121—171no—
392#121—171no—
393#121—341no—
394C4×Q8—171no—
395C4×D4—171no—
396C4×D4—171no—
397C4×D4—171no—
398C4×D4—341no—
399C4×D4—341no—
400#117—341no—
401C2×C42C22×D1711yescharacteristic
402#107—171no—
403#107—171no—
404#106—171no—
405#106—171no—
406C4⋊C8—171no—
407C4⋊C8—171no—
408C4⋊C8—171no—
409C4⋊C8—171no—
410C4⋊C8—341no—
411C4⋊C8—341no—
412C4⋊C8—341no—
413C4⋊C8D6811yescharacteristic
414C4⋊C8D6811yescharacteristic
415#103—171no—
416#103—171no—
417#102—171no—
418#102—171no—
419#102—171no—
420#102—171no—
421#102—171no—
422#102—171no—
423C22⋊C8—341no—
424C22⋊C8—341no—
425C22⋊C8—341no—
426C22⋊C8—341no—
427C22⋊C8—341no—
428C22⋊C8—341no—
429C22⋊C8—341no—
430C22⋊C8D6811yescharacteristic
431C22⋊C8D6811yescharacteristic
432#97—341no—
433#97—341no—
434#97C4×D1711yescharacteristic
435#97C4×D1711yescharacteristic
436C4×C8—21no—
437C4×C8—341no—
438C4×C8C22×D1711yescharacteristic
439C4×C8C22×D1711yescharacteristic
440C4×C8C22×D1711yescharacteristic
441C4×C8C22×D1711yescharacteristic
442C4×C8C22×D1711yescharacteristic
443C4×C8C22×D1711yescharacteristic
444C17#1798711yescharacteristic, complemented, Sylow
445#41—1361no—
446#41—1361no—
447C2×Q8—171no—
448C2×Q8—341no—
449C2×D4—171no—
450C2×D4—171no—
451C2×D4—171no—
452C2×D4—341no—
453C2×D4—341no—
454C2×D4—341no—
455C2×D4—341no—
456C2×D4—341no—
457C22×C4—341no—
458C22×C4—341no—
459C22×C4—341no—
460C22×C4C2×C4×D1711yescharacteristic
461C22×C4C2×D6811yescharacteristic
462C22×C4#6325211yescharacteristic
463SD16—681no—
464SD16—681no—
465D8—681no—
466D8—681no—
467M16—41no—
468M16—41no—
469M16—1361no—
470M16—1361no—
471M16—1361no—
472M16—1361no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—42no—
476C2×C8—341no—
477C2×C8—341no—
478C2×C8—341no—
479C2×C8—341no—
480C2×C8—1361no—
481C2×C8—1361no—
482C2×C8—1361no—
483C2×C8C2×C4×D1711yescharacteristic
484C2×C8C2×C4×D1711yescharacteristic
485C2×C8C2×C4×D1711yescharacteristic
486C2×C8C2×C4×D1711yescharacteristic
487C2×C8C2×D6811yescharacteristic
488C2×C8C2×D6811yescharacteristic
489C2×C8C2×D6811yescharacteristic
490C2×C8C2×D6811yescharacteristic
491C4⋊C4—171no—
492C4⋊C4—171no—
493C4⋊C4—171no—
494C4⋊C4—171no—
495C4⋊C4—341no—
496C4⋊C4—341no—
497C4⋊C4—341no—
498C4⋊C4—341no—
499C4⋊C4—341no—
500C22⋊C4—341no—
501C22⋊C4—341no—
502C22⋊C4—341no—
503C22⋊C4—341no—
504C22⋊C4—341no—
505C22⋊C4—341no—
506C22⋊C4—341no—
507C22⋊C4—341no—
508C22⋊C4—341no—
509C42—341no—
510C42C2×C4×D1711yescharacteristic
511C42C2×D6811yescharacteristic
512C42#6325211yescharacteristic
513C42C23×D1711yescharacteristic
514C23—341no—
515C23—341no—
516C23—341no—
517C23C4×D6811yescharacteristic
518Q8—341no—
519Q8—341no—
520Q8—1361no—
521D4—341no—
522D4—341no—
523D4—341no—
524D4—341no—
525D4—341no—
526D4—341no—
527D4—1361no—
528D4—1361no—
529D4—1361no—
530D4—1361no—
531D4—1361no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—41no—
537C2×C4—341no—
538C2×C4—341no—
539C2×C4—341no—
540C2×C4—341no—
541C2×C4—341no—
542C2×C4—681no—
543C2×C4—681no—
544C2×C4—681no—
545C2×C4—681no—
546C2×C4—681no—
547C2×C4—681no—
548C2×C4C4×D6811yescharacteristic
549C2×C4C4×D6811yescharacteristic
550C2×C4C4×D6811yescharacteristic
551C2×C4C22×C4×D1711yescharacteristic
552C2×C4C22×D6811yescharacteristic
553C2×C4C2×#6325211yescharacteristic
554C8—22no—
555C8—21no—
556C8—21no—
557C8—21no—
558C8—21no—
559C8—21no—
560C8—21no—
561C8—21no—
562C8—21no—
563C8—41no—
564C8—681no—
565C8—681no—
566C8—681no—
567C8—681no—
568C22—21no—
569C22—21no—
570C22—21no—
571C22—681no—
572C22—681no—
573C22—681no—
574C22—681no—
575C22—681no—
576C22—681no—
577C22—681no—
578C22—681no—
579C22—681no—
580C22C2×C4×D6811yescharacteristic
581C4—21no—
582C4—21no—
583C4—21no—
584C4—21no—
585C4—681no—
586C4—681no—
587C4—681no—
588C4—681no—
589C4—681no—
590C4#1176357511yescharacteristic
591C4#1176357511yescharacteristic
592C4#1176361411yescharacteristic
593C4#1176362111yescharacteristic
594C2—41no—
595C2—1361no—
596C2—1361no—
597C2—1361no—
598C2#1453750311yescharacteristic
599C2#1453761811yescharacteristic
600C2#1453769511yescharacteristic
subgroupG/H
centerC2×C4C22×D68
commutatorC2×C4×C17C23×C4
FrattiniC42C23×D17
FittingC17×#1451C2
socleC22×C17C2×C4×D4
prime radical#14539379C2
cosocleC42×C17C24
hypercenter#1451D17
hypocenterC17#17987
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ #431 ◁ #1451

Complements

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

NH ≅ G/Ntype
2. #14537935C2semidirect
3. #14537859C2semidirect
4. #14527664C2semidirect
5. #14527650C2semidirect
6. #14527650C2semidirect
7. #14527643C2semidirect
8. #14527629C2semidirect
9. #14527622C2semidirect
10. #14527615C2semidirect
11. #14527615C2semidirect
12. #14527551C2semidirect
13. #14527245C2semidirect
14. #14527236C2semidirect
15. C17×#1451C2semidirect
282. #1451D17semidirect
444. C17#17987semidirect

Maximal subgroups

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

subgroupindex
#145393792
#145379352
#145378592
#145276642
#145276502
#145276432
#145276292
#145276222
#145276152
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C17×#14512
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