Finite Group Databasebeta

← #17004461

Subgroups — #17004461

Order 4352.

638 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14538790C211yesmaximal, characteristic
2#14537880C211yesmaximal, characteristic, complemented
3#14537805C211yesmaximal, characteristic
4#14527643C211yesmaximal, characteristic, complemented
5#14527620C211yesmaximal, characteristic, complemented
6#14527618C211yesmaximal, characteristic, complemented
7SD16⋊#3622C211yesmaximal, characteristic, complemented
8#14527595C211yesmaximal, characteristic, complemented
9#14527587C211yesmaximal, characteristic, complemented
10#14527581C211yesmaximal, characteristic, complemented
11#14527563C211yesmaximal, characteristic, complemented
12#14527225C211yesmaximal, characteristic
13#14527203C211yesmaximal, characteristic, complemented
14#14527082C211yesmaximal, characteristic, complemented
15C17×#1585C211yesmaximal, characteristic, complemented
16#11763363C2211yescharacteristic
17C4×D4×D17C2211yescharacteristic
18#11763141C411yescharacteristic
19#11763138C411yescharacteristic
20#11763098C411yescharacteristic
21#11763097C411yescharacteristic
22#11763013C411yescharacteristic
23#11763012C411yescharacteristic
24#11762961C411yescharacteristic
25#11762958C411yescharacteristic
26#11762939C2211yescharacteristic, complemented
27#11762937—21no—
28#11762936—21no—
29Q8×#3622C2211yescharacteristic, complemented
30#11762933C2211yescharacteristic, complemented
31C4×#63219C2211yescharacteristic
32C4×#63230C2211yescharacteristic
33C4×#63229C2211yescharacteristic
34C8×D68C2211yescharacteristic
35D4×#3622C2211yescharacteristic
36#11762874C2211yescharacteristic
37C8×C22⋊D17—21no—
38#11762872—21no—
39#11762871—21no—
40#11762869—21no—
41#11762865C2211yescharacteristic
42#11762861C2211yescharacteristic
43#11762860C2211yescharacteristic
44#11762860C2211yescharacteristic
45C2×#10587491—21no—
46C22⋊C8×D17—21no—
47C4×#63218C2211yescharacteristic
48#11762562C2211yescharacteristic, complemented
49#11762559C2211yescharacteristic, complemented
50#11762559C2211yescharacteristic, complemented
51#11762541C2211yescharacteristic, complemented
52Q8⋊#3622C2211yescharacteristic, complemented
53#11762539C2211yescharacteristic, complemented
54#11762538C2211yescharacteristic
55D4⋊#3622C2211yescharacteristic
56#11762536C2211yescharacteristic
57#11762530C2211yescharacteristic, complemented
58#11762530C2211yescharacteristic, complemented
59C8×#3622C2211yescharacteristic, complemented
60C17×#446C2211yescharacteristic, complemented
61C4×SD16×C17C2211yescharacteristic
62C8×D4×C17C2211yescharacteristic
63C17×#335C2211yescharacteristic, complemented
64C17×Q8⋊C8C2211yescharacteristic, complemented
65C17×D4⋊C8C2211yescharacteristic
66C17×#322C2211yescharacteristic, complemented
67C2×D4×D17C2×C411yescharacteristic
68C22×C4×D17—21no—
69C2×SD16×C17C2×C411yescharacteristic
70C22×C8×C17—21no—
71C4×Q8×C17C2311yescharacteristic
72C4×D4×C17C2311yescharacteristic
73#10587632C2×C411yescharacteristic
74#10587630C2×C411yescharacteristic
75C2×#63230C2×C411yescharacteristic
76D4×Dic17C2×C411yescharacteristic
77C2×#63229C2×C411yescharacteristic
78C4×C22⋊D17—21no—
79C22×#3622—21no—
80C2×#63219C2×C411yescharacteristic
81C2×#63218—21no—
82C2×C8×D17—21no—
83C2×C8×D17—21no—
84#10587583C2×C411yescharacteristic
85#10587582—21no—
86#10587579C2×C411yescharacteristic
87C4⋊C4×D17C2×C411yescharacteristic
88#10587575—21no—
89#10587574C2×C411yescharacteristic
90#10587567—21no—
91C22⋊C4×D17—21no—
92C4×D68C2311yescharacteristic
93#10587558—21no—
94C42×D17C2311yescharacteristic
95C4×Dic34—21no—
96C4×Dic34C2311yescharacteristic
97C17×#106C2×C411yescharacteristic
98C17×C4⋊C8—21no—
99C17×C4⋊C8C2311yescharacteristic
100C17×C4⋊C8C2311yescharacteristic
101C17×#103C2×C411yescharacteristic
102C17×#102C2×C411yescharacteristic
103C17×C22⋊C8—21no—
104C17×#97—21no—
105C4×C8×C17C2311yescharacteristic
106C4×C8×C17C2311yescharacteristic
107C4×C8×C17C2311yescharacteristic
108#10587506C2×C411yescharacteristic
109#10587503C2×C411yescharacteristic
110C22⋊#3622—21no—
111#10587492C2×C411yescharacteristic
112#10587491—21no—
113#10587491—21no—
114#10587491—21no—
115#10587491—21no—
116#10587491C2×C411yescharacteristic
117#10587491C2×C411yescharacteristic
118#10587491D411yescharacteristic
119#10587491D411yescharacteristic
120#10587488C2×C411yescharacteristic
121#10587487C2×C411yescharacteristic
122#10587486—21no—
123#10587486—21no—
124#10587486—21no—
125#10587485—21no—
126#10587485—21no—
127#10587485C2×C411yescharacteristic
128#10587485C2×C411yescharacteristic
129#10587485D411yescharacteristic
130#10587485D411yescharacteristic
131C8×Dic17—21no—
132C8×Dic17—21no—
133#10587481C2×C411yescharacteristic
134#10587480C2×C411yescharacteristic
135#10587479C2×C411yescharacteristic
136#10587479C2×C411yescharacteristic
137C4⋊#3622—21no—
138C4⋊#3622C2311yescharacteristic
139C4⋊#3622C2311yescharacteristic
140C4×#3622—21no—
141C4×#3622C2311yescharacteristic
142C4×#3622C2311yescharacteristic
143C4×#3622C2311yescharacteristic
144C23×D17—21no—
145C2×Q8×C17C22×C411yescharacteristic
146C2×D4×C17C22×C411yescharacteristic
147C22×C4×C17—21no—
148C2×C22⋊D17—21no—
149C22×Dic17—21no—
150D4×D17—22no—
151D4×D17—22no—
152C2×D68C22×C411yescharacteristic
153C2×C4×D17—21no—
154C2×C4×D17—21no—
155C2×C4×D17—21no—
156C2×C4×D17—81no—
157C2×C4×D17—81no—
158C2×C4×D17C22×C411yescharacteristic
159C2×C4×D17C2×D411yescharacteristic
160C2×C4×D17#4111yescharacteristic
161C2×Dic34—21no—
162C2×Dic34C22×C411yescharacteristic
163SD16×C17—22no—
164C2×C8×C17—21no—
165C2×C8×C17—21no—
166C2×C8×C17—21no—
167C2×C8×C17—81no—
168C2×C8×C17C22×C411yescharacteristic
169C2×C8×C17C22×C411yescharacteristic
170C2×C8×C17C2×D411yescharacteristic
171C2×C8×C17C2×D411yescharacteristic
172C4⋊C4×C17—21no—
173C4⋊C4×C17C22×C411yescharacteristic
174C4⋊C4×C17C22×C411yescharacteristic
175C22⋊C4×C17—21no—
176C42×C17—21no—
177C42×C17C2411yescharacteristic
178C22⋊Dic17—21no—
179#63230—22no—
180#63229—22no—
181#63227—21no—
182#63227—21no—
183#63227—21no—
184#63227—21no—
185C4⋊Dic17—21no—
186C4⋊Dic17C22×C411yescharacteristic
187C4⋊Dic17C22×C411yescharacteristic
188#63225—21no—
189#63225—21no—
190#63225—21no—
191#63225—21no—
192#63225—21no—
193#63225—21no—
194C4×Dic17—21no—
195C4×Dic17C22×C411yescharacteristic
196C4×Dic17C2×D411yescharacteristic
197C4×Dic17#4111yescharacteristic
198C2×#3622—21no—
199C2×#3622—21no—
200C2×#3622—21no—
201C2×#3622—81no—
202C2×#3622C22×C411yescharacteristic
203C2×#3622C22×C411yescharacteristic
204C2×#3622C2×D411yescharacteristic
205C2×#3622C2×D411yescharacteristic
206#63219—22no—
207#63218—42no—
208C8×D17—81no—
209C8×D17—81no—
210#17924—171nomaximal, Sylow
211C23×C17—21no—
212C22×D17—21no—
213C22×D17—24no—
214C22×D17—81no—
215C22×D17—81no—
216C22×D17C4×D411yescharacteristic
217Q8×C17—21no—
218Q8×C17—21no—
219D4×C17—21no—
220D4×C17#13112yes—
221C2×C4×C17—21no—
222C2×C4×C17—21no—
223C2×C4×C17—21no—
224C2×C4×C17—41no—
225C2×C4×C17—41no—
226C2×C4×C17C23×C411yescharacteristic
227C2×C4×C17C22×D411yescharacteristic
228C2×C4×C17C2×#4111yescharacteristic
229C22⋊D17—24no—
230C2×Dic17—21no—
231C2×Dic17—21no—
232C2×Dic17—21no—
233C2×Dic17—81no—
234C2×Dic17C4×D411yescharacteristic
235C2×Dic17C4×D411yescharacteristic
236C2×Dic17C4×D411yescharacteristic
237D68—21no—
238D68#13112yes—
239C4×D17—21no—
240C4×D17—21no—
241C4×D17—21no—
242C4×D17—21no—
243C4×D17—41no—
244C4×D17—41no—
245C4×D17—41no—
246C4×D17—81no—
247C4×D17—81no—
248Dic34—21no—
249Dic34—21no—
250Dic34—81no—
251C8×C17—22no—
252C8×C17—21no—
253C8×C17—21no—
254C8×C17—21no—
255C8×C17—21no—
256C8×C17—41no—
257C8×C17—41no—
258#3622—21no—
259#3622—21no—
260#3622—21no—
261#3622—21no—
262#3622—41no—
263#3622—41no—
264#3622—41no—
265#3101—171no—
266#2985—171no—
267#2972—171no—
268#1585—171no—
269#1585D1711yescharacteristic, complemented
270#1582—171no—
271#1582—171no—
272SD16⋊C8—171no—
273SD16⋊C8—171no—
274C8×SD16—171no—
275C8×SD16—171no—
276#1572—171no—
277#1490—171no—
278#1485—171no—
279#1453—171no—
280C22×C17—22no—
281C22×C17—41no—
282C22×C17—41no—
283C22×C17C2×C4×D411yescharacteristic
284C2×D17—21no—
285C2×D17—22no—
286C2×D17—21no—
287C2×D17—21no—
288C2×D17—41no—
289C2×D17—41no—
290C2×D17—84no—
291C4×C17—21no—
292C4×C17—41no—
293C4×C17—41no—
294C4×C17—41no—
295C4×C17C2×#13111yescharacteristic
296C4×C17C2×#13111yescharacteristic
297C4×C17#57711yescharacteristic
298C4×C17#57711yescharacteristic
299Dic17—21no—
300Dic17—21no—
301Dic17—21no—
302Dic17—41no—
303Dic17—41no—
304Dic17—41no—
305#533—171no—
306C2×C4×D4—171no—
307#483—171no—
308#483—171no—
309#476—171no—
310#476—171no—
311#461—171no—
312#461—171no—
313#450—171no—
314#450—171no—
315#446—171no—
316#446—341no—
317#446—341no—
318#446C2×D1711yescharacteristic, complemented
319C8×Q8—171no—
320C8×Q8—171no—
321C4×SD16—171no—
322C4×SD16—171no—
323C4×SD16—171no—
324C4×SD16C2×D1711yescharacteristic
325C8×D4—171no—
326C8×D4—171no—
327C8×D4—171no—
328C8×D4—341no—
329C8×D4—341no—
330C8×D4C2×D1711yescharacteristic
331#433—341no—
332#433—341no—
333#432—171no—
334#431—171no—
335#431—171no—
336#431—171no—
337C2×C22⋊C8—341no—
338C2×C22⋊C8—341no—
339C4×M16—171no—
340#335—171no—
341#335C2×D1711yescharacteristic, complemented
342#334—171no—
343#334—171no—
344Q8⋊C8—171no—
345Q8⋊C8—171no—
346Q8⋊C8—171no—
347Q8⋊C8C2×D1711yescharacteristic, complemented
348D4⋊C8—171no—
349D4⋊C8—171no—
350D4⋊C8—171no—
351D4⋊C8C2×D1711yescharacteristic
352#322—171no—
353#322—171no—
354#322C2×D1711yescharacteristic, complemented
355C82—171no—
356C2×C17—42no—
357C2×C17#292911yescharacteristic
358C2×C17#294911yescharacteristic
359C2×C17#295611yescharacteristic
360D17—41no—
361D17—42no—
362C22×D4—171no—
363C23×C4—341no—
364C2×SD16—171no—
365C2×SD16—171no—
366C2×SD16—171no—
367C2×SD16C4×D1711yescharacteristic
368C2×M16—341no—
369C22×C8—21no—
370C22×C8—341no—
371C22×C8—341no—
372C22×C8—341no—
373C4⋊Q8—171no—
374C4⋊Q8—171no—
375#125—341no—
376C22⋊Q8—171no—
377C22⋊Q8—171no—
378C22⋊Q8—341no—
379C4×Q8—171no—
380C4×Q8—341no—
381C4×Q8C22×D1711yescharacteristic
382C4×D4—171no—
383C4×D4—171no—
384C4×D4—171no—
385C4×D4—341no—
386C4×D4—341no—
387C4×D4C22×D1711yescharacteristic
388#117—341no—
389C2×C4⋊C4—171no—
390C2×C22⋊C4—341no—
391C2×C42—171no—
392#106—171no—
393#106—171no—
394#106—171no—
395#106C4×D1711yescharacteristic
396C4⋊C8—21no—
397C4⋊C8—171no—
398C4⋊C8—171no—
399C4⋊C8—171no—
400C4⋊C8—171no—
401C4⋊C8—171no—
402C4⋊C8—171no—
403C4⋊C8—341no—
404C4⋊C8—341no—
405C4⋊C8—341no—
406C4⋊C8C22×D1711yescharacteristic
407C4⋊C8C22×D1711yescharacteristic
408#103—171no—
409#103—171no—
410#103—171no—
411#103C4×D1711yescharacteristic
412#102—171no—
413#102—171no—
414#102—171no—
415#102C4×D1711yescharacteristic
416C22⋊C8—21no—
417C22⋊C8—171no—
418C22⋊C8—171no—
419C22⋊C8—171no—
420C22⋊C8—171no—
421C22⋊C8—341no—
422C22⋊C8—341no—
423C22⋊C8—341no—
424C22⋊C8—341no—
425C22⋊C8—341no—
426#97—21no—
427#97—341no—
428#97—341no—
429#97—341no—
430C4×C8—171no—
431C4×C8—171no—
432C4×C8—171no—
433C4×C8—341no—
434C4×C8—341no—
435C4×C8—341no—
436C4×C8C22×D1711yescharacteristic
437C4×C8C22×D1711yescharacteristic
438C4×C8C22×D1711yescharacteristic
439C17#1792411yescharacteristic, complemented, Sylow
440C24—341no—
441C2×Q8—171no—
442C2×Q8—341no—
443C2×Q8C2×C4×D1711yescharacteristic
444C2×D4—171no—
445C2×D4—341no—
446C2×D4—342no—
447C2×D4—342no—
448C2×D4C2×C4×D1711yescharacteristic
449C22×C4—21no—
450C22×C4—171no—
451C22×C4—171no—
452C22×C4—171no—
453C22×C4—341no—
454C22×C4—341no—
455C22×C4—341no—
456C22×C4—341no—
457C22×C4—1361no—
458C22×C4—1361no—
459SD16—22no—
460SD16—342no—
461SD16—342no—
462SD16—342no—
463M16—682no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—81no—
468C2×C8—171no—
469C2×C8—171no—
470C2×C8—171no—
471C2×C8—171no—
472C2×C8—341no—
473C2×C8—341no—
474C2×C8—341no—
475C2×C8—1361no—
476C2×C8—1361no—
477C2×C8—1361no—
478C2×C8C2×C4×D1711yescharacteristic
479C2×C8C2×C4×D1711yescharacteristic
480C2×C8D4×D1711yescharacteristic
481C2×C8D4×D1711yescharacteristic
482C4⋊C4—21no—
483C4⋊C4—171no—
484C4⋊C4—171no—
485C4⋊C4—341no—
486C4⋊C4—341no—
487C4⋊C4—341no—
488C4⋊C4—341no—
489C4⋊C4—341no—
490C4⋊C4—341no—
491C4⋊C4—341no—
492C4⋊C4C2×C4×D1711yescharacteristic
493C4⋊C4C2×C4×D1711yescharacteristic
494C22⋊C4—21no—
495C22⋊C4—341no—
496C22⋊C4—341no—
497C22⋊C4—341no—
498C22⋊C4—341no—
499C22⋊C4—341no—
500C42—21no—
501C42—171no—
502C42—171no—
503C42—171no—
504C42—341no—
505C42C23×D1711yescharacteristic
506C23—21no—
507C23—171no—
508C23—344no—
509C23—341no—
510C23—1361no—
511C23—1361no—
512Q8—21no—
513Q8—21no—
514Q8—341no—
515Q8—341no—
516Q8—1361no—
517D4—21no—
518D4—172no—
519D4—344no—
520D4—341no—
521D4#1058759312yes—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—171no—
528C2×C4—171no—
529C2×C4—171no—
530C2×C4—341no—
531C2×C4—341no—
532C2×C4—341no—
533C2×C4—341no—
534C2×C4—341no—
535C2×C4—341no—
536C2×C4—341no—
537C2×C4—681no—
538C2×C4—681no—
539C2×C4—681no—
540C2×C4—1361no—
541C2×C4—1361no—
542C2×C4—1361no—
543C2×C4C22×C4×D1711yescharacteristic
544C2×C4C2×D4×D1711yescharacteristic
545C2×C4#41×D1711yescharacteristic
546C8—22no—
547C8—21no—
548C8—21no—
549C8—21no—
550C8—21no—
551C8—41no—
552C8—41no—
553C8—341no—
554C8—341no—
555C8—341no—
556C8—341no—
557C8—681no—
558C8—681no—
559C8—681no—
560C22—22no—
561C22—41no—
562C22—41no—
563C22—341no—
564C22—342no—
565C22—341no—
566C22—341no—
567C22—681no—
568C22—681no—
569C22—1364no—
570C22C4×D4×D1711yescharacteristic
571C4—21no—
572C4—41no—
573C4—41no—
574C4—41no—
575C4—341no—
576C4—341no—
577C4—341no—
578C4—681no—
579C4—681no—
580C4—681no—
581C4#131×D1711yescharacteristic
582C4C2×#1058759311yescharacteristic
583C4#1176361811yescharacteristic
584C4#1176361911yescharacteristic
585C2—42no—
586C2—681no—
587C2—682no—
588C2#1453747511yescharacteristic
589C2#1453764011yescharacteristic
590C2#1453768911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D17
commutatorC2×C4×C17C23×C4
FrattiniC42C23×D17
FittingC17×#1585C2
socleC22×C17C2×C4×D4
prime radicalC2×D4×D17C2×C4
cosocleC42×C17C24
hypercenter#1585D17
hypocenterC17#17924
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1585

Complements

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

NH ≅ G/Ntype
2. #14537880C2semidirect
4. #14527643C2semidirect
5. #14527620C2semidirect
6. #14527618C2semidirect
7. SD16⋊#3622C2semidirect
8. #14527595C2semidirect
9. #14527587C2semidirect
10. #14527581C2semidirect
11. #14527563C2semidirect
13. #14527203C2semidirect
14. #14527082C2semidirect
15. C17×#1585C2semidirect
26. #11762939C22semidirect
29. Q8×#3622C22semidirect
30. #11762933C22semidirect
48. #11762562C22semidirect
49. #11762559C22semidirect
50. #11762559C22semidirect
51. #11762541C22semidirect
52. Q8⋊#3622C22semidirect
53. #11762539C22semidirect
57. #11762530C22semidirect
58. #11762530C22semidirect
59. C8×#3622C22semidirect
60. C17×#446C22semidirect
63. C17×#335C22semidirect
64. C17×Q8⋊C8C22semidirect
66. C17×#322C22semidirect
269. #1585D17semidirect
318. #446C2×D17semidirect
341. #335C2×D17semidirect
347. Q8⋊C8C2×D17semidirect
354. #322C2×D17semidirect
439. C17#17924semidirect

Maximal subgroups

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

subgroupindex
#145387902
#145378802
#145378052
#145276432
#145276202
#145276182
SD16⋊#36222
#145275952
#145275872
#145275812
#145275632
#145272252
#145272032
#145270822
C17×#15852
#1792417