Finite Group Databasebeta

← #17005481

Subgroups — #17005481

Order 4352.

650 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14538835C211yesmaximal, characteristic
2#14537947C211yesmaximal, characteristic, complemented
3#14537817C211yesmaximal, characteristic, complemented
4#14527674C211yesmaximal, characteristic, complemented
5#14527668C211yesmaximal, characteristic, complemented
6#14527659C211yesmaximal, characteristic, complemented
7#14527650C211yesmaximal, characteristic, complemented
8#14527645C211yesmaximal, characteristic, complemented
9SD16×#3622C211yesmaximal, characteristic, complemented
10C8×#63228C211yesmaximal, characteristic, complemented
11#14527568C211yesmaximal, characteristic, complemented
12#14527243C211yesmaximal, characteristic, complemented
13D17×D4⋊C8C211yesmaximal, characteristic, complemented
14#14527069C211yesmaximal, characteristic, complemented
15C17×#1585C211yesmaximal, characteristic, complemented
16#11763346C2211yescharacteristic
17C4×D4×D17C2211yescharacteristic
18#11763143C411yescharacteristic
19#11763129C411yescharacteristic
20#11763108C411yescharacteristic
21#11763107C411yescharacteristic
22#11763027C411yescharacteristic
23#11763026C411yescharacteristic
24#11762958C411yescharacteristic
25#11762944C411yescharacteristic
26Q8×#3622C2211yescharacteristic, complemented
27C4×#63230C2211yescharacteristic
28C4×D136C2211yescharacteristic
29C4×#63228C2211yescharacteristic
30#11762888C2211yescharacteristic
31#11762886C2211yescharacteristic
32#11762886C2211yescharacteristic, complemented
33#11762882—21no—
34#11762880—21no—
35#11762877—21no—
36C8×D68C2211yescharacteristic, complemented
37D4×#3622C2211yescharacteristic
38#11762874—21no—
39#11762871—21no—
40#11762865C2211yescharacteristic
41#11762860C2211yescharacteristic
42#11762860C2211yescharacteristic
43#11762834—21no—
44C4⋊C8×D17C2211yescharacteristic
45#11762771—21no—
46C2×#10587491—21no—
47C4×C8×D17C2211yescharacteristic
48#11762561C2211yescharacteristic, complemented
49#11762560C2211yescharacteristic, complemented
50#11762559C2211yescharacteristic, complemented
51Q8⋊#3622C2211yescharacteristic, complemented
52#11762538C2211yescharacteristic
53#11762538C2211yescharacteristic, complemented
54D4⋊#3622C2211yescharacteristic
55#11762536C2211yescharacteristic
56#11762536C2211yescharacteristic, complemented
57#11762530C2211yescharacteristic, complemented
58C8×#3622C2211yescharacteristic, 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#10587633C2×C411yescharacteristic
74#10587632C2×C411yescharacteristic
75C2×#63230C2×C411yescharacteristic
76D4×Dic17C2×C411yescharacteristic
77C2×#63228C2×C411yescharacteristic
78C4×C22⋊D17—21no—
79C22×#3622—21no—
80C2×D136C2×C411yescharacteristic
81C2×#63218—21no—
82C2×#63218—21no—
83C2×#63218—21no—
84C2×C8×D17—21no—
85C2×C8×D17—21no—
86C2×C8×D17—21no—
87#10587584—21no—
88#10587581C2×C411yescharacteristic
89#10587580—21no—
90#10587579C2×C411yescharacteristic
91C4⋊C4×D17C2×C411yescharacteristic
92#10587576C2×C411yescharacteristic
93#10587567—21no—
94C22⋊C4×D17—21no—
95C4×D68—21no—
96C4×D68C2311yescharacteristic
97C4×D68C2311yescharacteristic
98#10587558—21no—
99C42×D17C2311yescharacteristic
100C17×#106C2×C411yescharacteristic
101C17×C4⋊C8—21no—
102C17×C4⋊C8C2311yescharacteristic
103C17×C4⋊C8C2311yescharacteristic
104C17×#103C2×C411yescharacteristic
105C17×#102C2×C411yescharacteristic
106C17×C22⋊C8—21no—
107C17×#97—21no—
108C4×C8×C17C2311yescharacteristic
109C4×C8×C17C2311yescharacteristic
110C4×C8×C17C2311yescharacteristic
111#10587506C2×C411yescharacteristic
112#10587503C2×C411yescharacteristic
113C22⋊#3622—21no—
114#10587492C2×C411yescharacteristic
115#10587492C2×C411yescharacteristic
116#10587491—21no—
117#10587491—21no—
118#10587491—21no—
119#10587491—21no—
120#10587491—21no—
121#10587491C2×C411yescharacteristic
122#10587491C2×C411yescharacteristic
123#10587491D411yescharacteristic
124#10587491D411yescharacteristic
125#10587489C2×C411yescharacteristic
126#10587486—21no—
127#10587485—21no—
128#10587485C2×C411yescharacteristic
129#10587485C2×C411yescharacteristic
130#10587485D411yescharacteristic
131#10587485D411yescharacteristic
132C8×Dic17—21no—
133#10587480C2×C411yescharacteristic
134#10587480C2×C411yescharacteristic
135#10587479C2×C411yescharacteristic
136#10587478C2×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—41no—
152C2×D68—21no—
153C2×D68C22×C411yescharacteristic
154C2×D68C22×C411yescharacteristic
155C2×C4×D17—21no—
156C2×C4×D17—21no—
157C2×C4×D17—21no—
158C2×C4×D17—21no—
159C2×C4×D17—81no—
160C2×C4×D17—81no—
161C2×C4×D17C22×C411yescharacteristic
162C2×C4×D17C2×D411yescharacteristic
163C2×C4×D17#4111yescharacteristic
164SD16×C17—22no—
165C2×C8×C17—21no—
166C2×C8×C17—21no—
167C2×C8×C17—21no—
168C2×C8×C17—81no—
169C2×C8×C17C22×C411yescharacteristic
170C2×C8×C17C22×C411yescharacteristic
171C2×C8×C17C2×D411yescharacteristic
172C2×C8×C17C2×D411yescharacteristic
173C4⋊C4×C17—21no—
174C4⋊C4×C17C22×C411yescharacteristic
175C4⋊C4×C17C22×C411yescharacteristic
176C22⋊C4×C17—21no—
177C42×C17—21no—
178C42×C17C2411yescharacteristic
179C22⋊Dic17—21no—
180#63230—41no—
181#63228—22no—
182#63227—21no—
183#63227—21no—
184#63227—21no—
185#63227—21no—
186#63227—21no—
187#63227—21no—
188#63227—21no—
189C4⋊Dic17—21no—
190C4⋊Dic17C22×C411yescharacteristic
191C4⋊Dic17C22×C411yescharacteristic
192#63225—21no—
193#63225—21no—
194#63225—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
206D136—41no—
207#63218—81no—
208#63218—81no—
209#63218—81no—
210C8×D17—24no—
211C8×D17—81no—
212C8×D17—81no—
213#18014—171nomaximal, Sylow
214C23×C17—21no—
215C22×D17—21no—
216C22×D17—21no—
217C22×D17—42no—
218C22×D17—42no—
219C22×D17—81no—
220C22×D17C4×D411yescharacteristic
221Q8×C17—21no—
222Q8×C17—21no—
223D4×C17—21no—
224D4×C17#13112yes—
225C2×C4×C17—21no—
226C2×C4×C17—21no—
227C2×C4×C17—21no—
228C2×C4×C17—41no—
229C2×C4×C17—41no—
230C2×C4×C17C23×C411yescharacteristic
231C2×C4×C17C22×D411yescharacteristic
232C2×C4×C17C2×#4111yescharacteristic
233C22⋊D17—42no—
234C2×Dic17—21no—
235C2×Dic17—21no—
236C2×Dic17—81no—
237C2×Dic17C4×D411yescharacteristic
238C2×Dic17C4×D411yescharacteristic
239C2×Dic17C4×D411yescharacteristic
240D68—21no—
241D68—21no—
242D68—21no—
243D68—21no—
244D68—42no—
245C4×D17—22no—
246C4×D17—21no—
247C4×D17—21no—
248C4×D17—21no—
249C4×D17—21no—
250C4×D17—41no—
251C4×D17—41no—
252C4×D17—41no—
253C4×D17—41no—
254C4×D17—81no—
255C4×D17—81no—
256C8×C17—22no—
257C8×C17—21no—
258C8×C17—21no—
259C8×C17—21no—
260C8×C17—21no—
261C8×C17—41no—
262C8×C17—41no—
263#3622—22no—
264#3622—21no—
265#3622—21no—
266#3622—21no—
267#3622—21no—
268#3622—41no—
269#3622—41no—
270#3105—171no—
271#2994—171no—
272#2974—171no—
273#1590—171no—
274#1589—171no—
275#1588—171no—
276#1586—171no—
277#1586—171no—
278#1585D1711yescharacteristic, complemented
279C8×SD16—171no—
280C8×D8—171no—
281#1573—171no—
282#1494—171no—
283C2×D4⋊C8—171no—
284#1450—171no—
285C22×C17—22no—
286C22×C17—41no—
287C22×C17—41no—
288C22×C17C2×C4×D411yescharacteristic
289C2×D17—21no—
290C2×D17—21no—
291C2×D17—41no—
292C2×D17—41no—
293C2×D17—41no—
294C2×D17—41no—
295C2×D17—41no—
296C2×D17—41no—
297C2×D17—84no—
298C2×D17#44312yes—
299C4×C17—21no—
300C4×C17—41no—
301C4×C17—41no—
302C4×C17—41no—
303C4×C17C2×#13111yescharacteristic
304C4×C17#56811yescharacteristic
305C4×C17#57611yescharacteristic
306C4×C17#57711yescharacteristic
307Dic17—21no—
308Dic17—21no—
309Dic17—21no—
310Dic17—41no—
311Dic17—41no—
312#529—171no—
313C2×C4×D4—171no—
314#484—171no—
315#481—171no—
316#478—171no—
317#478—171no—
318#463—171no—
319#463—171no—
320#450—171no—
321#447—171no—
322#446C2×D1711yescharacteristic, complemented
323C8×Q8—171no—
324C4×SD16—171no—
325C4×SD16C2×D1711yescharacteristic
326C4×D8—171no—
327C4×D8—171no—
328#436—171no—
329#436—171no—
330#436—171no—
331#435—341no—
332#435—341no—
333#435—341no—
334C8×D4—171no—
335C8×D4—171no—
336C8×D4—341no—
337C8×D4C2×D1711yescharacteristic
338#433—341no—
339#432—171no—
340#431—171no—
341#431—171no—
342#424—341no—
343C2×C4⋊C8—171no—
344#407—341no—
345C2×C22⋊C8—341no—
346C2×C4×C8—171no—
347#335—171no—
348#335C2×D1711yescharacteristic, complemented
349#334—171no—
350#334—171no—
351Q8⋊C8—171no—
352Q8⋊C8C2×D1711yescharacteristic, complemented
353D4⋊C8—171no—
354D4⋊C8—171no—
355D4⋊C8—171no—
356D4⋊C8—171no—
357D4⋊C8—171no—
358D4⋊C8C2×D1711yescharacteristic
359#322—171no—
360#322C2×D1711yescharacteristic, complemented
361C82—171no—
362C82—171no—
363C2×C17—42no—
364C2×C17#293311yescharacteristic
365C2×C17#294611yescharacteristic
366C2×C17C2×#44311yescharacteristic
367D17—22no—
368D17—81no—
369D17—81no—
370C22×D4—171no—
371C23×C4—341no—
372C2×SD16—171no—
373C2×SD16C4×D1711yescharacteristic
374C2×D8—171no—
375C2×D8—171no—
376C2×M16—341no—
377C2×M16—341no—
378C2×M16—341no—
379C22×C8—21no—
380C22×C8—341no—
381C22×C8—341no—
382C22×C8—341no—
383C22×C8—341no—
384#126—341no—
385#125—171no—
386#124—171no—
387#123—341no—
388C22⋊Q8—171no—
389#121—171no—
390C4×Q8C22×D1711yescharacteristic
391C4×D4—171no—
392C4×D4—171no—
393C4×D4—171no—
394C4×D4—171no—
395C4×D4—341no—
396C4×D4—341no—
397C4×D4—341no—
398C4×D4C22×D1711yescharacteristic
399#117—341no—
400C2×C4⋊C4—171no—
401C2×C22⋊C4—341no—
402C2×C42—171no—
403#107—171no—
404#107—171no—
405#106—171no—
406#106C4×D1711yescharacteristic
407C4⋊C8—21no—
408C4⋊C8—171no—
409C4⋊C8—171no—
410C4⋊C8—171no—
411C4⋊C8—171no—
412C4⋊C8—171no—
413C4⋊C8—171no—
414C4⋊C8—341no—
415C4⋊C8—341no—
416C4⋊C8C22×D1711yescharacteristic
417C4⋊C8C22×D1711yescharacteristic
418#103—171no—
419#103C4×D1711yescharacteristic
420#102—171no—
421#102—171no—
422#102—171no—
423#102—171no—
424#102—171no—
425#102C4×D1711yescharacteristic
426C22⋊C8—21no—
427C22⋊C8—171no—
428C22⋊C8—171no—
429C22⋊C8—171no—
430C22⋊C8—171no—
431C22⋊C8—341no—
432C22⋊C8—341no—
433C22⋊C8—341no—
434C22⋊C8—341no—
435C22⋊C8—341no—
436C22⋊C8—341no—
437#97—21no—
438#97—341no—
439C4×C8—171no—
440C4×C8—171no—
441C4×C8—171no—
442C4×C8—341no—
443C4×C8—341no—
444C4×C8C22×D1711yescharacteristic
445C4×C8C22×D1711yescharacteristic
446C4×C8C22×D1711yescharacteristic
447C17#1801411yescharacteristic, complemented, Sylow
448C24—341no—
449C2×Q8C2×C4×D1711yescharacteristic
450C2×D4—171no—
451C2×D4—171no—
452C2×D4—341no—
453C2×D4—341no—
454C2×D4—342no—
455C2×D4—681no—
456C2×D4C2×C4×D1711yescharacteristic
457C22×C4—21no—
458C22×C4—171no—
459C22×C4—171no—
460C22×C4—171no—
461C22×C4—341no—
462C22×C4—341no—
463C22×C4—341no—
464C22×C4—341no—
465C22×C4—341no—
466C22×C4—1361no—
467C22×C4—1361no—
468SD16—22no—
469SD16—681no—
470D8—342no—
471D8—681no—
472M16—1361no—
473M16—1361no—
474M16—1361no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—81no—
479C2×C8—171no—
480C2×C8—171no—
481C2×C8—171no—
482C2×C8—171no—
483C2×C8—344no—
484C2×C8—341no—
485C2×C8—341no—
486C2×C8—341no—
487C2×C8—1361no—
488C2×C8—1361no—
489C2×C8—1361no—
490C2×C8C2×C4×D1711yescharacteristic
491C2×C8C2×C4×D1711yescharacteristic
492C2×C8D4×D1711yescharacteristic
493C2×C8D4×D1711yescharacteristic
494C4⋊C4—21no—
495C4⋊C4—171no—
496C4⋊C4—171no—
497C4⋊C4—341no—
498C4⋊C4—341no—
499C4⋊C4—341no—
500C4⋊C4—341no—
501C4⋊C4C2×C4×D1711yescharacteristic
502C4⋊C4C2×C4×D1711yescharacteristic
503C22⋊C4—21no—
504C22⋊C4—341no—
505C22⋊C4—341no—
506C22⋊C4—341no—
507C22⋊C4—341no—
508C22⋊C4—341no—
509C22⋊C4—341no—
510C22⋊C4—341no—
511C22⋊C4—341no—
512C42—21no—
513C42—171no—
514C42—171no—
515C42—171no—
516C42C23×D1711yescharacteristic
517C23—21no—
518C23—171no—
519C23—341no—
520C23—341no—
521C23—682no—
522C23—682no—
523C23—1361no—
524Q8—21no—
525Q8—21no—
526D4—21no—
527D4—341no—
528D4—341no—
529D4—341no—
530D4—341no—
531D4—682no—
532D4—682no—
533D4#1058759312yes—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—171no—
540C2×C4—171no—
541C2×C4—171no—
542C2×C4—342no—
543C2×C4—341no—
544C2×C4—341no—
545C2×C4—341no—
546C2×C4—341no—
547C2×C4—341no—
548C2×C4—341no—
549C2×C4—681no—
550C2×C4—681no—
551C2×C4—681no—
552C2×C4—681no—
553C2×C4—1361no—
554C2×C4—1361no—
555C2×C4—1361no—
556C2×C4C22×C4×D1711yescharacteristic
557C2×C4C2×D4×D1711yescharacteristic
558C2×C4#41×D1711yescharacteristic
559C8—22no—
560C8—21no—
561C8—21no—
562C8—21no—
563C8—21no—
564C8—41no—
565C8—41no—
566C8—342no—
567C8—341no—
568C8—341no—
569C8—341no—
570C8—341no—
571C8—681no—
572C8—681no—
573C22—22no—
574C22—41no—
575C22—41no—
576C22—172no—
577C22—341no—
578C22—341no—
579C22—681no—
580C22—681no—
581C22—681no—
582C22—681no—
583C22—681no—
584C22—681no—
585C22—1364no—
586C22C4×D4×D1711yescharacteristic
587C4—21no—
588C4—41no—
589C4—41no—
590C4—41no—
591C4—341no—
592C4—341no—
593C4—341no—
594C4—681no—
595C4—681no—
596C4C2×#1058759311yescharacteristic
597C4#1176357411yescharacteristic
598C4#1176361311yescharacteristic
599C4#1176361811yescharacteristic
600C2—42no—
601C2—342no—
602C2—1361no—
603C2—1361no—
604C2#1453751011yescharacteristic
605C2#1453761511yescharacteristic
606C2D17×#44311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D17
commutatorC2×C4×C17C23×C4
FrattiniC42C23×D17
FittingC17×#1585C2
socleC22×C17C2×C4×D4
prime radical#11762944C4
cosocleC42×C17C24
hypercenter#1585D17
hypocenterC17#18014
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. #14537947C2semidirect
3. #14537817C2semidirect
4. #14527674C2semidirect
5. #14527668C2semidirect
6. #14527659C2semidirect
7. #14527650C2semidirect
8. #14527645C2semidirect
9. SD16×#3622C2semidirect
10. C8×#63228C2semidirect
11. #14527568C2semidirect
12. #14527243C2semidirect
13. D17×D4⋊C8C2semidirect
14. #14527069C2semidirect
15. C17×#1585C2semidirect
26. Q8×#3622C22semidirect
32. #11762886C22semidirect
36. C8×D68C22semidirect
48. #11762561C22semidirect
49. #11762560C22semidirect
50. #11762559C22semidirect
51. Q8⋊#3622C22semidirect
53. #11762538C22semidirect
56. #11762536C22semidirect
57. #11762530C22semidirect
58. C8×#3622C22semidirect
59. C8×#3622C22semidirect
60. C17×#446C22semidirect
63. C17×#335C22semidirect
64. C17×Q8⋊C8C22semidirect
66. C17×#322C22semidirect
278. #1585D17semidirect
322. #446C2×D17semidirect
348. #335C2×D17semidirect
352. Q8⋊C8C2×D17semidirect
360. #322C2×D17semidirect
447. C17#18014semidirect

Maximal subgroups

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

subgroupindex
#145388352
#145379472
#145378172
#145276742
#145276682
#145276592
#145276502
#145276452
SD16×#36222
C8×#632282
#145275682
#145272432
D17×D4⋊C82
#145270692
C17×#15852
#1801417