Finite Group Databasebeta

← #17004381

Subgroups — #17004381

Order 4352.

648 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#14538829C211yesmaximal, characteristic
2#14537934C211yesmaximal, characteristic, complemented
3#14537805C211yesmaximal, characteristic, complemented
4#14527651C211yesmaximal, characteristic, complemented
5#14527638C211yesmaximal, characteristic, complemented
6#14527619C211yesmaximal, characteristic, complemented
7#14527614C211yesmaximal, characteristic, complemented
8#14527598C211yesmaximal, characteristic, complemented
9C8×#63229C211yesmaximal, characteristic, complemented
10C8×#63228C211yesmaximal, characteristic, complemented
11#14527571C211yesmaximal, characteristic, complemented
12#14527207C211yesmaximal, characteristic, complemented
13#14527189C211yesmaximal, characteristic, complemented
14#14527085C211yesmaximal, characteristic, complemented
15C17×#1580C211yesmaximal, characteristic, complemented
16#11763341C2211yescharacteristic
17C4×D4×D17C2211yescharacteristic
18#11763146C411yescharacteristic
19#11763126C411yescharacteristic
20#11763112C411yescharacteristic
21#11763111C411yescharacteristic
22#11763023C411yescharacteristic
23#11763022C411yescharacteristic
24#11762961C411yescharacteristic
25#11762941C411yescharacteristic
26#11762936C2211yescharacteristic, complemented
27C8×Dic34C2211yescharacteristic, complemented
28C4×#63219C2211yescharacteristic
29C4×#63229C2211yescharacteristic
30C4×#63228C2211yescharacteristic
31#11762887C2211yescharacteristic, complemented
32#11762884—21no—
33#11762880—21no—
34C8×D68C2211yescharacteristic
35D4×#3622C2211yescharacteristic
36#11762874C2211yescharacteristic
37C8×C22⋊D17—21no—
38#11762872—21no—
39#11762867—21no—
40#11762861C2211yescharacteristic
41#11762860C2211yescharacteristic
42#11762860C2211yescharacteristic
43#11762860C2211yescharacteristic
44#11762835—21no—
45#11762831C2211yescharacteristic
46C2×#10587491—21no—
47C22⋊C8×D17—21no—
48#11762562C2211yescharacteristic, complemented
49#11762561C2211yescharacteristic, complemented
50#11762559C2211yescharacteristic, complemented
51#11762541C2211yescharacteristic, complemented
52#11762539C2211yescharacteristic, complemented
53#11762538C2211yescharacteristic
54D4⋊#3622C2211yescharacteristic
55D4⋊#3622C2211yescharacteristic, complemented
56#11762536C2211yescharacteristic
57#11762531C2211yescharacteristic, complemented
58#11762530C2211yescharacteristic, complemented
59C8×#3622C2211yescharacteristic, complemented
60C4×D8×C17C2211yescharacteristic
61C8×D4×C17C2211yescharacteristic
62C8×D4×C17C2211yescharacteristic, complemented
63C17×#334C2211yescharacteristic, complemented
64C17×D4⋊C8C2211yescharacteristic
65C17×D4⋊C8C2211yescharacteristic, complemented
66C17×#322C2211yescharacteristic, complemented
67C2×D4×D17C2×C411yescharacteristic
68C22×C4×D17—21no—
69C2×D8×C17C2×C411yescharacteristic
70C22×C8×C17—21no—
71C22×C8×C17—21no—
72C4×D4×C17C2311yescharacteristic
73C4×D4×C17C2311yescharacteristic
74#10587624C2×C411yescharacteristic
75#10587622C2×C411yescharacteristic
76D4×Dic17C2×C411yescharacteristic
77C2×#63229C2×C411yescharacteristic
78C2×#63228C2×C411yescharacteristic
79C4×C22⋊D17—21no—
80C4×C22⋊D17—21no—
81#10587612—21no—
82C2×#63223—21no—
83C22×#3622—21no—
84C2×#63219C2×C411yescharacteristic
85C2×#63218—21no—
86C2×C8×D17—21no—
87C2×C8×D17—21no—
88#10587583C2×C411yescharacteristic
89#10587579C2×C411yescharacteristic
90C4⋊C4×D17C2×C411yescharacteristic
91#10587576C2×C411yescharacteristic
92#10587569—21no—
93#10587567—21no—
94C22⋊C4×D17—21no—
95#10587565—21no—
96C4×D68C2311yescharacteristic
97C42×D17C2311yescharacteristic
98C4×Dic34C2311yescharacteristic
99C17×#107C2×C411yescharacteristic
100C17×C4⋊C8C2311yescharacteristic
101C17×C4⋊C8C2311yescharacteristic
102C17×#102C2×C411yescharacteristic
103C17×#102C2×C411yescharacteristic
104C17×C22⋊C8—21no—
105C17×C22⋊C8—21no—
106C4×C8×C17C2311yescharacteristic
107C4×C8×C17C2311yescharacteristic
108C4×C8×C17C2311yescharacteristic
109#10587503C2×C411yescharacteristic
110#10587503C2×C411yescharacteristic
111C22⋊#3622—21no—
112C22⋊#3622—21no—
113#10587492C2×C411yescharacteristic
114#10587491—21no—
115#10587491—21no—
116#10587491—21no—
117#10587491—21no—
118#10587491C2×C411yescharacteristic
119#10587491C2×C411yescharacteristic
120#10587491D411yescharacteristic
121#10587491D411yescharacteristic
122#10587488C2×C411yescharacteristic
123#10587487C2×C411yescharacteristic
124#10587486—21no—
125#10587485—21no—
126#10587485—21no—
127#10587485—21no—
128#10587485—21no—
129#10587485C2×C411yescharacteristic
130#10587485C2×C411yescharacteristic
131#10587485D411yescharacteristic
132#10587485D411yescharacteristic
133C8×Dic17—21no—
134C8×Dic17—21no—
135#10587481C2×C411yescharacteristic
136#10587480C2×C411yescharacteristic
137#10587479C2×C411yescharacteristic
138#10587478C2×C411yescharacteristic
139C4⋊#3622C2311yescharacteristic
140C4⋊#3622C2311yescharacteristic
141C4×#3622C2311yescharacteristic
142C4×#3622C2311yescharacteristic
143C4×#3622C2311yescharacteristic
144C23×D17—21no—
145C2×D4×C17C22×C411yescharacteristic
146C2×D4×C17C22×C411yescharacteristic
147C22×C4×C17—21no—
148C22×C4×C17—21no—
149C2×C22⋊D17—21no—
150C2×C22⋊D17—21no—
151C22×Dic17—21no—
152D4×D17—22no—
153D4×D17—22no—
154C2×D68C22×C411yescharacteristic
155C2×C4×D17—21no—
156C2×C4×D17—21no—
157C2×C4×D17—21no—
158C2×C4×D17—81no—
159C2×C4×D17—81no—
160C2×C4×D17C22×C411yescharacteristic
161C2×C4×D17C2×D411yescharacteristic
162C2×C4×D17#4111yescharacteristic
163C2×Dic34C22×C411yescharacteristic
164D8×C17—22no—
165C2×C8×C17—21no—
166C2×C8×C17—21no—
167C2×C8×C17—21no—
168C2×C8×C17—81no—
169C2×C8×C17—81no—
170C2×C8×C17C22×C411yescharacteristic
171C2×C8×C17C22×C411yescharacteristic
172C2×C8×C17C2×D411yescharacteristic
173C2×C8×C17C2×D411yescharacteristic
174C4⋊C4×C17C22×C411yescharacteristic
175C4⋊C4×C17C22×C411yescharacteristic
176C22⋊C4×C17—21no—
177C22⋊C4×C17—21no—
178C42×C17C2411yescharacteristic
179C22⋊Dic17—21no—
180C22⋊Dic17—21no—
181C22⋊Dic17—21no—
182C22⋊Dic17—21no—
183#63229—22no—
184#63228—22no—
185#63227—21no—
186#63227—21no—
187#63227—21no—
188C4⋊Dic17—21no—
189C4⋊Dic17—21no—
190C4⋊Dic17C22×C411yescharacteristic
191C4⋊Dic17C22×C411yescharacteristic
192#63225—21no—
193#63225—21no—
194#63225—21no—
195C4×Dic17—21no—
196C4×Dic17C22×C411yescharacteristic
197C4×Dic17C2×D411yescharacteristic
198C4×Dic17#4111yescharacteristic
199#63223—81no—
200C2×#3622—21no—
201C2×#3622—21no—
202C2×#3622—21no—
203C2×#3622—81no—
204C2×#3622C22×C411yescharacteristic
205C2×#3622C22×C411yescharacteristic
206C2×#3622C2×D411yescharacteristic
207C2×#3622C2×D411yescharacteristic
208#63219—22no—
209#63218—81no—
210C8×D17—81no—
211C8×D17—81no—
212#17918—171nomaximal, Sylow
213C23×C17—21no—
214C23×C17—21no—
215C22×D17—21no—
216C22×D17—24no—
217C22×D17—81no—
218C22×D17—81no—
219C22×D17C4×D411yescharacteristic
220D4×C17—21no—
221D4×C17—21no—
222D4×C17—21no—
223D4×C17#13112yes—
224C2×C4×C17—21no—
225C2×C4×C17—21no—
226C2×C4×C17—41no—
227C2×C4×C17—41no—
228C2×C4×C17—41no—
229C2×C4×C17—41no—
230C2×C4×C17C23×C411yescharacteristic
231C2×C4×C17C22×D411yescharacteristic
232C2×C4×C17C2×#4111yescharacteristic
233C22⋊D17—24no—
234C22⋊D17—81no—
235C2×Dic17—21no—
236C2×Dic17—21no—
237C2×Dic17—21no—
238C2×Dic17—81no—
239C2×Dic17C4×D411yescharacteristic
240C2×Dic17C4×D411yescharacteristic
241C2×Dic17C4×D411yescharacteristic
242D68—21no—
243D68#13112yes—
244C4×D17—21no—
245C4×D17—21no—
246C4×D17—21no—
247C4×D17—21no—
248C4×D17—41no—
249C4×D17—41no—
250C4×D17—41no—
251C4×D17—81no—
252C4×D17—81no—
253Dic34—21no—
254Dic34—21no—
255C8×C17—21no—
256C8×C17—21no—
257C8×C17—21no—
258C8×C17—21no—
259C8×C17—41no—
260C8×C17—41no—
261C8×C17—41no—
262#3622—21no—
263#3622—21no—
264#3622—21no—
265#3622—21no—
266#3622—41no—
267#3622—41no—
268#3622—41no—
269#3105—171no—
270#2993—171no—
271#2972—171no—
272#1586—171no—
273#1585—171no—
274#1582—171no—
275#1581—171no—
276#1580D1711yescharacteristic, complemented
277SD16⋊C8—171no—
278C8×SD16—171no—
279C8×D8—171no—
280#1574—171no—
281#1486—171no—
282#1482—171no—
283#1454—171no—
284C22×C17—22no—
285C22×C17—41no—
286C22×C17—41no—
287C22×C17—41no—
288C22×C17—41no—
289C22×C17—41no—
290C22×C17C2×C4×D411yescharacteristic
291C2×D17—21no—
292C2×D17—22no—
293C2×D17—21no—
294C2×D17—21no—
295C2×D17—41no—
296C2×D17—41no—
297C2×D17—84no—
298C4×C17—21no—
299C4×C17—41no—
300C4×C17—41no—
301C4×C17C2×#13111yescharacteristic
302C4×C17C2×#13111yescharacteristic
303C4×C17#57611yescharacteristic
304C4×C17#57711yescharacteristic
305Dic17—21no—
306Dic17—21no—
307Dic17—21no—
308Dic17—41no—
309Dic17—41no—
310Dic17—41no—
311#529—171no—
312C2×C4×D4—171no—
313#484—171no—
314#481—171no—
315#478—171no—
316#478—171no—
317#463—171no—
318#463—171no—
319#450—171no—
320#447—171no—
321#446—171no—
322C8×Q8—171no—
323C4×SD16—171no—
324C4×SD16—171no—
325C4×D8—171no—
326C4×D8C2×D1711yescharacteristic
327#436—171no—
328#436—341no—
329#435—341no—
330C8×D4—171no—
331C8×D4—171no—
332C8×D4—171no—
333C8×D4—341no—
334C8×D4—341no—
335C8×D4C2×D1711yescharacteristic
336C8×D4C2×D1711yescharacteristic, complemented
337#433—341no—
338#431—171no—
339#431—171no—
340#431—171no—
341#431—171no—
342#424—341no—
343#423—171no—
344C2×C22⋊C8—341no—
345C2×C22⋊C8—341no—
346#335—171no—
347#335—171no—
348#334—171no—
349#334C2×D1711yescharacteristic, complemented
350Q8⋊C8—171no—
351Q8⋊C8—171no—
352D4⋊C8—171no—
353D4⋊C8—171no—
354D4⋊C8—171no—
355D4⋊C8—171no—
356D4⋊C8C2×D1711yescharacteristic
357D4⋊C8C2×D1711yescharacteristic, complemented
358#322—171no—
359#322—171no—
360#322C2×D1711yescharacteristic, complemented
361C82—171no—
362C2×C17—42no—
363C2×C17—81no—
364C2×C17#292911yescharacteristic
365C2×C17#294611yescharacteristic
366C2×C17#295711yescharacteristic
367D17—41no—
368D17—42no—
369C22×D4—171no—
370C23×C4—341no—
371C2×SD16—171no—
372C2×SD16—171no—
373C2×D8—171no—
374C2×D8C4×D1711yescharacteristic
375C2×M16—341no—
376C2×M16—341no—
377C22×C8—21no—
378C22×C8—21no—
379C22×C8—341no—
380C22×C8—341no—
381C22×C8—341no—
382#126—341no—
383#125—171no—
384#124—171no—
385#123—341no—
386C22⋊Q8—171no—
387#121—171no—
388C4×Q8—171no—
389C4×D4—171no—
390C4×D4—171no—
391C4×D4—171no—
392C4×D4—341no—
393C4×D4—341no—
394C4×D4—341no—
395C4×D4C22×D1711yescharacteristic
396C4×D4C22×D1711yescharacteristic
397#117—341no—
398C2×C4⋊C4—171no—
399C2×C22⋊C4—341no—
400C2×C42—171no—
401#107—171no—
402#107C4×D1711yescharacteristic
403#106—171no—
404#106—171no—
405C4⋊C8—171no—
406C4⋊C8—171no—
407C4⋊C8—171no—
408C4⋊C8—171no—
409C4⋊C8—171no—
410C4⋊C8—171no—
411C4⋊C8—341no—
412C4⋊C8—341no—
413C4⋊C8—341no—
414C4⋊C8—341no—
415C4⋊C8C22×D1711yescharacteristic
416C4⋊C8C22×D1711yescharacteristic
417#103—171no—
418#103—171no—
419#102—171no—
420#102—171no—
421#102—171no—
422#102—171no—
423#102C4×D1711yescharacteristic
424#102C4×D1711yescharacteristic
425C22⋊C8—21no—
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—341no—
438C4×C8—171no—
439C4×C8—171no—
440C4×C8—171no—
441C4×C8—341no—
442C4×C8—341no—
443C4×C8C22×D1711yescharacteristic
444C4×C8C22×D1711yescharacteristic
445C4×C8C22×D1711yescharacteristic
446C17#1791811yescharacteristic, complemented, Sylow
447C24—341no—
448C2×Q8—171no—
449C2×D4—171no—
450C2×D4—341no—
451C2×D4—342no—
452C2×D4—342no—
453C2×D4—341no—
454C2×D4C2×C4×D1711yescharacteristic
455C2×D4C2×C4×D1711yescharacteristic
456C22×C4—21no—
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—1361no—
466C22×C4—1361no—
467SD16—342no—
468SD16—342no—
469D8—22no—
470D8—342no—
471M16—1361no—
472M16—1361no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—81no—
477C2×C8—81no—
478C2×C8—171no—
479C2×C8—171no—
480C2×C8—171no—
481C2×C8—171no—
482C2×C8—341no—
483C2×C8—341no—
484C2×C8—341no—
485C2×C8—1361no—
486C2×C8—1361no—
487C2×C8—1361no—
488C2×C8C2×C4×D1711yescharacteristic
489C2×C8C2×C4×D1711yescharacteristic
490C2×C8D4×D1711yescharacteristic
491C2×C8D4×D1711yescharacteristic
492C4⋊C4—171no—
493C4⋊C4—171no—
494C4⋊C4—341no—
495C4⋊C4—341no—
496C4⋊C4—341no—
497C4⋊C4—341no—
498C4⋊C4—341no—
499C4⋊C4C2×C4×D1711yescharacteristic
500C4⋊C4C2×C4×D1711yescharacteristic
501C22⋊C4—21no—
502C22⋊C4—21no—
503C22⋊C4—341no—
504C22⋊C4—341no—
505C22⋊C4—341no—
506C22⋊C4—341no—
507C22⋊C4—341no—
508C22⋊C4—341no—
509C22⋊C4—341no—
510C42—171no—
511C42—171no—
512C42—171no—
513C42—341no—
514C42C23×D1711yescharacteristic
515C23—21no—
516C23—21no—
517C23—171no—
518C23—344no—
519C23—341no—
520C23—1361no—
521C23—1361no—
522Q8—341no—
523Q8—341no—
524D4—21no—
525D4—21no—
526D4—21no—
527D4—172no—
528D4—344no—
529D4—341no—
530D4—1361no—
531D4#1058758712yes—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—171no—
539C2×C4—171no—
540C2×C4—171no—
541C2×C4—341no—
542C2×C4—341no—
543C2×C4—341no—
544C2×C4—341no—
545C2×C4—341no—
546C2×C4—341no—
547C2×C4—341no—
548C2×C4—681no—
549C2×C4—681no—
550C2×C4—681no—
551C2×C4—1361no—
552C2×C4—1361no—
553C2×C4—1361no—
554C2×C4C22×C4×D1711yescharacteristic
555C2×C4C2×D4×D1711yescharacteristic
556C2×C4#41×D1711yescharacteristic
557C8—21no—
558C8—21no—
559C8—21no—
560C8—21no—
561C8—41no—
562C8—41no—
563C8—41no—
564C8—341no—
565C8—341no—
566C8—341no—
567C8—341no—
568C8—681no—
569C8—681no—
570C8—681no—
571C22—22no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—341no—
578C22—342no—
579C22—341no—
580C22—341no—
581C22—681no—
582C22—681no—
583C22—1364no—
584C22C4×D4×D1711yescharacteristic
585C4—21no—
586C4—41no—
587C4—41no—
588C4—341no—
589C4—341no—
590C4—341no—
591C4—681no—
592C4—681no—
593C4—681no—
594C4#131×D1711yescharacteristic
595C4C2×#1058758711yescharacteristic
596C4#1176361311yescharacteristic
597C4#1176361911yescharacteristic
598C2—42no—
599C2—81no—
600C2—681no—
601C2—682no—
602C2#1453747311yescharacteristic
603C2#1453761311yescharacteristic
604C2#1453769811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D17
commutatorC2×C4×C17C23×C4
FrattiniC42C23×D17
FittingC17×#1580C2
socleC22×C17C2×C4×D4
prime radical#11762941C4
cosocleC42×C17C24
hypercenter#1580D17
hypocenterC17#17918
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1580

Complements

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

NH ≅ G/Ntype
2. #14537934C2semidirect
3. #14537805C2semidirect
4. #14527651C2semidirect
5. #14527638C2semidirect
6. #14527619C2semidirect
7. #14527614C2semidirect
8. #14527598C2semidirect
9. C8×#63229C2semidirect
10. C8×#63228C2semidirect
11. #14527571C2semidirect
12. #14527207C2semidirect
13. #14527189C2semidirect
14. #14527085C2semidirect
15. C17×#1580C2semidirect
26. #11762936C22semidirect
27. C8×Dic34C22semidirect
31. #11762887C22semidirect
48. #11762562C22semidirect
49. #11762561C22semidirect
50. #11762559C22semidirect
51. #11762541C22semidirect
52. #11762539C22semidirect
55. D4⋊#3622C22semidirect
57. #11762531C22semidirect
58. #11762530C22semidirect
59. C8×#3622C22semidirect
62. C8×D4×C17C22semidirect
63. C17×#334C22semidirect
65. C17×D4⋊C8C22semidirect
66. C17×#322C22semidirect
276. #1580D17semidirect
336. C8×D4C2×D17semidirect
349. #334C2×D17semidirect
357. D4⋊C8C2×D17semidirect
360. #322C2×D17semidirect
446. C17#17918semidirect

Maximal subgroups

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

subgroupindex
#145388292
#145379342
#145378052
#145276512
#145276382
#145276192
#145276142
#145275982
C8×#632292
C8×#632282
#145275712
#145272072
#145271892
#145270852
C17×#15802
#1791817