Finite Group Databasebeta

← #17005487

Subgroups — #17005487

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#14538829C211yesmaximal, characteristic
2#14537945C211yesmaximal, characteristic, complemented
3#14537816C211yesmaximal, characteristic, complemented
4#14527677C211yesmaximal, characteristic, complemented
5#14527660C211yesmaximal, characteristic, complemented
6#14527649C211yesmaximal, characteristic, complemented
7#14527646C211yesmaximal, characteristic, complemented
8#14527640C211yesmaximal, characteristic, complemented
9C8×#63219C211yesmaximal, characteristic, complemented
10#14527576C211yesmaximal, characteristic, complemented
11#14527568C211yesmaximal, characteristic, complemented
12#14527241C211yesmaximal, characteristic, complemented
13D17×D4⋊C8C211yesmaximal, characteristic, complemented
14#14527066C211yesmaximal, characteristic, complemented
15C17×#1589C211yesmaximal, 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
32#11762883—21no—
33#11762878—21no—
34#11762878—21no—
35C8×D68C2211yescharacteristic
36D4×#3622C2211yescharacteristic, complemented
37#11762874C2211yescharacteristic
38#11762872—21no—
39#11762867—21no—
40#11762865C2211yescharacteristic
41#11762860C2211yescharacteristic
42#11762860C2211yescharacteristic
43#11762837—21no—
44C4⋊C8×D17C2211yescharacteristic
45#11762772—21no—
46C22⋊C8×D17—21no—
47C4×C8×D17C2211yescharacteristic
48#11762561C2211yescharacteristic, complemented
49#11762560C2211yescharacteristic, complemented
50#11762559C2211yescharacteristic, complemented
51#11762541C2211yescharacteristic, complemented
52#11762539C2211yescharacteristic, complemented
53#11762538C2211yescharacteristic
54D4⋊#3622C2211yescharacteristic
55D4⋊#3622C2211yescharacteristic, complemented
56#11762536C2211yescharacteristic
57#11762531C2211yescharacteristic, complemented
58#11762531C2211yescharacteristic, complemented
59C8×#3622C2211yescharacteristic, complemented
60C4×D8×C17C2211yescharacteristic
61C17×#436C2211yescharacteristic
62C17×#436C2211yescharacteristic, complemented
63C17×#335C2211yescharacteristic, complemented
64C17×D4⋊C8C2211yescharacteristic
65C17×D4⋊C8C2211yescharacteristic, complemented
66C82×C17C2211yescharacteristic, complemented
67C2×D4×D17C2×C411yescharacteristic
68C22×C4×D17—21no—
69C2×D8×C17C2×C411yescharacteristic
70C2×M16×C17—21no—
71C2×M16×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×C8×D17—21no—
86C2×C8×D17—21no—
87C2×C8×D17—21no—
88C2×C8×D17—21no—
89#10587583C2×C411yescharacteristic
90#10587579C2×C411yescharacteristic
91C4⋊C4×D17C2×C411yescharacteristic
92#10587576C2×C411yescharacteristic
93#10587569—21no—
94#10587567—21no—
95C22⋊C4×D17—21no—
96#10587565—21no—
97C4×D68C2311yescharacteristic
98C42×D17C2311yescharacteristic
99C4×Dic34C2311yescharacteristic
100C17×#107C2×C411yescharacteristic
101C17×C4⋊C8C2311yescharacteristic
102C17×C4⋊C8C2311yescharacteristic
103C17×#102C2×C411yescharacteristic
104C17×#102C2×C411yescharacteristic
105C17×C22⋊C8—21no—
106C17×C22⋊C8—21no—
107C4×C8×C17C2311yescharacteristic
108C4×C8×C17C2311yescharacteristic
109C4×C8×C17C2311yescharacteristic
110#10587503C2×C411yescharacteristic
111#10587503C2×C411yescharacteristic
112C22⋊#3622—21no—
113C22⋊#3622—21no—
114#10587492C2×C411yescharacteristic
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#10587486—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—41no—
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—41no—
165M16×C17—81no—
166M16×C17—81no—
167C2×C8×C17—21no—
168C2×C8×C17—21no—
169C2×C8×C17—21no—
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—41no—
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—
209C8×D17—24no—
210C8×D17—81no—
211C8×D17—81no—
212C8×D17—81no—
213#18014—171nomaximal, Sylow
214C23×C17—21no—
215C23×C17—21no—
216C22×D17—21no—
217C22×D17—42no—
218C22×D17—42no—
219C22×D17—81no—
220C22×D17C4×D411yescharacteristic
221D4×C17—21no—
222D4×C17—21no—
223D4×C17—21no—
224D4×C17—21no—
225C2×C4×C17—21no—
226C2×C4×C17—21no—
227C2×C4×C17—41no—
228C2×C4×C17—41no—
229C2×C4×C17—41no—
230C2×C4×C17—41no—
231C2×C4×C17C23×C411yescharacteristic
232C2×C4×C17C22×D411yescharacteristic
233C2×C4×C17C2×#4111yescharacteristic
234C22⋊D17—42no—
235C22⋊D17—42no—
236C2×Dic17—21no—
237C2×Dic17—21no—
238C2×Dic17—21no—
239C2×Dic17—81no—
240C2×Dic17C4×D411yescharacteristic
241C2×Dic17C4×D411yescharacteristic
242C2×Dic17C4×D411yescharacteristic
243D68—21no—
244D68#13112yes—
245C4×D17—22no—
246C4×D17—21no—
247C4×D17—21no—
248C4×D17—21no—
249C4×D17—21no—
250C4×D17—41no—
251C4×D17—41no—
252C4×D17—81no—
253C4×D17—81no—
254Dic34—21no—
255Dic34—21no—
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#1589D1711yescharacteristic, complemented
275#1588—171no—
276#1586—171no—
277#1586—171no—
278#1585—171no—
279C8×SD16—171no—
280C8×D8—171no—
281#1573—171no—
282#1494—171no—
283C2×D4⋊C8—171no—
284#1450—171no—
285C22×C17—41no—
286C22×C17—41no—
287C22×C17—41no—
288C22×C17—41no—
289C22×C17—41no—
290C22×C17—41no—
291C22×C17C2×C4×D411yescharacteristic
292C2×D17—21no—
293C2×D17—21no—
294C2×D17—22no—
295C2×D17—41no—
296C2×D17—41no—
297C2×D17—84no—
298C2×D17#44312yes—
299C4×C17—21no—
300C4×C17—41no—
301C4×C17—41no—
302C4×C17C2×#13111yescharacteristic
303C4×C17#56811yescharacteristic
304C4×C17#57611yescharacteristic
305C4×C17#57711yescharacteristic
306Dic17—21no—
307Dic17—21no—
308Dic17—21no—
309Dic17—41no—
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#446—171no—
323C8×Q8—171no—
324C4×SD16—171no—
325C4×SD16—171no—
326C4×D8—171no—
327C4×D8C2×D1711yescharacteristic
328#436—171no—
329#436C2×D1711yescharacteristic
330#436C2×D1711yescharacteristic, complemented
331#435—341no—
332#435—341no—
333#435—341no—
334C8×D4—171no—
335C8×D4—171no—
336C8×D4—171no—
337C8×D4—341no—
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⋊C8—171no—
353D4⋊C8—171no—
354D4⋊C8—171no—
355D4⋊C8—171no—
356D4⋊C8—171no—
357D4⋊C8C2×D1711yescharacteristic
358D4⋊C8C2×D1711yescharacteristic, complemented
359#322—171no—
360#322—171no—
361C82—171no—
362C82C2×D1711yescharacteristic, complemented
363C2×C17—81no—
364C2×C17—81no—
365C2×C17#293311yescharacteristic
366C2×C17#294611yescharacteristic
367C2×C17C2×#44311yescharacteristic
368D17—22no—
369D17—42no—
370C22×D4—171no—
371C23×C4—341no—
372C2×SD16—171no—
373C2×SD16—171no—
374C2×D8—171no—
375C2×D8C4×D1711yescharacteristic
376C2×M16—21no—
377C2×M16—21no—
378C2×M16—341no—
379C22×C8—341no—
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×Q8—171no—
391C4×D4—171no—
392C4×D4—171no—
393C4×D4—171no—
394C4×D4—341no—
395C4×D4—341no—
396C4×D4—341no—
397C4×D4C22×D1711yescharacteristic
398C4×D4C22×D1711yescharacteristic
399#117—341no—
400C2×C4⋊C4—171no—
401C2×C22⋊C4—341no—
402C2×C42—171no—
403#107—171no—
404#107C4×D1711yescharacteristic
405#106—171no—
406#106—171no—
407C4⋊C8—171no—
408C4⋊C8—171no—
409C4⋊C8—171no—
410C4⋊C8—171no—
411C4⋊C8—171no—
412C4⋊C8—171no—
413C4⋊C8—341no—
414C4⋊C8—341no—
415C4⋊C8—341no—
416C4⋊C8C22×D1711yescharacteristic
417C4⋊C8C22×D1711yescharacteristic
418#103—171no—
419#103—171no—
420#102—171no—
421#102—171no—
422#102—171no—
423#102—171no—
424#102C4×D1711yescharacteristic
425#102C4×D1711yescharacteristic
426C22⋊C8—21no—
427C22⋊C8—21no—
428C22⋊C8—171no—
429C22⋊C8—171no—
430C22⋊C8—171no—
431C22⋊C8—171no—
432C22⋊C8—341no—
433C22⋊C8—341no—
434C22⋊C8—341no—
435C22⋊C8—341no—
436C22⋊C8—341no—
437#97—341no—
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×Q8—171no—
450C2×D4—171no—
451C2×D4—341no—
452C2×D4—342no—
453C2×D4—341no—
454C2×D4—681no—
455C2×D4C2×C4×D1711yescharacteristic
456C2×D4C2×C4×D1711yescharacteristic
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—171no—
460C22×C4—171no—
461C22×C4—171no—
462C22×C4—341no—
463C22×C4—341no—
464C22×C4—341no—
465C22×C4—341no—
466C22×C4—1361no—
467C22×C4—1361no—
468SD16—342no—
469SD16—681no—
470D8—41no—
471D8—342no—
472M16—81no—
473M16—81no—
474M16—1361no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—171no—
479C2×C8—171no—
480C2×C8—171no—
481C2×C8—171no—
482C2×C8—344no—
483C2×C8—341no—
484C2×C8—341no—
485C2×C8—341no—
486C2×C8—1361no—
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—171no—
495C4⋊C4—171no—
496C4⋊C4—341no—
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—21no—
505C22⋊C4—341no—
506C22⋊C4—341no—
507C22⋊C4—341no—
508C22⋊C4—341no—
509C22⋊C4—341no—
510C22⋊C4—341no—
511C22⋊C4—341no—
512C42—171no—
513C42—171no—
514C42—171no—
515C42—341no—
516C42C23×D1711yescharacteristic
517C23—21no—
518C23—21no—
519C23—171no—
520C23—341no—
521C23—682no—
522C23—682no—
523C23—1361no—
524Q8—341no—
525Q8—341no—
526D4—21no—
527D4—21no—
528D4—21no—
529D4—21no—
530D4—172no—
531D4—341no—
532D4—682no—
533D4—682no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—171no—
541C2×C4—171no—
542C2×C4—171no—
543C2×C4—342no—
544C2×C4—341no—
545C2×C4—341no—
546C2×C4—341no—
547C2×C4—341no—
548C2×C4—341no—
549C2×C4—341no—
550C2×C4—341no—
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—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—172no—
580C22—341no—
581C22—341no—
582C22—342no—
583C22—681no—
584C22—681no—
585C22—1364no—
586C22C4×D4×D1711yescharacteristic
587C4—21no—
588C4—41no—
589C4—41no—
590C4—341no—
591C4—341no—
592C4—341no—
593C4—681no—
594C4—681no—
595C4—681no—
596C4#131×D1711yescharacteristic
597C4#1176357511yescharacteristic
598C4#1176361011yescharacteristic
599C4#1176361611yescharacteristic
600C2—81no—
601C2—81no—
602C2—342no—
603C2—682no—
604C2#1453751311yescharacteristic
605C2#1453760911yescharacteristic
606C2D17×#44311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D17
commutatorC2×C4×C17C23×C4
FrattiniC42C23×D17
FittingC17×#1589C2
socleC22×C17C2×C4×D4
prime radical#11762941C4
cosocleC42×C17C24
hypercenter#1589D17
hypocenterC17#18014
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1589

Complements

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

NH ≅ G/Ntype
2. #14537945C2semidirect
3. #14537816C2semidirect
4. #14527677C2semidirect
5. #14527660C2semidirect
6. #14527649C2semidirect
7. #14527646C2semidirect
8. #14527640C2semidirect
9. C8×#63219C2semidirect
10. #14527576C2semidirect
11. #14527568C2semidirect
12. #14527241C2semidirect
13. D17×D4⋊C8C2semidirect
14. #14527066C2semidirect
15. C17×#1589C2semidirect
26. #11762936C22semidirect
27. C8×Dic34C22semidirect
36. D4×#3622C22semidirect
48. #11762561C22semidirect
49. #11762560C22semidirect
50. #11762559C22semidirect
51. #11762541C22semidirect
52. #11762539C22semidirect
55. D4⋊#3622C22semidirect
57. #11762531C22semidirect
58. #11762531C22semidirect
59. C8×#3622C22semidirect
62. C17×#436C22semidirect
63. C17×#335C22semidirect
65. C17×D4⋊C8C22semidirect
66. C82×C17C22semidirect
274. #1589D17semidirect
330. #436C2×D17semidirect
348. #335C2×D17semidirect
358. D4⋊C8C2×D17semidirect
362. C82C2×D17semidirect
447. C17#18014semidirect

Maximal subgroups

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

subgroupindex
#145388292
#145379452
#145378162
#145276772
#145276602
#145276492
#145276462
#145276402
C8×#632192
#145275762
#145275682
#145272412
D17×D4⋊C82
#145270662
C17×#15892
#1801417