Finite Group Databasebeta

← #17005478

Subgroups — #17005478

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#14538833C211yesmaximal, characteristic
2#14537940C211yesmaximal, characteristic, complemented
3#14537821C211yesmaximal, characteristic, complemented
4#14527673C211yesmaximal, characteristic, complemented
5#14527668C211yesmaximal, characteristic, complemented
6#14527661C211yesmaximal, characteristic, complemented
7#14527647C211yesmaximal, characteristic, complemented
8#14527647C211yesmaximal, characteristic, complemented
9#14527640C211yesmaximal, characteristic, complemented
10#14527583C211yesmaximal, characteristic, complemented
11#14527578C211yesmaximal, characteristic, complemented
12#14527242C211yesmaximal, characteristic, complemented
13C2×#11762536C211yesmaximal, characteristic, complemented
14#14527068C211yesmaximal, characteristic, complemented
15C17×#1573C211yesmaximal, characteristic, complemented
16#11763343C2211yescharacteristic
17C2×C4×D68C2211yescharacteristic
18#11763145C411yescharacteristic
19#11763128C411yescharacteristic
20#11763110C411yescharacteristic
21#11763110C411yescharacteristic
22#11763025C411yescharacteristic
23#11763025C411yescharacteristic
24#11762962C411yescharacteristic
25#11762945C411yescharacteristic
26#11762936C2211yescharacteristic, complemented
27#11762933C2211yescharacteristic, complemented
28C4×#63219C2211yescharacteristic
29C4×#63219C2211yescharacteristic
30C4×D136C2211yescharacteristic
31C4×D136C2211yescharacteristic
32#11762886C2211yescharacteristic
33#11762886C2211yescharacteristic
34#11762886C2211yescharacteristic, complemented
35#11762882—21no—
36#11762882—21no—
37#11762880—21no—
38#11762874C2211yescharacteristic
39#11762874C2211yescharacteristic
40#11762874C2211yescharacteristic, complemented
41C8×C22⋊D17—21no—
42#11762869—21no—
43#11762862C2211yescharacteristic
44#11762834—21no—
45#11762771—21no—
46C22⋊C8×D17—21no—
47C2×C4×#3622C2211yescharacteristic
48#11762539C2211yescharacteristic, complemented
49#11762539C2211yescharacteristic, complemented
50#11762536C2211yescharacteristic
51#11762536C2211yescharacteristic
52#11762536C2211yescharacteristic
53#11762536C2211yescharacteristic
54#11762536C2211yescharacteristic, complemented
55#11762536C2211yescharacteristic, complemented
56#11762531C2211yescharacteristic, complemented
57#11762531C2211yescharacteristic, complemented
58C8×#3622C2211yescharacteristic, complemented
59C8×#3622C2211yescharacteristic, complemented
60C17×#432C2211yescharacteristic
61C17×#431C2211yescharacteristic
62C2×C17×C4⋊C8C2211yescharacteristic
63C17×#335C2211yescharacteristic, complemented
64C17×#335C2211yescharacteristic, complemented
65C17×#334C2211yescharacteristic, complemented
66C17×#334C2211yescharacteristic, complemented
67C22×D68C2×C411yescharacteristic
68C22×C4×D17—21no—
69C22×C8×C17—21no—
70C2×C42×C17C2311yescharacteristic
71#10587616C2×C411yescharacteristic
72#10587615—21no—
73C4×C22⋊D17—21no—
74C2×#63227—21no—
75C2×C4⋊Dic17C2×C411yescharacteristic
76#10587610C2×C411yescharacteristic
77C22×#3622—21no—
78C2×D136C2×C411yescharacteristic
79C2×D136C2×C411yescharacteristic
80C2×#63219C2×C411yescharacteristic
81C2×#63219C2×C411yescharacteristic
82C2×#63218—21no—
83C2×#63218—21no—
84C2×#63218—21no—
85C2×C8×D17—21no—
86C2×C8×D17—21no—
87C2×C8×D17—21no—
88#10587562—21no—
89#10587561C2×C411yescharacteristic
90C4×D68—21no—
91C4×D68—21no—
92C4×D68C2×C411yescharacteristic
93C4×D68C2×C411yescharacteristic
94C4×D68C2311yescharacteristic
95C4×D68C2311yescharacteristic
96C4×D68C2311yescharacteristic
97#10587558—21no—
98#10587556C2×C411yescharacteristic
99C4×Dic34C2311yescharacteristic
100C17×C4⋊C8—21no—
101C17×C4⋊C8C2×C411yescharacteristic
102C17×C4⋊C8C2×C411yescharacteristic
103C17×C4⋊C8C2311yescharacteristic
104C17×C4⋊C8C2311yescharacteristic
105C17×C4⋊C8C2311yescharacteristic
106C17×C4⋊C8C2311yescharacteristic
107C17×C22⋊C8—21no—
108C17×C22⋊C8C2×C411yescharacteristic
109C17×C22⋊C8C2×C411yescharacteristic
110C17×#97—21no—
111C4×C8×C17C2311yescharacteristic
112C4×C8×C17C2311yescharacteristic
113C22⋊#3622D411yescharacteristic
114C22⋊#3622D411yescharacteristic
115#10587492C2×C411yescharacteristic
116#10587492C2×C411yescharacteristic
117#10587492C2×C411yescharacteristic
118#10587492C2×C411yescharacteristic
119#10587492C2×C411yescharacteristic
120#10587492C2×C411yescharacteristic
121#10587491—21no—
122#10587491—21no—
123#10587491—21no—
124#10587491—21no—
125#10587491—21no—
126#10587491—21no—
127#10587489C2×C411yescharacteristic
128#10587489C2×C411yescharacteristic
129#10587488C2×C411yescharacteristic
130#10587488C2×C411yescharacteristic
131#10587487C2×C411yescharacteristic
132#10587487C2×C411yescharacteristic
133#10587486—21no—
134#10587485—21no—
135#10587485—21no—
136C8×Dic17—21no—
137C4⋊#3622D411yescharacteristic
138C4⋊#3622D411yescharacteristic
139C4×#3622—21no—
140C4×#3622C2311yescharacteristic
141C4×#3622C2311yescharacteristic
142C4×#3622C2311yescharacteristic
143C4×#3622C2311yescharacteristic
144C23×D17—21no—
145C22×C4×C17C22×C411yescharacteristic
146C22×C4×C17C2×D411yescharacteristic
147C22×C4×C17#4111yescharacteristic
148C2×C22⋊D17—21no—
149C22×Dic17—21no—
150C2×D68—22no—
151C2×D68—21no—
152C2×D68—41no—
153C2×D68C22×C411yescharacteristic
154C2×D68C22×C411yescharacteristic
155C2×D68C22×C411yescharacteristic
156C2×C4×D17—21no—
157C2×C4×D17—21no—
158C2×C4×D17—21no—
159C2×C4×D17—21no—
160C2×C4×D17—21no—
161C2×C4×D17—81no—
162C2×C4×D17—81no—
163C2×Dic34C22×C411yescharacteristic
164C2×C8×C17—21no—
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×C17C22×C411yescharacteristic
172C2×C8×C17C22×C411yescharacteristic
173C42×C17C22×C411yescharacteristic
174C42×C17C2×D411yescharacteristic
175C42×C17#4111yescharacteristic
176C42×C17C2411yescharacteristic
177C22⋊Dic17—21no—
178#63227—21no—
179#63227—21no—
180#63227—21no—
181#63227—21no—
182#63227—21no—
183#63227—21no—
184#63227—21no—
185#63227—21no—
186C4⋊Dic17—21no—
187C4⋊Dic17C22×C411yescharacteristic
188C4⋊Dic17C22×C411yescharacteristic
189C4⋊Dic17C22×C411yescharacteristic
190C4⋊Dic17C22×C411yescharacteristic
191#63225—21no—
192#63225—21no—
193#63225—21no—
194#63225—21no—
195C4×Dic17—21no—
196C2×#3622—24no—
197C2×#3622—21no—
198C2×#3622—21no—
199C2×#3622C2×D411yescharacteristic
200C2×#3622C2×D411yescharacteristic
201C2×#3622C2×D411yescharacteristic
202C2×#3622C2×D411yescharacteristic
203D136—22no—
204D136—41no—
205#63219—22no—
206#63219—41no—
207#63218—81no—
208#63218—81no—
209#63218—81no—
210C8×D17—81no—
211C8×D17—81no—
212C8×D17—81no—
213#18014—171nomaximal, Sylow
214C23×C17C4×D411yescharacteristic
215C22×D17—21no—
216C22×D17—21no—
217C22×D17—21no—
218C22×D17—42no—
219C22×D17—42no—
220C22×D17—81no—
221C2×C4×C17—22no—
222C2×C4×C17—21no—
223C2×C4×C17—21no—
224C2×C4×C17—21no—
225C2×C4×C17—21no—
226C2×C4×C17C4×D411yescharacteristic
227C2×C4×C17C4×D411yescharacteristic
228C2×C4×C17C4×D411yescharacteristic
229C2×C4×C17C23×C411yescharacteristic
230C2×C4×C17C22×D411yescharacteristic
231C2×C4×C17C2×#4111yescharacteristic
232C22⋊D17—42no—
233C2×Dic17—21no—
234C2×Dic17—21no—
235C2×Dic17—21no—
236C2×Dic17—21no—
237C2×Dic17—21no—
238C2×Dic17—81no—
239D68—21no—
240D68—21no—
241D68—21no—
242D68—21no—
243D68—21no—
244D68—42no—
245D68#13112yes—
246C4×D17—41no—
247C4×D17—41no—
248C4×D17—41no—
249C4×D17—41no—
250C4×D17—41no—
251C4×D17—41no—
252C4×D17—81no—
253C4×D17—81no—
254Dic34—21no—
255Dic34—21no—
256C8×C17—21no—
257C8×C17—21no—
258C8×C17—21no—
259C8×C17—21no—
260C8×C17—41no—
261C8×C17—41no—
262C8×C17—41no—
263C8×C17—41no—
264#3622—22no—
265#3622—22no—
266#3622—21no—
267#3622—21no—
268#3622—21no—
269#3622—21no—
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#1585—171no—
279C8×SD16—171no—
280C8×D8—171no—
281#1573D1711yescharacteristic, complemented
282#1494—171no—
283C2×D4⋊C8—171no—
284#1450—171no—
285C22×C17—21no—
286C22×C17—21no—
287C22×C17#44312yes—
288C22×C17C2×C4×D411yescharacteristic
289C2×D17—22no—
290C2×D17—41no—
291C2×D17—41no—
292C2×D17—41no—
293C2×D17—41no—
294C2×D17—41no—
295C2×D17—41no—
296C2×D17—41no—
297C2×D17—41no—
298C2×D17—84no—
299C4×C17—21no—
300C4×C17—21no—
301C4×C17—21no—
302C4×C17—21no—
303C4×C17C2×#13111yescharacteristic
304C4×C17#56811yescharacteristic
305C4×C17#57611yescharacteristic
306C4×C17#57711yescharacteristic
307Dic17—41no—
308Dic17—41no—
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×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—171no—
337C8×D4—341no—
338#433—341no—
339#432C2×D1711yescharacteristic
340#431—171no—
341#431C2×D1711yescharacteristic
342#424—341no—
343C2×C4⋊C8C2×D1711yescharacteristic
344#407—341no—
345C2×C22⋊C8—341no—
346C2×C4×C8—171no—
347#335C2×D1711yescharacteristic, complemented
348#335C2×D1711yescharacteristic, complemented
349#334C2×D1711yescharacteristic, complemented
350#334C2×D1711yescharacteristic, complemented
351Q8⋊C8—171no—
352Q8⋊C8—171no—
353D4⋊C8—171no—
354D4⋊C8—171no—
355D4⋊C8—171no—
356D4⋊C8—171no—
357D4⋊C8—171no—
358D4⋊C8—171no—
359#322—171no—
360#322—171no—
361C82—171no—
362C82—171no—
363C2×C17—22no—
364C2×C17#293311yescharacteristic
365C2×C17#294611yescharacteristic
366C2×C17C2×#44311yescharacteristic
367D17—42no—
368D17—81no—
369D17—81no—
370C22×D4—171no—
371C23×C4—341no—
372C2×SD16—171no—
373C2×SD16—171no—
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×Q8—171no—
391C4×D4—171no—
392C4×D4—171no—
393C4×D4—171no—
394C4×D4—171no—
395C4×D4—171no—
396C4×D4—341no—
397C4×D4—341no—
398C4×D4—341no—
399#117—341no—
400C2×C4⋊C4—171no—
401C2×C22⋊C4—341no—
402C2×C42C22×D1711yescharacteristic
403#107—171no—
404#107—171no—
405#106—171no—
406#106—171no—
407C4⋊C8—21no—
408C4⋊C8—171no—
409C4⋊C8—171no—
410C4⋊C8—341no—
411C4⋊C8—341no—
412C4⋊C8C4×D1711yescharacteristic
413C4⋊C8C4×D1711yescharacteristic
414C4⋊C8C22×D1711yescharacteristic
415C4⋊C8C22×D1711yescharacteristic
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#102—171no—
425#102—171no—
426C22⋊C8—21no—
427C22⋊C8—171no—
428C22⋊C8—171no—
429C22⋊C8—341no—
430C22⋊C8—341no—
431C22⋊C8—341no—
432C22⋊C8—341no—
433C22⋊C8—341no—
434C22⋊C8—341no—
435C22⋊C8C4×D1711yescharacteristic
436C22⋊C8C4×D1711yescharacteristic
437#97—21no—
438#97—341no—
439C4×C8—171no—
440C4×C8—171no—
441C4×C8—171no—
442C4×C8—171no—
443C4×C8—341no—
444C4×C8—341no—
445C4×C8C22×D1711yescharacteristic
446C4×C8C22×D1711yescharacteristic
447C17#1801411yescharacteristic, complemented, Sylow
448C24—341no—
449C2×Q8—171no—
450C2×D4—171no—
451C2×D4—171no—
452C2×D4—171no—
453C2×D4—342no—
454C2×D4—341no—
455C2×D4—341no—
456C2×D4—681no—
457C22×C4—341no—
458C22×C4—341no—
459C22×C4—341no—
460C22×C4—341no—
461C22×C4—341no—
462C22×C4—341no—
463C22×C4—1361no—
464C22×C4—1361no—
465C22×C4C2×C4×D1711yescharacteristic
466C22×C4D4×D1711yescharacteristic
467C22×C4#6325611yescharacteristic
468SD16—342no—
469SD16—681no—
470D8—342no—
471D8—681no—
472M16—1361no—
473M16—1361no—
474M16—1361no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—81no—
480C2×C8—171no—
481C2×C8—171no—
482C2×C8—171no—
483C2×C8—171no—
484C2×C8—344no—
485C2×C8—341no—
486C2×C8—341no—
487C2×C8—1361no—
488C2×C8—1361no—
489C2×C8—1361no—
490C2×C8C2×C4×D1711yescharacteristic
491C2×C8C2×C4×D1711yescharacteristic
492C2×C8C2×C4×D1711yescharacteristic
493C2×C8C2×C4×D1711yescharacteristic
494C4⋊C4—171no—
495C4⋊C4—171no—
496C4⋊C4—171no—
497C4⋊C4—171no—
498C4⋊C4—341no—
499C4⋊C4—341no—
500C4⋊C4—341no—
501C4⋊C4—341no—
502C4⋊C4—341no—
503C22⋊C4—341no—
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—341no—
513C42C2×C4×D1711yescharacteristic
514C42D4×D1711yescharacteristic
515C42#6325611yescharacteristic
516C42C23×D1711yescharacteristic
517C23—341no—
518C23—341no—
519C23—341no—
520C23—682no—
521C23—682no—
522C23—1361no—
523C23#1058757911yescharacteristic
524Q8—341no—
525Q8—341no—
526D4—172no—
527D4—341no—
528D4—341no—
529D4—341no—
530D4—341no—
531D4—341no—
532D4—682no—
533D4—682no—
534C2×C4—22no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—341no—
540C2×C4—341no—
541C2×C4—341no—
542C2×C4—341no—
543C2×C4—341no—
544C2×C4—681no—
545C2×C4—681no—
546C2×C4—681no—
547C2×C4—681no—
548C2×C4—681no—
549C2×C4—681no—
550C2×C4—1361no—
551C2×C4—1361no—
552C2×C4—1361no—
553C2×C4#1058757911yescharacteristic
554C2×C4#1058757911yescharacteristic
555C2×C4#1058757911yescharacteristic
556C2×C4C22×C4×D1711yescharacteristic
557C2×C4C2×D4×D1711yescharacteristic
558C2×C4C2×#6325611yescharacteristic
559C8—21no—
560C8—21no—
561C8—21no—
562C8—21no—
563C8—41no—
564C8—41no—
565C8—41no—
566C8—41no—
567C8—342no—
568C8—342no—
569C8—341no—
570C8—341no—
571C8—341no—
572C8—341no—
573C22—21no—
574C22—21no—
575C22—342no—
576C22—681no—
577C22—681no—
578C22—681no—
579C22—681no—
580C22—681no—
581C22—681no—
582C22—681no—
583C22—681no—
584C22—1364no—
585C22#1176292512yes—
586C22C2×#1058757911yescharacteristic
587C4—21no—
588C4—21no—
589C4—21no—
590C4—21no—
591C4—681no—
592C4—681no—
593C4—681no—
594C4—681no—
595C4—681no—
596C4#131×D1711yescharacteristic
597C4#1176357411yescharacteristic
598C4#1176361311yescharacteristic
599C4#1176361811yescharacteristic
600C2—22no—
601C2—682no—
602C2—1361no—
603C2—1361no—
604C2#1453750811yescharacteristic
605C2#1453761411yescharacteristic
606C2C2×#1176292511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D17
commutatorC2×C4×C17C23×C4
FrattiniC42C23×D17
FittingC17×#1573C2
socleC22×C17C2×C4×D4
prime radical#11762945C4
cosocleC42×C17C24
hypercenter#1573D17
hypocenterC17#18014
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1573

Complements

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

NH ≅ G/Ntype
2. #14537940C2semidirect
3. #14537821C2semidirect
4. #14527673C2semidirect
5. #14527668C2semidirect
6. #14527661C2semidirect
7. #14527647C2semidirect
8. #14527647C2semidirect
9. #14527640C2semidirect
10. #14527583C2semidirect
11. #14527578C2semidirect
12. #14527242C2semidirect
13. C2×#11762536C2semidirect
14. #14527068C2semidirect
15. C17×#1573C2semidirect
26. #11762936C22semidirect
27. #11762933C22semidirect
34. #11762886C22semidirect
40. #11762874C22semidirect
48. #11762539C22semidirect
49. #11762539C22semidirect
54. #11762536C22semidirect
55. #11762536C22semidirect
56. #11762531C22semidirect
57. #11762531C22semidirect
58. C8×#3622C22semidirect
59. C8×#3622C22semidirect
63. C17×#335C22semidirect
64. C17×#335C22semidirect
65. C17×#334C22semidirect
66. C17×#334C22semidirect
281. #1573D17semidirect
347. #335C2×D17semidirect
348. #335C2×D17semidirect
349. #334C2×D17semidirect
350. #334C2×D17semidirect
447. C17#18014semidirect

Maximal subgroups

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

subgroupindex
#145388332
#145379402
#145378212
#145276732
#145276682
#145276612
#145276472
#145276402
#145275832
#145275782
#145272422
C2×#117625362
#145270682
C17×#15732
#1801417