Finite Group Databasebeta

← #17004410

Subgroups — #17004410

Order 4352.

638 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14538838C211yesmaximal, characteristic
2#14537892C211yesmaximal, characteristic, complemented
3#14527660C211yesmaximal, characteristic, complemented
4#14527646C211yesmaximal, characteristic, complemented
5#14527625C211yesmaximal, characteristic, complemented
6#14527611C211yesmaximal, characteristic, complemented
7#14527606C211yesmaximal, characteristic, complemented
8#14527596C211yesmaximal, characteristic, complemented
9C8×#63229C211yesmaximal, characteristic, complemented
10C8×#63228C211yesmaximal, characteristic, complemented
11#14527570C211yesmaximal, characteristic, complemented
12#14527216C211yesmaximal, characteristic, complemented
13#14527183C211yesmaximal, characteristic, complemented
14#14527084C211yesmaximal, characteristic, complemented
15C17×#2981C211yesmaximal, characteristic, complemented
16C4×#63252C2211yescharacteristic
17#11763130C411yescharacteristic
18#11763130C411yescharacteristic
19#11763101C411yescharacteristic
20#11763096C411yescharacteristic
21#11763006C411yescharacteristic
22#11763001C411yescharacteristic
23#11762952C411yescharacteristic
24#11762952C411yescharacteristic
25C8×Dic34C2211yescharacteristic
26C8×Dic34C2211yescharacteristic
27C4×#63229C2211yescharacteristic
28C4×#63229C2211yescharacteristic
29C4×#63228C2211yescharacteristic
30C4×#63228C2211yescharacteristic
31C8×D68C2211yescharacteristic
32C8×D68C2211yescharacteristic
33#11762872—21no—
34#11762872—21no—
35#11762862C2211yescharacteristic
36#11762862C2211yescharacteristic
37#11762861—21no—
38C2×C4⋊#3622C2211yescharacteristic
39C4⋊C8×D17—21no—
40#11762561C2211yescharacteristic
41#11762561C2211yescharacteristic
42#11762559C2211yescharacteristic
43#11762559C2211yescharacteristic
44#11762539C2211yescharacteristic
45#11762539C2211yescharacteristic
46D4⋊#3622C2211yescharacteristic
47D4⋊#3622C2211yescharacteristic
48D4⋊#3622C2211yescharacteristic
49D4⋊#3622C2211yescharacteristic
50#11762536C2211yescharacteristic
51#11762536C2211yescharacteristic
52#11762531C2211yescharacteristic
53#11762531C2211yescharacteristic
54#11762530C2211yescharacteristic
55C8×#3622C2211yescharacteristic
56C17×#532C2211yescharacteristic
57C17×#436C2211yescharacteristic
58C17×#436C2211yescharacteristic
59C17×#435—21no—
60C17×#435—21no—
61C8×D4×C17C2211yescharacteristic
62C8×D4×C17C2211yescharacteristic
63C17×#432C2211yescharacteristic
64C17×#431C2211yescharacteristic
65C17×#408—21no—
66C17×#408—21no—
67C2×#41×C17—21no—
68C2×#63252C2×C411yescharacteristic
69C2×M16×C17—21no—
70C2×M16×C17—21no—
71C22×C8×C17—21no—
72C22×C8×C17—21no—
73C17×C4⋊Q8C2×C411yescharacteristic
74C17×#127C2×C411yescharacteristic
75C17×#124—21no—
76C17×#121—21no—
77C17×#121C2×C411yescharacteristic
78C17×#121C2×C411yescharacteristic
79C4×D4×C17—21no—
80C4×D4×C17C2311yescharacteristic
81C4×D4×C17C2311yescharacteristic
82C2×C42×C17C2311yescharacteristic
83C2×#63229C2×C411yescharacteristic
84C2×#63229C2×C411yescharacteristic
85C2×#63228C2×C411yescharacteristic
86C2×#63228C2×C411yescharacteristic
87C4×C22⋊D17—21no—
88C4×C22⋊D17—21no—
89#10587612C2×C411yescharacteristic
90C22×#3622—21no—
91C2×C8×D17—21no—
92C2×C8×D17—21no—
93C4×D68C2×C411yescharacteristic
94C4×D68C2311yescharacteristic
95#10587558—21no—
96C42×D17—21no—
97C4×Dic34C2×C411yescharacteristic
98C4×Dic34C2311yescharacteristic
99C17×C4⋊C8D411yescharacteristic
100C17×C4⋊C8D411yescharacteristic
101C17×C4⋊C8C2311yescharacteristic
102C17×C4⋊C8C2311yescharacteristic
103C17×C22⋊C8—21no—
104C17×C22⋊C8—21no—
105C17×C22⋊C8—21no—
106C17×C22⋊C8—21no—
107C17×C22⋊C8—21no—
108C17×C22⋊C8D411yescharacteristic
109C17×C22⋊C8D411yescharacteristic
110C17×#97—21no—
111C4×C8×C17C2311yescharacteristic
112C4×C8×C17C2311yescharacteristic
113#10587503C2×C411yescharacteristic
114#10587503C2×C411yescharacteristic
115#10587503C2×C411yescharacteristic
116#10587503C2×C411yescharacteristic
117C22⋊#3622—21no—
118C22⋊#3622C2×C411yescharacteristic
119C22⋊#3622C2×C411yescharacteristic
120#10587491—21no—
121#10587491—21no—
122#10587485—21no—
123#10587485—21no—
124C8×Dic17—21no—
125C8×Dic17—21no—
126#10587481C2×C411yescharacteristic
127#10587481C2×C411yescharacteristic
128#10587480C2×C411yescharacteristic
129#10587480C2×C411yescharacteristic
130#10587479C2×C411yescharacteristic
131#10587479C2×C411yescharacteristic
132#10587478C2×C411yescharacteristic
133#10587478C2×C411yescharacteristic
134C4⋊#3622—21no—
135C4⋊#3622—21no—
136C4⋊#3622C2×C411yescharacteristic
137C4⋊#3622C2×C411yescharacteristic
138C4⋊#3622C2311yescharacteristic
139C4⋊#3622C2311yescharacteristic
140C4×#3622C2311yescharacteristic
141C4×#3622C2311yescharacteristic
142C4×#3622C2311yescharacteristic
143C4×#3622C2311yescharacteristic
144#41×C17—81no—
145#41×C17—81no—
146C2×Q8×C17—21no—
147C2×D4×C17—21no—
148C2×D4×C17—21no—
149C2×D4×C17—21no—
150C2×D4×C17—21no—
151C2×D4×C17C22×C411yescharacteristic
152C2×D4×C17C22×C411yescharacteristic
153C22×C4×C17—21no—
154C22×C4×C17—21no—
155C22×C4×C17C22×C411yescharacteristic
156C22×C4×C17C2×D411yescharacteristic
157C22×C4×C17#4111yescharacteristic
158C2×C22⋊D17—21no—
159#63252—22no—
160#63252—22no—
161C2×D68C22×C411yescharacteristic
162C2×C4×D17—21no—
163C2×C4×D17—21no—
164C2×C4×D17—21no—
165C2×Dic34C22×C411yescharacteristic
166M16×C17—81no—
167M16×C17—81no—
168C2×C8×C17—21no—
169C2×C8×C17—21no—
170C2×C8×C17—81no—
171C2×C8×C17—81no—
172C2×C8×C17C2×D411yescharacteristic
173C2×C8×C17C2×D411yescharacteristic
174C2×C8×C17C2×D411yescharacteristic
175C2×C8×C17C2×D411yescharacteristic
176C4⋊C4×C17—21no—
177C4⋊C4×C17C22×C411yescharacteristic
178C4⋊C4×C17C22×C411yescharacteristic
179C22⋊C4×C17—21no—
180C22⋊C4×C17—21no—
181C22⋊C4×C17—21no—
182C22⋊C4×C17—21no—
183C42×C17C22×C411yescharacteristic
184C42×C17C2×D411yescharacteristic
185C42×C17#4111yescharacteristic
186C42×C17C2411yescharacteristic
187C22⋊Dic17—21no—
188#63229—22no—
189#63229—22no—
190#63228—22no—
191#63228—22no—
192#63227—21no—
193#63227—21no—
194C4⋊Dic17C22×C411yescharacteristic
195C4⋊Dic17C22×C411yescharacteristic
196#63225—21no—
197#63225—21no—
198C4×Dic17—21no—
199C4×Dic17—21no—
200C4×Dic17—21no—
201C2×#3622—21no—
202C2×#3622—21no—
203C2×#3622—21no—
204C2×#3622—21no—
205C2×#3622—81no—
206C2×#3622C22×C411yescharacteristic
207C2×#3622C22×C411yescharacteristic
208C2×#3622C22×C411yescharacteristic
209C2×#3622C22×C411yescharacteristic
210C8×D17—81no—
211C8×D17—81no—
212#17920—171nomaximal, Sylow
213C23×C17—21no—
214C23×C17—21no—
215C23×C17C4×D411yescharacteristic
216C22×D17—21no—
217Q8×C17—81no—
218D4×C17—21no—
219D4×C17—21no—
220D4×C17—21no—
221D4×C17—21no—
222D4×C17—81no—
223D4×C17—81no—
224D4×C17—81no—
225D4×C17—81no—
226C2×C4×C17—21no—
227C2×C4×C17—21no—
228C2×C4×C17—21no—
229C2×C4×C17—21no—
230C2×C4×C17—21no—
231C2×C4×C17—21no—
232C2×C4×C17—41no—
233C2×C4×C17—41no—
234C2×C4×C17—41no—
235C2×C4×C17—41no—
236C2×C4×C17—41no—
237C2×C4×C17C4×D411yescharacteristic
238C2×C4×C17C4×D411yescharacteristic
239C2×C4×C17C4×D411yescharacteristic
240C2×C4×C17C23×C411yescharacteristic
241C2×C4×C17C22×D411yescharacteristic
242C2×C4×C17C2×#4111yescharacteristic
243C22⋊D17—24no—
244C2×Dic17—21no—
245C2×Dic17—21no—
246C2×Dic17—21no—
247D68—21no—
248D68#13112yes—
249C4×D17—24no—
250C4×D17—41no—
251C4×D17—41no—
252C4×D17—81no—
253Dic34—21no—
254Dic34#13112yes—
255C8×C17—21no—
256C8×C17—21no—
257C8×C17—21no—
258C8×C17—21no—
259C8×C17—41no—
260C8×C17—41no—
261#3622—21no—
262#3622—21no—
263#3622—21no—
264#3622—21no—
265#3622—41no—
266#3622—41no—
267#3622—41no—
268#3622—41no—
269#3106—171no—
270#2988—171no—
271#2981D1711yescharacteristic, complemented
272#1588—171no—
273#1586—171no—
274#1583—171no—
275#1581—171no—
276#1580—171no—
277SD16⋊C8—171no—
278C8×SD16—171no—
279C8×D8—171no—
280#1573—171no—
281#1488—171no—
282#1480—171no—
283#1454—171no—
284C22×C17—21no—
285C22×C17—21no—
286C22×C17—21no—
287C22×C17—41no—
288C22×C17—41no—
289C22×C17—41no—
290C22×C17—41no—
291C22×C17—41no—
292C22×C17—41no—
293C22×C17C2×C4×D411yescharacteristic
294C2×D17—22no—
295C2×D17—41no—
296C2×D17—41no—
297C4×C17—21no—
298C4×C17—21no—
299C4×C17—21no—
300C4×C17—21no—
301C4×C17—41no—
302C4×C17—41no—
303C4×C17C2×#13111yescharacteristic
304C4×C17C2×#13111yescharacteristic
305C4×C17#57611yescharacteristic
306C4×C17#57711yescharacteristic
307Dic17—22no—
308Dic17—41no—
309Dic17—41no—
310#532C2×D1711yescharacteristic
311C4×#41—171no—
312#482—171no—
313#482—171no—
314#477—171no—
315#476—171no—
316#460—171no—
317#459—171no—
318#449—171no—
319#449—171no—
320C8×Q8—171no—
321C8×Q8—171no—
322C4×SD16—171no—
323C4×SD16—171no—
324C4×D8—171no—
325C4×D8—171no—
326#436C2×D1711yescharacteristic
327#436C2×D1711yescharacteristic
328#435—21no—
329#435—21no—
330C8×D4—171no—
331C8×D4—171no—
332C8×D4—341no—
333C8×D4—341no—
334C8×D4C2×D1711yescharacteristic
335C8×D4C2×D1711yescharacteristic
336#432C2×D1711yescharacteristic
337#431—171no—
338#431—171no—
339#431—341no—
340#431C2×D1711yescharacteristic
341C2×C4⋊C8—171no—
342C2×C4⋊C8—341no—
343#408—21no—
344#408—21no—
345#335—171no—
346#335—171no—
347#334—171no—
348#334—171no—
349Q8⋊C8—171no—
350Q8⋊C8—171no—
351D4⋊C8—171no—
352D4⋊C8—171no—
353D4⋊C8—171no—
354D4⋊C8—171no—
355D4⋊C8—171no—
356D4⋊C8—171no—
357#322—171no—
358#322—171no—
359#322—171no—
360C82—171no—
361C2×C17—41no—
362C2×C17—81no—
363C2×C17—81no—
364C2×C17#292911yescharacteristic
365C2×C17#294611yescharacteristic
366C2×C17#295711yescharacteristic
367D17—42no—
368C2×#41—21no—
369C2×#41—171no—
370C2×SD16—171no—
371C2×SD16—171no—
372C2×D8—171no—
373C2×D8—171no—
374C2×M16—21no—
375C2×M16—21no—
376C22×C8—21no—
377C22×C8—21no—
378C22×C8—341no—
379C22×C8—341no—
380C22×C8—341no—
381C4⋊Q8C4×D1711yescharacteristic
382#127C4×D1711yescharacteristic
383#124—21no—
384#121—21no—
385#121C4×D1711yescharacteristic
386#121C4×D1711yescharacteristic
387C4×Q8—171no—
388C4×Q8—171no—
389C4×D4—21no—
390C4×D4—171no—
391C4×D4—171no—
392C4×D4—341no—
393C4×D4—341no—
394C4×D4C22×D1711yescharacteristic
395C4×D4C22×D1711yescharacteristic
396#117—171no—
397#117—341no—
398C2×C42—341no—
399C2×C42C22×D1711yescharacteristic
400#107—171no—
401#107—171no—
402#106—171no—
403#106—171no—
404C4⋊C8—171no—
405C4⋊C8—171no—
406C4⋊C8—171no—
407C4⋊C8—171no—
408C4⋊C8—341no—
409C4⋊C8—341no—
410C4⋊C8—341no—
411C4⋊C8—341no—
412C4⋊C8C22⋊D1711yescharacteristic
413C4⋊C8C22⋊D1711yescharacteristic
414C4⋊C8C22×D1711yescharacteristic
415C4⋊C8C22×D1711yescharacteristic
416#103—171no—
417#103—171no—
418#102—171no—
419#102—171no—
420#102—171no—
421#102—171no—
422#102—171no—
423#102—171no—
424C22⋊C8—21no—
425C22⋊C8—21no—
426C22⋊C8—21no—
427C22⋊C8—21no—
428C22⋊C8—21no—
429C22⋊C8—171no—
430C22⋊C8—171no—
431C22⋊C8—341no—
432C22⋊C8—341no—
433C22⋊C8—341no—
434C22⋊C8C22⋊D1711yescharacteristic
435C22⋊C8C22⋊D1711yescharacteristic
436#97—21no—
437C4×C8—171no—
438C4×C8—171no—
439C4×C8—171no—
440C4×C8—171no—
441C4×C8—341no—
442C4×C8—341no—
443C4×C8C22×D1711yescharacteristic
444C4×C8C22×D1711yescharacteristic
445C17#1792011yescharacteristic, complemented, Sylow
446#41—81no—
447#41—81no—
448#41—342no—
449#41—342no—
450C2×Q8—21no—
451C2×Q8—171no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—171no—
457C2×D4—341no—
458C2×D4C2×C4×D1711yescharacteristic
459C2×D4C2×C4×D1711yescharacteristic
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—341no—
463C22×C4—341no—
464C22×C4—341no—
465C22×C4C2×C4×D1711yescharacteristic
466C22×C4#6325211yescharacteristic
467C22×C4C2×C22⋊D1711yescharacteristic
468SD16—342no—
469SD16—342no—
470D8—342no—
471D8—342no—
472M16—81no—
473M16—81no—
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—341no—
486C2×C8—1361no—
487C2×C8—1361no—
488C2×C8—1361no—
489C2×C8C2×C22⋊D1711yescharacteristic
490C2×C8C2×C22⋊D1711yescharacteristic
491C2×C8C2×C22⋊D1711yescharacteristic
492C2×C8C2×C22⋊D1711yescharacteristic
493C4⋊C4—21no—
494C4⋊C4—171no—
495C4⋊C4—171no—
496C4⋊C4—341no—
497C4⋊C4—341no—
498C4⋊C4C2×C4×D1711yescharacteristic
499C4⋊C4C2×C4×D1711yescharacteristic
500C22⋊C4—21no—
501C22⋊C4—21no—
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—341no—
505C22⋊C4—341no—
506C22⋊C4—341no—
507C42—341no—
508C42—341no—
509C42—341no—
510C42C2×C4×D1711yescharacteristic
511C42#6325211yescharacteristic
512C42C2×C22⋊D1711yescharacteristic
513C42C23×D1711yescharacteristic
514C23—21no—
515C23—21no—
516C23—341no—
517C23C4×C22⋊D1711yescharacteristic
518Q8—81no—
519Q8—172no—
520Q8—341no—
521D4—21no—
522D4—21no—
523D4—21no—
524D4—21no—
525D4—81no—
526D4—81no—
527D4—81no—
528D4—81no—
529D4—172no—
530D4—344no—
531D4—341no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—344no—
544C2×C4—341no—
545C2×C4—341no—
546C2×C4—341no—
547C2×C4—681no—
548C2×C4—681no—
549C2×C4—1361no—
550C2×C4C4×C22⋊D1711yescharacteristic
551C2×C4C4×C22⋊D1711yescharacteristic
552C2×C4C4×C22⋊D1711yescharacteristic
553C2×C4C22×C4×D1711yescharacteristic
554C2×C4C2×#6325211yescharacteristic
555C2×C4C22×C22⋊D1711yescharacteristic
556C8—21no—
557C8—21no—
558C8—21no—
559C8—21no—
560C8—41no—
561C8—41no—
562C8—341no—
563C8—341no—
564C8—341no—
565C8—341no—
566C8—681no—
567C8—681no—
568C8—681no—
569C8—681no—
570C22—21no—
571C22—21no—
572C22—21no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—342no—
580C22—681no—
581C22—681no—
582C22C2×C4×C22⋊D1711yescharacteristic
583C4—21no—
584C4—21no—
585C4—21no—
586C4—21no—
587C4—41no—
588C4—41no—
589C4—342no—
590C4—681no—
591C4—681no—
592C4#131×D1711yescharacteristic
593C4#131×D1711yescharacteristic
594C4#1176361211yescharacteristic
595C4#1176362011yescharacteristic
596C2—41no—
597C2—81no—
598C2—81no—
599C2—682no—
600C2#1453747611yescharacteristic
601C2#1453761611yescharacteristic
602C2#1453769911yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D17
commutatorC2×C4×C17C23×C4
FrattiniC42C23×D17
FittingC17×#2981C2
socleC22×C17C2×C4×D4
prime radical#14538838C2
cosocleC42×C17C24
hypercenter#2981D17
hypocenterC17#17920
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2981

Complements

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

NH ≅ G/Ntype
2. #14537892C2semidirect
3. #14527660C2semidirect
4. #14527646C2semidirect
5. #14527625C2semidirect
6. #14527611C2semidirect
7. #14527606C2semidirect
8. #14527596C2semidirect
9. C8×#63229C2semidirect
10. C8×#63228C2semidirect
11. #14527570C2semidirect
12. #14527216C2semidirect
13. #14527183C2semidirect
14. #14527084C2semidirect
15. C17×#2981C2semidirect
271. #2981D17semidirect
445. C17#17920semidirect

Maximal subgroups

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

subgroupindex
#145388382
#145378922
#145276602
#145276462
#145276252
#145276112
#145276062
#145275962
C8×#632292
C8×#632282
#145275702
#145272162
#145271832
#145270842
C17×#29812
#1792017