Finite Group Databasebeta

← #17005154

Subgroups — #17005154

Order 4352.

566 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14539384C211yesmaximal, characteristic
2#14537935C211yesmaximal, characteristic
3#14527662C211yesmaximal, characteristic, complemented
4#14527655C211yesmaximal, characteristic, complemented
5#14527653C211yesmaximal, characteristic, complemented
6#14527639C211yesmaximal, characteristic, complemented
7#14527634C211yesmaximal, characteristic, complemented
8#14527632C211yesmaximal, characteristic, complemented
9#14527627C211yesmaximal, characteristic, complemented
10#14527618C211yesmaximal, characteristic, complemented
11#14527552C211yesmaximal, characteristic, complemented
12#14527242C211yesmaximal, characteristic
13#14527239C211yesmaximal, characteristic, complemented
14#14527074C211yesmaximal, characteristic, complemented
15C17×#2985C211yesmaximal, characteristic, complemented
16#11763343C2211yescharacteristic
17#11763215C411yescharacteristic
18#11763201C411yescharacteristic
19#11763177C411yescharacteristic
20#11763171C411yescharacteristic
21#11763065C411yescharacteristic
22#11763065C411yescharacteristic
23#11763057C411yescharacteristic
24#11763057C411yescharacteristic
25#11762939C2211yescharacteristic
26C8×Dic34C2211yescharacteristic
27C4×#63231C2211yescharacteristic
28C4×#63231C2211yescharacteristic
29C4×#63230C2211yescharacteristic
30C4×#63230C2211yescharacteristic
31#11762888C2211yescharacteristic
32#11762884—21no—
33#11762883—21no—
34C8×D68C2211yescharacteristic
35#11762869—21no—
36#11762834—21no—
37#11762833C2211yescharacteristic
38C4×#63223C2211yescharacteristic
39C2×C4×#3622C2211yescharacteristic
40#11762561C2211yescharacteristic
41#11762561C2211yescharacteristic
42#11762559C2211yescharacteristic
43#11762559C2211yescharacteristic
44Q8⋊#3622C2211yescharacteristic
45Q8⋊#3622C2211yescharacteristic
46Q8⋊#3622C2211yescharacteristic
47Q8⋊#3622C2211yescharacteristic
48#11762539C2211yescharacteristic
49#11762539C2211yescharacteristic
50#11762536C2211yescharacteristic
51#11762536C2211yescharacteristic
52#11762531C2211yescharacteristic
53#11762531C2211yescharacteristic
54#11762530C2211yescharacteristic
55#11762530C2211yescharacteristic
56C17×#533C2211yescharacteristic
57C17×#446—21no—
58C17×#446—21no—
59C17×#446C2211yescharacteristic
60C17×#446C2211yescharacteristic
61C8×Q8×C17C2211yescharacteristic
62C8×Q8×C17C2211yescharacteristic
63C17×#433—21no—
64C17×#433—21no—
65C17×#432C2211yescharacteristic
66C17×#431C2211yescharacteristic
67C17×C4⋊Q8C2×C411yescharacteristic
68C17×C4⋊Q8C2×C411yescharacteristic
69C17×#125—21no—
70C17×C22⋊Q8—21no—
71C17×C22⋊Q8C2×C411yescharacteristic
72C17×C22⋊Q8C2×C411yescharacteristic
73C4×Q8×C17—21no—
74C4×Q8×C17C2311yescharacteristic
75C4×Q8×C17C2311yescharacteristic
76C17×#117—21no—
77C2×C42×C17C2311yescharacteristic
78C2×#63231C2×C411yescharacteristic
79C2×#63231C2×C411yescharacteristic
80C2×#63230C2×C411yescharacteristic
81C2×#63230C2×C411yescharacteristic
82#10587616C2×C411yescharacteristic
83#10587615—21no—
84C4×C22⋊D17—21no—
85#10587610C2×C411yescharacteristic
86C2×#63223—21no—
87C2×#63223C2×C411yescharacteristic
88C2×#63223C2×C411yescharacteristic
89C22×#3622—21no—
90C2×#63218—21no—
91C2×C8×D17—21no—
92#10587562—21no—
93#10587561C2×C411yescharacteristic
94C4×D68C2311yescharacteristic
95#10587558—21no—
96#10587556C2×C411yescharacteristic
97C4×Dic34C2311yescharacteristic
98C17×C4⋊C8—21no—
99C17×C4⋊C8—21no—
100C17×C4⋊C8—21no—
101C17×C4⋊C8—21no—
102C17×C4⋊C8D411yescharacteristic
103C17×C4⋊C8D411yescharacteristic
104C17×C4⋊C8C2311yescharacteristic
105C17×C4⋊C8C2311yescharacteristic
106C17×C22⋊C8—21no—
107C17×C22⋊C8D411yescharacteristic
108C17×C22⋊C8D411yescharacteristic
109C17×#97—21no—
110C17×#97—21no—
111C17×#97—21no—
112C4×C8×C17—21no—
113C4×C8×C17—21no—
114C4×C8×C17C2311yescharacteristic
115C4×C8×C17C2311yescharacteristic
116#10587506C2×C411yescharacteristic
117#10587506C2×C411yescharacteristic
118#10587506C2×C411yescharacteristic
119#10587506C2×C411yescharacteristic
120#10587491—21no—
121#10587491—21no—
122#10587486—21no—
123#10587485—21no—
124#10587485—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⋊#3622C2311yescharacteristic
136C4⋊#3622C2311yescharacteristic
137#10587474C2×C411yescharacteristic
138#10587474C2×C411yescharacteristic
139C4×#3622—21no—
140C4×#3622C2311yescharacteristic
141C4×#3622C2311yescharacteristic
142C4×#3622C2311yescharacteristic
143C4×#3622C2311yescharacteristic
144C2×Q8×C17—21no—
145C2×Q8×C17C22×C411yescharacteristic
146C2×Q8×C17C22×C411yescharacteristic
147C22×C4×C17C22×C411yescharacteristic
148C22×C4×C17C2×D411yescharacteristic
149C22×C4×C17#4111yescharacteristic
150C2×C22⋊D17—21no—
151C2×D68C22×C411yescharacteristic
152C2×C4×D17—21no—
153C2×Dic34C22×C411yescharacteristic
154C2×C8×C17—21no—
155C2×C8×C17—21no—
156C2×C8×C17C2×D411yescharacteristic
157C2×C8×C17C2×D411yescharacteristic
158C2×C8×C17C2×D411yescharacteristic
159C2×C8×C17C2×D411yescharacteristic
160C4⋊C4×C17—21no—
161C4⋊C4×C17—21no—
162C4⋊C4×C17—21no—
163C4⋊C4×C17—21no—
164C4⋊C4×C17—21no—
165C4⋊C4×C17—21no—
166C4⋊C4×C17—21no—
167C4⋊C4×C17C22×C411yescharacteristic
168C4⋊C4×C17C22×C411yescharacteristic
169C22⋊C4×C17—21no—
170C22⋊C4×C17—21no—
171C42×C17—21no—
172C42×C17—21no—
173C42×C17C22×C411yescharacteristic
174C42×C17C2×D411yescharacteristic
175C42×C17#4111yescharacteristic
176C42×C17C2411yescharacteristic
177C22⋊Dic17—21no—
178#63231—41no—
179#63231—41no—
180#63230—41no—
181#63230—41no—
182#63227—21no—
183#63227—21no—
184#63227—21no—
185#63227—21no—
186C4⋊Dic17C22×C411yescharacteristic
187C4⋊Dic17C22×C411yescharacteristic
188#63225—21no—
189#63225—21no—
190#63225—21no—
191#63225—21no—
192C4×Dic17—21no—
193#63223—41no—
194#63223—41no—
195#63223—81no—
196C2×#3622—21no—
197C2×#3622—21no—
198C2×#3622—21no—
199C2×#3622—21no—
200C2×#3622—42no—
201C2×#3622C22×C411yescharacteristic
202C2×#3622C22×C411yescharacteristic
203C2×#3622C22×C411yescharacteristic
204C2×#3622C22×C411yescharacteristic
205#63218—81no—
206C8×D17—81no—
207#17988—171nomaximal, Sylow
208C23×C17C4×D411yescharacteristic
209C22×D17—21no—
210Q8×C17—21no—
211Q8×C17—21no—
212Q8×C17—21no—
213Q8×C17—21no—
214Q8×C17—81no—
215C2×C4×C17—21no—
216C2×C4×C17—21no—
217C2×C4×C17—21no—
218C2×C4×C17—21no—
219C2×C4×C17—21no—
220C2×C4×C17—21no—
221C2×C4×C17—21no—
222C2×C4×C17—21no—
223C2×C4×C17—41no—
224C2×C4×C17C4×D411yescharacteristic
225C2×C4×C17C4×D411yescharacteristic
226C2×C4×C17C4×D411yescharacteristic
227C2×C4×C17C23×C411yescharacteristic
228C2×C4×C17C22×D411yescharacteristic
229C2×C4×C17C2×#4111yescharacteristic
230C22⋊D17—81no—
231C2×Dic17—21no—
232C2×Dic17—21no—
233C2×Dic17—21no—
234D68—21no—
235D68—21no—
236C4×D17—41no—
237C4×D17—41no—
238Dic34—21no—
239Dic34—21no—
240C8×C17—21no—
241C8×C17—21no—
242C8×C17—21no—
243C8×C17—21no—
244C8×C17—41no—
245C8×C17—41no—
246#3622—22no—
247#3622—21no—
248#3622—21no—
249#3622—21no—
250#3622—21no—
251#3622—41no—
252#3622—41no—
253#3622—41no—
254#3172—171no—
255#2993—171no—
256#2985D1711yescharacteristic, complemented
257#1588—171no—
258#1587—171no—
259#1587—171no—
260#1585—171no—
261#1584—171no—
262#1584—171no—
263#1583—171no—
264#1582—171no—
265#1569—171no—
266#1494—171no—
267#1493—171no—
268#1451—171no—
269C22×C17—21no—
270C22×C17—21no—
271C22×C17—21no—
272C22×C17C2×C4×D411yescharacteristic
273C2×D17—41no—
274C2×D17—41no—
275C2×D17—41no—
276C4×C17—21no—
277C4×C17—21no—
278C4×C17—21no—
279C4×C17—21no—
280C4×C17—41no—
281C4×C17—41no—
282C4×C17—41no—
283C4×C17—41no—
284C4×C17#56811yescharacteristic
285C4×C17#56811yescharacteristic
286C4×C17#57711yescharacteristic
287C4×C17#57811yescharacteristic
288Dic17—41no—
289Dic17—41no—
290Dic17—41no—
291#533C2×D1711yescharacteristic
292#529—171no—
293#501—171no—
294#497—171no—
295#491—171no—
296#489—171no—
297#470—171no—
298#470—171no—
299#468—171no—
300#468—171no—
301#446—21no—
302#446—21no—
303#446—171no—
304#446C2×D1711yescharacteristic
305#446C2×D1711yescharacteristic
306C8×Q8—171no—
307C8×Q8C2×D1711yescharacteristic
308C8×Q8C2×D1711yescharacteristic
309C4×Q16—171no—
310C4×Q16—171no—
311C4×SD16—171no—
312C4×SD16—171no—
313#436—171no—
314#436—341no—
315#435—341no—
316C8×D4—171no—
317#433—21no—
318#433—21no—
319#433—341no—
320#432C2×D1711yescharacteristic
321#431C2×D1711yescharacteristic
322#424—341no—
323#423—171no—
324C4×M16—171no—
325C2×C4×C8—171no—
326#335—171no—
327#335—171no—
328#334—171no—
329#334—171no—
330Q8⋊C8—171no—
331Q8⋊C8—171no—
332Q8⋊C8—171no—
333Q8⋊C8—171no—
334Q8⋊C8—171no—
335Q8⋊C8—171no—
336D4⋊C8—171no—
337D4⋊C8—171no—
338#322—171no—
339#322—171no—
340#322—171no—
341#322—171no—
342C2×C17—41no—
343C2×C17#293211yescharacteristic
344C2×C17#294711yescharacteristic
345C2×C17#295611yescharacteristic
346D17—81no—
347C2×Q16—171no—
348C2×Q16—171no—
349C2×SD16—171no—
350C2×SD16—171no—
351C2×M16—171no—
352C2×M16—171no—
353C2×M16—341no—
354C2×M16—341no—
355C22×C8—341no—
356C22×C8—341no—
357C4⋊Q8C4×D1711yescharacteristic
358C4⋊Q8C4×D1711yescharacteristic
359#126—341no—
360#125—21no—
361#125—171no—
362#124—171no—
363#123—341no—
364C22⋊Q8—21no—
365C22⋊Q8—171no—
366C22⋊Q8C4×D1711yescharacteristic
367C22⋊Q8C4×D1711yescharacteristic
368#121—171no—
369C4×Q8—21no—
370C4×Q8—171no—
371C4×Q8C22×D1711yescharacteristic
372C4×Q8C22×D1711yescharacteristic
373C4×D4—171no—
374C4×D4—341no—
375#117—21no—
376#117—341no—
377C2×C42C22×D1711yescharacteristic
378#107—171no—
379#107—171no—
380#106—171no—
381#106—171no—
382C4⋊C8—21no—
383C4⋊C8—21no—
384C4⋊C8—21no—
385C4⋊C8—21no—
386C4⋊C8—171no—
387C4⋊C8—171no—
388C4⋊C8—341no—
389C4⋊C8—341no—
390C4⋊C8—341no—
391C4⋊C8C22⋊D1711yescharacteristic
392C4⋊C8C22⋊D1711yescharacteristic
393C4⋊C8C22×D1711yescharacteristic
394C4⋊C8C22×D1711yescharacteristic
395#103—171no—
396#103—171no—
397#103—171no—
398#103—171no—
399#103—171no—
400#103—171no—
401#102—171no—
402#102—171no—
403C22⋊C8—21no—
404C22⋊C8—341no—
405C22⋊C8—341no—
406C22⋊C8C22⋊D1711yescharacteristic
407C22⋊C8C22⋊D1711yescharacteristic
408#97—21no—
409#97—21no—
410#97—21no—
411#97—171no—
412#97—171no—
413#97—341no—
414C4×C8—21no—
415C4×C8—21no—
416C4×C8—171no—
417C4×C8—171no—
418C4×C8—171no—
419C4×C8—171no—
420C4×C8—341no—
421C4×C8—341no—
422C4×C8C22×D1711yescharacteristic
423C4×C8C22×D1711yescharacteristic
424C17#1798811yescharacteristic, complemented, Sylow
425C2×Q8—21no—
426C2×Q8—171no—
427C2×Q8C2×C4×D1711yescharacteristic
428C2×Q8C2×C4×D1711yescharacteristic
429C2×D4—171no—
430C2×D4—341no—
431C22×C4—341no—
432C22×C4C2×C4×D1711yescharacteristic
433C22×C4#6325211yescharacteristic
434C22×C4C2×C22⋊D1711yescharacteristic
435Q16—681no—
436Q16—681no—
437SD16—681no—
438SD16—681no—
439M16—681no—
440M16—681no—
441M16—1361no—
442M16—1361no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—171no—
446C2×C8—171no—
447C2×C8—171no—
448C2×C8—171no—
449C2×C8—341no—
450C2×C8—341no—
451C2×C8—341no—
452C2×C8—341no—
453C2×C8—682no—
454C2×C8—1361no—
455C2×C8C2×C22⋊D1711yescharacteristic
456C2×C8C2×C22⋊D1711yescharacteristic
457C2×C8C2×C22⋊D1711yescharacteristic
458C2×C8C2×C22⋊D1711yescharacteristic
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—171no—
467C4⋊C4—171no—
468C4⋊C4—341no—
469C4⋊C4—341no—
470C4⋊C4—341no—
471C4⋊C4—341no—
472C4⋊C4C2×C4×D1711yescharacteristic
473C4⋊C4C2×C4×D1711yescharacteristic
474C22⋊C4—21no—
475C22⋊C4—21no—
476C22⋊C4—341no—
477C22⋊C4—341no—
478C22⋊C4—341no—
479C22⋊C4—341no—
480C22⋊C4—341no—
481C42—21no—
482C42—21no—
483C42—341no—
484C42C2×C4×D1711yescharacteristic
485C42#6325211yescharacteristic
486C42C2×C22⋊D1711yescharacteristic
487C42C23×D1711yescharacteristic
488C23—341no—
489C23C4×C22⋊D1711yescharacteristic
490Q8—21no—
491Q8—21no—
492Q8—21no—
493Q8—21no—
494Q8—81no—
495Q8—341no—
496Q8—341no—
497D4—341no—
498D4—341no—
499D4—1361no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—41no—
509C2×C4—341no—
510C2×C4—341no—
511C2×C4—341no—
512C2×C4—681no—
513C2×C4—681no—
514C2×C4C4×C22⋊D1711yescharacteristic
515C2×C4C4×C22⋊D1711yescharacteristic
516C2×C4C4×C22⋊D1711yescharacteristic
517C2×C4C22×C4×D1711yescharacteristic
518C2×C4C2×#6325211yescharacteristic
519C2×C4C22×C22⋊D1711yescharacteristic
520C8—21no—
521C8—21no—
522C8—21no—
523C8—21no—
524C8—41no—
525C8—41no—
526C8—342no—
527C8—341no—
528C8—341no—
529C8—341no—
530C8—341no—
531C8—681no—
532C8—681no—
533C8—681no—
534C22—21no—
535C22—21no—
536C22—21no—
537C22—681no—
538C22—681no—
539C22—681no—
540C22C2×C4×C22⋊D1711yescharacteristic
541C4—21no—
542C4—21no—
543C4—21no—
544C4—21no—
545C4—41no—
546C4—41no—
547C4—41no—
548C4—41no—
549C4—681no—
550C4—681no—
551C4—681no—
552C4#1176357411yescharacteristic
553C4#1176357411yescharacteristic
554C4#1176361711yescharacteristic
555C4#1176362411yescharacteristic
556C2—41no—
557C2—1361no—
558C2#1453750011yescharacteristic
559C2#1453762711yescharacteristic
560C2#1453769111yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D17
commutatorC2×C4×C17C23×C4
FrattiniC42C23×D17
FittingC17×#2985C2
socleC22×C17C2×C4×D4
prime radical#10587616C2×C4
cosocleC42×C17C24
hypercenter#2985D17
hypocenterC17#17988
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2985

Complements

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

NH ≅ G/Ntype
3. #14527662C2semidirect
4. #14527655C2semidirect
5. #14527653C2semidirect
6. #14527639C2semidirect
7. #14527634C2semidirect
8. #14527632C2semidirect
9. #14527627C2semidirect
10. #14527618C2semidirect
11. #14527552C2semidirect
13. #14527239C2semidirect
14. #14527074C2semidirect
15. C17×#2985C2semidirect
256. #2985D17semidirect
424. C17#17988semidirect

Maximal subgroups

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

subgroupindex
#145393842
#145379352
#145276622
#145276552
#145276532
#145276392
#145276342
#145276322
#145276272
#145276182
#145275522
#145272422
#145272392
#145270742
C17×#29852
#1798817