Finite Group Databasebeta

← #17004425

Subgroups — #17004425

Order 4352.

598 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14538849C211yesmaximal, characteristic
2#14537892C211yesmaximal, characteristic
3#14527653C211yesmaximal, characteristic, complemented
4#14527639C211yesmaximal, characteristic, complemented
5#14527632C211yesmaximal, characteristic, complemented
6#14527618C211yesmaximal, characteristic, complemented
7#14527601C211yesmaximal, characteristic, complemented
8#14527594C211yesmaximal, characteristic, complemented
9C8×#63231C211yesmaximal, characteristic, complemented
10C8×#63230C211yesmaximal, characteristic, complemented
11#14527570C211yesmaximal, characteristic, complemented
12#14527216C211yesmaximal, characteristic
13#14527187C211yesmaximal, characteristic, complemented
14#14527084C211yesmaximal, characteristic, complemented
15C17×#2985C211yesmaximal, characteristic, complemented
16C4×#63252C2211yescharacteristic
17#11763147C411yescharacteristic
18#11763147C411yescharacteristic
19#11763091C411yescharacteristic
20#11763086C411yescharacteristic
21#11763016C411yescharacteristic
22#11763011C411yescharacteristic
23#11762969C411yescharacteristic
24#11762969C411yescharacteristic
25C8×Dic34C2211yescharacteristic
26C8×Dic34C2211yescharacteristic
27C4×#63231C2211yescharacteristic
28C4×#63231C2211yescharacteristic
29C4×#63230C2211yescharacteristic
30C4×#63230C2211yescharacteristic
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
44Q8⋊#3622C2211yescharacteristic
45Q8⋊#3622C2211yescharacteristic
46Q8⋊#3622C2211yescharacteristic
47Q8⋊#3622C2211yescharacteristic
48#11762539C2211yescharacteristic
49#11762539C2211yescharacteristic
50#11762536C2211yescharacteristic
51#11762536C2211yescharacteristic
52#11762531C2211yescharacteristic
53#11762531C2211yescharacteristic
54#11762530C2211yescharacteristic
55C8×#3622C2211yescharacteristic
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
67C2×#63252C2×C411yescharacteristic
68C17×C4⋊Q8C2×C411yescharacteristic
69C17×C4⋊Q8C2×C411yescharacteristic
70C17×#125—21no—
71C17×C22⋊Q8—21no—
72C17×C22⋊Q8C2×C411yescharacteristic
73C17×C22⋊Q8C2×C411yescharacteristic
74C4×Q8×C17—21no—
75C4×Q8×C17C2311yescharacteristic
76C4×Q8×C17C2311yescharacteristic
77C17×#117—21no—
78C2×C42×C17C2311yescharacteristic
79C2×#63231C2×C411yescharacteristic
80C2×#63231C2×C411yescharacteristic
81C2×#63230C2×C411yescharacteristic
82C2×#63230C2×C411yescharacteristic
83C4×C22⋊D17—21no—
84C4×C22⋊D17—21no—
85#10587612C2×C411yescharacteristic
86C22×#3622—21no—
87C2×C8×D17—21no—
88C2×C8×D17—21no—
89C4×D68C2×C411yescharacteristic
90C4×D68C2311yescharacteristic
91#10587558—21no—
92C42×D17—21no—
93C4×Dic34C2×C411yescharacteristic
94C4×Dic34C2311yescharacteristic
95C17×C4⋊C8—21no—
96C17×C4⋊C8—21no—
97C17×C4⋊C8—21no—
98C17×C4⋊C8—21no—
99C17×C4⋊C8D411yescharacteristic
100C17×C4⋊C8D411yescharacteristic
101C17×C4⋊C8C2311yescharacteristic
102C17×C4⋊C8C2311yescharacteristic
103C17×C22⋊C8—21no—
104C17×C22⋊C8D411yescharacteristic
105C17×C22⋊C8D411yescharacteristic
106C17×#97—21no—
107C17×#97—21no—
108C17×#97—21no—
109C4×C8×C17—21no—
110C4×C8×C17—21no—
111C4×C8×C17C2311yescharacteristic
112C4×C8×C17C2311yescharacteristic
113#10587506C2×C411yescharacteristic
114#10587506C2×C411yescharacteristic
115#10587506C2×C411yescharacteristic
116#10587506C2×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
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—
151#63252—22no—
152#63252—22no—
153C2×D68C22×C411yescharacteristic
154C2×C4×D17—21no—
155C2×C4×D17—21no—
156C2×C4×D17—21no—
157C2×Dic34C22×C411yescharacteristic
158C2×C8×C17—21no—
159C2×C8×C17—21no—
160C2×C8×C17C2×D411yescharacteristic
161C2×C8×C17C2×D411yescharacteristic
162C2×C8×C17C2×D411yescharacteristic
163C2×C8×C17C2×D411yescharacteristic
164C4⋊C4×C17—21no—
165C4⋊C4×C17—21no—
166C4⋊C4×C17—21no—
167C4⋊C4×C17—21no—
168C4⋊C4×C17—21no—
169C4⋊C4×C17—21no—
170C4⋊C4×C17—21no—
171C4⋊C4×C17C22×C411yescharacteristic
172C4⋊C4×C17C22×C411yescharacteristic
173C22⋊C4×C17—21no—
174C22⋊C4×C17—21no—
175C42×C17—21no—
176C42×C17—21no—
177C42×C17C22×C411yescharacteristic
178C42×C17C2×D411yescharacteristic
179C42×C17#4111yescharacteristic
180C42×C17C2411yescharacteristic
181C22⋊Dic17—21no—
182#63231—22no—
183#63231—22no—
184#63230—22no—
185#63230—22no—
186#63227—21no—
187#63227—21no—
188C4⋊Dic17C22×C411yescharacteristic
189C4⋊Dic17C22×C411yescharacteristic
190#63225—21no—
191#63225—21no—
192C4×Dic17—21no—
193C4×Dic17—21no—
194C4×Dic17—21no—
195C2×#3622—21no—
196C2×#3622—21no—
197C2×#3622—21no—
198C2×#3622—21no—
199C2×#3622—81no—
200C2×#3622C22×C411yescharacteristic
201C2×#3622C22×C411yescharacteristic
202C2×#3622C22×C411yescharacteristic
203C2×#3622C22×C411yescharacteristic
204C8×D17—81no—
205C8×D17—81no—
206#17921—171nomaximal, Sylow
207C23×C17C4×D411yescharacteristic
208C22×D17—21no—
209Q8×C17—21no—
210Q8×C17—21no—
211Q8×C17—21no—
212Q8×C17—21no—
213Q8×C17—81no—
214C2×C4×C17—21no—
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—41no—
223C2×C4×C17C4×D411yescharacteristic
224C2×C4×C17C4×D411yescharacteristic
225C2×C4×C17C4×D411yescharacteristic
226C2×C4×C17C23×C411yescharacteristic
227C2×C4×C17C22×D411yescharacteristic
228C2×C4×C17C2×#4111yescharacteristic
229C22⋊D17—24no—
230C2×Dic17—21no—
231C2×Dic17—21no—
232C2×Dic17—21no—
233D68—21no—
234D68#13112yes—
235C4×D17—24no—
236C4×D17—41no—
237C4×D17—41no—
238C4×D17—81no—
239Dic34—21no—
240Dic34#13112yes—
241C8×C17—21no—
242C8×C17—21no—
243C8×C17—21no—
244C8×C17—21no—
245C8×C17—41no—
246C8×C17—41no—
247#3622—21no—
248#3622—21no—
249#3622—21no—
250#3622—21no—
251#3622—41no—
252#3622—41no—
253#3622—41no—
254#3622—41no—
255#3107—171no—
256#2988—171no—
257#2985D1711yescharacteristic, complemented
258#1587—171no—
259#1585—171no—
260#1584—171no—
261#1582—171no—
262#1579—171no—
263SD16⋊C8—171no—
264C8×Q16—171no—
265C8×SD16—171no—
266#1573—171no—
267#1488—171no—
268#1481—171no—
269#1454—171no—
270C22×C17—21no—
271C22×C17—21no—
272C22×C17—21no—
273C22×C17C2×C4×D411yescharacteristic
274C2×D17—22no—
275C2×D17—41no—
276C2×D17—41no—
277C4×C17—21no—
278C4×C17—21no—
279C4×C17—21no—
280C4×C17—21no—
281C4×C17—41no—
282C4×C17—41no—
283C4×C17—41no—
284C4×C17—41no—
285C4×C17C2×#13111yescharacteristic
286C4×C17C2×#13111yescharacteristic
287C4×C17#57711yescharacteristic
288C4×C17#57811yescharacteristic
289Dic17—22no—
290Dic17—41no—
291Dic17—41no—
292#533C2×D1711yescharacteristic
293C4×#41—171no—
294#485—171no—
295#485—171no—
296#475—171no—
297#474—171no—
298#462—171no—
299#461—171no—
300#452—171no—
301#452—171no—
302#446—21no—
303#446—21no—
304#446C2×D1711yescharacteristic
305#446C2×D1711yescharacteristic
306C8×Q8—171no—
307C8×Q8—171no—
308C8×Q8C2×D1711yescharacteristic
309C8×Q8C2×D1711yescharacteristic
310C4×Q16—171no—
311C4×Q16—171no—
312C4×SD16—171no—
313C4×SD16—171no—
314C8×D4—171no—
315C8×D4—171no—
316C8×D4—341no—
317C8×D4—341no—
318#433—21no—
319#433—21no—
320#432C2×D1711yescharacteristic
321#431—171no—
322#431—171no—
323#431—341no—
324#431C2×D1711yescharacteristic
325C2×C4⋊C8—171no—
326C2×C4⋊C8—341no—
327#335—171no—
328#335—171no—
329#334—171no—
330#334—171no—
331Q8⋊C8—171no—
332Q8⋊C8—171no—
333Q8⋊C8—171no—
334Q8⋊C8—171no—
335Q8⋊C8—171no—
336Q8⋊C8—171no—
337D4⋊C8—171no—
338D4⋊C8—171no—
339#322—171no—
340#322—171no—
341#322—171no—
342C82—171no—
343C2×C17—41no—
344C2×C17#292911yescharacteristic
345C2×C17#294711yescharacteristic
346C2×C17#295711yescharacteristic
347D17—42no—
348C2×#41—171no—
349C2×Q16—171no—
350C2×Q16—171no—
351C2×SD16—171no—
352C2×SD16—171no—
353C22×C8—341no—
354C22×C8—341no—
355C22×C8—341no—
356C4⋊Q8C4×D1711yescharacteristic
357C4⋊Q8C4×D1711yescharacteristic
358#125—21no—
359C22⋊Q8—21no—
360C22⋊Q8C4×D1711yescharacteristic
361C22⋊Q8C4×D1711yescharacteristic
362C4×Q8—21no—
363C4×Q8—171no—
364C4×Q8—171no—
365C4×Q8C22×D1711yescharacteristic
366C4×Q8C22×D1711yescharacteristic
367C4×D4—171no—
368C4×D4—171no—
369C4×D4—341no—
370C4×D4—341no—
371#117—21no—
372#117—171no—
373#117—341no—
374C2×C42—341no—
375C2×C42C22×D1711yescharacteristic
376#107—171no—
377#107—171no—
378#106—171no—
379#106—171no—
380C4⋊C8—21no—
381C4⋊C8—21no—
382C4⋊C8—21no—
383C4⋊C8—21no—
384C4⋊C8—171no—
385C4⋊C8—171no—
386C4⋊C8—171no—
387C4⋊C8—171no—
388C4⋊C8—341no—
389C4⋊C8—341no—
390C4⋊C8—341no—
391C4⋊C8—341no—
392C4⋊C8C22⋊D1711yescharacteristic
393C4⋊C8C22⋊D1711yescharacteristic
394C4⋊C8C22×D1711yescharacteristic
395C4⋊C8C22×D1711yescharacteristic
396#103—171no—
397#103—171no—
398#103—171no—
399#103—171no—
400#103—171no—
401#103—171no—
402#102—171no—
403#102—171no—
404C22⋊C8—21no—
405C22⋊C8—171no—
406C22⋊C8—171no—
407C22⋊C8—341no—
408C22⋊C8—341no—
409C22⋊C8—341no—
410C22⋊C8C22⋊D1711yescharacteristic
411C22⋊C8C22⋊D1711yescharacteristic
412#97—21no—
413#97—21no—
414#97—21no—
415C4×C8—21no—
416C4×C8—21no—
417C4×C8—171no—
418C4×C8—171no—
419C4×C8—171no—
420C4×C8—171no—
421C4×C8—341no—
422C4×C8—341no—
423C4×C8C22×D1711yescharacteristic
424C4×C8C22×D1711yescharacteristic
425C17#1792111yescharacteristic, complemented, Sylow
426#41—342no—
427#41—342no—
428C2×Q8—21no—
429C2×Q8—171no—
430C2×Q8C2×C4×D1711yescharacteristic
431C2×Q8C2×C4×D1711yescharacteristic
432C2×D4—171no—
433C2×D4—341no—
434C22×C4—341no—
435C22×C4—341no—
436C22×C4—341no—
437C22×C4C2×C4×D1711yescharacteristic
438C22×C4#6325211yescharacteristic
439C22×C4C2×C22⋊D1711yescharacteristic
440Q16—342no—
441Q16—342no—
442SD16—342no—
443SD16—342no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—171no—
447C2×C8—171no—
448C2×C8—171no—
449C2×C8—171no—
450C2×C8—341no—
451C2×C8—341no—
452C2×C8—341no—
453C2×C8—341no—
454C2×C8—1361no—
455C2×C8—1361no—
456C2×C8—1361no—
457C2×C8C2×C22⋊D1711yescharacteristic
458C2×C8C2×C22⋊D1711yescharacteristic
459C2×C8C2×C22⋊D1711yescharacteristic
460C2×C8C2×C22⋊D1711yescharacteristic
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—171no—
469C4⋊C4—171no—
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—
479C42—21no—
480C42—21no—
481C42—341no—
482C42—341no—
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—172no—
496Q8—341no—
497D4—172no—
498D4—344no—
499D4—341no—
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—344no—
510C2×C4—341no—
511C2×C4—341no—
512C2×C4—341no—
513C2×C4—681no—
514C2×C4—681no—
515C2×C4—1361no—
516C2×C4C4×C22⋊D1711yescharacteristic
517C2×C4C4×C22⋊D1711yescharacteristic
518C2×C4C4×C22⋊D1711yescharacteristic
519C2×C4C22×C4×D1711yescharacteristic
520C2×C4C2×#6325211yescharacteristic
521C2×C4C22×C22⋊D1711yescharacteristic
522C8—21no—
523C8—21no—
524C8—21no—
525C8—21no—
526C8—41no—
527C8—41no—
528C8—341no—
529C8—341no—
530C8—341no—
531C8—341no—
532C8—681no—
533C8—681no—
534C8—681no—
535C8—681no—
536C22—21no—
537C22—21no—
538C22—21no—
539C22—342no—
540C22—681no—
541C22—681no—
542C22C2×C4×C22⋊D1711yescharacteristic
543C4—21no—
544C4—21no—
545C4—21no—
546C4—21no—
547C4—41no—
548C4—41no—
549C4—41no—
550C4—41no—
551C4—342no—
552C4—681no—
553C4—681no—
554C4#131×D1711yescharacteristic
555C4#131×D1711yescharacteristic
556C4#1176361711yescharacteristic
557C4#1176362411yescharacteristic
558C2—41no—
559C2—682no—
560C2#1453747611yescharacteristic
561C2#1453762711yescharacteristic
562C2#1453769911yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D17
commutatorC2×C4×C17C23×C4
FrattiniC42C23×D17
FittingC17×#2985C2
socleC22×C17C2×C4×D4
prime radicalC2×#63252C2×C4
cosocleC42×C17C24
hypercenter#2985D17
hypocenterC17#17921
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. #14527653C2semidirect
4. #14527639C2semidirect
5. #14527632C2semidirect
6. #14527618C2semidirect
7. #14527601C2semidirect
8. #14527594C2semidirect
9. C8×#63231C2semidirect
10. C8×#63230C2semidirect
11. #14527570C2semidirect
13. #14527187C2semidirect
14. #14527084C2semidirect
15. C17×#2985C2semidirect
257. #2985D17semidirect
425. C17#17921semidirect

Maximal subgroups

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

subgroupindex
#145388492
#145378922
#145276532
#145276392
#145276322
#145276182
#145276012
#145275942
C8×#632312
C8×#632302
#145275702
#145272162
#145271872
#145270842
C17×#29852
#1792117