Finite Group Databasebeta

← #17005523

Subgroups — #17005523

Order 4352.

600 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14538860C211yesmaximal, characteristic
2#14537944C211yesmaximal, characteristic
3#14537874C211yesmaximal, characteristic, complemented
4#14527678C211yesmaximal, characteristic, complemented
5#14527677C211yesmaximal, characteristic, complemented
6#14527665C211yesmaximal, characteristic, complemented
7#14527658C211yesmaximal, characteristic, complemented
8#14527652C211yesmaximal, characteristic, complemented
9#14527638C211yesmaximal, characteristic, complemented
10#14527588C211yesmaximal, characteristic, complemented
11#14527587C211yesmaximal, characteristic, complemented
12#14527570C211yesmaximal, characteristic, complemented
13C2×#11762541C211yesmaximal, characteristic, complemented
14#14527067C211yesmaximal, characteristic, complemented
15C17×#1494C211yesmaximal, characteristic
16C2×C4×Dic34C2211yescharacteristic
17#11763137C411yescharacteristic
18#11763120C411yescharacteristic
19#11763113C411yescharacteristic
20#11763113C411yescharacteristic
21#11763028C411yescharacteristic
22#11763028C411yescharacteristic
23#11762964C411yescharacteristic
24#11762947C411yescharacteristic
25#11762940C2211yescharacteristic
26#11762937—21no—
27#11762937—21no—
28#11762936C2211yescharacteristic
29#11762936C2211yescharacteristic
30Q8×#3622C2211yescharacteristic
31#11762933C2211yescharacteristic
32#11762933C2211yescharacteristic
33C4×#63231C2211yescharacteristic
34C4×#63231C2211yescharacteristic
35C4×#63229C2211yescharacteristic
36C4×#63229C2211yescharacteristic
37#11762887C2211yescharacteristic
38#11762881—21no—
39D4×#3622—21no—
40D4×#3622C2211yescharacteristic
41#11762870—21no—
42#11762863—21no—
43#11762862C2211yescharacteristic
44#11762862C2211yescharacteristic
45#11762859—21no—
46#11762836—21no—
47C2×C4⋊#3622C2211yescharacteristic
48#11762561C2211yescharacteristic
49#11762561C2211yescharacteristic
50#11762559C2211yescharacteristic
51#11762559C2211yescharacteristic
52#11762541C2211yescharacteristic
53#11762541C2211yescharacteristic
54#11762541C2211yescharacteristic
55#11762541C2211yescharacteristic
56#11762530C2211yescharacteristic
57#11762530C2211yescharacteristic
58C8×#3622C2211yescharacteristic
59C8×#3622C2211yescharacteristic
60C17×#529C2211yescharacteristic
61C17×#432C2211yescharacteristic
62C2×C4×C8×C17C2211yescharacteristic
63C17×Q8⋊C8C2211yescharacteristic
64C17×Q8⋊C8C2211yescharacteristic
65C17×D4⋊C8C2211yescharacteristic
66C17×D4⋊C8C2211yescharacteristic
67C22×Dic34C2×C411yescharacteristic
68C22×C8×C17—21no—
69C17×#126—21no—
70C17×#125C2×C411yescharacteristic
71C17×#124C2×C411yescharacteristic
72C17×#123—21no—
73C17×C22⋊Q8C2×C411yescharacteristic
74C17×#121C2×C411yescharacteristic
75C4×Q8×C17C2311yescharacteristic
76C4×D4×C17—21no—
77C4×D4×C17C2311yescharacteristic
78C17×#117—21no—
79C2×C42×C17C2311yescharacteristic
80C2×#63231C2×C411yescharacteristic
81C2×#63231C2×C411yescharacteristic
82C2×#63229C2×C411yescharacteristic
83C2×#63229C2×C411yescharacteristic
84C2×C4⋊Dic17C2×C411yescharacteristic
85C2×#63225—21no—
86C2×C4×Dic17—21no—
87C2×#63223—21no—
88C22×#3622—21no—
89C22×#3622—21no—
90C4×Dic34—21no—
91C4×Dic34—21no—
92C4×Dic34C2×C411yescharacteristic
93C4×Dic34C2×C411yescharacteristic
94C4×Dic34C2311yescharacteristic
95C4×Dic34C2311yescharacteristic
96C17×C4⋊C8C2311yescharacteristic
97C17×C4⋊C8C2311yescharacteristic
98C17×C22⋊C8—21no—
99C17×#97—21no—
100C4×C8×C17—21no—
101C4×C8×C17C2311yescharacteristic
102C4×C8×C17C2311yescharacteristic
103#10587506C2×C411yescharacteristic
104#10587506C2×C411yescharacteristic
105#10587503C2×C411yescharacteristic
106#10587503C2×C411yescharacteristic
107C22⋊#3622—21no—
108C22⋊#3622—21no—
109C22⋊#3622C2×C411yescharacteristic
110C22⋊#3622C2×C411yescharacteristic
111C22⋊#3622D411yescharacteristic
112C22⋊#3622D411yescharacteristic
113#10587486—21no—
114#10587486—21no—
115#10587485—21no—
116#10587485—21no—
117#10587485—21no—
118#10587485—21no—
119C8×Dic17—21no—
120C8×Dic17—21no—
121#10587481C2×C411yescharacteristic
122#10587481C2×C411yescharacteristic
123#10587481C2×C411yescharacteristic
124#10587481C2×C411yescharacteristic
125#10587479C2×C411yescharacteristic
126#10587479C2×C411yescharacteristic
127#10587478C2×C411yescharacteristic
128#10587478C2×C411yescharacteristic
129C4⋊#3622—21no—
130C4⋊#3622—21no—
131C4⋊#3622—21no—
132C4⋊#3622C2×C411yescharacteristic
133C4⋊#3622C2×C411yescharacteristic
134C4⋊#3622D411yescharacteristic
135C4⋊#3622D411yescharacteristic
136C4⋊#3622C2311yescharacteristic
137C4⋊#3622C2311yescharacteristic
138#10587474—21no—
139C4×#3622—21no—
140C4×#3622C2311yescharacteristic
141C4×#3622C2311yescharacteristic
142C4×#3622C2311yescharacteristic
143C4×#3622C2311yescharacteristic
144C2×Q8×C17C22×C411yescharacteristic
145C2×D4×C17—21no—
146C2×D4×C17C22×C411yescharacteristic
147C22×C4×C17—21no—
148C22×C4×C17C22×C411yescharacteristic
149C22×C4×C17C2×D411yescharacteristic
150C22×C4×C17#4111yescharacteristic
151C22×Dic17—21no—
152C22×Dic17—21no—
153C2×Dic34—22no—
154C2×Dic34—21no—
155C2×Dic34—41no—
156C2×Dic34C22×C411yescharacteristic
157C2×Dic34C22×C411yescharacteristic
158C2×C8×C17—24no—
159C2×C8×C17—21no—
160C2×C8×C17—21no—
161C2×C8×C17—21no—
162C2×C8×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—
171C22⋊C4×C17—21no—
172C22⋊C4×C17—21no—
173C22⋊C4×C17—21no—
174C42×C17—21no—
175C42×C17C22×C411yescharacteristic
176C42×C17C2×D411yescharacteristic
177C42×C17#4111yescharacteristic
178C42×C17C2411yescharacteristic
179#63231—22no—
180#63231—41no—
181#63229—22no—
182#63229—41no—
183C4⋊Dic17—21no—
184C4⋊Dic17C22×C411yescharacteristic
185C4⋊Dic17C22×C411yescharacteristic
186#63225—21no—
187#63225—21no—
188#63225—21no—
189#63225—21no—
190C4×Dic17—21no—
191C4×Dic17—21no—
192C4×Dic17—21no—
193C4×Dic17—21no—
194#63223—81no—
195C2×#3622—21no—
196C2×#3622—21no—
197C2×#3622—81no—
198C2×#3622—81no—
199C2×#3622C22×C411yescharacteristic
200C2×#3622C22×C411yescharacteristic
201C2×#3622C22×C411yescharacteristic
202C2×#3622C22×C411yescharacteristic
203C2×#3622C2×D411yescharacteristic
204C2×#3622C2×D411yescharacteristic
205C2×#3622C2×D411yescharacteristic
206C2×#3622C2×D411yescharacteristic
207#18017—171nomaximal, Sylow
208C23×C17—21no—
209C23×C17C4×D411yescharacteristic
210Q8×C17—21no—
211Q8×C17—21no—
212D4×C17—21no—
213D4×C17—21no—
214D4×C17—42no—
215C2×C4×C17—22no—
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×C17—41no—
225C2×C4×C17C4×D411yescharacteristic
226C2×C4×C17C4×D411yescharacteristic
227C2×C4×C17C4×D411yescharacteristic
228C2×C4×C17C23×C411yescharacteristic
229C2×C4×C17C22×D411yescharacteristic
230C2×C4×C17C2×#4111yescharacteristic
231C2×Dic17—21no—
232C2×Dic17—21no—
233C2×Dic17—21no—
234C2×Dic17—21no—
235C2×Dic17—42no—
236C2×Dic17—42no—
237Dic34—21no—
238Dic34—21no—
239Dic34—21no—
240Dic34—42no—
241Dic34#13112yes—
242C8×C17—22no—
243C8×C17—22no—
244C8×C17—41no—
245C8×C17—41no—
246#3622—21no—
247#3622—21no—
248#3622—21no—
249#3622—21no—
250#3622—21no—
251#3622—21no—
252#3622—21no—
253#3622—21no—
254#3622—41no—
255#3622—41no—
256#3108—171no—
257#2994—171no—
258#2984—171no—
259#1591—171no—
260#1590—171no—
261#1588—171no—
262#1587—171no—
263#1587—171no—
264#1585—171no—
265C8×Q16—171no—
266C8×SD16—171no—
267#1573—171no—
268#1494D1711yescharacteristic
269C2×Q8⋊C8—171no—
270#1450—171no—
271C22×C17—21no—
272C22×C17—21no—
273C22×C17—41no—
274C22×C17—41no—
275C22×C17—41no—
276C22×C17#44312yes—
277C22×C17C2×C4×D411yescharacteristic
278C4×C17—21no—
279C4×C17—21no—
280C4×C17—21no—
281C4×C17—21no—
282C4×C17—41no—
283C4×C17—41no—
284C4×C17—41no—
285C4×C17C2×#13111yescharacteristic
286C4×C17#56811yescharacteristic
287C4×C17#57711yescharacteristic
288C4×C17#57811yescharacteristic
289Dic17—22no—
290Dic17—41no—
291Dic17—41no—
292Dic17—41no—
293#529C2×D1711yescharacteristic
294C2×C4×Q8—171no—
295#483—171no—
296#480—171no—
297#479—171no—
298#479—171no—
299#464—171no—
300#464—171no—
301#451—171no—
302#448—171no—
303#446—171no—
304#446—171no—
305#446—171no—
306#446—341no—
307#446—341no—
308C8×Q8—171no—
309C8×Q8—171no—
310C8×Q8—171no—
311C4×Q16—171no—
312C4×Q16—171no—
313C4×SD16—171no—
314C4×SD16—171no—
315#436—171no—
316#435—341no—
317C8×D4—171no—
318C8×D4—341no—
319#433—341no—
320#432—341no—
321#432C2×D1711yescharacteristic
322#431—171no—
323#431—171no—
324#431—341no—
325#424—341no—
326C2×C4⋊C8—171no—
327C2×C4×C8C2×D1711yescharacteristic
328#335—171no—
329#335—171no—
330#334—171no—
331#334—171no—
332Q8⋊C8—171no—
333Q8⋊C8—171no—
334Q8⋊C8—171no—
335Q8⋊C8—171no—
336Q8⋊C8C2×D1711yescharacteristic
337Q8⋊C8C2×D1711yescharacteristic
338D4⋊C8C2×D1711yescharacteristic
339D4⋊C8C2×D1711yescharacteristic
340#322—171no—
341#322—171no—
342C82—171no—
343C82—171no—
344C2×C17—22no—
345C2×C17—81no—
346C2×C17#293311yescharacteristic
347C2×C17#294711yescharacteristic
348C2×C17C2×#44311yescharacteristic
349C22×Q8—171no—
350C2×Q16—171no—
351C2×Q16—171no—
352C2×SD16—171no—
353C2×SD16—171no—
354C2×M16—341no—
355C22×C8—21no—
356C22×C8—341no—
357C22×C8—341no—
358#126—21no—
359#125C4×D1711yescharacteristic
360#124C4×D1711yescharacteristic
361#123—21no—
362C22⋊Q8C4×D1711yescharacteristic
363#121C4×D1711yescharacteristic
364C4×Q8—171no—
365C4×Q8—171no—
366C4×Q8—171no—
367C4×Q8—171no—
368C4×Q8—341no—
369C4×Q8—341no—
370C4×Q8C22×D1711yescharacteristic
371C4×D4—21no—
372C4×D4C22×D1711yescharacteristic
373#117—21no—
374C2×C4⋊C4—171no—
375C2×C4⋊C4—341no—
376C2×C42—341no—
377C2×C42C22×D1711yescharacteristic
378#107—171no—
379#107—171no—
380#106—171no—
381#106—171no—
382C4⋊C8—171no—
383C4⋊C8—171no—
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⋊C8—341no—
393C4⋊C8—341no—
394C4⋊C8—341no—
395C4⋊C8C22×D1711yescharacteristic
396C4⋊C8C22×D1711yescharacteristic
397#103—171no—
398#103—171no—
399#103—171no—
400#103—171no—
401#103—171no—
402#103—171no—
403#102—171no—
404#102—171no—
405C22⋊C8—21no—
406C22⋊C8—171no—
407C22⋊C8—171no—
408C22⋊C8—171no—
409C22⋊C8—171no—
410C22⋊C8—341no—
411C22⋊C8—341no—
412#97—21no—
413#97—341no—
414#97—341no—
415#97—341no—
416C4×C8—21no—
417C4×C8—171no—
418C4×C8—171no—
419C4×C8—171no—
420C4×C8—171no—
421C4×C8—341no—
422C4×C8—341no—
423C4×C8—341no—
424C4×C8C22×D1711yescharacteristic
425C4×C8C22×D1711yescharacteristic
426C17#1801711yescharacteristic, complemented, Sylow
427C2×Q8—171no—
428C2×Q8—171no—
429C2×Q8—342no—
430C2×Q8—341no—
431C2×Q8—681no—
432C2×Q8C2×C4×D1711yescharacteristic
433C2×D4—21no—
434C2×D4C2×C4×D1711yescharacteristic
435C22×C4—21no—
436C22×C4—341no—
437C22×C4—341no—
438C22×C4C2×C4×D1711yescharacteristic
439C22×C4D4×D1711yescharacteristic
440C22×C4#6325411yescharacteristic
441Q16—342no—
442Q16—681no—
443SD16—342no—
444SD16—681no—
445M16—1361no—
446C2×C8—24no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—171no—
452C2×C8—171no—
453C2×C8—171no—
454C2×C8—171no—
455C2×C8—171no—
456C2×C8—171no—
457C2×C8—171no—
458C2×C8—171no—
459C2×C8—341no—
460C2×C8—341no—
461C2×C8—1361no—
462C2×C8—1361no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—171no—
468C4⋊C4—171no—
469C4⋊C4—341no—
470C4⋊C4—341no—
471C4⋊C4—341no—
472C4⋊C4—341no—
473C4⋊C4—341no—
474C4⋊C4C2×C4×D1711yescharacteristic
475C4⋊C4C2×C4×D1711yescharacteristic
476C22⋊C4—21no—
477C22⋊C4—21no—
478C22⋊C4—21no—
479C22⋊C4—21no—
480C22⋊C4—21no—
481C42—21no—
482C42—341no—
483C42—341no—
484C42—341no—
485C42—341no—
486C42C2×C4×D1711yescharacteristic
487C42D4×D1711yescharacteristic
488C42#6325411yescharacteristic
489C42C23×D1711yescharacteristic
490C23—21no—
491C23#1058756711yescharacteristic
492Q8—21no—
493Q8—21no—
494Q8—172no—
495Q8—341no—
496Q8—341no—
497Q8—341no—
498Q8—682no—
499D4—21no—
500D4—21no—
501D4—42no—
502C2×C4—22no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—341no—
513C2×C4—341no—
514C2×C4—341no—
515C2×C4—341no—
516C2×C4—682no—
517C2×C4—682no—
518C2×C4#1058756711yescharacteristic
519C2×C4#1058756711yescharacteristic
520C2×C4#1058756711yescharacteristic
521C2×C4C22×C4×D1711yescharacteristic
522C2×C4C2×D4×D1711yescharacteristic
523C2×C4C2×#6325411yescharacteristic
524C8—22no—
525C8—22no—
526C8—41no—
527C8—41no—
528C8—341no—
529C8—341no—
530C8—341no—
531C8—341no—
532C8—341no—
533C8—341no—
534C8—341no—
535C8—341no—
536C8—681no—
537C8—681no—
538C22—21no—
539C22—21no—
540C22—41no—
541C22—41no—
542C22—41no—
543C22#1176292312yes—
544C22C2×#1058756711yescharacteristic
545C4—21no—
546C4—21no—
547C4—21no—
548C4—21no—
549C4—41no—
550C4—41no—
551C4—41no—
552C4—342no—
553C4—681no—
554C4—681no—
555C4—681no—
556C4#131×D1711yescharacteristic
557C4#1176357411yescharacteristic
558C4#1176361611yescharacteristic
559C4#1176362311yescharacteristic
560C2—22no—
561C2—81no—
562C2#1453751411yescharacteristic
563C2#1453763011yescharacteristic
564C2C2×#1176292311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D17
commutatorC2×C4×C17C23×C4
FrattiniC42C23×D17
FittingC17×#1494C2
socleC22×C17C2×C4×D4
prime radicalC17×#121C2×C4
cosocleC42×C17C24
hypercenter#1494D17
hypocenterC17#18017
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1494

Complements

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

NH ≅ G/Ntype
3. #14537874C2semidirect
4. #14527678C2semidirect
5. #14527677C2semidirect
6. #14527665C2semidirect
7. #14527658C2semidirect
8. #14527652C2semidirect
9. #14527638C2semidirect
10. #14527588C2semidirect
11. #14527587C2semidirect
12. #14527570C2semidirect
13. C2×#11762541C2semidirect
14. #14527067C2semidirect
426. C17#18017semidirect

Maximal subgroups

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

subgroupindex
#145388602
#145379442
#145378742
#145276782
#145276772
#145276652
#145276582
#145276522
#145276382
#145275882
#145275872
#145275702
C2×#117625412
#145270672
C17×#14942
#1801717