Finite Group Databasebeta

← #17005456

Subgroups — #17005456

Order 4352.

592 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14538860C211yesmaximal, characteristic
2#14537789C211yesmaximal, characteristic
3#14537735C211yesmaximal, characteristic, complemented
4#14527690C211yesmaximal, characteristic, complemented
5#14527677C211yesmaximal, characteristic, complemented
6#14527658C211yesmaximal, characteristic, complemented
7#14527638C211yesmaximal, characteristic, complemented
8#14527631C211yesmaximal, characteristic, complemented
9#14527630C211yesmaximal, characteristic, complemented
10#14527593C211yesmaximal, characteristic, complemented
11#14527588C211yesmaximal, characteristic, complemented
12#14527575C211yesmaximal, characteristic, complemented
13#14527180C211yesmaximal, characteristic, complemented
14#14527079C211yesmaximal, characteristic, complemented
15C17×#1495C211yesmaximal, characteristic
16C2×C4×Dic34C2211yescharacteristic
17#11763137C411yescharacteristic
18#11763120C411yescharacteristic
19#11763113C411yescharacteristic
20#11763113C411yescharacteristic
21#11763028C411yescharacteristic
22#11763028C411yescharacteristic
23#11762964C411yescharacteristic
24#11762947C411yescharacteristic
25#11762940C2211yescharacteristic
26#11762938—21no—
27#11762938—21no—
28#11762936C2211yescharacteristic
29#11762936C2211yescharacteristic
30Q8×#3622C2211yescharacteristic
31#11762933C2211yescharacteristic
32#11762933C2211yescharacteristic
33C4×#63231C2211yescharacteristic
34C4×#63231C2211yescharacteristic
35C4×#63229C2211yescharacteristic
36C4×#63229C2211yescharacteristic
37#11762887—21no—
38#11762887C2211yescharacteristic
39#11762881—21no—
40D4×#3622C2211yescharacteristic
41#11762870—21no—
42#11762862C2211yescharacteristic
43#11762862C2211yescharacteristic
44#11762832—21no—
45#11762765—21no—
46C4×#63223C2211yescharacteristic
47M16×Dic17—21no—
48#11762561C2211yescharacteristic
49#11762561C2211yescharacteristic
50#11762559C2211yescharacteristic
51#11762559C2211yescharacteristic
52#11762541C2211yescharacteristic
53#11762541C2211yescharacteristic
54#11762541C2211yescharacteristic
55#11762541C2211yescharacteristic
56#11762531C2211yescharacteristic
57#11762531C2211yescharacteristic
58#11762530C2211yescharacteristic
59C8×#3622C2211yescharacteristic
60C17×#529C2211yescharacteristic
61C17×#431C2211yescharacteristic
62C17×#423C2211yescharacteristic
63C17×Q8⋊C8C2211yescharacteristic
64C17×Q8⋊C8C2211yescharacteristic
65C17×D4⋊C8C2211yescharacteristic
66C17×D4⋊C8C2211yescharacteristic
67C22×Dic34C2×C411yescharacteristic
68C2×M16×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—
88C2×#63223D411yescharacteristic
89C2×#63223D411yescharacteristic
90C22×#3622—21no—
91C4×Dic34—21no—
92C4×Dic34—21no—
93C4×Dic34C2×C411yescharacteristic
94C4×Dic34C2×C411yescharacteristic
95C4×Dic34C2311yescharacteristic
96C4×Dic34C2311yescharacteristic
97C17×C4⋊C8—21no—
98C17×C4⋊C8—21no—
99C17×C4⋊C8C2311yescharacteristic
100C17×C4⋊C8C2311yescharacteristic
101C17×C22⋊C8—21no—
102C4×C8×C17C2311yescharacteristic
103C4×C8×C17C2311yescharacteristic
104#10587506C2×C411yescharacteristic
105#10587506C2×C411yescharacteristic
106#10587503C2×C411yescharacteristic
107#10587503C2×C411yescharacteristic
108C22⋊#3622—21no—
109C22⋊#3622—21no—
110C22⋊#3622—21no—
111C22⋊#3622C2×C411yescharacteristic
112C22⋊#3622C2×C411yescharacteristic
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⋊#3622C2×C411yescharacteristic
132C4⋊#3622C2×C411yescharacteristic
133C4⋊#3622C2311yescharacteristic
134C4⋊#3622C2311yescharacteristic
135#10587474—21no—
136#10587474D411yescharacteristic
137#10587474D411yescharacteristic
138C4×#3622—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
158M16×C17—42no—
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—22no—
195#63223—41no—
196#63223—42no—
197C2×#3622—21no—
198C2×#3622—21no—
199C2×#3622—42no—
200C2×#3622C22×C411yescharacteristic
201C2×#3622C22×C411yescharacteristic
202C2×#3622C22×C411yescharacteristic
203C2×#3622C22×C411yescharacteristic
204C2×#3622C2×D411yescharacteristic
205C2×#3622C2×D411yescharacteristic
206C2×#3622C2×D411yescharacteristic
207C2×#3622C2×D411yescharacteristic
208#18012—171nomaximal, Sylow
209C23×C17—21no—
210C23×C17C4×D411yescharacteristic
211Q8×C17—21no—
212Q8×C17—21no—
213D4×C17—21no—
214D4×C17—21no—
215D4×C17—81no—
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×C17—41no—
226C2×C4×C17C4×D411yescharacteristic
227C2×C4×C17C4×D411yescharacteristic
228C2×C4×C17C4×D411yescharacteristic
229C2×C4×C17C23×C411yescharacteristic
230C2×C4×C17C22×D411yescharacteristic
231C2×C4×C17C2×#4111yescharacteristic
232C2×Dic17—21no—
233C2×Dic17—21no—
234C2×Dic17—21no—
235C2×Dic17—21no—
236C2×Dic17—42no—
237C2×Dic17—81no—
238Dic34—21no—
239Dic34—21no—
240Dic34—21no—
241Dic34—42no—
242Dic34#13112yes—
243C8×C17—41no—
244C8×C17—41no—
245C8×C17—41no—
246C8×C17—41no—
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#3622#13712yes—
257#3108—171no—
258#2969—171no—
259Q8×M16—171no—
260#1593—171no—
261#1590—171no—
262#1587—171no—
263#1585—171no—
264#1584—171no—
265#1583—171no—
266SD16⋊C8—171no—
267C8×Q16—171no—
268#1574—171no—
269#1495D1711yescharacteristic
270#1479—171no—
271#1453—171no—
272C22×C17—21no—
273C22×C17—21no—
274C22×C17—21no—
275C22×C17—41no—
276C22×C17—41no—
277C22×C17—41no—
278C22×C17C2×C4×D411yescharacteristic
279C4×C17—21no—
280C4×C17—21no—
281C4×C17—21no—
282C4×C17—21no—
283C4×C17—41no—
284C4×C17—41no—
285C4×C17—41no—
286C4×C17C2×#13111yescharacteristic
287C4×C17#56811yescharacteristic
288C4×C17C2×#13711yescharacteristic
289C4×C17#57511yescharacteristic
290Dic17—22no—
291Dic17—41no—
292Dic17—41no—
293Dic17—41no—
294#529C2×D1711yescharacteristic
295C2×C4×Q8—171no—
296#483—171no—
297#480—171no—
298#479—171no—
299#479—171no—
300#464—171no—
301#464—171no—
302#451—171no—
303#448—171no—
304#446—171no—
305#446—171no—
306#446—171no—
307#446—341no—
308#446—341no—
309C8×Q8—171no—
310C8×Q8—171no—
311C8×Q8—171no—
312C4×Q16—171no—
313C4×Q16—171no—
314C4×SD16—171no—
315C4×SD16—171no—
316#436—171no—
317#436—341no—
318#435—341no—
319C8×D4—171no—
320#433—341no—
321#431—171no—
322#431—171no—
323#431C2×D1711yescharacteristic
324#423—341no—
325#423C2×D1711yescharacteristic
326#405—341no—
327C4×M16—171no—
328C4×M16—341no—
329#335—171no—
330#335—171no—
331#334—171no—
332#334—171no—
333Q8⋊C8—171no—
334Q8⋊C8—171no—
335Q8⋊C8—171no—
336Q8⋊C8—171no—
337Q8⋊C8C2×D1711yescharacteristic
338Q8⋊C8C2×D1711yescharacteristic
339D4⋊C8C2×D1711yescharacteristic
340D4⋊C8C2×D1711yescharacteristic
341#322—171no—
342#322—171no—
343#322—171no—
344C82—171no—
345C2×C17—41no—
346C2×C17—81no—
347C2×C17#293311yescharacteristic
348C2×C17C4×#13711yescharacteristic
349C2×C17#295711yescharacteristic
350C22×Q8—171no—
351C2×Q16—171no—
352C2×Q16—171no—
353C2×SD16—171no—
354C2×SD16—171no—
355C2×M16—21no—
356C2×M16—171no—
357C2×M16—171no—
358C2×M16—341no—
359C22×C8—341no—
360#126—21no—
361#125C4×D1711yescharacteristic
362#124C4×D1711yescharacteristic
363#123—21no—
364C22⋊Q8C4×D1711yescharacteristic
365#121C4×D1711yescharacteristic
366C4×Q8—171no—
367C4×Q8—171no—
368C4×Q8—171no—
369C4×Q8—171no—
370C4×Q8—341no—
371C4×Q8—341no—
372C4×Q8C22×D1711yescharacteristic
373C4×D4—21no—
374C4×D4C22×D1711yescharacteristic
375#117—21no—
376C2×C4⋊C4—171no—
377C2×C4⋊C4—341no—
378C2×C42—341no—
379C2×C42C22×D1711yescharacteristic
380#107—171no—
381#107—171no—
382#106—171no—
383#106—171no—
384C4⋊C8—21no—
385C4⋊C8—21no—
386C4⋊C8—171no—
387C4⋊C8—171no—
388C4⋊C8—171no—
389C4⋊C8—171no—
390C4⋊C8—341no—
391C4⋊C8—341no—
392C4⋊C8—341no—
393C4⋊C8—341no—
394C4⋊C8—341no—
395C4⋊C8—341no—
396C4⋊C8C22×D1711yescharacteristic
397C4⋊C8C22×D1711yescharacteristic
398#103—171no—
399#103—171no—
400#103—171no—
401#103—171no—
402#103—171no—
403#103—171no—
404#102—171no—
405#102—171no—
406C22⋊C8—21no—
407C22⋊C8—171no—
408C22⋊C8—171no—
409C22⋊C8—341no—
410C22⋊C8—341no—
411C22⋊C8—341no—
412#97—171no—
413#97—171no—
414#97—341no—
415#97—341no—
416#97—341no—
417C4×C8—171no—
418C4×C8—171no—
419C4×C8—171no—
420C4×C8—171no—
421C4×C8—341no—
422C4×C8—341no—
423C4×C8—341no—
424C4×C8—341no—
425C4×C8C22×D1711yescharacteristic
426C4×C8C22×D1711yescharacteristic
427C17#1801211yescharacteristic, complemented, Sylow
428C2×Q8—171no—
429C2×Q8—171no—
430C2×Q8—342no—
431C2×Q8—341no—
432C2×Q8—681no—
433C2×Q8C2×C4×D1711yescharacteristic
434C2×D4—21no—
435C2×D4C2×C4×D1711yescharacteristic
436C22×C4—21no—
437C22×C4—341no—
438C22×C4—341no—
439C22×C4C2×C4×D1711yescharacteristic
440C22×C4D4×D1711yescharacteristic
441C22×C4#6325411yescharacteristic
442Q16—342no—
443Q16—681no—
444SD16—342no—
445SD16—681no—
446M16—42no—
447M16—342no—
448M16—682no—
449M16—681no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—171no—
455C2×C8—171no—
456C2×C8—171no—
457C2×C8—171no—
458C2×C8—171no—
459C2×C8—171no—
460C2×C8—171no—
461C2×C8—171no—
462C2×C8—341no—
463C2×C8—341no—
464C2×C8—682no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—171no—
470C4⋊C4—171no—
471C4⋊C4—341no—
472C4⋊C4—341no—
473C4⋊C4—341no—
474C4⋊C4—341no—
475C4⋊C4—341no—
476C4⋊C4C2×C4×D1711yescharacteristic
477C4⋊C4C2×C4×D1711yescharacteristic
478C22⋊C4—21no—
479C22⋊C4—21no—
480C22⋊C4—21no—
481C22⋊C4—21no—
482C22⋊C4—21no—
483C42—21no—
484C42—341no—
485C42—341no—
486C42—341no—
487C42—341no—
488C42C2×C4×D1711yescharacteristic
489C42D4×D1711yescharacteristic
490C42#6325411yescharacteristic
491C42C23×D1711yescharacteristic
492C23—21no—
493C23#1058756711yescharacteristic
494Q8—21no—
495Q8—21no—
496Q8—172no—
497Q8—341no—
498Q8—341no—
499Q8—341no—
500Q8—682no—
501D4—21no—
502D4—21no—
503D4—81no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—341no—
515C2×C4—341no—
516C2×C4—341no—
517C2×C4—341no—
518C2×C4—682no—
519C2×C4—1361no—
520C2×C4#1058756711yescharacteristic
521C2×C4#1058756711yescharacteristic
522C2×C4#1058756711yescharacteristic
523C2×C4C22×C4×D1711yescharacteristic
524C2×C4C2×D4×D1711yescharacteristic
525C2×C4C2×#6325411yescharacteristic
526C8—41no—
527C8—41no—
528C8—41no—
529C8—41no—
530C8—172no—
531C8—341no—
532C8—341no—
533C8—341no—
534C8—341no—
535C8—341no—
536C8—341no—
537C8—341no—
538C8—681no—
539C8—681no—
540C22—21no—
541C22—21no—
542C22—21no—
543C22—41no—
544C22—41no—
545C22—41no—
546C22C2×#1058756711yescharacteristic
547C4—21no—
548C4—21no—
549C4—21no—
550C4—21no—
551C4—41no—
552C4—41no—
553C4—41no—
554C4—342no—
555C4—681no—
556C4—681no—
557C4—681no—
558C4#131×D1711yescharacteristic
559C4#1176357411yescharacteristic
560C4#137×D1711yescharacteristic
561C4#1176360511yescharacteristic
562C2—41no—
563C2—81no—
564C2#1453751411yescharacteristic
565C2#1453760811yescharacteristic
566C2#1453769711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D17
commutatorC2×C4×C17C23×C4
FrattiniC42C23×D17
FittingC17×#1495C2
socleC22×C17C2×C4×D4
prime radicalC17×#121C2×C4
cosocleC42×C17C24
hypercenter#1495D17
hypocenterC17#18012
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1495

Complements

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

NH ≅ G/Ntype
3. #14537735C2semidirect
4. #14527690C2semidirect
5. #14527677C2semidirect
6. #14527658C2semidirect
7. #14527638C2semidirect
8. #14527631C2semidirect
9. #14527630C2semidirect
10. #14527593C2semidirect
11. #14527588C2semidirect
12. #14527575C2semidirect
13. #14527180C2semidirect
14. #14527079C2semidirect
427. C17#18012semidirect

Maximal subgroups

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

subgroupindex
#145388602
#145377892
#145377352
#145276902
#145276772
#145276582
#145276382
#145276312
#145276302
#145275932
#145275882
#145275752
#145271802
#145270792
C17×#14952
#1801217