Finite Group Databasebeta

← #17005471

Subgroups — #17005471

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#14538849C211yesmaximal, characteristic
2#14537801C211yesmaximal, characteristic
3#14537733C211yesmaximal, characteristic, complemented
4#14527689C211yesmaximal, characteristic, complemented
5#14527671C211yesmaximal, characteristic, complemented
6#14527659C211yesmaximal, characteristic, complemented
7#14527658C211yesmaximal, characteristic, complemented
8#14527637C211yesmaximal, characteristic, complemented
9#14527624C211yesmaximal, characteristic, complemented
10#14527600C211yesmaximal, characteristic, complemented
11#14527588C211yesmaximal, characteristic, complemented
12#14527570C211yesmaximal, characteristic, complemented
13#14527172C211yesmaximal, characteristic
14#14527079C211yesmaximal, characteristic, complemented
15C17×#1497C211yesmaximal, characteristic, complemented
16C4×#63252C2211yescharacteristic
17#11763147C411yescharacteristic
18#11763147C411yescharacteristic
19#11763091C411yescharacteristic
20#11763086C411yescharacteristic
21#11763016C411yescharacteristic
22#11763011C411yescharacteristic
23#11762969C411yescharacteristic
24#11762969C411yescharacteristic
25#11762940—21no—
26#11762940—21no—
27#11762940C2211yescharacteristic
28#11762940C2211yescharacteristic
29Q8×#3622C2211yescharacteristic
30Q8×#3622C2211yescharacteristic
31#11762933C2211yescharacteristic
32#11762933C2211yescharacteristic
33C4×#63231C2211yescharacteristic
34C4×#63231C2211yescharacteristic
35C4×#63230C2211yescharacteristic
36C4×#63230C2211yescharacteristic
37#11762886C2211yescharacteristic
38#11762886C2211yescharacteristic
39#11762884—21no—
40#11762884—21no—
41#11762864—21no—
42#11762862C2211yescharacteristic
43#11762836—21no—
44C2×C4⋊#3622C2211yescharacteristic
45#11762765—21no—
46C4×#63223C2211yescharacteristic
47#11762761—21no—
48#11762561C2211yescharacteristic
49#11762561C2211yescharacteristic
50#11762559C2211yescharacteristic
51#11762559C2211yescharacteristic
52#11762541C2211yescharacteristic
53#11762541C2211yescharacteristic
54#11762538C2211yescharacteristic
55#11762538C2211yescharacteristic
56#11762531C2211yescharacteristic
57#11762531C2211yescharacteristic
58#11762530C2211yescharacteristic
59C8×#3622C2211yescharacteristic
60C17×#533C2211yescharacteristic
61C17×#432C2211yescharacteristic
62C17×#431C2211yescharacteristic
63C17×Q8⋊C8C2211yescharacteristic
64C17×Q8⋊C8C2211yescharacteristic
65C17×Q8⋊C8C2211yescharacteristic
66C17×Q8⋊C8C2211yescharacteristic
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
86C2×#63223D411yescharacteristic
87C2×#63223D411yescharacteristic
88C22×#3622—21no—
89C2×#63218—21no—
90C2×#63218—21no—
91C4×D68C2×C411yescharacteristic
92C4×D68C2311yescharacteristic
93#10587558—21no—
94C42×D17—21no—
95C4×Dic34C2×C411yescharacteristic
96C4×Dic34C2311yescharacteristic
97C17×C4⋊C8—21no—
98C17×C4⋊C8C2311yescharacteristic
99C17×C4⋊C8C2311yescharacteristic
100C17×C22⋊C8—21no—
101C17×C22⋊C8—21no—
102C17×#97—21no—
103C4×C8×C17C2311yescharacteristic
104C4×C8×C17C2311yescharacteristic
105#10587506C2×C411yescharacteristic
106#10587506C2×C411yescharacteristic
107#10587506C2×C411yescharacteristic
108#10587506C2×C411yescharacteristic
109C22⋊#3622C2×C411yescharacteristic
110C22⋊#3622C2×C411yescharacteristic
111#10587491—21no—
112#10587491—21no—
113#10587485—21no—
114#10587485—21no—
115C8×Dic17—21no—
116C8×Dic17—21no—
117#10587481C2×C411yescharacteristic
118#10587481C2×C411yescharacteristic
119#10587480C2×C411yescharacteristic
120#10587480C2×C411yescharacteristic
121#10587479C2×C411yescharacteristic
122#10587479C2×C411yescharacteristic
123#10587478C2×C411yescharacteristic
124#10587478C2×C411yescharacteristic
125C4⋊#3622—21no—
126C4⋊#3622—21no—
127C4⋊#3622—21no—
128C4⋊#3622—21no—
129C4⋊#3622—21no—
130C4⋊#3622C2×C411yescharacteristic
131C4⋊#3622C2×C411yescharacteristic
132C4⋊#3622C2311yescharacteristic
133C4⋊#3622C2311yescharacteristic
134#10587474—21no—
135#10587474—21no—
136#10587474D411yescharacteristic
137#10587474D411yescharacteristic
138C4×#3622—21no—
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—
151#63252—22no—
152#63252—41no—
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×C17—21no—
161C2×C8×C17—21no—
162C4⋊C4×C17—21no—
163C4⋊C4×C17—21no—
164C4⋊C4×C17—21no—
165C4⋊C4×C17—21no—
166C4⋊C4×C17—21no—
167C4⋊C4×C17—21no—
168C4⋊C4×C17—21no—
169C4⋊C4×C17C22×C411yescharacteristic
170C4⋊C4×C17C22×C411yescharacteristic
171C22⋊C4×C17—21no—
172C22⋊C4×C17—21no—
173C42×C17—21no—
174C42×C17—21no—
175C42×C17C22×C411yescharacteristic
176C42×C17C2×D411yescharacteristic
177C42×C17#4111yescharacteristic
178C42×C17C2411yescharacteristic
179C22⋊Dic17—21no—
180#63231—22no—
181#63231—22no—
182#63230—41no—
183#63230—41no—
184#63227—21no—
185#63227—21no—
186C4⋊Dic17C22×C411yescharacteristic
187C4⋊Dic17C22×C411yescharacteristic
188#63225—21no—
189#63225—21no—
190C4×Dic17—21no—
191C4×Dic17—21no—
192C4×Dic17—21no—
193#63223—22no—
194#63223—41no—
195C2×#3622—21no—
196C2×#3622—21no—
197C2×#3622—42no—
198C2×#3622C22×C411yescharacteristic
199C2×#3622C22×C411yescharacteristic
200C2×#3622C22×C411yescharacteristic
201C2×#3622C22×C411yescharacteristic
202C2×#3622C2×D411yescharacteristic
203C2×#3622C2×D411yescharacteristic
204C2×#3622C2×D411yescharacteristic
205C2×#3622C2×D411yescharacteristic
206#63218—42no—
207#63218—42no—
208#18013—171nomaximal, Sylow
209C23×C17C4×D411yescharacteristic
210C22×D17—21no—
211Q8×C17—21no—
212Q8×C17—21no—
213Q8×C17—21no—
214Q8×C17—21no—
215Q8×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—21no—
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
231C22⋊D17—42no—
232C2×Dic17—21no—
233C2×Dic17—21no—
234C2×Dic17—21no—
235D68—21no—
236D68—21no—
237C4×D17—42no—
238C4×D17—41no—
239C4×D17—41no—
240C4×D17—81no—
241Dic34—21no—
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#3107—171no—
258#2971—171no—
259#2962—171no—
260#1592—171no—
261#1590—171no—
262#1588—171no—
263#1587—171no—
264#1584—171no—
265#1583—171no—
266#1579—171no—
267C8×Q16—171no—
268#1573—171no—
269#1497D1711yescharacteristic, complemented
270#1477—171no—
271#1453—171no—
272C22×C17—21no—
273C22×C17—21no—
274C22×C17—21no—
275C22×C17C2×C4×D411yescharacteristic
276C2×D17—41no—
277C2×D17—41no—
278C2×D17—41no—
279C4×C17—21no—
280C4×C17—21no—
281C4×C17—21no—
282C4×C17—21no—
283C4×C17—41no—
284C4×C17—41no—
285C4×C17—41no—
286C4×C17—41no—
287C4×C17C2×#13111yescharacteristic
288C4×C17#56811yescharacteristic
289C4×C17C2×#13711yescharacteristic
290C4×C17#57511yescharacteristic
291Dic17—22no—
292Dic17—41no—
293Dic17—41no—
294#533C2×D1711yescharacteristic
295C4×#41—171no—
296#485—171no—
297#485—171no—
298#475—171no—
299#474—171no—
300#462—171no—
301#461—171no—
302#452—171no—
303#452—171no—
304#446—171no—
305#446—171no—
306#446—341no—
307#446—341no—
308C8×Q8—171no—
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—171no—
318#436—341no—
319#436—341no—
320#432—341no—
321#432C2×D1711yescharacteristic
322#431—171no—
323#431C2×D1711yescharacteristic
324#424—341no—
325C2×C4⋊C8—171no—
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⋊C8C2×D1711yescharacteristic
336Q8⋊C8C2×D1711yescharacteristic
337Q8⋊C8C2×D1711yescharacteristic
338Q8⋊C8C2×D1711yescharacteristic
339D4⋊C8—171no—
340D4⋊C8—171no—
341#322—171no—
342#322—171no—
343#322—171no—
344C82—171no—
345C2×C17—41no—
346C2×C17#293311yescharacteristic
347C2×C17C4×#13711yescharacteristic
348C2×C17#295711yescharacteristic
349D17—81no—
350C2×#41—171no—
351C2×Q16—171no—
352C2×Q16—171no—
353C2×SD16—171no—
354C2×SD16—171no—
355C2×M16—171no—
356C2×M16—171no—
357C2×M16—341no—
358C2×M16—341no—
359C22×C8—341no—
360C4⋊Q8C4×D1711yescharacteristic
361C4⋊Q8C4×D1711yescharacteristic
362#125—21no—
363C22⋊Q8—21no—
364C22⋊Q8C4×D1711yescharacteristic
365C22⋊Q8C4×D1711yescharacteristic
366C4×Q8—21no—
367C4×Q8—171no—
368C4×Q8—171no—
369C4×Q8C22×D1711yescharacteristic
370C4×Q8C22×D1711yescharacteristic
371C4×D4—171no—
372C4×D4—171no—
373C4×D4—341no—
374C4×D4—341no—
375#117—21no—
376#117—171no—
377#117—341no—
378C2×C42—341no—
379C2×C42C22×D1711yescharacteristic
380#107—171no—
381#107—171no—
382#106—171no—
383#106—171no—
384C4⋊C8—21no—
385C4⋊C8—171no—
386C4⋊C8—171no—
387C4⋊C8—171no—
388C4⋊C8—171no—
389C4⋊C8—341no—
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—21no—
408C22⋊C8—171no—
409C22⋊C8—171no—
410C22⋊C8—341no—
411C22⋊C8—341no—
412#97—21no—
413#97—171no—
414#97—171no—
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#1801311yescharacteristic, complemented, Sylow
428#41—342no—
429#41—681no—
430C2×Q8—21no—
431C2×Q8—171no—
432C2×Q8C2×C4×D1711yescharacteristic
433C2×Q8C2×C4×D1711yescharacteristic
434C2×D4—171no—
435C2×D4—341no—
436C22×C4—341no—
437C22×C4—341no—
438C22×C4—341no—
439C22×C4C2×C4×D1711yescharacteristic
440C22×C4D4×D1711yescharacteristic
441C22×C4#6325411yescharacteristic
442Q16—342no—
443Q16—342no—
444SD16—681no—
445SD16—681no—
446M16—342no—
447M16—682no—
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—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—171no—
473C4⋊C4—171no—
474C4⋊C4—341no—
475C4⋊C4—341no—
476C4⋊C4C2×C4×D1711yescharacteristic
477C4⋊C4C2×C4×D1711yescharacteristic
478C22⋊C4—21no—
479C22⋊C4—21no—
480C22⋊C4—341no—
481C22⋊C4—341no—
482C22⋊C4—341no—
483C42—21no—
484C42—21no—
485C42—341no—
486C42—341no—
487C42—341no—
488C42C2×C4×D1711yescharacteristic
489C42D4×D1711yescharacteristic
490C42#6325411yescharacteristic
491C42C23×D1711yescharacteristic
492C23—341no—
493C23#1058756711yescharacteristic
494Q8—21no—
495Q8—21no—
496Q8—21no—
497Q8—21no—
498Q8—81no—
499Q8—172no—
500Q8—341no—
501D4—341no—
502D4—341no—
503D4—682no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—41no—
513C2×C4—341no—
514C2×C4—341no—
515C2×C4—341no—
516C2×C4—682no—
517C2×C4—681no—
518C2×C4—681no—
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—681no—
544C22—681no—
545C22—681no—
546C22C2×#1058756711yescharacteristic
547C4—21no—
548C4—21no—
549C4—21no—
550C4—21no—
551C4—41no—
552C4—41no—
553C4—41no—
554C4—41no—
555C4—342no—
556C4—681no—
557C4—681no—
558C4#131×D1711yescharacteristic
559C4#1176357411yescharacteristic
560C4#137×D1711yescharacteristic
561C4#1176360811yescharacteristic
562C2—41no—
563C2—1361no—
564C2#1453751411yescharacteristic
565C2#1453759911yescharacteristic
566C2#1453769711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D17
commutatorC2×C4×C17C23×C4
FrattiniC42C23×D17
FittingC17×#1497C2
socleC22×C17C2×C4×D4
prime radicalC2×#63252C2×C4
cosocleC42×C17C24
hypercenter#1497D17
hypocenterC17#18013
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1497

Complements

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

NH ≅ G/Ntype
3. #14537733C2semidirect
4. #14527689C2semidirect
5. #14527671C2semidirect
6. #14527659C2semidirect
7. #14527658C2semidirect
8. #14527637C2semidirect
9. #14527624C2semidirect
10. #14527600C2semidirect
11. #14527588C2semidirect
12. #14527570C2semidirect
14. #14527079C2semidirect
15. C17×#1497C2semidirect
269. #1497D17semidirect
427. C17#18013semidirect

Maximal subgroups

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

subgroupindex
#145388492
#145378012
#145377332
#145276892
#145276712
#145276592
#145276582
#145276372
#145276242
#145276002
#145275882
#145275702
#145271722
#145270792
C17×#14972
#1801317