Finite Group Databasebeta

← #17191289

Subgroups — #17191289

Order 4352.

602 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14540471C211yesmaximal, characteristic, complemented
2#14531023C211yesmaximal, characteristic, complemented
3#14530981C211yesmaximal, characteristic, complemented
4#14530969C211yesmaximal, characteristic, complemented
5#14530928C211yesmaximal, characteristic, complemented
6#14530885C211yesmaximal, characteristic, complemented
7#14530878C211yesmaximal, characteristic, complemented
8#14530839C211yesmaximal, characteristic, complemented
9#14530705C211yesmaximal, characteristic, complemented
10#14530695C211yesmaximal, characteristic, complemented
11#14530658C211yesmaximal, characteristic, complemented
12#14530610C211yesmaximal, characteristic, complemented
13#14530494C211yesmaximal, characteristic, complemented
14C2×#11762609C211yesmaximal, characteristic, complemented
15C17×#3334C211yesmaximal, characteristic, complemented
16C2×#10587590C2211yescharacteristic
17C22×D136C2211yescharacteristic
18#11763455—21no—
19C2×#10587498C2211yescharacteristic, complemented
20C2×#10587497C2211yescharacteristic
21C2×#10587497C2211yescharacteristic
22C2×#10587483C2211yescharacteristic, complemented
23C22×#63214C2211yescharacteristic
24#11763193C2211yescharacteristic
25#11763050C2211yescharacteristic
26#11763045C2211yescharacteristic
27#11763025—21no—
28#11762962—21no—
29#11762956—21no—
30C4×D136C2211yescharacteristic
31#11762636C2211yescharacteristic, complemented
32#11762636C2211yescharacteristic, complemented
33#11762636C2211yescharacteristic, complemented
34C4⋊#63214C2211yescharacteristic, complemented
35#11762612C2211yescharacteristic, complemented
36#11762612C2211yescharacteristic, complemented
37#11762612C2211yescharacteristic, complemented
38#11762610C2211yescharacteristic, complemented
39#11762609C2211yescharacteristic
40#11762609C2211yescharacteristic
41#11762609C2211yescharacteristic
42#11762609C2211yescharacteristic
43#11762609C2211yescharacteristic
44#11762609C2211yescharacteristic
45C22⋊#63214C2211yescharacteristic
46C22⋊#63214C2211yescharacteristic, complemented
47#11762585C2211yescharacteristic, complemented
48C17×#547—21no—
49C17×#500C2211yescharacteristic, complemented
50C17×#480—21no—
51C17×#480—21no—
52C17×#474—21no—
53C17×#466C2211yescharacteristic
54C17×#466C2211yescharacteristic, complemented
55C4×D8×C17C2211yescharacteristic, complemented
56C8×D4×C17C2211yescharacteristic
57C2×C17×#107C2211yescharacteristic
58C2×C17×#107C2211yescharacteristic, complemented
59C2×#41×C17—41no—
60C2×#63252—21no—
61C22×D68—21no—
62C2×D8×C17C2311yescharacteristic
63C22×C8×C17C2311yescharacteristic
64C22×C8×C17C2311yescharacteristic
65C17×C4⋊Q8—21no—
66C17×#123—41no—
67C17×#123—41no—
68C17×C22⋊Q8—41no—
69C17×#121—21no—
70C17×#121—21no—
71C4×D4×C17—21no—
72C4×D4×C17D411yescharacteristic
73C2×C4⋊C4×C17—21no—
74C2×C4⋊C4×C17—21no—
75#10587623—41no—
76#10587616—21no—
77#10587610—21no—
78C2×Dic68C2311yescharacteristic
79#10587590—22no—
80#10587590—41no—
81C2×D136—22no—
82C2×D136—21no—
83C2×D136—41no—
84C2×D136C2311yescharacteristic
85C2×D136C2311yescharacteristic
86C2×#63219—21no—
87C2×#63219—21no—
88#10587580—41no—
89#10587570—41no—
90C22⋊C4×D17—41no—
91#10587561—21no—
92C4×D68—21no—
93C17×#107—21no—
94C17×#107—21no—
95C17×#107—21no—
96C17×#107C2311yescharacteristic
97C17×#107C2311yescharacteristic
98C17×#107C2311yescharacteristic
99C17×C4⋊C8D411yescharacteristic
100C17×#102—21no—
101C17×#102—21no—
102C17×#102—21no—
103C17×C22⋊C8D411yescharacteristic
104C17×C22⋊C8D411yescharacteristic
105C4×C8×C17C2311yescharacteristic
106#10587498—41no—
107#10587497—22no—
108#10587497—41no—
109#10587492—21no—
110#10587492—21no—
111#10587489C2311yescharacteristic
112#10587487—21no—
113#10587483—41no—
114C2×#63214—41no—
115C2×#63214C2311yescharacteristic
116C2×#63214C2311yescharacteristic
117C2×#63214C2311yescharacteristic
118C2×#63214C2311yescharacteristic
119C23×D17—41no—
120#41×C17—84no—
121C2×Q8×C17—41no—
122C2×D4×C17—21no—
123C2×D4×C17—41no—
124C2×D4×C17—41no—
125C2×D4×C17D811yescharacteristic
126C22×C4×C17—41no—
127C22×C4×C17—41no—
128C22×C4×C17—41no—
129C22×C4×C17C2×D411yescharacteristic
130C22×C4×C17C2×D411yescharacteristic
131C2×C22⋊D17—41no—
132C2×C22⋊D17—41no—
133#63252—42no—
134#63252—81no—
135C2×D68—21no—
136C2×D68—21no—
137C2×D68—42no—
138C2×D68—41no—
139C2×D68—81no—
140C2×C4×D17—41no—
141C2×C4×D17—41no—
142C2×Dic34—21no—
143D8×C17—21no—
144D8×C17—21no—
145C2×C8×C17—21no—
146C2×C8×C17—21no—
147C2×C8×C17—21no—
148C2×C8×C17—21no—
149C2×C8×C17C2×D411yescharacteristic
150C2×C8×C17C2×D411yescharacteristic
151C2×C8×C17C2×D411yescharacteristic
152C2×C8×C17C2411yescharacteristic
153C4⋊C4×C17—21no—
154C4⋊C4×C17—21no—
155C4⋊C4×C17—21no—
156C4⋊C4×C17—41no—
157C4⋊C4×C17—41no—
158C4⋊C4×C17—41no—
159C4⋊C4×C17D811yescharacteristic
160C22⋊C4×C17—41no—
161C22⋊C4×C17—41no—
162C22⋊C4×C17—41no—
163C22⋊C4×C17D811yescharacteristic
164C22⋊C4×C17D811yescharacteristic
165C42×C17C2×D411yescharacteristic
166C22⋊Dic17—41no—
167#63227—41no—
168#63227—41no—
169#63227—41no—
170#63227—41no—
171C4⋊Dic17—21no—
172#63225—41no—
173Dic68—21no—
174Dic68—21no—
175D136—21no—
176D136—21no—
177D136—21no—
178D136—42no—
179D136#4112yescomplemented
180#63219—42no—
181#63219—81no—
182#63214—21no—
183#63214—21no—
184#63214—21no—
185#63214—21no—
186#33873—171nomaximal, Sylow
187C23×C17—41no—
188C23×C17C2×D811yescharacteristic
189C23×C17C2×D811yescharacteristic
190C22×D17—41no—
191C22×D17—41no—
192C22×D17—82no—
193C22×D17—82no—
194C22×D17—161no—
195Q8×C17—82no—
196D4×C17—22no—
197D4×C17—41no—
198D4×C17—41no—
199D4×C17—82no—
200D4×C17—82no—
201C2×C4×C17—21no—
202C2×C4×C17—21no—
203C2×C4×C17—21no—
204C2×C4×C17—21no—
205C2×C4×C17—41no—
206C2×C4×C17—41no—
207C2×C4×C17—41no—
208C2×C4×C17—82no—
209C2×C4×C17—82no—
210C2×C4×C17—82no—
211C2×C4×C17C2×D811yescharacteristic
212C2×C4×C17C2×D811yescharacteristic
213C2×C4×C17C2×D811yescharacteristic
214C2×C4×C17C2×D811yescharacteristic
215C2×C4×C17C22×D411yescharacteristic
216C22⋊D17—82no—
217C22⋊D17—161no—
218C2×Dic17—41no—
219C2×Dic17—41no—
220D68—22no—
221D68—41no—
222D68—41no—
223D68—41no—
224D68—82no—
225C4×D17—82no—
226C4×D17—161no—
227Dic34—41no—
228Dic34—41no—
229C8×C17—21no—
230C8×C17—21no—
231C8×C17—21no—
232C8×C17C2×#4111yescharacteristic
233C8×C17H(5,𝔽2)11yescharacteristic
234#3334D1711yescharacteristic, complemented
235#3280—171no—
236#2243—171no—
237#2235—171no—
238#2233—171no—
239#2226—171no—
240#2218—171no—
241#2217—171no—
242#2210—171no—
243#2186—171no—
244#2184—171no—
245#2177—171no—
246#2168—171no—
247#2139—171no—
248C2×#357—171no—
249C22×C17—21no—
250C22×C17—21no—
251C22×C17—21no—
252C22×C17—21no—
253C22×C17—21no—
254C22×C17—81no—
255C22×C17—81no—
256C22×C17—81no—
257C22×C17#50912yes—
258C22×C17C22×D811yescharacteristic
259C2×D17—42no—
260C2×D17—81no—
261C2×D17—81no—
262C2×D17—81no—
263C2×D17—81no—
264C2×D17—81no—
265C2×D17—164no—
266C4×C17—21no—
267C4×C17—21no—
268C4×C17—21no—
269C4×C17—21no—
270C4×C17—81no—
271C4×C17—81no—
272C4×C17—81no—
273C4×C17#54611yescharacteristic
274C4×C17#57711yescharacteristic
275Dic17—81no—
276Dic17—81no—
277C2×#135—171no—
278C22×D8—171no—
279#547—21no—
280#546—341no—
281C2×SD32—171no—
282C2×D16—171no—
283C2×D16—171no—
284C2×M32—171no—
285C22×C16—171no—
286#500C2×D1711yescharacteristic, complemented
287#495—171no—
288#480—21no—
289#480—21no—
290#474—21no—
291#467—171no—
292#466—171no—
293#466C2×D1711yescharacteristic
294#466C2×D1711yescharacteristic, complemented
295#463—341no—
296#450—341no—
297#449—341no—
298C4×D8—171no—
299C4×D8C2×D1711yescharacteristic, complemented
300C8×D4C2×D1711yescharacteristic
301C2×#107C2×D1711yescharacteristic
302C2×#107C2×D1711yescharacteristic, complemented
303#367—171no—
304#367—171no—
305#367—171no—
306C4⋊C16—171no—
307#358—171no—
308#358—171no—
309#358—171no—
310#357—171no—
311#357—171no—
312#357—171no—
313#357—171no—
314#357—171no—
315#357—171no—
316#357—171no—
317C22⋊C16—171no—
318C22⋊C16—171no—
319#346—171no—
320C2×C17—22no—
321C2×C17—41no—
322C2×C17—161no—
323C2×C17#329411yescharacteristic
324C2×C17C2×#50911yescharacteristic
325C2×C17#341611yescharacteristic
326D17—82no—
327D17—161no—
328C2×#41—41no—
329C2×#41—341no—
330C22×D4—341no—
331#135—342no—
332#135—681no—
333C2×Q16—171no—
334C2×SD16—341no—
335C2×SD16—341no—
336C2×D8—171no—
337C2×D8—171no—
338C2×D8—342no—
339C2×D8—341no—
340C2×D8—681no—
341C2×D8C22×D1711yescharacteristic
342C22×C8C22×D1711yescharacteristic
343C22×C8C22×D1711yescharacteristic
344C4⋊Q8—21no—
345#124—341no—
346#123—41no—
347#123—41no—
348#123—681no—
349C22⋊Q8—41no—
350C22⋊Q8—341no—
351#121—21no—
352#121—21no—
353#121—341no—
354#121—681no—
355#120—681no—
356C4×D4—21no—
357C4×D4—341no—
358C4×D4C22⋊D1711yescharacteristic
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C22⋊C4—681no—
362SD32—681no—
363D16—342no—
364D16—681no—
365M32—681no—
366C2×C16—171no—
367C2×C16—171no—
368C2×C16—171no—
369C2×C16—171no—
370C2×C16—681no—
371#107—21no—
372#107—21no—
373#107—21no—
374#107—171no—
375#107C22×D1711yescharacteristic
376#107C22×D1711yescharacteristic
377#107C22×D1711yescharacteristic
378C4⋊C8C22⋊D1711yescharacteristic
379#103—341no—
380#102—21no—
381#102—21no—
382#102—21no—
383#102—341no—
384#102—341no—
385C22⋊C8C22⋊D1711yescharacteristic
386C22⋊C8C22⋊D1711yescharacteristic
387C4×C8C22×D1711yescharacteristic
388C17#3387311yescharacteristic, complemented, Sylow
389C24—681no—
390#41—84no—
391#41—682no—
392#41—1361no—
393C2×Q8—41no—
394C2×Q8—341no—
395C2×D4—21no—
396C2×D4—41no—
397C2×D4—41no—
398C2×D4—341no—
399C2×D4—341no—
400C2×D4—682no—
401C2×D4—681no—
402C2×D4—681no—
403C2×D4—681no—
404C2×D4—1361no—
405C2×D4#6322811yescharacteristic
406C22×C4—41no—
407C22×C4—41no—
408C22×C4—41no—
409C22×C4—681no—
410C22×C4—681no—
411C22×C4C2×C22⋊D1711yescharacteristic
412C22×C4C2×C22⋊D1711yescharacteristic
413Q16—341no—
414Q16—341no—
415SD16—682no—
416SD16—1361no—
417D8—21no—
418D8—21no—
419D8—172no—
420D8—341no—
421D8—341no—
422D8—341no—
423D8—682no—
424C2×C8—21no—
425C2×C8—21no—
426C2×C8—21no—
427C2×C8—21no—
428C2×C8C2×C22⋊D1711yescharacteristic
429C2×C8C2×C22⋊D1711yescharacteristic
430C2×C8C2×C22⋊D1711yescharacteristic
431C2×C8C23×D1711yescharacteristic
432C4⋊C4—21no—
433C4⋊C4—21no—
434C4⋊C4—21no—
435C4⋊C4—41no—
436C4⋊C4—41no—
437C4⋊C4—41no—
438C4⋊C4—341no—
439C4⋊C4—681no—
440C4⋊C4#6322811yescharacteristic
441C22⋊C4—41no—
442C22⋊C4—41no—
443C22⋊C4—41no—
444C22⋊C4—681no—
445C22⋊C4—681no—
446C22⋊C4—681no—
447C22⋊C4—681no—
448C22⋊C4—681no—
449C22⋊C4#6322811yescharacteristic
450C22⋊C4#6322811yescharacteristic
451C42C2×C22⋊D1711yescharacteristic
452C16—341no—
453C16—341no—
454C16—341no—
455C16—341no—
456C23—41no—
457C23—2721no—
458C23—681no—
459C23—681no—
460C23—1362no—
461C23—1362no—
462C23C2×#6322811yescharacteristic
463C23C2×#6322811yescharacteristic
464Q8—82no—
465Q8—681no—
466Q8—681no—
467D4—22no—
468D4—41no—
469D4—41no—
470D4—82no—
471D4—82no—
472D4—2721no—
473D4—342no—
474D4—681no—
475D4—681no—
476D4—681no—
477D4—1362no—
478D4—1362no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—82no—
487C2×C4—82no—
488C2×C4—82no—
489C2×C4—2721no—
490C2×C4—681no—
491C2×C4—681no—
492C2×C4—1362no—
493C2×C4C2×#6322811yescharacteristic
494C2×C4C2×#6322811yescharacteristic
495C2×C4C2×#6322811yescharacteristic
496C2×C4C2×#6322811yescharacteristic
497C2×C4C22×C22⋊D1711yescharacteristic
498C8—21no—
499C8—21no—
500C8—21no—
501C8#41×D1711yescharacteristic
502C8#1058769611yescharacteristic
503C22—21no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—81no—
509C22—81no—
510C22—81no—
511C22—2724no—
512C22—682no—
513C22—1361no—
514C22—1361no—
515C22—1361no—
516C22—1361no—
517C22—1361no—
518C22#1176324512yes—
519C22C22×#6322811yescharacteristic
520C4—21no—
521C4—21no—
522C4—21no—
523C4—21no—
524C4—81no—
525C4—81no—
526C4—81no—
527C4—1361no—
528C4—1361no—
529C4#1176344711yescharacteristic
530C4#1176361711yescharacteristic
531C2—22no—
532C2—41no—
533C2—161no—
534C2—2721no—
535C2—1362no—
536C2#1454059111yescharacteristic
537C2C2×#1176324511yescharacteristic
538C2#1454192811yescharacteristic
subgroupG/H
centerC22C22×#63228
commutator, cosocleC2×C8×C17C24
FrattiniC2×C8C23×D17
FittingC17×#3334C2
socleC22×C17C22×D8
hypercenter#3334D17
hypocenterC17#33873
LCSG ▷ C2×C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #3334

Complements

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

NH ≅ G/Ntype
1. #14540471C2semidirect
2. #14531023C2semidirect
3. #14530981C2semidirect
4. #14530969C2semidirect
5. #14530928C2semidirect
6. #14530885C2semidirect
7. #14530878C2semidirect
8. #14530839C2semidirect
9. #14530705C2semidirect
10. #14530695C2semidirect
11. #14530658C2semidirect
12. #14530610C2semidirect
13. #14530494C2semidirect
14. C2×#11762609C2semidirect
15. C17×#3334C2semidirect
19. C2×#10587498C22semidirect
22. C2×#10587483C22semidirect
31. #11762636C22semidirect
32. #11762636C22semidirect
33. #11762636C22semidirect
34. C4⋊#63214C22semidirect
35. #11762612C22semidirect
36. #11762612C22semidirect
37. #11762612C22semidirect
38. #11762610C22semidirect
46. C22⋊#63214C22semidirect
47. #11762585C22semidirect
49. C17×#500C22semidirect
54. C17×#466C22semidirect
55. C4×D8×C17C22semidirect
58. C2×C17×#107C22semidirect
179. D136#41semidirect
234. #3334D17semidirect
286. #500C2×D17semidirect
294. #466C2×D17semidirect
299. C4×D8C2×D17semidirect
302. C2×#107C2×D17semidirect
388. C17#33873semidirect

Maximal subgroups

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

subgroupindex
#145404712
#145310232
#145309812
#145309692
#145309282
#145308852
#145308782
#145308392
#145307052
#145306952
#145306582
#145306102
#145304942
C2×#117626092
C17×#33342
#3387317