Finite Group Databasebeta

← #17005454

Subgroups — #17005454

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#14538866C211yesmaximal, characteristic
2#14537788C211yesmaximal, characteristic
3M16×Dic34C211yesmaximal, characteristic, complemented
4#14527694C211yesmaximal, characteristic, complemented
5#14527676C211yesmaximal, characteristic, complemented
6#14527657C211yesmaximal, characteristic, complemented
7#14527643C211yesmaximal, characteristic, complemented
8#14527636C211yesmaximal, characteristic, complemented
9#14527629C211yesmaximal, characteristic, complemented
10#14527598C211yesmaximal, characteristic, complemented
11C8×Dic68C211yesmaximal, characteristic, complemented
12#14527573C211yesmaximal, characteristic, complemented
13#14527250C211yesmaximal, characteristic
14#14527180C211yesmaximal, characteristic, complemented
15C17×#1453C211yesmaximal, characteristic, complemented
16#11763343C2211yescharacteristic
17C2×C4×Dic34C2211yescharacteristic
18#11763140C411yescharacteristic
19#11763123C411yescharacteristic
20#11763117C411yescharacteristic
21#11763117C411yescharacteristic
22#11763032C411yescharacteristic
23#11763032C411yescharacteristic
24#11762967C411yescharacteristic
25#11762950C411yescharacteristic
26#11762939C2211yescharacteristic
27#11762939C2211yescharacteristic
28#11762939C2211yescharacteristic
29#11762937—21no—
30#11762937—21no—
31C8×Dic34C2211yescharacteristic
32C8×Dic34C2211yescharacteristic
33C8×Dic34C2211yescharacteristic
34C4×Dic68C2211yescharacteristic
35C4×Dic68C2211yescharacteristic
36C4×#63219C2211yescharacteristic
37C4×#63219C2211yescharacteristic
38#11762888C2211yescharacteristic
39#11762885—21no—
40#11762878—21no—
41C8×D68C2211yescharacteristic
42#11762871—21no—
43#11762862C2211yescharacteristic
44#11762833C2211yescharacteristic
45#11762832—21no—
46#11762766—21no—
47M16×Dic17—21no—
48#11762562C2211yescharacteristic
49#11762562C2211yescharacteristic
50#11762560C2211yescharacteristic
51#11762560C2211yescharacteristic
52#11762541C2211yescharacteristic
53#11762541C2211yescharacteristic
54#11762541C2211yescharacteristic
55#11762541C2211yescharacteristic
56#11762541C2211yescharacteristic
57#11762541C2211yescharacteristic
58#11762538C2211yescharacteristic
59#11762538C2211yescharacteristic
60C17×#431C2211yescharacteristic
61C17×#431C2211yescharacteristic
62C4×M16×C17C2211yescharacteristic
63C17×#322C2211yescharacteristic
64C17×#322C2211yescharacteristic
65C17×#322C2211yescharacteristic
66C82×C17C2211yescharacteristic
67C22×Dic34C2×C411yescharacteristic
68C2×M16×C17D411yescharacteristic
69C2×M16×C17D411yescharacteristic
70C2×C42×C17C2311yescharacteristic
71#10587616C2×C411yescharacteristic
72#10587615—21no—
73C4×C22⋊D17—21no—
74C2×C4⋊Dic17C2×C411yescharacteristic
75#10587610C2×C411yescharacteristic
76C2×#63225—21no—
77C2×C4×Dic17—21no—
78C2×#63223—21no—
79C2×Dic68C2×C411yescharacteristic
80C2×Dic68C2×C411yescharacteristic
81C2×#63219C2×C411yescharacteristic
82C2×#63219C2×C411yescharacteristic
83C2×#63218—21no—
84C2×C8×D17—21no—
85#10587562—21no—
86#10587561C2×C411yescharacteristic
87C4×D68C2311yescharacteristic
88#10587558—21no—
89#10587556C2×C411yescharacteristic
90C4×Dic34—21no—
91C4×Dic34—21no—
92C4×Dic34C2×C411yescharacteristic
93C4×Dic34C2×C411yescharacteristic
94C4×Dic34C2311yescharacteristic
95C4×Dic34C2311yescharacteristic
96C4×Dic34C2311yescharacteristic
97C17×C4⋊C8—21no—
98C17×C4⋊C8C2×C411yescharacteristic
99C17×C4⋊C8C2×C411yescharacteristic
100C17×C22⋊C8—21no—
101C17×C22⋊C8C2×C411yescharacteristic
102C17×C22⋊C8C2×C411yescharacteristic
103C17×#97D411yescharacteristic
104C17×#97D411yescharacteristic
105C4×C8×C17C2311yescharacteristic
106C4×C8×C17C2311yescharacteristic
107C4×C8×C17C2311yescharacteristic
108C4×C8×C17C2311yescharacteristic
109C4×C8×C17C2311yescharacteristic
110C4×C8×C17C2311yescharacteristic
111C22⋊#3622—21no—
112#10587492C2×C411yescharacteristic
113#10587492C2×C411yescharacteristic
114#10587491—21no—
115#10587491—21no—
116#10587489C2×C411yescharacteristic
117#10587489C2×C411yescharacteristic
118#10587488C2×C411yescharacteristic
119#10587488C2×C411yescharacteristic
120#10587487C2×C411yescharacteristic
121#10587487C2×C411yescharacteristic
122#10587487C2×C411yescharacteristic
123#10587487C2×C411yescharacteristic
124#10587487C2×C411yescharacteristic
125#10587487C2×C411yescharacteristic
126#10587486—21no—
127#10587486—21no—
128#10587486—21no—
129#10587485—21no—
130#10587485—21no—
131#10587485—21no—
132#10587485—21no—
133#10587485—21no—
134#10587485—21no—
135C8×Dic17—21no—
136C8×Dic17—21no—
137C8×Dic17—21no—
138C4⋊#3622—21no—
139C4⋊#3622C2311yescharacteristic
140C4⋊#3622C2311yescharacteristic
141C4⋊#3622C2311yescharacteristic
142C4⋊#3622C2311yescharacteristic
143C4×#3622—21no—
144C22×C4×C17C22×C411yescharacteristic
145C22×C4×C17C2×D411yescharacteristic
146C22×C4×C17#4111yescharacteristic
147C2×C22⋊D17—21no—
148C22×Dic17—21no—
149C22×Dic17—21no—
150C2×D68C22×C411yescharacteristic
151C2×C4×D17—21no—
152C2×Dic34—22no—
153C2×Dic34—21no—
154C2×Dic34—41no—
155C2×Dic34C22×C411yescharacteristic
156C2×Dic34C22×C411yescharacteristic
157C2×Dic34C22×C411yescharacteristic
158M16×C17—22no—
159M16×C17—41no—
160C2×C8×C17—21no—
161C2×C8×C17—21no—
162C2×C8×C17C22×C411yescharacteristic
163C2×C8×C17C22×C411yescharacteristic
164C2×C8×C17C22×C411yescharacteristic
165C2×C8×C17C22×C411yescharacteristic
166C2×C8×C17C2×D411yescharacteristic
167C2×C8×C17C2×D411yescharacteristic
168C2×C8×C17C2×D411yescharacteristic
169C2×C8×C17C2×D411yescharacteristic
170C42×C17C22×C411yescharacteristic
171C42×C17C2×D411yescharacteristic
172C42×C17#4111yescharacteristic
173C42×C17C2411yescharacteristic
174C22⋊Dic17—21no—
175#63227—21no—
176#63227—21no—
177#63227—21no—
178#63227—21no—
179C4⋊Dic17—21no—
180C4⋊Dic17C22×C411yescharacteristic
181C4⋊Dic17C22×C411yescharacteristic
182C4⋊Dic17C22×C411yescharacteristic
183C4⋊Dic17C22×C411yescharacteristic
184#63225—21no—
185#63225—21no—
186#63225—21no—
187#63225—21no—
188#63225—21no—
189#63225—21no—
190#63225—21no—
191#63225—21no—
192C4×Dic17—21no—
193C4×Dic17—21no—
194C4×Dic17—21no—
195C4×Dic17—21no—
196C4×Dic17—21no—
197#63223—42no—
198C2×#3622—21no—
199C2×#3622—21no—
200C2×#3622—21no—
201C2×#3622—21no—
202Dic68—22no—
203Dic68—41no—
204#63219—22no—
205#63219—41no—
206#63218—42no—
207C8×D17—42no—
208#18012—171nomaximal, Sylow
209C23×C17C4×D411yescharacteristic
210C22×D17—21no—
211C2×C4×C17—21no—
212C2×C4×C17—21no—
213C2×C4×C17—21no—
214C2×C4×C17—21no—
215C2×C4×C17—41no—
216C2×C4×C17C4×D411yescharacteristic
217C2×C4×C17C4×D411yescharacteristic
218C2×C4×C17C4×D411yescharacteristic
219C2×C4×C17C23×C411yescharacteristic
220C2×C4×C17C22×D411yescharacteristic
221C2×C4×C17C2×#4111yescharacteristic
222C22⋊D17—81no—
223C2×Dic17—21no—
224C2×Dic17—21no—
225C2×Dic17—21no—
226C2×Dic17—21no—
227C2×Dic17—21no—
228C2×Dic17—21no—
229C2×Dic17—21no—
230C2×Dic17—42no—
231C2×Dic17—81no—
232D68—21no—
233D68—21no—
234C4×D17—41no—
235C4×D17—41no—
236Dic34—21no—
237Dic34—21no—
238Dic34—21no—
239Dic34—21no—
240Dic34—21no—
241Dic34—42no—
242Dic34#13112yes—
243C8×C17—21no—
244C8×C17—21no—
245C8×C17—21no—
246C8×C17—21no—
247C8×C17—21no—
248C8×C17—21no—
249C8×C17—21no—
250C8×C17—41no—
251C8×C17—41no—
252C8×C17#13712yes—
253#3622—41no—
254#3622—41no—
255#3622—41no—
256#3622—41no—
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#1495—171no—
270#1479—171no—
271#1453D1711yescharacteristic, complemented
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×C17C2×#13111yescharacteristic
284C4×C17#56811yescharacteristic
285C4×C17C2×#13711yescharacteristic
286C4×C17#57511yescharacteristic
287Dic17—22no—
288Dic17—41no—
289Dic17—41no—
290Dic17—41no—
291Dic17—41no—
292Dic17—41no—
293Dic17—41no—
294#529—171no—
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#431C2×D1711yescharacteristic
323#431C2×D1711yescharacteristic
324#423—171no—
325#423—341no—
326#405—341no—
327C4×M16—341no—
328C4×M16C2×D1711yescharacteristic
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⋊C8—171no—
338Q8⋊C8—171no—
339D4⋊C8—171no—
340D4⋊C8—171no—
341#322C2×D1711yescharacteristic
342#322C2×D1711yescharacteristic
343#322C2×D1711yescharacteristic
344C82C2×D1711yescharacteristic
345C2×C17—41no—
346C2×C17#293311yescharacteristic
347C2×C17C4×#13711yescharacteristic
348C2×C17#295711yescharacteristic
349D17—81no—
350C22×Q8—171no—
351C2×Q16—171no—
352C2×Q16—171no—
353C2×SD16—171no—
354C2×SD16—171no—
355C2×M16—341no—
356C2×M16—341no—
357C2×M16D6811yescharacteristic
358C2×M16D6811yescharacteristic
359C22×C8—341no—
360#126—341no—
361#125—171no—
362#124—171no—
363#123—341no—
364C22⋊Q8—171no—
365#121—171no—
366C4×Q8—171no—
367C4×Q8—171no—
368C4×Q8—171no—
369C4×Q8—171no—
370C4×Q8—171no—
371C4×Q8—341no—
372C4×Q8—341no—
373C4×D4—171no—
374C4×D4—341no—
375#117—341no—
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—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⋊C8C4×D1711yescharacteristic
397C4⋊C8C4×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—341no—
408C22⋊C8—341no—
409C22⋊C8—341no—
410C22⋊C8C4×D1711yescharacteristic
411C22⋊C8C4×D1711yescharacteristic
412#97—341no—
413#97—341no—
414#97—341no—
415#97D6811yescharacteristic
416#97D6811yescharacteristic
417C4×C8—341no—
418C4×C8—341no—
419C4×C8—341no—
420C4×C8—341no—
421C4×C8C22×D1711yescharacteristic
422C4×C8C22×D1711yescharacteristic
423C4×C8C22×D1711yescharacteristic
424C4×C8C22×D1711yescharacteristic
425C4×C8C22×D1711yescharacteristic
426C4×C8C22×D1711yescharacteristic
427C17#1801211yescharacteristic, complemented, Sylow
428C2×Q8—171no—
429C2×Q8—171no—
430C2×Q8—171no—
431C2×Q8—342no—
432C2×Q8—341no—
433C2×Q8—681no—
434C2×D4—171no—
435C2×D4—341no—
436C22×C4—341no—
437C22×C4—341no—
438C22×C4—341no—
439C22×C4C2×C4×D1711yescharacteristic
440C22×C4C2×D6811yescharacteristic
441C22×C4#6325211yescharacteristic
442Q16—342no—
443Q16—681no—
444SD16—342no—
445SD16—681no—
446M16—22no—
447M16—41no—
448M16—682no—
449M16—682no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—341no—
453C2×C8—341no—
454C2×C8—341no—
455C2×C8—341no—
456C2×C8—682no—
457C2×C8C2×C4×D1711yescharacteristic
458C2×C8C2×C4×D1711yescharacteristic
459C2×C8C2×C4×D1711yescharacteristic
460C2×C8C2×C4×D1711yescharacteristic
461C2×C8C2×D6811yescharacteristic
462C2×C8C2×D6811yescharacteristic
463C2×C8C2×D6811yescharacteristic
464C2×C8C2×D6811yescharacteristic
465C4⋊C4—171no—
466C4⋊C4—171no—
467C4⋊C4—171no—
468C4⋊C4—171no—
469C4⋊C4—341no—
470C4⋊C4—341no—
471C4⋊C4—341no—
472C4⋊C4—341no—
473C4⋊C4—341no—
474C4⋊C4—341no—
475C4⋊C4—341no—
476C4⋊C4—341no—
477C4⋊C4—341no—
478C22⋊C4—341no—
479C22⋊C4—341no—
480C22⋊C4—341no—
481C22⋊C4—341no—
482C22⋊C4—341no—
483C42—341no—
484C42—341no—
485C42—341no—
486C42—341no—
487C42—341no—
488C42C2×C4×D1711yescharacteristic
489C42C2×D6811yescharacteristic
490C42#6325211yescharacteristic
491C42C23×D1711yescharacteristic
492C23—341no—
493C23C4×D6811yescharacteristic
494Q8—172no—
495Q8—341no—
496Q8—341no—
497Q8—341no—
498Q8—341no—
499Q8—341no—
500Q8—682no—
501D4—341no—
502D4—341no—
503D4—1361no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—41no—
509C2×C4—341no—
510C2×C4—341no—
511C2×C4—341no—
512C2×C4—341no—
513C2×C4—341no—
514C2×C4—341no—
515C2×C4—341no—
516C2×C4—682no—
517C2×C4—681no—
518C2×C4—681no—
519C2×C4—1361no—
520C2×C4C4×D6811yescharacteristic
521C2×C4C4×D6811yescharacteristic
522C2×C4C4×D6811yescharacteristic
523C2×C4C22×C4×D1711yescharacteristic
524C2×C4C22×D6811yescharacteristic
525C2×C4C2×#6325211yescharacteristic
526C8—21no—
527C8—21no—
528C8—21no—
529C8—21no—
530C8—21no—
531C8—21no—
532C8—21no—
533C8—41no—
534C8—41no—
535C8—681no—
536C8—681no—
537C8—681no—
538C8—681no—
539C8#1058759512yes—
540C22—21no—
541C22—21no—
542C22—21no—
543C22—681no—
544C22—681no—
545C22—681no—
546C22C2×C4×D6811yescharacteristic
547C4—21no—
548C4—21no—
549C4—21no—
550C4—21no—
551C4—342no—
552C4—681no—
553C4—681no—
554C4—681no—
555C4—681no—
556C4—681no—
557C4—681no—
558C4#131×D1711yescharacteristic
559C4#1176357411yescharacteristic
560C4C2×#1058759511yescharacteristic
561C4#1176360911yescharacteristic
562C2—41no—
563C2—1361no—
564C2#1453751211yescharacteristic
565C2C4×#1058759511yescharacteristic
566C2#1453770211yescharacteristic
subgroupG/H
centerC2×C4C22×D68
commutatorC2×C4×C17C23×C4
FrattiniC42C23×D17
FittingC17×#1453C2
socleC22×C17C2×C4×D4
prime radical#10587616C2×C4
cosocleC42×C17C24
hypercenter#1453D17
hypocenterC17#18012
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C4×M16 ◁ #1453

Complements

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

NH ≅ G/Ntype
3. M16×Dic34C2semidirect
4. #14527694C2semidirect
5. #14527676C2semidirect
6. #14527657C2semidirect
7. #14527643C2semidirect
8. #14527636C2semidirect
9. #14527629C2semidirect
10. #14527598C2semidirect
11. C8×Dic68C2semidirect
12. #14527573C2semidirect
14. #14527180C2semidirect
15. C17×#1453C2semidirect
271. #1453D17semidirect
427. C17#18012semidirect

Maximal subgroups

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

subgroupindex
#145388662
#145377882
M16×Dic342
#145276942
#145276762
#145276572
#145276432
#145276362
#145276292
#145275982
C8×Dic682
#145275732
#145272502
#145271802
C17×#14532
#1801217