Finite Group Databasebeta

← #17004281

Subgroups — #17004281

Order 4352.

626 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14538802C211yesmaximal, characteristic
2#14537759C211yesmaximal, characteristic, complemented
3#14527662C211yesmaximal, characteristic, complemented
4#14527655C211yesmaximal, characteristic, complemented
5#14527648C211yesmaximal, characteristic, complemented
6#14527641C211yesmaximal, characteristic, complemented
7#14527606C211yesmaximal, characteristic, complemented
8#14527601C211yesmaximal, characteristic, complemented
9#14527596C211yesmaximal, characteristic, complemented
10#14527594C211yesmaximal, characteristic, complemented
11#14527562C211yesmaximal, characteristic, complemented
12#14527218C211yesmaximal, characteristic, complemented
13#14527190C211yesmaximal, characteristic, complemented
14#14527076C211yesmaximal, characteristic, complemented
15C8×#41×C17C211yesmaximal, characteristic, complemented
16#11763343C2211yescharacteristic
17#11763150C411yescharacteristic
18#11763133C411yescharacteristic
19#11763116C411yescharacteristic
20#11763109C411yescharacteristic
21#11763031C411yescharacteristic
22#11763024C411yescharacteristic
23#11762971C411yescharacteristic
24#11762954C411yescharacteristic
25#11762939C2211yescharacteristic
26C8×Dic34C2211yescharacteristic
27C4×#63231C2211yescharacteristic
28C4×#63230C2211yescharacteristic
29C4×#63229C2211yescharacteristic
30C4×#63228C2211yescharacteristic
31#11762888C2211yescharacteristic
32#11762880—21no—
33C8×D68C2211yescharacteristic
34C8×C22⋊D17—21no—
35#11762868—21no—
36#11762866C2211yescharacteristic
37#11762862C2211yescharacteristic
38#11762862C2211yescharacteristic
39#11762763—21no—
40#11762561C2211yescharacteristic
41#11762561C2211yescharacteristic
42#11762559C2211yescharacteristic
43#11762559C2211yescharacteristic
44Q8⋊#3622C2211yescharacteristic
45Q8⋊#3622C2211yescharacteristic
46#11762539C2211yescharacteristic
47#11762539C2211yescharacteristic
48D4⋊#3622C2211yescharacteristic
49D4⋊#3622C2211yescharacteristic
50#11762536C2211yescharacteristic
51#11762536C2211yescharacteristic
52#11762531C2211yescharacteristic
53#11762531C2211yescharacteristic
54#11762531C2211yescharacteristic
55#11762531C2211yescharacteristic
56C4×#41×C17C2211yescharacteristic
57C8×Q8×C17C2211yescharacteristic
58C8×Q8×C17C2211yescharacteristic
59C8×D4×C17—21no—
60C8×D4×C17—21no—
61C8×D4×C17C2211yescharacteristic
62C8×D4×C17C2211yescharacteristic
63C17×#431—21no—
64C17×#431C2211yescharacteristic
65C2×C4×C8×C17—21no—
66C2×C4×C8×C17C2211yescharacteristic
67C2×#41×C17C2×C411yescharacteristic
68C22×C8×C17—21no—
69C22×C8×C17—21no—
70C22×C8×C17D411yescharacteristic
71C22×C8×C17D411yescharacteristic
72C4×Q8×C17C2×C411yescharacteristic
73C4×Q8×C17C2311yescharacteristic
74C4×D4×C17—21no—
75C4×D4×C17—21no—
76C4×D4×C17C2×C411yescharacteristic
77C4×D4×C17C2311yescharacteristic
78C17×#117—21no—
79C17×#117C2×C411yescharacteristic
80C2×C42×C17—21no—
81C2×C42×C17C2311yescharacteristic
82C2×#63231C2×C411yescharacteristic
83C2×#63230C2×C411yescharacteristic
84C2×#63229C2×C411yescharacteristic
85C2×#63228C2×C411yescharacteristic
86#10587616C2×C411yescharacteristic
87#10587615—21no—
88C4×C22⋊D17—21no—
89#10587610C2×C411yescharacteristic
90C2×#63218—21no—
91C2×C8×D17—21no—
92#10587562—21no—
93#10587561C2×C411yescharacteristic
94C4×D68C2311yescharacteristic
95#10587558—21no—
96#10587556C2×C411yescharacteristic
97C4×Dic34C2311yescharacteristic
98C17×C4⋊C8—21no—
99C17×C4⋊C8—21no—
100C17×C4⋊C8C2311yescharacteristic
101C17×C4⋊C8C2311yescharacteristic
102C17×C22⋊C8—21no—
103C17×C22⋊C8—21no—
104C17×C22⋊C8—21no—
105C4×C8×C17—21no—
106C4×C8×C17—21no—
107C4×C8×C17—21no—
108C4×C8×C17D411yescharacteristic
109C4×C8×C17D411yescharacteristic
110C4×C8×C17C2311yescharacteristic
111C4×C8×C17C2311yescharacteristic
112#10587506C2×C411yescharacteristic
113#10587506C2×C411yescharacteristic
114#10587503C2×C411yescharacteristic
115#10587503C2×C411yescharacteristic
116C22⋊#3622—21no—
117C22⋊#3622—21no—
118C22⋊#3622C2×C411yescharacteristic
119C22⋊#3622C2×C411yescharacteristic
120#10587491—21no—
121#10587491—21no—
122#10587486—21no—
123#10587485—21no—
124#10587485—21no—
125C8×Dic17—21no—
126#10587481C2×C411yescharacteristic
127#10587481C2×C411yescharacteristic
128#10587480C2×C411yescharacteristic
129#10587480C2×C411yescharacteristic
130#10587479C2×C411yescharacteristic
131#10587479C2×C411yescharacteristic
132#10587478C2×C411yescharacteristic
133#10587478C2×C411yescharacteristic
134C4⋊#3622—21no—
135C4⋊#3622C2×C411yescharacteristic
136C4⋊#3622C2×C411yescharacteristic
137C4⋊#3622C2311yescharacteristic
138C4⋊#3622C2311yescharacteristic
139#10587474—21no—
140C4×#3622C2311yescharacteristic
141C4×#3622C2311yescharacteristic
142C4×#3622C2311yescharacteristic
143C4×#3622C2311yescharacteristic
144#41×C17—22no—
145#41×C17—22no—
146C2×Q8×C17C22×C411yescharacteristic
147C2×D4×C17—21no—
148C2×D4×C17C22×C411yescharacteristic
149C22×C4×C17—21no—
150C22×C4×C17—21no—
151C22×C4×C17—21no—
152C22×C4×C17C22×C411yescharacteristic
153C22×C4×C17C2×D411yescharacteristic
154C22×C4×C17#4111yescharacteristic
155C2×C22⋊D17—21no—
156C2×D68C22×C411yescharacteristic
157C2×C4×D17—21no—
158C2×Dic34C22×C411yescharacteristic
159C2×C8×C17—21no—
160C2×C8×C17—21no—
161C2×C8×C17—41no—
162C2×C8×C17—41no—
163C2×C8×C17—42no—
164C2×C8×C17—42no—
165C2×C8×C17C2×D411yescharacteristic
166C2×C8×C17C2×D411yescharacteristic
167C2×C8×C17C2×D411yescharacteristic
168C2×C8×C17C2×D411yescharacteristic
169C4⋊C4×C17—21no—
170C4⋊C4×C17—21no—
171C4⋊C4×C17C22×C411yescharacteristic
172C4⋊C4×C17C22×C411yescharacteristic
173C22⋊C4×C17—21no—
174C22⋊C4×C17—21no—
175C22⋊C4×C17—21no—
176C42×C17—21no—
177C42×C17—21no—
178C42×C17—21no—
179C42×C17C22×C411yescharacteristic
180C42×C17C2×D411yescharacteristic
181C42×C17#4111yescharacteristic
182C42×C17C2411yescharacteristic
183C22⋊Dic17—21no—
184#63231—22no—
185#63230—22no—
186#63229—22no—
187#63228—22no—
188#63227—21no—
189#63227—21no—
190#63227—21no—
191#63227—21no—
192C4⋊Dic17C22×C411yescharacteristic
193C4⋊Dic17C22×C411yescharacteristic
194#63225—21no—
195#63225—21no—
196#63225—21no—
197#63225—21no—
198C4×Dic17—21no—
199C2×#3622—21no—
200C2×#3622—21no—
201C2×#3622—21no—
202C2×#3622—21no—
203C2×#3622C22×C411yescharacteristic
204C2×#3622C22×C411yescharacteristic
205C2×#3622C22×C411yescharacteristic
206C2×#3622C22×C411yescharacteristic
207#63218—42no—
208C8×D17—42no—
209#17909—171nomaximal, Sylow
210C23×C17—21no—
211C23×C17C4×D411yescharacteristic
212C22×D17—21no—
213Q8×C17—21no—
214Q8×C17#13112yes—
215D4×C17—24no—
216D4×C17—21no—
217D4×C17#13112yes—
218C2×C4×C17—24no—
219C2×C4×C17—21no—
220C2×C4×C17—21no—
221C2×C4×C17—21no—
222C2×C4×C17—21no—
223C2×C4×C17—21no—
224C2×C4×C17—21no—
225C2×C4×C17—21no—
226C2×C4×C17—41no—
227C2×C4×C17—42no—
228C2×C4×C17—41no—
229C2×C4×C17—41no—
230C2×C4×C17C4×D411yescharacteristic
231C2×C4×C17C4×D411yescharacteristic
232C2×C4×C17C4×D411yescharacteristic
233C2×C4×C17C23×C411yescharacteristic
234C2×C4×C17C22×D411yescharacteristic
235C2×C4×C17C2×#4111yescharacteristic
236C22⋊D17—42no—
237C2×Dic17—21no—
238C2×Dic17—21no—
239C2×Dic17—21no—
240D68—21no—
241D68—21no—
242C4×D17—41no—
243C4×D17—41no—
244Dic34—21no—
245Dic34—21no—
246C8×C17—21no—
247C8×C17—21no—
248C8×C17—21no—
249C8×C17—21no—
250C8×C17—41no—
251C8×C17—41no—
252#3622—21no—
253#3622—21no—
254#3622—21no—
255#3622—21no—
256#3622—41no—
257#3622—41no—
258#3622—41no—
259#3622—41no—
260#3102—171no—
261#2966—171no—
262C8×#41D1711yescharacteristic, complemented
263#1588—171no—
264#1587—171no—
265#1586—171no—
266#1585—171no—
267#1580—171no—
268#1579—171no—
269SD16⋊C8—171no—
270SD16⋊C8—171no—
271#1572—171no—
272#1488—171no—
273#1482—171no—
274#1452—171no—
275C22×C17—21no—
276C22×C17—22no—
277C22×C17—21no—
278C22×C17—21no—
279C22×C17—41no—
280C22×C17—41no—
281C22×C17C2×C4×D411yescharacteristic
282C2×D17—41no—
283C2×D17—41no—
284C2×D17—41no—
285C4×C17—21no—
286C4×C17—22no—
287C4×C17—21no—
288C4×C17—21no—
289C4×C17—21no—
290C4×C17—41no—
291C4×C17—41no—
292C4×C17C2×#13111yescharacteristic
293C4×C17C2×#13111yescharacteristic
294C4×C17#57511yescharacteristic
295C4×C17#57511yescharacteristic
296Dic17—41no—
297Dic17—41no—
298Dic17—41no—
299#529—171no—
300C4×#41C2×D1711yescharacteristic
301#485—171no—
302#482—171no—
303#479—171no—
304#478—171no—
305#464—171no—
306#463—171no—
307#452—171no—
308#449—171no—
309#446—171no—
310C8×Q8—171no—
311C8×Q8C2×D1711yescharacteristic
312C8×Q8C2×D1711yescharacteristic
313C4×Q16—171no—
314C4×SD16—171no—
315C4×SD16—171no—
316C4×D8—171no—
317#436—171no—
318#435—341no—
319C8×D4—21no—
320C8×D4—21no—
321C8×D4—171no—
322C8×D4—341no—
323C8×D4C2×D1711yescharacteristic
324C8×D4C2×D1711yescharacteristic
325#433—341no—
326#432—171no—
327#431—21no—
328#431—171no—
329#431—171no—
330#431C2×D1711yescharacteristic
331#405—341no—
332C2×C4×C8—21no—
333C2×C4×C8C2×D1711yescharacteristic
334#335—171no—
335#335—171no—
336#334—171no—
337#334—171no—
338Q8⋊C8—171no—
339Q8⋊C8—171no—
340Q8⋊C8—171no—
341Q8⋊C8—171no—
342D4⋊C8—171no—
343D4⋊C8—171no—
344D4⋊C8—171no—
345D4⋊C8—171no—
346#322—171no—
347#322—171no—
348#322—171no—
349#322—171no—
350C2×C17—41no—
351C2×C17—42no—
352C2×C17#292911yescharacteristic
353C2×C17#294311yescharacteristic
354C2×C17#295511yescharacteristic
355D17—81no—
356C2×#41C4×D1711yescharacteristic
357C2×Q16—171no—
358C2×SD16—171no—
359C2×SD16—171no—
360C2×D8—171no—
361C2×M16—341no—
362C22×C8—21no—
363C22×C8—21no—
364C22×C8—341no—
365C22×C8C22⋊D1711yescharacteristic
366C22×C8C22⋊D1711yescharacteristic
367#126—341no—
368#125—171no—
369#124—171no—
370#123—341no—
371C22⋊Q8—171no—
372#121—171no—
373C4×Q8—171no—
374C4×Q8C4×D1711yescharacteristic
375C4×Q8C22×D1711yescharacteristic
376C4×D4—21no—
377C4×D4—21no—
378C4×D4—171no—
379C4×D4—341no—
380C4×D4C4×D1711yescharacteristic
381C4×D4C22×D1711yescharacteristic
382#117—21no—
383#117—341no—
384#117C4×D1711yescharacteristic
385C2×C42—21no—
386C2×C42C22×D1711yescharacteristic
387#107—171no—
388#107—171no—
389#106—171no—
390#106—171no—
391C4⋊C8—21no—
392C4⋊C8—21no—
393C4⋊C8—171no—
394C4⋊C8—171no—
395C4⋊C8—171no—
396C4⋊C8—171no—
397C4⋊C8—341no—
398C4⋊C8—341no—
399C4⋊C8—341no—
400C4⋊C8C22×D1711yescharacteristic
401C4⋊C8C22×D1711yescharacteristic
402#103—171no—
403#103—171no—
404#103—171no—
405#103—171no—
406#102—171no—
407#102—171no—
408#102—171no—
409#102—171no—
410C22⋊C8—21no—
411C22⋊C8—21no—
412C22⋊C8—21no—
413C22⋊C8—171no—
414C22⋊C8—171no—
415C22⋊C8—341no—
416C22⋊C8—341no—
417C22⋊C8—341no—
418C22⋊C8—341no—
419#97—341no—
420#97—341no—
421C4×C8—21no—
422C4×C8—21no—
423C4×C8—21no—
424C4×C8—171no—
425C4×C8—171no—
426C4×C8—171no—
427C4×C8—171no—
428C4×C8—341no—
429C4×C8C22⋊D1711yescharacteristic
430C4×C8C22⋊D1711yescharacteristic
431C4×C8C22×D1711yescharacteristic
432C4×C8C22×D1711yescharacteristic
433C17#1790911yescharacteristic, complemented, Sylow
434#41—22no—
435#41—22no—
436C2×Q8—171no—
437C2×Q8C2×C4×D1711yescharacteristic
438C2×D4—21no—
439C2×D4—171no—
440C2×D4—341no—
441C2×D4C2×C4×D1711yescharacteristic
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—341no—
446C22×C4C2×C4×D1711yescharacteristic
447C22×C4#6325211yescharacteristic
448C22×C4C2×C22⋊D1711yescharacteristic
449Q16—342no—
450SD16—342no—
451SD16—342no—
452D8—342no—
453M16—682no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—41no—
457C2×C8—41no—
458C2×C8—42no—
459C2×C8—42no—
460C2×C8—171no—
461C2×C8—171no—
462C2×C8—171no—
463C2×C8—171no—
464C2×C8—341no—
465C2×C8—341no—
466C2×C8—341no—
467C2×C8—341no—
468C2×C8—682no—
469C2×C8C2×C22⋊D1711yescharacteristic
470C2×C8C2×C22⋊D1711yescharacteristic
471C2×C8C2×C22⋊D1711yescharacteristic
472C2×C8C2×C22⋊D1711yescharacteristic
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—171no—
476C4⋊C4—171no—
477C4⋊C4—341no—
478C4⋊C4—341no—
479C4⋊C4—341no—
480C4⋊C4—341no—
481C4⋊C4C2×C4×D1711yescharacteristic
482C4⋊C4C2×C4×D1711yescharacteristic
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—341no—
487C22⋊C4—341no—
488C22⋊C4—341no—
489C22⋊C4—341no—
490C22⋊C4—341no—
491C42—21no—
492C42—21no—
493C42—21no—
494C42—341no—
495C42C2×C4×D1711yescharacteristic
496C42#6325211yescharacteristic
497C42C2×C22⋊D1711yescharacteristic
498C42C23×D1711yescharacteristic
499C23—21no—
500C23—341no—
501C23C4×C22⋊D1711yescharacteristic
502Q8—21no—
503Q8—341no—
504Q8—341no—
505Q8#1058758712yes—
506D4—24no—
507D4—21no—
508D4—341no—
509D4—341no—
510D4—682no—
511D4#1058758712yes—
512C2×C4—24no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—41no—
521C2×C4—42no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—341no—
525C2×C4—341no—
526C2×C4—341no—
527C2×C4—681no—
528C2×C4—681no—
529C2×C4C4×C22⋊D1711yescharacteristic
530C2×C4C4×C22⋊D1711yescharacteristic
531C2×C4C4×C22⋊D1711yescharacteristic
532C2×C4C22×C4×D1711yescharacteristic
533C2×C4C2×#6325211yescharacteristic
534C2×C4C22×C22⋊D1711yescharacteristic
535C8—21no—
536C8—21no—
537C8—21no—
538C8—21no—
539C8—41no—
540C8—41no—
541C8—341no—
542C8—341no—
543C8—341no—
544C8—341no—
545C8—681no—
546C8—681no—
547C8—681no—
548C8—681no—
549C22—21no—
550C22—22no—
551C22—21no—
552C22—21no—
553C22—41no—
554C22—41no—
555C22—681no—
556C22—681no—
557C22—681no—
558C22C2×C4×C22⋊D1711yescharacteristic
559C4—21no—
560C4—22no—
561C4—21no—
562C4—21no—
563C4—21no—
564C4—41no—
565C4—41no—
566C4—681no—
567C4—681no—
568C4—681no—
569C4C2×#1058758711yescharacteristic
570C4C2×#1058758711yescharacteristic
571C4#1176360711yescharacteristic
572C4#1176360711yescharacteristic
573C2—41no—
574C2—42no—
575C2—1361no—
576C2#1453747811yescharacteristic
577C2#1453758211yescharacteristic
578C2#1453768511yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D17
commutatorC2×C4×C17C23×C4
FrattiniC42C23×D17
FittingC8×#41×C17C2
socleC22×C17C2×C4×D4
prime radical#11762954C4
cosocleC42×C17C24
hypercenterC8×#41D17
hypocenterC17#17909
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C2×C4×C8 ◁ C8×#41

Complements

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

NH ≅ G/Ntype
2. #14537759C2semidirect
3. #14527662C2semidirect
4. #14527655C2semidirect
5. #14527648C2semidirect
6. #14527641C2semidirect
7. #14527606C2semidirect
8. #14527601C2semidirect
9. #14527596C2semidirect
10. #14527594C2semidirect
11. #14527562C2semidirect
12. #14527218C2semidirect
13. #14527190C2semidirect
14. #14527076C2semidirect
15. C8×#41×C17C2semidirect
262. C8×#41D17semidirect
433. C17#17909semidirect

Maximal subgroups

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

subgroupindex
#145388022
#145377592
#145276622
#145276552
#145276482
#145276412
#145276062
#145276012
#145275962
#145275942
#145275622
#145272182
#145271902
#145270762
C8×#41×C172
#1790917