Finite Group Databasebeta

← #17005197

Subgroups — #17005197

Order 4352.

576 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14539348C211yesmaximal, characteristic
2#14537933C211yesmaximal, characteristic, complemented
3#14537929C211yesmaximal, characteristic, complemented
4#14527658C211yesmaximal, characteristic, complemented
5#14527652C211yesmaximal, characteristic, complemented
6#14527651C211yesmaximal, characteristic, complemented
7#14527645C211yesmaximal, characteristic, complemented
8#14527630C211yesmaximal, characteristic, complemented
9#14527624C211yesmaximal, characteristic, complemented
10#14527623C211yesmaximal, characteristic, complemented
11#14527617C211yesmaximal, characteristic, complemented
12#14527539C211yesmaximal, characteristic, complemented
13#14527250C211yesmaximal, characteristic, complemented
14#14527077C211yesmaximal, characteristic, complemented
15C17×#1495C211yesmaximal, characteristic, complemented
16#11763343C2211yescharacteristic
17#11763208C411yescharacteristic
18#11763191C411yescharacteristic
19#11763166C411yescharacteristic
20#11763163C411yescharacteristic
21#11763048C411yescharacteristic
22#11763043C411yescharacteristic
23#11763040C411yescharacteristic
24#11763036C411yescharacteristic
25#11762940C2211yescharacteristic
26#11762936C2211yescharacteristic
27Q8×#3622C2211yescharacteristic
28#11762933C2211yescharacteristic
29C4×#63231C2211yescharacteristic
30C4×#63230C2211yescharacteristic
31C4×#63229C2211yescharacteristic
32C4×#63228C2211yescharacteristic
33#11762887—21no—
34#11762887C2211yescharacteristic
35#11762886C2211yescharacteristic
36#11762885—21no—
37#11762881—21no—
38#11762878—21no—
39D4×#3622C2211yescharacteristic
40#11762874C2211yescharacteristic
41#11762870—21no—
42#11762869—21no—
43#11762862C2211yescharacteristic
44#11762836—21no—
45#11762834—21no—
46#11762833C2211yescharacteristic
47C2×C4×#3622C2211yescharacteristic
48#11762559C2211yescharacteristic
49#11762559C2211yescharacteristic
50#11762559C2211yescharacteristic
51#11762559C2211yescharacteristic
52#11762541C2211yescharacteristic
53#11762541C2211yescharacteristic
54#11762538C2211yescharacteristic
55#11762538C2211yescharacteristic
56#11762531C2211yescharacteristic
57#11762531C2211yescharacteristic
58#11762530C2211yescharacteristic
59#11762530C2211yescharacteristic
60C17×#529C2211yescharacteristic
61C17×#431C2211yescharacteristic
62C17×#423C2211yescharacteristic
63C17×Q8⋊C8C2211yescharacteristic
64C17×Q8⋊C8C2211yescharacteristic
65C17×D4⋊C8C2211yescharacteristic
66C17×D4⋊C8C2211yescharacteristic
67C2×M16×C17—21no—
68C17×#126—21no—
69C17×#125C2×C411yescharacteristic
70C17×#124C2×C411yescharacteristic
71C17×#123—21no—
72C17×C22⋊Q8C2×C411yescharacteristic
73C17×#121C2×C411yescharacteristic
74C4×Q8×C17C2311yescharacteristic
75C4×D4×C17—21no—
76C4×D4×C17C2311yescharacteristic
77C17×#117—21no—
78C2×C42×C17C2311yescharacteristic
79C2×#63231C2×C411yescharacteristic
80C2×#63230C2×C411yescharacteristic
81C2×#63229C2×C411yescharacteristic
82C2×#63228C2×C411yescharacteristic
83#10587616C2×C411yescharacteristic
84#10587615—21no—
85C4×C22⋊D17—21no—
86#10587610C2×C411yescharacteristic
87C2×#63223—21no—
88C2×#63223—21no—
89C22×#3622—21no—
90C22×#3622C2×C411yescharacteristic
91C22×#3622C2×C411yescharacteristic
92C2×#63218—21no—
93C2×C8×D17—21no—
94#10587562—21no—
95#10587561C2×C411yescharacteristic
96C4×D68C2311yescharacteristic
97#10587558—21no—
98#10587556C2×C411yescharacteristic
99C4×Dic34C2311yescharacteristic
100C17×C4⋊C8—21no—
101C17×C4⋊C8—21no—
102C17×C4⋊C8C2311yescharacteristic
103C17×C4⋊C8C2311yescharacteristic
104C17×C22⋊C8—21no—
105C4×C8×C17C2311yescharacteristic
106C4×C8×C17C2311yescharacteristic
107#10587506C2×C411yescharacteristic
108#10587506C2×C411yescharacteristic
109#10587503C2×C411yescharacteristic
110#10587503C2×C411yescharacteristic
111C22⋊#3622—21no—
112C22⋊#3622—21no—
113C22⋊#3622D411yescharacteristic
114C22⋊#3622D411yescharacteristic
115#10587491—21no—
116#10587491—21no—
117#10587486—21no—
118#10587485—21no—
119#10587485—21no—
120C8×Dic17—21no—
121#10587481C2×C411yescharacteristic
122#10587481C2×C411yescharacteristic
123#10587480C2×C411yescharacteristic
124#10587480C2×C411yescharacteristic
125#10587479C2×C411yescharacteristic
126#10587479C2×C411yescharacteristic
127#10587478C2×C411yescharacteristic
128#10587478C2×C411yescharacteristic
129C4⋊#3622—21no—
130C4⋊#3622—21no—
131C4⋊#3622—21no—
132C4⋊#3622D411yescharacteristic
133C4⋊#3622D411yescharacteristic
134C4⋊#3622C2311yescharacteristic
135C4⋊#3622C2311yescharacteristic
136#10587474—21no—
137C4×#3622—21no—
138C4×#3622C2×C411yescharacteristic
139C4×#3622C2×C411yescharacteristic
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
151C2×C22⋊D17—21no—
152C2×D68C22×C411yescharacteristic
153C2×C4×D17—21no—
154C2×Dic34C22×C411yescharacteristic
155M16×C17—81no—
156C2×C8×C17—21no—
157C2×C8×C17—21no—
158C2×C8×C17—21no—
159C2×C8×C17—21no—
160C4⋊C4×C17—21no—
161C4⋊C4×C17—21no—
162C4⋊C4×C17—21no—
163C4⋊C4×C17—21no—
164C4⋊C4×C17C22×C411yescharacteristic
165C4⋊C4×C17C22×C411yescharacteristic
166C22⋊C4×C17—21no—
167C22⋊C4×C17—21no—
168C22⋊C4×C17—21no—
169C22⋊C4×C17—21no—
170C22⋊C4×C17—21no—
171C42×C17—21no—
172C42×C17C22×C411yescharacteristic
173C42×C17C2×D411yescharacteristic
174C42×C17#4111yescharacteristic
175C42×C17C2411yescharacteristic
176C22⋊Dic17—21no—
177#63231—41no—
178#63230—41no—
179#63229—41no—
180#63228—41no—
181#63227—21no—
182#63227—21no—
183#63227—21no—
184#63227—21no—
185C4⋊Dic17C22×C411yescharacteristic
186C4⋊Dic17C22×C411yescharacteristic
187#63225—21no—
188#63225—21no—
189#63225—21no—
190#63225—21no—
191C4×Dic17—21no—
192#63223—81no—
193#63223—81no—
194C2×#3622—21no—
195C2×#3622—21no—
196C2×#3622—41no—
197C2×#3622—41no—
198C2×#3622—81no—
199C2×#3622C22×C411yescharacteristic
200C2×#3622C22×C411yescharacteristic
201C2×#3622C22×C411yescharacteristic
202C2×#3622C22×C411yescharacteristic
203C2×#3622C2×D411yescharacteristic
204C2×#3622C2×D411yescharacteristic
205C2×#3622C2×D411yescharacteristic
206C2×#3622C2×D411yescharacteristic
207#63218—81no—
208C8×D17—81no—
209#17993—171nomaximal, Sylow
210C23×C17—21no—
211C23×C17C4×D411yescharacteristic
212C22×D17—21no—
213Q8×C17—21no—
214Q8×C17—21no—
215D4×C17—21no—
216D4×C17—21no—
217D4×C17—81no—
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—21no—
225C2×C4×C17—41no—
226C2×C4×C17—41no—
227C2×C4×C17—41no—
228C2×C4×C17C4×D411yescharacteristic
229C2×C4×C17C4×D411yescharacteristic
230C2×C4×C17C4×D411yescharacteristic
231C2×C4×C17C23×C411yescharacteristic
232C2×C4×C17C22×D411yescharacteristic
233C2×C4×C17C2×#4111yescharacteristic
234C22⋊D17—81no—
235C2×Dic17—21no—
236C2×Dic17—21no—
237C2×Dic17—21no—
238D68—21no—
239D68—21no—
240C4×D17—41no—
241C4×D17—41no—
242Dic34—21no—
243Dic34—21no—
244C8×C17—41no—
245C8×C17—41no—
246C8×C17—41no—
247C8×C17—41no—
248#3622—21no—
249#3622—21no—
250#3622—21no—
251#3622—21no—
252#3622—21no—
253#3622—21no—
254#3622—21no—
255#3622—21no—
256#3622—41no—
257#3622—41no—
258#3168—171no—
259#2993—171no—
260#2993—171no—
261#1587—171no—
262#1587—171no—
263#1586—171no—
264#1586—171no—
265#1583—171no—
266#1583—171no—
267#1582—171no—
268#1582—171no—
269#1566—171no—
270#1495—171no—
271#1495D1711yescharacteristic, complemented
272#1452—171no—
273C22×C17—21no—
274C22×C17—21no—
275C22×C17—21no—
276C22×C17—41no—
277C22×C17—41no—
278C22×C17—41no—
279C22×C17C2×C4×D411yescharacteristic
280C2×D17—41no—
281C2×D17—41no—
282C2×D17—41no—
283C4×C17—21no—
284C4×C17—21no—
285C4×C17—21no—
286C4×C17—21no—
287C4×C17—41no—
288C4×C17—41no—
289C4×C17—41no—
290C4×C17#56811yescharacteristic
291C4×C17#56811yescharacteristic
292C4×C17#57711yescharacteristic
293C4×C17#57711yescharacteristic
294Dic17—41no—
295Dic17—41no—
296Dic17—41no—
297#529—171no—
298#529C2×D1711yescharacteristic
299#499—171no—
300#495—171no—
301#488—171no—
302#488—171no—
303#467—171no—
304#466—171no—
305#465—171no—
306#465—171no—
307#446—171no—
308#446—171no—
309C8×Q8—171no—
310C8×Q8—171no—
311C4×Q16—171no—
312C4×SD16—171no—
313C4×SD16—171no—
314C4×D8—171no—
315#436—171no—
316#436—171no—
317#436—341no—
318#436—341no—
319#435—341no—
320#435—341no—
321C8×D4—171no—
322C8×D4—171no—
323#433—341no—
324#433—341no—
325#431—171no—
326#431C2×D1711yescharacteristic
327#424—341no—
328#424—341no—
329#423—171no—
330#423C2×D1711yescharacteristic
331C2×C4×C8—171no—
332#334—171no—
333#334—171no—
334#334—171no—
335#334—171no—
336Q8⋊C8—171no—
337Q8⋊C8—171no—
338Q8⋊C8C2×D1711yescharacteristic
339Q8⋊C8C2×D1711yescharacteristic
340D4⋊C8—171no—
341D4⋊C8—171no—
342D4⋊C8C2×D1711yescharacteristic
343D4⋊C8C2×D1711yescharacteristic
344#322—171no—
345#322—171no—
346#322—171no—
347#322—171no—
348C2×C17—41no—
349C2×C17—81no—
350C2×C17#293211yescharacteristic
351C2×C17#295211yescharacteristic
352C2×C17#295711yescharacteristic
353D17—81no—
354C2×Q16—171no—
355C2×SD16—171no—
356C2×SD16—171no—
357C2×D8—171no—
358C2×M16—21no—
359C2×M16—341no—
360C2×M16—341no—
361C2×M16—341no—
362C22×C8—171no—
363C22×C8—171no—
364C22×C8—341no—
365C22×C8—341no—
366#126—21no—
367#126—341no—
368#125—171no—
369#125C4×D1711yescharacteristic
370#124—171no—
371#124C4×D1711yescharacteristic
372#123—21no—
373#123—341no—
374C22⋊Q8—171no—
375C22⋊Q8C4×D1711yescharacteristic
376#121—171no—
377#121C4×D1711yescharacteristic
378C4×Q8—171no—
379C4×Q8C22×D1711yescharacteristic
380C4×D4—21no—
381C4×D4—171no—
382C4×D4—341no—
383C4×D4C22×D1711yescharacteristic
384#117—21no—
385#117—341no—
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⋊C8—341no—
401C4⋊C8—341no—
402C4⋊C8C22×D1711yescharacteristic
403C4⋊C8C22×D1711yescharacteristic
404#103—171no—
405#103—171no—
406#103—171no—
407#103—171no—
408#102—171no—
409#102—171no—
410#102—171no—
411#102—171no—
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—171no—
422C4×C8—171no—
423C4×C8—171no—
424C4×C8—171no—
425C4×C8—171no—
426C4×C8—171no—
427C4×C8—341no—
428C4×C8—341no—
429C4×C8C22×D1711yescharacteristic
430C4×C8C22×D1711yescharacteristic
431C17#1799311yescharacteristic, complemented, Sylow
432C2×Q8—171no—
433C2×Q8C2×C4×D1711yescharacteristic
434C2×D4—21no—
435C2×D4—171no—
436C2×D4—341no—
437C2×D4C2×C4×D1711yescharacteristic
438C22×C4—21no—
439C22×C4—341no—
440C22×C4C2×C4×D1711yescharacteristic
441C22×C4D4×D1711yescharacteristic
442C22×C4#6325411yescharacteristic
443Q16—681no—
444SD16—681no—
445SD16—681no—
446D8—681no—
447M16—81no—
448M16—1361no—
449M16—1361no—
450M16—1361no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—171no—
456C2×C8—171no—
457C2×C8—171no—
458C2×C8—171no—
459C2×C8—171no—
460C2×C8—171no—
461C2×C8—171no—
462C2×C8—171no—
463C2×C8—341no—
464C2×C8—341no—
465C2×C8—681no—
466C2×C8—681no—
467C2×C8—1361no—
468C2×C8—1361no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—171no—
474C4⋊C4—171no—
475C4⋊C4—341no—
476C4⋊C4—341no—
477C4⋊C4—341no—
478C4⋊C4—341no—
479C4⋊C4C2×C4×D1711yescharacteristic
480C4⋊C4C2×C4×D1711yescharacteristic
481C22⋊C4—21no—
482C22⋊C4—21no—
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—341no—
493C42C2×C4×D1711yescharacteristic
494C42D4×D1711yescharacteristic
495C42#6325411yescharacteristic
496C42C23×D1711yescharacteristic
497C23—21no—
498C23—341no—
499C23#1058756711yescharacteristic
500Q8—21no—
501Q8—21no—
502Q8—341no—
503Q8—341no—
504D4—21no—
505D4—21no—
506D4—81no—
507D4—341no—
508D4—341no—
509D4—1361no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—341no—
521C2×C4—341no—
522C2×C4—341no—
523C2×C4—681no—
524C2×C4—681no—
525C2×C4#1058756711yescharacteristic
526C2×C4#1058756711yescharacteristic
527C2×C4#1058756711yescharacteristic
528C2×C4C22×C4×D1711yescharacteristic
529C2×C4C2×D4×D1711yescharacteristic
530C2×C4C2×#6325411yescharacteristic
531C8—41no—
532C8—41no—
533C8—41no—
534C8—41no—
535C8—341no—
536C8—341no—
537C8—341no—
538C8—341no—
539C8—341no—
540C8—341no—
541C8—341no—
542C8—341no—
543C8—681no—
544C8—681no—
545C22—21no—
546C22—21no—
547C22—21no—
548C22—41no—
549C22—41no—
550C22—41no—
551C22—681no—
552C22—681no—
553C22—681no—
554C22C2×#1058756711yescharacteristic
555C4—21no—
556C4—21no—
557C4—21no—
558C4—21no—
559C4—41no—
560C4—41no—
561C4—41no—
562C4—681no—
563C4—681no—
564C4—681no—
565C4#1176357411yescharacteristic
566C4#1176357411yescharacteristic
567C4#1176361811yescharacteristic
568C4#1176361911yescharacteristic
569C2—41no—
570C2—81no—
571C2—1361no—
572C2#1453749911yescharacteristic
573C2#1453766311yescharacteristic
574C2#1453769711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D17
commutatorC2×C4×C17C23×C4
FrattiniC42C23×D17
FittingC17×#1495C2
socleC22×C17C2×C4×D4
prime radical#11763043C4
cosocleC42×C17C24
hypercenter#1495D17
hypocenterC17#17993
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
2. #14537933C2semidirect
3. #14537929C2semidirect
4. #14527658C2semidirect
5. #14527652C2semidirect
6. #14527651C2semidirect
7. #14527645C2semidirect
8. #14527630C2semidirect
9. #14527624C2semidirect
10. #14527623C2semidirect
11. #14527617C2semidirect
12. #14527539C2semidirect
13. #14527250C2semidirect
14. #14527077C2semidirect
15. C17×#1495C2semidirect
271. #1495D17semidirect
431. C17#17993semidirect

Maximal subgroups

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

subgroupindex
#145393482
#145379332
#145379292
#145276582
#145276522
#145276512
#145276452
#145276302
#145276242
#145276232
#145276172
#145275392
#145272502
#145270772
C17×#14952
#1799317