Finite Group Databasebeta

← #17064276

Subgroups — #17064276

Order 4352.

782 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14531405C211yesmaximal, characteristic
2#14531399C211yesmaximal, characteristic
3#14530356C211yesmaximal, characteristic, complemented
4#14530355C211yesmaximal, characteristic, complemented
5#14530353C211yesmaximal, characteristic, complemented
6#14530352C211yesmaximal, characteristic, complemented
7#14530350C211yesmaximal, characteristic, complemented
8#14530346C211yesmaximal, characteristic, complemented
9#14530344C211yesmaximal, characteristic, complemented
10#14528502C211yesmaximal, characteristic
11#14528502C211yesmaximal, characteristic
12#14528499C211yesmaximal, characteristic
13D17×#340C211yesmaximal, characteristic
14#14528479C211yesmaximal, characteristic
15C17×#2099C211yesmaximal, characteristic, complemented
16C22×#63218C2211yescharacteristic
17C22×C8×D17C2211yescharacteristic
18C2×#10587578C2211yescharacteristic
19C2×#10587578C2211yescharacteristic
20C2×#10587558C2211yescharacteristic
21C2×C4⋊C4×D17C2211yescharacteristic
22C2×C4⋊C4×D17C2211yescharacteristic
23#11762708C2211yescharacteristic
24#11762707C2211yescharacteristic
25#11762706—21no—
26#11762705C2211yescharacteristic
27#11762704—21no—
28#11762704—21no—
29#11762704—21no—
30#11762680—21no—
31#11762680—21no—
32#11762678C2211yescharacteristic
33#11762675C2211yescharacteristic
34#11762674C2211yescharacteristic
35#11762668—21no—
36#11762666—21no—
37#11762572C2211yescharacteristic
38#11762572C2211yescharacteristic
39#11762572C2211yescharacteristic
40#11762572C2211yescharacteristic
41#11762571C2211yescharacteristic
42#11762571C2211yescharacteristic
43#11762571C2211yescharacteristic
44#11762571C2211yescharacteristic
45#11762571C2211yescharacteristic
46#11762571C2211yescharacteristic
47#11762571C2211yescharacteristic
48#11762571C2211yescharacteristic
49#11762564C2211yescharacteristic
50#11762563C2211yescharacteristic
51#11762563C2211yescharacteristic
52C17×#389C2211yescharacteristic
53C17×#384C2211yescharacteristic
54C17×#340C2211yescharacteristic
55C17×#340C2211yescharacteristic
56C17×#340C2211yescharacteristic
57C17×#340C2211yescharacteristic
58C17×#336C2211yescharacteristic
59C22×C4×D17—21no—
60C22×C4×D17—21no—
61C22×C4×D17C2311yescharacteristic
62C22×C8×C17C2311yescharacteristic
63C22×C8×C17C2311yescharacteristic
64C2×C4⋊C4×C17—21no—
65C2×C4⋊C4×C17—21no—
66C2×C4⋊C4×C17—21no—
67C2×C4⋊C4×C17C2311yescharacteristic
68C2×C4⋊C4×C17C2311yescharacteristic
69C2×C4⋊C4×C17C2311yescharacteristic
70C2×C4⋊C4×C17C2311yescharacteristic
71C2×C42×C17C2311yescharacteristic
72C2×#63227—21no—
73C2×#63227—21no—
74C2×#63227D411yescharacteristic
75C2×#63227D411yescharacteristic
76C2×C4⋊Dic17—21no—
77C2×C4⋊Dic17C2311yescharacteristic
78C2×C4⋊Dic17C2311yescharacteristic
79C2×C4⋊Dic17C2311yescharacteristic
80C2×C4⋊Dic17C2311yescharacteristic
81C2×#63225—21no—
82C2×#63225—21no—
83C2×#63225—21no—
84C2×#63225—21no—
85C2×#63225—21no—
86C2×#63225—21no—
87C2×#63225D411yescharacteristic
88C2×#63225D411yescharacteristic
89C2×C4×Dic17—21no—
90C2×C4×Dic17—21no—
91C2×C4×Dic17C2311yescharacteristic
92C22×#3622C2311yescharacteristic
93C22×#3622C2311yescharacteristic
94C2×#63218—22no—
95C2×#63218—22no—
96C2×#63218—22no—
97C2×C8×D17—22no—
98C2×C8×D17—22no—
99C2×C8×D17—22no—
100#10587578—22no—
101#10587578—22no—
102#10587578—22no—
103#10587578—22no—
104C4⋊C4×D17—22no—
105C4⋊C4×D17—22no—
106C4⋊C4×D17—22no—
107C4⋊C4×D17Q814yes—
108#10587558—22no—
109#10587558—22no—
110C17×#95—21no—
111#10587502—21no—
112#10587502—21no—
113#10587502—21no—
114#10587502—21no—
115#10587502—21no—
116#10587502—21no—
117#10587502—21no—
118C23×D17C2×D411yescharacteristic
119C22×C4×C17—21no—
120C22×C4×C17—21no—
121C22×C4×C17—21no—
122C22×C4×C17—21no—
123C22×C4×C17C2×D411yescharacteristic
124C22×C4×C17C2×D411yescharacteristic
125C22×C4×C17C2411yescharacteristic
126C22×Dic17—21no—
127C22×Dic17—21no—
128C22×Dic17—21no—
129C22×Dic17—21no—
130C22×Dic17C2×D411yescharacteristic
131C22×Dic17C2×D411yescharacteristic
132C22×Dic17C2×D411yescharacteristic
133C2×C4×D17—24no—
134C2×C4×D17—42no—
135C2×C4×D17—81no—
136C2×C4×D17—81no—
137C2×C4×D17—81no—
138C2×C4×D17—81no—
139C2×C4×D17C2×Q812yes—
140C2×C4×D17#4112yes—
141C2×C4×D17#4112yes—
142C2×C4×D17#4112yes—
143C2×C4×D17#4112yes—
144C2×C4×D17#4112yes—
145C2×C8×C17—21no—
146C2×C8×C17—21no—
147C2×C8×C17—21no—
148C2×C8×C17—21no—
149C2×C8×C17—21no—
150C2×C8×C17—21no—
151C4⋊C4×C17—21no—
152C4⋊C4×C17—21no—
153C4⋊C4×C17—21no—
154C4⋊C4×C17—21no—
155C4⋊C4×C17—21no—
156C4⋊C4×C17—21no—
157C4⋊C4×C17—21no—
158C4⋊C4×C17—81no—
159C4⋊C4×C17—81no—
160C4⋊C4×C17—81no—
161C4⋊C4×C17C2×Q812yes—
162C42×C17—21no—
163C42×C17—21no—
164#63227—22no—
165#63227—22no—
166#63227—42no—
167#63227—42no—
168C4⋊Dic17—21no—
169C4⋊Dic17—21no—
170C4⋊Dic17—21no—
171C4⋊Dic17—21no—
172C4⋊Dic17—21no—
173C4⋊Dic17—21no—
174C4⋊Dic17—21no—
175C4⋊Dic17—81no—
176C4⋊Dic17C2×Q812yes—
177#63225—24no—
178#63225—22no—
179#63225—22no—
180#63225—42no—
181#63225—81no—
182#63225—81no—
183#63225—81no—
184#63225—81no—
185C4×Dic17—21no—
186C4×Dic17—21no—
187C4×Dic17—42no—
188C4×Dic17—42no—
189C2×#3622—21no—
190C2×#3622—21no—
191C2×#3622—21no—
192C2×#3622—21no—
193C2×#3622—21no—
194C2×#3622—21no—
195#63218—44no—
196C8×D17—44no—
197#23749—171nomaximal, Sylow
198C23×C17C22×D411yescharacteristic
199C22×D17—21no—
200C22×D17—21no—
201C22×D17—21no—
202C22×D17—21no—
203C22×D17C22⋊Q812yes—
204C22×D17#12312yes—
205C22×D17#12412yes—
206C2×C4×C17—22no—
207C2×C4×C17—21no—
208C2×C4×C17—21no—
209C2×C4×C17—21no—
210C2×C4×C17—21no—
211C2×C4×C17—21no—
212C2×C4×C17—21no—
213C2×C4×C17—41no—
214C2×C4×C17—41no—
215C2×C4×C17—41no—
216C2×C4×C17—41no—
217C2×C4×C17—41no—
218C2×C4×C17—41no—
219C2×C4×C17—41no—
220C2×C4×C17—41no—
221C2×C4×C17—41no—
222C2×C4×C17—41no—
223C2×C4×C17—41no—
224C2×C4×C17C22×Q811yescharacteristic
225C2×C4×C17C2×#4111yescharacteristic
226C2×C4×C17C2×#4111yescharacteristic
227C2×C4×C17C2×#4111yescharacteristic
228C2×C4×C17C2×#4111yescharacteristic
229C2×C4×C17C2×#4111yescharacteristic
230C2×Dic17—22no—
231C2×Dic17—21no—
232C2×Dic17—21no—
233C2×Dic17—21no—
234C2×Dic17—21no—
235C2×Dic17—21no—
236C2×Dic17—21no—
237C2×Dic17—41no—
238C2×Dic17—41no—
239C2×Dic17—41no—
240C2×Dic17—41no—
241C2×Dic17—41no—
242C2×Dic17—41no—
243C2×Dic17—41no—
244C2×Dic17—41no—
245C2×Dic17—41no—
246C2×Dic17—41no—
247C2×Dic17—41no—
248C2×Dic17C22⋊Q812yes—
249C2×Dic17#12312yes—
250C2×Dic17#12412yes—
251C4×D17—84no—
252C4×D17—84no—
253C4×D17#12514yes—
254C4×D17#12514yes—
255C4×D17#12614yes—
256C4×D17#12614yes—
257C8×C17—41no—
258C8×C17—41no—
259#3622—41no—
260#3622—41no—
261#2317—171no—
262#2316—171no—
263#2101—171no—
264#2101—171no—
265#2101—171no—
266#2101—171no—
267#2100—171no—
268#2100—171no—
269#2099—171no—
270#2099D1711yescharacteristic, complemented
271#1736—171no—
272#1736—171no—
273#1735—171no—
274C2×#340—171no—
275#1729—171no—
276C22×C17C2×C22⋊Q811yescharacteristic
277C22×C17C2×#12311yescharacteristic
278C22×C17C2×#12411yescharacteristic
279C22×C17#57611yescharacteristic
280C22×C17#57711yescharacteristic
281C22×C17#57711yescharacteristic
282C22×C17#57811yescharacteristic
283C2×D17—22no—
284C2×D17—22no—
285C2×D17—22no—
286C2×D17—22no—
287C2×D17—22no—
288C2×D17—22no—
289C2×D17#40014yes—
290C4×C17—42no—
291C4×C17—41no—
292C4×C17—41no—
293C4×C17—81no—
294C4×C17—81no—
295C4×C17—81no—
296C4×C17C2×#12511yescharacteristic
297C4×C17C2×#12511yescharacteristic
298C4×C17C2×#12611yescharacteristic
299C4×C17C2×#12611yescharacteristic
300Dic17—42no—
301Dic17—41no—
302Dic17—41no—
303Dic17—81no—
304Dic17—81no—
305Dic17—81no—
306Dic17#40014yes—
307C22×M16—171no—
308C23×C8—171no—
309C2×#117—171no—
310C2×#117—171no—
311C2×#117—171no—
312C22×C4⋊C4—171no—
313C22×C4⋊C4—171no—
314#389—171no—
315#389—171no—
316#389—171no—
317#389—341no—
318#389—341no—
319#389—341no—
320#389—341no—
321#389C2×D1711yescharacteristic
322#385—341no—
323#385—341no—
324#384—171no—
325#384C2×D1711yescharacteristic
326#382—171no—
327#382—171no—
328#380—341no—
329#380—341no—
330#340—171no—
331#340—171no—
332#340—171no—
333#340—171no—
334#340—171no—
335#340—171no—
336#340—171no—
337#340—171no—
338#340—171no—
339#340—171no—
340#340—171no—
341#340—171no—
342#340C2×D1711yescharacteristic
343#340C2×D1711yescharacteristic
344#340C2×D1711yescharacteristic
345#340C2×D1711yescharacteristic
346#336—171no—
347#336—171no—
348#336—171no—
349#336C2×D1711yescharacteristic
350C2×C17C2×#40011yescharacteristic
351C2×C17#308111yescharacteristic
352C2×C17#308211yescharacteristic
353C2×C17#309811yescharacteristic
354C2×C17#309911yescharacteristic
355C2×C17#313611yescharacteristic
356C2×C17#313711yescharacteristic
357D17—24no—
358C23×C4—171no—
359C23×C4—341no—
360C23×C4—341no—
361C2×M16—342no—
362C2×M16—342no—
363C2×M16—342no—
364C22×C8—171no—
365C22×C8—171no—
366C22×C8—342no—
367C22×C8—342no—
368C22×C8—342no—
369C22×C8C22×D1711yescharacteristic
370C22×C8C22×D1711yescharacteristic
371#117—342no—
372#117—342no—
373#117—342no—
374#117—342no—
375#117—342no—
376#117—342no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—171no—
381C2×C4⋊C4—174no—
382C2×C4⋊C4—171no—
383C2×C4⋊C4—171no—
384C2×C4⋊C4—171no—
385C2×C4⋊C4—171no—
386C2×C4⋊C4—171no—
387C2×C4⋊C4—342no—
388C2×C4⋊C4—342no—
389C2×C4⋊C4—342no—
390C2×C4⋊C4—341no—
391C2×C4⋊C4—341no—
392C2×C4⋊C4—341no—
393C2×C4⋊C4—341no—
394C2×C4⋊C4—341no—
395C2×C4⋊C4—341no—
396C2×C4⋊C4—341no—
397C2×C4⋊C4C22×D1711yescharacteristic
398C2×C4⋊C4C22×D1711yescharacteristic
399C2×C4⋊C4C22×D1711yescharacteristic
400C2×C4⋊C4C22×D1711yescharacteristic
401C2×C22⋊C4—171no—
402C2×C22⋊C4—171no—
403C2×C22⋊C4—341no—
404C2×C22⋊C4—341no—
405C2×C42—171no—
406C2×C42—341no—
407C2×C42—341no—
408C2×C42C22×D1711yescharacteristic
409#95—21no—
410#95—341no—
411#95—341no—
412#95—341no—
413#95—341no—
414#95—341no—
415#95—341no—
416#95—341no—
417C17#2374911yescharacteristic, complemented, Sylow
418C24—171no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—171no—
424C22×C4—172no—
425C22×C4—172no—
426C22×C4—172no—
427C22×C4—172no—
428C22×C4—172no—
429C22×C4—172no—
430C22×C4—171no—
431C22×C4—171no—
432C22×C4—344no—
433C22×C4—341no—
434C22×C4—341no—
435C22×C4—341no—
436C22×C4—341no—
437C22×C4—682no—
438C22×C4—1361no—
439C22×C4—1361no—
440C22×C4—1361no—
441C22×C4—1361no—
442C22×C4D4×D1711yescharacteristic
443C22×C4D4×D1711yescharacteristic
444C22×C4C23×D1711yescharacteristic
445M16—684no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—341no—
453C2×C8—341no—
454C2×C8—341no—
455C2×C8—341no—
456C2×C8—341no—
457C2×C8—341no—
458C2×C8—684no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—81no—
467C4⋊C4—81no—
468C4⋊C4—81no—
469C4⋊C4—172no—
470C4⋊C4—344no—
471C4⋊C4—342no—
472C4⋊C4—342no—
473C4⋊C4—341no—
474C4⋊C4—341no—
475C4⋊C4—341no—
476C4⋊C4—341no—
477C4⋊C4—341no—
478C4⋊C4—341no—
479C4⋊C4—341no—
480C4⋊C4—682no—
481C4⋊C4—1361no—
482C4⋊C4—1361no—
483C4⋊C4—1361no—
484C4⋊C4—1361no—
485C4⋊C4—1361no—
486C4⋊C4Q8×D1712yes—
487C22⋊C4—342no—
488C22⋊C4—342no—
489C22⋊C4—682no—
490C22⋊C4—682no—
491C42—21no—
492C42—21no—
493C42—341no—
494C42—341no—
495C42—682no—
496C42—682no—
497C23—172no—
498C23—172no—
499C23—172no—
500C23—341no—
501C23—341no—
502C23—341no—
503C23—341no—
504C23C2×D4×D1711yescharacteristic
505C2×C4—22no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—172no—
524C2×C4—172no—
525C2×C4—172no—
526C2×C4—174no—
527C2×C4—174no—
528C2×C4—174no—
529C2×C4—174no—
530C2×C4—342no—
531C2×C4—341no—
532C2×C4—341no—
533C2×C4—341no—
534C2×C4—341no—
535C2×C4—341no—
536C2×C4—341no—
537C2×C4—681no—
538C2×C4—681no—
539C2×C4—681no—
540C2×C4—681no—
541C2×C4—681no—
542C2×C4—681no—
543C2×C4—681no—
544C2×C4—681no—
545C2×C4—681no—
546C2×C4—681no—
547C2×C4—681no—
548C2×C4—1364no—
549C2×C4—1364no—
550C2×C4C2×Q8×D1711yescharacteristic
551C2×C4#41×D1711yescharacteristic
552C2×C4#41×D1711yescharacteristic
553C2×C4#41×D1711yescharacteristic
554C2×C4#41×D1711yescharacteristic
555C2×C4#41×D1711yescharacteristic
556C8—41no—
557C8—41no—
558C8—681no—
559C8—681no—
560C22—174no—
561C22—342no—
562C22—342no—
563C22—342no—
564C22—342no—
565C22—342no—
566C22—342no—
567C22C22⋊Q8×D1711yescharacteristic
568C22#123×D1711yescharacteristic
569C22#124×D1711yescharacteristic
570C22#1176361011yescharacteristic
571C22#1176361511yescharacteristic
572C22#1176361811yescharacteristic
573C22#1176362511yescharacteristic
574C4—41no—
575C4—41no—
576C4—42no—
577C4—81no—
578C4—81no—
579C4—81no—
580C4—174no—
581C4—681no—
582C4—681no—
583C4—682no—
584C4—1361no—
585C4—1361no—
586C4—1361no—
587C4#125×D1711yescharacteristic
588C4#125×D1711yescharacteristic
589C4#126×D1711yescharacteristic
590C4#126×D1711yescharacteristic
591C2—344no—
592C2D17×#40011yescharacteristic
593C2#1453860811yescharacteristic
594C2#1453861911yescharacteristic
595C2#1453875711yescharacteristic
596C2#1453876811yescharacteristic
597C2#1453913311yescharacteristic
598C2#1453915011yescharacteristic
subgroupG/H
centerC23C2×D4×D17
commutator, cosocleC22×C4×C17C24
FrattiniC22×C4C23×D17
FittingC17×#2099C2
socleC23×C17C22×D4
prime radicalC23×D17C2×D4
hypercenter#2099D17
hypocenterC17#23749
LCSG ▷ C22×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2099

Complements

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

NH ≅ G/Ntype
3. #14530356C2semidirect
4. #14530355C2semidirect
5. #14530353C2semidirect
6. #14530352C2semidirect
7. #14530350C2semidirect
8. #14530346C2semidirect
9. #14530344C2semidirect
15. C17×#2099C2semidirect
270. #2099D17semidirect
417. C17#23749semidirect

Maximal subgroups

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

subgroupindex
#145314052
#145313992
#145303562
#145303552
#145303532
#145303522
#145303502
#145303462
#145303442
#145285022
#145284992
D17×#3402
#145284792
C17×#20992
#2374917