Finite Group Databasebeta

← #17092388

Subgroups — #17092388

Order 4352.

696 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14531667C211yesmaximal, characteristic
2#14530351C211yesmaximal, characteristic, complemented
3#14530286C211yesmaximal, characteristic, complemented
4#14530286C211yesmaximal, characteristic, complemented
5#14530119C211yesmaximal, characteristic, complemented
6#14529742C211yesmaximal, characteristic, complemented
7#14529550C211yesmaximal, characteristic, complemented
8#14529359C211yesmaximal, characteristic, complemented
9#14529359C211yesmaximal, characteristic, complemented
10#14528977C211yesmaximal, characteristic
11#14528969C211yesmaximal, characteristic
12#14528876C211yesmaximal, characteristic
13#14528815C211yesmaximal, characteristic
14#14528503C211yesmaximal, characteristic
15C17×#2442C211yesmaximal, characteristic
16C22×#63223C2211yescharacteristic
17C2×#10587612C2211yescharacteristic
18C2×#10587478C2211yescharacteristic
19C2×#10587479C2211yescharacteristic
20C2×#10587479C2211yescharacteristic
21C2×#10587479C2211yescharacteristic
22C2×C4⋊#3622C2211yescharacteristic
23C2×C4⋊#3622C2211yescharacteristic
24C2×C22⋊#3622C2211yescharacteristic
25#11762707C2211yescharacteristic
26#11762707C2211yescharacteristic
27#11762697—21no—
28#11762697—21no—
29#11762673—21no—
30#11762669C2211yescharacteristic
31C4×C4⋊Dic17C2211yescharacteristic
32C4×C4⋊Dic17C2211yescharacteristic
33#11762654—21no—
34#11762571C2211yescharacteristic
35#11762571C2211yescharacteristic
36#11762571C2211yescharacteristic
37#11762571C2211yescharacteristic
38#11762571C2211yescharacteristic
39#11762571C2211yescharacteristic
40#11762571C2211yescharacteristic
41#11762571C2211yescharacteristic
42#11762571C2211yescharacteristic
43#11762571C2211yescharacteristic
44#11762571C2211yescharacteristic
45#11762571C2211yescharacteristic
46#11762564C2211yescharacteristic
47#11762564C2211yescharacteristic
48C2×C17×#125C2211yescharacteristic
49C22×C4⋊C4×C17C2211yescharacteristic
50C17×#400—21no—
51C17×#398—21no—
52C17×#389C2211yescharacteristic
53C17×#389C2211yescharacteristic
54C17×#385—21no—
55C17×#382C2211yescharacteristic
56C17×#380—21no—
57C17×#380C2211yescharacteristic
58C4×C22⋊C4×C17C2211yescharacteristic
59C23×C4×C17—21no—
60C23×C4×C17C2311yescharacteristic
61C17×#125—22no—
62C17×#125—41no—
63C2×C4⋊C4×C17—22no—
64C2×C4⋊C4×C17—21no—
65C2×C4⋊C4×C17—21no—
66C2×C4⋊C4×C17—21no—
67C2×C4⋊C4×C17—21no—
68C2×C4⋊C4×C17—21no—
69C2×C4⋊C4×C17—41no—
70C2×C4⋊C4×C17C2311yescharacteristic
71C2×C4⋊C4×C17C2311yescharacteristic
72C2×C4⋊C4×C17C2311yescharacteristic
73C2×C4⋊C4×C17C2311yescharacteristic
74C2×C22⋊C4×C17—21no—
75C2×C22⋊C4×C17D411yescharacteristic
76C2×C22⋊C4×C17D411yescharacteristic
77C2×C42×C17C2311yescharacteristic
78C2×C42×C17C2311yescharacteristic
79C2×C22⋊Dic17—21no—
80C2×C22⋊Dic17—21no—
81#10587612—22no—
82#10587612Q814yes—
83C2×C4⋊Dic17C2311yescharacteristic
84C2×C4⋊Dic17C2311yescharacteristic
85C2×C4⋊Dic17C2311yescharacteristic
86C2×C4⋊Dic17C2311yescharacteristic
87C2×#63225—21no—
88C2×#63225—21no—
89C2×C4×Dic17—21no—
90C2×C4×Dic17—21no—
91C2×C4×Dic17—21no—
92C2×#63223—22no—
93C2×#63223—22no—
94C2×#63223—41no—
95C22×#3622C2311yescharacteristic
96C22×#3622C2311yescharacteristic
97C22×#3622C2311yescharacteristic
98C22×#3622C2311yescharacteristic
99C17×#95—21no—
100C17×#95—21no—
101C17×#95—21no—
102C17×#95—21no—
103C17×#95—21no—
104C17×#95D411yescharacteristic
105C17×#95D411yescharacteristic
106#10587502—21no—
107#10587502—21no—
108#10587502—21no—
109#10587502—21no—
110#10587502—21no—
111C22⋊#3622—22no—
112#10587479—22no—
113#10587479—22no—
114#10587479—41no—
115#10587478—41no—
116C4⋊#3622—22no—
117C4⋊#3622—41no—
118C24×C17C2×D411yescharacteristic
119C22×C4×C17—21no—
120C22×C4×C17—21no—
121C22×C4×C17—21no—
122C22×C4×C17—21no—
123C22×C4×C17—21no—
124C22×C4×C17—21no—
125C22×C4×C17—21no—
126C22×C4×C17—21no—
127C22×C4×C17—42no—
128C22×C4×C17—42no—
129C22×C4×C17—81no—
130C22×C4×C17C2×D411yescharacteristic
131C22×C4×C17C2×D411yescharacteristic
132C22×C4×C17C2×D411yescharacteristic
133C22×C4×C17C2×D411yescharacteristic
134C22×C4×C17C2×D411yescharacteristic
135C22×C4×C17C2×Q812yes—
136C22×C4×C17#4112yes—
137C22×C4×C17C2411yescharacteristic
138C22×Dic17—21no—
139C22×Dic17—21no—
140C22×Dic17—21no—
141C22×Dic17—21no—
142C4⋊C4×C17—21no—
143C4⋊C4×C17—21no—
144C4⋊C4×C17—21no—
145C4⋊C4×C17—21no—
146C4⋊C4×C17—21no—
147C4⋊C4×C17—21no—
148C4⋊C4×C17—21no—
149C4⋊C4×C17—42no—
150C4⋊C4×C17—42no—
151C4⋊C4×C17—42no—
152C4⋊C4×C17—81no—
153C4⋊C4×C17—81no—
154C4⋊C4×C17#4112yes—
155C22⋊C4×C17—41no—
156C22⋊C4×C17—41no—
157C22⋊C4×C17—42no—
158C42×C17—21no—
159C42×C17—21no—
160C42×C17—21no—
161C42×C17—21no—
162C22⋊Dic17—24no—
163C22⋊Dic17—81no—
164C4⋊Dic17—21no—
165C4⋊Dic17—21no—
166C4⋊Dic17—21no—
167C4⋊Dic17—21no—
168C4⋊Dic17—21no—
169C4⋊Dic17—21no—
170C4⋊Dic17C2×Q812yes—
171C4⋊Dic17C2×Q812yes—
172#63225—81no—
173#63225—81no—
174C4×Dic17—24no—
175C4×Dic17—42no—
176C4×Dic17—42no—
177#63223—44no—
178C2×#3622—21no—
179C2×#3622—21no—
180C2×#3622—21no—
181C2×#3622—21no—
182C2×#3622—21no—
183C2×#3622—21no—
184C2×#3622—21no—
185C2×#3622—21no—
186C2×#3622—21no—
187C2×#3622—21no—
188C2×#3622—21no—
189C2×#3622#4112yes—
190#26019—171nomaximal, Sylow
191C23×C17—21no—
192C23×C17—21no—
193C23×C17—21no—
194C23×C17—21no—
195C23×C17—21no—
196C23×C17—21no—
197C23×C17C22⋊Q812yes—
198C23×C17C22×D411yescharacteristic
199C2×C4×C17—21no—
200C2×C4×C17—21no—
201C2×C4×C17—22no—
202C2×C4×C17—22no—
203C2×C4×C17—22no—
204C2×C4×C17—22no—
205C2×C4×C17—21no—
206C2×C4×C17—21no—
207C2×C4×C17—22no—
208C2×C4×C17—21no—
209C2×C4×C17—21no—
210C2×C4×C17—21no—
211C2×C4×C17—21no—
212C2×C4×C17—21no—
213C2×C4×C17—21no—
214C2×C4×C17—21no—
215C2×C4×C17—21no—
216C2×C4×C17—21no—
217C2×C4×C17—21no—
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×C17—41no—
225C2×C4×C17—41no—
226C2×C4×C17—41no—
227C2×C4×C17—41no—
228C2×C4×C17—41no—
229C2×C4×C17—84no—
230C2×C4×C17C22⋊Q812yes—
231C2×C4×C17C22×Q811yescharacteristic
232C2×C4×C17C2×#4111yescharacteristic
233C2×C4×C17C2×#4111yescharacteristic
234C2×C4×C17C2×#4111yescharacteristic
235C2×C4×C17H(5,𝔽2)11yescharacteristic
236C2×C4×C172−1+411yescharacteristic
237C2×Dic17—22no—
238C2×Dic17—22no—
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×Dic17—41no—
249#3622—22no—
250#3622—41no—
251#3622—41no—
252#3622—41no—
253#2442D1711yescharacteristic
254#2346—171no—
255#2101—171no—
256#2088—171no—
257#2088—171no—
258#2059—171no—
259#1989—171no—
260#1949—171no—
261#1919—171no—
262#1919—171no—
263#1853—171no—
264#1851—171no—
265#1825—171no—
266#1809—171no—
267#1736—171no—
268C22×C17—22no—
269C22×C17—22no—
270C22×C17—22no—
271C22×C17—41no—
272C22×C17—41no—
273C22×C17—41no—
274C22×C17—41no—
275C22×C17C2×C22⋊Q811yescharacteristic
276C22×C17#54611yescharacteristic
277C22×C17#54711yescharacteristic
278C22×C17#57511yescharacteristic
279C22×C17#57511yescharacteristic
280C22×C17#57711yescharacteristic
281C22×C17#57711yescharacteristic
282C4×C17—22no—
283C4×C17—41no—
284C4×C17—41no—
285C4×C17—41no—
286C4×C17—41no—
287C4×C17—42no—
288C4×C17—81no—
289C4×C17—81no—
290C4×C17—81no—
291C4×C17#53311yescharacteristic
292C4×C17#54411yescharacteristic
293C4×C17#55111yescharacteristic
294C4×C17#55211yescharacteristic
295Dic17—42no—
296Dic17—42no—
297Dic17—81no—
298Dic17—81no—
299C22×M16—171no—
300C2×#125C2×D1711yescharacteristic
301C2×#117—171no—
302C22×C4⋊C4C2×D1711yescharacteristic
303C2×#107—171no—
304C2×#106—171no—
305C2×#106—171no—
306C2×#106—171no—
307C2×C4⋊C8—171no—
308C2×C4⋊C8—171no—
309C2×C22⋊C8—171no—
310#400—21no—
311#398—21no—
312#389—171no—
313#389—171no—
314#389C2×D1711yescharacteristic
315#389C2×D1711yescharacteristic
316#388—341no—
317#388—341no—
318#385—21no—
319#382—341no—
320#382C2×D1711yescharacteristic
321#380—21no—
322#380—171no—
323#380C2×D1711yescharacteristic
324C4×C4⋊C4—171no—
325C4×C4⋊C4—171no—
326C4×C22⋊C4C2×D1711yescharacteristic
327#376—341no—
328#340—171no—
329#340—171no—
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#336—171no—
341#336—171no—
342C2×C17—42no—
343C2×C17#243811yescharacteristic
344C2×C17#308011yescharacteristic
345C2×C17#308411yescharacteristic
346C2×C17#332111yescharacteristic
347C2×C17#332311yescharacteristic
348C2×C17#334811yescharacteristic
349C2×C17#335111yescharacteristic
350C23×C4—21no—
351C23×C4C22×D1711yescharacteristic
352C2×M16—342no—
353C2×M16—342no—
354C2×M16—681no—
355C22×C8—171no—
356C22×C8—171no—
357C22×C8—171no—
358C22×C8—171no—
359#125—22no—
360#125—41no—
361#117—174no—
362#117—342no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—41no—
370C2×C4⋊C4—171no—
371C2×C4⋊C4—171no—
372C2×C4⋊C4—171no—
373C2×C4⋊C4—171no—
374C2×C4⋊C4—341no—
375C2×C4⋊C4—341no—
376C2×C4⋊C4C22×D1711yescharacteristic
377C2×C4⋊C4C22×D1711yescharacteristic
378C2×C4⋊C4C22×D1711yescharacteristic
379C2×C4⋊C4C22×D1711yescharacteristic
380C2×C22⋊C4—21no—
381C2×C22⋊C4—341no—
382C2×C22⋊C4—341no—
383C2×C22⋊C4C22⋊D1711yescharacteristic
384C2×C22⋊C4C22⋊D1711yescharacteristic
385C2×C42—341no—
386C2×C42—341no—
387C2×C42—341no—
388C2×C42C22×D1711yescharacteristic
389C2×C42C22×D1711yescharacteristic
390#107—681no—
391#106—342no—
392#106—342no—
393#106—681no—
394C4⋊C8—342no—
395C4⋊C8—681no—
396C22⋊C8—342no—
397#95—21no—
398#95—21no—
399#95—21no—
400#95—21no—
401#95—21no—
402#95—341no—
403#95—341no—
404#95—341no—
405#95—341no—
406#95—341no—
407#95C22⋊D1711yescharacteristic
408#95C22⋊D1711yescharacteristic
409C17#2601911yescharacteristic, complemented, Sylow
410C24C2×C22⋊D1711yescharacteristic
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—42no—
420C22×C4—42no—
421C22×C4—81no—
422C22×C4—341no—
423C22×C4—341no—
424C22×C4—341no—
425C22×C4—341no—
426C22×C4Q8×D1712yes—
427C22×C4#6325612yes—
428C22×C4C2×C22⋊D1711yescharacteristic
429C22×C4C2×C22⋊D1711yescharacteristic
430C22×C4C2×C22⋊D1711yescharacteristic
431C22×C4C2×C22⋊D1711yescharacteristic
432C22×C4C2×C22⋊D1711yescharacteristic
433C22×C4C23×D1711yescharacteristic
434M16—684no—
435C2×C8—172no—
436C2×C8—341no—
437C2×C8—341no—
438C2×C8—341no—
439C2×C8—341no—
440C2×C8—341no—
441C2×C8—341no—
442C2×C8—341no—
443C2×C8—341no—
444C2×C8—341no—
445C2×C8—341no—
446C2×C8—341no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—42no—
455C4⋊C4—42no—
456C4⋊C4—42no—
457C4⋊C4—81no—
458C4⋊C4—81no—
459C4⋊C4—172no—
460C4⋊C4—172no—
461C4⋊C4—341no—
462C4⋊C4—341no—
463C4⋊C4—341no—
464C4⋊C4—341no—
465C4⋊C4—341no—
466C4⋊C4—341no—
467C4⋊C4—1361no—
468C4⋊C4—1361no—
469C4⋊C4#6325412yes—
470C22⋊C4—41no—
471C22⋊C4—41no—
472C22⋊C4—42no—
473C22⋊C4—344no—
474C22⋊C4—1361no—
475C42—21no—
476C42—21no—
477C42—21no—
478C42—21no—
479C42—344no—
480C42—682no—
481C42—682no—
482C23—21no—
483C23—21no—
484C23—21no—
485C23—21no—
486C23—21no—
487C23—21no—
488C23#1058763212yes—
489C23C22×C22⋊D1711yescharacteristic
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—22no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
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—84no—
521C2×C4—342no—
522C2×C4—342no—
523C2×C4—681no—
524C2×C4—681no—
525C2×C4—681no—
526C2×C4—681no—
527C2×C4—681no—
528C2×C4—681no—
529C2×C4—681no—
530C2×C4—681no—
531C2×C4—681no—
532C2×C4—681no—
533C2×C4#1058763212yes—
534C2×C4C2×#6325411yescharacteristic
535C2×C4#1058769111yescharacteristic
536C2×C4C2×Q8×D1711yescharacteristic
537C2×C4C2×#6325611yescharacteristic
538C2×C4#41×D1711yescharacteristic
539C2×C4#1058769711yescharacteristic
540C8—342no—
541C8—681no—
542C8—681no—
543C8—681no—
544C22—22no—
545C22—22no—
546C22—22no—
547C22—41no—
548C22—41no—
549C22—41no—
550C22—41no—
551C22C2×#1058763211yescharacteristic
552C22#1176345311yescharacteristic
553C22#1176345811yescharacteristic
554C22#1176360711yescharacteristic
555C22#1176360711yescharacteristic
556C22#1176361711yescharacteristic
557C22#1176362011yescharacteristic
558C4—22no—
559C4—41no—
560C4—41no—
561C4—41no—
562C4—42no—
563C4—41no—
564C4—81no—
565C4—81no—
566C4—81no—
567C4—682no—
568C4—682no—
569C4—1361no—
570C4—1361no—
571C4#1176336111yescharacteristic
572C4#1176343811yescharacteristic
573C4#1176348611yescharacteristic
574C4#1176350111yescharacteristic
575C2—42no—
576C2#1453245611yescharacteristic
577C2#1453860211yescharacteristic
578C2#1453864211yescharacteristic
579C2#1454097011yescharacteristic
580C2#1454100011yescharacteristic
581C2#1454129311yescharacteristic
582C2#1454133811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D17
commutator, cosocleC22×C4×C17C24
FrattiniC22×C4C23×D17
FittingC17×#2442C2
socleC23×C17C22×D4
prime radicalC24×C17C2×D4
hypercenter#2442D17
hypocenterC17#26019
LCSG ▷ C22×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2442

Complements

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

NH ≅ G/Ntype
2. #14530351C2semidirect
3. #14530286C2semidirect
4. #14530286C2semidirect
5. #14530119C2semidirect
6. #14529742C2semidirect
7. #14529550C2semidirect
8. #14529359C2semidirect
9. #14529359C2semidirect
409. C17#26019semidirect

Maximal subgroups

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

subgroupindex
#145316672
#145303512
#145302862
#145301192
#145297422
#145295502
#145293592
#145289772
#145289692
#145288762
#145288152
#145285032
C17×#24422
#2601917