Finite Group Databasebeta

← #17005236

Subgroups — #17005236

Order 4352.

618 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14537798C211yesmaximal, characteristic, complemented
2#14537789C211yesmaximal, characteristic, complemented
3#14527681C211yesmaximal, characteristic, complemented
4#14527675C211yesmaximal, characteristic, complemented
5#14527635C211yesmaximal, characteristic, complemented
6#14527621C211yesmaximal, characteristic, complemented
7#14527621C211yesmaximal, characteristic, complemented
8#14527614C211yesmaximal, characteristic, complemented
9SD16×#3622C211yesmaximal, characteristic, complemented
10D8×#3622C211yesmaximal, characteristic, complemented
11#14527564C211yesmaximal, characteristic, complemented
12#14527244C211yesmaximal, characteristic, complemented
13#14527166C211yesmaximal, characteristic, complemented
14#14527065C211yesmaximal, characteristic, complemented
15C17×#3102C211yesmaximal, characteristic
16#11762940C2211yescharacteristic
17#11762940C2211yescharacteristic
18#11762940C2211yescharacteristic
19Q8×#3622C2211yescharacteristic
20#11762887—21no—
21#11762887C2211yescharacteristic
22#11762881—21no—
23#11762881—21no—
24#11762881—21no—
25D4×#3622C2211yescharacteristic
26D4×#3622C2211yescharacteristic
27D4×#3622C2211yescharacteristic
28#11762870—21no—
29#11762866—21no—
30#11762866C2211yescharacteristic
31#11762862C2211yescharacteristic
32#11762765—21no—
33C4×#63223C2211yescharacteristic
34C2×#10587474—21no—
35C2×C4×#3622C2211yescharacteristic
36#11762562C2211yescharacteristic
37#11762562C2211yescharacteristic
38#11762560C2211yescharacteristic
39#11762560C2211yescharacteristic
40Q8⋊#3622C2211yescharacteristic
41Q8⋊#3622C2211yescharacteristic
42Q8⋊#3622C2211yescharacteristic
43Q8⋊#3622C2211yescharacteristic
44D4⋊#3622C2211yescharacteristic
45D4⋊#3622C2211yescharacteristic
46D4⋊#3622C2211yescharacteristic
47D4⋊#3622C2211yescharacteristic
48#11762531C2211yescharacteristic
49#11762531C2211yescharacteristic
50C8×#3622C2211yescharacteristic
51C8×#3622C2211yescharacteristic
52C17×#529C2211yescharacteristic
53C4×#41×C17C2211yescharacteristic
54C17×#485C411yescharacteristic
55C17×#482C411yescharacteristic
56C17×#479C411yescharacteristic
57C17×#478C411yescharacteristic
58C17×#464C411yescharacteristic
59C17×#463C411yescharacteristic
60C17×#452C411yescharacteristic
61C17×#449C411yescharacteristic
62C4×Q16×C17C2211yescharacteristic
63C4×SD16×C17C2211yescharacteristic
64C4×SD16×C17C2211yescharacteristic
65C4×D8×C17C2211yescharacteristic
66C17×#431C2211yescharacteristic
67C2×#41×C17C2×C411yescharacteristic
68C2×Q16×C17C2×C411yescharacteristic
69C2×SD16×C17C2×C411yescharacteristic
70C2×SD16×C17C2×C411yescharacteristic
71C2×D8×C17C2×C411yescharacteristic
72C17×#126—21no—
73C17×#125C2×C411yescharacteristic
74C17×#124C2×C411yescharacteristic
75C17×#123—21no—
76C17×C22⋊Q8C2×C411yescharacteristic
77C17×#121C2×C411yescharacteristic
78C4×Q8×C17C2×C411yescharacteristic
79C4×Q8×C17C2311yescharacteristic
80C4×Q8×C17C2311yescharacteristic
81C4×D4×C17—21no—
82C4×D4×C17—21no—
83C4×D4×C17—21no—
84C4×D4×C17C2×C411yescharacteristic
85C4×D4×C17C2311yescharacteristic
86C4×D4×C17C2311yescharacteristic
87C17×#117—21no—
88C17×#117—21no—
89C17×#117C2×C411yescharacteristic
90C2×C42×C17—21no—
91C2×C42×C17C2311yescharacteristic
92C2×#63223—21no—
93C2×#63223D411yescharacteristic
94C2×#63223D411yescharacteristic
95C22×#3622—21no—
96C22×#3622—21no—
97C22×#3622—21no—
98C22×#3622—21no—
99C17×#107C2×C411yescharacteristic
100C17×#107C2×C411yescharacteristic
101C17×#106C2×C411yescharacteristic
102C17×#106C2×C411yescharacteristic
103C17×C4⋊C8C2×C411yescharacteristic
104C17×C4⋊C8C2×C411yescharacteristic
105C17×#103C2×C411yescharacteristic
106C17×#103C2×C411yescharacteristic
107C17×#103C2×C411yescharacteristic
108C17×#103C2×C411yescharacteristic
109C17×#102C2×C411yescharacteristic
110C17×#102C2×C411yescharacteristic
111C17×#102C2×C411yescharacteristic
112C17×#102C2×C411yescharacteristic
113C17×C22⋊C8C2×C411yescharacteristic
114C17×C22⋊C8C2×C411yescharacteristic
115C4×C8×C17C2311yescharacteristic
116C4×C8×C17C2311yescharacteristic
117C22⋊#3622—21no—
118C22⋊#3622—21no—
119C22⋊#3622—21no—
120C22⋊#3622—21no—
121C22⋊#3622—21no—
122C22⋊#3622—21no—
123C4⋊#3622—21no—
124C4⋊#3622—21no—
125C4⋊#3622—21no—
126C4⋊#3622—21no—
127C4⋊#3622C2311yescharacteristic
128C4⋊#3622C2311yescharacteristic
129C4⋊#3622C2311yescharacteristic
130C4⋊#3622C2311yescharacteristic
131#10587474—21no—
132#10587474—21no—
133#10587474—21no—
134#10587474—21no—
135#10587474D411yescharacteristic
136#10587474D411yescharacteristic
137C4×#3622—21no—
138C4×#3622—21no—
139C4×#3622—21no—
140C4×#3622C2311yescharacteristic
141C4×#3622C2311yescharacteristic
142C4×#3622C2311yescharacteristic
143C4×#3622C2311yescharacteristic
144#41×C17—22no—
145#41×C17—41no—
146C2×Q8×C17C22×C411yescharacteristic
147C2×Q8×C17C22×C411yescharacteristic
148C2×D4×C17—21no—
149C2×D4×C17—21no—
150C2×D4×C17C22×C411yescharacteristic
151C2×D4×C17C22×C411yescharacteristic
152C22×C4×C17—21no—
153C22×C4×C17—21no—
154C22×C4×C17—21no—
155C22×C4×C17—21no—
156C22×C4×C17C22×C411yescharacteristic
157C22×C4×C17C2×D411yescharacteristic
158C22×C4×C17#4111yescharacteristic
159Q16×C17—41no—
160SD16×C17—22no—
161SD16×C17—41no—
162D8×C17—22no—
163C2×C8×C17C22×C411yescharacteristic
164C2×C8×C17C22×C411yescharacteristic
165C2×C8×C17C22×C411yescharacteristic
166C2×C8×C17C22×C411yescharacteristic
167C4⋊C4×C17—21no—
168C4⋊C4×C17—21no—
169C4⋊C4×C17—21no—
170C4⋊C4×C17—21no—
171C4⋊C4×C17—21no—
172C4⋊C4×C17—21no—
173C4⋊C4×C17C22×C411yescharacteristic
174C4⋊C4×C17C22×C411yescharacteristic
175C4⋊C4×C17C22×C411yescharacteristic
176C4⋊C4×C17C22×C411yescharacteristic
177C22⋊C4×C17—21no—
178C22⋊C4×C17—21no—
179C22⋊C4×C17—21no—
180C22⋊C4×C17—21no—
181C22⋊C4×C17—21no—
182C22⋊C4×C17—21no—
183C22⋊C4×C17—21no—
184C22⋊C4×C17—21no—
185C42×C17—21no—
186C42×C17—21no—
187C42×C17—21no—
188C42×C17—21no—
189C42×C17C22×C411yescharacteristic
190C42×C17C2×D411yescharacteristic
191C42×C17#4111yescharacteristic
192C42×C17C2411yescharacteristic
193#63223—22no—
194#63223—22no—
195#63223—42no—
196C2×#3622—21no—
197C2×#3622—21no—
198C2×#3622—21no—
199C2×#3622—21no—
200C2×#3622—21no—
201C2×#3622—21no—
202C2×#3622—42no—
203C2×#3622—42no—
204C2×#3622—42no—
205C2×#3622—42no—
206C2×#3622C2×D411yescharacteristic
207C2×#3622C2×D411yescharacteristic
208C2×#3622C2×D411yescharacteristic
209C2×#3622C2×D411yescharacteristic
210#17996—171nomaximal, Sylow
211C23×C17—21no—
212C23×C17—21no—
213C23×C17C4×D411yescharacteristic
214Q8×C17—21no—
215Q8×C17—21no—
216Q8×C17—21no—
217Q8×C17—21no—
218D4×C17—21no—
219D4×C17—21no—
220D4×C17—21no—
221D4×C17—42no—
222D4×C17—81no—
223D4×C17#13112yes—
224C2×C4×C17—21no—
225C2×C4×C17—21no—
226C2×C4×C17—21no—
227C2×C4×C17—21no—
228C2×C4×C17—21no—
229C2×C4×C17—21no—
230C2×C4×C17—21no—
231C2×C4×C17—21no—
232C2×C4×C17—21no—
233C2×C4×C17—21no—
234C2×C4×C17—41no—
235C2×C4×C17—42no—
236C2×C4×C17—41no—
237C2×C4×C17—41no—
238C2×C4×C17—41no—
239C2×C4×C17—41no—
240C2×C4×C17—81no—
241C2×C4×C17C4×D411yescharacteristic
242C2×C4×C17C4×D411yescharacteristic
243C2×C4×C17C4×D411yescharacteristic
244C2×C4×C17C23×C411yescharacteristic
245C2×C4×C17C22×D411yescharacteristic
246C2×C4×C17C2×#4111yescharacteristic
247C8×C17—21no—
248C8×C17—21no—
249C8×C17—21no—
250C8×C17—21no—
251#3622—22no—
252#3622—21no—
253#3622—21no—
254#3622—41no—
255#3622—41no—
256#3622—41no—
257#3622—41no—
258#3622—41no—
259#3622#13512yes—
260#3622#13512yes—
261#3102D1711yescharacteristic
262#2970—171no—
263#2969—171no—
264#1591—171no—
265#1590—171no—
266#1584—171no—
267#1582—171no—
268#1582—171no—
269#1581—171no—
270C8×SD16—171no—
271C8×D8—171no—
272#1572—171no—
273#1494—171no—
274#1476—171no—
275C8×M16—171no—
276C22×C17—21no—
277C22×C17—22no—
278C22×C17—21no—
279C22×C17—21no—
280C22×C17—41no—
281C22×C17—41no—
282C22×C17—41no—
283C22×C17—41no—
284C22×C17—41no—
285C22×C17C2×C4×D411yescharacteristic
286C4×C17—21no—
287C4×C17—21no—
288C4×C17—21no—
289C4×C17—21no—
290C4×C17—41no—
291C4×C17—41no—
292C4×C17—41no—
293C4×C17—41no—
294C4×C17—41no—
295C4×C17—41no—
296C4×C17C2×#13111yescharacteristic
297C4×C17#56811yescharacteristic
298C4×C17C2×#13511yescharacteristic
299C4×C17C2×#13511yescharacteristic
300#529C2×D1711yescharacteristic
301C4×#41C2×D1711yescharacteristic
302#485Dic1711yescharacteristic
303#482Dic1711yescharacteristic
304#479Dic1711yescharacteristic
305#478Dic1711yescharacteristic
306#464Dic1711yescharacteristic
307#463Dic1711yescharacteristic
308#452Dic1711yescharacteristic
309#449Dic1711yescharacteristic
310#446—171no—
311#446—171no—
312#446—171no—
313C8×Q8—171no—
314C4×Q16C2×D1711yescharacteristic
315C4×SD16C2×D1711yescharacteristic
316C4×SD16C2×D1711yescharacteristic
317C4×D8C2×D1711yescharacteristic
318#436—171no—
319#436—341no—
320#435—341no—
321#435—341no—
322#435—341no—
323C8×D4—171no—
324C8×D4—171no—
325C8×D4—171no—
326#433—341no—
327#432—171no—
328#432—341no—
329#431—171no—
330#431C2×D1711yescharacteristic
331#405—341no—
332C4×M16—171no—
333C2×#97—341no—
334C2×C4×C8—171no—
335#335—171no—
336#335—171no—
337#334—171no—
338#334—171no—
339Q8⋊C8—171no—
340Q8⋊C8—171no—
341Q8⋊C8—171no—
342Q8⋊C8—171no—
343D4⋊C8—171no—
344D4⋊C8—171no—
345D4⋊C8—171no—
346D4⋊C8—171no—
347#322—171no—
348#322—171no—
349C82—171no—
350C82—171no—
351C2×C17—41no—
352C2×C17—42no—
353C2×C17—81no—
354C2×C17#293311yescharacteristic
355C2×C17C4×#13511yescharacteristic
356C2×C17#295611yescharacteristic
357C2×#41C2×Dic1711yescharacteristic
358C2×Q16C2×Dic1711yescharacteristic
359C2×SD16C2×Dic1711yescharacteristic
360C2×SD16C2×Dic1711yescharacteristic
361C2×D8C2×Dic1711yescharacteristic
362C2×M16—171no—
363C2×M16—171no—
364C2×M16—341no—
365C22×C8—341no—
366C22×C8—341no—
367C22×C8—341no—
368C22×C8—341no—
369#126—21no—
370#125C2×Dic1711yescharacteristic
371#124C2×Dic1711yescharacteristic
372#123—21no—
373C22⋊Q8C2×Dic1711yescharacteristic
374#121C2×Dic1711yescharacteristic
375C4×Q8C2×Dic1711yescharacteristic
376C4×Q8C22×D1711yescharacteristic
377C4×Q8C22×D1711yescharacteristic
378C4×D4—21no—
379C4×D4—21no—
380C4×D4—21no—
381C4×D4C2×Dic1711yescharacteristic
382C4×D4C22×D1711yescharacteristic
383C4×D4C22×D1711yescharacteristic
384#117—21no—
385#117—21no—
386#117C2×Dic1711yescharacteristic
387C2×C42—21no—
388C2×C42C22×D1711yescharacteristic
389#107C2×Dic1711yescharacteristic
390#107C2×Dic1711yescharacteristic
391#106C2×Dic1711yescharacteristic
392#106C2×Dic1711yescharacteristic
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⋊C8C2×Dic1711yescharacteristic
402C4⋊C8C2×Dic1711yescharacteristic
403#103C2×Dic1711yescharacteristic
404#103C2×Dic1711yescharacteristic
405#103C2×Dic1711yescharacteristic
406#103C2×Dic1711yescharacteristic
407#102C2×Dic1711yescharacteristic
408#102C2×Dic1711yescharacteristic
409#102C2×Dic1711yescharacteristic
410#102C2×Dic1711yescharacteristic
411C22⋊C8—341no—
412C22⋊C8—341no—
413C22⋊C8—341no—
414C22⋊C8—341no—
415C22⋊C8—341no—
416C22⋊C8—341no—
417C22⋊C8C2×Dic1711yescharacteristic
418C22⋊C8C2×Dic1711yescharacteristic
419#97—171no—
420#97—171no—
421#97—341no—
422#97—341no—
423#97—341no—
424#97—341no—
425C4×C8—171no—
426C4×C8—171no—
427C4×C8—171no—
428C4×C8—171no—
429C4×C8—341no—
430C4×C8—341no—
431C4×C8—341no—
432C4×C8C22×D1711yescharacteristic
433C4×C8C22×D1711yescharacteristic
434C17#1799611yescharacteristic, complemented, Sylow
435#41—22no—
436#41—41no—
437C2×Q8C22×Dic1711yescharacteristic
438C2×Q8C22×Dic1711yescharacteristic
439C2×D4—21no—
440C2×D4—21no—
441C2×D4C22×Dic1711yescharacteristic
442C2×D4C22×Dic1711yescharacteristic
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4D4×D1711yescharacteristic
448C22×C4#6325411yescharacteristic
449C22×C4C22×Dic1711yescharacteristic
450Q16—41no—
451SD16—22no—
452SD16—41no—
453D8—22no—
454M16—342no—
455M16—342no—
456M16—682no—
457C2×C8—171no—
458C2×C8—171no—
459C2×C8—171no—
460C2×C8—171no—
461C2×C8—341no—
462C2×C8—341no—
463C2×C8—341no—
464C2×C8—341no—
465C2×C8—341no—
466C2×C8—341no—
467C2×C8—682no—
468C2×C8—682no—
469C2×C8—682no—
470C2×C8—682no—
471C2×C8C22×Dic1711yescharacteristic
472C2×C8C22×Dic1711yescharacteristic
473C2×C8C22×Dic1711yescharacteristic
474C2×C8C22×Dic1711yescharacteristic
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4C22×Dic1711yescharacteristic
482C4⋊C4C22×Dic1711yescharacteristic
483C4⋊C4C22×Dic1711yescharacteristic
484C4⋊C4C22×Dic1711yescharacteristic
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—21no—
489C22⋊C4—21no—
490C22⋊C4—21no—
491C22⋊C4—21no—
492C22⋊C4—21no—
493C42—21no—
494C42—21no—
495C42—21no—
496C42—21no—
497C42D4×D1711yescharacteristic
498C42#6325411yescharacteristic
499C42C22×Dic1711yescharacteristic
500C42C23×D1711yescharacteristic
501C23—21no—
502C23—21no—
503C23D4×Dic1711yescharacteristic
504Q8—21no—
505Q8—21no—
506Q8—21no—
507Q8—21no—
508D4—21no—
509D4—21no—
510D4—21no—
511D4—42no—
512D4—81no—
513D4#1058763412yes—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—41no—
525C2×C4—42no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—81no—
531C2×C4D4×Dic1711yescharacteristic
532C2×C4D4×Dic1711yescharacteristic
533C2×C4D4×Dic1711yescharacteristic
534C2×C4C2×D4×D1711yescharacteristic
535C2×C4C2×#6325411yescharacteristic
536C2×C4C23×Dic1711yescharacteristic
537C8—21no—
538C8—21no—
539C8—21no—
540C8—21no—
541C8—172no—
542C8—172no—
543C8—342no—
544C8—341no—
545C8—341no—
546C8—681no—
547C8—681no—
548C8—681no—
549C8—681no—
550C8—681no—
551C22—21no—
552C22—22no—
553C22—21no—
554C22—21no—
555C22—41no—
556C22—41no—
557C22—41no—
558C22—41no—
559C22—41no—
560C22C2×D4×Dic1711yescharacteristic
561C4—21no—
562C4—21no—
563C4—21no—
564C4—21no—
565C4—41no—
566C4—41no—
567C4—41no—
568C4—41no—
569C4—41no—
570C4—41no—
571C4C2×#1058763411yescharacteristic
572C4#1176357611yescharacteristic
573C4#135×D1711yescharacteristic
574C4#135×D1711yescharacteristic
575C2—41no—
576C2—42no—
577C2—81no—
578C2#1453751111yescharacteristic
579C2#135×Dic1711yescharacteristic
580C2#1453769411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D17
commutatorC2×C4×C17C23×C4
FrattiniC42C23×D17
FittingC17×#3102C2
socleC22×C17C2×C4×D4
prime radicalC17×#449C4
cosocleC42×C17C24
hypercenter#3102D17
hypocenterC17#17996
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3102

Complements

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

NH ≅ G/Ntype
1. #14537798C2semidirect
2. #14537789C2semidirect
3. #14527681C2semidirect
4. #14527675C2semidirect
5. #14527635C2semidirect
6. #14527621C2semidirect
7. #14527621C2semidirect
8. #14527614C2semidirect
9. SD16×#3622C2semidirect
10. D8×#3622C2semidirect
11. #14527564C2semidirect
12. #14527244C2semidirect
13. #14527166C2semidirect
14. #14527065C2semidirect
434. C17#17996semidirect

Maximal subgroups

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

subgroupindex
#145377982
#145377892
#145276812
#145276752
#145276352
#145276212
#145276142
SD16×#36222
D8×#36222
#145275642
#145272442
#145271662
#145270652
C17×#31022
#1799617