Finite Group Databasebeta

← C17×#19857 #16877601

Subgroups — C17×#19857 #16877601

Order 4352.

582 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C17×#3400C211yesmaximal, characteristic, complemented
2C17×#3381C211yesmaximal, characteristic, complemented
3C17×#3361C211yesmaximal, characteristic
4C17×#3338C211yesmaximal, characteristic, complemented
5C17×#1714C211yesmaximal, characteristic, complemented
6C17×#1696C211yesmaximal, characteristic, complemented
7C17×#1678C211yesmaximal, characteristic, complemented
8C17×#1672C211yesmaximal, characteristic, complemented
9C17×#1665C211yesmaximal, characteristic
10C17×#1644C211yesmaximal, characteristic, complemented
11C17×#1636C211yesmaximal, characteristic, complemented
12C17×#1630C211yesmaximal, characteristic, complemented
13C17×#1622C211yesmaximal, characteristic
14C17×#1582C211yesmaximal, characteristic, complemented
15C17×#1579C211yesmaximal, characteristic, complemented
16C17×#559C2211yescharacteristic
17C17×#557C2211yescharacteristic
18C17×#554C2211yescharacteristic
19C17×#554C2211yescharacteristic
20C17×#500C2211yescharacteristic
21C17×#499—21no—
22C17×#498C2211yescharacteristic
23C17×#497—21no—
24C17×#492C2211yescharacteristic
25C17×#492C2211yescharacteristic
26C17×#488—21no—
27C17×#487C2211yescharacteristic
28C17×#486C2211yescharacteristic
29C17×#484—21no—
30C17×#484—21no—
31C17×#479—21no—
32C17×#478—21no—
33C17×#478—21no—
34C17×#477C2211yescharacteristic
35C17×#477C2211yescharacteristic
36C17×#477C2211yescharacteristic
37C17×#477C2211yescharacteristic
38C17×#474C2211yescharacteristic
39C17×#467—21no—
40C17×#464—21no—
41C17×#463—21no—
42C17×#462C2211yescharacteristic
43C17×#461—21no—
44C17×#460C2211yescharacteristic
45C17×#459C2211yescharacteristic
46C17×#446C2211yescharacteristic
47C8×Q8×C17C2211yescharacteristic
48C8×Q8×C17C2211yescharacteristic
49C17×#440—21no—
50C4×Q16×C17C2211yescharacteristic
51C4×SD16×C17—21no—
52C4×SD16×C17C2211yescharacteristic
53C4×D8×C17—21no—
54C8×D4×C17C2211yescharacteristic
55C2×C17×#107—21no—
56C17×#334C2211yescharacteristic
57C17×#334C2211yescharacteristic
58C17×#333C2211yescharacteristic
59C17×#333C2211yescharacteristic
60C17×#332C2211yescharacteristic
61C17×#331C2211yescharacteristic
62C17×Q8⋊C8C2211yescharacteristic
63C17×Q8⋊C8C2211yescharacteristic
64C17×Q8⋊C8C2211yescharacteristic
65C17×D4⋊C8C2211yescharacteristic
66C17×#322C2211yescharacteristic
67C2×Q16×C17—21no—
68C2×Q16×C17D411yescharacteristic
69C2×SD16×C17—21no—
70C2×SD16×C17—21no—
71C2×SD16×C17—21no—
72C2×SD16×C17—41no—
73C2×SD16×C17D411yescharacteristic
74C2×D8×C17—21no—
75C22×C8×C17—21no—
76C17×C4⋊Q8—21no—
77C17×C4⋊Q8C2311yescharacteristic
78C17×C4⋊Q8C2311yescharacteristic
79C17×C4⋊Q8C2311yescharacteristic
80C17×#127C2311yescharacteristic
81C17×#125—21no—
82C17×#125—21no—
83C17×#125—21no—
84C17×#125—41no—
85C17×#124—21no—
86C17×#124—21no—
87C17×#123—41no—
88C17×C22⋊Q8—21no—
89C17×C22⋊Q8—21no—
90C17×C22⋊Q8—41no—
91C17×C22⋊Q8—41no—
92C4×Q8×C17—21no—
93C4×Q8×C17—21no—
94C4×Q8×C17C2311yescharacteristic
95C4×Q8×C17C2311yescharacteristic
96C4×Q8×C17C2311yescharacteristic
97C4×D4×C17—21no—
98C4×D4×C17—21no—
99C4×D4×C17—21no—
100C4×D4×C17—21no—
101C4×D4×C17C2311yescharacteristic
102C2×C4⋊C4×C17—21no—
103C2×C4⋊C4×C17—21no—
104C17×#107—21no—
105C17×#107—21no—
106C17×#107—21no—
107C17×#107—21no—
108C17×#107—21no—
109C17×#107—21no—
110C17×#107—21no—
111C17×#107D411yescharacteristic
112C17×#106—21no—
113C17×#106—21no—
114C17×#106D411yescharacteristic
115C17×C4⋊C8—21no—
116C17×C4⋊C8—21no—
117C17×C4⋊C8—21no—
118C17×C4⋊C8C2311yescharacteristic
119C17×C4⋊C8C2311yescharacteristic
120C17×C4⋊C8C2311yescharacteristic
121C17×C4⋊C8C2311yescharacteristic
122C17×#103—21no—
123C17×#103—21no—
124C17×#103—21no—
125C17×#103—21no—
126C17×#103—21no—
127C17×#103—41no—
128C17×#103D411yescharacteristic
129C17×#103D411yescharacteristic
130C17×#103D411yescharacteristic
131C17×#102—21no—
132C17×#102—21no—
133C17×#102—21no—
134C17×#102—21no—
135C17×#102—21no—
136C17×#102D411yescharacteristic
137C17×C22⋊C8—21no—
138C17×#97—21no—
139C4×C8×C17—21no—
140C4×C8×C17—21no—
141C4×C8×C17C2311yescharacteristic
142C4×C8×C17C2311yescharacteristic
143C4×C8×C17C2311yescharacteristic
144C2×Q8×C17—21no—
145C2×Q8×C17—21no—
146C2×Q8×C17—21no—
147C2×Q8×C17C2×D411yescharacteristic
148C2×Q8×C17C2×D411yescharacteristic
149C2×Q8×C17C2×D411yescharacteristic
150C2×D4×C17—21no—
151C2×D4×C17—21no—
152C2×D4×C17—21no—
153C2×D4×C17C2×D411yescharacteristic
154C22×C4×C17—21no—
155C22×C4×C17—41no—
156C22×C4×C17—41no—
157C22×C4×C17—41no—
158Q16×C17—22no—
159Q16×C17—81no—
160SD16×C17—22no—
161SD16×C17—42no—
162SD16×C17—81no—
163SD16×C17—81no—
164SD16×C17—82no—
165D8×C17—42no—
166C2×C8×C17—21no—
167C2×C8×C17—21no—
168C2×C8×C17—21no—
169C2×C8×C17—21no—
170C2×C8×C17—21no—
171C2×C8×C17—42no—
172C2×C8×C17C2×D411yescharacteristic
173C2×C8×C17C2×D411yescharacteristic
174C2×C8×C17C2×D411yescharacteristic
175C2×C8×C17C2×D411yescharacteristic
176C4⋊C4×C17—21no—
177C4⋊C4×C17—21no—
178C4⋊C4×C17—21no—
179C4⋊C4×C17—21no—
180C4⋊C4×C17—21no—
181C4⋊C4×C17—21no—
182C4⋊C4×C17—21no—
183C4⋊C4×C17—21no—
184C4⋊C4×C17—21no—
185C4⋊C4×C17—41no—
186C4⋊C4×C17—41no—
187C4⋊C4×C17—41no—
188C4⋊C4×C17—41no—
189C4⋊C4×C17—41no—
190C4⋊C4×C17—41no—
191C4⋊C4×C17—41no—
192C4⋊C4×C17C2×D411yescharacteristic
193C4⋊C4×C17C2×D411yescharacteristic
194C4⋊C4×C17C2×D411yescharacteristic
195C4⋊C4×C17C2×D411yescharacteristic
196C22⋊C4×C17—21no—
197C22⋊C4×C17—41no—
198C22⋊C4×C17—41no—
199C22⋊C4×C17—41no—
200C22⋊C4×C17—41no—
201C22⋊C4×C17—41no—
202C42×C17—21no—
203C42×C17—21no—
204C42×C17—21no—
205C42×C17—41no—
206C42×C17C2411yescharacteristic
207#19857C1711yesmaximal, characteristic, direct product factor, Sylow
208C23×C17—21no—
209C23×C17—41no—
210Q8×C17—21no—
211Q8×C17—21no—
212Q8×C17—21no—
213Q8×C17—21no—
214Q8×C17—21no—
215Q8×C17—21no—
216Q8×C17—41no—
217Q8×C17—41no—
218Q8×C17—81no—
219Q8×C17—81no—
220D4×C17—21no—
221D4×C17—41no—
222D4×C17—41no—
223D4×C17—41no—
224D4×C17—41no—
225D4×C17—81no—
226D4×C17#13712yes—
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—41no—
236C2×C4×C17—41no—
237C2×C4×C17—41no—
238C2×C4×C17—41no—
239C2×C4×C17—161no—
240C2×C4×C17—161no—
241C2×C4×C17—161no—
242C2×C4×C17C22×D411yescharacteristic
243C2×C4×C17C22×D411yescharacteristic
244C2×C4×C17H(5,𝔽2)11yescharacteristic
245C8×C17—21no—
246C8×C17—21no—
247C8×C17—21no—
248C8×C17—41no—
249C8×C17—41no—
250C8×C17—41no—
251C8×C17—41no—
252C8×C17—41no—
253C8×C17#13512yes—
254#3400C2×C1711yescharacteristic, complemented
255#3381C2×C1711yescharacteristic, complemented
256#3361C2×C1711yescharacteristic
257#3338C2×C1711yescharacteristic, complemented
258#1714C2×C1711yescharacteristic, complemented
259#1696C2×C1711yescharacteristic, complemented
260#1678C2×C1711yescharacteristic, complemented
261#1672C2×C1711yescharacteristic, complemented
262#1665C2×C1711yescharacteristic
263#1644C2×C1711yescharacteristic, complemented
264#1636C2×C1711yescharacteristic, complemented
265#1630C2×C1711yescharacteristic, complemented
266#1622C2×C1711yescharacteristic
267#1582C2×C1711yescharacteristic, complemented
268#1579C2×C1711yescharacteristic, complemented
269C22×C17—22no—
270C22×C17—41no—
271C22×C17—41no—
272C22×C17—81no—
273C22×C17—81no—
274C22×C17—81no—
275C22×C17D4211yescharacteristic
276C4×C17—21no—
277C4×C17—41no—
278C4×C17—41no—
279C4×C17—41no—
280C4×C17—41no—
281C4×C17—41no—
282C4×C17—41no—
283C4×C17—41no—
284C4×C17—81no—
285C4×C17—81no—
286C4×C17—81no—
287C4×C17C2×#13511yescharacteristic
288C4×C17C2×#13711yescharacteristic
289C4×C17#57711yescharacteristic
290C4×C17#57811yescharacteristic
291#559C22×C1711yescharacteristic
292#557C22×C1711yescharacteristic
293#554C22×C1711yescharacteristic
294#554C22×C1711yescharacteristic
295#500C22×C1711yescharacteristic
296#499—21no—
297#498C22×C1711yescharacteristic
298#497—21no—
299#492C22×C1711yescharacteristic
300#492C22×C1711yescharacteristic
301#488—21no—
302#487C22×C1711yescharacteristic
303#486C22×C1711yescharacteristic
304#484—21no—
305#484—21no—
306#479—21no—
307#478—21no—
308#478—21no—
309#477C22×C1711yescharacteristic
310#477C22×C1711yescharacteristic
311#477C22×C1711yescharacteristic
312#477C22×C1711yescharacteristic
313#474C22×C1711yescharacteristic
314#467—21no—
315#464—21no—
316#463—21no—
317#462C22×C1711yescharacteristic
318#461—21no—
319#460C22×C1711yescharacteristic
320#459C22×C1711yescharacteristic
321#446C22×C1711yescharacteristic
322C8×Q8C22×C1711yescharacteristic
323C8×Q8C22×C1711yescharacteristic
324#440—21no—
325C4×Q16C22×C1711yescharacteristic
326C4×SD16—21no—
327C4×SD16C22×C1711yescharacteristic
328C4×D8—21no—
329C8×D4C22×C1711yescharacteristic
330C2×#107—21no—
331#334C22×C1711yescharacteristic
332#334C22×C1711yescharacteristic
333#333C22×C1711yescharacteristic
334#333C22×C1711yescharacteristic
335#332C22×C1711yescharacteristic
336#331C22×C1711yescharacteristic
337Q8⋊C8C22×C1711yescharacteristic
338Q8⋊C8C22×C1711yescharacteristic
339Q8⋊C8C22×C1711yescharacteristic
340D4⋊C8C22×C1711yescharacteristic
341#322C22×C1711yescharacteristic
342C2×C17—42no—
343C2×C17—161no—
344C2×C17#327011yescharacteristic
345C2×C17#328411yescharacteristic
346C2×C17#328811yescharacteristic
347C2×Q16—21no—
348C2×Q16D4×C1711yescharacteristic
349C2×SD16—21no—
350C2×SD16—21no—
351C2×SD16—21no—
352C2×SD16—41no—
353C2×SD16D4×C1711yescharacteristic
354C2×D8—21no—
355C22×C8—21no—
356C4⋊Q8—21no—
357C4⋊Q8C23×C1711yescharacteristic
358C4⋊Q8C23×C1711yescharacteristic
359C4⋊Q8C23×C1711yescharacteristic
360#127C23×C1711yescharacteristic
361#125—21no—
362#125—21no—
363#125—21no—
364#125—41no—
365#124—21no—
366#124—21no—
367#123—41no—
368C22⋊Q8—21no—
369C22⋊Q8—21no—
370C22⋊Q8—41no—
371C22⋊Q8—41no—
372C4×Q8—21no—
373C4×Q8—21no—
374C4×Q8C23×C1711yescharacteristic
375C4×Q8C23×C1711yescharacteristic
376C4×Q8C23×C1711yescharacteristic
377C4×D4—21no—
378C4×D4—21no—
379C4×D4—21no—
380C4×D4—21no—
381C4×D4C23×C1711yescharacteristic
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384#107—21no—
385#107—21no—
386#107—21no—
387#107—21no—
388#107—21no—
389#107—21no—
390#107—21no—
391#107D4×C1711yescharacteristic
392#106—21no—
393#106—21no—
394#106D4×C1711yescharacteristic
395C4⋊C8—21no—
396C4⋊C8—21no—
397C4⋊C8—21no—
398C4⋊C8C23×C1711yescharacteristic
399C4⋊C8C23×C1711yescharacteristic
400C4⋊C8C23×C1711yescharacteristic
401C4⋊C8C23×C1711yescharacteristic
402#103—21no—
403#103—21no—
404#103—21no—
405#103—21no—
406#103—21no—
407#103—41no—
408#103D4×C1711yescharacteristic
409#103D4×C1711yescharacteristic
410#103D4×C1711yescharacteristic
411#102—21no—
412#102—21no—
413#102—21no—
414#102—21no—
415#102—21no—
416#102D4×C1711yescharacteristic
417C22⋊C8—21no—
418#97—21no—
419C4×C8—21no—
420C4×C8—21no—
421C4×C8C23×C1711yescharacteristic
422C4×C8C23×C1711yescharacteristic
423C4×C8C23×C1711yescharacteristic
424C17#1985711yescharacteristic, direct product factor, Sylow
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8C2×D4×C1711yescharacteristic
429C2×Q8C2×D4×C1711yescharacteristic
430C2×Q8C2×D4×C1711yescharacteristic
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—21no—
434C2×D4C2×D4×C1711yescharacteristic
435C22×C4—21no—
436C22×C4—41no—
437C22×C4—41no—
438C22×C4—41no—
439Q16—22no—
440Q16—81no—
441SD16—22no—
442SD16—42no—
443SD16—81no—
444SD16—81no—
445SD16—82no—
446D8—42no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—42no—
453C2×C8C2×D4×C1711yescharacteristic
454C2×C8C2×D4×C1711yescharacteristic
455C2×C8C2×D4×C1711yescharacteristic
456C2×C8C2×D4×C1711yescharacteristic
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—41no—
467C4⋊C4—41no—
468C4⋊C4—41no—
469C4⋊C4—41no—
470C4⋊C4—41no—
471C4⋊C4—41no—
472C4⋊C4—41no—
473C4⋊C4C2×D4×C1711yescharacteristic
474C4⋊C4C2×D4×C1711yescharacteristic
475C4⋊C4C2×D4×C1711yescharacteristic
476C4⋊C4C2×D4×C1711yescharacteristic
477C22⋊C4—21no—
478C22⋊C4—41no—
479C22⋊C4—41no—
480C22⋊C4—41no—
481C22⋊C4—41no—
482C22⋊C4—41no—
483C42—21no—
484C42—21no—
485C42—21no—
486C42—41no—
487C42C24×C1711yescharacteristic
488C23—21no—
489C23—41no—
490Q8—21no—
491Q8—21no—
492Q8—21no—
493Q8—21no—
494Q8—21no—
495Q8—21no—
496Q8—41no—
497Q8—41no—
498Q8—81no—
499Q8—81no—
500D4—21no—
501D4—41no—
502D4—41no—
503D4—41no—
504D4—41no—
505D4—81no—
506D4C17×#13712yes—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—161no—
520C2×C4—161no—
521C2×C4—161no—
522C2×C4C22×D4×C1711yescharacteristic
523C2×C4C22×D4×C1711yescharacteristic
524C2×C4C17×H(5,𝔽2)11yescharacteristic
525C8—21no—
526C8—21no—
527C8—21no—
528C8—41no—
529C8—41no—
530C8—41no—
531C8—41no—
532C8—41no—
533C8C17×#13512yes—
534C22—22no—
535C22—41no—
536C22—41no—
537C22—81no—
538C22—81no—
539C22—81no—
540C22D42×C1711yescharacteristic
541C4—21no—
542C4—41no—
543C4—41no—
544C4—41no—
545C4—41no—
546C4—41no—
547C4—41no—
548C4—41no—
549C4—81no—
550C4—81no—
551C4—81no—
552C4C2×C17×#13511yescharacteristic
553C4C2×C17×#13711yescharacteristic
554C4C17×#57711yescharacteristic
555C4C17×#57811yescharacteristic
556C2—42no—
557C2—161no—
558C2C17×#327011yescharacteristic
559C2C17×#328411yescharacteristic
560C2C17×#328811yescharacteristic
subgroupG/H
center, socleC22×C17D42
commutator, Frattini, cosocleC42C24×C17
prime radicalC17×#459C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C17 ◁ C42×C17 ◁ G

Complements

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

NH ≅ G/Ntype
1. C17×#3400C2semidirect
2. C17×#3381C2semidirect
4. C17×#3338C2semidirect
5. C17×#1714C2semidirect
6. C17×#1696C2semidirect
7. C17×#1678C2semidirect
8. C17×#1672C2semidirect
10. C17×#1644C2semidirect
11. C17×#1636C2semidirect
12. C17×#1630C2semidirect
14. C17×#1582C2semidirect
15. C17×#1579C2semidirect
207. #19857C17direct (N × H)
254. #3400C2×C17semidirect
255. #3381C2×C17semidirect
257. #3338C2×C17semidirect
258. #1714C2×C17semidirect
259. #1696C2×C17semidirect
260. #1678C2×C17semidirect
261. #1672C2×C17semidirect
263. #1644C2×C17semidirect
264. #1636C2×C17semidirect
265. #1630C2×C17semidirect
267. #1582C2×C17semidirect
268. #1579C2×C17semidirect
424. C17#19857direct (N × H)

Maximal subgroups

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

subgroupindex
C17×#34002
C17×#33812
C17×#33612
C17×#33382
C17×#17142
C17×#16962
C17×#16782
C17×#16722
C17×#16652
C17×#16442
C17×#16362
C17×#16302
C17×#16222
C17×#15822
C17×#15792
#1985717