Finite Group Databasebeta

← C17×#19848 #16877592

Subgroups — C17×#19848 #16877592

Order 4352.

556 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C17×#3369C211yesmaximal, characteristic
2C17×#3364C211yesmaximal, characteristic
3C17×#3363C211yesmaximal, characteristic, complemented
4C17×#3342C211yesmaximal, characteristic
5C17×#1718C211yesmaximal, characteristic, complemented
6C17×#1700C211yesmaximal, characteristic, complemented
7C17×#1684C211yesmaximal, characteristic, complemented
8C17×#1683C211yesmaximal, characteristic
9C17×#1674C211yesmaximal, characteristic, complemented
10C17×#1653C211yesmaximal, characteristic, complemented
11C17×#1652C211yesmaximal, characteristic
12C17×#1645C211yesmaximal, characteristic, complemented
13C17×#1638C211yesmaximal, characteristic
14C17×#1584C211yesmaximal, characteristic, complemented
15C17×SD16⋊C8C211yesmaximal, characteristic
16Q82×C17C2211yescharacteristic
17C17×#557C2211yescharacteristic
18C17×#556C2211yescharacteristic
19C17×#556C2211yescharacteristic
20C17×#500C2211yescharacteristic
21C17×#498C2211yescharacteristic
22C17×#489—21no—
23C17×#488—21no—
24C17×#487—21no—
25C17×#487C2211yescharacteristic
26C17×#487C2211yescharacteristic
27C17×#487C2211yescharacteristic
28C17×#487C2211yescharacteristic
29C17×#485—21no—
30C17×#485—21no—
31C17×#479—21no—
32C17×#477—21no—
33C17×#477C2211yescharacteristic
34C17×#476C2211yescharacteristic
35C17×#475—21no—
36C17×#475C2211yescharacteristic
37C17×#475C2211yescharacteristic
38C17×#474C2211yescharacteristic
39C17×#467—21no—
40C17×#464—21no—
41C17×#464—21no—
42C17×#462—21no—
43C17×#462C2211yescharacteristic
44C17×#462C2211yescharacteristic
45C17×#462C2211yescharacteristic
46C17×#446C2211yescharacteristic
47C8×Q8×C17C2211yescharacteristic
48C8×Q8×C17C2211yescharacteristic
49C17×#441—21no—
50C4×Q16×C17—21no—
51C4×Q16×C17—21no—
52C4×Q16×C17C2211yescharacteristic
53C4×SD16×C17C2211yescharacteristic
54C8×D4×C17C2211yescharacteristic
55C17×#427—21no—
56C17×#335C2211yescharacteristic
57C17×#335C2211yescharacteristic
58C17×#333C2211yescharacteristic
59C17×#332C2211yescharacteristic
60C17×#332C2211yescharacteristic
61C17×#332C2211yescharacteristic
62C17×Q8⋊C8C2211yescharacteristic
63C17×Q8⋊C8C2211yescharacteristic
64C17×Q8⋊C8C2211yescharacteristic
65C17×D4⋊C8C2211yescharacteristic
66C17×#322C2211yescharacteristic
67C2×Q16×C17—21no—
68C2×Q16×C17—21no—
69C2×Q16×C17—21no—
70C2×Q16×C17D411yescharacteristic
71C2×SD16×C17D411yescharacteristic
72C22×C8×C17—21no—
73C17×C4⋊Q8—21no—
74C17×C4⋊Q8—21no—
75C17×C4⋊Q8—21no—
76C17×C4⋊Q8—41no—
77C17×C4⋊Q8C2311yescharacteristic
78C17×C4⋊Q8C2311yescharacteristic
79C17×C4⋊Q8C2311yescharacteristic
80C17×C4⋊Q8C2311yescharacteristic
81C17×#126—41no—
82C17×#126—41no—
83C17×#125—21no—
84C17×#125—41no—
85C17×#124—21no—
86C17×#124—21no—
87C17×C22⋊Q8—21no—
88C17×C22⋊Q8—21no—
89C4×Q8×C17—21no—
90C4×Q8×C17—21no—
91C4×Q8×C17—21no—
92C4×Q8×C17—21no—
93C4×Q8×C17—21no—
94C4×Q8×C17—21no—
95C4×Q8×C17C2311yescharacteristic
96C4×Q8×C17C2311yescharacteristic
97C4×Q8×C17C2311yescharacteristic
98C4×D4×C17C2311yescharacteristic
99C17×#117—21no—
100C17×#117—21no—
101C17×#107—21no—
102C17×#107—21no—
103C17×#107—21no—
104C17×#107—21no—
105C17×#107D411yescharacteristic
106C17×#106—21no—
107C17×#106—21no—
108C17×#106—21no—
109C17×#106—41no—
110C17×#106D411yescharacteristic
111C17×C4⋊C8—21no—
112C17×C4⋊C8—21no—
113C17×C4⋊C8—21no—
114C17×C4⋊C8C2311yescharacteristic
115C17×C4⋊C8C2311yescharacteristic
116C17×C4⋊C8C2311yescharacteristic
117C17×C4⋊C8C2311yescharacteristic
118C17×#103—21no—
119C17×#103—21no—
120C17×#103—21no—
121C17×#103—21no—
122C17×#103—21no—
123C17×#103—21no—
124C17×#103—21no—
125C17×#103—21no—
126C17×#103—21no—
127C17×#103—21no—
128C17×#103—21no—
129C17×#103—21no—
130C17×#103—41no—
131C17×#103D411yescharacteristic
132C17×#103D411yescharacteristic
133C17×#103D411yescharacteristic
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×C17—21no—
148C2×Q8×C17—41no—
149C2×Q8×C17C2×D411yescharacteristic
150C2×Q8×C17C2×D411yescharacteristic
151C2×Q8×C17C2×D411yescharacteristic
152C2×D4×C17C2×D411yescharacteristic
153C22×C4×C17—21no—
154Q16×C17—41no—
155Q16×C17—42no—
156Q16×C17—42no—
157Q16×C17—42no—
158SD16×C17—22no—
159C2×C8×C17—21no—
160C2×C8×C17—21no—
161C2×C8×C17—21no—
162C2×C8×C17—21no—
163C2×C8×C17—21no—
164C2×C8×C17—42no—
165C2×C8×C17C2×D411yescharacteristic
166C2×C8×C17C2×D411yescharacteristic
167C2×C8×C17C2×D411yescharacteristic
168C2×C8×C17C2×D411yescharacteristic
169C4⋊C4×C17—21no—
170C4⋊C4×C17—21no—
171C4⋊C4×C17—21no—
172C4⋊C4×C17—21no—
173C4⋊C4×C17—21no—
174C4⋊C4×C17—21no—
175C4⋊C4×C17—21no—
176C4⋊C4×C17—21no—
177C4⋊C4×C17—21no—
178C4⋊C4×C17—21no—
179C4⋊C4×C17—21no—
180C4⋊C4×C17—41no—
181C4⋊C4×C17—41no—
182C4⋊C4×C17—41no—
183C4⋊C4×C17—41no—
184C4⋊C4×C17—41no—
185C4⋊C4×C17—41no—
186C4⋊C4×C17—41no—
187C4⋊C4×C17C2×D411yescharacteristic
188C4⋊C4×C17C2×D411yescharacteristic
189C4⋊C4×C17C2×D411yescharacteristic
190C4⋊C4×C17C2×D411yescharacteristic
191C22⋊C4×C17—21no—
192C22⋊C4×C17—41no—
193C22⋊C4×C17—41no—
194C22⋊C4×C17—41no—
195C22⋊C4×C17—41no—
196C42×C17—21no—
197C42×C17—21no—
198C42×C17—21no—
199C42×C17—41no—
200C42×C17—41no—
201C42×C17—41no—
202C42×C17—41no—
203C42×C17C2411yescharacteristic
204#19848C1711yesmaximal, characteristic, direct product factor, Sylow
205C23×C17—21no—
206Q8×C17—21no—
207Q8×C17—21no—
208Q8×C17—21no—
209Q8×C17—21no—
210Q8×C17—21no—
211Q8×C17—41no—
212Q8×C17—41no—
213Q8×C17—41no—
214Q8×C17—41no—
215Q8×C17—41no—
216Q8×C17—41no—
217Q8×C17—81no—
218Q8×C17—161no—
219Q8×C17#13512yes—
220D4×C17—21no—
221D4×C17—21no—
222C2×C4×C17—21no—
223C2×C4×C17—21no—
224C2×C4×C17—21no—
225C2×C4×C17—21no—
226C2×C4×C17—21no—
227C2×C4×C17—21no—
228C2×C4×C17—21no—
229C2×C4×C17—41no—
230C2×C4×C17—41no—
231C2×C4×C17—41no—
232C2×C4×C17—41no—
233C2×C4×C17—41no—
234C2×C4×C17—41no—
235C2×C4×C17C22×D411yescharacteristic
236C2×C4×C17C22×D411yescharacteristic
237C2×C4×C17H(5,𝔽2)11yescharacteristic
238C8×C17—21no—
239C8×C17—21no—
240C8×C17—21no—
241C8×C17—21no—
242C8×C17—41no—
243C8×C17—41no—
244C8×C17—41no—
245C8×C17—41no—
246C8×C17—41no—
247#3369C2×C1711yescharacteristic
248#3364C2×C1711yescharacteristic
249#3363C2×C1711yescharacteristic, complemented
250#3342C2×C1711yescharacteristic
251#1718C2×C1711yescharacteristic, complemented
252#1700C2×C1711yescharacteristic, complemented
253#1684C2×C1711yescharacteristic, complemented
254#1683C2×C1711yescharacteristic
255#1674C2×C1711yescharacteristic, complemented
256#1653C2×C1711yescharacteristic, complemented
257#1652C2×C1711yescharacteristic
258#1645C2×C1711yescharacteristic, complemented
259#1638C2×C1711yescharacteristic
260#1584C2×C1711yescharacteristic, complemented
261SD16⋊C8C2×C1711yescharacteristic
262C22×C17—41no—
263C22×C17—41no—
264C22×C17—41no—
265C22×C17D4211yescharacteristic
266C4×C17—22no—
267C4×C17—21no—
268C4×C17—41no—
269C4×C17—41no—
270C4×C17—41no—
271C4×C17—41no—
272C4×C17—41no—
273C4×C17—41no—
274C4×C17—81no—
275C4×C17—81no—
276C4×C17—81no—
277C4×C17—81no—
278C4×C17C2×#13511yescharacteristic
279C4×C17#57511yescharacteristic
280C4×C17#57811yescharacteristic
281C4×C17#57811yescharacteristic
282Q82C22×C1711yescharacteristic
283#557C22×C1711yescharacteristic
284#556C22×C1711yescharacteristic
285#556C22×C1711yescharacteristic
286#500C22×C1711yescharacteristic
287#498C22×C1711yescharacteristic
288#489—21no—
289#488—21no—
290#487—21no—
291#487C22×C1711yescharacteristic
292#487C22×C1711yescharacteristic
293#487C22×C1711yescharacteristic
294#487C22×C1711yescharacteristic
295#485—21no—
296#485—21no—
297#479—21no—
298#477—21no—
299#477C22×C1711yescharacteristic
300#476C22×C1711yescharacteristic
301#475—21no—
302#475C22×C1711yescharacteristic
303#475C22×C1711yescharacteristic
304#474C22×C1711yescharacteristic
305#467—21no—
306#464—21no—
307#464—21no—
308#462—21no—
309#462C22×C1711yescharacteristic
310#462C22×C1711yescharacteristic
311#462C22×C1711yescharacteristic
312#446C22×C1711yescharacteristic
313C8×Q8C22×C1711yescharacteristic
314C8×Q8C22×C1711yescharacteristic
315#441—21no—
316C4×Q16—21no—
317C4×Q16—21no—
318C4×Q16C22×C1711yescharacteristic
319C4×SD16C22×C1711yescharacteristic
320C8×D4C22×C1711yescharacteristic
321#427—21no—
322#335C22×C1711yescharacteristic
323#335C22×C1711yescharacteristic
324#333C22×C1711yescharacteristic
325#332C22×C1711yescharacteristic
326#332C22×C1711yescharacteristic
327#332C22×C1711yescharacteristic
328Q8⋊C8C22×C1711yescharacteristic
329Q8⋊C8C22×C1711yescharacteristic
330Q8⋊C8C22×C1711yescharacteristic
331D4⋊C8C22×C1711yescharacteristic
332#322C22×C1711yescharacteristic
333C2×C17—81no—
334C2×C17#326911yescharacteristic
335C2×C17#328511yescharacteristic
336C2×C17#328911yescharacteristic
337C2×Q16—21no—
338C2×Q16—21no—
339C2×Q16—21no—
340C2×Q16D4×C1711yescharacteristic
341C2×SD16D4×C1711yescharacteristic
342C22×C8—21no—
343C4⋊Q8—21no—
344C4⋊Q8—21no—
345C4⋊Q8—21no—
346C4⋊Q8—41no—
347C4⋊Q8C23×C1711yescharacteristic
348C4⋊Q8C23×C1711yescharacteristic
349C4⋊Q8C23×C1711yescharacteristic
350C4⋊Q8C23×C1711yescharacteristic
351#126—41no—
352#126—41no—
353#125—21no—
354#125—41no—
355#124—21no—
356#124—21no—
357C22⋊Q8—21no—
358C22⋊Q8—21no—
359C4×Q8—21no—
360C4×Q8—21no—
361C4×Q8—21no—
362C4×Q8—21no—
363C4×Q8—21no—
364C4×Q8—21no—
365C4×Q8C23×C1711yescharacteristic
366C4×Q8C23×C1711yescharacteristic
367C4×Q8C23×C1711yescharacteristic
368C4×D4C23×C1711yescharacteristic
369#117—21no—
370#117—21no—
371#107—21no—
372#107—21no—
373#107—21no—
374#107—21no—
375#107D4×C1711yescharacteristic
376#106—21no—
377#106—21no—
378#106—21no—
379#106—41no—
380#106D4×C1711yescharacteristic
381C4⋊C8—21no—
382C4⋊C8—21no—
383C4⋊C8—21no—
384C4⋊C8C23×C1711yescharacteristic
385C4⋊C8C23×C1711yescharacteristic
386C4⋊C8C23×C1711yescharacteristic
387C4⋊C8C23×C1711yescharacteristic
388#103—21no—
389#103—21no—
390#103—21no—
391#103—21no—
392#103—21no—
393#103—21no—
394#103—21no—
395#103—21no—
396#103—21no—
397#103—21no—
398#103—21no—
399#103—21no—
400#103—41no—
401#103D4×C1711yescharacteristic
402#103D4×C1711yescharacteristic
403#103D4×C1711yescharacteristic
404#102—21no—
405#102—21no—
406#102D4×C1711yescharacteristic
407C22⋊C8—21no—
408#97—21no—
409C4×C8—21no—
410C4×C8—21no—
411C4×C8C23×C1711yescharacteristic
412C4×C8C23×C1711yescharacteristic
413C4×C8C23×C1711yescharacteristic
414C17#1984811yescharacteristic, direct product factor, Sylow
415C2×Q8—21no—
416C2×Q8—21no—
417C2×Q8—21no—
418C2×Q8—21no—
419C2×Q8—41no—
420C2×Q8C2×D4×C1711yescharacteristic
421C2×Q8C2×D4×C1711yescharacteristic
422C2×Q8C2×D4×C1711yescharacteristic
423C2×D4C2×D4×C1711yescharacteristic
424C22×C4—21no—
425Q16—41no—
426Q16—42no—
427Q16—42no—
428Q16—42no—
429SD16—22no—
430C2×C8—21no—
431C2×C8—21no—
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—21no—
435C2×C8—42no—
436C2×C8C2×D4×C1711yescharacteristic
437C2×C8C2×D4×C1711yescharacteristic
438C2×C8C2×D4×C1711yescharacteristic
439C2×C8C2×D4×C1711yescharacteristic
440C4⋊C4—21no—
441C4⋊C4—21no—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—41no—
452C4⋊C4—41no—
453C4⋊C4—41no—
454C4⋊C4—41no—
455C4⋊C4—41no—
456C4⋊C4—41no—
457C4⋊C4—41no—
458C4⋊C4C2×D4×C1711yescharacteristic
459C4⋊C4C2×D4×C1711yescharacteristic
460C4⋊C4C2×D4×C1711yescharacteristic
461C4⋊C4C2×D4×C1711yescharacteristic
462C22⋊C4—21no—
463C22⋊C4—41no—
464C22⋊C4—41no—
465C22⋊C4—41no—
466C22⋊C4—41no—
467C42—21no—
468C42—21no—
469C42—21no—
470C42—41no—
471C42—41no—
472C42—41no—
473C42—41no—
474C42C24×C1711yescharacteristic
475C23—21no—
476Q8—21no—
477Q8—21no—
478Q8—21no—
479Q8—21no—
480Q8—21no—
481Q8—41no—
482Q8—41no—
483Q8—41no—
484Q8—41no—
485Q8—41no—
486Q8—41no—
487Q8—81no—
488Q8—161no—
489Q8C17×#13512yes—
490D4—21no—
491D4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4C22×D4×C1711yescharacteristic
506C2×C4C22×D4×C1711yescharacteristic
507C2×C4C17×H(5,𝔽2)11yescharacteristic
508C8—21no—
509C8—21no—
510C8—21no—
511C8—21no—
512C8—41no—
513C8—41no—
514C8—41no—
515C8—41no—
516C8—41no—
517C22—41no—
518C22—41no—
519C22—41no—
520C22D42×C1711yescharacteristic
521C4—22no—
522C4—21no—
523C4—41no—
524C4—41no—
525C4—41no—
526C4—41no—
527C4—41no—
528C4—41no—
529C4—81no—
530C4—81no—
531C4—81no—
532C4—81no—
533C4C2×C17×#13511yescharacteristic
534C4C17×#57511yescharacteristic
535C4C17×#57811yescharacteristic
536C4C17×#57811yescharacteristic
537C2—81no—
538C2C17×#326911yescharacteristic
539C2C17×#328511yescharacteristic
540C2C17×#328911yescharacteristic
subgroupG/H
center, socleC22×C17D42
commutator, Frattini, cosocleC42C24×C17
prime radicalC2×D4×C17C2×D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C17 ◁ C42×C17 ◁ G

Complements

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

NH ≅ G/Ntype
3. C17×#3363C2semidirect
5. C17×#1718C2semidirect
6. C17×#1700C2semidirect
7. C17×#1684C2semidirect
9. C17×#1674C2semidirect
10. C17×#1653C2semidirect
12. C17×#1645C2semidirect
14. C17×#1584C2semidirect
204. #19848C17direct (N × H)
249. #3363C2×C17semidirect
251. #1718C2×C17semidirect
252. #1700C2×C17semidirect
253. #1684C2×C17semidirect
255. #1674C2×C17semidirect
256. #1653C2×C17semidirect
258. #1645C2×C17semidirect
260. #1584C2×C17semidirect
414. C17#19848direct (N × H)

Maximal subgroups

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

subgroupindex
C17×#33692
C17×#33642
C17×#33632
C17×#33422
C17×#17182
C17×#17002
C17×#16842
C17×#16832
C17×#16742
C17×#16532
C17×#16522
C17×#16452
C17×#16382
C17×#15842
C17×SD16⋊C82
#1984817