Finite Group Databasebeta

← C17×#33968 #16891712

Subgroups — C17×#33968 #16891712

Order 4352.

516 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C17×#3396C211yesmaximal, characteristic, complemented
2C17×#3393C211yesmaximal, characteristic, complemented
3C17×#2251C211yesmaximal, characteristic, complemented
4C17×#2250C211yesmaximal, characteristic
5C17×#2249C211yesmaximal, characteristic, complemented
6C17×#2211C211yesmaximal, characteristic, complemented
7C17×#2211C211yesmaximal, characteristic, complemented
8C17×#2210C211yesmaximal, characteristic, complemented
9C17×#2210C211yesmaximal, characteristic, complemented
10C17×#2208C211yesmaximal, characteristic, complemented
11C17×#2207C211yesmaximal, characteristic, complemented
12C17×#2183C211yesmaximal, characteristic, complemented
13C17×#2177C211yesmaximal, characteristic, complemented
14C17×#2176C211yesmaximal, characteristic, complemented
15C4×C17×SD32C211yesmaximal, characteristic, complemented
16C17×#559—21no—
17C17×#556—21no—
18C2×C17×Q32C2211yescharacteristic
19C2×C17×Q32C2211yescharacteristic
20C2×C17×SD32C2211yescharacteristic
21C2×C17×SD32C2211yescharacteristic
22C2×C17×SD32C2211yescharacteristic
23C2×C17×SD32C2211yescharacteristic
24C2×C17×SD32C2211yescharacteristic
25C2×C17×D16C2211yescharacteristic
26C2×C17×D16C2211yescharacteristic
27C17×#495C2211yescharacteristic
28C17×#495C2211yescharacteristic
29C17×#495C2211yescharacteristic
30C17×#495C2211yescharacteristic
31C17×#494C2211yescharacteristic
32C17×#493C2211yescharacteristic
33C17×#464—21no—
34C17×#464—21no—
35C17×#463—21no—
36C17×#463—21no—
37C17×#461—21no—
38C17×#460—21no—
39C8×Q8×C17C2211yescharacteristic
40C4×Q16×C17C2211yescharacteristic
41C4×Q16×C17C2211yescharacteristic
42C4×Q16×C17C2211yescharacteristic
43C4×D8×C17C2211yescharacteristic
44C4×D8×C17C2211yescharacteristic
45C4×D8×C17C2211yescharacteristic
46C17×#367C2211yescharacteristic
47C17×C4⋊C16C2211yescharacteristic
48C17×C4⋊C16C2211yescharacteristic
49C17×C4⋊C16C2211yescharacteristic
50C17×#358C2211yescharacteristic
51C17×#358C2211yescharacteristic
52C17×#358C2211yescharacteristic
53C17×#357C2211yescharacteristic
54C17×#357C2211yescharacteristic
55C17×#357C2211yescharacteristic
56C17×#346C2211yescharacteristic
57C17×#346C2211yescharacteristic
58C4×C16×C17C2211yescharacteristic
59C2×Q16×C17—21no—
60C2×Q16×C17C2311yescharacteristic
61C2×Q16×C17C2311yescharacteristic
62C2×Q16×C17C2311yescharacteristic
63C2×SD16×C17—21no—
64C2×SD16×C17—21no—
65C2×SD16×C17—21no—
66C2×SD16×C17—21no—
67C2×D8×C17—21no—
68C2×D8×C17C2311yescharacteristic
69C2×D8×C17C2311yescharacteristic
70C2×D8×C17C2311yescharacteristic
71C17×C4⋊Q8—21no—
72C17×#127—21no—
73C17×#126—41no—
74C17×#126—41no—
75C17×#124—21no—
76C17×#124—21no—
77C17×#124—21no—
78C17×#124—21no—
79C17×#124—41no—
80C17×#123—41no—
81C17×#123—41no—
82C17×C22⋊Q8—41no—
83C4×Q8×C17—21no—
84C4×Q8×C17—21no—
85C4×Q8×C17—21no—
86C4×Q8×C17D411yescharacteristic
87C4×D4×C17—21no—
88C4×D4×C17—21no—
89C4×D4×C17—21no—
90C4×D4×C17—41no—
91C17×#117—41no—
92C17×Q32—22no—
93C17×Q32—41no—
94C17×SD32—22no—
95C17×SD32—41no—
96C17×SD32—41no—
97C17×SD32—41no—
98C17×SD32—41no—
99C17×D16—22no—
100C17×D16—41no—
101C2×C16×C17C2311yescharacteristic
102C2×C16×C17C2311yescharacteristic
103C2×C16×C17C2311yescharacteristic
104C2×C16×C17C2311yescharacteristic
105C17×#107C2311yescharacteristic
106C17×#107C2311yescharacteristic
107C17×C4⋊C8D411yescharacteristic
108C17×C4⋊C8D411yescharacteristic
109C17×C4⋊C8D411yescharacteristic
110C17×#103—21no—
111C17×#103—21no—
112C17×#103—21no—
113C17×#102—21no—
114C17×#102—21no—
115C17×#102—21no—
116C4×C8×C17C2311yescharacteristic
117C4×C8×C17C2311yescharacteristic
118C4×C8×C17C2311yescharacteristic
119C2×Q8×C17—21no—
120C2×Q8×C17—21no—
121C2×Q8×C17—21no—
122C2×Q8×C17D811yescharacteristic
123C2×D4×C17—21no—
124C2×D4×C17—21no—
125C2×D4×C17—21no—
126C2×D4×C17—41no—
127C2×D4×C17—41no—
128C22×C4×C17—41no—
129C22×C4×C17—41no—
130C22×C4×C17—41no—
131Q16×C17—21no—
132Q16×C17—21no—
133Q16×C17—21no—
134Q16×C17—21no—
135Q16×C17—21no—
136Q16×C17—21no—
137Q16×C17—81no—
138SD16×C17—81no—
139SD16×C17—81no—
140SD16×C17—81no—
141SD16×C17—81no—
142D8×C17—21no—
143D8×C17—21no—
144D8×C17—21no—
145D8×C17—21no—
146D8×C17—21no—
147D8×C17—21no—
148D8×C17—81no—
149C2×C8×C17C2×D411yescharacteristic
150C2×C8×C17C2×D411yescharacteristic
151C2×C8×C17C2×D411yescharacteristic
152C2×C8×C17C2411yescharacteristic
153C4⋊C4×C17—21no—
154C4⋊C4×C17—21no—
155C4⋊C4×C17—41no—
156C4⋊C4×C17—41no—
157C4⋊C4×C17—41no—
158C4⋊C4×C17—41no—
159C4⋊C4×C17—41no—
160C4⋊C4×C17D811yescharacteristic
161C4⋊C4×C17D811yescharacteristic
162C4⋊C4×C17D811yescharacteristic
163C22⋊C4×C17—41no—
164C22⋊C4×C17—41no—
165C22⋊C4×C17—41no—
166C22⋊C4×C17—41no—
167C22⋊C4×C17—41no—
168C22⋊C4×C17—41no—
169C22⋊C4×C17—41no—
170C22⋊C4×C17—41no—
171C22⋊C4×C17—41no—
172C22⋊C4×C17—41no—
173C22⋊C4×C17—41no—
174C42×C17—41no—
175C42×C17—41no—
176C42×C17—41no—
177C42×C17C2×D411yescharacteristic
178C42×C17C2×D411yescharacteristic
179C42×C17C2×D411yescharacteristic
180C16×C17—21no—
181C16×C17—21no—
182C16×C17—21no—
183C16×C17#4112yes—
184#33968C1711yesmaximal, characteristic, direct product factor, Sylow
185C23×C17—41no—
186C23×C17—41no—
187C23×C17—41no—
188Q8×C17—41no—
189Q8×C17—41no—
190Q8×C17—41no—
191Q8×C17—41no—
192Q8×C17—41no—
193Q8×C17—41no—
194Q8×C17—41no—
195D4×C17—41no—
196D4×C17—41no—
197D4×C17—41no—
198D4×C17—41no—
199D4×C17—41no—
200D4×C17—41no—
201D4×C17—82no—
202D4×C17—161no—
203C2×C4×C17—41no—
204C2×C4×C17—41no—
205C2×C4×C17—41no—
206C2×C4×C17—41no—
207C2×C4×C17—41no—
208C2×C4×C17—82no—
209C2×C4×C17—161no—
210C2×C4×C17—161no—
211C2×C4×C17C2×D811yescharacteristic
212C2×C4×C17C2×D811yescharacteristic
213C2×C4×C17C2×D811yescharacteristic
214C2×C4×C17C2×D811yescharacteristic
215C2×C4×C17C2×D811yescharacteristic
216C2×C4×C17C2×D811yescharacteristic
217C2×C4×C17C22×D411yescharacteristic
218C8×C17—21no—
219C8×C17—21no—
220C8×C17—21no—
221C8×C17C2×#4111yescharacteristic
222C8×C17H(5,𝔽2)11yescharacteristic
223#3396C2×C1711yescharacteristic, complemented
224#3393C2×C1711yescharacteristic, complemented
225#2251C2×C1711yescharacteristic, complemented
226#2250C2×C1711yescharacteristic
227#2249C2×C1711yescharacteristic, complemented
228#2211C2×C1711yescharacteristic, complemented
229#2211C2×C1711yescharacteristic, complemented
230#2210C2×C1711yescharacteristic, complemented
231#2210C2×C1711yescharacteristic, complemented
232#2208C2×C1711yescharacteristic, complemented
233#2207C2×C1711yescharacteristic, complemented
234#2183C2×C1711yescharacteristic, complemented
235#2177C2×C1711yescharacteristic, complemented
236#2176C2×C1711yescharacteristic, complemented
237C4×SD32C2×C1711yescharacteristic, complemented
238C22×C17—81no—
239C22×C17—81no—
240C22×C17—81no—
241C22×C17—81no—
242C22×C17—81no—
243C22×C17—81no—
244C22×C17—81no—
245C22×C17—81no—
246C22×C17—81no—
247C22×C17C22×D811yescharacteristic
248C4×C17—21no—
249C4×C17—21no—
250C4×C17—21no—
251C4×C17—21no—
252C4×C17—21no—
253C4×C17—21no—
254C4×C17—81no—
255C4×C17—81no—
256C4×C17—81no—
257C4×C17—81no—
258C4×C17—81no—
259C4×C17#55011yescharacteristic
260C4×C17#57611yescharacteristic
261#559—21no—
262#556—21no—
263C2×Q32C22×C1711yescharacteristic
264C2×Q32C22×C1711yescharacteristic
265C2×SD32C22×C1711yescharacteristic
266C2×SD32C22×C1711yescharacteristic
267C2×SD32C22×C1711yescharacteristic
268C2×SD32C22×C1711yescharacteristic
269C2×SD32C22×C1711yescharacteristic
270C2×D16C22×C1711yescharacteristic
271C2×D16C22×C1711yescharacteristic
272#495C22×C1711yescharacteristic
273#495C22×C1711yescharacteristic
274#495C22×C1711yescharacteristic
275#495C22×C1711yescharacteristic
276#494C22×C1711yescharacteristic
277#493C22×C1711yescharacteristic
278#464—21no—
279#464—21no—
280#463—21no—
281#463—21no—
282#461—21no—
283#460—21no—
284C8×Q8C22×C1711yescharacteristic
285C4×Q16C22×C1711yescharacteristic
286C4×Q16C22×C1711yescharacteristic
287C4×Q16C22×C1711yescharacteristic
288C4×D8C22×C1711yescharacteristic
289C4×D8C22×C1711yescharacteristic
290C4×D8C22×C1711yescharacteristic
291#367C22×C1711yescharacteristic
292C4⋊C16C22×C1711yescharacteristic
293C4⋊C16C22×C1711yescharacteristic
294C4⋊C16C22×C1711yescharacteristic
295#358C22×C1711yescharacteristic
296#358C22×C1711yescharacteristic
297#358C22×C1711yescharacteristic
298#357C22×C1711yescharacteristic
299#357C22×C1711yescharacteristic
300#357C22×C1711yescharacteristic
301#346C22×C1711yescharacteristic
302#346C22×C1711yescharacteristic
303C4×C16C22×C1711yescharacteristic
304C2×C17—161no—
305C2×C17—161no—
306C2×C17—161no—
307C2×C17#339111yescharacteristic
308C2×C17#341411yescharacteristic
309C2×C17#341611yescharacteristic
310C2×Q16—21no—
311C2×Q16C23×C1711yescharacteristic
312C2×Q16C23×C1711yescharacteristic
313C2×Q16C23×C1711yescharacteristic
314C2×SD16—21no—
315C2×SD16—21no—
316C2×SD16—21no—
317C2×SD16—21no—
318C2×D8—21no—
319C2×D8C23×C1711yescharacteristic
320C2×D8C23×C1711yescharacteristic
321C2×D8C23×C1711yescharacteristic
322C4⋊Q8—21no—
323#127—21no—
324#126—41no—
325#126—41no—
326#124—21no—
327#124—21no—
328#124—21no—
329#124—21no—
330#124—41no—
331#123—41no—
332#123—41no—
333C22⋊Q8—41no—
334C4×Q8—21no—
335C4×Q8—21no—
336C4×Q8—21no—
337C4×Q8D4×C1711yescharacteristic
338C4×D4—21no—
339C4×D4—21no—
340C4×D4—21no—
341C4×D4—41no—
342#117—41no—
343Q32—22no—
344Q32—41no—
345SD32—22no—
346SD32—41no—
347SD32—41no—
348SD32—41no—
349SD32—41no—
350D16—22no—
351D16—41no—
352C2×C16C23×C1711yescharacteristic
353C2×C16C23×C1711yescharacteristic
354C2×C16C23×C1711yescharacteristic
355C2×C16C23×C1711yescharacteristic
356#107C23×C1711yescharacteristic
357#107C23×C1711yescharacteristic
358C4⋊C8D4×C1711yescharacteristic
359C4⋊C8D4×C1711yescharacteristic
360C4⋊C8D4×C1711yescharacteristic
361#103—21no—
362#103—21no—
363#103—21no—
364#102—21no—
365#102—21no—
366#102—21no—
367C4×C8C23×C1711yescharacteristic
368C4×C8C23×C1711yescharacteristic
369C4×C8C23×C1711yescharacteristic
370C17#3396811yescharacteristic, direct product factor, Sylow
371C2×Q8—21no—
372C2×Q8—21no—
373C2×Q8—21no—
374C2×Q8D8×C1711yescharacteristic
375C2×D4—21no—
376C2×D4—21no—
377C2×D4—21no—
378C2×D4—41no—
379C2×D4—41no—
380C22×C4—41no—
381C22×C4—41no—
382C22×C4—41no—
383Q16—21no—
384Q16—21no—
385Q16—21no—
386Q16—21no—
387Q16—21no—
388Q16—21no—
389Q16—81no—
390SD16—81no—
391SD16—81no—
392SD16—81no—
393SD16—81no—
394D8—21no—
395D8—21no—
396D8—21no—
397D8—21no—
398D8—21no—
399D8—21no—
400D8—81no—
401C2×C8C2×D4×C1711yescharacteristic
402C2×C8C2×D4×C1711yescharacteristic
403C2×C8C2×D4×C1711yescharacteristic
404C2×C8C24×C1711yescharacteristic
405C4⋊C4—21no—
406C4⋊C4—21no—
407C4⋊C4—41no—
408C4⋊C4—41no—
409C4⋊C4—41no—
410C4⋊C4—41no—
411C4⋊C4—41no—
412C4⋊C4D8×C1711yescharacteristic
413C4⋊C4D8×C1711yescharacteristic
414C4⋊C4D8×C1711yescharacteristic
415C22⋊C4—41no—
416C22⋊C4—41no—
417C22⋊C4—41no—
418C22⋊C4—41no—
419C22⋊C4—41no—
420C22⋊C4—41no—
421C22⋊C4—41no—
422C22⋊C4—41no—
423C22⋊C4—41no—
424C22⋊C4—41no—
425C22⋊C4—41no—
426C42—41no—
427C42—41no—
428C42—41no—
429C42C2×D4×C1711yescharacteristic
430C42C2×D4×C1711yescharacteristic
431C42C2×D4×C1711yescharacteristic
432C16—21no—
433C16—21no—
434C16—21no—
435C16#41×C1712yes—
436C23—41no—
437C23—41no—
438C23—41no—
439Q8—41no—
440Q8—41no—
441Q8—41no—
442Q8—41no—
443Q8—41no—
444Q8—41no—
445Q8—41no—
446D4—41no—
447D4—41no—
448D4—41no—
449D4—41no—
450D4—41no—
451D4—41no—
452D4—82no—
453D4—161no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—82no—
460C2×C4—161no—
461C2×C4—161no—
462C2×C4C2×D8×C1711yescharacteristic
463C2×C4C2×D8×C1711yescharacteristic
464C2×C4C2×D8×C1711yescharacteristic
465C2×C4C2×D8×C1711yescharacteristic
466C2×C4C2×D8×C1711yescharacteristic
467C2×C4C2×D8×C1711yescharacteristic
468C2×C4C22×D4×C1711yescharacteristic
469C8—21no—
470C8—21no—
471C8—21no—
472C8C2×#41×C1711yescharacteristic
473C8C17×H(5,𝔽2)11yescharacteristic
474C22—81no—
475C22—81no—
476C22—81no—
477C22—81no—
478C22—81no—
479C22—81no—
480C22—81no—
481C22—81no—
482C22—81no—
483C22C22×D8×C1711yescharacteristic
484C4—21no—
485C4—21no—
486C4—21no—
487C4—21no—
488C4—21no—
489C4—21no—
490C4—81no—
491C4—81no—
492C4—81no—
493C4—81no—
494C4—81no—
495C4C17×#55011yescharacteristic
496C4C17×#57611yescharacteristic
497C2—161no—
498C2—161no—
499C2—161no—
500C2C17×#339111yescharacteristic
501C2C17×#341411yescharacteristic
502C2C17×#341611yescharacteristic
subgroupG/H
center, socleC22×C17C22×D8
commutator, Frattini, cosocleC2×C8C24×C17
prime radicalC17×#2250C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C17 ◁ C4×Q8×C17 ◁ C8×Q8×C17 ◁ G

Complements

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

NH ≅ G/Ntype
1. C17×#3396C2semidirect
2. C17×#3393C2semidirect
3. C17×#2251C2semidirect
5. C17×#2249C2semidirect
6. C17×#2211C2semidirect
7. C17×#2211C2semidirect
8. C17×#2210C2semidirect
9. C17×#2210C2semidirect
10. C17×#2208C2semidirect
11. C17×#2207C2semidirect
12. C17×#2183C2semidirect
13. C17×#2177C2semidirect
14. C17×#2176C2semidirect
15. C4×C17×SD32C2semidirect
184. #33968C17direct (N × H)
223. #3396C2×C17semidirect
224. #3393C2×C17semidirect
225. #2251C2×C17semidirect
227. #2249C2×C17semidirect
228. #2211C2×C17semidirect
229. #2211C2×C17semidirect
230. #2210C2×C17semidirect
231. #2210C2×C17semidirect
232. #2208C2×C17semidirect
233. #2207C2×C17semidirect
234. #2183C2×C17semidirect
235. #2177C2×C17semidirect
236. #2176C2×C17semidirect
237. C4×SD32C2×C17semidirect
370. C17#33968direct (N × H)

Maximal subgroups

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

subgroupindex
C17×#33962
C17×#33932
C17×#22512
C17×#22502
C17×#22492
C17×#22112
C17×#22102
C17×#22082
C17×#22072
C17×#21832
C17×#21772
C17×#21762
C4×C17×SD322
#3396817