Finite Group Databasebeta

← C17×#33943 #16891687

Subgroups — C17×#33943 #16891687

Order 4352.

482 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C17×#3393C211yesmaximal, characteristic, complemented
2C17×#3380C211yesmaximal, characteristic, complemented
3C17×#2245C211yesmaximal, characteristic, complemented
4C17×#2243C211yesmaximal, characteristic, complemented
5C17×#2242C211yesmaximal, characteristic, complemented
6C17×#2229C211yesmaximal, characteristic, complemented
7C17×#2228C211yesmaximal, characteristic, complemented
8C17×#2225C211yesmaximal, characteristic, complemented
9C17×#2210C211yesmaximal, characteristic
10C17×#2210C211yesmaximal, characteristic
11C17×#2208C211yesmaximal, characteristic, complemented
12C17×#2183C211yesmaximal, characteristic, complemented
13C17×#2177C211yesmaximal, characteristic
14C17×#2175C211yesmaximal, characteristic, complemented
15C4×C17×SD32C211yesmaximal, characteristic, complemented
16C17×#556—21no—
17C17×#554—21no—
18C2×C17×SD32C2211yescharacteristic
19C2×C17×SD32C2211yescharacteristic
20C2×C17×D16C2211yescharacteristic
21C17×#500C2211yescharacteristic
22C17×#499C2211yescharacteristic
23C17×#499C2211yescharacteristic
24C17×#495C2211yescharacteristic
25C17×#495C2211yescharacteristic
26C17×#494C2211yescharacteristic
27C17×#478—21no—
28C17×#478—21no—
29C17×#476—21no—
30C17×#464—21no—
31C17×#464—21no—
32C17×#461—21no—
33C8×Q8×C17C2211yescharacteristic
34C4×Q16×C17C2211yescharacteristic
35C4×Q16×C17C2211yescharacteristic
36C4×D8×C17C2211yescharacteristic
37C4×D8×C17C2211yescharacteristic
38C4×D8×C17C2211yescharacteristic
39C4×D8×C17C2211yescharacteristic
40C17×#367C2211yescharacteristic
41C17×#367C2211yescharacteristic
42C17×#366C2211yescharacteristic
43C17×C4⋊C16C2211yescharacteristic
44C17×C4⋊C16C2211yescharacteristic
45C17×C4⋊C16C2211yescharacteristic
46C17×#358C2211yescharacteristic
47C17×#358C2211yescharacteristic
48C17×#358C2211yescharacteristic
49C17×#358C2211yescharacteristic
50C17×#358C2211yescharacteristic
51C17×#358C2211yescharacteristic
52C17×#357C2211yescharacteristic
53C17×#357C2211yescharacteristic
54C17×#357C2211yescharacteristic
55C17×#357C2211yescharacteristic
56C17×#346C2211yescharacteristic
57C17×#346C2211yescharacteristic
58C4×C16×C17C2211yescharacteristic
59C2×Q16×C17—21no—
60C2×Q16×C17C2311yescharacteristic
61C2×Q16×C17C2311yescharacteristic
62C2×SD16×C17—21no—
63C2×SD16×C17—21no—
64C2×D8×C17C2311yescharacteristic
65C2×D8×C17C2311yescharacteristic
66C17×C4⋊Q8—21no—
67C17×C4⋊Q8—21no—
68C17×#126—41no—
69C17×#126—41no—
70C17×#125—21no—
71C17×#125—21no—
72C17×#124—21no—
73C17×#124—21no—
74C17×C22⋊Q8—41no—
75C17×C22⋊Q8—41no—
76C17×C22⋊Q8—41no—
77C17×C22⋊Q8—41no—
78C4×Q8×C17—21no—
79C4×Q8×C17—21no—
80C4×Q8×C17D411yescharacteristic
81C4×D4×C17—21no—
82C4×D4×C17—21no—
83C4×D4×C17—21no—
84C4×D4×C17—21no—
85C17×#117—41no—
86C2×C4⋊C4×C17—41no—
87C17×SD32—22no—
88C17×SD32—22no—
89C17×D16—22no—
90C2×C16×C17C2311yescharacteristic
91C2×C16×C17C2311yescharacteristic
92C2×C16×C17C2311yescharacteristic
93C2×C16×C17C2311yescharacteristic
94C17×#107—21no—
95C17×#107C2311yescharacteristic
96C17×#107C2311yescharacteristic
97C17×#107C2311yescharacteristic
98C17×#107C2311yescharacteristic
99C17×#106—21no—
100C17×#106—21no—
101C17×C4⋊C8D411yescharacteristic
102C17×C4⋊C8D411yescharacteristic
103C17×C4⋊C8D411yescharacteristic
104C17×#103—21no—
105C17×#103—21no—
106C17×#102—21no—
107C17×#102—21no—
108C17×#102—21no—
109C17×#102—21no—
110C4×C8×C17C2311yescharacteristic
111C4×C8×C17C2311yescharacteristic
112C4×C8×C17C2311yescharacteristic
113C2×Q8×C17—21no—
114C2×Q8×C17—21no—
115C2×Q8×C17—41no—
116C2×Q8×C17D811yescharacteristic
117C2×D4×C17—21no—
118C2×D4×C17—21no—
119C22×C4×C17—41no—
120C22×C4×C17—41no—
121C22×C4×C17—41no—
122C22×C4×C17—41no—
123Q16×C17—21no—
124Q16×C17—21no—
125Q16×C17—21no—
126Q16×C17—21no—
127Q16×C17—81no—
128SD16×C17—81no—
129SD16×C17—81no—
130D8×C17—21no—
131D8×C17—21no—
132D8×C17—21no—
133D8×C17#4112yes—
134C2×C8×C17C2×D411yescharacteristic
135C2×C8×C17C2×D411yescharacteristic
136C2×C8×C17C2×D411yescharacteristic
137C2×C8×C17C2411yescharacteristic
138C4⋊C4×C17—21no—
139C4⋊C4×C17—21no—
140C4⋊C4×C17—21no—
141C4⋊C4×C17—21no—
142C4⋊C4×C17—41no—
143C4⋊C4×C17—41no—
144C4⋊C4×C17—41no—
145C4⋊C4×C17—41no—
146C4⋊C4×C17—41no—
147C4⋊C4×C17—41no—
148C4⋊C4×C17—41no—
149C4⋊C4×C17—41no—
150C4⋊C4×C17—41no—
151C4⋊C4×C17D811yescharacteristic
152C4⋊C4×C17D811yescharacteristic
153C4⋊C4×C17D811yescharacteristic
154C22⋊C4×C17—41no—
155C22⋊C4×C17—41no—
156C22⋊C4×C17—41no—
157C22⋊C4×C17—41no—
158C22⋊C4×C17—41no—
159C22⋊C4×C17—41no—
160C22⋊C4×C17—41no—
161C22⋊C4×C17—41no—
162C42×C17—41no—
163C42×C17—41no—
164C42×C17C2×D411yescharacteristic
165C42×C17C2×D411yescharacteristic
166C42×C17C2×D411yescharacteristic
167C16×C17—21no—
168C16×C17—21no—
169C16×C17—21no—
170C16×C17—21no—
171#33943C1711yesmaximal, characteristic, direct product factor, Sylow
172C23×C17—41no—
173C23×C17—41no—
174Q8×C17—41no—
175Q8×C17—41no—
176Q8×C17—41no—
177Q8×C17—41no—
178Q8×C17—41no—
179Q8×C17—161no—
180D4×C17—22no—
181D4×C17—41no—
182D4×C17—41no—
183D4×C17—41no—
184C2×C4×C17—41no—
185C2×C4×C17—41no—
186C2×C4×C17—41no—
187C2×C4×C17—41no—
188C2×C4×C17—41no—
189C2×C4×C17—41no—
190C2×C4×C17—82no—
191C2×C4×C17—82no—
192C2×C4×C17—161no—
193C2×C4×C17—161no—
194C2×C4×C17C2×D811yescharacteristic
195C2×C4×C17C2×D811yescharacteristic
196C2×C4×C17C2×D811yescharacteristic
197C2×C4×C17C2×D811yescharacteristic
198C2×C4×C17C2×D811yescharacteristic
199C2×C4×C17C2×D811yescharacteristic
200C2×C4×C17C22×D411yescharacteristic
201C8×C17—21no—
202C8×C17—21no—
203C8×C17—21no—
204C8×C17C2×#4111yescharacteristic
205C8×C172−1+411yescharacteristic
206#3393C2×C1711yescharacteristic, complemented
207#3380C2×C1711yescharacteristic, complemented
208#2245C2×C1711yescharacteristic, complemented
209#2243C2×C1711yescharacteristic, complemented
210#2242C2×C1711yescharacteristic, complemented
211#2229C2×C1711yescharacteristic, complemented
212#2228C2×C1711yescharacteristic, complemented
213#2225C2×C1711yescharacteristic, complemented
214#2210C2×C1711yescharacteristic
215#2210C2×C1711yescharacteristic
216#2208C2×C1711yescharacteristic, complemented
217#2183C2×C1711yescharacteristic, complemented
218#2177C2×C1711yescharacteristic
219#2175C2×C1711yescharacteristic, complemented
220C4×SD32C2×C1711yescharacteristic, complemented
221C22×C17—42no—
222C22×C17—81no—
223C22×C17—81no—
224C22×C17—81no—
225C22×C17—81no—
226C22×C17—81no—
227C22×C17C22×D811yescharacteristic
228C4×C17—21no—
229C4×C17—21no—
230C4×C17—21no—
231C4×C17—21no—
232C4×C17—21no—
233C4×C17—21no—
234C4×C17—81no—
235C4×C17—81no—
236C4×C17—81no—
237C4×C17—81no—
238C4×C17—81no—
239C4×C17—81no—
240C4×C17#54811yescharacteristic
241C4×C17#57711yescharacteristic
242#556—21no—
243#554—21no—
244C2×SD32C22×C1711yescharacteristic
245C2×SD32C22×C1711yescharacteristic
246C2×D16C22×C1711yescharacteristic
247#500C22×C1711yescharacteristic
248#499C22×C1711yescharacteristic
249#499C22×C1711yescharacteristic
250#495C22×C1711yescharacteristic
251#495C22×C1711yescharacteristic
252#494C22×C1711yescharacteristic
253#478—21no—
254#478—21no—
255#476—21no—
256#464—21no—
257#464—21no—
258#461—21no—
259C8×Q8C22×C1711yescharacteristic
260C4×Q16C22×C1711yescharacteristic
261C4×Q16C22×C1711yescharacteristic
262C4×D8C22×C1711yescharacteristic
263C4×D8C22×C1711yescharacteristic
264C4×D8C22×C1711yescharacteristic
265C4×D8C22×C1711yescharacteristic
266#367C22×C1711yescharacteristic
267#367C22×C1711yescharacteristic
268#366C22×C1711yescharacteristic
269C4⋊C16C22×C1711yescharacteristic
270C4⋊C16C22×C1711yescharacteristic
271C4⋊C16C22×C1711yescharacteristic
272#358C22×C1711yescharacteristic
273#358C22×C1711yescharacteristic
274#358C22×C1711yescharacteristic
275#358C22×C1711yescharacteristic
276#358C22×C1711yescharacteristic
277#358C22×C1711yescharacteristic
278#357C22×C1711yescharacteristic
279#357C22×C1711yescharacteristic
280#357C22×C1711yescharacteristic
281#357C22×C1711yescharacteristic
282#346C22×C1711yescharacteristic
283#346C22×C1711yescharacteristic
284C4×C16C22×C1711yescharacteristic
285C2×C17—82no—
286C2×C17—161no—
287C2×C17#335811yescharacteristic
288C2×C17#341411yescharacteristic
289C2×C17#341611yescharacteristic
290C2×Q16—21no—
291C2×Q16C23×C1711yescharacteristic
292C2×Q16C23×C1711yescharacteristic
293C2×SD16—21no—
294C2×SD16—21no—
295C2×D8C23×C1711yescharacteristic
296C2×D8C23×C1711yescharacteristic
297C4⋊Q8—21no—
298C4⋊Q8—21no—
299#126—41no—
300#126—41no—
301#125—21no—
302#125—21no—
303#124—21no—
304#124—21no—
305C22⋊Q8—41no—
306C22⋊Q8—41no—
307C22⋊Q8—41no—
308C22⋊Q8—41no—
309C4×Q8—21no—
310C4×Q8—21no—
311C4×Q8D4×C1711yescharacteristic
312C4×D4—21no—
313C4×D4—21no—
314C4×D4—21no—
315C4×D4—21no—
316#117—41no—
317C2×C4⋊C4—41no—
318SD32—22no—
319SD32—22no—
320D16—22no—
321C2×C16C23×C1711yescharacteristic
322C2×C16C23×C1711yescharacteristic
323C2×C16C23×C1711yescharacteristic
324C2×C16C23×C1711yescharacteristic
325#107—21no—
326#107C23×C1711yescharacteristic
327#107C23×C1711yescharacteristic
328#107C23×C1711yescharacteristic
329#107C23×C1711yescharacteristic
330#106—21no—
331#106—21no—
332C4⋊C8D4×C1711yescharacteristic
333C4⋊C8D4×C1711yescharacteristic
334C4⋊C8D4×C1711yescharacteristic
335#103—21no—
336#103—21no—
337#102—21no—
338#102—21no—
339#102—21no—
340#102—21no—
341C4×C8C23×C1711yescharacteristic
342C4×C8C23×C1711yescharacteristic
343C4×C8C23×C1711yescharacteristic
344C17#3394311yescharacteristic, direct product factor, Sylow
345C2×Q8—21no—
346C2×Q8—21no—
347C2×Q8—41no—
348C2×Q8D8×C1711yescharacteristic
349C2×D4—21no—
350C2×D4—21no—
351C22×C4—41no—
352C22×C4—41no—
353C22×C4—41no—
354C22×C4—41no—
355Q16—21no—
356Q16—21no—
357Q16—21no—
358Q16—21no—
359Q16—81no—
360SD16—81no—
361SD16—81no—
362D8—21no—
363D8—21no—
364D8—21no—
365D8#41×C1712yes—
366C2×C8C2×D4×C1711yescharacteristic
367C2×C8C2×D4×C1711yescharacteristic
368C2×C8C2×D4×C1711yescharacteristic
369C2×C8C24×C1711yescharacteristic
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—21no—
374C4⋊C4—41no—
375C4⋊C4—41no—
376C4⋊C4—41no—
377C4⋊C4—41no—
378C4⋊C4—41no—
379C4⋊C4—41no—
380C4⋊C4—41no—
381C4⋊C4—41no—
382C4⋊C4—41no—
383C4⋊C4D8×C1711yescharacteristic
384C4⋊C4D8×C1711yescharacteristic
385C4⋊C4D8×C1711yescharacteristic
386C22⋊C4—41no—
387C22⋊C4—41no—
388C22⋊C4—41no—
389C22⋊C4—41no—
390C22⋊C4—41no—
391C22⋊C4—41no—
392C22⋊C4—41no—
393C22⋊C4—41no—
394C42—41no—
395C42—41no—
396C42C2×D4×C1711yescharacteristic
397C42C2×D4×C1711yescharacteristic
398C42C2×D4×C1711yescharacteristic
399C16—21no—
400C16—21no—
401C16—21no—
402C16—21no—
403C23—41no—
404C23—41no—
405Q8—41no—
406Q8—41no—
407Q8—41no—
408Q8—41no—
409Q8—41no—
410Q8—161no—
411D4—22no—
412D4—41no—
413D4—41no—
414D4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—82no—
422C2×C4—82no—
423C2×C4—161no—
424C2×C4—161no—
425C2×C4C2×D8×C1711yescharacteristic
426C2×C4C2×D8×C1711yescharacteristic
427C2×C4C2×D8×C1711yescharacteristic
428C2×C4C2×D8×C1711yescharacteristic
429C2×C4C2×D8×C1711yescharacteristic
430C2×C4C2×D8×C1711yescharacteristic
431C2×C4C22×D4×C1711yescharacteristic
432C8—21no—
433C8—21no—
434C8—21no—
435C8C2×#41×C1711yescharacteristic
436C8C17×2−1+411yescharacteristic
437C22—42no—
438C22—81no—
439C22—81no—
440C22—81no—
441C22—81no—
442C22—81no—
443C22C22×D8×C1711yescharacteristic
444C4—21no—
445C4—21no—
446C4—21no—
447C4—21no—
448C4—21no—
449C4—21no—
450C4—81no—
451C4—81no—
452C4—81no—
453C4—81no—
454C4—81no—
455C4—81no—
456C4C17×#54811yescharacteristic
457C4C17×#57711yescharacteristic
458C2—82no—
459C2—161no—
460C2C17×#335811yescharacteristic
461C2C17×#341411yescharacteristic
462C2C17×#341611yescharacteristic
subgroupG/H
center, socleC22×C17C22×D8
commutator, Frattini, cosocleC2×C8C24×C17
prime radicalC2×C17×D16C22
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×#3393C2semidirect
2. C17×#3380C2semidirect
3. C17×#2245C2semidirect
4. C17×#2243C2semidirect
5. C17×#2242C2semidirect
6. C17×#2229C2semidirect
7. C17×#2228C2semidirect
8. C17×#2225C2semidirect
11. C17×#2208C2semidirect
12. C17×#2183C2semidirect
14. C17×#2175C2semidirect
15. C4×C17×SD32C2semidirect
171. #33943C17direct (N × H)
206. #3393C2×C17semidirect
207. #3380C2×C17semidirect
208. #2245C2×C17semidirect
209. #2243C2×C17semidirect
210. #2242C2×C17semidirect
211. #2229C2×C17semidirect
212. #2228C2×C17semidirect
213. #2225C2×C17semidirect
216. #2208C2×C17semidirect
217. #2183C2×C17semidirect
219. #2175C2×C17semidirect
220. C4×SD32C2×C17semidirect
344. C17#33943direct (N × H)

Maximal subgroups

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

subgroupindex
C17×#33932
C17×#33802
C17×#22452
C17×#22432
C17×#22422
C17×#22292
C17×#22282
C17×#22252
C17×#22102
C17×#22082
C17×#21832
C17×#21772
C17×#21752
C4×C17×SD322
#3394317