Finite Group Databasebeta

← C17×#33937 #16891681

Subgroups — C17×#33937 #16891681

Order 4352.

494 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C17×#3396C211yesmaximal, characteristic, complemented
2C17×#3380C211yesmaximal, characteristic, complemented
3C17×#2244C211yesmaximal, characteristic, complemented
4C17×#2243C211yesmaximal, characteristic, complemented
5C17×#2242C211yesmaximal, characteristic, complemented
6C17×#2229C211yesmaximal, characteristic, complemented
7C17×#2228C211yesmaximal, characteristic, complemented
8C17×#2224C211yesmaximal, characteristic, complemented
9C17×#2210C211yesmaximal, characteristic, complemented
10C17×#2210C211yesmaximal, characteristic, complemented
11C17×#2206C211yesmaximal, characteristic
12C17×#2183C211yesmaximal, characteristic, complemented
13C17×#2177C211yesmaximal, characteristic, complemented
14C17×#2175C211yesmaximal, characteristic, complemented
15C4×C17×D16C211yesmaximal, characteristic, complemented
16C17×#559—21no—
17C17×#554—21no—
18C2×C17×SD32C2211yescharacteristic
19C2×C17×D16C2211yescharacteristic
20C2×C17×D16C2211yescharacteristic
21C17×#500C2211yescharacteristic
22C17×#499C2211yescharacteristic
23C17×#499C2211yescharacteristic
24C17×#495C2211yescharacteristic
25C17×#495C2211yescharacteristic
26C17×#493C2211yescharacteristic
27C17×#478—21no—
28C17×#478—21no—
29C17×#476—21no—
30C17×#463—21no—
31C17×#463—21no—
32C17×#460—21no—
33C8×Q8×C17C2211yescharacteristic
34C4×Q16×C17C2211yescharacteristic
35C4×D8×C17C2211yescharacteristic
36C4×D8×C17C2211yescharacteristic
37C4×D8×C17C2211yescharacteristic
38C4×D8×C17C2211yescharacteristic
39C4×D8×C17C2211yescharacteristic
40C17×#367C2211yescharacteristic
41C17×#366C2211yescharacteristic
42C17×#366C2211yescharacteristic
43C17×C4⋊C16C2211yescharacteristic
44C17×C4⋊C16C2211yescharacteristic
45C17×C4⋊C16C2211yescharacteristic
46C17×#358C2211yescharacteristic
47C17×#358C2211yescharacteristic
48C17×#358C2211yescharacteristic
49C17×#357C2211yescharacteristic
50C17×#357C2211yescharacteristic
51C17×#357C2211yescharacteristic
52C17×#357C2211yescharacteristic
53C17×#357C2211yescharacteristic
54C17×#357C2211yescharacteristic
55C17×#357C2211yescharacteristic
56C17×#346C2211yescharacteristic
57C17×#346C2211yescharacteristic
58C4×C16×C17C2211yescharacteristic
59C2×Q16×C17C2311yescharacteristic
60C2×SD16×C17—21no—
61C2×SD16×C17—21no—
62C2×D8×C17—21no—
63C2×D8×C17C2311yescharacteristic
64C2×D8×C17C2311yescharacteristic
65C2×D8×C17C2311yescharacteristic
66C17×C4⋊Q8—21no—
67C17×#127—21no—
68C17×#125—21no—
69C17×#125—21no—
70C17×#124—21no—
71C17×#124—21no—
72C17×#124—41no—
73C17×#123—41no—
74C17×#123—41no—
75C17×C22⋊Q8—41no—
76C17×C22⋊Q8—41no—
77C17×C22⋊Q8—41no—
78C4×Q8×C17—21no—
79C4×Q8×C17D411yescharacteristic
80C4×D4×C17—21no—
81C4×D4×C17—21no—
82C4×D4×C17—21no—
83C4×D4×C17—21no—
84C4×D4×C17—21no—
85C4×D4×C17—41no—
86C2×C4⋊C4×C17—41no—
87C17×SD32—22no—
88C17×D16—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×#102—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—41no—
115C2×Q8×C17D811yescharacteristic
116C2×D4×C17—21no—
117C2×D4×C17—21no—
118C2×D4×C17—21no—
119C2×D4×C17—41no—
120C2×D4×C17—41no—
121C22×C4×C17—41no—
122C22×C4×C17—41no—
123C22×C4×C17—41no—
124C22×C4×C17—41no—
125C22×C4×C17—41no—
126Q16×C17—21no—
127Q16×C17—21no—
128SD16×C17—81no—
129SD16×C17—81no—
130D8×C17—21no—
131D8×C17—21no—
132D8×C17—21no—
133D8×C17—21no—
134D8×C17—21no—
135D8×C17—81no—
136D8×C17#4112yes—
137C2×C8×C17C2×D411yescharacteristic
138C2×C8×C17C2×D411yescharacteristic
139C2×C8×C17C2×D411yescharacteristic
140C2×C8×C17C2411yescharacteristic
141C4⋊C4×C17—21no—
142C4⋊C4×C17—21no—
143C4⋊C4×C17—21no—
144C4⋊C4×C17—21no—
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—
162C22⋊C4×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#33937C1711yesmaximal, characteristic, direct product factor, Sylow
172C23×C17—41no—
173C23×C17—41no—
174C23×C17—41no—
175Q8×C17—41no—
176Q8×C17—41no—
177Q8×C17—41no—
178Q8×C17—161no—
179D4×C17—22no—
180D4×C17—41no—
181D4×C17—41no—
182D4×C17—41no—
183D4×C17—41no—
184D4×C17—41no—
185D4×C17—82no—
186D4×C17—161no—
187C2×C4×C17—41no—
188C2×C4×C17—41no—
189C2×C4×C17—41no—
190C2×C4×C17—41no—
191C2×C4×C17—41no—
192C2×C4×C17—82no—
193C2×C4×C17—161no—
194C2×C4×C17—161no—
195C2×C4×C17—161no—
196C2×C4×C17—161no—
197C2×C4×C17C2×D811yescharacteristic
198C2×C4×C17C2×D811yescharacteristic
199C2×C4×C17C2×D811yescharacteristic
200C2×C4×C17C2×D811yescharacteristic
201C2×C4×C17C2×D811yescharacteristic
202C2×C4×C17C2×D811yescharacteristic
203C2×C4×C17C22×D411yescharacteristic
204C8×C17—21no—
205C8×C17—21no—
206C8×C17—21no—
207C8×C17C2×#4111yescharacteristic
208C8×C172−1+411yescharacteristic
209#3396C2×C1711yescharacteristic, complemented
210#3380C2×C1711yescharacteristic, complemented
211#2244C2×C1711yescharacteristic, complemented
212#2243C2×C1711yescharacteristic, complemented
213#2242C2×C1711yescharacteristic, complemented
214#2229C2×C1711yescharacteristic, complemented
215#2228C2×C1711yescharacteristic, complemented
216#2224C2×C1711yescharacteristic, complemented
217#2210C2×C1711yescharacteristic, complemented
218#2210C2×C1711yescharacteristic, complemented
219#2206C2×C1711yescharacteristic
220#2183C2×C1711yescharacteristic, complemented
221#2177C2×C1711yescharacteristic, complemented
222#2175C2×C1711yescharacteristic, complemented
223C4×D16C2×C1711yescharacteristic, complemented
224C22×C17—42no—
225C22×C17—81no—
226C22×C17—81no—
227C22×C17—81no—
228C22×C17—81no—
229C22×C17—81no—
230C22×C17—81no—
231C22×C17—81no—
232C22×C17—81no—
233C22×C17C22×D811yescharacteristic
234C4×C17—21no—
235C4×C17—21no—
236C4×C17—21no—
237C4×C17—21no—
238C4×C17—21no—
239C4×C17—21no—
240C4×C17—81no—
241C4×C17—81no—
242C4×C17—81no—
243C4×C17—81no—
244C4×C17—81no—
245C4×C17#54811yescharacteristic
246C4×C17#57711yescharacteristic
247#559—21no—
248#554—21no—
249C2×SD32C22×C1711yescharacteristic
250C2×D16C22×C1711yescharacteristic
251C2×D16C22×C1711yescharacteristic
252#500C22×C1711yescharacteristic
253#499C22×C1711yescharacteristic
254#499C22×C1711yescharacteristic
255#495C22×C1711yescharacteristic
256#495C22×C1711yescharacteristic
257#493C22×C1711yescharacteristic
258#478—21no—
259#478—21no—
260#476—21no—
261#463—21no—
262#463—21no—
263#460—21no—
264C8×Q8C22×C1711yescharacteristic
265C4×Q16C22×C1711yescharacteristic
266C4×D8C22×C1711yescharacteristic
267C4×D8C22×C1711yescharacteristic
268C4×D8C22×C1711yescharacteristic
269C4×D8C22×C1711yescharacteristic
270C4×D8C22×C1711yescharacteristic
271#367C22×C1711yescharacteristic
272#366C22×C1711yescharacteristic
273#366C22×C1711yescharacteristic
274C4⋊C16C22×C1711yescharacteristic
275C4⋊C16C22×C1711yescharacteristic
276C4⋊C16C22×C1711yescharacteristic
277#358C22×C1711yescharacteristic
278#358C22×C1711yescharacteristic
279#358C22×C1711yescharacteristic
280#357C22×C1711yescharacteristic
281#357C22×C1711yescharacteristic
282#357C22×C1711yescharacteristic
283#357C22×C1711yescharacteristic
284#357C22×C1711yescharacteristic
285#357C22×C1711yescharacteristic
286#357C22×C1711yescharacteristic
287#346C22×C1711yescharacteristic
288#346C22×C1711yescharacteristic
289C4×C16C22×C1711yescharacteristic
290C2×C17—82no—
291C2×C17—161no—
292C2×C17—161no—
293C2×C17#335811yescharacteristic
294C2×C17#341411yescharacteristic
295C2×C17#341511yescharacteristic
296C2×Q16C23×C1711yescharacteristic
297C2×SD16—21no—
298C2×SD16—21no—
299C2×D8—21no—
300C2×D8C23×C1711yescharacteristic
301C2×D8C23×C1711yescharacteristic
302C2×D8C23×C1711yescharacteristic
303C4⋊Q8—21no—
304#127—21no—
305#125—21no—
306#125—21no—
307#124—21no—
308#124—21no—
309#124—41no—
310#123—41no—
311#123—41no—
312C22⋊Q8—41no—
313C22⋊Q8—41no—
314C22⋊Q8—41no—
315C4×Q8—21no—
316C4×Q8D4×C1711yescharacteristic
317C4×D4—21no—
318C4×D4—21no—
319C4×D4—21no—
320C4×D4—21no—
321C4×D4—21no—
322C4×D4—41no—
323C2×C4⋊C4—41no—
324SD32—22no—
325D16—22no—
326D16—22no—
327C2×C16C23×C1711yescharacteristic
328C2×C16C23×C1711yescharacteristic
329C2×C16C23×C1711yescharacteristic
330C2×C16C23×C1711yescharacteristic
331#107—21no—
332#107C23×C1711yescharacteristic
333#107C23×C1711yescharacteristic
334#107C23×C1711yescharacteristic
335#107C23×C1711yescharacteristic
336#106—21no—
337#106—21no—
338C4⋊C8D4×C1711yescharacteristic
339C4⋊C8D4×C1711yescharacteristic
340C4⋊C8D4×C1711yescharacteristic
341#103—21no—
342#102—21no—
343#102—21no—
344#102—21no—
345#102—21no—
346#102—21no—
347C4×C8C23×C1711yescharacteristic
348C4×C8C23×C1711yescharacteristic
349C4×C8C23×C1711yescharacteristic
350C17#3393711yescharacteristic, direct product factor, Sylow
351C2×Q8—21no—
352C2×Q8—41no—
353C2×Q8D8×C1711yescharacteristic
354C2×D4—21no—
355C2×D4—21no—
356C2×D4—21no—
357C2×D4—41no—
358C2×D4—41no—
359C22×C4—41no—
360C22×C4—41no—
361C22×C4—41no—
362C22×C4—41no—
363C22×C4—41no—
364Q16—21no—
365Q16—21no—
366SD16—81no—
367SD16—81no—
368D8—21no—
369D8—21no—
370D8—21no—
371D8—21no—
372D8—21no—
373D8—81no—
374D8#41×C1712yes—
375C2×C8C2×D4×C1711yescharacteristic
376C2×C8C2×D4×C1711yescharacteristic
377C2×C8C2×D4×C1711yescharacteristic
378C2×C8C24×C1711yescharacteristic
379C4⋊C4—21no—
380C4⋊C4—21no—
381C4⋊C4—21no—
382C4⋊C4—21no—
383C4⋊C4—41no—
384C4⋊C4—41no—
385C4⋊C4—41no—
386C4⋊C4—41no—
387C4⋊C4—41no—
388C4⋊C4—41no—
389C4⋊C4D8×C1711yescharacteristic
390C4⋊C4D8×C1711yescharacteristic
391C4⋊C4D8×C1711yescharacteristic
392C22⋊C4—41no—
393C22⋊C4—41no—
394C22⋊C4—41no—
395C22⋊C4—41no—
396C22⋊C4—41no—
397C22⋊C4—41no—
398C22⋊C4—41no—
399C22⋊C4—41no—
400C22⋊C4—41no—
401C42—41no—
402C42C2×D4×C1711yescharacteristic
403C42C2×D4×C1711yescharacteristic
404C42C2×D4×C1711yescharacteristic
405C16—21no—
406C16—21no—
407C16—21no—
408C16—21no—
409C23—41no—
410C23—41no—
411C23—41no—
412Q8—41no—
413Q8—41no—
414Q8—41no—
415Q8—161no—
416D4—22no—
417D4—41no—
418D4—41no—
419D4—41no—
420D4—41no—
421D4—41no—
422D4—82no—
423D4—161no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—82no—
430C2×C4—161no—
431C2×C4—161no—
432C2×C4—161no—
433C2×C4—161no—
434C2×C4C2×D8×C1711yescharacteristic
435C2×C4C2×D8×C1711yescharacteristic
436C2×C4C2×D8×C1711yescharacteristic
437C2×C4C2×D8×C1711yescharacteristic
438C2×C4C2×D8×C1711yescharacteristic
439C2×C4C2×D8×C1711yescharacteristic
440C2×C4C22×D4×C1711yescharacteristic
441C8—21no—
442C8—21no—
443C8—21no—
444C8C2×#41×C1711yescharacteristic
445C8C17×2−1+411yescharacteristic
446C22—42no—
447C22—81no—
448C22—81no—
449C22—81no—
450C22—81no—
451C22—81no—
452C22—81no—
453C22—81no—
454C22—81no—
455C22C22×D8×C1711yescharacteristic
456C4—21no—
457C4—21no—
458C4—21no—
459C4—21no—
460C4—21no—
461C4—21no—
462C4—81no—
463C4—81no—
464C4—81no—
465C4—81no—
466C4—81no—
467C4C17×#54811yescharacteristic
468C4C17×#57711yescharacteristic
469C2—82no—
470C2—161no—
471C2—161no—
472C2C17×#335811yescharacteristic
473C2C17×#341411yescharacteristic
474C2C17×#341511yescharacteristic
subgroupG/H
center, socleC22×C17C22×D8
commutator, Frattini, cosocleC2×C8C24×C17
prime radicalC17×#2206C2
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×#3380C2semidirect
3. C17×#2244C2semidirect
4. C17×#2243C2semidirect
5. C17×#2242C2semidirect
6. C17×#2229C2semidirect
7. C17×#2228C2semidirect
8. C17×#2224C2semidirect
9. C17×#2210C2semidirect
10. C17×#2210C2semidirect
12. C17×#2183C2semidirect
13. C17×#2177C2semidirect
14. C17×#2175C2semidirect
15. C4×C17×D16C2semidirect
171. #33937C17direct (N × H)
209. #3396C2×C17semidirect
210. #3380C2×C17semidirect
211. #2244C2×C17semidirect
212. #2243C2×C17semidirect
213. #2242C2×C17semidirect
214. #2229C2×C17semidirect
215. #2228C2×C17semidirect
216. #2224C2×C17semidirect
217. #2210C2×C17semidirect
218. #2210C2×C17semidirect
220. #2183C2×C17semidirect
221. #2177C2×C17semidirect
222. #2175C2×C17semidirect
223. C4×D16C2×C17semidirect
350. C17#33937direct (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×#33802
C17×#22442
C17×#22432
C17×#22422
C17×#22292
C17×#22282
C17×#22242
C17×#22102
C17×#22062
C17×#21832
C17×#21772
C17×#21752
C4×C17×D162
#3393717