Finite Group Databasebeta

← C17×#33914 #16891658

Subgroups — C17×#33914 #16891658

Order 4352.

488 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×#3341C211yesmaximal, characteristic, complemented
2C17×#3339C211yesmaximal, characteristic, complemented
3C17×#2255C211yesmaximal, characteristic, complemented
4C17×#2234C211yesmaximal, characteristic, complemented
5C17×#2234C211yesmaximal, characteristic, complemented
6C17×#2234C211yesmaximal, characteristic, complemented
7C17×#2232C211yesmaximal, characteristic, complemented
8C17×#2228C211yesmaximal, characteristic, complemented
9C17×#2224C211yesmaximal, characteristic, complemented
10C17×#2218C211yesmaximal, characteristic, complemented
11C17×#2215C211yesmaximal, characteristic, complemented
12C17×#2177C211yesmaximal, characteristic, complemented
13C17×#2168C211yesmaximal, characteristic, complemented
14C17×#2159C211yesmaximal, characteristic, complemented
15C17×#2158C211yesmaximal, characteristic, complemented
16C17×#555—21no—
17C17×#553—21no—
18C2×C17×D16C2211yescharacteristic
19C2×C17×M32C2211yescharacteristic
20C22×C16×C17C2211yescharacteristic
21C17×#500C2211yescharacteristic
22C17×#499C2211yescharacteristic
23C17×#482—21no—
24C17×#482—21no—
25C17×#482—21no—
26C17×#481—21no—
27C17×#478—21no—
28C17×#476—21no—
29C17×#466C2211yescharacteristic
30C17×#466C2211yescharacteristic
31C17×#466C2211yescharacteristic
32C17×#466C2211yescharacteristic
33C4×D8×C17C2211yescharacteristic
34C4×D8×C17C2211yescharacteristic
35C8×D4×C17C2211yescharacteristic
36C17×#427C2211yescharacteristic
37C17×#427C2211yescharacteristic
38C17×#427C2211yescharacteristic
39C2×C17×#107C2211yescharacteristic
40C17×#367C2211yescharacteristic
41C17×#367C2211yescharacteristic
42C17×#367C2211yescharacteristic
43C17×#367C2211yescharacteristic
44C17×#366C2211yescharacteristic
45C17×#366C2211yescharacteristic
46C17×#366C2211yescharacteristic
47C17×#366C2211yescharacteristic
48C17×#366C2211yescharacteristic
49C17×C4⋊C16C2211yescharacteristic
50C17×#357C2211yescharacteristic
51C17×#357C2211yescharacteristic
52C17×#357C2211yescharacteristic
53C17×#357C2211yescharacteristic
54C17×#357C2211yescharacteristic
55C17×#357C2211yescharacteristic
56C17×C22⋊C16C2211yescharacteristic
57C17×C22⋊C16C2211yescharacteristic
58C17×#346C2211yescharacteristic
59C2×D8×C17C2311yescharacteristic
60C2×D8×C17C2311yescharacteristic
61C22×C8×C17C2311yescharacteristic
62C22×C8×C17C2311yescharacteristic
63C17×C4⋊Q8—21no—
64C17×#126—41no—
65C17×#125—21no—
66C17×#124—41no—
67C17×#124—41no—
68C17×#123—41no—
69C17×#121—21no—
70C17×#121—21no—
71C17×#121—21no—
72C17×#121—21no—
73C17×#121—41no—
74C17×#121—41no—
75C4×D4×C17—21no—
76C4×D4×C17—21no—
77C4×D4×C17—41no—
78C4×D4×C17D411yescharacteristic
79C17×#117—21no—
80C17×#117—21no—
81C17×#117—21no—
82C17×#117—41no—
83C2×C4⋊C4×C17—21no—
84C17×D16—22no—
85C17×M32—22no—
86C2×C16×C17—22no—
87C2×C16×C17C2311yescharacteristic
88C2×C16×C17C2311yescharacteristic
89C2×C16×C17C2311yescharacteristic
90C2×C16×C17C2311yescharacteristic
91C17×#107—21no—
92C17×#107—21no—
93C17×#107C2311yescharacteristic
94C17×#107C2311yescharacteristic
95C17×#107C2311yescharacteristic
96C17×#107C2311yescharacteristic
97C17×#107C2311yescharacteristic
98C17×#107C2311yescharacteristic
99C17×#106—21no—
100C17×#106—21no—
101C17×#106—21no—
102C17×#106—21no—
103C17×C4⋊C8D411yescharacteristic
104C17×#102—21no—
105C17×#102—21no—
106C17×#102—21no—
107C17×#102—21no—
108C17×#102—21no—
109C17×#102—21no—
110C17×C22⋊C8D411yescharacteristic
111C17×C22⋊C8D411yescharacteristic
112C4×C8×C17C2311yescharacteristic
113C2×Q8×C17—41no—
114C2×D4×C17—21no—
115C2×D4×C17—21no—
116C2×D4×C17—41no—
117C2×D4×C17—41no—
118C2×D4×C17—41no—
119C2×D4×C17—41no—
120C2×D4×C17D811yescharacteristic
121C22×C4×C17—41no—
122C22×C4×C17—41no—
123C22×C4×C17—41no—
124C22×C4×C17C2×D411yescharacteristic
125C22×C4×C17C2×D411yescharacteristic
126D8×C17—21no—
127D8×C17—21no—
128D8×C17—21no—
129D8×C17—21no—
130C2×C8×C17—21no—
131C2×C8×C17—21no—
132C2×C8×C17—21no—
133C2×C8×C17—21no—
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—21no—
143C4⋊C4×C17—21no—
144C4⋊C4×C17—41no—
145C4⋊C4×C17—41no—
146C4⋊C4×C17—41no—
147C4⋊C4×C17—41no—
148C4⋊C4×C17D811yescharacteristic
149C22⋊C4×C17—41no—
150C22⋊C4×C17—41no—
151C22⋊C4×C17—41no—
152C22⋊C4×C17—41no—
153C22⋊C4×C17—41no—
154C22⋊C4×C17—41no—
155C22⋊C4×C17—41no—
156C22⋊C4×C17—41no—
157C22⋊C4×C17—41no—
158C22⋊C4×C17D811yescharacteristic
159C22⋊C4×C17D811yescharacteristic
160C42×C17—41no—
161C42×C17—41no—
162C42×C17—41no—
163C42×C17C2×D411yescharacteristic
164C16×C17—21no—
165C16×C17—21no—
166C16×C17—21no—
167C16×C17#4112yes—
168#33914C1711yesmaximal, characteristic, direct product factor, Sylow
169C23×C17—41no—
170C23×C17—41no—
171C23×C17C2×D811yescharacteristic
172C23×C17C2×D811yescharacteristic
173Q8×C17—161no—
174D4×C17—41no—
175D4×C17—41no—
176D4×C17—41no—
177D4×C17—41no—
178D4×C17—41no—
179D4×C17—82no—
180D4×C17—161no—
181D4×C17—161no—
182D4×C17—161no—
183C2×C4×C17—21no—
184C2×C4×C17—21no—
185C2×C4×C17—21no—
186C2×C4×C17—21no—
187C2×C4×C17—41no—
188C2×C4×C17—41no—
189C2×C4×C17—41no—
190C2×C4×C17—41no—
191C2×C4×C17—41no—
192C2×C4×C17—41no—
193C2×C4×C17—82no—
194C2×C4×C17—161no—
195C2×C4×C17—161no—
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#3341C2×C1711yescharacteristic, complemented
207#3339C2×C1711yescharacteristic, complemented
208#2255C2×C1711yescharacteristic, complemented
209#2234C2×C1711yescharacteristic, complemented
210#2234C2×C1711yescharacteristic, complemented
211#2234C2×C1711yescharacteristic, complemented
212#2232C2×C1711yescharacteristic, complemented
213#2228C2×C1711yescharacteristic, complemented
214#2224C2×C1711yescharacteristic, complemented
215#2218C2×C1711yescharacteristic, complemented
216#2215C2×C1711yescharacteristic, complemented
217#2177C2×C1711yescharacteristic, complemented
218#2168C2×C1711yescharacteristic, complemented
219#2159C2×C1711yescharacteristic, complemented
220#2158C2×C1711yescharacteristic, complemented
221C22×C17—21no—
222C22×C17—21no—
223C22×C17—21no—
224C22×C17—21no—
225C22×C17—21no—
226C22×C17—21no—
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—81no—
239C4×C17—81no—
240C4×C17—81no—
241C4×C17—81no—
242C4×C17—81no—
243C4×C17—81no—
244C4×C17#54711yescharacteristic
245C4×C17#57811yescharacteristic
246#555—21no—
247#553—21no—
248C2×D16C22×C1711yescharacteristic
249C2×M32C22×C1711yescharacteristic
250C22×C16C22×C1711yescharacteristic
251#500C22×C1711yescharacteristic
252#499C22×C1711yescharacteristic
253#482—21no—
254#482—21no—
255#482—21no—
256#481—21no—
257#478—21no—
258#476—21no—
259#466C22×C1711yescharacteristic
260#466C22×C1711yescharacteristic
261#466C22×C1711yescharacteristic
262#466C22×C1711yescharacteristic
263C4×D8C22×C1711yescharacteristic
264C4×D8C22×C1711yescharacteristic
265C8×D4C22×C1711yescharacteristic
266#427C22×C1711yescharacteristic
267#427C22×C1711yescharacteristic
268#427C22×C1711yescharacteristic
269C2×#107C22×C1711yescharacteristic
270#367C22×C1711yescharacteristic
271#367C22×C1711yescharacteristic
272#367C22×C1711yescharacteristic
273#367C22×C1711yescharacteristic
274#366C22×C1711yescharacteristic
275#366C22×C1711yescharacteristic
276#366C22×C1711yescharacteristic
277#366C22×C1711yescharacteristic
278#366C22×C1711yescharacteristic
279C4⋊C16C22×C1711yescharacteristic
280#357C22×C1711yescharacteristic
281#357C22×C1711yescharacteristic
282#357C22×C1711yescharacteristic
283#357C22×C1711yescharacteristic
284#357C22×C1711yescharacteristic
285#357C22×C1711yescharacteristic
286C22⋊C16C22×C1711yescharacteristic
287C22⋊C16C22×C1711yescharacteristic
288#346C22×C1711yescharacteristic
289C2×C17—41no—
290C2×C17—41no—
291C2×C17—161no—
292C2×C17—161no—
293C2×C17#333411yescharacteristic
294C2×C17#341411yescharacteristic
295C2×C17#341511yescharacteristic
296C2×D8C23×C1711yescharacteristic
297C2×D8C23×C1711yescharacteristic
298C22×C8C23×C1711yescharacteristic
299C22×C8C23×C1711yescharacteristic
300C4⋊Q8—21no—
301#126—41no—
302#125—21no—
303#124—41no—
304#124—41no—
305#123—41no—
306#121—21no—
307#121—21no—
308#121—21no—
309#121—21no—
310#121—41no—
311#121—41no—
312C4×D4—21no—
313C4×D4—21no—
314C4×D4—41no—
315C4×D4D4×C1711yescharacteristic
316#117—21no—
317#117—21no—
318#117—21no—
319#117—41no—
320C2×C4⋊C4—21no—
321D16—22no—
322M32—22no—
323C2×C16—22no—
324C2×C16C23×C1711yescharacteristic
325C2×C16C23×C1711yescharacteristic
326C2×C16C23×C1711yescharacteristic
327C2×C16C23×C1711yescharacteristic
328#107—21no—
329#107—21no—
330#107C23×C1711yescharacteristic
331#107C23×C1711yescharacteristic
332#107C23×C1711yescharacteristic
333#107C23×C1711yescharacteristic
334#107C23×C1711yescharacteristic
335#107C23×C1711yescharacteristic
336#106—21no—
337#106—21no—
338#106—21no—
339#106—21no—
340C4⋊C8D4×C1711yescharacteristic
341#102—21no—
342#102—21no—
343#102—21no—
344#102—21no—
345#102—21no—
346#102—21no—
347C22⋊C8D4×C1711yescharacteristic
348C22⋊C8D4×C1711yescharacteristic
349C4×C8C23×C1711yescharacteristic
350C17#3391411yescharacteristic, direct product factor, Sylow
351C2×Q8—41no—
352C2×D4—21no—
353C2×D4—21no—
354C2×D4—41no—
355C2×D4—41no—
356C2×D4—41no—
357C2×D4—41no—
358C2×D4D8×C1711yescharacteristic
359C22×C4—41no—
360C22×C4—41no—
361C22×C4—41no—
362C22×C4C2×D4×C1711yescharacteristic
363C22×C4C2×D4×C1711yescharacteristic
364D8—21no—
365D8—21no—
366D8—21no—
367D8—21no—
368C2×C8—21no—
369C2×C8—21no—
370C2×C8—21no—
371C2×C8—21no—
372C2×C8C2×D4×C1711yescharacteristic
373C2×C8C2×D4×C1711yescharacteristic
374C2×C8C2×D4×C1711yescharacteristic
375C2×C8C24×C1711yescharacteristic
376C4⋊C4—21no—
377C4⋊C4—21no—
378C4⋊C4—21no—
379C4⋊C4—21no—
380C4⋊C4—21no—
381C4⋊C4—21no—
382C4⋊C4—41no—
383C4⋊C4—41no—
384C4⋊C4—41no—
385C4⋊C4—41no—
386C4⋊C4D8×C1711yescharacteristic
387C22⋊C4—41no—
388C22⋊C4—41no—
389C22⋊C4—41no—
390C22⋊C4—41no—
391C22⋊C4—41no—
392C22⋊C4—41no—
393C22⋊C4—41no—
394C22⋊C4—41no—
395C22⋊C4—41no—
396C22⋊C4D8×C1711yescharacteristic
397C22⋊C4D8×C1711yescharacteristic
398C42—41no—
399C42—41no—
400C42—41no—
401C42C2×D4×C1711yescharacteristic
402C16—21no—
403C16—21no—
404C16—21no—
405C16#41×C1712yes—
406C23—41no—
407C23—41no—
408C23C2×D8×C1711yescharacteristic
409C23C2×D8×C1711yescharacteristic
410Q8—161no—
411D4—41no—
412D4—41no—
413D4—41no—
414D4—41no—
415D4—41no—
416D4—82no—
417D4—161no—
418D4—161no—
419D4—161no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—82no—
431C2×C4—161no—
432C2×C4—161no—
433C2×C4C2×D8×C1711yescharacteristic
434C2×C4C2×D8×C1711yescharacteristic
435C2×C4C2×D8×C1711yescharacteristic
436C2×C4C2×D8×C1711yescharacteristic
437C2×C4C22×D4×C1711yescharacteristic
438C8—21no—
439C8—21no—
440C8—21no—
441C8C2×#41×C1711yescharacteristic
442C8C17×2−1+411yescharacteristic
443C22—21no—
444C22—21no—
445C22—21no—
446C22—21no—
447C22—21no—
448C22—21no—
449C22—81no—
450C22—81no—
451C22—81no—
452C22—81no—
453C22—81no—
454C22—81no—
455C22C22×D8×C1711yescharacteristic
456C4—21no—
457C4—21no—
458C4—21no—
459C4—21no—
460C4—81no—
461C4—81no—
462C4—81no—
463C4—81no—
464C4—81no—
465C4—81no—
466C4C17×#54711yescharacteristic
467C4C17×#57811yescharacteristic
468C2—41no—
469C2—41no—
470C2—161no—
471C2—161no—
472C2C17×#333411yescharacteristic
473C2C17×#341411yescharacteristic
474C2C17×#341511yescharacteristic
subgroupG/H
center, socleC22×C17C22×D8
commutator, Frattini, cosocleC2×C8C24×C17
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C17 ◁ C4×D4×C17 ◁ C8×D4×C17 ◁ G

Complements

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

NH ≅ G/Ntype
1. C17×#3341C2semidirect
2. C17×#3339C2semidirect
3. C17×#2255C2semidirect
4. C17×#2234C2semidirect
5. C17×#2234C2semidirect
6. C17×#2234C2semidirect
7. C17×#2232C2semidirect
8. C17×#2228C2semidirect
9. C17×#2224C2semidirect
10. C17×#2218C2semidirect
11. C17×#2215C2semidirect
12. C17×#2177C2semidirect
13. C17×#2168C2semidirect
14. C17×#2159C2semidirect
15. C17×#2158C2semidirect
168. #33914C17direct (N × H)
206. #3341C2×C17semidirect
207. #3339C2×C17semidirect
208. #2255C2×C17semidirect
209. #2234C2×C17semidirect
210. #2234C2×C17semidirect
211. #2234C2×C17semidirect
212. #2232C2×C17semidirect
213. #2228C2×C17semidirect
214. #2224C2×C17semidirect
215. #2218C2×C17semidirect
216. #2215C2×C17semidirect
217. #2177C2×C17semidirect
218. #2168C2×C17semidirect
219. #2159C2×C17semidirect
220. #2158C2×C17semidirect
350. C17#33914direct (N × H)

Maximal subgroups

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

subgroupindex
C17×#33412
C17×#33392
C17×#22552
C17×#22342
C17×#22322
C17×#22282
C17×#22242
C17×#22182
C17×#22152
C17×#21772
C17×#21682
C17×#21592
C17×#21582
#3391417