Finite Group Databasebeta

← C17×#33917 #16891661

Subgroups — C17×#33917 #16891661

Order 4352.

476 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×#3342C211yesmaximal, characteristic, complemented
2C17×#3339C211yesmaximal, characteristic
3C17×#2255C211yesmaximal, characteristic, complemented
4C17×#2237C211yesmaximal, characteristic, complemented
5C17×#2235C211yesmaximal, characteristic, complemented
6C17×#2234C211yesmaximal, characteristic, complemented
7C17×#2234C211yesmaximal, characteristic, complemented
8C17×#2229C211yesmaximal, characteristic, complemented
9C17×#2226C211yesmaximal, characteristic, complemented
10C17×#2220C211yesmaximal, characteristic, complemented
11C17×#2217C211yesmaximal, characteristic, complemented
12C17×#2175C211yesmaximal, characteristic, complemented
13C17×#2168C211yesmaximal, characteristic, complemented
14C17×#2159C211yesmaximal, characteristic, complemented
15C17×#2158C211yesmaximal, characteristic, complemented
16C17×#556—21no—
17C17×#553—21no—
18C2×C17×SD32C2211yescharacteristic
19C2×C17×M32C2211yescharacteristic
20C22×C16×C17C2211yescharacteristic
21C17×#500C2211yescharacteristic
22C17×#499C2211yescharacteristic
23C17×#485—21no—
24C17×#485—21no—
25C17×#482—21no—
26C17×#481—21no—
27C17×#478—21no—
28C17×#475—21no—
29C17×#467C2211yescharacteristic
30C17×#467C2211yescharacteristic
31C17×#466C2211yescharacteristic
32C17×#466C2211yescharacteristic
33C4×Q16×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×#367C2211yescharacteristic
45C17×#366C2211yescharacteristic
46C17×#366C2211yescharacteristic
47C17×#366C2211yescharacteristic
48C17×#366C2211yescharacteristic
49C17×C4⋊C16C2211yescharacteristic
50C17×#358C2211yescharacteristic
51C17×#358C2211yescharacteristic
52C17×#358C2211yescharacteristic
53C17×#357C2211yescharacteristic
54C17×#357C2211yescharacteristic
55C17×#357C2211yescharacteristic
56C17×C22⋊C16C2211yescharacteristic
57C17×C22⋊C16C2211yescharacteristic
58C17×#346C2211yescharacteristic
59C2×Q16×C17C2311yescharacteristic
60C2×D8×C17C2311yescharacteristic
61C22×C8×C17C2311yescharacteristic
62C22×C8×C17C2311yescharacteristic
63C17×C4⋊Q8—21no—
64C17×#126—41no—
65C17×#126—41no—
66C17×#126—41no—
67C17×#125—21no—
68C17×#124—41no—
69C17×#123—41no—
70C17×C22⋊Q8—21no—
71C17×C22⋊Q8—21no—
72C17×#121—21no—
73C17×#121—21no—
74C17×#121—41no—
75C4×Q8×C17—21no—
76C4×Q8×C17—41no—
77C4×D4×C17—21no—
78C4×D4×C17—41no—
79C4×D4×C17D411yescharacteristic
80C17×#117—21no—
81C17×#117—21no—
82C17×#117—21no—
83C2×C4⋊C4×C17—21no—
84C17×SD32—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×#103—21no—
105C17×#103—21no—
106C17×#103—21no—
107C17×#102—21no—
108C17×#102—21no—
109C17×#102—21no—
110C17×C22⋊C8D411yescharacteristic
111C17×C22⋊C8D411yescharacteristic
112C4×C8×C17C2311yescharacteristic
113C2×Q8×C17—21no—
114C2×Q8×C17—41no—
115C2×D4×C17—21no—
116C2×D4×C17—41no—
117C2×D4×C17—41no—
118C2×D4×C17D811yescharacteristic
119C22×C4×C17—41no—
120C22×C4×C17—41no—
121C22×C4×C17C2×D411yescharacteristic
122C22×C4×C17C2×D411yescharacteristic
123Q16×C17—21no—
124Q16×C17—21no—
125D8×C17—21no—
126D8×C17—21no—
127C2×C8×C17—21no—
128C2×C8×C17—21no—
129C2×C8×C17—21no—
130C2×C8×C17—21no—
131C2×C8×C17C2×D411yescharacteristic
132C2×C8×C17C2×D411yescharacteristic
133C2×C8×C17C2×D411yescharacteristic
134C2×C8×C17C2411yescharacteristic
135C4⋊C4×C17—21no—
136C4⋊C4×C17—21no—
137C4⋊C4×C17—21no—
138C4⋊C4×C17—21no—
139C4⋊C4×C17—21no—
140C4⋊C4×C17—21no—
141C4⋊C4×C17—41no—
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×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×C17D811yescharacteristic
158C22⋊C4×C17D811yescharacteristic
159C42×C17—41no—
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#33917C1711yesmaximal, characteristic, direct product factor, Sylow
169C23×C17—41no—
170C23×C17C2×D811yescharacteristic
171C23×C17C2×D811yescharacteristic
172Q8×C17—41no—
173Q8×C17—41no—
174Q8×C17—82no—
175D4×C17—41no—
176D4×C17—41no—
177D4×C17—41no—
178D4×C17—82no—
179D4×C17—161no—
180C2×C4×C17—21no—
181C2×C4×C17—21no—
182C2×C4×C17—21no—
183C2×C4×C17—21no—
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—41no—
191C2×C4×C17—161no—
192C2×C4×C17—161no—
193C2×C4×C17C2×D811yescharacteristic
194C2×C4×C17C2×D811yescharacteristic
195C2×C4×C17C2×D811yescharacteristic
196C2×C4×C17C2×D811yescharacteristic
197C2×C4×C17C22×D411yescharacteristic
198C8×C17—21no—
199C8×C17—21no—
200C8×C17—21no—
201C8×C17C2×#4111yescharacteristic
202C8×C172−1+411yescharacteristic
203#3342C2×C1711yescharacteristic, complemented
204#3339C2×C1711yescharacteristic
205#2255C2×C1711yescharacteristic, complemented
206#2237C2×C1711yescharacteristic, complemented
207#2235C2×C1711yescharacteristic, complemented
208#2234C2×C1711yescharacteristic, complemented
209#2234C2×C1711yescharacteristic, complemented
210#2229C2×C1711yescharacteristic, complemented
211#2226C2×C1711yescharacteristic, complemented
212#2220C2×C1711yescharacteristic, complemented
213#2217C2×C1711yescharacteristic, complemented
214#2175C2×C1711yescharacteristic, complemented
215#2168C2×C1711yescharacteristic, complemented
216#2159C2×C1711yescharacteristic, complemented
217#2158C2×C1711yescharacteristic, complemented
218C22×C17—21no—
219C22×C17—21no—
220C22×C17—21no—
221C22×C17—21no—
222C22×C17—21no—
223C22×C17—21no—
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—81no—
233C4×C17—81no—
234C4×C17—81no—
235C4×C17—81no—
236C4×C17—81no—
237C4×C17—81no—
238C4×C17—81no—
239C4×C17#54711yescharacteristic
240C4×C17#57811yescharacteristic
241#556—21no—
242#553—21no—
243C2×SD32C22×C1711yescharacteristic
244C2×M32C22×C1711yescharacteristic
245C22×C16C22×C1711yescharacteristic
246#500C22×C1711yescharacteristic
247#499C22×C1711yescharacteristic
248#485—21no—
249#485—21no—
250#482—21no—
251#481—21no—
252#478—21no—
253#475—21no—
254#467C22×C1711yescharacteristic
255#467C22×C1711yescharacteristic
256#466C22×C1711yescharacteristic
257#466C22×C1711yescharacteristic
258C4×Q16C22×C1711yescharacteristic
259C4×D8C22×C1711yescharacteristic
260C8×D4C22×C1711yescharacteristic
261#427C22×C1711yescharacteristic
262#427C22×C1711yescharacteristic
263#427C22×C1711yescharacteristic
264C2×#107C22×C1711yescharacteristic
265#367C22×C1711yescharacteristic
266#367C22×C1711yescharacteristic
267#367C22×C1711yescharacteristic
268#367C22×C1711yescharacteristic
269#367C22×C1711yescharacteristic
270#366C22×C1711yescharacteristic
271#366C22×C1711yescharacteristic
272#366C22×C1711yescharacteristic
273#366C22×C1711yescharacteristic
274C4⋊C16C22×C1711yescharacteristic
275#358C22×C1711yescharacteristic
276#358C22×C1711yescharacteristic
277#358C22×C1711yescharacteristic
278#357C22×C1711yescharacteristic
279#357C22×C1711yescharacteristic
280#357C22×C1711yescharacteristic
281C22⋊C16C22×C1711yescharacteristic
282C22⋊C16C22×C1711yescharacteristic
283#346C22×C1711yescharacteristic
284C2×C17—41no—
285C2×C17—41no—
286C2×C17—161no—
287C2×C17#333411yescharacteristic
288C2×C17#341411yescharacteristic
289C2×C17#341611yescharacteristic
290C2×Q16C23×C1711yescharacteristic
291C2×D8C23×C1711yescharacteristic
292C22×C8C23×C1711yescharacteristic
293C22×C8C23×C1711yescharacteristic
294C4⋊Q8—21no—
295#126—41no—
296#126—41no—
297#126—41no—
298#125—21no—
299#124—41no—
300#123—41no—
301C22⋊Q8—21no—
302C22⋊Q8—21no—
303#121—21no—
304#121—21no—
305#121—41no—
306C4×Q8—21no—
307C4×Q8—41no—
308C4×D4—21no—
309C4×D4—41no—
310C4×D4D4×C1711yescharacteristic
311#117—21no—
312#117—21no—
313#117—21no—
314C2×C4⋊C4—21no—
315SD32—22no—
316M32—22no—
317C2×C16—22no—
318C2×C16C23×C1711yescharacteristic
319C2×C16C23×C1711yescharacteristic
320C2×C16C23×C1711yescharacteristic
321C2×C16C23×C1711yescharacteristic
322#107—21no—
323#107—21no—
324#107C23×C1711yescharacteristic
325#107C23×C1711yescharacteristic
326#107C23×C1711yescharacteristic
327#107C23×C1711yescharacteristic
328#107C23×C1711yescharacteristic
329#107C23×C1711yescharacteristic
330#106—21no—
331#106—21no—
332#106—21no—
333#106—21no—
334C4⋊C8D4×C1711yescharacteristic
335#103—21no—
336#103—21no—
337#103—21no—
338#102—21no—
339#102—21no—
340#102—21no—
341C22⋊C8D4×C1711yescharacteristic
342C22⋊C8D4×C1711yescharacteristic
343C4×C8C23×C1711yescharacteristic
344C17#3391711yescharacteristic, direct product factor, Sylow
345C2×Q8—21no—
346C2×Q8—41no—
347C2×D4—21no—
348C2×D4—41no—
349C2×D4—41no—
350C2×D4D8×C1711yescharacteristic
351C22×C4—41no—
352C22×C4—41no—
353C22×C4C2×D4×C1711yescharacteristic
354C22×C4C2×D4×C1711yescharacteristic
355Q16—21no—
356Q16—21no—
357D8—21no—
358D8—21no—
359C2×C8—21no—
360C2×C8—21no—
361C2×C8—21no—
362C2×C8—21no—
363C2×C8C2×D4×C1711yescharacteristic
364C2×C8C2×D4×C1711yescharacteristic
365C2×C8C2×D4×C1711yescharacteristic
366C2×C8C24×C1711yescharacteristic
367C4⋊C4—21no—
368C4⋊C4—21no—
369C4⋊C4—21no—
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—41no—
374C4⋊C4—41no—
375C4⋊C4—41no—
376C4⋊C4—41no—
377C4⋊C4—41no—
378C4⋊C4—41no—
379C4⋊C4—41no—
380C4⋊C4D8×C1711yescharacteristic
381C22⋊C4—41no—
382C22⋊C4—41no—
383C22⋊C4—41no—
384C22⋊C4—41no—
385C22⋊C4—41no—
386C22⋊C4—41no—
387C22⋊C4—41no—
388C22⋊C4—41no—
389C22⋊C4D8×C1711yescharacteristic
390C22⋊C4D8×C1711yescharacteristic
391C42—41no—
392C42—41no—
393C42—41no—
394C42—41no—
395C42C2×D4×C1711yescharacteristic
396C16—21no—
397C16—21no—
398C16—21no—
399C16#41×C1712yes—
400C23—41no—
401C23C2×D8×C1711yescharacteristic
402C23C2×D8×C1711yescharacteristic
403Q8—41no—
404Q8—41no—
405Q8—82no—
406D4—41no—
407D4—41no—
408D4—41no—
409D4—82no—
410D4—161no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—161no—
423C2×C4—161no—
424C2×C4C2×D8×C1711yescharacteristic
425C2×C4C2×D8×C1711yescharacteristic
426C2×C4C2×D8×C1711yescharacteristic
427C2×C4C2×D8×C1711yescharacteristic
428C2×C4C22×D4×C1711yescharacteristic
429C8—21no—
430C8—21no—
431C8—21no—
432C8C2×#41×C1711yescharacteristic
433C8C17×2−1+411yescharacteristic
434C22—21no—
435C22—21no—
436C22—21no—
437C22—21no—
438C22—21no—
439C22—21no—
440C22—81no—
441C22—81no—
442C22—81no—
443C22C22×D8×C1711yescharacteristic
444C4—21no—
445C4—21no—
446C4—21no—
447C4—21no—
448C4—81no—
449C4—81no—
450C4—81no—
451C4—81no—
452C4—81no—
453C4—81no—
454C4—81no—
455C4C17×#54711yescharacteristic
456C4C17×#57811yescharacteristic
457C2—41no—
458C2—41no—
459C2—161no—
460C2C17×#333411yescharacteristic
461C2C17×#341411yescharacteristic
462C2C17×#341611yescharacteristic
subgroupG/H
center, socleC22×C17C22×D8
commutator, Frattini, cosocleC2×C8C24×C17
prime radicalC17×#3339C2
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×#3342C2semidirect
3. C17×#2255C2semidirect
4. C17×#2237C2semidirect
5. C17×#2235C2semidirect
6. C17×#2234C2semidirect
7. C17×#2234C2semidirect
8. C17×#2229C2semidirect
9. C17×#2226C2semidirect
10. C17×#2220C2semidirect
11. C17×#2217C2semidirect
12. C17×#2175C2semidirect
13. C17×#2168C2semidirect
14. C17×#2159C2semidirect
15. C17×#2158C2semidirect
168. #33917C17direct (N × H)
203. #3342C2×C17semidirect
205. #2255C2×C17semidirect
206. #2237C2×C17semidirect
207. #2235C2×C17semidirect
208. #2234C2×C17semidirect
209. #2234C2×C17semidirect
210. #2229C2×C17semidirect
211. #2226C2×C17semidirect
212. #2220C2×C17semidirect
213. #2217C2×C17semidirect
214. #2175C2×C17semidirect
215. #2168C2×C17semidirect
216. #2159C2×C17semidirect
217. #2158C2×C17semidirect
344. C17#33917direct (N × H)

Maximal subgroups

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

subgroupindex
C17×#33422
C17×#33392
C17×#22552
C17×#22372
C17×#22352
C17×#22342
C17×#22292
C17×#22262
C17×#22202
C17×#22172
C17×#21752
C17×#21682
C17×#21592
C17×#21582
#3391717