Finite Group Databasebeta

← C17×#3318 #14526324

Subgroups — C17×#3318 #14526324

Order 2176.

462 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C17×#553C211yesmaximal, characteristic, complemented
2D42×C17C211yesmaximal, characteristic, complemented
3C17×#490C211yesmaximal, characteristic, complemented
4C17×#482C211yesmaximal, characteristic, complemented
5C17×#481C211yesmaximal, characteristic, complemented
6C17×#478C211yesmaximal, characteristic, complemented
7C17×#469C211yesmaximal, characteristic, complemented
8C17×#466C211yesmaximal, characteristic, complemented
9C17×#459C211yesmaximal, characteristic, complemented
10C17×#447C211yesmaximal, characteristic, complemented
11C17×#447C211yesmaximal, characteristic, complemented
12C17×#442C211yesmaximal, characteristic, complemented
13C17×#435C211yesmaximal, characteristic, complemented
14C17×#418C211yesmaximal, characteristic, complemented
15C2×C17×#102C211yesmaximal, characteristic, complemented
16C22×D4×C17—21no—
17C22×D4×C17C2211yescharacteristic
18C22×D4×C17C2211yescharacteristic
19C2×D8×C17C2211yescharacteristic
20C2×D8×C17C2211yescharacteristic, complemented
21C2×D8×C17C2211yescharacteristic, complemented
22C2×M16×C17C2211yescharacteristic, complemented
23C22×C8×C17C2211yescharacteristic, complemented
24C17×#127C2211yescharacteristic
25C17×#126—21no—
26C17×#125C2211yescharacteristic, complemented
27C17×#123—21no—
28C17×#121—21no—
29C17×#121—21no—
30C17×#121C2211yescharacteristic
31C17×#121C2211yescharacteristic
32C17×#121C2211yescharacteristic, complemented
33C17×#121C2211yescharacteristic, complemented
34C17×#120—21no—
35C17×#120—21no—
36C4×D4×C17—21no—
37C4×D4×C17C2211yescharacteristic
38C4×D4×C17C2211yescharacteristic
39C4×D4×C17C2211yescharacteristic, complemented
40C17×#117C2211yescharacteristic, complemented
41C2×C4⋊C4×C17C2211yescharacteristic, complemented
42C17×#107C2211yescharacteristic, complemented
43C17×#106C2211yescharacteristic, complemented
44C17×#106C2211yescharacteristic, complemented
45C17×C4⋊C8C2211yescharacteristic, complemented
46C17×#102C2211yescharacteristic
47C17×#102C2211yescharacteristic
48C17×#102C2211yescharacteristic
49C17×#102C2211yescharacteristic, complemented
50C17×#102C2211yescharacteristic, complemented
51C17×#102C2211yescharacteristic, complemented
52C17×#102C2211yescharacteristic, complemented
53C17×#102C2211yescharacteristic, complemented
54C17×#102C2211yescharacteristic, complemented
55C17×#102C2211yescharacteristic, complemented
56C17×C22⋊C8C2211yescharacteristic, complemented
57C17×C22⋊C8C2211yescharacteristic, complemented
58C17×#97C2211yescharacteristic, complemented
59C24×C17—21no—
60C24×C17—21no—
61C2×D4×C17—22no—
62C2×D4×C17—22no—
63C2×D4×C17—21no—
64C2×D4×C17—21no—
65C2×D4×C17—21no—
66C2×D4×C17—21no—
67C2×D4×C17—21no—
68C2×D4×C17—21no—
69C2×D4×C17—21no—
70C2×D4×C17—21no—
71C2×D4×C17—41no—
72C2×D4×C17—41no—
73C2×D4×C17—44no—
74C2×D4×C17D411yescharacteristic
75C2×D4×C17C2311yescharacteristic
76C2×D4×C17C2311yescharacteristic
77C2×D4×C17C2311yescharacteristic
78C2×D4×C17C2311yescharacteristic
79C22×C4×C17—21no—
80C22×C4×C17—21no—
81C22×C4×C17—21no—
82C22×C4×C17C2311yescharacteristic
83C22×C4×C17C2311yescharacteristic
84D8×C17—22no—
85D8×C17—41no—
86D8×C17—41no—
87M16×C17—41no—
88C2×C8×C17—41no—
89C2×C8×C17C2311yescharacteristic
90C2×C8×C17C2311yescharacteristic
91C2×C8×C17C2311yescharacteristic
92C2×C8×C17C2311yescharacteristic
93C4⋊C4×C17—21no—
94C4⋊C4×C17—21no—
95C4⋊C4×C17—21no—
96C4⋊C4×C17D411yescharacteristic
97C4⋊C4×C17C2311yescharacteristic
98C4⋊C4×C17C2311yescharacteristic
99C4⋊C4×C17C2311yescharacteristic
100C4⋊C4×C17C2311yescharacteristic
101C22⋊C4×C17—21no—
102C22⋊C4×C17—21no—
103C22⋊C4×C17—21no—
104C22⋊C4×C17—21no—
105C22⋊C4×C17—21no—
106C22⋊C4×C17—21no—
107C22⋊C4×C17—21no—
108C22⋊C4×C17D411yescharacteristic
109C22⋊C4×C17D411yescharacteristic
110C42×C17—21no—
111C42×C17C2311yescharacteristic
112C23×C17—21no—
113C23×C17—21no—
114C23×C17—21no—
115C23×C17—21no—
116C23×C17—42no—
117C23×C17—42no—
118C23×C17—42no—
119C23×C17—42no—
120C23×C17—81no—
121C23×C17—81no—
122C23×C17C2×D411yescharacteristic
123C23×C17C2×D411yescharacteristic
124D4×C17—22no—
125D4×C17—21no—
126D4×C17—21no—
127D4×C17—21no—
128D4×C17—21no—
129D4×C17—21no—
130D4×C17—21no—
131D4×C17—21no—
132D4×C17—42no—
133D4×C17—42no—
134D4×C17—42no—
135D4×C17—42no—
136D4×C17—42no—
137D4×C17—42no—
138D4×C17—81no—
139D4×C17—81no—
140D4×C17#4112yes—
141C2×C4×C17—21no—
142C2×C4×C17—21no—
143C2×C4×C17—21no—
144C2×C4×C17—21no—
145C2×C4×C17—21no—
146C2×C4×C17—21no—
147C2×C4×C17—21no—
148C2×C4×C17—21no—
149C2×C4×C17—42no—
150C2×C4×C17—81no—
151C2×C4×C17—81no—
152C2×C4×C17C2×D411yescharacteristic
153C2×C4×C17C2×D411yescharacteristic
154C2×C4×C17C2×D411yescharacteristic
155C2×C4×C17C2×D411yescharacteristic
156C2×C4×C17C2411yescharacteristic
157C8×C17—21no—
158C8×C17—21no—
159C8×C17—21no—
160C8×C17—21no—
161#3318C1711yesmaximal, characteristic, direct product factor, Sylow
162C22×C17—21no—
163C22×C17—21no—
164C22×C17—21no—
165C22×C17—22no—
166C22×C17—21no—
167C22×C17—21no—
168C22×C17—41no—
169C22×C17—41no—
170C22×C17—41no—
171C22×C17—41no—
172C22×C17—41no—
173C22×C17—41no—
174C22×C17—41no—
175C22×C17—41no—
176C22×C17—41no—
177C22×C17—41no—
178C22×C17—41no—
179C22×C17—84no—
180C22×C17—84no—
181C22×C17AGL(1,ℤ/8)12yes—
182C22×C17C22×D411yescharacteristic
183C4×C17—21no—
184C4×C17—21no—
185C4×C17—21no—
186C4×C17—21no—
187C4×C17—41no—
188C4×C17—41no—
189C4×C17—41no—
190C4×C17—41no—
191C4×C17C2×#4111yescharacteristic
192C4×C17H(5,𝔽2)11yescharacteristic
193#553C2×C1711yescharacteristic, complemented
194D42C2×C1711yescharacteristic, complemented
195#490C2×C1711yescharacteristic, complemented
196#482C2×C1711yescharacteristic, complemented
197#481C2×C1711yescharacteristic, complemented
198#478C2×C1711yescharacteristic, complemented
199#469C2×C1711yescharacteristic, complemented
200#466C2×C1711yescharacteristic, complemented
201#459C2×C1711yescharacteristic, complemented
202#447C2×C1711yescharacteristic, complemented
203#447C2×C1711yescharacteristic, complemented
204#442C2×C1711yescharacteristic, complemented
205#435C2×C1711yescharacteristic, complemented
206#418C2×C1711yescharacteristic, complemented
207C2×#102C2×C1711yescharacteristic, complemented
208C2×C17—22no—
209C2×C17—41no—
210C2×C17—42no—
211C2×C17—81no—
212C2×C17—81no—
213C2×C17—81no—
214C2×C17#54611yescharacteristic
215C2×C17C2×AGL(1,ℤ/8)11yescharacteristic
216C2×C17#57611yescharacteristic
217C22×D4—21no—
218C22×D4C22×C1711yescharacteristic
219C22×D4C22×C1711yescharacteristic
220C2×D8C22×C1711yescharacteristic
221C2×D8C22×C1711yescharacteristic, complemented
222C2×D8C22×C1711yescharacteristic, complemented
223C2×M16C22×C1711yescharacteristic, complemented
224C22×C8C22×C1711yescharacteristic, complemented
225#127C22×C1711yescharacteristic
226#126—21no—
227#125C22×C1711yescharacteristic, complemented
228#123—21no—
229#121—21no—
230#121—21no—
231#121C22×C1711yescharacteristic
232#121C22×C1711yescharacteristic
233#121C22×C1711yescharacteristic, complemented
234#121C22×C1711yescharacteristic, complemented
235#120—21no—
236#120—21no—
237C4×D4—21no—
238C4×D4C22×C1711yescharacteristic
239C4×D4C22×C1711yescharacteristic
240C4×D4C22×C1711yescharacteristic, complemented
241#117C22×C1711yescharacteristic, complemented
242C2×C4⋊C4C22×C1711yescharacteristic, complemented
243#107C22×C1711yescharacteristic, complemented
244#106C22×C1711yescharacteristic, complemented
245#106C22×C1711yescharacteristic, complemented
246C4⋊C8C22×C1711yescharacteristic, complemented
247#102C22×C1711yescharacteristic
248#102C22×C1711yescharacteristic
249#102C22×C1711yescharacteristic
250#102C22×C1711yescharacteristic, complemented
251#102C22×C1711yescharacteristic, complemented
252#102C22×C1711yescharacteristic, complemented
253#102C22×C1711yescharacteristic, complemented
254#102C22×C1711yescharacteristic, complemented
255#102C22×C1711yescharacteristic, complemented
256#102C22×C1711yescharacteristic, complemented
257C22⋊C8C22×C1711yescharacteristic, complemented
258C22⋊C8C22×C1711yescharacteristic, complemented
259#97C22×C1711yescharacteristic, complemented
260C17#331811yescharacteristic, direct product factor, Sylow
261C24—21no—
262C24—21no—
263C2×D4—22no—
264C2×D4—22no—
265C2×D4—21no—
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—21no—
269C2×D4—21no—
270C2×D4—21no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—41no—
274C2×D4—41no—
275C2×D4—44no—
276C2×D4D4×C1711yescharacteristic
277C2×D4C23×C1711yescharacteristic
278C2×D4C23×C1711yescharacteristic
279C2×D4C23×C1711yescharacteristic
280C2×D4C23×C1711yescharacteristic
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4C23×C1711yescharacteristic
285C22×C4C23×C1711yescharacteristic
286D8—22no—
287D8—41no—
288D8—41no—
289M16—41no—
290C2×C8—41no—
291C2×C8C23×C1711yescharacteristic
292C2×C8C23×C1711yescharacteristic
293C2×C8C23×C1711yescharacteristic
294C2×C8C23×C1711yescharacteristic
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4D4×C1711yescharacteristic
299C4⋊C4C23×C1711yescharacteristic
300C4⋊C4C23×C1711yescharacteristic
301C4⋊C4C23×C1711yescharacteristic
302C4⋊C4C23×C1711yescharacteristic
303C22⋊C4—21no—
304C22⋊C4—21no—
305C22⋊C4—21no—
306C22⋊C4—21no—
307C22⋊C4—21no—
308C22⋊C4—21no—
309C22⋊C4—21no—
310C22⋊C4D4×C1711yescharacteristic
311C22⋊C4D4×C1711yescharacteristic
312C42—21no—
313C42C23×C1711yescharacteristic
314C23—21no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—42no—
319C23—42no—
320C23—42no—
321C23—42no—
322C23—81no—
323C23—81no—
324C23C2×D4×C1711yescharacteristic
325C23C2×D4×C1711yescharacteristic
326D4—22no—
327D4—21no—
328D4—21no—
329D4—21no—
330D4—21no—
331D4—21no—
332D4—21no—
333D4—21no—
334D4—42no—
335D4—42no—
336D4—42no—
337D4—42no—
338D4—42no—
339D4—42no—
340D4—81no—
341D4—81no—
342D4#41×C1712yes—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—42no—
352C2×C4—81no—
353C2×C4—81no—
354C2×C4C2×D4×C1711yescharacteristic
355C2×C4C2×D4×C1711yescharacteristic
356C2×C4C2×D4×C1711yescharacteristic
357C2×C4C2×D4×C1711yescharacteristic
358C2×C4C24×C1711yescharacteristic
359C8—21no—
360C8—21no—
361C8—21no—
362C8—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—22no—
367C22—21no—
368C22—21no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—84no—
381C22—84no—
382C22C17×AGL(1,ℤ/8)12yes—
383C22C22×D4×C1711yescharacteristic
384C4—21no—
385C4—21no—
386C4—21no—
387C4—21no—
388C4—41no—
389C4—41no—
390C4—41no—
391C4—41no—
392C4C2×#41×C1711yescharacteristic
393C4C17×H(5,𝔽2)11yescharacteristic
394C2—22no—
395C2—41no—
396C2—42no—
397C2—81no—
398C2—81no—
399C2—81no—
400C2C17×#54611yescharacteristic
401C2C2×C17×AGL(1,ℤ/8)11yescharacteristic
402C2C17×#57611yescharacteristic
subgroupG/H
center, socleC22×C17C22×D4
commutator, Frattini, cosocleC2×C4C24×C17
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C17 ◁ C4×D4×C17 ◁ G

Complements

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

NH ≅ G/Ntype
1. C17×#553C2semidirect
2. D42×C17C2semidirect
3. C17×#490C2semidirect
4. C17×#482C2semidirect
5. C17×#481C2semidirect
6. C17×#478C2semidirect
7. C17×#469C2semidirect
8. C17×#466C2semidirect
9. C17×#459C2semidirect
10. C17×#447C2semidirect
11. C17×#447C2semidirect
12. C17×#442C2semidirect
13. C17×#435C2semidirect
14. C17×#418C2semidirect
15. C2×C17×#102C2semidirect
20. C2×D8×C17C22semidirect
21. C2×D8×C17C22semidirect
22. C2×M16×C17C22semidirect
23. C22×C8×C17C22semidirect
26. C17×#125C22semidirect
32. C17×#121C22semidirect
33. C17×#121C22semidirect
39. C4×D4×C17C22semidirect
40. C17×#117C22semidirect
41. C2×C4⋊C4×C17C22semidirect
42. C17×#107C22semidirect
43. C17×#106C22semidirect
44. C17×#106C22semidirect
45. C17×C4⋊C8C22semidirect
49. C17×#102C22semidirect
50. C17×#102C22semidirect
51. C17×#102C22semidirect
52. C17×#102C22semidirect
53. C17×#102C22semidirect
54. C17×#102C22semidirect
55. C17×#102C22semidirect
56. C17×C22⋊C8C22semidirect
57. C17×C22⋊C8C22semidirect
58. C17×#97C22semidirect
161. #3318C17direct (N × H)
193. #553C2×C17semidirect
194. D42C2×C17semidirect
195. #490C2×C17semidirect
196. #482C2×C17semidirect
197. #481C2×C17semidirect
198. #478C2×C17semidirect
199. #469C2×C17semidirect
200. #466C2×C17semidirect
201. #459C2×C17semidirect
202. #447C2×C17semidirect
203. #447C2×C17semidirect
204. #442C2×C17semidirect
205. #435C2×C17semidirect
206. #418C2×C17semidirect
207. C2×#102C2×C17semidirect
221. C2×D8C22×C17semidirect
222. C2×D8C22×C17semidirect
223. C2×M16C22×C17semidirect
224. C22×C8C22×C17semidirect
227. #125C22×C17semidirect
233. #121C22×C17semidirect
234. #121C22×C17semidirect
240. C4×D4C22×C17semidirect
241. #117C22×C17semidirect
242. C2×C4⋊C4C22×C17semidirect
243. #107C22×C17semidirect
244. #106C22×C17semidirect
245. #106C22×C17semidirect
246. C4⋊C8C22×C17semidirect
250. #102C22×C17semidirect
251. #102C22×C17semidirect
252. #102C22×C17semidirect
253. #102C22×C17semidirect
254. #102C22×C17semidirect
255. #102C22×C17semidirect
256. #102C22×C17semidirect
257. C22⋊C8C22×C17semidirect
258. C22⋊C8C22×C17semidirect
259. #97C22×C17semidirect
260. C17#3318direct (N × H)

Maximal subgroups

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

subgroupindex
C17×#5532
D42×C172
C17×#4902
C17×#4822
C17×#4812
C17×#4782
C17×#4692
C17×#4662
C17×#4592
C17×#4472
C17×#4422
C17×#4352
C17×#4182
C2×C17×#1022
#331817