Finite Group Databasebeta

← C17×#3524 #14526530

Subgroups — C17×#3524 #14526530

Order 2176.

1030 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C17×#559C213yesmaximal, complemented
2C17×#557C211yesmaximal, characteristic, complemented
3C17×#555C213yesmaximal, complemented
4C17×#553C213yesmaximal, complemented
5C17×#552C213yesmaximal, complemented
6C17×#550C211yesmaximal, characteristic, complemented
7C17×#548C211yesmaximal, characteristic, complemented
8C17×#548C211yesmaximal, characteristic, complemented
9C17×#542C213yesmaximal, complemented
10C17×#540C213yesmaximal, complemented
11C17×#529C213yesmaximal, complemented
12C17×#529C213yesmaximal, complemented
13C17×#520C211yesmaximal, characteristic, complemented
14C17×#519C211yesmaximal, characteristic, complemented
15C4×#41×C17C211yesmaximal, characteristic, complemented
16C2×#41×C17C2211yescharacteristic
17C2×#41×C17C2211yescharacteristic
18C22×Q8×C17C2211yescharacteristic
19C17×C4⋊Q8C2213yes—
20C17×#127C2213yes—
21C17×#126C2211yescharacteristic
22C17×#126C2213yes—
23C17×#126C2216yes—
24C17×#125C2213yes—
25C17×#125C2213yes—
26C17×#125C2213yes—
27C17×#124C2213yes—
28C17×#124C2213yes—
29C17×#124C2213yes—
30C17×#124C2216yes—
31C17×#123C2216yes—
32C17×#123C2213yes—
33C17×#123C2213yes—
34C17×#123C2216yes—
35C17×C22⋊Q8C2213yes—
36C17×C22⋊Q8C2213yes—
37C17×C22⋊Q8C2213yes—
38C17×#121C2213yes—
39C17×#121C2213yes—
40C17×#121C2213yes—
41C17×#121C2213yes—
42C17×#121C2216yes—
43C17×#121C2213yes—
44C4×Q8×C17C2211yescharacteristic
45C4×Q8×C17C2211yescharacteristic
46C4×Q8×C17C2213yes—
47C4×Q8×C17C2211yescharacteristic
48C4×Q8×C17C2213yes—
49C4×Q8×C17C2211yescharacteristic
50C4×Q8×C17C2213yes—
51C4×D4×C17C2213yes—
52C4×D4×C17C2213yes—
53C4×D4×C17C2213yes—
54C4×D4×C17C2213yes—
55C4×D4×C17C2213yes—
56C4×D4×C17C2213yes—
57C4×D4×C17C2213yes—
58C4×D4×C17C2216yes—
59C17×#117C2213yes—
60C17×#117C2213yes—
61C17×#117C2213yes—
62C17×#117C2213yes—
63C17×#117C2216yes—
64C2×C4⋊C4×C17C2213yes—
65C2×C42×C17C2213yes—
66#41×C17—24no—
67#41×C17—24no—
68C2×Q8×C17—24no—
69C2×Q8×C17C2313yes—
70C2×Q8×C17C2313yes—
71C2×Q8×C17C2311yescharacteristic
72C2×D4×C17C2313yes—
73C2×D4×C17C2313yes—
74C2×D4×C17C2313yes—
75C2×D4×C17C2316yes—
76C2×D4×C17C2313yes—
77C2×D4×C17C2313yes—
78C22×C4×C17C2313yes—
79C22×C4×C17C2313yes—
80C22×C4×C17C2313yes—
81C22×C4×C17C2313yes—
82C22×C4×C17C2313yes—
83C22×C4×C17C2316yes—
84C4⋊C4×C17C2313yes—
85C4⋊C4×C17C2311yescharacteristic
86C4⋊C4×C17C2313yes—
87C4⋊C4×C17C2313yes—
88C4⋊C4×C17C2313yes—
89C4⋊C4×C17C2313yes—
90C4⋊C4×C17C2313yes—
91C4⋊C4×C17C2311yescharacteristic
92C4⋊C4×C17C2313yes—
93C4⋊C4×C17C2316yes—
94C4⋊C4×C17C2313yes—
95C4⋊C4×C17C2313yes—
96C4⋊C4×C17C2311yescharacteristic
97C4⋊C4×C17C2313yes—
98C4⋊C4×C17C2313yes—
99C22⋊C4×C17C2316yes—
100C22⋊C4×C17C2316yes—
101C22⋊C4×C17C2313yes—
102C22⋊C4×C17C2313yes—
103C22⋊C4×C17C2311yescharacteristic
104C22⋊C4×C17C2313yes—
105C22⋊C4×C17C2313yes—
106C22⋊C4×C17C2313yes—
107C22⋊C4×C17C2316yes—
108C22⋊C4×C17C2313yes—
109C22⋊C4×C17C2311yescharacteristic
110C22⋊C4×C17C2313yes—
111C22⋊C4×C17C2311yescharacteristic
112C42×C17C2313yes—
113C42×C17C2313yes—
114C42×C17C2316yes—
115C42×C17C2313yes—
116C42×C17C2313yes—
117C42×C17C2311yescharacteristic
118C42×C17C2313yes—
119C23×C17C2411yescharacteristic
120C23×C17C2413yes—
121C23×C17C2413yes—
122Q8×C17—26no—
123Q8×C17—43no—
124Q8×C17#4114yes—
125D4×C17—26no—
126D4×C17—26no—
127D4×C17—43no—
128D4×C17—43no—
129D4×C17—43no—
130D4×C17—46no—
131C2×C4×C17—26no—
132C2×C4×C17—26no—
133C2×C4×C17—26no—
134C2×C4×C17—43no—
135C2×C4×C17—46no—
136C2×C4×C17—43no—
137C2×C4×C17C2411yescharacteristic
138C2×C4×C17C2413yes—
139C2×C4×C17C2411yescharacteristic
140C2×C4×C17C2411yescharacteristic
141C2×C4×C17C2411yescharacteristic
142C2×C4×C17C2413yes—
143C2×C4×C17C2411yescharacteristic
144C2×C4×C17C2413yes—
145C2×C4×C17C2413yes—
146C2×C4×C17C2413yes—
147C2×C4×C17C2411yescharacteristic
148C2×C4×C17C2413yes—
149#3524C1711yesmaximal, characteristic, direct product factor, Sylow
150C22×C17—21no—
151C22×C17—23no—
152C22×C17—23no—
153C22×C17—23no—
154C22×C17—23no—
155C22×C17—23no—
156C22×C17—21no—
157C22×C17—21no—
158C22×C17—23no—
159C22×C17C2511yescharacteristic
160C4×C17—21no—
161C4×C17—21no—
162C4×C17—23no—
163C4×C17—21no—
164C4×C17—23no—
165C4×C17—21no—
166C4×C17—23no—
167C4×C17—23no—
168C4×C17—21no—
169C4×C17—23no—
170C4×C17—21no—
171C4×C17C2×#4116yes—
172#559C2×C1713yescomplemented
173#557C2×C1711yescharacteristic, complemented
174#555C2×C1713yescomplemented
175#553C2×C1713yescomplemented
176#552C2×C1713yescomplemented
177#550C2×C1711yescharacteristic, complemented
178#548C2×C1711yescharacteristic, complemented
179#548C2×C1711yescharacteristic, complemented
180#542C2×C1713yescomplemented
181#540C2×C1713yescomplemented
182#529C2×C1713yescomplemented
183#529C2×C1713yescomplemented
184#520C2×C1711yescharacteristic, complemented
185#519C2×C1711yescharacteristic, complemented
186C4×#41C2×C1711yescharacteristic, complemented
187C2×C17—41no—
188C2×C17—43no—
189C2×C17—43no—
190C2×C17C22×#4111yescharacteristic
191C2×C17#58511yescharacteristic
192C2×C17#58511yescharacteristic
193C2×#41C22×C1711yescharacteristic
194C2×#41C22×C1711yescharacteristic
195C22×Q8C22×C1711yescharacteristic
196C4⋊Q8C22×C1713yes—
197#127C22×C1713yes—
198#126C22×C1711yescharacteristic
199#126C22×C1713yes—
200#126C22×C1716yes—
201#125C22×C1713yes—
202#125C22×C1713yes—
203#125C22×C1713yes—
204#124C22×C1713yes—
205#124C22×C1713yes—
206#124C22×C1713yes—
207#124C22×C1716yes—
208#123C22×C1716yes—
209#123C22×C1713yes—
210#123C22×C1713yes—
211#123C22×C1716yes—
212C22⋊Q8C22×C1713yes—
213C22⋊Q8C22×C1713yes—
214C22⋊Q8C22×C1713yes—
215#121C22×C1713yes—
216#121C22×C1713yes—
217#121C22×C1713yes—
218#121C22×C1713yes—
219#121C22×C1716yes—
220#121C22×C1713yes—
221C4×Q8C22×C1711yescharacteristic
222C4×Q8C22×C1711yescharacteristic
223C4×Q8C22×C1713yes—
224C4×Q8C22×C1711yescharacteristic
225C4×Q8C22×C1713yes—
226C4×Q8C22×C1711yescharacteristic
227C4×Q8C22×C1713yes—
228C4×D4C22×C1713yes—
229C4×D4C22×C1713yes—
230C4×D4C22×C1713yes—
231C4×D4C22×C1713yes—
232C4×D4C22×C1713yes—
233C4×D4C22×C1713yes—
234C4×D4C22×C1713yes—
235C4×D4C22×C1716yes—
236#117C22×C1713yes—
237#117C22×C1713yes—
238#117C22×C1713yes—
239#117C22×C1713yes—
240#117C22×C1716yes—
241C2×C4⋊C4C22×C1713yes—
242C2×C42C22×C1713yes—
243C17#352411yescharacteristic, direct product factor, Sylow
244#41—24no—
245#41—24no—
246C2×Q8—24no—
247C2×Q8C23×C1713yes—
248C2×Q8C23×C1713yes—
249C2×Q8C23×C1711yescharacteristic
250C2×D4C23×C1713yes—
251C2×D4C23×C1713yes—
252C2×D4C23×C1713yes—
253C2×D4C23×C1713yes—
254C2×D4C23×C1716yes—
255C2×D4C23×C1713yes—
256C22×C4C23×C1713yes—
257C22×C4C23×C1713yes—
258C22×C4C23×C1713yes—
259C22×C4C23×C1713yes—
260C22×C4C23×C1713yes—
261C22×C4C23×C1716yes—
262C4⋊C4C23×C1713yes—
263C4⋊C4C23×C1713yes—
264C4⋊C4C23×C1713yes—
265C4⋊C4C23×C1711yescharacteristic
266C4⋊C4C23×C1713yes—
267C4⋊C4C23×C1713yes—
268C4⋊C4C23×C1713yes—
269C4⋊C4C23×C1713yes—
270C4⋊C4C23×C1713yes—
271C4⋊C4C23×C1716yes—
272C4⋊C4C23×C1711yescharacteristic
273C4⋊C4C23×C1713yes—
274C4⋊C4C23×C1713yes—
275C4⋊C4C23×C1711yescharacteristic
276C4⋊C4C23×C1713yes—
277C22⋊C4C23×C1711yescharacteristic
278C22⋊C4C23×C1713yes—
279C22⋊C4C23×C1713yes—
280C22⋊C4C23×C1713yes—
281C22⋊C4C23×C1716yes—
282C22⋊C4C23×C1713yes—
283C22⋊C4C23×C1716yes—
284C22⋊C4C23×C1711yescharacteristic
285C22⋊C4C23×C1713yes—
286C22⋊C4C23×C1711yescharacteristic
287C22⋊C4C23×C1713yes—
288C22⋊C4C23×C1716yes—
289C22⋊C4C23×C1713yes—
290C42C23×C1711yescharacteristic
291C42C23×C1713yes—
292C42C23×C1713yes—
293C42C23×C1713yes—
294C42C23×C1716yes—
295C42C23×C1713yes—
296C42C23×C1713yes—
297C23C24×C1711yescharacteristic
298C23C24×C1713yes—
299C23C24×C1713yes—
300Q8—26no—
301Q8—43no—
302Q8#41×C1714yes—
303D4—26no—
304D4—26no—
305D4—43no—
306D4—43no—
307D4—43no—
308D4—46no—
309C2×C4—26no—
310C2×C4—26no—
311C2×C4—26no—
312C2×C4—43no—
313C2×C4—46no—
314C2×C4—43no—
315C2×C4C24×C1711yescharacteristic
316C2×C4C24×C1711yescharacteristic
317C2×C4C24×C1711yescharacteristic
318C2×C4C24×C1713yes—
319C2×C4C24×C1711yescharacteristic
320C2×C4C24×C1713yes—
321C2×C4C24×C1711yescharacteristic
322C2×C4C24×C1713yes—
323C2×C4C24×C1713yes—
324C2×C4C24×C1713yes—
325C2×C4C24×C1711yescharacteristic
326C2×C4C24×C1713yes—
327C22—21no—
328C22—23no—
329C22—23no—
330C22—23no—
331C22—23no—
332C22—23no—
333C22—21no—
334C22—21no—
335C22—23no—
336C22C25×C1711yescharacteristic
337C4—21no—
338C4—21no—
339C4—23no—
340C4—21no—
341C4—23no—
342C4—21no—
343C4—23no—
344C4—23no—
345C4—21no—
346C4—23no—
347C4—21no—
348C4C2×#41×C1716yes—
349C2—41no—
350C2—43no—
351C2—43no—
352C2C22×#41×C1711yescharacteristic
353C2C17×#58511yescharacteristic
354C2C17×#58511yescharacteristic
subgroupG/H
center, socleC22×C17C25
commutator, Frattini, cosocleC22C25×C17
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C17 ◁ G

Complements

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

NH ≅ G/Ntype
1. C17×#559C2semidirect
2. C17×#557C2semidirect
3. C17×#555C2semidirect
4. C17×#553C2semidirect
5. C17×#552C2semidirect
6. C17×#550C2semidirect
7. C17×#548C2semidirect
8. C17×#548C2semidirect
9. C17×#542C2semidirect
10. C17×#540C2semidirect
11. C17×#529C2semidirect
12. C17×#529C2semidirect
13. C17×#520C2semidirect
14. C17×#519C2semidirect
15. C4×#41×C17C2semidirect
149. #3524C17direct (N × H)
172. #559C2×C17semidirect
173. #557C2×C17semidirect
174. #555C2×C17semidirect
175. #553C2×C17semidirect
176. #552C2×C17semidirect
177. #550C2×C17semidirect
178. #548C2×C17semidirect
179. #548C2×C17semidirect
180. #542C2×C17semidirect
181. #540C2×C17semidirect
182. #529C2×C17semidirect
183. #529C2×C17semidirect
184. #520C2×C17semidirect
185. #519C2×C17semidirect
186. C4×#41C2×C17semidirect
243. C17#3524direct (N × H)

Maximal subgroups

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

subgroupindex
C17×#5592
C17×#5572
C17×#5552
C17×#5532
C17×#5522
C17×#5502
C17×#5482
C17×#5422
C17×#5402
C17×#5292
C17×#5202
C17×#5192
C4×#41×C172
#352417