Finite Group Databasebeta

← C17×#34311 #16892055

Subgroups — C17×#34311 #16892055

Order 4352.

2860 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×Q8×C17C211yesmaximal, characteristic
2C2×C17×#519C212yesmaximal, complemented
3C17×#2365C213yesmaximal, complemented
4C17×#2362C216yesmaximal, complemented
5C17×#2354C213yesmaximal
6Q8×C4⋊C4×C17C211yesmaximal, characteristic, complemented
7Q8×C22⋊C4×C17C212yesmaximal, complemented
8C17×#2323C216yesmaximal, complemented
9C4×C17×C4⋊Q8C213yesmaximal, complemented
10C17×#2293C213yesmaximal
11C42×Q8×C17C211yesmaximal, characteristic, complemented
12C23×Q8×C17C2212yes—
13D4×Q8×C17C4116yescomplemented
14C2×C17×C4⋊Q8C2213yes—
15C2×C17×C22⋊Q8C2216yes—
16C17×#519—216no—
17C2×C4×Q8×C17C2211yescharacteristic
18C2×C4×Q8×C17C2216yes—
19C2×C4×Q8×C17C2212yes—
20C2×C4×Q8×C17C2216yes—
21C2×C4×Q8×C17C2211yescharacteristic
22C2×C4×Q8×C17C2211yescharacteristic
23C2×C4×D4×C17C2213yes—
24C2×C17×#117C2216yes—
25C2×C17×#117C2216yes—
26C17×#391C2216yes—
27C17×#391C2216yes—
28C17×#390C2211yescharacteristic
29C17×#390C2213yes—
30C17×#389C2213yes—
31C17×#389C2213yes—
32C17×#389C2216yes—
33C17×#389C2216yes—
34C17×#388C2216yes—
35C17×#388C2216yes—
36C17×#388C22112yes—
37C17×#387C22112yes—
38C17×#384C2213yes—
39C17×#380C2216yes—
40C4×C4⋊C4×C17C2213yes—
41C4×C4⋊C4×C17C2213yes—
42C4×C4⋊C4×C17C2213yes—
43C4×C4⋊C4×C17C2213yes—
44C4×C4⋊C4×C17C2216yes—
45C4×C4⋊C4×C17C2216yes—
46C4×C22⋊C4×C17C2216yes—
47C43×C17C2213yes—
48C22×Q8×C17—28no—
49C22×Q8×C17—28no—
50C22×Q8×C17C2×C4116yes—
51C22×Q8×C17C2316yes—
52C22×Q8×C17C2311yescharacteristic
53C22×D4×C17C2311yescharacteristic
54C23×C4×C17C2316yes—
55C17×C4⋊Q8C2×C4124yes—
56C17×C22⋊Q8C2×C4148yes—
57C4×Q8×C17—28no—
58C4×Q8×C17—24no—
59C4×Q8×C17—224no—
60C4×Q8×C17—224no—
61C4×Q8×C17C2×C418yes—
62C4×Q8×C17D418yescomplemented
63C4×D4×C17C2×C4124yes—
64C17×#117—224no—
65C17×#117—224no—
66C2×C4⋊C4×C17C2316yes—
67C2×C4⋊C4×C17C2316yes—
68C2×C4⋊C4×C17C2316yes—
69C2×C4⋊C4×C17C2313yes—
70C2×C4⋊C4×C17C2313yes—
71C2×C4⋊C4×C17C2311yescharacteristic
72C2×C4⋊C4×C17C2316yes—
73C2×C4⋊C4×C17C2313yes—
74C2×C4⋊C4×C17C2313yes—
75C2×C4⋊C4×C17C2316yes—
76C2×C4⋊C4×C17C2313yes—
77C2×C22⋊C4×C17C2312yes—
78C2×C22⋊C4×C17C2316yes—
79C2×C22⋊C4×C17C2312yes—
80C2×C22⋊C4×C17C2316yes—
81C2×C22⋊C4×C17C2316yes—
82C2×C42×C17C2316yes—
83C2×C42×C17C23112yes—
84C2×C42×C17C2313yes—
85C2×C42×C17C2311yescharacteristic
86C2×C42×C17C2313yes—
87C2×C42×C17C2313yes—
88C2×C42×C17C2313yes—
89C2×C42×C17C2313yes—
90C2×C42×C17C2313yes—
91C17×#95C2316yes—
92C17×#95C2316yes—
93C17×#95C2316yes—
94C17×#95C23112yes—
95C17×#95C2316yes—
96C24×C17C2412yes—
97C2×Q8×C17—264no—
98C2×Q8×C17—212no—
99C2×Q8×C17—212no—
100C2×Q8×C17C22×C4124yes—
101C2×Q8×C17C22×C414yes—
102C2×Q8×C17C2×D414yes—
103C2×Q8×C17#4114yes—
104C2×D4×C17—22no—
105C2×D4×C17—22no—
106C2×D4×C17C22×C414yes—
107C22×C4×C17—212no—
108C22×C4×C17—212no—
109C22×C4×C17C22×C4124yes—
110C22×C4×C17C2413yes—
111C22×C4×C17C2412yes—
112C22×C4×C17C2416yes—
113C22×C4×C17C2416yes—
114C22×C4×C17C2413yes—
115C22×C4×C17C2413yes—
116C22×C4×C17C2411yescharacteristic
117C22×C4×C17C2411yescharacteristic
118C22×C4×C17C2413yes—
119C22×C4×C17C2411yescharacteristic
120C4⋊C4×C17—212no—
121C4⋊C4×C17—212no—
122C4⋊C4×C17—212no—
123C4⋊C4×C17—26no—
124C4⋊C4×C17—22no—
125C4⋊C4×C17—26no—
126C4⋊C4×C17—46no—
127C4⋊C4×C17C22×C4124yes—
128C4⋊C4×C17C22×C4112yes—
129C4⋊C4×C17C22×C4112yes—
130C4⋊C4×C17C2×D4112yes—
131C22⋊C4×C17—212no—
132C22⋊C4×C17—24no—
133C22⋊C4×C17—24no—
134C22⋊C4×C17—46no—
135C22⋊C4×C17C22×C4124yes—
136C42×C17—224no—
137C42×C17—212no—
138C42×C17—26no—
139C42×C17—26no—
140C42×C17—22no—
141C42×C17—26no—
142C42×C17—43no—
143C42×C17C22×C4112yes—
144C42×C17C2×D4112yes—
145#34311C1711yesmaximal, characteristic, direct product factor, Sylow
146C23×C17—22no—
147C23×C17—22no—
148C23×C17—22no—
149C23×C17—22no—
150C23×C17—22no—
151C23×C17—22no—
152C23×C17C23×C414yes—
153C23×C17C2511yescharacteristic
154Q8×C17—248no—
155Q8×C17C4×D4116yes—
156D4×C17—28no—
157C2×C4×C17—26no—
158C2×C4×C17—21no—
159C2×C4×C17—26no—
160C2×C4×C17—23no—
161C2×C4×C17—21no—
162C2×C4×C17—23no—
163C2×C4×C17—23no—
164C2×C4×C17—21no—
165C2×C4×C17—21no—
166C2×C4×C17—23no—
167C2×C4×C17—248no—
168C2×C4×C17—26no—
169C2×C4×C17—22no—
170C2×C4×C17—23no—
171C2×C4×C17—23no—
172C2×C4×C17—22no—
173C2×C4×C17—26no—
174C2×C4×C17—22no—
175C2×C4×C17—23no—
176C2×C4×C17—26no—
177C2×C4×C17C23×C416yes—
178C2×C4×C17C23×C4112yes—
179C2×C4×C17C23×C416yes—
180C2×C4×C17C23×C412yes—
181C2×C4×C17C22×D416yes—
182C2×C4×C17C22×D412yes—
183C2×C4×C17C22×D416yes—
184C2×C4×C17C2×#4116yes—
185C2×C4×C172−1+412yes—
186C2×C4×C172−1+412yes—
187C2×C4×C172−1+412yes—
188C2×D4×Q8C2×C1711yescharacteristic
189C2×#519C2×C1712yescomplemented
190#2365C2×C1713yescomplemented
191#2362C2×C1716yescomplemented
192#2354C2×C1713yes—
193Q8×C4⋊C4C2×C1711yescharacteristic, complemented
194Q8×C22⋊C4C2×C1712yescomplemented
195#2323C2×C1716yescomplemented
196C4×C4⋊Q8C2×C1713yescomplemented
197#2293C2×C1713yes—
198C42×Q8C2×C1711yescharacteristic, complemented
199C22×C17—24no—
200C22×C17—24no—
201C22×C17—24no—
202C22×C17—42no—
203C22×C17—42no—
204C22×C17—42no—
205C22×C17—42no—
206C22×C17C24×C411yescharacteristic
207C22×C17C23×D411yescharacteristic
208C22×C17C22×#4111yescharacteristic
209C22×C17C2×2−1+411yescharacteristic
210C22×C17C2×2−1+411yescharacteristic
211C22×C17C2×2−1+411yescharacteristic
212C22×C17#58511yescharacteristic
213C4×C17—212no—
214C4×C17—26no—
215C4×C17—22no—
216C4×C17—26no—
217C4×C17—22no—
218C4×C17—46no—
219C4×C17—42no—
220C4×C17—43no—
221C4×C17C2×C4×D4112yes—
222C4×C17#51914yescomplemented
223C23×Q8C22×C1712yes—
224D4×Q8C4×C17116yescomplemented
225C2×C4⋊Q8C22×C1713yes—
226C2×C22⋊Q8C22×C1716yes—
227#519—216no—
228C2×C4×Q8C22×C1716yes—
229C2×C4×Q8C22×C1711yescharacteristic
230C2×C4×Q8C22×C1712yes—
231C2×C4×Q8C22×C1716yes—
232C2×C4×Q8C22×C1711yescharacteristic
233C2×C4×Q8C22×C1711yescharacteristic
234C2×C4×D4C22×C1713yes—
235C2×#117C22×C1716yes—
236C2×#117C22×C1716yes—
237#391C22×C1716yes—
238#391C22×C1716yes—
239#390C22×C1713yes—
240#390C22×C1711yescharacteristic
241#389C22×C1713yes—
242#389C22×C1716yes—
243#389C22×C1716yes—
244#389C22×C1713yes—
245#388C22×C1716yes—
246#388C22×C17112yes—
247#388C22×C1716yes—
248#387C22×C17112yes—
249#384C22×C1713yes—
250#380C22×C1716yes—
251C4×C4⋊C4C22×C1716yes—
252C4×C4⋊C4C22×C1716yes—
253C4×C4⋊C4C22×C1713yes—
254C4×C4⋊C4C22×C1713yes—
255C4×C4⋊C4C22×C1713yes—
256C4×C4⋊C4C22×C1713yes—
257C4×C22⋊C4C22×C1716yes—
258C43C22×C1713yes—
259C2×C17—44no—
260C2×C17C22×C4×D411yescharacteristic
261C2×C17C2×#51911yescharacteristic
262C2×C17C4×2−1+411yescharacteristic
263C2×C17#349711yescharacteristic
264C2×C17#349911yescharacteristic
265C2×C17#351811yescharacteristic
266C2×C17#352311yescharacteristic
267C22×Q8—28no—
268C22×Q8—28no—
269C22×Q8C2×C4×C17116yes—
270C22×Q8C23×C1716yes—
271C22×Q8C23×C1711yescharacteristic
272C22×D4C23×C1711yescharacteristic
273C23×C4C23×C1716yes—
274C4⋊Q8C2×C4×C17124yes—
275C22⋊Q8C2×C4×C17148yes—
276C4×Q8—28no—
277C4×Q8—24no—
278C4×Q8—224no—
279C4×Q8—224no—
280C4×Q8C2×C4×C1718yes—
281C4×Q8D4×C1718yescomplemented
282C4×D4C2×C4×C17124yes—
283#117—224no—
284#117—224no—
285C2×C4⋊C4C23×C1716yes—
286C2×C4⋊C4C23×C1716yes—
287C2×C4⋊C4C23×C1716yes—
288C2×C4⋊C4C23×C1713yes—
289C2×C4⋊C4C23×C1713yes—
290C2×C4⋊C4C23×C1711yescharacteristic
291C2×C4⋊C4C23×C1716yes—
292C2×C4⋊C4C23×C1713yes—
293C2×C4⋊C4C23×C1713yes—
294C2×C4⋊C4C23×C1716yes—
295C2×C4⋊C4C23×C1713yes—
296C2×C22⋊C4C23×C1712yes—
297C2×C22⋊C4C23×C1716yes—
298C2×C22⋊C4C23×C1712yes—
299C2×C22⋊C4C23×C1716yes—
300C2×C22⋊C4C23×C1716yes—
301C2×C42C23×C1716yes—
302C2×C42C23×C17112yes—
303C2×C42C23×C1713yes—
304C2×C42C23×C1711yescharacteristic
305C2×C42C23×C1713yes—
306C2×C42C23×C1713yes—
307C2×C42C23×C1713yes—
308C2×C42C23×C1713yes—
309C2×C42C23×C1713yes—
310#95C23×C1716yes—
311#95C23×C1716yes—
312#95C23×C1716yes—
313#95C23×C17112yes—
314#95C23×C1716yes—
315C17#3431111yescharacteristic, direct product factor, Sylow
316C24C24×C1712yes—
317C2×Q8—264no—
318C2×Q8—212no—
319C2×Q8—212no—
320C2×Q8C22×C4×C17124yes—
321C2×Q8C22×C4×C1714yes—
322C2×Q8C2×D4×C1714yes—
323C2×Q8#41×C1714yes—
324C2×D4—22no—
325C2×D4—22no—
326C2×D4C22×C4×C1714yes—
327C22×C4—212no—
328C22×C4—212no—
329C22×C4C22×C4×C17124yes—
330C22×C4C24×C1713yes—
331C22×C4C24×C1712yes—
332C22×C4C24×C1716yes—
333C22×C4C24×C1713yes—
334C22×C4C24×C1716yes—
335C22×C4C24×C1713yes—
336C22×C4C24×C1711yescharacteristic
337C22×C4C24×C1711yescharacteristic
338C22×C4C24×C1713yes—
339C22×C4C24×C1711yescharacteristic
340C4⋊C4—212no—
341C4⋊C4—212no—
342C4⋊C4—212no—
343C4⋊C4—26no—
344C4⋊C4—22no—
345C4⋊C4—26no—
346C4⋊C4—46no—
347C4⋊C4C22×C4×C17112yes—
348C4⋊C4C22×C4×C17112yes—
349C4⋊C4C22×C4×C17124yes—
350C4⋊C4C2×D4×C17112yes—
351C22⋊C4—212no—
352C22⋊C4—24no—
353C22⋊C4—24no—
354C22⋊C4—46no—
355C22⋊C4C22×C4×C17124yes—
356C42—224no—
357C42—212no—
358C42—26no—
359C42—26no—
360C42—22no—
361C42—26no—
362C42—43no—
363C42C22×C4×C17112yes—
364C42C2×D4×C17112yes—
365C23—22no—
366C23—22no—
367C23—22no—
368C23—22no—
369C23—22no—
370C23—22no—
371C23C23×C4×C1714yes—
372C23C25×C1711yescharacteristic
373Q8—248no—
374Q8C4×D4×C17116yes—
375D4—28no—
376C2×C4—26no—
377C2×C4—21no—
378C2×C4—26no—
379C2×C4—21no—
380C2×C4—23no—
381C2×C4—23no—
382C2×C4—21no—
383C2×C4—23no—
384C2×C4—21no—
385C2×C4—23no—
386C2×C4—248no—
387C2×C4—26no—
388C2×C4—22no—
389C2×C4—23no—
390C2×C4—23no—
391C2×C4—22no—
392C2×C4—26no—
393C2×C4—22no—
394C2×C4—23no—
395C2×C4—26no—
396C2×C4C23×C4×C1716yes—
397C2×C4C23×C4×C17112yes—
398C2×C4C23×C4×C1716yes—
399C2×C4C23×C4×C1712yes—
400C2×C4C22×D4×C1716yes—
401C2×C4C22×D4×C1712yes—
402C2×C4C22×D4×C1716yes—
403C2×C4C2×#41×C1716yes—
404C2×C4C17×2−1+412yes—
405C2×C4C17×2−1+412yes—
406C2×C4C17×2−1+412yes—
407C22—24no—
408C22—24no—
409C22—24no—
410C22—42no—
411C22—42no—
412C22—42no—
413C22—42no—
414C22C24×C4×C1711yescharacteristic
415C22C23×D4×C1711yescharacteristic
416C22C22×#41×C1711yescharacteristic
417C22C2×C17×2−1+411yescharacteristic
418C22C2×C17×2−1+411yescharacteristic
419C22C2×C17×2−1+411yescharacteristic
420C22C17×#58511yescharacteristic
421C4—22no—
422C4—26no—
423C4—22no—
424C4—212no—
425C4—26no—
426C4—46no—
427C4—42no—
428C4—43no—
429C4C2×C4×D4×C17112yes—
430C4C17×#51914yescomplemented
431C2—44no—
432C2C22×C4×D4×C1711yescharacteristic
433C2C2×C17×#51911yescharacteristic
434C2C4×C17×2−1+411yescharacteristic
435C2C17×#349711yescharacteristic
436C2C17×#349911yescharacteristic
437C2C17×#351811yescharacteristic
438C2C17×#352311yescharacteristic
subgroupG/H
center, socleC23×C17C25
commutatorC22C24×C4×C17
Frattini, cosocleC23C25×C17
prime radicalC22×D4×C17C23
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C17 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C17×#519C2semidirect
3. C17×#2365C2semidirect
4. C17×#2362C2semidirect
6. Q8×C4⋊C4×C17C2semidirect
7. Q8×C22⋊C4×C17C2semidirect
8. C17×#2323C2semidirect
9. C4×C17×C4⋊Q8C2semidirect
11. C42×Q8×C17C2semidirect
13. D4×Q8×C17C4semidirect
62. C4×Q8×C17D4semidirect
145. #34311C17direct (N × H)
189. C2×#519C2×C17semidirect
190. #2365C2×C17semidirect
191. #2362C2×C17semidirect
193. Q8×C4⋊C4C2×C17semidirect
194. Q8×C22⋊C4C2×C17semidirect
195. #2323C2×C17semidirect
196. C4×C4⋊Q8C2×C17semidirect
198. C42×Q8C2×C17semidirect
222. C4×C17#519semidirect
224. D4×Q8C4×C17semidirect
281. C4×Q8D4×C17semidirect
315. C17#34311direct (N × H)
430. C4C17×#519semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Q8×C172
C2×C17×#5192
C17×#23652
C17×#23622
C17×#23542
Q8×C4⋊C4×C172
Q8×C22⋊C4×C172
C17×#23232
C4×C17×C4⋊Q82
C17×#22932
C42×Q8×C172
#3431117