Finite Group Databasebeta

← C17×#19416 #16877160

Subgroups — C17×#19416 #16877160

Order 4352.

694 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C17×#3226C211yesmaximal, characteristic, complemented
2C17×#3039C211yesmaximal, characteristic, complemented
3C17×#3035C211yesmaximal, characteristic
4C17×#2988C211yesmaximal, characteristic, complemented
5C17×#1682C212yesmaximal, complemented
6C17×#1681C212yesmaximal, complemented
7C17×#1674C212yesmaximal, complemented
8C17×#1673C212yesmaximal, complemented
9C17×#1571C211yesmaximal, characteristic, complemented
10C17×#1547C211yesmaximal, characteristic, complemented
11C2×C17×#332C211yesmaximal, characteristic, complemented
12C2×C17×#137—21no—
13C2×C17×#135—21no—
14C17×#532C2211yescharacteristic
15C2×C17×C4⋊Q8C2211yescharacteristic
16C4×#41×C17C2211yescharacteristic
17C17×#500C2212yes—
18C17×#486C2212yes—
19C17×#480—22no—
20C17×#474—21no—
21C17×#474—21no—
22C17×#464—21no—
23C17×#463—21no—
24C17×#462—21no—
25C17×#462C2211yescharacteristic
26C17×#462C2212yes—
27C17×#461—21no—
28C17×#461C2211yescharacteristic
29C17×#461C2212yes—
30C17×#460C2211yescharacteristic
31C17×#459C2211yescharacteristic
32C8×Q8×C17C2212yes—
33C8×D4×C17—22no—
34C8×D4×C17C2212yes—
35C17×#431—21no—
36C17×#431C2211yescharacteristic
37C17×#423C2211yescharacteristic
38C2×C17×C4⋊C8—21no—
39C2×C17×C4⋊C8C2211yescharacteristic
40C2×C17×C4⋊C8C2211yescharacteristic
41C17×#419—21no—
42C17×#416—21no—
43C17×#335C2212yes—
44C17×#335C2212yes—
45C17×#332C2212yes—
46C17×#332C2212yes—
47C17×#332C2212yes—
48C17×#331C2212yes—
49C2×#41×C17—21no—
50C2×#41×C17D411yescharacteristic
51C22×Q8×C17—21no—
52C17×#137—44no—
53C17×#135—44no—
54C2×Q16×C17—21no—
55C2×Q16×C17—22no—
56C2×SD16×C17—21no—
57C2×SD16×C17—21no—
58C2×SD16×C17—22no—
59C2×D8×C17—21no—
60C2×M16×C17—21no—
61C22×C8×C17—21no—
62C22×C8×C17—21no—
63C22×C8×C17—22no—
64C17×C4⋊Q8—21no—
65C17×C4⋊Q8—21no—
66C17×C4⋊Q8—21no—
67C17×C4⋊Q8C2311yescharacteristic
68C17×C4⋊Q8C2312yes—
69C17×#127C2311yescharacteristic
70C17×#124—21no—
71C17×#121—21no—
72C17×#121—21no—
73C4×Q8×C17D411yescharacteristic
74C4×Q8×C17C2311yescharacteristic
75C4×D4×C17—21no—
76C4×D4×C17—21no—
77C4×D4×C17—21no—
78C4×D4×C17—21no—
79C4×D4×C17D411yescharacteristic
80C4×D4×C17C2311yescharacteristic
81C17×#117—21no—
82C17×#117D411yescharacteristic
83C2×C4⋊C4×C17—21no—
84C2×C4⋊C4×C17—21no—
85C2×C42×C17—21no—
86C2×C42×C17C2311yescharacteristic
87C17×#107—22no—
88C17×#107—22no—
89C17×C4⋊C8—22no—
90C17×C4⋊C8—21no—
91C17×C4⋊C8—21no—
92C17×C4⋊C8—21no—
93C17×C4⋊C8D411yescharacteristic
94C17×C4⋊C8D411yescharacteristic
95C17×C4⋊C8C2312yes—
96C17×C4⋊C8C2312yes—
97C17×C4⋊C8C2311yescharacteristic
98C17×C4⋊C8C2311yescharacteristic
99C17×#103—21no—
100C17×#103—21no—
101C17×#103—22no—
102C17×#103—22no—
103C17×#102—22no—
104C17×#102—22no—
105C17×#102—21no—
106C17×#102—21no—
107C17×C22⋊C8—22no—
108C17×C22⋊C8D412yes—
109C4×C8×C17—22no—
110C4×C8×C17C2312yes—
111#41×C17—22no—
112#41×C17—42no—
113#41×C17—42no—
114#41×C17D814yes—
115C2×Q8×C17—21no—
116C2×Q8×C17—22no—
117C2×Q8×C17—41no—
118C2×Q8×C17—42no—
119C2×Q8×C17—42no—
120C2×Q8×C17C2×D411yescharacteristic
121C2×D4×C17—21no—
122C2×D4×C17—21no—
123C2×D4×C17—21no—
124C2×D4×C17—21no—
125C2×D4×C17—41no—
126C2×D4×C17C2×D411yescharacteristic
127C22×C4×C17—21no—
128C22×C4×C17—21no—
129C22×C4×C17—21no—
130C22×C4×C17—41no—
131C22×C4×C17—41no—
132C22×C4×C17C2×D411yescharacteristic
133C22×C4×C17C2×D411yescharacteristic
134C22×C4×C17#4111yescharacteristic
135Q16×C17—42no—
136Q16×C17—44no—
137SD16×C17—42no—
138SD16×C17—42no—
139SD16×C17—44no—
140D8×C17—42no—
141M16×C17—42no—
142C2×C8×C17—22no—
143C2×C8×C17—21no—
144C2×C8×C17—21no—
145C2×C8×C17—22no—
146C2×C8×C17—42no—
147C2×C8×C17—82no—
148C2×C8×C17—81no—
149C2×C8×C17C2×D412yes—
150C2×C8×C17C2×D412yes—
151C4⋊C4×C17—21no—
152C4⋊C4×C17—21no—
153C4⋊C4×C17—22no—
154C4⋊C4×C17—21no—
155C4⋊C4×C17—22no—
156C4⋊C4×C17—21no—
157C4⋊C4×C17—41no—
158C4⋊C4×C17—41no—
159C4⋊C4×C17C2×D411yescharacteristic
160C4⋊C4×C17C2×D411yescharacteristic
161C22⋊C4×C17—21no—
162C22⋊C4×C17—21no—
163C22⋊C4×C17—21no—
164C22⋊C4×C17—41no—
165C22⋊C4×C17—41no—
166C42×C17—21no—
167C42×C17—21no—
168C42×C17—21no—
169C42×C17C2×D411yescharacteristic
170C42×C17C2×D411yescharacteristic
171C42×C17#4111yescharacteristic
172C42×C17C2411yescharacteristic
173#19416C1711yesmaximal, characteristic, direct product factor, Sylow
174C23×C17—21no—
175C23×C17—41no—
176C23×C17#12111yescharacteristic
177Q8×C17—21no—
178Q8×C17—42no—
179Q8×C17—41no—
180Q8×C17—42no—
181Q8×C17—41no—
182Q8×C17—82no—
183Q8×C17C2×D812yes—
184D4×C17—24no—
185D4×C17—21no—
186D4×C17—41no—
187D4×C17—41no—
188D4×C17—41no—
189D4×C17—41no—
190D4×C17—81no—
191D4×C17—82no—
192D4×C17C2×D812yes—
193C2×C4×C17—21no—
194C2×C4×C17—21no—
195C2×C4×C17—21no—
196C2×C4×C17—24no—
197C2×C4×C17—21no—
198C2×C4×C17—21no—
199C2×C4×C17—41no—
200C2×C4×C17—41no—
201C2×C4×C17—41no—
202C2×C4×C17—41no—
203C2×C4×C17—42no—
204C2×C4×C17—81no—
205C2×C4×C17—82no—
206C2×C4×C17—82no—
207C2×C4×C17#12111yescharacteristic
208C2×C4×C17#12111yescharacteristic
209C2×C4×C17#12111yescharacteristic
210C2×C4×C17C2×D812yes—
211C2×C4×C17#13512yes—
212C2×C4×C17C22×D411yescharacteristic
213C2×C4×C17C22×D411yescharacteristic
214C2×C4×C17C2×#4111yescharacteristic
215C8×C17—22no—
216C8×C17—22no—
217C8×C17—41no—
218C8×C17—41no—
219C8×C17—42no—
220C8×C17—42no—
221#3226C2×C1711yescharacteristic, complemented
222#3039C2×C1711yescharacteristic, complemented
223#3035C2×C1711yescharacteristic
224#2988C2×C1711yescharacteristic, complemented
225#1682C2×C1712yescomplemented
226#1681C2×C1712yescomplemented
227#1674C2×C1712yescomplemented
228#1673C2×C1712yescomplemented
229#1571C2×C1711yescharacteristic, complemented
230#1547C2×C1711yescharacteristic, complemented
231C2×#332C2×C1711yescharacteristic, complemented
232C22×C17—21no—
233C22×C17—21no—
234C22×C17—22no—
235C22×C17—41no—
236C22×C17—41no—
237C22×C17—81no—
238C22×C17—81no—
239C22×C17—81no—
240C22×C17#46612yes—
241C22×C17C2×#12111yescharacteristic
242C4×C17—21no—
243C4×C17—22no—
244C4×C17—21no—
245C4×C17—21no—
246C4×C17—41no—
247C4×C17—41no—
248C4×C17—81no—
249C4×C17—82no—
250C4×C17#46612yes—
251C4×C17C22×D811yescharacteristic
252C4×C17C2×#13511yescharacteristic
253C4×C17#57711yescharacteristic
254C4×C17#57811yescharacteristic
255C2×#137—21no—
256C2×#135—21no—
257#532C22×C1711yescharacteristic
258C2×C4⋊Q8C22×C1711yescharacteristic
259C4×#41C22×C1711yescharacteristic
260#500C22×C1712yes—
261#486C22×C1712yes—
262#480—22no—
263#474—21no—
264#474—21no—
265#464—21no—
266#463—21no—
267#462—21no—
268#462C22×C1711yescharacteristic
269#462C22×C1712yes—
270#461—21no—
271#461C22×C1711yescharacteristic
272#461C22×C1712yes—
273#460C22×C1711yescharacteristic
274#459C22×C1711yescharacteristic
275C8×Q8C22×C1712yes—
276C8×D4—22no—
277C8×D4C22×C1712yes—
278#431—21no—
279#431C22×C1711yescharacteristic
280#423C22×C1711yescharacteristic
281C2×C4⋊C8—21no—
282C2×C4⋊C8C22×C1711yescharacteristic
283C2×C4⋊C8C22×C1711yescharacteristic
284#419—21no—
285#416—21no—
286#335C22×C1712yes—
287#335C22×C1712yes—
288#332C22×C1712yes—
289#332C22×C1712yes—
290#332C22×C1712yes—
291#331C22×C1712yes—
292C2×C17—22no—
293C2×C17—42no—
294C2×C17—161no—
295C2×C17#304611yescharacteristic
296C2×C17C2×#46611yescharacteristic
297C2×C17#306911yescharacteristic
298C2×#41—21no—
299C2×#41D4×C1711yescharacteristic
300C22×Q8—21no—
301#137—44no—
302#135—44no—
303C2×Q16—21no—
304C2×Q16—22no—
305C2×SD16—21no—
306C2×SD16—21no—
307C2×SD16—22no—
308C2×D8—21no—
309C2×M16—21no—
310C22×C8—21no—
311C22×C8—21no—
312C22×C8—22no—
313C4⋊Q8—21no—
314C4⋊Q8—21no—
315C4⋊Q8—21no—
316C4⋊Q8C23×C1712yes—
317C4⋊Q8C23×C1711yescharacteristic
318#127C23×C1711yescharacteristic
319#124—21no—
320#121—21no—
321#121—21no—
322C4×Q8D4×C1711yescharacteristic
323C4×Q8C23×C1711yescharacteristic
324C4×D4—21no—
325C4×D4—21no—
326C4×D4—21no—
327C4×D4—21no—
328C4×D4D4×C1711yescharacteristic
329C4×D4C23×C1711yescharacteristic
330#117—21no—
331#117D4×C1711yescharacteristic
332C2×C4⋊C4—21no—
333C2×C4⋊C4—21no—
334C2×C42—21no—
335C2×C42C23×C1711yescharacteristic
336#107—22no—
337#107—22no—
338C4⋊C8—22no—
339C4⋊C8—21no—
340C4⋊C8—21no—
341C4⋊C8—21no—
342C4⋊C8D4×C1711yescharacteristic
343C4⋊C8D4×C1711yescharacteristic
344C4⋊C8C23×C1712yes—
345C4⋊C8C23×C1712yes—
346C4⋊C8C23×C1711yescharacteristic
347C4⋊C8C23×C1711yescharacteristic
348#103—21no—
349#103—21no—
350#103—22no—
351#103—22no—
352#102—22no—
353#102—22no—
354#102—21no—
355#102—21no—
356C22⋊C8—22no—
357C22⋊C8D4×C1712yes—
358C4×C8—22no—
359C4×C8C23×C1712yes—
360C17#1941611yescharacteristic, direct product factor, Sylow
361#41—22no—
362#41—42no—
363#41—42no—
364#41D8×C1714yes—
365C2×Q8—21no—
366C2×Q8—22no—
367C2×Q8—41no—
368C2×Q8—42no—
369C2×Q8—42no—
370C2×Q8C2×D4×C1711yescharacteristic
371C2×D4—21no—
372C2×D4—21no—
373C2×D4—21no—
374C2×D4—21no—
375C2×D4—41no—
376C2×D4C2×D4×C1711yescharacteristic
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—41no—
381C22×C4—41no—
382C22×C4C2×D4×C1711yescharacteristic
383C22×C4C2×D4×C1711yescharacteristic
384C22×C4#41×C1711yescharacteristic
385Q16—42no—
386Q16—44no—
387SD16—42no—
388SD16—42no—
389SD16—44no—
390D8—42no—
391M16—42no—
392C2×C8—22no—
393C2×C8—21no—
394C2×C8—21no—
395C2×C8—22no—
396C2×C8—42no—
397C2×C8—82no—
398C2×C8—81no—
399C2×C8C2×D4×C1712yes—
400C2×C8C2×D4×C1712yes—
401C4⋊C4—21no—
402C4⋊C4—21no—
403C4⋊C4—22no—
404C4⋊C4—21no—
405C4⋊C4—22no—
406C4⋊C4—21no—
407C4⋊C4—41no—
408C4⋊C4—41no—
409C4⋊C4C2×D4×C1711yescharacteristic
410C4⋊C4C2×D4×C1711yescharacteristic
411C22⋊C4—21no—
412C22⋊C4—21no—
413C22⋊C4—21no—
414C22⋊C4—41no—
415C22⋊C4—41no—
416C42—21no—
417C42—21no—
418C42—21no—
419C42C2×D4×C1711yescharacteristic
420C42C2×D4×C1711yescharacteristic
421C42#41×C1711yescharacteristic
422C42C24×C1711yescharacteristic
423C23—21no—
424C23—41no—
425C23C17×#12111yescharacteristic
426Q8—21no—
427Q8—42no—
428Q8—41no—
429Q8—42no—
430Q8—41no—
431Q8—82no—
432Q8C2×D8×C1712yes—
433D4—24no—
434D4—21no—
435D4—41no—
436D4—41no—
437D4—41no—
438D4—41no—
439D4—81no—
440D4—82no—
441D4C2×D8×C1712yes—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—24no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—42no—
453C2×C4—81no—
454C2×C4—82no—
455C2×C4—82no—
456C2×C4C17×#12111yescharacteristic
457C2×C4C17×#12111yescharacteristic
458C2×C4C17×#12111yescharacteristic
459C2×C4C2×D8×C1712yes—
460C2×C4C17×#13512yes—
461C2×C4C22×D4×C1711yescharacteristic
462C2×C4C22×D4×C1711yescharacteristic
463C2×C4C2×#41×C1711yescharacteristic
464C8—22no—
465C8—22no—
466C8—41no—
467C8—41no—
468C8—42no—
469C8—42no—
470C22—21no—
471C22—21no—
472C22—22no—
473C22—41no—
474C22—41no—
475C22—81no—
476C22—81no—
477C22—81no—
478C22C17×#46612yes—
479C22C2×C17×#12111yescharacteristic
480C4—21no—
481C4—22no—
482C4—21no—
483C4—21no—
484C4—41no—
485C4—41no—
486C4—81no—
487C4—82no—
488C4C17×#46612yes—
489C4C22×D8×C1711yescharacteristic
490C4C2×C17×#13511yescharacteristic
491C4C17×#57711yescharacteristic
492C4C17×#57811yescharacteristic
493C2—22no—
494C2—42no—
495C2—161no—
496C2C17×#304611yescharacteristic
497C2C2×C17×#46611yescharacteristic
498C2C17×#306911yescharacteristic
subgroupG/H
center, socleC22×C17C2×#121
commutator, Frattini, cosocleC42C24×C17
prime radicalC17×#3035C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C17 ◁ C2×C42×C17 ◁ G

Complements

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

NH ≅ G/Ntype
1. C17×#3226C2semidirect
2. C17×#3039C2semidirect
4. C17×#2988C2semidirect
5. C17×#1682C2semidirect
6. C17×#1681C2semidirect
7. C17×#1674C2semidirect
8. C17×#1673C2semidirect
9. C17×#1571C2semidirect
10. C17×#1547C2semidirect
11. C2×C17×#332C2semidirect
173. #19416C17direct (N × H)
221. #3226C2×C17semidirect
222. #3039C2×C17semidirect
224. #2988C2×C17semidirect
225. #1682C2×C17semidirect
226. #1681C2×C17semidirect
227. #1674C2×C17semidirect
228. #1673C2×C17semidirect
229. #1571C2×C17semidirect
230. #1547C2×C17semidirect
231. C2×#332C2×C17semidirect
360. C17#19416direct (N × H)

Maximal subgroups

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

subgroupindex
C17×#32262
C17×#30392
C17×#30352
C17×#29882
C17×#16822
C17×#16812
C17×#16742
C17×#16732
C17×#15712
C17×#15472
C2×C17×#3322
#1941617