Finite Group Databasebeta

← C17×#19457 #16877201

Subgroups — C17×#19457 #16877201

Order 4352.

660 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C17×#3206C211yesmaximal, characteristic, complemented
2C17×#3109C211yesmaximal, characteristic
3C2×C17×#474C211yesmaximal, characteristic, complemented
4C17×#2974C211yesmaximal, characteristic, complemented
5C17×#1703C212yesmaximal, complemented
6C17×#1685C212yesmaximal, complemented
7C17×#1683C212yesmaximal, complemented
8C17×#1665C212yesmaximal, complemented
9C17×#1573C211yesmaximal, characteristic, complemented
10C17×#1556C211yesmaximal, characteristic, complemented
11C17×#1551C211yesmaximal, characteristic, complemented
12C17×#532C2211yescharacteristic
13C2×C17×C4⋊Q8C2211yescharacteristic
14C2×C4×D4×C17C2211yescharacteristic
15C17×#492C2212yescomplemented
16C17×#487C2212yescomplemented
17C17×#481—21no—
18C17×#476C2211yescharacteristic
19C17×#476C2211yescharacteristic
20C17×#474—21no—
21C17×#474—21no—
22C17×#474C2212yes—
23C17×#474C2212yes—
24C17×#461—22no—
25C17×#459C2211yescharacteristic
26C17×#459C2211yescharacteristic
27C17×#448—21no—
28C17×#448—21no—
29C17×#447—21no—
30C17×#442—21no—
31C17×#442—21no—
32C17×#436C2212yes—
33C17×#435—22no—
34C8×D4×C17C2212yes—
35C17×#432C2211yescharacteristic
36C17×#432C2211yescharacteristic
37C17×#431C2211yescharacteristic
38C2×C17×#107—21no—
39C2×C17×C4⋊C8C2211yescharacteristic
40C2×C17×#102—21no—
41C17×#407—21no—
42C2×C17×C22⋊C8—21no—
43C17×#335C2212yescomplemented
44C17×#334C2212yescomplemented
45C17×#333C2212yescomplemented
46C17×#332C2212yescomplemented
47C17×#332C2212yescomplemented
48C17×#331C2212yescomplemented
49C2×#41×C17—21no—
50C22×Q8×C17—21no—
51C22×D4×C17D411yescharacteristic
52C23×C4×C17—21no—
53C2×SD16×C17—22no—
54C2×SD16×C17—22no—
55C2×D8×C17—21no—
56C2×D8×C17—21no—
57C2×M16×C17—22no—
58C22×C8×C17—21no—
59C22×C8×C17—22no—
60C17×C4⋊Q8—21no—
61C17×C4⋊Q8—21no—
62C17×C4⋊Q8—21no—
63C17×C4⋊Q8C2312yes—
64C17×C4⋊Q8C2311yescharacteristic
65C17×#127C2311yescharacteristic
66C17×#124—21no—
67C17×#121—21no—
68C17×#121—21no—
69C4×D4×C17—21no—
70C4×D4×C17—21no—
71C4×D4×C17—21no—
72C4×D4×C17—21no—
73C4×D4×C17D411yescharacteristic
74C4×D4×C17D411yescharacteristic
75C4×D4×C17C2311yescharacteristic
76C4×D4×C17C2311yescharacteristic
77C2×C4⋊C4×C17—21no—
78C2×C4⋊C4×C17—21no—
79C2×C4⋊C4×C17D411yescharacteristic
80C2×C22⋊C4×C17—21no—
81C2×C42×C17C2311yescharacteristic
82C17×#107—22no—
83C17×#107—22no—
84C17×#106—21no—
85C17×#106—21no—
86C17×C4⋊C8—21no—
87C17×C4⋊C8D412yes—
88C17×C4⋊C8C2312yes—
89C17×C4⋊C8C2312yes—
90C17×C4⋊C8C2311yescharacteristic
91C17×C4⋊C8C2311yescharacteristic
92C17×#103—22no—
93C17×#103—22no—
94C17×#102—22no—
95C17×#102—22no—
96C17×#102—21no—
97C17×#102—21no—
98C17×#102—21no—
99C17×#102—21no—
100C17×C22⋊C8—21no—
101C17×C22⋊C8—21no—
102C17×C22⋊C8—22no—
103C17×C22⋊C8—22no—
104C17×C22⋊C8D411yescharacteristic
105C17×C22⋊C8D411yescharacteristic
106C17×#97—21no—
107C17×#97—21no—
108C4×C8×C17C2312yes—
109C24×C17—21no—
110#41×C17—82no—
111C2×Q8×C17—22no—
112C2×Q8×C17—21no—
113C2×Q8×C17—41no—
114C2×Q8×C17—82no—
115C2×D4×C17—22no—
116C2×D4×C17—21no—
117C2×D4×C17—21no—
118C2×D4×C17—21no—
119C2×D4×C17—21no—
120C2×D4×C17—41no—
121C2×D4×C17—41no—
122C2×D4×C17C2×D411yescharacteristic
123C2×D4×C17C2×D411yescharacteristic
124C22×C4×C17—21no—
125C22×C4×C17—21no—
126C22×C4×C17—21no—
127C22×C4×C17—21no—
128C22×C4×C17—21no—
129C22×C4×C17—41no—
130C22×C4×C17—41no—
131C22×C4×C17—82no—
132C22×C4×C17C2×D411yescharacteristic
133C22×C4×C17C2×D411yescharacteristic
134C22×C4×C17#4111yescharacteristic
135SD16×C17—82no—
136SD16×C17—82no—
137D8×C17—42no—
138D8×C17—42no—
139M16×C17—82no—
140C2×C8×C17—22no—
141C2×C8×C17—22no—
142C2×C8×C17—21no—
143C2×C8×C17—21no—
144C2×C8×C17—42no—
145C2×C8×C17—82no—
146C2×C8×C17C2×D412yes—
147C2×C8×C17C2×D412yes—
148C4⋊C4×C17—21no—
149C4⋊C4×C17—22no—
150C4⋊C4×C17—21no—
151C4⋊C4×C17—21no—
152C4⋊C4×C17—22no—
153C4⋊C4×C17—41no—
154C4⋊C4×C17—41no—
155C4⋊C4×C17C2×D411yescharacteristic
156C4⋊C4×C17C2×D411yescharacteristic
157C22⋊C4×C17—21no—
158C22⋊C4×C17—21no—
159C22⋊C4×C17—21no—
160C22⋊C4×C17—21no—
161C22⋊C4×C17—41no—
162C22⋊C4×C17—41no—
163C42×C17C2×D411yescharacteristic
164C42×C17C2×D411yescharacteristic
165C42×C17#4111yescharacteristic
166C42×C17C2411yescharacteristic
167#19457C1711yesmaximal, characteristic, direct product factor, Sylow
168C23×C17—21no—
169C23×C17—21no—
170C23×C17—42no—
171C23×C17—42no—
172C23×C17—41no—
173C23×C17—81no—
174C23×C17#12111yescharacteristic
175Q8×C17—42no—
176Q8×C17—42no—
177Q8×C17—81no—
178Q8×C17—82no—
179D4×C17—21no—
180D4×C17—21no—
181D4×C17—21no—
182D4×C17—42no—
183D4×C17—41no—
184D4×C17—41no—
185D4×C17—42no—
186D4×C17—81no—
187D4×C17—82no—
188D4×C17#13712yes—
189C2×C4×C17—22no—
190C2×C4×C17—21no—
191C2×C4×C17—21no—
192C2×C4×C17—22no—
193C2×C4×C17—21no—
194C2×C4×C17—21no—
195C2×C4×C17—42no—
196C2×C4×C17—42no—
197C2×C4×C17—41no—
198C2×C4×C17—42no—
199C2×C4×C17—81no—
200C2×C4×C17—81no—
201C2×C4×C17—82no—
202C2×C4×C17—81no—
203C2×C4×C17—82no—
204C2×C4×C17#12111yescharacteristic
205C2×C4×C17#12111yescharacteristic
206C2×C4×C17#12111yescharacteristic
207C2×C4×C17C22×D411yescharacteristic
208C2×C4×C17C22×D411yescharacteristic
209C2×C4×C17C2×#4111yescharacteristic
210C8×C17—22no—
211C8×C17—22no—
212C8×C17—41no—
213C8×C17—42no—
214C8×C17—41no—
215C8×C17—42no—
216#3206C2×C1711yescharacteristic, complemented
217#3109C2×C1711yescharacteristic
218C2×#474C2×C1711yescharacteristic, complemented
219#2974C2×C1711yescharacteristic, complemented
220#1703C2×C1712yescomplemented
221#1685C2×C1712yescomplemented
222#1683C2×C1712yescomplemented
223#1665C2×C1712yescomplemented
224#1573C2×C1711yescharacteristic, complemented
225#1556C2×C1711yescharacteristic, complemented
226#1551C2×C1711yescharacteristic, complemented
227C22×C17—21no—
228C22×C17—21no—
229C22×C17—22no—
230C22×C17—41no—
231C22×C17—41no—
232C22×C17—41no—
233C22×C17—41no—
234C22×C17—41no—
235C22×C17—84no—
236C22×C17—81no—
237C22×C17—81no—
238C22×C17—81no—
239C22×C17#47112yes—
240C22×C17C2×#12111yescharacteristic
241C4×C17—21no—
242C4×C17—21no—
243C4×C17—21no—
244C4×C17—21no—
245C4×C17—41no—
246C4×C17—41no—
247C4×C17—82no—
248C4×C17—81no—
249C4×C17C2×#13711yescharacteristic
250C4×C17#57511yescharacteristic
251C4×C17#57612yes—
252#532C22×C1711yescharacteristic
253C2×C4⋊Q8C22×C1711yescharacteristic
254C2×C4×D4C22×C1711yescharacteristic
255#492C22×C1712yescomplemented
256#487C22×C1712yescomplemented
257#481—21no—
258#476C22×C1711yescharacteristic
259#476C22×C1711yescharacteristic
260#474—21no—
261#474—21no—
262#474C22×C1712yes—
263#474C22×C1712yes—
264#461—22no—
265#459C22×C1711yescharacteristic
266#459C22×C1711yescharacteristic
267#448—21no—
268#448—21no—
269#447—21no—
270#442—21no—
271#442—21no—
272#436C22×C1712yes—
273#435—22no—
274C8×D4C22×C1712yes—
275#432C22×C1711yescharacteristic
276#432C22×C1711yescharacteristic
277#431C22×C1711yescharacteristic
278C2×#107—21no—
279C2×C4⋊C8C22×C1711yescharacteristic
280C2×#102—21no—
281#407—21no—
282C2×C22⋊C8—21no—
283#335C22×C1712yescomplemented
284#334C22×C1712yescomplemented
285#333C22×C1712yescomplemented
286#332C22×C1712yescomplemented
287#332C22×C1712yescomplemented
288#331C22×C1712yescomplemented
289C2×C17—22no—
290C2×C17—42no—
291C2×C17—81no—
292C2×C17—161no—
293C2×C17#304111yescharacteristic
294C2×C17#305611yescharacteristic
295C2×C17C2×#47111yescharacteristic
296C2×#41—21no—
297C22×Q8—21no—
298C22×D4D4×C1711yescharacteristic
299C23×C4—21no—
300C2×SD16—22no—
301C2×SD16—22no—
302C2×D8—21no—
303C2×D8—21no—
304C2×M16—22no—
305C22×C8—21no—
306C22×C8—22no—
307C4⋊Q8—21no—
308C4⋊Q8—21no—
309C4⋊Q8—21no—
310C4⋊Q8C23×C1712yes—
311C4⋊Q8C23×C1711yescharacteristic
312#127C23×C1711yescharacteristic
313#124—21no—
314#121—21no—
315#121—21no—
316C4×D4—21no—
317C4×D4—21no—
318C4×D4—21no—
319C4×D4—21no—
320C4×D4D4×C1711yescharacteristic
321C4×D4D4×C1711yescharacteristic
322C4×D4C23×C1711yescharacteristic
323C4×D4C23×C1711yescharacteristic
324C2×C4⋊C4—21no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4D4×C1711yescharacteristic
327C2×C22⋊C4—21no—
328C2×C42C23×C1711yescharacteristic
329#107—22no—
330#107—22no—
331#106—21no—
332#106—21no—
333C4⋊C8—21no—
334C4⋊C8D4×C1712yes—
335C4⋊C8C23×C1712yes—
336C4⋊C8C23×C1712yes—
337C4⋊C8C23×C1711yescharacteristic
338C4⋊C8C23×C1711yescharacteristic
339#103—22no—
340#103—22no—
341#102—22no—
342#102—22no—
343#102—21no—
344#102—21no—
345#102—21no—
346#102—21no—
347C22⋊C8—21no—
348C22⋊C8—21no—
349C22⋊C8—22no—
350C22⋊C8—22no—
351C22⋊C8D4×C1711yescharacteristic
352C22⋊C8D4×C1711yescharacteristic
353#97—21no—
354#97—21no—
355C4×C8C23×C1712yes—
356C17#1945711yescharacteristic, direct product factor, Sylow
357C24—21no—
358#41—82no—
359C2×Q8—22no—
360C2×Q8—21no—
361C2×Q8—41no—
362C2×Q8—82no—
363C2×D4—22no—
364C2×D4—21no—
365C2×D4—21no—
366C2×D4—21no—
367C2×D4—21no—
368C2×D4—41no—
369C2×D4—41no—
370C2×D4C2×D4×C1711yescharacteristic
371C2×D4C2×D4×C1711yescharacteristic
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—41no—
378C22×C4—41no—
379C22×C4—82no—
380C22×C4C2×D4×C1711yescharacteristic
381C22×C4C2×D4×C1711yescharacteristic
382C22×C4#41×C1711yescharacteristic
383SD16—82no—
384SD16—82no—
385D8—42no—
386D8—42no—
387M16—82no—
388C2×C8—22no—
389C2×C8—21no—
390C2×C8—21no—
391C2×C8—22no—
392C2×C8—42no—
393C2×C8—82no—
394C2×C8C2×D4×C1712yes—
395C2×C8C2×D4×C1712yes—
396C4⋊C4—21no—
397C4⋊C4—21no—
398C4⋊C4—22no—
399C4⋊C4—21no—
400C4⋊C4—22no—
401C4⋊C4—41no—
402C4⋊C4—41no—
403C4⋊C4C2×D4×C1711yescharacteristic
404C4⋊C4C2×D4×C1711yescharacteristic
405C22⋊C4—21no—
406C22⋊C4—21no—
407C22⋊C4—21no—
408C22⋊C4—21no—
409C22⋊C4—41no—
410C22⋊C4—41no—
411C42C2×D4×C1711yescharacteristic
412C42C2×D4×C1711yescharacteristic
413C42#41×C1711yescharacteristic
414C42C24×C1711yescharacteristic
415C23—21no—
416C23—21no—
417C23—42no—
418C23—42no—
419C23—41no—
420C23—81no—
421C23C17×#12111yescharacteristic
422Q8—42no—
423Q8—42no—
424Q8—81no—
425Q8—82no—
426D4—21no—
427D4—21no—
428D4—21no—
429D4—42no—
430D4—41no—
431D4—41no—
432D4—42no—
433D4—81no—
434D4—82no—
435D4C17×#13712yes—
436C2×C4—22no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—22no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—42no—
443C2×C4—42no—
444C2×C4—41no—
445C2×C4—42no—
446C2×C4—81no—
447C2×C4—81no—
448C2×C4—82no—
449C2×C4—81no—
450C2×C4—82no—
451C2×C4C17×#12111yescharacteristic
452C2×C4C17×#12111yescharacteristic
453C2×C4C17×#12111yescharacteristic
454C2×C4C22×D4×C1711yescharacteristic
455C2×C4C22×D4×C1711yescharacteristic
456C2×C4C2×#41×C1711yescharacteristic
457C8—22no—
458C8—22no—
459C8—41no—
460C8—42no—
461C8—41no—
462C8—42no—
463C22—21no—
464C22—21no—
465C22—22no—
466C22—41no—
467C22—41no—
468C22—41no—
469C22—41no—
470C22—41no—
471C22—84no—
472C22—81no—
473C22—81no—
474C22—81no—
475C22C17×#47112yes—
476C22C2×C17×#12111yescharacteristic
477C4—21no—
478C4—21no—
479C4—21no—
480C4—21no—
481C4—41no—
482C4—41no—
483C4—82no—
484C4—81no—
485C4C2×C17×#13711yescharacteristic
486C4C17×#57511yescharacteristic
487C4C17×#57612yes—
488C2—22no—
489C2—42no—
490C2—81no—
491C2—161no—
492C2C17×#304111yescharacteristic
493C2C17×#305611yescharacteristic
494C2C2×C17×#47111yescharacteristic
subgroupG/H
center, socleC22×C17C2×#121
commutator, Frattini, cosocleC42C24×C17
prime radicalC17×#3109C2
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×#3206C2semidirect
3. C2×C17×#474C2semidirect
4. C17×#2974C2semidirect
5. C17×#1703C2semidirect
6. C17×#1685C2semidirect
7. C17×#1683C2semidirect
8. C17×#1665C2semidirect
9. C17×#1573C2semidirect
10. C17×#1556C2semidirect
11. C17×#1551C2semidirect
15. C17×#492C22semidirect
16. C17×#487C22semidirect
43. C17×#335C22semidirect
44. C17×#334C22semidirect
45. C17×#333C22semidirect
46. C17×#332C22semidirect
47. C17×#332C22semidirect
48. C17×#331C22semidirect
167. #19457C17direct (N × H)
216. #3206C2×C17semidirect
218. C2×#474C2×C17semidirect
219. #2974C2×C17semidirect
220. #1703C2×C17semidirect
221. #1685C2×C17semidirect
222. #1683C2×C17semidirect
223. #1665C2×C17semidirect
224. #1573C2×C17semidirect
225. #1556C2×C17semidirect
226. #1551C2×C17semidirect
255. #492C22×C17semidirect
256. #487C22×C17semidirect
283. #335C22×C17semidirect
284. #334C22×C17semidirect
285. #333C22×C17semidirect
286. #332C22×C17semidirect
287. #332C22×C17semidirect
288. #331C22×C17semidirect
356. C17#19457direct (N × H)

Maximal subgroups

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

subgroupindex
C17×#32062
C17×#31092
C2×C17×#4742
C17×#29742
C17×#17032
C17×#16852
C17×#16832
C17×#16652
C17×#15732
C17×#15562
C17×#15512
#1945717