Finite Group Databasebeta

← C17×#18360 #16876104

Subgroups — C17×#18360 #16876104

Order 4352.

928 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C17×#3507C211yesmaximal, characteristic, complemented
2C17×#3215C211yesmaximal, characteristic, complemented
3C17×#3213C211yesmaximal, characteristic
4C17×#2632C211yesmaximal, characteristic, complemented
5C17×#1603C214yesmaximal, complemented
6C17×#1597C214yesmaximal, complemented
7C17×#1515C211yesmaximal, characteristic, complemented
8C17×#1514C211yesmaximal, characteristic, complemented
9C17×#1467C211yesmaximal, characteristic, complemented
10C17×#559—21no—
11C17×#557—21no—
12C17×#556—22no—
13C17×#556—21no—
14C17×#554—21no—
15C17×#552—22no—
16C17×#539C2214yes—
17C17×#536—21no—
18C17×#533C2211yescharacteristic
19C17×#532C2211yescharacteristic
20C17×#529—22no—
21C2×C17×#124C2211yescharacteristic
22C17×#520—21no—
23C2×C4×Q8×C17C2211yescharacteristic
24C17×#497—21no—
25C17×#496—21no—
26C17×#489—21no—
27C17×#489—21no—
28C17×#464—22no—
29C17×#463—22no—
30C17×#451C2212yes—
31C17×#450C2212yes—
32C17×#448C2212yes—
33C17×#447C2212yes—
34C17×#432C2211yescharacteristic
35C17×#432C2211yescharacteristic
36C17×#399—21no—
37C17×#395C2212yes—
38C17×#394C2212yes—
39C17×#393—21no—
40C17×#388—22no—
41C17×#383C2211yescharacteristic
42C17×#328C2214yes—
43C17×#327C2214yes—
44C17×#324C2214yes—
45C2×#41×C17—21no—
46C22×Q8×C17D411yescharacteristic
47C22×Q8×C17C2311yescharacteristic
48C22×D4×C17C2311yescharacteristic
49C2×Q16×C17—22no—
50C2×SD16×C17—22no—
51C2×SD16×C17—22no—
52C2×D8×C17—22no—
53C17×C4⋊Q8—22no—
54C17×C4⋊Q8D411yescharacteristic
55C17×C4⋊Q8D411yescharacteristic
56C17×C4⋊Q8D411yescharacteristic
57C17×#127D411yescharacteristic
58C17×#126—24no—
59C17×#126—24no—
60C17×#125—22no—
61C17×#125—24no—
62C17×#125—21no—
63C17×#124—22no—
64C17×#124—22no—
65C17×#124—21no—
66C17×#124—21no—
67C17×#124—21no—
68C17×#124—21no—
69C17×#124—21no—
70C17×#123—24no—
71C17×#123—24no—
72C17×C22⋊Q8—22no—
73C17×C22⋊Q8—22no—
74C17×C22⋊Q8—24no—
75C17×C22⋊Q8—21no—
76C17×C22⋊Q8C2312yes—
77C17×#121—21no—
78C17×#121C2312yes—
79C4×Q8×C17—22no—
80C4×Q8×C17—22no—
81C4×Q8×C17—21no—
82C4×Q8×C17—21no—
83C4×Q8×C17—21no—
84C4×Q8×C17—21no—
85C4×Q8×C17—21no—
86C4×Q8×C17D412yes—
87C4×D4×C17—22no—
88C4×D4×C17—22no—
89C4×D4×C17—24no—
90C4×D4×C17—21no—
91C4×D4×C17D412yes—
92C17×#117—22no—
93C17×#117—24no—
94C17×#117—21no—
95C2×C4⋊C4×C17—22no—
96C2×C4⋊C4×C17—22no—
97C2×C4⋊C4×C17D411yescharacteristic
98C2×C4⋊C4×C17C2312yes—
99C2×C22⋊C4×C17—21no—
100C2×C22⋊C4×C17—21no—
101C2×C22⋊C4×C17—22no—
102C2×C22⋊C4×C17—22no—
103C2×C42×C17D412yes—
104C2×C42×C17C2311yescharacteristic
105C17×C4⋊C8—21no—
106C17×C4⋊C8—21no—
107C17×#103—22no—
108C17×#103—22no—
109C17×#102—22no—
110C17×#102—22no—
111C17×C22⋊C8C2312yes—
112C17×C22⋊C8C2312yes—
113C17×#97—21no—
114C17×#97—21no—
115C17×#95—21no—
116C17×#95—21no—
117C17×#95—22no—
118C17×#95C2312yes—
119C24×C17—21no—
120#41×C17—44no—
121C2×Q8×C17—21no—
122C2×Q8×C17—21no—
123C2×Q8×C17—21no—
124C2×Q8×C17—21no—
125C2×Q8×C17—21no—
126C2×Q8×C17—21no—
127C2×Q8×C17—42no—
128C2×Q8×C17—81no—
129C2×Q8×C17C2×D412yes—
130C2×D4×C17—22no—
131C2×D4×C17—21no—
132C2×D4×C17—21no—
133C2×D4×C17—21no—
134C2×D4×C17—21no—
135C2×D4×C17—81no—
136C2×D4×C17C2×D412yes—
137C22×C4×C17—24no—
138C22×C4×C17—22no—
139C22×C4×C17—21no—
140C22×C4×C17—22no—
141C22×C4×C17C2×D412yes—
142C22×C4×C17C2×D411yescharacteristic
143C22×C4×C17C2×D412yes—
144C22×C4×C17C2×D411yescharacteristic
145C22×C4×C17C2411yescharacteristic
146Q16×C17—82no—
147SD16×C17—82no—
148SD16×C17—82no—
149D8×C17—82no—
150C2×C8×C17—22no—
151C2×C8×C17—22no—
152C4⋊C4×C17—24no—
153C4⋊C4×C17—24no—
154C4⋊C4×C17—24no—
155C4⋊C4×C17—21no—
156C4⋊C4×C17—21no—
157C4⋊C4×C17—21no—
158C4⋊C4×C17—22no—
159C4⋊C4×C17—21no—
160C4⋊C4×C17—21no—
161C4⋊C4×C17—21no—
162C4⋊C4×C17—22no—
163C4⋊C4×C17—22no—
164C4⋊C4×C17—22no—
165C4⋊C4×C17—82no—
166C4⋊C4×C17C2×D412yes—
167C4⋊C4×C17C2×D412yes—
168C22⋊C4×C17—24no—
169C22⋊C4×C17—24no—
170C22⋊C4×C17—24no—
171C22⋊C4×C17—22no—
172C22⋊C4×C17—22no—
173C22⋊C4×C17—22no—
174C22⋊C4×C17—44no—
175C22⋊C4×C17—41no—
176C22⋊C4×C17—41no—
177C22⋊C4×C17—41no—
178C22⋊C4×C17—41no—
179C22⋊C4×C17—82no—
180C42×C17—24no—
181C42×C17—22no—
182C42×C17—22no—
183C42×C17—22no—
184C42×C17C2×D411yescharacteristic
185C42×C17C2×D411yescharacteristic
186C42×C17C2×D411yescharacteristic
187C42×C17C2×D411yescharacteristic
188#18360C1711yesmaximal, characteristic, direct product factor, Sylow
189C23×C17—22no—
190C23×C17—42no—
191C23×C17—42no—
192C23×C17—41no—
193C23×C17—42no—
194C23×C17C22×D411yescharacteristic
195Q8×C17—42no—
196Q8×C17—42no—
197Q8×C17—42no—
198Q8×C17—42no—
199Q8×C17—42no—
200Q8×C17—42no—
201Q8×C17—42no—
202D4×C17—42no—
203D4×C17—42no—
204D4×C17—42no—
205D4×C17—42no—
206D4×C17—42no—
207D4×C17—44no—
208C2×C4×C17—22no—
209C2×C4×C17—22no—
210C2×C4×C17—22no—
211C2×C4×C17—22no—
212C2×C4×C17—22no—
213C2×C4×C17—22no—
214C2×C4×C17—22no—
215C2×C4×C17—22no—
216C2×C4×C17—41no—
217C2×C4×C17—41no—
218C2×C4×C17—44no—
219C2×C4×C17—42no—
220C2×C4×C17—42no—
221C2×C4×C17—42no—
222C2×C4×C17—42no—
223C2×C4×C17—41no—
224C2×C4×C17—42no—
225C2×C4×C17—84no—
226C2×C4×C17#12011yescharacteristic
227C2×C4×C17#12011yescharacteristic
228C2×C4×C17#12011yescharacteristic
229C2×C4×C17#12011yescharacteristic
230C2×C4×C17C22×D411yescharacteristic
231C2×C4×C17C22×D411yescharacteristic
232C8×C17—42no—
233C8×C17—42no—
234#3507C2×C1711yescharacteristic, complemented
235#3215C2×C1711yescharacteristic, complemented
236#3213C2×C1711yescharacteristic
237#2632C2×C1711yescharacteristic, complemented
238#1603C2×C1714yescomplemented
239#1597C2×C1714yescomplemented
240#1515C2×C1711yescharacteristic, complemented
241#1514C2×C1711yescharacteristic, complemented
242#1467C2×C1711yescharacteristic, complemented
243C22×C17—21no—
244C22×C17—21no—
245C22×C17—42no—
246C22×C17—42no—
247C22×C17—42no—
248C22×C17—84no—
249C22×C17—81no—
250C22×C17—81no—
251C22×C17—81no—
252C22×C17C2×#12011yescharacteristic
253C22×C17#57512yes—
254C4×C17—21no—
255C4×C17—21no—
256C4×C17—21no—
257C4×C17—21no—
258C4×C17—21no—
259C4×C17—21no—
260C4×C17—42no—
261C4×C17—42no—
262C4×C17—42no—
263C4×C17—42no—
264C4×C17—42no—
265C4×C17—82no—
266C4×C17—81no—
267#559—21no—
268#557—21no—
269#556—21no—
270#556—22no—
271#554—21no—
272#552—22no—
273#539C22×C1714yes—
274#536—21no—
275#533C22×C1711yescharacteristic
276#532C22×C1711yescharacteristic
277#529—22no—
278C2×#124C22×C1711yescharacteristic
279#520—21no—
280C2×C4×Q8C22×C1711yescharacteristic
281#497—21no—
282#496—21no—
283#489—21no—
284#489—21no—
285#464—22no—
286#463—22no—
287#451C22×C1712yes—
288#450C22×C1712yes—
289#448C22×C1712yes—
290#447C22×C1712yes—
291#432C22×C1711yescharacteristic
292#432C22×C1711yescharacteristic
293#399—21no—
294#395C22×C1712yes—
295#394C22×C1712yes—
296#393—21no—
297#388—22no—
298#383C22×C1711yescharacteristic
299#328C22×C1714yes—
300#327C22×C1714yes—
301#324C22×C1714yes—
302C2×C17—22no—
303C2×C17—82no—
304C2×C17—161no—
305C2×C17#300511yescharacteristic
306C2×C17#302011yescharacteristic
307C2×C17#302711yescharacteristic
308C2×#41—21no—
309C22×Q8D4×C1711yescharacteristic
310C22×Q8C23×C1711yescharacteristic
311C22×D4C23×C1711yescharacteristic
312C2×Q16—22no—
313C2×SD16—22no—
314C2×SD16—22no—
315C2×D8—22no—
316C4⋊Q8—22no—
317C4⋊Q8D4×C1711yescharacteristic
318C4⋊Q8D4×C1711yescharacteristic
319C4⋊Q8D4×C1711yescharacteristic
320#127D4×C1711yescharacteristic
321#126—24no—
322#126—24no—
323#125—22no—
324#125—24no—
325#125—21no—
326#124—22no—
327#124—22no—
328#124—21no—
329#124—21no—
330#124—21no—
331#124—21no—
332#124—21no—
333#123—24no—
334#123—24no—
335C22⋊Q8—22no—
336C22⋊Q8—22no—
337C22⋊Q8—24no—
338C22⋊Q8—21no—
339C22⋊Q8C23×C1712yes—
340#121—21no—
341#121C23×C1712yes—
342C4×Q8—22no—
343C4×Q8—22no—
344C4×Q8—21no—
345C4×Q8—21no—
346C4×Q8—21no—
347C4×Q8—21no—
348C4×Q8—21no—
349C4×Q8D4×C1712yes—
350C4×D4—22no—
351C4×D4—22no—
352C4×D4—24no—
353C4×D4—21no—
354C4×D4D4×C1712yes—
355#117—22no—
356#117—24no—
357#117—21no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4D4×C1711yescharacteristic
361C2×C4⋊C4C23×C1712yes—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—21no—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—22no—
366C2×C42D4×C1712yes—
367C2×C42C23×C1711yescharacteristic
368C4⋊C8—21no—
369C4⋊C8—21no—
370#103—22no—
371#103—22no—
372#102—22no—
373#102—22no—
374C22⋊C8C23×C1712yes—
375C22⋊C8C23×C1712yes—
376#97—21no—
377#97—21no—
378#95—21no—
379#95—21no—
380#95—22no—
381#95C23×C1712yes—
382C17#1836011yescharacteristic, direct product factor, Sylow
383C24—21no—
384#41—44no—
385C2×Q8—21no—
386C2×Q8—21no—
387C2×Q8—21no—
388C2×Q8—21no—
389C2×Q8—21no—
390C2×Q8—21no—
391C2×Q8—42no—
392C2×Q8—81no—
393C2×Q8C2×D4×C1712yes—
394C2×D4—22no—
395C2×D4—21no—
396C2×D4—21no—
397C2×D4—21no—
398C2×D4—21no—
399C2×D4—81no—
400C2×D4C2×D4×C1712yes—
401C22×C4—24no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—21no—
405C22×C4C2×D4×C1712yes—
406C22×C4C2×D4×C1711yescharacteristic
407C22×C4C2×D4×C1712yes—
408C22×C4C2×D4×C1711yescharacteristic
409C22×C4C24×C1711yescharacteristic
410Q16—82no—
411SD16—82no—
412SD16—82no—
413D8—82no—
414C2×C8—22no—
415C2×C8—22no—
416C4⋊C4—24no—
417C4⋊C4—24no—
418C4⋊C4—24no—
419C4⋊C4—22no—
420C4⋊C4—22no—
421C4⋊C4—22no—
422C4⋊C4—21no—
423C4⋊C4—21no—
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—22no—
427C4⋊C4—21no—
428C4⋊C4—21no—
429C4⋊C4—82no—
430C4⋊C4C2×D4×C1712yes—
431C4⋊C4C2×D4×C1712yes—
432C22⋊C4—24no—
433C22⋊C4—24no—
434C22⋊C4—24no—
435C22⋊C4—22no—
436C22⋊C4—22no—
437C22⋊C4—22no—
438C22⋊C4—44no—
439C22⋊C4—41no—
440C22⋊C4—41no—
441C22⋊C4—41no—
442C22⋊C4—41no—
443C22⋊C4—82no—
444C42—24no—
445C42—22no—
446C42—22no—
447C42—22no—
448C42C2×D4×C1711yescharacteristic
449C42C2×D4×C1711yescharacteristic
450C42C2×D4×C1711yescharacteristic
451C42C2×D4×C1711yescharacteristic
452C23—22no—
453C23—42no—
454C23—42no—
455C23—41no—
456C23—42no—
457C23C22×D4×C1711yescharacteristic
458Q8—42no—
459Q8—42no—
460Q8—42no—
461Q8—42no—
462Q8—42no—
463Q8—42no—
464Q8—42no—
465D4—42no—
466D4—42no—
467D4—42no—
468D4—42no—
469D4—42no—
470D4—44no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—44no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—41no—
487C2×C4—42no—
488C2×C4—84no—
489C2×C4C17×#12011yescharacteristic
490C2×C4C17×#12011yescharacteristic
491C2×C4C17×#12011yescharacteristic
492C2×C4C17×#12011yescharacteristic
493C2×C4C22×D4×C1711yescharacteristic
494C2×C4C22×D4×C1711yescharacteristic
495C8—42no—
496C8—42no—
497C22—21no—
498C22—21no—
499C22—42no—
500C22—42no—
501C22—42no—
502C22—84no—
503C22—81no—
504C22—81no—
505C22—81no—
506C22C2×C17×#12011yescharacteristic
507C22C17×#57512yes—
508C4—21no—
509C4—21no—
510C4—21no—
511C4—21no—
512C4—21no—
513C4—21no—
514C4—42no—
515C4—42no—
516C4—42no—
517C4—42no—
518C4—42no—
519C4—82no—
520C4—81no—
521C2—22no—
522C2—82no—
523C2—161no—
524C2C17×#300511yescharacteristic
525C2C17×#302011yescharacteristic
526C2C17×#302711yescharacteristic
subgroupG/H
center, socleC22×C17C2×#120
commutator, Frattini, cosocleC22×C4C24×C17
prime radicalC17×#3213C2
LCSG ▷ C22×C4 ▷ 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×#3507C2semidirect
2. C17×#3215C2semidirect
4. C17×#2632C2semidirect
5. C17×#1603C2semidirect
6. C17×#1597C2semidirect
7. C17×#1515C2semidirect
8. C17×#1514C2semidirect
9. C17×#1467C2semidirect
188. #18360C17direct (N × H)
234. #3507C2×C17semidirect
235. #3215C2×C17semidirect
237. #2632C2×C17semidirect
238. #1603C2×C17semidirect
239. #1597C2×C17semidirect
240. #1515C2×C17semidirect
241. #1514C2×C17semidirect
242. #1467C2×C17semidirect
382. C17#18360direct (N × H)

Maximal subgroups

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

subgroupindex
C17×#35072
C17×#32152
C17×#32132
C17×#26322
C17×#16032
C17×#15972
C17×#15152
C17×#15142
C17×#14672
#1836017