Finite Group Databasebeta

← C17×#18154 #16875898

Subgroups — C17×#18154 #16875898

Order 4352.

960 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C17×#3458C211yesmaximal, characteristic, complemented
2C17×#3110C212yesmaximal, complemented
3C17×#2598C211yesmaximal, characteristic
4C17×#1617C212yesmaximal, complemented
5C17×#1614C212yesmaximal, complemented
6C17×#1599C212yesmaximal, complemented
7C17×#1596C212yesmaximal
8C17×#1515C212yesmaximal, complemented
9C17×#1464C211yesmaximal, characteristic, complemented
10C17×#544—21no—
11C17×#544—22no—
12C17×#544—22no—
13C17×#544C2212yes—
14C17×#543—21no—
15C17×#543C2212yes—
16C17×#533—24no—
17C17×#533—21no—
18C17×#533C2212yes—
19C2×C4×D4×C17C2211yescharacteristic
20C2×C17×#117—21no—
21C2×C17×#117C2211yescharacteristic
22C17×#484C2214yes—
23C17×#474—22no—
24C17×#461—22no—
25C17×#450C2214yes—
26C17×#440—24no—
27C17×#432C2212yes—
28C17×#400C2211yescharacteristic
29C17×#399C2211yescharacteristic
30C17×#394C2211yescharacteristic
31C17×#392C2211yescharacteristic
32C17×#388—21no—
33C17×#386—21no—
34C17×#386—21no—
35C17×#385—21no—
36C17×#383C2211yescharacteristic
37C17×#328C2214yes—
38C17×#328C2214yes—
39C17×#324C2212yes—
40C17×#323C2212yes—
41C22×D4×C17—21no—
42C22×D4×C17C2311yescharacteristic
43C23×C4×C17—21no—
44C23×C4×C17D411yescharacteristic
45C2×SD16×C17—24no—
46C17×C4⋊Q8—24no—
47C17×C4⋊Q8—21no—
48C17×C4⋊Q8—21no—
49C17×C4⋊Q8—24no—
50C17×C4⋊Q8D412yescomplemented
51C17×C4⋊Q8D412yescomplemented
52C17×#125—24no—
53C17×#125—22no—
54C17×#125—24no—
55C17×#125—22no—
56C17×C22⋊Q8—24no—
57C17×C22⋊Q8—24no—
58C17×C22⋊Q8—24no—
59C17×C22⋊Q8—22no—
60C17×C22⋊Q8—22no—
61C17×C22⋊Q8—22no—
62C17×C22⋊Q8—24no—
63C17×C22⋊Q8C2314yes—
64C4×Q8×C17—22no—
65C4×Q8×C17—22no—
66C4×Q8×C17—22no—
67C4×Q8×C17D414yescomplemented
68C4×D4×C17—22no—
69C4×D4×C17—22no—
70C17×#117—22no—
71C17×#117—22no—
72C17×#117—22no—
73C17×#117—22no—
74C17×#117—22no—
75C17×#117—22no—
76C2×C4⋊C4×C17—21no—
77C2×C4⋊C4×C17—21no—
78C2×C4⋊C4×C17—21no—
79C2×C4⋊C4×C17D411yescharacteristic
80C2×C4⋊C4×C17C2311yescharacteristic
81C2×C4⋊C4×C17C2311yescharacteristic
82C2×C22⋊C4×C17—22no—
83C2×C22⋊C4×C17—21no—
84C2×C22⋊C4×C17—21no—
85C2×C22⋊C4×C17—21no—
86C2×C22⋊C4×C17—21no—
87C2×C22⋊C4×C17—21no—
88C2×C22⋊C4×C17D411yescharacteristic
89C2×C22⋊C4×C17C2311yescharacteristic
90C2×C42×C17—22no—
91C2×C42×C17D411yescharacteristic
92C2×C42×C17C2311yescharacteristic
93C17×#107—24no—
94C17×C4⋊C8—22no—
95C17×#103—24no—
96C17×#102—24no—
97C17×C22⋊C8C2314yes—
98C17×#97—22no—
99C17×#95—21no—
100C17×#95—21no—
101C17×#95—21no—
102C17×#95—21no—
103C17×#95C2311yescharacteristic
104C17×#95C2311yescharacteristic
105C24×C17—21no—
106C24×C17C2×D411yescharacteristic
107C2×Q8×C17—22no—
108C2×Q8×C17—22no—
109C2×Q8×C17—22no—
110C2×Q8×C17C2×D414yes—
111C2×D4×C17—22no—
112C2×D4×C17—42no—
113C2×D4×C17—42no—
114C2×D4×C17—42no—
115C2×D4×C17—81no—
116C22×C4×C17—22no—
117C22×C4×C17—21no—
118C22×C4×C17—21no—
119C22×C4×C17—22no—
120C22×C4×C17—22no—
121C22×C4×C17—22no—
122C22×C4×C17—21no—
123C22×C4×C17—21no—
124C22×C4×C17—21no—
125C22×C4×C17—42no—
126C22×C4×C17—81no—
127C22×C4×C17—81no—
128C22×C4×C17C2×D411yescharacteristic
129C22×C4×C17C2×D411yescharacteristic
130C22×C4×C17C2×D411yescharacteristic
131C22×C4×C17C2×D411yescharacteristic
132C22×C4×C17C2×D411yescharacteristic
133C22×C4×C17C2411yescharacteristic
134SD16×C17—48no—
135C2×C8×C17—24no—
136C4⋊C4×C17—22no—
137C4⋊C4×C17—24no—
138C4⋊C4×C17—24no—
139C4⋊C4×C17—22no—
140C4⋊C4×C17—22no—
141C4⋊C4×C17—22no—
142C4⋊C4×C17—24no—
143C4⋊C4×C17—22no—
144C4⋊C4×C17—22no—
145C4⋊C4×C17—22no—
146C4⋊C4×C17—22no—
147C4⋊C4×C17—24no—
148C4⋊C4×C17—22no—
149C4⋊C4×C17—22no—
150C4⋊C4×C17—81no—
151C4⋊C4×C17C2×D414yes—
152C22⋊C4×C17—24no—
153C22⋊C4×C17—24no—
154C22⋊C4×C17—22no—
155C22⋊C4×C17—22no—
156C22⋊C4×C17—42no—
157C22⋊C4×C17—41no—
158C22⋊C4×C17—41no—
159C22⋊C4×C17—42no—
160C22⋊C4×C17—81no—
161C22⋊C4×C17—81no—
162C42×C17—24no—
163C42×C17—21no—
164C42×C17—24no—
165C42×C17—21no—
166C42×C17C2×D412yes—
167C42×C17C2×D412yes—
168#18154C1711yesmaximal, characteristic, direct product factor, Sylow
169C23×C17—21no—
170C23×C17—21no—
171C23×C17—22no—
172C23×C17—41no—
173C23×C17—41no—
174C23×C17—41no—
175C23×C17—41no—
176C23×C17—41no—
177C23×C17—41no—
178C23×C17—41no—
179C23×C17—41no—
180C23×C17#13712yes—
181C23×C17C22×D411yescharacteristic
182Q8×C17—44no—
183Q8×C17—82no—
184Q8×C17—82no—
185Q8×C17—82no—
186D4×C17—24no—
187D4×C17—42no—
188D4×C17—84no—
189C2×C4×C17—24no—
190C2×C4×C17—24no—
191C2×C4×C17—21no—
192C2×C4×C17—21no—
193C2×C4×C17—21no—
194C2×C4×C17—21no—
195C2×C4×C17—24no—
196C2×C4×C17—21no—
197C2×C4×C17—21no—
198C2×C4×C17—24no—
199C2×C4×C17—41no—
200C2×C4×C17—41no—
201C2×C4×C17—41no—
202C2×C4×C17—41no—
203C2×C4×C17—41no—
204C2×C4×C17—41no—
205C2×C4×C17—41no—
206C2×C4×C17—41no—
207C2×C4×C17—41no—
208C2×C4×C17—41no—
209C2×C4×C17—41no—
210C2×C4×C17—41no—
211C2×C4×C17—41no—
212C2×C4×C17—84no—
213C2×C4×C17—82no—
214C2×C4×C17—82no—
215C2×C4×C17#12011yescharacteristic
216C2×C4×C17#12011yescharacteristic
217C2×C4×C17#12012yes—
218C2×C4×C17#13712yes—
219C2×C4×C17C22×D412yes—
220C8×C17—44no—
221#3458C2×C1711yescharacteristic, complemented
222#3110C2×C1712yescomplemented
223#2598C2×C1711yescharacteristic
224#1617C2×C1712yescomplemented
225#1614C2×C1712yescomplemented
226#1599C2×C1712yescomplemented
227#1596C2×C1712yes—
228#1515C2×C1712yescomplemented
229#1464C2×C1711yescharacteristic, complemented
230C22×C17—21no—
231C22×C17—21no—
232C22×C17—22no—
233C22×C17—42no—
234C22×C17—42no—
235C22×C17—42no—
236C22×C17—41no—
237C22×C17—41no—
238C22×C17—42no—
239C22×C17—81no—
240C22×C17—81no—
241C22×C17—81no—
242C22×C17—81no—
243C22×C17—81no—
244C22×C17C2×#12011yescharacteristic
245C22×C17C2×#13711yescharacteristic
246C22×C17C2×#13711yescharacteristic
247C4×C17—21no—
248C4×C17—21no—
249C4×C17—22no—
250C4×C17—22no—
251C4×C17—22no—
252C4×C17—41no—
253C4×C17—44no—
254C4×C17—41no—
255C4×C17—44no—
256C4×C17—81no—
257C4×C17—81no—
258C4×C17—81no—
259#544—22no—
260#544—22no—
261#544—21no—
262#544C22×C1712yes—
263#543—21no—
264#543C22×C1712yes—
265#533—24no—
266#533—21no—
267#533C22×C1712yes—
268C2×C4×D4C22×C1711yescharacteristic
269C2×#117—21no—
270C2×#117C22×C1711yescharacteristic
271#484C22×C1714yes—
272#474—22no—
273#461—22no—
274#450C22×C1714yes—
275#440—24no—
276#432C22×C1712yes—
277#400C22×C1711yescharacteristic
278#399C22×C1711yescharacteristic
279#394C22×C1711yescharacteristic
280#392C22×C1711yescharacteristic
281#388—21no—
282#386—21no—
283#386—21no—
284#385—21no—
285#383C22×C1711yescharacteristic
286#328C22×C1714yes—
287#328C22×C1714yes—
288#324C22×C1712yes—
289#323C22×C1712yes—
290C2×C17—21no—
291C2×C17—21no—
292C2×C17—42no—
293C2×C17—82no—
294C2×C17#300411yescharacteristic
295C2×C17#302111yescharacteristic
296C2×C17#302511yescharacteristic
297C22×D4—21no—
298C22×D4C23×C1711yescharacteristic
299C23×C4—21no—
300C23×C4D4×C1711yescharacteristic
301C2×SD16—24no—
302C4⋊Q8—24no—
303C4⋊Q8—21no—
304C4⋊Q8—21no—
305C4⋊Q8—24no—
306C4⋊Q8D4×C1712yescomplemented
307C4⋊Q8D4×C1712yescomplemented
308#125—24no—
309#125—22no—
310#125—24no—
311#125—22no—
312C22⋊Q8—24no—
313C22⋊Q8—24no—
314C22⋊Q8—24no—
315C22⋊Q8—22no—
316C22⋊Q8—22no—
317C22⋊Q8—22no—
318C22⋊Q8—24no—
319C22⋊Q8C23×C1714yes—
320C4×Q8—22no—
321C4×Q8—22no—
322C4×Q8—22no—
323C4×Q8D4×C1714yescomplemented
324C4×D4—22no—
325C4×D4—22no—
326#117—22no—
327#117—22no—
328#117—22no—
329#117—22no—
330#117—22no—
331#117—22no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4D4×C1711yescharacteristic
336C2×C4⋊C4C23×C1711yescharacteristic
337C2×C4⋊C4C23×C1711yescharacteristic
338C2×C22⋊C4—22no—
339C2×C22⋊C4—21no—
340C2×C22⋊C4—21no—
341C2×C22⋊C4—21no—
342C2×C22⋊C4—21no—
343C2×C22⋊C4—21no—
344C2×C22⋊C4D4×C1711yescharacteristic
345C2×C22⋊C4C23×C1711yescharacteristic
346C2×C42—22no—
347C2×C42D4×C1711yescharacteristic
348C2×C42C23×C1711yescharacteristic
349#107—24no—
350C4⋊C8—22no—
351#103—24no—
352#102—24no—
353C22⋊C8C23×C1714yes—
354#97—22no—
355#95—21no—
356#95—21no—
357#95—21no—
358#95—21no—
359#95C23×C1711yescharacteristic
360#95C23×C1711yescharacteristic
361C17#1815411yescharacteristic, direct product factor, Sylow
362C24—21no—
363C24C2×D4×C1711yescharacteristic
364C2×Q8—22no—
365C2×Q8—22no—
366C2×Q8—22no—
367C2×Q8C2×D4×C1714yes—
368C2×D4—22no—
369C2×D4—42no—
370C2×D4—42no—
371C2×D4—42no—
372C2×D4—81no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—42no—
383C22×C4—81no—
384C22×C4—81no—
385C22×C4C2×D4×C1711yescharacteristic
386C22×C4C2×D4×C1711yescharacteristic
387C22×C4C2×D4×C1711yescharacteristic
388C22×C4C2×D4×C1711yescharacteristic
389C22×C4C2×D4×C1711yescharacteristic
390C22×C4C24×C1711yescharacteristic
391SD16—48no—
392C2×C8—24no—
393C4⋊C4—22no—
394C4⋊C4—22no—
395C4⋊C4—22no—
396C4⋊C4—24no—
397C4⋊C4—24no—
398C4⋊C4—22no—
399C4⋊C4—22no—
400C4⋊C4—24no—
401C4⋊C4—22no—
402C4⋊C4—22no—
403C4⋊C4—22no—
404C4⋊C4—22no—
405C4⋊C4—24no—
406C4⋊C4—22no—
407C4⋊C4—81no—
408C4⋊C4C2×D4×C1714yes—
409C22⋊C4—24no—
410C22⋊C4—24no—
411C22⋊C4—22no—
412C22⋊C4—22no—
413C22⋊C4—42no—
414C22⋊C4—42no—
415C22⋊C4—41no—
416C22⋊C4—41no—
417C22⋊C4—81no—
418C22⋊C4—81no—
419C42—24no—
420C42—24no—
421C42—21no—
422C42—21no—
423C42C2×D4×C1712yes—
424C42C2×D4×C1712yes—
425C23—21no—
426C23—21no—
427C23—22no—
428C23—41no—
429C23—41no—
430C23—41no—
431C23—41no—
432C23—41no—
433C23—41no—
434C23—41no—
435C23—41no—
436C23C17×#13712yes—
437C23C22×D4×C1711yescharacteristic
438Q8—44no—
439Q8—82no—
440Q8—82no—
441Q8—82no—
442D4—24no—
443D4—42no—
444D4—84no—
445C2×C4—24no—
446C2×C4—24no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—24no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—24no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—84no—
469C2×C4—82no—
470C2×C4—82no—
471C2×C4C17×#12011yescharacteristic
472C2×C4C17×#12011yescharacteristic
473C2×C4C17×#12012yes—
474C2×C4C17×#13712yes—
475C2×C4C22×D4×C1712yes—
476C8—44no—
477C22—21no—
478C22—21no—
479C22—22no—
480C22—42no—
481C22—42no—
482C22—42no—
483C22—41no—
484C22—41no—
485C22—42no—
486C22—81no—
487C22—81no—
488C22—81no—
489C22—81no—
490C22—81no—
491C22C2×C17×#12011yescharacteristic
492C22C2×C17×#13711yescharacteristic
493C22C2×C17×#13711yescharacteristic
494C4—22no—
495C4—21no—
496C4—21no—
497C4—22no—
498C4—22no—
499C4—41no—
500C4—44no—
501C4—41no—
502C4—44no—
503C4—81no—
504C4—81no—
505C4—81no—
506C2—21no—
507C2—21no—
508C2—42no—
509C2—82no—
510C2C17×#300411yescharacteristic
511C2C17×#302111yescharacteristic
512C2C17×#302511yescharacteristic
subgroupG/H
center, socleC22×C17C2×#120
commutator, Frattini, cosocleC22×C4C24×C17
prime radicalC17×#392C22
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×#3458C2semidirect
2. C17×#3110C2semidirect
4. C17×#1617C2semidirect
5. C17×#1614C2semidirect
6. C17×#1599C2semidirect
8. C17×#1515C2semidirect
9. C17×#1464C2semidirect
50. C17×C4⋊Q8D4semidirect
51. C17×C4⋊Q8D4semidirect
67. C4×Q8×C17D4semidirect
168. #18154C17direct (N × H)
221. #3458C2×C17semidirect
222. #3110C2×C17semidirect
224. #1617C2×C17semidirect
225. #1614C2×C17semidirect
226. #1599C2×C17semidirect
228. #1515C2×C17semidirect
229. #1464C2×C17semidirect
306. C4⋊Q8D4×C17semidirect
307. C4⋊Q8D4×C17semidirect
323. C4×Q8D4×C17semidirect
361. C17#18154direct (N × H)

Maximal subgroups

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

subgroupindex
C17×#34582
C17×#31102
C17×#25982
C17×#16172
C17×#16142
C17×#15992
C17×#15962
C17×#15152
C17×#14642
#1815417