Finite Group Databasebeta

← C17×#18191 #16875935

Subgroups — C17×#18191 #16875935

Order 4352.

990 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C17×#3506C211yesmaximal, characteristic
2C17×#3113C211yesmaximal, characteristic, complemented
3C17×#3112C211yesmaximal, characteristic, complemented
4C17×#2398C211yesmaximal, characteristic, complemented
5C17×#1612C214yesmaximal, complemented
6C17×#1606C214yesmaximal, complemented
7C17×#1506C211yesmaximal, characteristic, complemented
8C17×#1505C211yesmaximal, characteristic, complemented
9C17×#1466C211yesmaximal, characteristic, complemented
10C17×#559—22no—
11C17×#556—21no—
12C17×#555—21no—
13C17×#553—22no—
14C17×#550—21no—
15C17×#547—21no—
16C17×#538C2214yes—
17C17×#535—21no—
18C17×#533C2211yescharacteristic
19C17×#532C2211yescharacteristic
20C17×#525—22no—
21C17×#520—21no—
22C2×C4×Q8×C17C2211yescharacteristic
23C2×C4×D4×C17C2211yescharacteristic
24C17×#483C2212yes—
25C17×#480C2212yes—
26C17×#477—21no—
27C17×#475—21no—
28C17×#462—21no—
29C17×#460—21no—
30C17×#451C2212yes—
31C17×#448C2212yes—
32C17×#441—22no—
33C17×#440—22no—
34C17×#432C2211yescharacteristic
35C17×#432C2211yescharacteristic
36C17×#400—21no—
37C17×#397C2212yes—
38C17×#394—21no—
39C17×#393C2212yes—
40C4×C22⋊C4×C17—22no—
41C17×#376C2211yescharacteristic
42C17×#328C2214yes—
43C17×#327C2214yes—
44C17×#323C2214yes—
45C2×#41×C17—22no—
46C2×#41×C17—21no—
47C22×Q8×C17C2311yescharacteristic
48C22×D4×C17D411yescharacteristic
49C23×C4×C17D412yes—
50C2×Q16×C17—22no—
51C2×SD16×C17—22no—
52C17×C4⋊Q8D411yescharacteristic
53C17×C4⋊Q8D411yescharacteristic
54C17×C4⋊Q8D411yescharacteristic
55C17×#127—22no—
56C17×#127D411yescharacteristic
57C17×#126—24no—
58C17×#125—21no—
59C17×#124—22no—
60C17×#124—24no—
61C17×#124—21no—
62C17×#123—24no—
63C17×#123—24no—
64C17×C22⋊Q8—22no—
65C17×C22⋊Q8—21no—
66C17×C22⋊Q8C2312yes—
67C17×#121—22no—
68C17×#121—22no—
69C17×#121—22no—
70C17×#121—24no—
71C17×#121—21no—
72C17×#121C2312yes—
73C17×#120—24no—
74C4×Q8×C17—22no—
75C4×Q8×C17—21no—
76C4×Q8×C17—21no—
77C4×Q8×C17—21no—
78C4×Q8×C17—21no—
79C4×Q8×C17—21no—
80C4×Q8×C17D412yes—
81C4×D4×C17—22no—
82C4×D4×C17—24no—
83C4×D4×C17—24no—
84C4×D4×C17—21no—
85C4×D4×C17—21no—
86C4×D4×C17—21no—
87C4×D4×C17—21no—
88C4×D4×C17—21no—
89C4×D4×C17D412yes—
90C17×#117—22no—
91C17×#117—22no—
92C17×#117—21no—
93C2×C4⋊C4×C17—22no—
94C2×C4⋊C4×C17—21no—
95C2×C4⋊C4×C17D411yescharacteristic
96C2×C4⋊C4×C17C2311yescharacteristic
97C2×C22⋊C4×C17—22no—
98C2×C22⋊C4×C17—22no—
99C2×C22⋊C4×C17C2312yes—
100C2×C42×C17—21no—
101C2×C42×C17—21no—
102C2×C42×C17C2311yescharacteristic
103C17×#107—22no—
104C17×#106—22no—
105C17×C4⋊C8—21no—
106C17×C4⋊C8—21no—
107C17×#103—22no—
108C17×#103—22no—
109C17×#103—22no—
110C17×#102—22no—
111C17×C22⋊C8C2312yes—
112C17×C22⋊C8C2312yes—
113C17×#97—21no—
114C17×#97—21no—
115C17×#95—21no—
116C17×#95—22no—
117C17×#95—22no—
118C17×#95C2312yes—
119C24×C17C2×D412yes—
120#41×C17—44no—
121#41×C17—84no—
122C2×Q8×C17—21no—
123C2×Q8×C17—21no—
124C2×Q8×C17—21no—
125C2×Q8×C17—21no—
126C2×Q8×C17—42no—
127C2×Q8×C17C2×D412yes—
128C2×D4×C17—22no—
129C2×D4×C17—24no—
130C2×D4×C17—24no—
131C2×D4×C17—21no—
132C2×D4×C17—21no—
133C2×D4×C17—21no—
134C2×D4×C17—21no—
135C2×D4×C17—42no—
136C2×D4×C17C2×D412yes—
137C22×C4×C17—21no—
138C22×C4×C17—24no—
139C22×C4×C17—22no—
140C22×C4×C17—22no—
141C22×C4×C17—22no—
142C22×C4×C17—22no—
143C22×C4×C17—21no—
144C22×C4×C17—44no—
145C22×C4×C17C2×D411yescharacteristic
146C22×C4×C17C2×D411yescharacteristic
147C22×C4×C17C2×D412yes—
148C22×C4×C17C2411yescharacteristic
149Q16×C17—44no—
150SD16×C17—44no—
151C2×C8×C17—22no—
152C2×C8×C17—22no—
153C4⋊C4×C17—24no—
154C4⋊C4×C17—21no—
155C4⋊C4×C17—22no—
156C4⋊C4×C17—21no—
157C4⋊C4×C17—21no—
158C4⋊C4×C17—21no—
159C4⋊C4×C17—21no—
160C4⋊C4×C17—21no—
161C4⋊C4×C17—22no—
162C4⋊C4×C17—21no—
163C4⋊C4×C17—21no—
164C4⋊C4×C17—41no—
165C4⋊C4×C17—41no—
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—22no—
175C22⋊C4×C17—22no—
176C22⋊C4×C17—44no—
177C22⋊C4×C17—44no—
178C42×C17—24no—
179C42×C17—22no—
180C42×C17—42no—
181C42×C17—41no—
182C42×C17—41no—
183C42×C17C2×D411yescharacteristic
184C42×C17C2×D411yescharacteristic
185C42×C17C2×D411yescharacteristic
186C42×C17C2×D411yescharacteristic
187#18191C1711yesmaximal, characteristic, direct product factor, Sylow
188C23×C17—22no—
189C23×C17—22no—
190C23×C17—22no—
191C23×C17—22no—
192C23×C17—42no—
193C23×C17—42no—
194C23×C17C22×D411yescharacteristic
195Q8×C17—22no—
196Q8×C17—22no—
197Q8×C17—42no—
198Q8×C17—41no—
199Q8×C17—41no—
200Q8×C17—42no—
201Q8×C17—42no—
202D4×C17—42no—
203D4×C17—42no—
204D4×C17—42no—
205D4×C17—42no—
206D4×C17—44no—
207D4×C17—42no—
208D4×C17—84no—
209D4×C17—84no—
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—22no—
217C2×C4×C17—41no—
218C2×C4×C17—44no—
219C2×C4×C17—41no—
220C2×C4×C17—41no—
221C2×C4×C17—44no—
222C2×C4×C17—42no—
223C2×C4×C17—42no—
224C2×C4×C17—42no—
225C2×C4×C17—41no—
226C2×C4×C17—42no—
227C2×C4×C17—42no—
228C2×C4×C17—82no—
229C2×C4×C17—84no—
230C2×C4×C17#12011yescharacteristic
231C2×C4×C17#12011yescharacteristic
232C2×C4×C17#12011yescharacteristic
233C2×C4×C17#12011yescharacteristic
234C2×C4×C17C22×D411yescharacteristic
235C2×C4×C17C22×D411yescharacteristic
236C8×C17—42no—
237C8×C17—42no—
238#3506C2×C1711yescharacteristic
239#3113C2×C1711yescharacteristic, complemented
240#3112C2×C1711yescharacteristic, complemented
241#2398C2×C1711yescharacteristic, complemented
242#1612C2×C1714yescomplemented
243#1606C2×C1714yescomplemented
244#1506C2×C1711yescharacteristic, complemented
245#1505C2×C1711yescharacteristic, complemented
246#1466C2×C1711yescharacteristic, complemented
247C22×C17—21no—
248C22×C17—21no—
249C22×C17—44no—
250C22×C17—42no—
251C22×C17—42no—
252C22×C17—42no—
253C22×C17—42no—
254C22×C17—42no—
255C22×C17—42no—
256C22×C17—82no—
257C22×C17C2×#12011yescharacteristic
258C22×C17#57512yes—
259C4×C17—21no—
260C4×C17—21no—
261C4×C17—21no—
262C4×C17—21no—
263C4×C17—21no—
264C4×C17—42no—
265C4×C17—42no—
266C4×C17—42no—
267C4×C17—42no—
268C4×C17—42no—
269C4×C17—82no—
270C4×C17—81no—
271C4×C17#45512yes—
272#559—22no—
273#556—21no—
274#555—21no—
275#553—22no—
276#550—21no—
277#547—21no—
278#538C22×C1714yes—
279#535—21no—
280#533C22×C1711yescharacteristic
281#532C22×C1711yescharacteristic
282#525—22no—
283#520—21no—
284C2×C4×Q8C22×C1711yescharacteristic
285C2×C4×D4C22×C1711yescharacteristic
286#483C22×C1712yes—
287#480C22×C1712yes—
288#477—21no—
289#475—21no—
290#462—21no—
291#460—21no—
292#451C22×C1712yes—
293#448C22×C1712yes—
294#441—22no—
295#440—22no—
296#432C22×C1711yescharacteristic
297#432C22×C1711yescharacteristic
298#400—21no—
299#397C22×C1712yes—
300#394—21no—
301#393C22×C1712yes—
302C4×C22⋊C4—22no—
303#376C22×C1711yescharacteristic
304#328C22×C1714yes—
305#327C22×C1714yes—
306#323C22×C1714yes—
307C2×C17—22no—
308C2×C17—82no—
309C2×C17—82no—
310C2×C17#300511yescharacteristic
311C2×C17C2×#45511yescharacteristic
312C2×C17#302511yescharacteristic
313C2×#41—22no—
314C2×#41—21no—
315C22×Q8C23×C1711yescharacteristic
316C22×D4D4×C1711yescharacteristic
317C23×C4D4×C1712yes—
318C2×Q16—22no—
319C2×SD16—22no—
320C4⋊Q8D4×C1711yescharacteristic
321C4⋊Q8D4×C1711yescharacteristic
322C4⋊Q8D4×C1711yescharacteristic
323#127—22no—
324#127D4×C1711yescharacteristic
325#126—24no—
326#125—21no—
327#124—22no—
328#124—24no—
329#124—21no—
330#123—24no—
331#123—24no—
332C22⋊Q8—22no—
333C22⋊Q8—21no—
334C22⋊Q8C23×C1712yes—
335#121—22no—
336#121—22no—
337#121—22no—
338#121—24no—
339#121—21no—
340#121C23×C1712yes—
341#120—24no—
342C4×Q8—22no—
343C4×Q8—21no—
344C4×Q8—21no—
345C4×Q8—21no—
346C4×Q8—21no—
347C4×Q8—21no—
348C4×Q8D4×C1712yes—
349C4×D4—22no—
350C4×D4—24no—
351C4×D4—24no—
352C4×D4—21no—
353C4×D4—21no—
354C4×D4—21no—
355C4×D4—21no—
356C4×D4—21no—
357C4×D4D4×C1712yes—
358#117—22no—
359#117—22no—
360#117—21no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4D4×C1711yescharacteristic
364C2×C4⋊C4C23×C1711yescharacteristic
365C2×C22⋊C4—22no—
366C2×C22⋊C4—22no—
367C2×C22⋊C4C23×C1712yes—
368C2×C42—21no—
369C2×C42—21no—
370C2×C42C23×C1711yescharacteristic
371#107—22no—
372#106—22no—
373C4⋊C8—21no—
374C4⋊C8—21no—
375#103—22no—
376#103—22no—
377#103—22no—
378#102—22no—
379C22⋊C8C23×C1712yes—
380C22⋊C8C23×C1712yes—
381#97—21no—
382#97—21no—
383#95—21no—
384#95—22no—
385#95—22no—
386#95C23×C1712yes—
387C17#1819111yescharacteristic, direct product factor, Sylow
388C24C2×D4×C1712yes—
389#41—44no—
390#41—84no—
391C2×Q8—21no—
392C2×Q8—21no—
393C2×Q8—21no—
394C2×Q8—21no—
395C2×Q8—42no—
396C2×Q8C2×D4×C1712yes—
397C2×D4—22no—
398C2×D4—24no—
399C2×D4—24no—
400C2×D4—21no—
401C2×D4—21no—
402C2×D4—21no—
403C2×D4—21no—
404C2×D4—42no—
405C2×D4C2×D4×C1712yes—
406C22×C4—21no—
407C22×C4—24no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—21no—
413C22×C4—44no—
414C22×C4C2×D4×C1711yescharacteristic
415C22×C4C2×D4×C1711yescharacteristic
416C22×C4C2×D4×C1712yes—
417C22×C4C24×C1711yescharacteristic
418Q16—44no—
419SD16—44no—
420C2×C8—22no—
421C2×C8—22no—
422C4⋊C4—24no—
423C4⋊C4—22no—
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—21no—
429C4⋊C4—21no—
430C4⋊C4—22no—
431C4⋊C4—21no—
432C4⋊C4—21no—
433C4⋊C4—41no—
434C4⋊C4—41no—
435C4⋊C4C2×D4×C1712yes—
436C4⋊C4C2×D4×C1712yes—
437C22⋊C4—24no—
438C22⋊C4—24no—
439C22⋊C4—24no—
440C22⋊C4—22no—
441C22⋊C4—22no—
442C22⋊C4—22no—
443C22⋊C4—22no—
444C22⋊C4—22no—
445C22⋊C4—44no—
446C22⋊C4—44no—
447C42—24no—
448C42—22no—
449C42—42no—
450C42—41no—
451C42—41no—
452C42C2×D4×C1711yescharacteristic
453C42C2×D4×C1711yescharacteristic
454C42C2×D4×C1711yescharacteristic
455C42C2×D4×C1711yescharacteristic
456C23—22no—
457C23—22no—
458C23—22no—
459C23—22no—
460C23—42no—
461C23—42no—
462C23C22×D4×C1711yescharacteristic
463Q8—22no—
464Q8—22no—
465Q8—42no—
466Q8—41no—
467Q8—41no—
468Q8—42no—
469Q8—42no—
470D4—42no—
471D4—42no—
472D4—42no—
473D4—42no—
474D4—44no—
475D4—42no—
476D4—84no—
477D4—84no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—41no—
486C2×C4—44no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—44no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—41no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—82no—
497C2×C4—84no—
498C2×C4C17×#12011yescharacteristic
499C2×C4C17×#12011yescharacteristic
500C2×C4C17×#12011yescharacteristic
501C2×C4C17×#12011yescharacteristic
502C2×C4C22×D4×C1711yescharacteristic
503C2×C4C22×D4×C1711yescharacteristic
504C8—42no—
505C8—42no—
506C22—21no—
507C22—21no—
508C22—44no—
509C22—42no—
510C22—42no—
511C22—42no—
512C22—42no—
513C22—42no—
514C22—42no—
515C22—82no—
516C22C2×C17×#12011yescharacteristic
517C22C17×#57512yes—
518C4—21no—
519C4—21no—
520C4—21no—
521C4—21no—
522C4—21no—
523C4—42no—
524C4—42no—
525C4—42no—
526C4—42no—
527C4—42no—
528C4—82no—
529C4—81no—
530C4C17×#45512yes—
531C2—22no—
532C2—82no—
533C2—82no—
534C2C17×#300511yescharacteristic
535C2C2×C17×#45511yescharacteristic
536C2C17×#302511yescharacteristic
subgroupG/H
center, socleC22×C17C2×#120
commutator, Frattini, cosocleC22×C4C24×C17
prime radicalC17×#3506C2
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
2. C17×#3113C2semidirect
3. C17×#3112C2semidirect
4. C17×#2398C2semidirect
5. C17×#1612C2semidirect
6. C17×#1606C2semidirect
7. C17×#1506C2semidirect
8. C17×#1505C2semidirect
9. C17×#1466C2semidirect
187. #18191C17direct (N × H)
239. #3113C2×C17semidirect
240. #3112C2×C17semidirect
241. #2398C2×C17semidirect
242. #1612C2×C17semidirect
243. #1606C2×C17semidirect
244. #1506C2×C17semidirect
245. #1505C2×C17semidirect
246. #1466C2×C17semidirect
387. C17#18191direct (N × H)

Maximal subgroups

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

subgroupindex
C17×#35062
C17×#31132
C17×#31122
C17×#23982
C17×#16122
C17×#16062
C17×#15062
C17×#15052
C17×#14662
#1819117