Finite Group Databasebeta

← D17×#2043 #17062002

Subgroups — D17×#2043 #17062002

Order 4352.

1542 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊Q8×D17C211yesmaximal, characteristic
2C2×#103×D17C212yesmaximal
3C2×#103×D17C212yesmaximal
4D17×#389C211yesmaximal, characteristic
5#14530031C211yesmaximal, characteristic, complemented
6#14530030C211yesmaximal, characteristic, complemented
7#14530029C212yesmaximal, complemented
8#14530028C212yesmaximal, complemented
9#14530027C211yesmaximal, characteristic, complemented
10D17×#336C211yesmaximal, characteristic
11C17×#2043C211yesmaximal, characteristic, complemented
12C22×Q8×D17C2212yes—
13C22×C8×D17C2212yes—
14C2×#10587555C2211yescharacteristic
15C2×#10587574—21no—
16C2×#10587574—21no—
17C2×#10587630C2212yes—
18C4⋊Q8×D17—28no—
19C2×C4⋊C4×D17—21no—
20C2×C4⋊C4×D17—21no—
21C2×C4⋊C4×D17—21no—
22C2×C4⋊C4×D17C2211yescharacteristic
23C2×C4⋊C4×D17C2211yescharacteristic
24C2×C42×D17C2211yescharacteristic
25C2×#10587487C2212yes—
26C2×#10587487C2212yes—
27C2×#10587506C2212yes—
28C2×#10587506C2212yes—
29C2×#10587481C2212yes—
30C2×#10587481C2212yes—
31#103×D17—28no—
32#103×D17—28no—
33#11762708C2211yescharacteristic
34#11762707C2211yescharacteristic
35#11762706—21no—
36#11762705C2211yescharacteristic
37#11762704—21no—
38#95×D17—21no—
39#11762564C2211yescharacteristic
40#11762563C2212yes—
41C2×C17×C4⋊Q8C2211yescharacteristic
42C2×C17×#103C2212yes—
43C2×C17×#103C2212yes—
44C17×#389C2211yescharacteristic
45C17×#336C2211yescharacteristic
46C22×Q8×C17C2312yes—
47C2×Q8×D17—24no—
48C2×Q8×D17—24no—
49C2×Q8×D17—24no—
50C2×Q8×D17—24no—
51C2×Q8×D17—24no—
52C2×Q8×D17D418yes—
53C22×C4×D17—22no—
54C22×C4×D17—21no—
55C22×C4×D17—21no—
56C22×C4×D17D411yescharacteristic
57C22×C4×D17D411yescharacteristic
58C22×C4×D17C2311yescharacteristic
59C22×Dic34—22no—
60C22×Dic34C2312yes—
61C22×C8×C17C2312yes—
62C17×C4⋊Q8—24no—
63C2×C4⋊C4×C17—21no—
64C2×C4⋊C4×C17—21no—
65C2×C4⋊C4×C17—21no—
66C2×C4⋊C4×C17C2311yescharacteristic
67C2×C4⋊C4×C17C2311yescharacteristic
68C2×C42×C17C2311yescharacteristic
69#10587630—24no—
70#10587630—24no—
71C2×C4⋊Dic17—21no—
72C2×C4⋊Dic17—21no—
73C2×C4⋊Dic17—21no—
74C2×C4⋊Dic17C2311yescharacteristic
75C2×C4⋊Dic17C2311yescharacteristic
76C2×#63225—21no—
77C2×#63225—21no—
78C2×#63225—22no—
79C2×#63225—22no—
80C2×#63225—21no—
81C2×#63225—21no—
82C2×C4×Dic17D411yescharacteristic
83C2×C4×Dic17D411yescharacteristic
84C2×C4×Dic17C2311yescharacteristic
85C22×#3622C2312yes—
86C2×C8×D17—24no—
87C2×C8×D17—24no—
88C2×C8×D17—24no—
89C4⋊C4×D17—28no—
90C4⋊C4×D17—28no—
91C4⋊C4×D17—22no—
92C4⋊C4×D17—24no—
93C4⋊C4×D17—44no—
94C4⋊C4×D17D414yes—
95#10587574—28no—
96#10587574—28no—
97C42×D17—24no—
98#10587555—24no—
99C17×#103—24no—
100C17×#103—24no—
101C17×#95—21no—
102#10587506—24no—
103#10587506—24no—
104#10587502—21no—
105#10587502—21no—
106#10587502—21no—
107#10587487—24no—
108#10587487—24no—
109#10587481—24no—
110#10587481—24no—
111C23×D17C2×D411yescharacteristic
112C2×Q8×C17—22no—
113C2×Q8×C17—22no—
114C2×Q8×C17—22no—
115C2×Q8×C17—22no—
116C2×Q8×C17—22no—
117C2×Q8×C17C2×D414yes—
118C22×C4×C17—22no—
119C22×C4×C17—21no—
120C22×C4×C17—21no—
121C22×C4×C17C2×D411yescharacteristic
122C22×C4×C17C2×D411yescharacteristic
123C22×C4×C17C2411yescharacteristic
124C22×Dic17—22no—
125C22×Dic17—21no—
126C22×Dic17—21no—
127C22×Dic17C2×D411yescharacteristic
128C22×Dic17C2×D411yescharacteristic
129C22×Dic17C2×D411yescharacteristic
130Q8×D17—216no—
131Q8×D17—216no—
132Q8×D17—48no—
133Q8×D17—48no—
134C2×C4×D17—22no—
135C2×C4×D17—22no—
136C2×C4×D17—22no—
137C2×C4×D17—22no—
138C2×C4×D17—28no—
139C2×C4×D17—24no—
140C2×C4×D17—44no—
141C2×C4×D17—44no—
142C2×C4×D17—42no—
143C2×C4×D17—42no—
144C2×C4×D17—42no—
145C2×C4×D17—42no—
146C2×C4×D17—42no—
147C2×C4×D17SD1614yes—
148C2×C4×D17Q1614yes—
149C2×C4×D17C2×D412yes—
150C2×C4×D17C2×D414yes—
151C2×C4×D17#4114yes—
152C2×C4×D17#4112yes—
153C2×Dic34—22no—
154C2×Dic34—22no—
155C2×Dic34—22no—
156C2×Dic34—22no—
157C2×Dic34—22no—
158C2×Dic34—28no—
159C2×Dic34—44no—
160C2×Dic34—44no—
161C2×Dic34C2×D414yes—
162C2×C8×C17—22no—
163C2×C8×C17—22no—
164C2×C8×C17—22no—
165C4⋊C4×C17—24no—
166C4⋊C4×C17—24no—
167C4⋊C4×C17—21no—
168C4⋊C4×C17—22no—
169C4⋊C4×C17—42no—
170C4⋊C4×C17C2×D412yes—
171C42×C17—22no—
172C4⋊Dic17—24no—
173C4⋊Dic17—24no—
174C4⋊Dic17—21no—
175C4⋊Dic17—22no—
176C4⋊Dic17—42no—
177C4⋊Dic17C2×D412yes—
178#63225—28no—
179#63225—28no—
180#63225—24no—
181#63225—42no—
182#63225—42no—
183#63225—42no—
184C4×Dic17—22no—
185C4×Dic17—22no—
186C4×Dic17—22no—
187C2×#3622—22no—
188C2×#3622—22no—
189C2×#3622—22no—
190C8×D17—48no—
191C2×#2043—171nomaximal, Sylow
192C23×C17C22×D411yescharacteristic
193C22×D17#12012yes—
194C22×D17#12112yes—
195C22×D17#12412yes—
196C22×D17C2×SD1612yes—
197C22×D17C2×Q1612yes—
198C22×D17#13712yes—
199C22×D17#13712yes—
200Q8×C17—24no—
201Q8×C17—24no—
202Q8×C17—42no—
203Q8×C17—42no—
204C2×C4×C17—21no—
205C2×C4×C17—21no—
206C2×C4×C17—21no—
207C2×C4×C17—21no—
208C2×C4×C17—24no—
209C2×C4×C17—22no—
210C2×C4×C17—42no—
211C2×C4×C17—42no—
212C2×C4×C17—41no—
213C2×C4×C17—41no—
214C2×C4×C17—41no—
215C2×C4×C17—41no—
216C2×C4×C17—41no—
217C2×C4×C17C2×SD1612yes—
218C2×C4×C17C2×Q1612yes—
219C2×C4×C17C22×D411yescharacteristic
220C2×C4×C17C22×D412yes—
221C2×C4×C17C2×#4112yes—
222C2×C4×C17C2×#4111yescharacteristic
223C2×Dic17—21no—
224C2×Dic17—21no—
225C2×Dic17—21no—
226C2×Dic17—21no—
227C2×Dic17—24no—
228C2×Dic17—22no—
229C2×Dic17—42no—
230C2×Dic17—42no—
231C2×Dic17—41no—
232C2×Dic17—41no—
233C2×Dic17—41no—
234C2×Dic17—41no—
235C2×Dic17—41no—
236C2×Dic17#12012yes—
237C2×Dic17#12112yes—
238C2×Dic17#12412yes—
239C2×Dic17C2×SD1612yes—
240C2×Dic17C2×Q1612yes—
241C4×D17—28no—
242C4×D17—28no—
243C4×D17—416no—
244C4×D17—48no—
245C4×D17—84no—
246C4×D17#12118yes—
247C4×D17#12318yes—
248Dic34—24no—
249Dic34—24no—
250Dic34—42no—
251Dic34—42no—
252Dic34—416no—
253C8×C17—42no—
254#3622—42no—
255C22×C4⋊Q8—171no—
256C22×#103—172no—
257C22×#103—172no—
258C2×#389—171no—
259#2043—172no—
260#2043—172no—
261#2043—171no—
262#2043—171no—
263#2043—171no—
264#2043D1711yescharacteristic, direct product factor
265C2×#336—171no—
266C22×C17C2×#12011yescharacteristic
267C22×C17C2×#12111yescharacteristic
268C22×C17C2×#12411yescharacteristic
269C22×C17C22×SD1611yescharacteristic
270C22×C17C22×Q1611yescharacteristic
271C22×C17C2×#13711yescharacteristic
272C22×C17C2×#13711yescharacteristic
273C2×D17#39414yes—
274C2×D17#44814yes—
275C2×D17#45114yes—
276C2×D17#46114yes—
277C2×D17#46214yes—
278C2×D17#48714yes—
279C2×D17#49114yes—
280C4×C17—22no—
281C4×C17—22no—
282C4×C17—44no—
283C4×C17—42no—
284C4×C17—81no—
285C4×C17C2×#12112yes—
286C4×C17C2×#12312yes—
287Dic17—22no—
288Dic17—22no—
289Dic17—44no—
290Dic17—42no—
291Dic17—81no—
292Dic17#39414yes—
293C23×Q8—172no—
294C23×C8—172no—
295C2×C4⋊Q8—172no—
296C2×C4⋊Q8—171no—
297C2×C4⋊Q8—341no—
298C2×C4⋊Q8—341no—
299C2×C4⋊Q8—348no—
300C2×C4⋊Q8C2×D1711yescharacteristic
301C22×C4⋊C4—171no—
302C22×C4⋊C4—171no—
303C22×C4⋊C4—341no—
304C22×C4⋊C4—341no—
305C22×C4⋊C4—341no—
306C22×C42—171no—
307C2×#103—172no—
308C2×#103—172no—
309C2×#103—172no—
310C2×#103—172no—
311C2×#103—172no—
312C2×#103—172no—
313C2×#103—348no—
314C2×#103—348no—
315C2×#103C2×D1712yes—
316C2×#103C2×D1712yes—
317#389—171no—
318#389—171no—
319#389—171no—
320#389—341no—
321#389—341no—
322#389C2×D1711yescharacteristic
323C2×#95—341no—
324#336—172no—
325#336—171no—
326#336C2×D1711yescharacteristic
327C2×C17C2×#39411yescharacteristic
328C2×C17C2×#44811yescharacteristic
329C2×C17C2×#45111yescharacteristic
330C2×C17C2×#46111yescharacteristic
331C2×C17C2×#46211yescharacteristic
332C2×C17C2×#48711yescharacteristic
333C2×C17C2×#49111yescharacteristic
334D17#204318yesdirect product factor
335C22×Q8—178no—
336C22×Q8—172no—
337C22×Q8—342no—
338C22×Q8—344no—
339C22×Q8—344no—
340C22×Q8—344no—
341C22×Q8—344no—
342C22×Q8—344no—
343C22×Q8C22×D1712yes—
344C23×C4—171no—
345C23×C4—171no—
346C23×C4—171no—
347C23×C4—341no—
348C23×C4—342no—
349C23×C4—341no—
350C22×C8—172no—
351C22×C8—344no—
352C22×C8—344no—
353C22×C8—344no—
354C22×C8C22×D1712yes—
355C4⋊Q8—24no—
356C4⋊Q8—344no—
357C4⋊Q8—348no—
358C4⋊Q8—348no—
359C4⋊Q8—344no—
360C4⋊Q8—344no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—171no—
365C2×C4⋊C4—174no—
366C2×C4⋊C4—171no—
367C2×C4⋊C4—342no—
368C2×C4⋊C4—348no—
369C2×C4⋊C4—348no—
370C2×C4⋊C4—344no—
371C2×C4⋊C4—341no—
372C2×C4⋊C4—342no—
373C2×C4⋊C4—342no—
374C2×C4⋊C4—341no—
375C2×C4⋊C4—341no—
376C2×C4⋊C4—341no—
377C2×C4⋊C4—341no—
378C2×C4⋊C4—341no—
379C2×C4⋊C4—341no—
380C2×C4⋊C4—684no—
381C2×C4⋊C4C22×D1711yescharacteristic
382C2×C4⋊C4C22×D1711yescharacteristic
383C2×C42—171no—
384C2×C42—171no—
385C2×C42—171no—
386C2×C42—344no—
387C2×C42C22×D1711yescharacteristic
388#103—24no—
389#103—24no—
390#103—344no—
391#103—344no—
392#103—344no—
393#103—344no—
394#103—344no—
395#103—344no—
396#95—21no—
397#95—341no—
398#95—341no—
399#95—341no—
400C17C2×#204311yescharacteristic, complemented, Sylow
401C24—171no—
402C2×Q8—22no—
403C2×Q8—22no—
404C2×Q8—22no—
405C2×Q8—22no—
406C2×Q8—22no—
407C2×Q8—174no—
408C2×Q8—348no—
409C2×Q8—3416no—
410C2×Q8—3416no—
411C2×Q8—342no—
412C2×Q8—342no—
413C2×Q8—342no—
414C2×Q8—342no—
415C2×Q8—342no—
416C2×Q8—684no—
417C2×Q8—684no—
418C2×Q8—688no—
419C2×Q8—688no—
420C2×Q8D4×D1714yes—
421C22×C4—21no—
422C22×C4—22no—
423C22×C4—21no—
424C22×C4—171no—
425C22×C4—174no—
426C22×C4—172no—
427C22×C4—172no—
428C22×C4—174no—
429C22×C4—171no—
430C22×C4—171no—
431C22×C4—174no—
432C22×C4—174no—
433C22×C4—342no—
434C22×C4—342no—
435C22×C4—342no—
436C22×C4—342no—
437C22×C4—344no—
438C22×C4—348no—
439C22×C4—341no—
440C22×C4—342no—
441C22×C4—341no—
442C22×C4—682no—
443C22×C4—682no—
444C22×C4—684no—
445C22×C4—684no—
446C22×C4—682no—
447C22×C4—682no—
448C22×C4—682no—
449C22×C4D4×D1711yescharacteristic
450C22×C4D4×D1711yescharacteristic
451C22×C4C23×D1711yescharacteristic
452C2×C8—22no—
453C2×C8—22no—
454C2×C8—22no—
455C2×C8—342no—
456C2×C8—342no—
457C2×C8—342no—
458C2×C8—688no—
459C4⋊C4—24no—
460C4⋊C4—24no—
461C4⋊C4—21no—
462C4⋊C4—22no—
463C4⋊C4—42no—
464C4⋊C4—172no—
465C4⋊C4—344no—
466C4⋊C4—348no—
467C4⋊C4—348no—
468C4⋊C4—344no—
469C4⋊C4—344no—
470C4⋊C4—341no—
471C4⋊C4—342no—
472C4⋊C4—682no—
473C4⋊C4—682no—
474C4⋊C4—682no—
475C4⋊C4—682no—
476C4⋊C4D4×D1712yes—
477C42—22no—
478C42—342no—
479C42—342no—
480C42—342no—
481C23—172no—
482C23—172no—
483C23—172no—
484C23—172no—
485C23—172no—
486C23—172no—
487C23—172no—
488C23C2×D4×D1711yescharacteristic
489Q8—24no—
490Q8—24no—
491Q8—42no—
492Q8—42no—
493Q8—344no—
494Q8—344no—
495Q8—6816no—
496Q8—682no—
497Q8—682no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—24no—
503C2×C4—22no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—172no—
512C2×C4—172no—
513C2×C4—172no—
514C2×C4—178no—
515C2×C4—178no—
516C2×C4—172no—
517C2×C4—172no—
518C2×C4—348no—
519C2×C4—348no—
520C2×C4—341no—
521C2×C4—341no—
522C2×C4—341no—
523C2×C4—341no—
524C2×C4—344no—
525C2×C4—342no—
526C2×C4—6816no—
527C2×C4—688no—
528C2×C4—682no—
529C2×C4—682no—
530C2×C4—681no—
531C2×C4—681no—
532C2×C4—681no—
533C2×C4—681no—
534C2×C4—681no—
535C2×C4—1364no—
536C2×C4SD16×D1712yes—
537C2×C4Q16×D1712yes—
538C2×C4C2×D4×D1711yescharacteristic
539C2×C4C2×D4×D1712yes—
540C2×C4#41×D1712yes—
541C2×C4#41×D1711yescharacteristic
542C8—42no—
543C8—682no—
544C22—174no—
545C22—174no—
546C22—174no—
547C22—174no—
548C22—174no—
549C22—174no—
550C22—174no—
551C22#120×D1711yescharacteristic
552C22#121×D1711yescharacteristic
553C22#124×D1711yescharacteristic
554C22C2×SD16×D1711yescharacteristic
555C22C2×Q16×D1711yescharacteristic
556C22#137×D1711yescharacteristic
557C22#137×D1711yescharacteristic
558C4—22no—
559C4—22no—
560C4—44no—
561C4—42no—
562C4—81no—
563C4—174no—
564C4—342no—
565C4—342no—
566C4—684no—
567C4—682no—
568C4—1361no—
569C4#121×D1712yes—
570C4#123×D1712yes—
571C2—178no—
572C2D17×#39411yescharacteristic
573C2D17×#44811yescharacteristic
574C2D17×#45111yescharacteristic
575C2D17×#46111yescharacteristic
576C2D17×#46211yescharacteristic
577C2D17×#48711yescharacteristic
578C2D17×#49111yescharacteristic
subgroupG/H
centerC23C2×D4×D17
commutator, cosocleC22×C4×C17C24
FrattiniC22×C4C23×D17
FittingC17×#2043C2
socleC23×C17C22×D4
prime radicalC23×D17C2×D4
hypercenter#2043D17
hypocenterC17C2×#2043
LCSG ▷ C22×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2043

Complements

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

NH ≅ G/Ntype
5. #14530031C2semidirect
6. #14530030C2semidirect
7. #14530029C2semidirect
8. #14530028C2semidirect
9. #14530027C2semidirect
11. C17×#2043C2semidirect
264. #2043D17direct (N × H)
334. D17#2043direct (N × H)
400. C17C2×#2043semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊Q8×D172
C2×#103×D172
D17×#3892
#145300312
#145300302
#145300292
#145300282
#145300272
D17×#3362
C17×#20432
C2×#204317