Finite Group Databasebeta

← D17×#2059 #17062353

Subgroups — D17×#2059 #17062353

Order 4352.

1238 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#125×D17C211yesmaximal, characteristic
2C2×#107×D17C211yesmaximal, characteristic
3C2×#106×D17C211yesmaximal, characteristic
4D17×#389C211yesmaximal, characteristic
5#14530125C211yesmaximal, characteristic, complemented
6#14530124C211yesmaximal, characteristic, complemented
7#14530123C211yesmaximal, characteristic, complemented
8#14530122C211yesmaximal, characteristic, complemented
9#14530121C211yesmaximal, characteristic, complemented
10#14530120C211yesmaximal, characteristic, complemented
11#14530119C211yesmaximal, characteristic, complemented
12D17×#340C211yesmaximal, characteristic
13D17×#340C211yesmaximal, characteristic
14D17×#336C211yesmaximal, characteristic
15C17×#2059C211yesmaximal, characteristic, complemented
16C22×C8×D17C2211yescharacteristic
17C22×C8×D17C2211yescharacteristic
18C2×#10587556C2211yescharacteristic
19C2×#10587576C2211yescharacteristic
20C2×#10587576C2211yescharacteristic
21C2×#10587575—21no—
22C2×#10587575—21no—
23#125×D17—24no—
24#125×D17—24no—
25C2×C4⋊C4×D17—21no—
26C2×C4⋊C4×D17—21no—
27C2×C4⋊C4×D17—21no—
28C2×C4⋊C4×D17C2211yescharacteristic
29C2×C4⋊C4×D17C2211yescharacteristic
30C2×C4⋊C4×D17C2211yescharacteristic
31C2×C4⋊C4×D17C2211yescharacteristic
32C2×C42×D17C2211yescharacteristic
33C2×#10587489C2211yescharacteristic
34C2×#10587478C2211yescharacteristic
35C2×#10587478C2211yescharacteristic
36#107×D17—24no—
37C2×#10587488C2211yescharacteristic
38C2×#10587479C2211yescharacteristic
39C2×#10587479C2211yescharacteristic
40#106×D17—24no—
41#11762708C2211yescharacteristic
42#11762707C2211yescharacteristic
43#11762706—21no—
44#11762705C2211yescharacteristic
45#11762704—21no—
46#95×D17—21no—
47#11762572C2211yescharacteristic
48#11762572C2211yescharacteristic
49#11762571C2211yescharacteristic
50#11762571C2211yescharacteristic
51#11762571C2211yescharacteristic
52#11762571C2211yescharacteristic
53#11762564C2211yescharacteristic
54#11762563C2211yescharacteristic
55#11762563C2211yescharacteristic
56C2×C17×#125C2211yescharacteristic
57C2×C17×#107C2211yescharacteristic
58C2×C17×#106C2211yescharacteristic
59C17×#389C2211yescharacteristic
60C17×#340C2211yescharacteristic
61C17×#340C2211yescharacteristic
62C17×#336C2211yescharacteristic
63C22×C4×D17—21no—
64C22×C4×D17—21no—
65C22×C4×D17—21no—
66C22×C4×D17—21no—
67C22×C4×D17D411yescharacteristic
68C22×C4×D17D411yescharacteristic
69C22×C4×D17C2311yescharacteristic
70C22×C8×C17C2311yescharacteristic
71C22×C8×C17C2311yescharacteristic
72C17×#125—22no—
73C17×#125—22no—
74C2×C4⋊C4×C17—21no—
75C2×C4⋊C4×C17—21no—
76C2×C4⋊C4×C17—21no—
77C2×C4⋊C4×C17C2311yescharacteristic
78C2×C4⋊C4×C17C2311yescharacteristic
79C2×C4⋊C4×C17C2311yescharacteristic
80C2×C4⋊C4×C17C2311yescharacteristic
81C2×C42×C17C2311yescharacteristic
82C2×C4⋊Dic17—21no—
83C2×C4⋊Dic17—21no—
84C2×C4⋊Dic17—21no—
85C2×C4⋊Dic17C2311yescharacteristic
86C2×C4⋊Dic17C2311yescharacteristic
87C2×C4⋊Dic17C2311yescharacteristic
88C2×C4⋊Dic17C2311yescharacteristic
89C2×#63225—21no—
90C2×#63225—21no—
91C2×#63225—21no—
92C2×#63225—21no—
93C2×#63225—21no—
94C2×#63225—21no—
95C2×#63225—21no—
96C2×#63225—21no—
97C2×#63225—21no—
98C2×#63225—21no—
99C2×C4×Dic17D411yescharacteristic
100C2×C4×Dic17D411yescharacteristic
101C2×C4×Dic17C2311yescharacteristic
102C22×#3622C2311yescharacteristic
103C22×#3622C2311yescharacteristic
104C2×C8×D17—22no—
105C2×C8×D17—22no—
106C2×C8×D17—22no—
107C2×C8×D17—22no—
108C2×C8×D17Q814yes—
109C2×C8×D17Q814yes—
110C4⋊C4×D17—28no—
111C4⋊C4×D17—28no—
112C4⋊C4×D17—22no—
113C4⋊C4×D17—22no—
114C4⋊C4×D17—22no—
115C4⋊C4×D17—22no—
116C4⋊C4×D17—22no—
117C4⋊C4×D17—44no—
118C4⋊C4×D17D414yes—
119C4⋊C4×D17D414yes—
120C4⋊C4×D17Q814yes—
121#10587576—22no—
122#10587576—22no—
123#10587576—22no—
124#10587576—22no—
125#10587575—28no—
126#10587575—28no—
127C42×D17—22no—
128C42×D17—22no—
129#10587556—22no—
130#10587556—22no—
131C17×#107—22no—
132C17×#106—22no—
133C17×#95—21no—
134#10587502—21no—
135#10587502—21no—
136#10587502—21no—
137#10587489—22no—
138#10587488—22no—
139#10587479—22no—
140#10587479—22no—
141#10587478—22no—
142#10587478—22no—
143C23×D17C2×D411yescharacteristic
144C22×C4×C17—21no—
145C22×C4×C17—21no—
146C22×C4×C17—21no—
147C22×C4×C17—21no—
148C22×C4×C17C2×D411yescharacteristic
149C22×C4×C17C2×D411yescharacteristic
150C22×C4×C17C2411yescharacteristic
151C22×Dic17—21no—
152C22×Dic17—21no—
153C22×Dic17—21no—
154C22×Dic17—21no—
155C22×Dic17C2×D411yescharacteristic
156C22×Dic17C2×D411yescharacteristic
157C22×Dic17C2×D411yescharacteristic
158C2×C4×D17—24no—
159C2×C4×D17—24no—
160C2×C4×D17—22no—
161C2×C4×D17—22no—
162C2×C4×D17—24no—
163C2×C4×D17—22no—
164C2×C4×D17—22no—
165C2×C4×D17—22no—
166C2×C4×D17—22no—
167C2×C4×D17—42no—
168C2×C4×D17—42no—
169C2×C4×D17—42no—
170C2×C4×D17—42no—
171C2×C4×D17—42no—
172C2×C4×D17—42no—
173C2×C4×D17—42no—
174C2×C4×D17—42no—
175C2×C4×D17—42no—
176C2×C4×D17C2×D412yes—
177C2×C4×D17C2×D412yes—
178C2×C4×D17C2×Q812yes—
179C2×C4×D17C2×Q812yes—
180C2×C4×D17C2×Q812yes—
181C2×C4×D17#4112yes—
182C2×C8×C17—21no—
183C2×C8×C17—21no—
184C2×C8×C17—21no—
185C2×C8×C17—21no—
186C2×C8×C17C2×Q812yes—
187C2×C8×C17C2×Q812yes—
188C4⋊C4×C17—24no—
189C4⋊C4×C17—24no—
190C4⋊C4×C17—21no—
191C4⋊C4×C17—21no—
192C4⋊C4×C17—21no—
193C4⋊C4×C17—21no—
194C4⋊C4×C17—21no—
195C4⋊C4×C17—42no—
196C4⋊C4×C17C2×D412yes—
197C4⋊C4×C17C2×D412yes—
198C4⋊C4×C17C2×Q812yes—
199C42×C17—21no—
200C42×C17—21no—
201C4⋊Dic17—24no—
202C4⋊Dic17—24no—
203C4⋊Dic17—21no—
204C4⋊Dic17—21no—
205C4⋊Dic17—21no—
206C4⋊Dic17—21no—
207C4⋊Dic17—21no—
208C4⋊Dic17—42no—
209C4⋊Dic17C2×D412yes—
210C4⋊Dic17C2×D412yes—
211C4⋊Dic17C2×Q812yes—
212#63225—24no—
213#63225—24no—
214#63225—24no—
215#63225—24no—
216#63225—24no—
217#63225—24no—
218#63225—24no—
219#63225—42no—
220#63225—42no—
221#63225—42no—
222C4×Dic17—21no—
223C4×Dic17—21no—
224C4×Dic17—22no—
225C4×Dic17—22no—
226C2×#3622—21no—
227C2×#3622—21no—
228C2×#3622—21no—
229C2×#3622—21no—
230C2×#3622C2×Q812yes—
231C2×#3622C2×Q812yes—
232C8×D17—28no—
233C8×D17—28no—
234C2×#2059—171nomaximal, Sylow
235C23×C17C22×D411yescharacteristic
236C22×D17#12012yes—
237C22×D17C22⋊Q812yes—
238C22×D17C4⋊Q812yes—
239C22×D17#13512yes—
240C22×D17#13512yes—
241C22×D17AGL(1,ℤ/8)12yes—
242C22×D17#13712yes—
243C2×C4×C17—21no—
244C2×C4×C17—21no—
245C2×C4×C17—22no—
246C2×C4×C17—22no—
247C2×C4×C17—22no—
248C2×C4×C17—21no—
249C2×C4×C17—21no—
250C2×C4×C17—21no—
251C2×C4×C17—21no—
252C2×C4×C17—41no—
253C2×C4×C17—41no—
254C2×C4×C17—41no—
255C2×C4×C17—41no—
256C2×C4×C17—41no—
257C2×C4×C17—41no—
258C2×C4×C17—41no—
259C2×C4×C17—41no—
260C2×C4×C17—41no—
261C2×C4×C17C22×D411yescharacteristic
262C2×C4×C17C22×D411yescharacteristic
263C2×C4×C17C22×Q811yescharacteristic
264C2×C4×C17C22×Q811yescharacteristic
265C2×C4×C17C22×Q811yescharacteristic
266C2×C4×C17C2×#4111yescharacteristic
267C2×Dic17—22no—
268C2×Dic17—22no—
269C2×Dic17—21no—
270C2×Dic17—21no—
271C2×Dic17—22no—
272C2×Dic17—21no—
273C2×Dic17—21no—
274C2×Dic17—21no—
275C2×Dic17—21no—
276C2×Dic17—41no—
277C2×Dic17—41no—
278C2×Dic17—41no—
279C2×Dic17—41no—
280C2×Dic17—41no—
281C2×Dic17—41no—
282C2×Dic17—41no—
283C2×Dic17—41no—
284C2×Dic17—41no—
285C2×Dic17#12012yes—
286C2×Dic17C22⋊Q812yes—
287C2×Dic17C4⋊Q812yes—
288C4×D17—44no—
289C4×D17—48no—
290C4×D17—44no—
291C4×D17—48no—
292C4×D17—48no—
293C4×D17—84no—
294C4×D17C22⋊Q814yes—
295C4×D17C22⋊Q814yes—
296C4×D17C4⋊Q814yes—
297C4×D17C4⋊Q814yes—
298C8×C17—22no—
299C8×C17—22no—
300#3622—22no—
301#3622—22no—
302C22×#125—171no—
303C22×#107—171no—
304C22×#106—171no—
305C2×#389—171no—
306#2059—171no—
307#2059—171no—
308#2059—171no—
309#2059—171no—
310#2059—171no—
311#2059—171no—
312#2059—171no—
313#2059D1711yescharacteristic, direct product factor
314C2×#340—171no—
315C2×#340—171no—
316C2×#336—171no—
317C22×C17C2×#12011yescharacteristic
318C22×C17C2×C22⋊Q811yescharacteristic
319C22×C17C2×C4⋊Q811yescharacteristic
320C22×C17C2×#13511yescharacteristic
321C22×C17C2×#13511yescharacteristic
322C22×C17C2×AGL(1,ℤ/8)11yescharacteristic
323C22×C17C2×#13711yescharacteristic
324C2×D17#39514yes—
325C2×D17#44914yes—
326C2×D17#45214yes—
327C2×D17#47814yes—
328C2×D17#47914yes—
329C2×D17#49914yes—
330C2×D17#50114yes—
331C4×C17—42no—
332C4×C17—41no—
333C4×C17—42no—
334C4×C17—41no—
335C4×C17—42no—
336C4×C17—81no—
337C4×C17C2×C22⋊Q811yescharacteristic
338C4×C17C2×C22⋊Q811yescharacteristic
339C4×C17C2×C4⋊Q811yescharacteristic
340C4×C17C2×C4⋊Q811yescharacteristic
341Dic17—42no—
342Dic17—41no—
343Dic17—42no—
344Dic17—41no—
345Dic17—42no—
346Dic17—81no—
347Dic17#39514yes—
348C23×C8—171no—
349C23×C8—171no—
350C2×#125—171no—
351C2×#125—171no—
352C2×#125—171no—
353C2×#125—341no—
354C2×#125—341no—
355C2×#125—344no—
356C2×#125—344no—
357C2×#125C2×D1711yescharacteristic
358C22×C4⋊C4—171no—
359C22×C4⋊C4—171no—
360C22×C4⋊C4—171no—
361C22×C4⋊C4—171no—
362C22×C4⋊C4—341no—
363C22×C4⋊C4—341no—
364C22×C4⋊C4—341no—
365C22×C42—171no—
366C2×#107—171no—
367C2×#107—171no—
368C2×#107—171no—
369C2×#107—344no—
370C2×#107C2×D1711yescharacteristic
371C2×#106—171no—
372C2×#106—171no—
373C2×#106—171no—
374C2×#106—344no—
375C2×#106C2×D1711yescharacteristic
376#389—171no—
377#389—171no—
378#389—171no—
379#389—341no—
380#389—341no—
381#389C2×D1711yescharacteristic
382C2×#95—341no—
383#340—171no—
384#340—171no—
385#340—171no—
386#340—171no—
387#340—171no—
388#340—171no—
389#340C2×D1711yescharacteristic
390#340C2×D1711yescharacteristic
391#336—171no—
392#336—171no—
393#336—171no—
394#336C2×D1711yescharacteristic
395C2×C17C2×#39511yescharacteristic
396C2×C17C2×#44911yescharacteristic
397C2×C17C2×#45211yescharacteristic
398C2×C17C2×#47811yescharacteristic
399C2×C17C2×#47911yescharacteristic
400C2×C17C2×#49911yescharacteristic
401C2×C17C2×#50111yescharacteristic
402D17#205918yesdirect product factor
403C23×C4—171no—
404C23×C4—171no—
405C23×C4—171no—
406C23×C4—341no—
407C23×C4—341no—
408C23×C4—341no—
409C23×C4—341no—
410C22×C8—171no—
411C22×C8—171no—
412C22×C8—174no—
413C22×C8—174no—
414C22×C8—342no—
415C22×C8—342no—
416C22×C8—342no—
417C22×C8—342no—
418C22×C8C22×D1711yescharacteristic
419C22×C8C22×D1711yescharacteristic
420#125—22no—
421#125—22no—
422#125—342no—
423#125—342no—
424#125—342no—
425#125—342no—
426#125—348no—
427#125—348no—
428#125—342no—
429#125—342no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—171no—
434C2×C4⋊C4—171no—
435C2×C4⋊C4—171no—
436C2×C4⋊C4—174no—
437C2×C4⋊C4—174no—
438C2×C4⋊C4—174no—
439C2×C4⋊C4—171no—
440C2×C4⋊C4—342no—
441C2×C4⋊C4—342no—
442C2×C4⋊C4—342no—
443C2×C4⋊C4—348no—
444C2×C4⋊C4—348no—
445C2×C4⋊C4—342no—
446C2×C4⋊C4—342no—
447C2×C4⋊C4—341no—
448C2×C4⋊C4—341no—
449C2×C4⋊C4—341no—
450C2×C4⋊C4—341no—
451C2×C4⋊C4—341no—
452C2×C4⋊C4—341no—
453C2×C4⋊C4—341no—
454C2×C4⋊C4—341no—
455C2×C4⋊C4—341no—
456C2×C4⋊C4—341no—
457C2×C4⋊C4—341no—
458C2×C4⋊C4—341no—
459C2×C4⋊C4—341no—
460C2×C4⋊C4—684no—
461C2×C4⋊C4C22×D1711yescharacteristic
462C2×C4⋊C4C22×D1711yescharacteristic
463C2×C4⋊C4C22×D1711yescharacteristic
464C2×C4⋊C4C22×D1711yescharacteristic
465C2×C42—171no—
466C2×C42—171no—
467C2×C42—171no—
468C2×C42—342no—
469C2×C42—342no—
470C2×C42C22×D1711yescharacteristic
471#107—22no—
472#107—342no—
473#107—342no—
474#107—342no—
475#106—22no—
476#106—342no—
477#106—342no—
478#106—342no—
479#95—21no—
480#95—341no—
481#95—341no—
482#95—341no—
483C17C2×#205911yescharacteristic, complemented, Sylow
484C24—171no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—171no—
490C22×C4—172no—
491C22×C4—172no—
492C22×C4—172no—
493C22×C4—172no—
494C22×C4—172no—
495C22×C4—172no—
496C22×C4—171no—
497C22×C4—171no—
498C22×C4—342no—
499C22×C4—342no—
500C22×C4—344no—
501C22×C4—344no—
502C22×C4—344no—
503C22×C4—342no—
504C22×C4—342no—
505C22×C4—342no—
506C22×C4—342no—
507C22×C4—341no—
508C22×C4—341no—
509C22×C4—341no—
510C22×C4—341no—
511C22×C4—682no—
512C22×C4—682no—
513C22×C4—682no—
514C22×C4—682no—
515C22×C4—682no—
516C22×C4—682no—
517C22×C4—682no—
518C22×C4—682no—
519C22×C4—682no—
520C22×C4D4×D1711yescharacteristic
521C22×C4D4×D1711yescharacteristic
522C22×C4C23×D1711yescharacteristic
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—172no—
528C2×C8—172no—
529C2×C8—348no—
530C2×C8—348no—
531C2×C8—341no—
532C2×C8—341no—
533C2×C8—341no—
534C2×C8—341no—
535C2×C8Q8×D1712yes—
536C2×C8Q8×D1712yes—
537C4⋊C4—24no—
538C4⋊C4—24no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—42no—
545C4⋊C4—172no—
546C4⋊C4—172no—
547C4⋊C4—172no—
548C4⋊C4—344no—
549C4⋊C4—344no—
550C4⋊C4—344no—
551C4⋊C4—344no—
552C4⋊C4—344no—
553C4⋊C4—344no—
554C4⋊C4—344no—
555C4⋊C4—344no—
556C4⋊C4—344no—
557C4⋊C4—341no—
558C4⋊C4—341no—
559C4⋊C4—341no—
560C4⋊C4—341no—
561C4⋊C4—341no—
562C4⋊C4—682no—
563C4⋊C4—682no—
564C4⋊C4—682no—
565C4⋊C4—682no—
566C4⋊C4D4×D1712yes—
567C4⋊C4D4×D1712yes—
568C4⋊C4Q8×D1712yes—
569C42—21no—
570C42—21no—
571C42—342no—
572C42—342no—
573C42—341no—
574C42—341no—
575C23—172no—
576C23—172no—
577C23—172no—
578C23—172no—
579C23—172no—
580C23—172no—
581C23—172no—
582C23C2×D4×D1711yescharacteristic
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—172no—
602C2×C4—172no—
603C2×C4—172no—
604C2×C4—174no—
605C2×C4—174no—
606C2×C4—174no—
607C2×C4—174no—
608C2×C4—341no—
609C2×C4—341no—
610C2×C4—342no—
611C2×C4—342no—
612C2×C4—342no—
613C2×C4—341no—
614C2×C4—341no—
615C2×C4—341no—
616C2×C4—341no—
617C2×C4—684no—
618C2×C4—684no—
619C2×C4—688no—
620C2×C4—688no—
621C2×C4—688no—
622C2×C4—681no—
623C2×C4—681no—
624C2×C4—681no—
625C2×C4—681no—
626C2×C4—681no—
627C2×C4—681no—
628C2×C4—681no—
629C2×C4—681no—
630C2×C4—681no—
631C2×C4—1364no—
632C2×C4C2×D4×D1711yescharacteristic
633C2×C4C2×D4×D1711yescharacteristic
634C2×C4C2×Q8×D1711yescharacteristic
635C2×C4C2×Q8×D1711yescharacteristic
636C2×C4C2×Q8×D1711yescharacteristic
637C2×C4#41×D1711yescharacteristic
638C8—22no—
639C8—22no—
640C8—342no—
641C8—342no—
642C22—174no—
643C22—174no—
644C22—174no—
645C22—174no—
646C22—174no—
647C22—174no—
648C22—174no—
649C22#120×D1711yescharacteristic
650C22C22⋊Q8×D1711yescharacteristic
651C22C4⋊Q8×D1711yescharacteristic
652C22#135×D1711yescharacteristic
653C22#135×D1711yescharacteristic
654C22AGL(1,ℤ/8)×D1711yescharacteristic
655C22#137×D1711yescharacteristic
656C4—41no—
657C4—42no—
658C4—42no—
659C4—41no—
660C4—42no—
661C4—81no—
662C4—174no—
663C4—681no—
664C4—682no—
665C4—682no—
666C4—681no—
667C4—682no—
668C4—1361no—
669C4C22⋊Q8×D1711yescharacteristic
670C4C22⋊Q8×D1711yescharacteristic
671C4C4⋊Q8×D1711yescharacteristic
672C4C4⋊Q8×D1711yescharacteristic
673C2—178no—
674C2D17×#39511yescharacteristic
675C2D17×#44911yescharacteristic
676C2D17×#45211yescharacteristic
677C2D17×#47811yescharacteristic
678C2D17×#47911yescharacteristic
679C2D17×#49911yescharacteristic
680C2D17×#50111yescharacteristic
subgroupG/H
centerC23C2×D4×D17
commutator, cosocleC22×C4×C17C24
FrattiniC22×C4C23×D17
FittingC17×#2059C2
socleC23×C17C22×D4
prime radicalC23×D17C2×D4
hypercenter#2059D17
hypocenterC17C2×#2059
LCSG ▷ C22×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2059

Complements

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

NH ≅ G/Ntype
5. #14530125C2semidirect
6. #14530124C2semidirect
7. #14530123C2semidirect
8. #14530122C2semidirect
9. #14530121C2semidirect
10. #14530120C2semidirect
11. #14530119C2semidirect
15. C17×#2059C2semidirect
313. #2059D17direct (N × H)
402. D17#2059direct (N × H)
483. C17C2×#2059semidirect

Maximal subgroups

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

subgroupindex
C2×#125×D172
C2×#107×D172
C2×#106×D172
D17×#3892
#145301252
#145301242
#145301232
#145301222
#145301212
#145301202
#145301192
D17×#3402
D17×#3362
C17×#20592
C2×#205917