Finite Group Databasebeta

← D17×#1809 #17033893

Subgroups — D17×#1809 #17033893

Order 4352.

1662 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×M16×D17C211yesmaximal, characteristic
2C2×#107×D17C211yesmaximal, characteristic, complemented
3C2×#106×D17C211yesmaximal, characteristic, complemented
4D17×#380C212yesmaximal
5#14528818C211yesmaximal, characteristic, complemented
6#14528817C211yesmaximal, characteristic, complemented
7#14528816C212yesmaximal, complemented
8#14528815C212yesmaximal, complemented
9#14528814C211yesmaximal, characteristic, complemented
10D17×#340C212yesmaximal, complemented
11C17×#1809C211yesmaximal, characteristic, complemented
12C23×C4×D17C2211yescharacteristic
13C22×#63223C2211yescharacteristic
14C22×#63218C2211yescharacteristic
15C22×#63218C2211yescharacteristic
16C2×M16×D17—24no—
17C2×M16×D17—24no—
18C2×M16×D17C418yescomplemented
19C22×C8×D17C2211yescharacteristic
20C22×C8×D17C2211yescharacteristic
21C2×C4⋊C4×D17C2212yes—
22C2×C4⋊C4×D17C2212yes—
23C2×C22⋊C4×D17—22no—
24C2×#10587489C2211yescharacteristic, complemented
25C2×#10587478C2212yescomplemented
26#107×D17—24no—
27C2×#10587488C2211yescharacteristic, complemented
28C2×#10587479C2212yescomplemented
29#106×D17—24no—
30#11762669C2212yes—
31#11762668—22no—
32#11762667—22no—
33#11762666C2212yes—
34#11762666C2212yes—
35#95×D17—22no—
36#11762572C2212yescomplemented
37#11762571C2212yescomplemented
38#11762571C2212yescomplemented
39C22×M16×C17C2211yescharacteristic
40C2×C17×#107C2211yescharacteristic, complemented
41C2×C17×#106C2211yescharacteristic, complemented
42C17×#380C2212yes—
43C17×#340C2212yescomplemented
44C24×D17D411yescharacteristic
45C23×C4×C17C2311yescharacteristic
46C23×Dic17D411yescharacteristic
47C22×C4×D17—22no—
48C22×C4×D17—22no—
49C22×C4×D17—22no—
50C22×C4×D17—22no—
51C22×C4×D17—22no—
52C22×C4×D17—22no—
53C22×C4×D17C2×C414yes—
54C22×C4×D17D411yescharacteristic
55C22×C4×D17D411yescharacteristic
56C22×C4×D17Q814yes—
57C22×C4×D17C2311yescharacteristic
58C22×C4×D17C2311yescharacteristic
59C2×M16×C17—22no—
60C2×M16×C17—22no—
61C2×M16×C17C2×C414yescomplemented
62C22×C8×C17C2311yescharacteristic
63C22×C8×C17C2311yescharacteristic
64C2×C4⋊C4×C17C2312yes—
65C2×C4⋊C4×C17C2312yes—
66C2×C22⋊C4×C17—22no—
67C2×C22⋊Dic17—22no—
68C2×#63227—22no—
69C2×#63227—22no—
70C2×C4⋊Dic17C2312yes—
71C2×C4⋊Dic17C2312yes—
72C2×#63225—22no—
73C2×#63225—22no—
74C2×#63223—22no—
75C2×#63223—22no—
76C2×#63223C2×C414yescomplemented
77C22×#3622C2311yescharacteristic
78C22×#3622C2311yescharacteristic
79M16×D17—232no—
80C2×#63218—22no—
81C2×#63218—22no—
82C2×#63218—22no—
83C2×#63218—22no—
84C2×#63218C2×C414yescomplemented
85C2×#63218C2×C414yescomplemented
86C2×C8×D17—22no—
87C2×C8×D17—22no—
88C2×C8×D17C2×C414yes—
89C2×C8×D17C2×C414yes—
90C2×C8×D17D414yes—
91C2×C8×D17D414yes—
92C4⋊C4×D17—24no—
93C4⋊C4×D17—24no—
94C4⋊C4×D17—24no—
95C4⋊C4×D17—24no—
96C22⋊C4×D17—48no—
97C17×#107—22no—
98C17×#106—22no—
99C17×#95—22no—
100#10587502—22no—
101#10587502—22no—
102#10587502—22no—
103#10587489—22no—
104#10587488—22no—
105#10587479—24no—
106#10587478—24no—
107C24×C17C2×D411yescharacteristic
108C23×D17—22no—
109C23×D17—22no—
110C23×D17—24no—
111C23×D17—24no—
112C23×D17C4⋊C414yes—
113C23×D17C2×D411yescharacteristic
114C23×D17C2×D411yescharacteristic
115C22×C4×C17—21no—
116C22×C4×C17—21no—
117C22×C4×C17—21no—
118C22×C4×C17—21no—
119C22×C4×C17—22no—
120C22×C4×C17—22no—
121C22×C4×C17C22×C412yes—
122C22×C4×C17C2×D411yescharacteristic
123C22×C4×C17C2×Q812yes—
124C22×C4×C17C2411yescharacteristic
125C22×Dic17—22no—
126C22×Dic17—22no—
127C22×Dic17—22no—
128C22×Dic17—22no—
129C22×Dic17C4⋊C414yes—
130C22×Dic17C2×D411yescharacteristic
131C22×Dic17C2×D411yescharacteristic
132C2×C4×D17—22no—
133C2×C4×D17—22no—
134C2×C4×D17—21no—
135C2×C4×D17—21no—
136C2×C4×D17—21no—
137C2×C4×D17—21no—
138C2×C4×D17—22no—
139C2×C4×D17—22no—
140C2×C4×D17—28no—
141C2×C4×D17—28no—
142C2×C4×D17—28no—
143C2×C4×D17—28no—
144C2×C4×D17—44no—
145C2×C4×D17—44no—
146C2×C4×D17—44no—
147C2×C4×D17—44no—
148C2×C4×D17—44no—
149C2×C4×D17—44no—
150C2×C4×D17C4⋊C414yes—
151C2×C4×D17C4⋊C414yes—
152C2×C4×D17C22×C412yes—
153C2×C4×D17C22×C412yes—
154C2×C4×D17C2×D412yes—
155C2×C4×D17C2×D412yes—
156C2×C4×D17C2×Q812yes—
157C2×C4×D17C2×Q812yes—
158C2×C4×D17#4112yes—
159C2×C4×D17#4112yes—
160M16×C17—28no—
161C2×C8×C17—21no—
162C2×C8×C17—21no—
163C2×C8×C17C22×C412yes—
164C2×C8×C17C22×C412yes—
165C2×C8×C17C2×D412yes—
166C2×C8×C17C2×D412yes—
167C4⋊C4×C17—22no—
168C4⋊C4×C17—22no—
169C4⋊C4×C17—22no—
170C4⋊C4×C17—22no—
171C22⋊C4×C17—44no—
172C22⋊Dic17—44no—
173#63227—44no—
174#63227—44no—
175C4⋊Dic17—22no—
176C4⋊Dic17—22no—
177C4⋊Dic17—22no—
178C4⋊Dic17—22no—
179#63225—44no—
180#63225—44no—
181#63223—28no—
182C2×#3622—21no—
183C2×#3622—21no—
184C2×#3622C22×C412yes—
185C2×#3622C22×C412yes—
186C2×#3622C2×D412yes—
187C2×#3622C2×D412yes—
188#63218—28no—
189#63218—28no—
190C8×D17—28no—
191C8×D17C22⋊C4116yescomplemented
192C2×#1809—171nomaximal, Sylow
193C23×C17—21no—
194C23×C17—21no—
195C23×C17—22no—
196C23×C17—22no—
197C23×C17C2×C4⋊C412yes—
198C23×C17C22×D411yescharacteristic
199C22×D17—21no—
200C22×D17—21no—
201C22×D17—22no—
202C22×D17—22no—
203C22×D17—28no—
204C22×D17—216no—
205C22×D17—48no—
206C22×D17—44no—
207C22×D17—44no—
208C22×D17C2×C4⋊C412yes—
209C22×D17C2×C4⋊C412yes—
210C22×D17#12112yes—
211C22×D17#12112yes—
212C22×D17AGL(1,ℤ/8)14yes—
213C22×D17#13714yes—
214C2×C4×C17—21no—
215C2×C4×C17—21no—
216C2×C4×C17—22no—
217C2×C4×C17—22no—
218C2×C4×C17—22no—
219C2×C4×C17—22no—
220C2×C4×C17—42no—
221C2×C4×C17—42no—
222C2×C4×C17—42no—
223C2×C4×C17—42no—
224C2×C4×C17—42no—
225C2×C4×C17—42no—
226C2×C4×C17C2×C4⋊C412yes—
227C2×C4×C17C23×C411yescharacteristic
228C2×C4×C17C22×D411yescharacteristic
229C2×C4×C17C22×D411yescharacteristic
230C2×C4×C17C22×Q811yescharacteristic
231C2×C4×C17C2×#4111yescharacteristic
232C2×C4×C17C2×#4111yescharacteristic
233C2×Dic17—21no—
234C2×Dic17—21no—
235C2×Dic17—28no—
236C2×Dic17—42no—
237C2×Dic17—42no—
238C2×Dic17—42no—
239C2×Dic17—42no—
240C2×Dic17—42no—
241C2×Dic17—42no—
242C2×Dic17C2×C4⋊C412yes—
243C2×Dic17C2×C4⋊C412yes—
244C2×Dic17#12112yes—
245C2×Dic17#12112yes—
246C4×D17—28no—
247C4×D17—22no—
248C4×D17—22no—
249C4×D17—22no—
250C4×D17—22no—
251C4×D17—28no—
252C4×D17—88no—
253C4×D17—88no—
254C4×D17C2×C22⋊C414yes—
255C4×D17#11714yes—
256C4×D17C22⋊Q814yes—
257C4×D17C22⋊Q814yes—
258C8×C17—22no—
259C8×C17C2×C22⋊C414yescomplemented
260#3622—22no—
261#3622C2×C22⋊C414yescomplemented
262C23×M16—171no—
263C22×#107—171no—
264C22×#106—171no—
265C2×#380—172no—
266#1809—171no—
267#1809—171no—
268#1809—172no—
269#1809—172no—
270#1809—171no—
271#1809D1711yescharacteristic, direct product factor
272C2×#340—172no—
273C22×C17—24no—
274C22×C17—22no—
275C22×C17—42no—
276C22×C17—41no—
277C22×C17—41no—
278C22×C17C22×C4⋊C411yescharacteristic
279C22×C17C2×#12111yescharacteristic
280C22×C17C2×#12111yescharacteristic
281C22×C17C2×AGL(1,ℤ/8)12yes—
282C22×C17C2×#13712yes—
283C2×D17—24no—
284C2×D17—22no—
285C2×D17—42no—
286C2×D17—41no—
287C2×D17—41no—
288C2×D17—416no—
289C2×D17#38014yes—
290C2×D17#42818yes—
291C2×D17#46818yes—
292C2×D17#46914yes—
293C2×D17#47014yes—
294C4×C17—22no—
295C4×C17—82no—
296C4×C17—82no—
297C4×C17C22×C22⋊C411yescharacteristic
298C4×C17C2×#11711yescharacteristic
299C4×C17C2×C22⋊Q811yescharacteristic
300C4×C17C2×C22⋊Q811yescharacteristic
301Dic17—22no—
302Dic17—82no—
303Dic17—82no—
304Dic17#38014yes—
305C24×C4—171no—
306C22×M16—171no—
307C22×M16—178no—
308C22×M16—171no—
309C22×M16—171no—
310C22×M16—344no—
311C22×M16—344no—
312C22×M16C2×D1711yescharacteristic
313C23×C8—171no—
314C23×C8—171no—
315C22×C4⋊C4—172no—
316C22×C4⋊C4—172no—
317C22×C22⋊C4—342no—
318C2×#107—171no—
319C2×#107—172no—
320C2×#107—344no—
321C2×#107C2×D1711yescharacteristic, complemented
322C2×#106—171no—
323C2×#106—172no—
324C2×#106—344no—
325C2×#106C2×D1711yescharacteristic, complemented
326#380—172no—
327#380—172no—
328#380—172no—
329#380—342no—
330#380—342no—
331#380C2×D1712yes—
332C2×#95—342no—
333#340—172no—
334#340—172no—
335#340—172no—
336#340C2×D1712yescomplemented
337C2×C17—42no—
338C2×C17C2×#38011yescharacteristic
339C2×C17C2×#42812yes—
340C2×C17C2×#46812yes—
341C2×C17C2×#46911yescharacteristic
342C2×C17C2×#47011yescharacteristic
343D17—42no—
344D17#180918yesdirect product factor
345C25—171no—
346C23×C4—171no—
347C23×C4—171no—
348C23×C4—174no—
349C23×C4—171no—
350C23×C4—171no—
351C23×C4—174no—
352C23×C4—171no—
353C23×C4—342no—
354C23×C4—342no—
355C23×C4—342no—
356C23×C4—342no—
357C23×C4—342no—
358C23×C4—342no—
359C23×C4C22×D1711yescharacteristic
360C2×M16—22no—
361C2×M16—22no—
362C2×M16—174no—
363C2×M16—174no—
364C2×M16—174no—
365C2×M16—342no—
366C2×M16—342no—
367C2×M16—3432no—
368C2×M16—342no—
369C2×M16—342no—
370C2×M16—342no—
371C2×M16—342no—
372C2×M16C4×D1714yescomplemented
373C22×C8—171no—
374C22×C8—174no—
375C22×C8—174no—
376C22×C8—174no—
377C22×C8—171no—
378C22×C8—174no—
379C22×C8—342no—
380C22×C8—342no—
381C22×C8C22×D1711yescharacteristic
382C22×C8C22×D1711yescharacteristic
383C2×C4⋊C4—172no—
384C2×C4⋊C4—172no—
385C2×C4⋊C4—344no—
386C2×C4⋊C4—344no—
387C2×C4⋊C4—344no—
388C2×C4⋊C4—344no—
389C2×C4⋊C4—342no—
390C2×C4⋊C4—342no—
391C2×C4⋊C4C22×D1712yes—
392C2×C4⋊C4C22×D1712yes—
393C2×C22⋊C4—22no—
394C2×C22⋊C4—342no—
395C2×C22⋊C4—342no—
396C2×C22⋊C4—342no—
397C2×C22⋊C4—688no—
398#107—22no—
399#107—344no—
400#107—342no—
401#106—22no—
402#106—344no—
403#106—342no—
404#95—22no—
405#95—342no—
406#95—342no—
407#95—342no—
408C17C2×#180911yescharacteristic, complemented, Sylow
409C24—171no—
410C24—171no—
411C24—174no—
412C24—344no—
413C24—342no—
414C24—342no—
415C24—344no—
416C24D4×D1711yescharacteristic
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—171no—
424C22×C4—172no—
425C22×C4—172no—
426C22×C4—172no—
427C22×C4—172no—
428C22×C4—172no—
429C22×C4—172no—
430C22×C4—171no—
431C22×C4—174no—
432C22×C4—172no—
433C22×C4—172no—
434C22×C4—174no—
435C22×C4—174no—
436C22×C4—348no—
437C22×C4—342no—
438C22×C4—342no—
439C22×C4—348no—
440C22×C4—348no—
441C22×C4—348no—
442C22×C4—342no—
443C22×C4—342no—
444C22×C4—342no—
445C22×C4—342no—
446C22×C4—341no—
447C22×C4—341no—
448C22×C4—341no—
449C22×C4—341no—
450C22×C4—342no—
451C22×C4—342no—
452C22×C4—684no—
453C22×C4—684no—
454C22×C4—684no—
455C22×C4—684no—
456C22×C4—684no—
457C22×C4—684no—
458C22×C4C2×C4×D1712yes—
459C22×C4D4×D1711yescharacteristic
460C22×C4Q8×D1712yes—
461C22×C4C23×D1711yescharacteristic
462M16—28no—
463M16—348no—
464M16—348no—
465M16—348no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—172no—
469C2×C8—172no—
470C2×C8—172no—
471C2×C8—1716no—
472C2×C8—172no—
473C2×C8—348no—
474C2×C8—341no—
475C2×C8—341no—
476C2×C8C2×C4×D1712yes—
477C2×C8C2×C4×D1712yes—
478C2×C8D4×D1712yes—
479C2×C8D4×D1712yes—
480C4⋊C4—22no—
481C4⋊C4—22no—
482C4⋊C4—22no—
483C4⋊C4—22no—
484C4⋊C4—342no—
485C4⋊C4—342no—
486C4⋊C4—342no—
487C4⋊C4—342no—
488C4⋊C4—684no—
489C4⋊C4—684no—
490C22⋊C4—44no—
491C22⋊C4—684no—
492C22⋊C4—684no—
493C22⋊C4—684no—
494C23—21no—
495C23—21no—
496C23—22no—
497C23—22no—
498C23—172no—
499C23—172no—
500C23—172no—
501C23—174no—
502C23—174no—
503C23—172no—
504C23—348no—
505C23—3416no—
506C23—341no—
507C23—341no—
508C23—342no—
509C23—342no—
510C23—688no—
511C23—684no—
512C23—684no—
513C23C4⋊C4×D1712yes—
514C23C2×D4×D1711yescharacteristic
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—172no—
528C2×C4—172no—
529C2×C4—172no—
530C2×C4—174no—
531C2×C4—174no—
532C2×C4—174no—
533C2×C4—174no—
534C2×C4—172no—
535C2×C4—348no—
536C2×C4—348no—
537C2×C4—348no—
538C2×C4—341no—
539C2×C4—341no—
540C2×C4—342no—
541C2×C4—342no—
542C2×C4—342no—
543C2×C4—342no—
544C2×C4—682no—
545C2×C4—682no—
546C2×C4—682no—
547C2×C4—682no—
548C2×C4—682no—
549C2×C4—682no—
550C2×C4—1368no—
551C2×C4—1368no—
552C2×C4C4⋊C4×D1712yes—
553C2×C4C22×C4×D1711yescharacteristic
554C2×C4C2×D4×D1711yescharacteristic
555C2×C4C2×D4×D1711yescharacteristic
556C2×C4C2×Q8×D1711yescharacteristic
557C2×C4#41×D1711yescharacteristic
558C2×C4#41×D1711yescharacteristic
559C8—22no—
560C8—174no—
561C8—342no—
562C8C22⋊C4×D1714yescomplemented
563C22—22no—
564C22—24no—
565C22—42no—
566C22—41no—
567C22—41no—
568C22—174no—
569C22—178no—
570C22—174no—
571C22—174no—
572C22—178no—
573C22—342no—
574C22—344no—
575C22—6816no—
576C22—682no—
577C22—681no—
578C22—681no—
579C22C2×C4⋊C4×D1711yescharacteristic
580C22#121×D1711yescharacteristic
581C22#121×D1711yescharacteristic
582C22AGL(1,ℤ/8)×D1712yes—
583C22#137×D1712yes—
584C4—22no—
585C4—82no—
586C4—82no—
587C4—174no—
588C4—342no—
589C4—1362no—
590C4—1362no—
591C4C2×C22⋊C4×D1711yescharacteristic
592C4#117×D1711yescharacteristic
593C4C22⋊Q8×D1711yescharacteristic
594C4C22⋊Q8×D1711yescharacteristic
595C2—42no—
596C2—178no—
597C2—682no—
598C2D17×#38011yescharacteristic
599C2D17×#42812yes—
600C2D17×#46812yes—
601C2D17×#46911yescharacteristic
602C2D17×#47011yescharacteristic
subgroupG/H
centerC23C2×D4×D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC17×#1809C2
socleC23×C17C22×D4
prime radicalC24×D17D4
cosocleC22×C4×C17C24
hypercenter#1809D17
hypocenterC17C2×#1809
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1809

Complements

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

NH ≅ G/Ntype
2. C2×#107×D17C2semidirect
3. C2×#106×D17C2semidirect
5. #14528818C2semidirect
6. #14528817C2semidirect
7. #14528816C2semidirect
8. #14528815C2semidirect
9. #14528814C2semidirect
10. D17×#340C2semidirect
11. C17×#1809C2semidirect
18. C2×M16×D17C4semidirect
24. C2×#10587489C22semidirect
25. C2×#10587478C22semidirect
27. C2×#10587488C22semidirect
28. C2×#10587479C22semidirect
36. #11762572C22semidirect
37. #11762571C22semidirect
38. #11762571C22semidirect
40. C2×C17×#107C22semidirect
41. C2×C17×#106C22semidirect
43. C17×#340C22semidirect
61. C2×M16×C17C2×C4semidirect
76. C2×#63223C2×C4semidirect
84. C2×#63218C2×C4semidirect
85. C2×#63218C2×C4semidirect
191. C8×D17C22⋊C4semidirect
259. C8×C17C2×C22⋊C4semidirect
261. #3622C2×C22⋊C4semidirect
271. #1809D17direct (N × H)
321. C2×#107C2×D17semidirect
325. C2×#106C2×D17semidirect
336. #340C2×D17semidirect
344. D17#1809direct (N × H)
372. C2×M16C4×D17semidirect
408. C17C2×#1809semidirect
562. C8C22⋊C4×D17semidirect

Maximal subgroups

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

subgroupindex
C22×M16×D172
C2×#107×D172
C2×#106×D172
D17×#3802
#145288182
#145288172
#145288162
#145288152
#145288142
D17×#3402
C17×#18092
C2×#180917