Finite Group Databasebeta

← #17070392

Subgroups — #17070392

Order 4352.

1378 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊Q8×D17C211yesmaximal, characteristic, complemented
2C2×#11763099C211yesmaximal, characteristic, complemented
3C4×#10587624C211yesmaximal, characteristic
4#14530115C212yesmaximal, complemented
5#14529918C212yesmaximal, complemented
6#14529733C211yesmaximal, characteristic, complemented
7#14529731C211yesmaximal, characteristic, complemented
8#14529098C212yesmaximal
9#14528975C212yesmaximal, complemented
10#14528761C211yesmaximal, characteristic, complemented
11C2×C17×#476C211yesmaximal, characteristic, complemented
12C22×Q8×D17—21no—
13C2×#10587555C2211yescharacteristic
14C2×#10587574—21no—
15C2×#10587574C2212yes—
16C2×#10587630—21no—
17C4⋊Q8×D17—24no—
18C4⋊Q8×D17—24no—
19C2×#10587624C2211yescharacteristic
20C2×C4×C22⋊D17—21no—
21C2×C4⋊C4×D17—21no—
22C2×C4⋊C4×D17C2212yes—
23C2×C42×D17C2211yescharacteristic
24#11763099—24no—
25C2×#10587479C2212yes—
26C2×C4⋊#3622C2211yescharacteristic
27C2×#10587503C2212yes—
28C2×#10587491C2212yes—
29#11762712C2211yescharacteristic
30#11762705C2211yescharacteristic
31#11762697—21no—
32#11762685—21no—
33#11762666C2211yescharacteristic
34C4×C4⋊Dic17C2211yescharacteristic
35C4×C22⋊Dic17—21no—
36#11762572C2212yes—
37#11762572C2212yes—
38#11762571C2212yes—
39#11762571C2212yes—
40#11762563C2212yes—
41C2×C17×C4⋊Q8C2211yescharacteristic
42C2×C4×D4×C17C2211yescharacteristic
43C17×#476—24no—
44C2×C17×#106C2212yes—
45C2×C17×C4⋊C8C2211yescharacteristic
46C2×C17×#102C2212yes—
47C22×Q8×C17—21no—
48C22×D4×C17C2311yescharacteristic
49C23×C4×C17—21no—
50C22×C22⋊D17—21no—
51C2×Q8×D17—28no—
52C2×Q8×D17—44no—
53C2×Q8×D17—44no—
54C22×C4×D17—22no—
55C22×C4×D17D411yescharacteristic
56C22×C4×D17D411yescharacteristic
57C22×C4×D17C2311yescharacteristic
58C22×Dic34—21no—
59C22×Dic34—22no—
60C22×C8×C17C2312yes—
61C17×C4⋊Q8—22no—
62C17×C4⋊Q8D414yescomplemented
63C4×D4×C17—22no—
64C4×D4×C17—22no—
65C2×C4⋊C4×C17—21no—
66C2×C4⋊C4×C17C2311yescharacteristic
67C2×C4⋊C4×C17C2312yes—
68C2×C22⋊C4×C17—21no—
69C2×C42×C17C2311yescharacteristic
70C2×C22⋊Dic17—21no—
71C2×C22⋊Dic17—21no—
72C2×C22⋊Dic17—21no—
73#10587630—28no—
74#10587624—22no—
75#10587624Q814yescomplemented
76C4×C22⋊D17—44no—
77C2×#63227—21no—
78C2×C4⋊Dic17—21no—
79C2×C4⋊Dic17C2311yescharacteristic
80C2×C4⋊Dic17C2312yes—
81C2×C4⋊Dic17C2311yescharacteristic
82C2×#63225—22no—
83C2×#63225—22no—
84C2×#63225—21no—
85C2×C4×Dic17—21no—
86C2×C4×Dic17D411yescharacteristic
87C2×C4×Dic17D411yescharacteristic
88C2×C4×Dic17C2311yescharacteristic
89C22×#3622C2312yes—
90C4⋊C4×D17—28no—
91C4⋊C4×D17—24no—
92C4⋊C4×D17—24no—
93#10587574—28no—
94#10587574—24no—
95#10587574—24no—
96C42×D17—22no—
97C42×D17—22no—
98#10587555—22no—
99#10587555D414yescomplemented
100C17×#106—24no—
101C17×C4⋊C8—22no—
102C17×#102—24no—
103#10587503—24no—
104#10587502—21no—
105#10587502—21no—
106#10587502—21no—
107#10587491—24no—
108#10587479—24no—
109C4⋊#3622—22no—
110C24×C17—21no—
111C23×D17C2×D411yescharacteristic
112C2×Q8×C17—24no—
113C2×Q8×C17—42no—
114C2×Q8×C17—42no—
115C2×D4×C17—21no—
116C2×D4×C17—21no—
117C2×D4×C17—21no—
118C2×D4×C17—21no—
119C2×D4×C17—21no—
120C2×D4×C17C2×Q812yescomplemented
121C22×C4×C17—22no—
122C22×C4×C17—21no—
123C22×C4×C17—42no—
124C22×C4×C17—42no—
125C22×C4×C17—42no—
126C22×C4×C17C2×D411yescharacteristic
127C22×C4×C17C2×D411yescharacteristic
128C22×C4×C17C2411yescharacteristic
129C2×C22⋊D17—24no—
130C2×C22⋊D17—42no—
131C2×C22⋊D17—42no—
132C22×Dic17—22no—
133C22×Dic17—21no—
134C22×Dic17—21no—
135C22×Dic17C2×D411yescharacteristic
136C22×Dic17C2×D411yescharacteristic
137C22×Dic17C2×D411yescharacteristic
138Q8×D17—432no—
139C2×C4×D17—22no—
140C2×C4×D17—22no—
141C2×C4×D17—22no—
142C2×C4×D17—22no—
143C2×C4×D17—21no—
144C2×C4×D17—21no—
145C2×C4×D17—21no—
146C2×C4×D17—21no—
147C2×C4×D17—22no—
148C2×C4×D17—28no—
149C2×C4×D17—44no—
150C2×C4×D17—44no—
151C2×C4×D17SD1614yes—
152C2×C4×D17C2×Q812yes—
153C2×C4×D17#4112yes—
154C2×Dic34—28no—
155C2×Dic34—24no—
156C2×Dic34—44no—
157C2×Dic34—42no—
158C2×Dic34—42no—
159C2×Dic34—44no—
160C2×C8×C17—22no—
161C2×C8×C17—22no—
162C2×C8×C17—22no—
163C4⋊C4×C17—24no—
164C4⋊C4×C17—22no—
165C4⋊C4×C17—21no—
166C4⋊C4×C17—21no—
167C4⋊C4×C17C2×D414yes—
168C22⋊C4×C17—42no—
169C42×C17C2×D412yes—
170C42×C17C2×D412yes—
171C22⋊Dic17—24no—
172C22⋊Dic17—42no—
173C22⋊Dic17—42no—
174#63227—42no—
175C4⋊Dic17—24no—
176C4⋊Dic17—22no—
177C4⋊Dic17—21no—
178C4⋊Dic17—21no—
179C4⋊Dic17—21no—
180C4⋊Dic17C2×D414yes—
181C4⋊Dic17C2×Q812yescomplemented
182#63225—28no—
183#63225—28no—
184#63225—42no—
185C4×Dic17—22no—
186C4×Dic17—22no—
187C4×Dic17—21no—
188C4×Dic17—21no—
189C4×Dic17—42no—
190C2×#3622—22no—
191C2×#3622—22no—
192C2×#3622—22no—
193#24299—171nomaximal, Sylow
194C23×C17—22no—
195C23×C17—41no—
196C23×C17—41no—
197C23×C17—41no—
198C23×C17—41no—
199C23×C17—41no—
200C23×C17—41no—
201C23×C17C22×D411yescharacteristic
202C22×D17—21no—
203C22×D17—21no—
204C22×D17—21no—
205C22×D17—21no—
206C22×D17C22⋊Q812yes—
207C22×D17C2×SD1612yes—
208C22×D17AGL(1,ℤ/8)12yes—
209Q8×C17—48no—
210D4×C17—22no—
211D4×C17—22no—
212D4×C17—41no—
213D4×C17—41no—
214C2×C4×C17—21no—
215C2×C4×C17—21no—
216C2×C4×C17—24no—
217C2×C4×C17—42no—
218C2×C4×C17—42no—
219C2×C4×C17—41no—
220C2×C4×C17—41no—
221C2×C4×C17—41no—
222C2×C4×C17—84no—
223C2×C4×C17#12012yes—
224C2×C4×C17#12012yes—
225C2×C4×C17C2×SD1612yes—
226C2×C4×C17#13712yes—
227C2×C4×C17C22×D411yescharacteristic
228C2×C4×C17C22×D411yescharacteristic
229C2×C4×C17C22×Q811yescharacteristic
230C2×C4×C17C2×#4111yescharacteristic
231C2×C4×C172−1+411yescharacteristic
232C2×C4×C172−1+411yescharacteristic
233C22⋊D17—48no—
234C2×Dic17—21no—
235C2×Dic17—21no—
236C2×Dic17—21no—
237C2×Dic17—21no—
238C2×Dic17—21no—
239C2×Dic17—21no—
240C2×Dic17—24no—
241C2×Dic17—22no—
242C2×Dic17—41no—
243C2×Dic17—42no—
244C2×Dic17—42no—
245C2×Dic17—41no—
246C2×Dic17—41no—
247C2×Dic17—41no—
248C2×Dic17—41no—
249C2×Dic17C22⋊Q812yes—
250C2×Dic17C2×SD1612yes—
251C2×Dic17AGL(1,ℤ/8)12yes—
252C4×D17—28no—
253C4×D17—22no—
254C4×D17—22no—
255C4×D17—22no—
256C4×D17—22no—
257C4×D17—28no—
258C4×D17—416no—
259Dic34—416no—
260Dic34—48no—
261C8×C17—42no—
262#3622—42no—
263C22×C4⋊Q8—171no—
264C2×#476—171no—
265C2×#476D1711yescharacteristic, complemented
266C4×#121—171no—
267#2058—172no—
268#2023—172no—
269#1987—171no—
270#1987—171no—
271#1874—172no—
272#1853—172no—
273#1797—171no—
274C22×C17—42no—
275C22×C17—42no—
276C22×C17—42no—
277C22×C17—81no—
278C22×C17—81no—
279C22×C17—81no—
280C22×C17—81no—
281C22×C17C2×#12011yescharacteristic
282C22×C17C2×C22⋊Q811yescharacteristic
283C22×C17#53611yescharacteristic
284C22×C17C22×SD1611yescharacteristic
285C22×C17C2×AGL(1,ℤ/8)11yescharacteristic
286C22×C17C2×AGL(1,ℤ/8)11yescharacteristic
287C22×C17C2×#13711yescharacteristic
288C2×D17—22no—
289C2×D17—22no—
290C2×D17—22no—
291C2×D17—22no—
292C2×D17—22no—
293C2×D17—22no—
294C2×D17#47614yescomplemented
295C4×C17—22no—
296C4×C17—44no—
297C4×C17—81no—
298C4×C17#44814yes—
299C4×C17#54811yescharacteristic
300C4×C17#54811yescharacteristic
301C4×C17D4×Q811yescharacteristic
302C4×C17D4×Q811yescharacteristic
303Dic17—22no—
304Dic17—22no—
305Dic17—22no—
306Dic17—44no—
307Dic17—42no—
308Dic17—81no—
309C23×Q8—341no—
310C2×C4⋊Q8—172no—
311C2×C4⋊Q8—171no—
312C2×C4⋊Q8—341no—
313C2×C4⋊Q8—341no—
314C2×C4⋊Q8—344no—
315C2×C4⋊Q8—344no—
316C2×C4⋊Q8C2×D1711yescharacteristic
317C2×#121—171no—
318C2×C4×D4—341no—
319C2×C4×D4C2×D1711yescharacteristic
320C22×C4⋊C4—172no—
321C22×C4⋊C4—341no—
322C22×C42—171no—
323#476—24no—
324#476—344no—
325C2×#106—172no—
326C2×#106C2×D1712yes—
327C2×C4⋊C8—171no—
328C2×C4⋊C8C2×D1711yescharacteristic
329C2×#102—172no—
330C2×#102C2×D1712yes—
331C2×C22⋊C8—172no—
332#390—171no—
333#389—171no—
334#388—341no—
335#386—341no—
336#380—171no—
337C4×C4⋊C4—171no—
338C4×C22⋊C4—341no—
339#340—172no—
340#340—172no—
341#340—172no—
342#340—172no—
343#336—172no—
344C2×C17—82no—
345C2×C17#240911yescharacteristic
346C2×C17C2×#44811yescharacteristic
347C2×C17#300311yescharacteristic
348C2×C17C2×#47611yescharacteristic
349C2×C17#307911yescharacteristic
350C2×C17#322711yescharacteristic
351C2×C17#323811yescharacteristic
352D17—24no—
353C22×Q8—21no—
354C22×Q8—342no—
355C22×Q8—348no—
356C22×Q8—341no—
357C22×Q8—684no—
358C22×Q8—684no—
359C22×D4—341no—
360C22×D4C22×D1711yescharacteristic
361C23×C4—21no—
362C23×C4—171no—
363C23×C4—171no—
364C23×C4—171no—
365C23×C4—342no—
366C22×C8—172no—
367C22×C8C22×D1712yes—
368C4⋊Q8—22no—
369C4⋊Q8—174no—
370C4⋊Q8—344no—
371C4⋊Q8—348no—
372C4⋊Q8—348no—
373C4⋊Q8—344no—
374C4⋊Q8—342no—
375C4⋊Q8C22⋊D1714yescomplemented
376#121—174no—
377#121—342no—
378C4×D4—22no—
379C4×D4—22no—
380C4×D4—684no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—172no—
383C2×C4⋊C4—171no—
384C2×C4⋊C4—171no—
385C2×C4⋊C4—344no—
386C2×C4⋊C4—348no—
387C2×C4⋊C4—342no—
388C2×C4⋊C4—342no—
389C2×C4⋊C4—341no—
390C2×C4⋊C4—344no—
391C2×C4⋊C4—341no—
392C2×C4⋊C4C22×D1711yescharacteristic
393C2×C4⋊C4C22×D1712yes—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—341no—
396C2×C22⋊C4—341no—
397C2×C22⋊C4—341no—
398C2×C22⋊C4—341no—
399C2×C42—171no—
400C2×C42—171no—
401C2×C42—171no—
402C2×C42—342no—
403C2×C42—342no—
404C2×C42—341no—
405C2×C42C22×D1711yescharacteristic
406#106—24no—
407#106—344no—
408C4⋊C8—22no—
409C4⋊C8—342no—
410#102—24no—
411#102—344no—
412C22⋊C8—344no—
413#95—341no—
414#95—341no—
415#95—341no—
416C17#2429911yescharacteristic, complemented, Sylow
417C24—21no—
418C24—171no—
419C2×Q8—24no—
420C2×Q8—42no—
421C2×Q8—42no—
422C2×Q8—348no—
423C2×Q8—344no—
424C2×Q8—682no—
425C2×Q8—682no—
426C2×Q8—684no—
427C2×Q8—684no—
428C2×Q8—6832no—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—21no—
434C2×D4—344no—
435C2×D4—682no—
436C2×D4—682no—
437C2×D4Q8×D1712yescomplemented
438C22×C4—22no—
439C22×C4—21no—
440C22×C4—42no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—171no—
444C22×C4—171no—
445C22×C4—171no—
446C22×C4—172no—
447C22×C4—172no—
448C22×C4—174no—
449C22×C4—342no—
450C22×C4—342no—
451C22×C4—348no—
452C22×C4—341no—
453C22×C4—341no—
454C22×C4—341no—
455C22×C4—341no—
456C22×C4—342no—
457C22×C4—342no—
458C22×C4—342no—
459C22×C4—341no—
460C22×C4—342no—
461C22×C4—341no—
462C22×C4—684no—
463C22×C4—684no—
464C22×C4D4×D1711yescharacteristic
465C22×C4D4×D1711yescharacteristic
466C22×C4C23×D1711yescharacteristic
467C2×C8—22no—
468C2×C8—22no—
469C2×C8—22no—
470C2×C8—342no—
471C2×C8—342no—
472C2×C8—342no—
473C4⋊C4—22no—
474C4⋊C4—24no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—174no—
478C4⋊C4—172no—
479C4⋊C4—348no—
480C4⋊C4—348no—
481C4⋊C4—341no—
482C4⋊C4—342no—
483C4⋊C4—344no—
484C4⋊C4—341no—
485C4⋊C4—341no—
486C4⋊C4—682no—
487C4⋊C4C2×C22⋊D1714yes—
488C22⋊C4—42no—
489C22⋊C4—344no—
490C22⋊C4—682no—
491C22⋊C4—682no—
492C22⋊C4—682no—
493C42—341no—
494C42—341no—
495C42—342no—
496C42—342no—
497C42—682no—
498C42D4×D1712yes—
499C42C2×C22⋊D1712yes—
500C23—22no—
501C23—41no—
502C23—41no—
503C23—41no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23—172no—
508C23—172no—
509C23—172no—
510C23—341no—
511C23—341no—
512C23—341no—
513C23—341no—
514C23C2×D4×D1711yescharacteristic
515Q8—48no—
516Q8—688no—
517Q8—6816no—
518D4—22no—
519D4—22no—
520D4—41no—
521D4—41no—
522D4—688no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—24no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—84no—
532C2×C4—172no—
533C2×C4—172no—
534C2×C4—172no—
535C2×C4—348no—
536C2×C4—341no—
537C2×C4—341no—
538C2×C4—341no—
539C2×C4—341no—
540C2×C4—341no—
541C2×C4—341no—
542C2×C4—348no—
543C2×C4—342no—
544C2×C4—342no—
545C2×C4—342no—
546C2×C4—342no—
547C2×C4—344no—
548C2×C4—342no—
549C2×C4—6816no—
550C2×C4—681no—
551C2×C4—682no—
552C2×C4—682no—
553C2×C4—681no—
554C2×C4—681no—
555C2×C4—681no—
556C2×C4—681no—
557C2×C4SD16×D1712yes—
558C2×C4#1058760112yes—
559C2×C4#1058762312yes—
560C2×C4#1058762312yes—
561C2×C4C2×D4×D1711yescharacteristic
562C2×C4C2×Q8×D1711yescharacteristic
563C2×C4#1058769411yescharacteristic
564C2×C4#41×D1711yescharacteristic
565C2×C4#1058769711yescharacteristic
566C2×C4C22×C22⋊D1711yescharacteristic
567C8—42no—
568C8—682no—
569C22—42no—
570C22—42no—
571C22—42no—
572C22—81no—
573C22—81no—
574C22—81no—
575C22—81no—
576C22—174no—
577C22—342no—
578C22—342no—
579C22—342no—
580C22—342no—
581C22—342no—
582C22—342no—
583C22C2×#1058762311yescharacteristic
584C22C22⋊Q8×D1711yescharacteristic
585C22#1176338211yescharacteristic
586C22C2×SD16×D1711yescharacteristic
587C22AGL(1,ℤ/8)×D1711yescharacteristic
588C22AGL(1,ℤ/8)×D1711yescharacteristic
589C22C2×#1058760111yescharacteristic
590C4—22no—
591C4—44no—
592C4—81no—
593C4—342no—
594C4—342no—
595C4—342no—
596C4—684no—
597C4—682no—
598C4—1361no—
599C4#1176294614yes—
600C4#1176346611yescharacteristic
601C4#1176346911yescharacteristic
602C4#1176347211yescharacteristic
603C4Q8×C22⋊D1711yescharacteristic
604C2—82no—
605C2—344no—
606C2#1453214511yescharacteristic
607C2C2×#1176294611yescharacteristic
608C2#1453800911yescharacteristic
609C2D17×#47611yescharacteristic
610C2#1453859611yescharacteristic
611C2#1453991111yescharacteristic
612C2#1454000411yescharacteristic
subgroupG/H
centerC23C2×D4×D17
commutator, cosocleC22×C4×C17C24
FrattiniC22×C4C23×D17
FittingC2×C17×#476C2
socleC23×C17C22×D4
prime radicalC2×#10587624C22
hypercenterC2×#476D17
hypocenterC17#24299
LCSG ▷ C22×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#476

Complements

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

NH ≅ G/Ntype
1. C2×C4⋊Q8×D17C2semidirect
2. C2×#11763099C2semidirect
4. #14530115C2semidirect
5. #14529918C2semidirect
6. #14529733C2semidirect
7. #14529731C2semidirect
9. #14528975C2semidirect
10. #14528761C2semidirect
11. C2×C17×#476C2semidirect
62. C17×C4⋊Q8D4semidirect
75. #10587624Q8semidirect
99. #10587555D4semidirect
120. C2×D4×C17C2×Q8semidirect
181. C4⋊Dic17C2×Q8semidirect
265. C2×#476D17semidirect
294. C2×D17#476semidirect
375. C4⋊Q8C22⋊D17semidirect
416. C17#24299semidirect
437. C2×D4Q8×D17semidirect

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×#117630992
C4×#105876242
#145301152
#145299182
#145297332
#145297312
#145290982
#145289752
#145287612
C2×C17×#4762
#2429917