Finite Group Databasebeta

← #17045452

Subgroups — #17045452

Order 4352.

1308 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762943C211yesmaximal, characteristic
2#14531290C211yesmaximal, characteristic, complemented
3C2×#11762712C211yesmaximal, characteristic, complemented
4#14529647C212yesmaximal, complemented
5#14529464C212yesmaximal, complemented
6#14529407C212yesmaximal, complemented
7#14529129C212yesmaximal, complemented
8#14529099C211yesmaximal, characteristic, complemented
9#14528971C211yesmaximal, characteristic, complemented
10C22⋊C8×Dic17C211yesmaximal, characteristic, complemented
11C17×#1786C211yesmaximal, characteristic, complemented
12C22×#63228C2212yes—
13C2×#10587616C2211yescharacteristic
14C2×#10587579C2211yescharacteristic, complemented
15C2×#10587567—21no—
16C22×C4⋊Dic17C2211yescharacteristic
17C22×C22⋊Dic17—21no—
18C22×C22⋊Dic17—21no—
19C22×C4×Dic17C2211yescharacteristic
20#11762943C418yescomplemented
21C2×#10587478C2212yescomplemented
22C2×#10587492C2212yescomplemented
23C2×#10587503C2212yes—
24C2×C22⋊#3622C2211yescharacteristic
25C2×C8×Dic17C2212yescomplemented
26#11762712—21no—
27#11762712—21no—
28#11762712C2212yes—
29#11762712C2212yes—
30#11762710C2211yescharacteristic, complemented
31#11762705C2211yescharacteristic, complemented
32#11762698—21no—
33#11762686—21no—
34C4⋊C4×Dic17C2211yescharacteristic, complemented
35#11762656—21no—
36#11762572C2212yescomplemented
37#11762571C2212yescomplemented
38#11762563C2212yescomplemented
39C23×D4×C17C2211yescharacteristic
40C2×C17×#102C2212yes—
41C2×C17×#102C2212yes—
42C2×C17×C22⋊C8C2211yescharacteristic
43C17×#380C2211yescharacteristic
44C25×C17—21no—
45C22×D4×C17—21no—
46C22×D4×C17—22no—
47C22×D4×C17—42no—
48C22×D4×C17—42no—
49C22×D4×C17C2×C414yescomplemented
50C22×D4×C17C2312yes—
51C23×C4×C17C2311yescharacteristic
52C22×C22⋊D17—21no—
53C23×Dic17—21no—
54C23×Dic17D411yescharacteristic
55C23×Dic17D411yescharacteristic
56C22×D68C2311yescharacteristic
57C22×C4×D17—21no—
58C22×C8×C17C2312yes—
59C2×C4⋊C4×C17C2311yescharacteristic
60C2×C4⋊C4×C17C2311yescharacteristic
61C2×C22⋊C4×C17—21no—
62C2×C22⋊Dic17—22no—
63C2×C22⋊Dic17—22no—
64C2×C22⋊Dic17—22no—
65C2×C22⋊Dic17—22no—
66C2×C22⋊Dic17—44no—
67C2×C22⋊Dic17—44no—
68C2×#63228—42no—
69C2×#63228—42no—
70C2×#63228C2×C418yescomplemented
71#10587616—22no—
72#10587616C2×C414yes—
73C2×#63227—21no—
74C2×#63227—21no—
75C2×#63227—21no—
76C2×#63227—21no—
77C2×C4⋊Dic17—21no—
78C2×C4⋊Dic17—42no—
79C2×C4⋊Dic17C2312yes—
80C2×C4⋊Dic17C2311yescharacteristic
81C2×#63225—21no—
82C2×C4×Dic17—21no—
83C2×C4×Dic17—42no—
84C2×C4×Dic17D411yescharacteristic
85C2×C4×Dic17D411yescharacteristic
86C2×C4×Dic17C2311yescharacteristic
87C2×C4×Dic17C2311yescharacteristic
88C22×#3622C2312yes—
89#10587579—42no—
90#10587567—44no—
91C17×#102—42no—
92C17×#102—42no—
93C17×C22⋊C8—22no—
94C17×#95—21no—
95#10587503C2×C418yescomplemented
96#10587502—21no—
97#10587502—21no—
98C22⋊#3622C2×C414yescomplemented
99#10587492—42no—
100C8×Dic17—42no—
101#10587478—42no—
102C24×C17—24no—
103C24×C17—22no—
104C24×C17—42no—
105C24×C17—42no—
106C24×C17—42no—
107C24×C17—42no—
108C24×C17—42no—
109C24×C17—42no—
110C24×C17C2×D411yescharacteristic
111C23×D17—21no—
112C2×D4×C17—24no—
113C2×D4×C17—22no—
114C2×D4×C17—22no—
115C2×D4×C17—22no—
116C2×D4×C17—22no—
117C2×D4×C17—22no—
118C2×D4×C17—48no—
119C2×D4×C17—42no—
120C2×D4×C17—42no—
121C2×D4×C17—48no—
122C2×D4×C17C22×C414yes—
123C22×C4×C17—22no—
124C22×C4×C17—22no—
125C22×C4×C17—21no—
126C22×C4×C17—21no—
127C22×C4×C17C22×C412yes—
128C22×C4×C17C2×D411yescharacteristic
129C22×C4×C17#4112yes—
130C22×C4×C17C2411yescharacteristic
131C2×C22⋊D17—24no—
132C2×C22⋊D17—42no—
133C2×C22⋊D17—42no—
134C22×Dic17—22no—
135C22×Dic17—21no—
136C22×Dic17—22no—
137C22×Dic17—22no—
138C22×Dic17—41no—
139C22×Dic17—41no—
140C22×Dic17—41no—
141C22×Dic17—42no—
142C22×Dic17—42no—
143C22×Dic17—42no—
144C22×Dic17D814yescomplemented
145C22×Dic17C2×D411yescharacteristic
146C22×Dic17C2×D411yescharacteristic
147C22×Dic17C2×D411yescharacteristic
148C22×Dic17C2×D411yescharacteristic
149C2×D68—22no—
150C2×D68—22no—
151C2×D68—21no—
152C2×D68C22×C412yes—
153C2×C4×D17—42no—
154C2×C4×D17—42no—
155C2×C4×D17—42no—
156C2×C8×C17—22no—
157C2×C8×C17—22no—
158C2×C8×C17—22no—
159C4⋊C4×C17—22no—
160C4⋊C4×C17—22no—
161C22⋊C4×C17—42no—
162C22⋊Dic17—44no—
163C22⋊Dic17—44no—
164C22⋊Dic17—44no—
165C22⋊Dic17—44no—
166#63228—48no—
167#63227—24no—
168#63227—42no—
169#63227—42no—
170#63227—42no—
171C4⋊Dic17—21no—
172C4⋊Dic17—22no—
173C4⋊Dic17—22no—
174C4⋊Dic17—42no—
175C4⋊Dic17C22×C412yes—
176#63225—42no—
177C4×Dic17—22no—
178C4×Dic17—22no—
179C4×Dic17—41no—
180C4×Dic17—41no—
181C4×Dic17—42no—
182C2×#3622—22no—
183C2×#3622—22no—
184C2×#3622C22×C414yes—
185#22040—171nomaximal, Sylow
186C23×C17—21no—
187C23×C17—21no—
188C23×C17—21no—
189C23×C17—21no—
190C23×C17—24no—
191C23×C17—48no—
192C23×C17—48no—
193C23×C17—42no—
194C23×C17—42no—
195C23×C17—42no—
196C23×C17—42no—
197C23×C17—42no—
198C23×C17—42no—
199C23×C17—48no—
200C23×C17—84no—
201C23×C17—84no—
202C23×C17—84no—
203C23×C17—84no—
204C23×C17C4×D412yes—
205C23×C17C2×D812yes—
206C23×C17#13512yes—
207C23×C17C22×D411yescharacteristic
208C22×D17—22no—
209C22×D17—41no—
210C22×D17—41no—
211C22×D17—41no—
212C22×D17—41no—
213C22×D17—41no—
214C22×D17—41no—
215D4×C17—24no—
216D4×C17—24no—
217D4×C17—48no—
218D4×C17—42no—
219D4×C17—42no—
220C2×C4×C17—21no—
221C2×C4×C17—21no—
222C2×C4×C17—24no—
223C2×C4×C17—24no—
224C2×C4×C17—41no—
225C2×C4×C17—41no—
226C2×C4×C17—41no—
227C2×C4×C17—41no—
228C2×C4×C17—41no—
229C2×C4×C17—41no—
230C2×C4×C17C4×D412yes—
231C2×C4×C17C23×C411yescharacteristic
232C2×C4×C17C2×#4111yescharacteristic
233C2×C4×C17H(5,𝔽2)12yes—
234C2×C4×C17H(5,𝔽2)12yes—
235C22⋊D17—48no—
236C2×Dic17—21no—
237C2×Dic17—21no—
238C2×Dic17—21no—
239C2×Dic17—21no—
240C2×Dic17—21no—
241C2×Dic17—21no—
242C2×Dic17—22no—
243C2×Dic17—21no—
244C2×Dic17—21no—
245C2×Dic17—21no—
246C2×Dic17—44no—
247C2×Dic17—44no—
248C2×Dic17—41no—
249C2×Dic17—41no—
250C2×Dic17—42no—
251C2×Dic17—42no—
252C2×Dic17—42no—
253C2×Dic17—84no—
254C2×Dic17C2×D812yes—
255C2×Dic17C2×D812yes—
256C2×Dic17AGL(1,ℤ/8)12yes—
257D68—24no—
258D68—42no—
259C4×D17—84no—
260C8×C17—42no—
261#3622—24no—
262C2×#447—171no—
263C4×#121—171no—
264C2×#390—171no—
265#1970—172no—
266#1934—172no—
267#1925—172no—
268#1879—172no—
269#1874—171no—
270#1852—171no—
271#1786D1711yescharacteristic, complemented
272C4×C22⋊C8—171no—
273C22×C17—22no—
274C22×C17—22no—
275C22×C17—22no—
276C22×C17—22no—
277C22×C17—22no—
278C22×C17—22no—
279C22×C17—44no—
280C22×C17—44no—
281C22×C17—44no—
282C22×C17—816no—
283C22×C17—82no—
284C22×C17—82no—
285C22×C17—82no—
286C22×C17—82no—
287C22×C17C4×D814yes—
288C22×C17C2×C4×D411yescharacteristic
289C22×C17#53411yescharacteristic
290C22×C17#53511yescharacteristic
291C22×C17C22×D811yescharacteristic
292C22×C17C2×#13511yescharacteristic
293C22×C17C2×AGL(1,ℤ/8)11yescharacteristic
294C22×C17#57511yescharacteristic
295C2×D17—42no—
296C2×D17—42no—
297C2×D17—42no—
298C2×D17—81no—
299C2×D17—81no—
300C2×D17—81no—
301C2×D17—81no—
302C4×C17—22no—
303C4×C17—81no—
304C4×C17—81no—
305C4×C17#51812yes—
306C4×C17#53812yes—
307Dic17—22no—
308Dic17—22no—
309Dic17—22no—
310Dic17—41no—
311Dic17—42no—
312Dic17—82no—
313C23×D4C2×D1711yescharacteristic
314C22×D8—172no—
315C2×#121—171no—
316C2×C4×D4—171no—
317C2×C4×D4—341no—
318C22×C4⋊C4—171no—
319C22×C22⋊C4—341no—
320C22×C22⋊C4—341no—
321C22×C42—171no—
322#447—178no—
323C2×#107—172no—
324C2×#102—172no—
325C2×#102—172no—
326C2×#102C2×D1712yes—
327C2×#102C2×D1712yes—
328C2×C22⋊C8—171no—
329C2×C22⋊C8C2×D1711yescharacteristic
330C2×C4×C8—172no—
331#390—172no—
332#390—172no—
333#390—171no—
334#390—341no—
335#390—341no—
336#389—171no—
337#388—341no—
338#386—341no—
339#380C2×D1711yescharacteristic
340C4×C4⋊C4—171no—
341C4×C22⋊C4—341no—
342#340—172no—
343#340—172no—
344#336—172no—
345C2×C17—24no—
346C2×C17—84no—
347C2×C17#232111yescharacteristic
348C2×C17C2×C4×D811yescharacteristic
349C2×C17C4×AGL(1,ℤ/8)11yescharacteristic
350C2×C17#318611yescharacteristic
351C2×C17#318811yescharacteristic
352C2×C17#320511yescharacteristic
353C2×C17#321111yescharacteristic
354D17—82no—
355C25—21no—
356C22×D4—21no—
357C22×D4—22no—
358C22×D4—42no—
359C22×D4—42no—
360C22×D4—171no—
361C22×D4—341no—
362C22×D4C4×D1714yescomplemented
363C22×D4C22×D1712yes—
364C23×C4—171no—
365C23×C4—171no—
366C23×C4—341no—
367C23×C4—341no—
368C23×C4C22×D1711yescharacteristic
369C2×D8—178no—
370C2×D8—682no—
371C2×D8—682no—
372C22×C8—172no—
373C22×C8C22×D1712yes—
374#121—174no—
375#121—342no—
376C4×D4—682no—
377C4×D4—684no—
378C2×C4⋊C4—171no—
379C2×C4⋊C4—172no—
380C2×C4⋊C4—341no—
381C2×C4⋊C4—341no—
382C2×C4⋊C4—682no—
383C2×C4⋊C4C22×D1711yescharacteristic
384C2×C4⋊C4C22×D1711yescharacteristic
385C2×C22⋊C4—21no—
386C2×C22⋊C4—341no—
387C2×C22⋊C4—341no—
388C2×C22⋊C4—341no—
389C2×C22⋊C4—341no—
390C2×C22⋊C4—342no—
391C2×C22⋊C4—342no—
392C2×C22⋊C4—342no—
393C2×C22⋊C4—342no—
394C2×C22⋊C4—684no—
395C2×C22⋊C4—684no—
396C2×C42—171no—
397C2×C42—171no—
398C2×C42—171no—
399C2×C42—171no—
400C2×C42—341no—
401C2×C42—682no—
402#107—682no—
403#102—42no—
404#102—42no—
405#102—178no—
406#102—682no—
407C22⋊C8—22no—
408C22⋊C8—174no—
409C4×C8—682no—
410#95—21no—
411#95—341no—
412#95—341no—
413C17#2204011yescharacteristic, complemented, Sylow
414C24—22no—
415C24—24no—
416C24—42no—
417C24—42no—
418C24—42no—
419C24—42no—
420C24—42no—
421C24—42no—
422C24—341no—
423C24D4×D1711yescharacteristic
424C2×D4—22no—
425C2×D4—22no—
426C2×D4—22no—
427C2×D4—22no—
428C2×D4—22no—
429C2×D4—24no—
430C2×D4—48no—
431C2×D4—42no—
432C2×D4—42no—
433C2×D4—48no—
434C2×D4—172no—
435C2×D4—344no—
436C2×D4—341no—
437C2×D4—342no—
438C2×D4—342no—
439C2×D4—682no—
440C2×D4—682no—
441C2×D4C2×C4×D1714yes—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—171no—
447C22×C4—171no—
448C22×C4—171no—
449C22×C4—174no—
450C22×C4—171no—
451C22×C4—342no—
452C22×C4—341no—
453C22×C4—342no—
454C22×C4—342no—
455C22×C4—682no—
456C22×C4—682no—
457C22×C4—682no—
458C22×C4—681no—
459C22×C4—681no—
460C22×C4—681no—
461C22×C4—682no—
462C22×C4—682no—
463C22×C4—682no—
464C22×C4C2×C4×D1712yes—
465C22×C4D4×D1711yescharacteristic
466C22×C4#6325412yes—
467C22×C4C23×D1711yescharacteristic
468D8—688no—
469C2×C8—22no—
470C2×C8—22no—
471C2×C8—22no—
472C2×C8—174no—
473C2×C8—342no—
474C2×C8—342no—
475C4⋊C4—22no—
476C4⋊C4—22no—
477C4⋊C4—172no—
478C4⋊C4—341no—
479C4⋊C4—342no—
480C4⋊C4—342no—
481C4⋊C4—682no—
482C4⋊C4—682no—
483C22⋊C4—42no—
484C22⋊C4—344no—
485C22⋊C4—682no—
486C22⋊C4—682no—
487C22⋊C4—682no—
488C22⋊C4—684no—
489C22⋊C4—684no—
490C22⋊C4—684no—
491C22⋊C4—684no—
492C42—342no—
493C42—342no—
494C42—681no—
495C42—681no—
496C42—682no—
497C23—21no—
498C23—21no—
499C23—21no—
500C23—21no—
501C23—24no—
502C23—48no—
503C23—48no—
504C23—42no—
505C23—42no—
506C23—42no—
507C23—42no—
508C23—42no—
509C23—42no—
510C23—48no—
511C23—84no—
512C23—84no—
513C23—84no—
514C23—84no—
515C23—342no—
516C23—681no—
517C23—681no—
518C23—681no—
519C23—681no—
520C23—681no—
521C23—681no—
522C23#1058756712yes—
523C23D8×D1712yes—
524C23#1058760212yes—
525C23C2×D4×D1711yescharacteristic
526D4—24no—
527D4—24no—
528D4—48no—
529D4—42no—
530D4—42no—
531D4—344no—
532D4—688no—
533D4—682no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—24no—
537C2×C4—24no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—172no—
545C2×C4—172no—
546C2×C4—172no—
547C2×C4—341no—
548C2×C4—341no—
549C2×C4—341no—
550C2×C4—341no—
551C2×C4—341no—
552C2×C4—341no—
553C2×C4—342no—
554C2×C4—341no—
555C2×C4—341no—
556C2×C4—341no—
557C2×C4—684no—
558C2×C4—684no—
559C2×C4—681no—
560C2×C4—681no—
561C2×C4—682no—
562C2×C4—682no—
563C2×C4—682no—
564C2×C4—1364no—
565C2×C4—1364no—
566C2×C4#1058756712yes—
567C2×C4C22×C4×D1711yescharacteristic
568C2×C4C2×#6325411yescharacteristic
569C2×C4#1058769112yes—
570C2×C4#1058769112yes—
571C8—42no—
572C8—344no—
573C22—22no—
574C22—22no—
575C22—22no—
576C22—22no—
577C22—22no—
578C22—22no—
579C22—44no—
580C22—44no—
581C22—44no—
582C22—816no—
583C22—82no—
584C22—82no—
585C22—82no—
586C22—82no—
587C22—682no—
588C22—682no—
589C22—682no—
590C22—1361no—
591C22—1361no—
592C22—1361no—
593C22—1361no—
594C22#1176288914yes—
595C22C2×#1058756711yescharacteristic
596C22#1176336911yescharacteristic
597C22#1176337411yescharacteristic
598C22C2×D8×D1711yescharacteristic
599C22C2×#1058760211yescharacteristic
600C22AGL(1,ℤ/8)×D1711yescharacteristic
601C22#1176360511yescharacteristic
602C4—22no—
603C4—81no—
604C4—81no—
605C4—342no—
606C4—342no—
607C4—342no—
608C4—681no—
609C4—682no—
610C4—1362no—
611C4#1176328212yes—
612C4#1176339412yes—
613C2—24no—
614C2—84no—
615C2—1362no—
616C2#1453143911yescharacteristic
617C2C2×#1176288911yescharacteristic
618C2#1453758811yescharacteristic
619C2#1453953311yescharacteristic
620C2#1453955211yescharacteristic
621C2#1453970011yescharacteristic
622C2#1453975211yescharacteristic
subgroupG/H
centerC23C2×D4×D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC17×#1786C2
socleC23×C17C22×D4
prime radicalC2×#11762943C2
cosocleC22×C4×C17C24
hypercenter#1786D17
hypocenterC17#22040
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1786

Complements

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

NH ≅ G/Ntype
2. #14531290C2semidirect
3. C2×#11762712C2semidirect
4. #14529647C2semidirect
5. #14529464C2semidirect
6. #14529407C2semidirect
7. #14529129C2semidirect
8. #14529099C2semidirect
9. #14528971C2semidirect
10. C22⋊C8×Dic17C2semidirect
11. C17×#1786C2semidirect
14. C2×#10587579C22semidirect
20. #11762943C4semidirect
21. C2×#10587478C22semidirect
22. C2×#10587492C22semidirect
25. C2×C8×Dic17C22semidirect
30. #11762710C22semidirect
31. #11762705C22semidirect
34. C4⋊C4×Dic17C22semidirect
36. #11762572C22semidirect
37. #11762571C22semidirect
38. #11762563C22semidirect
49. C22×D4×C17C2×C4semidirect
70. C2×#63228C2×C4semidirect
95. #10587503C2×C4semidirect
98. C22⋊#3622C2×C4semidirect
144. C22×Dic17D8semidirect
271. #1786D17semidirect
362. C22×D4C4×D17semidirect
413. C17#22040semidirect

Maximal subgroups

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

subgroupindex
C2×#117629432
#145312902
C2×#117627122
#145296472
#145294642
#145294072
#145291292
#145290992
#145289712
C22⋊C8×Dic172
C17×#17862
#2204017