Finite Group Databasebeta

← #17036118

Subgroups — #17036118

Order 4352.

1994 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763320C211yesmaximal, characteristic
2C2×#11762782C212yesmaximal, complemented
3#14531167C211yesmaximal, characteristic, complemented
4#14529242C214yesmaximal, complemented
5#14529237C214yesmaximal, complemented
6#14528516C212yesmaximal, complemented
7C22×C17×#117C211yesmaximal, characteristic, complemented
8C22×#63252C2211yescharacteristic
9#11763320—22no—
10#11763320—22no—
11#11763320—21no—
12#11763320—21no—
13#11763320—21no—
14#11763320—21no—
15C2×#10587615C2212yes—
16C2×#10587610C412yescomplemented
17C2×#10587616C412yescomplemented
18C2×#10587639C2212yes—
19C2×C4×C22⋊D17C414yescomplemented
20C2×#10587612C2212yes—
21C2×#10587612C2211yescharacteristic
22#11762782—28no—
23C2×#10587477C2218yes—
24#11762672C2212yes—
25#11762669—22no—
26#11762665C2212yes—
27C4×C22⋊Dic17—22no—
28#11762575C2218yes—
29C24×C4×C17C2211yescharacteristic
30C2×C17×#117—28no—
31C2×C17×#117—21no—
32C2×C17×#117—21no—
33C2×C17×#117C2212yes—
34C2×C17×#117C2212yes—
35C22×C4⋊C4×C17—21no—
36C22×C22⋊C4×C17C2212yes—
37C22×C42×C17—21no—
38C25×C17C2311yescharacteristic
39C23×C4×C17—24no—
40C23×C4×C17—24no—
41C23×C4×C17—22no—
42C23×C4×C17C2×C412yes—
43C23×C4×C17C2×C412yes—
44C23×C4×C17D412yes—
45C23×C4×C17D412yes—
46C23×C4×C17D411yescharacteristic
47C23×C4×C17D411yescharacteristic
48C23×C4×C17D411yescharacteristic
49C23×C4×C17D411yescharacteristic
50C23×C4×C17C2311yescharacteristic
51C23×C4×C17C2311yescharacteristic
52C22×C22⋊D17C2×C414yes—
53C22×C22⋊D17C2312yes—
54C2×#63252—24no—
55C2×#63252—21no—
56C2×#63252—21no—
57C2×#63252—21no—
58C2×#63252—21no—
59C2×#63252—24no—
60C22×D68C2×C411yescharacteristic, complemented
61C22×C4×D17C2×C412yescomplemented
62C22×Dic34C2×C411yescharacteristic, complemented
63C17×#117—28no—
64C17×#117—28no—
65C17×#117—24no—
66C17×#117—28no—
67C17×#117D418yescomplemented
68C2×C4⋊C4×C17—28no—
69C2×C4⋊C4×C17—22no—
70C2×C4⋊C4×C17—22no—
71C2×C22⋊C4×C17—22no—
72C2×C22⋊C4×C17—28no—
73C2×C22⋊C4×C17C2314yes—
74C2×C42×C17—28no—
75C2×C42×C17—22no—
76C2×C42×C17—22no—
77#10587639—24no—
78#10587639—22no—
79#10587639—22no—
80C2×C22⋊Dic17—24no—
81C2×C22⋊Dic17C2×C414yes—
82C2×C22⋊Dic17C2314yes—
83C2×C22⋊Dic17C2312yes—
84#10587616—22no—
85#10587616—22no—
86#10587616—22no—
87#10587616—22no—
88#10587615—24no—
89#10587615—22no—
90#10587615—22no—
91C4×C22⋊D17—24no—
92C4×C22⋊D17—24no—
93C4×C22⋊D17—24no—
94C4×C22⋊D17—24no—
95C2×#63227C2×C414yescomplemented
96#10587612—21no—
97#10587612—21no—
98#10587612—21no—
99#10587612—21no—
100#10587612—24no—
101#10587612—24no—
102C2×C4⋊Dic17—22no—
103C2×C4⋊Dic17C2×C412yescomplemented
104#10587610—22no—
105#10587610—22no—
106#10587610—22no—
107#10587610—22no—
108C2×#63225C2×C414yescomplemented
109C2×C4×Dic17—22no—
110C2×C4×Dic17C2×C412yescomplemented
111#10587502—24no—
112#10587477—216no—
113C24×C17—22no—
114C24×C17—22no—
115C24×C17—44no—
116C24×C17C22×C412yes—
117C24×C17C2×D412yes—
118C24×C17C2×D411yescharacteristic
119C24×C17C2×D411yescharacteristic
120C24×C17C2411yescharacteristic
121C23×D17C22×C412yes—
122C22×C4×C17—22no—
123C22×C4×C17—22no—
124C22×C4×C17—28no—
125C22×C4×C17—28no—
126C22×C4×C17—22no—
127C22×C4×C17—22no—
128C22×C4×C17—22no—
129C22×C4×C17—22no—
130C22×C4×C17—28no—
131C22×C4×C17—28no—
132C22×C4×C17—22no—
133C22×C4×C17—22no—
134C22×C4×C17—22no—
135C22×C4×C17—22no—
136C22×C4×C17—28no—
137C22×C4×C17—24no—
138C22×C4×C17—48no—
139C22×C4×C17C22⋊C412yes—
140C22×C4×C17C22⋊C412yes—
141C22×C4×C17C22⋊C412yes—
142C22×C4×C17C22⋊C412yes—
143C22×C4×C17C22⋊C412yes—
144C22×C4×C17C22⋊C412yes—
145C22×C4×C17C22⋊C412yes—
146C22×C4×C17C22⋊C412yes—
147C22×C4×C17C22×C412yes—
148C22×C4×C17C22×C411yescharacteristic
149C22×C4×C17C22×C411yescharacteristic
150C22×C4×C17C2×D412yes—
151C22×C4×C17C2×D411yescharacteristic
152C22×C4×C17C2×D411yescharacteristic
153C22×C4×C17C2×D411yescharacteristic
154C22×C4×C17C2×D411yescharacteristic
155C22×C4×C17C2×D411yescharacteristic
156C22×C4×C17C2×D411yescharacteristic
157C22×C4×C17C2×D414yes—
158C22×C4×C17#4114yes—
159C2×C22⋊D17—24no—
160C2×C22⋊D17—24no—
161C2×C22⋊D17—24no—
162C2×C22⋊D17—22no—
163C2×C22⋊D17—22no—
164C2×C22⋊D17—24no—
165C2×C22⋊D17—48no—
166C22×Dic17—24no—
167C22×Dic17C22×C412yes—
168C22×Dic17C22×C414yes—
169#63252—42no—
170#63252—42no—
171#63252—44no—
172#63252—44no—
173#63252—42no—
174#63252—42no—
175C2×D68—21no—
176C2×D68—21no—
177C2×D68—24no—
178C2×C4×D17—22no—
179C2×C4×D17—22no—
180C2×C4×D17—28no—
181C2×Dic34—21no—
182C2×Dic34—21no—
183C2×Dic34—24no—
184C4⋊C4×C17—28no—
185C4⋊C4×C17—28no—
186C22⋊C4×C17—28no—
187C22⋊C4×C17—24no—
188C22⋊C4×C17C2×D418yes—
189C42×C17—28no—
190C42×C17—28no—
191C22⋊Dic17—24no—
192C22⋊Dic17—24no—
193C22⋊Dic17—22no—
194C22⋊Dic17—22no—
195C22⋊Dic17—24no—
196C22⋊Dic17—24no—
197C22⋊Dic17—48no—
198#63227—24no—
199#63227—24no—
200C4⋊Dic17—22no—
201C4⋊Dic17—22no—
202C4⋊Dic17—44no—
203#63225—24no—
204#63225—24no—
205C4×Dic17—22no—
206C4×Dic17—22no—
207C4×Dic17—44no—
208#20983—171nomaximal, Sylow
209C23×C17—21no—
210C23×C17—21no—
211C23×C17—24no—
212C23×C17—24no—
213C23×C17—21no—
214C23×C17—24no—
215C23×C17—21no—
216C23×C17—24no—
217C23×C17—24no—
218C23×C17—42no—
219C23×C17—42no—
220C23×C17—42no—
221C23×C17—42no—
222C23×C17—48no—
223C23×C17—48no—
224C23×C17C2×C22⋊C412yes—
225C23×C17C2×C22⋊C412yes—
226C23×C17C23×C411yescharacteristic
227C23×C17C22×D411yescharacteristic
228C23×C17C22×D411yescharacteristic
229C23×C17C22×D412yes—
230C23×C17C2×#4112yes—
231C22×D17—22no—
232C22×D17—24no—
233C22×D17—44no—
234C2×C4×C17—24no—
235C2×C4×C17—21no—
236C2×C4×C17—21no—
237C2×C4×C17—24no—
238C2×C4×C17—21no—
239C2×C4×C17—21no—
240C2×C4×C17—24no—
241C2×C4×C17—24no—
242C2×C4×C17—24no—
243C2×C4×C17—24no—
244C2×C4×C17—24no—
245C2×C4×C17—24no—
246C2×C4×C17—24no—
247C2×C4×C17—24no—
248C2×C4×C17—28no—
249C2×C4×C17—416no—
250C2×C4×C17—48no—
251C2×C4×C17C2×C22⋊C412yes—
252C2×C4×C17C2×C22⋊C412yes—
253C2×C4×C17C2×C22⋊C411yescharacteristic
254C2×C4×C17C2×C22⋊C411yescharacteristic
255C2×C4×C17C2×C22⋊C411yescharacteristic
256C2×C4×C17C2×C22⋊C411yescharacteristic
257C2×C4×C17C4×D414yes—
258C2×C4×C17C4×D414yes—
259C2×C4×C17#12012yes—
260C2×C4×C17#12012yes—
261C2×C4×C17#12114yes—
262C2×C4×C17#12114yes—
263C2×C4×C17#12312yes—
264C2×C4×C17#12312yes—
265C22⋊D17—48no—
266C22⋊D17—42no—
267C22⋊D17—44no—
268C22⋊D17—42no—
269C22⋊D17—48no—
270C2×Dic17—22no—
271C2×Dic17—24no—
272C2×Dic17—24no—
273C2×Dic17—44no—
274C2×Dic17—48no—
275C2×Dic17—44no—
276D68—42no—
277D68—42no—
278C4×D17—44no—
279C4×D17—44no—
280Dic34—42no—
281Dic34—42no—
282C2×#525—171no—
283C22×#117D1711yescharacteristic, complemented
284C2×#410—172no—
285#2280—171no—
286#1899—174no—
287#1898—174no—
288#1740—172no—
289C22×C17—24no—
290C22×C17—24no—
291C22×C17—22no—
292C22×C17—22no—
293C22×C17—22no—
294C22×C17—22no—
295C22×C17—22no—
296C22×C17—22no—
297C22×C17—22no—
298C22×C17—22no—
299C22×C17—42no—
300C22×C17—42no—
301C22×C17—48no—
302C22×C17—48no—
303C22×C17—42no—
304C22×C17—42no—
305C22×C17#41014yescomplemented
306C22×C17C22×C22⋊C411yescharacteristic
307C22×C17C2×C4×D412yes—
308C22×C17C2×#12011yescharacteristic
309C22×C17C2×#12112yes—
310C22×C17C2×#12311yescharacteristic
311C2×D17—44no—
312C2×D17—42no—
313C2×D17—84no—
314C4×C17—22no—
315C4×C17—22no—
316C4×C17—48no—
317C4×C17#38612yes—
318C4×C17#38612yes—
319C4×C17#38612yes—
320C4×C17#38612yes—
321Dic17—44no—
322Dic17—42no—
323Dic17—84no—
324C22×#41—171no—
325C24×C4C2×D1711yescharacteristic
326#525—342no—
327#525—342no—
328#525—341no—
329#525—341no—
330#525—341no—
331#525—341no—
332C2×#123—172no—
333C2×C22⋊Q8—172no—
334C2×#121—172no—
335C2×#120—172no—
336C2×C4×D4—174no—
337C2×#117—21no—
338C2×#117—21no—
339C2×#117—28no—
340C2×#117—171no—
341C2×#117—172no—
342C2×#117C2×D1712yes—
343C2×#117C2×D1712yes—
344C22×C4⋊C4—21no—
345C22×C22⋊C4C2×D1712yes—
346C22×C42—21no—
347#410—348no—
348C2×#99—178no—
349#381—172no—
350#380—342no—
351#379—172no—
352C4×C22⋊C4—342no—
353#342—178no—
354C2×C17—22no—
355C2×C17—21no—
356C2×C17—22no—
357C2×C17—21no—
358C2×C17—24no—
359C2×C17—42no—
360C2×C17C2×#38611yescharacteristic
361C2×C17C2×#41012yes—
362D17—82no—
363C25C22×D1711yescharacteristic
364C2×#41—341no—
365C2×#41—341no—
366C2×#41—344no—
367C2×#41—341no—
368C2×#41—341no—
369C2×#41—344no—
370C22×Q8—171no—
371C22×D4—172no—
372C22×D4—174no—
373C22×D4—171no—
374C23×C4—24no—
375C23×C4—24no—
376C23×C4—22no—
377C23×C4—172no—
378C23×C4C4×D1712yes—
379C23×C4C4×D1712yes—
380C23×C4D6812yes—
381C23×C4D6812yes—
382C23×C4C22⋊D1711yescharacteristic
383C23×C4C22⋊D1711yescharacteristic
384C23×C4C22⋊D1711yescharacteristic
385C23×C4C22⋊D1711yescharacteristic
386C23×C4C22×D1711yescharacteristic
387C23×C4C22×D1711yescharacteristic
388#123—344no—
389#123—342no—
390#123—342no—
391C22⋊Q8—342no—
392C22⋊Q8—342no—
393C22⋊Q8—342no—
394C22⋊Q8—342no—
395#121—342no—
396#121—342no—
397#121—342no—
398#121—342no—
399#120—344no—
400#120—342no—
401#120—342no—
402C4×D4—344no—
403C4×D4—344no—
404C4×D4—344no—
405C4×D4—344no—
406#117—28no—
407#117—28no—
408#117—24no—
409#117—28no—
410#117—341no—
411#117—341no—
412#117—341no—
413#117—341no—
414#117—344no—
415#117—344no—
416#117C22⋊D1718yescomplemented
417C2×C4⋊C4—28no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—172no—
421C2×C4⋊C4—174no—
422C2×C4⋊C4—342no—
423C2×C22⋊C4—22no—
424C2×C22⋊C4—28no—
425C2×C22⋊C4—174no—
426C2×C22⋊C4—172no—
427C2×C22⋊C4—174no—
428C2×C22⋊C4—174no—
429C2×C22⋊C4—344no—
430C2×C22⋊C4C22×D1714yes—
431C2×C42—28no—
432C2×C42—22no—
433C2×C42—22no—
434C2×C42—172no—
435C2×C42—342no—
436#99—3416no—
437#95—344no—
438C17#2098311yescharacteristic, complemented, Sylow
439C24—22no—
440C24—22no—
441C24—44no—
442C24—172no—
443C24C2×C4×D1712yes—
444C24C2×D6812yes—
445C24C2×C22⋊D1711yescharacteristic
446C24C2×C22⋊D1711yescharacteristic
447C24C23×D1711yescharacteristic
448#41—682no—
449#41—682no—
450#41—684no—
451#41—684no—
452#41—682no—
453#41—682no—
454C2×Q8—341no—
455C2×Q8—341no—
456C2×Q8—344no—
457C2×D4—342no—
458C2×D4—344no—
459C2×D4—344no—
460C2×D4—342no—
461C2×D4—344no—
462C2×D4—344no—
463C2×D4—341no—
464C2×D4—341no—
465C2×D4—344no—
466C2×D4—688no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—28no—
470C22×C4—28no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—28no—
476C22×C4—28no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—28no—
482C22×C4—24no—
483C22×C4—48no—
484C22×C4—172no—
485C22×C4—174no—
486C22×C4—342no—
487C22×C4—342no—
488C22×C4—348no—
489C22×C4—344no—
490C22×C4#6322712yes—
491C22×C4#6322712yes—
492C22×C4#6322712yes—
493C22×C4#6322712yes—
494C22×C4#6322712yes—
495C22×C4#6322712yes—
496C22×C4#6322712yes—
497C22×C4#6322712yes—
498C22×C4C2×C4×D1712yes—
499C22×C4C2×C4×D1711yescharacteristic
500C22×C4C2×C4×D1711yescharacteristic
501C22×C4C2×D6812yes—
502C22×C4C2×D6811yescharacteristic
503C22×C4C2×D6811yescharacteristic
504C22×C4#6325214yes—
505C22×C4C2×C22⋊D1711yescharacteristic
506C22×C4C2×C22⋊D1711yescharacteristic
507C22×C4C2×C22⋊D1711yescharacteristic
508C22×C4C2×C22⋊D1711yescharacteristic
509C22×C4C2×C22⋊D1714yes—
510C4⋊C4—28no—
511C4⋊C4—28no—
512C4⋊C4—342no—
513C4⋊C4—342no—
514C4⋊C4—344no—
515C4⋊C4—344no—
516C4⋊C4—684no—
517C22⋊C4—28no—
518C22⋊C4—24no—
519C22⋊C4—342no—
520C22⋊C4—342no—
521C22⋊C4—344no—
522C22⋊C4—344no—
523C22⋊C4—344no—
524C22⋊C4—344no—
525C22⋊C4—344no—
526C22⋊C4—344no—
527C22⋊C4—688no—
528C22⋊C4C2×C22⋊D1718yes—
529C42—28no—
530C42—28no—
531C42—342no—
532C42—342no—
533C42—684no—
534C23—24no—
535C23—21no—
536C23—21no—
537C23—24no—
538C23—24no—
539C23—24no—
540C23—21no—
541C23—24no—
542C23—21no—
543C23—42no—
544C23—42no—
545C23—42no—
546C23—42no—
547C23—48no—
548C23—48no—
549C23—342no—
550C23—344no—
551C23—684no—
552C23C2×#6322712yes—
553C23C2×#6322712yes—
554C23C22×C4×D1711yescharacteristic
555C23C22×D6811yescharacteristic
556C23C2×#6325212yes—
557C23C22×C22⋊D1711yescharacteristic
558C23C22×C22⋊D1712yes—
559Q8—682no—
560Q8—682no—
561D4—688no—
562D4—688no—
563D4—682no—
564D4—684no—
565D4—682no—
566D4—682no—
567D4—682no—
568C2×C4—24no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—24no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—24no—
575C2×C4—24no—
576C2×C4—24no—
577C2×C4—24no—
578C2×C4—24no—
579C2×C4—24no—
580C2×C4—24no—
581C2×C4—24no—
582C2×C4—28no—
583C2×C4—416no—
584C2×C4—48no—
585C2×C4—344no—
586C2×C4—342no—
587C2×C4—344no—
588C2×C4—684no—
589C2×C4—684no—
590C2×C4—684no—
591C2×C4—688no—
592C2×C4—684no—
593C2×C4C2×#6322712yes—
594C2×C4C2×#6322712yes—
595C2×C4C2×#6322711yescharacteristic
596C2×C4C2×#6322711yescharacteristic
597C2×C4C2×#6322711yescharacteristic
598C2×C4C2×#6322711yescharacteristic
599C2×C4C4×C22⋊D1714yes—
600C2×C4C4×C22⋊D1714yes—
601C2×C4#1058761512yes—
602C2×C4#1058761512yes—
603C2×C4#1058761614yes—
604C2×C4#1058761614yes—
605C2×C4#1058763912yes—
606C2×C4#1058763912yes—
607C22—24no—
608C22—24no—
609C22—22no—
610C22—22no—
611C22—22no—
612C22—22no—
613C22—22no—
614C22—22no—
615C22—22no—
616C22—22no—
617C22—42no—
618C22—42no—
619C22—48no—
620C22—48no—
621C22—42no—
622C22—42no—
623C22—684no—
624C22—682no—
625C22—1364no—
626C22#1176278214yescomplemented
627C22C22×#6322711yescharacteristic
628C22C2×C4×C22⋊D1712yes—
629C22C2×#1058763911yescharacteristic
630C22C2×#1058761612yes—
631C22C2×#1058761511yescharacteristic
632C4—22no—
633C4—22no—
634C4—48no—
635C4—684no—
636C4—682no—
637C4—1364no—
638C4#1176268812yes—
639C4#1176268812yes—
640C4#1176268812yes—
641C4#1176268812yes—
642C2—21no—
643C2—22no—
644C2—24no—
645C2—21no—
646C2—22no—
647C2—42no—
648C2—1362no—
649C2C2×#1176268811yescharacteristic
650C2C2×#1176278212yes—
subgroupG/H
centerC2×C4C2×#63227
commutatorC23×C17C23×C4
FrattiniC24C23×D17
FittingC22×C17×#117C2
socleC22×C17C22×C22⋊C4
prime radicalC2×#11763320C2
cosocleC24×C17C24
hypercenterC22×#117D17
hypocenterC17#20983
LCSG ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C24×C4 ◁ C22×#117

Complements

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

NH ≅ G/Ntype
2. C2×#11762782C2semidirect
3. #14531167C2semidirect
4. #14529242C2semidirect
5. #14529237C2semidirect
6. #14528516C2semidirect
7. C22×C17×#117C2semidirect
16. C2×#10587610C4semidirect
17. C2×#10587616C4semidirect
19. C2×C4×C22⋊D17C4semidirect
60. C22×D68C2×C4semidirect
61. C22×C4×D17C2×C4semidirect
62. C22×Dic34C2×C4semidirect
67. C17×#117D4semidirect
95. C2×#63227C2×C4semidirect
103. C2×C4⋊Dic17C2×C4semidirect
108. C2×#63225C2×C4semidirect
110. C2×C4×Dic17C2×C4semidirect
283. C22×#117D17semidirect
305. C22×C17#410semidirect
416. #117C22⋊D17semidirect
438. C17#20983semidirect
626. C22#11762782semidirect

Maximal subgroups

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

subgroupindex
C2×#117633202
C2×#117627822
#145311672
#145292422
#145292372
#145285162
C22×C17×#1172
#2098317