Finite Group Databasebeta

← #17968372

Subgroups — #17968372

Order 4352.

1834 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D17⋊#99C212yesmaximal
2#14545220C212yesmaximal, complemented
3#14544531C212yesmaximal, complemented
4C4×#10587539C212yesmaximal, complemented
5#14544529C212yesmaximal, complemented
6C4×#10587551C212yesmaximal, complemented
7C2×#11763687C212yesmaximal, complemented
8C2×#11763281C211yesmaximal, characteristic
9C22×C22⋊#595C2214yes—
10C2×#10587539C2214yes—
11D17⋊#99C4116yescomplemented
12C2×#10587551C2214yes—
13C22⋊C4×#595—28no—
14C4×C22⋊#595C2214yescomplemented
15C4×C22⋊#595C2214yescomplemented
16#11763687C2214yescomplemented
17#11763687C2214yescomplemented
18C22×D4×D17C2211yescharacteristic
19#11763281—28no—
20C2×C4×D68C2211yescharacteristic
21C2×D4×Dic17C411yescharacteristic, complemented
22C2×#10587579C2211yescharacteristic
23C2×C4×C22⋊D17C411yescharacteristic, complemented
24C2×C4×C22⋊D17C2211yescharacteristic
25C2×#10587567C411yescharacteristic, complemented
26C2×#10587567C2211yescharacteristic
27C2×#10587578C411yescharacteristic, complemented
28C2×#10587558C411yescharacteristic, complemented
29C22×#63227C411yescharacteristic, complemented
30C22×#63227C2211yescharacteristic
31C2×C22⋊C4×D17C411yescharacteristic, complemented
32C2×C22⋊C4×D17C2211yescharacteristic
33C2×C4×D4×C17C411yescharacteristic, complemented
34C24×D17C2×C411yescharacteristic
35C24×D17C2311yescharacteristic
36C23×#595—24no—
37C22×D4×C17C2×C411yescharacteristic
38C23×C4×C17C2×C411yescharacteristic
39C23×C4×C17C2×C411yescharacteristic, complemented
40C22×C22⋊D17C2×C411yescharacteristic
41C22×C22⋊D17C2311yescharacteristic
42C23×Dic17C2×C411yescharacteristic
43C23×Dic17C2×C411yescharacteristic, complemented
44C2×D4×D17—24no—
45C2×D4×D17—24no—
46C2×D4×D17C2×C418yes—
47C22×D68C2311yescharacteristic
48C22×C4×D17C2×C411yescharacteristic
49C22×C4×D17C2×C411yescharacteristic, complemented
50C22×C4×D17C2×C411yescharacteristic, complemented
51C22×C4×D17C2311yescharacteristic
52C22×C4×D17C2311yescharacteristic
53C2×C22⋊#595—24no—
54C2×C22⋊#595—28no—
55C2×C22⋊#595C2×C4116yescomplemented
56C2×C22⋊#595C2318yes—
57C2×C4×#595—24no—
58C2×C4×#595—24no—
59C4×D4×C17—24no—
60C2×C4⋊C4×C17C2×C411yescharacteristic, complemented
61C2×C22⋊C4×C17C2×C411yescharacteristic
62C2×C22⋊C4×C17C2×C411yescharacteristic, complemented
63C2×C42×C17C2×C411yescharacteristic, complemented
64C2×C22⋊Dic17C2×C411yescharacteristic
65C2×C22⋊Dic17C2×C411yescharacteristic, complemented
66D4×Dic17—24no—
67C4×C22⋊D17—24no—
68C4×C22⋊D17—24no—
69C2×#63227—24no—
70C2×#63227—24no—
71C2×#63227C2×C411yescharacteristic
72C2×#63227C2×C411yescharacteristic
73C2×#63227C2×C411yescharacteristic
74C2×#63227C2×C411yescharacteristic
75C2×#63227C2×C411yescharacteristic, complemented
76C2×#63227C2×C411yescharacteristic, complemented
77C2×#63227C2311yescharacteristic
78C2×#63227C2311yescharacteristic
79C2×C4⋊Dic17C2×C411yescharacteristic, complemented
80C2×#63225C2×C411yescharacteristic, complemented
81C2×#63225C2×C411yescharacteristic, complemented
82C2×C4×Dic17C2×C411yescharacteristic, complemented
83C2×C4×Dic17C2×C411yescharacteristic, complemented
84C2×C4×Dic17C2×C411yescharacteristic, complemented
85#10587579—24no—
86#10587578—24no—
87#10587567—24no—
88#10587567—24no—
89C22⋊C4×D17—24no—
90C22⋊C4×D17D418yes—
91C4×D68—24no—
92#10587558—24no—
93#10587551C2×C4116yescomplemented
94(C2×#595)⋊C4—24no—
95(C2×#595)⋊C4—24no—
96#10587539C2×C4116yescomplemented
97C24×C17C22×C411yescharacteristic
98C24×C17C22×C411yescharacteristic
99C23×D17—22no—
100C23×D17—22no—
101C23×D17—81no—
102C23×D17—81no—
103C23×D17—81no—
104C23×D17—81no—
105C23×D17C4214yescomplemented
106C23×D17C22×C411yescharacteristic
107C23×D17C22×C411yescharacteristic
108C23×D17C22×C414yes—
109C23×D17C2×D414yes—
110C23×D17#4114yes—
111C23×D17C2411yescharacteristic
112C22×#595—28no—
113C22×#595—216no—
114C22×#595—84no—
115C22×#595—84no—
116C2×D4×C17—22no—
117C2×D4×C17—22no—
118C2×D4×C17C4214yescomplemented
119C22×C4×C17—22no—
120C22×C4×C17—22no—
121C22×C4×C17—81no—
122C22×C4×C17—81no—
123C22×C4×C17C22×C411yescharacteristic
124C22×C4×C17C22×C411yescharacteristic
125C22×C4×C17C22×C411yescharacteristic
126C22×C4×C17C22×C411yescharacteristic
127C22×C4×C17C22×C411yescharacteristic
128C2×C22⋊D17—22no—
129C2×C22⋊D17—22no—
130C2×C22⋊D17—22no—
131C2×C22⋊D17—22no—
132C2×C22⋊D17C4214yescomplemented
133C2×C22⋊D17C22×C414yes—
134C22×Dic17—22no—
135C22×Dic17—22no—
136C22×Dic17—81no—
137C22×Dic17—81no—
138C22×Dic17C22×C411yescharacteristic
139C22×Dic17C22×C411yescharacteristic
140C22×Dic17C22×C411yescharacteristic
141C22×Dic17C22×C411yescharacteristic
142C22×Dic17C22×C411yescharacteristic
143D4×D17—216no—
144D4×D17—216no—
145C2×D68—22no—
146C2×D68—22no—
147C2×D68C22×C414yes—
148C2×C4×D17—22no—
149C2×C4×D17—22no—
150C2×C4×D17—22no—
151C2×C4×D17—22no—
152C2×C4×D17—81no—
153C2×C4×D17—81no—
154C2×C4×D17—81no—
155C2×C4×D17—81no—
156C2×C4×D17C4214yescomplemented
157C2×C4×D17C2×D414yes—
158C2×C4×D17C2×D414yes—
159C22⋊#595—216no—
160C22⋊#595—28no—
161C22⋊#595C22×C4116yes—
162C4×#595—84no—
163C4×#595—84no—
164C4⋊C4×C17—22no—
165C22⋊C4×C17—22no—
166C22⋊C4×C17C22⋊C414yes—
167C42×C17—22no—
168C22⋊Dic17—22no—
169C22⋊Dic17C22⋊C414yes—
170#63227—22no—
171#63227—22no—
172#63227—22no—
173#63227—22no—
174#63227—22no—
175#63227—22no—
176#63227C22⋊C414yes—
177#63227C22⋊C414yes—
178C4⋊Dic17—22no—
179#63225—22no—
180#63225—22no—
181C4×Dic17—22no—
182C4×Dic17—22no—
183C4×Dic17—22no—
184#20392—171nomaximal, Sylow
185C23×C17—21no—
186C23×C17—21no—
187C23×C17—41no—
188C23×C17—41no—
189C23×C17—41no—
190C23×C17—41no—
191C23×C17C2×C4212yes—
192C23×C17C2×C4212yes—
193C23×C17C2×C22⋊C412yes—
194C23×C17#11712yes—
195C23×C17C23×C411yescharacteristic
196C22×D17—21no—
197C22×D17—21no—
198C22×D17—28no—
199C22×D17—41no—
200C22×D17—41no—
201C22×D17—44no—
202C22×D17—44no—
203C22×D17—41no—
204C22×D17—41no—
205C22×D17—41no—
206C22×D17—41no—
207C22×D17—82no—
208C22×D17—82no—
209C22×D17—84no—
210C22×D17—84no—
211C22×D17—84no—
212C22×D17—84no—
213C22×D17C2×C4212yes—
214C22×D17C2×C4212yes—
215C22×D17C2×C22⋊C412yes—
216C22×D17#11712yes—
217C22×D17C4×D418yes—
218C22×D17C4×D418yes—
219C22×D17C23×C412yes—
220C22×D17C22×D412yes—
221C22×D17C2×#4112yes—
222C2×#595—216no—
223C2×#595—48no—
224C2×#595—48no—
225C2×#595—816no—
226D4×C17—28no—
227C2×C4×C17—21no—
228C2×C4×C17—21no—
229C2×C4×C17—21no—
230C2×C4×C17—21no—
231C2×C4×C17—41no—
232C2×C4×C17—41no—
233C2×C4×C17—41no—
234C2×C4×C17—41no—
235C2×C4×C17—82no—
236C2×C4×C17—82no—
237C2×C4×C17C2×C4212yes—
238C2×C4×C17C2×C22⋊C412yes—
239C2×C4×C17C2×C22⋊C412yes—
240C22⋊D17—28no—
241C22⋊D17—28no—
242C2×Dic17—21no—
243C2×Dic17—21no—
244C2×Dic17—21no—
245C2×Dic17—21no—
246C2×Dic17—41no—
247C2×Dic17—41no—
248C2×Dic17—41no—
249C2×Dic17—41no—
250C2×Dic17—82no—
251C2×Dic17—82no—
252C2×Dic17C2×C4212yes—
253C2×Dic17C2×C22⋊C412yes—
254C2×Dic17C2×C22⋊C412yes—
255D68—28no—
256C4×D17—28no—
257C4×D17—44no—
258C4×D17—44no—
259C4×D17—82no—
260C4×D17—82no—
261C2×#518—171no—
262C22×#99—172no—
263#2273—172no—
264C4×#99—172no—
265C4×#99—172no—
266C4×#99—172no—
267C4×#99—172no—
268C2×#342—172no—
269C22×C17—21no—
270C22×C17—21no—
271C22×C17—22no—
272C22×C17—22no—
273C22×C17—22no—
274C22×C17—42no—
275C22×C17—42no—
276C22×C17—42no—
277C22×C17—42no—
278C22×C17—41no—
279C22×C17—41no—
280C22×C17C4×C22⋊C414yes—
281C22×C17C22×C4211yescharacteristic
282C22×C17C22×C22⋊C411yescharacteristic
283C22×C17C2×#11711yescharacteristic
284C2×D17—22no—
285C2×D17—22no—
286C2×D17—22no—
287C2×D17—22no—
288C2×D17—22no—
289C2×D17—48no—
290C2×D17—42no—
291C2×D17—42no—
292C2×D17—48no—
293C2×D17—42no—
294C2×D17—42no—
295C2×D17—42no—
296C2×D17—41no—
297C2×D17—41no—
298C2×D17—42no—
299C2×D17—88no—
300C2×D17C4×C22⋊C414yes—
301C2×D17C2×C4×D414yes—
302#595—416no—
303C4×C17—22no—
304C4×C17—22no—
305C4×C17—22no—
306C4×C17—41no—
307C4×C17—41no—
308Dic17—22no—
309Dic17—22no—
310Dic17—22no—
311Dic17—41no—
312Dic17—41no—
313C23×D4—171no—
314#518—348no—
315C2×C4×D4—171no—
316C2×C4×D4—171no—
317C2×C4×D4—171no—
318C2×C4×D4—171no—
319C2×C4×D4—171no—
320C2×C4×D4—171no—
321C2×C4×D4—171no—
322C2×C4×D4#59511yescharacteristic, complemented
323C2×#117—171no—
324C2×#117—171no—
325C22×C22⋊C4—171no—
326C22×C22⋊C4—174no—
327C22×C22⋊C4—171no—
328C22×C22⋊C4—171no—
329C22×C22⋊C4—171no—
330C2×#99—174no—
331C2×#99—1716no—
332C2×#99—174no—
333C4×C22⋊C4—174no—
334C4×C22⋊C4—174no—
335C4×C22⋊C4—348no—
336#342—174no—
337#342—174no—
338C2×C17—21no—
339C2×C17—21no—
340C2×C17—24no—
341C2×C17—42no—
342C2×C17C2×C4×C22⋊C411yescharacteristic
343C2×C17#288311yescharacteristic
344C2×C17#288311yescharacteristic
345D17—24no—
346D17—24no—
347D17—42no—
348C25—171no—
349C25—171no—
350C22×D4—171no—
351C22×D4—171no—
352C22×D4—178no—
353C22×D4—171no—
354C22×D4—344no—
355C22×D4—344no—
356C22×D4C2×#59511yescharacteristic
357C23×C4—171no—
358C23×C4—171no—
359C23×C4—171no—
360C23×C4—171no—
361C23×C4—171no—
362C23×C4—171no—
363C23×C4—171no—
364C23×C4—344no—
365C23×C4C2×#59511yescharacteristic
366C23×C4C2×#59511yescharacteristic, complemented
367C4×D4—24no—
368C4×D4—344no—
369C4×D4—344no—
370C4×D4—344no—
371C4×D4—344no—
372C4×D4—344no—
373C4×D4—344no—
374C4×D4—344no—
375#117—344no—
376#117—344no—
377C2×C4⋊C4—171no—
378C2×C4⋊C4—171no—
379C2×C4⋊C4—171no—
380C2×C4⋊C4C2×#59511yescharacteristic, complemented
381C2×C22⋊C4—171no—
382C2×C22⋊C4—171no—
383C2×C22⋊C4—171no—
384C2×C22⋊C4—178no—
385C2×C22⋊C4—1716no—
386C2×C22⋊C4—178no—
387C2×C22⋊C4—171no—
388C2×C22⋊C4—171no—
389C2×C22⋊C4—171no—
390C2×C22⋊C4—171no—
391C2×C22⋊C4—171no—
392C2×C22⋊C4—171no—
393C2×C22⋊C4—171no—
394C2×C22⋊C4—344no—
395C2×C22⋊C4—344no—
396C2×C22⋊C4—344no—
397C2×C22⋊C4—348no—
398C2×C22⋊C4—344no—
399C2×C22⋊C4C2×#59511yescharacteristic
400C2×C22⋊C4C2×#59511yescharacteristic, complemented
401C2×C42—171no—
402C2×C42—171no—
403C2×C42—171no—
404C2×C42—344no—
405C2×C42—344no—
406C2×C42C2×#59511yescharacteristic, complemented
407#99—1716no—
408#99—1716no—
409#95—344no—
410#95—344no—
411C17#2039211yescharacteristic, complemented, Sylow
412C24—174no—
413C24—171no—
414C24—171no—
415C24—174no—
416C24—174no—
417C24—171no—
418C24—174no—
419C24—342no—
420C24—342no—
421C24—1361no—
422C24—1361no—
423C24—1361no—
424C24—1361no—
425C24C22×#59511yescharacteristic
426C24C22×#59511yescharacteristic
427C2×D4—22no—
428C2×D4—22no—
429C2×D4—174no—
430C2×D4—174no—
431C2×D4—174no—
432C2×D4—342no—
433C2×D4—342no—
434C2×D4—3416no—
435C2×D4—3416no—
436C2×D4—342no—
437C2×D4—342no—
438C2×D4—342no—
439C2×D4—342no—
440C2×D4C4×#59514yescomplemented
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—81no—
444C22×C4—81no—
445C22×C4—171no—
446C22×C4—171no—
447C22×C4—171no—
448C22×C4—174no—
449C22×C4—174no—
450C22×C4—174no—
451C22×C4—171no—
452C22×C4—171no—
453C22×C4—342no—
454C22×C4—342no—
455C22×C4—342no—
456C22×C4—342no—
457C22×C4—348no—
458C22×C4—3416no—
459C22×C4—342no—
460C22×C4—342no—
461C22×C4—1361no—
462C22×C4—1361no—
463C22×C4—1361no—
464C22×C4—1361no—
465C22×C4—1364no—
466C22×C4—1364no—
467C22×C4—1361no—
468C22×C4—1361no—
469C22×C4C22×#59511yescharacteristic
470C22×C4C22×#59511yescharacteristic
471C22×C4C22×#59511yescharacteristic
472C22×C4C22×#59511yescharacteristic
473C22×C4C22×#59511yescharacteristic
474C4⋊C4—22no—
475C4⋊C4—342no—
476C4⋊C4—342no—
477C4⋊C4—342no—
478C22⋊C4—22no—
479C22⋊C4—174no—
480C22⋊C4—174no—
481C22⋊C4—174no—
482C22⋊C4—1716no—
483C22⋊C4—342no—
484C22⋊C4—342no—
485C22⋊C4—342no—
486C22⋊C4—342no—
487C22⋊C4—342no—
488C22⋊C4—342no—
489C22⋊C4—3416no—
490C22⋊C4—348no—
491C22⋊C4—342no—
492C22⋊C4C22⋊#59514yes—
493C42—22no—
494C42—342no—
495C42—342no—
496C42—342no—
497C42—1364no—
498C42—1364no—
499C23—21no—
500C23—21no—
501C23—41no—
502C23—41no—
503C23—41no—
504C23—41no—
505C23—172no—
506C23—172no—
507C23—178no—
508C23—178no—
509C23—172no—
510C23—172no—
511C23—172no—
512C23—172no—
513C23—172no—
514C23—348no—
515C23—341no—
516C23—341no—
517C23—681no—
518C23—684no—
519C23—681no—
520C23—684no—
521C23—681no—
522C23—681no—
523C23—681no—
524C23—681no—
525C23—1362no—
526C23—1362no—
527C23—1364no—
528C23—1364no—
529C23—1364no—
530C23—1364no—
531C23C2×C4×#59512yes—
532C23C2×C4×#59512yes—
533C23#1058767712yes—
534C23C2×C22⋊#59512yes—
535C23C23×#59511yescharacteristic
536D4—28no—
537D4—348no—
538D4—348no—
539D4—348no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—82no—
549C2×C4—82no—
550C2×C4—172no—
551C2×C4—172no—
552C2×C4—172no—
553C2×C4—348no—
554C2×C4—341no—
555C2×C4—341no—
556C2×C4—3416no—
557C2×C4—341no—
558C2×C4—341no—
559C2×C4—684no—
560C2×C4—684no—
561C2×C4—681no—
562C2×C4—681no—
563C2×C4—688no—
564C2×C4—688no—
565C2×C4—681no—
566C2×C4—681no—
567C2×C4—1362no—
568C2×C4—1362no—
569C2×C4—1362no—
570C2×C4—1362no—
571C2×C4—13616no—
572C2×C4C2×C4×#59512yes—
573C2×C4C2×C22⋊#59512yes—
574C2×C4C2×C22⋊#59512yes—
575C22—21no—
576C22—22no—
577C22—21no—
578C22—22no—
579C22—22no—
580C22—42no—
581C22—42no—
582C22—42no—
583C22—42no—
584C22—41no—
585C22—41no—
586C22—174no—
587C22—174no—
588C22—342no—
589C22—342no—
590C22—342no—
591C22—342no—
592C22—342no—
593C22—688no—
594C22—682no—
595C22—682no—
596C22—682no—
597C22—682no—
598C22—688no—
599C22—682no—
600C22—682no—
601C22—681no—
602C22—681no—
603C22—1368no—
604C22C4×C22⋊#59514yes—
605C22C22×C4×#59511yescharacteristic
606C22C22×C22⋊#59511yescharacteristic
607C22C2×#1058767711yescharacteristic
608C4—22no—
609C4—22no—
610C4—22no—
611C4—41no—
612C4—41no—
613C4—342no—
614C4—342no—
615C4—342no—
616C4—6816no—
617C4—681no—
618C4—681no—
619C2—21no—
620C2—21no—
621C2—24no—
622C2—42no—
623C2—344no—
624C2—344no—
625C2—682no—
626C2C2×C4×C22⋊#59511yescharacteristic
627C2#1454538311yescharacteristic
628C2#1454538411yescharacteristic
subgroupG/H
centerC22C22×C22⋊#595
commutatorC22×C17C22×C42
FrattiniC23C23×#595
FittingC2×C4×D4×C17C4
socleC22×C17C22×C22⋊C4
prime radicalC22×D4×D17C22
cosocleC23×D17C24
hypercenterC2×C4×D4#595
hypocenterC17#20392
LCSG ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×C22⋊C4 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
2. #14545220C2semidirect
3. #14544531C2semidirect
4. C4×#10587539C2semidirect
5. #14544529C2semidirect
6. C4×#10587551C2semidirect
7. C2×#11763687C2semidirect
11. D17⋊#99C4semidirect
14. C4×C22⋊#595C22semidirect
15. C4×C22⋊#595C22semidirect
16. #11763687C22semidirect
17. #11763687C22semidirect
21. C2×D4×Dic17C4semidirect
23. C2×C4×C22⋊D17C4semidirect
25. C2×#10587567C4semidirect
27. C2×#10587578C4semidirect
28. C2×#10587558C4semidirect
29. C22×#63227C4semidirect
31. C2×C22⋊C4×D17C4semidirect
33. C2×C4×D4×C17C4semidirect
39. C23×C4×C17C2×C4semidirect
43. C23×Dic17C2×C4semidirect
49. C22×C4×D17C2×C4semidirect
50. C22×C4×D17C2×C4semidirect
55. C2×C22⋊#595C2×C4semidirect
60. C2×C4⋊C4×C17C2×C4semidirect
62. C2×C22⋊C4×C17C2×C4semidirect
63. C2×C42×C17C2×C4semidirect
65. C2×C22⋊Dic17C2×C4semidirect
75. C2×#63227C2×C4semidirect
76. C2×#63227C2×C4semidirect
79. C2×C4⋊Dic17C2×C4semidirect
80. C2×#63225C2×C4semidirect
81. C2×#63225C2×C4semidirect
82. C2×C4×Dic17C2×C4semidirect
83. C2×C4×Dic17C2×C4semidirect
84. C2×C4×Dic17C2×C4semidirect
93. #10587551C2×C4semidirect
96. #10587539C2×C4semidirect
105. C23×D17C42semidirect
118. C2×D4×C17C42semidirect
132. C2×C22⋊D17C42semidirect
156. C2×C4×D17C42semidirect
322. C2×C4×D4#595semidirect
366. C23×C4C2×#595semidirect
380. C2×C4⋊C4C2×#595semidirect
400. C2×C22⋊C4C2×#595semidirect
406. C2×C42C2×#595semidirect
411. C17#20392semidirect
440. C2×D4C4×#595semidirect

Maximal subgroups

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

subgroupindex
C2×D17⋊#992
#145452202
#145445312
C4×#105875392
#145445292
C4×#105875512
C2×#117636872
C2×#117632812
#2039217