Finite Group Databasebeta

← #17050627

Subgroups — #17050627

Order 4352.

1194 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762881C211yesmaximal, characteristic, complemented
2#14531713C211yesmaximal, characteristic, complemented
3#14529758C211yesmaximal, characteristic, complemented
4#14529737C211yesmaximal, characteristic, complemented
5#14529223C211yesmaximal, characteristic, complemented
6#14529213C211yesmaximal, characteristic, complemented
7#14529107C211yesmaximal, characteristic, complemented
8#14529102C211yesmaximal, characteristic, complemented
9#14528879C211yesmaximal, characteristic, complemented
10#14528879C211yesmaximal, characteristic, complemented
11#14528794C211yesmaximal, characteristic, complemented
12#14528609C211yesmaximal, characteristic, complemented
13#14528505C211yesmaximal, characteristic, complemented
14#14528500C211yesmaximal, characteristic, complemented
15C2×C17×#555C211yesmaximal, characteristic
16C22×#63223C2211yescharacteristic
17C23×#3622C2211yescharacteristic
18C2×#10587612C2211yescharacteristic
19C22×C4⋊Dic17C2211yescharacteristic
20#11762881—24no—
21C2×C4⋊#3622C2211yescharacteristic
22C2×#10587503C2211yescharacteristic
23C2×#10587503C2211yescharacteristic
24C2×#10587503C2211yescharacteristic
25C2×#10587503C2211yescharacteristic
26C2×C22⋊#3622C2211yescharacteristic
27C2×C22⋊#3622C2211yescharacteristic
28C2×#10587474C2211yescharacteristic
29#11762702—21no—
30#11762695—21no—
31#11762689—21no—
32#11762675C2211yescharacteristic
33#11762669C2211yescharacteristic
34#11762669C2211yescharacteristic
35C4×C4⋊Dic17C2211yescharacteristic
36C22⋊C4×Dic17—21no—
37#11762571C2211yescharacteristic
38#11762571C2211yescharacteristic
39#11762571C2211yescharacteristic
40#11762571C2211yescharacteristic
41#11762571C2211yescharacteristic
42#11762571C2211yescharacteristic
43#11762571C2211yescharacteristic
44#11762571C2211yescharacteristic
45#11762571C2211yescharacteristic
46#11762571C2211yescharacteristic
47#11762571C2211yescharacteristic
48#11762571C2211yescharacteristic
49C17×#555—24no—
50C17×#555C418yescomplemented
51C2×C17×C4⋊Q8C2211yescharacteristic
52C2×C17×#124—21no—
53C2×C17×#124—21no—
54C2×C17×#121—21no—
55C2×C17×#121C2211yescharacteristic
56C2×C17×#121C2211yescharacteristic
57C2×C4×D4×C17C2211yescharacteristic
58C2×C4×D4×C17C2211yescharacteristic
59C2×C17×#117—21no—
60C2×C17×#117C2211yescharacteristic
61C2×C17×#117C2211yescharacteristic
62C22×Q8×C17—21no—
63C22×D4×C17—21no—
64C22×D4×C17—21no—
65C22×D4×C17D411yescharacteristic
66C22×D4×C17C2311yescharacteristic
67C23×C4×C17—21no—
68C23×C4×C17C2311yescharacteristic
69C23×C4×C17C2311yescharacteristic
70C23×Dic17—21no—
71C17×C4⋊Q8—22no—
72C17×C4⋊Q8C2×C414yescomplemented
73C17×#124—28no—
74C17×#124—28no—
75C17×#121—28no—
76C17×#121—22no—
77C17×#121—22no—
78C17×#121C2×C414yes—
79C17×#121C2×C414yescomplemented
80C4×D4×C17—22no—
81C4×D4×C17C2×C414yes—
82C4×D4×C17C2×C414yescomplemented
83C4×D4×C17D414yes—
84C17×#117—22no—
85C17×#117—22no—
86C17×#117—28no—
87C17×#117C2×C414yes—
88C17×#117C2×C414yescomplemented
89C2×C4⋊C4×C17—21no—
90C2×C4⋊C4×C17D411yescharacteristic
91C2×C4⋊C4×C17C2311yescharacteristic
92C2×C4⋊C4×C17C2311yescharacteristic
93C2×C4⋊C4×C17C2311yescharacteristic
94C2×C22⋊C4×C17—21no—
95C2×C22⋊C4×C17—21no—
96C2×C22⋊C4×C17—21no—
97C2×C22⋊C4×C17—21no—
98C2×C22⋊C4×C17—21no—
99C2×C22⋊C4×C17D411yescharacteristic
100C2×C22⋊C4×C17D411yescharacteristic
101C2×C42×C17—21no—
102C2×C42×C17—21no—
103C2×C42×C17C2311yescharacteristic
104C2×C22⋊Dic17—21no—
105C2×C22⋊Dic17—21no—
106C2×C22⋊Dic17—21no—
107#10587612—22no—
108#10587612—41no—
109C2×C4⋊Dic17—21no—
110C2×C4⋊Dic17—22no—
111C2×C4⋊Dic17—41no—
112C2×C4⋊Dic17C2311yescharacteristic
113C2×C4⋊Dic17C2311yescharacteristic
114C2×C4⋊Dic17C2311yescharacteristic
115C2×C4⋊Dic17C2311yescharacteristic
116C2×C4×Dic17—21no—
117C2×C4×Dic17—21no—
118C2×#63223—22no—
119C2×#63223—22no—
120C2×#63223—41no—
121C22×#3622—22no—
122C22×#3622—22no—
123C22×#3622—41no—
124C22×#3622C2311yescharacteristic
125C22×#3622C2311yescharacteristic
126C22×#3622C2311yescharacteristic
127C22×#3622C2311yescharacteristic
128#10587503—22no—
129#10587503—22no—
130#10587503—41no—
131#10587503—41no—
132#10587502—21no—
133#10587502—21no—
134#10587502—21no—
135#10587502—21no—
136#10587502—21no—
137C22⋊#3622—22no—
138C22⋊#3622—22no—
139C4⋊#3622—22no—
140#10587474—22no—
141C24×C17—21no—
142C24×C17C2×D411yescharacteristic
143C24×C17C2×D411yescharacteristic
144C2×Q8×C17—24no—
145C2×Q8×C17—81no—
146C2×Q8×C17—81no—
147C2×D4×C17—24no—
148C2×D4×C17—24no—
149C2×D4×C17—21no—
150C2×D4×C17—21no—
151C2×D4×C17—21no—
152C2×D4×C17—21no—
153C2×D4×C17—21no—
154C2×D4×C17—41no—
155C2×D4×C17—41no—
156C2×D4×C17—81no—
157C2×D4×C17—81no—
158C2×D4×C17—81no—
159C2×D4×C17—81no—
160C2×D4×C17C22⋊C414yes—
161C2×D4×C17C22×C412yes—
162C22×C4×C17—21no—
163C22×C4×C17—21no—
164C22×C4×C17—21no—
165C22×C4×C17—21no—
166C22×C4×C17—21no—
167C22×C4×C17—21no—
168C22×C4×C17—21no—
169C22×C4×C17—21no—
170C22×C4×C17—21no—
171C22×C4×C17—21no—
172C22×C4×C17—21no—
173C22×C4×C17—24no—
174C22×C4×C17—42no—
175C22×C4×C17—42no—
176C22×C4×C17C22×C412yes—
177C22×C4×C17C22×C412yes—
178C22×C4×C17C2×D411yescharacteristic
179C22×C4×C17C2×D411yescharacteristic
180C22×C4×C17C2×D411yescharacteristic
181C22×C4×C17C2×D411yescharacteristic
182C22×C4×C17C2×D412yes—
183C22×C4×C17C2×D412yes—
184C22×C4×C17C2411yescharacteristic
185C22×Dic17—21no—
186C22×Dic17—21no—
187C22×Dic17—21no—
188C22×Dic17—21no—
189C22×Dic17—42no—
190C22×Dic17—42no—
191C22×Dic17—81no—
192C4⋊C4×C17—24no—
193C4⋊C4×C17—21no—
194C4⋊C4×C17—21no—
195C4⋊C4×C17—21no—
196C4⋊C4×C17C22⋊C414yes—
197C4⋊C4×C17C22×C412yes—
198C4⋊C4×C17C22×C412yes—
199C4⋊C4×C17C22×C412yes—
200C22⋊C4×C17—24no—
201C22⋊C4×C17—24no—
202C22⋊C4×C17—24no—
203C22⋊C4×C17—24no—
204C22⋊C4×C17—24no—
205C22⋊C4×C17C22⋊C414yes—
206C22⋊C4×C17C22⋊C414yes—
207C42×C17—24no—
208C42×C17—24no—
209C42×C17C22×C412yes—
210C42×C17C2×D412yes—
211C22⋊Dic17—42no—
212C22⋊Dic17—42no—
213C22⋊Dic17—81no—
214C4⋊Dic17—21no—
215C4⋊Dic17—21no—
216C4⋊Dic17—21no—
217C4⋊Dic17—21no—
218C4⋊Dic17—21no—
219C4⋊Dic17—21no—
220C4⋊Dic17—21no—
221C4⋊Dic17—42no—
222C4⋊Dic17#4112yes—
223C4×Dic17—42no—
224C4×Dic17—81no—
225#63223—44no—
226C2×#3622—21no—
227C2×#3622—21no—
228C2×#3622—21no—
229C2×#3622—21no—
230C2×#3622—21no—
231C2×#3622—21no—
232C2×#3622—21no—
233C2×#3622—21no—
234C2×#3622—21no—
235C2×#3622—21no—
236C2×#3622—21no—
237C2×#3622—44no—
238C2×#3622#4112yes—
239#22492—171nomaximal, Sylow
240C23×C17—21no—
241C23×C17—21no—
242C23×C17—21no—
243C23×C17—21no—
244C23×C17—21no—
245C23×C17—21no—
246C23×C17—21no—
247C23×C17—21no—
248C23×C17—21no—
249C23×C17—21no—
250C23×C17—21no—
251C23×C17—21no—
252C23×C17—22no—
253C23×C17—41no—
254C23×C17—41no—
255C23×C17—41no—
256C23×C17—41no—
257C23×C17—41no—
258C23×C17—41no—
259C23×C17C2×C22⋊C412yes—
260C23×C17C2×C22⋊C412yes—
261C23×C17C22×D411yescharacteristic
262Q8×C17—84no—
263D4×C17—22no—
264D4×C17—22no—
265D4×C17—44no—
266D4×C17—41no—
267D4×C17—41no—
268D4×C17—84no—
269D4×C17—84no—
270C2×C4×C17—21no—
271C2×C4×C17—21no—
272C2×C4×C17—21no—
273C2×C4×C17—21no—
274C2×C4×C17—21no—
275C2×C4×C17—21no—
276C2×C4×C17—21no—
277C2×C4×C17—21no—
278C2×C4×C17—22no—
279C2×C4×C17—22no—
280C2×C4×C17—22no—
281C2×C4×C17—22no—
282C2×C4×C17—22no—
283C2×C4×C17—22no—
284C2×C4×C17—22no—
285C2×C4×C17—22no—
286C2×C4×C17—22no—
287C2×C4×C17—22no—
288C2×C4×C17—22no—
289C2×C4×C17—48no—
290C2×C4×C17—41no—
291C2×C4×C17—41no—
292C2×C4×C17—41no—
293C2×C4×C17—41no—
294C2×C4×C17—41no—
295C2×C4×C17—41no—
296C2×C4×C17C2×C22⋊C412yes—
297C2×C4×C17C2×C22⋊C412yes—
298C2×C4×C17C2×C22⋊C412yes—
299C2×C4×C17C2×C22⋊C412yes—
300C2×C4×C17C23×C411yescharacteristic
301C2×C4×C17C22×D411yescharacteristic
302C2×C4×C17C2×#4111yescharacteristic
303C2×C4×C17C2×#4111yescharacteristic
304C2×C4×C17H(5,𝔽2)11yescharacteristic
305C2×C4×C172−1+411yescharacteristic
306C2×Dic17—22no—
307C2×Dic17—41no—
308C2×Dic17—41no—
309C2×Dic17—41no—
310C2×Dic17—41no—
311C2×Dic17—41no—
312C2×Dic17—41no—
313C2×Dic17—41no—
314C2×Dic17—41no—
315C2×Dic17—41no—
316C2×Dic17—41no—
317C2×Dic17—41no—
318C2×Dic17—84no—
319#3622—22no—
320#3622—41no—
321#3622—41no—
322#3622—41no—
323C2×#555D1711yescharacteristic
324C2×#435—171no—
325#2352—171no—
326#1993—171no—
327#1988—171no—
328#1895—171no—
329#1893—171no—
330#1875—171no—
331#1874—171no—
332#1825—171no—
333#1825—171no—
334#1804—171no—
335#1762—171no—
336#1736—171no—
337#1735—171no—
338C22×C17—22no—
339C22×C17—22no—
340C22×C17—22no—
341C22×C17—22no—
342C22×C17—22no—
343C22×C17—22no—
344C22×C17—41no—
345C22×C17—41no—
346C22×C17—41no—
347C22×C17—41no—
348C22×C17—41no—
349C22×C17—41no—
350C22×C17—41no—
351C22×C17—41no—
352C22×C17—42no—
353C22×C17—42no—
354C22×C17—42no—
355C22×C17—81no—
356C22×C17—81no—
357C22×C17—81no—
358C22×C17—81no—
359C22×C17C22×C22⋊C411yescharacteristic
360C22×C17#54611yescharacteristic
361C22×C17#54711yescharacteristic
362C22×C17#57511yescharacteristic
363C22×C17#57511yescharacteristic
364C22×C17#57611yescharacteristic
365C22×C17#57711yescharacteristic
366C4×C17—22no—
367C4×C17—22no—
368C4×C17—22no—
369C4×C17—22no—
370C4×C17—42no—
371C4×C17—42no—
372C4×C17—42no—
373C4×C17C4×#4111yescharacteristic
374C4×C17#52011yescharacteristic
375C4×C17#54611yescharacteristic
376C4×C17#54711yescharacteristic
377Dic17—42no—
378Dic17—81no—
379Dic17—81no—
380Dic17—81no—
381C22×M16—171no—
382C23×C8—171no—
383#555—24no—
384#555Dic1718yescomplemented
385C2×C4⋊Q8C2×D1711yescharacteristic
386C2×#124—21no—
387C2×#124—21no—
388C2×#121—21no—
389C2×#121C2×D1711yescharacteristic
390C2×#121C2×D1711yescharacteristic
391C2×C4×D4C2×D1711yescharacteristic
392C2×C4×D4C2×D1711yescharacteristic
393C2×#117—21no—
394C2×#117—171no—
395C2×#117C2×D1711yescharacteristic
396C2×#117C2×D1711yescharacteristic
397C22×C4⋊C4—171no—
398#435—344no—
399C2×C4⋊C8—171no—
400C2×#102—171no—
401C2×#102—171no—
402C2×#102—171no—
403C2×#102—171no—
404C2×C22⋊C8—171no—
405C2×C22⋊C8—171no—
406C2×#97—171no—
407#388—341no—
408#387—341no—
409#386—341no—
410#382—171no—
411#380—171no—
412#380—171no—
413C4×C4⋊C4—171no—
414C4×C22⋊C4—341no—
415#340—171no—
416#340—171no—
417#340—171no—
418#340—171no—
419#340—171no—
420#340—171no—
421#340—171no—
422#340—171no—
423#340—171no—
424#340—171no—
425#340—171no—
426#340—171no—
427C2×C17—42no—
428C2×C17—42no—
429C2×C17—82no—
430C2×C17#233911yescharacteristic
431C2×C17#289611yescharacteristic
432C2×C17#289711yescharacteristic
433C2×C17#331911yescharacteristic
434C2×C17#332111yescharacteristic
435C2×C17#334711yescharacteristic
436C2×C17#334811yescharacteristic
437C22×Q8—21no—
438C22×D4—21no—
439C22×D4—21no—
440C22×D4C22⋊D1711yescharacteristic
441C22×D4C22×D1711yescharacteristic
442C23×C4—21no—
443C23×C4—341no—
444C23×C4C22×D1711yescharacteristic
445C23×C4C22×D1711yescharacteristic
446C2×M16—342no—
447C2×M16—342no—
448C2×M16—681no—
449C22×C8—171no—
450C22×C8—171no—
451C22×C8—171no—
452C22×C8—171no—
453C22×C8—342no—
454C22×C8—342no—
455C22×C8—681no—
456C4⋊Q8—22no—
457C4⋊Q8C2×Dic1714yescomplemented
458#124—28no—
459#124—28no—
460#121—28no—
461#121—22no—
462#121—22no—
463#121C2×Dic1714yes—
464#121C2×Dic1714yescomplemented
465C4×D4—22no—
466C4×D4C2×Dic1714yes—
467C4×D4C2×Dic1714yescomplemented
468C4×D4C22⋊D1714yes—
469#117—22no—
470#117—22no—
471#117—28no—
472#117—342no—
473#117—681no—
474#117C2×Dic1714yes—
475#117C2×Dic1714yescomplemented
476C2×C4⋊C4—21no—
477C2×C4⋊C4—171no—
478C2×C4⋊C4—171no—
479C2×C4⋊C4—171no—
480C2×C4⋊C4—171no—
481C2×C4⋊C4—342no—
482C2×C4⋊C4—341no—
483C2×C4⋊C4—681no—
484C2×C4⋊C4C22⋊D1711yescharacteristic
485C2×C4⋊C4C22×D1711yescharacteristic
486C2×C4⋊C4C22×D1711yescharacteristic
487C2×C4⋊C4C22×D1711yescharacteristic
488C2×C22⋊C4—21no—
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—341no—
494C2×C22⋊C4—341no—
495C2×C22⋊C4—341no—
496C2×C22⋊C4C22⋊D1711yescharacteristic
497C2×C22⋊C4C22⋊D1711yescharacteristic
498C2×C42—21no—
499C2×C42—21no—
500C2×C42—341no—
501C2×C42—341no—
502C2×C42C22×D1711yescharacteristic
503C4⋊C8—342no—
504#102—342no—
505#102—342no—
506#102—681no—
507#102—681no—
508C22⋊C8—342no—
509C22⋊C8—342no—
510#97—342no—
511#95—341no—
512#95—341no—
513#95—341no—
514#95—341no—
515#95—341no—
516C17#2249211yescharacteristic, complemented, Sylow
517C24—21no—
518C24C2×C22⋊D1711yescharacteristic
519C24C2×C22⋊D1711yescharacteristic
520C2×Q8—24no—
521C2×Q8—81no—
522C2×Q8—81no—
523C2×D4—24no—
524C2×D4—24no—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—41no—
531C2×D4—41no—
532C2×D4—81no—
533C2×D4—81no—
534C2×D4—81no—
535C2×D4—81no—
536C2×D4C22⋊Dic1714yes—
537C2×D4C22×Dic1712yes—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—24no—
550C22×C4—42no—
551C22×C4—42no—
552C22×C4—341no—
553C22×C4—341no—
554C22×C4—341no—
555C22×C4—341no—
556C22×C4—682no—
557C22×C4—682no—
558C22×C4—1361no—
559C22×C4C22×Dic1712yes—
560C22×C4C22×Dic1712yes—
561C22×C4C2×C22⋊D1712yes—
562C22×C4C2×C22⋊D1712yes—
563C22×C4C2×C22⋊D1711yescharacteristic
564C22×C4C2×C22⋊D1711yescharacteristic
565C22×C4C2×C22⋊D1711yescharacteristic
566C22×C4C2×C22⋊D1711yescharacteristic
567C22×C4C23×D1711yescharacteristic
568M16—684no—
569C2×C8—172no—
570C2×C8—341no—
571C2×C8—341no—
572C2×C8—341no—
573C2×C8—341no—
574C2×C8—341no—
575C2×C8—341no—
576C2×C8—341no—
577C2×C8—341no—
578C2×C8—341no—
579C2×C8—341no—
580C2×C8—341no—
581C2×C8—684no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—24no—
586C4⋊C4—172no—
587C4⋊C4—341no—
588C4⋊C4—341no—
589C4⋊C4—341no—
590C4⋊C4—341no—
591C4⋊C4—341no—
592C4⋊C4—341no—
593C4⋊C4—341no—
594C4⋊C4—682no—
595C4⋊C4C22⋊Dic1714yes—
596C4⋊C4C22×Dic1712yes—
597C4⋊C4C22×Dic1712yes—
598C4⋊C4C22×Dic1712yes—
599C22⋊C4—24no—
600C22⋊C4—24no—
601C22⋊C4—24no—
602C22⋊C4—24no—
603C22⋊C4—24no—
604C22⋊C4—682no—
605C22⋊C4—682no—
606C22⋊C4—1361no—
607C22⋊C4C22⋊Dic1714yes—
608C22⋊C4C22⋊Dic1714yes—
609C42—24no—
610C42—24no—
611C42—682no—
612C42—1361no—
613C42C22×Dic1712yes—
614C42C2×C22⋊D1712yes—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—22no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23C2×C22⋊Dic1712yes—
635C23C2×C22⋊Dic1712yes—
636C23C22×C22⋊D1711yescharacteristic
637Q8—84no—
638D4—22no—
639D4—22no—
640D4—44no—
641D4—41no—
642D4—41no—
643D4—84no—
644D4—84no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—48no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—342no—
672C2×C4—681no—
673C2×C4—681no—
674C2×C4—681no—
675C2×C4—681no—
676C2×C4—681no—
677C2×C4—681no—
678C2×C4—681no—
679C2×C4—681no—
680C2×C4—681no—
681C2×C4—681no—
682C2×C4—681no—
683C2×C4—1364no—
684C2×C4C2×C22⋊Dic1712yes—
685C2×C4C2×C22⋊Dic1712yes—
686C2×C4C2×C22⋊Dic1712yes—
687C2×C4C2×C22⋊Dic1712yes—
688C2×C4#41×D1711yescharacteristic
689C2×C4#41×D1711yescharacteristic
690C2×C4#1058769611yescharacteristic
691C2×C4#1058769711yescharacteristic
692C2×C4C23×Dic1711yescharacteristic
693C2×C4C22×C22⋊D1711yescharacteristic
694C8—342no—
695C8—681no—
696C8—681no—
697C8—681no—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—42no—
713C22—42no—
714C22—42no—
715C22—81no—
716C22—81no—
717C22—81no—
718C22—81no—
719C22C22×C22⋊Dic1711yescharacteristic
720C22#1176344711yescharacteristic
721C22#1176345811yescharacteristic
722C22#1176360711yescharacteristic
723C22#1176360711yescharacteristic
724C22#1176361211yescharacteristic
725C22#1176362011yescharacteristic
726C4—22no—
727C4—22no—
728C4—22no—
729C4—22no—
730C4—42no—
731C4—42no—
732C4—42no—
733C4—682no—
734C4—1361no—
735C4—1361no—
736C4—1361no—
737C4#41×Dic1711yescharacteristic
738C4#1176329211yescharacteristic
739C4#1176344711yescharacteristic
740C4#1176345811yescharacteristic
741C2—42no—
742C2—42no—
743C2—82no—
744C2#1453161411yescharacteristic
745C2#1453730311yescharacteristic
746C2#1453731011yescharacteristic
747C2#1454093411yescharacteristic
748C2#1454096411yescharacteristic
749C2#1454128411yescharacteristic
750C2#1454129911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
Fitting, prime radicalC2×C17×#555C2
socleC23×C17C22×D4
cosocleC22×C4×C17C24
hypercenterC2×#555D17
hypocenterC17#22492
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#555

Complements

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

NH ≅ G/Ntype
1. C2×#11762881C2semidirect
2. #14531713C2semidirect
3. #14529758C2semidirect
4. #14529737C2semidirect
5. #14529223C2semidirect
6. #14529213C2semidirect
7. #14529107C2semidirect
8. #14529102C2semidirect
9. #14528879C2semidirect
10. #14528879C2semidirect
11. #14528794C2semidirect
12. #14528609C2semidirect
13. #14528505C2semidirect
14. #14528500C2semidirect
50. C17×#555C4semidirect
72. C17×C4⋊Q8C2×C4semidirect
79. C17×#121C2×C4semidirect
82. C4×D4×C17C2×C4semidirect
88. C17×#117C2×C4semidirect
384. #555Dic17semidirect
457. C4⋊Q8C2×Dic17semidirect
464. #121C2×Dic17semidirect
467. C4×D4C2×Dic17semidirect
475. #117C2×Dic17semidirect
516. C17#22492semidirect

Maximal subgroups

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

subgroupindex
C2×#117628812
#145317132
#145297582
#145297372
#145292232
#145292132
#145291072
#145291022
#145288792
#145287942
#145286092
#145285052
#145285002
C2×C17×#5552
#2249217