Finite Group Databasebeta

← #17050642

Subgroups — #17050642

Order 4352.

1258 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762881C211yesmaximal, characteristic, complemented
2D4×C4⋊Dic17C211yesmaximal, characteristic, complemented
3#14529754C211yesmaximal, characteristic, complemented
4#14529742C211yesmaximal, characteristic, complemented
5#14529223C211yesmaximal, characteristic, complemented
6#14529213C211yesmaximal, characteristic, complemented
7#14529102C211yesmaximal, characteristic, complemented
8#14529102C211yesmaximal, characteristic, complemented
9#14528879C211yesmaximal, characteristic, complemented
10#14528874C211yesmaximal, characteristic, complemented
11#14528784C211yesmaximal, characteristic, complemented
12#14528609C211yesmaximal, characteristic, complemented
13#14528505C211yesmaximal, characteristic, complemented
14C2×#11762571C211yesmaximal, characteristic, complemented
15C2×C17×#553C211yesmaximal, characteristic
16C22×#63223C2211yescharacteristic
17C23×#3622C2211yescharacteristic
18C2×D4×Dic17—21no—
19C22×C4⋊Dic17C2211yescharacteristic
20C22×C4⋊Dic17C2211yescharacteristic
21#11762881—24no—
22C2×C4⋊#3622C2211yescharacteristic
23C2×#10587503C2211yescharacteristic
24C2×#10587503C2211yescharacteristic
25C2×#10587503C2211yescharacteristic
26C2×#10587503C2211yescharacteristic
27C2×C22⋊#3622C2211yescharacteristic
28C2×C22⋊#3622C2211yescharacteristic
29C2×#10587474C2211yescharacteristic
30#11762708—21no—
31#11762684—21no—
32#11762684—21no—
33#11762679C2211yescharacteristic
34#11762669C2211yescharacteristic
35#11762669C2211yescharacteristic
36C4×C4⋊Dic17C2211yescharacteristic
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×#553—24no—
50C17×#553C418yescomplemented
51C2×C17×#126—21no—
52C2×C17×#125C2211yescharacteristic
53C2×C17×#123—21no—
54C2×C17×#121—21no—
55C2×C17×#121C2211yescharacteristic
56C2×C17×#121C2211yescharacteristic
57C2×C4×D4×C17—21no—
58C2×C4×D4×C17C2211yescharacteristic
59C2×C4×D4×C17C2211yescharacteristic
60C2×C17×#117C2211yescharacteristic
61C22×C4⋊C4×C17C2211yescharacteristic
62C22×D4×C17—21no—
63C22×D4×C17—21no—
64C22×D4×C17D411yescharacteristic
65C22×D4×C17C2311yescharacteristic
66C23×C4×C17—21no—
67C23×C4×C17—21no—
68C23×C4×C17C2311yescharacteristic
69C23×C4×C17C2311yescharacteristic
70C23×Dic17—21no—
71C23×Dic17—21no—
72C17×#126—28no—
73C17×#125—22no—
74C17×#125C2×C414yescomplemented
75C17×#123—28no—
76C17×#121—28no—
77C17×#121—22no—
78C17×#121—22no—
79C17×#121C2×C414yescomplemented
80C17×#121C2×C414yescomplemented
81C4×D4×C17—28no—
82C4×D4×C17—22no—
83C4×D4×C17C2×C414yes—
84C4×D4×C17C2×C414yescomplemented
85C4×D4×C17D414yes—
86C17×#117—22no—
87C17×#117C2×C414yescomplemented
88C2×C4⋊C4×C17—21no—
89C2×C4⋊C4×C17—22no—
90C2×C4⋊C4×C17—21no—
91C2×C4⋊C4×C17—21no—
92C2×C4⋊C4×C17C2×C414yescomplemented
93C2×C4⋊C4×C17D411yescharacteristic
94C2×C4⋊C4×C17C2311yescharacteristic
95C2×C4⋊C4×C17C2311yescharacteristic
96C2×C4⋊C4×C17C2311yescharacteristic
97C2×C22⋊C4×C17—21no—
98C2×C22⋊C4×C17—21no—
99C2×C22⋊C4×C17—21no—
100C2×C22⋊C4×C17—21no—
101C2×C22⋊C4×C17D411yescharacteristic
102C2×C22⋊C4×C17D411yescharacteristic
103C2×C42×C17—21no—
104C2×C42×C17C2311yescharacteristic
105C2×C22⋊Dic17—21no—
106C2×C22⋊Dic17—21no—
107D4×Dic17—44no—
108C2×C4⋊Dic17—21no—
109C2×C4⋊Dic17—21no—
110C2×C4⋊Dic17—21no—
111C2×C4⋊Dic17—21no—
112C2×C4⋊Dic17—22no—
113C2×C4⋊Dic17—22no—
114C2×C4⋊Dic17—41no—
115C2×C4⋊Dic17—41no—
116C2×C4⋊Dic17C2311yescharacteristic
117C2×C4⋊Dic17C2311yescharacteristic
118C2×C4⋊Dic17C2311yescharacteristic
119C2×C4⋊Dic17C2311yescharacteristic
120C2×C4×Dic17—21no—
121C2×#63223—22no—
122C2×#63223—22no—
123C2×#63223—41no—
124C22×#3622—22no—
125C22×#3622—22no—
126C22×#3622—41no—
127C22×#3622C2311yescharacteristic
128C22×#3622C2311yescharacteristic
129C22×#3622C2311yescharacteristic
130C22×#3622C2311yescharacteristic
131#10587503—22no—
132#10587503—22no—
133#10587503—41no—
134#10587503—41no—
135#10587502—21no—
136#10587502—21no—
137#10587502—21no—
138C22⋊#3622—22no—
139C22⋊#3622—22no—
140C4⋊#3622—22no—
141#10587474—22no—
142C24×C17—21no—
143C24×C17C2×D411yescharacteristic
144C24×C17C2×D411yescharacteristic
145C2×D4×C17—22no—
146C2×D4×C17—22no—
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—42no—
155C2×D4×C17—42no—
156C2×D4×C17—81no—
157C2×D4×C17—81no—
158C2×D4×C17C22⋊C414yes—
159C2×D4×C17C22×C412yes—
160C22×C4×C17—21no—
161C22×C4×C17—21no—
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—24no—
172C22×C4×C17—24no—
173C22×C4×C17—81no—
174C22×C4×C17—81no—
175C22×C4×C17—81no—
176C22×C4×C17—81no—
177C22×C4×C17C22×C412yes—
178C22×C4×C17C22×C412yes—
179C22×C4×C17C2×D411yescharacteristic
180C22×C4×C17C2×D411yescharacteristic
181C22×C4×C17C2×D411yescharacteristic
182C22×C4×C17C2×D411yescharacteristic
183C22×C4×C17C2×D412yes—
184C22×C4×C17C2×D412yes—
185C22×C4×C17C2411yescharacteristic
186C22×Dic17—21no—
187C22×Dic17—21no—
188C22×Dic17—21no—
189C22×Dic17—21no—
190C22×Dic17—42no—
191C22×Dic17—42no—
192C22×Dic17—42no—
193C22×Dic17—42no—
194C22×Dic17—81no—
195C22×Dic17—81no—
196C4⋊C4×C17—24no—
197C4⋊C4×C17—24no—
198C4⋊C4×C17—24no—
199C4⋊C4×C17—21no—
200C4⋊C4×C17—21no—
201C4⋊C4×C17—21no—
202C4⋊C4×C17C22⋊C414yes—
203C4⋊C4×C17C22×C412yes—
204C4⋊C4×C17C22×C412yes—
205C4⋊C4×C17C22×C412yes—
206C22⋊C4×C17—24no—
207C22⋊C4×C17—24no—
208C22⋊C4×C17—24no—
209C22⋊C4×C17—24no—
210C22⋊C4×C17C22⋊C414yes—
211C22⋊C4×C17C22⋊C414yes—
212C42×C17—24no—
213C42×C17C22×C412yes—
214C42×C17C2×D412yes—
215C22⋊Dic17—42no—
216C22⋊Dic17—42no—
217C4⋊Dic17—21no—
218C4⋊Dic17—21no—
219C4⋊Dic17—21no—
220C4⋊Dic17—21no—
221C4⋊Dic17—21no—
222C4⋊Dic17—21no—
223C4⋊Dic17—21no—
224C4⋊Dic17—42no—
225C4⋊Dic17—42no—
226C4⋊Dic17—42no—
227C4⋊Dic17—81no—
228C4⋊Dic17#4112yes—
229C4×Dic17—42no—
230#63223—44no—
231C2×#3622—21no—
232C2×#3622—21no—
233C2×#3622—21no—
234C2×#3622—21no—
235C2×#3622—21no—
236C2×#3622—21no—
237C2×#3622—21no—
238C2×#3622—21no—
239C2×#3622—21no—
240C2×#3622—21no—
241C2×#3622—21no—
242C2×#3622—44no—
243C2×#3622#4112yes—
244#22493—171nomaximal, Sylow
245C23×C17—21no—
246C23×C17—21no—
247C23×C17—21no—
248C23×C17—21no—
249C23×C17—21no—
250C23×C17—21no—
251C23×C17—21no—
252C23×C17—21no—
253C23×C17—21no—
254C23×C17—21no—
255C23×C17—22no—
256C23×C17—41no—
257C23×C17—41no—
258C23×C17—41no—
259C23×C17—41no—
260C23×C17—41no—
261C23×C17—41no—
262C23×C17C2×C22⋊C412yes—
263C23×C17C2×C22⋊C412yes—
264C23×C17AGL(1,ℤ/8)12yes—
265C23×C17#13712yes—
266C23×C17C22×D411yescharacteristic
267D4×C17—28no—
268D4×C17—22no—
269D4×C17—22no—
270D4×C17—48no—
271D4×C17—41no—
272D4×C17—41no—
273D4×C17—84no—
274C2×C4×C17—21no—
275C2×C4×C17—21no—
276C2×C4×C17—21no—
277C2×C4×C17—21no—
278C2×C4×C17—21no—
279C2×C4×C17—21no—
280C2×C4×C17—21no—
281C2×C4×C17—21no—
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—22no—
290C2×C4×C17—22no—
291C2×C4×C17—22no—
292C2×C4×C17—22no—
293C2×C4×C17—41no—
294C2×C4×C17—41no—
295C2×C4×C17—41no—
296C2×C4×C17—41no—
297C2×C4×C17—41no—
298C2×C4×C17—41no—
299C2×C4×C17—84no—
300C2×C4×C17—84no—
301C2×C4×C17C2×C22⋊C412yes—
302C2×C4×C17C2×C22⋊C412yes—
303C2×C4×C17C2×C22⋊C412yes—
304C2×C4×C17C2×C22⋊C412yes—
305C2×C4×C17C23×C411yescharacteristic
306C2×C4×C17C22×D411yescharacteristic
307C2×C4×C17C2×#4111yescharacteristic
308C2×C4×C17C2×#4111yescharacteristic
309C2×C4×C17H(5,𝔽2)11yescharacteristic
310C2×C4×C172−1+411yescharacteristic
311C2×Dic17—22no—
312C2×Dic17—41no—
313C2×Dic17—41no—
314C2×Dic17—41no—
315C2×Dic17—41no—
316C2×Dic17—41no—
317C2×Dic17—41no—
318C2×Dic17—41no—
319C2×Dic17—41no—
320C2×Dic17—41no—
321C2×Dic17—41no—
322C2×Dic17—41no—
323C2×Dic17—84no—
324C2×Dic17—84no—
325#3622—22no—
326#3622—41no—
327#3622—41no—
328#3622—41no—
329C2×#553D1711yescharacteristic
330C2×#435—171no—
331D4×C4⋊C4—171no—
332#1992—171no—
333#1989—171no—
334#1895—171no—
335#1893—171no—
336#1874—171no—
337#1874—171no—
338#1825—171no—
339#1824—171no—
340#1802—171no—
341#1762—171no—
342#1736—171no—
343C2×#340—171no—
344C22×C17—22no—
345C22×C17—22no—
346C22×C17—22no—
347C22×C17—22no—
348C22×C17—22no—
349C22×C17—22no—
350C22×C17—22no—
351C22×C17—22no—
352C22×C17—22no—
353C22×C17—41no—
354C22×C17—41no—
355C22×C17—41no—
356C22×C17—41no—
357C22×C17—42no—
358C22×C17—42no—
359C22×C17—42no—
360C22×C17—81no—
361C22×C17—81no—
362C22×C17—81no—
363C22×C17—81no—
364C22×C17#41714yes—
365C22×C17C22×C22⋊C411yescharacteristic
366C22×C17#54611yescharacteristic
367C22×C17#54711yescharacteristic
368C22×C17C2×AGL(1,ℤ/8)11yescharacteristic
369C22×C17C2×#13711yescharacteristic
370C22×C17#57611yescharacteristic
371C22×C17#57711yescharacteristic
372C4×C17—22no—
373C4×C17—22no—
374C4×C17—22no—
375C4×C17—22no—
376C4×C17—42no—
377C4×C17—42no—
378C4×C17—42no—
379C4×C17C4×#4111yescharacteristic
380C4×C17#52011yescharacteristic
381C4×C17#54611yescharacteristic
382C4×C17#54711yescharacteristic
383Dic17—42no—
384Dic17—81no—
385Dic17—81no—
386Dic17—81no—
387C22×M16—171no—
388C23×C8—171no—
389#553—24no—
390#553Dic1718yescomplemented
391C2×#126—21no—
392C2×#125C2×D1711yescharacteristic
393C2×#123—21no—
394C2×#121—21no—
395C2×#121C2×D1711yescharacteristic
396C2×#121C2×D1711yescharacteristic
397C2×C4×D4—21no—
398C2×C4×D4—341no—
399C2×C4×D4C2×D1711yescharacteristic
400C2×C4×D4C2×D1711yescharacteristic
401C2×#117C2×D1711yescharacteristic
402C22×C4⋊C4—171no—
403C22×C4⋊C4—171no—
404C22×C4⋊C4C2×D1711yescharacteristic
405#435—344no—
406C2×C4⋊C8—171no—
407C2×#102—171no—
408C2×#102—171no—
409C2×#102—171no—
410C2×#102—171no—
411C2×C22⋊C8—171no—
412C2×C22⋊C8—171no—
413C2×#97—171no—
414#389—341no—
415#385—341no—
416#385—341no—
417#384—171no—
418#380—171no—
419#380—171no—
420C4×C4⋊C4—171no—
421#340—171no—
422#340—171no—
423#340—171no—
424#340—171no—
425#340—171no—
426#340—171no—
427#340—171no—
428#340—171no—
429#340—171no—
430#340—171no—
431#340—171no—
432#340—171no—
433C2×C17—24no—
434C2×C17—42no—
435C2×C17—82no—
436C2×C17#233911yescharacteristic
437C2×C17C2×#41711yescharacteristic
438C2×C17#289711yescharacteristic
439C2×C17#331811yescharacteristic
440C2×C17#332011yescharacteristic
441C2×C17#334511yescharacteristic
442C2×C17#334611yescharacteristic
443C22×D4—21no—
444C22×D4—21no—
445C22×D4C22⋊D1711yescharacteristic
446C22×D4C22×D1711yescharacteristic
447C23×C4—21no—
448C23×C4—21no—
449C23×C4—341no—
450C23×C4—341no—
451C23×C4C22×D1711yescharacteristic
452C23×C4C22×D1711yescharacteristic
453C2×M16—342no—
454C2×M16—342no—
455C2×M16—681no—
456C22×C8—171no—
457C22×C8—171no—
458C22×C8—171no—
459C22×C8—171no—
460C22×C8—342no—
461C22×C8—342no—
462C22×C8—681no—
463#126—28no—
464#125—22no—
465#125C2×Dic1714yescomplemented
466#123—28no—
467#121—28no—
468#121—22no—
469#121—22no—
470#121C2×Dic1714yescomplemented
471#121C2×Dic1714yescomplemented
472C4×D4—28no—
473C4×D4—22no—
474C4×D4—684no—
475C4×D4C2×Dic1714yes—
476C4×D4C2×Dic1714yescomplemented
477C4×D4C22⋊D1714yes—
478#117—22no—
479#117C2×Dic1714yescomplemented
480C2×C4⋊C4—21no—
481C2×C4⋊C4—22no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—171no—
485C2×C4⋊C4—171no—
486C2×C4⋊C4—171no—
487C2×C4⋊C4—171no—
488C2×C4⋊C4—342no—
489C2×C4⋊C4—342no—
490C2×C4⋊C4—341no—
491C2×C4⋊C4—341no—
492C2×C4⋊C4—341no—
493C2×C4⋊C4—341no—
494C2×C4⋊C4—681no—
495C2×C4⋊C4—681no—
496C2×C4⋊C4C2×Dic1714yescomplemented
497C2×C4⋊C4C22⋊D1711yescharacteristic
498C2×C4⋊C4C22×D1711yescharacteristic
499C2×C4⋊C4C22×D1711yescharacteristic
500C2×C4⋊C4C22×D1711yescharacteristic
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—341no—
506C2×C22⋊C4—341no—
507C2×C22⋊C4C22⋊D1711yescharacteristic
508C2×C22⋊C4C22⋊D1711yescharacteristic
509C2×C42—21no—
510C2×C42—341no—
511C2×C42C22×D1711yescharacteristic
512C4⋊C8—342no—
513#102—342no—
514#102—342no—
515#102—681no—
516#102—681no—
517C22⋊C8—342no—
518C22⋊C8—342no—
519#97—342no—
520#95—341no—
521#95—341no—
522#95—341no—
523C17#2249311yescharacteristic, complemented, Sylow
524C24—21no—
525C24C2×C22⋊D1711yescharacteristic
526C24C2×C22⋊D1711yescharacteristic
527C2×D4—22no—
528C2×D4—22no—
529C2×D4—24no—
530C2×D4—24no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—42no—
537C2×D4—42no—
538C2×D4—81no—
539C2×D4—81no—
540C2×D4C22⋊Dic1714yes—
541C2×D4C22×Dic1712yes—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—24no—
554C22×C4—24no—
555C22×C4—81no—
556C22×C4—81no—
557C22×C4—81no—
558C22×C4—81no—
559C22×C4—341no—
560C22×C4—341no—
561C22×C4—341no—
562C22×C4—341no—
563C22×C4—682no—
564C22×C4—682no—
565C22×C4—682no—
566C22×C4—682no—
567C22×C4—1361no—
568C22×C4—1361no—
569C22×C4C22×Dic1712yes—
570C22×C4C22×Dic1712yes—
571C22×C4C2×C22⋊D1712yes—
572C22×C4C2×C22⋊D1712yes—
573C22×C4C2×C22⋊D1711yescharacteristic
574C22×C4C2×C22⋊D1711yescharacteristic
575C22×C4C2×C22⋊D1711yescharacteristic
576C22×C4C2×C22⋊D1711yescharacteristic
577C22×C4C23×D1711yescharacteristic
578M16—684no—
579C2×C8—172no—
580C2×C8—341no—
581C2×C8—341no—
582C2×C8—341no—
583C2×C8—341no—
584C2×C8—341no—
585C2×C8—341no—
586C2×C8—341no—
587C2×C8—341no—
588C2×C8—341no—
589C2×C8—341no—
590C2×C8—341no—
591C2×C8—684no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—24no—
596C4⋊C4—24no—
597C4⋊C4—24no—
598C4⋊C4—172no—
599C4⋊C4—341no—
600C4⋊C4—341no—
601C4⋊C4—341no—
602C4⋊C4—341no—
603C4⋊C4—341no—
604C4⋊C4—341no—
605C4⋊C4—341no—
606C4⋊C4—682no—
607C4⋊C4—682no—
608C4⋊C4—682no—
609C4⋊C4—1361no—
610C4⋊C4C22⋊Dic1714yes—
611C4⋊C4C22×Dic1712yes—
612C4⋊C4C22×Dic1712yes—
613C4⋊C4C22×Dic1712yes—
614C22⋊C4—24no—
615C22⋊C4—24no—
616C22⋊C4—24no—
617C22⋊C4—24no—
618C22⋊C4—682no—
619C22⋊C4—682no—
620C22⋊C4C22⋊Dic1714yes—
621C22⋊C4C22⋊Dic1714yes—
622C42—24no—
623C42—682no—
624C42C22×Dic1712yes—
625C42C2×C22⋊D1712yes—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—22no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23#1058763512yes—
644C23#1058763712yes—
645C23C2×C22⋊Dic1712yes—
646C23C2×C22⋊Dic1712yes—
647C23C22×C22⋊D1711yescharacteristic
648D4—28no—
649D4—22no—
650D4—22no—
651D4—48no—
652D4—41no—
653D4—41no—
654D4—84no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—84no—
681C2×C4—84no—
682C2×C4—342no—
683C2×C4—681no—
684C2×C4—681no—
685C2×C4—681no—
686C2×C4—681no—
687C2×C4—681no—
688C2×C4—681no—
689C2×C4—681no—
690C2×C4—681no—
691C2×C4—681no—
692C2×C4—681no—
693C2×C4—681no—
694C2×C4—1364no—
695C2×C4—1364no—
696C2×C4C2×C22⋊Dic1712yes—
697C2×C4C2×C22⋊Dic1712yes—
698C2×C4C2×C22⋊Dic1712yes—
699C2×C4C2×C22⋊Dic1712yes—
700C2×C4#41×D1711yescharacteristic
701C2×C4#41×D1711yescharacteristic
702C2×C4#1058769611yescharacteristic
703C2×C4#1058769711yescharacteristic
704C2×C4C23×Dic1711yescharacteristic
705C2×C4C22×C22⋊D1711yescharacteristic
706C8—342no—
707C8—681no—
708C8—681no—
709C8—681no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—22no—
716C22—22no—
717C22—22no—
718C22—22no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—42no—
724C22—42no—
725C22—42no—
726C22—81no—
727C22—81no—
728C22—81no—
729C22—81no—
730C22#1176281014yes—
731C22C22×C22⋊Dic1711yescharacteristic
732C22#1176344711yescharacteristic
733C22#1176345811yescharacteristic
734C22C2×#1058763511yescharacteristic
735C22C2×#1058763711yescharacteristic
736C22#1176361211yescharacteristic
737C22#1176362011yescharacteristic
738C4—22no—
739C4—22no—
740C4—22no—
741C4—22no—
742C4—42no—
743C4—42no—
744C4—42no—
745C4—682no—
746C4—1361no—
747C4—1361no—
748C4—1361no—
749C4#41×Dic1711yescharacteristic
750C4#1176329211yescharacteristic
751C4#1176344711yescharacteristic
752C4#1176345811yescharacteristic
753C2—24no—
754C2—42no—
755C2—82no—
756C2#1453161411yescharacteristic
757C2C2×#1176281011yescharacteristic
758C2#1453731011yescharacteristic
759C2#1454091911yescharacteristic
760C2#1454094911yescharacteristic
761C2#1454124811yescharacteristic
762C2#1454126911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
Fitting, prime radicalC2×C17×#553C2
socleC23×C17C22×D4
cosocleC22×C4×C17C24
hypercenterC2×#553D17
hypocenterC17#22493
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#553

Complements

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

NH ≅ G/Ntype
1. C2×#11762881C2semidirect
2. D4×C4⋊Dic17C2semidirect
3. #14529754C2semidirect
4. #14529742C2semidirect
5. #14529223C2semidirect
6. #14529213C2semidirect
7. #14529102C2semidirect
8. #14529102C2semidirect
9. #14528879C2semidirect
10. #14528874C2semidirect
11. #14528784C2semidirect
12. #14528609C2semidirect
13. #14528505C2semidirect
14. C2×#11762571C2semidirect
50. C17×#553C4semidirect
74. C17×#125C2×C4semidirect
79. C17×#121C2×C4semidirect
80. C17×#121C2×C4semidirect
84. C4×D4×C17C2×C4semidirect
87. C17×#117C2×C4semidirect
92. C2×C4⋊C4×C17C2×C4semidirect
390. #553Dic17semidirect
465. #125C2×Dic17semidirect
470. #121C2×Dic17semidirect
471. #121C2×Dic17semidirect
476. C4×D4C2×Dic17semidirect
479. #117C2×Dic17semidirect
496. C2×C4⋊C4C2×Dic17semidirect
523. C17#22493semidirect

Maximal subgroups

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

subgroupindex
C2×#117628812
D4×C4⋊Dic172
#145297542
#145297422
#145292232
#145292132
#145291022
#145288792
#145288742
#145287842
#145286092
#145285052
C2×#117625712
C2×C17×#5532
#2249317