Finite Group Databasebeta

← #17050621

Subgroups — #17050621

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×#11763524C211yesmaximal, characteristic
2C2×#11762881C211yesmaximal, characteristic, complemented
3#14529756C211yesmaximal, characteristic, complemented
4#14529736C211yesmaximal, characteristic, complemented
5#14529220C211yesmaximal, characteristic, complemented
6#14529210C211yesmaximal, characteristic, complemented
7#14529106C211yesmaximal, characteristic, complemented
8#14529101C211yesmaximal, characteristic, complemented
9#14528876C211yesmaximal, characteristic, complemented
10#14528876C211yesmaximal, characteristic, complemented
11#14528791C211yesmaximal, characteristic, complemented
12#14528612C211yesmaximal, characteristic, complemented
13#14528503C211yesmaximal, characteristic, complemented
14#14528500C211yesmaximal, characteristic, complemented
15C17×#2352C211yesmaximal, characteristic, complemented
16C22×#63223C2211yescharacteristic
17C23×#3622C2211yescharacteristic
18#11763524—24no—
19#11763524C418yescomplemented
20C2×#10587555C2211yescharacteristic
21C2×#10587571—21no—
22C2×#10587571—21no—
23C2×#10587616C2211yescharacteristic
24C2×#10587616C2211yescharacteristic
25C2×#10587624—21no—
26C2×C4×D68C2211yescharacteristic
27C2×#10587612C2211yescharacteristic
28C2×#10587612C2211yescharacteristic
29C2×#10587578—21no—
30#11762881—24no—
31C2×C4⋊#3622C2211yescharacteristic
32C2×#10587480C2211yescharacteristic
33C2×#10587480C2211yescharacteristic
34C2×#10587480C2211yescharacteristic
35C2×#10587480C2211yescharacteristic
36C2×C22⋊#3622C2211yescharacteristic
37C2×C22⋊#3622C2211yescharacteristic
38C2×#10587474C2211yescharacteristic
39#11762571C2211yescharacteristic
40#11762571C2211yescharacteristic
41#11762571C2211yescharacteristic
42#11762571C2211yescharacteristic
43#11762571C2211yescharacteristic
44#11762571C2211yescharacteristic
45#11762571C2211yescharacteristic
46#11762571C2211yescharacteristic
47#11762571C2211yescharacteristic
48#11762571C2211yescharacteristic
49#11762571C2211yescharacteristic
50#11762571C2211yescharacteristic
51C2×C4×D4×C17C2211yescharacteristic
52C2×C17×#117C2211yescharacteristic
53C22×C4⋊C4×C17C2211yescharacteristic
54C17×#388—21no—
55C17×#387—21no—
56C17×#386—21no—
57C17×#382C2211yescharacteristic
58C17×#380C2211yescharacteristic
59C17×#380C2211yescharacteristic
60C4×C4⋊C4×C17C2211yescharacteristic
61C4×C22⋊C4×C17—21no—
62C22×D4×C17D411yescharacteristic
63C23×C4×C17—21no—
64C23×C4×C17C2311yescharacteristic
65C23×C4×C17C2311yescharacteristic
66C22×C22⋊D17—21no—
67C22×C22⋊D17—21no—
68C22×D68C2311yescharacteristic
69C22×C4×D17—21no—
70C22×Dic34—21no—
71C4×D4×C17C2×C414yes—
72C4×D4×C17D414yes—
73C17×#117—22no—
74C17×#117—41no—
75C2×C4⋊C4×C17—22no—
76C2×C4⋊C4×C17—21no—
77C2×C4⋊C4×C17—41no—
78C2×C4⋊C4×C17D411yescharacteristic
79C2×C4⋊C4×C17C2311yescharacteristic
80C2×C4⋊C4×C17C2311yescharacteristic
81C2×C4⋊C4×C17C2311yescharacteristic
82C2×C4⋊C4×C17C2311yescharacteristic
83C2×C22⋊C4×C17—21no—
84C2×C22⋊C4×C17—21no—
85C2×C22⋊C4×C17—21no—
86C2×C22⋊C4×C17D411yescharacteristic
87C2×C22⋊C4×C17D411yescharacteristic
88C2×C42×C17—21no—
89C2×C42×C17—21no—
90C2×C42×C17C2311yescharacteristic
91C2×C22⋊Dic17—21no—
92C2×C22⋊Dic17—21no—
93#10587624—28no—
94#10587616—22no—
95#10587616—22no—
96#10587616C2×C414yes—
97#10587616C2×C414yescomplemented
98C2×#63227—21no—
99C2×#63227—21no—
100C2×#63227—21no—
101#10587612—22no—
102#10587612—22no—
103#10587612C2×C414yes—
104#10587612C2×C414yescomplemented
105C2×C4⋊Dic17—21no—
106C2×C4⋊Dic17C2311yescharacteristic
107C2×C4⋊Dic17C2311yescharacteristic
108C2×C4⋊Dic17C2311yescharacteristic
109C2×C4×Dic17—21no—
110C2×C4×Dic17—21no—
111C2×#63223—22no—
112C2×#63223—22no—
113C2×#63223—41no—
114C22×#3622—22no—
115C22×#3622—22no—
116C22×#3622—41no—
117C22×#3622C2311yescharacteristic
118C22×#3622C2311yescharacteristic
119C22×#3622C2311yescharacteristic
120C22×#3622C2311yescharacteristic
121#10587578—28no—
122#10587571—28no—
123#10587571—28no—
124C4×D68—22no—
125C4×D68C2×C414yescomplemented
126#10587555—22no—
127#10587555C2×C414yescomplemented
128C17×#95—21no—
129C17×#95—21no—
130C17×#95—21no—
131C17×#95—21no—
132C17×#95—21no—
133C22⋊#3622—22no—
134C22⋊#3622—22no—
135#10587480—22no—
136#10587480—22no—
137#10587480—41no—
138#10587480—41no—
139C4⋊#3622—22no—
140#10587474—22no—
141C24×C17C2×D411yescharacteristic
142C24×C17C2×D411yescharacteristic
143C23×D17—21no—
144C2×D4×C17—41no—
145C2×D4×C17—41no—
146C2×D4×C17C22⋊C414yes—
147C22×C4×C17—21no—
148C22×C4×C17—21no—
149C22×C4×C17—21no—
150C22×C4×C17—21no—
151C22×C4×C17—21no—
152C22×C4×C17—21no—
153C22×C4×C17—21no—
154C22×C4×C17—21no—
155C22×C4×C17—21no—
156C22×C4×C17—21no—
157C22×C4×C17—21no—
158C22×C4×C17—21no—
159C22×C4×C17—42no—
160C22×C4×C17—42no—
161C22×C4×C17—81no—
162C22×C4×C17C22×C412yes—
163C22×C4×C17C22×C412yes—
164C22×C4×C17C2×D412yes—
165C22×C4×C17C2×D412yes—
166C22×C4×C17C2×D411yescharacteristic
167C22×C4×C17C2×D411yescharacteristic
168C22×C4×C17C2×D411yescharacteristic
169C22×C4×C17C2×D411yescharacteristic
170C22×C4×C17C2411yescharacteristic
171C2×C22⋊D17—24no—
172C2×C22⋊D17—24no—
173C2×C22⋊D17—81no—
174C2×C22⋊D17—81no—
175C2×C22⋊D17—81no—
176C2×C22⋊D17—81no—
177C22×Dic17—21no—
178C22×Dic17—21no—
179C22×Dic17—21no—
180C2×D68—21no—
181C2×D68—21no—
182C2×D68—21no—
183C2×D68—21no—
184C2×D68—21no—
185C2×D68C22×C412yes—
186C2×C4×D17—24no—
187C2×C4×D17—42no—
188C2×C4×D17—42no—
189C2×Dic34—24no—
190C2×Dic34—81no—
191C2×Dic34—81no—
192C4⋊C4×C17—21no—
193C4⋊C4×C17—21no—
194C4⋊C4×C17—21no—
195C4⋊C4×C17—21no—
196C4⋊C4×C17—21no—
197C4⋊C4×C17—21no—
198C4⋊C4×C17—21no—
199C4⋊C4×C17—42no—
200C4⋊C4×C17C22⋊C414yes—
201C4⋊C4×C17#4112yes—
202C22⋊C4×C17—42no—
203C22⋊C4×C17—42no—
204C22⋊C4×C17—81no—
205C22⋊C4×C17C22⋊C414yes—
206C22⋊C4×C17C22⋊C414yes—
207C42×C17—42no—
208C42×C17—81no—
209C42×C17C22×C412yes—
210C42×C17C2×D412yes—
211C22⋊Dic17—24no—
212C22⋊Dic17—24no—
213#63227—24no—
214#63227—24no—
215#63227—24no—
216C4⋊Dic17—24no—
217C4⋊Dic17—21no—
218C4⋊Dic17—21no—
219C4⋊Dic17—21no—
220C4⋊Dic17C22×C412yes—
221C4⋊Dic17C22×C412yes—
222C4⋊Dic17C22×C412yes—
223C4×Dic17—24no—
224C4×Dic17—24no—
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×C17C2×C22⋊C412yes—
253C23×C17C2×C22⋊C412yes—
254C23×C17C22×D411yescharacteristic
255C22×D17—22no—
256C22×D17—41no—
257C22×D17—41no—
258C22×D17—41no—
259C22×D17—41no—
260C22×D17—41no—
261C22×D17—41no—
262D4×C17—44no—
263C2×C4×C17—21no—
264C2×C4×C17—21no—
265C2×C4×C17—21no—
266C2×C4×C17—21no—
267C2×C4×C17—21no—
268C2×C4×C17—21no—
269C2×C4×C17—21no—
270C2×C4×C17—21no—
271C2×C4×C17—22no—
272C2×C4×C17—22no—
273C2×C4×C17—22no—
274C2×C4×C17—22no—
275C2×C4×C17—22no—
276C2×C4×C17—22no—
277C2×C4×C17—22no—
278C2×C4×C17—22no—
279C2×C4×C17—22no—
280C2×C4×C17—41no—
281C2×C4×C17—41no—
282C2×C4×C17—41no—
283C2×C4×C17—41no—
284C2×C4×C17—41no—
285C2×C4×C17—41no—
286C2×C4×C17—41no—
287C2×C4×C17—41no—
288C2×C4×C17—41no—
289C2×C4×C17—41no—
290C2×C4×C17—41no—
291C2×C4×C17—84no—
292C2×C4×C17C2×C22⋊C412yes—
293C2×C4×C17C2×C22⋊C412yes—
294C2×C4×C17C2×C22⋊C412yes—
295C2×C4×C17C2×C22⋊C412yes—
296C2×C4×C17C23×C411yescharacteristic
297C2×C4×C17C22×D411yescharacteristic
298C2×C4×C17C2×#4111yescharacteristic
299C2×C4×C17C2×#4111yescharacteristic
300C2×C4×C17H(5,𝔽2)11yescharacteristic
301C2×C4×C172−1+411yescharacteristic
302C22⋊D17—84no—
303C22⋊D17—84no—
304C2×Dic17—22no—
305C2×Dic17—22no—
306C2×Dic17—22no—
307C2×Dic17—41no—
308C2×Dic17—41no—
309C2×Dic17—41no—
310C2×Dic17—41no—
311C2×Dic17—41no—
312C2×Dic17—41no—
313D68—22no—
314D68—22no—
315D68—41no—
316D68—41no—
317C4×D17—48no—
318Dic34—84no—
319#3622—22no—
320#3622—41no—
321#3622—41no—
322#3622—41no—
323C2×#555—171no—
324C2×#435—171no—
325#2352D1711yescharacteristic, complemented
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×C17C22×C22⋊C411yescharacteristic
353C22×C17#54611yescharacteristic
354C22×C17#54711yescharacteristic
355C22×C17#57511yescharacteristic
356C22×C17#57511yescharacteristic
357C22×C17#57611yescharacteristic
358C22×C17#57711yescharacteristic
359C2×D17—42no—
360C2×D17—42no—
361C2×D17—42no—
362C2×D17—81no—
363C2×D17—81no—
364C2×D17—81no—
365C2×D17—81no—
366C4×C17—22no—
367C4×C17—22no—
368C4×C17—22no—
369C4×C17—22no—
370C4×C17—42no—
371C4×C17—81no—
372C4×C17—81no—
373C4×C17—81no—
374C4×C17C4×#4111yescharacteristic
375C4×C17#52011yescharacteristic
376C4×C17#54611yescharacteristic
377C4×C17#54711yescharacteristic
378Dic17—42no—
379Dic17—42no—
380Dic17—42no—
381C22×M16—171no—
382C23×C8—171no—
383#555—178no—
384#555—344no—
385C2×C4⋊Q8—171no—
386C2×#124—341no—
387C2×#124—341no—
388C2×#121—171no—
389C2×#121—171no—
390C2×#121—341no—
391C2×C4×D4—171no—
392C2×C4×D4C2×D1711yescharacteristic
393C2×#117—171no—
394C2×#117—171no—
395C2×#117—341no—
396C2×#117C2×D1711yescharacteristic
397C22×C4⋊C4C2×D1711yescharacteristic
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—21no—
408#387—21no—
409#386—21no—
410#382C2×D1711yescharacteristic
411#380C2×D1711yescharacteristic
412#380C2×D1711yescharacteristic
413C4×C4⋊C4C2×D1711yescharacteristic
414C4×C22⋊C4—21no—
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#233911yescharacteristic
430C2×C17#289611yescharacteristic
431C2×C17#289711yescharacteristic
432C2×C17#331911yescharacteristic
433C2×C17#332111yescharacteristic
434C2×C17#334711yescharacteristic
435C2×C17#334811yescharacteristic
436D17—82no—
437C22×Q8—341no—
438C22×D4—171no—
439C22×D4—341no—
440C22×D4—341no—
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—174no—
457C4⋊Q8—342no—
458#124—348no—
459#124—348no—
460#121—174no—
461#121—174no—
462#121—348no—
463#121—342no—
464#121—342no—
465C4×D4—174no—
466C4×D4—342no—
467C4×D4C4×D1714yes—
468C4×D4D6814yes—
469#117—22no—
470#117—41no—
471#117—174no—
472#117—174no—
473#117—342no—
474#117—342no—
475#117—348no—
476C2×C4⋊C4—22no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—41no—
479C2×C4⋊C4—171no—
480C2×C4⋊C4—171no—
481C2×C4⋊C4—171no—
482C2×C4⋊C4—341no—
483C2×C4⋊C4C22⋊D1711yescharacteristic
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—341no—
492C2×C22⋊C4—341no—
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—21no—
512#95—21no—
513#95—21no—
514#95—21no—
515#95—21no—
516C17#2249211yescharacteristic, complemented, Sylow
517C24—341no—
518C24C2×C22⋊D1711yescharacteristic
519C24C2×C22⋊D1711yescharacteristic
520C2×Q8—344no—
521C2×Q8—1361no—
522C2×Q8—1361no—
523C2×D4—41no—
524C2×D4—41no—
525C2×D4—172no—
526C2×D4—344no—
527C2×D4—344no—
528C2×D4—341no—
529C2×D4—341no—
530C2×D4—341no—
531C2×D4—341no—
532C2×D4—341no—
533C2×D4—1361no—
534C2×D4—1361no—
535C2×D4—1361no—
536C2×D4—1361no—
537C2×D4#6322714yes—
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—21no—
550C22×C4—42no—
551C22×C4—42no—
552C22×C4—81no—
553C22×C4—341no—
554C22×C4—341no—
555C22×C4—341no—
556C22×C4—344no—
557C22×C4—682no—
558C22×C4—682no—
559C22×C4C2×C4×D1712yes—
560C22×C4C2×C4×D1712yes—
561C22×C4C2×D6812yes—
562C22×C4C2×D6812yes—
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—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—42no—
590C4⋊C4—172no—
591C4⋊C4—172no—
592C4⋊C4—172no—
593C4⋊C4—341no—
594C4⋊C4—341no—
595C4⋊C4—341no—
596C4⋊C4—344no—
597C4⋊C4#6322714yes—
598C4⋊C4#6325412yes—
599C22⋊C4—42no—
600C22⋊C4—42no—
601C22⋊C4—81no—
602C22⋊C4—344no—
603C22⋊C4—344no—
604C22⋊C4—344no—
605C22⋊C4—344no—
606C22⋊C4—344no—
607C22⋊C4#6322714yes—
608C22⋊C4#6322714yes—
609C42—42no—
610C42—81no—
611C42—344no—
612C42—344no—
613C42C2×C4×D1712yes—
614C42C2×D6812yes—
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—342no—
628C23—681no—
629C23—681no—
630C23—681no—
631C23—681no—
632C23—681no—
633C23—681no—
634C23C2×#6322712yes—
635C23C2×#6322712yes—
636C23C22×C22⋊D1711yescharacteristic
637Q8—1364no—
638D4—44no—
639D4—342no—
640D4—342no—
641D4—681no—
642D4—681no—
643D4—1364no—
644D4—1364no—
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—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—84no—
674C2×C4—342no—
675C2×C4—342no—
676C2×C4—342no—
677C2×C4—688no—
678C2×C4—681no—
679C2×C4—681no—
680C2×C4—681no—
681C2×C4—681no—
682C2×C4—681no—
683C2×C4—681no—
684C2×C4C2×#6322712yes—
685C2×C4C2×#6322712yes—
686C2×C4C2×#6322712yes—
687C2×C4C2×#6322712yes—
688C2×C4C22×C4×D1711yescharacteristic
689C2×C4C22×D6811yescharacteristic
690C2×C4C2×#6325411yescharacteristic
691C2×C4#1058769111yescharacteristic
692C2×C4#41×D1711yescharacteristic
693C2×C4#1058769711yescharacteristic
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—682no—
713C22—682no—
714C22—682no—
715C22—1361no—
716C22—1361no—
717C22—1361no—
718C22—1361no—
719C22C22×#6322711yescharacteristic
720C22#1176345311yescharacteristic
721C22#1176345811yescharacteristic
722C22#1176360711yescharacteristic
723C22#1176360711yescharacteristic
724C22#1176361211yescharacteristic
725C22#1176361711yescharacteristic
726C4—22no—
727C4—22no—
728C4—22no—
729C4—22no—
730C4—42no—
731C4—81no—
732C4—81no—
733C4—81no—
734C4—682no—
735C4—682no—
736C4—682no—
737C4C4×#6325411yescharacteristic
738C4#1176328811yescharacteristic
739C4#1176345411yescharacteristic
740C4#1176346311yescharacteristic
741C2—42no—
742C2—42no—
743C2—1362no—
744C2#1453160911yescharacteristic
745C2#1453730111yescharacteristic
746C2#1453730711yescharacteristic
747C2#1454094011yescharacteristic
748C2#1454097011yescharacteristic
749C2#1454127811yescharacteristic
750C2#1454129311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC17×#2352C2
socleC23×C17C22×D4
prime radicalC2×#11763524C2
cosocleC22×C4×C17C24
hypercenter#2352D17
hypocenterC17#22492
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2352

Complements

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

NH ≅ G/Ntype
2. C2×#11762881C2semidirect
3. #14529756C2semidirect
4. #14529736C2semidirect
5. #14529220C2semidirect
6. #14529210C2semidirect
7. #14529106C2semidirect
8. #14529101C2semidirect
9. #14528876C2semidirect
10. #14528876C2semidirect
11. #14528791C2semidirect
12. #14528612C2semidirect
13. #14528503C2semidirect
14. #14528500C2semidirect
15. C17×#2352C2semidirect
19. #11763524C4semidirect
97. #10587616C2×C4semidirect
104. #10587612C2×C4semidirect
125. C4×D68C2×C4semidirect
127. #10587555C2×C4semidirect
325. #2352D17semidirect
516. C17#22492semidirect

Maximal subgroups

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

subgroupindex
C2×#117635242
C2×#117628812
#145297562
#145297362
#145292202
#145292102
#145291062
#145291012
#145288762
#145287912
#145286122
#145285032
#145285002
C17×#23522
#2249217