Finite Group Databasebeta

← #17045516

Subgroups — #17045516

Order 4352.

1096 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762954C211yesmaximal, characteristic
2C4×#10587616C211yesmaximal, characteristic, complemented
3#14529649C211yesmaximal, characteristic, complemented
4#14529641C211yesmaximal, characteristic, complemented
5#14529470C211yesmaximal, characteristic, complemented
6#14529463C211yesmaximal, characteristic, complemented
7#14529422C211yesmaximal, characteristic, complemented
8#14529408C211yesmaximal, characteristic, complemented
9#14529135C211yesmaximal, characteristic, complemented
10#14529121C211yesmaximal, characteristic, complemented
11#14529106C211yesmaximal, characteristic, complemented
12#14528983C211yesmaximal, characteristic, complemented
13#14528724C211yesmaximal, characteristic, complemented
14C4×C22⋊#3622C211yesmaximal, characteristic, complemented
15C17×#2297C211yesmaximal, characteristic, complemented
16C22×#63230C2211yescharacteristic
17C22×#63228C2211yescharacteristic
18C2×#10587616C2211yescharacteristic
19C2×C4×D68C2211yescharacteristic
20C2×C4×C22⋊D17—21no—
21#11762954C418yescomplemented
22C2×#10587478C2211yescharacteristic
23C2×#10587479C2211yescharacteristic
24C2×#10587506C2211yescharacteristic
25C2×#10587506C2211yescharacteristic
26C2×#10587506C2211yescharacteristic
27C2×#10587503C2211yescharacteristic
28C2×#10587503C2211yescharacteristic
29C2×#10587503C2211yescharacteristic
30C2×#10587480C2211yescharacteristic
31C2×#10587480C2211yescharacteristic
32C2×C22⋊#3622C2211yescharacteristic
33C2×C22⋊#3622C2211yescharacteristic
34C2×C4×#3622C2211yescharacteristic
35C2×C4×#3622C2211yescharacteristic
36#11762711C2211yescharacteristic
37#11762707C2211yescharacteristic
38#11762700—21no—
39#11762688—21no—
40#11762669C2211yescharacteristic
41C4×C4⋊Dic17C2211yescharacteristic
42C4×#63227—21no—
43#11762571C2211yescharacteristic
44#11762571C2211yescharacteristic
45#11762571C2211yescharacteristic
46#11762571C2211yescharacteristic
47#11762564C2211yescharacteristic
48#11762564C2211yescharacteristic
49C22×#41×C17C2211yescharacteristic
50C2×C17×#117C2211yescharacteristic
51C22×C42×C17C2211yescharacteristic
52C17×#391C2211yescharacteristic
53C17×#391C2211yescharacteristic
54C17×#390C2211yescharacteristic
55C17×#390C2211yescharacteristic
56C17×#386—21no—
57C17×#386—21no—
58C4×C22⋊C4×C17—21no—
59C4×C22⋊C4×C17—21no—
60C2×#41×C17—22no—
61C2×#41×C17—41no—
62C2×#41×C17—41no—
63C2×#41×C17—41no—
64C2×#41×C17—41no—
65C2×#41×C17C2×C414yescomplemented
66C22×Q8×C17C2311yescharacteristic
67C22×D4×C17—21no—
68C22×D4×C17C2311yescharacteristic
69C23×C4×C17—21no—
70C23×C4×C17D411yescharacteristic
71C23×C4×C17D411yescharacteristic
72C23×C4×C17C2311yescharacteristic
73C22×C22⋊D17—21no—
74C22×D68C2311yescharacteristic
75C22×C4×D17—21no—
76C17×#117—41no—
77C17×#117—41no—
78C2×C4⋊C4×C17C2311yescharacteristic
79C2×C4⋊C4×C17C2311yescharacteristic
80C2×C22⋊C4×C17—21no—
81C2×C22⋊C4×C17—21no—
82C2×C22⋊C4×C17—21no—
83C2×C22⋊C4×C17—21no—
84C2×C22⋊C4×C17—21no—
85C2×C42×C17—21no—
86C2×C42×C17—41no—
87C2×C42×C17—41no—
88C2×C42×C17D411yescharacteristic
89C2×C42×C17D411yescharacteristic
90C2×C42×C17C2311yescharacteristic
91C2×C42×C17C2311yescharacteristic
92C2×C22⋊Dic17—21no—
93C2×#63230—41no—
94C2×#63230—41no—
95C2×#63230C2×C414yescomplemented
96C2×#63228—41no—
97C2×#63228—41no—
98C2×#63228C2×C414yescomplemented
99#10587616—22no—
100#10587616C2×C414yes—
101C4×C22⋊D17—44no—
102C2×#63227—21no—
103C2×#63227—21no—
104C2×#63227—21no—
105C2×#63227—21no—
106C2×C4⋊Dic17C2311yescharacteristic
107C2×C4⋊Dic17C2311yescharacteristic
108C2×C4⋊Dic17C2311yescharacteristic
109C2×#63225—21no—
110C2×C4×Dic17—21no—
111C22×#3622C2311yescharacteristic
112C22×#3622C2311yescharacteristic
113C22×#3622C2311yescharacteristic
114C22×#3622C2311yescharacteristic
115C4×D68—41no—
116C4×D68—41no—
117C17×#95—21no—
118C17×#95—21no—
119C17×#95—21no—
120C17×#95—21no—
121#10587506—41no—
122#10587506—41no—
123#10587506C2×C414yescomplemented
124#10587503—41no—
125#10587503—41no—
126#10587503C2×C414yescomplemented
127#10587502—21no—
128#10587502—21no—
129#10587502—21no—
130C22⋊#3622—22no—
131C22⋊#3622C2×C414yescomplemented
132#10587480—41no—
133#10587480—41no—
134#10587479—41no—
135#10587478—41no—
136C4×#3622—41no—
137C4×#3622—41no—
138C24×C17—21no—
139C24×C17C2×D411yescharacteristic
140C23×D17—21no—
141#41×C17—44no—
142#41×C17—44no—
143#41×C17—44no—
144#41×C17—44no—
145C2×Q8×C17—21no—
146C2×Q8×C17—21no—
147C2×Q8×C17—21no—
148C2×Q8×C17—21no—
149C2×Q8×C17—21no—
150C2×Q8×C17C22×C412yes—
151C2×D4×C17—24no—
152C2×D4×C17—21no—
153C2×D4×C17—21no—
154C2×D4×C17—21no—
155C2×D4×C17—21no—
156C2×D4×C17—21no—
157C2×D4×C17—42no—
158C2×D4×C17—42no—
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—24no—
166C22×C4×C17—22no—
167C22×C4×C17—22no—
168C22×C4×C17—22no—
169C22×C4×C17—21no—
170C22×C4×C17—21no—
171C22×C4×C17—41no—
172C22×C4×C17—41no—
173C22×C4×C17—41no—
174C22×C4×C17—42no—
175C22×C4×C17—42no—
176C22×C4×C17C22×C412yes—
177C22×C4×C17C2×D411yescharacteristic
178C22×C4×C17C2×D411yescharacteristic
179C22×C4×C17C2×D411yescharacteristic
180C22×C4×C17C2×D411yescharacteristic
181C22×C4×C17C2×D411yescharacteristic
182C22×C4×C17#4112yes—
183C22×C4×C17C2411yescharacteristic
184C2×C22⋊D17—24no—
185C2×C22⋊D17—42no—
186C2×C22⋊D17—42no—
187C22×Dic17—21no—
188C22×Dic17—21no—
189C22×Dic17—21no—
190C2×D68—21no—
191C2×D68—21no—
192C2×D68—21no—
193C2×D68—21no—
194C2×D68—21no—
195C2×D68C22×C412yes—
196C2×C4×D17—42no—
197C2×C4×D17—42no—
198C2×C4×D17—42no—
199C4⋊C4×C17—21no—
200C4⋊C4×C17—21no—
201C4⋊C4×C17—21no—
202C4⋊C4×C17—21no—
203C22⋊C4×C17—42no—
204C22⋊C4×C17—42no—
205C22⋊C4×C17—42no—
206C22⋊C4×C17—42no—
207C22⋊C4×C17—42no—
208C42×C17—21no—
209C42×C17—21no—
210C42×C17—21no—
211C42×C17—21no—
212C42×C17—41no—
213C42×C17—41no—
214C42×C17—42no—
215C22⋊Dic17—42no—
216#63230—44no—
217#63228—44no—
218#63227—24no—
219#63227—42no—
220#63227—42no—
221#63227—42no—
222C4⋊Dic17—21no—
223C4⋊Dic17—21no—
224C4⋊Dic17—21no—
225C4⋊Dic17—21no—
226C4⋊Dic17—21no—
227C4⋊Dic17C22×C412yes—
228#63225—42no—
229C4×Dic17—42no—
230C2×#3622—21no—
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×#3622C22×C412yes—
241C2×#3622C22×C412yes—
242#22045—171nomaximal, Sylow
243C23×C17—21no—
244C23×C17—21no—
245C23×C17—21no—
246C23×C17—21no—
247C23×C17—21no—
248C23×C17—21no—
249C23×C17—22no—
250C23×C17—41no—
251C23×C17—41no—
252C23×C17—41no—
253C23×C17—41no—
254C23×C17—41no—
255C23×C17—41no—
256C23×C17C4×D412yes—
257C23×C17C22×D411yescharacteristic
258C22×D17—22no—
259C22×D17—41no—
260C22×D17—41no—
261C22×D17—41no—
262C22×D17—41no—
263C22×D17—41no—
264C22×D17—41no—
265Q8×C17—22no—
266Q8×C17—22no—
267Q8×C17—41no—
268Q8×C17—41no—
269D4×C17—22no—
270D4×C17—22no—
271D4×C17—48no—
272D4×C17—41no—
273D4×C17—41no—
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—21no—
288C2×C4×C17—21no—
289C2×C4×C17—21no—
290C2×C4×C17—44no—
291C2×C4×C17—44no—
292C2×C4×C17—48no—
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—41no—
300C2×C4×C17—41no—
301C2×C4×C17C4×D412yes—
302C2×C4×C17#13512yes—
303C2×C4×C17#13512yes—
304C2×C4×C17AGL(1,ℤ/8)12yes—
305C2×C4×C17C23×C411yescharacteristic
306C2×C4×C17C2×#4111yescharacteristic
307C2×C4×C17H(5,𝔽2)11yescharacteristic
308C2×C4×C17H(5,𝔽2)11yescharacteristic
309C2×C4×C17H(5,𝔽2)11yescharacteristic
310C2×C4×C17H(5,𝔽2)11yescharacteristic
311C22⋊D17—48no—
312C2×Dic17—22no—
313C2×Dic17—41no—
314C2×Dic17—41no—
315C2×Dic17—41no—
316C2×Dic17—41no—
317C2×Dic17—41no—
318C2×Dic17—41no—
319C2×Dic17—41no—
320C2×Dic17—41no—
321D68—22no—
322D68—22no—
323D68—41no—
324D68—41no—
325C4×D17—84no—
326#3622—22no—
327#3622—22no—
328#3622—41no—
329#3622—41no—
330C2×#449—171no—
331C4×#121—171no—
332#2297D1711yescharacteristic, complemented
333#1970—171no—
334#1968—171no—
335#1934—171no—
336#1933—171no—
337#1928—171no—
338#1926—171no—
339#1879—171no—
340#1877—171no—
341#1875—171no—
342#1854—171no—
343#1788—171no—
344C4×C22⋊C8—171no—
345C22×C17—22no—
346C22×C17—22no—
347C22×C17—22no—
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×C17C2×C4×D411yescharacteristic
360C22×C17#53411yescharacteristic
361C22×C17#53511yescharacteristic
362C22×C17C2×#13511yescharacteristic
363C22×C17C2×#13511yescharacteristic
364C22×C17C2×AGL(1,ℤ/8)11yescharacteristic
365C22×C17#57511yescharacteristic
366C2×D17—42no—
367C2×D17—42no—
368C2×D17—42no—
369C2×D17—81no—
370C2×D17—81no—
371C2×D17—81no—
372C2×D17—81no—
373C4×C17—22no—
374C4×C17—22no—
375C4×C17—22no—
376C4×C17—22no—
377C4×C17—42no—
378C4×C17—41no—
379C4×C17—81no—
380C4×C17—81no—
381C4×C17#51811yescharacteristic
382C4×C17#51811yescharacteristic
383C4×C17#53811yescharacteristic
384C4×C17#53811yescharacteristic
385Dic17—42no—
386Dic17—81no—
387Dic17—81no—
388C22×#41C2×D1711yescharacteristic
389C22×SD16—171no—
390C22×D8—171no—
391C2×#121—171no—
392C2×C4×D4—171no—
393C2×C4×D4—341no—
394C2×#117C2×D1711yescharacteristic
395C22×C42C2×D1711yescharacteristic
396#449—178no—
397C2×#107—171no—
398C2×#106—171no—
399C2×#103—171no—
400C2×#103—171no—
401C2×#103—171no—
402C2×#102—171no—
403C2×#102—171no—
404C2×#102—171no—
405C2×#102—171no—
406C2×#102—171no—
407C2×C22⋊C8—171no—
408C2×C22⋊C8—171no—
409C2×C4×C8—171no—
410C2×C4×C8—171no—
411#391C2×D1711yescharacteristic
412#391C2×D1711yescharacteristic
413#390—171no—
414#390C2×D1711yescharacteristic
415#390C2×D1711yescharacteristic
416#389—171no—
417#388—341no—
418#386—21no—
419#386—21no—
420#386—341no—
421#380—171no—
422C4×C4⋊C4—171no—
423C4×C22⋊C4—21no—
424C4×C22⋊C4—21no—
425C4×C22⋊C4—341no—
426#340—171no—
427#340—171no—
428#340—171no—
429#340—171no—
430#336—171no—
431#336—171no—
432C2×C17—42no—
433C2×C17—82no—
434C2×C17#232111yescharacteristic
435C2×C17C4×#13511yescharacteristic
436C2×C17C4×AGL(1,ℤ/8)11yescharacteristic
437C2×C17#318811yescharacteristic
438C2×C17#319111yescharacteristic
439C2×C17#320711yescharacteristic
440C2×C17#321211yescharacteristic
441D17—82no—
442C2×#41—22no—
443C2×#41—41no—
444C2×#41—41no—
445C2×#41—41no—
446C2×#41—41no—
447C2×#41C4×D1714yescomplemented
448C22×Q8C22×D1711yescharacteristic
449C22×D4—21no—
450C22×D4—171no—
451C22×D4—341no—
452C22×D4C22×D1711yescharacteristic
453C23×C4—21no—
454C23×C4—341no—
455C23×C4C22⋊D1711yescharacteristic
456C23×C4C22⋊D1711yescharacteristic
457C23×C4C22×D1711yescharacteristic
458C2×SD16—174no—
459C2×SD16—681no—
460C2×SD16—681no—
461C2×D8—174no—
462C2×D8—681no—
463C2×D8—681no—
464C22×C8—171no—
465C22×C8—171no—
466C22×C8—171no—
467C22×C8—171no—
468#121—174no—
469#121—342no—
470C4×D4—681no—
471C4×D4—681no—
472C4×D4—684no—
473#117—41no—
474#117—41no—
475C2×C4⋊C4—171no—
476C2×C4⋊C4—171no—
477C2×C4⋊C4—171no—
478C2×C4⋊C4—341no—
479C2×C4⋊C4C22×D1711yescharacteristic
480C2×C4⋊C4C22×D1711yescharacteristic
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—341no—
487C2×C22⋊C4—341no—
488C2×C22⋊C4—341no—
489C2×C22⋊C4—341no—
490C2×C22⋊C4—341no—
491C2×C42—21no—
492C2×C42—41no—
493C2×C42—41no—
494C2×C42—341no—
495C2×C42C22⋊D1711yescharacteristic
496C2×C42C22⋊D1711yescharacteristic
497C2×C42C22×D1711yescharacteristic
498C2×C42C22×D1711yescharacteristic
499#107—681no—
500#106—681no—
501#103—174no—
502#103—681no—
503#103—681no—
504#102—174no—
505#102—681no—
506#102—681no—
507#102—681no—
508#102—681no—
509C22⋊C8—174no—
510C22⋊C8—342no—
511C4×C8—681no—
512C4×C8—681no—
513#95—21no—
514#95—21no—
515#95—21no—
516#95—21no—
517#95—341no—
518#95—341no—
519#95—341no—
520C17#2204511yescharacteristic, complemented, Sylow
521C24—21no—
522C24—341no—
523C24C2×C22⋊D1711yescharacteristic
524#41—44no—
525#41—44no—
526#41—44no—
527#41—44no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8C2×C4×D1712yes—
534C2×D4—24no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—42no—
541C2×D4—42no—
542C2×D4—172no—
543C2×D4—344no—
544C2×D4—341no—
545C2×D4—341no—
546C2×D4—341no—
547C2×D4—341no—
548C2×D4—341no—
549C2×D4—682no—
550C2×D4—682no—
551C2×D4C2×C4×D1712yes—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—24no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—41no—
564C22×C4—41no—
565C22×C4—41no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4—341no—
569C22×C4—341no—
570C22×C4—341no—
571C22×C4—682no—
572C22×C4—682no—
573C22×C4—682no—
574C22×C4C2×C4×D1712yes—
575C22×C4#6325212yes—
576C22×C4C2×C22⋊D1711yescharacteristic
577C22×C4C2×C22⋊D1711yescharacteristic
578C22×C4C2×C22⋊D1711yescharacteristic
579C22×C4C2×C22⋊D1711yescharacteristic
580C22×C4C2×C22⋊D1711yescharacteristic
581C22×C4C23×D1711yescharacteristic
582SD16—684no—
583D8—684no—
584C2×C8—172no—
585C2×C8—172no—
586C2×C8—341no—
587C2×C8—341no—
588C2×C8—341no—
589C2×C8—341no—
590C2×C8—341no—
591C2×C8—341no—
592C2×C8—341no—
593C2×C8—341no—
594C2×C8—341no—
595C2×C8—341no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—172no—
601C4⋊C4—341no—
602C4⋊C4—341no—
603C4⋊C4—341no—
604C4⋊C4—341no—
605C4⋊C4—341no—
606C4⋊C4—682no—
607C22⋊C4—42no—
608C22⋊C4—42no—
609C22⋊C4—42no—
610C22⋊C4—42no—
611C22⋊C4—42no—
612C22⋊C4—344no—
613C22⋊C4—682no—
614C22⋊C4—682no—
615C22⋊C4—682no—
616C22⋊C4—682no—
617C42—21no—
618C42—21no—
619C42—21no—
620C42—21no—
621C42—41no—
622C42—41no—
623C42—42no—
624C42—682no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—22no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—342no—
639C23—681no—
640C23—681no—
641C23—681no—
642C23—681no—
643C23—681no—
644C23—681no—
645C23C4×C22⋊D1712yes—
646C23C22×C22⋊D1711yescharacteristic
647Q8—22no—
648Q8—22no—
649Q8—41no—
650Q8—41no—
651D4—22no—
652D4—22no—
653D4—48no—
654D4—41no—
655D4—41no—
656D4—342no—
657D4—342no—
658D4—688no—
659D4—681no—
660D4—681no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—44no—
678C2×C4—48no—
679C2×C4—44no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—342no—
689C2×C4—681no—
690C2×C4—681no—
691C2×C4—681no—
692C2×C4—681no—
693C2×C4—681no—
694C2×C4—681no—
695C2×C4—681no—
696C2×C4—681no—
697C2×C4—1364no—
698C2×C4C4×C22⋊D1712yes—
699C2×C4#1058763512yes—
700C2×C4#1058763612yes—
701C2×C4#1058763612yes—
702C2×C4C22×C4×D1711yescharacteristic
703C2×C4C2×#6325211yescharacteristic
704C2×C4#1058769111yescharacteristic
705C2×C4#1058769111yescharacteristic
706C2×C4#1058769111yescharacteristic
707C2×C4#1058769111yescharacteristic
708C8—342no—
709C8—342no—
710C8—681no—
711C8—681no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—42no—
720C22—42no—
721C22—42no—
722C22—81no—
723C22—81no—
724C22—81no—
725C22—81no—
726C22—682no—
727C22—682no—
728C22—682no—
729C22—1361no—
730C22—1361no—
731C22—1361no—
732C22—1361no—
733C22C2×C4×C22⋊D1711yescharacteristic
734C22#1176336811yescharacteristic
735C22#1176337611yescharacteristic
736C22C2×#1058763611yescharacteristic
737C22C2×#1058763611yescharacteristic
738C22C2×#1058763511yescharacteristic
739C22#1176360711yescharacteristic
740C4—22no—
741C4—22no—
742C4—22no—
743C4—22no—
744C4—41no—
745C4—42no—
746C4—81no—
747C4—81no—
748C4—682no—
749C4—1361no—
750C4—1361no—
751C4#1176328211yescharacteristic
752C4#1176328211yescharacteristic
753C4#1176339711yescharacteristic
754C4#1176339711yescharacteristic
755C2—42no—
756C2—82no—
757C2—1362no—
758C2#1453144211yescharacteristic
759C2C4×#1058763611yescharacteristic
760C2C4×#1058763511yescharacteristic
761C2#1453954511yescharacteristic
762C2#1453957211yescharacteristic
763C2#1453971711yescharacteristic
764C2#1453976011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC17×#2297C2
socleC23×C17C22×D4
prime radicalC2×#11762954C2
cosocleC22×C4×C17C24
hypercenter#2297D17
hypocenterC17#22045
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2297

Complements

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

NH ≅ G/Ntype
2. C4×#10587616C2semidirect
3. #14529649C2semidirect
4. #14529641C2semidirect
5. #14529470C2semidirect
6. #14529463C2semidirect
7. #14529422C2semidirect
8. #14529408C2semidirect
9. #14529135C2semidirect
10. #14529121C2semidirect
11. #14529106C2semidirect
12. #14528983C2semidirect
13. #14528724C2semidirect
14. C4×C22⋊#3622C2semidirect
15. C17×#2297C2semidirect
21. #11762954C4semidirect
65. C2×#41×C17C2×C4semidirect
95. C2×#63230C2×C4semidirect
98. C2×#63228C2×C4semidirect
123. #10587506C2×C4semidirect
126. #10587503C2×C4semidirect
131. C22⋊#3622C2×C4semidirect
332. #2297D17semidirect
447. C2×#41C4×D17semidirect
520. C17#22045semidirect

Maximal subgroups

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

subgroupindex
C2×#117629542
C4×#105876162
#145296492
#145296412
#145294702
#145294632
#145294222
#145294082
#145291352
#145291212
#145291062
#145289832
#145287242
C4×C22⋊#36222
C17×#22972
#2204517