Finite Group Databasebeta

← #17968819

Subgroups — #17968819

Order 4352.

1130 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763848C211yesmaximal, characteristic
2C2×SD16×#595C211yesmaximal, characteristic
3#14545224C211yesmaximal, characteristic, complemented
4#14545223C211yesmaximal, characteristic
5#14544599C211yesmaximal, characteristic, complemented
6#14544598C211yesmaximal, characteristic, complemented
7#107×#595C211yesmaximal, characteristic, complemented
8#14544557C211yesmaximal, characteristic, complemented
9#14544555C211yesmaximal, characteristic
10#103×#595C211yesmaximal, characteristic, complemented
11C4×#10587549C211yesmaximal, characteristic, complemented
12#102×#595C211yesmaximal, characteristic
13C4×#10587547C211yesmaximal, characteristic
14#14544442C211yesmaximal, characteristic, complemented
15D17×#440C211yesmaximal, characteristic
16C2×Q8×#595C2211yescharacteristic
17C2×Q8×#595C2211yescharacteristic
18C2×D4×#595C2211yescharacteristic
19C2×D4×#595C2211yescharacteristic
20#11763848C418yescomplemented
21SD16×#595C418yescomplemented
22C2×#10587534C2211yescharacteristic
23C2×#10587533C2211yescharacteristic
24C2×#10587549C2211yescharacteristic
25C2×#10587549C2211yescharacteristic
26C2×#10587547C2211yescharacteristic
27C2×#10587547C2211yescharacteristic
28C2×#10587532C2211yescharacteristic
29C2×#10587532C2211yescharacteristic
30C4×#63242C2211yescharacteristic
31C2×C8×#595C2211yescharacteristic
32C2×C8×#595C2211yescharacteristic
33C4⋊C4×#595—21no—
34C4⋊C4×#595—21no—
35C4⋊C4×#595C2211yescharacteristic
36C4⋊C4×#595C2211yescharacteristic
37C4⋊C4×#595C2211yescharacteristic
38C4⋊C4×#595C2211yescharacteristic
39C4×C4⋊#595—21no—
40C4×C4⋊#595C2211yescharacteristic
41C4×C4⋊#595C2211yescharacteristic
42C22⋊C4×#595—21no—
43C22⋊C4×#595—21no—
44C4×C22⋊#595—21no—
45#11763745—21no—
46#11763745C2211yescharacteristic
47C2×(C2×#595)⋊C4—21no—
48#11763683C2211yescharacteristic
49#11763683C2211yescharacteristic
50#11763682C2211yescharacteristic
51#11763682C2211yescharacteristic
52#11763682C2211yescharacteristic
53#11763682C2211yescharacteristic
54C2×SD16×D17C2211yescharacteristic
55C4×Q8×D17C2211yescharacteristic
56C4×D4×D17C2211yescharacteristic
57#11762912C411yescharacteristic, complemented
58#11762911C411yescharacteristic, complemented
59#11762910C411yescharacteristic, complemented
60#11762909C411yescharacteristic, complemented
61#11762908C411yescharacteristic, complemented
62#11762907C411yescharacteristic, complemented
63#11762906C411yescharacteristic, complemented
64#107×D17C2211yescharacteristic
65#103×D17C2211yescharacteristic
66#102×D17C2211yescharacteristic
67#97×D17C2211yescharacteristic
68C17×#440C411yescharacteristic, complemented
69C23×#595—21no—
70C23×#595—21no—
71C2×Q8×D17C2311yescharacteristic
72C2×D4×D17C2311yescharacteristic
73C22×C4×D17—21no—
74C2×C22⋊#595—21no—
75C2×C22⋊#595—21no—
76Q8×#595—22no—
77Q8×#595—22no—
78Q8×#595C2×C414yescomplemented
79Q8×#595C2×C414yescomplemented
80D4×#595—22no—
81D4×#595—22no—
82D4×#595C2×C414yes—
83D4×#595C2×C414yes—
84C2×C4⋊#595—21no—
85C2×C4⋊#595—21no—
86C2×C4⋊#595C2311yescharacteristic
87C2×C4⋊#595C2311yescharacteristic
88C2×C4⋊#595C2311yescharacteristic
89C2×C4⋊#595C2311yescharacteristic
90C2×C4×#595—21no—
91C2×C4×#595—21no—
92C2×C4×#595—21no—
93C2×C4×#595—21no—
94C2×C4×#595—21no—
95C2×C4×#595—21no—
96C2×C4×#595—21no—
97C2×C4×#595—21no—
98C2×C4×#595C2311yescharacteristic
99C2×C4×#595C2311yescharacteristic
100C2×#63242C2311yescharacteristic
101C2×#63242C2311yescharacteristic
102C2×SD16×C17C2×C411yescharacteristic
103C4×Q8×C17C2×C411yescharacteristic, complemented
104C4×D4×C17C2×C411yescharacteristic
105Q8×Dic17C2×C411yescharacteristic, complemented
106C2×#63230C2×C411yescharacteristic
107D4×Dic17C2×C411yescharacteristic
108C2×#63229C2×C411yescharacteristic
109C4×C22⋊D17—21no—
110SD16×D17C2×C414yes—
111SD16×D17C2×C414yes—
112C2×#63219C2×C411yescharacteristic
113C2×C8×D17C2311yescharacteristic
114C2×C8×D17C2311yescharacteristic
115#10587579C2×C411yescharacteristic
116C4⋊C4×D17—21no—
117C4⋊C4×D17C2311yescharacteristic
118C4⋊C4×D17C2311yescharacteristic
119#10587573—21no—
120#10587573C2×C411yescharacteristic, complemented
121#10587567—21no—
122C22⋊C4×D17—21no—
123C4×D68C2×C411yescharacteristic
124C42×D17—21no—
125C42×D17C2311yescharacteristic
126C4×Dic34—21no—
127C4×Dic34C2×C411yescharacteristic, complemented
128#10587549C2×C414yescomplemented
129#10587549C2×C414yescomplemented
130#10587547C2×C414yes—
131#10587547C2×C414yes—
132(C2×#595)⋊C4—21no—
133(C2×#595)⋊C4—21no—
134(C2×#595)⋊C4—21no—
135(C2×#595)⋊C4—21no—
136(C2×#595)⋊C4—21no—
137(C2×#595)⋊C4—21no—
138(C2×#595)⋊C4D411yescharacteristic
139(C2×#595)⋊C4D411yescharacteristic
140(C2×#595)⋊C4D411yescharacteristic
141(C2×#595)⋊C4D411yescharacteristic
142C4×#3624—21no—
143C4×#3624—21no—
144#10587534C2×C414yescomplemented
145#10587533C2×C414yescomplemented
146#10587532—22no—
147#10587532C2×C414yescomplemented
148C8×#595—22no—
149C8×#595C2×C414yescomplemented
150C17×#107C2×C411yescharacteristic, complemented
151C17×#103C2×C411yescharacteristic, complemented
152C17×#102C2×C411yescharacteristic
153C17×#97C2×C411yescharacteristic, complemented
154#10587506C2×C411yescharacteristic, complemented
155#10587503C2×C411yescharacteristic
156#10587492C2×C411yescharacteristic
157#10587489C2×C411yescharacteristic, complemented
158#10587487C2×C411yescharacteristic, complemented
159#10587486C2×C411yescharacteristic, complemented
160#10587486C2×C411yescharacteristic, complemented
161#10587481C2×C411yescharacteristic, complemented
162#10587480C2×C411yescharacteristic
163#10587478C2×C411yescharacteristic, complemented
164#10587478C2×C411yescharacteristic, complemented
165#10587474C2×C411yescharacteristic, complemented
166C23×D17—21no—
167C22×#595—21no—
168C22×#595—21no—
169C22×#595—21no—
170C22×#595—21no—
171C22×#595—24no—
172C22×#595—24no—
173C22×#595—81no—
174C22×#595—81no—
175C22×#595—81no—
176C22×#595—81no—
177C22×#595C2×D411yescharacteristic
178C22×#595C2×D411yescharacteristic
179C22×#595C2×D411yescharacteristic
180C22×#595C2×D411yescharacteristic
181C2×Q8×C17C22×C411yescharacteristic
182C2×D4×C17C22×C411yescharacteristic
183C22×C4×C17—21no—
184C2×C22⋊D17—21no—
185C22×Dic17—21no—
186Q8×D17—21no—
187Q8×D17—21no—
188Q8×D17C22×C412yes—
189Q8×D17C22×C412yes—
190D4×D17—21no—
191D4×D17—21no—
192D4×D17C22×C412yes—
193D4×D17C22×C412yes—
194C2×D68C22×C411yescharacteristic
195C2×C4×D17—21no—
196C2×C4×D17—21no—
197C2×C4×D17—21no—
198C2×C4×D17—21no—
199C2×C4×D17—21no—
200C2×C4×D17—81no—
201C2×C4×D17—81no—
202C2×C4×D17C2×D411yescharacteristic
203C2×C4×D17C2×D411yescharacteristic
204C2×C4×D17C2411yescharacteristic
205C2×Dic34—21no—
206C2×Dic34C22×C411yescharacteristic
207C22⋊#595—24no—
208C22⋊#595—24no—
209C2×#3624—21no—
210C2×#3624—21no—
211C4⋊#595—24no—
212C4⋊#595—24no—
213C4⋊#595—21no—
214C4⋊#595—21no—
215C4⋊#595—21no—
216C4⋊#595—21no—
217C4⋊#595C22×C412yes—
218C4⋊#595C22×C412yes—
219C4⋊#595C22×C412yes—
220C4⋊#595C22×C412yes—
221C4×#595—24no—
222C4×#595—24no—
223C4×#595—81no—
224C4×#595—81no—
225C4×#595—81no—
226C4×#595—81no—
227C4×#595—81no—
228C4×#595—81no—
229C4×#595C22×C412yes—
230C4×#595C22×C412yes—
231C4×#595#4112yes—
232C4×#595#4112yes—
233#63242—21no—
234#63242—21no—
235#63242C22×C412yes—
236#63242C22×C412yes—
237SD16×C17C4214yescomplemented
238C2×C8×C17C22×C411yescharacteristic
239C2×C8×C17C22×C411yescharacteristic
240C4⋊C4×C17—21no—
241C4⋊C4×C17C22×C411yescharacteristic
242C4⋊C4×C17C22×C411yescharacteristic
243C22⋊C4×C17—21no—
244C42×C17—21no—
245C42×C17C22×C411yescharacteristic
246C22⋊Dic17—21no—
247#63230C4214yescomplemented
248#63229C4214yescomplemented
249#63227—21no—
250#63227—21no—
251C4⋊Dic17—21no—
252C4⋊Dic17C22×C411yescharacteristic
253C4⋊Dic17C22×C411yescharacteristic
254#63225—21no—
255#63225—21no—
256#63225—21no—
257#63225—21no—
258C4×Dic17—21no—
259C4×Dic17—21no—
260C4×Dic17—21no—
261C4×Dic17C22×C411yescharacteristic
262C4×Dic17#4111yescharacteristic
263C4×Dic17#4111yescharacteristic
264C2×#3622C22×C411yescharacteristic
265C2×#3622C22×C411yescharacteristic
266#63219C4214yescomplemented
267C8×D17—21no—
268C8×D17—21no—
269C8×D17C22×C412yes—
270C8×D17C22×C412yes—
271#20504—171nomaximal, Sylow
272C23×C17—21no—
273C22×D17—21no—
274C22×D17—22no—
275C22×D17—22no—
276C22×D17—41no—
277C22×D17—41no—
278C22×D17—41no—
279C22×D17—41no—
280C22×D17C22×D411yescharacteristic
281C2×#595—21no—
282C2×#595—21no—
283C2×#595—21no—
284C2×#595—21no—
285C2×#595—21no—
286C2×#595—21no—
287C2×#595—21no—
288C2×#595—21no—
289C2×#595—22no—
290C2×#595—22no—
291C2×#595—22no—
292C2×#595—22no—
293C2×#595—41no—
294C2×#595—41no—
295C2×#595—41no—
296C2×#595—41no—
297C2×#595—41no—
298C2×#595—41no—
299C2×#595—41no—
300C2×#595—41no—
301C2×#595—84no—
302C2×#595—84no—
303C2×#595C4×D412yes—
304C2×#595C4×D412yes—
305C2×#595C4×D412yes—
306C2×#595C4×D412yes—
307Q8×C17—21no—
308Q8×C17C2×C4212yes—
309D4×C17—21no—
310D4×C17C2×C4212yes—
311C2×C4×C17—21no—
312C2×C4×C17—21no—
313C2×C4×C17—21no—
314C2×C4×C17—81no—
315C2×C4×C17C4×D411yescharacteristic
316C2×C4×C17C4×D411yescharacteristic
317C2×C4×C17C23×C411yescharacteristic
318C22⋊D17—22no—
319C22⋊D17—22no—
320C2×Dic17—21no—
321C2×Dic17—21no—
322C2×Dic17—21no—
323C2×Dic17—81no—
324C2×Dic17C4×D411yescharacteristic
325C2×Dic17C4×D411yescharacteristic
326C2×Dic17C2×#4111yescharacteristic
327D68—21no—
328D68C2×C4212yes—
329C4×D17—22no—
330C4×D17—22no—
331C4×D17—21no—
332C4×D17—21no—
333C4×D17—21no—
334C4×D17—21no—
335C4×D17—41no—
336C4×D17—41no—
337C4×D17—41no—
338C4×D17—41no—
339C4×D17—81no—
340C4×D17—81no—
341C4×D17C23×C411yescharacteristic
342C4×D17C23×C411yescharacteristic
343C4×D17C2×#4111yescharacteristic
344C4×D17C2×#4111yescharacteristic
345Dic34—21no—
346Dic34—22no—
347Dic34—22no—
348Dic34C2×C4212yes—
349#3624—22no—
350#3624—22no—
351C8×C17—21no—
352C8×C17C2×C4212yes—
353#3622—21no—
354#3622C2×C4212yes—
355C2×#440—171no—
356C2×#440—171no—
357C2×C4×SD16—171no—
358#2276—171no—
359#2275—171no—
360#1776—171no—
361#1776—171no—
362C4×#107—171no—
363#1763—171no—
364#1762—171no—
365C4×#103—171no—
366C4×#103—171no—
367C4×#102—171no—
368C4×#102—171no—
369#1726—171no—
370C22×C17—22no—
371C22×C17—41no—
372C22×C17—41no—
373C22×C17C2×C4×D411yescharacteristic
374C2×D17—22no—
375C2×D17—41no—
376C2×D17—41no—
377C2×D17—42no—
378C2×D17—42no—
379C2×D17—42no—
380C2×D17—42no—
381C2×D17C2×C4×D411yescharacteristic
382C2×D17C2×C4×D411yescharacteristic
383C2×D17#57611yescharacteristic
384C2×D17#57711yescharacteristic
385C2×D17#57711yescharacteristic
386C2×D17#57811yescharacteristic
387#595—22no—
388#595—22no—
389#595—22no—
390#595—22no—
391#595—42no—
392#595—42no—
393#595—42no—
394#595—42no—
395C4×C17—21no—
396C4×C17—21no—
397C4×C17—22no—
398C4×C17—41no—
399C4×C17—41no—
400C4×C17C22×C4211yescharacteristic
401C4×C17C4×#4111yescharacteristic
402Dic17—21no—
403Dic17—21no—
404Dic17—22no—
405Dic17—41no—
406Dic17—41no—
407Dic17C4×#4111yescharacteristic
408Dic17C4×#4111yescharacteristic
409C22×SD16—171no—
410C2×C4×Q8—171no—
411C2×C4×Q8—171no—
412C2×C4×Q8—171no—
413C2×C4×D4—171no—
414C2×C4×D4—171no—
415C2×C4×D4—171no—
416#440—178no—
417#440—171no—
418#440—171no—
419#440—171no—
420#440—171no—
421#440—171no—
422#440—171no—
423#440—171no—
424#440#59511yescharacteristic, complemented
425C4×SD16—178no—
426C2×#107—171no—
427C2×#107—171no—
428C2×#106—171no—
429C2×#103—171no—
430C2×#103—171no—
431C2×#103—171no—
432C2×#102—171no—
433C2×#102—171no—
434C2×#102—171no—
435C2×#97—171no—
436C2×#97—171no—
437C2×#97—171no—
438C2×C4×C8—171no—
439C2×C4×C8—171no—
440C2×C4×C8—171no—
441C4×C4⋊C4—171no—
442C4×C4⋊C4—171no—
443C4×C4⋊C4—171no—
444C4×C4⋊C4—171no—
445C4×C4⋊C4—171no—
446C4×C4⋊C4—171no—
447C4×C4⋊C4—341no—
448C4×C4⋊C4—341no—
449C4×C4⋊C4—341no—
450C4×C22⋊C4—341no—
451C4×C22⋊C4—341no—
452C4×C22⋊C4—341no—
453#376—171no—
454#376—341no—
455C2×#95—341no—
456#340—171no—
457#340—171no—
458#340—171no—
459#340—171no—
460#340—171no—
461#340—171no—
462C2×C17—42no—
463C2×C17C42×D411yescharacteristic
464C2×C17#294611yescharacteristic
465C2×C17#294711yescharacteristic
466D17—42no—
467D17#294611yescharacteristic
468D17#294711yescharacteristic
469D17#294911yescharacteristic
470D17#295111yescharacteristic
471C22×Q8—171no—
472C22×D4—171no—
473C23×C4—341no—
474C23×C4—341no—
475C23×C4—341no—
476C2×SD16—171no—
477C2×SD16—171no—
478C2×SD16—174no—
479C2×SD16—174no—
480C2×SD16—171no—
481C2×SD16C2×#59511yescharacteristic
482C22×C8—171no—
483C22×C8—171no—
484C22×C8—171no—
485C22×C8—171no—
486C4×Q8—174no—
487C4×Q8—174no—
488C4×Q8—171no—
489C4×Q8—171no—
490C4×Q8—171no—
491C4×Q8—341no—
492C4×Q8—341no—
493C4×Q8—342no—
494C4×Q8—342no—
495C4×Q8C2×#59511yescharacteristic, complemented
496C4×D4—174no—
497C4×D4—174no—
498C4×D4—171no—
499C4×D4—171no—
500C4×D4—171no—
501C4×D4—341no—
502C4×D4—341no—
503C4×D4—342no—
504C4×D4—342no—
505C4×D4C2×#59511yescharacteristic
506C2×C4⋊C4—171no—
507C2×C4⋊C4—171no—
508C2×C4⋊C4—171no—
509C2×C4⋊C4—171no—
510C2×C4⋊C4—171no—
511C2×C4⋊C4—171no—
512C2×C4⋊C4—341no—
513C2×C4⋊C4—341no—
514C2×C4⋊C4—341no—
515C2×C22⋊C4—341no—
516C2×C22⋊C4—341no—
517C2×C22⋊C4—341no—
518C2×C42—171no—
519C2×C42—171no—
520C2×C42—171no—
521C2×C42—341no—
522C2×C42—341no—
523C2×C42—341no—
524C2×C42—341no—
525C2×C42—341no—
526C2×C42—341no—
527C2×C42—341no—
528C2×C42—341no—
529C2×C42—341no—
530#107—174no—
531#107—171no—
532#107—171no—
533#107—171no—
534#107C2×#59511yescharacteristic, complemented
535#106—174no—
536#103—174no—
537#103—174no—
538#103—171no—
539#103—171no—
540#103—171no—
541#103C2×#59511yescharacteristic, complemented
542#102—174no—
543#102—174no—
544#102—171no—
545#102—171no—
546#102—171no—
547#102C2×#59511yescharacteristic
548#97—174no—
549#97—171no—
550#97—171no—
551#97—171no—
552#97—342no—
553#97C2×#59511yescharacteristic, complemented
554C4×C8—174no—
555C4×C8—342no—
556C4×C8—341no—
557C4×C8—341no—
558#95—171no—
559#95—171no—
560#95—171no—
561#95—171no—
562#95—341no—
563#95—341no—
564#95—341no—
565#95—341no—
566#95—341no—
567#95—341no—
568C17#2050411yescharacteristic, complemented, Sylow
569C24—341no—
570C2×Q8—172no—
571C2×Q8—172no—
572C2×Q8—171no—
573C2×Q8—341no—
574C2×Q8—341no—
575C2×Q8—341no—
576C2×Q8C22×#59511yescharacteristic
577C2×D4—172no—
578C2×D4—172no—
579C2×D4—171no—
580C2×D4—341no—
581C2×D4—341no—
582C2×D4—341no—
583C2×D4C22×#59511yescharacteristic
584C22×C4—21no—
585C22×C4—171no—
586C22×C4—171no—
587C22×C4—171no—
588C22×C4—171no—
589C22×C4—171no—
590C22×C4—171no—
591C22×C4—171no—
592C22×C4—341no—
593C22×C4—341no—
594C22×C4—341no—
595C22×C4—341no—
596C22×C4—341no—
597C22×C4—344no—
598C22×C4—344no—
599C22×C4—341no—
600C22×C4—341no—
601C22×C4—341no—
602C22×C4—341no—
603C22×C4—341no—
604C22×C4—1361no—
605C22×C4—1361no—
606C22×C4—1361no—
607C22×C4—1361no—
608C22×C4—1361no—
609C22×C4—1361no—
610SD16—174no—
611SD16—174no—
612SD16—174no—
613SD16C4×#59514yescomplemented
614C2×C8—171no—
615C2×C8—172no—
616C2×C8—172no—
617C2×C8—172no—
618C2×C8—172no—
619C2×C8—171no—
620C2×C8—341no—
621C2×C8—341no—
622C2×C8—341no—
623C2×C8—341no—
624C2×C8—341no—
625C2×C8—341no—
626C2×C8C22×#59511yescharacteristic
627C2×C8C22×#59511yescharacteristic
628C4⋊C4—21no—
629C4⋊C4—172no—
630C4⋊C4—172no—
631C4⋊C4—172no—
632C4⋊C4—172no—
633C4⋊C4—171no—
634C4⋊C4—171no—
635C4⋊C4—341no—
636C4⋊C4—341no—
637C4⋊C4—341no—
638C4⋊C4—341no—
639C4⋊C4—341no—
640C4⋊C4—341no—
641C4⋊C4—341no—
642C4⋊C4—341no—
643C4⋊C4—344no—
644C4⋊C4—344no—
645C4⋊C4—341no—
646C4⋊C4C22×#59511yescharacteristic
647C4⋊C4C22×#59511yescharacteristic
648C22⋊C4—21no—
649C22⋊C4—341no—
650C22⋊C4—341no—
651C22⋊C4—344no—
652C22⋊C4—344no—
653C22⋊C4—341no—
654C42—21no—
655C42—172no—
656C42—172no—
657C42—172no—
658C42—172no—
659C42—171no—
660C42—171no—
661C42—171no—
662C42—341no—
663C42—341no—
664C42—344no—
665C42—344no—
666C42—341no—
667C42—1361no—
668C42—1361no—
669C42—1361no—
670C42—1361no—
671C42—1361no—
672C42—1361no—
673C42C22×#59511yescharacteristic
674C23—21no—
675C23—171no—
676C23—342no—
677C23—342no—
678C23—341no—
679C23—681no—
680C23—681no—
681C23—681no—
682C23—681no—
683Q8—21no—
684Q8—172no—
685Q8—342no—
686Q8—342no—
687Q8—341no—
688Q8C2×C4×#59512yes—
689D4—21no—
690D4—172no—
691D4—342no—
692D4—342no—
693D4—341no—
694D4C2×C4×#59512yes—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—81no—
699C2×C4—171no—
700C2×C4—171no—
701C2×C4—171no—
702C2×C4—171no—
703C2×C4—171no—
704C2×C4—172no—
705C2×C4—172no—
706C2×C4—172no—
707C2×C4—172no—
708C2×C4—171no—
709C2×C4—171no—
710C2×C4—342no—
711C2×C4—342no—
712C2×C4—341no—
713C2×C4—341no—
714C2×C4—341no—
715C2×C4—341no—
716C2×C4—341no—
717C2×C4—341no—
718C2×C4—341no—
719C2×C4—341no—
720C2×C4—341no—
721C2×C4—341no—
722C2×C4—341no—
723C2×C4—341no—
724C2×C4—341no—
725C2×C4—342no—
726C2×C4—342no—
727C2×C4—342no—
728C2×C4—342no—
729C2×C4—341no—
730C2×C4—341no—
731C2×C4—681no—
732C2×C4—681no—
733C2×C4—681no—
734C2×C4—681no—
735C2×C4—681no—
736C2×C4—681no—
737C2×C4—681no—
738C2×C4—681no—
739C2×C4—681no—
740C2×C4—681no—
741C2×C4—681no—
742C2×C4—681no—
743C2×C4—1361no—
744C2×C4—1361no—
745C2×C4—1361no—
746C2×C4—1364no—
747C2×C4—1364no—
748C2×C4D4×#59511yescharacteristic
749C2×C4D4×#59511yescharacteristic
750C2×C4C23×#59511yescharacteristic
751C8—21no—
752C8—172no—
753C8—342no—
754C8—342no—
755C8—341no—
756C8C2×C4×#59512yes—
757C22—22no—
758C22—41no—
759C22—41no—
760C22—171no—
761C22—171no—
762C22—171no—
763C22—171no—
764C22—171no—
765C22—171no—
766C22—342no—
767C22—682no—
768C22—682no—
769C22—682no—
770C22—682no—
771C22—681no—
772C22—681no—
773C22C2×D4×#59511yescharacteristic
774C4—22no—
775C4—21no—
776C4—21no—
777C4—41no—
778C4—41no—
779C4—171no—
780C4—171no—
781C4—342no—
782C4—342no—
783C4—342no—
784C4—342no—
785C4—342no—
786C4—341no—
787C4—341no—
788C4—682no—
789C4—682no—
790C4—682no—
791C4—682no—
792C4—681no—
793C4—681no—
794C4C22×C4×#59511yescharacteristic
795C4#41×#59511yescharacteristic
796C2—42no—
797C2—171no—
798C2—171no—
799C2—171no—
800C2—171no—
801C2—682no—
802C2C4×D4×#59511yescharacteristic
803C2#1454554111yescharacteristic
804C2#1454554211yescharacteristic
subgroupG/H
centerC22C2×D4×#595
commutatorC4×C17C22×C42
FrattiniC2×C4C23×#595
FittingC17×#440C4
socleC22×C17C2×C4×D4
prime radicalC2×D4×D17C23
cosocleC2×C4×D17C24
hypercenter#440#595
hypocenterC17#20504
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
3. #14545224C2semidirect
5. #14544599C2semidirect
6. #14544598C2semidirect
7. #107×#595C2semidirect
8. #14544557C2semidirect
10. #103×#595C2semidirect
11. C4×#10587549C2semidirect
14. #14544442C2semidirect
20. #11763848C4semidirect
21. SD16×#595C4semidirect
57. #11762912C4semidirect
58. #11762911C4semidirect
59. #11762910C4semidirect
60. #11762909C4semidirect
61. #11762908C4semidirect
62. #11762907C4semidirect
63. #11762906C4semidirect
68. C17×#440C4semidirect
78. Q8×#595C2×C4semidirect
79. Q8×#595C2×C4semidirect
103. C4×Q8×C17C2×C4semidirect
105. Q8×Dic17C2×C4semidirect
120. #10587573C2×C4semidirect
127. C4×Dic34C2×C4semidirect
128. #10587549C2×C4semidirect
129. #10587549C2×C4semidirect
144. #10587534C2×C4semidirect
145. #10587533C2×C4semidirect
147. #10587532C2×C4semidirect
149. C8×#595C2×C4semidirect
150. C17×#107C2×C4semidirect
151. C17×#103C2×C4semidirect
153. C17×#97C2×C4semidirect
154. #10587506C2×C4semidirect
157. #10587489C2×C4semidirect
158. #10587487C2×C4semidirect
159. #10587486C2×C4semidirect
160. #10587486C2×C4semidirect
161. #10587481C2×C4semidirect
163. #10587478C2×C4semidirect
164. #10587478C2×C4semidirect
165. #10587474C2×C4semidirect
237. SD16×C17C42semidirect
247. #63230C42semidirect
248. #63229C42semidirect
266. #63219C42semidirect
424. #440#595semidirect
495. C4×Q8C2×#595semidirect
534. #107C2×#595semidirect
541. #103C2×#595semidirect
553. #97C2×#595semidirect
568. C17#20504semidirect
613. SD16C4×#595semidirect

Maximal subgroups

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

subgroupindex
C2×#117638482
C2×SD16×#5952
#145452242
#145452232
#145445992
#145445982
#107×#5952
#145445572
#145445552
#103×#5952
C4×#105875492
#102×#5952
C4×#105875472
#145444422
D17×#4402
#2050417