Finite Group Databasebeta

← #17001337

Subgroups — #17001337

Order 4352.

1010 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14542394C211yesmaximal, characteristic
2#14537909C211yesmaximal, characteristic, complemented
3#14527254C211yesmaximal, characteristic, complemented
4#14527250C211yesmaximal, characteristic, complemented
5#14527245C211yesmaximal, characteristic, complemented
6#14527228C211yesmaximal, characteristic, complemented
7#14527219C211yesmaximal, characteristic, complemented
8#14527210C211yesmaximal, characteristic, complemented
9#14527198C211yesmaximal, characteristic, complemented
10#14527193C211yesmaximal, characteristic, complemented
11#14527184C211yesmaximal, characteristic, complemented
12#14527176C211yesmaximal, characteristic, complemented
13#14527172C211yesmaximal, characteristic, complemented
14C2×#11762538C211yesmaximal, characteristic, complemented
15C17×#2922C211yesmaximal, characteristic, complemented
16#11763544C411yescharacteristic
17#11763519C411yescharacteristic
18#11763516C411yescharacteristic
19#11763505C411yescharacteristic
20#11763505C411yescharacteristic
21#11763503—21no—
22#11763483—21no—
23#11763483—21no—
24#11763455C411yescharacteristic
25#11763455C411yescharacteristic
26#11763447—21no—
27D4×D68C411yescharacteristic
28#11763359C2211yescharacteristic
29#11763346—21no—
30#11763343C2211yescharacteristic
31#11763343C2211yescharacteristic
32#11763318—21no—
33#11763318—21no—
34C4×#63252C2211yescharacteristic
35C2×C4×D68C2211yescharacteristic
36C2×C4×D68C2211yescharacteristic
37C4×D4×D17—21no—
38#11762940—21no—
39#11762881—21no—
40#11762881—21no—
41D4×#3622—21no—
42#11762866C2211yescharacteristic, complemented
43#11762866C2211yescharacteristic, complemented
44#11762862C2211yescharacteristic, complemented
45#11762833C2211yescharacteristic, complemented
46C2×C4⋊#3622C2211yescharacteristic, complemented
47C2×C4⋊#3622C2211yescharacteristic, complemented
48#11762541C2211yescharacteristic, complemented
49#11762541C2211yescharacteristic, complemented
50#11762541C2211yescharacteristic, complemented
51#11762541C2211yescharacteristic, complemented
52#11762538C2211yescharacteristic
53#11762538C2211yescharacteristic
54#11762538C2211yescharacteristic
55#11762538C2211yescharacteristic
56#11762538C2211yescharacteristic, complemented
57#11762538C2211yescharacteristic, complemented
58#11762538C2211yescharacteristic, complemented
59#11762538C2211yescharacteristic, complemented
60#11762538C2211yescharacteristic, complemented
61#11762538C2211yescharacteristic, complemented
62#11762538C2211yescharacteristic, complemented
63#11762538C2211yescharacteristic, complemented
64C4×#41×C17C2211yescharacteristic
65C17×#433—21no—
66C17×#433—21no—
67C17×#431C2211yescharacteristic, complemented
68C17×#431C2211yescharacteristic, complemented
69C17×#431C2211yescharacteristic, complemented
70C17×#431C2211yescharacteristic, complemented
71C17×#424—21no—
72C17×#408—21no—
73C4×M16×C17C2211yescharacteristic, complemented
74C2×C4×C8×C17C2211yescharacteristic, complemented
75C2×#41×C17D411yescharacteristic
76C2×D4×D17—21no—
77C2×#63252—21no—
78C2×#63252C2×C411yescharacteristic
79C22×D68C2×C411yescharacteristic
80C22×D68C2×C411yescharacteristic
81C22×C4×D17—21no—
82C22×C4×D17—21no—
83C2×M16×C17—21no—
84C22×C8×C17—21no—
85C4×Q8×C17C2×C411yescharacteristic
86C4×Q8×C17D411yescharacteristic
87C4×D4×C17C2×C411yescharacteristic
88C4×D4×C17C2×C411yescharacteristic
89C4×D4×C17C2×C411yescharacteristic
90C4×D4×C17D411yescharacteristic
91C4×D4×C17D411yescharacteristic
92C4×D4×C17D411yescharacteristic
93C17×#117D411yescharacteristic
94C17×#117D411yescharacteristic
95C17×#117D411yescharacteristic
96C2×C42×C17C2311yescharacteristic
97C2×C42×C17C2311yescharacteristic
98C2×C42×C17C2311yescharacteristic
99#10587633—21no—
100#10587632—21no—
101#10587625—21no—
102#10587625—21no—
103#10587623—21no—
104#10587623—21no—
105D4×Dic17—21no—
106#10587616—21no—
107#10587616C2×C411yescharacteristic
108#10587616C2×C411yescharacteristic
109#10587616C2×C411yescharacteristic
110#10587616C2×C411yescharacteristic
111#10587615—21no—
112#10587615—21no—
113C4×C22⋊D17—21no—
114C4×C22⋊D17—21no—
115C4×C22⋊D17—21no—
116C4×C22⋊D17—21no—
117C2×#63227—21no—
118C2×#63227—21no—
119#10587612C2×C411yescharacteristic
120C2×C4⋊Dic17C2×C411yescharacteristic
121C2×C4⋊Dic17C2×C411yescharacteristic
122#10587610C2×C411yescharacteristic
123#10587610C2×C411yescharacteristic
124C2×#63223—21no—
125C22×#3622—21no—
126C22×#3622—21no—
127#10587584—21no—
128#10587584—21no—
129#10587582—21no—
130#10587582—21no—
131#10587581—21no—
132#10587580—21no—
133#10587580—21no—
134#10587580—21no—
135#10587580—21no—
136#10587579—21no—
137C4⋊C4×D17—21no—
138#10587576—21no—
139#10587570—21no—
140#10587570—21no—
141#10587569—21no—
142#10587569—21no—
143#10587568—21no—
144#10587568—21no—
145#10587567—21no—
146#10587567—21no—
147C22⋊C4×D17—21no—
148C22⋊C4×D17—21no—
149#10587564—21no—
150#10587564—21no—
151#10587562—21no—
152#10587562—21no—
153#10587561—21no—
154#10587561C2×C411yescharacteristic
155#10587561C2×C411yescharacteristic
156#10587560C2×C411yescharacteristic
157C4×D68—21no—
158C4×D68—21no—
159C4×D68—21no—
160C4×D68—21no—
161C4×D68—21no—
162C4×D68C2×C411yescharacteristic
163C4×D68C2×C411yescharacteristic
164C4×D68C2×C411yescharacteristic
165C4×D68C2×C411yescharacteristic
166C4×D68C2×C411yescharacteristic
167C4×D68C2311yescharacteristic
168C4×D68C2311yescharacteristic
169C4×D68C2311yescharacteristic
170#10587558—21no—
171#10587558—21no—
172#10587558—21no—
173C42×D17—21no—
174#10587556C2×C411yescharacteristic
175#10587556C2×C411yescharacteristic
176#10587555C2×C411yescharacteristic
177C4×Dic34C2×C411yescharacteristic
178C4×Dic34C2311yescharacteristic
179C17×C4⋊C8—21no—
180C17×C4⋊C8—21no—
181C17×C4⋊C8—21no—
182C17×C4⋊C8—21no—
183C17×C22⋊C8—21no—
184C17×C22⋊C8—21no—
185C17×C22⋊C8—21no—
186C17×C22⋊C8—21no—
187C17×#97—21no—
188C4×C8×C17—21no—
189C4×C8×C17C2311yescharacteristic
190C4×C8×C17C2311yescharacteristic
191C4×C8×C17C2311yescharacteristic
192C4×C8×C17C2311yescharacteristic
193C22⋊#3622—21no—
194C22⋊#3622—21no—
195C22⋊#3622—21no—
196C4⋊#3622—21no—
197C4⋊#3622—21no—
198C4⋊#3622—21no—
199C4⋊#3622C2311yescharacteristic
200C4⋊#3622C2311yescharacteristic
201C4⋊#3622C2311yescharacteristic
202C4⋊#3622C2311yescharacteristic
203#10587474—21no—
204#10587474—21no—
205C4×#3622—21no—
206C23×D17—21no—
207C23×D17—21no—
208#41×C17—42no—
209C2×Q8×C17C22⋊C411yescharacteristic
210C2×D4×C17C22⋊C411yescharacteristic
211C2×D4×C17C22⋊C411yescharacteristic
212C2×D4×C17C22⋊C411yescharacteristic
213C22×C4×C17C22×C411yescharacteristic
214C22×C4×C17C22×C411yescharacteristic
215C22×C4×C17C22×C411yescharacteristic
216C22×C4×C17C2×D411yescharacteristic
217C22×C4×C17C2×D411yescharacteristic
218C22×C4×C17C2×D411yescharacteristic
219C22×C4×C17C2×D411yescharacteristic
220C22×C4×C17C2×D411yescharacteristic
221C22×C4×C17C2×D411yescharacteristic
222C2×C22⋊D17—21no—
223C2×C22⋊D17—21no—
224C2×C22⋊D17—21no—
225C2×C22⋊D17—21no—
226C2×C22⋊D17—21no—
227C22×Dic17—21no—
228C22×Dic17—21no—
229D4×D17—44no—
230#63252—22no—
231#63252—41no—
232#63252—81no—
233#63252—81no—
234C2×D68—22no—
235C2×D68—22no—
236C2×D68—21no—
237C2×D68—21no—
238C2×D68—21no—
239C2×D68—21no—
240C2×D68—41no—
241C2×D68—41no—
242C2×D68C22×C411yescharacteristic
243C2×D68C22×C411yescharacteristic
244C2×D68C22×C411yescharacteristic
245C2×C4×D17—21no—
246C2×C4×D17—21no—
247C2×C4×D17—21no—
248C2×C4×D17—21no—
249C2×C4×D17—21no—
250C2×C4×D17—21no—
251C2×C4×D17—21no—
252C2×C4×D17—21no—
253C2×C4×D17—21no—
254C2×C4×D17—81no—
255C2×C4×D17—81no—
256C2×C4×D17—81no—
257C2×C4×D17—81no—
258C2×Dic34—21no—
259C2×Dic34C22×C411yescharacteristic
260M16×C17—42no—
261C2×C8×C17—21no—
262C2×C8×C17—21no—
263C2×C8×C17—21no—
264C2×C8×C17—21no—
265C2×C8×C17—42no—
266C4⋊C4×C17C22⋊C411yescharacteristic
267C4⋊C4×C17C22⋊C411yescharacteristic
268C4⋊C4×C17C22⋊C411yescharacteristic
269C4⋊C4×C17C22⋊C411yescharacteristic
270C4⋊C4×C17C22⋊C411yescharacteristic
271C4⋊C4×C17C22⋊C411yescharacteristic
272C22⋊C4×C17C22⋊C411yescharacteristic
273C22⋊C4×C17C22⋊C411yescharacteristic
274C22⋊C4×C17C22⋊C411yescharacteristic
275C22⋊C4×C17C22⋊C411yescharacteristic
276C22⋊C4×C17C22⋊C411yescharacteristic
277C22⋊C4×C17C22⋊C411yescharacteristic
278C42×C17C22×C411yescharacteristic
279C42×C17C22×C411yescharacteristic
280C42×C17C22×C411yescharacteristic
281C42×C17C2×D411yescharacteristic
282C42×C17C2×D411yescharacteristic
283C42×C17C2×D411yescharacteristic
284C42×C17C2×D411yescharacteristic
285C42×C17C2×D411yescharacteristic
286C42×C17C2×D411yescharacteristic
287C42×C17C2411yescharacteristic
288C22⋊Dic17—21no—
289C22⋊Dic17—21no—
290C22⋊Dic17—21no—
291#63227—21no—
292#63227—21no—
293#63227—21no—
294#63227—21no—
295#63227—21no—
296#63227—21no—
297#63227—21no—
298#63227—21no—
299#63227—21no—
300#63227—21no—
301#63227—21no—
302#63227—21no—
303#63227—21no—
304#63227—21no—
305#63227—21no—
306#63227—21no—
307C4⋊Dic17—21no—
308C4⋊Dic17—21no—
309C4⋊Dic17—21no—
310C4⋊Dic17C22×C411yescharacteristic
311C4⋊Dic17C22×C411yescharacteristic
312C4⋊Dic17C22×C411yescharacteristic
313C4⋊Dic17C22×C411yescharacteristic
314#63225—21no—
315#63225—21no—
316#63225—21no—
317#63225—21no—
318#63225—21no—
319#63225—21no—
320#63225—21no—
321#63225—21no—
322C4×Dic17—21no—
323C4×Dic17—21no—
324C4×Dic17—21no—
325#63223—81no—
326C2×#3622—21no—
327C2×#3622—21no—
328C2×#3622—21no—
329C2×#3622—21no—
330C2×#3622—81no—
331C2×#3622—81no—
332#17521—171nomaximal, Sylow
333C23×C17C2×C22⋊C411yescharacteristic
334C23×C17C2×C22⋊C411yescharacteristic
335C23×C17C2×C22⋊C411yescharacteristic
336C22×D17—21no—
337C22×D17—21no—
338C22×D17—21no—
339C22×D17—42no—
340C22×D17—42no—
341C22×D17—42no—
342C22×D17—42no—
343C22×D17—81no—
344C22×D17—81no—
345Q8×C17—41no—
346D4×C17—22no—
347D4×C17—22no—
348D4×C17—41no—
349C2×C4×C17—22no—
350C2×C4×C17—21no—
351C2×C4×C17—21no—
352C2×C4×C17—21no—
353C2×C4×C17—21no—
354C2×C4×C17—21no—
355C2×C4×C17—21no—
356C2×C4×C17—21no—
357C2×C4×C17—21no—
358C2×C4×C17—21no—
359C2×C4×C17—21no—
360C2×C4×C17—21no—
361C2×C4×C17—21no—
362C2×C4×C17—41no—
363C2×C4×C17—41no—
364C2×C4×C17C2×C22⋊C411yescharacteristic
365C2×C4×C17C2×C22⋊C411yescharacteristic
366C2×C4×C17C2×C22⋊C411yescharacteristic
367C2×C4×C17C2×C22⋊C411yescharacteristic
368C2×C4×C17C2×C22⋊C411yescharacteristic
369C2×C4×C17C2×C22⋊C411yescharacteristic
370C2×C4×C17C2×C22⋊C411yescharacteristic
371C2×C4×C17C2×C22⋊C411yescharacteristic
372C2×C4×C17C2×C22⋊C411yescharacteristic
373C2×C4×C17C23×C411yescharacteristic
374C2×C4×C17C22×D411yescharacteristic
375C2×C4×C17C22×D411yescharacteristic
376C22⋊D17—42no—
377C22⋊D17—42no—
378C22⋊D17—42no—
379C22⋊D17—81no—
380C22⋊D17—81no—
381C2×Dic17—21no—
382C2×Dic17—21no—
383C2×Dic17—21no—
384C2×Dic17—21no—
385C2×Dic17—21no—
386C2×Dic17—81no—
387C2×Dic17—81no—
388D68—21no—
389D68—21no—
390D68—21no—
391D68—21no—
392D68—21no—
393D68—42no—
394D68—42no—
395D68—42no—
396D68—81no—
397D68#13112yes—
398C4×D17—42no—
399C4×D17—42no—
400C4×D17—41no—
401C4×D17—41no—
402C4×D17—41no—
403C4×D17—41no—
404C4×D17—41no—
405C4×D17—41no—
406C4×D17—81no—
407C4×D17—81no—
408C4×D17—81no—
409C4×D17—81no—
410Dic34—21no—
411Dic34—21no—
412Dic34—81no—
413C8×C17—41no—
414C8×C17—41no—
415C8×C17—41no—
416C8×C17—41no—
417#3622—41no—
418#3622—41no—
419#3622—41no—
420#3622—41no—
421#3481—171no—
422#2990—171no—
423#2922D1711yescharacteristic, complemented
424#1496—171no—
425#1495—171no—
426#1494—171no—
427#1490—171no—
428#1488—171no—
429#1486—171no—
430#1483—171no—
431#1482—171no—
432#1480—171no—
433#1478—171no—
434#1477—171no—
435C2×D4⋊C8—171no—
436C22×C17—21no—
437C22×C17—21no—
438C22×C17—21no—
439C22×C17—21no—
440C22×C17—21no—
441C22×C17—21no—
442C22×C17—21no—
443C22×C17—21no—
444C22×C17#42112yes—
445C22×C17C22×C22⋊C411yescharacteristic
446C2×D17—22no—
447C2×D17—41no—
448C2×D17—41no—
449C2×D17—41no—
450C2×D17—41no—
451C2×D17—41no—
452C2×D17—41no—
453C2×D17—41no—
454C2×D17—41no—
455C2×D17—84no—
456C2×D17—84no—
457C4×C17—21no—
458C4×C17—21no—
459C4×C17—21no—
460C4×C17—21no—
461C4×C17—21no—
462C4×C17—21no—
463C4×C17—21no—
464C4×C17—21no—
465C4×C17—21no—
466C4×C17—21no—
467C4×C17C2×#13111yescharacteristic
468C4×C17#56811yescharacteristic
469C4×C17#57611yescharacteristic
470C4×C17#57711yescharacteristic
471Dic17—41no—
472Dic17—41no—
473Dic17—41no—
474Dic17—41no—
475Dic17—41no—
476#559—171no—
477#554—171no—
478#554—171no—
479#553—171no—
480#553—171no—
481#553—341no—
482#551—341no—
483#551—341no—
484#546—171no—
485#546—171no—
486#546—341no—
487D42—171no—
488#532—171no—
489#529—171no—
490#529—171no—
491#529—341no—
492#525—341no—
493#525—341no—
494C4×#41—171no—
495C4×#41C2×D1711yescharacteristic
496C2×C4×D4—171no—
497C2×C4×D4—171no—
498C2×C4×D4—341no—
499#446—341no—
500#435—341no—
501#435—341no—
502C8×D4—341no—
503#433—21no—
504#433—21no—
505#432—171no—
506#432—171no—
507#431—171no—
508#431C2×D1711yescharacteristic, complemented
509#431C2×D1711yescharacteristic, complemented
510#431C2×D1711yescharacteristic, complemented
511#431C2×D1711yescharacteristic, complemented
512#424—21no—
513#423—171no—
514C2×C4⋊C8—171no—
515C2×C4⋊C8—171no—
516#408—21no—
517C4×M16C2×D1711yescharacteristic, complemented
518C2×C4×C8C2×D1711yescharacteristic, complemented
519Q8⋊C8—171no—
520Q8⋊C8—171no—
521Q8⋊C8—171no—
522Q8⋊C8—171no—
523D4⋊C8—171no—
524D4⋊C8—171no—
525D4⋊C8—171no—
526D4⋊C8—171no—
527D4⋊C8—171no—
528D4⋊C8—171no—
529D4⋊C8—171no—
530D4⋊C8—171no—
531D4⋊C8—171no—
532D4⋊C8—171no—
533D4⋊C8—171no—
534D4⋊C8—171no—
535C2×C17—22no—
536C2×C17—41no—
537C2×C17—41no—
538C2×C17#288011yescharacteristic
539C2×C17#289711yescharacteristic
540C2×C17C2×#42111yescharacteristic
541D17—42no—
542D17—81no—
543D17—81no—
544C2×#41—171no—
545C2×#41—341no—
546C2×#41C22⋊D1711yescharacteristic
547C22×D4—171no—
548C22×D4—171no—
549C22×D4—341no—
550C23×C4—341no—
551C23×C4—341no—
552C2×M16—21no—
553C2×M16—341no—
554C22×C8—21no—
555C22×C8—341no—
556C22×C8—341no—
557C4⋊Q8—171no—
558#127—171no—
559#126—341no—
560#126—341no—
561#126—341no—
562#126—341no—
563#125—171no—
564#125—171no—
565#125—341no—
566#124—171no—
567#124—171no—
568#124—341no—
569#124—341no—
570#123—341no—
571#123—341no—
572#123—341no—
573#123—341no—
574#123—341no—
575#123—341no—
576#123—341no—
577#123—341no—
578C22⋊Q8—171no—
579C22⋊Q8—171no—
580C22⋊Q8—341no—
581C22⋊Q8—341no—
582C22⋊Q8—341no—
583C22⋊Q8—341no—
584C22⋊Q8—341no—
585#121—171no—
586#121—171no—
587#121—171no—
588#121—171no—
589#121—341no—
590#121—341no—
591#121—341no—
592#121—341no—
593#121—341no—
594#121—341no—
595#120—341no—
596#120—341no—
597#120—341no—
598#120—341no—
599C4×Q8—171no—
600C4×Q8—171no—
601C4×Q8C4×D1711yescharacteristic
602C4×Q8D6811yescharacteristic
603C4×D4—171no—
604C4×D4—171no—
605C4×D4—171no—
606C4×D4—171no—
607C4×D4—171no—
608C4×D4—171no—
609C4×D4—171no—
610C4×D4—171no—
611C4×D4—341no—
612C4×D4—341no—
613C4×D4—341no—
614C4×D4—341no—
615C4×D4—341no—
616C4×D4—341no—
617C4×D4—341no—
618C4×D4—341no—
619C4×D4—341no—
620C4×D4—341no—
621C4×D4—341no—
622C4×D4—341no—
623C4×D4—341no—
624C4×D4C4×D1711yescharacteristic
625C4×D4C4×D1711yescharacteristic
626C4×D4C4×D1711yescharacteristic
627C4×D4D6811yescharacteristic
628C4×D4D6811yescharacteristic
629C4×D4D6811yescharacteristic
630#117—171no—
631#117—341no—
632#117—341no—
633#117—341no—
634#117C22⋊D1711yescharacteristic
635#117C22⋊D1711yescharacteristic
636#117C22⋊D1711yescharacteristic
637C2×C4⋊C4—171no—
638C2×C4⋊C4—171no—
639C2×C4⋊C4—341no—
640C2×C22⋊C4—341no—
641C2×C22⋊C4—341no—
642C2×C22⋊C4—341no—
643C2×C22⋊C4—341no—
644C2×C42—341no—
645C2×C42C22×D1711yescharacteristic
646C2×C42C22×D1711yescharacteristic
647C2×C42C22×D1711yescharacteristic
648C4⋊C8—21no—
649C4⋊C8—21no—
650C4⋊C8—21no—
651C4⋊C8—21no—
652C4⋊C8—171no—
653C4⋊C8—171no—
654C4⋊C8—171no—
655C4⋊C8—171no—
656C4⋊C8—341no—
657C4⋊C8—341no—
658C4⋊C8—341no—
659C22⋊C8—21no—
660C22⋊C8—21no—
661C22⋊C8—21no—
662C22⋊C8—21no—
663C22⋊C8—341no—
664C22⋊C8—341no—
665C22⋊C8—341no—
666#97—21no—
667#97—341no—
668#97—341no—
669C4×C8—21no—
670C4×C8—341no—
671C4×C8C22×D1711yescharacteristic
672C4×C8C22×D1711yescharacteristic
673C4×C8C22×D1711yescharacteristic
674C4×C8C22×D1711yescharacteristic
675C17#1752111yescharacteristic, complemented, Sylow
676C24—341no—
677C24—341no—
678#41—42no—
679#41—342no—
680#41—681no—
681#41—1361no—
682#41—1361no—
683C2×Q8—171no—
684C2×Q8—341no—
685C2×Q8#6322711yescharacteristic
686C2×D4—171no—
687C2×D4—171no—
688C2×D4—171no—
689C2×D4—342no—
690C2×D4—342no—
691C2×D4—341no—
692C2×D4—341no—
693C2×D4—341no—
694C2×D4—341no—
695C2×D4—341no—
696C2×D4—341no—
697C2×D4—341no—
698C2×D4—341no—
699C2×D4—341no—
700C2×D4—681no—
701C2×D4—681no—
702C2×D4—684no—
703C2×D4#6322711yescharacteristic
704C2×D4#6322711yescharacteristic
705C2×D4#6322711yescharacteristic
706C22×C4—341no—
707C22×C4—341no—
708C22×C4—341no—
709C22×C4—341no—
710C22×C4—341no—
711C22×C4—341no—
712C22×C4—341no—
713C22×C4—341no—
714C22×C4—341no—
715C22×C4—341no—
716C22×C4—341no—
717C22×C4—1361no—
718C22×C4—1361no—
719C22×C4—1361no—
720C22×C4—1361no—
721C22×C4C2×C4×D1711yescharacteristic
722C22×C4C2×C4×D1711yescharacteristic
723C22×C4C2×C4×D1711yescharacteristic
724C22×C4C2×D6811yescharacteristic
725C22×C4C2×D6811yescharacteristic
726C22×C4C2×D6811yescharacteristic
727C22×C4C2×C22⋊D1711yescharacteristic
728C22×C4C2×C22⋊D1711yescharacteristic
729C22×C4C2×C22⋊D1711yescharacteristic
730M16—42no—
731M16—1361no—
732C2×C8—21no—
733C2×C8—21no—
734C2×C8—21no—
735C2×C8—21no—
736C2×C8—42no—
737C2×C8—341no—
738C2×C8—341no—
739C2×C8—341no—
740C2×C8—341no—
741C2×C8—1361no—
742C2×C8—1361no—
743C4⋊C4—171no—
744C4⋊C4—171no—
745C4⋊C4—171no—
746C4⋊C4—171no—
747C4⋊C4—341no—
748C4⋊C4—341no—
749C4⋊C4—341no—
750C4⋊C4—341no—
751C4⋊C4—341no—
752C4⋊C4—341no—
753C4⋊C4—341no—
754C4⋊C4—341no—
755C4⋊C4—341no—
756C4⋊C4—341no—
757C4⋊C4—341no—
758C4⋊C4#6322711yescharacteristic
759C4⋊C4#6322711yescharacteristic
760C4⋊C4#6322711yescharacteristic
761C4⋊C4#6322711yescharacteristic
762C4⋊C4#6322711yescharacteristic
763C4⋊C4#6322711yescharacteristic
764C22⋊C4—341no—
765C22⋊C4—341no—
766C22⋊C4—341no—
767C22⋊C4—341no—
768C22⋊C4—341no—
769C22⋊C4—341no—
770C22⋊C4—341no—
771C22⋊C4—341no—
772C22⋊C4—341no—
773C22⋊C4—341no—
774C22⋊C4—341no—
775C22⋊C4—341no—
776C22⋊C4—341no—
777C22⋊C4—341no—
778C22⋊C4—341no—
779C22⋊C4—341no—
780C22⋊C4—341no—
781C22⋊C4—341no—
782C22⋊C4—341no—
783C22⋊C4#6322711yescharacteristic
784C22⋊C4#6322711yescharacteristic
785C22⋊C4#6322711yescharacteristic
786C22⋊C4#6322711yescharacteristic
787C22⋊C4#6322711yescharacteristic
788C22⋊C4#6322711yescharacteristic
789C42—341no—
790C42—341no—
791C42—341no—
792C42C2×C4×D1711yescharacteristic
793C42C2×C4×D1711yescharacteristic
794C42C2×C4×D1711yescharacteristic
795C42C2×D6811yescharacteristic
796C42C2×D6811yescharacteristic
797C42C2×D6811yescharacteristic
798C42C2×C22⋊D1711yescharacteristic
799C42C2×C22⋊D1711yescharacteristic
800C42C2×C22⋊D1711yescharacteristic
801C42C23×D1711yescharacteristic
802C23—341no—
803C23—341no—
804C23—341no—
805C23—682no—
806C23—682no—
807C23—682no—
808C23—682no—
809C23—1361no—
810C23—1361no—
811C23C2×#6322711yescharacteristic
812C23C2×#6322711yescharacteristic
813C23C2×#6322711yescharacteristic
814Q8—41no—
815Q8—341no—
816Q8—341no—
817Q8—1361no—
818D4—22no—
819D4—22no—
820D4—41no—
821D4—172no—
822D4—341no—
823D4—341no—
824D4—341no—
825D4—341no—
826D4—341no—
827D4—682no—
828D4—682no—
829D4—682no—
830D4—682no—
831D4—682no—
832D4—682no—
833D4—1361no—
834D4—1361no—
835D4—1361no—
836C2×C4—22no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—341no—
852C2×C4—341no—
853C2×C4—341no—
854C2×C4—341no—
855C2×C4—341no—
856C2×C4—682no—
857C2×C4—682no—
858C2×C4—681no—
859C2×C4—681no—
860C2×C4—681no—
861C2×C4—681no—
862C2×C4—681no—
863C2×C4—681no—
864C2×C4—1361no—
865C2×C4—1361no—
866C2×C4—1361no—
867C2×C4—1361no—
868C2×C4—1361no—
869C2×C4—1361no—
870C2×C4C2×#6322711yescharacteristic
871C2×C4C2×#6322711yescharacteristic
872C2×C4C2×#6322711yescharacteristic
873C2×C4C2×#6322711yescharacteristic
874C2×C4C2×#6322711yescharacteristic
875C2×C4C2×#6322711yescharacteristic
876C2×C4C2×#6322711yescharacteristic
877C2×C4C2×#6322711yescharacteristic
878C2×C4C2×#6322711yescharacteristic
879C2×C4C22×C4×D1711yescharacteristic
880C2×C4C22×D6811yescharacteristic
881C2×C4C22×C22⋊D1711yescharacteristic
882C8—41no—
883C8—41no—
884C8—41no—
885C8—41no—
886C8—681no—
887C8—681no—
888C8—681no—
889C8—681no—
890C22—21no—
891C22—21no—
892C22—21no—
893C22—21no—
894C22—21no—
895C22—21no—
896C22—21no—
897C22—21no—
898C22—342no—
899C22—681no—
900C22—681no—
901C22—681no—
902C22—681no—
903C22—681no—
904C22—681no—
905C22—681no—
906C22—681no—
907C22—1364no—
908C22—1364no—
909C22#1176282712yes—
910C22C22×#6322711yescharacteristic
911C4—21no—
912C4—21no—
913C4—21no—
914C4—21no—
915C4—21no—
916C4—21no—
917C4—21no—
918C4—21no—
919C4—21no—
920C4—21no—
921C4—681no—
922C4—681no—
923C4—681no—
924C4—681no—
925C4—681no—
926C4#131×D1711yescharacteristic
927C4#1176357411yescharacteristic
928C4#1176361411yescharacteristic
929C4#1176362111yescharacteristic
930C2—22no—
931C2—41no—
932C2—41no—
933C2—682no—
934C2—1361no—
935C2—1361no—
936C2#1453723111yescharacteristic
937C2#1453731111yescharacteristic
938C2C2×#1176282711yescharacteristic
subgroupG/H
centerC2×C4C22×D68
commutatorC2×C4×C17C23×C4
FrattiniC42C23×D17
FittingC17×#2922C2
socleC22×C17C22×C22⋊C4
prime radical#14542394C2
cosocleC42×C17C24
hypercenter#2922D17
hypocenterC17#17521
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ #2922

Complements

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

NH ≅ G/Ntype
2. #14537909C2semidirect
3. #14527254C2semidirect
4. #14527250C2semidirect
5. #14527245C2semidirect
6. #14527228C2semidirect
7. #14527219C2semidirect
8. #14527210C2semidirect
9. #14527198C2semidirect
10. #14527193C2semidirect
11. #14527184C2semidirect
12. #14527176C2semidirect
13. #14527172C2semidirect
14. C2×#11762538C2semidirect
15. C17×#2922C2semidirect
42. #11762866C22semidirect
43. #11762866C22semidirect
44. #11762862C22semidirect
45. #11762833C22semidirect
46. C2×C4⋊#3622C22semidirect
47. C2×C4⋊#3622C22semidirect
48. #11762541C22semidirect
49. #11762541C22semidirect
50. #11762541C22semidirect
51. #11762541C22semidirect
56. #11762538C22semidirect
57. #11762538C22semidirect
58. #11762538C22semidirect
59. #11762538C22semidirect
60. #11762538C22semidirect
61. #11762538C22semidirect
62. #11762538C22semidirect
63. #11762538C22semidirect
67. C17×#431C22semidirect
68. C17×#431C22semidirect
69. C17×#431C22semidirect
70. C17×#431C22semidirect
73. C4×M16×C17C22semidirect
74. C2×C4×C8×C17C22semidirect
423. #2922D17semidirect
508. #431C2×D17semidirect
509. #431C2×D17semidirect
510. #431C2×D17semidirect
511. #431C2×D17semidirect
517. C4×M16C2×D17semidirect
518. C2×C4×C8C2×D17semidirect
675. C17#17521semidirect

Maximal subgroups

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

subgroupindex
#145423942
#145379092
#145272542
#145272502
#145272452
#145272282
#145272192
#145272102
#145271982
#145271932
#145271842
#145271762
#145271722
C2×#117625382
C17×#29222
#1752117