Finite Group Databasebeta

← #17001853

Subgroups — #17001853

Order 4352.

1060 conjugacy classes of subgroups.

The subgroup lattice has 1012 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14542816C211yesmaximal, characteristic
2#14531417C211yesmaximal, characteristic, complemented
3#14527362C211yesmaximal, characteristic, complemented
4#14527353C211yesmaximal, characteristic, complemented
5#14527345C211yesmaximal, characteristic, complemented
6#14527341C211yesmaximal, characteristic, complemented
7#14527332C211yesmaximal, characteristic, complemented
8#14527328C211yesmaximal, characteristic, complemented
9#14527323C211yesmaximal, characteristic, complemented
10#14527314C211yesmaximal, characteristic, complemented
11#14527301C211yesmaximal, characteristic, complemented
12#14527289C211yesmaximal, characteristic, complemented
13#14527276C211yesmaximal, characteristic, complemented
14C2×#11762544C211yesmaximal, characteristic, complemented
15C17×#2974C211yesmaximal, characteristic, complemented
16#11763524C411yescharacteristic, complemented
17#11763516C411yescharacteristic, complemented
18#11763507—21no—
19#11763505C411yescharacteristic, complemented
20#11763505C411yescharacteristic, complemented
21#11763480C411yescharacteristic, complemented
22#11763455C411yescharacteristic, complemented
23#11763455C411yescharacteristic, complemented
24#11763449—21no—
25#11763449—21no—
26D4×D68C411yescharacteristic, complemented
27D4×C22⋊D17—21no—
28#11763410—21no—
29#11763392—21no—
30#11763392—21no—
31#11763359C2211yescharacteristic
32#11763343C2211yescharacteristic
33#11763320C2211yescharacteristic
34#11763320C2211yescharacteristic
35C2×#10587616C2211yescharacteristic
36C2×#10587616C2211yescharacteristic
37#11763281—21no—
38#11762702—21no—
39#11762695—21no—
40#11762689—21no—
41#11762684—21no—
42#11762677C2211yescharacteristic, complemented
43#11762675C2211yescharacteristic, complemented
44#11762672C2211yescharacteristic, complemented
45#11762669C2211yescharacteristic, complemented
46C4×C22⋊Dic17C2211yescharacteristic, complemented
47C2×#10587502C2211yescharacteristic, complemented
48#11762547C2211yescharacteristic, complemented
49#11762547C2211yescharacteristic, complemented
50#11762547C2211yescharacteristic, complemented
51#11762547C2211yescharacteristic, complemented
52#11762544C2211yescharacteristic
53#11762544C2211yescharacteristic
54#11762544C2211yescharacteristic
55#11762544C2211yescharacteristic
56#11762544C2211yescharacteristic, complemented
57#11762544C2211yescharacteristic, complemented
58#11762544C2211yescharacteristic, complemented
59#11762544C2211yescharacteristic, complemented
60#11762544C2211yescharacteristic, complemented
61#11762544C2211yescharacteristic, complemented
62#11762544C2211yescharacteristic, complemented
63#11762544C2211yescharacteristic, complemented
64C2×C4×D4×C17C2211yescharacteristic
65C17×#436—21no—
66C17×#435—21no—
67C17×#435—21no—
68C8×D4×C17—21no—
69C17×#432C2211yescharacteristic, complemented
70C17×#431C2211yescharacteristic, complemented
71C17×#407C2211yescharacteristic, complemented
72C17×#407C2211yescharacteristic, complemented
73C2×C17×C22⋊C8C2211yescharacteristic, complemented
74C2×C17×C22⋊C8C2211yescharacteristic, complemented
75C22×D4×C17D411yescharacteristic
76C23×C4×C17C2311yescharacteristic
77C23×C4×C17C2311yescharacteristic
78C22×C22⋊D17—21no—
79C22×C22⋊D17—21no—
80C23×Dic17—21no—
81C2×D4×D17—21no—
82C2×#63252—21no—
83C2×#63252C2×C411yescharacteristic
84C2×#63252C2×C411yescharacteristic, complemented
85C22×D68C2×C411yescharacteristic
86C22×D68C2×C411yescharacteristic, complemented
87C2×M16×C17—21no—
88C2×M16×C17—21no—
89C22×C8×C17—21no—
90C22×C8×C17—21no—
91C4×D4×C17C2×C411yescharacteristic
92C4×D4×C17C2×C411yescharacteristic
93C4×D4×C17C2×C411yescharacteristic
94C4×D4×C17C2×C411yescharacteristic
95C4×D4×C17D411yescharacteristic
96C4×D4×C17D411yescharacteristic
97C4×D4×C17D411yescharacteristic
98C4×D4×C17D411yescharacteristic
99C2×C4⋊C4×C17D411yescharacteristic
100C2×C22⋊C4×C17D411yescharacteristic
101C2×C22⋊C4×C17D411yescharacteristic
102C2×C42×C17C2311yescharacteristic
103#10587639—21no—
104#10587639—21no—
105C2×C22⋊Dic17—21no—
106C2×C22⋊Dic17—21no—
107C2×C22⋊Dic17—21no—
108#10587626—21no—
109#10587625—21no—
110#10587625—21no—
111#10587624—21no—
112#10587623—21no—
113#10587623—21no—
114D4×Dic17—21no—
115#10587616—21no—
116#10587616—21no—
117#10587616—21no—
118#10587616—21no—
119#10587616—21no—
120#10587616C2×C411yescharacteristic
121#10587616C2×C411yescharacteristic
122#10587616C2×C411yescharacteristic
123#10587616C2×C411yescharacteristic, complemented
124#10587616C2×C411yescharacteristic, complemented
125#10587616C2×C411yescharacteristic, complemented
126#10587616C2311yescharacteristic
127#10587616C2311yescharacteristic
128#10587616C2311yescharacteristic
129#10587615—21no—
130#10587615—21no—
131#10587615—21no—
132C4×C22⋊D17—21no—
133C4×C22⋊D17—21no—
134C4×C22⋊D17—21no—
135C4×C22⋊D17—21no—
136C4×C22⋊D17—21no—
137C2×#63227—21no—
138C2×#63227—21no—
139#10587612C2×C411yescharacteristic
140#10587612C2×C411yescharacteristic, complemented
141C2×C4⋊Dic17—21no—
142C2×C4⋊Dic17—21no—
143C2×C4⋊Dic17C2×C411yescharacteristic
144C2×C4⋊Dic17C2×C411yescharacteristic, complemented
145#10587610C2×C411yescharacteristic
146#10587610C2×C411yescharacteristic, complemented
147#10587610C2311yescharacteristic
148C2×C4×Dic17—21no—
149#10587584—21no—
150#10587584—21no—
151#10587581—21no—
152#10587580—21no—
153#10587580—21no—
154#10587579—21no—
155#10587578—21no—
156#10587576—21no—
157#10587571—21no—
158#10587571—21no—
159#10587570—21no—
160#10587570—21no—
161#10587570—21no—
162#10587570—21no—
163#10587569—21no—
164#10587569—21no—
165#10587568—21no—
166#10587568—21no—
167#10587567—21no—
168#10587567—21no—
169C22⋊C4×D17—21no—
170C22⋊C4×D17—21no—
171#10587564—21no—
172#10587564—21no—
173#10587562—21no—
174#10587561—21no—
175#10587561C2×C411yescharacteristic, complemented
176#10587560C2×C411yescharacteristic, complemented
177C4×D68—21no—
178C4×D68C2×C411yescharacteristic, complemented
179C4×D68C2×C411yescharacteristic, complemented
180C4×D68C2×C411yescharacteristic, complemented
181#10587558—21no—
182#10587556C2×C411yescharacteristic, complemented
183#10587555C2×C411yescharacteristic, complemented
184C4×Dic34C2×C411yescharacteristic, complemented
185C17×C4⋊C8—21no—
186C17×C4⋊C8—21no—
187C17×C22⋊C8—21no—
188C17×C22⋊C8—21no—
189C17×C22⋊C8—21no—
190C17×C22⋊C8—21no—
191C17×C22⋊C8C2311yescharacteristic
192C17×C22⋊C8C2311yescharacteristic
193C17×C22⋊C8C2311yescharacteristic
194C17×C22⋊C8C2311yescharacteristic
195C17×#97—21no—
196C4×C8×C17—21no—
197#10587502—21no—
198#10587502—21no—
199#10587502—21no—
200#10587502—21no—
201#10587502—21no—
202#10587502C2311yescharacteristic
203#10587502C2311yescharacteristic
204#10587502C2311yescharacteristic
205#10587502C2311yescharacteristic
206C24×C17C2×D411yescharacteristic
207C24×C17C2×D411yescharacteristic
208C23×D17—21no—
209C23×D17—21no—
210C2×D4×C17—42no—
211C2×D4×C17C22⋊C411yescharacteristic
212C2×D4×C17C22⋊C411yescharacteristic
213C2×D4×C17C22⋊C411yescharacteristic
214C2×D4×C17C22⋊C411yescharacteristic
215C22×C4×C17—81no—
216C22×C4×C17—81no—
217C22×C4×C17C22×C411yescharacteristic
218C22×C4×C17C22×C411yescharacteristic
219C22×C4×C17C22×C411yescharacteristic
220C22×C4×C17C22×C411yescharacteristic
221C22×C4×C17C2×D411yescharacteristic
222C22×C4×C17C2×D411yescharacteristic
223C22×C4×C17C2×D411yescharacteristic
224C22×C4×C17C2×D411yescharacteristic
225C22×C4×C17C2×D411yescharacteristic
226C22×C4×C17C2×D411yescharacteristic
227C22×C4×C17C2×D411yescharacteristic
228C22×C4×C17C2×D411yescharacteristic
229C22×C4×C17C2411yescharacteristic
230C2×C22⋊D17—21no—
231C2×C22⋊D17—21no—
232C2×C22⋊D17—21no—
233C2×C22⋊D17—21no—
234C2×C22⋊D17—21no—
235C2×C22⋊D17—21no—
236C2×C22⋊D17—21no—
237C2×C22⋊D17—21no—
238C2×C22⋊D17—21no—
239C2×C22⋊D17—21no—
240C2×C22⋊D17—21no—
241C2×C22⋊D17—81no—
242C2×C22⋊D17—81no—
243C2×C22⋊D17—81no—
244C2×C22⋊D17—81no—
245C22×Dic17—21no—
246C22×Dic17—21no—
247C22×Dic17—21no—
248C22×Dic17—21no—
249C22×Dic17—21no—
250C22×Dic17—21no—
251C22×Dic17—42no—
252C22×Dic17—81no—
253C22×Dic17—81no—
254D4×D17—44no—
255#63252—81no—
256#63252—81no—
257#63252—81no—
258#63252—81no—
259C2×D68—21no—
260C2×D68—21no—
261C2×D68—21no—
262C2×D68—21no—
263C2×D68—81no—
264C2×D68—81no—
265C2×D68C22×C411yescharacteristic
266C2×D68C22×C411yescharacteristic
267C2×D68C22×C411yescharacteristic
268C2×C4×D17—21no—
269C2×C4×D17—21no—
270C2×C4×D17—21no—
271C2×C4×D17—21no—
272C2×C4×D17—21no—
273C2×Dic34—21no—
274C2×Dic34C22×C411yescharacteristic
275M16×C17—81no—
276M16×C17—81no—
277C2×C8×C17—21no—
278C2×C8×C17—21no—
279C2×C8×C17—21no—
280C2×C8×C17—21no—
281C2×C8×C17—81no—
282C2×C8×C17—81no—
283C4⋊C4×C17C22⋊C411yescharacteristic
284C4⋊C4×C17C22⋊C411yescharacteristic
285C4⋊C4×C17C22⋊C411yescharacteristic
286C4⋊C4×C17C22⋊C411yescharacteristic
287C22⋊C4×C17C22⋊C411yescharacteristic
288C22⋊C4×C17C22⋊C411yescharacteristic
289C22⋊C4×C17C22⋊C411yescharacteristic
290C22⋊C4×C17C22⋊C411yescharacteristic
291C22⋊C4×C17C22⋊C411yescharacteristic
292C22⋊C4×C17C22⋊C411yescharacteristic
293C22⋊C4×C17C22⋊C411yescharacteristic
294C22⋊C4×C17C22⋊C411yescharacteristic
295C42×C17C22×C411yescharacteristic
296C42×C17C22×C411yescharacteristic
297C42×C17C2×D411yescharacteristic
298C42×C17C2×D411yescharacteristic
299C22⋊Dic17—21no—
300C22⋊Dic17—21no—
301C22⋊Dic17—21no—
302C22⋊Dic17—21no—
303C22⋊Dic17—21no—
304C22⋊Dic17—42no—
305C22⋊Dic17—81no—
306C22⋊Dic17—81no—
307#63227—21no—
308#63227—21no—
309#63227—21no—
310#63227—21no—
311#63227—21no—
312#63227—21no—
313#63227—21no—
314#63227—21no—
315#63227—21no—
316#63227—21no—
317#63227—21no—
318#63227—21no—
319#63227—21no—
320#63227—21no—
321C4⋊Dic17—21no—
322C4⋊Dic17—21no—
323C4⋊Dic17—21no—
324C4⋊Dic17—81no—
325C4⋊Dic17—81no—
326C4⋊Dic17C22×C411yescharacteristic
327C4⋊Dic17C22×C411yescharacteristic
328C4⋊Dic17C22×C411yescharacteristic
329C4⋊Dic17C22×C411yescharacteristic
330#63225—21no—
331#63225—21no—
332#63225—21no—
333#63225—21no—
334#63225—21no—
335#63225—21no—
336C4×Dic17—21no—
337C4×Dic17—21no—
338C4×Dic17—21no—
339C4×Dic17—81no—
340#17597—171nomaximal, Sylow
341C23×C17—21no—
342C23×C17—21no—
343C23×C17—22no—
344C23×C17—21no—
345C23×C17—21no—
346C23×C17—41no—
347C23×C17—41no—
348C23×C17—41no—
349C23×C17C2×C22⋊C411yescharacteristic
350C23×C17C2×C22⋊C411yescharacteristic
351C23×C17C2×C22⋊C411yescharacteristic
352C23×C17C2×C22⋊C411yescharacteristic
353C23×C17C22×D411yescharacteristic
354C22×D17—21no—
355C22×D17—21no—
356C22×D17—21no—
357C22×D17—42no—
358C22×D17—42no—
359C22×D17—81no—
360C22×D17—81no—
361C22×D17—81no—
362C22×D17—81no—
363D4×C17—22no—
364D4×C17—22no—
365D4×C17—41no—
366D4×C17—41no—
367C2×C4×C17—21no—
368C2×C4×C17—21no—
369C2×C4×C17—41no—
370C2×C4×C17—41no—
371C2×C4×C17—41no—
372C2×C4×C17—41no—
373C2×C4×C17—41no—
374C2×C4×C17—41no—
375C2×C4×C17—41no—
376C2×C4×C17—41no—
377C2×C4×C17—41no—
378C2×C4×C17—41no—
379C2×C4×C17—41no—
380C2×C4×C17—41no—
381C2×C4×C17C2×C22⋊C411yescharacteristic
382C2×C4×C17C2×C22⋊C411yescharacteristic
383C2×C4×C17C2×C22⋊C411yescharacteristic
384C2×C4×C17C2×C22⋊C411yescharacteristic
385C2×C4×C17C2×C22⋊C411yescharacteristic
386C2×C4×C17C2×C22⋊C411yescharacteristic
387C2×C4×C17C2×C22⋊C411yescharacteristic
388C2×C4×C17C2×C22⋊C411yescharacteristic
389C2×C4×C17C23×C411yescharacteristic
390C2×C4×C17C22×D411yescharacteristic
391C22⋊D17—42no—
392C22⋊D17—41no—
393C22⋊D17—41no—
394C22⋊D17—41no—
395C22⋊D17—41no—
396C22⋊D17—41no—
397C22⋊D17—41no—
398C22⋊D17—42no—
399C22⋊D17—81no—
400C22⋊D17—81no—
401C22⋊D17—81no—
402C22⋊D17—81no—
403C22⋊D17—81no—
404C22⋊D17—81no—
405C2×Dic17—21no—
406C2×Dic17—21no—
407C2×Dic17—21no—
408C2×Dic17—21no—
409C2×Dic17—21no—
410C2×Dic17—41no—
411C2×Dic17—41no—
412C2×Dic17—41no—
413C2×Dic17—41no—
414C2×Dic17—41no—
415C2×Dic17—41no—
416C2×Dic17—41no—
417C2×Dic17—41no—
418C2×Dic17—41no—
419C2×Dic17—41no—
420C2×Dic17—41no—
421C2×Dic17—41no—
422C2×Dic17—81no—
423C2×Dic17—81no—
424C2×Dic17—84no—
425D68—41no—
426D68—41no—
427D68—41no—
428D68—42no—
429D68—81no—
430D68—81no—
431D68—81no—
432C4×D17—42no—
433C4×D17—81no—
434C4×D17—81no—
435C4×D17—81no—
436C4×D17—81no—
437Dic34—41no—
438Dic34—81no—
439C8×C17—41no—
440C8×C17—41no—
441C8×C17—41no—
442C8×C17—41no—
443#3519—171no—
444#2974D1711yescharacteristic, complemented
445#2318—171no—
446#1521—171no—
447#1519—171no—
448#1517—171no—
449#1516—171no—
450#1514—171no—
451#1513—171no—
452#1512—171no—
453#1510—171no—
454#1507—171no—
455#1504—171no—
456#1501—171no—
457C2×#327—171no—
458C22×C17—21no—
459C22×C17—21no—
460C22×C17—21no—
461C22×C17—21no—
462C22×C17—21no—
463C22×C17—21no—
464C22×C17—21no—
465C22×C17—21no—
466C22×C17—21no—
467C22×C17—21no—
468C22×C17—21no—
469C22×C17—21no—
470C22×C17—21no—
471C22×C17—42no—
472C22×C17—42no—
473C22×C17—81no—
474C22×C17—81no—
475C22×C17#42112yes—
476C22×C17C22×C22⋊C411yescharacteristic
477C22×C17#57611yescharacteristic
478C22×C17#57711yescharacteristic
479C2×D17—41no—
480C2×D17—41no—
481C2×D17—41no—
482C2×D17—41no—
483C2×D17—41no—
484C2×D17—41no—
485C2×D17—41no—
486C2×D17—41no—
487C2×D17—41no—
488C2×D17—162no—
489C2×D17—162no—
490C4×C17—21no—
491C4×C17—21no—
492C4×C17—21no—
493C4×C17—21no—
494C4×C17—21no—
495C4×C17—21no—
496C4×C17—21no—
497C4×C17—21no—
498C4×C17—21no—
499C4×C17—21no—
500Dic17—41no—
501Dic17—41no—
502Dic17—41no—
503Dic17—41no—
504Dic17—41no—
505Dic17—81no—
506Dic17—81no—
507Dic17—81no—
508Dic17—81no—
509#555—171no—
510#554—171no—
511#553—171no—
512#553—171no—
513#553—341no—
514#550—171no—
515#546—171no—
516#546—171no—
517#546—341no—
518#546—341no—
519D42—171no—
520D42—341no—
521#540—341no—
522#538—341no—
523#538—341no—
524#532—171no—
525#529—171no—
526#525—171no—
527#525—171no—
528C2×#121—171no—
529C2×#121—171no—
530#518—341no—
531C2×C4×D4C2×D1711yescharacteristic
532#436—21no—
533#435—21no—
534#435—21no—
535C8×D4—21no—
536#432C2×D1711yescharacteristic, complemented
537#431C2×D1711yescharacteristic, complemented
538#407C2×D1711yescharacteristic, complemented
539#407C2×D1711yescharacteristic, complemented
540C2×C22⋊C8C2×D1711yescharacteristic, complemented
541C2×C22⋊C8C2×D1711yescharacteristic, complemented
542#388—341no—
543#387—341no—
544#386—341no—
545#385—341no—
546#383—171no—
547#382—171no—
548#381—171no—
549#380—171no—
550C4×C22⋊C4—171no—
551C2×#95—171no—
552#328—171no—
553#328—171no—
554#328—171no—
555#328—171no—
556#327—171no—
557#327—171no—
558#327—171no—
559#327—171no—
560#327—171no—
561#327—171no—
562#327—171no—
563#327—171no—
564#327—171no—
565#327—171no—
566#327—171no—
567#327—171no—
568C2×C17—21no—
569C2×C17—21no—
570C2×C17—22no—
571C2×C17—41no—
572C2×C17—41no—
573C2×C17—41no—
574C2×C17#288311yescharacteristic
575C2×C17#289711yescharacteristic
576C2×C17C2×#42111yescharacteristic
577D17—81no—
578D17—81no—
579D17—81no—
580C2×#41—171no—
581C2×#41—171no—
582C2×#41—341no—
583C22×D4—171no—
584C22×D4—171no—
585C22×D4—341no—
586C22×D4—341no—
587C22×D4—341no—
588C22×D4D6811yescharacteristic
589C23×C4—341no—
590C23×C4C22×D1711yescharacteristic
591C23×C4C22×D1711yescharacteristic
592C2×M16—21no—
593C2×M16—21no—
594C22×C8—21no—
595C22×C8—21no—
596C4⋊Q8—171no—
597#127—171no—
598#127—341no—
599#126—341no—
600#126—341no—
601#126—341no—
602#125—171no—
603#125—341no—
604#124—171no—
605#124—341no—
606#124—341no—
607#124—341no—
608#123—341no—
609#123—341no—
610#123—341no—
611#123—341no—
612#123—341no—
613#123—341no—
614#123—341no—
615C22⋊Q8—171no—
616C22⋊Q8—171no—
617C22⋊Q8—171no—
618C22⋊Q8—341no—
619C22⋊Q8—341no—
620#121—171no—
621#121—171no—
622#121—171no—
623#121—171no—
624#121—171no—
625#121—171no—
626#121—171no—
627#121—171no—
628#121—171no—
629#121—341no—
630#121—341no—
631#121—341no—
632#121—341no—
633#121—341no—
634#121—341no—
635#121—341no—
636#121—341no—
637#121—341no—
638#121—341no—
639#121—341no—
640#121—341no—
641#121—341no—
642#120—341no—
643#120—341no—
644#120—341no—
645#120—341no—
646#120—341no—
647#120—341no—
648C4×Q8—171no—
649C4×D4—171no—
650C4×D4—171no—
651C4×D4—171no—
652C4×D4—341no—
653C4×D4—341no—
654C4×D4—341no—
655C4×D4—341no—
656C4×D4—341no—
657C4×D4—341no—
658C4×D4—341no—
659C4×D4—341no—
660C4×D4—341no—
661C4×D4—341no—
662C4×D4C4×D1711yescharacteristic
663C4×D4C4×D1711yescharacteristic
664C4×D4C4×D1711yescharacteristic
665C4×D4C4×D1711yescharacteristic
666C4×D4C22⋊D1711yescharacteristic
667C4×D4C22⋊D1711yescharacteristic
668C4×D4C22⋊D1711yescharacteristic
669C4×D4C22⋊D1711yescharacteristic
670#117—171no—
671#117—171no—
672#117—341no—
673#117—341no—
674C2×C4⋊C4—171no—
675C2×C4⋊C4—171no—
676C2×C4⋊C4—341no—
677C2×C4⋊C4—341no—
678C2×C4⋊C4D6811yescharacteristic
679C2×C22⋊C4—341no—
680C2×C22⋊C4—341no—
681C2×C22⋊C4—341no—
682C2×C22⋊C4—341no—
683C2×C22⋊C4—341no—
684C2×C22⋊C4—341no—
685C2×C22⋊C4—341no—
686C2×C22⋊C4D6811yescharacteristic
687C2×C22⋊C4D6811yescharacteristic
688C2×C42—341no—
689C2×C42C22×D1711yescharacteristic
690C4⋊C8—21no—
691C4⋊C8—21no—
692C22⋊C8—21no—
693C22⋊C8—21no—
694C22⋊C8—21no—
695C22⋊C8—21no—
696C22⋊C8C22×D1711yescharacteristic
697C22⋊C8C22×D1711yescharacteristic
698C22⋊C8C22×D1711yescharacteristic
699C22⋊C8C22×D1711yescharacteristic
700#97—21no—
701C4×C8—21no—
702#95—171no—
703#95—171no—
704#95—171no—
705#95—171no—
706#95—341no—
707#95—341no—
708#95—341no—
709#95—341no—
710#95—341no—
711C17#1759711yescharacteristic, complemented, Sylow
712C24—341no—
713C24—341no—
714C24C2×D6811yescharacteristic
715C24C2×D6811yescharacteristic
716#41—1361no—
717#41—1361no—
718#41—1361no—
719#41—1361no—
720C2×Q8—171no—
721C2×Q8—341no—
722C2×D4—42no—
723C2×D4—171no—
724C2×D4—171no—
725C2×D4—171no—
726C2×D4—341no—
727C2×D4—341no—
728C2×D4—341no—
729C2×D4—341no—
730C2×D4—341no—
731C2×D4—341no—
732C2×D4—341no—
733C2×D4—341no—
734C2×D4—341no—
735C2×D4—341no—
736C2×D4—341no—
737C2×D4—341no—
738C2×D4—341no—
739C2×D4—341no—
740C2×D4—341no—
741C2×D4—684no—
742C2×D4—1361no—
743C2×D4—1361no—
744C2×D4—1361no—
745C2×D4—1361no—
746C2×D4—1361no—
747C2×D4—1361no—
748C2×D4#6322711yescharacteristic
749C2×D4#6322711yescharacteristic
750C2×D4#6322711yescharacteristic
751C2×D4#6322711yescharacteristic
752C22×C4—81no—
753C22×C4—81no—
754C22×C4—341no—
755C22×C4—341no—
756C22×C4—341no—
757C22×C4—341no—
758C22×C4—341no—
759C22×C4—341no—
760C22×C4—341no—
761C22×C4—341no—
762C22×C4—341no—
763C22×C4—341no—
764C22×C4—341no—
765C22×C4—682no—
766C22×C4—1361no—
767C22×C4—1361no—
768C22×C4C2×C4×D1711yescharacteristic
769C22×C4C2×C4×D1711yescharacteristic
770C22×C4C2×C4×D1711yescharacteristic
771C22×C4C2×C4×D1711yescharacteristic
772C22×C4C2×D6811yescharacteristic
773C22×C4C2×D6811yescharacteristic
774C22×C4C2×D6811yescharacteristic
775C22×C4C2×D6811yescharacteristic
776C22×C4C2×C22⋊D1711yescharacteristic
777C22×C4C2×C22⋊D1711yescharacteristic
778C22×C4C2×C22⋊D1711yescharacteristic
779C22×C4C2×C22⋊D1711yescharacteristic
780C22×C4C23×D1711yescharacteristic
781M16—81no—
782M16—81no—
783C2×C8—21no—
784C2×C8—21no—
785C2×C8—21no—
786C2×C8—21no—
787C2×C8—81no—
788C2×C8—81no—
789C4⋊C4—171no—
790C4⋊C4—171no—
791C4⋊C4—171no—
792C4⋊C4—171no—
793C4⋊C4—341no—
794C4⋊C4—341no—
795C4⋊C4—341no—
796C4⋊C4—341no—
797C4⋊C4—341no—
798C4⋊C4—341no—
799C4⋊C4—341no—
800C4⋊C4—341no—
801C4⋊C4—341no—
802C4⋊C4—1361no—
803C4⋊C4—1361no—
804C4⋊C4#6322711yescharacteristic
805C4⋊C4#6322711yescharacteristic
806C4⋊C4#6322711yescharacteristic
807C4⋊C4#6322711yescharacteristic
808C22⋊C4—341no—
809C22⋊C4—341no—
810C22⋊C4—341no—
811C22⋊C4—341no—
812C22⋊C4—341no—
813C22⋊C4—341no—
814C22⋊C4—341no—
815C22⋊C4—341no—
816C22⋊C4—341no—
817C22⋊C4—341no—
818C22⋊C4—341no—
819C22⋊C4—341no—
820C22⋊C4—341no—
821C22⋊C4—341no—
822C22⋊C4—341no—
823C22⋊C4—341no—
824C22⋊C4—341no—
825C22⋊C4—341no—
826C22⋊C4—341no—
827C22⋊C4—682no—
828C22⋊C4—1361no—
829C22⋊C4—1361no—
830C22⋊C4#6322711yescharacteristic
831C22⋊C4#6322711yescharacteristic
832C22⋊C4#6322711yescharacteristic
833C22⋊C4#6322711yescharacteristic
834C22⋊C4#6322711yescharacteristic
835C22⋊C4#6322711yescharacteristic
836C22⋊C4#6322711yescharacteristic
837C22⋊C4#6322711yescharacteristic
838C42—341no—
839C42—341no—
840C42—341no—
841C42—1361no—
842C42C2×C4×D1711yescharacteristic
843C42C2×C4×D1711yescharacteristic
844C42C2×C22⋊D1711yescharacteristic
845C42C2×C22⋊D1711yescharacteristic
846C23—22no—
847C23—21no—
848C23—21no—
849C23—21no—
850C23—21no—
851C23—41no—
852C23—41no—
853C23—41no—
854C23—341no—
855C23—341no—
856C23—341no—
857C23—682no—
858C23—682no—
859C23—1361no—
860C23—1361no—
861C23—1361no—
862C23—1361no—
863C23C2×#6322711yescharacteristic
864C23C2×#6322711yescharacteristic
865C23C2×#6322711yescharacteristic
866C23C2×#6322711yescharacteristic
867C23C22×D6811yescharacteristic
868Q8—681no—
869Q8—1361no—
870D4—22no—
871D4—22no—
872D4—41no—
873D4—41no—
874D4—681no—
875D4—681no—
876D4—681no—
877D4—682no—
878D4—682no—
879D4—682no—
880D4—681no—
881D4—681no—
882D4—681no—
883D4—681no—
884D4—681no—
885D4—681no—
886D4—1361no—
887D4—1361no—
888D4—1361no—
889D4—1361no—
890D4—1361no—
891D4—1361no—
892D4—1361no—
893D4—1361no—
894D4—1361no—
895C2×C4—21no—
896C2×C4—21no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—341no—
910C2×C4—341no—
911C2×C4—341no—
912C2×C4—341no—
913C2×C4—341no—
914C2×C4—682no—
915C2×C4—681no—
916C2×C4—681no—
917C2×C4—681no—
918C2×C4—681no—
919C2×C4—681no—
920C2×C4—681no—
921C2×C4—681no—
922C2×C4—681no—
923C2×C4—681no—
924C2×C4—681no—
925C2×C4—681no—
926C2×C4—681no—
927C2×C4—1361no—
928C2×C4—1361no—
929C2×C4—1361no—
930C2×C4—1361no—
931C2×C4—1361no—
932C2×C4—1361no—
933C2×C4—1364no—
934C2×C4C2×#6322711yescharacteristic
935C2×C4C2×#6322711yescharacteristic
936C2×C4C2×#6322711yescharacteristic
937C2×C4C2×#6322711yescharacteristic
938C2×C4C2×#6322711yescharacteristic
939C2×C4C2×#6322711yescharacteristic
940C2×C4C2×#6322711yescharacteristic
941C2×C4C2×#6322711yescharacteristic
942C2×C4C22×C4×D1711yescharacteristic
943C2×C4C22×C22⋊D1711yescharacteristic
944C8—41no—
945C8—41no—
946C8—41no—
947C8—41no—
948C22—21no—
949C22—21no—
950C22—21no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—21no—
955C22—21no—
956C22—21no—
957C22—21no—
958C22—21no—
959C22—21no—
960C22—21no—
961C22—42no—
962C22—42no—
963C22—81no—
964C22—81no—
965C22—2722no—
966C22—2722no—
967C22—681no—
968C22—681no—
969C22—681no—
970C22—681no—
971C22—681no—
972C22—681no—
973C22—681no—
974C22—681no—
975C22—681no—
976C22#1176282512yes—
977C22C22×#6322711yescharacteristic
978C22#1176361411yescharacteristic
979C22#1176362111yescharacteristic
980C4—21no—
981C4—21no—
982C4—21no—
983C4—21no—
984C4—21no—
985C4—21no—
986C4—21no—
987C4—21no—
988C4—21no—
989C4—21no—
990C4—681no—
991C4—681no—
992C4—681no—
993C4—681no—
994C4—681no—
995C4—1361no—
996C4—1361no—
997C4—1361no—
998C4—1361no—
999C2—21no—
1000C2—21no—
1001C2—22no—
1002C2—41no—
1003C2—41no—
1004C2—41no—
1005C2—1361no—
1006C2—1361no—
1007C2—1361no—
1008C2#1453724411yescharacteristic
1009C2#1453731111yescharacteristic
1010C2C2×#1176282511yescharacteristic
subgroupG/H
centerC22C22×#63227
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC17×#2974C2
socleC22×C17C22×C22⋊C4
prime radical#14542816C2
cosocleC22×C4×C17C24
hypercenter#2974D17
hypocenterC17#17597
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #2974

Complements

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

NH ≅ G/Ntype
2. #14531417C2semidirect
3. #14527362C2semidirect
4. #14527353C2semidirect
5. #14527345C2semidirect
6. #14527341C2semidirect
7. #14527332C2semidirect
8. #14527328C2semidirect
9. #14527323C2semidirect
10. #14527314C2semidirect
11. #14527301C2semidirect
12. #14527289C2semidirect
13. #14527276C2semidirect
14. C2×#11762544C2semidirect
15. C17×#2974C2semidirect
16. #11763524C4semidirect
17. #11763516C4semidirect
19. #11763505C4semidirect
20. #11763505C4semidirect
21. #11763480C4semidirect
22. #11763455C4semidirect
23. #11763455C4semidirect
26. D4×D68C4semidirect
42. #11762677C22semidirect
43. #11762675C22semidirect
44. #11762672C22semidirect
45. #11762669C22semidirect
46. C4×C22⋊Dic17C22semidirect
47. C2×#10587502C22semidirect
48. #11762547C22semidirect
49. #11762547C22semidirect
50. #11762547C22semidirect
51. #11762547C22semidirect
56. #11762544C22semidirect
57. #11762544C22semidirect
58. #11762544C22semidirect
59. #11762544C22semidirect
60. #11762544C22semidirect
61. #11762544C22semidirect
62. #11762544C22semidirect
63. #11762544C22semidirect
69. C17×#432C22semidirect
70. C17×#431C22semidirect
71. C17×#407C22semidirect
72. C17×#407C22semidirect
73. C2×C17×C22⋊C8C22semidirect
74. C2×C17×C22⋊C8C22semidirect
84. C2×#63252C2×C4semidirect
86. C22×D68C2×C4semidirect
123. #10587616C2×C4semidirect
124. #10587616C2×C4semidirect
125. #10587616C2×C4semidirect
140. #10587612C2×C4semidirect
144. C2×C4⋊Dic17C2×C4semidirect
146. #10587610C2×C4semidirect
175. #10587561C2×C4semidirect
176. #10587560C2×C4semidirect
178. C4×D68C2×C4semidirect
179. C4×D68C2×C4semidirect
180. C4×D68C2×C4semidirect
182. #10587556C2×C4semidirect
183. #10587555C2×C4semidirect
184. C4×Dic34C2×C4semidirect
444. #2974D17semidirect
536. #432C2×D17semidirect
537. #431C2×D17semidirect
538. #407C2×D17semidirect
539. #407C2×D17semidirect
540. C2×C22⋊C8C2×D17semidirect
541. C2×C22⋊C8C2×D17semidirect
711. C17#17597semidirect

Maximal subgroups

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

subgroupindex
#145428162
#145314172
#145273622
#145273532
#145273452
#145273412
#145273322
#145273282
#145273232
#145273142
#145273012
#145272892
#145272762
C2×#117625442
C17×#29742
#1759717