Finite Group Databasebeta

← #17001868

Subgroups — #17001868

Order 4352.

996 conjugacy classes of subgroups.

The subgroup lattice has 952 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14542833C211yesmaximal, characteristic
2#14531417C211yesmaximal, characteristic, complemented
3#14527362C211yesmaximal, characteristic, complemented
4#14527357C211yesmaximal, characteristic, complemented
5#14527349C211yesmaximal, characteristic, complemented
6#14527341C211yesmaximal, characteristic, complemented
7#14527336C211yesmaximal, characteristic, complemented
8#14527328C211yesmaximal, characteristic, complemented
9#14527323C211yesmaximal, characteristic, complemented
10#14527318C211yesmaximal, characteristic, complemented
11#14527305C211yesmaximal, characteristic, complemented
12#14527289C211yesmaximal, characteristic, complemented
13#14527276C211yesmaximal, characteristic, complemented
14C2×#11762547C211yesmaximal, characteristic, complemented
15C17×#2974C211yesmaximal, characteristic, complemented
16#11763529C411yescharacteristic, complemented
17#11763514—21no—
18#11763499C411yescharacteristic, complemented
19#11763499C411yescharacteristic, complemented
20#11763485—21no—
21#11763485—21no—
22D4×Dic34C411yescharacteristic, complemented
23#11763468C411yescharacteristic, complemented
24#11763468C411yescharacteristic, complemented
25#11763464C411yescharacteristic, complemented
26#11763463C411yescharacteristic, complemented
27#11763453—21no—
28#11763424—21no—
29#11763401—21no—
30#11763401—21no—
31#11763366C2211yescharacteristic
32#11763343C2211yescharacteristic
33#11763320C2211yescharacteristic
34#11763320C2211yescharacteristic
35C2×#10587610C2211yescharacteristic
36C2×#10587610C2211yescharacteristic
37#11763288—21no—
38#11762702—21no—
39#11762695—21no—
40#11762689—21no—
41#11762684—21no—
42#11762677C2211yescharacteristic
43#11762675C2211yescharacteristic
44#11762672C2211yescharacteristic
45#11762669C2211yescharacteristic
46C4×C22⋊Dic17C2211yescharacteristic
47C2×#10587502C2211yescharacteristic
48#11762547C2211yescharacteristic
49#11762547C2211yescharacteristic
50#11762547C2211yescharacteristic
51#11762547C2211yescharacteristic
52#11762547C2211yescharacteristic
53#11762547C2211yescharacteristic
54#11762547C2211yescharacteristic
55#11762547C2211yescharacteristic
56#11762547C2211yescharacteristic
57#11762547C2211yescharacteristic
58#11762547C2211yescharacteristic
59#11762547C2211yescharacteristic
60#11762544C2211yescharacteristic
61#11762544C2211yescharacteristic
62#11762544C2211yescharacteristic
63#11762544C2211yescharacteristic
64C2×C4×D4×C17C2211yescharacteristic
65C17×#436—21no—
66C17×#435—21no—
67C17×#435—21no—
68C8×D4×C17—21no—
69C17×#432C2211yescharacteristic
70C17×#431C2211yescharacteristic
71C17×#407C2211yescharacteristic
72C17×#407C2211yescharacteristic
73C2×C17×C22⋊C8C2211yescharacteristic
74C2×C17×C22⋊C8C2211yescharacteristic
75C22×D4×C17D411yescharacteristic
76C23×C4×C17C2311yescharacteristic
77C23×C4×C17C2311yescharacteristic
78C23×Dic17—21no—
79C2×#63254—21no—
80C2×#63252C2×C411yescharacteristic
81C2×#63252C2×C411yescharacteristic, complemented
82C22×Dic34C2×C411yescharacteristic
83C22×Dic34C2×C411yescharacteristic, complemented
84C2×M16×C17—21no—
85C2×M16×C17—21no—
86C22×C8×C17—21no—
87C22×C8×C17—21no—
88C4×D4×C17C2×C411yescharacteristic
89C4×D4×C17C2×C411yescharacteristic
90C4×D4×C17C2×C411yescharacteristic
91C4×D4×C17C2×C411yescharacteristic
92C4×D4×C17D411yescharacteristic
93C4×D4×C17D411yescharacteristic
94C4×D4×C17D411yescharacteristic
95C4×D4×C17D411yescharacteristic
96C2×C4⋊C4×C17D411yescharacteristic
97C2×C22⋊C4×C17D411yescharacteristic
98C2×C22⋊C4×C17D411yescharacteristic
99C2×C42×C17C2311yescharacteristic
100#10587639—21no—
101#10587639—21no—
102C2×C22⋊Dic17—21no—
103C2×C22⋊Dic17—21no—
104C2×C22⋊Dic17—21no—
105C2×C22⋊Dic17—21no—
106C2×C22⋊Dic17—21no—
107#10587625—21no—
108#10587625—21no—
109#10587624—21no—
110#10587622—21no—
111#10587621—21no—
112#10587621—21no—
113D4×Dic17—21no—
114#10587616C2×C411yescharacteristic
115#10587616C2×C411yescharacteristic, complemented
116#10587616C2311yescharacteristic
117#10587615—21no—
118#10587615—21no—
119#10587615—21no—
120C4×C22⋊D17—21no—
121C4×C22⋊D17—21no—
122C4×C22⋊D17—21no—
123C4×C22⋊D17—21no—
124C4×C22⋊D17—21no—
125#10587612—21no—
126#10587612C2×C411yescharacteristic
127#10587612C2×C411yescharacteristic, complemented
128C2×C4⋊Dic17—21no—
129C2×C4⋊Dic17—21no—
130C2×C4⋊Dic17C2×C411yescharacteristic
131C2×C4⋊Dic17C2×C411yescharacteristic, complemented
132#10587610—21no—
133#10587610—21no—
134#10587610—21no—
135#10587610—21no—
136#10587610—21no—
137#10587610C2×C411yescharacteristic
138#10587610C2×C411yescharacteristic
139#10587610C2×C411yescharacteristic
140#10587610C2×C411yescharacteristic, complemented
141#10587610C2×C411yescharacteristic, complemented
142#10587610C2×C411yescharacteristic, complemented
143#10587610C2311yescharacteristic
144#10587610C2311yescharacteristic
145#10587610C2311yescharacteristic
146C2×#63225—21no—
147C2×#63225—21no—
148C2×C4×Dic17—21no—
149#10587583—21no—
150#10587582—21no—
151#10587582—21no—
152C4⋊C4×D17—21no—
153#10587575—21no—
154#10587575—21no—
155#10587574—21no—
156#10587573—21no—
157#10587572—21no—
158#10587572—21no—
159#10587571—21no—
160#10587571—21no—
161#10587569—21no—
162#10587569—21no—
163#10587567—21no—
164#10587567—21no—
165#10587565—21no—
166#10587565—21no—
167#10587565—21no—
168#10587565—21no—
169#10587564—21no—
170#10587564—21no—
171#10587563—21no—
172#10587563—21no—
173#10587562—21no—
174#10587561C2×C411yescharacteristic, complemented
175C4×D68C2×C411yescharacteristic, complemented
176#10587558—21no—
177#10587556—21no—
178#10587556C2×C411yescharacteristic, complemented
179#10587555C2×C411yescharacteristic, complemented
180#10587555C2×C411yescharacteristic, complemented
181C4×Dic34—21no—
182C4×Dic34C2×C411yescharacteristic, complemented
183C4×Dic34C2×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
208C2×D4×C17—42no—
209C2×D4×C17C22⋊C411yescharacteristic
210C2×D4×C17C22⋊C411yescharacteristic
211C2×D4×C17C22⋊C411yescharacteristic
212C2×D4×C17C22⋊C411yescharacteristic
213C22×C4×C17—81no—
214C22×C4×C17—81no—
215C22×C4×C17C22×C411yescharacteristic
216C22×C4×C17C22×C411yescharacteristic
217C22×C4×C17C22×C411yescharacteristic
218C22×C4×C17C22×C411yescharacteristic
219C22×C4×C17C2×D411yescharacteristic
220C22×C4×C17C2×D411yescharacteristic
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×C17C2411yescharacteristic
228C2×C22⋊D17—21no—
229C2×C22⋊D17—21no—
230C2×C22⋊D17—21no—
231C2×C22⋊D17—21no—
232C2×C22⋊D17—21no—
233C22×Dic17—21no—
234C22×Dic17—21no—
235C22×Dic17—21no—
236C22×Dic17—21no—
237C22×Dic17—21no—
238C22×Dic17—21no—
239C22×Dic17—21no—
240C22×Dic17—21no—
241C22×Dic17—42no—
242C22×Dic17—81no—
243C22×Dic17—81no—
244#63254—44no—
245#63252—81no—
246#63252—81no—
247C2×D68C22×C411yescharacteristic
248C2×C4×D17—21no—
249C2×C4×D17—21no—
250C2×C4×D17—21no—
251C2×Dic34—21no—
252C2×Dic34—21no—
253C2×Dic34—21no—
254C2×Dic34—81no—
255C2×Dic34—81no—
256C2×Dic34C22×C411yescharacteristic
257C2×Dic34C22×C411yescharacteristic
258C2×Dic34C22×C411yescharacteristic
259M16×C17—81no—
260M16×C17—81no—
261C2×C8×C17—21no—
262C2×C8×C17—21no—
263C2×C8×C17—21no—
264C2×C8×C17—21no—
265C2×C8×C17—81no—
266C2×C8×C17—81no—
267C4⋊C4×C17C22⋊C411yescharacteristic
268C4⋊C4×C17C22⋊C411yescharacteristic
269C4⋊C4×C17C22⋊C411yescharacteristic
270C4⋊C4×C17C22⋊C411yescharacteristic
271C22⋊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
278C22⋊C4×C17C22⋊C411yescharacteristic
279C42×C17C22×C411yescharacteristic
280C42×C17C22×C411yescharacteristic
281C42×C17C2×D411yescharacteristic
282C42×C17C2×D411yescharacteristic
283C22⋊Dic17—21no—
284C22⋊Dic17—21no—
285C22⋊Dic17—21no—
286C22⋊Dic17—21no—
287C22⋊Dic17—21no—
288C22⋊Dic17—21no—
289C22⋊Dic17—21no—
290C22⋊Dic17—21no—
291C22⋊Dic17—21no—
292C22⋊Dic17—21no—
293C22⋊Dic17—21no—
294C22⋊Dic17—42no—
295C22⋊Dic17—81no—
296C22⋊Dic17—81no—
297#63227—21no—
298#63227—21no—
299#63227—21no—
300#63227—21no—
301#63227—21no—
302#63227—21no—
303C4⋊Dic17—21no—
304C4⋊Dic17—21no—
305C4⋊Dic17—21no—
306C4⋊Dic17—21no—
307C4⋊Dic17—21no—
308C4⋊Dic17—81no—
309C4⋊Dic17—81no—
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—
322#63225—21no—
323#63225—21no—
324#63225—21no—
325#63225—21no—
326#63225—21no—
327#63225—21no—
328C4×Dic17—21no—
329C4×Dic17—21no—
330C4×Dic17—21no—
331C4×Dic17—21no—
332C4×Dic17—21no—
333C4×Dic17—81no—
334#17598—171nomaximal, Sylow
335C23×C17—21no—
336C23×C17—21no—
337C23×C17—22no—
338C23×C17—21no—
339C23×C17—21no—
340C23×C17—41no—
341C23×C17—41no—
342C23×C17—41no—
343C23×C17C2×C22⋊C411yescharacteristic
344C23×C17C2×C22⋊C411yescharacteristic
345C23×C17C2×C22⋊C411yescharacteristic
346C23×C17C2×C22⋊C411yescharacteristic
347C23×C17C22×D411yescharacteristic
348C22×D17—21no—
349D4×C17—22no—
350D4×C17—22no—
351D4×C17—41no—
352D4×C17—41no—
353C2×C4×C17—21no—
354C2×C4×C17—21no—
355C2×C4×C17—41no—
356C2×C4×C17—41no—
357C2×C4×C17—41no—
358C2×C4×C17—41no—
359C2×C4×C17—41no—
360C2×C4×C17—41no—
361C2×C4×C17—41no—
362C2×C4×C17—41no—
363C2×C4×C17—41no—
364C2×C4×C17—41no—
365C2×C4×C17—41no—
366C2×C4×C17—41no—
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×C17C2×C22⋊C411yescharacteristic
374C2×C4×C17C2×C22⋊C411yescharacteristic
375C2×C4×C17C23×C411yescharacteristic
376C2×C4×C17C22×D411yescharacteristic
377C22⋊D17—42no—
378C22⋊D17—41no—
379C22⋊D17—41no—
380C22⋊D17—42no—
381C22⋊D17—81no—
382C22⋊D17—81no—
383C2×Dic17—21no—
384C2×Dic17—21no—
385C2×Dic17—21no—
386C2×Dic17—21no—
387C2×Dic17—21no—
388C2×Dic17—21no—
389C2×Dic17—21no—
390C2×Dic17—42no—
391C2×Dic17—42no—
392C2×Dic17—41no—
393C2×Dic17—41no—
394C2×Dic17—41no—
395C2×Dic17—41no—
396C2×Dic17—41no—
397C2×Dic17—41no—
398C2×Dic17—41no—
399C2×Dic17—41no—
400C2×Dic17—41no—
401C2×Dic17—41no—
402C2×Dic17—41no—
403C2×Dic17—41no—
404C2×Dic17—81no—
405C2×Dic17—81no—
406C2×Dic17—84no—
407D68—41no—
408C4×D17—42no—
409C4×D17—81no—
410C4×D17—81no—
411Dic34—42no—
412Dic34—41no—
413Dic34—41no—
414Dic34—41no—
415Dic34—81no—
416Dic34—81no—
417C8×C17—41no—
418C8×C17—41no—
419C8×C17—41no—
420C8×C17—41no—
421#3520—171no—
422#2974D1711yescharacteristic, complemented
423#2318—171no—
424#1521—171no—
425#1520—171no—
426#1518—171no—
427#1516—171no—
428#1515—171no—
429#1513—171no—
430#1512—171no—
431#1511—171no—
432#1508—171no—
433#1504—171no—
434#1501—171no—
435C2×#328—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—21no—
445C22×C17—21no—
446C22×C17—21no—
447C22×C17—21no—
448C22×C17—21no—
449C22×C17—42no—
450C22×C17—42no—
451C22×C17—81no—
452C22×C17—81no—
453C22×C17#42112yes—
454C22×C17C22×C22⋊C411yescharacteristic
455C22×C17#57711yescharacteristic
456C22×C17#57811yescharacteristic
457C2×D17—41no—
458C2×D17—41no—
459C2×D17—41no—
460C4×C17—21no—
461C4×C17—21no—
462C4×C17—21no—
463C4×C17—21no—
464C4×C17—21no—
465C4×C17—21no—
466C4×C17—21no—
467C4×C17—21no—
468C4×C17—21no—
469C4×C17—21no—
470Dic17—41no—
471Dic17—41no—
472Dic17—41no—
473Dic17—41no—
474Dic17—41no—
475Dic17—41no—
476Dic17—41no—
477Dic17—81no—
478Dic17—81no—
479Dic17—81no—
480Dic17—81no—
481#556—171no—
482#554—341no—
483#552—171no—
484#552—171no—
485#551—341no—
486#551—341no—
487D4×Q8—171no—
488#548—171no—
489#548—171no—
490#547—171no—
491#547—171no—
492#546—341no—
493#542—341no—
494#539—341no—
495#539—341no—
496#533—171no—
497#529—171no—
498#525—171no—
499#525—171no—
500C2×C22⋊Q8—171no—
501C2×C22⋊Q8—171no—
502#520—341no—
503C2×C4×D4C2×D1711yescharacteristic
504#436—21no—
505#435—21no—
506#435—21no—
507C8×D4—21no—
508#432C2×D1711yescharacteristic
509#431C2×D1711yescharacteristic
510#407C2×D1711yescharacteristic
511#407C2×D1711yescharacteristic
512C2×C22⋊C8C2×D1711yescharacteristic
513C2×C22⋊C8C2×D1711yescharacteristic
514#388—341no—
515#387—341no—
516#386—341no—
517#385—341no—
518#383—171no—
519#382—171no—
520#381—171no—
521#380—171no—
522C4×C22⋊C4—171no—
523C2×#95—171no—
524#328—171no—
525#328—171no—
526#328—171no—
527#328—171no—
528#328—171no—
529#328—171no—
530#328—171no—
531#328—171no—
532#328—171no—
533#328—171no—
534#328—171no—
535#328—171no—
536#327—171no—
537#327—171no—
538#327—171no—
539#327—171no—
540C2×C17—21no—
541C2×C17—21no—
542C2×C17—22no—
543C2×C17—41no—
544C2×C17—41no—
545C2×C17—41no—
546C2×C17#288311yescharacteristic
547C2×C17#289811yescharacteristic
548C2×C17C2×#42111yescharacteristic
549D17—81no—
550C2×#41—171no—
551C2×#41—171no—
552C2×#41—341no—
553C22×Q8—171no—
554C22×Q8—171no—
555C22×D4D6811yescharacteristic
556C23×C4—341no—
557C23×C4C22×D1711yescharacteristic
558C23×C4C22×D1711yescharacteristic
559C2×M16—21no—
560C2×M16—21no—
561C22×C8—21no—
562C22×C8—21no—
563C4⋊Q8—171no—
564C4⋊Q8—171no—
565C4⋊Q8—341no—
566#126—341no—
567#126—341no—
568#126—341no—
569#126—341no—
570#126—341no—
571#125—171no—
572#125—341no—
573#125—341no—
574#125—341no—
575#124—171no—
576#124—341no—
577#124—341no—
578#124—341no—
579#123—341no—
580#123—341no—
581#123—341no—
582#123—341no—
583#123—341no—
584#123—341no—
585#123—341no—
586#123—341no—
587#123—341no—
588C22⋊Q8—171no—
589C22⋊Q8—171no—
590C22⋊Q8—171no—
591C22⋊Q8—171no—
592C22⋊Q8—171no—
593C22⋊Q8—171no—
594C22⋊Q8—171no—
595C22⋊Q8—171no—
596C22⋊Q8—171no—
597C22⋊Q8—341no—
598C22⋊Q8—341no—
599C22⋊Q8—341no—
600C22⋊Q8—341no—
601C22⋊Q8—341no—
602C22⋊Q8—341no—
603C22⋊Q8—341no—
604C22⋊Q8—341no—
605C22⋊Q8—341no—
606C22⋊Q8—341no—
607#121—171no—
608#121—171no—
609#121—171no—
610#121—341no—
611#121—341no—
612#121—341no—
613#120—341no—
614#120—341no—
615C4×Q8—171no—
616C4×Q8—171no—
617C4×Q8—171no—
618C4×Q8—341no—
619C4×Q8—341no—
620C4×D4—171no—
621C4×D4—341no—
622C4×D4—341no—
623C4×D4—341no—
624C4×D4—341no—
625C4×D4—341no—
626C4×D4—341no—
627C4×D4—341no—
628C4×D4—341no—
629C4×D4C4×D1711yescharacteristic
630C4×D4C4×D1711yescharacteristic
631C4×D4C4×D1711yescharacteristic
632C4×D4C4×D1711yescharacteristic
633C4×D4C22⋊D1711yescharacteristic
634C4×D4C22⋊D1711yescharacteristic
635C4×D4C22⋊D1711yescharacteristic
636C4×D4C22⋊D1711yescharacteristic
637#117—171no—
638#117—171no—
639#117—341no—
640#117—341no—
641#117—341no—
642#117—341no—
643C2×C4⋊C4—171no—
644C2×C4⋊C4—171no—
645C2×C4⋊C4—341no—
646C2×C4⋊C4—341no—
647C2×C4⋊C4—341no—
648C2×C4⋊C4—341no—
649C2×C4⋊C4—341no—
650C2×C4⋊C4D6811yescharacteristic
651C2×C22⋊C4—341no—
652C2×C22⋊C4—341no—
653C2×C22⋊C4—341no—
654C2×C22⋊C4—341no—
655C2×C22⋊C4—341no—
656C2×C22⋊C4D6811yescharacteristic
657C2×C22⋊C4D6811yescharacteristic
658C2×C42—341no—
659C2×C42C22×D1711yescharacteristic
660C4⋊C8—21no—
661C4⋊C8—21no—
662C22⋊C8—21no—
663C22⋊C8—21no—
664C22⋊C8—21no—
665C22⋊C8—21no—
666C22⋊C8C22×D1711yescharacteristic
667C22⋊C8C22×D1711yescharacteristic
668C22⋊C8C22×D1711yescharacteristic
669C22⋊C8C22×D1711yescharacteristic
670#97—21no—
671C4×C8—21no—
672#95—171no—
673#95—171no—
674#95—171no—
675#95—171no—
676#95—341no—
677#95—341no—
678#95—341no—
679#95—341no—
680#95—341no—
681C17#1759811yescharacteristic, complemented, Sylow
682C24C2×D6811yescharacteristic
683C24C2×D6811yescharacteristic
684#41—684no—
685#41—1361no—
686#41—1361no—
687C2×Q8—171no—
688C2×Q8—171no—
689C2×Q8—171no—
690C2×Q8—341no—
691C2×Q8—341no—
692C2×Q8—341no—
693C2×Q8—1361no—
694C2×Q8—1361no—
695C2×D4—42no—
696C2×D4—171no—
697C2×D4—341no—
698C2×D4—341no—
699C2×D4—341no—
700C2×D4—341no—
701C2×D4—341no—
702C2×D4#6322711yescharacteristic
703C2×D4#6322711yescharacteristic
704C2×D4#6322711yescharacteristic
705C2×D4#6322711yescharacteristic
706C22×C4—81no—
707C22×C4—81no—
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—341no—
718C22×C4—341no—
719C22×C4—682no—
720C22×C4—1361no—
721C22×C4—1361no—
722C22×C4C2×C4×D1711yescharacteristic
723C22×C4C2×C4×D1711yescharacteristic
724C22×C4C2×C4×D1711yescharacteristic
725C22×C4C2×C4×D1711yescharacteristic
726C22×C4C2×D6811yescharacteristic
727C22×C4C2×D6811yescharacteristic
728C22×C4C2×D6811yescharacteristic
729C22×C4C2×D6811yescharacteristic
730C22×C4C2×C22⋊D1711yescharacteristic
731C22×C4C2×C22⋊D1711yescharacteristic
732C22×C4C2×C22⋊D1711yescharacteristic
733C22×C4C2×C22⋊D1711yescharacteristic
734C22×C4C23×D1711yescharacteristic
735M16—81no—
736M16—81no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—81no—
742C2×C8—81no—
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—341no—
759C4⋊C4—341no—
760C4⋊C4—341no—
761C4⋊C4—341no—
762C4⋊C4—341no—
763C4⋊C4—341no—
764C4⋊C4—341no—
765C4⋊C4—341no—
766C4⋊C4—1361no—
767C4⋊C4—1361no—
768C4⋊C4#6322711yescharacteristic
769C4⋊C4#6322711yescharacteristic
770C4⋊C4#6322711yescharacteristic
771C4⋊C4#6322711yescharacteristic
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—341no—
784C22⋊C4—341no—
785C22⋊C4—341no—
786C22⋊C4—341no—
787C22⋊C4—341no—
788C22⋊C4—341no—
789C22⋊C4—682no—
790C22⋊C4—1361no—
791C22⋊C4—1361no—
792C22⋊C4#6322711yescharacteristic
793C22⋊C4#6322711yescharacteristic
794C22⋊C4#6322711yescharacteristic
795C22⋊C4#6322711yescharacteristic
796C22⋊C4#6322711yescharacteristic
797C22⋊C4#6322711yescharacteristic
798C22⋊C4#6322711yescharacteristic
799C22⋊C4#6322711yescharacteristic
800C42—341no—
801C42—341no—
802C42—341no—
803C42—341no—
804C42—341no—
805C42—1361no—
806C42C2×C4×D1711yescharacteristic
807C42C2×C4×D1711yescharacteristic
808C42C2×C22⋊D1711yescharacteristic
809C42C2×C22⋊D1711yescharacteristic
810C23—22no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—21no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—341no—
819C23C2×#6322711yescharacteristic
820C23C2×#6322711yescharacteristic
821C23C2×#6322711yescharacteristic
822C23C2×#6322711yescharacteristic
823C23C22×D6811yescharacteristic
824Q8—681no—
825Q8—681no—
826Q8—681no—
827Q8—682no—
828Q8—1361no—
829Q8—1361no—
830D4—22no—
831D4—22no—
832D4—41no—
833D4—41no—
834D4—681no—
835D4—682no—
836D4—682no—
837D4—681no—
838D4—681no—
839D4—1361no—
840D4—1361no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—341no—
856C2×C4—341no—
857C2×C4—341no—
858C2×C4—341no—
859C2×C4—341no—
860C2×C4—341no—
861C2×C4—341no—
862C2×C4—682no—
863C2×C4—682no—
864C2×C4—682no—
865C2×C4—681no—
866C2×C4—681no—
867C2×C4—681no—
868C2×C4—681no—
869C2×C4—681no—
870C2×C4—681no—
871C2×C4—681no—
872C2×C4—681no—
873C2×C4—681no—
874C2×C4—681no—
875C2×C4—681no—
876C2×C4—681no—
877C2×C4—1361no—
878C2×C4—1361no—
879C2×C4—1361no—
880C2×C4—1361no—
881C2×C4—1364no—
882C2×C4C2×#6322711yescharacteristic
883C2×C4C2×#6322711yescharacteristic
884C2×C4C2×#6322711yescharacteristic
885C2×C4C2×#6322711yescharacteristic
886C2×C4C2×#6322711yescharacteristic
887C2×C4C2×#6322711yescharacteristic
888C2×C4C2×#6322711yescharacteristic
889C2×C4C2×#6322711yescharacteristic
890C2×C4C22×C4×D1711yescharacteristic
891C2×C4C22×C22⋊D1711yescharacteristic
892C8—41no—
893C8—41no—
894C8—41no—
895C8—41no—
896C22—21no—
897C22—21no—
898C22—21no—
899C22—21no—
900C22—21no—
901C22—21no—
902C22—21no—
903C22—21no—
904C22—21no—
905C22—21no—
906C22—21no—
907C22—21no—
908C22—21no—
909C22—42no—
910C22—42no—
911C22—81no—
912C22—81no—
913C22—681no—
914C22—681no—
915C22—681no—
916C22#1176282512yes—
917C22C22×#6322711yescharacteristic
918C22#1176362111yescharacteristic
919C22#1176362611yescharacteristic
920C4—21no—
921C4—21no—
922C4—21no—
923C4—21no—
924C4—21no—
925C4—21no—
926C4—21no—
927C4—21no—
928C4—21no—
929C4—21no—
930C4—681no—
931C4—681no—
932C4—681no—
933C4—681no—
934C4—681no—
935C4—681no—
936C4—681no—
937C4—1361no—
938C4—1361no—
939C4—1361no—
940C4—1361no—
941C2—21no—
942C2—21no—
943C2—22no—
944C2—41no—
945C2—41no—
946C2—41no—
947C2—1361no—
948C2#1453724411yescharacteristic
949C2#1453731811yescharacteristic
950C2C2×#1176282511yescharacteristic
subgroupG/H
centerC22C22×#63227
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC17×#2974C2
socleC22×C17C22×C22⋊C4
prime radical#14542833C2
cosocleC22×C4×C17C24
hypercenter#2974D17
hypocenterC17#17598
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. #14527357C2semidirect
5. #14527349C2semidirect
6. #14527341C2semidirect
7. #14527336C2semidirect
8. #14527328C2semidirect
9. #14527323C2semidirect
10. #14527318C2semidirect
11. #14527305C2semidirect
12. #14527289C2semidirect
13. #14527276C2semidirect
14. C2×#11762547C2semidirect
15. C17×#2974C2semidirect
16. #11763529C4semidirect
18. #11763499C4semidirect
19. #11763499C4semidirect
22. D4×Dic34C4semidirect
23. #11763468C4semidirect
24. #11763468C4semidirect
25. #11763464C4semidirect
26. #11763463C4semidirect
81. C2×#63252C2×C4semidirect
83. C22×Dic34C2×C4semidirect
115. #10587616C2×C4semidirect
127. #10587612C2×C4semidirect
131. C2×C4⋊Dic17C2×C4semidirect
140. #10587610C2×C4semidirect
141. #10587610C2×C4semidirect
142. #10587610C2×C4semidirect
174. #10587561C2×C4semidirect
175. C4×D68C2×C4semidirect
178. #10587556C2×C4semidirect
179. #10587555C2×C4semidirect
180. #10587555C2×C4semidirect
182. C4×Dic34C2×C4semidirect
183. C4×Dic34C2×C4semidirect
184. C4×Dic34C2×C4semidirect
422. #2974D17semidirect
681. C17#17598semidirect

Maximal subgroups

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

subgroupindex
#145428332
#145314172
#145273622
#145273572
#145273492
#145273412
#145273362
#145273282
#145273232
#145273182
#145273052
#145272892
#145272762
C2×#117625472
C17×#29742
#1759817