Finite Group Databasebeta

← #15831060

Subgroups — #15831060

Order 3328.

942 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13128797C211yesmaximal, characteristic
2#13123850C211yesmaximal, characteristic, complemented
3#13113470C211yesmaximal, characteristic, complemented
4#13113468C211yesmaximal, characteristic, complemented
5#13113465C211yesmaximal, characteristic, complemented
6#13113459C211yesmaximal, characteristic, complemented
7#13113457C211yesmaximal, characteristic, complemented
8#13113454C211yesmaximal, characteristic, complemented
9#13113448C211yesmaximal, characteristic, complemented
10#13113444C211yesmaximal, characteristic, complemented
11#13113435C211yesmaximal, characteristic, complemented
12#13113433C211yesmaximal, characteristic, complemented
13#13113425C211yesmaximal, characteristic, complemented
14C2×#11718056C211yesmaximal, characteristic, complemented
15C13×#2923C211yesmaximal, characteristic, complemented
16C4×C13×#41C2211yescharacteristic
17#11719534—21no—
18#11719290C411yescharacteristic
19#11719289C411yescharacteristic
20#11719287—21no—
21#11719265—21no—
22#11719265—21no—
23#11719257C411yescharacteristic
24#11719257C411yescharacteristic
25#11719255C411yescharacteristic
26#11719255C411yescharacteristic
27D4×D52C411yescharacteristic
28#11719250—21no—
29D4×Dic26C411yescharacteristic
30#11719237—21no—
31#11719232—21no—
32#11719232—21no—
33#11719184C2211yescharacteristic
34#11719184C2211yescharacteristic
35#11719184C2211yescharacteristic
36#11719182C2211yescharacteristic
37C2×#88129C2211yescharacteristic
38C2×#88129C2211yescharacteristic
39C13×#433—21no—
40C13×#433—21no—
41C13×#432C2211yescharacteristic, complemented
42C13×#432C2211yescharacteristic, complemented
43C13×#432C2211yescharacteristic, complemented
44C13×#432C2211yescharacteristic, complemented
45C13×#424—21no—
46C13×#408—21no—
47C4×C13×M16C2211yescharacteristic, complemented
48C2×C13×#97C2211yescharacteristic, complemented
49#11718685—21no—
50#11718672—21no—
51#11718672—21no—
52D4×#1055—21no—
53#11718587C2211yescharacteristic, complemented
54#11718587C2211yescharacteristic, complemented
55#11718587C2211yescharacteristic, complemented
56C4×#6099C2211yescharacteristic, complemented
57C2×#88043C2211yescharacteristic, complemented
58C2×#88043C2211yescharacteristic, complemented
59#11718057C2211yescharacteristic, complemented
60#11718057C2211yescharacteristic, complemented
61#11718057C2211yescharacteristic, complemented
62#11718057C2211yescharacteristic, complemented
63#11718056C2211yescharacteristic
64#11718056C2211yescharacteristic
65#11718056C2211yescharacteristic
66#11718056C2211yescharacteristic
67#11718056C2211yescharacteristic, complemented
68#11718056C2211yescharacteristic, complemented
69#11718056C2211yescharacteristic, complemented
70#11718056C2211yescharacteristic, complemented
71#11718056C2211yescharacteristic, complemented
72#11718056C2211yescharacteristic, complemented
73#11718056C2211yescharacteristic, complemented
74#11718056C2211yescharacteristic, complemented
75C2×C13×#41D411yescharacteristic
76C2×D4×D13—21no—
77C2×#6127C2×C411yescharacteristic
78C2×#6127C2×C411yescharacteristic
79C22×D52C2×C411yescharacteristic
80C22×D52C2×C411yescharacteristic
81C22×Dic26C2×C411yescharacteristic
82C22×Dic26C2×C411yescharacteristic
83C2×C13×M16—21no—
84C22×C8×C13—21no—
85C4×Q8×C13C2×C411yescharacteristic
86C4×Q8×C13D411yescharacteristic
87C4×D4×C13C2×C411yescharacteristic
88C4×D4×C13C2×C411yescharacteristic
89C4×D4×C13C2×C411yescharacteristic
90C4×D4×C13D411yescharacteristic
91C4×D4×C13D411yescharacteristic
92C4×D4×C13D411yescharacteristic
93C13×#117D411yescharacteristic
94C13×#117D411yescharacteristic
95C13×#117D411yescharacteristic
96C2×C42×C13C2311yescharacteristic
97C2×C42×C13C2311yescharacteristic
98C2×C42×C13C2311yescharacteristic
99#88201—21no—
100#88200—21no—
101#88193—21no—
102#88193—21no—
103#88191—21no—
104#88191—21no—
105D4×Dic13—21no—
106#88184—21no—
107#88184—21no—
108#88184C2×C411yescharacteristic
109#88184C2×C411yescharacteristic
110#88184C2×C411yescharacteristic
111#88183—21no—
112#88183—21no—
113#88183—21no—
114C4×C22⋊D13—21no—
115C4×C22⋊D13—21no—
116C4×C22⋊D13—21no—
117C2×#6103—21no—
118C2×#6103—21no—
119C2×#6103—21no—
120C2×#6103—21no—
121#88178C2×C411yescharacteristic
122#88178C2×C411yescharacteristic
123#88178C2×C411yescharacteristic
124C2×#6099—21no—
125C22×#1055—21no—
126C22×#1055—21no—
127#88152—21no—
128#88152—21no—
129#88150—21no—
130#88150—21no—
131#88149—21no—
132#88148—21no—
133#88148—21no—
134#88148—21no—
135#88148—21no—
136#88147—21no—
137#88146—21no—
138#88142—21no—
139#88139—21no—
140#88139—21no—
141#88138—21no—
142#88138—21no—
143#88136—21no—
144#88136—21no—
145#88135—21no—
146#88135—21no—
147C22⋊C4×D13—21no—
148C22⋊C4×D13—21no—
149#88132—21no—
150#88132—21no—
151#88130—21no—
152#88130—21no—
153#88130—21no—
154#88129—21no—
155#88129—21no—
156#88129—21no—
157#88129—21no—
158#88129C2×C411yescharacteristic
159#88129C2×C411yescharacteristic
160#88129C2×C411yescharacteristic
161#88129C2×C411yescharacteristic
162#88129C2311yescharacteristic
163#88129C2311yescharacteristic
164#88129C2311yescharacteristic
165#88128C2×C411yescharacteristic
166C4×D52—21no—
167C4×D52—21no—
168C4×D52C2×C411yescharacteristic
169C4×D52C2×C411yescharacteristic
170C4×D52C2×C411yescharacteristic
171#88126—21no—
172#88126—21no—
173#88126—21no—
174#88124C2311yescharacteristic
175#88123C2×C411yescharacteristic
176C4×Dic26C2×C411yescharacteristic
177C4×Dic26C2×C411yescharacteristic
178C4×Dic26C2×C411yescharacteristic
179C13×C4⋊C8—21no—
180C13×C4⋊C8—21no—
181C13×C4⋊C8—21no—
182C13×C4⋊C8—21no—
183C13×C22⋊C8—21no—
184C13×C22⋊C8—21no—
185C13×C22⋊C8—21no—
186C13×C22⋊C8—21no—
187C13×#97—21no—
188C13×#97C2311yescharacteristic
189C13×#97C2311yescharacteristic
190C13×#97C2311yescharacteristic
191C13×#97C2311yescharacteristic
192C4×C8×C13—21no—
193C22⋊#1055—21no—
194C22⋊#1055—21no—
195C22⋊#1055—21no—
196C4⋊#1055—21no—
197C4⋊#1055—21no—
198C4⋊#1055—21no—
199#88043—21no—
200#88043—21no—
201#88043C2311yescharacteristic
202#88043C2311yescharacteristic
203#88043C2311yescharacteristic
204#88043C2311yescharacteristic
205C4×#1055—21no—
206#17679—131nomaximal, Sylow
207C23×D13—21no—
208C23×D13—21no—
209C13×#41—42no—
210C2×Q8×C13C22⋊C411yescharacteristic
211C2×D4×C13C22⋊C411yescharacteristic
212C2×D4×C13C22⋊C411yescharacteristic
213C2×D4×C13C22⋊C411yescharacteristic
214C22×C4×C13C22×C411yescharacteristic
215C22×C4×C13C22×C411yescharacteristic
216C22×C4×C13C22×C411yescharacteristic
217C22×C4×C13C2×D411yescharacteristic
218C22×C4×C13C2×D411yescharacteristic
219C22×C4×C13C2×D411yescharacteristic
220C22×C4×C13C2×D411yescharacteristic
221C22×C4×C13C2×D411yescharacteristic
222C22×C4×C13C2×D411yescharacteristic
223C2×C22⋊D13—21no—
224C2×C22⋊D13—21no—
225C2×C22⋊D13—21no—
226C2×C22⋊D13—21no—
227C2×C22⋊D13—21no—
228C22×Dic13—21no—
229C22×Dic13—21no—
230D4×D13—44no—
231#6127—81no—
232#6127—81no—
233C2×D52—21no—
234C2×D52—21no—
235C2×D52—21no—
236C2×D52—21no—
237C2×D52—81no—
238C2×D52—81no—
239C2×D52C22×C411yescharacteristic
240C2×D52C22×C411yescharacteristic
241C2×D52C22×C411yescharacteristic
242C2×C4×D13—21no—
243C2×C4×D13—21no—
244C2×C4×D13—21no—
245C2×C4×D13—21no—
246C2×C4×D13—21no—
247C2×Dic26—21no—
248C2×Dic26—21no—
249C2×Dic26—81no—
250C2×Dic26—81no—
251C2×Dic26C22×C411yescharacteristic
252C2×Dic26C22×C411yescharacteristic
253C2×Dic26C22×C411yescharacteristic
254C13×M16—42no—
255C2×C8×C13—21no—
256C2×C8×C13—21no—
257C2×C8×C13—21no—
258C2×C8×C13—21no—
259C2×C8×C13—42no—
260C13×C4⋊C4C22⋊C411yescharacteristic
261C13×C4⋊C4C22⋊C411yescharacteristic
262C13×C4⋊C4C22⋊C411yescharacteristic
263C13×C4⋊C4C22⋊C411yescharacteristic
264C13×C4⋊C4C22⋊C411yescharacteristic
265C13×C4⋊C4C22⋊C411yescharacteristic
266C13×C22⋊C4C22⋊C411yescharacteristic
267C13×C22⋊C4C22⋊C411yescharacteristic
268C13×C22⋊C4C22⋊C411yescharacteristic
269C13×C22⋊C4C22⋊C411yescharacteristic
270C13×C22⋊C4C22⋊C411yescharacteristic
271C13×C22⋊C4C22⋊C411yescharacteristic
272C42×C13C22×C411yescharacteristic
273C42×C13C22×C411yescharacteristic
274C42×C13C22×C411yescharacteristic
275C42×C13C2×D411yescharacteristic
276C42×C13C2×D411yescharacteristic
277C42×C13C2×D411yescharacteristic
278C42×C13C2×D411yescharacteristic
279C42×C13C2×D411yescharacteristic
280C42×C13C2×D411yescharacteristic
281C42×C13C2411yescharacteristic
282C22⋊Dic13—21no—
283C22⋊Dic13—21no—
284C22⋊Dic13—21no—
285#6103—21no—
286#6103—21no—
287#6103—21no—
288#6103—21no—
289#6103—21no—
290#6103—21no—
291#6103—21no—
292#6103—21no—
293#6103—21no—
294#6103—21no—
295#6103—21no—
296#6103—21no—
297#6103—21no—
298#6103—21no—
299#6103—21no—
300#6103—21no—
301#6103—21no—
302#6103—21no—
303#6103—21no—
304#6103—21no—
305C4⋊Dic13—21no—
306C4⋊Dic13—21no—
307C4⋊Dic13C22×C411yescharacteristic
308C4⋊Dic13C22×C411yescharacteristic
309#6101—21no—
310#6101—21no—
311#6101—21no—
312#6101—21no—
313#6101—21no—
314#6101—21no—
315#6101—21no—
316#6101—21no—
317C4×Dic13—21no—
318C4×Dic13—21no—
319C4×Dic13—21no—
320#6099—42no—
321C2×#1055—21no—
322C2×#1055—21no—
323C2×#1055—21no—
324C2×#1055—21no—
325C2×#1055—42no—
326C2×#1055—42no—
327#3514—131no—
328#2970—131no—
329#2923D1311yescharacteristic, complemented
330#1536—131no—
331#1535—131no—
332#1535—131no—
333#1533—131no—
334#1532—131no—
335#1532—131no—
336#1530—131no—
337#1529—131no—
338#1527—131no—
339#1527—131no—
340#1524—131no—
341C2×#329—131no—
342C23×C13C2×C22⋊C411yescharacteristic
343C23×C13C2×C22⋊C411yescharacteristic
344C23×C13C2×C22⋊C411yescharacteristic
345C22×D13—21no—
346C22×D13—21no—
347C22×D13—21no—
348C22×D13—42no—
349C22×D13—42no—
350C22×D13—81no—
351C22×D13—81no—
352C22×D13—81no—
353C22×D13—81no—
354Q8×C13—41no—
355D4×C13—22no—
356D4×C13—22no—
357D4×C13—41no—
358C2×C4×C13—22no—
359C2×C4×C13—41no—
360C2×C4×C13—41no—
361C2×C4×C13—41no—
362C2×C4×C13—41no—
363C2×C4×C13—41no—
364C2×C4×C13—41no—
365C2×C4×C13—41no—
366C2×C4×C13—41no—
367C2×C4×C13C2×C22⋊C411yescharacteristic
368C2×C4×C13C2×C22⋊C411yescharacteristic
369C2×C4×C13C2×C22⋊C411yescharacteristic
370C2×C4×C13C2×C22⋊C411yescharacteristic
371C2×C4×C13C2×C22⋊C411yescharacteristic
372C2×C4×C13C2×C22⋊C411yescharacteristic
373C2×C4×C13C2×C22⋊C411yescharacteristic
374C2×C4×C13C2×C22⋊C411yescharacteristic
375C2×C4×C13C2×C22⋊C411yescharacteristic
376C2×C4×C13C23×C411yescharacteristic
377C2×C4×C13C22×D411yescharacteristic
378C2×C4×C13C22×D411yescharacteristic
379C22⋊D13—42no—
380C22⋊D13—42no—
381C22⋊D13—81no—
382C22⋊D13—81no—
383C22⋊D13—81no—
384C2×Dic13—21no—
385C2×Dic13—21no—
386C2×Dic13—21no—
387C2×Dic13—21no—
388C2×Dic13—21no—
389C2×Dic13—81no—
390C2×Dic13—81no—
391D52—42no—
392D52—41no—
393D52—41no—
394D52—41no—
395D52—81no—
396D52—81no—
397D52—81no—
398C4×D13—42no—
399C4×D13—81no—
400C4×D13—81no—
401C4×D13—81no—
402C4×D13—81no—
403Dic26—41no—
404Dic26—41no—
405Dic26—41no—
406Dic26—81no—
407Dic26—81no—
408C8×C13—41no—
409C8×C13—41no—
410C8×C13—41no—
411C8×C13—41no—
412#1055—22no—
413#1055—41no—
414#1055—41no—
415#1055—41no—
416#559—131no—
417#556—131no—
418#555—261no—
419#551—261no—
420#551—261no—
421D4×Q8—131no—
422#548—131no—
423#548—131no—
424#546—131no—
425#546—131no—
426#546—261no—
427D42—131no—
428#542—261no—
429#538—261no—
430#538—261no—
431#532—131no—
432#529—131no—
433#529—131no—
434#529—131no—
435C2×#124—131no—
436C2×#124—131no—
437#518—261no—
438C4×#41C2×D1311yescharacteristic
439#446—261no—
440#435—261no—
441#435—261no—
442C8×D4—261no—
443#433—21no—
444#433—21no—
445#432—131no—
446#432—131no—
447#432—131no—
448#432C2×D1311yescharacteristic, complemented
449#432C2×D1311yescharacteristic, complemented
450#432C2×D1311yescharacteristic, complemented
451#432C2×D1311yescharacteristic, complemented
452#424—21no—
453#408—21no—
454C4×M16—131no—
455C4×M16C2×D1311yescharacteristic, complemented
456C2×#97—131no—
457C2×#97—131no—
458C2×#97C2×D1311yescharacteristic, complemented
459#330—131no—
460#330—131no—
461#330—131no—
462#330—131no—
463#329—131no—
464#329—131no—
465#329—131no—
466#329—131no—
467#329—131no—
468#329—131no—
469#329—131no—
470#329—131no—
471#329—131no—
472#329—131no—
473#329—131no—
474#329—131no—
475C22×C13—21no—
476C22×C13—21no—
477C22×C13—21no—
478C22×C13—21no—
479C22×C13—21no—
480C22×C13—21no—
481C22×C13—21no—
482C22×C13—21no—
483C22×C13#42112yes—
484C22×C13C22×C22⋊C411yescharacteristic
485C2×D13—41no—
486C2×D13—41no—
487C2×D13—41no—
488C2×D13—41no—
489C2×D13—41no—
490C2×D13—41no—
491C2×D13—41no—
492C2×D13—41no—
493C2×D13—41no—
494C2×D13—162no—
495C2×D13—162no—
496C4×C13—21no—
497C4×C13—21no—
498C4×C13—21no—
499C4×C13—21no—
500C4×C13—21no—
501C4×C13—21no—
502C4×C13—21no—
503C4×C13—21no—
504C4×C13—21no—
505C4×C13—21no—
506C4×C13—21no—
507C4×C13—21no—
508Dic13—41no—
509Dic13—41no—
510Dic13—41no—
511Dic13—41no—
512Dic13—41no—
513C2×#41—131no—
514C2×#41—131no—
515C2×#41C22⋊D1311yescharacteristic
516C22×Q8—131no—
517C22×Q8—131no—
518C22×D4—131no—
519C22×D4—131no—
520C22×D4—261no—
521C2×M16—21no—
522C2×M16—261no—
523C22×C8—21no—
524C22×C8—261no—
525C22×C8—261no—
526C4⋊Q8—131no—
527C4⋊Q8—261no—
528#127—131no—
529#126—261no—
530#126—261no—
531#126—261no—
532#126—261no—
533#126—261no—
534#125—131no—
535#124—131no—
536#124—131no—
537#124—131no—
538#124—131no—
539#124—131no—
540#124—131no—
541#124—131no—
542#124—261no—
543#124—261no—
544#124—261no—
545#124—261no—
546#124—261no—
547#124—261no—
548#124—261no—
549#123—261no—
550#123—261no—
551#123—261no—
552#123—261no—
553#123—261no—
554#123—261no—
555#123—261no—
556C22⋊Q8—131no—
557C22⋊Q8—131no—
558C22⋊Q8—131no—
559C22⋊Q8—261no—
560C22⋊Q8—261no—
561C22⋊Q8—261no—
562C22⋊Q8—261no—
563C22⋊Q8—261no—
564#121—131no—
565#121—131no—
566#121—131no—
567#121—261no—
568#121—261no—
569#121—261no—
570#121—261no—
571#121—261no—
572#121—261no—
573#121—261no—
574#120—261no—
575#120—261no—
576#120—261no—
577#120—261no—
578C4×Q8—131no—
579C4×Q8—131no—
580C4×Q8—131no—
581C4×Q8C4×D1311yescharacteristic
582C4×Q8D5211yescharacteristic
583C4×D4—131no—
584C4×D4—131no—
585C4×D4—131no—
586C4×D4—261no—
587C4×D4—261no—
588C4×D4—261no—
589C4×D4—261no—
590C4×D4—261no—
591C4×D4—261no—
592C4×D4—261no—
593C4×D4—261no—
594C4×D4—261no—
595C4×D4C4×D1311yescharacteristic
596C4×D4C4×D1311yescharacteristic
597C4×D4C4×D1311yescharacteristic
598C4×D4D5211yescharacteristic
599C4×D4D5211yescharacteristic
600C4×D4D5211yescharacteristic
601#117—261no—
602#117—261no—
603#117—261no—
604#117—261no—
605#117C22⋊D1311yescharacteristic
606#117C22⋊D1311yescharacteristic
607#117C22⋊D1311yescharacteristic
608C2×C22⋊C4—261no—
609C2×C22⋊C4—261no—
610C2×C22⋊C4—261no—
611C2×C22⋊C4—261no—
612C2×C22⋊C4—261no—
613C2×C22⋊C4—261no—
614C2×C42C22×D1311yescharacteristic
615C2×C42C22×D1311yescharacteristic
616C2×C42C22×D1311yescharacteristic
617C4⋊C8—21no—
618C4⋊C8—21no—
619C4⋊C8—21no—
620C4⋊C8—21no—
621C4⋊C8—261no—
622C4⋊C8—261no—
623C4⋊C8—261no—
624C22⋊C8—21no—
625C22⋊C8—21no—
626C22⋊C8—21no—
627C22⋊C8—21no—
628C22⋊C8—261no—
629C22⋊C8—261no—
630C22⋊C8—261no—
631#97—21no—
632#97—131no—
633#97—131no—
634#97—131no—
635#97—131no—
636#97—261no—
637#97—261no—
638#97C22×D1311yescharacteristic
639#97C22×D1311yescharacteristic
640#97C22×D1311yescharacteristic
641#97C22×D1311yescharacteristic
642C4×C8—21no—
643C4×C8—261no—
644C2×C13—22no—
645C2×C13—41no—
646C2×C13—41no—
647C2×C13#288811yescharacteristic
648C2×C13C2×#42111yescharacteristic
649C2×C13#290111yescharacteristic
650D13—81no—
651D13—81no—
652D13—81no—
653C24—261no—
654C24—261no—
655#41—42no—
656#41—1041no—
657#41—1041no—
658C2×Q8—131no—
659C2×Q8—131no—
660C2×Q8—131no—
661C2×Q8—261no—
662C2×Q8—261no—
663C2×Q8—1041no—
664C2×Q8—1041no—
665C2×Q8#610311yescharacteristic
666C2×D4—131no—
667C2×D4—131no—
668C2×D4—131no—
669C2×D4—261no—
670C2×D4—261no—
671C2×D4—261no—
672C2×D4—261no—
673C2×D4—261no—
674C2×D4—261no—
675C2×D4—261no—
676C2×D4—261no—
677C2×D4—261no—
678C2×D4—524no—
679C2×D4—1041no—
680C2×D4—1041no—
681C2×D4#610311yescharacteristic
682C2×D4#610311yescharacteristic
683C2×D4#610311yescharacteristic
684C22×C4—261no—
685C22×C4—261no—
686C22×C4—261no—
687C22×C4—261no—
688C22×C4—261no—
689C22×C4—261no—
690C22×C4—261no—
691C22×C4C2×C4×D1311yescharacteristic
692C22×C4C2×C4×D1311yescharacteristic
693C22×C4C2×C4×D1311yescharacteristic
694C22×C4C2×D5211yescharacteristic
695C22×C4C2×D5211yescharacteristic
696C22×C4C2×D5211yescharacteristic
697C22×C4C2×C22⋊D1311yescharacteristic
698C22×C4C2×C22⋊D1311yescharacteristic
699C22×C4C2×C22⋊D1311yescharacteristic
700M16—42no—
701M16—522no—
702C2×C8—21no—
703C2×C8—21no—
704C2×C8—21no—
705C2×C8—21no—
706C2×C8—42no—
707C2×C8—261no—
708C2×C8—261no—
709C2×C8—261no—
710C2×C8—261no—
711C2×C8—522no—
712C2×C8—522no—
713C4⋊C4—131no—
714C4⋊C4—131no—
715C4⋊C4—261no—
716C4⋊C4—261no—
717C4⋊C4—261no—
718C4⋊C4—261no—
719C4⋊C4—261no—
720C4⋊C4—261no—
721C4⋊C4—261no—
722C4⋊C4—261no—
723C4⋊C4—261no—
724C4⋊C4—261no—
725C4⋊C4#610311yescharacteristic
726C4⋊C4#610311yescharacteristic
727C4⋊C4#610311yescharacteristic
728C4⋊C4#610311yescharacteristic
729C4⋊C4#610311yescharacteristic
730C4⋊C4#610311yescharacteristic
731C22⋊C4—261no—
732C22⋊C4—261no—
733C22⋊C4—261no—
734C22⋊C4—261no—
735C22⋊C4—261no—
736C22⋊C4—261no—
737C22⋊C4—261no—
738C22⋊C4—261no—
739C22⋊C4—261no—
740C22⋊C4—261no—
741C22⋊C4—261no—
742C22⋊C4—261no—
743C22⋊C4—261no—
744C22⋊C4—261no—
745C22⋊C4—261no—
746C22⋊C4—261no—
747C22⋊C4—261no—
748C22⋊C4—261no—
749C22⋊C4—261no—
750C22⋊C4—261no—
751C22⋊C4—261no—
752C22⋊C4—261no—
753C22⋊C4—261no—
754C22⋊C4#610311yescharacteristic
755C22⋊C4#610311yescharacteristic
756C22⋊C4#610311yescharacteristic
757C22⋊C4#610311yescharacteristic
758C22⋊C4#610311yescharacteristic
759C22⋊C4#610311yescharacteristic
760C42—261no—
761C42—261no—
762C42—261no—
763C42C2×C4×D1311yescharacteristic
764C42C2×C4×D1311yescharacteristic
765C42C2×C4×D1311yescharacteristic
766C42C2×D5211yescharacteristic
767C42C2×D5211yescharacteristic
768C42C2×D5211yescharacteristic
769C42C2×C22⋊D1311yescharacteristic
770C42C2×C22⋊D1311yescharacteristic
771C42C2×C22⋊D1311yescharacteristic
772C42C23×D1311yescharacteristic
773C13#1767911yescharacteristic, complemented, Sylow
774C23—261no—
775C23—261no—
776C23—261no—
777C23—522no—
778C23—522no—
779C23—1041no—
780C23—1041no—
781C23—1041no—
782C23—1041no—
783C23C2×#610311yescharacteristic
784C23C2×#610311yescharacteristic
785C23C2×#610311yescharacteristic
786Q8—41no—
787Q8—521no—
788Q8—521no—
789Q8—521no—
790Q8—1041no—
791Q8—1041no—
792D4—22no—
793D4—22no—
794D4—41no—
795D4—521no—
796D4—521no—
797D4—521no—
798D4—522no—
799D4—522no—
800D4—522no—
801D4—1041no—
802D4—1041no—
803D4—1041no—
804D4—1041no—
805D4—1041no—
806D4—1041no—
807C2×C4—22no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—261no—
817C2×C4—261no—
818C2×C4—261no—
819C2×C4—261no—
820C2×C4—261no—
821C2×C4—522no—
822C2×C4—1041no—
823C2×C4—1041no—
824C2×C4—1041no—
825C2×C4—1041no—
826C2×C4—1041no—
827C2×C4—1041no—
828C2×C4C2×#610311yescharacteristic
829C2×C4C2×#610311yescharacteristic
830C2×C4C2×#610311yescharacteristic
831C2×C4C2×#610311yescharacteristic
832C2×C4C2×#610311yescharacteristic
833C2×C4C2×#610311yescharacteristic
834C2×C4C2×#610311yescharacteristic
835C2×C4C2×#610311yescharacteristic
836C2×C4C2×#610311yescharacteristic
837C2×C4C22×C4×D1311yescharacteristic
838C2×C4C22×D5211yescharacteristic
839C2×C4C22×C22⋊D1311yescharacteristic
840C8—41no—
841C8—41no—
842C8—41no—
843C8—41no—
844C8—262no—
845C8—521no—
846C8—521no—
847C8—521no—
848C22—21no—
849C22—21no—
850C22—21no—
851C22—21no—
852C22—21no—
853C22—21no—
854C22—21no—
855C22—21no—
856C22—521no—
857C22—521no—
858C22—521no—
859C22—521no—
860C22—521no—
861C22—521no—
862C22—521no—
863C22—521no—
864C22—521no—
865C22—2082no—
866C22—2082no—
867C22#1171866612yes—
868C22C22×#610311yescharacteristic
869C4—21no—
870C4—21no—
871C4—21no—
872C4—21no—
873C4—21no—
874C4—21no—
875C4—21no—
876C4—21no—
877C4—21no—
878C4—21no—
879C4—21no—
880C4—21no—
881C4—521no—
882C4—521no—
883C4—521no—
884C4—521no—
885C4—521no—
886C2—22no—
887C2—41no—
888C2—41no—
889C2—1041no—
890C2—1041no—
891C2—1041no—
892C2#1312331411yescharacteristic
893C2C2×#1171866611yescharacteristic
894C2#1312338111yescharacteristic
subgroupG/H
centerC22C22×#6103
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#2923C2
socleC22×C13C22×C22⋊C4
prime radical#13128797C2
cosocleC42×C13C24
hypercenter#2923D13
hypocenterC13#17679
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×#41 ◁ #2923

Complements

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

NH ≅ G/Ntype
2. #13123850C2semidirect
3. #13113470C2semidirect
4. #13113468C2semidirect
5. #13113465C2semidirect
6. #13113459C2semidirect
7. #13113457C2semidirect
8. #13113454C2semidirect
9. #13113448C2semidirect
10. #13113444C2semidirect
11. #13113435C2semidirect
12. #13113433C2semidirect
13. #13113425C2semidirect
14. C2×#11718056C2semidirect
15. C13×#2923C2semidirect
41. C13×#432C22semidirect
42. C13×#432C22semidirect
43. C13×#432C22semidirect
44. C13×#432C22semidirect
47. C4×C13×M16C22semidirect
48. C2×C13×#97C22semidirect
53. #11718587C22semidirect
54. #11718587C22semidirect
55. #11718587C22semidirect
56. C4×#6099C22semidirect
57. C2×#88043C22semidirect
58. C2×#88043C22semidirect
59. #11718057C22semidirect
60. #11718057C22semidirect
61. #11718057C22semidirect
62. #11718057C22semidirect
67. #11718056C22semidirect
68. #11718056C22semidirect
69. #11718056C22semidirect
70. #11718056C22semidirect
71. #11718056C22semidirect
72. #11718056C22semidirect
73. #11718056C22semidirect
74. #11718056C22semidirect
329. #2923D13semidirect
448. #432C2×D13semidirect
449. #432C2×D13semidirect
450. #432C2×D13semidirect
451. #432C2×D13semidirect
455. C4×M16C2×D13semidirect
458. C2×#97C2×D13semidirect
773. C13#17679semidirect

Maximal subgroups

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

subgroupindex
#131287972
#131238502
#131134702
#131134682
#131134652
#131134592
#131134572
#131134542
#131134482
#131134442
#131134352
#131134332
#131134252
C2×#117180562
C13×#29232
#1767913