Finite Group Databasebeta

← #15830455

Subgroups — #15830455

Order 3328.

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#13128885C211yesmaximal, characteristic
2#13123871C211yesmaximal, characteristic, complemented
3#13113411C211yesmaximal, characteristic, complemented
4#13113407C211yesmaximal, characteristic, complemented
5#13113399C211yesmaximal, characteristic, complemented
6#13113390C211yesmaximal, characteristic, complemented
7#13113386C211yesmaximal, characteristic, complemented
8#13113377C211yesmaximal, characteristic, complemented
9#13113372C211yesmaximal, characteristic, complemented
10#13113368C211yesmaximal, characteristic, complemented
11#13113355C211yesmaximal, characteristic, complemented
12#13113338C211yesmaximal, characteristic, complemented
13#13113325C211yesmaximal, characteristic, complemented
14C2×#11718044C211yesmaximal, characteristic, complemented
15C13×#2318C211yesmaximal, characteristic, complemented
16C2×C4×D4×C13C2211yescharacteristic
17#11719511—21no—
18#11719496C2211yescharacteristic
19#11719496C2211yescharacteristic
20C2×#88178C2211yescharacteristic
21C2×#88178C2211yescharacteristic
22#11719269—21no—
23#11719269—21no—
24#11719266—21no—
25#11719260C411yescharacteristic, complemented
26#11719257C411yescharacteristic, complemented
27#11719257C411yescharacteristic, complemented
28#11719256C411yescharacteristic, complemented
29#11719251—21no—
30#11719247C411yescharacteristic, complemented
31#11719246C411yescharacteristic, complemented
32#11719246C411yescharacteristic, complemented
33D4×Dic26C411yescharacteristic, complemented
34#11719216—21no—
35#11719200—21no—
36#11719200—21no—
37#11719184C2211yescharacteristic
38#11719175C2211yescharacteristic
39C13×#388—21no—
40C13×#387—21no—
41C13×#386—21no—
42C13×#385—21no—
43C13×#383C2211yescharacteristic
44C13×#382C2211yescharacteristic
45C13×#381C2211yescharacteristic
46C13×#380C2211yescharacteristic
47C4×C13×C22⋊C4C2211yescharacteristic
48C2×C13×#95C2211yescharacteristic
49#11718868C2211yescharacteristic
50#11718868C2211yescharacteristic
51C2×C22⋊#1055C2211yescharacteristic
52C2×C22⋊#1055C2211yescharacteristic
53#11718673—21no—
54#11718672—21no—
55#11718672—21no—
56D4×#1055—21no—
57#11718587C2211yescharacteristic
58#11718586C2211yescharacteristic
59#11718044C2211yescharacteristic
60#11718044C2211yescharacteristic
61#11718044C2211yescharacteristic
62#11718044C2211yescharacteristic
63#11718044C2211yescharacteristic
64#11718044C2211yescharacteristic
65#11718044C2211yescharacteristic
66#11718044C2211yescharacteristic
67#11718044C2211yescharacteristic
68#11718044C2211yescharacteristic
69#11718044C2211yescharacteristic
70#11718044C2211yescharacteristic
71#11718043C2211yescharacteristic
72#11718043C2211yescharacteristic
73#11718043C2211yescharacteristic
74#11718043C2211yescharacteristic
75C22×D4×C13D411yescharacteristic
76C23×C4×C13—21no—
77C23×C4×C13C2311yescharacteristic
78C23×C4×C13C2311yescharacteristic
79C2×#6129—21no—
80C2×#6127C2×C411yescharacteristic
81C2×#6127C2×C411yescharacteristic, complemented
82C22×Dic26C2×C411yescharacteristic
83C22×Dic26C2×C411yescharacteristic, complemented
84C4×D4×C13C2×C411yescharacteristic
85C4×D4×C13C2×C411yescharacteristic
86C4×D4×C13C2×C411yescharacteristic
87C4×D4×C13C2×C411yescharacteristic
88C4×D4×C13D411yescharacteristic
89C4×D4×C13D411yescharacteristic
90C4×D4×C13D411yescharacteristic
91C4×D4×C13D411yescharacteristic
92C2×C13×C4⋊C4—21no—
93C2×C13×C4⋊C4—21no—
94C2×C13×C4⋊C4D411yescharacteristic
95C2×C13×C22⋊C4—21no—
96C2×C13×C22⋊C4—21no—
97C2×C13×C22⋊C4—21no—
98C2×C13×C22⋊C4D411yescharacteristic
99C2×C13×C22⋊C4D411yescharacteristic
100C2×C42×C13—21no—
101C2×C42×C13C2311yescharacteristic
102#88207—21no—
103#88207—21no—
104C2×C22⋊Dic13—21no—
105C2×C22⋊Dic13—21no—
106#88193—21no—
107#88193—21no—
108#88192—21no—
109#88190—21no—
110#88189—21no—
111#88189—21no—
112D4×Dic13—21no—
113#88184C2×C411yescharacteristic
114#88184C2×C411yescharacteristic, complemented
115#88184C2311yescharacteristic
116#88183—21no—
117#88183—21no—
118#88183—21no—
119C4×C22⋊D13—21no—
120C4×C22⋊D13—21no—
121C4×C22⋊D13—21no—
122C4×C22⋊D13—21no—
123C4×C22⋊D13—21no—
124#88180—21no—
125#88180C2×C411yescharacteristic
126#88180C2×C411yescharacteristic, complemented
127C2×C4⋊Dic13C2×C411yescharacteristic
128C2×C4⋊Dic13C2×C411yescharacteristic, complemented
129#88178—21no—
130#88178—21no—
131#88178—21no—
132#88178—21no—
133#88178—21no—
134#88178C2×C411yescharacteristic
135#88178C2×C411yescharacteristic
136#88178C2×C411yescharacteristic
137#88178C2×C411yescharacteristic, complemented
138#88178C2×C411yescharacteristic, complemented
139#88178C2×C411yescharacteristic, complemented
140#88178C2311yescharacteristic
141#88178C2311yescharacteristic
142#88178C2311yescharacteristic
143C2×#6101—21no—
144C2×#6101—21no—
145C2×#6099—21no—
146C2×#6099—21no—
147C22×#1055—21no—
148C22×#1055—21no—
149#88151—21no—
150#88150—21no—
151#88150—21no—
152C4⋊C4×D13—21no—
153#88143—21no—
154#88143—21no—
155#88142—21no—
156#88141—21no—
157#88140—21no—
158#88140—21no—
159#88139—21no—
160#88139—21no—
161#88137—21no—
162#88137—21no—
163#88135—21no—
164#88135—21no—
165#88133—21no—
166#88133—21no—
167#88133—21no—
168#88133—21no—
169#88132—21no—
170#88132—21no—
171#88131—21no—
172#88131—21no—
173#88130—21no—
174#88129C2×C411yescharacteristic, complemented
175C4×D52C2×C411yescharacteristic, complemented
176#88126—21no—
177#88124—21no—
178#88124C2×C411yescharacteristic, complemented
179#88123C2×C411yescharacteristic, complemented
180#88123C2×C411yescharacteristic, complemented
181C4×Dic26—21no—
182C4×Dic26C2×C411yescharacteristic, complemented
183C4×Dic26C2×C411yescharacteristic, complemented
184C4×Dic26C2×C411yescharacteristic, complemented
185C13×#95—21no—
186C13×#95—21no—
187C13×#95—21no—
188C13×#95—21no—
189C13×#95—21no—
190C13×#95C2311yescharacteristic
191C13×#95C2311yescharacteristic
192C13×#95C2311yescharacteristic
193C13×#95C2311yescharacteristic
194C22⋊#1055—21no—
195C22⋊#1055—21no—
196C22⋊#1055—21no—
197C22⋊#1055—21no—
198C22⋊#1055C2311yescharacteristic
199C22⋊#1055C2311yescharacteristic
200C22⋊#1055C2311yescharacteristic
201C22⋊#1055C2311yescharacteristic
202C4⋊#1055—21no—
203C4⋊#1055—21no—
204#88043—21no—
205C4×#1055—21no—
206#17598—131nomaximal, Sylow
207C24×C13C2×D411yescharacteristic
208C24×C13C2×D411yescharacteristic
209C2×D4×C13—42no—
210C2×D4×C13C22⋊C411yescharacteristic
211C2×D4×C13C22⋊C411yescharacteristic
212C2×D4×C13C22⋊C411yescharacteristic
213C2×D4×C13C22⋊C411yescharacteristic
214C22×C4×C13—21no—
215C22×C4×C13—21no—
216C22×C4×C13—21no—
217C22×C4×C13—21no—
218C22×C4×C13—42no—
219C22×C4×C13—81no—
220C22×C4×C13—81no—
221C22×C4×C13—81no—
222C22×C4×C13—81no—
223C22×C4×C13C22×C411yescharacteristic
224C22×C4×C13C22×C411yescharacteristic
225C22×C4×C13C22×C411yescharacteristic
226C22×C4×C13C22×C411yescharacteristic
227C22×C4×C13C2×D411yescharacteristic
228C22×C4×C13C2×D411yescharacteristic
229C22×C4×C13C2×D411yescharacteristic
230C22×C4×C13C2×D411yescharacteristic
231C22×C4×C13C2×D411yescharacteristic
232C22×C4×C13C2×D411yescharacteristic
233C22×C4×C13C2×D411yescharacteristic
234C22×C4×C13C2×D411yescharacteristic
235C22×C4×C13C2411yescharacteristic
236C2×C22⋊D13—21no—
237C2×C22⋊D13—21no—
238C2×C22⋊D13—21no—
239C2×C22⋊D13—21no—
240C2×C22⋊D13—21no—
241C22×Dic13—21no—
242C22×Dic13—21no—
243C22×Dic13—21no—
244C22×Dic13—21no—
245#6129—44no—
246#6127—81no—
247#6127—81no—
248C2×D52C22×C411yescharacteristic
249C2×C4×D13—21no—
250C2×C4×D13—21no—
251C2×C4×D13—21no—
252C2×Dic26—21no—
253C2×Dic26—21no—
254C2×Dic26—21no—
255C2×Dic26—81no—
256C2×Dic26—81no—
257C2×Dic26C22×C411yescharacteristic
258C2×Dic26C22×C411yescharacteristic
259C2×Dic26C22×C411yescharacteristic
260C13×C4⋊C4—81no—
261C13×C4⋊C4—81no—
262C13×C4⋊C4C22⋊C411yescharacteristic
263C13×C4⋊C4C22⋊C411yescharacteristic
264C13×C4⋊C4C22⋊C411yescharacteristic
265C13×C4⋊C4C22⋊C411yescharacteristic
266C13×C22⋊C4—42no—
267C13×C22⋊C4—81no—
268C13×C22⋊C4—81no—
269C13×C22⋊C4C22⋊C411yescharacteristic
270C13×C22⋊C4C22⋊C411yescharacteristic
271C13×C22⋊C4C22⋊C411yescharacteristic
272C13×C22⋊C4C22⋊C411yescharacteristic
273C13×C22⋊C4C22⋊C411yescharacteristic
274C13×C22⋊C4C22⋊C411yescharacteristic
275C13×C22⋊C4C22⋊C411yescharacteristic
276C13×C22⋊C4C22⋊C411yescharacteristic
277C42×C13—81no—
278C42×C13C22×C411yescharacteristic
279C42×C13C22×C411yescharacteristic
280C42×C13C2×D411yescharacteristic
281C42×C13C2×D411yescharacteristic
282C22⋊Dic13—21no—
283C22⋊Dic13—21no—
284C22⋊Dic13—21no—
285C22⋊Dic13—21no—
286C22⋊Dic13—21no—
287C22⋊Dic13—21no—
288C22⋊Dic13—21no—
289C22⋊Dic13—21no—
290C22⋊Dic13—21no—
291C22⋊Dic13—21no—
292C22⋊Dic13—21no—
293#6103—21no—
294#6103—21no—
295#6103—21no—
296#6103—21no—
297#6103—21no—
298#6103—21no—
299C4⋊Dic13—21no—
300C4⋊Dic13—21no—
301C4⋊Dic13—21no—
302C4⋊Dic13—21no—
303C4⋊Dic13—21no—
304C4⋊Dic13C22×C411yescharacteristic
305C4⋊Dic13C22×C411yescharacteristic
306C4⋊Dic13C22×C411yescharacteristic
307C4⋊Dic13C22×C411yescharacteristic
308#6101—21no—
309#6101—21no—
310#6101—21no—
311#6101—21no—
312#6101—21no—
313#6101—21no—
314#6101—21no—
315#6101—21no—
316#6101—21no—
317#6101—21no—
318#6101—21no—
319#6101—21no—
320#6101—21no—
321#6101—21no—
322C4×Dic13—21no—
323C4×Dic13—21no—
324C4×Dic13—21no—
325C4×Dic13—21no—
326C4×Dic13—21no—
327#6099—81no—
328#6099—81no—
329C2×#1055—21no—
330C2×#1055—21no—
331C2×#1055—21no—
332C2×#1055—21no—
333C2×#1055—81no—
334C2×#1055—81no—
335#3520—131no—
336#2974—131no—
337#2318D1311yescharacteristic, complemented
338#1521—131no—
339#1520—131no—
340#1518—131no—
341#1516—131no—
342#1515—131no—
343#1513—131no—
344#1512—131no—
345#1511—131no—
346#1508—131no—
347#1504—131no—
348#1501—131no—
349C2×#328—131no—
350C23×C13—21no—
351C23×C13—21no—
352C23×C13—22no—
353C23×C13—21no—
354C23×C13—21no—
355C23×C13—41no—
356C23×C13—41no—
357C23×C13—41no—
358C23×C13C2×C22⋊C411yescharacteristic
359C23×C13C2×C22⋊C411yescharacteristic
360C23×C13C2×C22⋊C411yescharacteristic
361C23×C13C2×C22⋊C411yescharacteristic
362C23×C13C22×D411yescharacteristic
363C22×D13—21no—
364D4×C13—22no—
365D4×C13—22no—
366D4×C13—41no—
367D4×C13—41no—
368C2×C4×C13—21no—
369C2×C4×C13—21no—
370C2×C4×C13—41no—
371C2×C4×C13—41no—
372C2×C4×C13—41no—
373C2×C4×C13—41no—
374C2×C4×C13—41no—
375C2×C4×C13—41no—
376C2×C4×C13—41no—
377C2×C4×C13—41no—
378C2×C4×C13—41no—
379C2×C4×C13—41no—
380C2×C4×C13—41no—
381C2×C4×C13—41no—
382C2×C4×C13—41no—
383C2×C4×C13—41no—
384C2×C4×C13—41no—
385C2×C4×C13—41no—
386C2×C4×C13—41no—
387C2×C4×C13—41no—
388C2×C4×C13—41no—
389C2×C4×C13—41no—
390C2×C4×C13—41no—
391C2×C4×C13—41no—
392C2×C4×C13—41no—
393C2×C4×C13—41no—
394C2×C4×C13—84no—
395C2×C4×C13C2×C22⋊C411yescharacteristic
396C2×C4×C13C2×C22⋊C411yescharacteristic
397C2×C4×C13C2×C22⋊C411yescharacteristic
398C2×C4×C13C2×C22⋊C411yescharacteristic
399C2×C4×C13C2×C22⋊C411yescharacteristic
400C2×C4×C13C2×C22⋊C411yescharacteristic
401C2×C4×C13C2×C22⋊C411yescharacteristic
402C2×C4×C13C2×C22⋊C411yescharacteristic
403C2×C4×C13C23×C411yescharacteristic
404C2×C4×C13C22×D411yescharacteristic
405C22⋊D13—42no—
406C22⋊D13—41no—
407C22⋊D13—41no—
408C22⋊D13—42no—
409C22⋊D13—81no—
410C22⋊D13—81no—
411C2×Dic13—21no—
412C2×Dic13—21no—
413C2×Dic13—21no—
414C2×Dic13—21no—
415C2×Dic13—21no—
416C2×Dic13—21no—
417C2×Dic13—21no—
418C2×Dic13—42no—
419C2×Dic13—42no—
420C2×Dic13—81no—
421C2×Dic13—81no—
422D52—41no—
423C4×D13—42no—
424C4×D13—81no—
425C4×D13—81no—
426Dic26—42no—
427Dic26—41no—
428Dic26—41no—
429Dic26—41no—
430Dic26—81no—
431Dic26—81no—
432#1055—41no—
433#1055—41no—
434#1055—41no—
435#1055—41no—
436#556—131no—
437#554—261no—
438#552—131no—
439#552—131no—
440#551—261no—
441#551—261no—
442D4×Q8—131no—
443#548—131no—
444#548—131no—
445#547—131no—
446#547—131no—
447#546—261no—
448#542—261no—
449#539—261no—
450#539—261no—
451#533—131no—
452#529—131no—
453#525—131no—
454#525—131no—
455C2×C22⋊Q8—131no—
456C2×C22⋊Q8—131no—
457#520—261no—
458C2×C4×D4C2×D1311yescharacteristic
459#436—261no—
460#435—261no—
461#435—261no—
462C8×D4—261no—
463#432—131no—
464#431—131no—
465#407—131no—
466#407—131no—
467C2×C22⋊C8—131no—
468C2×C22⋊C8—131no—
469#388—21no—
470#387—21no—
471#386—21no—
472#385—21no—
473#383C2×D1311yescharacteristic
474#382C2×D1311yescharacteristic
475#381C2×D1311yescharacteristic
476#380C2×D1311yescharacteristic
477C4×C22⋊C4C2×D1311yescharacteristic
478C2×#95C2×D1311yescharacteristic
479#328—131no—
480#328—131no—
481#328—131no—
482#328—131no—
483#328—131no—
484#328—131no—
485#328—131no—
486#328—131no—
487#328—131no—
488#328—131no—
489#328—131no—
490#328—131no—
491#327—131no—
492#327—131no—
493#327—131no—
494#327—131no—
495C22×C13—21no—
496C22×C13—21no—
497C22×C13—21no—
498C22×C13—21no—
499C22×C13—21no—
500C22×C13—21no—
501C22×C13—21no—
502C22×C13—21no—
503C22×C13—21no—
504C22×C13—21no—
505C22×C13—21no—
506C22×C13—21no—
507C22×C13—21no—
508C22×C13—42no—
509C22×C13—42no—
510C22×C13—81no—
511C22×C13—81no—
512C22×C13#42112yes—
513C22×C13C22×C22⋊C411yescharacteristic
514C22×C13#57711yescharacteristic
515C22×C13#57811yescharacteristic
516C2×D13—41no—
517C2×D13—41no—
518C2×D13—41no—
519C4×C13—21no—
520C4×C13—21no—
521C4×C13—21no—
522C4×C13—21no—
523C4×C13—21no—
524C4×C13—21no—
525C4×C13—21no—
526C4×C13—21no—
527C4×C13—21no—
528C4×C13—21no—
529C4×C13—81no—
530C4×C13—81no—
531C4×C13—81no—
532C4×C13—81no—
533Dic13—41no—
534Dic13—41no—
535Dic13—41no—
536Dic13—41no—
537Dic13—41no—
538Dic13—41no—
539Dic13—41no—
540C2×#41—131no—
541C2×#41—131no—
542C2×#41—261no—
543C22×Q8—131no—
544C22×Q8—131no—
545C22×D4C22⋊D1311yescharacteristic
546C23×C4—21no—
547C23×C4C22×D1311yescharacteristic
548C23×C4C22×D1311yescharacteristic
549C2×M16—261no—
550C2×M16—261no—
551C22×C8—261no—
552C22×C8—261no—
553C4⋊Q8—131no—
554C4⋊Q8—131no—
555C4⋊Q8—261no—
556#126—261no—
557#126—261no—
558#126—261no—
559#126—261no—
560#126—261no—
561#125—131no—
562#125—261no—
563#125—261no—
564#125—261no—
565#124—131no—
566#124—261no—
567#124—261no—
568#124—261no—
569#123—261no—
570#123—261no—
571#123—261no—
572#123—261no—
573#123—261no—
574#123—261no—
575#123—261no—
576#123—261no—
577#123—261no—
578C22⋊Q8—131no—
579C22⋊Q8—131no—
580C22⋊Q8—131no—
581C22⋊Q8—131no—
582C22⋊Q8—131no—
583C22⋊Q8—131no—
584C22⋊Q8—131no—
585C22⋊Q8—131no—
586C22⋊Q8—131no—
587C22⋊Q8—261no—
588C22⋊Q8—261no—
589C22⋊Q8—261no—
590C22⋊Q8—261no—
591C22⋊Q8—261no—
592C22⋊Q8—261no—
593C22⋊Q8—261no—
594C22⋊Q8—261no—
595C22⋊Q8—261no—
596C22⋊Q8—261no—
597#121—131no—
598#121—131no—
599#121—131no—
600#121—261no—
601#121—261no—
602#121—261no—
603#120—261no—
604#120—261no—
605C4×Q8—131no—
606C4×Q8—131no—
607C4×Q8—131no—
608C4×Q8—261no—
609C4×Q8—261no—
610C4×D4—131no—
611C4×D4—261no—
612C4×D4—261no—
613C4×D4—261no—
614C4×D4—261no—
615C4×D4—261no—
616C4×D4—261no—
617C4×D4—261no—
618C4×D4—261no—
619C4×D4C4×D1311yescharacteristic
620C4×D4C4×D1311yescharacteristic
621C4×D4C4×D1311yescharacteristic
622C4×D4C4×D1311yescharacteristic
623C4×D4D5211yescharacteristic
624C4×D4D5211yescharacteristic
625C4×D4D5211yescharacteristic
626C4×D4D5211yescharacteristic
627#117—131no—
628#117—131no—
629#117—261no—
630#117—261no—
631#117—261no—
632#117—261no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—131no—
636C2×C4⋊C4—131no—
637C2×C4⋊C4—261no—
638C2×C4⋊C4—261no—
639C2×C4⋊C4—261no—
640C2×C4⋊C4C22⋊D1311yescharacteristic
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—261no—
645C2×C22⋊C4—261no—
646C2×C22⋊C4C22⋊D1311yescharacteristic
647C2×C22⋊C4C22⋊D1311yescharacteristic
648C2×C42—21no—
649C2×C42C22×D1311yescharacteristic
650C4⋊C8—261no—
651C4⋊C8—261no—
652C22⋊C8—131no—
653C22⋊C8—131no—
654C22⋊C8—131no—
655C22⋊C8—131no—
656C22⋊C8—261no—
657C22⋊C8—261no—
658C22⋊C8—261no—
659C22⋊C8—261no—
660#97—261no—
661C4×C8—261no—
662#95—21no—
663#95—21no—
664#95—21no—
665#95—21no—
666#95—21no—
667#95C22×D1311yescharacteristic
668#95C22×D1311yescharacteristic
669#95C22×D1311yescharacteristic
670#95C22×D1311yescharacteristic
671C2×C13—21no—
672C2×C13—21no—
673C2×C13—22no—
674C2×C13—41no—
675C2×C13—41no—
676C2×C13—41no—
677C2×C13#288311yescharacteristic
678C2×C13#289811yescharacteristic
679C2×C13C2×#42111yescharacteristic
680D13—81no—
681C24C2×C22⋊D1311yescharacteristic
682C24C2×C22⋊D1311yescharacteristic
683#41—524no—
684#41—1041no—
685#41—1041no—
686C2×Q8—131no—
687C2×Q8—131no—
688C2×Q8—131no—
689C2×Q8—261no—
690C2×Q8—261no—
691C2×Q8—261no—
692C2×Q8—1041no—
693C2×Q8—1041no—
694C2×D4—42no—
695C2×D4—131no—
696C2×D4—261no—
697C2×D4—261no—
698C2×D4—261no—
699C2×D4—261no—
700C2×D4—261no—
701C2×D4#610311yescharacteristic
702C2×D4#610311yescharacteristic
703C2×D4#610311yescharacteristic
704C2×D4#610311yescharacteristic
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—42no—
710C22×C4—81no—
711C22×C4—81no—
712C22×C4—81no—
713C22×C4—81no—
714C22×C4—261no—
715C22×C4—261no—
716C22×C4—261no—
717C22×C4—261no—
718C22×C4—261no—
719C22×C4—261no—
720C22×C4—261no—
721C22×C4C2×C4×D1311yescharacteristic
722C22×C4C2×C4×D1311yescharacteristic
723C22×C4C2×C4×D1311yescharacteristic
724C22×C4C2×C4×D1311yescharacteristic
725C22×C4C2×D5211yescharacteristic
726C22×C4C2×D5211yescharacteristic
727C22×C4C2×D5211yescharacteristic
728C22×C4C2×D5211yescharacteristic
729C22×C4C2×C22⋊D1311yescharacteristic
730C22×C4C2×C22⋊D1311yescharacteristic
731C22×C4C2×C22⋊D1311yescharacteristic
732C22×C4C2×C22⋊D1311yescharacteristic
733C22×C4C23×D1311yescharacteristic
734M16—1041no—
735M16—1041no—
736C2×C8—261no—
737C2×C8—261no—
738C2×C8—261no—
739C2×C8—261no—
740C2×C8—1041no—
741C2×C8—1041no—
742C4⋊C4—81no—
743C4⋊C4—81no—
744C4⋊C4—131no—
745C4⋊C4—131no—
746C4⋊C4—131no—
747C4⋊C4—131no—
748C4⋊C4—261no—
749C4⋊C4—261no—
750C4⋊C4—261no—
751C4⋊C4—261no—
752C4⋊C4—261no—
753C4⋊C4—261no—
754C4⋊C4—261no—
755C4⋊C4—261no—
756C4⋊C4—261no—
757C4⋊C4—261no—
758C4⋊C4—261no—
759C4⋊C4—261no—
760C4⋊C4—261no—
761C4⋊C4—261no—
762C4⋊C4—261no—
763C4⋊C4—261no—
764C4⋊C4—261no—
765C4⋊C4—261no—
766C4⋊C4—261no—
767C4⋊C4#610311yescharacteristic
768C4⋊C4#610311yescharacteristic
769C4⋊C4#610311yescharacteristic
770C4⋊C4#610311yescharacteristic
771C22⋊C4—42no—
772C22⋊C4—81no—
773C22⋊C4—81no—
774C22⋊C4—261no—
775C22⋊C4—261no—
776C22⋊C4—261no—
777C22⋊C4—261no—
778C22⋊C4—261no—
779C22⋊C4—261no—
780C22⋊C4—261no—
781C22⋊C4—261no—
782C22⋊C4—261no—
783C22⋊C4—261no—
784C22⋊C4—261no—
785C22⋊C4—261no—
786C22⋊C4—261no—
787C22⋊C4—261no—
788C22⋊C4—261no—
789C22⋊C4—261no—
790C22⋊C4—261no—
791C22⋊C4#610311yescharacteristic
792C22⋊C4#610311yescharacteristic
793C22⋊C4#610311yescharacteristic
794C22⋊C4#610311yescharacteristic
795C22⋊C4#610311yescharacteristic
796C22⋊C4#610311yescharacteristic
797C22⋊C4#610311yescharacteristic
798C22⋊C4#610311yescharacteristic
799C42—81no—
800C42—261no—
801C42—261no—
802C42—261no—
803C42—261no—
804C42—261no—
805C42C2×C4×D1311yescharacteristic
806C42C2×C4×D1311yescharacteristic
807C42C2×D5211yescharacteristic
808C42C2×D5211yescharacteristic
809C13#1759811yescharacteristic, complemented, Sylow
810C23—22no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—21no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—261no—
819C23C2×#610311yescharacteristic
820C23C2×#610311yescharacteristic
821C23C2×#610311yescharacteristic
822C23C2×#610311yescharacteristic
823C23C22×C22⋊D1311yescharacteristic
824Q8—521no—
825Q8—521no—
826Q8—521no—
827Q8—522no—
828Q8—1041no—
829Q8—1041no—
830D4—22no—
831D4—22no—
832D4—41no—
833D4—41no—
834D4—521no—
835D4—522no—
836D4—522no—
837D4—521no—
838D4—521no—
839D4—1041no—
840D4—1041no—
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—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—84no—
868C2×C4—261no—
869C2×C4—261no—
870C2×C4—261no—
871C2×C4—261no—
872C2×C4—261no—
873C2×C4—261no—
874C2×C4—261no—
875C2×C4—522no—
876C2×C4—522no—
877C2×C4—522no—
878C2×C4—1041no—
879C2×C4—1041no—
880C2×C4—1041no—
881C2×C4—1041no—
882C2×C4C2×#610311yescharacteristic
883C2×C4C2×#610311yescharacteristic
884C2×C4C2×#610311yescharacteristic
885C2×C4C2×#610311yescharacteristic
886C2×C4C2×#610311yescharacteristic
887C2×C4C2×#610311yescharacteristic
888C2×C4C2×#610311yescharacteristic
889C2×C4C2×#610311yescharacteristic
890C2×C4C22×C4×D1311yescharacteristic
891C2×C4C22×D5211yescharacteristic
892C8—521no—
893C8—521no—
894C8—521no—
895C8—521no—
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—521no—
914C22—521no—
915C22—521no—
916C22#1171866612yes—
917C22C22×#610311yescharacteristic
918C22#1171954111yescharacteristic
919C22#1171954311yescharacteristic
920C4—21no—
921C4—21no—
922C4—21no—
923C4—21no—
924C4—21no—
925C4—21no—
926C4—21no—
927C4—21no—
928C4—21no—
929C4—21no—
930C4—81no—
931C4—81no—
932C4—81no—
933C4—81no—
934C4—521no—
935C4—521no—
936C4—521no—
937C4—521no—
938C4—521no—
939C4—521no—
940C4—521no—
941C2—21no—
942C2—21no—
943C2—22no—
944C2—41no—
945C2—41no—
946C2—41no—
947C2—1041no—
948C2#1312329611yescharacteristic
949C2#1312336611yescharacteristic
950C2C2×#1171866611yescharacteristic
subgroupG/H
centerC22C22×#6103
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#2318C2
socleC22×C13C22×C22⋊C4
prime radical#13128885C2
cosocleC22×C4×C13C24
hypercenter#2318D13
hypocenterC13#17598
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #2318

Complements

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

NH ≅ G/Ntype
2. #13123871C2semidirect
3. #13113411C2semidirect
4. #13113407C2semidirect
5. #13113399C2semidirect
6. #13113390C2semidirect
7. #13113386C2semidirect
8. #13113377C2semidirect
9. #13113372C2semidirect
10. #13113368C2semidirect
11. #13113355C2semidirect
12. #13113338C2semidirect
13. #13113325C2semidirect
14. C2×#11718044C2semidirect
15. C13×#2318C2semidirect
25. #11719260C4semidirect
26. #11719257C4semidirect
27. #11719257C4semidirect
28. #11719256C4semidirect
30. #11719247C4semidirect
31. #11719246C4semidirect
32. #11719246C4semidirect
33. D4×Dic26C4semidirect
81. C2×#6127C2×C4semidirect
83. C22×Dic26C2×C4semidirect
114. #88184C2×C4semidirect
126. #88180C2×C4semidirect
128. C2×C4⋊Dic13C2×C4semidirect
137. #88178C2×C4semidirect
138. #88178C2×C4semidirect
139. #88178C2×C4semidirect
174. #88129C2×C4semidirect
175. C4×D52C2×C4semidirect
178. #88124C2×C4semidirect
179. #88123C2×C4semidirect
180. #88123C2×C4semidirect
182. C4×Dic26C2×C4semidirect
183. C4×Dic26C2×C4semidirect
184. C4×Dic26C2×C4semidirect
337. #2318D13semidirect
809. C13#17598semidirect

Maximal subgroups

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

subgroupindex
#131288852
#131238712
#131134112
#131134072
#131133992
#131133902
#131133862
#131133772
#131133722
#131133682
#131133552
#131133382
#131133252
C2×#117180442
C13×#23182
#1759813