Finite Group Databasebeta

← #16808521

Subgroups — #16808521

Order 3328.

1962 conjugacy classes of subgroups.

The subgroup lattice has 910 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13131678C212yesmaximal, complemented
2#13131677C212yesmaximal, complemented
3#13131676C212yesmaximal, complemented
4#13131675C212yesmaximal, complemented
5#13131666C214yesmaximal, complemented
6#13131665C212yesmaximal, complemented
7#13131662C212yesmaximal, complemented
8#13131627C212yesmaximal, complemented
9#13131564C212yesmaximal, complemented
10#13131553C214yesmaximal, complemented
11#13131522C212yesmaximal, complemented
12#13131514C211yesmaximal, characteristic, complemented
13#13131407C212yesmaximal, complemented
14C2×#11719047C211yesmaximal, characteristic, complemented
15#13128130C211yesmaximal, characteristic
16C2×#88238C2214yes—
17C22×D13⋊C8C2212yes—
18C13×#529C411yescharacteristic
19#11719411C412yes—
20#11719411C2212yes—
21#11719396C2211yescharacteristic
22#11719393C411yescharacteristic
23#11719385C2211yescharacteristic
24#11719373C411yescharacteristic
25#11719361C2212yes—
26#11719354C412yes—
27#11719332C411yescharacteristic
28#11719327C2211yescharacteristic
29#11719311C411yescharacteristic
30#11719301C2211yescharacteristic
31#11719283C411yescharacteristic
32C4×#6131C2211yescharacteristic
33#11719253C411yescharacteristic
34#11719252C412yes—
35C4×#6129C2211yescharacteristic
36C4×#6129C2212yes—
37#11719233C412yes—
38#11719227C2212yes—
39#11719184C411yescharacteristic
40C2×C42×D13C2211yescharacteristic
41#11719158C2214yescomplemented
42#11719146C2214yes—
43#11719144C2214yescomplemented
44#11719130C2212yescomplemented
45#11719129C2212yes—
46#11719128C2212yescomplemented
47#11719126C2212yes—
48C4×#6122C2212yes—
49C4×#6122C2212yescomplemented
50C2×#88110C2211yescharacteristic
51C2×#88110C2212yes—
52C2×#88110C2211yescharacteristic
53C2×#88110C2212yescomplemented
54#11719080C2214yescomplemented
55#11719078C2214yescomplemented
56#11719078C2214yescomplemented
57#11719077C2214yescomplemented
58#11719075C2214yes—
59#11719075C2214yes—
60#11719075C2214yescomplemented
61#11719073C2214yes—
62#11719073C2214yes—
63#11719072C2214yescomplemented
64#11719068C2214yescomplemented
65#11719067C2214yes—
66#11719065C2214yes—
67#11719065C2214yes—
68#11719065C2214yescomplemented
69#11719064C2214yescomplemented
70#11719063C2214yes—
71#11719063C2214yes—
72#11719062C2214yes—
73#11719062C2214yescomplemented
74#11719055C2212yes—
75#11719055C2212yescomplemented
76#11719054C2211yescharacteristic
77#11719054C2211yescharacteristic
78#11719054C2212yescomplemented
79#11719051C2212yes—
80#11719049C2212yes—
81C4×#6118C2212yescomplemented
82#11719047C2212yes—
83#11719047C2212yes—
84#11719047C2212yes—
85#11719047C2212yes—
86#11719047C2212yescomplemented
87C2×#6131C2×C411yescharacteristic
88C2×#6129C2×C411yescharacteristic
89C2×#6129C2312yes—
90C2×#6127C2×C412yes—
91C22×C4×D13C2×C411yescharacteristic
92C22×C4×D13C2×C411yescharacteristic
93C22×C4×D13C2311yescharacteristic
94C2×#6122C2314yes—
95C2×#6122C2314yes—
96C22×#1057C2314yes—
97C22×#1057C2312yes—
98C22×#1057C2312yes—
99#88238—216no—
100C2×#6118C2314yes—
101C2×D13⋊C8—28no—
102C2×D13⋊C8C2314yes—
103C2×D13⋊C8C2314yes—
104C2×D13⋊C8C2314yes—
105C13×#126C2×C412yes—
106C13×#125C2×C411yescharacteristic
107C13×#124C2×C411yescharacteristic
108C13×#123C2×C412yes—
109C13×C22⋊Q8C2×C411yescharacteristic
110C13×#121C2×C411yescharacteristic
111C4×Q8×C13C2×C411yescharacteristic
112C4×D4×C13C2×C412yes—
113C4×D4×C13C2×C411yescharacteristic
114C13×#117C2×C412yes—
115C2×C42×C13C2×C411yescharacteristic
116#88200C2×C411yescharacteristic
117Q8×Dic13C2311yescharacteristic
118#88198C2×C411yescharacteristic
119#88194C2×C411yescharacteristic
120#88193C2×C412yes—
121#88192C2×C411yescharacteristic
122#88191C2×C412yes—
123D4×Dic13C2×C412yes—
124D4×Dic13C2311yescharacteristic
125#88184C2×C411yescharacteristic
126#88183C2×C412yes—
127C4×C22⋊D13C2×C412yes—
128C4×C22⋊D13C2×C412yes—
129C4×C22⋊D13C2×C412yes—
130#88178C2×C411yescharacteristic
131C2×C4×Dic13C2×C411yescharacteristic
132C2×C4×Dic13C2311yescharacteristic
133C2×C4×Dic13C2311yescharacteristic
134C2×C4×Dic13C2312yes—
135#88152C2×C412yes—
136#88151C2×C411yescharacteristic
137#88150C2×C412yes—
138#88150C2×C412yes—
139#88150C2×C412yes—
140#88149C2×C411yescharacteristic
141#88148C2×C412yes—
142#88148C2×C412yes—
143#88147C2×C412yes—
144#88147C2312yes—
145#88147C2311yescharacteristic
146#88147C2312yes—
147#88146C2×C411yescharacteristic
148#88146C2×C411yescharacteristic
149#88146C2×C412yes—
150#88146C2312yes—
151#88143C2×C412yes—
152#88143C2×C412yes—
153#88142C2×C411yescharacteristic
154#88142C2×C411yescharacteristic
155#88141C2×C412yes—
156#88141C2×C412yes—
157#88141C2312yes—
158#88141C2311yescharacteristic
159#88139C2×C412yes—
160#88139C2×C412yes—
161#88138C2×C412yes—
162#88138C2×C412yes—
163#88138C2×C412yes—
164#88137C2×C412yes—
165#88137C2×C412yes—
166#88136C2×C412yes—
167#88135C2×C412yes—
168#88135C2×C412yes—
169#88135C2×C412yes—
170#88135C2×C412yes—
171#88135C2312yes—
172#88135C2312yes—
173#88135C2312yes—
174#88133C2×C412yes—
175#88132C2×C412yes—
176#88131C2×C412yes—
177#88131C2312yes—
178#88131C2312yes—
179#88130C2×C412yes—
180#88129C2×C411yescharacteristic
181C4×D52C2×C411yescharacteristic
182C4×D52C2×C412yes—
183#88126C2×C412yes—
184#88126C2×C412yes—
185C42×D13C2×C411yescharacteristic
186C42×D13C2×C411yescharacteristic
187C42×D13C2×C411yescharacteristic
188C42×D13C2×C411yescharacteristic
189C42×D13C2311yescharacteristic
190C42×D13C2311yescharacteristic
191C42×D13C2311yescharacteristic
192C42×D13C2311yescharacteristic
193C42×D13C2312yes—
194#88124C2×C411yescharacteristic
195C4×Dic26C2×C411yescharacteristic
196C4×Dic26C2×C412yes—
197C22⋊#1057C2314yes—
198C22⋊#1057C2314yes—
199#88112C2314yes—
200#88112C2314yes—
201#88112C2314yes—
202#88111C2312yes—
203#88111C2312yes—
204#88111C2314yes—
205#88111C2314yes—
206#88111C2314yes—
207#88110C2312yes—
208#88110C2312yes—
209#88110C2312yes—
210#88110C2314yes—
211#88110C2312yes—
212#88110C2314yes—
213#88110C2312yes—
214#88110C2314yes—
215#88110C2312yes—
216#88110C2314yes—
217C4⋊#1057C2312yes—
218C4⋊#1057C2312yes—
219C4⋊#1057C2314yes—
220C4⋊#1057C2314yes—
221C4×#1057C2314yes—
222C4×#1057C2314yes—
223C4×#1057C2314yes—
224#60207—131nomaximal, Sylow
225C23×D13C22×C411yescharacteristic
226C2×Q8×C13C22×C411yescharacteristic
227C2×D4×C13C22×C412yes—
228C2×D4×C13C22×C411yescharacteristic
229C22×C4×C13C22×C411yescharacteristic
230C22×C4×C13C22×C411yescharacteristic
231C22×C4×C13C22×C411yescharacteristic
232C22×C4×C13C22×C412yes—
233C2×C22⋊D13C22×C412yes—
234C2×C22⋊D13C22×C412yes—
235C2×C22⋊D13C22×C412yes—
236C2×C22⋊D13C22×C412yes—
237C2×C22⋊D13C22×C412yes—
238C22×Dic13C22×C412yes—
239C22×Dic13C22×C411yescharacteristic
240C22×Dic13C22×C411yescharacteristic
241C22×Dic13C2412yes—
242C22×Dic13C2411yescharacteristic
243#6131—42no—
244#6129—28no—
245#6129—42no—
246#6127—44no—
247C2×D52C22×C412yes—
248C2×D52C22×C412yes—
249C2×D52C22×C411yescharacteristic
250C2×C4×D13—24no—
251C2×C4×D13—42no—
252C2×C4×D13—42no—
253C2×C4×D13C22×C411yescharacteristic
254C2×C4×D13C22×C411yescharacteristic
255C2×C4×D13C22×C411yescharacteristic
256C2×C4×D13C22×C411yescharacteristic
257C2×C4×D13C22×C411yescharacteristic
258C2×C4×D13C22×C411yescharacteristic
259C2×C4×D13C22×C411yescharacteristic
260C2×C4×D13C22×C411yescharacteristic
261C2×C4×D13C22×C411yescharacteristic
262C2×C4×D13C22×C411yescharacteristic
263C2×C4×D13C22×C412yes—
264C2×C4×D13C22×C412yes—
265C2×C4×D13C2411yescharacteristic
266C2×C4×D13C2411yescharacteristic
267C2×C4×D13C2412yes—
268C2×Dic26C22×C412yes—
269C2×Dic26C22×C411yescharacteristic
270C2×Dic26C22×C412yes—
271#6122—28no—
272#6122—28no—
273C2×#1057—24no—
274C2×#1057—28no—
275C2×#1057#4118yescomplemented
276C2×#1057C2414yes—
277C2×#1057C2414yes—
278C2×#1057C2414yes—
279C2×#1057C2414yes—
280#6118—28no—
281D13⋊C8—28no—
282D13⋊C8—28no—
283D13⋊C8—28no—
284C13×C4⋊C4C22×C412yes—
285C13×C4⋊C4C22×C412yes—
286C13×C4⋊C4C22×C411yescharacteristic
287C13×C4⋊C4C22×C412yes—
288C13×C4⋊C4C22×C411yescharacteristic
289C13×C4⋊C4C22×C412yes—
290C13×C22⋊C4C22×C412yes—
291C13×C22⋊C4C22×C412yes—
292C13×C22⋊C4C22×C412yes—
293C13×C22⋊C4C22×C412yes—
294C13×C22⋊C4C22×C412yes—
295C42×C13C22×C411yescharacteristic
296C42×C13C22×C412yes—
297C42×C13C22×C411yescharacteristic
298C42×C13C22×C411yescharacteristic
299C42×C13C22×C411yescharacteristic
300C22⋊Dic13C22×C412yes—
301C22⋊Dic13C22×C412yes—
302C22⋊Dic13C22×C412yes—
303#6103C22×C412yes—
304#6103C22×C412yes—
305#6103C22×C412yes—
306#6103C22×C412yes—
307#6103C22×C412yes—
308#6103C22×C412yes—
309#6103C22×C412yes—
310#6103C22×C412yes—
311#6103C22×C412yes—
312#6103C22×C412yes—
313C4⋊Dic13C22×C411yescharacteristic
314C4⋊Dic13C22×C412yes—
315C4⋊Dic13C22×C411yescharacteristic
316C4⋊Dic13C22×C412yes—
317#6101C22×C412yes—
318#6101C22×C412yes—
319#6101C22×C412yes—
320#6101C22×C412yes—
321#6101C22×C412yes—
322#6101C22×C412yes—
323#6101C22×C412yes—
324#6101C22×C412yes—
325#6101C22×C412yes—
326#6101C22×C412yes—
327C4×Dic13C22×C411yescharacteristic
328C4×Dic13C22×C412yes—
329C4×Dic13C22×C411yescharacteristic
330C4×Dic13C22×C411yescharacteristic
331C4×Dic13C22×C411yescharacteristic
332C4×Dic13C22×C411yescharacteristic
333C4×Dic13C22×C411yescharacteristic
334C4×Dic13C22×C411yescharacteristic
335C4×Dic13C22×C411yescharacteristic
336C4×Dic13C22×C412yes—
337C4×Dic13C22×C412yes—
338C4×Dic13C2411yescharacteristic
339C4×Dic13C2412yes—
340C4×Dic13C2412yes—
341C4×Dic13C2411yescharacteristic
342C4×Dic13C2411yescharacteristic
343C4×Dic13C2411yescharacteristic
344#3444—131no—
345#2970—132no—
346#2970—132no—
347#2970—132no—
348#2970—132no—
349#2968—132no—
350#2968—132no—
351#2968—134no—
352#2961—132no—
353#2932—132no—
354#2929—134no—
355#2923—132no—
356#2920—131no—
357#2875—132no—
358C22×#97—131no—
359C23×C13C23×C412yes—
360C23×C13C23×C411yescharacteristic
361C22×D13—22no—
362C22×D13—22no—
363C22×D13—22no—
364C22×D13C23×C412yes—
365C22×D13C23×C411yescharacteristic
366C22×D13C23×C411yescharacteristic
367Q8×C13—41no—
368D4×C13—24no—
369D4×C13—41no—
370C2×C4×C13—22no—
371C2×C4×C13—41no—
372C2×C4×C13—41no—
373C2×C4×C13—42no—
374C2×C4×C13C23×C411yescharacteristic
375C2×C4×C13C23×C411yescharacteristic
376C2×C4×C13C23×C411yescharacteristic
377C2×C4×C13C23×C411yescharacteristic
378C2×C4×C13C23×C411yescharacteristic
379C2×C4×C13C23×C412yes—
380C2×C4×C13C23×C411yescharacteristic
381C2×C4×C13C23×C412yes—
382C2×C4×C13C23×C412yes—
383C22⋊D13—24no—
384C22⋊D13—24no—
385C22⋊D13—24no—
386C22⋊D13—24no—
387C22⋊D13—42no—
388C2×Dic13—24no—
389C2×Dic13—41no—
390C2×Dic13—41no—
391C2×Dic13—42no—
392C2×Dic13C23×C411yescharacteristic
393C2×Dic13C23×C411yescharacteristic
394C2×Dic13C23×C411yescharacteristic
395C2×Dic13C23×C411yescharacteristic
396C2×Dic13C23×C412yes—
397C2×Dic13C23×C412yes—
398C2×Dic13C23×C412yes—
399C2×Dic13C23×C411yescharacteristic
400C2×Dic13C2×#4114yes—
401C2×Dic13C2511yescharacteristic
402D52—24no—
403D52—24no—
404D52—41no—
405C4×D13—22no—
406C4×D13—22no—
407C4×D13—22no—
408C4×D13—22no—
409C4×D13—22no—
410C4×D13—22no—
411C4×D13—22no—
412C4×D13—22no—
413C4×D13—24no—
414C4×D13—41no—
415C4×D13—41no—
416C4×D13—41no—
417C4×D13—41no—
418C4×D13—42no—
419C4×D13—42no—
420Dic26—24no—
421Dic26—42no—
422Dic26—41no—
423#1057—24no—
424#1057—24no—
425#1057—24no—
426#1057C2×#4118yes—
427C2×#131—134no—
428C23×C8—132no—
429#533—131no—
430#533—131no—
431#533—131no—
432#532—131no—
433#532—131no—
434#532—131no—
435#529—132no—
436#529—132no—
437#529—131no—
438#529—131no—
439#529—132no—
440#529—132no—
441#529—131no—
442#529#26111yescharacteristic
443#525—132no—
444#525—131no—
445#525—131no—
446#525—132no—
447C4×#41—131no—
448C4×#41—132no—
449C4×#41—131no—
450C4×#41—132no—
451C22×C42—131no—
452#446—134no—
453#446—134no—
454#446—134no—
455#446—134no—
456#435—134no—
457#435—134no—
458#435—134no—
459#435—134no—
460#435—134no—
461#435—134no—
462#435—134no—
463#435—134no—
464C8×D4—134no—
465C8×D4—134no—
466C8×D4—134no—
467C8×D4—134no—
468#433—134no—
469#433—134no—
470#432—131no—
471#432—131no—
472#432—132no—
473#432—132no—
474#432—132no—
475#432—132no—
476#432—132no—
477#431—132no—
478#431—132no—
479#424—134no—
480#423—132no—
481#408—134no—
482#407—132no—
483#405—134no—
484#405—134no—
485#405—134no—
486C4×M16—132no—
487C4×M16—132no—
488C4×M16—132no—
489C2×#97—131no—
490C2×#97—131no—
491C2×#97—132no—
492C2×#97—132no—
493C2×#97—132no—
494C2×#97—132no—
495C2×#97—132no—
496C2×#97—132no—
497C2×#97—132no—
498C22×C13—21no—
499C22×C13—21no—
500C22×C13—22no—
501C22×C13—22no—
502C22×C13—22no—
503C22×C13C4×#4112yes—
504C22×C13C24×C411yescharacteristic
505C2×D13—28no—
506C2×D13—21no—
507C2×D13—21no—
508C2×D13—21no—
509C2×D13—21no—
510C2×D13—22no—
511C2×D13—22no—
512C2×D13—22no—
513C2×D13#56812yes—
514C2×D13#56812yes—
515C4×C13—22no—
516C4×C13—21no—
517C4×C13—21no—
518C4×C13—21no—
519C4×C13—22no—
520C4×C13—21no—
521C4×C13—21no—
522C4×C13—21no—
523C4×C13—22no—
524Dic13—22no—
525Dic13—21no—
526Dic13—22no—
527Dic13—22no—
528Dic13—21no—
529Dic13—21no—
530Dic13—21no—
531Dic13C4×#4112yes—
532Dic13C22×#4112yes—
533C2×#41—131no—
534C2×#41—132no—
535C2×#41—131no—
536C2×#41—132no—
537C23×C4—131no—
538C23×C4—131no—
539C23×C4—131no—
540#131—2616no—
541C2×M16—134no—
542C2×M16—134no—
543C2×M16—134no—
544C22×C8—132no—
545C22×C8—132no—
546C22×C8—134no—
547C22×C8—134no—
548C22×C8—134no—
549C22×C8—134no—
550C22×C8—268no—
551C4⋊Q8—131no—
552C4⋊Q8—131no—
553C4⋊Q8—131no—
554#127—131no—
555#126—132no—
556#126—132no—
557#126—132no—
558#126C2×#26112yes—
559#125—132no—
560#125—132no—
561#125—131no—
562#125C2×#26111yescharacteristic
563#124—132no—
564#124—132no—
565#124—131no—
566#124C2×#26111yescharacteristic
567#123—132no—
568#123—132no—
569#123—132no—
570#123—132no—
571#123—132no—
572#123C2×#26112yes—
573C22⋊Q8—131no—
574C22⋊Q8—131no—
575C22⋊Q8—132no—
576C22⋊Q8—132no—
577C22⋊Q8—132no—
578C22⋊Q8—131no—
579C22⋊Q8—132no—
580C22⋊Q8C2×#26111yescharacteristic
581#121—131no—
582#121—132no—
583#121—131no—
584#121—131no—
585#121—132no—
586#121—132no—
587#121—132no—
588#121C2×#26111yescharacteristic
589#120—132no—
590#120—132no—
591C4×Q8—131no—
592C4×Q8—132no—
593C4×Q8—132no—
594C4×Q8—132no—
595C4×Q8—131no—
596C4×Q8—132no—
597C4×Q8—131no—
598C4×Q8C2×#26111yescharacteristic
599C4×D4—132no—
600C4×D4—131no—
601C4×D4—132no—
602C4×D4—132no—
603C4×D4—132no—
604C4×D4—132no—
605C4×D4—132no—
606C4×D4—132no—
607C4×D4—131no—
608C4×D4—132no—
609C4×D4—132no—
610C4×D4—132no—
611C4×D4—132no—
612C4×D4—132no—
613C4×D4—132no—
614C4×D4—132no—
615C4×D4—132no—
616C4×D4—131no—
617C4×D4C2×#26112yes—
618C4×D4C2×#26111yescharacteristic
619#117—131no—
620#117—131no—
621#117—132no—
622#117—132no—
623#117—132no—
624#117—132no—
625#117—132no—
626#117—132no—
627#117—132no—
628#117C2×#26112yes—
629C2×C42—132no—
630C2×C42—131no—
631C2×C42—131no—
632C2×C42—131no—
633C2×C42—132no—
634C2×C42—131no—
635C2×C42—131no—
636C2×C42—131no—
637C2×C42—131no—
638C2×C42—131no—
639C2×C42—131no—
640C2×C42—131no—
641C2×C42—131no—
642C2×C42C2×#26111yescharacteristic
643C4⋊C8—132no—
644C4⋊C8—132no—
645C4⋊C8—134no—
646C4⋊C8—134no—
647C4⋊C8—134no—
648C4⋊C8—134no—
649C4⋊C8—134no—
650C22⋊C8—132no—
651C22⋊C8—132no—
652C22⋊C8—134no—
653C22⋊C8—134no—
654C22⋊C8—134no—
655C22⋊C8—134no—
656C22⋊C8—134no—
657#97—132no—
658#97—132no—
659#97—132no—
660#97—132no—
661#97—134no—
662#97—134no—
663#97—132no—
664#97—132no—
665#97—134no—
666#97—134no—
667C4×C8—134no—
668C4×C8—134no—
669C4×C8—134no—
670C2×C13—22no—
671C2×C13—42no—
672C2×C13C2×C4×#4111yescharacteristic
673C2×C13C2×#56811yescharacteristic
674C2×C13C2×#56811yescharacteristic
675D13—22no—
676D13—22no—
677D13—42no—
678C24—131no—
679#41—268no—
680#41—524no—
681#41—522no—
682#41—522no—
683C2×Q8—132no—
684C2×Q8—132no—
685C2×Q8—131no—
686C2×Q8C22×#26111yescharacteristic
687C2×D4—132no—
688C2×D4—132no—
689C2×D4—132no—
690C2×D4—132no—
691C2×D4—132no—
692C2×D4—132no—
693C2×D4—132no—
694C2×D4—131no—
695C2×D4C22×#26112yes—
696C2×D4C22×#26111yescharacteristic
697C22×C4—131no—
698C22×C4—132no—
699C22×C4—131no—
700C22×C4—131no—
701C22×C4—132no—
702C22×C4—131no—
703C22×C4—131no—
704C22×C4—132no—
705C22×C4—131no—
706C22×C4—131no—
707C22×C4—131no—
708C22×C4—131no—
709C22×C4—131no—
710C22×C4—131no—
711C22×C4—131no—
712C22×C4—131no—
713C22×C4—131no—
714C22×C4—131no—
715C22×C4—132no—
716C22×C4—132no—
717C22×C4—264no—
718C22×C4—522no—
719C22×C4—522no—
720C22×C4C22×#26111yescharacteristic
721C22×C4C22×#26111yescharacteristic
722C22×C4C22×#26111yescharacteristic
723C22×C4C22×#26112yes—
724M16—268no—
725M16—268no—
726M16—268no—
727C2×C8—134no—
728C2×C8—138no—
729C2×C8—134no—
730C2×C8—134no—
731C2×C8—134no—
732C2×C8—268no—
733C2×C8—268no—
734C2×C8—268no—
735C2×C8—268no—
736C2×C8—264no—
737C4⋊C4—132no—
738C4⋊C4—132no—
739C4⋊C4—132no—
740C4⋊C4—132no—
741C4⋊C4—131no—
742C4⋊C4—131no—
743C4⋊C4—132no—
744C4⋊C4—132no—
745C4⋊C4—132no—
746C4⋊C4—132no—
747C4⋊C4—132no—
748C4⋊C4—132no—
749C4⋊C4—132no—
750C4⋊C4—132no—
751C4⋊C4C22×#26111yescharacteristic
752C4⋊C4C22×#26112yes—
753C4⋊C4C22×#26111yescharacteristic
754C4⋊C4C22×#26112yes—
755C4⋊C4C22×#26112yes—
756C4⋊C4C22×#26112yes—
757C22⋊C4—132no—
758C22⋊C4—132no—
759C22⋊C4—132no—
760C22⋊C4—132no—
761C22⋊C4—132no—
762C22⋊C4—132no—
763C22⋊C4—132no—
764C22⋊C4—132no—
765C22⋊C4—132no—
766C22⋊C4—132no—
767C22⋊C4—132no—
768C22⋊C4—132no—
769C22⋊C4—132no—
770C22⋊C4C22×#26112yes—
771C22⋊C4C22×#26112yes—
772C22⋊C4C22×#26112yes—
773C22⋊C4C22×#26112yes—
774C22⋊C4C22×#26112yes—
775C42—131no—
776C42—132no—
777C42—132no—
778C42—131no—
779C42—131no—
780C42—131no—
781C42—131no—
782C42—131no—
783C42—131no—
784C42—131no—
785C42—131no—
786C42—131no—
787C42—131no—
788C42—131no—
789C42—132no—
790C42—132no—
791C42—132no—
792C42C22×#26111yescharacteristic
793C42C22×#26111yescharacteristic
794C42C22×#26111yescharacteristic
795C42C22×#26111yescharacteristic
796C42C22×#26112yes—
797C13#6020711yescharacteristic, complemented, Sylow
798C23—131no—
799C23—131no—
800C23—132no—
801C23—262no—
802C23—262no—
803C23—262no—
804C23C23×#26112yes—
805C23C23×#26111yescharacteristic
806Q8—41no—
807Q8—264no—
808Q8—521no—
809Q8—522no—
810D4—24no—
811D4—41no—
812D4—264no—
813D4—264no—
814D4—264no—
815D4—264no—
816D4—264no—
817D4—264no—
818D4—521no—
819D4—522no—
820C2×C4—22no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—42no—
824C2×C4—134no—
825C2×C4—131no—
826C2×C4—131no—
827C2×C4—131no—
828C2×C4—131no—
829C2×C4—131no—
830C2×C4—131no—
831C2×C4—132no—
832C2×C4—132no—
833C2×C4—132no—
834C2×C4—262no—
835C2×C4—262no—
836C2×C4—264no—
837C2×C4—262no—
838C2×C4—262no—
839C2×C4—262no—
840C2×C4—262no—
841C2×C4—262no—
842C2×C4—262no—
843C2×C4—264no—
844C2×C4—521no—
845C2×C4—521no—
846C2×C4—521no—
847C2×C4—521no—
848C2×C4—522no—
849C2×C4—522no—
850C2×C4—521no—
851C2×C4—521no—
852C2×C4—522no—
853C2×C4C23×#26111yescharacteristic
854C2×C4C23×#26111yescharacteristic
855C2×C4C23×#26111yescharacteristic
856C2×C4C23×#26111yescharacteristic
857C2×C4C23×#26111yescharacteristic
858C2×C4C23×#26111yescharacteristic
859C2×C4C23×#26112yes—
860C2×C4C23×#26112yes—
861C2×C4C23×#26112yes—
862C8—138no—
863C8—264no—
864C8—264no—
865C8—264no—
866C22—21no—
867C22—21no—
868C22—22no—
869C22—22no—
870C22—22no—
871C22—132no—
872C22—132no—
873C22—268no—
874C22—261no—
875C22—261no—
876C22—261no—
877C22—261no—
878C22—262no—
879C22—262no—
880C22—262no—
881C22#41×#26112yes—
882C22C24×#26111yescharacteristic
883C4—21no—
884C4—21no—
885C4—22no—
886C4—21no—
887C4—21no—
888C4—21no—
889C4—21no—
890C4—22no—
891C4—22no—
892C4—132no—
893C4—132no—
894C4—262no—
895C4—261no—
896C4—261no—
897C4—261no—
898C4—261no—
899C4—262no—
900C4—262no—
901C2—22no—
902C2—42no—
903C2—262no—
904C2—262no—
905C2—522no—
906C2C2×#41×#26111yescharacteristic
907C2D13⋊#56811yescharacteristic
908C2D13⋊#56811yescharacteristic
subgroupG/H
center, FrattiniC22C24×#261
commutator, socleC22×C13C24×C4
FittingC13×#529C4
prime radical#13128130C2
cosocleC2×Dic13C25
hypercenter#529#261
hypocenterC13#60207
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ #529

Complements

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

NH ≅ G/Ntype
1. #13131678C2semidirect
2. #13131677C2semidirect
3. #13131676C2semidirect
4. #13131675C2semidirect
5. #13131666C2semidirect
6. #13131665C2semidirect
7. #13131662C2semidirect
8. #13131627C2semidirect
9. #13131564C2semidirect
10. #13131553C2semidirect
11. #13131522C2semidirect
12. #13131514C2semidirect
13. #13131407C2semidirect
14. C2×#11719047C2semidirect
41. #11719158C22semidirect
43. #11719144C22semidirect
44. #11719130C22semidirect
46. #11719128C22semidirect
49. C4×#6122C22semidirect
53. C2×#88110C22semidirect
54. #11719080C22semidirect
55. #11719078C22semidirect
56. #11719078C22semidirect
57. #11719077C22semidirect
60. #11719075C22semidirect
63. #11719072C22semidirect
64. #11719068C22semidirect
68. #11719065C22semidirect
69. #11719064C22semidirect
73. #11719062C22semidirect
75. #11719055C22semidirect
78. #11719054C22semidirect
81. C4×#6118C22semidirect
86. #11719047C22semidirect
275. C2×#1057#41semidirect
797. C13#60207semidirect

Maximal subgroups

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

subgroupindex
#131316782
#131316772
#131316762
#131316752
#131316662
#131316652
#131316622
#131316272
#131315642
#131315532
#131315222
#131315142
#131314072
C2×#117190472
#131281302
#6020713