Finite Group Databasebeta

← #16808509

Subgroups — #16808509

Order 3328.

1950 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#13131658C214yesmaximal, complemented
2#13131657C212yesmaximal, complemented
3#13131655C212yesmaximal, complemented
4#13131648C212yesmaximal, complemented
5#13131647C212yesmaximal, complemented
6#13131646C212yesmaximal, complemented
7#13131645C212yesmaximal, complemented
8#13131627C212yesmaximal, complemented
9#13131564C212yesmaximal, complemented
10#13131555C214yesmaximal, complemented
11#13131519C212yesmaximal, complemented
12#13131512C211yesmaximal, characteristic, complemented
13C4×#88238C212yesmaximal, complemented
14C2×C4×#6122C211yesmaximal, characteristic, complemented
15#13128128C211yesmaximal, characteristic
16C22×#6122C2212yes—
17C2×#88238C2214yes—
18C13×#525C411yescharacteristic
19#11719537C411yescharacteristic
20#41×Dic13C2211yescharacteristic
21#11719496C411yescharacteristic
22C22×C4×Dic13C2211yescharacteristic
23#11719354C412yes—
24#11719354C2212yes—
25#11719329C411yescharacteristic
26#11719329C2211yescharacteristic
27#11719327C411yescharacteristic
28#11719327C2211yescharacteristic
29#11719305C411yescharacteristic
30#11719305C2211yescharacteristic
31#11719301C411yescharacteristic
32#11719301C2211yescharacteristic
33#11719291C412yes—
34#11719291C2212yes—
35#11719243C412yes—
36#11719243C412yes—
37C4×#6129C2212yes—
38C4×#6129C2212yes—
39#11719227C2211yescharacteristic
40#11719222C411yescharacteristic
41#11719169C2212yes—
42#11719158C2214yescomplemented
43#11719146C2214yes—
44#11719145C2214yes—
45#11719145C2214yes—
46#11719144C2214yes—
47#11719144C2214yes—
48#11719144C2214yescomplemented
49#11719130C2212yes—
50#11719129C2212yes—
51#11719128C2212yes—
52#11719125C2212yes—
53#11719125C2212yescomplemented
54C4×#6122C2212yes—
55C4×#6122C2212yes—
56C4×#6122C2212yes—
57C4×#6122C2212yes—
58C4×#6122C2212yes—
59C4×#6122C2212yescomplemented
60C2×#88110C2212yes—
61#11719119C2211yescharacteristic
62#11719119C2211yescharacteristic
63#11719119C2212yescomplemented
64C2×C4×#1057C2211yescharacteristic
65C2×C4×#1057C2211yescharacteristic
66C2×C4×#1057C2212yescomplemented
67#11719080C2214yescomplemented
68#11719078C2214yescomplemented
69#11719078C2214yescomplemented
70#11719077C2214yescomplemented
71#11719075C2214yescomplemented
72#11719072C2214yescomplemented
73#11719068C2214yescomplemented
74#11719067C2214yes—
75#11719066C2214yes—
76#11719066C2214yes—
77#11719065C2214yes—
78#11719065C2214yes—
79#11719065C2214yescomplemented
80#11719064C2214yescomplemented
81#11719062C2214yes—
82#11719062C2214yescomplemented
83#11719051C2212yescomplemented
84#11719049C2212yescomplemented
85C4×#6118C2212yescomplemented
86C4×D13⋊C8C2212yescomplemented
87C2×C13×#41C2×C411yescharacteristic
88C23×C4×C13C2×C411yescharacteristic
89C23×Dic13C2×C411yescharacteristic
90C23×Dic13C2311yescharacteristic
91C2×#6129C2×C412yes—
92C2×#6129C2312yes—
93C2×#6127C2×C411yescharacteristic
94C2×#6122—28no—
95C2×#6122C2314yes—
96C2×#6122C2314yes—
97C2×#6122C2314yes—
98C2×#6122C2314yes—
99C22×#1057C2314yes—
100C22×#1057C2312yes—
101C22×#1057C2312yes—
102#88238—216no—
103C2×#6118C2314yes—
104C2×D13⋊C8C2314yes—
105C13×#123C2×C412yes—
106C13×C22⋊Q8C2×C411yescharacteristic
107C13×C22⋊Q8C2×C411yescharacteristic
108C13×#121C2×C411yescharacteristic
109C13×#121C2×C411yescharacteristic
110C13×#120C2×C412yes—
111C4×D4×C13C2×C412yes—
112C4×D4×C13C2×C412yes—
113C13×#117C2×C411yescharacteristic
114#88207C2×C412yes—
115#88201C2×C411yescharacteristic
116Q8×Dic13C2×C411yescharacteristic
117Q8×Dic13C2311yescharacteristic
118#88198C2×C411yescharacteristic
119#88194C2×C411yescharacteristic
120#88193C2×C412yes—
121#88193C2×C412yes—
122#88193C2×C412yes—
123#88193C2×C412yes—
124#88190C2×C411yescharacteristic
125#88189C2×C412yes—
126#88189C2×C412yes—
127D4×Dic13C2×C412yes—
128D4×Dic13C2×C412yes—
129D4×Dic13C2×C411yescharacteristic
130D4×Dic13C2312yes—
131D4×Dic13C2312yes—
132D4×Dic13C2311yescharacteristic
133#88184C2×C411yescharacteristic
134#88184C2×C411yescharacteristic
135#88183C2×C412yes—
136C4×C22⋊D13C2×C412yes—
137C4×C22⋊D13C2×C412yes—
138C4×C22⋊D13C2×C412yes—
139C4×C22⋊D13C2×C412yes—
140#88180C2×C411yescharacteristic
141#88180C2×C412yes—
142#88178C2×C411yescharacteristic
143#88178C2×C411yescharacteristic
144C2×C4×Dic13C2×C411yescharacteristic
145C2×C4×Dic13C2×C411yescharacteristic
146C2×C4×Dic13C2×C411yescharacteristic
147C2×C4×Dic13C2×C411yescharacteristic
148C2×C4×Dic13C2×C411yescharacteristic
149C2×C4×Dic13C2×C411yescharacteristic
150C2×C4×Dic13C2311yescharacteristic
151C2×C4×Dic13C2311yescharacteristic
152C2×C4×Dic13C2311yescharacteristic
153C2×C4×Dic13C2311yescharacteristic
154C2×C4×Dic13C2311yescharacteristic
155C2×C4×Dic13C2311yescharacteristic
156C2×C4×Dic13C2312yes—
157#88152C2×C412yes—
158#88152C2×C412yes—
159#88147C2×C411yescharacteristic
160#88147C2311yescharacteristic
161#88146C2×C412yes—
162#88146C2312yes—
163#88144C2×C411yescharacteristic
164#88144C2×C411yescharacteristic
165#88143C2×C412yes—
166#88143C2×C412yes—
167#88142C2×C411yescharacteristic
168#88142C2×C411yescharacteristic
169#88141C2×C411yescharacteristic
170#88141C2×C412yes—
171#88141C2311yescharacteristic
172#88141C2312yes—
173#88140C2×C412yes—
174#88140C2×C412yes—
175#88139C2×C412yes—
176#88139C2×C412yes—
177#88135C2×C412yes—
178#88135C2×C412yes—
179#88135C2×C412yes—
180#88135C2312yes—
181#88135C2312yes—
182#88135C2312yes—
183#88133C2×C412yes—
184#88133C2×C412yes—
185#88132C2×C412yes—
186#88132C2×C412yes—
187#88132C2×C412yes—
188#88132C2×C412yes—
189#88131C2×C412yes—
190#88131C2×C412yes—
191#88131C2312yes—
192#88131C2312yes—
193#88126C2×C412yes—
194C42×D13C2312yes—
195C4×Dic26C2×C412yes—
196C4×Dic26C2×C412yes—
197C22⋊#1057C2312yes—
198C22⋊#1057C2314yes—
199C22⋊#1057C2312yes—
200C22⋊#1057C2314yes—
201C22⋊#1057C2314yes—
202#88112C2314yes—
203#88112C2314yes—
204#88112C2314yes—
205#88111C2314yes—
206#88111C2314yes—
207#88110C2314yes—
208#88110C2314yes—
209#88110C2314yes—
210#88110C2314yes—
211#88110C2314yes—
212C4⋊#1057C2314yes—
213C4⋊#1057C2312yes—
214C4⋊#1057C2314yes—
215C4⋊#1057C2312yes—
216C4×#1057C2312yes—
217C4×#1057C2312yes—
218C4×#1057C2314yes—
219C4×#1057C2312yes—
220C4×#1057C2312yes—
221C4×#1057C2314yes—
222C4×#1057C2312yes—
223C4×#1057C2312yes—
224#60205—131nomaximal, Sylow
225C24×C13C22×C411yescharacteristic
226C13×#41—42no—
227C2×Q8×C13C22×C411yescharacteristic
228C2×D4×C13C22×C412yes—
229C2×D4×C13C22×C411yescharacteristic
230C2×D4×C13C22×C412yes—
231C2×D4×C13C22×C412yes—
232C22×C4×C13—42no—
233C22×C4×C13C22×C411yescharacteristic
234C22×C4×C13C22×C411yescharacteristic
235C22×C4×C13C22×C411yescharacteristic
236C22×C4×C13C22×C412yes—
237C22×C4×C13C22×C411yescharacteristic
238C22×C4×C13C22×C411yescharacteristic
239C22×C4×C13C22×C411yescharacteristic
240C2×C22⋊D13C22×C412yes—
241C2×C22⋊D13C22×C412yes—
242C2×C22⋊D13C22×C412yes—
243C2×C22⋊D13C22×C412yes—
244C2×C22⋊D13C22×C412yes—
245C22×Dic13—24no—
246C22×Dic13—42no—
247C22×Dic13C22×C411yescharacteristic
248C22×Dic13C22×C412yes—
249C22×Dic13C22×C411yescharacteristic
250C22×Dic13C22×C411yescharacteristic
251C22×Dic13C22×C411yescharacteristic
252C22×Dic13C22×C411yescharacteristic
253C22×Dic13C22×C411yescharacteristic
254C22×Dic13C22×C411yescharacteristic
255C22×Dic13C22×C411yescharacteristic
256C22×Dic13C22×C411yescharacteristic
257C22×Dic13C2412yes—
258C22×Dic13C2411yescharacteristic
259C22×Dic13C2411yescharacteristic
260C22×Dic13C2411yescharacteristic
261#6129—28no—
262#6129—44no—
263#6127—42no—
264C2×D52C22×C411yescharacteristic
265C2×C4×D13C22×C412yes—
266C2×C4×D13C22×C412yes—
267C2×C4×D13C2412yes—
268C2×Dic26C22×C412yes—
269C2×Dic26C22×C412yes—
270C2×Dic26C22×C411yescharacteristic
271#6122—28no—
272#6122—28no—
273#6122—28no—
274#6122—28no—
275C2×#1057—24no—
276C2×#1057—28no—
277C2×#1057#4118yescomplemented
278C2×#1057C2414yes—
279C2×#1057C2414yes—
280C2×#1057C2414yes—
281C2×#1057C2414yes—
282#6118—28no—
283D13⋊C8—28no—
284C13×C4⋊C4C22×C411yescharacteristic
285C13×C4⋊C4C22×C412yes—
286C13×C4⋊C4C22×C411yescharacteristic
287C13×C4⋊C4C22×C412yes—
288C13×C22⋊C4C22×C412yes—
289C13×C22⋊C4C22×C412yes—
290C13×C22⋊C4C22×C412yes—
291C13×C22⋊C4C22×C412yes—
292C13×C22⋊C4C22×C412yes—
293C42×C13C22×C412yes—
294C22⋊Dic13C22×C412yes—
295C22⋊Dic13C22×C412yes—
296C22⋊Dic13C22×C412yes—
297C22⋊Dic13C22×C412yes—
298C22⋊Dic13C22×C412yes—
299C22⋊Dic13C22×C412yes—
300C22⋊Dic13C22×C412yes—
301#6103C22×C412yes—
302#6103C22×C412yes—
303#6103C22×C412yes—
304#6103C22×C412yes—
305#6103C22×C412yes—
306#6103C22×C412yes—
307C4⋊Dic13C22×C412yes—
308C4⋊Dic13C22×C412yes—
309C4⋊Dic13C22×C412yes—
310C4⋊Dic13C22×C412yes—
311C4⋊Dic13C22×C411yescharacteristic
312C4⋊Dic13C22×C411yescharacteristic
313#6101C22×C412yes—
314#6101C22×C412yes—
315#6101C22×C412yes—
316#6101C22×C412yes—
317#6101C22×C412yes—
318#6101C22×C412yes—
319#6101C22×C412yes—
320#6101C22×C412yes—
321#6101C22×C412yes—
322#6101C22×C412yes—
323C4×Dic13C22×C411yescharacteristic
324C4×Dic13C22×C411yescharacteristic
325C4×Dic13C22×C412yes—
326C4×Dic13C22×C412yes—
327C4×Dic13C22×C411yescharacteristic
328C4×Dic13C22×C411yescharacteristic
329C4×Dic13C22×C412yes—
330C4×Dic13C22×C411yescharacteristic
331C4×Dic13C22×C411yescharacteristic
332C4×Dic13C22×C411yescharacteristic
333C4×Dic13C22×C411yescharacteristic
334C4×Dic13C22×C411yescharacteristic
335C4×Dic13C22×C411yescharacteristic
336C4×Dic13C22×C411yescharacteristic
337C4×Dic13C22×C411yescharacteristic
338C4×Dic13C2411yescharacteristic
339C4×Dic13C2411yescharacteristic
340C4×Dic13C2412yes—
341C4×Dic13C2412yes—
342C4×Dic13C2411yescharacteristic
343C4×Dic13C2411yescharacteristic
344#3444—131no—
345#2967—132no—
346#2967—132no—
347#2967—134no—
348#2965—132no—
349#2965—132no—
350#2965—132no—
351#2965—132no—
352#2961—132no—
353#2932—132no—
354#2930—134no—
355#2922—132no—
356#2920—131no—
357C4×#131—132no—
358C2×C4×M16—131no—
359C23×C13—22no—
360C23×C13—41no—
361C23×C13—41no—
362C23×C13C23×C412yes—
363C23×C13C23×C411yescharacteristic
364C23×C13C23×C411yescharacteristic
365C23×C13C23×C411yescharacteristic
366C22×D13C23×C412yes—
367Q8×C13—41no—
368D4×C13—24no—
369D4×C13—42no—
370D4×C13—41no—
371D4×C13—42no—
372C2×C4×C13—22no—
373C2×C4×C13—22no—
374C2×C4×C13—22no—
375C2×C4×C13—24no—
376C2×C4×C13—41no—
377C2×C4×C13—41no—
378C2×C4×C13—41no—
379C2×C4×C13C23×C411yescharacteristic
380C2×C4×C13C23×C411yescharacteristic
381C2×C4×C13C23×C411yescharacteristic
382C2×C4×C13C23×C412yes—
383C2×C4×C13C23×C412yes—
384C2×C4×C13C23×C412yes—
385C2×C4×C13C23×C411yescharacteristic
386C22⋊D13—24no—
387C22⋊D13—24no—
388C22⋊D13—42no—
389C22⋊D13—42no—
390C22⋊D13—42no—
391C2×Dic13—22no—
392C2×Dic13—22no—
393C2×Dic13—22no—
394C2×Dic13—22no—
395C2×Dic13—24no—
396C2×Dic13—22no—
397C2×Dic13—22no—
398C2×Dic13—24no—
399C2×Dic13—22no—
400C2×Dic13—22no—
401C2×Dic13—41no—
402C2×Dic13—41no—
403C2×Dic13—41no—
404C2×Dic13C23×C411yescharacteristic
405C2×Dic13C23×C411yescharacteristic
406C2×Dic13C23×C411yescharacteristic
407C2×Dic13C23×C411yescharacteristic
408C2×Dic13C23×C411yescharacteristic
409C2×Dic13C23×C412yes—
410C2×Dic13C23×C412yes—
411C2×Dic13C23×C412yes—
412C2×Dic13C23×C411yescharacteristic
413C2×Dic13C23×C411yescharacteristic
414C2×Dic13C2×#4114yes—
415C2×Dic13C2511yescharacteristic
416D52—41no—
417C4×D13—24no—
418C4×D13—24no—
419C4×D13—24no—
420Dic26—24no—
421Dic26—41no—
422Dic26—42no—
423#1057—24no—
424#1057—24no—
425#1057—24no—
426#1057C2×#4118yes—
427C2×#131—134no—
428C22×M16—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—131no—
440#529—131no—
441#529—132no—
442#529—132no—
443#525—131no—
444#525—132no—
445#525—132no—
446#525#26111yescharacteristic
447C4×#41—131no—
448C4×#41—132no—
449C4×#41—132no—
450C4×#41—131no—
451C22×C42—131no—
452#446—134no—
453#446—134no—
454#446—134no—
455#446—134no—
456#436—134no—
457#436—134no—
458#436—134no—
459#436—134no—
460#435—134no—
461#435—134no—
462#435—134no—
463#435—134no—
464#435—134no—
465#435—134no—
466#435—134no—
467#435—134no—
468#433—134no—
469#433—134no—
470#432—132no—
471#432—132no—
472#431—131no—
473#431—131no—
474#431—132no—
475#431—132no—
476#431—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—
489C4×M16—132no—
490C4×M16—132no—
491C4×M16—132no—
492C4×M16—132no—
493C2×#97—132no—
494C2×C4×C8—131no—
495C2×C4×C8—131no—
496C2×C4×C8—132no—
497C2×C4×C8—132no—
498C22×C13—21no—
499C22×C13—21no—
500C22×C13—21no—
501C22×C13—21no—
502C22×C13—22no—
503C22×C13—21no—
504C22×C13—21no—
505C22×C13—22no—
506C22×C13—21no—
507C22×C13—21no—
508C22×C13—22no—
509C22×C13—44no—
510C22×C13C4×#4112yes—
511C22×C13C24×C411yescharacteristic
512C2×D13—22no—
513C2×D13—22no—
514C2×D13—22no—
515C4×C13—22no—
516C4×C13—22no—
517C4×C13—21no—
518C4×C13—21no—
519C4×C13—21no—
520C4×C13—22no—
521C4×C13#56812yes—
522Dic13—22no—
523Dic13—21no—
524Dic13—21no—
525Dic13—21no—
526Dic13—22no—
527Dic13—22no—
528Dic13—21no—
529Dic13—21no—
530Dic13C4×#4112yes—
531Dic13#56812yes—
532Dic13C22×#4112yes—
533C2×#41—132no—
534C2×#41—132no—
535C2×#41—131no—
536C2×#41C2×#26111yescharacteristic
537C23×C4—131no—
538C23×C4—131no—
539C23×C4C2×#26111yescharacteristic
540#131—2616no—
541C2×M16—134no—
542C2×M16—134no—
543C2×M16—134no—
544C2×M16—134no—
545C2×M16—134no—
546C2×M16—268no—
547C22×C8—132no—
548C22×C8—132no—
549C22×C8—134no—
550C22×C8—134no—
551C4⋊Q8—131no—
552C4⋊Q8—131no—
553C4⋊Q8—131no—
554#127—131no—
555#126—132no—
556#126—132no—
557#126—132no—
558#126—132no—
559#125—132no—
560#125—132no—
561#125—131no—
562#125—131no—
563#124—131no—
564#124—131no—
565#124—132no—
566#124—132no—
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—132no—
579C22⋊Q8C2×#26111yescharacteristic
580C22⋊Q8C2×#26111yescharacteristic
581#121—132no—
582#121—132no—
583#121—132no—
584#121—132no—
585#121—131no—
586#121—131no—
587#121C2×#26111yescharacteristic
588#121C2×#26111yescharacteristic
589#120—132no—
590#120C2×#26112yes—
591C4×Q8—131no—
592C4×Q8—131no—
593C4×Q8—132no—
594C4×Q8—131no—
595C4×Q8—132no—
596C4×Q8—131no—
597C4×Q8—132no—
598C4×Q8—132no—
599C4×D4—132no—
600C4×D4—132no—
601C4×D4—132no—
602C4×D4—132no—
603C4×D4—131no—
604C4×D4—131no—
605C4×D4—132no—
606C4×D4—132no—
607C4×D4—132no—
608C4×D4—132no—
609C4×D4—131no—
610C4×D4—131no—
611C4×D4—132no—
612C4×D4—132no—
613C4×D4—132no—
614C4×D4—132no—
615C4×D4—132no—
616C4×D4—132no—
617C4×D4C2×#26112yes—
618C4×D4C2×#26112yes—
619#117—131no—
620#117—132no—
621#117—132no—
622#117—132no—
623#117—132no—
624#117—132no—
625#117—132no—
626#117—132no—
627#117—132no—
628#117C2×#26111yescharacteristic
629C2×C42—132no—
630C2×C42—131no—
631C2×C42—131no—
632C2×C42—131no—
633C2×C42—131no—
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×C42—132no—
643C4⋊C8—132no—
644C4⋊C8—132no—
645C4⋊C8—134no—
646C4⋊C8—134no—
647C4⋊C8—134no—
648C4⋊C8—134no—
649C4⋊C8—134no—
650C22⋊C8—134no—
651C22⋊C8—134no—
652C22⋊C8—132no—
653C22⋊C8—134no—
654C22⋊C8—132no—
655C22⋊C8—134no—
656C22⋊C8—134no—
657#97—134no—
658#97—134no—
659#97—134no—
660#97—134no—
661#97—134no—
662C4×C8—132no—
663C4×C8—132no—
664C4×C8—132no—
665C4×C8—132no—
666C4×C8—132no—
667C4×C8—132no—
668C4×C8—134no—
669C4×C8—134no—
670C2×C13—22no—
671C2×C13—42no—
672C2×C13—41no—
673C2×C13—41no—
674C2×C13C2×C4×#4111yescharacteristic
675C2×C13C2×#56811yescharacteristic
676C2×C13C2×#56811yescharacteristic
677D13—42no—
678C24C22×#26111yescharacteristic
679#41—42no—
680#41—268no—
681#41—522no—
682#41—524no—
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—131no—
693C2×D4C22×#26112yes—
694C2×D4C22×#26112yes—
695C2×D4C22×#26111yescharacteristic
696C2×D4C22×#26112yes—
697C22×C4—42no—
698C22×C4—131no—
699C22×C4—131no—
700C22×C4—131no—
701C22×C4—132no—
702C22×C4—131no—
703C22×C4—131no—
704C22×C4—131no—
705C22×C4—131no—
706C22×C4—131no—
707C22×C4—131no—
708C22×C4—132no—
709C22×C4—131no—
710C22×C4—131no—
711C22×C4—131no—
712C22×C4—132no—
713C22×C4—132no—
714C22×C4—132no—
715C22×C4—264no—
716C22×C4—522no—
717C22×C4C22×#26111yescharacteristic
718C22×C4C22×#26111yescharacteristic
719C22×C4C22×#26111yescharacteristic
720C22×C4C22×#26112yes—
721C22×C4C22×#26111yescharacteristic
722C22×C4C22×#26111yescharacteristic
723C22×C4C22×#26111yescharacteristic
724M16—268no—
725M16—268no—
726M16—268no—
727M16—268no—
728M16—268no—
729C2×C8—134no—
730C2×C8—138no—
731C2×C8—134no—
732C2×C8—134no—
733C2×C8—134no—
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⋊C4—132no—
752C4⋊C4—132no—
753C4⋊C4C22×#26112yes—
754C4⋊C4C22×#26112yes—
755C4⋊C4C22×#26111yescharacteristic
756C4⋊C4C22×#26111yescharacteristic
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—131no—
792C42—131no—
793C42—131no—
794C42—131no—
795C42—132no—
796C42C22×#26112yes—
797C13#6020511yescharacteristic, complemented, Sylow
798C23—22no—
799C23—41no—
800C23—41no—
801C23—132no—
802C23C23×#26112yes—
803C23C23×#26111yescharacteristic
804C23C23×#26111yescharacteristic
805C23C23×#26111yescharacteristic
806Q8—41no—
807Q8—264no—
808Q8—521no—
809Q8—522no—
810D4—24no—
811D4—41no—
812D4—42no—
813D4—42no—
814D4—264no—
815D4—264no—
816D4—521no—
817D4—522no—
818D4—522no—
819D4—522no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—24no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—134no—
828C2×C4—131no—
829C2×C4—131no—
830C2×C4—131no—
831C2×C4—131no—
832C2×C4—131no—
833C2×C4—131no—
834C2×C4—131no—
835C2×C4—131no—
836C2×C4—132no—
837C2×C4—132no—
838C2×C4—132no—
839C2×C4—264no—
840C2×C4—264no—
841C2×C4—264no—
842C2×C4—262no—
843C2×C4—262no—
844C2×C4—262no—
845C2×C4—262no—
846C2×C4—262no—
847C2×C4—262no—
848C2×C4—262no—
849C2×C4—264no—
850C2×C4—262no—
851C2×C4—264no—
852C2×C4—521no—
853C2×C4—521no—
854C2×C4—521no—
855C2×C4C23×#26111yescharacteristic
856C2×C4C23×#26111yescharacteristic
857C2×C4C23×#26111yescharacteristic
858C2×C4C23×#26112yes—
859C2×C4C23×#26112yes—
860C2×C4C23×#26112yes—
861C2×C4C23×#26111yescharacteristic
862C8—138no—
863C8—264no—
864C8—264no—
865C8—264no—
866C22—21no—
867C22—21no—
868C22—21no—
869C22—21no—
870C22—22no—
871C22—21no—
872C22—21no—
873C22—22no—
874C22—21no—
875C22—21no—
876C22—22no—
877C22—44no—
878C22—262no—
879C22—262no—
880C22—262no—
881C22#41×#26112yes—
882C22C24×#26111yescharacteristic
883C4—22no—
884C4—21no—
885C4—21no—
886C4—21no—
887C4—22no—
888C4—22no—
889C4—132no—
890C4—132no—
891C4—132no—
892C4—261no—
893C4—261no—
894C4—262no—
895C4—262no—
896C4—261no—
897C4—261no—
898C4—261no—
899C4—262no—
900C4#1171962112yes—
901C2—22no—
902C2—41no—
903C2—41no—
904C2—42no—
905C2—522no—
906C2C2×#41×#26111yescharacteristic
907C2C2×#1171962111yescharacteristic
908C2D13⋊#56811yescharacteristic
subgroupG/H
centerC2×C4C23×#261
commutator, socleC22×C13C24×C4
FrattiniC22C24×#261
FittingC13×#525C4
prime radical#13128128C2
cosocleC2×Dic13C25
hypercenter#525#261
hypocenterC13#60205
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. #13131658C2semidirect
2. #13131657C2semidirect
3. #13131655C2semidirect
4. #13131648C2semidirect
5. #13131647C2semidirect
6. #13131646C2semidirect
7. #13131645C2semidirect
8. #13131627C2semidirect
9. #13131564C2semidirect
10. #13131555C2semidirect
11. #13131519C2semidirect
12. #13131512C2semidirect
13. C4×#88238C2semidirect
14. C2×C4×#6122C2semidirect
42. #11719158C22semidirect
48. #11719144C22semidirect
53. #11719125C22semidirect
59. C4×#6122C22semidirect
63. #11719119C22semidirect
66. C2×C4×#1057C22semidirect
67. #11719080C22semidirect
68. #11719078C22semidirect
69. #11719078C22semidirect
70. #11719077C22semidirect
71. #11719075C22semidirect
72. #11719072C22semidirect
73. #11719068C22semidirect
79. #11719065C22semidirect
80. #11719064C22semidirect
82. #11719062C22semidirect
83. #11719051C22semidirect
84. #11719049C22semidirect
85. C4×#6118C22semidirect
86. C4×D13⋊C8C22semidirect
277. C2×#1057#41semidirect
797. C13#60205semidirect

Maximal subgroups

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

subgroupindex
#131316582
#131316572
#131316552
#131316482
#131316472
#131316462
#131316452
#131316272
#131315642
#131315552
#131315192
#131315122
C4×#882382
C2×C4×#61222
#131281282
#6020513