Finite Group Databasebeta

← #16735268

Subgroups — #16735268

Order 3328.

1686 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13128226C211yesmaximal, characteristic
2#13126134C214yesmaximal, complemented
3#13126119C214yesmaximal, complemented
4#13126104C214yesmaximal, complemented
5#13126089C214yesmaximal, complemented
6#13125385C211yesmaximal, characteristic, complemented
7#13125378C211yesmaximal, characteristic, complemented
8#13125239C211yesmaximal, characteristic, complemented
9#13125232C211yesmaximal, characteristic, complemented
10#13124767C212yesmaximal, complemented
11#13124759C212yesmaximal, complemented
12#13124654C212yesmaximal, complemented
13#13124645C212yesmaximal, complemented
14#13123474C211yesmaximal, characteristic, complemented
15C2×C13×#544C211yesmaximal, characteristic, complemented
16C13×#544—22no—
17C13×#544—22no—
18C13×#544C2214yes—
19C13×#544C2214yes—
20C2×C13×C4⋊Q8—21no—
21C2×C13×C4⋊Q8C2211yescharacteristic
22C2×C13×C4⋊Q8C2211yescharacteristic
23C2×C13×#125—21no—
24C2×C13×#125C2211yescharacteristic
25C2×C13×#125C2211yescharacteristic
26C2×C13×C22⋊Q8—21no—
27C2×C13×C22⋊Q8—21no—
28C2×C13×#117C2211yescharacteristic
29C2×C13×#117C2211yescharacteristic
30C22×C13×C4⋊C4C2211yescharacteristic
31#11719496C2212yes—
32#11719240C2212yes—
33#11719239C2212yes—
34#11719239C2212yes—
35#11719233—22no—
36#11719233—22no—
37#11719223C2212yes—
38#11719220—21no—
39#11719220—21no—
40#11719199—21no—
41#11719199—21no—
42#11719182C2211yescharacteristic
43C4×#6127C2212yes—
44#11719175C2211yescharacteristic
45#11718868C2212yes—
46#11718755C2214yescomplemented
47#11718754C2212yescomplemented
48#11718752C2214yescomplemented
49#11718750C2214yescomplemented
50#11718749C2212yescomplemented
51#11718748C2214yescomplemented
52#11718745C2214yescomplemented
53#11718741C2214yescomplemented
54#11718740C2212yescomplemented
55#11718739C2212yescomplemented
56#11718730C2212yescomplemented
57#11718729C2214yescomplemented
58#11718728C2212yescomplemented
59#11718727C2214yescomplemented
60#11718727C2214yescomplemented
61#11718726C2212yescomplemented
62#11718726C2212yescomplemented
63#11718725C2214yescomplemented
64#11718724C2214yescomplemented
65#11718724C2214yescomplemented
66#11718664C2214yes—
67#11718664C2214yes—
68#11718661C2214yes—
69#11718661C2214yes—
70#11718657C2214yes—
71#11718657C2214yes—
72#11718632C2214yes—
73#11718631C2214yes—
74#11718629C2214yes—
75#11718628C2214yes—
76#11718627C2212yes—
77#11718627C2212yes—
78#11718627C2212yes—
79#11718627C2212yes—
80#11718625C2212yes—
81#11718625C2212yes—
82#11718625C2212yes—
83#11718625C2212yes—
84#11718585C2212yes—
85C4×#6099C2211yescharacteristic
86C4×#6099C2211yescharacteristic
87C22×Q8×C13—21no—
88C22×Q8×C13—21no—
89C23×C4×C13—21no—
90C23×C4×C13C2311yescharacteristic
91C2×#6127C2312yes—
92C13×C4⋊Q8—24no—
93C13×C4⋊Q8—24no—
94C13×C4⋊Q8—21no—
95C13×C4⋊Q8—21no—
96C13×C4⋊Q8—22no—
97C13×C4⋊Q8C2312yes—
98C13×C4⋊Q8C2312yes—
99C13×C4⋊Q8C2314yes—
100C13×#125—24no—
101C13×#125—24no—
102C13×#125—21no—
103C13×#125—21no—
104C13×#125—22no—
105C13×#125C2314yes—
106C13×#125C2312yes—
107C13×#125C2312yes—
108C13×C22⋊Q8—24no—
109C13×C22⋊Q8—24no—
110C13×C22⋊Q8—24no—
111C13×C22⋊Q8—24no—
112C13×#117—22no—
113C13×#117D412yes—
114C13×#117D412yes—
115C13×#117C2314yes—
116C13×#117C2312yes—
117C13×#117C2312yes—
118C2×C13×C4⋊C4—21no—
119C2×C13×C4⋊C4—22no—
120C2×C13×C4⋊C4—21no—
121C2×C13×C4⋊C4—21no—
122C2×C13×C4⋊C4—21no—
123C2×C13×C4⋊C4—21no—
124C2×C13×C4⋊C4—21no—
125C2×C13×C4⋊C4—21no—
126C2×C13×C4⋊C4D411yescharacteristic
127C2×C13×C4⋊C4D411yescharacteristic
128C2×C13×C4⋊C4C2311yescharacteristic
129C2×C13×C4⋊C4C2311yescharacteristic
130C2×C13×C4⋊C4C2314yes—
131C2×C13×C4⋊C4C2311yescharacteristic
132C2×C13×C4⋊C4C2311yescharacteristic
133C2×C13×C22⋊C4—21no—
134C2×C13×C22⋊C4D411yescharacteristic
135C2×C13×C22⋊C4D411yescharacteristic
136C2×C42×C13—21no—
137C2×C42×C13C2311yescharacteristic
138C2×C42×C13C2311yescharacteristic
139#88207—22no—
140#88184—21no—
141#88184—21no—
142#88184C2312yes—
143#88184C2312yes—
144#88183—22no—
145C4×C22⋊D13—22no—
146C4×C22⋊D13—22no—
147C4×C22⋊D13—22no—
148C4×C22⋊D13—22no—
149#88180C2312yes—
150#88178—21no—
151#88178—21no—
152#88178C2312yes—
153#88178C2312yes—
154C2×#6099C2312yes—
155C2×#6099C2312yes—
156#88152—22no—
157#88152—22no—
158#88150—22no—
159#88150—22no—
160#88148—22no—
161#88148—22no—
162#88143—22no—
163#88143—22no—
164#88139—22no—
165#88139—22no—
166#88138—22no—
167#88138—22no—
168#88137—22no—
169#88137—22no—
170#88133—22no—
171#88133—22no—
172#88129C2312yes—
173#88128C2311yescharacteristic
174C4×D52—21no—
175C4×D52—21no—
176C4×D52C2312yes—
177C4×D52C2312yes—
178#88126—22no—
179C42×D13—22no—
180#88124C2312yes—
181#88123C2311yescharacteristic
182#88123C2311yescharacteristic
183#88123C2311yescharacteristic
184C4×Dic26—21no—
185C4×Dic26—21no—
186C4×Dic26C2312yes—
187C4×Dic26C2312yes—
188C22⋊#1055C2314yes—
189C22⋊#1055C2314yes—
190#88050C2314yes—
191#88050C2314yes—
192#88050C2314yes—
193#88050C2314yes—
194#88049C2314yes—
195#88049C2314yes—
196#88049C2314yes—
197#88049C2314yes—
198#88048C2314yes—
199#88048C2314yes—
200#88048C2314yes—
201#88048C2314yes—
202#88047C2314yes—
203#88047C2314yes—
204#88047C2314yes—
205#88047C2314yes—
206C4⋊#1055C2314yes—
207C4⋊#1055C2314yes—
208#88043C2312yes—
209#88043C2312yes—
210C4×#1055C2312yes—
211C4×#1055C2312yes—
212#60867—131nomaximal, Sylow
213C24×C13C2×D411yescharacteristic
214C2×Q8×C13—24no—
215C2×Q8×C13—22no—
216C2×Q8×C13—22no—
217C2×Q8×C13—82no—
218C2×Q8×C13—82no—
219C22×C4×C13—24no—
220C22×C4×C13—21no—
221C22×C4×C13—21no—
222C22×C4×C13—21no—
223C22×C4×C13—21no—
224C22×C4×C13—24no—
225C22×C4×C13—82no—
226C22×C4×C13C2×D412yes—
227C22×C4×C13C2×D411yescharacteristic
228C22×C4×C13C2×D411yescharacteristic
229C22×C4×C13C2×D411yescharacteristic
230C22×C4×C13C2×D411yescharacteristic
231C22×C4×C13C2×D411yescharacteristic
232C22×C4×C13C2412yes—
233C22×C4×C13C2411yescharacteristic
234C2×C22⋊D13—22no—
235C2×C22⋊D13—22no—
236C2×C22⋊D13—22no—
237#6127—28no—
238C2×D52—21no—
239C2×D52—21no—
240C2×D52C2412yes—
241C2×C4×D13—22no—
242C2×C4×D13—22no—
243C2×C4×D13—22no—
244C2×Dic26—21no—
245C2×Dic26—21no—
246C2×Dic26C2412yes—
247C13×C4⋊C4—24no—
248C13×C4⋊C4—21no—
249C13×C4⋊C4—21no—
250C13×C4⋊C4—24no—
251C13×C4⋊C4—22no—
252C13×C4⋊C4—22no—
253C13×C4⋊C4—24no—
254C13×C4⋊C4—22no—
255C13×C4⋊C4—22no—
256C13×C4⋊C4—24no—
257C13×C4⋊C4—22no—
258C13×C4⋊C4—22no—
259C13×C4⋊C4—21no—
260C13×C4⋊C4—21no—
261C13×C4⋊C4C2×D412yes—
262C13×C4⋊C4C2×D412yes—
263C13×C4⋊C4C2×D412yes—
264C13×C4⋊C4C2×D412yes—
265C13×C4⋊C4C2412yes—
266C13×C4⋊C4C2412yes—
267C13×C4⋊C4C2412yes—
268C13×C4⋊C4C2412yes—
269C13×C22⋊C4—24no—
270C13×C22⋊C4C2×D412yes—
271C13×C22⋊C4C2×D412yes—
272C13×C22⋊C4C2×D412yes—
273C13×C22⋊C4C2×D412yes—
274C42×C13—24no—
275C42×C13C2×D411yescharacteristic
276C42×C13C2×D411yescharacteristic
277C42×C13C2×D412yes—
278C42×C13C2412yes—
279C42×C13C2411yescharacteristic
280C42×C13C2411yescharacteristic
281C22⋊Dic13—22no—
282C22⋊Dic13—22no—
283C22⋊Dic13—22no—
284#6103—22no—
285#6103—22no—
286#6103—22no—
287#6103—22no—
288#6103—22no—
289#6103—22no—
290C4⋊Dic13—21no—
291C4⋊Dic13—21no—
292C4⋊Dic13—21no—
293C4⋊Dic13—21no—
294C4⋊Dic13C2412yes—
295C4⋊Dic13C2412yes—
296#6101—22no—
297#6101—22no—
298#6101—22no—
299#6101—22no—
300#6101—22no—
301#6101—22no—
302C4×Dic13—22no—
303C4×Dic13—22no—
304C4×Dic13—22no—
305#6099—24no—
306#6099—24no—
307C2×#1055C2414yes—
308C2×#1055C2414yes—
309C2×#544D1311yescharacteristic, complemented
310#3455—131no—
311#3244—134no—
312#3243—134no—
313#3242—134no—
314#3241—134no—
315#3166—131no—
316#3165—131no—
317#3142—131no—
318#3141—131no—
319#3093—132no—
320#3092—132no—
321#3080—132no—
322#3079—132no—
323#2921—131no—
324C23×C13—22no—
325C23×C13—41no—
326C23×C13—41no—
327C23×C13C22×D412yes—
328C23×C13C22×D411yescharacteristic
329C22×D13—22no—
330Q8×C13—82no—
331Q8×C13—84no—
332Q8×C13—82no—
333C2×C4×C13—22no—
334C2×C4×C13—24no—
335C2×C4×C13—24no—
336C2×C4×C13—22no—
337C2×C4×C13—22no—
338C2×C4×C13—22no—
339C2×C4×C13—22no—
340C2×C4×C13—41no—
341C2×C4×C13—41no—
342C2×C4×C13—41no—
343C2×C4×C13—41no—
344C2×C4×C13—42no—
345C2×C4×C13—42no—
346C2×C4×C13—42no—
347C2×C4×C13—42no—
348C2×C4×C13—84no—
349C2×C4×C13C22×D412yes—
350C2×C4×C13C22×D412yes—
351C2×C4×C13C22×D411yescharacteristic
352C2×C4×C13C22×D411yescharacteristic
353C2×C4×C13C22×D412yes—
354C2×C4×C13C22×D411yescharacteristic
355C2×C4×C13C22×D411yescharacteristic
356C2×C4×C13C22×D411yescharacteristic
357C2×C4×C132−1+414yes—
358C2×C4×C13C2511yescharacteristic
359C22⋊D13—44no—
360C22⋊D13—82no—
361C22⋊D13—82no—
362C2×Dic13—22no—
363C2×Dic13—22no—
364C2×Dic13—22no—
365D52—24no—
366D52—81no—
367D52—81no—
368C4×D13—44no—
369C4×D13—82no—
370C4×D13—82no—
371Dic26—24no—
372Dic26—81no—
373Dic26—81no—
374#1055—24no—
375#1055—24no—
376#544—22no—
377#544—22no—
378#544C2×D1314yes—
379#544C2×D1314yes—
380#542—132no—
381#542—132no—
382#541—132no—
383#540—132no—
384#539—261no—
385#539—261no—
386#538—261no—
387#538—261no—
388#533—131no—
389#532—131no—
390C2×C4⋊Q8—21no—
391C2×C4⋊Q8C2×D1311yescharacteristic
392C2×C4⋊Q8C2×D1311yescharacteristic
393#529—262no—
394#529—262no—
395C2×#125—21no—
396C2×#125C2×D1311yescharacteristic
397C2×#125C2×D1311yescharacteristic
398#525—132no—
399C2×C22⋊Q8—21no—
400C2×C22⋊Q8—21no—
401C4×#41—132no—
402C2×#117C2×D1311yescharacteristic
403C2×#117C2×D1311yescharacteristic
404C22×C4⋊C4C2×D1311yescharacteristic
405#501—134no—
406#501—132no—
407#501—132no—
408#500—132no—
409#499—134no—
410#498—132no—
411#491—132no—
412#490—132no—
413#489—134no—
414#488—134no—
415#487—132no—
416#486—132no—
417#485—134no—
418#485—134no—
419#484—134no—
420#483—134no—
421#482—134no—
422#482—134no—
423#481—134no—
424#480—134no—
425#479—134no—
426#479—134no—
427#478—134no—
428#478—134no—
429#477—134no—
430#476—134no—
431#475—134no—
432#474—134no—
433#433—134no—
434#433—134no—
435#428—132no—
436#428—132no—
437#428—132no—
438#428—132no—
439#423—132no—
440#417—132no—
441#417—132no—
442#417—132no—
443#417—132no—
444#407—132no—
445C4×M16—131no—
446C4×M16—131no—
447C22×C13—21no—
448C22×C13—21no—
449C22×C13—22no—
450C22×C13—22no—
451C22×C13—22no—
452C22×C13—44no—
453C22×C13#53612yes—
454C22×C13C23×D411yescharacteristic
455C2×D13—42no—
456C2×D13—42no—
457C2×D13—42no—
458C4×C13—21no—
459C4×C13—22no—
460C4×C13—21no—
461C4×C13—21no—
462C4×C13—22no—
463C4×C13—21no—
464C4×C13—22no—
465C4×C13—42no—
466C4×C13—42no—
467C4×C13—42no—
468C4×C13—42no—
469C4×C13#53612yes—
470C4×C13C2×2−1+412yes—
471Dic13—42no—
472Dic13—42no—
473Dic13—42no—
474C2×#41—132no—
475C22×Q8—21no—
476C22×Q8—21no—
477C23×C4—21no—
478C23×C4C22×D1311yescharacteristic
479C2×M16—132no—
480C2×M16—132no—
481C4⋊Q8—24no—
482C4⋊Q8—24no—
483C4⋊Q8—22no—
484C4⋊Q8—21no—
485C4⋊Q8—21no—
486C4⋊Q8—131no—
487C4⋊Q8—131no—
488C4⋊Q8—131no—
489C4⋊Q8C22×D1314yes—
490C4⋊Q8C22×D1312yes—
491C4⋊Q8C22×D1312yes—
492#127—131no—
493#126—262no—
494#126—262no—
495#126—262no—
496#126—262no—
497#125—24no—
498#125—24no—
499#125—22no—
500#125—21no—
501#125—21no—
502#125—132no—
503#125—262no—
504#125—262no—
505#125C22×D1314yes—
506#125C22×D1312yes—
507#125C22×D1312yes—
508#124—132no—
509#124—262no—
510#124—262no—
511#123—262no—
512#123—262no—
513#123—262no—
514#123—262no—
515#123—262no—
516C22⋊Q8—24no—
517C22⋊Q8—24no—
518C22⋊Q8—24no—
519C22⋊Q8—24no—
520C22⋊Q8—132no—
521C22⋊Q8—132no—
522C22⋊Q8—261no—
523C22⋊Q8—261no—
524C22⋊Q8—262no—
525C22⋊Q8—262no—
526#121—132no—
527#121—132no—
528#121—261no—
529#121—261no—
530#121—262no—
531#121—262no—
532#120—262no—
533C4×Q8—132no—
534C4×Q8—132no—
535C4×Q8—261no—
536C4×Q8—261no—
537C4×D4—132no—
538C4×D4—132no—
539C4×D4—262no—
540C4×D4—262no—
541C4×D4—262no—
542C4×D4—262no—
543C4×D4—261no—
544C4×D4—261no—
545#117—22no—
546#117—132no—
547#117—262no—
548#117C22⋊D1312yes—
549#117C22⋊D1312yes—
550#117C22×D1314yes—
551#117C22×D1312yes—
552#117C22×D1312yes—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—22no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—21no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4C22⋊D1311yescharacteristic
562C2×C4⋊C4C22⋊D1311yescharacteristic
563C2×C4⋊C4C22×D1311yescharacteristic
564C2×C4⋊C4C22×D1311yescharacteristic
565C2×C4⋊C4C22×D1314yes—
566C2×C4⋊C4C22×D1311yescharacteristic
567C2×C4⋊C4C22×D1311yescharacteristic
568C2×C22⋊C4—21no—
569C2×C22⋊C4C22⋊D1311yescharacteristic
570C2×C22⋊C4C22⋊D1311yescharacteristic
571C2×C42—21no—
572C2×C42—262no—
573C2×C42C22×D1311yescharacteristic
574C2×C42C22×D1311yescharacteristic
575#107—134no—
576#107—134no—
577#107—134no—
578#107—134no—
579#106—134no—
580#106—134no—
581#106—134no—
582#106—134no—
583C4⋊C8—134no—
584C4⋊C8—134no—
585#103—134no—
586#103—134no—
587#103—134no—
588#103—134no—
589#102—134no—
590#102—134no—
591#102—134no—
592#102—134no—
593C22⋊C8—134no—
594C22⋊C8—134no—
595#97—132no—
596#97—132no—
597C4×C8—132no—
598C4×C8—132no—
599C2×C13—22no—
600C2×C13—42no—
601C2×C13C2×#53611yescharacteristic
602C2×C13#358511yescharacteristic
603C2×C13#358611yescharacteristic
604D13—82no—
605C24C2×C22⋊D1311yescharacteristic
606#41—268no—
607C2×Q8—24no—
608C2×Q8—22no—
609C2×Q8—22no—
610C2×Q8—82no—
611C2×Q8—82no—
612C2×Q8—132no—
613C2×Q8—261no—
614C2×Q8—261no—
615C2×D4—132no—
616C2×D4—262no—
617C2×D4—262no—
618C2×D4—262no—
619C2×D4—261no—
620C2×D4—261no—
621C22×C4—24no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—24no—
627C22×C4—82no—
628C22×C4—262no—
629C22×C4—262no—
630C22×C4—262no—
631C22×C4C2×C22⋊D1311yescharacteristic
632C22×C4C2×C22⋊D1312yes—
633C22×C4C2×C22⋊D1311yescharacteristic
634C22×C4C2×C22⋊D1311yescharacteristic
635C22×C4C2×C22⋊D1311yescharacteristic
636C22×C4C2×C22⋊D1311yescharacteristic
637C22×C4C23×D1312yes—
638C22×C4C23×D1311yescharacteristic
639M16—264no—
640M16—264no—
641C2×C8—134no—
642C2×C8—134no—
643C4⋊C4—24no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—24no—
647C4⋊C4—22no—
648C4⋊C4—22no—
649C4⋊C4—24no—
650C4⋊C4—22no—
651C4⋊C4—22no—
652C4⋊C4—24no—
653C4⋊C4—22no—
654C4⋊C4—22no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—132no—
658C4⋊C4—132no—
659C4⋊C4—262no—
660C4⋊C4—262no—
661C4⋊C4—261no—
662C4⋊C4—261no—
663C4⋊C4—262no—
664C4⋊C4—262no—
665C4⋊C4—262no—
666C4⋊C4—262no—
667C4⋊C4—261no—
668C4⋊C4—261no—
669C4⋊C4C2×C22⋊D1312yes—
670C4⋊C4C2×C22⋊D1312yes—
671C4⋊C4C2×C22⋊D1312yes—
672C4⋊C4C2×C22⋊D1312yes—
673C4⋊C4C23×D1312yes—
674C4⋊C4C23×D1312yes—
675C4⋊C4C23×D1312yes—
676C4⋊C4C23×D1312yes—
677C22⋊C4—24no—
678C22⋊C4—262no—
679C22⋊C4—262no—
680C22⋊C4—262no—
681C22⋊C4—262no—
682C22⋊C4—262no—
683C22⋊C4—262no—
684C22⋊C4—262no—
685C22⋊C4—262no—
686C22⋊C4—262no—
687C22⋊C4C2×C22⋊D1312yes—
688C22⋊C4C2×C22⋊D1312yes—
689C22⋊C4C2×C22⋊D1312yes—
690C22⋊C4C2×C22⋊D1312yes—
691C42—24no—
692C42—262no—
693C42—262no—
694C42—262no—
695C42C2×C22⋊D1312yes—
696C42C2×C22⋊D1311yescharacteristic
697C42C2×C22⋊D1311yescharacteristic
698C42C23×D1311yescharacteristic
699C42C23×D1311yescharacteristic
700C42C23×D1312yes—
701C13#6086711yescharacteristic, complemented, Sylow
702C23—22no—
703C23—41no—
704C23—41no—
705C23—262no—
706C23C22×C22⋊D1312yes—
707C23C22×C22⋊D1311yescharacteristic
708Q8—84no—
709Q8—82no—
710Q8—82no—
711Q8—264no—
712Q8—1041no—
713Q8—1041no—
714D4—264no—
715D4—524no—
716D4—1041no—
717D4—1041no—
718D4—1042no—
719D4—1042no—
720C2×C4—22no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—84no—
736C2×C4—262no—
737C2×C4—262no—
738C2×C4—262no—
739C2×C4—524no—
740C2×C4—1042no—
741C2×C4—1042no—
742C2×C4#8825414yes—
743C2×C4C22×C22⋊D1312yes—
744C2×C4C22×C22⋊D1312yes—
745C2×C4C22×C22⋊D1312yes—
746C2×C4C22×C22⋊D1311yescharacteristic
747C2×C4C22×C22⋊D1311yescharacteristic
748C2×C4C22×C22⋊D1311yescharacteristic
749C2×C4C22×C22⋊D1311yescharacteristic
750C2×C4C22×C22⋊D1311yescharacteristic
751C2×C4C24×D1311yescharacteristic
752C8—264no—
753C8—264no—
754C22—21no—
755C22—21no—
756C22—22no—
757C22—22no—
758C22—22no—
759C22—44no—
760C22—522no—
761C22—522no—
762C22—522no—
763C22#1171952112yes—
764C22C23×C22⋊D1311yescharacteristic
765C4—22no—
766C4—21no—
767C4—21no—
768C4—22no—
769C4—21no—
770C4—21no—
771C4—22no—
772C4—42no—
773C4—42no—
774C4—42no—
775C4—42no—
776C4—522no—
777C4—522no—
778C4—522no—
779C4#1171952112yes—
780C4C2×#8825412yes—
781C2—22no—
782C2—42no—
783C2—1042no—
784C2C2×#1171952111yescharacteristic
785C2#1312961611yescharacteristic
786C2#1312962311yescharacteristic
subgroupG/H
centerC22C23×C22⋊D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#544C2
socleC22×C13C23×D4
prime radical#13128226C2
hypercenterC2×#544D13
hypocenterC13#60867
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×#117 ◁ C2×#544

Complements

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

NH ≅ G/Ntype
2. #13126134C2semidirect
3. #13126119C2semidirect
4. #13126104C2semidirect
5. #13126089C2semidirect
6. #13125385C2semidirect
7. #13125378C2semidirect
8. #13125239C2semidirect
9. #13125232C2semidirect
10. #13124767C2semidirect
11. #13124759C2semidirect
12. #13124654C2semidirect
13. #13124645C2semidirect
14. #13123474C2semidirect
15. C2×C13×#544C2semidirect
46. #11718755C22semidirect
47. #11718754C22semidirect
48. #11718752C22semidirect
49. #11718750C22semidirect
50. #11718749C22semidirect
51. #11718748C22semidirect
52. #11718745C22semidirect
53. #11718741C22semidirect
54. #11718740C22semidirect
55. #11718739C22semidirect
56. #11718730C22semidirect
57. #11718729C22semidirect
58. #11718728C22semidirect
59. #11718727C22semidirect
60. #11718727C22semidirect
61. #11718726C22semidirect
62. #11718726C22semidirect
63. #11718725C22semidirect
64. #11718724C22semidirect
65. #11718724C22semidirect
309. C2×#544D13semidirect
701. C13#60867semidirect

Maximal subgroups

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

subgroupindex
#131282262
#131261342
#131261192
#131261042
#131260892
#131253852
#131253782
#131252392
#131252322
#131247672
#131247592
#131246542
#131246452
#131234742
C2×C13×#5442
#6086713