Finite Group Databasebeta

← #16752993

Subgroups — #16752993

Order 3328.

1750 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13128701C211yesmaximal, characteristic, complemented
2#13127790C214yesmaximal, complemented
3#13127781C214yesmaximal, complemented
4#13127663C214yesmaximal, complemented
5#13127589C214yesmaximal, complemented
6#13126066C212yesmaximal, complemented
7#13126042C211yesmaximal, characteristic, complemented
8#13126026C211yesmaximal, characteristic, complemented
9#13126004C212yesmaximal, complemented
10#13124974C212yesmaximal, complemented
11#13124935C211yesmaximal, characteristic, complemented
12#13124927C211yesmaximal, characteristic
13#13124883C212yesmaximal, complemented
14#13123921C211yesmaximal, characteristic, complemented
15C2×C13×#554C211yesmaximal, characteristic, complemented
16C13×#554—22no—
17C13×#554—22no—
18C13×#554C2214yes—
19C13×#554C2214yes—
20C2×C13×C4⋊Q8C2211yescharacteristic
21C2×C13×#125C2211yescharacteristic
22C2×C13×#125C2211yescharacteristic
23C2×C13×C22⋊Q8—21no—
24C2×C13×C22⋊Q8—21no—
25C2×C13×C22⋊Q8—21no—
26C2×C4×Q8×C13C2211yescharacteristic
27C2×C4×D4×C13C2211yescharacteristic
28C2×C4×D4×C13C2211yescharacteristic
29C2×C4×D4×C13C2211yescharacteristic
30C22×C13×C4⋊C4—21no—
31#11719521—21no—
32#11719290C2212yescomplemented
33#11719289C2212yescomplemented
34#11719286—22no—
35#11719284C2212yescomplemented
36#11719273—22no—
37#11719272C2212yescomplemented
38#11719220—21no—
39#11719220—21no—
40#11719209—21no—
41#11719184C2212yes—
42#11719184C2212yes—
43#11719182C2211yescharacteristic
44#11719175C2211yescharacteristic
45#11718879C2212yes—
46#11718878C2212yes—
47#11718755C2214yescomplemented
48#11718750C2214yescomplemented
49#11718748C2214yescomplemented
50#11718741C2214yescomplemented
51#11718730C2212yescomplemented
52#11718729C2214yescomplemented
53#11718728C2212yescomplemented
54#11718727C2214yescomplemented
55#11718727C2214yescomplemented
56#11718726C2212yescomplemented
57#11718726C2212yescomplemented
58#11718725C2214yescomplemented
59#11718724C2214yescomplemented
60#11718724C2214yescomplemented
61#11718685C2214yescomplemented
62#11718685C2214yescomplemented
63#11718680C2212yes—
64#11718679C2214yes—
65#11718679C2214yes—
66C4×#6105C2214yes—
67#11718677C2214yes—
68#11718677C2214yes—
69#11718676C2212yes—
70#11718675C2214yes—
71#11718675C2214yes—
72C4×#6104C2214yes—
73#11718670C2214yes—
74#11718670C2214yes—
75#11718669C2212yes—
76#11718668C2212yes—
77#11718632C2212yes—
78#11718631C2212yes—
79#11718631C2212yes—
80#11718629C2212yes—
81#11718629C2212yes—
82#11718628C2212yes—
83#11718587C2211yescharacteristic
84#11718587C2211yescharacteristic
85#11718587C2212yes—
86#11718586C2212yes—
87C22×Q8×C13—21no—
88C22×Q8×C13D411yescharacteristic
89C22×D4×C13C2311yescharacteristic
90C23×C4×C13—21no—
91C23×C4×C13—21no—
92C23×C4×C13—21no—
93C2×#6127—21no—
94C13×C4⋊Q8—22no—
95C13×C4⋊Q8C2314yes—
96C13×#125—21no—
97C13×#125—21no—
98C13×#125—22no—
99C13×#125C2312yes—
100C13×#125C2314yes—
101C13×#125C2312yes—
102C13×C22⋊Q8—24no—
103C13×C22⋊Q8—24no—
104C13×C22⋊Q8—24no—
105C13×C22⋊Q8—24no—
106C13×C22⋊Q8—24no—
107C13×C22⋊Q8—24no—
108C4×Q8×C13D412yes—
109C4×Q8×C13D412yes—
110C4×Q8×C13C2312yes—
111C4×Q8×C13C2312yes—
112C4×D4×C13—21no—
113C4×D4×C13—21no—
114C4×D4×C13—22no—
115C4×D4×C13—22no—
116C4×D4×C13C2312yes—
117C4×D4×C13C2312yes—
118C4×D4×C13C2314yes—
119C4×D4×C13C2314yes—
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—24no—
126C2×C13×C4⋊C4—24no—
127C2×C13×C4⋊C4D411yescharacteristic
128C2×C13×C4⋊C4D411yescharacteristic
129C2×C13×C4⋊C4D411yescharacteristic
130C2×C13×C4⋊C4C2311yescharacteristic
131C2×C13×C4⋊C4C2311yescharacteristic
132C2×C13×C4⋊C4C2311yescharacteristic
133C2×C13×C22⋊C4—21no—
134C2×C13×C22⋊C4—21no—
135C2×C13×C22⋊C4—21no—
136C2×C42×C13C2311yescharacteristic
137C2×C42×C13C2311yescharacteristic
138C2×C42×C13C2311yescharacteristic
139#88201—22no—
140#88200—22no—
141#88200—22no—
142#88198—22no—
143C2×#6105C2314yes—
144C2×#6104C2314yes—
145#88184—21no—
146#88184C2312yes—
147#88183—22no—
148#88183—22no—
149C4×C22⋊D13—22no—
150C4×C22⋊D13—22no—
151#88180—21no—
152#88178—21no—
153#88178C2312yes—
154#88152—22no—
155#88152—22no—
156#88150—22no—
157#88150—22no—
158#88148—22no—
159#88148—22no—
160#88147—22no—
161#88146—22no—
162C4⋊C4×D13—22no—
163#88143—22no—
164#88143—22no—
165#88141—22no—
166#88130—22no—
167#88130—22no—
168#88129—21no—
169#88129C2312yes—
170#88129C2312yes—
171#88128C2311yescharacteristic
172C4×D52—21no—
173C4×D52C2312yes—
174C4×D52C2312yes—
175C4×D52C2312yes—
176#88126—22no—
177#88126—22no—
178#88124—21no—
179#88124C2312yes—
180#88124C2312yes—
181#88123C2311yescharacteristic
182#88123C2311yescharacteristic
183#88123C2311yescharacteristic
184C4×Dic26—21no—
185C4×Dic26C2312yes—
186C4×Dic26C2312yes—
187C4×Dic26C2312yes—
188#88072C2314yes—
189#88072C2314yes—
190C22⋊#1055C2312yes—
191C22⋊#1055C2312yes—
192#88050C2314yes—
193#88050C2314yes—
194#88050C2314yes—
195#88049C2314yes—
196#88049C2314yes—
197#88049C2314yes—
198#88048C2314yes—
199#88048C2314yes—
200#88048C2314yes—
201#88047C2314yes—
202#88047C2314yes—
203#88047C2314yes—
204C4⋊#1055C2312yes—
205C4⋊#1055C2312yes—
206C4⋊#1055C2314yes—
207C4⋊#1055C2314yes—
208#88043C2312yes—
209#88043C2314yes—
210#88043C2312yes—
211C4×#1055C2314yes—
212#61831—131nomaximal, Sylow
213C24×C13—21no—
214C2×Q8×C13—24no—
215C2×Q8×C13—42no—
216C2×Q8×C13—82no—
217C2×Q8×C13C2×D412yes—
218C2×Q8×C13C2×D412yes—
219C2×D4×C13—24no—
220C2×D4×C13—21no—
221C2×D4×C13C2412yes—
222C22×C4×C13—21no—
223C22×C4×C13—21no—
224C22×C4×C13—21no—
225C22×C4×C13—24no—
226C22×C4×C13—24no—
227C22×C4×C13—22no—
228C22×C4×C13—22no—
229C22×C4×C13—44no—
230C22×C4×C13—82no—
231C22×C4×C13—82no—
232C22×C4×C13C2×D411yescharacteristic
233C22×C4×C13C2×D411yescharacteristic
234C22×C4×C13C2×D411yescharacteristic
235C22×C4×C13C2×D411yescharacteristic
236C22×C4×C13C2×D411yescharacteristic
237C22×C4×C13C2×D411yescharacteristic
238C22×C4×C13C2411yescharacteristic
239C2×C22⋊D13—22no—
240#6127—44no—
241C2×D52—21no—
242C2×D52—21no—
243C2×D52C2412yes—
244C2×C4×D13—22no—
245C2×C4×D13—22no—
246C2×C4×D13—22no—
247C2×Dic26—21no—
248C2×Dic26—21no—
249C2×Dic26C2412yes—
250C13×C4⋊C4—24no—
251C13×C4⋊C4—22no—
252C13×C4⋊C4—22no—
253C13×C4⋊C4—24no—
254C13×C4⋊C4—22no—
255C13×C4⋊C4—24no—
256C13×C4⋊C4—22no—
257C13×C4⋊C4—21no—
258C13×C4⋊C4—21no—
259C13×C4⋊C4—21no—
260C13×C4⋊C4C2×D412yes—
261C13×C4⋊C4C2×D412yes—
262C13×C4⋊C4C2×D412yes—
263C13×C4⋊C4C2×D412yes—
264C13×C4⋊C4C2×D412yes—
265C13×C4⋊C4C2×D412yes—
266C13×C4⋊C4C2412yes—
267C13×C4⋊C4C2412yes—
268C13×C4⋊C4C2412yes—
269C13×C22⋊C4—24no—
270C13×C22⋊C4—22no—
271C13×C22⋊C4—24no—
272C13×C22⋊C4—22no—
273C42×C13C2×D411yescharacteristic
274C42×C13C2×D411yescharacteristic
275C42×C13C2×D412yes—
276C42×C13C2×D412yes—
277C42×C13C2411yescharacteristic
278C42×C13C2412yes—
279C42×C13C2412yes—
280C42×C13C2411yescharacteristic
281C22⋊Dic13—22no—
282#6105—28no—
283#6104—28no—
284#6103—22no—
285#6103—22no—
286#6103—22no—
287#6103—22no—
288#6103—22no—
289#6103—22no—
290#6103—22no—
291#6103—22no—
292C4⋊Dic13—21no—
293C4⋊Dic13—21no—
294C4⋊Dic13—21no—
295C4⋊Dic13—21no—
296C4⋊Dic13C2412yes—
297C4⋊Dic13C2412yes—
298#6101—22no—
299#6101—22no—
300#6101—22no—
301#6101—22no—
302#6101—22no—
303#6101—22no—
304#6101—22no—
305#6101—22no—
306C4×Dic13—22no—
307C4×Dic13—22no—
308C4×Dic13—22no—
309C2×#1055C2414yes—
310C2×#1055C2414yes—
311#3507—131no—
312C2×#554D1311yescharacteristic, complemented
313#3389—134no—
314#3388—134no—
315#3376—134no—
316#3370—134no—
317#3239—132no—
318#3236—131no—
319#3234—131no—
320#3232—132no—
321#3114—132no—
322#3110—131no—
323#3109—131no—
324#3105—132no—
325#2983—131no—
326C23×C13—24no—
327C23×C13—22no—
328C23×C13—42no—
329C23×C13—42no—
330C23×C13C22×D411yescharacteristic
331C22×D13—22no—
332Q8×C13—42no—
333Q8×C13—42no—
334Q8×C13—84no—
335D4×C13—24no—
336D4×C13—22no—
337D4×C132−1+414yes—
338C2×C4×C13—22no—
339C2×C4×C13—22no—
340C2×C4×C13—22no—
341C2×C4×C13—22no—
342C2×C4×C13—22no—
343C2×C4×C13—22no—
344C2×C4×C13—22no—
345C2×C4×C13—41no—
346C2×C4×C13—41no—
347C2×C4×C13—41no—
348C2×C4×C13—48no—
349C2×C4×C13—42no—
350C2×C4×C13—42no—
351C2×C4×C13—42no—
352C2×C4×C13—82no—
353C2×C4×C13—84no—
354C2×C4×C13—82no—
355C2×C4×C13C22×D411yescharacteristic
356C2×C4×C13C22×D412yes—
357C2×C4×C13C22×D412yes—
358C2×C4×C13C22×D411yescharacteristic
359C2×C4×C13C22×D411yescharacteristic
360C2×C4×C13C22×D412yes—
361C2×C4×C13C22×D412yes—
362C2×C4×C13C22×D411yescharacteristic
363C2×C4×C13C22×D411yescharacteristic
364C2×C4×C13C2511yescharacteristic
365C22⋊D13—44no—
366C2×Dic13—22no—
367C2×Dic13—22no—
368C2×Dic13—22no—
369D52—24no—
370D52—42no—
371D52—81no—
372C4×D13—44no—
373C4×D13—82no—
374C4×D13—82no—
375Dic26—24no—
376Dic26—42no—
377Dic26—81no—
378#1055—24no—
379#1055—24no—
380#559—132no—
381#557—132no—
382#556—132no—
383#556—262no—
384#554—22no—
385#554—22no—
386#554—132no—
387#554C2×D1314yes—
388#554C2×D1314yes—
389#552—262no—
390#539—261no—
391#539—261no—
392#536—261no—
393#533—131no—
394#532—131no—
395C2×C4⋊Q8C2×D1311yescharacteristic
396#529—132no—
397#529—132no—
398C2×#125C2×D1311yescharacteristic
399C2×#125C2×D1311yescharacteristic
400C2×C22⋊Q8—21no—
401C2×C22⋊Q8—21no—
402C2×C22⋊Q8—21no—
403#520—261no—
404C2×C4×Q8C2×D1311yescharacteristic
405C2×C4×D4C2×D1311yescharacteristic
406C2×C4×D4C2×D1311yescharacteristic
407C2×C4×D4C2×D1311yescharacteristic
408C22×C4⋊C4—21no—
409#501—134no—
410#501—132no—
411#501—132no—
412#499—134no—
413#491—132no—
414#490—132no—
415#489—134no—
416#488—134no—
417#484—132no—
418#484—132no—
419#483—132no—
420#481—132no—
421#481—132no—
422#480—132no—
423#479—134no—
424#479—134no—
425#478—134no—
426#478—134no—
427#478—134no—
428#478—134no—
429#476—132no—
430#475—134no—
431#474—134no—
432#474—132no—
433#463—134no—
434#463—134no—
435#461—132no—
436#459—132no—
437#450—132no—
438#447—132no—
439#446—134no—
440#446—134no—
441#442—134no—
442#442—134no—
443#440—134no—
444#440—134no—
445C4×SD16—134no—
446C4×D8—134no—
447#432—131no—
448#432—131no—
449#432—132no—
450#431—132no—
451C22×C13—21no—
452C22×C13—21no—
453C22×C13—24no—
454C22×C13—48no—
455C22×C13—42no—
456C22×C13—42no—
457C22×C13#57512yes—
458C22×C13C23×D411yescharacteristic
459C2×D13—42no—
460C2×D13—42no—
461C2×D13—42no—
462C4×C13—21no—
463C4×C13—22no—
464C4×C13—22no—
465C4×C13—21no—
466C4×C13—21no—
467C4×C13—21no—
468C4×C13—21no—
469C4×C13—22no—
470C4×C13—22no—
471C4×C13—42no—
472C4×C13—42no—
473C4×C13—42no—
474C4×C13C2×2−1+412yes—
475Dic13—42no—
476Dic13—42no—
477Dic13—42no—
478C2×#41—261no—
479C22×Q8—21no—
480C22×Q8C22⋊D1311yescharacteristic
481C22×D4C22×D1311yescharacteristic
482C23×C4—21no—
483C23×C4—21no—
484C23×C4—21no—
485C2×SD16—134no—
486C2×D8—134no—
487C4⋊Q8—22no—
488C4⋊Q8—131no—
489C4⋊Q8—131no—
490C4⋊Q8—131no—
491C4⋊Q8—262no—
492C4⋊Q8C22×D1314yes—
493#127—131no—
494#126—262no—
495#126—262no—
496#126—262no—
497#126—262no—
498#125—22no—
499#125—21no—
500#125—21no—
501#125—132no—
502#125—132no—
503#125—262no—
504#125—262no—
505#125—261no—
506#125C22×D1312yes—
507#125C22×D1314yes—
508#125C22×D1312yes—
509#124—132no—
510#124—132no—
511#124—262no—
512#124—261no—
513#123—262no—
514#123—262no—
515#123—262no—
516#123—262no—
517C22⋊Q8—24no—
518C22⋊Q8—24no—
519C22⋊Q8—24no—
520C22⋊Q8—24no—
521C22⋊Q8—24no—
522C22⋊Q8—24no—
523C22⋊Q8—132no—
524C22⋊Q8—262no—
525C22⋊Q8—262no—
526C22⋊Q8—261no—
527C22⋊Q8—262no—
528C22⋊Q8—262no—
529#121—132no—
530#121—261no—
531C4×Q8—132no—
532C4×Q8—132no—
533C4×Q8—132no—
534C4×Q8—262no—
535C4×Q8—261no—
536C4×Q8C22⋊D1312yes—
537C4×Q8C22⋊D1312yes—
538C4×Q8C22×D1312yes—
539C4×Q8C22×D1312yes—
540C4×D4—22no—
541C4×D4—22no—
542C4×D4—21no—
543C4×D4—21no—
544C4×D4—132no—
545C4×D4—132no—
546C4×D4—132no—
547C4×D4—262no—
548C4×D4—262no—
549C4×D4—262no—
550C4×D4—261no—
551C4×D4C22×D1314yes—
552C4×D4C22×D1312yes—
553C4×D4C22×D1314yes—
554C4×D4C22×D1312yes—
555#117—261no—
556#117—262no—
557#117—262no—
558#117—262no—
559C2×C4⋊C4—21no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4—21no—
564C2×C4⋊C4—24no—
565C2×C4⋊C4—24no—
566C2×C4⋊C4—262no—
567C2×C4⋊C4C22⋊D1311yescharacteristic
568C2×C4⋊C4C22⋊D1311yescharacteristic
569C2×C4⋊C4C22⋊D1311yescharacteristic
570C2×C4⋊C4C22×D1311yescharacteristic
571C2×C4⋊C4C22×D1311yescharacteristic
572C2×C4⋊C4C22×D1311yescharacteristic
573C2×C22⋊C4—21no—
574C2×C22⋊C4—21no—
575C2×C22⋊C4—21no—
576C2×C42C22×D1311yescharacteristic
577C2×C42C22×D1311yescharacteristic
578C2×C42C22×D1311yescharacteristic
579#107—134no—
580#107—134no—
581#107—134no—
582#106—134no—
583#106—134no—
584#106—134no—
585C4⋊C8—134no—
586C4⋊C8—132no—
587C4⋊C8—132no—
588C4⋊C8—134no—
589#103—134no—
590#103—134no—
591#103—134no—
592#102—134no—
593#102—134no—
594#102—134no—
595#102—134no—
596#102—134no—
597C22⋊C8—132no—
598C22⋊C8—132no—
599#97—132no—
600#97—134no—
601#97—132no—
602C4×C8—134no—
603C2×C13—22no—
604C2×C13—44no—
605C2×C13#348611yescharacteristic
606C2×C13C2×#57511yescharacteristic
607C2×C13#358511yescharacteristic
608D13—82no—
609C24—21no—
610#41—524no—
611C2×Q8—24no—
612C2×Q8—42no—
613C2×Q8—82no—
614C2×Q8—132no—
615C2×Q8—261no—
616C2×Q8—261no—
617C2×Q8C2×C22⋊D1312yes—
618C2×Q8C2×C22⋊D1312yes—
619C2×D4—24no—
620C2×D4—21no—
621C2×D4—132no—
622C2×D4—262no—
623C2×D4—261no—
624C2×D4—261no—
625C2×D4C23×D1312yes—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—24no—
630C22×C4—24no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—44no—
634C22×C4—82no—
635C22×C4—82no—
636C22×C4—262no—
637C22×C4—262no—
638C22×C4—262no—
639C22×C4C2×C22⋊D1311yescharacteristic
640C22×C4C2×C22⋊D1311yescharacteristic
641C22×C4C2×C22⋊D1311yescharacteristic
642C22×C4C2×C22⋊D1311yescharacteristic
643C22×C4C2×C22⋊D1311yescharacteristic
644C22×C4C2×C22⋊D1311yescharacteristic
645C22×C4C23×D1311yescharacteristic
646SD16—268no—
647D8—268no—
648C2×C8—134no—
649C2×C8—134no—
650C4⋊C4—24no—
651C4⋊C4—22no—
652C4⋊C4—22no—
653C4⋊C4—24no—
654C4⋊C4—22no—
655C4⋊C4—24no—
656C4⋊C4—22no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—132no—
661C4⋊C4—132no—
662C4⋊C4—261no—
663C4⋊C4—262no—
664C4⋊C4—262no—
665C4⋊C4—261no—
666C4⋊C4—262no—
667C4⋊C4—262no—
668C4⋊C4—262no—
669C4⋊C4—261no—
670C4⋊C4—262no—
671C4⋊C4—262no—
672C4⋊C4—262no—
673C4⋊C4—261no—
674C4⋊C4C2×C22⋊D1312yes—
675C4⋊C4C2×C22⋊D1312yes—
676C4⋊C4C2×C22⋊D1312yes—
677C4⋊C4C2×C22⋊D1312yes—
678C4⋊C4C2×C22⋊D1312yes—
679C4⋊C4C2×C22⋊D1312yes—
680C4⋊C4C23×D1312yes—
681C4⋊C4C23×D1312yes—
682C4⋊C4C23×D1312yes—
683C22⋊C4—24no—
684C22⋊C4—22no—
685C22⋊C4—24no—
686C22⋊C4—22no—
687C22⋊C4—262no—
688C22⋊C4—262no—
689C22⋊C4—262no—
690C22⋊C4—262no—
691C22⋊C4—262no—
692C22⋊C4—262no—
693C22⋊C4—262no—
694C22⋊C4—262no—
695C22⋊C4—262no—
696C42—262no—
697C42—262no—
698C42—262no—
699C42C2×C22⋊D1312yes—
700C42C2×C22⋊D1312yes—
701C42C2×C22⋊D1311yescharacteristic
702C42C2×C22⋊D1311yescharacteristic
703C42C23×D1312yes—
704C42C23×D1311yescharacteristic
705C42C23×D1312yes—
706C42C23×D1311yescharacteristic
707C13#6183111yescharacteristic, complemented, Sylow
708C23—24no—
709C23—22no—
710C23—42no—
711C23—42no—
712C23—262no—
713C23C22×C22⋊D1311yescharacteristic
714Q8—42no—
715Q8—42no—
716Q8—84no—
717Q8—264no—
718Q8—522no—
719Q8—1041no—
720D4—24no—
721D4—22no—
722D4—264no—
723D4—522no—
724D4—524no—
725D4—1041no—
726D4#8825414yes—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—48no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—84no—
742C2×C4—82no—
743C2×C4—82no—
744C2×C4—262no—
745C2×C4—262no—
746C2×C4—262no—
747C2×C4—524no—
748C2×C4—1042no—
749C2×C4—1042no—
750C2×C4C22×C22⋊D1311yescharacteristic
751C2×C4C22×C22⋊D1312yes—
752C2×C4C22×C22⋊D1312yes—
753C2×C4C22×C22⋊D1311yescharacteristic
754C2×C4C22×C22⋊D1312yes—
755C2×C4C22×C22⋊D1311yescharacteristic
756C2×C4C22×C22⋊D1312yes—
757C2×C4C22×C22⋊D1311yescharacteristic
758C2×C4C22×C22⋊D1311yescharacteristic
759C2×C4C24×D1311yescharacteristic
760C8—264no—
761C8—264no—
762C22—21no—
763C22—21no—
764C22—24no—
765C22—48no—
766C22—42no—
767C22—42no—
768C22—522no—
769C22—522no—
770C22—522no—
771C22#1171952712yes—
772C22C23×C22⋊D1311yescharacteristic
773C4—21no—
774C4—22no—
775C4—21no—
776C4—21no—
777C4—22no—
778C4—22no—
779C4—21no—
780C4—21no—
781C4—22no—
782C4—42no—
783C4—42no—
784C4—42no—
785C4—522no—
786C4—522no—
787C4—522no—
788C4C2×#8825412yes—
789C2—22no—
790C2—44no—
791C2—1042no—
792C2#1312848711yescharacteristic
793C2C2×#1171952711yescharacteristic
794C2#1312961611yescharacteristic
subgroupG/H
centerC22C23×C22⋊D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#554C2
socleC22×C13C23×D4
prime radical#13124927C2
hypercenterC2×#554D13
hypocenterC13#61831
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C4×Q8 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. #13128701C2semidirect
2. #13127790C2semidirect
3. #13127781C2semidirect
4. #13127663C2semidirect
5. #13127589C2semidirect
6. #13126066C2semidirect
7. #13126042C2semidirect
8. #13126026C2semidirect
9. #13126004C2semidirect
10. #13124974C2semidirect
11. #13124935C2semidirect
13. #13124883C2semidirect
14. #13123921C2semidirect
15. C2×C13×#554C2semidirect
32. #11719290C22semidirect
33. #11719289C22semidirect
35. #11719284C22semidirect
37. #11719272C22semidirect
47. #11718755C22semidirect
48. #11718750C22semidirect
49. #11718748C22semidirect
50. #11718741C22semidirect
51. #11718730C22semidirect
52. #11718729C22semidirect
53. #11718728C22semidirect
54. #11718727C22semidirect
55. #11718727C22semidirect
56. #11718726C22semidirect
57. #11718726C22semidirect
58. #11718725C22semidirect
59. #11718724C22semidirect
60. #11718724C22semidirect
61. #11718685C22semidirect
62. #11718685C22semidirect
312. C2×#554D13semidirect
707. C13#61831semidirect

Maximal subgroups

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

subgroupindex
#131287012
#131277902
#131277812
#131276632
#131275892
#131260662
#131260422
#131260262
#131260042
#131249742
#131249352
#131249272
#131248832
#131239212
C2×C13×#5542
#6183113