Finite Group Databasebeta

← #16735965

Subgroups — #16735965

Order 3328.

1822 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13128226C211yesmaximal, characteristic, complemented
2#13126301C214yesmaximal, complemented
3#13126292C214yesmaximal, complemented
4#13126262C214yesmaximal, complemented
5#13126247C214yesmaximal, complemented
6#13124645C212yesmaximal, complemented
7#13124641C211yesmaximal, characteristic, complemented
8#13124633C211yesmaximal, characteristic, complemented
9#13124462C212yesmaximal, complemented
10#13124451C212yesmaximal, complemented
11#13124326C212yesmaximal, complemented
12#13124308C211yesmaximal, characteristic, complemented
13#13124300C211yesmaximal, characteristic, complemented
14#13123400C211yesmaximal, characteristic, complemented
15C2×C13×#542C211yesmaximal, characteristic, complemented
16C13×#542—22no—
17C13×#542—22no—
18C13×#542C2214yes—
19C13×#542C2214yes—
20C2×C13×C4⋊Q8C2211yescharacteristic
21C2×C13×#126—21no—
22C2×C13×#124—21no—
23C2×C13×#124C2211yescharacteristic
24C2×C13×#123—21no—
25C2×C13×C22⋊Q8—21no—
26C2×C13×C22⋊Q8C2211yescharacteristic
27C2×C13×#121C2211yescharacteristic
28C2×C4×Q8×C13C2211yescharacteristic
29C2×C4×D4×C13C2211yescharacteristic
30C2×C13×#117C2211yescharacteristic
31C2×#88196C2212yes—
32C2×#88186C2212yes—
33#11719496C2212yes—
34C22×#6099C2212yes—
35#11719240C2212yescomplemented
36#11719239C2212yescomplemented
37#11719239C2212yescomplemented
38#11719233—22no—
39#11719233—22no—
40#11719223C2212yescomplemented
41#11719220—21no—
42#11719220—21no—
43#11719199—21no—
44#11719199—21no—
45#11719182C2211yescharacteristic
46C4×#6127C2212yes—
47#11719175C2211yescharacteristic
48#11718886C2212yes—
49#11718876C2212yes—
50#11718755C2214yescomplemented
51#11718752C2214yescomplemented
52#11718748C2214yescomplemented
53#11718745C2214yescomplemented
54#11718718C2214yescomplemented
55#11718718C2214yescomplemented
56#11718715C2214yescomplemented
57#11718715C2214yescomplemented
58#11718713C2214yescomplemented
59#11718712C2214yescomplemented
60#11718710C2214yescomplemented
61#11718709C2214yescomplemented
62#11718703C2214yes—
63#11718702C2214yes—
64#11718700C2214yes—
65#11718699C2214yes—
66#11718692C2212yescomplemented
67#11718689C2214yescomplemented
68#11718688C2212yescomplemented
69#11718683C2214yescomplemented
70#11718682C2212yescomplemented
71#11718681C2212yescomplemented
72#11718680C2212yescomplemented
73#11718677C2214yescomplemented
74#11718676C2212yescomplemented
75#11718670C2214yescomplemented
76#11718669C2212yescomplemented
77#11718668C2212yescomplemented
78#11718660C2214yescomplemented
79#11718660C2214yescomplemented
80#11718627C2212yes—
81#11718627C2212yes—
82#11718625C2212yes—
83#11718625C2212yes—
84#11718585C2211yescharacteristic
85#11718585C2211yescharacteristic
86#11718585C2212yes—
87C22×Q8×C13—21no—
88C22×Q8×C13C2311yescharacteristic
89C22×D4×C13—21no—
90C22×D4×C13C2311yescharacteristic
91C23×C4×C13—21no—
92C23×C4×C13C2311yescharacteristic
93C2×#6127C2312yes—
94C13×C4⋊Q8—22no—
95C13×C4⋊Q8C2314yes—
96C13×#126—24no—
97C13×#126—24no—
98C13×#124—24no—
99C13×#124—24no—
100C13×#124—22no—
101C13×#124C2314yes—
102C13×#123—24no—
103C13×#123—24no—
104C13×C22⋊Q8—22no—
105C13×C22⋊Q8—24no—
106C13×C22⋊Q8—24no—
107C13×C22⋊Q8C2314yes—
108C13×#121—22no—
109C13×#121C2314yes—
110C4×Q8×C13—21no—
111C4×Q8×C13—21no—
112C4×Q8×C13C2312yes—
113C4×Q8×C13C2312yes—
114C4×D4×C13—21no—
115C4×D4×C13—21no—
116C4×D4×C13C2312yes—
117C4×D4×C13C2312yes—
118C13×#117D412yes—
119C13×#117D412yes—
120C13×#117C2312yes—
121C13×#117C2312yes—
122C2×C13×C4⋊C4—21no—
123C2×C13×C4⋊C4—21no—
124C2×C13×C4⋊C4—21no—
125C2×C13×C4⋊C4D411yescharacteristic
126C2×C13×C4⋊C4D411yescharacteristic
127C2×C13×C4⋊C4C2311yescharacteristic
128C2×C13×C4⋊C4C2311yescharacteristic
129C2×C13×C22⋊C4—21no—
130C2×C13×C22⋊C4—21no—
131C2×C13×C22⋊C4—21no—
132C2×C13×C22⋊C4—21no—
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—
140C2×#6107C2314yes—
141#88196—44no—
142C2×#6106C2314yes—
143C2×#6105C2314yes—
144#88186—44no—
145C2×#6104C2314yes—
146#88184—21no—
147#88184—21no—
148#88184C2312yes—
149#88184C2312yes—
150#88183—22no—
151C4×C22⋊D13—22no—
152C4×C22⋊D13—22no—
153C4×C22⋊D13—22no—
154C4×C22⋊D13—22no—
155#88180C2312yes—
156#88178—21no—
157#88178—21no—
158#88178C2312yes—
159#88178C2312yes—
160C2×#6099—44no—
161C2×#6099C2312yes—
162C2×#6099C2312yes—
163C2×#6099C2314yes—
164C22×#1055C2314yes—
165#88152—22no—
166#88152—22no—
167#88150—22no—
168#88150—22no—
169#88148—22no—
170#88148—22no—
171#88143—22no—
172#88143—22no—
173#88139—22no—
174#88139—22no—
175#88138—22no—
176#88138—22no—
177#88137—22no—
178#88137—22no—
179#88133—22no—
180#88133—22no—
181#88129C2312yes—
182#88128C2311yescharacteristic
183C4×D52—21no—
184C4×D52—21no—
185C4×D52C2312yes—
186C4×D52C2312yes—
187#88126—22no—
188C42×D13—22no—
189#88124C2312yes—
190#88123C2311yescharacteristic
191#88123C2311yescharacteristic
192#88123C2311yescharacteristic
193C4×Dic26—21no—
194C4×Dic26—21no—
195C4×Dic26C2312yes—
196C4×Dic26C2312yes—
197#88075C2314yes—
198#88075C2314yes—
199#88072C2314yes—
200#88072C2314yes—
201#88050C2314yes—
202#88050C2314yes—
203#88049C2314yes—
204#88049C2314yes—
205#88048C2314yes—
206#88048C2314yes—
207#88047C2314yes—
208#88047C2314yes—
209C4⋊#1055C2312yes—
210C4⋊#1055C2312yes—
211C4⋊#1055C2312yes—
212C4⋊#1055C2312yes—
213C4⋊#1055C2314yes—
214C4⋊#1055C2314yes—
215#60919—131nomaximal, Sylow
216C24×C13—21no—
217C24×C13C2×D411yescharacteristic
218C2×Q8×C13—21no—
219C2×Q8×C13—24no—
220C2×Q8×C13—22no—
221C2×Q8×C13—22no—
222C2×Q8×C13—82no—
223C2×Q8×C13C2412yes—
224C2×D4×C13—24no—
225C2×D4×C13—21no—
226C2×D4×C13—22no—
227C2×D4×C13—22no—
228C2×D4×C13—82no—
229C2×D4×C13C2412yes—
230C22×C4×C13—22no—
231C22×C4×C13—22no—
232C22×C4×C13—21no—
233C22×C4×C13—21no—
234C22×C4×C13—21no—
235C22×C4×C13—22no—
236C22×C4×C13—22no—
237C22×C4×C13—82no—
238C22×C4×C13C2×D412yes—
239C22×C4×C13C2×D411yescharacteristic
240C22×C4×C13C2×D411yescharacteristic
241C22×C4×C13C2×D411yescharacteristic
242C22×C4×C13C2×D411yescharacteristic
243C22×C4×C13C2×D411yescharacteristic
244C22×C4×C13C2412yes—
245C22×C4×C13C2411yescharacteristic
246C2×C22⋊D13—22no—
247C2×C22⋊D13—22no—
248C2×C22⋊D13—22no—
249#6127—24no—
250#6127—24no—
251C2×D52—21no—
252C2×D52—21no—
253C2×D52C2412yes—
254C2×C4×D13—22no—
255C2×C4×D13—22no—
256C2×C4×D13—22no—
257C2×Dic26—21no—
258C2×Dic26—21no—
259C2×Dic26C2412yes—
260C13×C4⋊C4—22no—
261C13×C4⋊C4—22no—
262C13×C4⋊C4—24no—
263C13×C4⋊C4—24no—
264C13×C4⋊C4—21no—
265C13×C4⋊C4—21no—
266C13×C4⋊C4C2×D412yes—
267C13×C4⋊C4C2×D412yes—
268C13×C4⋊C4C2×D412yes—
269C13×C4⋊C4C2×D412yes—
270C13×C4⋊C4C2412yes—
271C13×C4⋊C4C2412yes—
272C13×C22⋊C4—24no—
273C13×C22⋊C4—22no—
274C13×C22⋊C4—22no—
275C13×C22⋊C4—24no—
276C13×C22⋊C4—24no—
277C13×C22⋊C4—24no—
278C13×C22⋊C4C2×D412yes—
279C13×C22⋊C4C2×D412yes—
280C13×C22⋊C4C2×D412yes—
281C13×C22⋊C4C2×D412yes—
282C42×C13—22no—
283C42×C13—22no—
284C42×C13C2×D411yescharacteristic
285C42×C13C2×D411yescharacteristic
286C42×C13C2×D412yes—
287C42×C13C2412yes—
288C42×C13C2411yescharacteristic
289C42×C13C2411yescharacteristic
290C22⋊Dic13—22no—
291C22⋊Dic13—22no—
292C22⋊Dic13—22no—
293#6107—44no—
294#6106—44no—
295#6105—44no—
296#6104—44no—
297#6103—22no—
298#6103—22no—
299#6103—22no—
300#6103—22no—
301#6103—22no—
302#6103—22no—
303C4⋊Dic13—21no—
304C4⋊Dic13—21no—
305C4⋊Dic13—21no—
306C4⋊Dic13—21no—
307C4⋊Dic13C2412yes—
308C4⋊Dic13C2412yes—
309#6101—22no—
310#6101—22no—
311#6101—22no—
312#6101—22no—
313#6101—22no—
314#6101—22no—
315C4×Dic13—22no—
316C4×Dic13—22no—
317C4×Dic13—22no—
318#6099—24no—
319#6099—24no—
320#6099—44no—
321C2×#1055—44no—
322C2×#1055C2414yes—
323C2×#1055C2414yes—
324#3455—131no—
325C2×#542D1311yescharacteristic, complemented
326#3263—134no—
327#3262—134no—
328#3258—134no—
329#3257—134no—
330#3079—132no—
331#3078—131no—
332#3077—131no—
333#3056—132no—
334#3055—132no—
335#3040—132no—
336#3037—131no—
337#3036—131no—
338#2905—131no—
339C23×C13—22no—
340C23×C13—22no—
341C23×C13—41no—
342C23×C13—41no—
343C23×C13—42no—
344C23×C13—42no—
345C23×C13—42no—
346C23×C13C22×D412yes—
347C23×C13C22×D411yescharacteristic
348C22×D13—22no—
349Q8×C13—22no—
350Q8×C13—22no—
351Q8×C13—42no—
352Q8×C13—84no—
353D4×C13—22no—
354D4×C13—22no—
355D4×C13—42no—
356D4×C13—84no—
357C2×C4×C13—22no—
358C2×C4×C13—24no—
359C2×C4×C13—22no—
360C2×C4×C13—22no—
361C2×C4×C13—22no—
362C2×C4×C13—22no—
363C2×C4×C13—22no—
364C2×C4×C13—41no—
365C2×C4×C13—41no—
366C2×C4×C13—41no—
367C2×C4×C13—41no—
368C2×C4×C13—42no—
369C2×C4×C13—42no—
370C2×C4×C13—42no—
371C2×C4×C13—82no—
372C2×C4×C13—82no—
373C2×C4×C13C22×D412yes—
374C2×C4×C13C22×D412yes—
375C2×C4×C13C22×D411yescharacteristic
376C2×C4×C13C22×D411yescharacteristic
377C2×C4×C13C22×D412yes—
378C2×C4×C13C22×D411yescharacteristic
379C2×C4×C13C22×D411yescharacteristic
380C2×C4×C13C22×D411yescharacteristic
381C2×C4×C13H(5,𝔽2)12yes—
382C2×C4×C132−1+412yes—
383C2×C4×C13C2511yescharacteristic
384C22⋊D13—44no—
385C22⋊D13—82no—
386C22⋊D13—82no—
387C2×Dic13—22no—
388C2×Dic13—22no—
389C2×Dic13—22no—
390D52—22no—
391D52—22no—
392D52—81no—
393D52—81no—
394C4×D13—44no—
395C4×D13—82no—
396C4×D13—82no—
397Dic26—22no—
398Dic26—22no—
399Dic26—81no—
400Dic26—81no—
401#1055—24no—
402#1055—24no—
403C2×#137—132no—
404C2×AGL(1,ℤ/8)—132no—
405C22×M16—132no—
406#542—22no—
407#542—22no—
408#542—132no—
409#542—132no—
410#542C2×D1314yes—
411#542C2×D1314yes—
412#541—132no—
413#540—132no—
414#539—261no—
415#539—261no—
416#538—261no—
417#538—261no—
418#533—131no—
419#532—131no—
420C2×C4⋊Q8C2×D1311yescharacteristic
421#529—262no—
422#529—262no—
423C2×#126—21no—
424C2×#124—21no—
425C2×#124C2×D1311yescharacteristic
426#525—132no—
427C2×#123—21no—
428C2×C22⋊Q8—21no—
429C2×C22⋊Q8C2×D1311yescharacteristic
430C2×#121C2×D1311yescharacteristic
431C4×#41—132no—
432C2×C4×Q8C2×D1311yescharacteristic
433C2×C4×D4C2×D1311yescharacteristic
434C2×#117C2×D1311yescharacteristic
435#479—134no—
436#478—134no—
437#477—134no—
438#477—132no—
439#476—134no—
440#476—132no—
441#475—134no—
442#475—132no—
443#474—134no—
444#474—132no—
445#470—134no—
446#469—134no—
447#468—134no—
448#468—134no—
449#467—134no—
450#466—134no—
451#465—134no—
452#465—134no—
453#464—134no—
454#464—134no—
455#464—134no—
456#463—134no—
457#463—134no—
458#463—134no—
459#462—132no—
460#461—132no—
461#460—132no—
462#459—132no—
463#428—132no—
464#428—132no—
465#424—134no—
466#424—134no—
467#423—131no—
468#423—131no—
469#423—132no—
470#419—132no—
471#418—132no—
472#417—132no—
473#417—132no—
474C22×C13—21no—
475C22×C13—21no—
476C22×C13—22no—
477C22×C13—22no—
478C22×C13—22no—
479C22×C13—42no—
480C22×C13—42no—
481C22×C13—42no—
482C22×C13—82no—
483C22×C13—84no—
484C22×C13#53712yes—
485C22×C13C23×D411yescharacteristic
486C2×D13—42no—
487C2×D13—42no—
488C2×D13—42no—
489C4×C13—21no—
490C4×C13—22no—
491C4×C13—21no—
492C4×C13—21no—
493C4×C13—22no—
494C4×C13—21no—
495C4×C13—22no—
496C4×C13—42no—
497C4×C13—42no—
498C4×C13—42no—
499C4×C13#53712yes—
500C4×C13C2×H(5,𝔽2)11yescharacteristic
501C4×C13C2×2−1+411yescharacteristic
502Dic13—42no—
503Dic13—42no—
504Dic13—42no—
505C2×#41—132no—
506C22×Q8—21no—
507C22×Q8C22×D1311yescharacteristic
508C22×D4—21no—
509C22×D4C22×D1311yescharacteristic
510C23×C4—21no—
511C23×C4C22×D1311yescharacteristic
512#137—524no—
513AGL(1,ℤ/8)—524no—
514C2×Q16—134no—
515C2×SD16—134no—
516C2×SD16—134no—
517C2×D8—134no—
518C2×M16—132no—
519C2×M16—132no—
520C2×M16—134no—
521C2×M16—524no—
522C22×C8—134no—
523C4⋊Q8—22no—
524C4⋊Q8—131no—
525C4⋊Q8—131no—
526C4⋊Q8—131no—
527C4⋊Q8C22×D1314yes—
528#127—131no—
529#126—24no—
530#126—24no—
531#126—262no—
532#126—262no—
533#126—262no—
534#126—262no—
535#125—132no—
536#125—262no—
537#125—262no—
538#124—24no—
539#124—24no—
540#124—22no—
541#124—132no—
542#124—262no—
543#124—262no—
544#124C22×D1314yes—
545#123—24no—
546#123—24no—
547#123—262no—
548#123—262no—
549#123—262no—
550#123—262no—
551#123—262no—
552C22⋊Q8—22no—
553C22⋊Q8—24no—
554C22⋊Q8—24no—
555C22⋊Q8—132no—
556C22⋊Q8—132no—
557C22⋊Q8—261no—
558C22⋊Q8—261no—
559C22⋊Q8—262no—
560C22⋊Q8—262no—
561C22⋊Q8C22×D1314yes—
562#121—22no—
563#121—132no—
564#121—132no—
565#121—261no—
566#121—261no—
567#121—262no—
568#121—262no—
569#121C22×D1314yes—
570#120—262no—
571C4×Q8—21no—
572C4×Q8—21no—
573C4×Q8—132no—
574C4×Q8—132no—
575C4×Q8—261no—
576C4×Q8—261no—
577C4×Q8C22×D1312yes—
578C4×Q8C22×D1312yes—
579C4×D4—21no—
580C4×D4—21no—
581C4×D4—132no—
582C4×D4—132no—
583C4×D4—262no—
584C4×D4—262no—
585C4×D4—262no—
586C4×D4—262no—
587C4×D4—261no—
588C4×D4—261no—
589C4×D4C22×D1312yes—
590C4×D4C22×D1312yes—
591#117—132no—
592#117—262no—
593#117C22⋊D1312yes—
594#117C22⋊D1312yes—
595#117C22×D1312yes—
596#117C22×D1312yes—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4C22⋊D1311yescharacteristic
601C2×C4⋊C4C22⋊D1311yescharacteristic
602C2×C4⋊C4C22×D1311yescharacteristic
603C2×C4⋊C4C22×D1311yescharacteristic
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—21no—
609C2×C22⋊C4C22⋊D1311yescharacteristic
610C2×C22⋊C4C22⋊D1311yescharacteristic
611C2×C42—21no—
612C2×C42—262no—
613C2×C42C22×D1311yescharacteristic
614C2×C42C22×D1311yescharacteristic
615#107—134no—
616#107—134no—
617#106—134no—
618#106—134no—
619C4⋊C8—132no—
620C4⋊C8—132no—
621C4⋊C8—132no—
622C4⋊C8—134no—
623C4⋊C8—134no—
624C4⋊C8—132no—
625#103—134no—
626#103—134no—
627#103—134no—
628#103—134no—
629#102—134no—
630#102—134no—
631#102—134no—
632#102—134no—
633C2×C13—22no—
634C2×C13—42no—
635C2×C13—82no—
636C2×C13C2×#53711yescharacteristic
637C2×C13#358511yescharacteristic
638C2×C13#358611yescharacteristic
639D13—82no—
640C24—21no—
641C24C2×C22⋊D1311yescharacteristic
642#41—264no—
643#41—264no—
644C2×Q8—21no—
645C2×Q8—24no—
646C2×Q8—22no—
647C2×Q8—22no—
648C2×Q8—82no—
649C2×Q8—132no—
650C2×Q8—261no—
651C2×Q8—261no—
652C2×Q8C23×D1312yes—
653C2×D4—24no—
654C2×D4—22no—
655C2×D4—22no—
656C2×D4—21no—
657C2×D4—82no—
658C2×D4—132no—
659C2×D4—262no—
660C2×D4—262no—
661C2×D4—262no—
662C2×D4—261no—
663C2×D4—261no—
664C2×D4C23×D1312yes—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—82no—
673C22×C4—262no—
674C22×C4—262no—
675C22×C4—262no—
676C22×C4C2×C22⋊D1311yescharacteristic
677C22×C4C2×C22⋊D1312yes—
678C22×C4C2×C22⋊D1311yescharacteristic
679C22×C4C2×C22⋊D1311yescharacteristic
680C22×C4C2×C22⋊D1311yescharacteristic
681C22×C4C2×C22⋊D1311yescharacteristic
682C22×C4C23×D1312yes—
683C22×C4C23×D1311yescharacteristic
684Q16—524no—
685SD16—524no—
686SD16—524no—
687D8—524no—
688M16—264no—
689M16—264no—
690M16—524no—
691C2×C8—134no—
692C2×C8—134no—
693C2×C8—524no—
694C4⋊C4—22no—
695C4⋊C4—22no—
696C4⋊C4—24no—
697C4⋊C4—24no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—132no—
701C4⋊C4—132no—
702C4⋊C4—262no—
703C4⋊C4—262no—
704C4⋊C4—261no—
705C4⋊C4—261no—
706C4⋊C4—262no—
707C4⋊C4—262no—
708C4⋊C4—262no—
709C4⋊C4—262no—
710C4⋊C4—261no—
711C4⋊C4—261no—
712C4⋊C4C2×C22⋊D1312yes—
713C4⋊C4C2×C22⋊D1312yes—
714C4⋊C4C2×C22⋊D1312yes—
715C4⋊C4C2×C22⋊D1312yes—
716C4⋊C4C23×D1312yes—
717C4⋊C4C23×D1312yes—
718C22⋊C4—24no—
719C22⋊C4—22no—
720C22⋊C4—22no—
721C22⋊C4—24no—
722C22⋊C4—24no—
723C22⋊C4—24no—
724C22⋊C4—262no—
725C22⋊C4—262no—
726C22⋊C4—262no—
727C22⋊C4—262no—
728C22⋊C4—262no—
729C22⋊C4—262no—
730C22⋊C4—262no—
731C22⋊C4—262no—
732C22⋊C4—262no—
733C22⋊C4C2×C22⋊D1312yes—
734C22⋊C4C2×C22⋊D1312yes—
735C22⋊C4C2×C22⋊D1312yes—
736C22⋊C4C2×C22⋊D1312yes—
737C42—22no—
738C42—22no—
739C42—262no—
740C42—262no—
741C42—262no—
742C42C2×C22⋊D1312yes—
743C42C2×C22⋊D1311yescharacteristic
744C42C2×C22⋊D1311yescharacteristic
745C42C23×D1312yes—
746C42C23×D1311yescharacteristic
747C42C23×D1311yescharacteristic
748C13#6091911yescharacteristic, complemented, Sylow
749C23—22no—
750C23—22no—
751C23—41no—
752C23—41no—
753C23—42no—
754C23—42no—
755C23—42no—
756C23—262no—
757C23C22×C22⋊D1312yes—
758C23C22×C22⋊D1311yescharacteristic
759Q8—22no—
760Q8—22no—
761Q8—42no—
762Q8—84no—
763Q8—262no—
764Q8—262no—
765Q8—1041no—
766Q8—1041no—
767D4—22no—
768D4—22no—
769D4—42no—
770D4—84no—
771D4—262no—
772D4—262no—
773D4—524no—
774D4—1041no—
775D4—1041no—
776D4—1042no—
777D4—1042no—
778C2×C4—22no—
779C2×C4—24no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—82no—
793C2×C4—82no—
794C2×C4—262no—
795C2×C4—262no—
796C2×C4—262no—
797C2×C4—524no—
798C2×C4—1042no—
799C2×C4—1042no—
800C2×C4#8825612yes—
801C2×C4#8825712yes—
802C2×C4C22×C22⋊D1311yescharacteristic
803C2×C4C22×C22⋊D1311yescharacteristic
804C2×C4C22×C22⋊D1312yes—
805C2×C4C22×C22⋊D1312yes—
806C2×C4C22×C22⋊D1311yescharacteristic
807C2×C4C22×C22⋊D1311yescharacteristic
808C2×C4C22×C22⋊D1312yes—
809C2×C4C22×C22⋊D1311yescharacteristic
810C2×C4C24×D1311yescharacteristic
811C8—264no—
812C8—264no—
813C22—21no—
814C22—21no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—42no—
819C22—42no—
820C22—42no—
821C22—82no—
822C22—84no—
823C22—522no—
824C22—522no—
825C22—522no—
826C22#1171953812yes—
827C22C23×C22⋊D1311yescharacteristic
828C4—21no—
829C4—21no—
830C4—22no—
831C4—22no—
832C4—21no—
833C4—21no—
834C4—22no—
835C4—42no—
836C4—42no—
837C4—42no—
838C4—522no—
839C4—522no—
840C4—522no—
841C4#1171953812yes—
842C4C2×#8825611yescharacteristic
843C4C2×#8825711yescharacteristic
844C2—22no—
845C2—42no—
846C2—82no—
847C2—1042no—
848C2C2×#1171953811yescharacteristic
849C2#1312961611yescharacteristic
850C2#1312962311yescharacteristic
subgroupG/H
centerC22C23×C22⋊D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#542C2
socleC22×C13C23×D4
hypercenterC2×#542D13
hypocenterC13#60919
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. #13128226C2semidirect
2. #13126301C2semidirect
3. #13126292C2semidirect
4. #13126262C2semidirect
5. #13126247C2semidirect
6. #13124645C2semidirect
7. #13124641C2semidirect
8. #13124633C2semidirect
9. #13124462C2semidirect
10. #13124451C2semidirect
11. #13124326C2semidirect
12. #13124308C2semidirect
13. #13124300C2semidirect
14. #13123400C2semidirect
15. C2×C13×#542C2semidirect
35. #11719240C22semidirect
36. #11719239C22semidirect
37. #11719239C22semidirect
40. #11719223C22semidirect
50. #11718755C22semidirect
51. #11718752C22semidirect
52. #11718748C22semidirect
53. #11718745C22semidirect
54. #11718718C22semidirect
55. #11718718C22semidirect
56. #11718715C22semidirect
57. #11718715C22semidirect
58. #11718713C22semidirect
59. #11718712C22semidirect
60. #11718710C22semidirect
61. #11718709C22semidirect
66. #11718692C22semidirect
67. #11718689C22semidirect
68. #11718688C22semidirect
69. #11718683C22semidirect
70. #11718682C22semidirect
71. #11718681C22semidirect
72. #11718680C22semidirect
73. #11718677C22semidirect
74. #11718676C22semidirect
75. #11718670C22semidirect
76. #11718669C22semidirect
77. #11718668C22semidirect
78. #11718660C22semidirect
79. #11718660C22semidirect
325. C2×#542D13semidirect
748. C13#60919semidirect

Maximal subgroups

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

subgroupindex
#131282262
#131263012
#131262922
#131262622
#131262472
#131246452
#131246412
#131246332
#131244622
#131244512
#131243262
#131243082
#131243002
#131234002
C2×C13×#5422
#6091913