Finite Group Databasebeta

← #16015716

Subgroups — #16015716

Order 3328.

1252 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13128165C211yesmaximal, characteristic
2C2×#11718901C211yesmaximal, characteristic, complemented
3#13116510C212yesmaximal, complemented
4#13116507C212yesmaximal, complemented
5#13116503C214yesmaximal, complemented
6#13116499C214yesmaximal, complemented
7C2×C13×#410C211yesmaximal, characteristic, complemented
8C22×C13×#41C2211yescharacteristic
9C22×#6127C411yescharacteristic, complemented
10C2×C13×#117—21no—
11#11719538—21no—
12#11719538—21no—
13#11719537C412yescomplemented
14#11719537C2212yes—
15#11719535C411yescharacteristic, complemented
16#11719535C2211yescharacteristic
17#11719533—21no—
18#11719533—21no—
19#11719530C411yescharacteristic, complemented
20#11719530C2211yescharacteristic
21#11719521C412yescomplemented
22#11719510C2212yes—
23#11719509—21no—
24#11719509—21no—
25#11719496—21no—
26#11719496—21no—
27C2×#88180—21no—
28C2×#88180C411yescharacteristic, complemented
29C13×#410—21no—
30C13×#410—21no—
31C13×#410C2212yes—
32C13×#410C2212yescomplemented
33C2×C13×#99—21no—
34C2×C13×#99C2212yescomplemented
35#11718901—21no—
36#11718901—21no—
37#11718901C2212yes—
38#11718901C2212yescomplemented
39C2×#88074—21no—
40C2×#88074C2212yescomplemented
41#11718066C2218yescomplemented
42#11718065C2218yescomplemented
43C2×C13×#41—41no—
44C2×C13×#41—41no—
45C2×C13×#41—41no—
46C2×C13×#41—41no—
47C2×C13×#41C2×C411yescharacteristic
48C2×C13×#41C2×C411yescharacteristic
49C2×C13×#41D411yescharacteristic
50C2×C13×#41D411yescharacteristic
51C2×C13×#41D411yescharacteristic
52C2×C13×#41D411yescharacteristic
53C2×C13×#41C2311yescharacteristic
54C2×C13×#41C2311yescharacteristic
55C22×Q8×C13C2×C411yescharacteristic
56C22×D4×C13D411yescharacteristic
57C22×D4×C13D411yescharacteristic
58C22×D4×C13C2311yescharacteristic
59C23×C4×C13C2×C411yescharacteristic
60C23×C4×C13D411yescharacteristic
61C23×C4×C13D411yescharacteristic
62C22×C22⋊D13—21no—
63C2×#6127—21no—
64C2×#6127—21no—
65C2×#6127—41no—
66C2×#6127—41no—
67C2×#6127—41no—
68C2×#6127—41no—
69C2×#6127C2×C412yes—
70C2×#6127C2×C412yescomplemented
71C22×D52C2×C411yescharacteristic, complemented
72C22×C4×D13—21no—
73C22×Dic26C2×C411yescharacteristic, complemented
74C13×#117—22no—
75C13×#117—22no—
76C13×#117—41no—
77C13×#117—41no—
78C2×C13×C4⋊C4—41no—
79C2×C13×C22⋊C4—22no—
80C2×C42×C13—41no—
81#88207—22no—
82#88207—22no—
83C2×C22⋊Dic13—21no—
84C2×C22⋊Dic13—22no—
85#88201C2×C412yescomplemented
86#88201C2×C412yescomplemented
87#88200—22no—
88#88200—22no—
89#88198C2×C412yescomplemented
90#88198C2×C412yescomplemented
91#88194C2×C412yes—
92#88194C2312yes—
93#88193—22no—
94#88193—22no—
95#88193—22no—
96#88193—22no—
97#88192—22no—
98#88192—22no—
99#88191—21no—
100#88191—21no—
101#88191—21no—
102#88191—21no—
103#88190C2×C412yes—
104#88190C2312yes—
105#88189—21no—
106#88189—21no—
107#88189—21no—
108#88189—21no—
109#88184—21no—
110#88184—21no—
111#88184—21no—
112#88184—21no—
113#88183—22no—
114#88183—22no—
115C4×C22⋊D13—22no—
116C4×C22⋊D13—22no—
117C4×C22⋊D13—22no—
118C4×C22⋊D13—22no—
119#88180—21no—
120#88180—21no—
121#88180—22no—
122#88180—22no—
123#88180—41no—
124#88180—41no—
125#88180C2×C412yes—
126#88180C2×C411yescharacteristic, complemented
127#88180C2×C411yescharacteristic, complemented
128C2×C4⋊Dic13—21no—
129C2×C4⋊Dic13—41no—
130#88178—21no—
131#88178—21no—
132#88178—21no—
133#88178—21no—
134C2×C4×Dic13—41no—
135C2×C4×Dic13C2×C412yescomplemented
136C13×#99—22no—
137C13×#99—22no—
138C13×#99—22no—
139C13×#99C2314yes—
140#88074—22no—
141#88074—22no—
142#88074—22no—
143#88074C2314yes—
144#33358—131nomaximal, Sylow
145C24×C13C22⋊C411yescharacteristic
146C24×C13C2×D411yescharacteristic
147C24×C13C2×D411yescharacteristic
148C23×D13—21no—
149C13×#41—41no—
150C13×#41—41no—
151C13×#41—41no—
152C13×#41—41no—
153C13×#41—41no—
154C13×#41—41no—
155C13×#41—41no—
156C13×#41—41no—
157C13×#41—41no—
158C13×#41—41no—
159C13×#41—41no—
160C13×#41—41no—
161C13×#41—41no—
162C13×#41—41no—
163C13×#41—41no—
164C13×#41—41no—
165C2×Q8×C13—41no—
166C2×Q8×C13—41no—
167C2×Q8×C13C22⋊C411yescharacteristic
168C2×Q8×C13C22⋊C411yescharacteristic
169C2×Q8×C13C22×C411yescharacteristic
170C2×Q8×C13C22×C411yescharacteristic
171C2×D4×C13—41no—
172C2×D4×C13—41no—
173C2×D4×C13—41no—
174C2×D4×C13—41no—
175C2×D4×C13—41no—
176C2×D4×C13—41no—
177C2×D4×C13C22⋊C411yescharacteristic
178C2×D4×C13C22⋊C411yescharacteristic
179C2×D4×C13C22⋊C411yescharacteristic
180C2×D4×C13C22⋊C411yescharacteristic
181C2×D4×C13C22×C411yescharacteristic
182C2×D4×C13C2×D411yescharacteristic
183C2×D4×C13C2×D411yescharacteristic
184C2×D4×C13C2×D411yescharacteristic
185C2×D4×C13C2×D411yescharacteristic
186C2×D4×C13C2×D411yescharacteristic
187C2×D4×C13C2×D411yescharacteristic
188C2×D4×C13C2411yescharacteristic
189C22×C4×C13—21no—
190C22×C4×C13—21no—
191C22×C4×C13—21no—
192C22×C4×C13—21no—
193C22×C4×C13—21no—
194C22×C4×C13—21no—
195C22×C4×C13—21no—
196C22×C4×C13—21no—
197C22×C4×C13—21no—
198C22×C4×C13—21no—
199C22×C4×C13—21no—
200C22×C4×C13—21no—
201C22×C4×C13—42no—
202C22×C4×C13C22⋊C411yescharacteristic
203C22×C4×C13C22⋊C411yescharacteristic
204C22×C4×C13C22⋊C411yescharacteristic
205C22×C4×C13C22⋊C411yescharacteristic
206C22×C4×C13C22⋊C411yescharacteristic
207C22×C4×C13C22⋊C411yescharacteristic
208C22×C4×C13C22⋊C411yescharacteristic
209C22×C4×C13C22⋊C411yescharacteristic
210C22×C4×C13C22⋊C411yescharacteristic
211C22×C4×C13C22×C411yescharacteristic
212C22×C4×C13C22×C411yescharacteristic
213C22×C4×C13C22×C411yescharacteristic
214C22×C4×C13C2×D411yescharacteristic
215C22×C4×C13C2×D411yescharacteristic
216C22×C4×C13C2×D411yescharacteristic
217C22×C4×C13C2×D411yescharacteristic
218C2×C22⋊D13—22no—
219C2×C22⋊D13—22no—
220C2×C22⋊D13—22no—
221C2×C22⋊D13—22no—
222C2×C22⋊D13—22no—
223C2×C22⋊D13—22no—
224C2×C22⋊D13—42no—
225C2×C22⋊D13—42no—
226C22×Dic13—21no—
227C22×Dic13—22no—
228C22×Dic13—42no—
229#6127—42no—
230#6127—42no—
231#6127—41no—
232#6127—41no—
233#6127—41no—
234#6127—41no—
235#6127—42no—
236#6127—42no—
237#6127—42no—
238#6127—42no—
239C2×D52—21no—
240C2×D52—41no—
241C2×D52—41no—
242C2×D52C22×C412yes—
243C2×C4×D13—22no—
244C2×C4×D13—22no—
245C2×C4×D13—42no—
246C2×C4×D13—42no—
247C2×Dic26—21no—
248C2×Dic26—41no—
249C2×Dic26—41no—
250C2×Dic26C22×C412yes—
251C13×C4⋊C4—42no—
252C13×C4⋊C4—42no—
253C13×C22⋊C4—24no—
254C13×C22⋊C4—42no—
255C42×C13—42no—
256C42×C13—42no—
257C22⋊Dic13—22no—
258C22⋊Dic13—22no—
259C22⋊Dic13—22no—
260C22⋊Dic13—21no—
261C22⋊Dic13—21no—
262C22⋊Dic13—22no—
263C22⋊Dic13—22no—
264C22⋊Dic13—24no—
265C22⋊Dic13—42no—
266#6103—22no—
267#6103—22no—
268#6103—22no—
269#6103—22no—
270C4⋊Dic13—21no—
271C4⋊Dic13—21no—
272C4⋊Dic13—22no—
273C4⋊Dic13—42no—
274C4⋊Dic13—42no—
275#6101—22no—
276#6101—22no—
277#6101—22no—
278#6101—22no—
279C4×Dic13—22no—
280C4×Dic13—42no—
281C4×Dic13—42no—
282C4×Dic13C22×C412yes—
283C4×Dic13C22×C412yes—
284#3449—131no—
285C2×#410—131no—
286C2×#410D1311yescharacteristic, complemented
287#2129—132no—
288#2128—132no—
289#2127—134no—
290#2126—134no—
291C23×C13—21no—
292C23×C13—21no—
293C23×C13—21no—
294C23×C13—21no—
295C23×C13—21no—
296C23×C13—21no—
297C23×C13—81no—
298C23×C13—81no—
299C23×C13—81no—
300C23×C13C2×C22⋊C411yescharacteristic
301C23×C13C2×C22⋊C411yescharacteristic
302C23×C13C2×C22⋊C411yescharacteristic
303C23×C13C2×C22⋊C411yescharacteristic
304C23×C13C2×C22⋊C411yescharacteristic
305C23×C13C22×D411yescharacteristic
306C23×C13C22×D411yescharacteristic
307C22×D13—22no—
308C22×D13—42no—
309C22×D13—82no—
310Q8×C13—41no—
311Q8×C13—41no—
312Q8×C13—41no—
313Q8×C13—41no—
314D4×C13—41no—
315D4×C13—41no—
316D4×C13—41no—
317D4×C13—41no—
318D4×C13—41no—
319D4×C13—41no—
320D4×C13—41no—
321D4×C13—41no—
322D4×C13—41no—
323D4×C13—41no—
324D4×C13—41no—
325D4×C13—41no—
326C2×C4×C13—21no—
327C2×C4×C13—21no—
328C2×C4×C13—21no—
329C2×C4×C13—21no—
330C2×C4×C13—21no—
331C2×C4×C13—21no—
332C2×C4×C13—21no—
333C2×C4×C13—21no—
334C2×C4×C13—21no—
335C2×C4×C13—21no—
336C2×C4×C13—21no—
337C2×C4×C13—21no—
338C2×C4×C13—21no—
339C2×C4×C13—21no—
340C2×C4×C13—21no—
341C2×C4×C13—21no—
342C2×C4×C13—21no—
343C2×C4×C13—21no—
344C2×C4×C13—21no—
345C2×C4×C13—21no—
346C2×C4×C13—21no—
347C2×C4×C13—21no—
348C2×C4×C13—21no—
349C2×C4×C13—21no—
350C2×C4×C13—21no—
351C2×C4×C13—21no—
352C2×C4×C13—21no—
353C2×C4×C13—21no—
354C2×C4×C13—21no—
355C2×C4×C13—21no—
356C2×C4×C13—44no—
357C2×C4×C13—84no—
358C2×C4×C13#9911yescharacteristic
359C2×C4×C13#9911yescharacteristic
360C2×C4×C13#9911yescharacteristic
361C2×C4×C13#9911yescharacteristic
362C2×C4×C13C2×C22⋊C411yescharacteristic
363C2×C4×C13C2×C22⋊C411yescharacteristic
364C2×C4×C13C2×C22⋊C411yescharacteristic
365C2×C4×C13C2×C22⋊C411yescharacteristic
366C2×C4×C13C2×C22⋊C411yescharacteristic
367C2×C4×C13C2×C22⋊C411yescharacteristic
368C2×C4×C13C2×C22⋊C411yescharacteristic
369C2×C4×C13C23×C411yescharacteristic
370C22⋊D13—44no—
371C22⋊D13—42no—
372C22⋊D13—42no—
373C22⋊D13—82no—
374C22⋊D13—82no—
375C22⋊D13—82no—
376C22⋊D13—82no—
377C2×Dic13—22no—
378C2×Dic13—22no—
379C2×Dic13—22no—
380C2×Dic13—42no—
381C2×Dic13—44no—
382C2×Dic13—82no—
383C2×Dic13—84no—
384D52—42no—
385D52—41no—
386D52—41no—
387C4×D13—44no—
388C4×D13—42no—
389C4×D13—42no—
390Dic26—41no—
391Dic26—41no—
392Dic26—42no—
393C22×#41—131no—
394C22×#41C2×D1311yescharacteristic
395#537—261no—
396#537—261no—
397#536—131no—
398#536—131no—
399#536—132no—
400#535—131no—
401#535—131no—
402#535—132no—
403#534—261no—
404#534—261no—
405#532—132no—
406#532—132no—
407#525—261no—
408#525—261no—
409#525—261no—
410#525—261no—
411C2×#117—21no—
412C2×#117—131no—
413C2×#117—261no—
414#410—21no—
415#410—21no—
416#410—132no—
417#410—132no—
418#410—261no—
419#410—261no—
420#410C2×D1312yes—
421#410C2×D1312yescomplemented
422C2×#99—21no—
423C2×#99—132no—
424C2×#99—261no—
425C2×#99C2×D1312yescomplemented
426#354—138no—
427#353—138no—
428C22×C13—21no—
429C22×C13—21no—
430C22×C13—21no—
431C22×C13—21no—
432C22×C13—21no—
433C22×C13—21no—
434C22×C13—41no—
435C22×C13—41no—
436C22×C13—41no—
437C22×C13—41no—
438C22×C13—41no—
439C22×C13—41no—
440C22×C13—41no—
441C22×C13—42no—
442C22×C13—42no—
443C22×C13—81no—
444C22×C13—81no—
445C22×C13—81no—
446C22×C13—81no—
447C22×C13C2×#9911yescharacteristic
448C22×C13C2×#9911yescharacteristic
449C22×C13C22×C22⋊C411yescharacteristic
450C2×D13—42no—
451C2×D13—42no—
452C2×D13—42no—
453C2×D13—84no—
454C4×C13—21no—
455C4×C13—21no—
456C4×C13—21no—
457C4×C13—21no—
458C4×C13—21no—
459C4×C13—21no—
460C4×C13—84no—
461C4×C13C2×#9911yescharacteristic
462C4×C13C2×#9911yescharacteristic
463C4×C13C2×#9911yescharacteristic
464C4×C13C2×#9911yescharacteristic
465Dic13—42no—
466Dic13—42no—
467Dic13—42no—
468Dic13—84no—
469C2×#41—41no—
470C2×#41—41no—
471C2×#41—41no—
472C2×#41—41no—
473C2×#41—132no—
474C2×#41—132no—
475C2×#41—261no—
476C2×#41—261no—
477C2×#41—521no—
478C2×#41—521no—
479C2×#41—521no—
480C2×#41—521no—
481C2×#41C4×D1311yescharacteristic
482C2×#41C4×D1311yescharacteristic
483C2×#41D5211yescharacteristic
484C2×#41D5211yescharacteristic
485C2×#41C22⋊D1311yescharacteristic
486C2×#41C22⋊D1311yescharacteristic
487C2×#41C22×D1311yescharacteristic
488C2×#41C22×D1311yescharacteristic
489C22×Q8—131no—
490C22×Q8C4×D1311yescharacteristic
491C22×D4—131no—
492C22×D4—261no—
493C22×D4D5211yescharacteristic
494C22×D4C22⋊D1311yescharacteristic
495C22×D4C22×D1311yescharacteristic
496C23×C4—261no—
497C23×C4C4×D1311yescharacteristic
498C23×C4D5211yescharacteristic
499C23×C4C22⋊D1311yescharacteristic
500C4⋊Q8—132no—
501C4⋊Q8—132no—
502#127—132no—
503#127—132no—
504#124—132no—
505#124—132no—
506#124—132no—
507#124—132no—
508#123—261no—
509#123—261no—
510#123—261no—
511#123—261no—
512#123—262no—
513#123—262no—
514C22⋊Q8—262no—
515C22⋊Q8—262no—
516C22⋊Q8—261no—
517C22⋊Q8—261no—
518C22⋊Q8—261no—
519C22⋊Q8—261no—
520#121—262no—
521#121—262no—
522#121—262no—
523#121—262no—
524#121—262no—
525#121—262no—
526#121—261no—
527#121—261no—
528#121—261no—
529#121—261no—
530#120—262no—
531#120—262no—
532#120—261no—
533#120—261no—
534#120—261no—
535#120—261no—
536C4×D4—262no—
537C4×D4—262no—
538C4×D4—262no—
539C4×D4—262no—
540#117—22no—
541#117—22no—
542#117—41no—
543#117—41no—
544#117—132no—
545#117—131no—
546#117—131no—
547#117—261no—
548#117—261no—
549#117—262no—
550#117—262no—
551#117—521no—
552#117—521no—
553C2×C4⋊C4—41no—
554C2×C4⋊C4—261no—
555C2×C4⋊C4—521no—
556C2×C22⋊C4—22no—
557C2×C22⋊C4—261no—
558C2×C22⋊C4—262no—
559C2×C42—41no—
560C2×C42—132no—
561C2×C42—521no—
562#99—22no—
563#99—22no—
564#99—22no—
565#99—134no—
566#99—262no—
567#99—262no—
568#99—262no—
569#99C22×D1314yes—
570C2×C13—21no—
571C2×C13—21no—
572C2×C13—21no—
573C2×C13—41no—
574C2×C13—41no—
575C2×C13—41no—
576C2×C13—41no—
577C2×C13—41no—
578C2×C13—41no—
579C2×C13C22×#9911yescharacteristic
580D13—82no—
581C24—261no—
582C24#610311yescharacteristic
583C24C2×D5211yescharacteristic
584C24C2×C22⋊D1311yescharacteristic
585#41—41no—
586#41—41no—
587#41—41no—
588#41—41no—
589#41—41no—
590#41—41no—
591#41—41no—
592#41—41no—
593#41—41no—
594#41—41no—
595#41—41no—
596#41—41no—
597#41—41no—
598#41—41no—
599#41—41no—
600#41—41no—
601#41—522no—
602#41—522no—
603#41—522no—
604#41—522no—
605#41—522no—
606#41—522no—
607#41—521no—
608#41—521no—
609#41—521no—
610#41—521no—
611C2×Q8—41no—
612C2×Q8—41no—
613C2×Q8—132no—
614C2×Q8—261no—
615C2×Q8—521no—
616C2×Q8—521no—
617C2×Q8#610311yescharacteristic
618C2×Q8#610311yescharacteristic
619C2×Q8C2×C4×D1311yescharacteristic
620C2×Q8C2×C4×D1311yescharacteristic
621C2×D4—41no—
622C2×D4—41no—
623C2×D4—41no—
624C2×D4—41no—
625C2×D4—41no—
626C2×D4—41no—
627C2×D4—132no—
628C2×D4—262no—
629C2×D4—262no—
630C2×D4—262no—
631C2×D4—262no—
632C2×D4—262no—
633C2×D4—262no—
634C2×D4—261no—
635C2×D4—521no—
636C2×D4—521no—
637C2×D4—522no—
638C2×D4—522no—
639C2×D4#610311yescharacteristic
640C2×D4#610311yescharacteristic
641C2×D4#610311yescharacteristic
642C2×D4#610311yescharacteristic
643C2×D4C2×C4×D1311yescharacteristic
644C2×D4C2×D5211yescharacteristic
645C2×D4C2×D5211yescharacteristic
646C2×D4C2×D5211yescharacteristic
647C2×D4C2×C22⋊D1311yescharacteristic
648C2×D4C2×C22⋊D1311yescharacteristic
649C2×D4C2×C22⋊D1311yescharacteristic
650C2×D4C23×D1311yescharacteristic
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—42no—
664C22×C4—261no—
665C22×C4—262no—
666C22×C4—262no—
667C22×C4—262no—
668C22×C4—522no—
669C22×C4—522no—
670C22×C4—522no—
671C22×C4#610311yescharacteristic
672C22×C4#610311yescharacteristic
673C22×C4#610311yescharacteristic
674C22×C4#610311yescharacteristic
675C22×C4#610311yescharacteristic
676C22×C4#610311yescharacteristic
677C22×C4#610311yescharacteristic
678C22×C4#610311yescharacteristic
679C22×C4#610311yescharacteristic
680C22×C4C2×C4×D1311yescharacteristic
681C22×C4C2×C4×D1311yescharacteristic
682C22×C4C2×C4×D1311yescharacteristic
683C22×C4C2×D5211yescharacteristic
684C22×C4C2×D5211yescharacteristic
685C22×C4C2×C22⋊D1311yescharacteristic
686C22×C4C2×C22⋊D1311yescharacteristic
687C4⋊C4—42no—
688C4⋊C4—42no—
689C4⋊C4—262no—
690C4⋊C4—261no—
691C4⋊C4—261no—
692C4⋊C4—262no—
693C4⋊C4—262no—
694C4⋊C4—262no—
695C4⋊C4—262no—
696C4⋊C4—522no—
697C4⋊C4—522no—
698C22⋊C4—24no—
699C22⋊C4—42no—
700C22⋊C4—261no—
701C22⋊C4—261no—
702C22⋊C4—262no—
703C22⋊C4—262no—
704C22⋊C4—262no—
705C22⋊C4—262no—
706C22⋊C4—262no—
707C22⋊C4—262no—
708C22⋊C4—262no—
709C22⋊C4—262no—
710C22⋊C4—262no—
711C22⋊C4—264no—
712C22⋊C4—522no—
713C42—42no—
714C42—42no—
715C42—132no—
716C42—132no—
717C42—262no—
718C42—522no—
719C42—522no—
720C13#3335811yescharacteristic, complemented, Sylow
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—81no—
728C23—81no—
729C23—81no—
730C23—262no—
731C23—522no—
732C23—1042no—
733C23C2×#610311yescharacteristic
734C23C2×#610311yescharacteristic
735C23C2×#610311yescharacteristic
736C23C2×#610311yescharacteristic
737C23C2×#610311yescharacteristic
738C23C22×D5211yescharacteristic
739C23C22×C22⋊D1311yescharacteristic
740Q8—41no—
741Q8—41no—
742Q8—41no—
743Q8—41no—
744Q8—522no—
745Q8—521no—
746Q8—521no—
747D4—41no—
748D4—41no—
749D4—41no—
750D4—41no—
751D4—41no—
752D4—41no—
753D4—41no—
754D4—41no—
755D4—41no—
756D4—41no—
757D4—41no—
758D4—41no—
759D4—522no—
760D4—524no—
761D4—522no—
762D4—522no—
763D4—521no—
764D4—521no—
765D4—1042no—
766D4—1042no—
767D4—1042no—
768D4—1042no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—44no—
800C2×C4—84no—
801C2×C4—262no—
802C2×C4—262no—
803C2×C4—262no—
804C2×C4—524no—
805C2×C4—522no—
806C2×C4—522no—
807C2×C4—522no—
808C2×C4—524no—
809C2×C4—1042no—
810C2×C4—1044no—
811C2×C4#8804611yescharacteristic
812C2×C4#8804611yescharacteristic
813C2×C4#8804611yescharacteristic
814C2×C4#8804611yescharacteristic
815C2×C4C2×#610311yescharacteristic
816C2×C4C2×#610311yescharacteristic
817C2×C4C2×#610311yescharacteristic
818C2×C4C2×#610311yescharacteristic
819C2×C4C2×#610311yescharacteristic
820C2×C4C2×#610311yescharacteristic
821C2×C4C2×#610311yescharacteristic
822C2×C4C22×C4×D1311yescharacteristic
823C22—21no—
824C22—21no—
825C22—21no—
826C22—21no—
827C22—21no—
828C22—21no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—42no—
837C22—42no—
838C22—81no—
839C22—81no—
840C22—81no—
841C22—81no—
842C22—522no—
843C22—522no—
844C22—522no—
845C22—1044no—
846C22C2×#8804611yescharacteristic
847C22C2×#8804611yescharacteristic
848C22C22×#610311yescharacteristic
849C4—21no—
850C4—21no—
851C4—21no—
852C4—21no—
853C4—21no—
854C4—21no—
855C4—84no—
856C4—522no—
857C4—522no—
858C4—522no—
859C4—1044no—
860C4C2×#8804611yescharacteristic
861C4C2×#8804611yescharacteristic
862C4C2×#8804611yescharacteristic
863C4C2×#8804611yescharacteristic
864C2—21no—
865C2—21no—
866C2—21no—
867C2—41no—
868C2—41no—
869C2—41no—
870C2—41no—
871C2—41no—
872C2—41no—
873C2—1042no—
874C2C22×#8804611yescharacteristic
subgroupG/H
centerC4C2×#88046
commutatorC2×C4×C13C23×C4
FrattiniC2×D4C23×D13
FittingC2×C13×#410C2
socleC2×C13C22×#99
prime radical#13128165C2
cosocleC2×D4×C13C24
hypercenterC2×#410D13
hypocenterC13#33358
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C22×C4 ◁ C22×#41 ◁ C2×#410

Complements

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

NH ≅ G/Ntype
2. C2×#11718901C2semidirect
3. #13116510C2semidirect
4. #13116507C2semidirect
5. #13116503C2semidirect
6. #13116499C2semidirect
7. C2×C13×#410C2semidirect
9. C22×#6127C4semidirect
13. #11719537C4semidirect
15. #11719535C4semidirect
19. #11719530C4semidirect
21. #11719521C4semidirect
28. C2×#88180C4semidirect
32. C13×#410C22semidirect
34. C2×C13×#99C22semidirect
38. #11718901C22semidirect
40. C2×#88074C22semidirect
41. #11718066C22semidirect
42. #11718065C22semidirect
70. C2×#6127C2×C4semidirect
71. C22×D52C2×C4semidirect
73. C22×Dic26C2×C4semidirect
85. #88201C2×C4semidirect
86. #88201C2×C4semidirect
89. #88198C2×C4semidirect
90. #88198C2×C4semidirect
126. #88180C2×C4semidirect
127. #88180C2×C4semidirect
135. C2×C4×Dic13C2×C4semidirect
286. C2×#410D13semidirect
421. #410C2×D13semidirect
425. C2×#99C2×D13semidirect
720. C13#33358semidirect

Maximal subgroups

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

subgroupindex
#131281652
C2×#117189012
#131165102
#131165072
#131165032
#131164992
C2×C13×#4102
#3335813