Finite Group Databasebeta

← #16735099

Subgroups — #16735099

Order 3328.

1780 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13128132C211yesmaximal, characteristic
2C2×#11719175C211yesmaximal, characteristic, complemented
3#13126078C214yesmaximal, complemented
4#13126068C212yesmaximal, complemented
5#13126059C212yesmaximal, complemented
6#13126052C212yesmaximal, complemented
7#13126044C212yesmaximal, complemented
8#13126036C212yesmaximal, complemented
9#13126028C212yesmaximal, complemented
10#13125360C212yesmaximal, complemented
11#13125182C212yesmaximal, complemented
12#13124751C214yesmaximal, complemented
13#13124626C214yesmaximal, complemented
14C2×C13×#432C211yesmaximal, characteristic, complemented
15C22×C42×C13C2211yescharacteristic
16#11719496—21no—
17#11719496—21no—
18#11719496C2212yes—
19C2×#88180C2212yes—
20C2×#88178—21no—
21C2×#88178—21no—
22#11719184—21no—
23#11719184—21no—
24#11719184—21no—
25#11719184—21no—
26#11719184C2212yes—
27#11719184C2212yes—
28#11719182C2211yescharacteristic
29#11719182C2211yescharacteristic
30#11719182C2211yescharacteristic
31C4×#6127—21no—
32C4×#6127—21no—
33C4×#6127C2212yes—
34#11719175—21no—
35#11719175—21no—
36#11719175—21no—
37#11719175—21no—
38#11719175C2212yes—
39#11719175C2212yes—
40#11719175C2212yes—
41#11719175C2212yes—
42#11719175C2211yescharacteristic
43#11719175C2211yescharacteristic
44#11719175C2211yescharacteristic
45C2×#88124C2212yes—
46C2×#88123C2211yescharacteristic
47C2×#88123C2211yescharacteristic
48C2×C4×Dic26—21no—
49C2×C4×Dic26—21no—
50C13×#432C2212yes—
51C13×#432C2212yes—
52C13×#432C2212yes—
53C13×#432C2212yes—
54C2×C13×C4⋊C8C2212yes—
55C2×C13×C22⋊C8C2212yes—
56C2×C13×#97C2212yes—
57#11718774C2218yes—
58#11718767C2218yes—
59#11718512C2214yescomplemented
60#11718511C2214yescomplemented
61#11718508C2218yescomplemented
62#11718507C2214yescomplemented
63#11718503C2214yescomplemented
64#11718490C2218yescomplemented
65#11718398C2218yes—
66#11718397C2214yes—
67#11718396C2214yes—
68#11718384C2218yes—
69#11718383C2214yes—
70#11718382C2214yes—
71#11718375C2214yescomplemented
72#11718375C2214yescomplemented
73#11718374C2214yescomplemented
74#11718364C2214yescomplemented
75#11718363C2214yescomplemented
76#11718363C2214yescomplemented
77#11718363C2214yescomplemented
78#11718363C2214yescomplemented
79C23×C4×C13D411yescharacteristic
80C23×C4×C13D411yescharacteristic
81C23×C4×C13C2311yescharacteristic
82C2×#6127—21no—
83C2×#6127—21no—
84C2×#6127C2312yes—
85C22×Dic26—21no—
86C22×Dic26—21no—
87C22×C8×C13C2314yes—
88C2×C42×C13D411yescharacteristic
89C2×C42×C13D411yescharacteristic
90C2×C42×C13D411yescharacteristic
91C2×C42×C13D411yescharacteristic
92C2×C42×C13D411yescharacteristic
93C2×C42×C13D411yescharacteristic
94C2×C42×C13C2311yescharacteristic
95C2×C42×C13C2311yescharacteristic
96C2×C42×C13C2311yescharacteristic
97C2×C42×C13C2311yescharacteristic
98C2×C42×C13C2311yescharacteristic
99C2×C42×C13C2311yescharacteristic
100#88207—22no—
101C2×C22⋊Dic13—22no—
102#88184—21no—
103#88184—21no—
104#88184—21no—
105#88184—21no—
106#88184C2312yes—
107#88184C2312yes—
108#88183—22no—
109#88183—22no—
110#88183—22no—
111C4×C22⋊D13—22no—
112C4×C22⋊D13—22no—
113C4×C22⋊D13—22no—
114C4×C22⋊D13—22no—
115C4×C22⋊D13—22no—
116C4×C22⋊D13—22no—
117#88180—22no—
118#88180—22no—
119#88180—21no—
120#88180—21no—
121#88180C2314yes—
122#88180C2314yes—
123#88180C2312yes—
124C2×C4⋊Dic13—21no—
125C2×C4⋊Dic13—21no—
126C2×C4⋊Dic13C2312yes—
127C2×C4⋊Dic13C2312yes—
128#88178—22no—
129#88178—22no—
130#88178—22no—
131#88178—22no—
132#88178—22no—
133#88178—22no—
134#88178—22no—
135#88178—22no—
136#88178—21no—
137#88178—21no—
138#88178—21no—
139#88178—21no—
140#88178C2312yes—
141#88178C2312yes—
142C2×#6101—22no—
143C2×#6101—22no—
144C2×C4×Dic13—22no—
145#88130—22no—
146#88130—22no—
147#88129—21no—
148#88129—21no—
149#88129C2312yes—
150#88128C2311yescharacteristic
151C4×D52—21no—
152C4×D52—21no—
153C4×D52—21no—
154C4×D52—21no—
155C4×D52C2312yes—
156C4×D52C2312yes—
157#88126—22no—
158#88126—22no—
159#88126—22no—
160C42×D13—22no—
161#88124—22no—
162#88124—22no—
163#88124—21no—
164#88124—21no—
165#88124C2314yes—
166#88124C2314yes—
167#88124C2312yes—
168#88123—21no—
169#88123—21no—
170#88123—21no—
171#88123—21no—
172#88123C2311yescharacteristic
173#88123C2312yes—
174#88123C2312yes—
175#88123C2312yes—
176#88123C2312yes—
177#88123C2311yescharacteristic
178#88123C2311yescharacteristic
179C4×Dic26—22no—
180C4×Dic26—22no—
181C4×Dic26—22no—
182C4×Dic26—22no—
183C4×Dic26—22no—
184C4×Dic26—22no—
185C4×Dic26—22no—
186C4×Dic26—22no—
187C4×Dic26—21no—
188C4×Dic26—21no—
189C4×Dic26—21no—
190C4×Dic26—21no—
191C4×Dic26C2312yes—
192C4×Dic26C2312yes—
193C13×C4⋊C8C2314yes—
194C13×C4⋊C8C2314yes—
195C13×C22⋊C8C2314yes—
196C13×C22⋊C8C2314yes—
197C13×#97C2314yes—
198C13×#97C2314yes—
199#88061C2318yes—
200#88061C2318yes—
201#88058C2318yes—
202#88058C2318yes—
203#88057C2318yes—
204#88057C2318yes—
205#88056C2318yes—
206#88056C2318yes—
207#60854—131nomaximal, Sylow
208C24×C13C2×D411yescharacteristic
209C22×C4×C13—24no—
210C22×C4×C13—42no—
211C22×C4×C13—42no—
212C22×C4×C13C2×D411yescharacteristic
213C22×C4×C13C2×D411yescharacteristic
214C22×C4×C13C2×D411yescharacteristic
215C22×C4×C13C2×D411yescharacteristic
216C22×C4×C13C2×D411yescharacteristic
217C22×C4×C13C2×D411yescharacteristic
218C22×C4×C13C2×D411yescharacteristic
219C22×C4×C13C2×D411yescharacteristic
220C22×C4×C13C2×D411yescharacteristic
221C22×C4×C13C2×D411yescharacteristic
222C22×C4×C13C2×D411yescharacteristic
223C22×C4×C13C2×D411yescharacteristic
224C22×C4×C13C2×D411yescharacteristic
225C22×C4×C13C2×D411yescharacteristic
226C22×C4×C13C2×D411yescharacteristic
227C22×C4×C13C2411yescharacteristic
228C22×C4×C13C2411yescharacteristic
229C22×C4×C13C2411yescharacteristic
230C2×C22⋊D13—22no—
231C2×C22⋊D13—22no—
232C2×C22⋊D13—22no—
233C22×Dic13—22no—
234C22×Dic13—22no—
235#6127—28no—
236#6127—44no—
237#6127—44no—
238C2×D52—21no—
239C2×D52—21no—
240C2×D52C2412yes—
241C2×C4×D13—22no—
242C2×C4×D13—22no—
243C2×C4×D13—22no—
244C2×Dic26—22no—
245C2×Dic26—22no—
246C2×Dic26—22no—
247C2×Dic26—22no—
248C2×Dic26—21no—
249C2×Dic26—21no—
250C2×Dic26—44no—
251C2×Dic26—44no—
252C2×Dic26C2412yes—
253C2×C8×C13—28no—
254C2×C8×C13C2418yes—
255C42×C13C2×D411yescharacteristic
256C42×C13C2×D411yescharacteristic
257C42×C13C2×D411yescharacteristic
258C42×C13C2×D411yescharacteristic
259C42×C13C2×D411yescharacteristic
260C42×C13C2×D411yescharacteristic
261C42×C13C2×D411yescharacteristic
262C42×C13C2×D411yescharacteristic
263C42×C13C2×D411yescharacteristic
264C42×C13C2×D411yescharacteristic
265C42×C13C2×D411yescharacteristic
266C42×C13C2×D411yescharacteristic
267C42×C13C2411yescharacteristic
268C42×C13C2411yescharacteristic
269C42×C13C2411yescharacteristic
270C42×C13C2411yescharacteristic
271C22⋊Dic13—24no—
272C22⋊Dic13—24no—
273C22⋊Dic13—22no—
274C22⋊Dic13—22no—
275C22⋊Dic13—22no—
276#6103—22no—
277#6103—22no—
278#6103—22no—
279#6103—22no—
280#6103—22no—
281#6103—22no—
282C4⋊Dic13—22no—
283C4⋊Dic13—22no—
284C4⋊Dic13—22no—
285C4⋊Dic13—22no—
286C4⋊Dic13—21no—
287C4⋊Dic13—21no—
288C4⋊Dic13—21no—
289C4⋊Dic13—21no—
290C4⋊Dic13—22no—
291C4⋊Dic13—22no—
292C4⋊Dic13C2412yes—
293C4⋊Dic13C2412yes—
294C4⋊Dic13C2414yes—
295C4⋊Dic13C2414yes—
296#6101—24no—
297#6101—24no—
298#6101—24no—
299#6101—24no—
300#6101—22no—
301#6101—22no—
302#6101—22no—
303#6101—22no—
304#6101—22no—
305#6101—22no—
306C4×Dic13—24no—
307C4×Dic13—24no—
308C4×Dic13—22no—
309C4×Dic13—22no—
310C4×Dic13—22no—
311#3444—131no—
312C2×#533—131no—
313#3240—134no—
314#3239—132no—
315#3238—132no—
316#3237—132no—
317#3236—132no—
318#3235—132no—
319#3234—132no—
320#3162—132no—
321#3135—132no—
322#3091—134no—
323#3076—134no—
324C2×#432D1311yescharacteristic, complemented
325C23×C13—22no—
326C23×C13—22no—
327C23×C13—41no—
328C23×C13C22×D411yescharacteristic
329C23×C13C22×D411yescharacteristic
330C23×C13C22×D411yescharacteristic
331C22×D13—22no—
332C2×C4×C13—22no—
333C2×C4×C13—22no—
334C2×C4×C13—22no—
335C2×C4×C13—22no—
336C2×C4×C13—22no—
337C2×C4×C13—22no—
338C2×C4×C13—22no—
339C2×C4×C13—22no—
340C2×C4×C13—22no—
341C2×C4×C13—22no—
342C2×C4×C13—41no—
343C2×C4×C13—41no—
344C2×C4×C13—41no—
345C2×C4×C13—41no—
346C2×C4×C13—41no—
347C2×C4×C13—41no—
348C2×C4×C13—41no—
349C2×C4×C13C22×D411yescharacteristic
350C2×C4×C13C22×D411yescharacteristic
351C2×C4×C13C22×D411yescharacteristic
352C2×C4×C13C22×D411yescharacteristic
353C2×C4×C13C22×D411yescharacteristic
354C2×C4×C13C22×D411yescharacteristic
355C2×C4×C13C22×D411yescharacteristic
356C2×C4×C13C22×D411yescharacteristic
357C2×C4×C13C22×D411yescharacteristic
358C2×C4×C13C22×D411yescharacteristic
359C2×C4×C13C22×D411yescharacteristic
360C2×C4×C132−1+414yes—
361C2×C4×C13C2511yescharacteristic
362C22⋊D13—44no—
363C22⋊D13—44no—
364C22⋊D13—44no—
365C2×Dic13—24no—
366C2×Dic13—24no—
367C2×Dic13—22no—
368C2×Dic13—22no—
369C2×Dic13—22no—
370C2×Dic13—44no—
371C2×Dic13—44no—
372D52—24no—
373D52—42no—
374D52—42no—
375C4×D13—44no—
376C4×D13—44no—
377C4×D13—44no—
378Dic26—24no—
379Dic26—44no—
380Dic26—44no—
381Dic26—44no—
382Dic26—42no—
383Dic26—42no—
384Dic26—44no—
385C8×C13—28no—
386#533—132no—
387#533—132no—
388#533—131no—
389#533—132no—
390#533—132no—
391#533—131no—
392#533—131no—
393#533—261no—
394#533—261no—
395#533—261no—
396#533—261no—
397#532—131no—
398#532—131no—
399#532—131no—
400C2×C4⋊Q8—131no—
401C2×C4⋊Q8—131no—
402#529—132no—
403#529—132no—
404#529—261no—
405#529—261no—
406#529—261no—
407#529—261no—
408C2×#125—132no—
409#525—132no—
410#525—261no—
411#525—261no—
412C2×C22⋊Q8—261no—
413C2×C22⋊Q8—261no—
414C4×#41—132no—
415C4×#41—261no—
416C4×#41—261no—
417C2×C4×Q8—261no—
418C2×C4×Q8—261no—
419C2×#117—132no—
420C22×C42C2×D1311yescharacteristic
421#501—134no—
422#501—134no—
423#501—134no—
424#501—134no—
425#491—134no—
426#490—134no—
427#489—134no—
428#489—134no—
429#485—138no—
430#484—134no—
431#483—134no—
432#482—138no—
433#481—134no—
434#480—134no—
435#479—138no—
436#478—138no—
437#477—134no—
438#476—134no—
439#475—134no—
440#474—134no—
441#432C2×D1312yes—
442#432C2×D1312yes—
443#432C2×D1312yes—
444#432C2×D1312yes—
445#427—138no—
446C2×C4⋊C8C2×D1312yes—
447#416—138no—
448C2×C22⋊C8C2×D1312yes—
449C2×#97C2×D1312yes—
450C22×C13—21no—
451C22×C13—21no—
452C22×C13—21no—
453C22×C13—21no—
454C22×C13—21no—
455C22×C13—21no—
456C22×C13—21no—
457C22×C13—44no—
458C22×C13#53612yes—
459C22×C13#57512yes—
460C22×C13C23×D411yescharacteristic
461C2×D13—42no—
462C2×D13—42no—
463C2×D13—42no—
464C4×C13—21no—
465C4×C13—21no—
466C4×C13—21no—
467C4×C13—21no—
468C4×C13—21no—
469C4×C13—21no—
470C4×C13—21no—
471C4×C13—21no—
472C4×C13—21no—
473C4×C13#53612yes—
474C4×C13#57512yes—
475C4×C13C2×2−1+412yes—
476Dic13—42no—
477Dic13—44no—
478Dic13—44no—
479Dic13—42no—
480Dic13—42no—
481C2×#41—132no—
482C2×#41—261no—
483C2×#41—261no—
484C22×Q8—261no—
485C22×Q8—261no—
486C23×C4D5211yescharacteristic
487C23×C4D5211yescharacteristic
488C23×C4C22×D1311yescharacteristic
489C22×C8C22×D1314yes—
490C4⋊Q8—132no—
491C4⋊Q8—132no—
492C4⋊Q8—132no—
493C4⋊Q8—132no—
494C4⋊Q8—131no—
495C4⋊Q8—131no—
496C4⋊Q8—131no—
497C4⋊Q8—261no—
498C4⋊Q8—261no—
499C4⋊Q8—261no—
500C4⋊Q8—261no—
501#127—131no—
502#126—262no—
503#126—262no—
504#125—134no—
505#125—134no—
506#125—132no—
507#125—262no—
508#125—262no—
509#125—261no—
510#125—261no—
511#124—132no—
512#124—261no—
513#124—261no—
514#123—262no—
515#123—262no—
516#123—262no—
517C22⋊Q8—132no—
518C22⋊Q8—132no—
519C22⋊Q8—262no—
520C22⋊Q8—262no—
521C22⋊Q8—262no—
522C22⋊Q8—262no—
523C22⋊Q8—262no—
524C22⋊Q8—262no—
525C22⋊Q8—262no—
526C22⋊Q8—262no—
527C22⋊Q8—261no—
528C22⋊Q8—261no—
529C22⋊Q8—261no—
530C22⋊Q8—261no—
531#121—132no—
532#121—132no—
533#121—261no—
534#121—261no—
535#121—261no—
536#121—261no—
537#120—262no—
538C4×Q8—132no—
539C4×Q8—132no—
540C4×Q8—262no—
541C4×Q8—262no—
542C4×Q8—262no—
543C4×Q8—262no—
544C4×Q8—262no—
545C4×Q8—262no—
546C4×Q8—262no—
547C4×Q8—262no—
548C4×Q8—261no—
549C4×Q8—261no—
550C4×Q8—261no—
551C4×Q8—261no—
552C4×D4—132no—
553C4×D4—132no—
554C4×D4—262no—
555C4×D4—262no—
556C4×D4—262no—
557C4×D4—262no—
558C4×D4—262no—
559C4×D4—262no—
560C4×D4—261no—
561C4×D4—261no—
562C4×D4—261no—
563C4×D4—261no—
564#117—134no—
565#117—134no—
566#117—132no—
567#117—262no—
568#117—262no—
569#117—261no—
570#117—261no—
571#117—262no—
572#117—262no—
573#117—262no—
574C2×C4⋊C4—132no—
575C2×C4⋊C4—132no—
576C2×C4⋊C4—262no—
577C2×C4⋊C4—262no—
578C2×C4⋊C4—261no—
579C2×C4⋊C4—261no—
580C2×C22⋊C4—262no—
581C2×C42—262no—
582C2×C42—262no—
583C2×C42D5211yescharacteristic
584C2×C42D5211yescharacteristic
585C2×C42D5211yescharacteristic
586C2×C42D5211yescharacteristic
587C2×C42D5211yescharacteristic
588C2×C42D5211yescharacteristic
589C2×C42C22×D1311yescharacteristic
590C2×C42C22×D1311yescharacteristic
591C2×C42C22×D1311yescharacteristic
592C2×C42C22×D1311yescharacteristic
593C2×C42C22×D1311yescharacteristic
594C2×C42C22×D1311yescharacteristic
595#107—138no—
596#107—138no—
597#106—138no—
598#106—138no—
599C4⋊C8C22×D1314yes—
600C4⋊C8C22×D1314yes—
601#103—138no—
602#103—138no—
603#102—138no—
604#102—138no—
605C22⋊C8C22×D1314yes—
606C22⋊C8C22×D1314yes—
607#97C22×D1314yes—
608#97C22×D1314yes—
609C2×C13—22no—
610C2×C13—22no—
611C2×C13—41no—
612C2×C13C2×#53611yescharacteristic
613C2×C13C2×#57511yescharacteristic
614C2×C13C2×#57511yescharacteristic
615D13—82no—
616C24C2×D5211yescharacteristic
617#41—268no—
618#41—524no—
619#41—524no—
620C2×Q8—132no—
621C2×Q8—261no—
622C2×Q8—261no—
623C2×Q8—262no—
624C2×Q8—262no—
625C2×Q8—262no—
626C2×Q8—262no—
627C2×Q8—524no—
628C2×Q8—524no—
629C2×D4—132no—
630C2×D4—262no—
631C2×D4—262no—
632C2×D4—262no—
633C2×D4—261no—
634C2×D4—261no—
635C22×C4—24no—
636C22×C4—42no—
637C22×C4—42no—
638C22×C4—262no—
639C22×C4—262no—
640C22×C4—262no—
641C22×C4—262no—
642C22×C4—262no—
643C22×C4C2×D5211yescharacteristic
644C22×C4C2×D5211yescharacteristic
645C22×C4C2×D5211yescharacteristic
646C22×C4C2×D5211yescharacteristic
647C22×C4C2×D5211yescharacteristic
648C22×C4C2×D5211yescharacteristic
649C22×C4C2×D5211yescharacteristic
650C22×C4C2×D5211yescharacteristic
651C22×C4C2×D5211yescharacteristic
652C22×C4C2×D5211yescharacteristic
653C22×C4C2×D5211yescharacteristic
654C22×C4C2×D5211yescharacteristic
655C22×C4C2×D5211yescharacteristic
656C22×C4C2×D5211yescharacteristic
657C22×C4C2×D5211yescharacteristic
658C22×C4C23×D1311yescharacteristic
659C22×C4C23×D1311yescharacteristic
660C22×C4C23×D1311yescharacteristic
661C2×C8—28no—
662C2×C8C23×D1318yes—
663C4⋊C4—134no—
664C4⋊C4—134no—
665C4⋊C4—132no—
666C4⋊C4—132no—
667C4⋊C4—262no—
668C4⋊C4—262no—
669C4⋊C4—264no—
670C4⋊C4—264no—
671C4⋊C4—264no—
672C4⋊C4—264no—
673C4⋊C4—262no—
674C4⋊C4—262no—
675C4⋊C4—262no—
676C4⋊C4—262no—
677C4⋊C4—262no—
678C4⋊C4—262no—
679C4⋊C4—261no—
680C4⋊C4—261no—
681C4⋊C4—261no—
682C4⋊C4—261no—
683C4⋊C4—262no—
684C4⋊C4—262no—
685C4⋊C4—262no—
686C4⋊C4—262no—
687C22⋊C4—264no—
688C22⋊C4—264no—
689C22⋊C4—262no—
690C22⋊C4—262no—
691C22⋊C4—262no—
692C22⋊C4—262no—
693C22⋊C4—262no—
694C22⋊C4—262no—
695C22⋊C4—262no—
696C22⋊C4—262no—
697C22⋊C4—262no—
698C42—264no—
699C42—262no—
700C42—262no—
701C42—262no—
702C42—264no—
703C42C2×D5211yescharacteristic
704C42C2×D5211yescharacteristic
705C42C2×D5211yescharacteristic
706C42C2×D5211yescharacteristic
707C42C2×D5211yescharacteristic
708C42C2×D5211yescharacteristic
709C42C2×D5211yescharacteristic
710C42C2×D5211yescharacteristic
711C42C2×D5211yescharacteristic
712C42C2×D5211yescharacteristic
713C42C2×D5211yescharacteristic
714C42C2×D5211yescharacteristic
715C42C23×D1311yescharacteristic
716C42C23×D1311yescharacteristic
717C42C23×D1311yescharacteristic
718C42C23×D1311yescharacteristic
719C13#6085411yescharacteristic, complemented, Sylow
720C23—22no—
721C23—22no—
722C23—41no—
723C23—262no—
724C23C22×D5211yescharacteristic
725C23C22×D5211yescharacteristic
726C23C22×D5211yescharacteristic
727Q8—264no—
728Q8—524no—
729Q8—524no—
730Q8—524no—
731Q8—522no—
732Q8—522no—
733Q8—524no—
734D4—264no—
735D4—522no—
736D4—522no—
737D4—524no—
738D4—524no—
739D4—524no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—262no—
758C2×C4—262no—
759C2×C4—262no—
760C2×C4—264no—
761C2×C4—264no—
762C2×C4—524no—
763C2×C4—524no—
764C2×C4—524no—
765C2×C4—524no—
766C2×C4—524no—
767C2×C4C22×D5211yescharacteristic
768C2×C4C22×D5211yescharacteristic
769C2×C4C22×D5211yescharacteristic
770C2×C4C22×D5211yescharacteristic
771C2×C4C22×D5211yescharacteristic
772C2×C4C22×D5211yescharacteristic
773C2×C4C22×D5211yescharacteristic
774C2×C4C22×D5211yescharacteristic
775C2×C4C22×D5211yescharacteristic
776C2×C4C22×D5211yescharacteristic
777C2×C4C22×D5211yescharacteristic
778C2×C4#8825714yes—
779C2×C4C24×D1311yescharacteristic
780C8—28no—
781C22—21no—
782C22—21no—
783C22—21no—
784C22—21no—
785C22—21no—
786C22—21no—
787C22—21no—
788C22—44no—
789C22—522no—
790C22—522no—
791C22—522no—
792C22#1171923112yes—
793C22#1171945312yes—
794C22C23×D5211yescharacteristic
795C4—21no—
796C4—21no—
797C4—21no—
798C4—21no—
799C4—21no—
800C4—21no—
801C4—21no—
802C4—21no—
803C4—21no—
804C4—522no—
805C4—522no—
806C4—524no—
807C4—524no—
808C4—522no—
809C4#1171923112yes—
810C4#1171945312yes—
811C4C2×#8825712yes—
812C2—22no—
813C2—22no—
814C2—41no—
815C2—1042no—
816C2C2×#1171923111yescharacteristic
817C2C2×#1171945311yescharacteristic
818C2C2×#1171945311yescharacteristic
subgroupG/H
centerC2×C4C22×D52
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#432C2
socleC22×C13C23×D4
prime radical#13128132C2
hypercenterC2×#432D13
hypocenterC13#60854
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ C2×#432

Complements

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

NH ≅ G/Ntype
2. C2×#11719175C2semidirect
3. #13126078C2semidirect
4. #13126068C2semidirect
5. #13126059C2semidirect
6. #13126052C2semidirect
7. #13126044C2semidirect
8. #13126036C2semidirect
9. #13126028C2semidirect
10. #13125360C2semidirect
11. #13125182C2semidirect
12. #13124751C2semidirect
13. #13124626C2semidirect
14. C2×C13×#432C2semidirect
59. #11718512C22semidirect
60. #11718511C22semidirect
61. #11718508C22semidirect
62. #11718507C22semidirect
63. #11718503C22semidirect
64. #11718490C22semidirect
71. #11718375C22semidirect
72. #11718375C22semidirect
73. #11718374C22semidirect
74. #11718364C22semidirect
75. #11718363C22semidirect
76. #11718363C22semidirect
77. #11718363C22semidirect
78. #11718363C22semidirect
324. C2×#432D13semidirect
719. C13#60854semidirect

Maximal subgroups

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

subgroupindex
#131281322
C2×#117191752
#131260782
#131260682
#131260592
#131260522
#131260442
#131260362
#131260282
#131253602
#131251822
#131247512
#131246262
C2×C13×#4322
#6085413