Finite Group Databasebeta

← #16735016

Subgroups — #16735016

Order 3328.

1800 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13128132C211yesmaximal, characteristic
2C2×#11719175C211yesmaximal, characteristic, complemented
3#13126017C214yesmaximal, complemented
4#13126006C214yesmaximal, complemented
5#13125997C212yesmaximal, complemented
6#13125989C211yesmaximal, characteristic, complemented
7#13125982C211yesmaximal, characteristic, complemented
8#13125974C212yesmaximal, complemented
9#13125966C211yesmaximal, characteristic, complemented
10#13125959C211yesmaximal, characteristic, complemented
11#13125350C212yesmaximal, complemented
12#13125159C212yesmaximal, complemented
13#13124751C214yesmaximal, complemented
14#13124626C214yesmaximal, complemented
15C2×C13×#431C211yesmaximal, characteristic, complemented
16C22×C42×C13C2211yescharacteristic
17#11719496—21no—
18#11719496—21no—
19#11719496C2212yes—
20C2×#88180C2212yes—
21C2×#88178—21no—
22C2×#88178—21no—
23#11719184—21no—
24#11719184—21no—
25#11719184—21no—
26#11719184—21no—
27#11719184C2212yes—
28#11719184C2212yes—
29#11719182C2211yescharacteristic
30#11719182C2211yescharacteristic
31#11719182C2211yescharacteristic
32C4×#6127—21no—
33C4×#6127—21no—
34C4×#6127C2212yes—
35#11719175—21no—
36#11719175—21no—
37#11719175—21no—
38#11719175—21no—
39#11719175C2212yes—
40#11719175C2212yes—
41#11719175C2212yes—
42#11719175C2212yes—
43#11719175C2211yescharacteristic
44#11719175C2211yescharacteristic
45#11719175C2211yescharacteristic
46C2×#88124C2212yes—
47C2×#88123C2211yescharacteristic
48C2×#88123C2211yescharacteristic
49C2×C4×Dic26—21no—
50C2×C4×Dic26—21no—
51C13×#431C2211yescharacteristic
52C13×#431C2211yescharacteristic
53C13×#431C2212yes—
54C13×#431C2212yes—
55C13×#431C2212yes—
56C2×C13×C4⋊C8C2212yes—
57C2×C13×C22⋊C8C2212yes—
58C2×C4×C8×C13C2212yes—
59#11718774C2218yes—
60#11718767C2218yes—
61#11718512C2214yescomplemented
62#11718511C2214yescomplemented
63#11718508C2218yescomplemented
64#11718507C2214yescomplemented
65#11718503C2214yescomplemented
66#11718490C2218yescomplemented
67#11718398C2218yes—
68#11718397C2214yes—
69#11718396C2214yes—
70#11718384C2218yes—
71#11718383C2214yes—
72#11718382C2214yes—
73#11718358C2218yescomplemented
74#11718355C2212yescomplemented
75#11718355C2212yescomplemented
76#11718344C2218yescomplemented
77#11718343C2212yescomplemented
78#11718343C2212yescomplemented
79#11718342C2212yescomplemented
80#11718342C2212yescomplemented
81#11718341C2212yescomplemented
82#11718341C2212yescomplemented
83C23×C4×C13D411yescharacteristic
84C23×C4×C13D411yescharacteristic
85C23×C4×C13C2311yescharacteristic
86C2×#6127—21no—
87C2×#6127—21no—
88C2×#6127C2312yes—
89C22×Dic26—21no—
90C22×Dic26—21no—
91C22×C8×C13C2314yes—
92C2×C42×C13D411yescharacteristic
93C2×C42×C13D411yescharacteristic
94C2×C42×C13D411yescharacteristic
95C2×C42×C13D411yescharacteristic
96C2×C42×C13D411yescharacteristic
97C2×C42×C13D411yescharacteristic
98C2×C42×C13C2311yescharacteristic
99C2×C42×C13C2311yescharacteristic
100C2×C42×C13C2311yescharacteristic
101C2×C42×C13C2311yescharacteristic
102C2×C42×C13C2311yescharacteristic
103C2×C42×C13C2311yescharacteristic
104#88207—22no—
105C2×C22⋊Dic13—22no—
106#88184—21no—
107#88184—21no—
108#88184—21no—
109#88184—21no—
110#88184C2312yes—
111#88184C2312yes—
112#88183—22no—
113#88183—22no—
114#88183—22no—
115C4×C22⋊D13—22no—
116C4×C22⋊D13—22no—
117C4×C22⋊D13—22no—
118C4×C22⋊D13—22no—
119C4×C22⋊D13—22no—
120C4×C22⋊D13—22no—
121#88180—22no—
122#88180—22no—
123#88180—21no—
124#88180—21no—
125#88180C2314yes—
126#88180C2314yes—
127#88180C2312yes—
128C2×C4⋊Dic13—21no—
129C2×C4⋊Dic13—21no—
130C2×C4⋊Dic13C2312yes—
131C2×C4⋊Dic13C2312yes—
132#88178—22no—
133#88178—22no—
134#88178—22no—
135#88178—22no—
136#88178—22no—
137#88178—22no—
138#88178—22no—
139#88178—22no—
140#88178—21no—
141#88178—21no—
142#88178—21no—
143#88178—21no—
144#88178C2312yes—
145#88178C2312yes—
146C2×#6101—22no—
147C2×#6101—22no—
148C2×C4×Dic13—22no—
149#88130—22no—
150#88130—22no—
151#88129—21no—
152#88129—21no—
153#88129C2312yes—
154#88128C2311yescharacteristic
155C4×D52—21no—
156C4×D52—21no—
157C4×D52—21no—
158C4×D52—21no—
159C4×D52C2312yes—
160C4×D52C2312yes—
161#88126—22no—
162#88126—22no—
163#88126—22no—
164C42×D13—22no—
165#88124—22no—
166#88124—22no—
167#88124—21no—
168#88124—21no—
169#88124C2314yes—
170#88124C2314yes—
171#88124C2312yes—
172#88123—21no—
173#88123—21no—
174#88123—21no—
175#88123—21no—
176#88123C2311yescharacteristic
177#88123C2312yes—
178#88123C2312yes—
179#88123C2312yes—
180#88123C2312yes—
181#88123C2311yescharacteristic
182#88123C2311yescharacteristic
183C4×Dic26—22no—
184C4×Dic26—22no—
185C4×Dic26—22no—
186C4×Dic26—22no—
187C4×Dic26—22no—
188C4×Dic26—22no—
189C4×Dic26—22no—
190C4×Dic26—22no—
191C4×Dic26—21no—
192C4×Dic26—21no—
193C4×Dic26—21no—
194C4×Dic26—21no—
195C4×Dic26C2312yes—
196C4×Dic26C2312yes—
197C13×C4⋊C8C2314yes—
198C13×C4⋊C8C2312yes—
199C13×C4⋊C8C2312yes—
200C13×C22⋊C8C2312yes—
201C13×C22⋊C8C2312yes—
202C13×C22⋊C8C2314yes—
203C4×C8×C13C2312yes—
204C4×C8×C13C2312yes—
205C4×C8×C13C2314yes—
206#88061C2318yes—
207#88061C2318yes—
208#88058C2318yes—
209#88058C2318yes—
210#88057C2318yes—
211#88057C2318yes—
212#88056C2318yes—
213#88056C2318yes—
214#60846—131nomaximal, Sylow
215C24×C13C2×D411yescharacteristic
216C22×C4×C13—24no—
217C22×C4×C13—24no—
218C22×C4×C13—42no—
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×C13C2×D411yescharacteristic
228C22×C4×C13C2×D411yescharacteristic
229C22×C4×C13C2×D411yescharacteristic
230C22×C4×C13C2×D411yescharacteristic
231C22×C4×C13C2×D411yescharacteristic
232C22×C4×C13C2×D411yescharacteristic
233C22×C4×C13C2×D411yescharacteristic
234C22×C4×C13C2411yescharacteristic
235C22×C4×C13C2411yescharacteristic
236C22×C4×C13C2411yescharacteristic
237C2×C22⋊D13—22no—
238C2×C22⋊D13—22no—
239C2×C22⋊D13—22no—
240C22×Dic13—22no—
241C22×Dic13—22no—
242#6127—28no—
243#6127—44no—
244#6127—44no—
245C2×D52—21no—
246C2×D52—21no—
247C2×D52C2412yes—
248C2×C4×D13—22no—
249C2×C4×D13—22no—
250C2×C4×D13—22no—
251C2×Dic26—22no—
252C2×Dic26—22no—
253C2×Dic26—22no—
254C2×Dic26—22no—
255C2×Dic26—21no—
256C2×Dic26—21no—
257C2×Dic26—44no—
258C2×Dic26—44no—
259C2×Dic26C2412yes—
260C2×C8×C13—28no—
261C2×C8×C13C2414yes—
262C2×C8×C13C2414yes—
263C42×C13C2×D411yescharacteristic
264C42×C13C2×D411yescharacteristic
265C42×C13C2×D411yescharacteristic
266C42×C13C2×D411yescharacteristic
267C42×C13C2×D411yescharacteristic
268C42×C13C2×D411yescharacteristic
269C42×C13C2×D411yescharacteristic
270C42×C13C2×D411yescharacteristic
271C42×C13C2×D411yescharacteristic
272C42×C13C2×D411yescharacteristic
273C42×C13C2×D411yescharacteristic
274C42×C13C2×D411yescharacteristic
275C42×C13C2411yescharacteristic
276C42×C13C2411yescharacteristic
277C42×C13C2411yescharacteristic
278C42×C13C2411yescharacteristic
279C22⋊Dic13—24no—
280C22⋊Dic13—24no—
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—22no—
291C4⋊Dic13—22no—
292C4⋊Dic13—22no—
293C4⋊Dic13—22no—
294C4⋊Dic13—21no—
295C4⋊Dic13—21no—
296C4⋊Dic13—21no—
297C4⋊Dic13—21no—
298C4⋊Dic13—22no—
299C4⋊Dic13—22no—
300C4⋊Dic13C2412yes—
301C4⋊Dic13C2412yes—
302C4⋊Dic13C2414yes—
303C4⋊Dic13C2414yes—
304#6101—24no—
305#6101—24no—
306#6101—24no—
307#6101—24no—
308#6101—22no—
309#6101—22no—
310#6101—22no—
311#6101—22no—
312#6101—22no—
313#6101—22no—
314C4×Dic13—24no—
315C4×Dic13—24no—
316C4×Dic13—22no—
317C4×Dic13—22no—
318C4×Dic13—22no—
319#3444—131no—
320C2×#533—131no—
321#3233—134no—
322#3232—134no—
323#3231—132no—
324#3230—131no—
325#3229—131no—
326#3228—132no—
327#3227—131no—
328#3226—131no—
329#3160—132no—
330#3131—132no—
331#3091—134no—
332#3076—134no—
333C2×#431D1311yescharacteristic, complemented
334C23×C13—22no—
335C23×C13—22no—
336C23×C13—41no—
337C23×C13C22×D411yescharacteristic
338C23×C13C22×D411yescharacteristic
339C23×C13C22×D411yescharacteristic
340C22×D13—22no—
341C2×C4×C13—22no—
342C2×C4×C13—22no—
343C2×C4×C13—22no—
344C2×C4×C13—22no—
345C2×C4×C13—22no—
346C2×C4×C13—22no—
347C2×C4×C13—22no—
348C2×C4×C13—22no—
349C2×C4×C13—22no—
350C2×C4×C13—22no—
351C2×C4×C13—22no—
352C2×C4×C13—22no—
353C2×C4×C13—22no—
354C2×C4×C13—41no—
355C2×C4×C13—41no—
356C2×C4×C13—41no—
357C2×C4×C13#13514yes—
358C2×C4×C13C22×D411yescharacteristic
359C2×C4×C13C22×D411yescharacteristic
360C2×C4×C13C22×D411yescharacteristic
361C2×C4×C13C22×D411yescharacteristic
362C2×C4×C13C22×D411yescharacteristic
363C2×C4×C13C22×D411yescharacteristic
364C2×C4×C13C22×D411yescharacteristic
365C2×C4×C13C22×D411yescharacteristic
366C2×C4×C13C22×D411yescharacteristic
367C2×C4×C13C22×D411yescharacteristic
368C2×C4×C13C22×D411yescharacteristic
369C2×C4×C132−1+414yes—
370C2×C4×C13C2511yescharacteristic
371C22⋊D13—44no—
372C22⋊D13—44no—
373C22⋊D13—44no—
374C2×Dic13—24no—
375C2×Dic13—24no—
376C2×Dic13—22no—
377C2×Dic13—22no—
378C2×Dic13—22no—
379C2×Dic13—44no—
380C2×Dic13—44no—
381D52—24no—
382D52—42no—
383D52—42no—
384C4×D13—44no—
385C4×D13—44no—
386C4×D13—44no—
387Dic26—24no—
388Dic26—44no—
389Dic26—44no—
390Dic26—44no—
391Dic26—42no—
392Dic26—44no—
393Dic26—42no—
394C8×C13—24no—
395C8×C13—24no—
396#533—132no—
397#533—132no—
398#533—131no—
399#533—132no—
400#533—132no—
401#533—131no—
402#533—131no—
403#533—261no—
404#533—261no—
405#533—261no—
406#533—261no—
407#532—131no—
408#532—131no—
409#532—131no—
410C2×C4⋊Q8—131no—
411C2×C4⋊Q8—131no—
412#529—132no—
413#529—132no—
414#529—261no—
415#529—261no—
416#529—261no—
417#529—261no—
418C2×#125—132no—
419#525—132no—
420#525—261no—
421#525—261no—
422C2×C22⋊Q8—261no—
423C2×C22⋊Q8—261no—
424C4×#41—132no—
425C4×#41—261no—
426C4×#41—261no—
427C2×C4×Q8—261no—
428C2×C4×Q8—261no—
429C2×#117—132no—
430C22×C42C2×D1311yescharacteristic
431#500—132no—
432#500—132no—
433#499—138no—
434#498—132no—
435#498—132no—
436#488—138no—
437#487—132no—
438#487—132no—
439#486—132no—
440#486—132no—
441#485—138no—
442#484—134no—
443#483—134no—
444#482—138no—
445#481—134no—
446#480—134no—
447#479—138no—
448#478—138no—
449#477—134no—
450#476—134no—
451#475—134no—
452#474—134no—
453#431C2×D1311yescharacteristic
454#431C2×D1311yescharacteristic
455#431C2×D1312yes—
456#431C2×D1312yes—
457#431C2×D1312yes—
458#427—138no—
459C2×C4⋊C8C2×D1312yes—
460#416—138no—
461C2×C22⋊C8C2×D1312yes—
462C2×C4×C8C2×D1312yes—
463C22×C13—21no—
464C22×C13—21no—
465C22×C13—21no—
466C22×C13—21no—
467C22×C13—21no—
468C22×C13—21no—
469C22×C13—21no—
470C22×C13—44no—
471C22×C13#53612yes—
472C22×C13C2×#13512yes—
473C22×C13C23×D411yescharacteristic
474C2×D13—42no—
475C2×D13—42no—
476C2×D13—42no—
477C4×C13—21no—
478C4×C13—21no—
479C4×C13—21no—
480C4×C13—21no—
481C4×C13—21no—
482C4×C13—21no—
483C4×C13—21no—
484C4×C13#53612yes—
485C4×C13C2×#13512yes—
486C4×C13C2×#13512yes—
487C4×C13#57512yes—
488C4×C13C2×2−1+412yes—
489Dic13—42no—
490Dic13—44no—
491Dic13—42no—
492Dic13—44no—
493Dic13—42no—
494C2×#41—132no—
495C2×#41—261no—
496C2×#41—261no—
497C22×Q8—261no—
498C22×Q8—261no—
499C23×C4D5211yescharacteristic
500C23×C4D5211yescharacteristic
501C23×C4C22×D1311yescharacteristic
502C22×C8C22×D1314yes—
503C4⋊Q8—132no—
504C4⋊Q8—132no—
505C4⋊Q8—132no—
506C4⋊Q8—132no—
507C4⋊Q8—131no—
508C4⋊Q8—131no—
509C4⋊Q8—131no—
510C4⋊Q8—261no—
511C4⋊Q8—261no—
512C4⋊Q8—261no—
513C4⋊Q8—261no—
514#127—131no—
515#126—262no—
516#126—262no—
517#125—134no—
518#125—134no—
519#125—132no—
520#125—262no—
521#125—262no—
522#125—261no—
523#125—261no—
524#124—132no—
525#124—261no—
526#124—261no—
527#123—262no—
528#123—262no—
529#123—262no—
530C22⋊Q8—132no—
531C22⋊Q8—132no—
532C22⋊Q8—262no—
533C22⋊Q8—262no—
534C22⋊Q8—262no—
535C22⋊Q8—262no—
536C22⋊Q8—262no—
537C22⋊Q8—262no—
538C22⋊Q8—262no—
539C22⋊Q8—262no—
540C22⋊Q8—261no—
541C22⋊Q8—261no—
542C22⋊Q8—261no—
543C22⋊Q8—261no—
544#121—132no—
545#121—132no—
546#121—261no—
547#121—261no—
548#121—261no—
549#121—261no—
550#120—262no—
551C4×Q8—132no—
552C4×Q8—132no—
553C4×Q8—262no—
554C4×Q8—262no—
555C4×Q8—262no—
556C4×Q8—262no—
557C4×Q8—262no—
558C4×Q8—262no—
559C4×Q8—262no—
560C4×Q8—262no—
561C4×Q8—261no—
562C4×Q8—261no—
563C4×Q8—261no—
564C4×Q8—261no—
565C4×D4—132no—
566C4×D4—132no—
567C4×D4—262no—
568C4×D4—262no—
569C4×D4—262no—
570C4×D4—262no—
571C4×D4—262no—
572C4×D4—262no—
573C4×D4—261no—
574C4×D4—261no—
575C4×D4—261no—
576C4×D4—261no—
577#117—134no—
578#117—134no—
579#117—132no—
580#117—262no—
581#117—262no—
582#117—261no—
583#117—261no—
584#117—262no—
585#117—262no—
586#117—262no—
587C2×C4⋊C4—132no—
588C2×C4⋊C4—132no—
589C2×C4⋊C4—262no—
590C2×C4⋊C4—262no—
591C2×C4⋊C4—261no—
592C2×C4⋊C4—261no—
593C2×C22⋊C4—262no—
594C2×C42—262no—
595C2×C42—262no—
596C2×C42D5211yescharacteristic
597C2×C42D5211yescharacteristic
598C2×C42D5211yescharacteristic
599C2×C42D5211yescharacteristic
600C2×C42D5211yescharacteristic
601C2×C42D5211yescharacteristic
602C2×C42C22×D1311yescharacteristic
603C2×C42C22×D1311yescharacteristic
604C2×C42C22×D1311yescharacteristic
605C2×C42C22×D1311yescharacteristic
606C2×C42C22×D1311yescharacteristic
607C2×C42C22×D1311yescharacteristic
608#107—138no—
609#107—138no—
610#106—138no—
611#106—138no—
612C4⋊C8C22×D1312yes—
613C4⋊C8C22×D1312yes—
614C4⋊C8C22×D1314yes—
615#103—138no—
616#103—138no—
617#102—138no—
618#102—138no—
619C22⋊C8C22×D1312yes—
620C22⋊C8C22×D1312yes—
621C22⋊C8C22×D1314yes—
622C4×C8C22×D1312yes—
623C4×C8C22×D1312yes—
624C4×C8C22×D1314yes—
625C2×C13—22no—
626C2×C13—22no—
627C2×C13—41no—
628C2×C13C2×#53611yescharacteristic
629C2×C13C22×#13511yescharacteristic
630C2×C13C2×#57511yescharacteristic
631D13—82no—
632C24C2×D5211yescharacteristic
633#41—268no—
634#41—524no—
635#41—524no—
636C2×Q8—132no—
637C2×Q8—261no—
638C2×Q8—261no—
639C2×Q8—262no—
640C2×Q8—262no—
641C2×Q8—262no—
642C2×Q8—262no—
643C2×Q8—524no—
644C2×Q8—524no—
645C2×D4—132no—
646C2×D4—262no—
647C2×D4—262no—
648C2×D4—262no—
649C2×D4—261no—
650C2×D4—261no—
651C22×C4—24no—
652C22×C4—24no—
653C22×C4—42no—
654C22×C4—262no—
655C22×C4—262no—
656C22×C4—262no—
657C22×C4—262no—
658C22×C4—262no—
659C22×C4C2×D5211yescharacteristic
660C22×C4C2×D5211yescharacteristic
661C22×C4C2×D5211yescharacteristic
662C22×C4C2×D5211yescharacteristic
663C22×C4C2×D5211yescharacteristic
664C22×C4C2×D5211yescharacteristic
665C22×C4C2×D5211yescharacteristic
666C22×C4C2×D5211yescharacteristic
667C22×C4C2×D5211yescharacteristic
668C22×C4C2×D5211yescharacteristic
669C22×C4C2×D5211yescharacteristic
670C22×C4C2×D5211yescharacteristic
671C22×C4C2×D5211yescharacteristic
672C22×C4C2×D5211yescharacteristic
673C22×C4C2×D5211yescharacteristic
674C22×C4C23×D1311yescharacteristic
675C22×C4C23×D1311yescharacteristic
676C22×C4C23×D1311yescharacteristic
677C2×C8—28no—
678C2×C8C23×D1314yes—
679C2×C8C23×D1314yes—
680C4⋊C4—134no—
681C4⋊C4—134no—
682C4⋊C4—132no—
683C4⋊C4—132no—
684C4⋊C4—262no—
685C4⋊C4—262no—
686C4⋊C4—264no—
687C4⋊C4—264no—
688C4⋊C4—264no—
689C4⋊C4—264no—
690C4⋊C4—262no—
691C4⋊C4—262no—
692C4⋊C4—262no—
693C4⋊C4—262no—
694C4⋊C4—262no—
695C4⋊C4—262no—
696C4⋊C4—261no—
697C4⋊C4—261no—
698C4⋊C4—261no—
699C4⋊C4—261no—
700C4⋊C4—262no—
701C4⋊C4—262no—
702C4⋊C4—262no—
703C4⋊C4—262no—
704C22⋊C4—264no—
705C22⋊C4—264no—
706C22⋊C4—262no—
707C22⋊C4—262no—
708C22⋊C4—262no—
709C22⋊C4—262no—
710C22⋊C4—262no—
711C22⋊C4—262no—
712C22⋊C4—262no—
713C22⋊C4—262no—
714C22⋊C4—262no—
715C42—264no—
716C42—262no—
717C42—262no—
718C42—262no—
719C42—264no—
720C42C2×D5211yescharacteristic
721C42C2×D5211yescharacteristic
722C42C2×D5211yescharacteristic
723C42C2×D5211yescharacteristic
724C42C2×D5211yescharacteristic
725C42C2×D5211yescharacteristic
726C42C2×D5211yescharacteristic
727C42C2×D5211yescharacteristic
728C42C2×D5211yescharacteristic
729C42C2×D5211yescharacteristic
730C42C2×D5211yescharacteristic
731C42C2×D5211yescharacteristic
732C42C23×D1311yescharacteristic
733C42C23×D1311yescharacteristic
734C42C23×D1311yescharacteristic
735C42C23×D1311yescharacteristic
736C13#6084611yescharacteristic, complemented, Sylow
737C23—22no—
738C23—22no—
739C23—41no—
740C23—262no—
741C23C22×D5211yescharacteristic
742C23C22×D5211yescharacteristic
743C23C22×D5211yescharacteristic
744Q8—264no—
745Q8—524no—
746Q8—524no—
747Q8—524no—
748Q8—522no—
749Q8—524no—
750Q8—522no—
751D4—264no—
752D4—524no—
753D4—524no—
754D4—524no—
755D4—522no—
756D4—522no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—262no—
774C2×C4—262no—
775C2×C4—262no—
776C2×C4—264no—
777C2×C4—264no—
778C2×C4—524no—
779C2×C4—524no—
780C2×C4—524no—
781C2×C4—524no—
782C2×C4—524no—
783C2×C4#8815814yes—
784C2×C4C22×D5211yescharacteristic
785C2×C4C22×D5211yescharacteristic
786C2×C4C22×D5211yescharacteristic
787C2×C4C22×D5211yescharacteristic
788C2×C4C22×D5211yescharacteristic
789C2×C4C22×D5211yescharacteristic
790C2×C4C22×D5211yescharacteristic
791C2×C4C22×D5211yescharacteristic
792C2×C4C22×D5211yescharacteristic
793C2×C4C22×D5211yescharacteristic
794C2×C4C22×D5211yescharacteristic
795C2×C4#8825714yes—
796C2×C4C24×D1311yescharacteristic
797C8—24no—
798C8—24no—
799C22—21no—
800C22—21no—
801C22—21no—
802C22—21no—
803C22—21no—
804C22—21no—
805C22—21no—
806C22—44no—
807C22—522no—
808C22—522no—
809C22—522no—
810C22#1171923112yes—
811C22C2×#8815812yes—
812C22C23×D5211yescharacteristic
813C4—21no—
814C4—21no—
815C4—21no—
816C4—21no—
817C4—21no—
818C4—21no—
819C4—21no—
820C4—522no—
821C4—524no—
822C4—522no—
823C4—524no—
824C4—522no—
825C4#1171923112yes—
826C4C2×#8815812yes—
827C4C2×#8815812yes—
828C4#1171945312yes—
829C4C2×#8825712yes—
830C2—22no—
831C2—22no—
832C2—41no—
833C2—1042no—
834C2C2×#1171923111yescharacteristic
835C2C22×#8815811yescharacteristic
836C2C2×#1171945311yescharacteristic
subgroupG/H
centerC2×C4C22×D52
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#431C2
socleC22×C13C23×D4
prime radical#13128132C2
hypercenterC2×#431D13
hypocenterC13#60846
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ C2×#431

Complements

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

NH ≅ G/Ntype
2. C2×#11719175C2semidirect
3. #13126017C2semidirect
4. #13126006C2semidirect
5. #13125997C2semidirect
6. #13125989C2semidirect
7. #13125982C2semidirect
8. #13125974C2semidirect
9. #13125966C2semidirect
10. #13125959C2semidirect
11. #13125350C2semidirect
12. #13125159C2semidirect
13. #13124751C2semidirect
14. #13124626C2semidirect
15. C2×C13×#431C2semidirect
61. #11718512C22semidirect
62. #11718511C22semidirect
63. #11718508C22semidirect
64. #11718507C22semidirect
65. #11718503C22semidirect
66. #11718490C22semidirect
73. #11718358C22semidirect
74. #11718355C22semidirect
75. #11718355C22semidirect
76. #11718344C22semidirect
77. #11718343C22semidirect
78. #11718343C22semidirect
79. #11718342C22semidirect
80. #11718342C22semidirect
81. #11718341C22semidirect
82. #11718341C22semidirect
333. C2×#431D13semidirect
736. C13#60846semidirect

Maximal subgroups

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

subgroupindex
#131281322
C2×#117191752
#131260172
#131260062
#131259972
#131259892
#131259822
#131259742
#131259662
#131259592
#131253502
#131251592
#131247512
#131246262
C2×C13×#4312
#6084613