Finite Group Databasebeta

← #16808223

Subgroups — #16808223

Order 3328.

2042 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13131534C214yesmaximal, complemented
2#13131531C214yesmaximal, complemented
3#13131530C212yesmaximal, complemented
4#13131529C212yesmaximal, complemented
5#13131527C212yesmaximal, complemented
6#13131526C212yesmaximal, complemented
7#13131524C212yesmaximal, complemented
8#13131523C212yesmaximal, complemented
9#13131521C212yesmaximal, complemented
10#13131520C212yesmaximal, complemented
11#13131480C211yesmaximal, characteristic, complemented
12C2×#11719079C211yesmaximal, characteristic, complemented
13#13131421C211yesmaximal, characteristic
14D13⋊#408C211yesmaximal, characteristic
15#13131401C211yesmaximal, characteristic, complemented
16#13131396C211yesmaximal, characteristic, complemented
17#13128036C211yesmaximal, characteristic
18C2×#41×D13C2211yescharacteristic
19C2×D13⋊M16C2211yescharacteristic
20C2×D13⋊M16C2211yescharacteristic
21C22×#6118C2211yescharacteristic
22C22×D13⋊C8C2211yescharacteristic
23C13×#520C411yescharacteristic
24#11719532C411yescharacteristic
25C4×#6131C2212yes—
26#11719277C412yes—
27#11719250C414yes—
28#11719250C412yes—
29C4×#6129C2212yes—
30C4×#6129C2214yes—
31#11719228C411yescharacteristic
32#11719228C412yes—
33D13×#117C2212yes—
34D13×#117C2211yescharacteristic
35#11719209C411yescharacteristic
36#11719209C412yes—
37C2×#88146C2212yes—
38C2×#88146C2211yescharacteristic
39#11719159C2211yescharacteristic
40#11719159C2212yes—
41#11719159C2211yescharacteristic
42#11719147C2211yescharacteristic
43#11719147C2212yes—
44#11719147C2211yescharacteristic
45#11719146C2212yes—
46#11719146C2214yes—
47#11719146C2212yes—
48#11719130C2214yescomplemented
49#11719129C2214yescomplemented
50#11719128C2214yescomplemented
51#11719127C2212yes—
52#11719127C2212yes—
53#11719125C2214yescomplemented
54D13⋊(C22⋊C8)C2212yes—
55D13⋊(C22⋊C8)C2212yes—
56C2×#88112C2212yescomplemented
57#11719119C2214yescomplemented
58C2×C4⋊#1057C2212yescomplemented
59#11719079C2212yes—
60#11719079C2212yes—
61#11719079C2212yes—
62#11719079C2212yes—
63#11719079C2212yescomplemented
64#11719079C2212yescomplemented
65#11719079C2212yescomplemented
66#11719079C2212yescomplemented
67#11719077C2214yescomplemented
68#11719077C2214yescomplemented
69#11719077C2214yescomplemented
70#11719077C2214yescomplemented
71#11719072C2211yescharacteristic
72#11719072C2212yes—
73#11719072C2211yescharacteristic
74#11719072C2211yescharacteristic
75#11719072C2212yes—
76#11719072C2211yescharacteristic
77#11719068C2214yescomplemented
78#11719068C2214yescomplemented
79#11719068C2214yescomplemented
80#11719068C2214yescomplemented
81#11719062C2212yescomplemented
82#11719062C2214yescomplemented
83#11719062C2212yescomplemented
84#11719055C2214yescomplemented
85#11719054C2214yescomplemented
86#11719051C2214yescomplemented
87#11719049C2214yescomplemented
88C4×#6118C2212yescomplemented
89C4×#6118C2212yescomplemented
90#11719047C2212yescomplemented
91C4×D13⋊C8C2212yescomplemented
92C2×C13×#41C2×C411yescharacteristic
93#41×D13—24no—
94#41×D13—24no—
95C2×#6131C2311yescharacteristic
96C2×Q8×D13C2×C411yescharacteristic
97C2×#6129C2312yes—
98C2×#6129C2311yescharacteristic
99C2×D4×D13C2×C412yes—
100C2×D4×D13C2×C411yescharacteristic
101C2×#6127C2×C411yescharacteristic
102C2×#6127C2×C412yes—
103C22×C4×D13C2312yes—
104C22×C4×D13C2311yescharacteristic
105C2×#6122C2312yes—
106C2×#6122C2312yes—
107C22×#1057C2311yescharacteristic
108C22×#1057C2311yescharacteristic
109C22×#1057C2312yes—
110D13⋊M16—24no—
111D13⋊M16—24no—
112C2×#6118—24no—
113C2×#6118C2312yes—
114C2×#6118C2311yescharacteristic
115C2×#6118C2311yescharacteristic
116C2×#6118C2312yes—
117C2×#6118C2311yescharacteristic
118C2×#6118C2311yescharacteristic
119C2×D13⋊C8—24no—
120C2×D13⋊C8C2311yescharacteristic
121C2×D13⋊C8C2312yes—
122C2×D13⋊C8C2311yescharacteristic
123C2×D13⋊C8C2311yescharacteristic
124C2×D13⋊C8C2311yescharacteristic
125C2×D13⋊C8C2312yes—
126C4×Q8×C13C2×C412yes—
127C4×D4×C13C2×C412yes—
128C4×D4×C13C2×C414yes—
129C13×#117C2×C412yes—
130C13×#117C2×C411yescharacteristic
131C2×C13×C4⋊C4C2×C412yes—
132C2×C13×C4⋊C4C2×C411yescharacteristic
133Q8×Dic13C2×C412yes—
134D4×Dic13C2×C412yes—
135D4×Dic13C2×C414yes—
136C4×C22⋊D13C2×C414yes—
137C4×C22⋊D13C2×C414yes—
138C4×C22⋊D13C2×C414yes—
139C2×#6103C2×C414yes—
140C2×#6103C2×C412yes—
141#88180C2×C412yes—
142#88180C2×C411yescharacteristic
143C2×C4⋊Dic13C2×C412yes—
144C2×C4⋊Dic13C2×C411yescharacteristic
145C2×C4×Dic13C2312yes—
146C2×C4×Dic13C2314yes—
147#88147C2×C414yes—
148#88147C2×C412yes—
149#88146C2×C412yes—
150#88146C2×C412yes—
151#88146C2×C412yes—
152#88146C2×C414yes—
153#88146C2×C412yes—
154#88146C2311yescharacteristic
155#88146C2312yes—
156#88146C2314yes—
157#88146C2312yes—
158#88146C2311yescharacteristic
159C4⋊C4×D13C2×C412yes—
160C4⋊C4×D13C2×C411yescharacteristic
161C4⋊C4×D13C2×C412yes—
162C4⋊C4×D13C2×C411yescharacteristic
163#88141C2×C412yes—
164#88141C2×C414yes—
165#88135C2×C414yes—
166#88135C2×C414yes—
167#88135C2×C414yes—
168C22⋊C4×D13C2×C414yes—
169C22⋊C4×D13C2×C412yes—
170#88131C2312yes—
171#88131C2314yes—
172C4×D52C2×C414yes—
173C4×D52C2×C412yes—
174#88126C2×C414yes—
175#88126C2×C412yes—
176C42×D13C2312yes—
177C42×D13C2314yes—
178C4×Dic26C2×C412yes—
179C4×Dic26C2×C414yes—
180C22⋊#1057C2312yes—
181C22⋊#1057C2314yes—
182C22⋊#1057C2312yes—
183C22⋊#1057C2312yes—
184C22⋊#1057C2312yes—
185C22⋊#1057C2314yes—
186#88112C2314yes—
187#88112C2314yes—
188#88112C2314yes—
189#88112C2314yes—
190#88111C2312yes—
191#88111C2314yes—
192#88111C2312yes—
193#88111C2314yes—
194#88111C2312yes—
195#88111C2312yes—
196#88110C2312yes—
197#88110C2312yes—
198#88110C2312yes—
199#88110C2312yes—
200#88110C2314yes—
201#88110C2314yes—
202C4⋊#1057C2314yes—
203C4⋊#1057C2314yes—
204C4⋊#1057C2314yes—
205C4⋊#1057C2314yes—
206C4×#1057C2312yes—
207C4×#1057C2312yes—
208C4×#1057C2312yes—
209C4×#1057C2312yes—
210C4×#1057C2314yes—
211C4×#1057C2314yes—
212#60126—131nomaximal, Sylow
213C23×D13C22×C412yes—
214C23×D13C22×C411yescharacteristic
215C13×#41—24no—
216C2×Q8×C13C22×C411yescharacteristic
217C2×D4×C13C22×C412yes—
218C2×D4×C13C22×C411yescharacteristic
219C22×C4×C13C22×C412yes—
220C22×C4×C13C22×C414yes—
221C22×C4×C13C22×C412yes—
222C22×C4×C13C22×C411yescharacteristic
223C2×C22⋊D13C22×C412yes—
224C2×C22⋊D13C22×C412yes—
225C2×C22⋊D13C22×C412yes—
226C22×Dic13C22×C414yes—
227C22×Dic13C22×C412yes—
228C22×Dic13C2412yes—
229C22×Dic13C2411yescharacteristic
230#6131—22no—
231#6131—22no—
232Q8×D13—24no—
233#6129—24no—
234#6129—24no—
235#6129—22no—
236#6129—22no—
237D4×D13—28no—
238D4×D13—24no—
239#6127—24no—
240#6127—28no—
241C2×D52C22×C412yes—
242C2×D52C22×C411yescharacteristic
243C2×C4×D13—24no—
244C2×C4×D13—24no—
245C2×C4×D13C22×C412yes—
246C2×C4×D13C22×C412yes—
247C2×C4×D13C22×C414yes—
248C2×C4×D13C22×C412yes—
249C2×C4×D13C22×C414yes—
250C2×C4×D13C22×C412yes—
251C2×C4×D13C22×C411yescharacteristic
252C2×C4×D13C22×C411yescharacteristic
253C2×C4×D13#4114yes—
254C2×C4×D13#4114yes—
255C2×C4×D13C2412yes—
256C2×C4×D13C2411yescharacteristic
257C2×C4×D13C2411yescharacteristic
258C2×Dic26C22×C411yescharacteristic
259C2×Dic26C22×C412yes—
260#6122—24no—
261#6122—24no—
262C2×#1057—22no—
263C2×#1057—22no—
264C2×#1057—24no—
265C2×#1057C2411yescharacteristic
266C2×#1057C2411yescharacteristic
267C2×#1057C2412yes—
268C2×#1057C2412yes—
269C2×#1057C2412yes—
270C2×#1057C2412yes—
271C2×#1057C2414yes—
272C2×#1057C2411yescharacteristic
273C2×#1057C2411yescharacteristic
274#6118—24no—
275#6118—24no—
276#6118—22no—
277#6118—22no—
278#6118—22no—
279#6118—22no—
280D13⋊C8—22no—
281D13⋊C8—22no—
282D13⋊C8—22no—
283D13⋊C8—22no—
284D13⋊C8—24no—
285D13⋊C8—24no—
286C13×C4⋊C4C22×C414yes—
287C13×C4⋊C4C22×C412yes—
288C13×C4⋊C4C22×C411yescharacteristic
289C13×C4⋊C4C22×C411yescharacteristic
290C13×C4⋊C4C22×C412yes—
291C13×C22⋊C4C22×C414yes—
292C13×C22⋊C4C22×C412yes—
293C42×C13C22×C414yes—
294C42×C13C22×C412yes—
295C22⋊Dic13C22×C414yes—
296C22⋊Dic13C22×C412yes—
297#6103C22×C412yes—
298#6103C22×C412yes—
299#6103C22×C414yes—
300#6103C22×C414yes—
301#6103C22×C414yes—
302#6103C22×C414yes—
303C4⋊Dic13C22×C414yes—
304C4⋊Dic13C22×C412yes—
305C4⋊Dic13C22×C411yescharacteristic
306C4⋊Dic13C22×C411yescharacteristic
307C4⋊Dic13C22×C412yes—
308#6101C22×C414yes—
309#6101C22×C412yes—
310#6101C22×C414yes—
311#6101C22×C412yes—
312C4×Dic13C22×C414yes—
313C4×Dic13C22×C414yes—
314C4×Dic13C22×C414yes—
315C4×Dic13C22×C414yes—
316C4×Dic13C22×C412yes—
317C4×Dic13C2412yes—
318C4×Dic13C2412yes—
319C4×Dic13C2414yes—
320#3428—131no—
321#2925—134no—
322#2925—134no—
323#2924—132no—
324#2924—132no—
325#2924—132no—
326#2924—132no—
327#2923—132no—
328#2923—132no—
329#2922—132no—
330#2922—132no—
331#2905—131no—
332C2×#424—131no—
333#2879—131no—
334C2×#408—131no—
335#2873—131no—
336C2×#405—131no—
337C23×C13C23×C412yes—
338C23×C13C23×C411yescharacteristic
339C22×D13—24no—
340C22×D13—41no—
341C22×D13—41no—
342C22×D13—42no—
343C22×D13—42no—
344C22×D13#11714yes—
345C22×D13C23×C412yes—
346C22×D13C23×C411yescharacteristic
347C22×D13C23×C411yescharacteristic
348Q8×C13—22no—
349D4×C13—24no—
350D4×C13—22no—
351C2×C4×C13—24no—
352C2×C4×C13—42no—
353C2×C4×C13—44no—
354C2×C4×C13#11714yes—
355C2×C4×C13C23×C412yes—
356C2×C4×C13C23×C414yes—
357C2×C4×C13C23×C412yes—
358C2×C4×C13C23×C412yes—
359C2×C4×C13C23×C411yescharacteristic
360C2×C4×C13C23×C411yescharacteristic
361C22⋊D13—24no—
362C22⋊D13—24no—
363C22⋊D13—24no—
364C2×Dic13—22no—
365C2×Dic13—22no—
366C2×Dic13—42no—
367C2×Dic13—44no—
368C2×Dic13C23×C412yes—
369C2×Dic13C23×C412yes—
370C2×Dic13C23×C412yes—
371C2×Dic13C23×C414yes—
372C2×Dic13C23×C411yescharacteristic
373C2×Dic13C2×#4112yes—
374C2×Dic13C2×#4112yes—
375C2×Dic13C2511yescharacteristic
376D52—24no—
377D52—22no—
378C4×D13—24no—
379C4×D13—24no—
380C4×D13—22no—
381C4×D13—22no—
382C4×D13—42no—
383C4×D13—44no—
384C4×D13—42no—
385C4×D13—44no—
386C4×D13#11714yes—
387C4×D13#11714yes—
388C4×D13C2×#4112yes—
389C4×D13C2×#4112yes—
390C4×D13C2×#4112yes—
391C4×D13C2×#4112yes—
392Dic26—22no—
393Dic26—24no—
394#1057—21no—
395#1057—21no—
396#1057—21no—
397#1057—21no—
398#1057—22no—
399#1057—22no—
400#1057—22no—
401#1057—22no—
402#1057—24no—
403C22×#41—131no—
404C22×M16—131no—
405C22×M16—131no—
406C22×M16—131no—
407C23×C8—131no—
408#520—131no—
409#520—132no—
410#520—131no—
411#520—132no—
412#520—131no—
413#520#26111yescharacteristic
414#519—132no—
415#518—134no—
416#518—132no—
417C4×#41—132no—
418C4×#41—132no—
419C4×#41—134no—
420C2×#117—131no—
421C2×#117—132no—
422C2×#117—131no—
423C2×#117—132no—
424#433—134no—
425#433—134no—
426#433—134no—
427#433—134no—
428#433—134no—
429#433—134no—
430#433—134no—
431#433—134no—
432#432—134no—
433#432—134no—
434#432—134no—
435#432—134no—
436#431—134no—
437#431—134no—
438#431—134no—
439#431—134no—
440#424—132no—
441#424—132no—
442#424—132no—
443#424—132no—
444#424—132no—
445#424—132no—
446#424—132no—
447#424—132no—
448#423—134no—
449C2×C4⋊C8—132no—
450C2×C4⋊C8—132no—
451#408—131no—
452#408—131no—
453#408—131no—
454#408—131no—
455#408—132no—
456#408—132no—
457#408—132no—
458#408—132no—
459#408—134no—
460#407—132no—
461#407—132no—
462C2×C22⋊C8—132no—
463C2×C22⋊C8—132no—
464#405—131no—
465#405—131no—
466#405—131no—
467#405—131no—
468#405—132no—
469#405—132no—
470#405—132no—
471#405—132no—
472#405—134no—
473C4×M16—132no—
474C4×M16—132no—
475C2×#97—132no—
476C2×C4×C8—132no—
477C22×C13—21no—
478C22×C13—21no—
479C22×C13—22no—
480C22×C13—22no—
481C22×C13—22no—
482C22×C13C2×#11712yes—
483C22×C13C24×C411yescharacteristic
484C2×D13—21no—
485C2×D13—21no—
486C2×D13—21no—
487C2×D13—21no—
488C2×D13—22no—
489C2×D13—22no—
490C2×D13—22no—
491C2×D13—44no—
492C2×D13—84no—
493C2×D13C2×#11712yes—
494C2×D13C2×#11712yes—
495C4×C13—22no—
496C4×C13—22no—
497C4×C13—22no—
498C4×C13—24no—
499C4×C13C2×#11712yes—
500C4×C13C2×#11712yes—
501Dic13—22no—
502Dic13—22no—
503Dic13—22no—
504Dic13—24no—
505Dic13C2×#11712yes—
506Dic13C22×#4111yescharacteristic
507Dic13C22×#4111yescharacteristic
508C2×#41—131no—
509C2×#41—132no—
510C2×#41—131no—
511C2×#41—132no—
512C2×#41—131no—
513C2×#41—264no—
514C2×#41—264no—
515C2×#41C2×#26111yescharacteristic
516C22×Q8—131no—
517C22×D4—131no—
518C22×D4—132no—
519C23×C4—131no—
520C23×C4—132no—
521C2×M16—131no—
522C2×M16—131no—
523C2×M16—132no—
524C2×M16—131no—
525C2×M16—131no—
526C2×M16—132no—
527C2×M16—132no—
528C2×M16—132no—
529C2×M16—264no—
530C2×M16—264no—
531C2×M16—264no—
532C22×C8—131no—
533C22×C8—131no—
534C22×C8—131no—
535C22×C8—131no—
536C22×C8—131no—
537C22×C8—131no—
538C22×C8—132no—
539C22×C8—132no—
540C22×C8—132no—
541C22×C8—264no—
542C4×Q8—132no—
543C4×Q8—132no—
544C4×Q8—134no—
545C4×Q8—132no—
546C4×Q8—134no—
547C4×Q8C2×#26112yes—
548C4×D4—132no—
549C4×D4—134no—
550C4×D4—134no—
551C4×D4—134no—
552C4×D4—134no—
553C4×D4—134no—
554C4×D4—132no—
555C4×D4—134no—
556C4×D4—134no—
557C4×D4—134no—
558C4×D4—134no—
559C4×D4—132no—
560C4×D4C2×#26112yes—
561C4×D4C2×#26114yes—
562#117—132no—
563#117—131no—
564#117—131no—
565#117—131no—
566#117—132no—
567#117—132no—
568#117—134no—
569#117—132no—
570#117—134no—
571#117—132no—
572#117—132no—
573#117—132no—
574#117—132no—
575#117—134no—
576#117—132no—
577#117—134no—
578#117C2×#26112yes—
579#117C2×#26111yescharacteristic
580C2×C4⋊C4—132no—
581C2×C4⋊C4—131no—
582C2×C4⋊C4—131no—
583C2×C4⋊C4—132no—
584C2×C4⋊C4—131no—
585C2×C4⋊C4—132no—
586C2×C4⋊C4C2×#26112yes—
587C2×C4⋊C4C2×#26111yescharacteristic
588C2×C22⋊C4—132no—
589C2×C22⋊C4—134no—
590C2×C22⋊C4—132no—
591C2×C22⋊C4—134no—
592C2×C42—132no—
593C2×C42—134no—
594C2×C42—132no—
595C2×C42—134no—
596C4⋊C8—134no—
597C4⋊C8—134no—
598C4⋊C8—134no—
599C4⋊C8—134no—
600C4⋊C8—134no—
601C4⋊C8—134no—
602C4⋊C8—134no—
603C4⋊C8—134no—
604C22⋊C8—132no—
605C22⋊C8—132no—
606C22⋊C8—132no—
607C22⋊C8—132no—
608C22⋊C8—134no—
609C22⋊C8—134no—
610C22⋊C8—132no—
611C22⋊C8—132no—
612C22⋊C8—132no—
613C22⋊C8—132no—
614C22⋊C8—134no—
615C22⋊C8—134no—
616#97—132no—
617#97—132no—
618#97—132no—
619#97—132no—
620#97—134no—
621#97—134no—
622C4×C8—132no—
623C4×C8—132no—
624C4×C8—132no—
625C4×C8—132no—
626C4×C8—134no—
627C4×C8—134no—
628C2×C13—22no—
629C2×C13—42no—
630C2×C13C22×#11711yescharacteristic
631C2×C13#357311yescharacteristic
632C2×C13#357311yescharacteristic
633D13—22no—
634D13—22no—
635D13—42no—
636C24—131no—
637C24—132no—
638#41—24no—
639#41—268no—
640#41—264no—
641#41—264no—
642#41—262no—
643#41—262no—
644#41—262no—
645#41—262no—
646#41—264no—
647C2×Q8—132no—
648C2×Q8—131no—
649C2×Q8—264no—
650C2×Q8C22×#26111yescharacteristic
651C2×D4—132no—
652C2×D4—132no—
653C2×D4—132no—
654C2×D4—132no—
655C2×D4—131no—
656C2×D4—264no—
657C2×D4—268no—
658C2×D4C22×#26112yes—
659C2×D4C22×#26111yescharacteristic
660C22×C4—131no—
661C22×C4—134no—
662C22×C4—134no—
663C22×C4—131no—
664C22×C4—131no—
665C22×C4—131no—
666C22×C4—131no—
667C22×C4—132no—
668C22×C4—134no—
669C22×C4—132no—
670C22×C4—132no—
671C22×C4—132no—
672C22×C4—132no—
673C22×C4—132no—
674C22×C4—134no—
675C22×C4—132no—
676C22×C4—134no—
677C22×C4—264no—
678C22×C4—264no—
679C22×C4C22×#26112yes—
680C22×C4C22×#26114yes—
681C22×C4C22×#26112yes—
682C22×C4C22×#26111yescharacteristic
683M16—264no—
684M16—262no—
685M16—262no—
686M16—264no—
687M16—262no—
688M16—262no—
689M16—264no—
690M16—264no—
691C2×C8—131no—
692C2×C8—131no—
693C2×C8—132no—
694C2×C8—132no—
695C2×C8—132no—
696C2×C8—132no—
697C2×C8—134no—
698C2×C8—131no—
699C2×C8—131no—
700C2×C8—262no—
701C2×C8—262no—
702C2×C8—262no—
703C2×C8—262no—
704C2×C8—262no—
705C2×C8—262no—
706C2×C8—264no—
707C2×C8—264no—
708C2×C8—264no—
709C4⋊C4—131no—
710C4⋊C4—132no—
711C4⋊C4—131no—
712C4⋊C4—132no—
713C4⋊C4—132no—
714C4⋊C4—134no—
715C4⋊C4—134no—
716C4⋊C4—134no—
717C4⋊C4—132no—
718C4⋊C4C22×#26111yescharacteristic
719C4⋊C4C22×#26111yescharacteristic
720C4⋊C4C22×#26112yes—
721C4⋊C4C22×#26114yes—
722C4⋊C4C22×#26112yes—
723C22⋊C4—134no—
724C22⋊C4—132no—
725C22⋊C4—132no—
726C22⋊C4—134no—
727C22⋊C4—132no—
728C22⋊C4—134no—
729C22⋊C4—134no—
730C22⋊C4—134no—
731C22⋊C4C22×#26114yes—
732C22⋊C4C22×#26112yes—
733C42—132no—
734C42—132no—
735C42—134no—
736C42—134no—
737C42—134no—
738C42—132no—
739C42—134no—
740C42—134no—
741C42C22×#26114yes—
742C42C22×#26112yes—
743C13#6012611yescharacteristic, complemented, Sylow
744C23—131no—
745C23—131no—
746C23—134no—
747C23—132no—
748C23—264no—
749C23—521no—
750C23—521no—
751C23—522no—
752C23—522no—
753C23C23×#26112yes—
754C23C23×#26111yescharacteristic
755Q8—22no—
756Q8—264no—
757Q8—262no—
758D4—24no—
759D4—22no—
760D4—264no—
761D4—264no—
762D4—264no—
763D4—264no—
764D4—262no—
765C2×C4—24no—
766C2×C4—42no—
767C2×C4—44no—
768C2×C4—132no—
769C2×C4—132no—
770C2×C4—131no—
771C2×C4—131no—
772C2×C4—132no—
773C2×C4—132no—
774C2×C4—132no—
775C2×C4—132no—
776C2×C4—134no—
777C2×C4—134no—
778C2×C4—132no—
779C2×C4—132no—
780C2×C4—134no—
781C2×C4—132no—
782C2×C4—262no—
783C2×C4—262no—
784C2×C4—264no—
785C2×C4—262no—
786C2×C4—262no—
787C2×C4—264no—
788C2×C4—522no—
789C2×C4—524no—
790C2×C4—522no—
791C2×C4—524no—
792C2×C4—522no—
793C2×C4—524no—
794C2×C4#8823714yes—
795C2×C4C23×#26112yes—
796C2×C4C23×#26114yes—
797C2×C4C23×#26112yes—
798C2×C4C23×#26112yes—
799C2×C4C23×#26111yescharacteristic
800C2×C4C23×#26111yescharacteristic
801C8—261no—
802C8—261no—
803C8—261no—
804C8—261no—
805C8—262no—
806C8—262no—
807C8—262no—
808C8—262no—
809C8—264no—
810C22—21no—
811C22—21no—
812C22—22no—
813C22—22no—
814C22—22no—
815C22—132no—
816C22—132no—
817C22—261no—
818C22—261no—
819C22—261no—
820C22—261no—
821C22—262no—
822C22—262no—
823C22—262no—
824C22—524no—
825C22—1044no—
826C22C2×#8823712yes—
827C22C24×#26111yescharacteristic
828C4—22no—
829C4—24no—
830C4—22no—
831C4—22no—
832C4—132no—
833C4—131no—
834C4—131no—
835C4—262no—
836C4—262no—
837C4—262no—
838C4—264no—
839C4C2×#8823712yes—
840C4C2×#8823712yes—
841C2—22no—
842C2—42no—
843C2—262no—
844C2—262no—
845C2—522no—
846C2C22×#8823711yescharacteristic
847C2#1313183111yescharacteristic
848C2#1313183211yescharacteristic
subgroupG/H
center, FrattiniC22C24×#261
commutator, socleC22×C13C24×C4
FittingC13×#520C4
prime radicalC2×#41×D13C22
cosocleC2×Dic13C25
hypercenter#520#261
hypocenterC13#60126
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ #520

Complements

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

NH ≅ G/Ntype
1. #13131534C2semidirect
2. #13131531C2semidirect
3. #13131530C2semidirect
4. #13131529C2semidirect
5. #13131527C2semidirect
6. #13131526C2semidirect
7. #13131524C2semidirect
8. #13131523C2semidirect
9. #13131521C2semidirect
10. #13131520C2semidirect
11. #13131480C2semidirect
12. C2×#11719079C2semidirect
15. #13131401C2semidirect
16. #13131396C2semidirect
48. #11719130C22semidirect
49. #11719129C22semidirect
50. #11719128C22semidirect
53. #11719125C22semidirect
56. C2×#88112C22semidirect
57. #11719119C22semidirect
58. C2×C4⋊#1057C22semidirect
63. #11719079C22semidirect
64. #11719079C22semidirect
65. #11719079C22semidirect
66. #11719079C22semidirect
67. #11719077C22semidirect
68. #11719077C22semidirect
69. #11719077C22semidirect
70. #11719077C22semidirect
77. #11719068C22semidirect
78. #11719068C22semidirect
79. #11719068C22semidirect
80. #11719068C22semidirect
81. #11719062C22semidirect
82. #11719062C22semidirect
83. #11719062C22semidirect
84. #11719055C22semidirect
85. #11719054C22semidirect
86. #11719051C22semidirect
87. #11719049C22semidirect
88. C4×#6118C22semidirect
89. C4×#6118C22semidirect
90. #11719047C22semidirect
91. C4×D13⋊C8C22semidirect
743. C13#60126semidirect

Maximal subgroups

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

subgroupindex
#131315342
#131315312
#131315302
#131315292
#131315272
#131315262
#131315242
#131315232
#131315212
#131315202
#131314802
C2×#117190792
#131314212
D13⋊#4082
#131314012
#131313962
#131280362
#6012613