Finite Group Databasebeta

← #16808976

Subgroups — #16808976

Order 3328.

1864 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13131794C214yesmaximal, complemented
2#13131775C214yesmaximal, complemented
3#13131765C214yesmaximal, complemented
4#13131760C214yesmaximal, complemented
5#13131629C212yesmaximal, complemented
6#13131569C214yesmaximal, complemented
7#13131563C212yesmaximal, complemented
8#13131535C212yesmaximal, complemented
9D13⋊#432C211yesmaximal, characteristic, complemented
10#13131484C212yesmaximal, complemented
11C2×#11719053C211yesmaximal, characteristic, complemented
12#13128133C211yesmaximal, characteristic
13C2×#88240C2214yes—
14C22×#6118C2212yes—
15C13×#533C411yescharacteristic
16#11719433C411yescharacteristic
17#11719433C2211yescharacteristic
18#11719430C411yescharacteristic
19#11719430C2211yescharacteristic
20#11719396C412yes—
21#11719396C2212yes—
22#11719332C412yes—
23#11719332C2212yes—
24#11719329C412yes—
25#11719329C2212yes—
26#11719285C412yes—
27#11719285C412yes—
28C4×#6131C2212yes—
29C4×#6131C2212yes—
30#11719229C412yes—
31#11719227C2212yes—
32#11719182C411yescharacteristic
33C2×C42×D13C2211yescharacteristic
34#11719159C2214yes—
35#11719158C2218yescomplemented
36#11719130C2212yes—
37#11719128C2212yes—
38D13⋊(C22⋊C8)C2212yes—
39C2×#88112C2212yes—
40C2×#88112C2212yes—
41#11719079C2214yes—
42#11719079C2218yescomplemented
43#11719078C2218yescomplemented
44#11719077C2218yescomplemented
45#11719076C2218yes—
46#11719075C2218yes—
47#11719075C2218yescomplemented
48#11719075C2218yescomplemented
49#11719072C2214yes—
50#11719064C2218yes—
51#11719063C2218yes—
52#11719055C2212yes—
53#11719055C2214yescomplemented
54#11719054C2212yes—
55#11719053C2212yes—
56#11719053C2212yes—
57#11719053C2212yes—
58#11719053C2212yes—
59#11719053C2214yescomplemented
60D13⋊(C4⋊C8)C2211yescharacteristic
61D13⋊(C4⋊C8)C2211yescharacteristic
62D13⋊(C4⋊C8)C2214yescomplemented
63#11719049C2214yescomplemented
64#11719047C2212yes—
65C2×#6131C2×C412yes—
66C2×#6131C2312yes—
67C2×#6127C2×C412yes—
68C22×C4×D13C2×C411yescharacteristic
69C22×C4×D13C2×C411yescharacteristic
70C22×C4×D13C2311yescharacteristic
71C22×#1057C2314yes—
72#88240—48no—
73C2×#6118—44no—
74C2×#6118C2314yes—
75C2×#6118C2314yes—
76C2×#6118C2318yes—
77C2×D13⋊C8C2312yes—
78C2×D13⋊C8C2312yes—
79C2×D13⋊C8C2318yes—
80C13×C4⋊Q8C2×C411yescharacteristic
81C13×C4⋊Q8C2×C411yescharacteristic
82C13×#125C2×C412yes—
83C13×C22⋊Q8C2×C412yes—
84C13×C22⋊Q8C2×C412yes—
85C4×Q8×C13C2×C412yes—
86C4×Q8×C13C2×C412yes—
87C13×#117C2×C412yes—
88C2×C42×C13C2×C411yescharacteristic
89#88201C2×C412yes—
90#88201C2×C412yes—
91#88200C2×C412yes—
92#88200C2×C412yes—
93Q8×Dic13C2×C412yes—
94Q8×Dic13C2312yes—
95#88184C2×C412yes—
96#88184C2×C412yes—
97C2×C4×Dic13C2×C411yescharacteristic
98C2×C4×Dic13C2311yescharacteristic
99C2×C4×Dic13C2311yescharacteristic
100#88152C2×C414yes—
101#88152C2×C414yes—
102#88151C2×C412yes—
103#88151C2×C412yes—
104#88149C2×C412yes—
105#88149C2×C412yes—
106#88149C2×C412yes—
107#88149C2×C412yes—
108#88148C2×C414yes—
109#88148C2×C414yes—
110#88147C2×C412yes—
111#88147C2×C412yes—
112#88147C2×C414yes—
113#88147C2312yes—
114#88147C2312yes—
115#88147C2314yes—
116#88146C2×C412yes—
117#88146C2×C414yes—
118#88146C2312yes—
119#88146C2314yes—
120#88144C2×C412yes—
121#88144C2×C412yes—
122#88141C2×C412yes—
123#88141C2312yes—
124#88140C2×C414yes—
125#88136C2×C414yes—
126#88135C2×C414yes—
127#88135C2314yes—
128#88129C2×C412yes—
129#88128C2×C411yescharacteristic
130C4×D52C2×C412yes—
131C4×D52C2×C412yes—
132C4×D52C2×C414yes—
133C4×D52C2×C414yes—
134#88126C2×C414yes—
135C42×D13C2×C411yescharacteristic
136C42×D13C2×C411yescharacteristic
137C42×D13C2×C411yescharacteristic
138C42×D13C2×C411yescharacteristic
139C42×D13C2311yescharacteristic
140C42×D13C2311yescharacteristic
141C42×D13C2311yescharacteristic
142C42×D13C2311yescharacteristic
143C42×D13C2314yes—
144#88123C2×C411yescharacteristic
145C22⋊#1057C2314yes—
146#88112C2312yes—
147#88112C2314yes—
148#88112C2312yes—
149#88112C2314yes—
150#88112C2314yes—
151#88112C2314yes—
152#88112C2318yes—
153#88111C2318yes—
154#88111C2314yes—
155#88111C2318yes—
156#88110C2314yes—
157#88110C2314yes—
158#88110C2318yes—
159C4⋊#1057C2312yes—
160C4⋊#1057C2312yes—
161C4⋊#1057C2318yes—
162C4×#1057C2318yes—
163#60269—131nomaximal, Sylow
164C23×D13C22×C411yescharacteristic
165C2×Q8×C13C22×C412yes—
166C2×Q8×C13C22×C412yes—
167C22×C4×C13C22×C411yescharacteristic
168C22×C4×C13C22×C411yescharacteristic
169C22×C4×C13C22×C411yescharacteristic
170C2×C22⋊D13C22×C414yes—
171C22×Dic13C22×C411yescharacteristic
172C22×Dic13C22×C411yescharacteristic
173C22×Dic13C2411yescharacteristic
174#6131—24no—
175#6131—24no—
176#6131—44no—
177#6127—44no—
178C2×D52C22×C412yes—
179C2×D52C22×C414yes—
180C2×D52C22×C412yes—
181C2×D52C22×C414yes—
182C2×D52C22×C412yes—
183C2×C4×D13—22no—
184C2×C4×D13—22no—
185C2×C4×D13—42no—
186C2×C4×D13—42no—
187C2×C4×D13C22×C411yescharacteristic
188C2×C4×D13C22×C411yescharacteristic
189C2×C4×D13C22×C411yescharacteristic
190C2×C4×D13C22×C411yescharacteristic
191C2×C4×D13C22×C414yes—
192C2×C4×D13C22×C411yescharacteristic
193C2×C4×D13C22×C411yescharacteristic
194C2×C4×D13C22×C411yescharacteristic
195C2×C4×D13C22×C411yescharacteristic
196C2×C4×D13C22×C411yescharacteristic
197C2×C4×D13C22×C411yescharacteristic
198C2×C4×D13C22×C414yes—
199C2×C4×D13C2411yescharacteristic
200C2×C4×D13C2414yes—
201C2×C4×D13C2411yescharacteristic
202C2×Dic26C22×C412yes—
203C2×#1057—44no—
204C2×#1057C2414yes—
205C2×#1057C2418yes—
206C2×#1057C2414yes—
207#6118—28no—
208#6118—44no—
209#6118—48no—
210D13⋊C8—24no—
211D13⋊C8—24no—
212D13⋊C8—48no—
213C13×C4⋊C4C22×C412yes—
214C13×C4⋊C4C22×C412yes—
215C13×C4⋊C4C22×C412yes—
216C13×C4⋊C4C22×C412yes—
217C13×C4⋊C4C22×C414yes—
218C13×C4⋊C4C22×C414yes—
219C13×C22⋊C4C22×C414yes—
220C42×C13C22×C411yescharacteristic
221C42×C13C22×C411yescharacteristic
222C42×C13C22×C411yescharacteristic
223C42×C13C22×C411yescharacteristic
224C42×C13C22×C414yes—
225#6103C22×C414yes—
226#6103C22×C414yes—
227#6103C22×C414yes—
228#6103C22×C414yes—
229#6103C22×C414yes—
230#6103C22×C414yes—
231#6103C22×C414yes—
232#6103C22×C414yes—
233C4⋊Dic13C22×C412yes—
234C4⋊Dic13C22×C412yes—
235C4⋊Dic13C22×C414yes—
236C4⋊Dic13C22×C414yes—
237#6101C22×C414yes—
238#6101C22×C414yes—
239C4×Dic13C22×C411yescharacteristic
240C4×Dic13C22×C411yescharacteristic
241C4×Dic13C22×C411yescharacteristic
242C4×Dic13C22×C411yescharacteristic
243C4×Dic13C22×C411yescharacteristic
244C4×Dic13C22×C411yescharacteristic
245C4×Dic13C22×C411yescharacteristic
246C4×Dic13C22×C411yescharacteristic
247C4×Dic13C22×C414yes—
248C4×Dic13C2414yes—
249C4×Dic13C2411yescharacteristic
250C4×Dic13C2411yescharacteristic
251C4×Dic13C2411yescharacteristic
252C4×Dic13C2411yescharacteristic
253#3444—131no—
254#2995—134no—
255#2992—134no—
256#2990—134no—
257#2989—134no—
258#2961—132no—
259#2933—134no—
260#2932—132no—
261#2925—132no—
262C2×#432—131no—
263#2906—132no—
264C2×#423—131no—
265C23×C13C23×C411yescharacteristic
266C22×D13—22no—
267C22×D13—22no—
268C22×D13—41no—
269C22×D13C23×C414yes—
270C22×D13C23×C411yescharacteristic
271C22×D13C23×C411yescharacteristic
272Q8×C13—24no—
273Q8×C13—42no—
274C2×C4×C13—22no—
275C2×C4×C13—22no—
276C2×C4×C13—41no—
277C2×C4×C13C23×C411yescharacteristic
278C2×C4×C13C23×C411yescharacteristic
279C2×C4×C13C23×C411yescharacteristic
280C2×C4×C13C23×C411yescharacteristic
281C2×C4×C13C23×C411yescharacteristic
282C2×C4×C13C23×C414yes—
283C2×C4×C13C23×C414yes—
284C2×C4×C13C23×C411yescharacteristic
285C22⋊D13—28no—
286C2×Dic13—22no—
287C2×Dic13—22no—
288C2×Dic13—21no—
289C2×Dic13—21no—
290C2×Dic13C23×C411yescharacteristic
291C2×Dic13C23×C411yescharacteristic
292C2×Dic13C23×C411yescharacteristic
293C2×Dic13C23×C411yescharacteristic
294C2×Dic13C23×C414yes—
295C2×Dic13C23×C411yescharacteristic
296C2×Dic13C2511yescharacteristic
297D52—28no—
298D52—24no—
299D52—42no—
300D52—42no—
301D52—44no—
302C4×D13—22no—
303C4×D13—22no—
304C4×D13—22no—
305C4×D13—22no—
306C4×D13—28no—
307C4×D13—24no—
308C4×D13—21no—
309C4×D13—21no—
310C4×D13—24no—
311C4×D13—41no—
312C4×D13—41no—
313C4×D13—41no—
314C4×D13—41no—
315C4×D13—41no—
316C4×D13—41no—
317C4×D13—44no—
318C4×D13H(5,𝔽2)12yes—
319C4×D132−1+412yes—
320Dic26—42no—
321#1057—24no—
322#1057—28no—
323#1057—24no—
324C2×#131—134no—
325C22×M16—132no—
326#533—131no—
327#533—131no—
328#533#26111yescharacteristic
329#532—131no—
330#532—131no—
331#532—131no—
332#529—132no—
333#529—132no—
334#529—132no—
335#529—132no—
336#529—132no—
337#529—132no—
338#525—132no—
339#525—132no—
340#525—132no—
341C4×#41—132no—
342C4×#41—132no—
343C4×#41—132no—
344C22×C42—131no—
345#446—138no—
346#446—138no—
347#436—138no—
348#435—138no—
349#435—138no—
350#435—138no—
351#435—138no—
352C8×D4—138no—
353#433—138no—
354#432—132no—
355#432—132no—
356#432—132no—
357#432—132no—
358#432—134no—
359#431—134no—
360#424—134no—
361#424—138no—
362#423—132no—
363#423—132no—
364#423—132no—
365#423—132no—
366#423—134no—
367C2×C4⋊C8—132no—
368C2×C4⋊C8—132no—
369C2×C4⋊C8—131no—
370C2×C4⋊C8—134no—
371C2×C4⋊C8—131no—
372#408—134no—
373C2×C22⋊C8—132no—
374#405—134no—
375C2×#97—132no—
376C22×C13—21no—
377C22×C13—21no—
378C22×C13#56812yes—
379C22×C13C24×C411yescharacteristic
380C2×D13—21no—
381C2×D13—21no—
382C2×D13—21no—
383C2×D13—24no—
384C2×D13—21no—
385C2×D13—24no—
386C2×D13—21no—
387C2×D13—24no—
388C2×D13—44no—
389C2×D13#52012yes—
390C4×C13—21no—
391C4×C13—24no—
392C4×C13—21no—
393C4×C13—21no—
394C4×C13—21no—
395C4×C13—24no—
396C4×C13—21no—
397C4×C13#52012yes—
398Dic13—21no—
399Dic13—24no—
400Dic13—21no—
401Dic13—21no—
402Dic13—21no—
403Dic13#56812yes—
404Dic13C2×H(5,𝔽2)11yescharacteristic
405Dic13C2×2−1+411yescharacteristic
406C2×#41—132no—
407C2×#41—132no—
408C2×#41—132no—
409C23×C4—131no—
410C23×C4—131no—
411C23×C4—131no—
412#131—528no—
413C2×M16—134no—
414C2×M16—134no—
415C2×M16—138no—
416C2×M16—524no—
417C22×C8—132no—
418C22×C8—132no—
419C22×C8—134no—
420C22×C8—138no—
421C4⋊Q8—131no—
422C4⋊Q8C2×#26111yescharacteristic
423C4⋊Q8C2×#26111yescharacteristic
424#127—131no—
425#126—134no—
426#126—134no—
427#125—132no—
428#125—132no—
429#125C2×#26112yes—
430#124—132no—
431#124—132no—
432#124—132no—
433#123—134no—
434#123—134no—
435#123—134no—
436C22⋊Q8—132no—
437C22⋊Q8—132no—
438C22⋊Q8—132no—
439C22⋊Q8—132no—
440C22⋊Q8C2×#26112yes—
441C22⋊Q8C2×#26112yes—
442#121—132no—
443#121—132no—
444#121—132no—
445#121—132no—
446#121—132no—
447#121—132no—
448#120—134no—
449C4×Q8—132no—
450C4×Q8—132no—
451C4×Q8—132no—
452C4×Q8—132no—
453C4×Q8C2×#26112yes—
454C4×Q8C2×#26112yes—
455C4×D4—134no—
456C4×D4—134no—
457C4×D4—132no—
458C4×D4—132no—
459C4×D4—132no—
460C4×D4—132no—
461C4×D4—134no—
462C4×D4—134no—
463C4×D4—134no—
464C4×D4—134no—
465C4×D4—132no—
466C4×D4—132no—
467#117—132no—
468#117—132no—
469#117—134no—
470#117—134no—
471#117—134no—
472#117C2×#26112yes—
473C2×C42—131no—
474C2×C42—131no—
475C2×C42—131no—
476C2×C42—134no—
477C2×C42—131no—
478C2×C42—131no—
479C2×C42—131no—
480C2×C42—131no—
481C2×C42—131no—
482C2×C42—131no—
483C2×C42—131no—
484C2×C42—131no—
485C2×C42C2×#26111yescharacteristic
486C4⋊C8—132no—
487C4⋊C8—138no—
488C4⋊C8—132no—
489C4⋊C8—132no—
490C4⋊C8—134no—
491C4⋊C8—134no—
492C4⋊C8—134no—
493C4⋊C8—134no—
494C4⋊C8—132no—
495C4⋊C8—138no—
496C22⋊C8—134no—
497C22⋊C8—138no—
498C22⋊C8—138no—
499C22⋊C8—134no—
500#97—134no—
501#97—134no—
502#97—138no—
503C4×C8—138no—
504C2×C13—22no—
505C2×C13C2×#52011yescharacteristic
506C2×C13C2×#56811yescharacteristic
507C2×C13C2×#56811yescharacteristic
508D13—22no—
509D13—44no—
510D13—41no—
511C24—131no—
512#41—264no—
513#41—264no—
514#41—524no—
515#41—524no—
516C2×Q8—132no—
517C2×Q8C22×#26112yes—
518C2×Q8C22×#26112yes—
519C2×D4—134no—
520C2×D4—134no—
521C2×D4—132no—
522C2×D4—134no—
523C2×D4—132no—
524C2×D4—132no—
525C22×C4—131no—
526C22×C4—131no—
527C22×C4—131no—
528C22×C4—131no—
529C22×C4—131no—
530C22×C4—134no—
531C22×C4—131no—
532C22×C4—131no—
533C22×C4—131no—
534C22×C4—131no—
535C22×C4—134no—
536C22×C4—131no—
537C22×C4—131no—
538C22×C4—131no—
539C22×C4—131no—
540C22×C4—131no—
541C22×C4—131no—
542C22×C4—134no—
543C22×C4—262no—
544C22×C4—262no—
545C22×C4—522no—
546C22×C4—522no—
547C22×C4C22×#26111yescharacteristic
548C22×C4C22×#26111yescharacteristic
549C22×C4C22×#26111yescharacteristic
550M16—268no—
551M16—524no—
552M16—528no—
553C2×C8—134no—
554C2×C8—138no—
555C2×C8—134no—
556C2×C8—264no—
557C2×C8—264no—
558C2×C8—524no—
559C2×C8—528no—
560C4⋊C4—132no—
561C4⋊C4—132no—
562C4⋊C4—134no—
563C4⋊C4—134no—
564C4⋊C4—134no—
565C4⋊C4—134no—
566C4⋊C4C22×#26112yes—
567C4⋊C4C22×#26112yes—
568C4⋊C4C22×#26114yes—
569C4⋊C4C22×#26114yes—
570C4⋊C4C22×#26112yes—
571C4⋊C4C22×#26112yes—
572C22⋊C4—134no—
573C22⋊C4—134no—
574C22⋊C4—134no—
575C22⋊C4—134no—
576C22⋊C4—134no—
577C22⋊C4—134no—
578C22⋊C4—134no—
579C22⋊C4—134no—
580C22⋊C4C22×#26114yes—
581C42—134no—
582C42—131no—
583C42—131no—
584C42—131no—
585C42—131no—
586C42—131no—
587C42—131no—
588C42—131no—
589C42—131no—
590C42—131no—
591C42—131no—
592C42—131no—
593C42—131no—
594C42—134no—
595C42C22×#26111yescharacteristic
596C42C22×#26111yescharacteristic
597C42C22×#26111yescharacteristic
598C42C22×#26111yescharacteristic
599C42C22×#26114yes—
600C13#6026911yescharacteristic, complemented, Sylow
601C23—131no—
602C23—134no—
603C23—131no—
604C23—262no—
605C23—262no—
606C23—521no—
607C23C23×#26111yescharacteristic
608Q8—24no—
609Q8—42no—
610Q8—522no—
611D4—268no—
612D4—268no—
613D4—264no—
614D4—522no—
615D4—524no—
616D4—522no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—41no—
620C2×C4—131no—
621C2×C4—131no—
622C2×C4—132no—
623C2×C4—132no—
624C2×C4—131no—
625C2×C4—131no—
626C2×C4—131no—
627C2×C4—131no—
628C2×C4—134no—
629C2×C4—264no—
630C2×C4—261no—
631C2×C4—261no—
632C2×C4—262no—
633C2×C4—262no—
634C2×C4—264no—
635C2×C4—268no—
636C2×C4—262no—
637C2×C4—261no—
638C2×C4—261no—
639C2×C4—262no—
640C2×C4—262no—
641C2×C4—262no—
642C2×C4—521no—
643C2×C4—521no—
644C2×C4—521no—
645C2×C4—521no—
646C2×C4—521no—
647C2×C4—521no—
648C2×C4—524no—
649C2×C4C23×#26111yescharacteristic
650C2×C4C23×#26111yescharacteristic
651C2×C4C23×#26111yescharacteristic
652C2×C4C23×#26111yescharacteristic
653C2×C4C23×#26111yescharacteristic
654C2×C4C23×#26114yes—
655C2×C4C23×#26114yes—
656C2×C4C23×#26111yescharacteristic
657C8—264no—
658C8—264no—
659C8—268no—
660C22—21no—
661C22—21no—
662C22—132no—
663C22—261no—
664C22—261no—
665C22—261no—
666C22—264no—
667C22—261no—
668C22—264no—
669C22—261no—
670C22—264no—
671C22—524no—
672C22#1171962512yes—
673C22C24×#26111yescharacteristic
674C4—21no—
675C4—24no—
676C4—21no—
677C4—21no—
678C4—24no—
679C4—21no—
680C4—21no—
681C4—131no—
682C4—131no—
683C4—132no—
684C4—261no—
685C4—261no—
686C4—261no—
687C4—261no—
688C4—264no—
689C4#1171963112yes—
690C2—22no—
691C2—262no—
692C2—521no—
693C2—524no—
694C2C2×#1171963111yescharacteristic
695C2D13⋊#56811yescharacteristic
696C2C2×#1171962511yescharacteristic
subgroupG/H
center, FrattiniC22C24×#261
commutator, socleC22×C13C24×C4
FittingC13×#533C4
prime radical#13128133C2
cosocleC2×Dic13C25
hypercenter#533#261
hypocenterC13#60269
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ #533

Complements

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

NH ≅ G/Ntype
1. #13131794C2semidirect
2. #13131775C2semidirect
3. #13131765C2semidirect
4. #13131760C2semidirect
5. #13131629C2semidirect
6. #13131569C2semidirect
7. #13131563C2semidirect
8. #13131535C2semidirect
9. D13⋊#432C2semidirect
10. #13131484C2semidirect
11. C2×#11719053C2semidirect
35. #11719158C22semidirect
42. #11719079C22semidirect
43. #11719078C22semidirect
44. #11719077C22semidirect
47. #11719075C22semidirect
48. #11719075C22semidirect
53. #11719055C22semidirect
59. #11719053C22semidirect
62. D13⋊(C4⋊C8)C22semidirect
63. #11719049C22semidirect
600. C13#60269semidirect

Maximal subgroups

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

subgroupindex
#131317942
#131317752
#131317652
#131317602
#131316292
#131315692
#131315632
#131315352
D13⋊#4322
#131314842
C2×#117190532
#131281332
#6026913