Finite Group Databasebeta

← #16808536

Subgroups — #16808536

Order 3328.

1996 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13131672C214yesmaximal, complemented
2#13131664C214yesmaximal, complemented
3#13131644C214yesmaximal, complemented
4#13131643C212yesmaximal, complemented
5#13131640C212yesmaximal, complemented
6#13131632C212yesmaximal, complemented
7#13131582C212yesmaximal, complemented
8#13131569C214yesmaximal, complemented
9#13131521C212yesmaximal, complemented
10D13⋊#431C211yesmaximal, characteristic, complemented
11C4×#88240C212yesmaximal, complemented
12C2×C4×#6118C211yesmaximal, characteristic, complemented
13#13128133C211yesmaximal, characteristic
14C2×#88240C2214yes—
15C22×#6118C2212yes—
16C13×#533C411yescharacteristic
17#11719433C411yescharacteristic
18#11719433C2211yescharacteristic
19#11719430C411yescharacteristic
20#11719430C2211yescharacteristic
21#11719396C412yes—
22#11719396C2212yes—
23#11719332C412yes—
24#11719332C2212yes—
25#11719329C412yes—
26#11719329C2212yes—
27#11719285C412yes—
28#11719285C412yes—
29C4×#6131C2212yes—
30C4×#6131C2212yes—
31#11719229C412yes—
32#11719227C2212yes—
33#11719182C411yescharacteristic
34C2×C42×D13C2211yescharacteristic
35#11719159C2214yes—
36#11719158C2218yescomplemented
37#11719125C2212yes—
38D13⋊(C22⋊C8)C2212yes—
39C2×#88110C2212yes—
40#11719119C2211yescharacteristic
41#11719119C2211yescharacteristic
42C2×C4×#1057C2212yes—
43#11719080C2214yescomplemented
44#11719079C2214yes—
45#11719077C2218yescomplemented
46#11719076C2218yes—
47#11719076C2214yescomplemented
48#11719075C2218yes—
49#11719075C2218yescomplemented
50#11719074C2214yescomplemented
51#11719073C2214yescomplemented
52#11719072C2214yes—
53#11719072C2218yescomplemented
54#11719064C2218yes—
55#11719063C2218yes—
56#11719051C2212yes—
57#11719051C2214yescomplemented
58D13⋊(C4⋊C8)C2212yes—
59#11719049C2212yes—
60#11719049C2214yescomplemented
61C4×#6118C2211yescharacteristic
62C4×#6118C2212yes—
63C4×#6118C2212yes—
64C4×#6118C2211yescharacteristic
65C4×#6118C2212yes—
66C4×#6118C2214yescomplemented
67C4×D13⋊C8C2212yes—
68C4×D13⋊C8C2214yescomplemented
69C2×#6131C2×C412yes—
70C2×#6131C2312yes—
71C2×#6127C2×C412yes—
72C22×C4×D13C2×C411yescharacteristic
73C22×C4×D13C2×C411yescharacteristic
74C22×C4×D13C2311yescharacteristic
75C22×#1057C2314yes—
76#88240—216no—
77C2×#6118—28no—
78C2×#6118C2314yes—
79C2×#6118C2312yes—
80C2×#6118C2318yes—
81C2×#6118C2312yes—
82C2×D13⋊C8C2314yes—
83C2×D13⋊C8C2318yes—
84C13×C4⋊Q8C2×C411yescharacteristic
85C13×C4⋊Q8C2×C411yescharacteristic
86C13×#125C2×C412yes—
87C13×C22⋊Q8C2×C412yes—
88C13×C22⋊Q8C2×C412yes—
89C4×Q8×C13C2×C412yes—
90C4×Q8×C13C2×C412yes—
91C13×#117C2×C412yes—
92C2×C42×C13C2×C411yescharacteristic
93#88201C2×C412yes—
94#88201C2×C412yes—
95#88200C2×C412yes—
96#88200C2×C412yes—
97Q8×Dic13C2×C412yes—
98Q8×Dic13C2312yes—
99#88184C2×C412yes—
100#88184C2×C412yes—
101C2×C4×Dic13C2×C411yescharacteristic
102C2×C4×Dic13C2311yescharacteristic
103C2×C4×Dic13C2311yescharacteristic
104#88152C2×C414yes—
105#88152C2×C414yes—
106#88151C2×C412yes—
107#88151C2×C412yes—
108#88149C2×C412yes—
109#88149C2×C412yes—
110#88149C2×C412yes—
111#88149C2×C412yes—
112#88148C2×C414yes—
113#88148C2×C414yes—
114#88147C2×C412yes—
115#88147C2×C412yes—
116#88147C2×C414yes—
117#88147C2312yes—
118#88147C2312yes—
119#88147C2314yes—
120#88146C2×C412yes—
121#88146C2×C414yes—
122#88146C2312yes—
123#88146C2314yes—
124#88144C2×C412yes—
125#88144C2×C412yes—
126#88141C2×C412yes—
127#88141C2312yes—
128#88140C2×C414yes—
129#88136C2×C414yes—
130#88135C2×C414yes—
131#88135C2314yes—
132#88129C2×C412yes—
133#88128C2×C411yescharacteristic
134C4×D52C2×C412yes—
135C4×D52C2×C412yes—
136C4×D52C2×C414yes—
137C4×D52C2×C414yes—
138#88126C2×C414yes—
139C42×D13C2×C411yescharacteristic
140C42×D13C2×C411yescharacteristic
141C42×D13C2×C411yescharacteristic
142C42×D13C2×C411yescharacteristic
143C42×D13C2311yescharacteristic
144C42×D13C2311yescharacteristic
145C42×D13C2311yescharacteristic
146C42×D13C2311yescharacteristic
147C42×D13C2314yes—
148#88123C2×C411yescharacteristic
149C22⋊#1057C2312yes—
150C22⋊#1057C2312yes—
151#88112C2314yes—
152#88112C2318yes—
153#88111C2314yes—
154#88111C2318yes—
155#88111C2318yes—
156#88110C2312yes—
157#88110C2314yes—
158#88110C2312yes—
159#88110C2318yes—
160C4⋊#1057C2312yes—
161C4⋊#1057C2312yes—
162C4⋊#1057C2318yes—
163C4×#1057C2312yes—
164C4×#1057C2312yes—
165C4×#1057C2314yes—
166C4×#1057C2312yes—
167C4×#1057C2318yes—
168C4×#1057C2312yes—
169C4×#1057C2314yes—
170#60210—131nomaximal, Sylow
171C23×D13C22×C411yescharacteristic
172C2×Q8×C13C22×C412yes—
173C2×Q8×C13C22×C412yes—
174C22×C4×C13C22×C411yescharacteristic
175C22×C4×C13C22×C411yescharacteristic
176C22×C4×C13C22×C411yescharacteristic
177C2×C22⋊D13C22×C414yes—
178C22×Dic13C22×C411yescharacteristic
179C22×Dic13C22×C411yescharacteristic
180C22×Dic13C2411yescharacteristic
181#6131—28no—
182#6131—44no—
183#6127—28no—
184C2×D52C22×C412yes—
185C2×D52C22×C414yes—
186C2×D52C22×C412yes—
187C2×D52C22×C412yes—
188C2×D52C22×C414yes—
189C2×C4×D13—24no—
190C2×C4×D13—24no—
191C2×C4×D13—42no—
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×C411yescharacteristic
199C2×C4×D13C22×C411yescharacteristic
200C2×C4×D13C22×C414yes—
201C2×C4×D13C22×C414yes—
202C2×C4×D13C22×C411yescharacteristic
203C2×C4×D13C22×C411yescharacteristic
204C2×C4×D13C2411yescharacteristic
205C2×C4×D13C2414yes—
206C2×C4×D13C2411yescharacteristic
207C2×Dic26C22×C412yes—
208C2×#1057—28no—
209C2×#1057C2414yes—
210C2×#1057C2414yes—
211C2×#1057C2414yes—
212C2×#1057C2414yes—
213#6118—24no—
214#6118—28no—
215#6118—216no—
216#6118#4118yescomplemented
217D13⋊C8—28no—
218D13⋊C8—216no—
219C13×C4⋊C4C22×C412yes—
220C13×C4⋊C4C22×C412yes—
221C13×C4⋊C4C22×C412yes—
222C13×C4⋊C4C22×C412yes—
223C13×C4⋊C4C22×C414yes—
224C13×C4⋊C4C22×C414yes—
225C13×C22⋊C4C22×C414yes—
226C42×C13C22×C411yescharacteristic
227C42×C13C22×C411yescharacteristic
228C42×C13C22×C411yescharacteristic
229C42×C13C22×C411yescharacteristic
230C42×C13C22×C414yes—
231#6103C22×C414yes—
232#6103C22×C414yes—
233#6103C22×C414yes—
234#6103C22×C414yes—
235#6103C22×C414yes—
236#6103C22×C414yes—
237#6103C22×C414yes—
238#6103C22×C414yes—
239C4⋊Dic13C22×C412yes—
240C4⋊Dic13C22×C412yes—
241C4⋊Dic13C22×C414yes—
242C4⋊Dic13C22×C414yes—
243#6101C22×C414yes—
244#6101C22×C414yes—
245C4×Dic13C22×C411yescharacteristic
246C4×Dic13C22×C411yescharacteristic
247C4×Dic13C22×C411yescharacteristic
248C4×Dic13C22×C411yescharacteristic
249C4×Dic13C22×C411yescharacteristic
250C4×Dic13C22×C411yescharacteristic
251C4×Dic13C22×C411yescharacteristic
252C4×Dic13C22×C411yescharacteristic
253C4×Dic13C22×C414yes—
254C4×Dic13C2411yescharacteristic
255C4×Dic13C2411yescharacteristic
256C4×Dic13C2411yescharacteristic
257C4×Dic13C2414yes—
258C4×Dic13C2411yescharacteristic
259#3444—131no—
260#2969—134no—
261#2968—134no—
262#2965—132no—
263#2965—134no—
264C8×#41—132no—
265#2962—132no—
266#2935—132no—
267#2933—134no—
268#2922—132no—
269C2×#431—131no—
270C4×#131—132no—
271C2×C4×M16—131no—
272C23×C13C23×C411yescharacteristic
273C22×D13—22no—
274C22×D13—22no—
275C22×D13—41no—
276C22×D13C23×C414yes—
277C22×D13C23×C411yescharacteristic
278C22×D13C23×C411yescharacteristic
279Q8×C13—24no—
280Q8×C13—42no—
281C2×C4×C13—22no—
282C2×C4×C13—41no—
283C2×C4×C13#13114yescomplemented
284C2×C4×C13C23×C411yescharacteristic
285C2×C4×C13C23×C411yescharacteristic
286C2×C4×C13C23×C411yescharacteristic
287C2×C4×C13C23×C414yes—
288C2×C4×C13C23×C414yes—
289C2×C4×C13C23×C411yescharacteristic
290C2×C4×C13C23×C411yescharacteristic
291C2×C4×C13C23×C411yescharacteristic
292C22⋊D13—28no—
293C2×Dic13—22no—
294C2×Dic13—22no—
295C2×Dic13—22no—
296C2×Dic13C23×C411yescharacteristic
297C2×Dic13C23×C411yescharacteristic
298C2×Dic13C23×C411yescharacteristic
299C2×Dic13C23×C411yescharacteristic
300C2×Dic13C23×C414yes—
301C2×Dic13C23×C411yescharacteristic
302C2×Dic13C2511yescharacteristic
303D52—28no—
304D52—24no—
305D52—24no—
306D52—42no—
307D52—44no—
308C4×D13—22no—
309C4×D13—22no—
310C4×D13—22no—
311C4×D13—22no—
312C4×D13—22no—
313C4×D13—22no—
314C4×D13—28no—
315C4×D13—22no—
316C4×D13—22no—
317C4×D13—28no—
318C4×D13—28no—
319C4×D13—22no—
320C4×D13—41no—
321C4×D13—41no—
322C4×D13C2×#4114yes—
323Dic26—24no—
324#1057—24no—
325#1057—24no—
326#1057—24no—
327#1057C2×#4118yes—
328C2×#131—134no—
329C22×M16—132no—
330#533—131no—
331#533—131no—
332#533#26111yescharacteristic
333#532—131no—
334#532—131no—
335#532—131no—
336#529—132no—
337#529—132no—
338#529—132no—
339#529—132no—
340#529—132no—
341#529—132no—
342#525—132no—
343#525—132no—
344#525—132no—
345C4×#41—132no—
346C4×#41—132no—
347C4×#41—132no—
348C22×C42—131no—
349#446—138no—
350#446—134no—
351C8×Q8—134no—
352#436—138no—
353#436—134no—
354#435—138no—
355#435—138no—
356#435—138no—
357C8×D4—138no—
358C8×D4—134no—
359#433—138no—
360#431—132no—
361#431—132no—
362#431—131no—
363#431—131no—
364#431—132no—
365#431—134no—
366#431—134no—
367#424—134no—
368C2×C4⋊C8—132no—
369#408—134no—
370C2×C22⋊C8—132no—
371#405—134no—
372#405—138no—
373C4×M16—131no—
374C4×M16—131no—
375C4×M16—132no—
376C4×M16—132no—
377C4×M16—132no—
378C4×M16—134no—
379C2×#97—132no—
380C2×C4×C8—132no—
381C2×C4×C8—132no—
382C2×C4×C8—134no—
383C22×C13—21no—
384C22×C13—21no—
385C22×C13C2×#13112yes—
386C22×C13C24×C411yescharacteristic
387C2×D13—21no—
388C2×D13—21no—
389C2×D13—21no—
390C2×D13—24no—
391C2×D13—21no—
392C2×D13—24no—
393C2×D13—21no—
394C2×D13—24no—
395C2×D13—44no—
396C2×D13C4×#4112yes—
397C4×C13—21no—
398C4×C13—24no—
399C4×C13—21no—
400C4×C13—21no—
401C4×C13—24no—
402C4×C13C4×#4112yes—
403C4×C13C2×#13112yes—
404C4×C13C2×#13112yes—
405Dic13—21no—
406Dic13—24no—
407Dic13—21no—
408Dic13—21no—
409Dic13—21no—
410Dic13#56812yes—
411Dic13C22×#4112yes—
412C2×#41—132no—
413C2×#41—132no—
414C2×#41—132no—
415C23×C4—131no—
416C23×C4—131no—
417C23×C4—131no—
418#131—2616no—
419C2×M16—132no—
420C2×M16—132no—
421C2×M16—134no—
422C2×M16—138no—
423C2×M16—268no—
424C22×C8—134no—
425C22×C8—134no—
426C22×C8—138no—
427C4⋊Q8—131no—
428C4⋊Q8C2×#26111yescharacteristic
429C4⋊Q8C2×#26111yescharacteristic
430#127—131no—
431#126—134no—
432#126—134no—
433#125—132no—
434#125—132no—
435#125C2×#26112yes—
436#124—132no—
437#124—132no—
438#124—132no—
439#123—134no—
440#123—134no—
441#123—134no—
442C22⋊Q8—132no—
443C22⋊Q8—132no—
444C22⋊Q8—132no—
445C22⋊Q8—132no—
446C22⋊Q8C2×#26112yes—
447C22⋊Q8C2×#26112yes—
448#121—132no—
449#121—132no—
450#121—132no—
451#121—132no—
452#121—132no—
453#121—132no—
454#120—134no—
455C4×Q8—132no—
456C4×Q8—132no—
457C4×Q8—132no—
458C4×Q8—132no—
459C4×Q8C2×#26112yes—
460C4×Q8C2×#26112yes—
461C4×D4—134no—
462C4×D4—134no—
463C4×D4—132no—
464C4×D4—132no—
465C4×D4—132no—
466C4×D4—132no—
467C4×D4—134no—
468C4×D4—134no—
469C4×D4—134no—
470C4×D4—134no—
471C4×D4—132no—
472C4×D4—132no—
473#117—132no—
474#117—132no—
475#117—134no—
476#117—134no—
477#117—134no—
478#117C2×#26112yes—
479C2×C42—131no—
480C2×C42—131no—
481C2×C42—131no—
482C2×C42—134no—
483C2×C42—131no—
484C2×C42—131no—
485C2×C42—131no—
486C2×C42—131no—
487C2×C42—131no—
488C2×C42—131no—
489C2×C42—131no—
490C2×C42—131no—
491C2×C42C2×#26111yescharacteristic
492C4⋊C8—132no—
493C4⋊C8—132no—
494C4⋊C8—138no—
495C4⋊C8—134no—
496C4⋊C8—138no—
497C22⋊C8—134no—
498C22⋊C8—138no—
499C22⋊C8—138no—
500C22⋊C8—132no—
501C22⋊C8—132no—
502#97—132no—
503#97—132no—
504#97—134no—
505#97—138no—
506C4×C8—132no—
507C4×C8—132no—
508C4×C8—132no—
509C4×C8—132no—
510C4×C8—134no—
511C4×C8—134no—
512C4×C8—138no—
513C2×C13—22no—
514C2×C13C2×C4×#4111yescharacteristic
515C2×C13C22×#13111yescharacteristic
516C2×C13C2×#56811yescharacteristic
517D13—22no—
518D13—44no—
519D13—41no—
520C24—131no—
521#41—268no—
522#41—268no—
523#41—524no—
524C2×Q8—132no—
525C2×Q8C22×#26112yes—
526C2×Q8C22×#26112yes—
527C2×D4—134no—
528C2×D4—134no—
529C2×D4—132no—
530C2×D4—132no—
531C2×D4—134no—
532C2×D4—132no—
533C22×C4—131no—
534C22×C4—131no—
535C22×C4—131no—
536C22×C4—131no—
537C22×C4—131no—
538C22×C4—134no—
539C22×C4—131no—
540C22×C4—131no—
541C22×C4—131no—
542C22×C4—131no—
543C22×C4—131no—
544C22×C4—131no—
545C22×C4—134no—
546C22×C4—131no—
547C22×C4—131no—
548C22×C4—134no—
549C22×C4—131no—
550C22×C4—131no—
551C22×C4—264no—
552C22×C4—264no—
553C22×C4—522no—
554C22×C4C22×#26111yescharacteristic
555C22×C4C22×#26111yescharacteristic
556C22×C4C22×#26111yescharacteristic
557M16—138no—
558M16—268no—
559M16—2616no—
560M16—264no—
561C2×C8—134no—
562C2×C8—134no—
563C2×C8—134no—
564C2×C8—134no—
565C2×C8—268no—
566C2×C8—2616no—
567C2×C8—268no—
568C4⋊C4—132no—
569C4⋊C4—132no—
570C4⋊C4—134no—
571C4⋊C4—134no—
572C4⋊C4—134no—
573C4⋊C4—134no—
574C4⋊C4C22×#26112yes—
575C4⋊C4C22×#26112yes—
576C4⋊C4C22×#26114yes—
577C4⋊C4C22×#26114yes—
578C4⋊C4C22×#26112yes—
579C4⋊C4C22×#26112yes—
580C22⋊C4—134no—
581C22⋊C4—134no—
582C22⋊C4—134no—
583C22⋊C4—134no—
584C22⋊C4—134no—
585C22⋊C4—134no—
586C22⋊C4—134no—
587C22⋊C4—134no—
588C22⋊C4C22×#26114yes—
589C42—131no—
590C42—131no—
591C42—134no—
592C42—131no—
593C42—131no—
594C42—131no—
595C42—131no—
596C42—131no—
597C42—131no—
598C42—131no—
599C42—131no—
600C42—134no—
601C42—131no—
602C42—131no—
603C42C22×#26111yescharacteristic
604C42C22×#26111yescharacteristic
605C42C22×#26111yescharacteristic
606C42C22×#26111yescharacteristic
607C42C22×#26114yes—
608C13#6021011yescharacteristic, complemented, Sylow
609C23—131no—
610C23—134no—
611C23—131no—
612C23—262no—
613C23—262no—
614C23—521no—
615C23C23×#26111yescharacteristic
616Q8—24no—
617Q8—42no—
618Q8—264no—
619D4—268no—
620D4—268no—
621D4—264no—
622D4—264no—
623D4—522no—
624D4—524no—
625C2×C4—22no—
626C2×C4—41no—
627C2×C4—131no—
628C2×C4—131no—
629C2×C4—134no—
630C2×C4—131no—
631C2×C4—131no—
632C2×C4—131no—
633C2×C4—131no—
634C2×C4—134no—
635C2×C4—268no—
636C2×C4—262no—
637C2×C4—262no—
638C2×C4—262no—
639C2×C4—268no—
640C2×C4—262no—
641C2×C4—262no—
642C2×C4—262no—
643C2×C4—262no—
644C2×C4—262no—
645C2×C4—262no—
646C2×C4—262no—
647C2×C4—262no—
648C2×C4—268no—
649C2×C4—262no—
650C2×C4—521no—
651C2×C4—521no—
652C2×C4#8824014yescomplemented
653C2×C4C23×#26111yescharacteristic
654C2×C4C23×#26111yescharacteristic
655C2×C4C23×#26111yescharacteristic
656C2×C4C23×#26114yes—
657C2×C4C23×#26114yes—
658C2×C4C23×#26111yescharacteristic
659C2×C4C23×#26111yescharacteristic
660C2×C4C23×#26111yescharacteristic
661C8—138no—
662C8—264no—
663C8—264no—
664C8—264no—
665C22—21no—
666C22—21no—
667C22—132no—
668C22—261no—
669C22—261no—
670C22—261no—
671C22—264no—
672C22—261no—
673C22—264no—
674C22—261no—
675C22—264no—
676C22—524no—
677C22C2×#8824012yes—
678C22C24×#26111yescharacteristic
679C4—21no—
680C4—24no—
681C4—21no—
682C4—21no—
683C4—24no—
684C4—132no—
685C4—132no—
686C4—261no—
687C4—261no—
688C4—261no—
689C4—264no—
690C4—261no—
691C4C2×#8824012yes—
692C4C2×#8824012yes—
693C4#41×#26112yes—
694C2—22no—
695C2—262no—
696C2—521no—
697C2—524no—
698C2C2×#41×#26111yescharacteristic
699C2C22×#8824011yescharacteristic
700C2D13⋊#56811yescharacteristic
subgroupG/H
centerC2×C4C23×#261
commutator, socleC22×C13C24×C4
FrattiniC22C24×#261
FittingC13×#533C4
prime radical#13128133C2
cosocleC2×Dic13C25
hypercenter#533#261
hypocenterC13#60210
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ #533

Complements

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

NH ≅ G/Ntype
1. #13131672C2semidirect
2. #13131664C2semidirect
3. #13131644C2semidirect
4. #13131643C2semidirect
5. #13131640C2semidirect
6. #13131632C2semidirect
7. #13131582C2semidirect
8. #13131569C2semidirect
9. #13131521C2semidirect
10. D13⋊#431C2semidirect
11. C4×#88240C2semidirect
12. C2×C4×#6118C2semidirect
36. #11719158C22semidirect
43. #11719080C22semidirect
45. #11719077C22semidirect
47. #11719076C22semidirect
49. #11719075C22semidirect
50. #11719074C22semidirect
51. #11719073C22semidirect
53. #11719072C22semidirect
57. #11719051C22semidirect
60. #11719049C22semidirect
66. C4×#6118C22semidirect
68. C4×D13⋊C8C22semidirect
216. #6118#41semidirect
283. C2×C4×C13#131semidirect
608. C13#60210semidirect
652. C2×C4#88240semidirect

Maximal subgroups

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

subgroupindex
#131316722
#131316642
#131316442
#131316432
#131316402
#131316322
#131315822
#131315692
#131315212
D13⋊#4312
C4×#882402
C2×C4×#61182
#131281332
#6021013