Finite Group Databasebeta

← #16808573

Subgroups — #16808573

Order 3328.

1960 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13131672C214yesmaximal, complemented
2#13131665C214yesmaximal, complemented
3#13131660C214yesmaximal, complemented
4#13131653C214yesmaximal, complemented
5#13131637C212yesmaximal, complemented
6#13131576C214yesmaximal, complemented
7#13131576C212yesmaximal, complemented
8#13131518C212yesmaximal, complemented
9#13131514C211yesmaximal, characteristic, complemented
10#13131402C212yesmaximal, complemented
11C4×D13⋊M16C211yesmaximal, characteristic, complemented
12C2×#11719396C211yesmaximal, characteristic
13C2×D13⋊M16C2212yes—
14C2×D13⋊M16C2214yes—
15C2×C13×#125C411yescharacteristic
16#11719396C412yes—
17#11719396C412yes—
18#11719396C412yes—
19#11719396C412yes—
20#11719396C2212yes—
21#11719396C2212yes—
22#11719396C2212yes—
23#11719396C2212yes—
24C2×#88152C412yes—
25C2×#88151C411yescharacteristic
26C2×#88149C411yescharacteristic
27C2×#88148C412yes—
28C2×#88147C2212yes—
29C2×#88147C2211yescharacteristic
30C2×#88146C2212yes—
31C2×#88141C2211yescharacteristic
32C2×#88129C411yescharacteristic
33C2×C42×D13C2211yescharacteristic
34#11719129C2212yes—
35#11719129C2214yes—
36#11719126C2212yes—
37#11719126C2214yes—
38C4×#6122C2212yes—
39C4×#6122C2214yes—
40C4×#6122C2211yescharacteristic
41C4×#6122C2211yescharacteristic
42C4×#6122C2212yes—
43#11719080C2214yescomplemented
44#11719078C2218yescomplemented
45#11719077C2218yescomplemented
46#11719077C2218yescomplemented
47#11719076C2214yescomplemented
48#11719076C2218yescomplemented
49#11719075C2218yescomplemented
50#11719075C2218yescomplemented
51#11719075C2218yescomplemented
52#11719074C2214yescomplemented
53#11719073C2218yescomplemented
54#11719073C2214yescomplemented
55#11719072C2218yescomplemented
56#11719072C2218yescomplemented
57#11719055C2212yescomplemented
58#11719054C2212yescomplemented
59#11719051C2212yescomplemented
60#11719049C2212yescomplemented
61C4×#6118C2212yescomplemented
62C4×#6118C2212yescomplemented
63#11719047C2212yescomplemented
64C4×D13⋊C8C2212yescomplemented
65C22×D52C2×C411yescharacteristic
66C22×D52C2×C412yes—
67C22×C4×D13C2×C411yescharacteristic
68C22×C4×D13C2×C411yescharacteristic
69C22×C4×D13C2311yescharacteristic
70C22×C4×D13C2312yes—
71C22×Dic26C2×C411yescharacteristic
72C2×#6122C2312yes—
73C2×#6122C2314yes—
74C2×#6122C2312yes—
75D13⋊M16—28no—
76D13⋊M16—216no—
77C2×#6118C2314yes—
78C2×#6118C2318yes—
79C2×D13⋊C8C2314yes—
80C2×D13⋊C8C2318yes—
81C13×#125C2×C412yes—
82C13×#125C2×C412yes—
83C13×#125C2×C412yes—
84C13×#125C2×C412yes—
85C2×C13×C4⋊C4C2×C411yescharacteristic
86C2×C13×C4⋊C4C2×C412yes—
87C2×C13×C4⋊C4C2×C411yescharacteristic
88C2×C13×C4⋊C4C2×C412yes—
89C2×C42×C13C2×C411yescharacteristic
90C2×#6103C2×C412yes—
91C2×#6103C2×C412yes—
92C2×#6103C2×C412yes—
93C2×#6103C2×C412yes—
94C2×#6103C2×C412yes—
95C2×C4⋊Dic13C2×C412yes—
96C2×#6101C2×C412yes—
97C2×C4×Dic13C2×C411yescharacteristic
98C2×C4×Dic13C2311yescharacteristic
99C2×C4×Dic13C2311yescharacteristic
100C2×C4×Dic13C2312yes—
101#88152C2×C414yes—
102#88152C2×C414yes—
103#88152C2×C414yes—
104#88152C2×C414yes—
105#88151C2×C412yes—
106#88151C2×C412yes—
107#88151C2×C412yes—
108#88151C2×C412yes—
109#88149C2×C412yes—
110#88149C2×C412yes—
111#88149C2×C412yes—
112#88149C2×C412yes—
113#88148C2×C414yes—
114#88148C2×C414yes—
115#88148C2×C414yes—
116#88148C2×C414yes—
117#88147C2×C412yes—
118#88147C2×C412yes—
119#88147C2×C414yes—
120#88147C2×C414yes—
121#88147C2314yes—
122#88147C2312yes—
123#88147C2312yes—
124#88147C2314yes—
125#88146C2×C414yes—
126#88146C2×C414yes—
127#88146C2314yes—
128#88146C2314yes—
129#88141C2×C412yes—
130#88141C2×C412yes—
131#88141C2312yes—
132#88141C2312yes—
133#88129C2×C412yes—
134#88129C2×C412yes—
135#88129C2×C412yes—
136#88129C2×C412yes—
137C42×D13C2×C411yescharacteristic
138C42×D13C2×C411yescharacteristic
139C42×D13C2×C411yescharacteristic
140C42×D13C2×C411yescharacteristic
141C42×D13C2311yescharacteristic
142C42×D13C2311yescharacteristic
143C42×D13C2311yescharacteristic
144C42×D13C2311yescharacteristic
145#88112C2314yes—
146#88112C2318yes—
147#88111C2314yes—
148#88111C2314yes—
149#88111C2318yes—
150#88111C2318yes—
151#88110C2312yes—
152#88110C2314yes—
153#88110C2312yes—
154#88110C2314yes—
155#88110C2318yes—
156C4⋊#1057C2314yes—
157C4⋊#1057C2318yes—
158C4×#1057C2312yes—
159C4×#1057C2314yes—
160C4×#1057C2312yes—
161C4×#1057C2314yes—
162C4×#1057C2318yes—
163#60214—131nomaximal, Sylow
164C23×D13C22×C411yescharacteristic
165C23×D13C22×C412yes—
166C22×C4×C13C22×C411yescharacteristic
167C22×C4×C13C22×C411yescharacteristic
168C22×C4×C13C22×C412yes—
169C22×C4×C13C22×C412yes—
170C22×C4×C13C22×C411yescharacteristic
171C22×Dic13C22×C411yescharacteristic
172C22×Dic13C22×C411yescharacteristic
173C22×Dic13C22×C412yes—
174C22×Dic13C2411yescharacteristic
175C2×D52—42no—
176C2×D52—44no—
177C2×D52C22×C412yes—
178C2×D52C22×C414yes—
179C2×D52C22×C412yes—
180C2×D52C22×C414yes—
181C2×C4×D13—24no—
182C2×C4×D13—28no—
183C2×C4×D13—42no—
184C2×C4×D13—42no—
185C2×C4×D13C22×C411yescharacteristic
186C2×C4×D13C22×C411yescharacteristic
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×D13C2411yescharacteristic
197C2×C4×D13C2411yescharacteristic
198C2×C4×D13C2414yes—
199C2×Dic26—42no—
200C2×Dic26C22×C412yes—
201C2×Dic26C22×C412yes—
202#6122—24no—
203#6122—28no—
204#6122#4118yes—
205C2×#1057C2414yes—
206C2×#1057C2418yes—
207C2×#1057C2414yes—
208#6118—28no—
209#6118—216no—
210D13⋊C8—28no—
211D13⋊C8—216no—
212C13×C4⋊C4C22×C412yes—
213C13×C4⋊C4C22×C412yes—
214C13×C4⋊C4C22×C414yes—
215C13×C4⋊C4C22×C414yes—
216C13×C4⋊C4C22×C412yes—
217C13×C4⋊C4C22×C412yes—
218C13×C4⋊C4C22×C414yes—
219C13×C4⋊C4C22×C414yes—
220C42×C13C22×C411yescharacteristic
221C42×C13C22×C411yescharacteristic
222C42×C13C22×C411yescharacteristic
223C42×C13C22×C411yescharacteristic
224#6103C22×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—
233#6103C22×C414yes—
234C4⋊Dic13C22×C414yes—
235C4⋊Dic13C22×C414yes—
236#6101C22×C414yes—
237#6101C22×C414yes—
238C4×Dic13C22×C411yescharacteristic
239C4×Dic13C22×C411yescharacteristic
240C4×Dic13C22×C411yescharacteristic
241C4×Dic13C22×C411yescharacteristic
242C4×Dic13C22×C411yescharacteristic
243C4×Dic13C22×C411yescharacteristic
244C4×Dic13C22×C411yescharacteristic
245C4×Dic13C22×C411yescharacteristic
246C4×Dic13C22×C414yes—
247C4×Dic13C2411yescharacteristic
248C4×Dic13C2411yescharacteristic
249C4×Dic13C2411yescharacteristic
250C4×Dic13C2414yes—
251C4×Dic13C2411yescharacteristic
252C2×#529—131no—
253#2969—134no—
254#2968—134no—
255#2967—134no—
256#2966—134no—
257Q8×M16—132no—
258D4×M16—134no—
259D4×M16—132no—
260#2921—132no—
261#2920—131no—
262#2873—132no—
263C2×C4×M16—131no—
264C23×C13C23×C411yescharacteristic
265C22×D13—22no—
266C22×D13—24no—
267C22×D13—22no—
268C22×D13—41no—
269C22×D13—42no—
270C22×D13—42no—
271C22×D13C23×C414yes—
272C22×D13C23×C411yescharacteristic
273C22×D13C23×C411yescharacteristic
274C2×C4×C13—22no—
275C2×C4×C13—24no—
276C2×C4×C13—22no—
277C2×C4×C13—41no—
278C2×C4×C13—42no—
279C2×C4×C13C23×C411yescharacteristic
280C2×C4×C13C23×C411yescharacteristic
281C2×C4×C13C23×C414yes—
282C2×C4×C13C23×C411yescharacteristic
283C2×C4×C13C23×C411yescharacteristic
284C2×C4×C13C23×C411yescharacteristic
285C2×C4×C13C23×C414yes—
286C2×C4×C13C23×C411yescharacteristic
287C2×Dic13—42no—
288C2×Dic13—41no—
289C2×Dic13—41no—
290C2×Dic13C23×C411yescharacteristic
291C2×Dic13C23×C411yescharacteristic
292C2×Dic13C23×C411yescharacteristic
293C2×Dic13C23×C411yescharacteristic
294C2×Dic13C23×C414yes—
295C2×Dic13C23×C411yescharacteristic
296C2×Dic13C2×#4114yes—
297C2×Dic13C2511yescharacteristic
298D52—28no—
299D52—24no—
300D52—42no—
301D52—44no—
302C4×D13—22no—
303C4×D13—22no—
304C4×D13—22no—
305C4×D13—22no—
306C4×D13—22no—
307C4×D13—22no—
308C4×D13—28no—
309C4×D13—22no—
310C4×D13—24no—
311C4×D13—22no—
312C4×D13—24no—
313C4×D13—41no—
314C4×D13—41no—
315C4×D13—41no—
316C4×D13—41no—
317Dic26—24no—
318Dic26—42no—
319#1057—24no—
320#1057—28no—
321#1057C2×#4118yes—
322C22×M16—132no—
323C22×M16—134no—
324#529—132no—
325#529—132no—
326#529—132no—
327#529—132no—
328#529—132no—
329#529—132no—
330#529—132no—
331#529—132no—
332C2×#126—132no—
333C2×#125#26111yescharacteristic
334C2×#124—131no—
335C2×#123—132no—
336C2×C22⋊Q8—131no—
337C2×#121—131no—
338C2×C4×Q8—131no—
339C2×C4×D4—132no—
340C2×C4×D4—131no—
341C2×#117—132no—
342C22×C42—131no—
343#446—134no—
344#446—138no—
345C8×Q8—134no—
346#436—134no—
347#436—138no—
348#435—138no—
349#435—138no—
350#435—138no—
351C8×D4—138no—
352C8×D4—134no—
353#433—138no—
354#433—138no—
355#432—132no—
356#432—132no—
357#431—132no—
358#431—132no—
359#423—132no—
360#423—134no—
361#407—132no—
362#407—134no—
363#405—138no—
364#405—138no—
365C4×M16—131no—
366C4×M16—131no—
367C4×M16—132no—
368C4×M16—132no—
369C4×M16—132no—
370C4×M16—132no—
371C4×M16—134no—
372C2×#97—132no—
373C2×C4×C8—132no—
374C22×C13—21no—
375C22×C13—21no—
376C22×C13C4×#4112yes—
377C22×C13C24×C411yescharacteristic
378C2×D13—21no—
379C2×D13—21no—
380C2×D13—21no—
381C2×D13—24no—
382C2×D13—21no—
383C2×D13—21no—
384C2×D13—24no—
385C2×D13—24no—
386C2×D13—44no—
387C2×D13—84no—
388C2×D13#56812yes—
389C4×C13—21no—
390C4×C13—24no—
391C4×C13—21no—
392C4×C13—21no—
393C4×C13—21no—
394C4×C13—21no—
395C4×C13—24no—
396C4×C13#56812yes—
397Dic13—24no—
398Dic13—21no—
399Dic13—21no—
400Dic13—21no—
401Dic13—21no—
402Dic13C4×#4112yes—
403Dic13C22×#4112yes—
404C22×Q8—131no—
405C22×D4—132no—
406C22×D4—131no—
407C23×C4—132no—
408C23×C4—131no—
409C23×C4—131no—
410C23×C4—131no—
411C2×M16—132no—
412C2×M16—132no—
413C2×M16—134no—
414C2×M16—134no—
415C2×M16—138no—
416C2×M16—268no—
417C2×M16—2616no—
418C22×C8—134no—
419C22×C8—138no—
420#126—134no—
421#126—134no—
422#126—134no—
423#126—134no—
424#125C2×#26112yes—
425#125C2×#26112yes—
426#125C2×#26112yes—
427#125C2×#26112yes—
428#124—132no—
429#124—132no—
430#124—132no—
431#124—132no—
432#123—134no—
433#123—134no—
434#123—134no—
435#123—134no—
436C22⋊Q8—132no—
437C22⋊Q8—132no—
438C22⋊Q8—132no—
439C22⋊Q8—132no—
440#121—132no—
441#121—132no—
442#121—132no—
443#121—132no—
444C4×Q8—132no—
445C4×Q8—132no—
446C4×Q8—132no—
447C4×Q8—132no—
448C4×D4—132no—
449C4×D4—132no—
450C4×D4—134no—
451C4×D4—134no—
452C4×D4—134no—
453C4×D4—132no—
454C4×D4—132no—
455C4×D4—134no—
456#117—134no—
457#117—134no—
458#117—134no—
459#117—134no—
460C2×C4⋊C4—132no—
461C2×C4⋊C4—132no—
462C2×C4⋊C4C2×#26112yes—
463C2×C4⋊C4C2×#26111yescharacteristic
464C2×C4⋊C4C2×#26112yes—
465C2×C4⋊C4C2×#26111yescharacteristic
466C2×C22⋊C4—132no—
467C2×C22⋊C4—132no—
468C2×C22⋊C4—132no—
469C2×C22⋊C4—132no—
470C2×C22⋊C4—132no—
471C2×C42—131no—
472C2×C42—132no—
473C2×C42—131no—
474C2×C42—131no—
475C2×C42—131no—
476C2×C42—131no—
477C2×C42—131no—
478C2×C42—131no—
479C2×C42—131no—
480C2×C42—131no—
481C2×C42—131no—
482C2×C42—131no—
483C2×C42C2×#26111yescharacteristic
484C4⋊C8—134no—
485C4⋊C8—138no—
486C4⋊C8—134no—
487C4⋊C8—138no—
488C22⋊C8—134no—
489C22⋊C8—134no—
490C22⋊C8—138no—
491C22⋊C8—138no—
492#97—132no—
493#97—132no—
494#97—134no—
495#97—134no—
496#97—138no—
497C4×C8—132no—
498C4×C8—132no—
499C4×C8—134no—
500C4×C8—134no—
501C4×C8—138no—
502C2×C13—22no—
503C2×C13C2×C4×#4111yescharacteristic
504C2×C13C2×#56811yescharacteristic
505C2×C13C2×#56811yescharacteristic
506D13—22no—
507D13—41no—
508D13—44no—
509C24—131no—
510C24—132no—
511C2×Q8—132no—
512C2×Q8—132no—
513C2×Q8—522no—
514C2×D4—134no—
515C2×D4—132no—
516C2×D4—134no—
517C2×D4—132no—
518C2×D4—522no—
519C2×D4—524no—
520C22×C4—131no—
521C22×C4—131no—
522C22×C4—131no—
523C22×C4—132no—
524C22×C4—131no—
525C22×C4—131no—
526C22×C4—134no—
527C22×C4—131no—
528C22×C4—131no—
529C22×C4—131no—
530C22×C4—131no—
531C22×C4—131no—
532C22×C4—131no—
533C22×C4—134no—
534C22×C4—131no—
535C22×C4—131no—
536C22×C4—131no—
537C22×C4—131no—
538C22×C4—264no—
539C22×C4—268no—
540C22×C4—522no—
541C22×C4—522no—
542C22×C4C22×#26111yescharacteristic
543C22×C4C22×#26111yescharacteristic
544C22×C4C22×#26112yes—
545C22×C4C22×#26111yescharacteristic
546C22×C4C22×#26112yes—
547M16—138no—
548M16—268no—
549M16—2616no—
550M16—264no—
551M16—268no—
552C2×C8—134no—
553C2×C8—134no—
554C2×C8—138no—
555C2×C8—268no—
556C2×C8—2616no—
557C4⋊C4—134no—
558C4⋊C4—134no—
559C4⋊C4—134no—
560C4⋊C4—134no—
561C4⋊C4C22×#26114yes—
562C4⋊C4C22×#26114yes—
563C4⋊C4C22×#26112yes—
564C4⋊C4C22×#26112yes—
565C4⋊C4C22×#26114yes—
566C4⋊C4C22×#26114yes—
567C4⋊C4C22×#26112yes—
568C4⋊C4C22×#26112yes—
569C22⋊C4—134no—
570C22⋊C4—134no—
571C22⋊C4—134no—
572C22⋊C4—134no—
573C22⋊C4—134no—
574C22⋊C4—134no—
575C22⋊C4—134no—
576C22⋊C4—134no—
577C22⋊C4—134no—
578C22⋊C4—134no—
579C42—131no—
580C42—131no—
581C42—131no—
582C42—134no—
583C42—131no—
584C42—131no—
585C42—131no—
586C42—131no—
587C42—131no—
588C42—131no—
589C42—131no—
590C42—131no—
591C42—131no—
592C42—134no—
593C42C22×#26111yescharacteristic
594C42C22×#26111yescharacteristic
595C42C22×#26111yescharacteristic
596C42C22×#26111yescharacteristic
597C13#6021411yescharacteristic, complemented, Sylow
598C23—131no—
599C23—134no—
600C23—131no—
601C23—262no—
602C23—262no—
603C23—264no—
604C23—521no—
605C23—522no—
606C23—522no—
607C23C23×#26111yescharacteristic
608Q8—264no—
609Q8—522no—
610D4—268no—
611D4—264no—
612D4—524no—
613D4—522no—
614C2×C4—22no—
615C2×C4—24no—
616C2×C4—22no—
617C2×C4—41no—
618C2×C4—42no—
619C2×C4—134no—
620C2×C4—131no—
621C2×C4—131no—
622C2×C4—131no—
623C2×C4—131no—
624C2×C4—131no—
625C2×C4—131no—
626C2×C4—134no—
627C2×C4—262no—
628C2×C4—264no—
629C2×C4—262no—
630C2×C4—264no—
631C2×C4—262no—
632C2×C4—262no—
633C2×C4—268no—
634C2×C4—262no—
635C2×C4—262no—
636C2×C4—262no—
637C2×C4—262no—
638C2×C4—521no—
639C2×C4—521no—
640C2×C4—521no—
641C2×C4—521no—
642C2×C4—521no—
643C2×C4—521no—
644C2×C4—522no—
645C2×C4C23×#26111yescharacteristic
646C2×C4C23×#26111yescharacteristic
647C2×C4C23×#26111yescharacteristic
648C2×C4C23×#26111yescharacteristic
649C2×C4C23×#26111yescharacteristic
650C2×C4C23×#26114yes—
651C2×C4C23×#26114yes—
652C2×C4C23×#26111yescharacteristic
653C8—138no—
654C8—264no—
655C8—268no—
656C22—21no—
657C22—21no—
658C22—132no—
659C22—261no—
660C22—261no—
661C22—261no—
662C22—264no—
663C22—261no—
664C22—264no—
665C22—261no—
666C22—264no—
667C22—524no—
668C22—1044no—
669C22#41×#26112yes—
670C22C24×#26111yescharacteristic
671C4—21no—
672C4—24no—
673C4—21no—
674C4—21no—
675C4—21no—
676C4—24no—
677C4—21no—
678C4—132no—
679C4—132no—
680C4—261no—
681C4—261no—
682C4—261no—
683C4—261no—
684C4—264no—
685C4#1171962512yes—
686C2—22no—
687C2—262no—
688C2—521no—
689C2—524no—
690C2C2×#41×#26111yescharacteristic
691C2D13⋊#56811yescharacteristic
692C2C2×#1171962511yescharacteristic
subgroupG/H
center, FrattiniC22C24×#261
commutator, socleC22×C13C24×C4
FittingC2×C13×#125C4
prime radicalC2×#88149C4
cosocleC2×Dic13C25
hypercenterC2×#125#261
hypocenterC13#60214
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
1. #13131672C2semidirect
2. #13131665C2semidirect
3. #13131660C2semidirect
4. #13131653C2semidirect
5. #13131637C2semidirect
6. #13131576C2semidirect
7. #13131576C2semidirect
8. #13131518C2semidirect
9. #13131514C2semidirect
10. #13131402C2semidirect
11. C4×D13⋊M16C2semidirect
43. #11719080C22semidirect
44. #11719078C22semidirect
45. #11719077C22semidirect
46. #11719077C22semidirect
47. #11719076C22semidirect
48. #11719076C22semidirect
49. #11719075C22semidirect
50. #11719075C22semidirect
51. #11719075C22semidirect
52. #11719074C22semidirect
53. #11719073C22semidirect
54. #11719073C22semidirect
55. #11719072C22semidirect
56. #11719072C22semidirect
57. #11719055C22semidirect
58. #11719054C22semidirect
59. #11719051C22semidirect
60. #11719049C22semidirect
61. C4×#6118C22semidirect
62. C4×#6118C22semidirect
63. #11719047C22semidirect
64. C4×D13⋊C8C22semidirect
597. C13#60214semidirect

Maximal subgroups

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

subgroupindex
#131316722
#131316652
#131316602
#131316532
#131316372
#131315762
#131315182
#131315142
#131314022
C4×D13⋊M162
C2×#117193962
#6021413