Finite Group Databasebeta

← #16808825

Subgroups — #16808825

Order 3328.

1748 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13131745C214yesmaximal, complemented
2#13131740C214yesmaximal, complemented
3#13131738C212yesmaximal, complemented
4#13131737C212yesmaximal, complemented
5#13131733C212yesmaximal, complemented
6#13131730C212yesmaximal, complemented
7#13131634C214yesmaximal, complemented
8#13131625C212yesmaximal, complemented
9#13131625C212yesmaximal, complemented
10#13131530C212yesmaximal
11#13131529C212yesmaximal
12#13131513C211yesmaximal, characteristic
13D13⋊#431C211yesmaximal, characteristic
14D13×#533C211yesmaximal, characteristic
15C13×#533C411yescharacteristic
16#11719433C2211yescharacteristic
17#11719433C2211yescharacteristic
18D13×C4⋊Q8C411yescharacteristic
19D13×C4⋊Q8C411yescharacteristic
20#11719393C2212yes—
21D13×#125C412yes—
22D13×C22⋊Q8C412yes—
23D13×C22⋊Q8C412yes—
24#11719327C2212yes—
25#11719327C2212yes—
26#11719283C412yes—
27#11719283C412yes—
28C4×Q8×D13C2212yes—
29C4×Q8×D13C2212yes—
30D13×#117C2212yes—
31#11719222C412yes—
32C2×C42×D13C2211yescharacteristic
33#11719175C411yescharacteristic
34#11719158C2214yescomplemented
35#11719158C2214yescomplemented
36Q8×#1057C2214yescomplemented
37Q8×#1057C2214yescomplemented
38#11719130C2212yes—
39#11719127C2212yes—
40#11719125C2212yes—
41D13⋊(C22⋊C8)C2211yescharacteristic
42D13⋊(C22⋊C8)C2211yescharacteristic
43#11719119C2212yes—
44#11719119C2212yes—
45#11719080C2214yescomplemented
46#11719080C2214yescomplemented
47#11719080C2218yescomplemented
48#11719079C2214yes—
49#11719079C2214yes—
50#11719078C2218yescomplemented
51#11719078C2218yescomplemented
52#11719074C2214yescomplemented
53#11719074C2214yescomplemented
54#11719074C2218yescomplemented
55#11719072C2214yes—
56#11719072C2214yes—
57#11719068C2218yes—
58#11719068C2218yes—
59#11719055C2214yes—
60#11719054C2214yes—
61#11719054C2212yes—
62#11719052C2212yes—
63#11719051C2214yes—
64#11719051C2212yes—
65#11719051C2211yescharacteristic
66#11719051C2211yescharacteristic
67D13⋊(C4⋊C8)C2212yes—
68#11719049C2214yes—
69#11719049C2211yescharacteristic
70#11719049C2211yescharacteristic
71C4×#6118C2212yes—
72C4×D13⋊C8C2212yes—
73C2×Q8×D13C2×C412yes—
74C2×Q8×D13C2×C412yes—
75C22×C4×D13C2×C411yescharacteristic
76C22×C4×D13C2×C411yescharacteristic
77C22×C4×D13C2311yescharacteristic
78C2×#6118C2314yes—
79C2×D13⋊C8C2312yes—
80C2×D13⋊C8C2312yes—
81C13×C4⋊Q8C2×C411yescharacteristic
82C13×C4⋊Q8C2×C411yescharacteristic
83C13×#125C2×C412yes—
84C13×C22⋊Q8C2×C412yes—
85C13×C22⋊Q8C2×C412yes—
86C4×Q8×C13C2×C412yes—
87C4×Q8×C13C2×C412yes—
88C13×#117C2×C412yes—
89C2×C42×C13C2×C411yescharacteristic
90#88200C2×C412yes—
91#88200C2×C412yes—
92Q8×Dic13C2312yes—
93Q8×Dic13C2312yes—
94#88198C2×C412yes—
95#88198C2×C412yes—
96#88180C2×C412yes—
97#88178C2×C412yes—
98#88178C2×C412yes—
99C2×C4×Dic13C2×C411yescharacteristic
100C2×C4×Dic13C2311yescharacteristic
101C2×C4×Dic13C2311yescharacteristic
102#88151C2×C412yes—
103#88151C2×C412yes—
104#88150C2×C414yes—
105#88150C2×C414yes—
106#88146C2312yes—
107#88146C2312yes—
108C4⋊C4×D13C2×C412yes—
109C4⋊C4×D13C2×C412yes—
110C4⋊C4×D13C2×C412yes—
111C4⋊C4×D13C2×C412yes—
112C4⋊C4×D13C2×C414yes—
113C4⋊C4×D13C2×C414yes—
114#88144C2×C412yes—
115#88144C2×C412yes—
116#88143C2×C414yes—
117#88143C2×C414yes—
118#88142C2×C412yes—
119#88142C2×C412yes—
120#88142C2×C412yes—
121#88142C2×C412yes—
122#88141C2312yes—
123#88141C2312yes—
124#88141C2314yes—
125#88141C2314yes—
126C22⋊C4×D13C2×C414yes—
127#88132C2×C414yes—
128#88132C2×C414yes—
129#88131C2314yes—
130#88126C2×C414yes—
131C42×D13C2×C411yescharacteristic
132C42×D13C2×C411yescharacteristic
133C42×D13C2×C411yescharacteristic
134C42×D13C2×C411yescharacteristic
135C42×D13C2311yescharacteristic
136C42×D13C2311yescharacteristic
137C42×D13C2311yescharacteristic
138C42×D13C2311yescharacteristic
139C42×D13C2314yes—
140#88124C2×C412yes—
141#88123C2×C411yescharacteristic
142#88123C2×C411yescharacteristic
143C4×Dic26C2×C412yes—
144C4×Dic26C2×C412yes—
145C4×Dic26C2×C414yes—
146C4×Dic26C2×C414yes—
147C22⋊#1057C2312yes—
148C22⋊#1057C2312yes—
149C22⋊#1057C2314yes—
150#88112C2312yes—
151#88112C2312yes—
152#88112C2318yes—
153#88112C2318yes—
154#88111C2311yescharacteristic
155#88111C2311yescharacteristic
156#88111C2314yes—
157#88111C2311yescharacteristic
158#88111C2311yescharacteristic
159#88110C2314yes—
160#88110C2318yes—
161#88110C2318yes—
162C4⋊#1057C2312yes—
163C4⋊#1057C2312yes—
164C4⋊#1057C2314yes—
165C4⋊#1057C2318yes—
166C4⋊#1057C2314yes—
167C4⋊#1057C2318yes—
168C4×#1057C2312yes—
169C4×#1057C2312yes—
170C4×#1057C2312yes—
171C4×#1057C2312yes—
172C4×#1057C2314yes—
173C4×#1057C2318yes—
174C4×#1057C2318yes—
175#60250—131nomaximal, Sylow
176C23×D13C22×C411yescharacteristic
177C2×Q8×C13C22×C412yes—
178C2×Q8×C13C22×C412yes—
179C22×C4×C13C22×C411yescharacteristic
180C22×C4×C13C22×C411yescharacteristic
181C22×C4×C13C22×C411yescharacteristic
182C22×Dic13C22×C411yescharacteristic
183C22×Dic13C22×C411yescharacteristic
184C22×Dic13C2411yescharacteristic
185Q8×D13—28no—
186Q8×D13—44no—
187C2×C4×D13—24no—
188C2×C4×D13—24no—
189C2×C4×D13—42no—
190C2×C4×D13C22×C411yescharacteristic
191C2×C4×D13C22×C411yescharacteristic
192C2×C4×D13C22×C411yescharacteristic
193C2×C4×D13C22×C411yescharacteristic
194C2×C4×D13C22×C411yescharacteristic
195C2×C4×D13C22×C411yescharacteristic
196C2×C4×D13C22×C411yescharacteristic
197C2×C4×D13C22×C414yes—
198C2×C4×D13C22×C411yescharacteristic
199C2×C4×D13C22×C411yescharacteristic
200C2×C4×D13C22×C414yes—
201C2×C4×D13C22×C411yescharacteristic
202C2×C4×D13C2411yescharacteristic
203C2×C4×D13C2411yescharacteristic
204C2×Dic26C22×C412yes—
205C2×Dic26C22×C412yes—
206C2×Dic26C22×C414yes—
207C2×Dic26C22×C414yes—
208C2×#1057C2412yes—
209C2×#1057C2412yes—
210C2×#1057C2418yes—
211C2×#1057C2412yes—
212C2×#1057C2412yes—
213#6118—28no—
214D13⋊C8—24no—
215D13⋊C8—24no—
216C13×C4⋊C4C22×C412yes—
217C13×C4⋊C4C22×C412yes—
218C13×C4⋊C4C22×C414yes—
219C13×C4⋊C4C22×C414yes—
220C13×C4⋊C4C22×C412yes—
221C13×C4⋊C4C22×C412yes—
222C13×C22⋊C4C22×C414yes—
223C42×C13C22×C411yescharacteristic
224C42×C13C22×C411yescharacteristic
225C42×C13C22×C414yes—
226C42×C13C22×C411yescharacteristic
227C42×C13C22×C411yescharacteristic
228C22⋊Dic13C22×C414yes—
229#6103C22×C414yes—
230#6103C22×C414yes—
231C4⋊Dic13C22×C412yes—
232C4⋊Dic13C22×C412yes—
233C4⋊Dic13C22×C414yes—
234C4⋊Dic13C22×C414yes—
235C4⋊Dic13C22×C412yes—
236C4⋊Dic13C22×C412yes—
237#6101C22×C414yes—
238#6101C22×C414yes—
239#6101C22×C414yes—
240#6101C22×C414yes—
241#6101C22×C414yes—
242#6101C22×C414yes—
243#6101C22×C414yes—
244#6101C22×C414yes—
245C4×Dic13C22×C411yescharacteristic
246C4×Dic13C22×C411yescharacteristic
247C4×Dic13C22×C414yes—
248C4×Dic13C22×C411yescharacteristic
249C4×Dic13C22×C411yescharacteristic
250C4×Dic13C22×C411yescharacteristic
251C4×Dic13C22×C411yescharacteristic
252C4×Dic13C22×C411yescharacteristic
253C4×Dic13C22×C411yescharacteristic
254C4×Dic13C2411yescharacteristic
255C4×Dic13C2411yescharacteristic
256C4×Dic13C2411yescharacteristic
257C4×Dic13C2414yes—
258C4×Dic13C2414yes—
259C4×Dic13C2411yescharacteristic
260C2×#533—131no—
261#2986—134no—
262#2985—134no—
263#2984—132no—
264#2984—132no—
265#2983—132no—
266#2982—132no—
267#2962—134no—
268#2960—132no—
269#2960—132no—
270#2924—132no—
271#2924—132no—
272#2920—131no—
273C2×#431—131no—
274C23×C13C23×C411yescharacteristic
275C22×D13—22no—
276C22×D13—22no—
277C22×D13—41no—
278C22×D13C23×C411yescharacteristic
279C22×D13C23×C411yescharacteristic
280Q8×C13—24no—
281Q8×C13—24no—
282C2×C4×C13—22no—
283C2×C4×C13—22no—
284C2×C4×C13—22no—
285C2×C4×C13C23×C411yescharacteristic
286C2×C4×C13C23×C411yescharacteristic
287C2×C4×C13C23×C411yescharacteristic
288C2×C4×C13C23×C414yes—
289C2×C4×C13C23×C414yes—
290C2×C4×C13C23×C411yescharacteristic
291C2×C4×C13C23×C411yescharacteristic
292C2×C4×C13C23×C411yescharacteristic
293C2×Dic13—22no—
294C2×Dic13—22no—
295C2×Dic13—41no—
296C2×Dic13C23×C411yescharacteristic
297C2×Dic13C23×C411yescharacteristic
298C2×Dic13C23×C411yescharacteristic
299C2×Dic13C23×C411yescharacteristic
300C2×Dic13C23×C414yes—
301C2×Dic13C23×C414yes—
302C2×Dic13C23×C411yescharacteristic
303C2×Dic13C2511yescharacteristic
304C4×D13—22no—
305C4×D13—22no—
306C4×D13—28no—
307C4×D13—22no—
308C4×D13—22no—
309C4×D13—22no—
310C4×D13—22no—
311C4×D13—22no—
312C4×D13—22no—
313C4×D13—41no—
314C4×D13—41no—
315C4×D13—44no—
316C4×D13#13114yes—
317C4×D132−1+414yes—
318Dic26—24no—
319Dic26—24no—
320Dic26—28no—
321Dic26—44no—
322#1057—22no—
323#1057—22no—
324#1057—22no—
325#1057—22no—
326#1057—28no—
327#533—131no—
328#533—131no—
329#533—132no—
330#533—132no—
331#533—132no—
332#533—132no—
333#533—132no—
334#533—132no—
335#533—131no—
336#533#26111yescharacteristic
337C2×C4⋊Q8—131no—
338C2×C4⋊Q8—131no—
339C2×#125—132no—
340C2×C22⋊Q8—132no—
341C2×C22⋊Q8—132no—
342C2×C4×Q8—132no—
343C2×C4×Q8—132no—
344C2×#117—132no—
345C22×C42—131no—
346#446—134no—
347#446—134no—
348#446—134no—
349#446—134no—
350#446—138no—
351#446—138no—
352#446—138no—
353C8×Q8—134no—
354C8×Q8—134no—
355C8×Q8—134no—
356C8×Q8—134no—
357C8×Q8—138no—
358#433—138no—
359#433—138no—
360#432—132no—
361#432—132no—
362#432—134no—
363#432—134no—
364#431—131no—
365#431—131no—
366#431—131no—
367#431—131no—
368#431—132no—
369#431—132no—
370#431—132no—
371#431—132no—
372#431—134no—
373#431—134no—
374#424—134no—
375#424—134no—
376#423—132no—
377C2×C4⋊C8—132no—
378#407—132no—
379C2×C22⋊C8—131no—
380C2×C22⋊C8—131no—
381#405—134no—
382#405—134no—
383C4×M16—132no—
384C2×C4×C8—132no—
385C22×C13—21no—
386C22×C13—21no—
387C22×C13—21no—
388C22×C13C24×C411yescharacteristic
389C2×D13—21no—
390C2×D13—21no—
391C2×D13—21no—
392C2×D13—21no—
393C2×D13—44no—
394C2×D13#51912yes—
395C2×D13C2×#13112yes—
396C4×C13—21no—
397C4×C13—24no—
398C4×C13—21no—
399C4×C13—24no—
400C4×C13—21no—
401C4×C13#51912yes—
402C4×C13C2×#13112yes—
403C4×C13#56812yes—
404Dic13—21no—
405Dic13—24no—
406Dic13—21no—
407Dic13—24no—
408Dic13—21no—
409Dic13—21no—
410Dic13C2×#13112yes—
411Dic13C2×2−1+412yes—
412C22×Q8—132no—
413C22×Q8—132no—
414C23×C4—131no—
415C23×C4—131no—
416C23×C4—131no—
417C2×M16—134no—
418C22×C8—132no—
419C22×C8—132no—
420C4⋊Q8—132no—
421C4⋊Q8—132no—
422C4⋊Q8—132no—
423C4⋊Q8—132no—
424C4⋊Q8—132no—
425C4⋊Q8—132no—
426C4⋊Q8—131no—
427C4⋊Q8—131no—
428C4⋊Q8C2×#26111yescharacteristic
429C4⋊Q8C2×#26111yescharacteristic
430#125—134no—
431#125—134no—
432#125—132no—
433#125—132no—
434#125—132no—
435#125C2×#26112yes—
436C22⋊Q8—132no—
437C22⋊Q8—132no—
438C22⋊Q8—132no—
439C22⋊Q8—132no—
440C22⋊Q8—134no—
441C22⋊Q8—134no—
442C22⋊Q8—132no—
443C22⋊Q8—132no—
444C22⋊Q8—134no—
445C22⋊Q8—134no—
446C22⋊Q8C2×#26112yes—
447C22⋊Q8C2×#26112yes—
448C4×Q8—132no—
449C4×Q8—132no—
450C4×Q8—132no—
451C4×Q8—132no—
452C4×Q8—134no—
453C4×Q8—134no—
454C4×Q8—134no—
455C4×Q8—134no—
456C4×Q8—132no—
457C4×Q8—132no—
458C4×Q8C2×#26112yes—
459C4×Q8C2×#26112yes—
460#117—132no—
461#117—132no—
462#117—132no—
463#117—134no—
464#117—134no—
465#117C2×#26112yes—
466C2×C4⋊C4—132no—
467C2×C4⋊C4—132no—
468C2×C4⋊C4—134no—
469C2×C4⋊C4—134no—
470C2×C4⋊C4—132no—
471C2×C4⋊C4—132no—
472C2×C22⋊C4—134no—
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—132no—
488C4⋊C8—134no—
489C4⋊C8—134no—
490C4⋊C8—138no—
491C4⋊C8—138no—
492C4⋊C8—132no—
493C4⋊C8—132no—
494C4⋊C8—138no—
495C4⋊C8—138no—
496C22⋊C8—131no—
497C22⋊C8—131no—
498C22⋊C8—131no—
499C22⋊C8—131no—
500C22⋊C8—134no—
501C22⋊C8—132no—
502C22⋊C8—132no—
503C22⋊C8—134no—
504#97—134no—
505#97—138no—
506#97—138no—
507C4×C8—132no—
508C4×C8—132no—
509C4×C8—132no—
510C4×C8—132no—
511C4×C8—134no—
512C4×C8—138no—
513C4×C8—138no—
514C2×C13—41no—
515C2×C13C2×#51911yescharacteristic
516C2×C13C22×#13111yescharacteristic
517C2×C13C2×#56811yescharacteristic
518D13—22no—
519D13—22no—
520C24—131no—
521C2×Q8—134no—
522C2×Q8—132no—
523C2×Q8—132no—
524C2×Q8—134no—
525C2×Q8—268no—
526C2×Q8—524no—
527C2×Q8C22×#26112yes—
528C2×Q8C22×#26112yes—
529C22×C4—131no—
530C22×C4—131no—
531C22×C4—131no—
532C22×C4—131no—
533C22×C4—131no—
534C22×C4—131no—
535C22×C4—131no—
536C22×C4—131no—
537C22×C4—131no—
538C22×C4—131no—
539C22×C4—131no—
540C22×C4—131no—
541C22×C4—131no—
542C22×C4—134no—
543C22×C4—131no—
544C22×C4—131no—
545C22×C4—134no—
546C22×C4—264no—
547C22×C4—264no—
548C22×C4—522no—
549C22×C4C22×#26111yescharacteristic
550C22×C4C22×#26111yescharacteristic
551C22×C4C22×#26111yescharacteristic
552M16—268no—
553C2×C8—132no—
554C2×C8—132no—
555C2×C8—138no—
556C2×C8—132no—
557C2×C8—132no—
558C2×C8—264no—
559C2×C8—264no—
560C4⋊C4—134no—
561C4⋊C4—134no—
562C4⋊C4—132no—
563C4⋊C4—132no—
564C4⋊C4—134no—
565C4⋊C4—134no—
566C4⋊C4—134no—
567C4⋊C4—134no—
568C4⋊C4—134no—
569C4⋊C4—134no—
570C4⋊C4—134no—
571C4⋊C4—134no—
572C4⋊C4—132no—
573C4⋊C4—132no—
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⋊C4C22×#26114yes—
584C42—131no—
585C42—131no—
586C42—131no—
587C42—134no—
588C42—134no—
589C42—131no—
590C42—131no—
591C42—131no—
592C42—131no—
593C42—131no—
594C42—131no—
595C42—131no—
596C42—131no—
597C42—131no—
598C42—134no—
599C42C22×#26111yescharacteristic
600C42C22×#26111yescharacteristic
601C42C22×#26111yescharacteristic
602C42C22×#26111yescharacteristic
603C42C22×#26114yes—
604C13#6025011yescharacteristic, complemented, Sylow
605C23—131no—
606C23—131no—
607C23—262no—
608C23—262no—
609C23—521no—
610C23C23×#26111yescharacteristic
611Q8—24no—
612Q8—24no—
613Q8—268no—
614Q8—264no—
615Q8—264no—
616Q8—524no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—131no—
621C2×C4—131no—
622C2×C4—134no—
623C2×C4—134no—
624C2×C4—131no—
625C2×C4—131no—
626C2×C4—131no—
627C2×C4—131no—
628C2×C4—134no—
629C2×C4—134no—
630C2×C4—262no—
631C2×C4—262no—
632C2×C4—262no—
633C2×C4—262no—
634C2×C4—268no—
635C2×C4—262no—
636C2×C4—262no—
637C2×C4—262no—
638C2×C4—262no—
639C2×C4—262no—
640C2×C4—262no—
641C2×C4—521no—
642C2×C4—521no—
643C2×C4—524no—
644C2×C4—521no—
645C2×C4C23×#26111yescharacteristic
646C2×C4C23×#26111yescharacteristic
647C2×C4C23×#26111yescharacteristic
648C2×C4C23×#26114yes—
649C2×C4C23×#26114yes—
650C2×C4C23×#26111yescharacteristic
651C2×C4C23×#26111yescharacteristic
652C2×C4C23×#26111yescharacteristic
653C8—262no—
654C8—262no—
655C8—262no—
656C8—262no—
657C8—268no—
658C22—21no—
659C22—21no—
660C22—21no—
661C22—132no—
662C22—132no—
663C22—261no—
664C22—261no—
665C22—261no—
666C22—261no—
667C22—524no—
668C22C24×#26111yescharacteristic
669C4—21no—
670C4—21no—
671C4—24no—
672C4—21no—
673C4—24no—
674C4—132no—
675C4—132no—
676C4—261no—
677C4—261no—
678C4—264no—
679C4—261no—
680C4—261no—
681C4—264no—
682C4#1171962712yes—
683C4D13⋊#13112yes—
684C4#1171962912yes—
685C2—41no—
686C2—262no—
687C2—262no—
688C2C2×#1171962711yescharacteristic
689C2C2×D13⋊#13111yescharacteristic
690C2C2×#1171962911yescharacteristic
subgroupG/H
center, FrattiniC22C24×#261
commutator, socleC22×C13C24×C4
FittingC13×#533C4
prime radicalC23×D13C22×C4
cosocleC2×Dic13C25
hypercenter#533#261
hypocenterC13#60250
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ #533

Complements

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

NH ≅ G/Ntype
1. #13131745C2semidirect
2. #13131740C2semidirect
3. #13131738C2semidirect
4. #13131737C2semidirect
5. #13131733C2semidirect
6. #13131730C2semidirect
7. #13131634C2semidirect
8. #13131625C2semidirect
9. #13131625C2semidirect
34. #11719158C22semidirect
35. #11719158C22semidirect
36. Q8×#1057C22semidirect
37. Q8×#1057C22semidirect
45. #11719080C22semidirect
46. #11719080C22semidirect
47. #11719080C22semidirect
50. #11719078C22semidirect
51. #11719078C22semidirect
52. #11719074C22semidirect
53. #11719074C22semidirect
54. #11719074C22semidirect
604. C13#60250semidirect

Maximal subgroups

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

subgroupindex
#131317452
#131317402
#131317382
#131317372
#131317332
#131317302
#131316342
#131316252
#131315302
#131315292
#131315132
D13⋊#4312
D13×#5332
#6025013