Finite Group Databasebeta

← #14926827

Subgroups — #14926827

Order 2816.

1978 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076924C212yesmaximal, complemented
2#13076900C212yesmaximal
3#13074730C211yesmaximal, characteristic, complemented
4#13074424C212yesmaximal
5#13073893C214yesmaximal, complemented
6#13073703C214yesmaximal, complemented
7#13073337C214yesmaximal, complemented
8#13072640C214yesmaximal, complemented
9#13071351C212yesmaximal, complemented
10#13071213C212yesmaximal
11#13071144C212yesmaximal, complemented
12C2×#10622279C211yesmaximal, characteristic
13C11×#2659C211yesmaximal, characteristic, complemented
14C23×C4×D11C2211yescharacteristic
15C2×C11×C22⋊Q8C2212yes—
16C2×#66999C2212yes—
17C2×#66999C2212yes—
18C22×(C2×D11)⋊C4C2211yescharacteristic
19C22×(C2×D11)⋊C4C2211yescharacteristic
20C2×#66977C2212yes—
21C22×C4×Dic11C2211yescharacteristic
22C22×C4×Dic11C2211yescharacteristic
23C2×#66943C2212yescomplemented
24C2×#66940C2212yescomplemented
25C11×#398C2214yescomplemented
26C11×#395C2214yescomplemented
27C11×#380C2212yes—
28C11×#380C2212yes—
29C2×C11×#95C2211yescharacteristic
30#10622843C2214yescomplemented
31#10622825C2212yes—
32#10622825C2212yes—
33C2×C11⋊#95C2211yescharacteristic
34#10622607C2214yes—
35#10622607C2214yes—
36#10622603C2214yes—
37#10622603C2214yes—
38#10622602C2214yes—
39#10622602C2214yes—
40#10622600C2212yes—
41#10622600C2212yes—
42#10622598C2214yescomplemented
43#10622598C2212yescomplemented
44#10622594C2214yescomplemented
45#10622594C2214yescomplemented
46#10622590C2212yescomplemented
47C4⋊C4×Dic11C2212yescomplemented
48#10622587C2212yescomplemented
49#10622586C2212yescomplemented
50#10622586C2212yescomplemented
51#10622568C2214yes—
52#10622563C2214yes—
53#10622559C2214yes—
54C22⋊C4×Dic11C2214yes—
55#10622290C2214yes—
56#10622286C2214yes—
57#10622283C2214yes—
58#10622283C2214yes—
59#10622279C2214yes—
60#10622279C2214yes—
61#10622274C2214yescomplemented
62#10622269C2214yescomplemented
63#10622268C2214yescomplemented
64#10622267C2214yescomplemented
65#10622265C2214yescomplemented
66#10622262C2214yescomplemented
67C24×D11C2311yescharacteristic
68C22×Q8×C11C2312yes—
69C23×C4×C11C2311yescharacteristic
70C23×C4×C11C2311yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C23×Dic11C2311yescharacteristic
73C23×Dic11C2311yescharacteristic
74C23×Dic11C2311yescharacteristic
75C22×C4×D11—24no—
76C22×C4×D11—42no—
77C22×C4×D11—42no—
78C22×C4×D11C2312yes—
79C22×C4×D11C2312yes—
80C22×Dic22C2312yes—
81C11×C22⋊Q8—28no—
82C2×C11×C4⋊C4C2312yes—
83C2×C11×C4⋊C4C2314yes—
84C2×C11×C4⋊C4C2312yes—
85C2×C11×C4⋊C4C2312yes—
86C2×C11×C4⋊C4C2312yes—
87C2×C11×C4⋊C4C2312yes—
88C2×C11×C22⋊C4C2314yes—
89C2×C22⋊Dic11C2314yes—
90#66999—44no—
91#66999—44no—
92C2×(C2×D11)⋊C4—24no—
93C2×(C2×D11)⋊C4Q818yescomplemented
94C2×(C2×D11)⋊C4C2314yes—
95C2×(C2×D11)⋊C4C2314yes—
96C2×(C2×D11)⋊C4C2314yes—
97C2×(C2×D11)⋊C4C2314yes—
98C2×(C2×D11)⋊C4C2314yes—
99C2×(C2×D11)⋊C4C2314yes—
100C2×C4⋊Dic11C2312yes—
101C2×C4⋊Dic11C2314yes—
102C2×C4⋊Dic11C2312yes—
103C2×C4⋊Dic11C2314yes—
104C2×C4⋊Dic11C2312yes—
105C2×C4⋊Dic11C2312yes—
106C2×C4⋊Dic11C2312yes—
107#66977—28no—
108C2×Dic11⋊C4C2314yes—
109C2×Dic11⋊C4C2314yes—
110C2×Dic11⋊C4C2314yes—
111C2×C4×Dic11—42no—
112C2×C4×Dic11—42no—
113C2×C4×Dic11C2312yes—
114C2×C4×Dic11C2312yes—
115C2×C4×Dic11C2314yes—
116C2×C4×Dic11C2312yes—
117C2×C4×Dic11C2314yes—
118C2×C4×Dic11C2312yes—
119#66943—44no—
120#66940—44no—
121C11×#95C2314yes—
122C11×#95C2314yes—
123C11×#95C2314yes—
124C11⋊#95C2314yes—
125C11⋊#95C2314yes—
126C11⋊#95C2314yes—
127C11⋊#95C2314yes—
128C11⋊#95C2314yes—
129C11⋊#95C2314yes—
130C11⋊#95C2314yes—
131C11⋊#95C2314yes—
132C11⋊#95C2314yes—
133#35012—111nomaximal, Sylow
134C24×C11C2411yescharacteristic
135C23×D11—22no—
136C23×D11—22no—
137C23×D11—41no—
138C23×D11—41no—
139C23×D11—41no—
140C23×D11—41no—
141C23×D11C2×Q814yes—
142C23×D11C2412yes—
143C2×Q8×C11—24no—
144C2×Q8×C11—42no—
145C2×Q8×C11—42no—
146C22×C4×C11—41no—
147C22×C4×C11—41no—
148C22×C4×C11—41no—
149C22×C4×C11—41no—
150C22×C4×C11—41no—
151C22×C4×C11—41no—
152C22×C4×C11C2×Q814yes—
153C22×C4×C11#4114yes—
154C22×C4×C11#4114yes—
155C22×C4×C11C2414yes—
156C22×C4×C11C2414yes—
157C22×C4×C11C2412yes—
158C22×C4×C11C2412yes—
159C22×C4×C11C2412yes—
160C22×Dic11—22no—
161C22×Dic11—22no—
162C22×Dic11—22no—
163C22×Dic11—22no—
164C22×Dic11—41no—
165C22×Dic11—41no—
166C22×Dic11—41no—
167C22×Dic11—41no—
168C22×Dic11C2×Q814yes—
169C22×Dic11C2412yes—
170C22×Dic11C2414yes—
171C22×Dic11C2414yes—
172C22×Dic11C2412yes—
173C22×Dic11C2411yescharacteristic
174C22×Dic11C2411yescharacteristic
175C2×C4×D11—24no—
176C2×C4×D11—24no—
177C2×C4×D11—24no—
178C2×C4×D11—24no—
179C2×C4×D11—42no—
180C2×C4×D11—42no—
181C2×C4×D11—416no—
182C2×Dic22—24no—
183C2×Dic22—42no—
184C2×Dic22—42no—
185C11×C4⋊C4—24no—
186C11×C4⋊C4—28no—
187C11×C4⋊C4—42no—
188C11×C4⋊C4—42no—
189C11×C4⋊C4—42no—
190C11×C4⋊C4—42no—
191C11×C22⋊C4—28no—
192C22⋊Dic11—28no—
193(C2×D11)⋊C4—28no—
194(C2×D11)⋊C4—44no—
195(C2×D11)⋊C4—44no—
196(C2×D11)⋊C4—44no—
197(C2×D11)⋊C4—44no—
198(C2×D11)⋊C4C2×Q8116yes—
199C4⋊Dic11—24no—
200C4⋊Dic11—42no—
201C4⋊Dic11—44no—
202C4⋊Dic11—42no—
203C4⋊Dic11—44no—
204C4⋊Dic11—42no—
205C4⋊Dic11—42no—
206Dic11⋊C4—28no—
207Dic11⋊C4—28no—
208Dic11⋊C4—28no—
209C4×Dic11—24no—
210C4×Dic11—24no—
211C4×Dic11—44no—
212C4×Dic11—42no—
213C4×Dic11—42no—
214C4×Dic11—44no—
215#2851—112no—
216#2848—112no—
217#2659—111no—
218#2659D1111yescharacteristic, complemented
219#2626—112no—
220#2574—114no—
221#2556—114no—
222#2522—114no—
223#2465—114no—
224#2329—112no—
225#2312—112no—
226C4×C22⋊Q8—112no—
227C2×C4×C22⋊C4—111no—
228C23×C11—21no—
229C23×C11—21no—
230C23×C11—21no—
231C23×C11—21no—
232C23×C11C22×Q812yes—
233C23×C11C2×#4112yes—
234C23×C11C2×#4112yes—
235C23×C11C2511yescharacteristic
236C22×D11—28no—
237C22×D11—22no—
238C22×D11—22no—
239C22×D11—22no—
240C22×D11—22no—
241C22×D11—22no—
242C22×D11—22no—
243C22×D11—44no—
244C22×D11—44no—
245C22×D11—44no—
246C22×D11—44no—
247C22×D11—44no—
248C22×D11—44no—
249C22×D11C22×Q814yes—
250Q8×C11—84no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—22no—
255C2×C4×C11—22no—
256C2×C4×C11—22no—
257C2×C4×C11—24no—
258C2×C4×C11—24no—
259C2×C4×C11—24no—
260C2×C4×C11—24no—
261C2×C4×C11—24no—
262C2×C4×C11—24no—
263C2×C4×C11—44no—
264C2×C4×C11—44no—
265C2×C4×C11—44no—
266C2×C4×C11C22×Q814yes—
267C2×C4×C11C2×#4114yes—
268C2×C4×C11C2×#4114yes—
269C2×Dic11—28no—
270C2×Dic11—21no—
271C2×Dic11—21no—
272C2×Dic11—22no—
273C2×Dic11—21no—
274C2×Dic11—21no—
275C2×Dic11—22no—
276C2×Dic11—24no—
277C2×Dic11—24no—
278C2×Dic11—22no—
279C2×Dic11—22no—
280C2×Dic11—24no—
281C2×Dic11—24no—
282C2×Dic11—24no—
283C2×Dic11—22no—
284C2×Dic11—24no—
285C2×Dic11—44no—
286C2×Dic11—44no—
287C2×Dic11C22×Q814yes—
288C2×Dic11H(5,𝔽2)12yes—
289C2×Dic11H(5,𝔽2)12yes—
290C4×D11—48no—
291C4×D11—48no—
292Dic22—48no—
293C24×C4—111no—
294C2×#125—112no—
295C2×C22⋊Q8—112no—
296C2×C22⋊Q8—112no—
297C2×C22⋊Q8—112no—
298C2×C22⋊Q8C2×D1112yes—
299C2×C4×Q8—112no—
300C22×C22⋊C4—111no—
301C22×C22⋊C4—111no—
302C22×C42—111no—
303C22×C42—111no—
304#399—114no—
305#398—114no—
306#398C2×D1114yescomplemented
307#396—114no—
308#396—114no—
309#395—114no—
310#395C2×D1114yescomplemented
311#393—114no—
312#391—114no—
313#391—112no—
314#389—114no—
315#389—112no—
316#389—112no—
317#389—112no—
318#388—114no—
319#388—114no—
320#388—114no—
321#388—114no—
322#387—114no—
323#387—114no—
324#387—114no—
325#387—114no—
326#387—114no—
327#385—114no—
328#385—114no—
329#385—114no—
330#385—114no—
331#382—112no—
332#380—112no—
333#380—112no—
334#380—112no—
335#380—112no—
336#380C2×D1112yes—
337#380C2×D1112yes—
338#379—114no—
339C4×C4⋊C4—112no—
340C4×C4⋊C4—114no—
341C4×C22⋊C4—114no—
342C4×C22⋊C4—114no—
343C4×C22⋊C4—114no—
344C2×#95—111no—
345C2×#95C2×D1111yescharacteristic
346C22×C11—22no—
347C22×C11—22no—
348C22×C11—22no—
349C22×C11—22no—
350C22×C11—22no—
351C22×C11—22no—
352C22×C11#53314yes—
353C22×C11C23×Q811yescharacteristic
354C22×C11C22×#4111yescharacteristic
355C22×C11C22×#4111yescharacteristic
356C22×C11C2×H(5,𝔽2)11yescharacteristic
357C22×C11C2×H(5,𝔽2)11yescharacteristic
358C22×C11#58511yescharacteristic
359C22×C11#58511yescharacteristic
360C2×D11—24no—
361C2×D11—24no—
362C2×D11—24no—
363C2×D11—416no—
364C2×D11—42no—
365C2×D11—42no—
366C2×D11—42no—
367C2×D11—42no—
368C4×C11—24no—
369C4×C11—24no—
370C4×C11—24no—
371C4×C11—44no—
372C4×C11—44no—
373Dic11—22no—
374Dic11—22no—
375Dic11—24no—
376Dic11—44no—
377Dic11—44no—
378Dic11—42no—
379C25—111no—
380C22×Q8—112no—
381C22×Q8C22×D1112yes—
382C23×C4—111no—
383C23×C4—111no—
384C23×C4—111no—
385C23×C4—112no—
386C23×C4—112no—
387C23×C4—224no—
388C23×C4—442no—
389C23×C4—442no—
390C23×C4C22×D1111yescharacteristic
391C23×C4C22×D1111yescharacteristic
392C23×C4C22×D1111yescharacteristic
393#125—444no—
394C22⋊Q8—28no—
395C22⋊Q8—228no—
396C22⋊Q8—444no—
397C22⋊Q8—444no—
398C4×Q8—444no—
399C2×C4⋊C4—114no—
400C2×C4⋊C4—114no—
401C2×C4⋊C4—114no—
402C2×C4⋊C4—112no—
403C2×C4⋊C4—112no—
404C2×C4⋊C4—112no—
405C2×C4⋊C4—112no—
406C2×C4⋊C4—114no—
407C2×C4⋊C4—112no—
408C2×C4⋊C4—114no—
409C2×C4⋊C4C22×D1112yes—
410C2×C4⋊C4C22×D1114yes—
411C2×C4⋊C4C22×D1112yes—
412C2×C4⋊C4C22×D1112yes—
413C2×C4⋊C4C22×D1112yes—
414C2×C4⋊C4C22×D1112yes—
415C2×C22⋊C4—118no—
416C2×C22⋊C4—114no—
417C2×C22⋊C4—114no—
418C2×C22⋊C4—114no—
419C2×C22⋊C4—114no—
420C2×C22⋊C4—114no—
421C2×C22⋊C4—114no—
422C2×C22⋊C4—114no—
423C2×C22⋊C4—224no—
424C2×C22⋊C4C22×D1114yes—
425C2×C42—112no—
426C2×C42—112no—
427C2×C42—114no—
428C2×C42—112no—
429C2×C42—112no—
430C2×C42—114no—
431C2×C42—442no—
432C2×C42—442no—
433#95—114no—
434#95—114no—
435#95—114no—
436#95—114no—
437#95—114no—
438#95—114no—
439#95—114no—
440#95—114no—
441#95—114no—
442#95C22×D1114yes—
443#95C22×D1114yes—
444#95C22×D1114yes—
445C2×C11—24no—
446C2×C11C2×#53311yescharacteristic
447C2×C11#345911yescharacteristic
448C2×C11#346011yescharacteristic
449C2×C11#349011yescharacteristic
450C2×C11#349311yescharacteristic
451C2×C11#350111yescharacteristic
452C2×C11#350111yescharacteristic
453D11—44no—
454C24—112no—
455C24—114no—
456C24—222no—
457C24—222no—
458C24—441no—
459C24—441no—
460C24—441no—
461C24—441no—
462C24C23×D1111yescharacteristic
463C2×Q8—24no—
464C2×Q8—42no—
465C2×Q8—42no—
466C2×Q8—224no—
467C2×Q8—442no—
468C2×Q8—442no—
469C22×C4—41no—
470C22×C4—41no—
471C22×C4—41no—
472C22×C4—41no—
473C22×C4—41no—
474C22×C4—41no—
475C22×C4—112no—
476C22×C4—111no—
477C22×C4—111no—
478C22×C4—114no—
479C22×C4—112no—
480C22×C4—114no—
481C22×C4—114no—
482C22×C4—224no—
483C22×C4—224no—
484C22×C4—222no—
485C22×C4—222no—
486C22×C4—222no—
487C22×C4—222no—
488C22×C4—224no—
489C22×C4—224no—
490C22×C4—442no—
491C22×C4—442no—
492C22×C4—4416no—
493C22×C4—441no—
494C22×C4—441no—
495C22×C4—441no—
496C22×C4—441no—
497C22×C4#434114yes—
498C22×C4Q8×D1114yes—
499C22×C4#434314yes—
500C22×C4C23×D1114yes—
501C22×C4C23×D1114yes—
502C22×C4C23×D1112yes—
503C22×C4C23×D1112yes—
504C22×C4C23×D1112yes—
505C4⋊C4—24no—
506C4⋊C4—28no—
507C4⋊C4—42no—
508C4⋊C4—42no—
509C4⋊C4—42no—
510C4⋊C4—42no—
511C4⋊C4—228no—
512C4⋊C4—228no—
513C4⋊C4—228no—
514C4⋊C4—224no—
515C4⋊C4—442no—
516C4⋊C4—442no—
517C4⋊C4—442no—
518C4⋊C4—444no—
519C4⋊C4—442no—
520C4⋊C4—444no—
521C22⋊C4—28no—
522C22⋊C4—1116no—
523C22⋊C4—228no—
524C22⋊C4—228no—
525C22⋊C4—444no—
526C22⋊C4—444no—
527C22⋊C4—444no—
528C22⋊C4—444no—
529C42—224no—
530C42—224no—
531C42—442no—
532C42—442no—
533C42—444no—
534C42—444no—
535C11#3501211yescharacteristic, complemented, Sylow
536C23—21no—
537C23—21no—
538C23—21no—
539C23—21no—
540C23—114no—
541C23—228no—
542C23—222no—
543C23—222no—
544C23—222no—
545C23—222no—
546C23—222no—
547C23—222no—
548C23—444no—
549C23—444no—
550C23—444no—
551C23—444no—
552C23—444no—
553C23—444no—
554C23C2×#434112yes—
555C23C2×Q8×D1112yes—
556C23C2×#434312yes—
557C23C24×D1111yescharacteristic
558Q8—84no—
559Q8—448no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—24no—
570C2×C4—24no—
571C2×C4—24no—
572C2×C4—44no—
573C2×C4—44no—
574C2×C4—44no—
575C2×C4—114no—
576C2×C4—112no—
577C2×C4—112no—
578C2×C4—228no—
579C2×C4—221no—
580C2×C4—221no—
581C2×C4—222no—
582C2×C4—221no—
583C2×C4—221no—
584C2×C4—222no—
585C2×C4—222no—
586C2×C4—224no—
587C2×C4—224no—
588C2×C4—222no—
589C2×C4—224no—
590C2×C4—224no—
591C2×C4—224no—
592C2×C4—224no—
593C2×C4—222no—
594C2×C4—448no—
595C2×C4—448no—
596C2×C4—444no—
597C2×C4—444no—
598C2×C4C2×#434114yes—
599C2×C4C2×Q8×D1114yes—
600C2×C4C2×#434314yes—
601C22—22no—
602C22—22no—
603C22—22no—
604C22—22no—
605C22—22no—
606C22—22no—
607C22—224no—
608C22—224no—
609C22—224no—
610C22—4416no—
611C22—442no—
612C22—442no—
613C22—442no—
614C22—442no—
615C22#1062325914yes—
616C22C22×#434111yescharacteristic
617C22C22×Q8×D1111yescharacteristic
618C22C22×#434311yescharacteristic
619C22D11×H(5,𝔽2)11yescharacteristic
620C22D11×H(5,𝔽2)11yescharacteristic
621C22#1062345511yescharacteristic
622C22#1062345711yescharacteristic
623C4—24no—
624C4—24no—
625C4—24no—
626C4—44no—
627C4—44no—
628C4—224no—
629C4—222no—
630C4—222no—
631C4—444no—
632C4—442no—
633C4—444no—
634C2—24no—
635C2—444no—
636C2C2×#1062325911yescharacteristic
637C2#1308202811yescharacteristic
638C2#1308203911yescharacteristic
639C2#1308230411yescharacteristic
640C2#1308233511yescharacteristic
641C2#1308241611yescharacteristic
642C2#1308241811yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2659C2
prime radicalC24×D11C23
hypercenter#2659D11
hypocenterC11#35012
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2659

Complements

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

NH ≅ G/Ntype
1. #13076924C2semidirect
3. #13074730C2semidirect
5. #13073893C2semidirect
6. #13073703C2semidirect
7. #13073337C2semidirect
8. #13072640C2semidirect
9. #13071351C2semidirect
11. #13071144C2semidirect
13. C11×#2659C2semidirect
23. C2×#66943C22semidirect
24. C2×#66940C22semidirect
25. C11×#398C22semidirect
26. C11×#395C22semidirect
30. #10622843C22semidirect
42. #10622598C22semidirect
43. #10622598C22semidirect
44. #10622594C22semidirect
45. #10622594C22semidirect
46. #10622590C22semidirect
47. C4⋊C4×Dic11C22semidirect
48. #10622587C22semidirect
49. #10622586C22semidirect
50. #10622586C22semidirect
61. #10622274C22semidirect
62. #10622269C22semidirect
63. #10622268C22semidirect
64. #10622267C22semidirect
65. #10622265C22semidirect
66. #10622262C22semidirect
93. C2×(C2×D11)⋊C4Q8semidirect
218. #2659D11semidirect
306. #398C2×D11semidirect
310. #395C2×D11semidirect
535. C11#35012semidirect

Maximal subgroups

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

subgroupindex
#130769242
#130769002
#130747302
#130744242
#130738932
#130737032
#130733372
#130726402
#130713512
#130712132
#130711442
C2×#106222792
C11×#26592
#3501211