Finite Group Databasebeta

← #14755415

Subgroups — #14755415

Order 2816.

1742 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623347C211yesmaximal, characteristic
2#13081817C211yesmaximal, characteristic
3C2×#10622619C211yesmaximal, characteristic
4#13071202C211yesmaximal, characteristic, complemented
5#13069026C218yesmaximal, complemented
6#13068349C211yesmaximal, characteristic, complemented
7#13068348C211yesmaximal, characteristic, complemented
8C11×#2310C211yesmaximal, characteristic, complemented
9C23×Q8×C11C2211yescharacteristic
10C22×#4339C2211yescharacteristic
11C2×C11×#117C2211yescharacteristic
12C2×C11×#117C2211yescharacteristic
13#10623347—24no—
14#10623347C418yescomplemented
15C2×#67000—21no—
16C2×#66999—22no—
17C2×#66997—21no—
18C2×#66982C2214yes—
19C2×#66979C2211yescharacteristic
20C2×#66979C2211yescharacteristic
21C2×#66979C2211yescharacteristic
22#10623054—22no—
23#10623053—22no—
24#10623052—21no—
25D11×#117—22no—
26#10623047—21no—
27#10623035—22no—
28#10623017C2214yes—
29C4×#4339—22no—
30C11×#391—22no—
31C11×#391—22no—
32C11×#381C2214yes—
33#10622843—22no—
34#10622843—22no—
35#10622824C2214yes—
36#10622619—24no—
37C2×#66870C2214yes—
38#10622165C2214yes—
39#10622164C2214yes—
40C22×Q8×C11—21no—
41C22×Q8×C11—21no—
42C22×Q8×C11—22no—
43C22×Q8×C11—21no—
44C22×Q8×C11—21no—
45C22×Q8×C11—21no—
46C22×Q8×C11—21no—
47C22×Q8×C11—22no—
48C22×Q8×C11—22no—
49C22×Q8×C11C2×C414yescomplemented
50C23×C4×C11C2312yes—
51C23×C4×C11C2311yescharacteristic
52C22×C22⋊D11C2312yes—
53C2×#4339—21no—
54C2×#4339—21no—
55C2×#4339—21no—
56C2×#4339—21no—
57C2×#4339—22no—
58C2×#4339—22no—
59C2×#4339C2×C414yes—
60C2×#4339D414yes—
61C22×D44D411yescharacteristic
62C22×C4×D11D412yes—
63C22×Dic22D411yescharacteristic
64C11×#117—21no—
65C11×#117—21no—
66C11×#117—21no—
67C11×#117—21no—
68C11×#117—22no—
69C11×#117—22no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4D412yes—
72C2×C11×C22⋊C4C2312yes—
73C2×C11×C22⋊C4C2312yes—
74C2×C42×C11—21no—
75C2×C42×C11D412yes—
76C2×C22⋊Dic11C2312yes—
77C2×C22⋊Dic11C2312yes—
78C2×C22⋊Dic11C2312yes—
79#67000—28no—
80#66999—216no—
81#66997—28no—
82#66982—28no—
83#66982C2×C4116yescomplemented
84C4×C22⋊D11—28no—
85C2×(C2×D11)⋊C4—24no—
86#66979—21no—
87#66979—21no—
88#66979—21no—
89#66979—21no—
90#66979—22no—
91#66979—22no—
92#66979—22no—
93#66979C2×C414yescomplemented
94C2×C4⋊Dic11—21no—
95C2×C4⋊Dic11—21no—
96C2×C4⋊Dic11D412yes—
97C2×Dic11⋊C4—24no—
98C2×C4×Dic11—21no—
99C2×C4×Dic11—21no—
100C2×C4×Dic11D412yes—
101#66946—24no—
102#66945—24no—
103C4⋊C4×D11—24no—
104#66940—24no—
105(C22⋊D11)⋊C4—28no—
106C22⋊C4×D11—24no—
107#66930—24no—
108C4×D44—24no—
109#66925—24no—
110C42×D11—24no—
111C4×Dic22—24no—
112C11×#95—28no—
113C11⋊#95—28no—
114#66870—28no—
115#20962—111nomaximal, Sylow
116C24×C11C2411yescharacteristic
117C23×D11C2×D412yes—
118C2×Q8×C11—24no—
119C2×Q8×C11—24no—
120C2×Q8×C11—24no—
121C2×Q8×C11—24no—
122C2×Q8×C11—24no—
123C2×Q8×C11—24no—
124C2×Q8×C11—41no—
125C2×Q8×C11—41no—
126C2×Q8×C11—41no—
127C2×Q8×C11—41no—
128C2×Q8×C11—42no—
129C2×Q8×C11—42no—
130C2×Q8×C11—42no—
131C2×Q8×C11—42no—
132C2×Q8×C11—42no—
133C2×Q8×C11—42no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11C22×C414yes—
142C22×C4×C11C22×C412yes—
143C22×C4×C11C2×D414yes—
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D412yes—
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11#4112yes—
152C22×C4×C11#4112yes—
153C2×C22⋊D11—22no—
154C2×C22⋊D11—22no—
155C2×C22⋊D11—22no—
156C2×C22⋊D11—22no—
157C2×C22⋊D11C22×C414yes—
158C2×C22⋊D11C2×D414yes—
159C22×Dic11—22no—
160C22×Dic11—22no—
161C22×Dic11C2×D412yes—
162C22×Dic11C2×D414yes—
163#4339—24no—
164#4339—24no—
165#4339—24no—
166#4339—24no—
167#4339—24no—
168#4339—24no—
169#4339—24no—
170#4339—24no—
171C2×D44—21no—
172C2×D44—21no—
173C2×D44—22no—
174C2×D44C22⋊C414yes—
175C2×C4×D11—28no—
176C2×C4×D11—22no—
177C2×C4×D11—22no—
178C2×C4×D11—24no—
179C2×C4×D11C22⋊C418yes—
180C2×Dic22—21no—
181C2×Dic22—21no—
182C2×Dic22—22no—
183C2×Dic22C22⋊C414yes—
184C11×C4⋊C4—22no—
185C11×C4⋊C4—22no—
186C11×C4⋊C4—42no—
187C11×C22⋊C4—22no—
188C11×C22⋊C4—22no—
189C11×C22⋊C4—22no—
190C11×C22⋊C4—22no—
191C42×C11—22no—
192C42×C11—22no—
193C42×C11—42no—
194C22⋊Dic11—22no—
195C22⋊Dic11—22no—
196C22⋊Dic11—22no—
197C22⋊Dic11—22no—
198C22⋊Dic11—22no—
199C22⋊Dic11C22×C414yes—
200(C2×D11)⋊C4—28no—
201(C2×D11)⋊C4—216no—
202C4⋊Dic11—24no—
203C4⋊Dic11—22no—
204C4⋊Dic11—22no—
205C4⋊Dic11—42no—
206Dic11⋊C4—28no—
207Dic11⋊C4—216no—
208C4×Dic11—28no—
209C4×Dic11—24no—
210C4×Dic11—22no—
211C4×Dic11—22no—
212C4×Dic11—42no—
213C2×#536—111no—
214#3428—111no—
215C2×#410—111no—
216#2310—111no—
217#2310D1111yescharacteristic, complemented
218#1890—118no—
219#1740—111no—
220#1740—111no—
221C23×C11—42no—
222C23×C11C23×C411yescharacteristic
223C23×C11C22×D411yescharacteristic
224C23×C11C22×D411yescharacteristic
225C23×C11C22×D411yescharacteristic
226C23×C11C22×D411yescharacteristic
227C23×C11C2×#4111yescharacteristic
228C23×C11C2×#4111yescharacteristic
229C22×D11—22no—
230C22×D11—22no—
231C22×D11—44no—
232C22×D11C2×C22⋊C414yes—
233Q8×C11—44no—
234Q8×C11—44no—
235Q8×C11—44no—
236Q8×C11—44no—
237C2×C4×C11—24no—
238C2×C4×C11—24no—
239C2×C4×C11—24no—
240C2×C4×C11—24no—
241C2×C4×C11—42no—
242C2×C4×C11—42no—
243C2×C4×C11—42no—
244C2×C4×C11—42no—
245C2×C4×C11—44no—
246C2×C4×C11—44no—
247C2×C4×C11—42no—
248C2×C4×C11C2×C22⋊C412yes—
249C2×C4×C11C2×C22⋊C412yes—
250C2×C4×C11C4×D412yes—
251C2×C4×C11C4×D412yes—
252C2×C4×C11C4×D412yes—
253C2×C4×C11C4×D412yes—
254C2×C4×C11#12011yescharacteristic
255C2×C4×C11#12011yescharacteristic
256C2×C4×C11#12011yescharacteristic
257C2×C4×C11#12011yescharacteristic
258C2×C4×C11#12112yes—
259C2×C4×C11#12112yes—
260C2×C4×C11#12112yes—
261C2×C4×C11#12112yes—
262C2×C4×C11#12312yes—
263C2×C4×C11#12312yes—
264C22⋊D11—24no—
265C22⋊D11—24no—
266C22⋊D11—24no—
267C22⋊D11—24no—
268C2×Dic11—22no—
269C2×Dic11—22no—
270C2×Dic11—24no—
271C2×Dic11—24no—
272C2×Dic11—44no—
273C2×Dic11—44no—
274C2×Dic11—44no—
275C2×Dic11—42no—
276C2×Dic11C2×C22⋊C414yes—
277D44—24no—
278D44—24no—
279C4×D11—28no—
280C4×D11—28no—
281C4×D11—88no—
282Dic22—24no—
283Dic22—24no—
284C22×#41—111no—
285C23×Q8C2×D1111yescharacteristic
286#536—118no—
287#536—224no—
288C2×C4⋊Q8—221no—
289C2×#124—221no—
290C2×#123—114no—
291C2×C22⋊Q8—222no—
292#520—222no—
293#520—222no—
294#519—221no—
295#518—114no—
296#518—221no—
297C4×#41—222no—
298C4×#41—222no—
299C2×#117—111no—
300C2×#117—111no—
301C2×#117—111no—
302C2×#117—222no—
303C2×#117C2×D1111yescharacteristic
304C2×#117C2×D1111yescharacteristic
305#410—224no—
306C2×#99—114no—
307#391—22no—
308#391—22no—
309#391—222no—
310#391—222no—
311#381—114no—
312#381C2×D1114yes—
313#342—114no—
314#342—114no—
315C22×C11—22no—
316C22×C11—22no—
317C22×C11—22no—
318C22×C11—41no—
319C22×C11—41no—
320C22×C11—41no—
321C22×C11—41no—
322C22×C11C22×C22⋊C411yescharacteristic
323C22×C11C2×C4×D411yescharacteristic
324C22×C11C2×C4×D411yescharacteristic
325C22×C11C2×#12011yescharacteristic
326C22×C11C2×#12111yescharacteristic
327C22×C11C2×#12111yescharacteristic
328C22×C11C2×#12311yescharacteristic
329C2×D11—24no—
330C2×D11—44no—
331C2×D11—44no—
332C2×D11—82no—
333C4×C11—44no—
334C4×C11—44no—
335C4×C11—82no—
336C4×C11#38612yes—
337C4×C11#38612yes—
338C4×C11#38612yes—
339C4×C11#38612yes—
340Dic11—24no—
341Dic11—44no—
342Dic11—44no—
343Dic11—82no—
344C2×#41—114no—
345C2×#41—114no—
346C2×#41—222no—
347C2×#41—221no—
348C2×#41—221no—
349C2×#41—222no—
350C2×#41—221no—
351C2×#41—221no—
352C22×Q8—22no—
353C22×Q8—21no—
354C22×Q8—21no—
355C22×Q8—22no—
356C22×Q8—21no—
357C22×Q8—21no—
358C22×Q8—22no—
359C22×Q8—21no—
360C22×Q8—21no—
361C22×Q8—111no—
362C22×Q8C4×D1114yescomplemented
363C22×D4—112no—
364C22×D4—111no—
365C23×C4—112no—
366C23×C4C22×D1112yes—
367C23×C4C22×D1111yescharacteristic
368C4⋊Q8—228no—
369#124—228no—
370#123—1116no—
371#123—228no—
372C22⋊Q8—2216no—
373C4×Q8—224no—
374C4×Q8—224no—
375C4×D4—224no—
376C4×D4—228no—
377C4×D4—224no—
378C4×D4—228no—
379#117—21no—
380#117—21no—
381#117—21no—
382#117—21no—
383#117—22no—
384#117—22no—
385#117—114no—
386#117—224no—
387#117—224no—
388#117—224no—
389#117—221no—
390#117—221no—
391#117—222no—
392#117—221no—
393#117—221no—
394#117—222no—
395#117—222no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—112no—
398C2×C4⋊C4—224no—
399C2×C4⋊C4—224no—
400C2×C4⋊C4—221no—
401C2×C4⋊C4—221no—
402C2×C4⋊C4C22⋊D1112yes—
403C2×C22⋊C4—112no—
404C2×C22⋊C4—112no—
405C2×C22⋊C4—112no—
406C2×C22⋊C4—224no—
407C2×C22⋊C4—224no—
408C2×C22⋊C4C22×D1112yes—
409C2×C22⋊C4C22×D1112yes—
410C2×C42—21no—
411C2×C42—112no—
412C2×C42—224no—
413C2×C42—221no—
414C2×C42—221no—
415C2×C42C22⋊D1112yes—
416#99—228no—
417#95—28no—
418#95—228no—
419C2×C11—21no—
420C2×C11—21no—
421C2×C11—21no—
422C2×C11—21no—
423C2×C11—21no—
424C2×C11—21no—
425C2×C11C2×#38611yescharacteristic
426C2×C11#302812yes—
427D11—44no—
428C24—112no—
429C24C23×D1111yescharacteristic
430#41—224no—
431#41—224no—
432#41—224no—
433#41—224no—
434#41—224no—
435#41—224no—
436#41—224no—
437#41—224no—
438C2×Q8—24no—
439C2×Q8—24no—
440C2×Q8—24no—
441C2×Q8—24no—
442C2×Q8—24no—
443C2×Q8—24no—
444C2×Q8—42no—
445C2×Q8—42no—
446C2×Q8—42no—
447C2×Q8—42no—
448C2×Q8—41no—
449C2×Q8—41no—
450C2×Q8—41no—
451C2×Q8—41no—
452C2×Q8—42no—
453C2×Q8—42no—
454C2×Q8—114no—
455C2×Q8—222no—
456C2×Q8—221no—
457C2×Q8—221no—
458C2×D4—114no—
459C2×D4—114no—
460C2×D4—114no—
461C2×D4—222no—
462C2×D4—222no—
463C2×D4—222no—
464C2×D4—222no—
465C2×D4—222no—
466C2×D4—221no—
467C2×D4—221no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—112no—
476C22×C4—118no—
477C22×C4—114no—
478C22×C4—228no—
479C22×C4—224no—
480C22×C4—222no—
481C22×C4—222no—
482C22×C4—222no—
483C22×C4—222no—
484C22×C4C2×C4×D1114yes—
485C22×C4C2×C4×D1112yes—
486C22×C4#433912yes—
487C22×C4D4×D1111yescharacteristic
488C22×C4D4×D1111yescharacteristic
489C22×C4D4×D1112yes—
490C22×C4D4×D1111yescharacteristic
491C22×C4D4×D1111yescharacteristic
492C22×C4#434112yes—
493C22×C4C2×C22⋊D1114yes—
494C22×C4C2×C22⋊D1111yescharacteristic
495C22×C4C2×C22⋊D1111yescharacteristic
496C4⋊C4—22no—
497C4⋊C4—22no—
498C4⋊C4—42no—
499C4⋊C4—2216no—
500C4⋊C4—228no—
501C4⋊C4—224no—
502C4⋊C4—222no—
503C4⋊C4—222no—
504C4⋊C4—442no—
505C22⋊C4—22no—
506C22⋊C4—22no—
507C22⋊C4—22no—
508C22⋊C4—22no—
509C22⋊C4—114no—
510C22⋊C4—2216no—
511C22⋊C4—228no—
512C22⋊C4—222no—
513C22⋊C4—222no—
514C22⋊C4—222no—
515C22⋊C4—222no—
516C22⋊C4—222no—
517C42—22no—
518C42—22no—
519C42—42no—
520C42—228no—
521C42—224no—
522C42—222no—
523C42—222no—
524C42—442no—
525C11#2096211yescharacteristic, complemented, Sylow
526C23—42no—
527C23—114no—
528C23—222no—
529C23—222no—
530C23—444no—
531C23C22×C4×D1111yescharacteristic
532C23C2×#433911yescharacteristic
533C23C2×D4×D1111yescharacteristic
534C23C2×D4×D1111yescharacteristic
535C23C2×D4×D1111yescharacteristic
536C23C2×#434111yescharacteristic
537C23C22×C22⋊D1111yescharacteristic
538Q8—44no—
539Q8—44no—
540Q8—44no—
541Q8—44no—
542Q8—224no—
543Q8—224no—
544D4—224no—
545D4—224no—
546D4—224no—
547D4—224no—
548D4—224no—
549D4—224no—
550C2×C4—24no—
551C2×C4—24no—
552C2×C4—24no—
553C2×C4—24no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—44no—
559C2×C4—44no—
560C2×C4—42no—
561C2×C4—114no—
562C2×C4—222no—
563C2×C4—222no—
564C2×C4—228no—
565C2×C4—228no—
566C2×C4—224no—
567C2×C4—224no—
568C2×C4—444no—
569C2×C4—444no—
570C2×C4—444no—
571C2×C4—442no—
572C2×C4—888no—
573C2×C4C22⋊C4×D1112yes—
574C2×C4C22⋊C4×D1112yes—
575C2×C4(C22⋊D11)⋊C412yes—
576C2×C4(C22⋊D11)⋊C412yes—
577C2×C4#6693612yes—
578C2×C4#6693612yes—
579C2×C4#6693712yes—
580C2×C4#6693712yes—
581C2×C4C4×C22⋊D1112yes—
582C2×C4C4×C22⋊D1112yes—
583C2×C4#6699011yescharacteristic
584C2×C4#6699011yescharacteristic
585C2×C4#6699011yescharacteristic
586C2×C4#6699011yescharacteristic
587C2×C4#6699112yes—
588C2×C4#6699112yes—
589C22—22no—
590C22—22no—
591C22—22no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—224no—
597C22—444no—
598C22—444no—
599C22—882no—
600C22C2×C22⋊C4×D1111yescharacteristic
601C22C2×(C22⋊D11)⋊C411yescharacteristic
602C22C2×#6693611yescharacteristic
603C22C2×#6693711yescharacteristic
604C22C2×C4×C22⋊D1111yescharacteristic
605C22C2×#6699011yescharacteristic
606C22C2×#6699111yescharacteristic
607C4—44no—
608C4—44no—
609C4—82no—
610C4—224no—
611C4—444no—
612C4—444no—
613C4—882no—
614C4#1062256912yes—
615C4#1062256912yes—
616C4#1062256912yes—
617C4#1062256912yes—
618C2—21no—
619C2—21no—
620C2—21no—
621C2—21no—
622C2—21no—
623C2—21no—
624C2—444no—
625C2C2×#1062256911yescharacteristic
626C2#1307802112yes—
subgroupG/H
centerC22C2×#66990
commutatorC23×C11C23×C4
FrattiniC24C23×D11
FittingC11×#2310C2
socleC22×C11C2×#120
prime radicalC22×#4339C22
cosocleC24×C11C24
hypercenter#2310D11
hypocenterC11#20962
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2310

Complements

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

NH ≅ G/Ntype
4. #13071202C2semidirect
5. #13069026C2semidirect
6. #13068349C2semidirect
7. #13068348C2semidirect
8. C11×#2310C2semidirect
14. #10623347C4semidirect
49. C22×Q8×C11C2×C4semidirect
83. #66982C2×C4semidirect
93. #66979C2×C4semidirect
217. #2310D11semidirect
362. C22×Q8C4×D11semidirect
525. C11#20962semidirect

Maximal subgroups

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

subgroupindex
C2×#106233472
#130818172
C2×#106226192
#130712022
#130690262
#130683492
#130683482
C11×#23102
#2096211