Finite Group Databasebeta

← #14757407

Subgroups — #14757407

Order 2816.

1662 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623363C211yesmaximal, characteristic
2C2×#10622726C211yesmaximal, characteristic, complemented
3C2×#10622846C211yesmaximal, characteristic, complemented
4C2×#10622615C211yesmaximal, characteristic, complemented
5C22×C8×Dic11C211yesmaximal, characteristic, complemented
6#13071019C211yesmaximal, characteristic, complemented
7#13069426C212yesmaximal, complemented
8#13069424C212yesmaximal, complemented
9#13069420C212yesmaximal, complemented
10#13069416C212yesmaximal, complemented
11C2×C11×#416C211yesmaximal, characteristic, complemented
12C22×C11×#41C2211yescharacteristic
13C22×#4339C2211yescharacteristic
14C23×C8×C11C2211yescharacteristic
15C2×C11×#117C2211yescharacteristic
16#10623363—24no—
17#10623363C418yescomplemented
18C2×#67000C2211yescharacteristic
19C2×#66997C2211yescharacteristic
20C2×#66993C2211yescharacteristic
21C2×#66992—22no—
22C2×#66989C2211yescharacteristic
23C2×C4×C22⋊D11—22no—
24C2×#66979C2211yescharacteristic
25C22×C4×Dic11C2211yescharacteristic
26C23×C11⋊C8C2211yescharacteristic
27C11×#416—24no—
28C2×C11×#103C2212yes—
29C2×C11×#102C2212yes—
30#10622846—24no—
31C2×#66899C2212yes—
32C2×#66896C2212yes—
33#10622726—24no—
34C2×#66885C2212yes—
35C2×#66880C2212yes—
36C2×C8×Dic11—24no—
37C2×C8×Dic11C2212yes—
38C2×C8×Dic11C2212yes—
39#10622615—24no—
40#10622590C2212yes—
41#10622589C2212yes—
42C2×#66874C2212yes—
43C2×#66873C2212yes—
44#10622555—22no—
45C4×Dic11⋊C4—22no—
46C2×C11×#41—22no—
47C2×C11×#41—22no—
48C2×C11×#41—22no—
49C2×C11×#41—22no—
50C2×C11×#41—22no—
51C2×C11×#41C2×C414yes—
52C22×Q8×C11C2311yescharacteristic
53C22×D4×C11—21no—
54C22×D4×C11C2311yescharacteristic
55C23×C4×C11—21no—
56C23×C4×C11C2311yescharacteristic
57C22×C22⋊D11—21no—
58C22×C22⋊D11—22no—
59C23×Dic11D412yes—
60C2×#4339—22no—
61C2×#4339—22no—
62C2×#4339—22no—
63C2×#4339—22no—
64C2×#4339—22no—
65C2×#4339C2×C414yes—
66C22×D44C2311yescharacteristic
67C22×C4×D11—21no—
68C22×Dic22C2311yescharacteristic
69C22×C8×C11—22no—
70C22×C8×C11—22no—
71C22×C8×C11D414yescomplemented
72C22×C8×C11C2312yes—
73C11×#117—22no—
74C11×#117—22no—
75C2×C11×C4⋊C4C2312yes—
76C2×C11×C22⋊C4—21no—
77C2×C42×C11—21no—
78C2×C22⋊Dic11—22no—
79C2×C22⋊Dic11—21no—
80#67000—22no—
81#67000C2×C414yes—
82#66997—22no—
83#66997C2×C414yes—
84#66993—22no—
85#66993C2×C414yes—
86#66992—216no—
87#66989—22no—
88#66989C2×C414yes—
89C4×C22⋊D11—216no—
90C2×(C2×D11)⋊C4—22no—
91#66979—22no—
92#66979—22no—
93C2×C4⋊Dic11C2312yes—
94C2×Dic11⋊C4—22no—
95C2×Dic11⋊C4—24no—
96C2×C4×Dic11—21no—
97C2×C4×Dic11C2×C414yes—
98C2×C4×Dic11D412yes—
99C2×C4×Dic11D414yes—
100C2×C4×Dic11C2311yescharacteristic
101C2×C4×Dic11C2311yescharacteristic
102C22×C11⋊C8—22no—
103C22×C11⋊C8—22no—
104C22×C11⋊C8D414yescomplemented
105C22×C11⋊C8C2312yes—
106C11×#103—24no—
107C11×#102—24no—
108#66899—24no—
109#66896—24no—
110C11⋊#95—24no—
111#66885—24no—
112#66880—24no—
113C8×Dic11—24no—
114C8×Dic11—24no—
115#66874—24no—
116#66873—24no—
117#21195—111nomaximal, Sylow
118C24×C11—21no—
119C24×C11C2×D411yescharacteristic
120C23×D11—21no—
121C11×#41—28no—
122C11×#41—28no—
123C11×#41—44no—
124C11×#41—44no—
125C2×Q8×C11—21no—
126C2×Q8×C11—21no—
127C2×Q8×C11—21no—
128C2×Q8×C11—21no—
129C2×Q8×C11—21no—
130C2×Q8×C11C22×C412yes—
131C2×D4×C11—24no—
132C2×D4×C11—21no—
133C2×D4×C11—21no—
134C2×D4×C11—21no—
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11—42no—
138C2×D4×C11—42no—
139C2×D4×C11C22×C412yes—
140C22×C4×C11—21no—
141C22×C4×C11—24no—
142C22×C4×C11—22no—
143C22×C4×C11—42no—
144C22×C4×C11—42no—
145C22×C4×C11C22×C412yes—
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D412yes—
148C22×C4×C11C2×D412yes—
149C22×C4×C11C2×D412yes—
150C22×C4×C11#4112yes—
151C22×C4×C11#4112yes—
152C22×C4×C11C2411yescharacteristic
153C2×C22⋊D11—28no—
154C2×C22⋊D11—24no—
155C2×C22⋊D11—48no—
156C2×C22⋊D11—42no—
157C2×C22⋊D11—42no—
158C22×Dic11—28no—
159C22×Dic11—21no—
160C22×Dic11—22no—
161C22×Dic11C22⋊C418yes—
162C22×Dic11C2×D412yes—
163C22×Dic11C2×D412yes—
164#4339—28no—
165#4339—28no—
166#4339—44no—
167#4339—44no—
168C2×D44—21no—
169C2×D44—21no—
170C2×D44—21no—
171C2×D44—21no—
172C2×D44—21no—
173C2×D44C22×C412yes—
174C2×C4×D11—24no—
175C2×C4×D11—42no—
176C2×C4×D11—42no—
177C2×Dic22—21no—
178C2×Dic22—21no—
179C2×Dic22—21no—
180C2×Dic22—21no—
181C2×Dic22—21no—
182C2×Dic22C22×C412yes—
183C2×C8×C11—28no—
184C2×C8×C11—22no—
185C2×C8×C11—22no—
186C2×C8×C11C2×D414yes—
187C11×C4⋊C4—22no—
188C11×C4⋊C4—22no—
189C11×C22⋊C4—42no—
190C42×C11—42no—
191C22⋊Dic11—28no—
192C22⋊Dic11—42no—
193(C2×D11)⋊C4—28no—
194C4⋊Dic11—22no—
195C4⋊Dic11—22no—
196Dic11⋊C4—28no—
197Dic11⋊C4—48no—
198C4×Dic11—42no—
199C4×Dic11C22⋊C418yes—
200C4×Dic11C22×C412yes—
201C4×Dic11C22×C412yes—
202C4×Dic11C2×D412yes—
203C4×Dic11C2×D412yes—
204C2×C11⋊C8—28no—
205C2×C11⋊C8—22no—
206C2×C11⋊C8—22no—
207C2×C11⋊C8C2×D414yes—
208C2×#532—111no—
209C2×#416—111no—
210C2×#416—111no—
211C2×#416—111no—
212C2×#416D1111yescharacteristic, complemented
213C22×C4×C8—111no—
214#2285—111no—
215#1958—112no—
216#1958—112no—
217#1957—112no—
218#1956—112no—
219C23×C11—24no—
220C23×C11—22no—
221C23×C11—41no—
222C23×C11—41no—
223C23×C11—44no—
224C23×C11C2×C22⋊C412yes—
225C23×C11#12412yes—
226C23×C11#12712yes—
227C23×C11C22×D411yescharacteristic
228C22×D11—22no—
229C22×D11—41no—
230C22×D11—41no—
231C22×D11—44no—
232Q8×C11—22no—
233Q8×C11—22no—
234Q8×C11—41no—
235Q8×C11—41no—
236D4×C11—22no—
237D4×C11—22no—
238D4×C11—48no—
239D4×C11—41no—
240D4×C11—41no—
241C2×C4×C11—22no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—48no—
245C2×C4×C11—42no—
246C2×C4×C11—44no—
247C2×C4×C11C2×C22⋊C412yes—
248C2×C4×C11C4×D414yes—
249C2×C4×C11C4×D414yes—
250C2×C4×C11#12114yes—
251C2×C4×C11#12114yes—
252C2×C4×C11#12412yes—
253C2×C4×C11#12712yes—
254C2×C4×C11C23×C411yescharacteristic
255C2×C4×C11C22×D411yescharacteristic
256C2×C4×C11C22×D411yescharacteristic
257C2×C4×C11C22×D411yescharacteristic
258C2×C4×C11C2×#4111yescharacteristic
259C2×C4×C11C2×#4111yescharacteristic
260C22⋊D11—48no—
261C22⋊D11—416no—
262C2×Dic11—24no—
263C2×Dic11—216no—
264C2×Dic11—22no—
265C2×Dic11—41no—
266C2×Dic11—41no—
267C2×Dic11—42no—
268C2×Dic11—44no—
269C2×Dic11C2×C22⋊C414yes—
270C2×Dic11C2×C22⋊C414yes—
271C2×Dic11#13518yes—
272D44—22no—
273D44—22no—
274D44—41no—
275D44—41no—
276C4×D11—48no—
277Dic22—22no—
278Dic22—22no—
279Dic22—41no—
280Dic22—41no—
281C8×C11—24no—
282C11⋊C8—24no—
283C22×#41—111no—
284C22×#41C2×D1111yescharacteristic
285C23×C8—111no—
286C23×C8C2×D1111yescharacteristic
287#532—118no—
288#532—224no—
289C2×C4⋊Q8—111no—
290C2×#127—111no—
291C2×#124—111no—
292C2×#124—111no—
293C2×#121—222no—
294C2×C4×D4—222no—
295C2×#117—111no—
296C2×#117C2×D1111yescharacteristic
297C22×C42—111no—
298#416—24no—
299#416—224no—
300#416—224no—
301#416—224no—
302C2×#103—112no—
303C2×#103—112no—
304C2×#103—112no—
305C2×#103C2×D1112yes—
306C2×#102—112no—
307C2×#102—112no—
308C2×#102—112no—
309C2×#102C2×D1112yes—
310C2×C4×C8—112no—
311C2×C4×C8—112no—
312C2×C4×C8—224no—
313#384—112no—
314#382—112no—
315#380—222no—
316C4×C4⋊C4—222no—
317C22×C11—24no—
318C22×C11—24no—
319C22×C11—24no—
320C22×C11—44no—
321C22×C11—42no—
322C22×C11—82no—
323C22×C11—82no—
324C22×C11#39014yes—
325C22×C11C22×C22⋊C411yescharacteristic
326C22×C11C2×#12411yescharacteristic
327C22×C11C2×#12711yescharacteristic
328C22×C11C2×#13514yes—
329C2×D11—44no—
330C2×D11—42no—
331C2×D11—82no—
332C2×D11—82no—
333C4×C11—42no—
334C4×C11—82no—
335C4×C11#39014yes—
336C4×C11C2×C4×D411yescharacteristic
337C4×C11C2×C4×D411yescharacteristic
338C4×C11C2×#12111yescharacteristic
339C4×C11C2×#12111yescharacteristic
340Dic11—24no—
341Dic11—42no—
342Dic11—82no—
343Dic11#41618yescomplemented
344C2×#41—22no—
345C2×#41—22no—
346C2×#41—22no—
347C2×#41—22no—
348C2×#41—22no—
349C2×#41—114no—
350C2×#41—222no—
351C2×#41—222no—
352C2×#41—222no—
353C2×#41—222no—
354C2×#41—222no—
355C2×#41C4×D1114yes—
356C22×Q8—111no—
357C22×Q8C22×D1111yescharacteristic
358C22×D4—21no—
359C22×D4—111no—
360C22×D4—222no—
361C22×D4—221no—
362C22×D4C22×D1111yescharacteristic
363C23×C4—21no—
364C23×C4—112no—
365C23×C4—221no—
366C23×C4C22×D1111yescharacteristic
367C22×C8—22no—
368C22×C8—22no—
369C22×C8—114no—
370C22×C8—112no—
371C22×C8—222no—
372C22×C8—222no—
373C22×C8C22⋊D1114yescomplemented
374C22×C8C22×D1112yes—
375C4⋊Q8—114no—
376C4⋊Q8—222no—
377#127—114no—
378#127—222no—
379#124—114no—
380#124—114no—
381#124—222no—
382#124—222no—
383#121—2216no—
384C4×D4—2216no—
385#117—22no—
386#117—22no—
387#117—222no—
388#117—222no—
389C2×C4⋊C4—112no—
390C2×C4⋊C4—222no—
391C2×C4⋊C4—224no—
392C2×C4⋊C4C22×D1112yes—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—222no—
395C2×C22⋊C4—222no—
396C2×C22⋊C4—221no—
397C2×C42—21no—
398C2×C42—114no—
399C2×C42—114no—
400C2×C42—112no—
401C2×C42—111no—
402C2×C42—111no—
403C2×C42—221no—
404#103—24no—
405#103—224no—
406#103—224no—
407#103—224no—
408#102—24no—
409#102—224no—
410#102—224no—
411#102—224no—
412C4×C8—224no—
413C4×C8—224no—
414#95—224no—
415C2×C11—24no—
416C2×C11—82no—
417C2×C11C2×#39011yescharacteristic
418C2×C11C2×#41612yes—
419C2×C11#313112yes—
420C2×C11#314712yes—
421D11—82no—
422C24—21no—
423C24—221no—
424C24D4×D1111yescharacteristic
425#41—28no—
426#41—28no—
427#41—44no—
428#41—44no—
429#41—228no—
430#41—228no—
431#41—444no—
432#41—444no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—112no—
439C2×Q8—221no—
440C2×Q8—221no—
441C2×Q8—221no—
442C2×Q8—221no—
443C2×Q8—221no—
444C2×Q8C2×C4×D1112yes—
445C2×D4—24no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—42no—
452C2×D4—42no—
453C2×D4—112no—
454C2×D4—228no—
455C2×D4—224no—
456C2×D4—221no—
457C2×D4—221no—
458C2×D4—221no—
459C2×D4—221no—
460C2×D4—221no—
461C2×D4—448no—
462C2×D4—442no—
463C2×D4—442no—
464C2×D4C2×C4×D1112yes—
465C22×C4—21no—
466C22×C4—24no—
467C22×C4—22no—
468C22×C4—42no—
469C22×C4—42no—
470C22×C4—112no—
471C22×C4—118no—
472C22×C4—112no—
473C22×C4—228no—
474C22×C4—221no—
475C22×C4—224no—
476C22×C4—222no—
477C22×C4—442no—
478C22×C4—442no—
479C22×C4C2×C4×D1112yes—
480C22×C4#433912yes—
481C22×C4D4×D1112yes—
482C22×C4D4×D1112yes—
483C22×C4D4×D1111yescharacteristic
484C22×C4#434112yes—
485C22×C4C2×C22⋊D1112yes—
486C22×C4C23×D1111yescharacteristic
487C2×C8—28no—
488C2×C8—22no—
489C2×C8—22no—
490C2×C8—114no—
491C2×C8—228no—
492C2×C8—222no—
493C2×C8—222no—
494C2×C8C2×C22⋊D1114yes—
495C4⋊C4—22no—
496C4⋊C4—22no—
497C4⋊C4—228no—
498C4⋊C4—222no—
499C4⋊C4—222no—
500C4⋊C4—448no—
501C22⋊C4—42no—
502C22⋊C4—228no—
503C22⋊C4—228no—
504C22⋊C4—442no—
505C42—42no—
506C42—118no—
507C42—112no—
508C42—112no—
509C42—112no—
510C42—112no—
511C42—442no—
512C11#2119511yescharacteristic, complemented, Sylow
513C23—24no—
514C23—22no—
515C23—41no—
516C23—44no—
517C23—41no—
518C23—222no—
519C23—441no—
520C23—444no—
521C23—441no—
522C23C22⋊C4×D1112yes—
523C23#6693812yes—
524C23#6699312yes—
525C23C2×D4×D1111yescharacteristic
526Q8—22no—
527Q8—22no—
528Q8—41no—
529Q8—41no—
530Q8—222no—
531Q8—222no—
532Q8—441no—
533Q8—441no—
534D4—22no—
535D4—22no—
536D4—48no—
537D4—41no—
538D4—41no—
539D4—222no—
540D4—222no—
541D4—4416no—
542D4—448no—
543D4—441no—
544D4—441no—
545C2×C4—22no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—48no—
549C2×C4—44no—
550C2×C4—42no—
551C2×C4—114no—
552C2×C4—118no—
553C2×C4—114no—
554C2×C4—2216no—
555C2×C4—224no—
556C2×C4—222no—
557C2×C4—441no—
558C2×C4—441no—
559C2×C4—448no—
560C2×C4—444no—
561C2×C4—442no—
562C2×C4C22⋊C4×D1112yes—
563C2×C4(C22⋊D11)⋊C414yes—
564C2×C4#6693714yes—
565C2×C4#6693812yes—
566C2×C4C4×C22⋊D1114yes—
567C2×C4#6699214yes—
568C2×C4#6699312yes—
569C2×C4C22×C4×D1111yescharacteristic
570C2×C4C2×#433911yescharacteristic
571C2×C4C2×D4×D1111yescharacteristic
572C2×C4C2×D4×D1111yescharacteristic
573C2×C4C2×#434111yescharacteristic
574C2×C4C22×C22⋊D1111yescharacteristic
575C8—24no—
576C8—224no—
577C22—24no—
578C22—24no—
579C22—24no—
580C22—44no—
581C22—42no—
582C22—82no—
583C22—82no—
584C22—444no—
585C22—442no—
586C22—882no—
587C22—882no—
588C22#1062257014yes—
589C22C2×C22⋊C4×D1111yescharacteristic
590C22C2×#6693811yescharacteristic
591C22D11×#13514yes—
592C22C2×#6699311yescharacteristic
593C4—42no—
594C4—82no—
595C4—118no—
596C4—224no—
597C4—442no—
598C4—882no—
599C4#1062257014yes—
600C4C2×(C22⋊D11)⋊C411yescharacteristic
601C4C2×#6693711yescharacteristic
602C4C2×C4×C22⋊D1111yescharacteristic
603C4C2×#6699211yescharacteristic
604C2—24no—
605C2—82no—
606C2—882no—
607C2C2×#1062257011yescharacteristic
608C2D11×#41612yes—
609C2#1307893612yes—
610C2#1307904012yes—
subgroupG/H
centerC22×C4D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#416C2
socleC23×C11C22×D4
prime radicalC2×#10623363C2
cosocleC22×C4×C11C24
hypercenterC2×#416D11
hypocenterC11#21195
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C2×#416

Complements

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

NH ≅ G/Ntype
2. C2×#10622726C2semidirect
3. C2×#10622846C2semidirect
4. C2×#10622615C2semidirect
5. C22×C8×Dic11C2semidirect
6. #13071019C2semidirect
7. #13069426C2semidirect
8. #13069424C2semidirect
9. #13069420C2semidirect
10. #13069416C2semidirect
11. C2×C11×#416C2semidirect
17. #10623363C4semidirect
71. C22×C8×C11D4semidirect
104. C22×C11⋊C8D4semidirect
212. C2×#416D11semidirect
343. Dic11#416semidirect
373. C22×C8C22⋊D11semidirect
512. C11#21195semidirect

Maximal subgroups

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

subgroupindex
C2×#106233632
C2×#106227262
C2×#106228462
C2×#106226152
C22×C8×Dic112
#130710192
#130694262
#130694242
#130694202
#130694162
C2×C11×#4162
#2119511