Finite Group Databasebeta

← #14757485

Subgroups — #14757485

Order 2816.

1718 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×#10623361C211yesmaximal, characteristic
2C2×#10622744C211yesmaximal, characteristic, complemented
3C2×#10622846C211yesmaximal, characteristic, complemented
4C22×#66873C211yesmaximal, characteristic, complemented
5C2×#10622735C211yesmaximal, characteristic, complemented
6#13071240C211yesmaximal, characteristic, complemented
7#13069438C212yesmaximal, complemented
8#13069429C212yesmaximal, complemented
9#13069424C212yesmaximal, complemented
10#13069420C212yesmaximal, complemented
11C2×C11×#417C211yesmaximal, characteristic, complemented
12C22×C11×#41C2211yescharacteristic
13C23×D44C2211yescharacteristic
14C22×C11×M16C2211yescharacteristic
15C22×C11×C4⋊C4C2211yescharacteristic
16#10623361—24no—
17#10623361C418yescomplemented
18C2×#67000C2212yes—
19C2×#66993C2212yes—
20C2×#66990—22no—
21C2×#66983—22no—
22C2×#66979C2211yescharacteristic
23C2×#66979C2211yescharacteristic
24C23×C11⋊C8C2211yescharacteristic
25C11×#417—24no—
26C2×C11×#103C2212yescomplemented
27C2×C11×#102C2212yescomplemented
28#10622846—24no—
29C2×#66899C2211yescharacteristic, complemented
30C2×#66899C2211yescharacteristic, complemented
31C2×#66896C2211yescharacteristic, complemented
32C2×#66896C2211yescharacteristic, complemented
33#10622823—22no—
34#10622744—24no—
35#10622735—24no—
36C2×#66885C2212yes—
37C2×#66885C2212yes—
38C2×#66879C2212yescomplemented
39C2×C8×Dic11C2212yescomplemented
40#10622590C2212yescomplemented
41#10622589C2212yescomplemented
42#10622586—22no—
43C2×#66873—24no—
44C2×#66873C2212yes—
45C2×#66873C2212yes—
46C24×D11—21no—
47C2×C11×#41—22no—
48C2×C11×#41—22no—
49C2×C11×#41—22no—
50C2×C11×#41—22no—
51C2×C11×#41—22no—
52C2×C11×#41C2×C414yes—
53C22×Q8×C11C2311yescharacteristic
54C22×D4×C11—21no—
55C22×D4×C11C2311yescharacteristic
56C23×C4×C11—21no—
57C23×C4×C11—21no—
58C23×C4×C11C2311yescharacteristic
59C22×C22⋊D11—24no—
60C22×D44—22no—
61C22×D44—22no—
62C22×D44—22no—
63C22×D44—22no—
64C22×D44—21no—
65C22×D44—22no—
66C22×D44C2×C414yes—
67C22×D44C2312yes—
68C2×C11×M16—22no—
69C2×C11×M16—22no—
70C2×C11×M16D414yescomplemented
71C22×C8×C11C2312yes—
72C2×C11×C4⋊C4—22no—
73C2×C11×C4⋊C4—22no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4C2312yes—
76C2×C22⋊Dic11—21no—
77C2×C22⋊Dic11D412yes—
78#67000—24no—
79#67000C2×C418yescomplemented
80#66993—24no—
81#66993C2×C418yescomplemented
82#66990—216no—
83#66983—216no—
84C2×(C2×D11)⋊C4—24no—
85#66979—22no—
86#66979—22no—
87#66979C2×C414yes—
88#66979D414yes—
89C2×C4⋊Dic11D412yes—
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×Dic11⋊C4—24no—
93C2×C4×Dic11—21no—
94C2×C4×Dic11C2312yes—
95C22×C11⋊C8—22no—
96C22×C11⋊C8—22no—
97C22×C11⋊C8D414yescomplemented
98C22×C11⋊C8C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100C11×#103—24no—
101C11×#102—24no—
102#66899—22no—
103#66899—22no—
104#66896—22no—
105#66896—22no—
106C11⋊#95—24no—
107#66885—24no—
108#66885—24no—
109#66879—24no—
110C8×Dic11—24no—
111#66873—24no—
112#66873—24no—
113#21206—111nomaximal, Sylow
114C24×C11—21no—
115C24×C11C2×D411yescharacteristic
116C23×D11—22no—
117C23×D11—24no—
118C23×D11—42no—
119C23×D11—42no—
120C23×D11—82no—
121C23×D11—82no—
122C11×#41—28no—
123C11×#41—28no—
124C11×#41—44no—
125C11×#41—44no—
126C2×Q8×C11—21no—
127C2×Q8×C11—21no—
128C2×Q8×C11—21no—
129C2×Q8×C11—21no—
130C2×Q8×C11—21no—
131C2×Q8×C11C22×C412yes—
132C2×D4×C11—24no—
133C2×D4×C11—21no—
134C2×D4×C11—21no—
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11—21no—
138C2×D4×C11—42no—
139C2×D4×C11—42no—
140C2×D4×C11C22×C412yes—
141C22×C4×C11—21no—
142C22×C4×C11—24no—
143C22×C4×C11—22no—
144C22×C4×C11—42no—
145C22×C4×C11—42no—
146C22×C4×C11—42no—
147C22×C4×C11—82no—
148C22×C4×C11C22×C412yes—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D412yes—
151C22×C4×C11C2×D412yes—
152C22×C4×C11C2×D412yes—
153C22×C4×C11#4112yes—
154C22×C4×C11#4112yes—
155C22×C4×C11C2411yescharacteristic
156C2×C22⋊D11—216no—
157C2×C22⋊D11—84no—
158C2×C22⋊D11—84no—
159C22×Dic11—21no—
160C22×Dic11—21no—
161C22×Dic11C2×D414yes—
162C2×D44—24no—
163C2×D44—28no—
164C2×D44—28no—
165C2×D44—22no—
166C2×D44—22no—
167C2×D44—22no—
168C2×D44—22no—
169C2×D44—22no—
170C2×D44—44no—
171C2×D44—44no—
172C2×D44—42no—
173C2×D44—42no—
174C2×D44C22×C414yes—
175C11×M16—28no—
176C2×C8×C11—22no—
177C2×C8×C11—22no—
178C2×C8×C11C2×D414yes—
179C11×C4⋊C4—22no—
180C11×C4⋊C4—22no—
181C11×C4⋊C4—42no—
182C22⋊Dic11—42no—
183C22⋊Dic11C22⋊C418yes—
184(C2×D11)⋊C4—216no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11C22⋊C418yes—
190Dic11⋊C4—84no—
191C4×Dic11—42no—
192C4×Dic11C22×C414yes—
193C4×Dic11C2×D414yes—
194C2×C11⋊C8—28no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8C2×D412yes—
200C2×C11⋊C8C2×D412yes—
201C2×#535—111no—
202C2×#417D1111yescharacteristic, complemented
203C2×#418—111no—
204C2×#416—111no—
205C22×#102—111no—
206C2×#405—111no—
207#2317—111no—
208#1961—112no—
209#1959—112no—
210#1958—112no—
211#1957—112no—
212C23×C11—22no—
213C23×C11—22no—
214C23×C11—22no—
215C23×C11—41no—
216C23×C11—41no—
217C23×C11—42no—
218C23×C11—42no—
219C23×C11C2×C22⋊C412yes—
220C23×C11#12412yes—
221C23×C11#12712yes—
222C23×C11C22×D411yescharacteristic
223C22×D11—24no—
224C22×D11—42no—
225C22×D11—42no—
226C22×D11—44no—
227C22×D11—44no—
228C22×D11—48no—
229C22×D11—88no—
230C22×D11—88no—
231C22×D11—84no—
232C22×D11—84no—
233Q8×C11—22no—
234Q8×C11—22no—
235Q8×C11—41no—
236Q8×C11—41no—
237D4×C11—22no—
238D4×C11—22no—
239D4×C11—48no—
240D4×C11—41no—
241D4×C11—41no—
242C2×C4×C11—22no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—48no—
246C2×C4×C11—42no—
247C2×C4×C11—44no—
248C2×C4×C11—84no—
249C2×C4×C11C2×C22⋊C412yes—
250C2×C4×C11C4×D414yes—
251C2×C4×C11C4×D414yes—
252C2×C4×C11#12114yes—
253C2×C4×C11#12114yes—
254C2×C4×C11#12412yes—
255C2×C4×C11#12712yes—
256C2×C4×C11C23×C411yescharacteristic
257C2×C4×C11C22×D411yescharacteristic
258C2×C4×C11C22×D411yescharacteristic
259C2×C4×C11C22×D411yescharacteristic
260C2×C4×C11C2×#4111yescharacteristic
261C2×C4×C11C2×#4111yescharacteristic
262C22⋊D11—816no—
263C2×Dic11—24no—
264C2×Dic11—24no—
265C2×Dic11—41no—
266C2×Dic11—41no—
267C2×Dic11—42no—
268C2×Dic11—42no—
269C2×Dic11C2×C22⋊C418yes—
270D44—24no—
271D44—24no—
272D44—42no—
273D44—42no—
274D44—48no—
275C8×C11—24no—
276C11⋊C8—22no—
277C11⋊C8—22no—
278C22×#41C2×D1111yescharacteristic
279C23×D4—111no—
280C22×M16C2×D1111yescharacteristic
281C23×C8—111no—
282#535—118no—
283#535—224no—
284C2×#127—112no—
285C2×#124—112no—
286C2×#121—222no—
287C2×#120—222no—
288C2×#117—111no—
289C2×#117—111no—
290C22×C4⋊C4C2×D1111yescharacteristic
291#418—224no—
292#417—24no—
293#416—224no—
294C2×#103—111no—
295C2×#103—111no—
296C2×#103C2×D1112yescomplemented
297C2×#102—111no—
298C2×#102—111no—
299C2×#102—112no—
300C2×#102—112no—
301C2×#102—112no—
302C2×#102—112no—
303C2×#102—224no—
304C2×#102C2×D1112yescomplemented
305#405—224no—
306C2×#97—112no—
307C2×C4×C8—112no—
308#389—222no—
309#385—222no—
310#384—112no—
311#382—112no—
312C22×C11—24no—
313C22×C11—24no—
314C22×C11—22no—
315C22×C11—22no—
316C22×C11—44no—
317C22×C11—42no—
318C22×C11—82no—
319C22×C11—81no—
320C22×C11—81no—
321C22×C11#39014yes—
322C22×C11C22×C22⋊C411yescharacteristic
323C22×C11C2×#12411yescharacteristic
324C22×C11C2×#12711yescharacteristic
325C22×C11#57612yes—
326C22×C11#57712yes—
327C2×D11—48no—
328C2×D11—44no—
329C2×D11—816no—
330C2×D11—84no—
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—28no—
341Dic11—81no—
342Dic11—81no—
343C25—221no—
344C2×#41—22no—
345C2×#41—22no—
346C2×#41—22no—
347C2×#41—22no—
348C2×#41—22no—
349C2×#41C4×D1114yes—
350C22×Q8C22×D1111yescharacteristic
351C22×D4—21no—
352C22×D4—114no—
353C22×D4—112no—
354C22×D4—224no—
355C22×D4—222no—
356C22×D4—222no—
357C22×D4—221no—
358C22×D4—222no—
359C22×D4—222no—
360C22×D4—222no—
361C22×D4C22×D1111yescharacteristic
362C23×C4—21no—
363C23×C4—21no—
364C23×C4C22×D1111yescharacteristic
365C2×M16—22no—
366C2×M16—22no—
367C2×M16C22⋊D1114yescomplemented
368C22×C8—114no—
369C22×C8—111no—
370C22×C8—111no—
371C22×C8—222no—
372C22×C8—222no—
373C22×C8C22×D1112yes—
374#127—118no—
375#127—224no—
376#124—118no—
377#124—224no—
378#121—2216no—
379#120—2216no—
380#117—114no—
381#117—114no—
382#117—222no—
383#117—222no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—112no—
388C2×C4⋊C4—111no—
389C2×C4⋊C4—111no—
390C2×C4⋊C4—224no—
391C2×C4⋊C4C22×D1112yes—
392C2×C22⋊C4—112no—
393C2×C22⋊C4—224no—
394C2×C22⋊C4—221no—
395C2×C42—112no—
396C2×C42—221no—
397#103—24no—
398#103—222no—
399#103—222no—
400#102—24no—
401#102—224no—
402#102—224no—
403#102—222no—
404#102—222no—
405#102—224no—
406#102—224no—
407#97—224no—
408C4×C8—224no—
409#95—224no—
410C2×C11—24no—
411C2×C11—82no—
412C2×C11C2×#39011yescharacteristic
413C2×C11#289712yes—
414C2×C11#313612yes—
415C2×C11#315411yescharacteristic
416C2×C11#315511yescharacteristic
417D11—84no—
418C24—21no—
419C24—222no—
420C24—224no—
421C24—442no—
422C24—442no—
423C24—882no—
424C24—882no—
425C24D4×D1111yescharacteristic
426#41—28no—
427#41—28no—
428#41—44no—
429#41—44no—
430C2×Q8—21no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8C2×C4×D1112yes—
436C2×D4—24no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—42no—
443C2×D4—42no—
444C2×D4—114no—
445C2×D4—2216no—
446C2×D4—224no—
447C2×D4—228no—
448C2×D4—228no—
449C2×D4—222no—
450C2×D4—222no—
451C2×D4—222no—
452C2×D4—222no—
453C2×D4—222no—
454C2×D4—444no—
455C2×D4—442no—
456C2×D4—444no—
457C2×D4—442no—
458C2×D4—884no—
459C2×D4—884no—
460C2×D4C2×C4×D1112yes—
461C22×C4—21no—
462C22×C4—24no—
463C22×C4—22no—
464C22×C4—42no—
465C22×C4—42no—
466C22×C4—42no—
467C22×C4—82no—
468C22×C4—114no—
469C22×C4—221no—
470C22×C4—221no—
471C22×C4C2×C4×D1112yes—
472C22×C4#433912yes—
473C22×C4D4×D1111yescharacteristic
474C22×C4D4×D1112yes—
475C22×C4D4×D1112yes—
476C22×C4#434112yes—
477C22×C4C2×C22⋊D1112yes—
478C22×C4C23×D1111yescharacteristic
479M16—28no—
480C2×C8—22no—
481C2×C8—22no—
482C2×C8—112no—
483C2×C8—112no—
484C2×C8—228no—
485C2×C8—221no—
486C2×C8—221no—
487C2×C8—221no—
488C2×C8—221no—
489C2×C8C2×C22⋊D1114yes—
490C4⋊C4—22no—
491C4⋊C4—22no—
492C4⋊C4—42no—
493C4⋊C4—118no—
494C4⋊C4—221no—
495C4⋊C4—221no—
496C4⋊C4—221no—
497C4⋊C4—221no—
498C4⋊C4—884no—
499C22⋊C4—118no—
500C22⋊C4—2216no—
501C22⋊C4—442no—
502C42—114no—
503C42—114no—
504C42—442no—
505C11#2120611yescharacteristic, complemented, Sylow
506C23—22no—
507C23—22no—
508C23—22no—
509C23—41no—
510C23—42no—
511C23—42no—
512C23—41no—
513C23—224no—
514C23—442no—
515C23—444no—
516C23—444no—
517C23—442no—
518C23—448no—
519C23—888no—
520C23—884no—
521C23—884no—
522C23—888no—
523C23C22⋊C4×D1112yes—
524C23#6693812yes—
525C23#6699312yes—
526C23C2×D4×D1111yescharacteristic
527Q8—22no—
528Q8—22no—
529Q8—41no—
530Q8—41no—
531D4—22no—
532D4—22no—
533D4—48no—
534D4—41no—
535D4—41no—
536D4—224no—
537D4—224no—
538D4—442no—
539D4—442no—
540D4—448no—
541D4—8816no—
542C2×C4—22no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—48no—
546C2×C4—44no—
547C2×C4—42no—
548C2×C4—84no—
549C2×C4—118no—
550C2×C4—224no—
551C2×C4—224no—
552C2×C4—442no—
553C2×C4—442no—
554C2×C4—441no—
555C2×C4—441no—
556C2×C4C22⋊C4×D1112yes—
557C2×C4(C22⋊D11)⋊C414yes—
558C2×C4#6693714yes—
559C2×C4#6693812yes—
560C2×C4C4×C22⋊D1114yes—
561C2×C4#6699214yes—
562C2×C4#6699312yes—
563C2×C4C22×C4×D1111yescharacteristic
564C2×C4C2×#433911yescharacteristic
565C2×C4C2×D4×D1111yescharacteristic
566C2×C4C2×D4×D1111yescharacteristic
567C2×C4C2×#434111yescharacteristic
568C2×C4C22×C22⋊D1111yescharacteristic
569C8—24no—
570C8—222no—
571C8—222no—
572C22—22no—
573C22—22no—
574C22—24no—
575C22—24no—
576C22—44no—
577C22—42no—
578C22—81no—
579C22—81no—
580C22—82no—
581C22—448no—
582C22—444no—
583C22—8816no—
584C22—882no—
585C22—882no—
586C22—884no—
587C22#1062257014yes—
588C22C2×C22⋊C4×D1111yescharacteristic
589C22C2×#6693811yescharacteristic
590C22#1062330512yes—
591C22#1062330912yes—
592C22C2×#6699311yescharacteristic
593C4—42no—
594C4—82no—
595C4—228no—
596C4—881no—
597C4—881no—
598C4#1062257014yes—
599C4C2×(C22⋊D11)⋊C411yescharacteristic
600C4C2×#6693711yescharacteristic
601C4C2×C4×C22⋊D1111yescharacteristic
602C4C2×#6699211yescharacteristic
603C2—24no—
604C2—82no—
605C2—884no—
606C2C2×#1062257011yescharacteristic
607C2#1307714012yes—
608C2#1307897312yes—
609C2#1307909511yescharacteristic
610C2#1307910111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#417C2
socleC23×C11C22×D4
prime radicalC2×#10623361C2
cosocleC22×C4×C11C24
hypercenterC2×#417D11
hypocenterC11#21206
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
2. C2×#10622744C2semidirect
3. C2×#10622846C2semidirect
4. C22×#66873C2semidirect
5. C2×#10622735C2semidirect
6. #13071240C2semidirect
7. #13069438C2semidirect
8. #13069429C2semidirect
9. #13069424C2semidirect
10. #13069420C2semidirect
11. C2×C11×#417C2semidirect
17. #10623361C4semidirect
26. C2×C11×#103C22semidirect
27. C2×C11×#102C22semidirect
29. C2×#66899C22semidirect
30. C2×#66899C22semidirect
31. C2×#66896C22semidirect
32. C2×#66896C22semidirect
38. C2×#66879C22semidirect
39. C2×C8×Dic11C22semidirect
40. #10622590C22semidirect
41. #10622589C22semidirect
70. C2×C11×M16D4semidirect
79. #67000C2×C4semidirect
81. #66993C2×C4semidirect
97. C22×C11⋊C8D4semidirect
202. C2×#417D11semidirect
296. C2×#103C2×D11semidirect
304. C2×#102C2×D11semidirect
367. C2×M16C22⋊D11semidirect
505. C11#21206semidirect

Maximal subgroups

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

subgroupindex
C2×#106233612
C2×#106227442
C2×#106228462
C22×#668732
C2×#106227352
#130712402
#130694382
#130694292
#130694242
#130694202
C2×C11×#4172
#2120611