Finite Group Databasebeta

← #14780794

Subgroups — #14780794

Order 2816.

1980 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
1#13081945C212yesmaximal, complemented
2C2×#10622849C212yesmaximal, complemented
3#13077060C211yesmaximal, characteristic, complemented
4#13069680C218yesmaximal, complemented
5C2×#10622195C211yesmaximal, characteristic, complemented
6C2×C11×#575C211yesmaximal, characteristic, complemented
7C22×C11×#41C2212yes—
8C22×#4339C2211yescharacteristic
9C11×#575—24no—
10C11×#575—22no—
11C11×#575C2214yes—
12C2×C11×#137—22no—
13C2×C11×AGL(1,ℤ/8)—22no—
14C2×C11×#135—22no—
15C22×C11×M16C2211yescharacteristic
16#10623364—24no—
17#10623363—24no—
18#10623361—22no—
19#10623359C2218yescomplemented
20#10623356—22no—
21#10623347—22no—
22#10623336—22no—
23#10623335—24no—
24#10623322—24no—
25C2×#66979C2212yes—
26C22×#4318C2211yescharacteristic
27#10622849—24no—
28#10622849C2218yescomplemented
29C2×#66901—24no—
30#10622742—22no—
31#10622739C2214yescomplemented
32#10622723—22no—
33#10622195C2214yescomplemented
34C2×C11×#41—22no—
35C2×C11×#41—22no—
36C2×C11×#41—22no—
37C2×C11×#41—22no—
38C2×C11×#41—22no—
39C2×C11×#41—22no—
40C2×C11×#41—22no—
41C2×C11×#41—22no—
42C2×C11×#41—22no—
43C2×C11×#41—22no—
44C2×C11×#41D414yescomplemented
45C2×C11×#41C2314yes—
46C22×Q8×C11D412yescomplemented
47C22×D4×C11—22no—
48C22×D4×C11D412yescomplemented
49C23×C4×C11—22no—
50C23×C4×C11C2311yescharacteristic
51C22×C22⋊D11D412yes—
52C2×#4339—21no—
53C2×#4339—21no—
54C2×#4339—22no—
55C2×#4339—22no—
56C2×#4339—22no—
57C2×#4339—22no—
58C2×#4339—21no—
59C2×#4339—21no—
60C22×D44D411yescharacteristic
61C22×C4×D11C2312yes—
62C22×Dic22D411yescharacteristic
63C11×#137—28no—
64C11×#137—28no—
65C11×AGL(1,ℤ/8)—28no—
66C11×AGL(1,ℤ/8)—28no—
67C11×#135—28no—
68C11×#135—28no—
69C2×C11×Q16—22no—
70C2×C11×SD16—24no—
71C2×C11×D8—22no—
72C2×C11×M16—22no—
73C2×C11×M16—22no—
74C2×C11×M16D412yescomplemented
75C2×C11×M16C2312yes—
76C22×C8×C11D412yescomplemented
77#67006—28no—
78C2×C22⋊Dic11—22no—
79#67000—24no—
80#66999—28no—
81#66997—24no—
82#66993—24no—
83#66992—216no—
84#66991—28no—
85#66990—28no—
86#66989—24no—
87#66988—28no—
88#66983—28no—
89#66982—28no—
90C4×C22⋊D11—216no—
91#66979—22no—
92#66979—22no—
93#66979D414yescomplemented
94#66979C2314yes—
95C2×C4⋊Dic11—22no—
96#66977—28no—
97C2×C4×Dic11D414yescomplemented
98C2×#4318—21no—
99C2×#4318—22no—
100C2×#4318—22no—
101C2×#4318C2312yes—
102C22×C11⋊C8—21no—
103#66901—216no—
104(C2×D11)⋊C8—28no—
105#23414—111nomaximal, Sylow
106C24×C11—22no—
107C24×C11C2×D411yescharacteristic
108C23×D11C2×D412yes—
109C11×#41—24no—
110C11×#41—24no—
111C11×#41—24no—
112C11×#41—24no—
113C11×#41—24no—
114C11×#41—24no—
115C11×#41—24no—
116C11×#41—24no—
117C11×#41—42no—
118C11×#41—42no—
119C11×#41—42no—
120C11×#41—42no—
121C11×#41—42no—
122C11×#41—42no—
123C11×#41—42no—
124C11×#41—42no—
125C2×Q8×C11—22no—
126C2×Q8×C11—22no—
127C2×Q8×C11—22no—
128C2×Q8×C11—22no—
129C2×Q8×C11—22no—
130C2×Q8×C11C2×D414yes—
131C2×D4×C11—24no—
132C2×D4×C11—24no—
133C2×D4×C11—22no—
134C2×D4×C11—22no—
135C2×D4×C11—22no—
136C2×D4×C11—22no—
137C2×D4×C11—22no—
138C2×D4×C11—42no—
139C2×D4×C11—42no—
140C2×D4×C11—42no—
141C2×D4×C11—42no—
142C2×D4×C11C2×D414yes—
143C22×C4×C11—22no—
144C22×C4×C11—24no—
145C22×C4×C11—24no—
146C22×C4×C11—42no—
147C22×C4×C11—42no—
148C22×C4×C11—42no—
149C22×C4×C11—42no—
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D412yes—
152C22×C4×C11C2×D412yes—
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D412yes—
156C22×C4×C11C2×D412yes—
157C22×C4×C11#4111yescharacteristic
158C22×C4×C11#4111yescharacteristic
159C22×C4×C11C2411yescharacteristic
160C2×C22⋊D11—216no—
161C2×C22⋊D11—24no—
162C2×C22⋊D11—24no—
163C2×C22⋊D11—22no—
164C2×C22⋊D11—22no—
165C22×Dic11—24no—
166C22×Dic11C2×D412yes—
167#4339—41no—
168#4339—41no—
169#4339—42no—
170#4339—42no—
171#4339—42no—
172#4339—42no—
173#4339—42no—
174#4339—42no—
175#4339—41no—
176#4339—41no—
177C2×D44—22no—
178C2×D44—22no—
179C2×D44—21no—
180C2×D44—21no—
181C2×C4×D11—22no—
182C2×C4×D11—24no—
183C2×C4×D11—24no—
184C2×C4×D11—22no—
185C2×Dic22—22no—
186C2×Dic22—22no—
187C2×Dic22—21no—
188C2×Dic22—21no—
189C11×Q16—28no—
190C11×SD16—216no—
191C11×D8—28no—
192C11×M16—24no—
193C11×M16—24no—
194C2×C8×C11—22no—
195C2×C8×C11—22no—
196C2×C8×C11C2×D414yes—
197C22⋊Dic11—216no—
198C22⋊Dic11—24no—
199C22⋊Dic11—24no—
200(C2×D11)⋊C4—216no—
201C4⋊Dic11—24no—
202C4⋊Dic11—24no—
203Dic11⋊C4—216no—
204C4×Dic11—24no—
205C4×Dic11C2×D418yes—
206#4318—24no—
207#4318—41no—
208#4318—41no—
209C2×C11⋊C8—22no—
210C2×C11⋊C8—42no—
211C2×#575D1111yescharacteristic, complemented
212#3449—112no—
213C2×#421—112no—
214#2879—111no—
215#2010—118no—
216C2×H(3,ℤ/4)—111no—
217C23×C11—24no—
218C23×C11—42no—
219C23×C11—42no—
220C23×C11—81no—
221C23×C11—84no—
222C23×C11#12012yes—
223C23×C11#12012yes—
224C23×C11#12111yescharacteristic
225C23×C11#12111yescharacteristic
226C23×C11C22×D411yescharacteristic
227C22×D11—24no—
228C22×D11—22no—
229C22×D11—82no—
230Q8×C11—24no—
231Q8×C11—24no—
232Q8×C11—42no—
233Q8×C11—42no—
234D4×C11—24no—
235D4×C11—24no—
236D4×C11—44no—
237D4×C11—44no—
238D4×C11—44no—
239D4×C11—44no—
240D4×C11—42no—
241D4×C11—42no—
242C2×C4×C11—24no—
243C2×C4×C11—42no—
244C2×C4×C11—42no—
245C2×C4×C11—44no—
246C2×C4×C11—44no—
247C2×C4×C11—44no—
248C2×C4×C11—44no—
249C2×C4×C11#12012yes—
250C2×C4×C11#12012yes—
251C2×C4×C11#12011yescharacteristic
252C2×C4×C11#12011yescharacteristic
253C2×C4×C11#12012yes—
254C2×C4×C11#12111yescharacteristic
255C2×C4×C11#12111yescharacteristic
256C2×C4×C11#12112yes—
257C2×C4×C11#12112yes—
258C2×C4×C11#12112yes—
259C2×C4×C11#12112yes—
260C2×C4×C11#12712yes—
261C2×C4×C11#12711yescharacteristic
262C2×C4×C11#12711yescharacteristic
263C2×C4×C11C22×D412yes—
264C2×C4×C11C22×D412yes—
265C2×C4×C11C22×D411yescharacteristic
266C2×C4×C11C2×#4111yescharacteristic
267C22⋊D11—42no—
268C22⋊D11—44no—
269C22⋊D11—42no—
270C22⋊D11—816no—
271C2×Dic11—28no—
272C2×Dic11—24no—
273C2×Dic11—22no—
274C2×Dic11—84no—
275D44—41no—
276D44—42no—
277D44—41no—
278C4×D11—42no—
279C4×D11—44no—
280C4×D11—42no—
281Dic22—41no—
282Dic22—42no—
283Dic22—41no—
284C8×C11—24no—
285C11⋊C8—42no—
286C22×#41—111no—
287C22×#41C2×D1112yes—
288#575—24no—
289#575—22no—
290#575C2×D1114yes—
291C2×#137—22no—
292C2×AGL(1,ℤ/8)—22no—
293C2×#135—22no—
294C22×M16—111no—
295C22×M16C2×D1111yescharacteristic
296#537—224no—
297#536—222no—
298#536—222no—
299#535—222no—
300#535—222no—
301#534—224no—
302#532—224no—
303#525—118no—
304#525—224no—
305C2×#117—112no—
306#421—118no—
307#421—224no—
308C2×#104—224no—
309#408—222no—
310#408—222no—
311#407—114no—
312H(3,ℤ/4)—114no—
313C22×C11—41no—
314C22×C11—42no—
315C22×C11—42no—
316C22×C11—41no—
317C22×C11—41no—
318C22×C11—48no—
319C22×C11—44no—
320C22×C11—84no—
321C22×C11—84no—
322C22×C11#39211yescharacteristic
323C22×C11#39212yes—
324C22×C11#39211yescharacteristic
325C22×C11C2×#12012yes—
326C22×C11C2×#12111yescharacteristic
327C2×D11—44no—
328C2×D11—48no—
329C2×D11—42no—
330C4×C11—44no—
331C4×C11#39211yescharacteristic
332C4×C11#39212yes—
333C4×C11#39211yescharacteristic
334C4×C11C2×#12011yescharacteristic
335C4×C11C2×#12112yes—
336C4×C11C2×#12711yescharacteristic
337Dic11—48no—
338Dic11—42no—
339C2×#41—22no—
340C2×#41—22no—
341C2×#41—22no—
342C2×#41—22no—
343C2×#41—22no—
344C2×#41—22no—
345C2×#41—22no—
346C2×#41—22no—
347C2×#41—22no—
348C2×#41—22no—
349C2×#41—222no—
350C2×#41—222no—
351C2×#41—221no—
352C2×#41—221no—
353C2×#41—222no—
354C2×#41—222no—
355C2×#41—221no—
356C2×#41—221no—
357C2×#41C22⋊D1114yescomplemented
358C2×#41C22×D1114yes—
359C22×Q8—111no—
360C22×Q8C22⋊D1112yescomplemented
361C22×D4—22no—
362C22×D4—112no—
363C22×D4—111no—
364C22×D4C22⋊D1112yescomplemented
365C23×C4—22no—
366C23×C4—112no—
367C23×C4C22×D1111yescharacteristic
368#137—28no—
369#137—28no—
370AGL(1,ℤ/8)—28no—
371AGL(1,ℤ/8)—28no—
372#135—28no—
373#135—28no—
374C2×Q16—22no—
375C2×SD16—24no—
376C2×D8—22no—
377C2×M16—22no—
378C2×M16—22no—
379C2×M16—112no—
380C2×M16—221no—
381C2×M16—222no—
382C2×M16—222no—
383C2×M16C22⋊D1112yescomplemented
384C2×M16C22×D1112yes—
385C22×C8—221no—
386C22×C8C22⋊D1112yescomplemented
387C4⋊Q8—224no—
388#127—224no—
389#124—224no—
390#124—224no—
391#123—228no—
392#123—228no—
393C22⋊Q8—228no—
394C22⋊Q8—228no—
395#121—228no—
396#121—2216no—
397#121—228no—
398#120—228no—
399#120—228no—
400C4×D4—2216no—
401#117—114no—
402#117—114no—
403#117—222no—
404#117—222no—
405C2×C4⋊C4—222no—
406C2×C22⋊C4—222no—
407C2×C42—114no—
408#104—2216no—
409C22⋊C8—228no—
410C2×C11—22no—
411C2×C11—21no—
412C2×C11—21no—
413C2×C11—22no—
414C2×C11—21no—
415C2×C11—84no—
416C2×C11C2×#39211yescharacteristic
417D11—82no—
418C24—22no—
419C24—112no—
420C24D4×D1111yescharacteristic
421#41—24no—
422#41—24no—
423#41—24no—
424#41—24no—
425#41—24no—
426#41—24no—
427#41—24no—
428#41—24no—
429#41—42no—
430#41—42no—
431#41—42no—
432#41—42no—
433#41—42no—
434#41—42no—
435#41—42no—
436#41—42no—
437#41—442no—
438#41—442no—
439#41—442no—
440#41—442no—
441#41—442no—
442#41—441no—
443#41—441no—
444#41—441no—
445#41—441no—
446#41—442no—
447C2×Q8—22no—
448C2×Q8—22no—
449C2×Q8—22no—
450C2×Q8—22no—
451C2×Q8—22no—
452C2×Q8—222no—
453C2×Q8—222no—
454C2×Q8—221no—
455C2×Q8—221no—
456C2×Q8C2×C22⋊D1114yes—
457C2×D4—24no—
458C2×D4—24no—
459C2×D4—22no—
460C2×D4—22no—
461C2×D4—22no—
462C2×D4—22no—
463C2×D4—22no—
464C2×D4—42no—
465C2×D4—42no—
466C2×D4—42no—
467C2×D4—42no—
468C2×D4—224no—
469C2×D4—224no—
470C2×D4—222no—
471C2×D4—222no—
472C2×D4—2216no—
473C2×D4—222no—
474C2×D4—222no—
475C2×D4—221no—
476C2×D4—221no—
477C2×D4C2×C22⋊D1114yes—
478C22×C4—22no—
479C22×C4—24no—
480C22×C4—24no—
481C22×C4—42no—
482C22×C4—42no—
483C22×C4—42no—
484C22×C4—42no—
485C22×C4—112no—
486C22×C4—224no—
487C22×C4—224no—
488C22×C4—222no—
489C22×C4—222no—
490C22×C4—224no—
491C22×C4D4×D1111yescharacteristic
492C22×C4D4×D1112yes—
493C22×C4D4×D1112yes—
494C22×C4#434111yescharacteristic
495C22×C4#434111yescharacteristic
496C22×C4C2×C22⋊D1112yes—
497C22×C4C2×C22⋊D1112yes—
498C22×C4C2×C22⋊D1111yescharacteristic
499C22×C4C2×C22⋊D1111yescharacteristic
500C22×C4C23×D1111yescharacteristic
501Q16—28no—
502SD16—216no—
503D8—28no—
504M16—24no—
505M16—24no—
506M16—224no—
507M16—441no—
508M16—441no—
509C2×C8—22no—
510C2×C8—22no—
511C2×C8—222no—
512C2×C8—442no—
513C2×C8C2×C22⋊D1114yes—
514C4⋊C4—2216no—
515C4⋊C4—224no—
516C4⋊C4—224no—
517C22⋊C4—2216no—
518C22⋊C4—2216no—
519C22⋊C4—224no—
520C22⋊C4—224no—
521C42—118no—
522C42—224no—
523C11#2341411yescharacteristic, complemented, Sylow
524C23—24no—
525C23—42no—
526C23—42no—
527C23—81no—
528C23—84no—
529C23—224no—
530C23—222no—
531C23—882no—
532C23#6699012yes—
533C23#6699012yes—
534C23#6699111yescharacteristic
535C23#6699111yescharacteristic
536C23C2×D4×D1111yescharacteristic
537Q8—24no—
538Q8—24no—
539Q8—42no—
540Q8—42no—
541Q8—441no—
542Q8—442no—
543Q8—441no—
544D4—24no—
545D4—24no—
546D4—44no—
547D4—44no—
548D4—44no—
549D4—44no—
550D4—42no—
551D4—42no—
552D4—442no—
553D4—444no—
554D4—442no—
555D4—441no—
556D4—442no—
557D4—441no—
558D4—8816no—
559C2×C4—24no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—44no—
563C2×C4—44no—
564C2×C4—44no—
565C2×C4—44no—
566C2×C4—228no—
567C2×C4—224no—
568C2×C4—222no—
569C2×C4—444no—
570C2×C4—442no—
571C2×C4—442no—
572C2×C4—884no—
573C2×C4#6699012yes—
574C2×C4#6699012yes—
575C2×C4#6699111yescharacteristic
576C2×C4#6699111yescharacteristic
577C2×C4#6699212yes—
578C2×C4#6699212yes—
579C2×C4#6699212yes—
580C2×C4#6699212yes—
581C2×C4#6699312yes—
582C2×C4#6699311yescharacteristic
583C2×C4#6699311yescharacteristic
584C2×C4#6700611yescharacteristic
585C2×C4#6700611yescharacteristic
586C2×C4#6700612yes—
587C2×C4C2×D4×D1112yes—
588C2×C4C2×#434111yescharacteristic
589C2×C4C22×C22⋊D1112yes—
590C2×C4C22×C22⋊D1111yescharacteristic
591C8—24no—
592C8—442no—
593C22—42no—
594C22—42no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—48no—
599C22—44no—
600C22—84no—
601C22—84no—
602C22—448no—
603C22—444no—
604C22—442no—
605C22#1062283611yescharacteristic
606C22#1062283612yes—
607C22#1062283611yescharacteristic
608C22C2×#6699012yes—
609C22C2×#6699111yescharacteristic
610C4—44no—
611C4—448no—
612C4—442no—
613C4#1062283611yescharacteristic
614C4#1062283612yes—
615C4#1062283611yescharacteristic
616C4C2×#6699212yes—
617C4C2×#6699311yescharacteristic
618C4C2×#6700611yescharacteristic
619C2—22no—
620C2—21no—
621C2—22no—
622C2—21no—
623C2—21no—
624C2—84no—
625C2—882no—
626C2C2×#1062283611yescharacteristic
subgroupG/H
centerC4C2×#66993
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#575C2
socleC2×C11C2×#392
hypercenterC2×#575D11
hypocenterC11#23414
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×#575

Complements

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

NH ≅ G/Ntype
1. #13081945C2semidirect
2. C2×#10622849C2semidirect
3. #13077060C2semidirect
4. #13069680C2semidirect
5. C2×#10622195C2semidirect
6. C2×C11×#575C2semidirect
19. #10623359C22semidirect
28. #10622849C22semidirect
31. #10622739C22semidirect
33. #10622195C22semidirect
44. C2×C11×#41D4semidirect
46. C22×Q8×C11D4semidirect
48. C22×D4×C11D4semidirect
74. C2×C11×M16D4semidirect
76. C22×C8×C11D4semidirect
93. #66979D4semidirect
97. C2×C4×Dic11D4semidirect
211. C2×#575D11semidirect
357. C2×#41C22⋊D11semidirect
360. C22×Q8C22⋊D11semidirect
364. C22×D4C22⋊D11semidirect
383. C2×M16C22⋊D11semidirect
386. C22×C8C22⋊D11semidirect
523. C11#23414semidirect

Maximal subgroups

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

subgroupindex
#130819452
C2×#106228492
#130770602
#130696802
C2×#106221952
C2×C11×#5752
#2341411