Finite Group Databasebeta

← #14726434

Subgroups — #14726434

Order 2816.

1498 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077866C212yesmaximal, complemented
2#13071831C211yesmaximal, characteristic, complemented
3#13067585C212yesmaximal, complemented
4#13067568C212yesmaximal, complemented
5#13067551C212yesmaximal, complemented
6#13067534C212yesmaximal, complemented
7#13067132C212yesmaximal, complemented
8#13066954C211yesmaximal, characteristic, complemented
9C11×#3496C211yesmaximal, characteristic, complemented
10C2×C11×H(5,𝔽2)—21no—
11C22×#4339C2211yescharacteristic, complemented
12C11×#547—22no—
13C11×#546—24no—
14D42×C11—22no—
15C11×#537C2212yes—
16C11×#534—21no—
17C11×#534C2212yes—
18C11×#532—21no—
19C2×C11×#121—21no—
20C2×C11×#121C2212yes—
21C2×C4×D4×C11C2211yescharacteristic
22C2×#66985—22no—
23C2×C4×C22⋊D11—21no—
24#10622836—21no—
25C4×C22⋊Dic11C2211yescharacteristic, complemented
26#10622820C2212yescomplemented
27#10622653C2214yescomplemented
28#10622650—24no—
29#10622649C2214yescomplemented
30#10622604C2211yescharacteristic, complemented
31#10622592C2211yescharacteristic, complemented
32#10622579—22no—
33#10622573C2211yescharacteristic, complemented
34#10622572—21no—
35#10622560C2211yescharacteristic, complemented
36C4×(C2×D11)⋊C4—21no—
37#10622175C2214yescomplemented
38#10622175C2214yescomplemented
39#10622166C2212yescomplemented
40#10622163C2212yescomplemented
41C11×H(5,𝔽2)—44no—
42C11×H(5,𝔽2)—44no—
43C2×C11×#41—24no—
44C2×C11×#41—22no—
45C22×D4×C11—24no—
46C22×D4×C11—22no—
47C22×D4×C11—22no—
48C22×D4×C11—21no—
49C22×D4×C11D411yescharacteristic
50C22×D4×C11D412yescomplemented
51C23×C4×C11D411yescharacteristic
52C23×C4×C11C2311yescharacteristic
53C22×C22⋊D11—21no—
54C22×C22⋊D11—21no—
55C2×#4339—22no—
56C2×#4339—22no—
57C2×#4339—44no—
58C22×D44C2311yescharacteristic
59C22×C4×D11—21no—
60C22×Dic22C2311yescharacteristic
61C11×C4⋊Q8—21no—
62C11×#127—21no—
63C11×#124—22no—
64C11×#123—24no—
65C11×#123—24no—
66C11×C22⋊Q8—24no—
67C11×#121—22no—
68C11×#121—22no—
69C11×#121—24no—
70C11×#121—22no—
71C11×#121—22no—
72C11×#121—22no—
73C11×#121—22no—
74C11×#121D414yescomplemented
75C11×#121C2314yes—
76C11×#120—24no—
77C11×#120—24no—
78C4×D4×C11—22no—
79C4×D4×C11—22no—
80C4×D4×C11—22no—
81C4×D4×C11—22no—
82C2×C11×C4⋊C4—21no—
83C2×C11×C4⋊C4D412yescomplemented
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C22⋊C4—22no—
86C2×C11×C22⋊C4—22no—
87C2×C11×C22⋊C4D411yescharacteristic
88C2×C11×C22⋊C4C2311yescharacteristic
89C2×C42×C11D411yescharacteristic
90C2×C22⋊Dic11—21no—
91C2×C22⋊Dic11—21no—
92C2×#4324—24no—
93#66985—48no—
94C2×#4323—24no—
95C4×C22⋊D11—44no—
96C2×(C2×D11)⋊C4—21no—
97C2×(C2×D11)⋊C4—21no—
98C2×(C2×D11)⋊C4—21no—
99C2×Dic11⋊C4—21no—
100C2×C4×Dic11—21no—
101C2×#4318—22no—
102C11⋊#95—21no—
103C11⋊#95—21no—
104C11⋊#95C2311yescharacteristic
105C11⋊#95C2311yescharacteristic
106C22⋊(C11⋊C8)—22no—
107C22⋊(C11⋊C8)C2314yes—
108#66874—24no—
109#66873—24no—
110#18166—111nomaximal, Sylow
111C24×C11—22no—
112C24×C11—22no—
113C24×C11C2×D411yescharacteristic
114C24×C11C2×D411yescharacteristic
115C23×D11—21no—
116C11×#41—44no—
117C11×#41—416no—
118C11×#41—44no—
119C2×Q8×C11—22no—
120C2×D4×C11—22no—
121C2×D4×C11—22no—
122C2×D4×C11—24no—
123C2×D4×C11—22no—
124C2×D4×C11—24no—
125C2×D4×C11—24no—
126C2×D4×C11—22no—
127C2×D4×C11—22no—
128C2×D4×C11—22no—
129C2×D4×C11—22no—
130C2×D4×C11—44no—
131C2×D4×C11—416no—
132C2×D4×C11—44no—
133C2×D4×C11—44no—
134C2×D4×C11—44no—
135C2×D4×C11—44no—
136C2×D4×C11—82no—
137C2×D4×C11C2×D414yes—
138C22×C4×C11—22no—
139C22×C4×C11—24no—
140C22×C4×C11—22no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—42no—
144C22×C4×C11—42no—
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D412yes—
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D412yes—
151C22×C4×C11C2411yescharacteristic
152C2×C22⋊D11—42no—
153C2×C22⋊D11—42no—
154C2×C22⋊D11—42no—
155C2×C22⋊D11—42no—
156C2×C22⋊D11—42no—
157C2×C22⋊D11—42no—
158C22×Dic11—21no—
159C22×Dic11—21no—
160C22×Dic11—21no—
161#4339—28no—
162#4339—44no—
163#4339—44no—
164#4339—44no—
165C2×D44—22no—
166C2×D44—42no—
167C2×C4×D11—24no—
168C2×C4×D11—42no—
169C2×C4×D11—41no—
170C2×C4×D11—41no—
171C2×Dic22—22no—
172C2×Dic22—42no—
173C11×C4⋊C4—22no—
174C11×C4⋊C4—22no—
175C11×C4⋊C4—22no—
176C11×C4⋊C4—22no—
177C11×C4⋊C4C2×D414yes—
178C11×C22⋊C4—24no—
179C11×C22⋊C4—24no—
180C11×C22⋊C4—22no—
181C11×C22⋊C4—24no—
182C11×C22⋊C4—24no—
183C11×C22⋊C4—22no—
184C42×C11—21no—
185C42×C11—21no—
186C22⋊Dic11—42no—
187C22⋊Dic11—42no—
188#4324—48no—
189#4323—48no—
190(C2×D11)⋊C4—42no—
191(C2×D11)⋊C4—42no—
192(C2×D11)⋊C4—42no—
193Dic11⋊C4—42no—
194C4×Dic11—42no—
195#4318—44no—
196C2×C11⋊C8—24no—
197#3496D1111yescharacteristic, complemented
198#3006—112no—
199#2388—111no—
200#1604—112no—
201#1601—112no—
202#1598—112no—
203#1595—112no—
204#1507—112no—
205#1465—111no—
206C23×C11—21no—
207C23×C11—21no—
208C23×C11—21no—
209C23×C11—21no—
210C23×C11—24no—
211C23×C11—41no—
212C23×C11—41no—
213C23×C11—41no—
214C23×C11—41no—
215C23×C11—44no—
216C23×C11—44no—
217C23×C11—82no—
218C23×C11—82no—
219C23×C11—82no—
220C23×C11—82no—
221C23×C11#12012yes—
222C23×C11AGL(1,ℤ/8)12yescomplemented
223C23×C11C22×D411yescharacteristic
224C22×D11—22no—
225C22×D11—41no—
226C22×D11—41no—
227C22×D11—41no—
228C22×D11—41no—
229C22×D11—41no—
230C22×D11—41no—
231Q8×C11—44no—
232D4×C11—28no—
233D4×C11—44no—
234D4×C11—44no—
235D4×C11—48no—
236D4×C11—48no—
237D4×C11—44no—
238D4×C11—44no—
239D4×C11—44no—
240D4×C11—82no—
241D4×C11—82no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—24no—
245C2×C4×C11—22no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—24no—
249C2×C4×C11—41no—
250C2×C4×C11—42no—
251C2×C4×C11—48no—
252C2×C4×C11—44no—
253C2×C4×C11—44no—
254C2×C4×C11—42no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—81no—
258C2×C4×C11#12011yescharacteristic
259C2×C4×C11#12011yescharacteristic
260C2×C4×C11AGL(1,ℤ/8)12yescomplemented
261C2×C4×C11C22×D412yes—
262C22⋊D11—48no—
263C22⋊D11—48no—
264C2×Dic11—22no—
265C2×Dic11—22no—
266C2×Dic11—41no—
267C2×Dic11—41no—
268C2×Dic11—41no—
269C2×Dic11—41no—
270C2×Dic11—41no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273D44—24no—
274D44—42no—
275C4×D11—44no—
276C4×D11—44no—
277Dic22—24no—
278Dic22—42no—
279C11⋊C8—44no—
280C2×H(5,𝔽2)—21no—
281C22×#41—111no—
282C2×AGL(1,ℤ/8)—222no—
283#547—22no—
284#546—24no—
285D42—22no—
286#537C2×D1112yes—
287#534—21no—
288#534C2×D1112yes—
289#532—21no—
290C2×#121—21no—
291C2×#121C2×D1112yes—
292C2×C4×D4—221no—
293C2×C4×D4C2×D1111yescharacteristic
294#449—224no—
295#448—114no—
296#447—114no—
297#417—222no—
298#407—112no—
299#395—111no—
300#394—111no—
301#394—221no—
302#393—111no—
303#392—111no—
304#392—221no—
305C4×C22⋊C4—111no—
306C4×C22⋊C4—221no—
307#327—114no—
308#327—114no—
309#324—112no—
310#323—112no—
311C22×C11—21no—
312C22×C11—21no—
313C22×C11—22no—
314C22×C11—22no—
315C22×C11—22no—
316C22×C11—22no—
317C22×C11—42no—
318C22×C11—41no—
319C22×C11—41no—
320C22×C11—44no—
321C22×C11—44no—
322C22×C11—44no—
323C22×C11—81no—
324C22×C11—81no—
325C22×C11—81no—
326C22×C11—164no—
327C22×C11—164no—
328C22×C11C2×#12011yescharacteristic
329C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
330C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
331C2×D11—42no—
332C2×D11—42no—
333C2×D11—42no—
334C2×D11—81no—
335C2×D11—81no—
336C2×D11—81no—
337C2×D11—81no—
338C4×C11—22no—
339C4×C11—21no—
340C4×C11—22no—
341C4×C11—44no—
342C4×C11—41no—
343C4×C11—41no—
344C4×C11B(4,𝔽2)12yes—
345Dic11—42no—
346Dic11—42no—
347Dic11—81no—
348H(5,𝔽2)—44no—
349H(5,𝔽2)—44no—
350C2×#41—24no—
351C2×#41—22no—
352C2×#41—222no—
353C2×#41—222no—
354C2×#41—444no—
355C22×Q8—111no—
356C22×D4—24no—
357C22×D4—22no—
358C22×D4—22no—
359C22×D4—21no—
360C22×D4—111no—
361C22×D4—221no—
362C22×D4—221no—
363C22×D4C22⋊D1111yescharacteristic
364C22×D4C22⋊D1112yescomplemented
365C23×C4—221no—
366C23×C4C22⋊D1111yescharacteristic
367C23×C4C22×D1111yescharacteristic
368AGL(1,ℤ/8)—448no—
369C2×SD16—224no—
370C2×D8—224no—
371C2×M16—222no—
372C4⋊Q8—21no—
373#127—21no—
374#124—22no—
375#123—24no—
376#123—24no—
377C22⋊Q8—24no—
378#121—22no—
379#121—22no—
380#121—24no—
381#121—22no—
382#121—22no—
383#121—22no—
384#121—22no—
385#121C22⋊D1114yescomplemented
386#121C22×D1114yes—
387#120—24no—
388#120—24no—
389C4×D4—22no—
390C4×D4—22no—
391C4×D4—22no—
392C4×D4—22no—
393C4×D4—444no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—221no—
396C2×C4⋊C4C22⋊D1112yescomplemented
397C2×C4⋊C4C22×D1111yescharacteristic
398C2×C22⋊C4—22no—
399C2×C22⋊C4—22no—
400C2×C22⋊C4—221no—
401C2×C22⋊C4—221no—
402C2×C22⋊C4—221no—
403C2×C22⋊C4—221no—
404C2×C22⋊C4—221no—
405C2×C22⋊C4C22⋊D1111yescharacteristic
406C2×C22⋊C4C22×D1111yescharacteristic
407C2×C42—221no—
408C2×C42C22⋊D1111yescharacteristic
409#103—224no—
410#102—224no—
411C22⋊C8—114no—
412C22⋊C8—222no—
413#95—111no—
414#95—111no—
415#95—221no—
416#95—221no—
417C2×C11—21no—
418C2×C11—21no—
419C2×C11—42no—
420C2×C11—42no—
421C2×C11—84no—
422C2×C11#300311yescharacteristic
423C2×C11#301811yescharacteristic
424C2×C11C2×B(4,𝔽2)11yescharacteristic
425D11—82no—
426C24—22no—
427C24—22no—
428C24—221no—
429C24C2×C22⋊D1111yescharacteristic
430C24C2×C22⋊D1111yescharacteristic
431#41—44no—
432#41—416no—
433#41—44no—
434#41—228no—
435#41—444no—
436#41—444no—
437#41—444no—
438C2×Q8—22no—
439C2×Q8—222no—
440C2×Q8—442no—
441C2×D4—22no—
442C2×D4—22no—
443C2×D4—24no—
444C2×D4—22no—
445C2×D4—24no—
446C2×D4—24no—
447C2×D4—22no—
448C2×D4—22no—
449C2×D4—22no—
450C2×D4—22no—
451C2×D4—44no—
452C2×D4—416no—
453C2×D4—44no—
454C2×D4—44no—
455C2×D4—44no—
456C2×D4—44no—
457C2×D4—82no—
458C2×D4—222no—
459C2×D4—442no—
460C2×D4—442no—
461C2×D4—442no—
462C2×D4—442no—
463C2×D4—442no—
464C2×D4—442no—
465C2×D4—442no—
466C2×D4C2×C22⋊D1114yes—
467C22×C4—22no—
468C22×C4—24no—
469C22×C4—22no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—42no—
473C22×C4—42no—
474C22×C4—224no—
475C22×C4—221no—
476C22×C4—221no—
477C22×C4—221no—
478C22×C4—442no—
479C22×C4—441no—
480C22×C4—441no—
481C22×C4C2×C22⋊D1111yescharacteristic
482C22×C4C2×C22⋊D1111yescharacteristic
483C22×C4C2×C22⋊D1112yes—
484C22×C4C2×C22⋊D1111yescharacteristic
485C22×C4C2×C22⋊D1111yescharacteristic
486C22×C4C2×C22⋊D1112yes—
487C22×C4C23×D1111yescharacteristic
488SD16—448no—
489D8—448no—
490M16—444no—
491C2×C8—224no—
492C4⋊C4—22no—
493C4⋊C4—22no—
494C4⋊C4—22no—
495C4⋊C4—22no—
496C4⋊C4—442no—
497C4⋊C4C2×C22⋊D1114yes—
498C22⋊C4—24no—
499C22⋊C4—24no—
500C22⋊C4—22no—
501C22⋊C4—24no—
502C22⋊C4—24no—
503C22⋊C4—22no—
504C22⋊C4—442no—
505C22⋊C4—442no—
506C22⋊C4—442no—
507C22⋊C4—442no—
508C22⋊C4—442no—
509C42—21no—
510C42—21no—
511C42—442no—
512C11#1816611yescharacteristic, complemented, Sylow
513C23—21no—
514C23—21no—
515C23—21no—
516C23—21no—
517C23—24no—
518C23—41no—
519C23—41no—
520C23—41no—
521C23—41no—
522C23—44no—
523C23—44no—
524C23—82no—
525C23—82no—
526C23—82no—
527C23—82no—
528C23—222no—
529C23—441no—
530C23—441no—
531C23—441no—
532C23—441no—
533C23—441no—
534C23—441no—
535C23#6698512yescomplemented
536C23#6700612yes—
537C23C22×C22⋊D1111yescharacteristic
538Q8—44no—
539Q8—224no—
540Q8—442no—
541D4—28no—
542D4—44no—
543D4—44no—
544D4—48no—
545D4—48no—
546D4—44no—
547D4—44no—
548D4—44no—
549D4—82no—
550D4—82no—
551D4—224no—
552D4—442no—
553D4—448no—
554D4—448no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—22no—
558C2×C4—24no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—24no—
562C2×C4—42no—
563C2×C4—41no—
564C2×C4—48no—
565C2×C4—44no—
566C2×C4—44no—
567C2×C4—42no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—81no—
571C2×C4—222no—
572C2×C4—222no—
573C2×C4—444no—
574C2×C4—441no—
575C2×C4—441no—
576C2×C4—441no—
577C2×C4—441no—
578C2×C4—444no—
579C2×C4—441no—
580C2×C4—441no—
581C2×C4—441no—
582C2×C4#6698512yescomplemented
583C2×C4#6700611yescharacteristic
584C2×C4#6700611yescharacteristic
585C2×C4C22×C22⋊D1112yes—
586C8—444no—
587C22—21no—
588C22—21no—
589C22—22no—
590C22—22no—
591C22—22no—
592C22—22no—
593C22—42no—
594C22—41no—
595C22—41no—
596C22—44no—
597C22—44no—
598C22—44no—
599C22—81no—
600C22—81no—
601C22—81no—
602C22—164no—
603C22—164no—
604C22—442no—
605C22—442no—
606C22—442no—
607C22—881no—
608C22—881no—
609C22—881no—
610C22—881no—
611C22C2×#6698511yescharacteristic
612C22C2×#6698511yescharacteristic
613C22C2×#6700611yescharacteristic
614C4—22no—
615C4—22no—
616C4—21no—
617C4—44no—
618C4—41no—
619C4—41no—
620C4—442no—
621C4—442no—
622C4—881no—
623C4#1062285712yes—
624C2—21no—
625C2—21no—
626C2—42no—
627C2—42no—
628C2—84no—
629C2—882no—
630C2#1307784311yescharacteristic
631C2#1307796511yescharacteristic
632C2C2×#1062285711yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#3496C2
socleC22×C11C2×#120
hypercenter#3496D11
hypocenterC11#18166
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3496

Complements

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

NH ≅ G/Ntype
1. #13077866C2semidirect
2. #13071831C2semidirect
3. #13067585C2semidirect
4. #13067568C2semidirect
5. #13067551C2semidirect
6. #13067534C2semidirect
7. #13067132C2semidirect
8. #13066954C2semidirect
9. C11×#3496C2semidirect
11. C22×#4339C22semidirect
25. C4×C22⋊Dic11C22semidirect
26. #10622820C22semidirect
27. #10622653C22semidirect
29. #10622649C22semidirect
30. #10622604C22semidirect
31. #10622592C22semidirect
33. #10622573C22semidirect
35. #10622560C22semidirect
37. #10622175C22semidirect
38. #10622175C22semidirect
39. #10622166C22semidirect
40. #10622163C22semidirect
50. C22×D4×C11D4semidirect
74. C11×#121D4semidirect
83. C2×C11×C4⋊C4D4semidirect
197. #3496D11semidirect
222. C23×C11AGL(1,ℤ/8)semidirect
260. C2×C4×C11AGL(1,ℤ/8)semidirect
364. C22×D4C22⋊D11semidirect
385. #121C22⋊D11semidirect
396. C2×C4⋊C4C22⋊D11semidirect
512. C11#18166semidirect
535. C23#66985semidirect
582. C2×C4#66985semidirect

Maximal subgroups

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

subgroupindex
#130778662
#130718312
#130675852
#130675682
#130675512
#130675342
#130671322
#130669542
C11×#34962
#1816611