Finite Group Databasebeta

← #14787664

Subgroups — #14787664

Order 2816.

1434 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623086C211yesmaximal, characteristic, complemented
2C2×#10622459C211yesmaximal, characteristic, complemented
3C2×C4×D88C211yesmaximal, characteristic, complemented
4#13073529C211yesmaximal, characteristic, complemented
5#13069799C212yesmaximal, complemented
6#13069614C212yesmaximal, complemented
7#13069577C211yesmaximal, characteristic, complemented
8#13068931C212yesmaximal, complemented
9#13068806C212yesmaximal, complemented
10#13068617C211yesmaximal, characteristic, complemented
11C11×#1954C211yesmaximal, characteristic, complemented
12C22×#4341—21no—
13C2×C4×D4×C11C2211yescharacteristic
14C2×#66991—21no—
15C2×#66983C2212yes—
16C2×#66983C2212yes—
17C22×C4⋊Dic11C2212yes—
18C22×D88C2211yescharacteristic
19#10623086—24no—
20#10623086—24no—
21C2×#66950—21no—
22C2×#66939—22no—
23C2×C4×D44C2211yescharacteristic
24C2×C4×D44C2211yescharacteristic
25C2×#66922C2211yescharacteristic
26C2×C11×C4⋊C8C2211yescharacteristic
27C2×C11×C22⋊C8C2212yes—
28C2×C11×C22⋊C8C2212yes—
29C2×C4×C8×C11C2211yescharacteristic
30#10622825C2212yes—
31C2×#66885C2212yes—
32C2×#66885C2211yescharacteristic
33C2×#66885C2211yescharacteristic
34C2×#66885C2212yes—
35C2×#66882C2211yescharacteristic
36C2×#66882C2212yes—
37#10622600—21no—
38#10622574—22no—
39#10622548C2211yescharacteristic
40#10622459—24no—
41C4×D88—24no—
42#10622189C2212yes—
43#10622189C2212yes—
44#10622189C2212yes—
45C22×D4×C11D411yescharacteristic
46C23×C4×C11C2312yes—
47C22×C22⋊D11—22no—
48C22×C22⋊D11—22no—
49C23×Dic11—22no—
50C2×#4341—28no—
51C2×#4341—44no—
52C2×#4341—44no—
53C22×D44C2311yescharacteristic
54C22×D44C2311yescharacteristic
55C22×C4×D11—21no—
56C22×C4×D11—21no—
57C22×Dic22—21no—
58C22×C8×C11C2311yescharacteristic
59C22×C8×C11C2312yes—
60C22×C8×C11C2311yescharacteristic
61C4×D4×C11—22no—
62C4×D4×C11—22no—
63C2×C11×C4⋊C4D411yescharacteristic
64C2×C11×C22⋊C4D412yes—
65C2×C42×C11C2311yescharacteristic
66C2×C22⋊Dic11—22no—
67#66991—44no—
68#66983—24no—
69#66983—24no—
70#66983—24no—
71#66983—42no—
72C2×(C2×D11)⋊C4—21no—
73C2×(C2×D11)⋊C4—22no—
74C2×(C2×D11)⋊C4—21no—
75C2×(C2×D11)⋊C4—22no—
76C2×C4⋊Dic11—21no—
77C2×C4⋊Dic11—22no—
78C2×C4⋊Dic11—24no—
79C2×C4⋊Dic11—24no—
80C2×C4⋊Dic11—21no—
81C2×C4⋊Dic11—21no—
82C2×C4⋊Dic11C2311yescharacteristic
83C2×C4⋊Dic11C2312yes—
84C2×C4⋊Dic11C2312yes—
85C2×C4⋊Dic11C2311yescharacteristic
86C2×D88—22no—
87C2×D88—22no—
88C2×D88—22no—
89#66950—28no—
90#66939—216no—
91C4×D44—22no—
92C4×D44—22no—
93C4×D44—22no—
94C4×D44D414yescomplemented
95#66922—22no—
96#66922D414yescomplemented
97C11×C4⋊C8—22no—
98C11×C22⋊C8—24no—
99C11×C22⋊C8—42no—
100C4×C8×C11—22no—
101C11⋊#95—22no—
102#66885—22no—
103#66885—22no—
104#66885—24no—
105#66885—42no—
106#66882—22no—
107#66882—24no—
108#24116—111nomaximal, Sylow
109C24×C11C2×D412yes—
110C23×D11—21no—
111C23×D11—21no—
112C2×D4×C11—22no—
113C2×D4×C11—22no—
114C2×D4×C11D814yescomplemented
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11C2×D412yes—
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2411yescharacteristic
125C2×C22⋊D11—28no—
126C2×C22⋊D11—44no—
127C2×C22⋊D11—44no—
128C2×C22⋊D11—44no—
129C2×C22⋊D11—44no—
130C2×C22⋊D11—82no—
131C22×Dic11—28no—
132C22×Dic11—22no—
133C22×Dic11—21no—
134C22×Dic11—21no—
135C22×Dic11—22no—
136C22×Dic11—44no—
137C22×Dic11—44no—
138#4341—432no—
139C2×D44—21no—
140C2×D44—21no—
141C2×D44—21no—
142C2×D44—21no—
143C2×D44—21no—
144C2×D44—21no—
145C2×D44—21no—
146C2×D44—21no—
147C2×D44—21no—
148C2×D44—21no—
149C2×D44C2×D412yes—
150C2×D44#4112yescomplemented
151C2×C4×D11—24no—
152C2×C4×D11—42no—
153C2×C4×D11—42no—
154C2×C4×D11—42no—
155C2×C4×D11—42no—
156C2×C4×D11—42no—
157C2×Dic22—24no—
158C2×Dic22—42no—
159C2×Dic22—42no—
160C2×C8×C11—21no—
161C2×C8×C11—22no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11—22no—
165C2×C8×C11—22no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11#4112yescomplemented
169C11×C4⋊C4—22no—
170C11×C22⋊C4—24no—
171C42×C11C2×D412yes—
172C42×C11C2×D412yes—
173C22⋊Dic11—44no—
174(C2×D11)⋊C4—28no—
175(C2×D11)⋊C4—24no—
176(C2×D11)⋊C4—44no—
177(C2×D11)⋊C4—42no—
178C4⋊Dic11—28no—
179C4⋊Dic11—24no—
180C4⋊Dic11—22no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—22no—
185C4⋊Dic11—22no—
186C4⋊Dic11—42no—
187C4⋊Dic11—81no—
188C4⋊Dic11C2×D414yes—
189C4⋊Dic11C2×D412yes—
190D88—28no—
191C2×#547—111no—
192C2×#474—111no—
193C2×C4×D8—111no—
194#2537—111no—
195#2033—112no—
196#1999—112no—
197#1990—111no—
198#1954D1111yescharacteristic, complemented
199#1874—112no—
200#1852—112no—
201#1802—111no—
202C23×C11—22no—
203C23×C11—22no—
204C23×C11—22no—
205C23×C11—22no—
206C23×C11—22no—
207C23×C11—22no—
208C23×C11C2×D814yes—
209C23×C11C22×D411yescharacteristic
210C22×D11—22no—
211C22×D11—22no—
212C22×D11—41no—
213C22×D11—41no—
214C22×D11—41no—
215C22×D11—41no—
216C22×D11—41no—
217C22×D11—41no—
218C22×D11—41no—
219C22×D11—41no—
220C22×D11—41no—
221C22×D11—41no—
222C22×D11—41no—
223C22×D11—41no—
224D4×C11—28no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—42no—
231C2×C4×C11—42no—
232C2×C4×C11—42no—
233C2×C4×C11—42no—
234C2×C4×C11#12012yes—
235C2×C4×C11#12012yes—
236C2×C4×C11C2×D812yes—
237C2×C4×C11AGL(1,ℤ/8)12yes—
238C2×C4×C11C22×D411yescharacteristic
239C2×C4×C11C22×D411yescharacteristic
240C2×C4×C11C2×#4111yescharacteristic
241C2×C4×C11C2×#4111yescharacteristic
242C2×C4×C11H(5,𝔽2)11yescharacteristic
243C2×C4×C112−1+411yescharacteristic
244C22⋊D11—416no—
245C22⋊D11—88no—
246C2×Dic11—24no—
247C2×Dic11—22no—
248C2×Dic11—416no—
249C2×Dic11—42no—
250C2×Dic11—41no—
251C2×Dic11—42no—
252C2×Dic11—41no—
253C2×Dic11—41no—
254C2×Dic11—42no—
255C2×Dic11—42no—
256C2×Dic11—41no—
257C2×Dic11—41no—
258C2×Dic11—42no—
259D44—22no—
260D44—22no—
261D44—22no—
262D44—22no—
263D44—41no—
264D44—41no—
265D44—41no—
266D44—41no—
267C4×D11—48no—
268C4×D11—84no—
269Dic22—48no—
270C8×C11—22no—
271C8×C11—41no—
272C8×C11—42no—
273C22×#41—221no—
274C22×D8—111no—
275#547—224no—
276#547—224no—
277C2×C4⋊Q8—111no—
278C2×#123—222no—
279C2×C22⋊Q8—221no—
280C2×#121—112no—
281C2×#121—112no—
282C2×#121—221no—
283C2×C4×D4—111no—
284C2×C4×D4—111no—
285C2×C4×D4C2×D1111yescharacteristic
286C22×C4⋊C4—112no—
287#474—224no—
288C4×D8—224no—
289C2×#107—111no—
290C2×#107—112no—
291C2×C4⋊C8C2×D1111yescharacteristic
292C2×#102—111no—
293C2×#102—112no—
294C2×#102—111no—
295C2×#102—112no—
296C2×C22⋊C8C2×D1112yes—
297C2×C22⋊C8C2×D1112yes—
298C2×C4×C8C2×D1111yescharacteristic
299#394—222no—
300#384—111no—
301#380—112no—
302#380—221no—
303#340—112no—
304#340—112no—
305#340—112no—
306C22×C11—24no—
307C22×C11—24no—
308C22×C11—24no—
309C22×C11—42no—
310C22×C11—42no—
311C22×C11—42no—
312C22×C11—42no—
313C22×C11C2×#12011yescharacteristic
314C22×C11#54611yescharacteristic
315C22×C11#54711yescharacteristic
316C22×C11C22×D811yescharacteristic
317C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
318C22×C11#57711yescharacteristic
319C22×C11#57811yescharacteristic
320C2×D11—42no—
321C2×D11—42no—
322C2×D11—42no—
323C2×D11—42no—
324C2×D11—42no—
325C2×D11—42no—
326C2×D11—81no—
327C2×D11—81no—
328C2×D11—81no—
329C2×D11—81no—
330C2×D11—81no—
331C2×D11—81no—
332C2×D11—81no—
333C2×D11—81no—
334C4×C11—22no—
335C4×C11—42no—
336C4×C11#44714yes—
337C4×C11#52511yescharacteristic
338C4×C11#53711yescharacteristic
339C4×C11#54811yescharacteristic
340C4×C11#55011yescharacteristic
341Dic11—44no—
342Dic11—42no—
343Dic11—81no—
344Dic11—82no—
345C2×#41—228no—
346C2×#41—444no—
347C2×#41—444no—
348C22×Q8—221no—
349C22×D4—111no—
350C22×D4—111no—
351C22×D4—222no—
352C22×D4—222no—
353C22×D4D4411yescharacteristic
354C23×C4—222no—
355C23×C4—221no—
356C23×C4—221no—
357C23×C4C22×D1112yes—
358C2×D8—222no—
359C2×D8—222no—
360C2×D8—222no—
361C22×C8C22×D1111yescharacteristic
362C22×C8C22×D1112yes—
363C22×C8C22×D1111yescharacteristic
364C4⋊Q8—114no—
365C4⋊Q8—222no—
366#123—2216no—
367C22⋊Q8—228no—
368#121—224no—
369#121—224no—
370#121—224no—
371#121—442no—
372#121—444no—
373C4×D4—22no—
374C4×D4—22no—
375C4×D4—114no—
376C4×D4—222no—
377C4×D4—222no—
378C4×D4—222no—
379C2×C4⋊C4—111no—
380C2×C4⋊C4—112no—
381C2×C4⋊C4—111no—
382C2×C4⋊C4—112no—
383C2×C4⋊C4—224no—
384C2×C4⋊C4—224no—
385C2×C4⋊C4—222no—
386C2×C4⋊C4—221no—
387C2×C4⋊C4—221no—
388C2×C4⋊C4—221no—
389C2×C4⋊C4D4411yescharacteristic
390C2×C22⋊C4—221no—
391C2×C22⋊C4—222no—
392C2×C22⋊C4—222no—
393C2×C22⋊C4—221no—
394C2×C22⋊C4—222no—
395C2×C22⋊C4D4412yes—
396C2×C42C22×D1111yescharacteristic
397#107—222no—
398#107—224no—
399C4⋊C8—22no—
400#102—222no—
401#102—224no—
402#102—222no—
403#102—442no—
404C22⋊C8—24no—
405C22⋊C8—42no—
406C4×C8—22no—
407#95—222no—
408C2×C11—44no—
409C2×C11#240711yescharacteristic
410C2×C11C2×#44711yescharacteristic
411C2×C11#301311yescharacteristic
412C2×C11#329411yescharacteristic
413C2×C11#333011yescharacteristic
414C2×C11#333411yescharacteristic
415C2×C11#335411yescharacteristic
416D11—82no—
417D11—82no—
418C24—221no—
419C24—221no—
420C24C2×D4412yes—
421#41—4432no—
422C2×Q8—224no—
423C2×Q8—442no—
424C2×Q8—442no—
425C2×D4—22no—
426C2×D4—22no—
427C2×D4—112no—
428C2×D4—112no—
429C2×D4—228no—
430C2×D4—221no—
431C2×D4—221no—
432C2×D4—221no—
433C2×D4—221no—
434C2×D4—221no—
435C2×D4—221no—
436C2×D4—221no—
437C2×D4—221no—
438C2×D4—221no—
439C2×D4—221no—
440C2×D4—444no—
441C2×D4—444no—
442C2×D4—444no—
443C2×D4—444no—
444C2×D4—882no—
445C2×D4D8814yescomplemented
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—228no—
453C22×C4—221no—
454C22×C4—222no—
455C22×C4—224no—
456C22×C4—221no—
457C22×C4—222no—
458C22×C4—444no—
459C22×C4—444no—
460C22×C4—442no—
461C22×C4—442no—
462C22×C4—442no—
463C22×C4—442no—
464C22×C4—442no—
465C22×C4C2×D4412yes—
466C22×C4C2×D4411yescharacteristic
467C22×C4C2×D4411yescharacteristic
468C22×C4C23×D1111yescharacteristic
469D8—228no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—22no—
474C2×C8—22no—
475C2×C8—21no—
476C2×C8—22no—
477C2×C8—21no—
478C2×C8#434112yescomplemented
479C4⋊C4—22no—
480C4⋊C4—112no—
481C4⋊C4—114no—
482C4⋊C4—228no—
483C4⋊C4—224no—
484C4⋊C4—221no—
485C4⋊C4—222no—
486C4⋊C4—221no—
487C4⋊C4—221no—
488C4⋊C4—222no—
489C4⋊C4—222no—
490C4⋊C4—442no—
491C4⋊C4—881no—
492C22⋊C4—24no—
493C22⋊C4—228no—
494C22⋊C4—224no—
495C22⋊C4—444no—
496C22⋊C4—444no—
497C22⋊C4—442no—
498C42D4×D1112yes—
499C42D4×D1112yes—
500C11#2411611yescharacteristic, complemented, Sylow
501C23—22no—
502C23—22no—
503C23—22no—
504C23—22no—
505C23—22no—
506C23—22no—
507C23—222no—
508C23—222no—
509C23—441no—
510C23—441no—
511C23—441no—
512C23—441no—
513C23—441no—
514C23—441no—
515C23—441no—
516C23—441no—
517C23—441no—
518C23—441no—
519C23—441no—
520C23—441no—
521C23C2×D8814yes—
522C23C22×D4411yescharacteristic
523Q8—448no—
524D4—28no—
525D4—222no—
526D4—222no—
527D4—222no—
528D4—222no—
529D4—4416no—
530D4—441no—
531D4—441no—
532D4—441no—
533D4—441no—
534D4—888no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—222no—
545C2×C4—224no—
546C2×C4—4416no—
547C2×C4—441no—
548C2×C4—442no—
549C2×C4—441no—
550C2×C4—442no—
551C2×C4—448no—
552C2×C4—441no—
553C2×C4—442no—
554C2×C4—441no—
555C2×C4—441no—
556C2×C4—442no—
557C2×C4—442no—
558C2×C4—884no—
559C2×C4#6693512yes—
560C2×C4#6693512yes—
561C2×C4C2×D8812yes—
562C2×C4#6696112yes—
563C2×C4C2×D4×D1111yescharacteristic
564C2×C4C2×D4×D1111yescharacteristic
565C2×C4C2×#434111yescharacteristic
566C2×C4#6703711yescharacteristic
567C2×C4#41×D1111yescharacteristic
568C2×C4#6704311yescharacteristic
569C8—22no—
570C8—42no—
571C8—41no—
572C22—24no—
573C22—24no—
574C22—24no—
575C22—42no—
576C22—42no—
577C22—42no—
578C22—42no—
579C22—442no—
580C22—442no—
581C22—442no—
582C22—442no—
583C22—442no—
584C22—442no—
585C22—881no—
586C22—881no—
587C22—881no—
588C22—881no—
589C22—881no—
590C22—881no—
591C22—881no—
592C22—881no—
593C22C2×#6693511yescharacteristic
594C22#1062308511yescharacteristic
595C22#1062308611yescharacteristic
596C22C22×D8811yescharacteristic
597C22C2×#6696111yescharacteristic
598C22#1062328211yescharacteristic
599C22#1062328411yescharacteristic
600C4—22no—
601C4—42no—
602C4—442no—
603C4—444no—
604C4—881no—
605C4—882no—
606C4#1062234514yes—
607C4#1062313711yescharacteristic
608C4#1062313911yescharacteristic
609C4#1062320811yescharacteristic
610C4#1062324911yescharacteristic
611C2—44no—
612C2—882no—
613C2—882no—
614C2#1307195911yescharacteristic
615C2C2×#1062234511yescharacteristic
616C2#1307793411yescharacteristic
617C2#1308043011yescharacteristic
618C2#1308092211yescharacteristic
619C2#1308096411yescharacteristic
620C2#1308121211yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1954C2
socleC23×C11C22×D4
hypercenter#1954D11
hypocenterC11#24116
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #1954

Complements

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

NH ≅ G/Ntype
1. C2×#10623086C2semidirect
2. C2×#10622459C2semidirect
3. C2×C4×D88C2semidirect
4. #13073529C2semidirect
5. #13069799C2semidirect
6. #13069614C2semidirect
7. #13069577C2semidirect
8. #13068931C2semidirect
9. #13068806C2semidirect
10. #13068617C2semidirect
11. C11×#1954C2semidirect
94. C4×D44D4semidirect
96. #66922D4semidirect
114. C2×D4×C11D8semidirect
150. C2×D44#41semidirect
168. C2×C8×C11#41semidirect
198. #1954D11semidirect
445. C2×D4D88semidirect
478. C2×C8#4341semidirect
500. C11#24116semidirect

Maximal subgroups

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

subgroupindex
C2×#106230862
C2×#106224592
C2×C4×D882
#130735292
#130697992
#130696142
#130695772
#130689312
#130688062
#130686172
C11×#19542
#2411611