Finite Group Databasebeta

← #14788800

Subgroups — #14788800

Order 2816.

2202 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622685C212yesmaximal, complemented
2C2×#10622830C212yesmaximal, complemented
3C4×#66983C211yesmaximal, characteristic, complemented
4#13069847C212yesmaximal, complemented
5#13069687C212yesmaximal, complemented
6#13069544C212yesmaximal, complemented
7#13068596C211yesmaximal, characteristic, complemented
8#13068547C212yesmaximal, complemented
9C22×C11×#127C211yesmaximal, characteristic, complemented
10C23×D4×C11—21no—
11C23×D4×C11—21no—
12C23×D4×C11C2212yes—
13C2×C11×#127—28no—
14C2×C11×#127—21no—
15C2×C11×#127—21no—
16C2×C11×#127C2212yes—
17C2×C11×#127C2212yes—
18C22×C42×C11C2211yescharacteristic
19C22×#4323C2214yescomplemented
20C2×#66983C2211yescharacteristic
21C2×C4×C22⋊D11—21no—
22C2×C4×D44C2211yescharacteristic, complemented
23#10622830—28no—
24C2×#66896C2214yescomplemented
25C2×#66896C2214yescomplemented
26C2×#66896C2214yescomplemented
27#10622826—21no—
28#10622825C2211yescharacteristic
29C2×C22⋊(C11⋊C8)C2212yes—
30#10622685—28no—
31#10622553—21no—
32#10622552C2211yescharacteristic, complemented
33C4×(C2×D11)⋊C4—21no—
34C4×C4⋊Dic11C2211yescharacteristic, complemented
35#10622541C2211yescharacteristic, complemented
36C2×C4⋊(C11⋊C8)C2212yescomplemented
37#10622162C2212yescomplemented
38C25×C11—22no—
39C22×D4×C11—28no—
40C22×D4×C11—28no—
41C22×D4×C11—28no—
42C22×D4×C11—22no—
43C22×D4×C11—22no—
44C22×D4×C11—22no—
45C22×D4×C11—22no—
46C22×D4×C11—22no—
47C22×D4×C11—24no—
48C22×D4×C11—24no—
49C22×D4×C11—44no—
50C22×D4×C11—44no—
51C22×D4×C11—44no—
52C22×D4×C11—44no—
53C22×D4×C11—44no—
54C22×D4×C11C2314yes—
55C23×C4×C11D411yescharacteristic
56C23×C4×C11D411yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C22×C22⋊D11—21no—
59C22×D44C2311yescharacteristic
60C22×C4×D11—21no—
61C11×#127—28no—
62C11×#127—28no—
63C11×#127—28no—
64C11×#127—24no—
65C11×#127D418yescomplemented
66C2×C42×C11—24no—
67C2×C42×C11D411yescharacteristic
68C2×C42×C11D411yescharacteristic
69C2×C42×C11C2311yescharacteristic
70C2×C42×C11C2311yescharacteristic
71C2×C22⋊Dic11—21no—
72C2×#4323—28no—
73C2×#4323—28no—
74C2×#4323—44no—
75#66983—22no—
76#66983D414yescomplemented
77C4×C22⋊D11—44no—
78C2×(C2×D11)⋊C4—21no—
79C2×(C2×D11)⋊C4—21no—
80C2×(C2×D11)⋊C4—21no—
81C2×(C2×D11)⋊C4—21no—
82C2×C4⋊Dic11C2311yescharacteristic
83C2×C4⋊Dic11C2311yescharacteristic
84C2×C4⋊Dic11C2311yescharacteristic
85C2×Dic11⋊C4—21no—
86C2×C4×Dic11—21no—
87C22×C11⋊C8C2314yes—
88C4×D44—24no—
89#66896—28no—
90#66896—28no—
91#66896—44no—
92C11⋊#95—21no—
93C11⋊#95—21no—
94C11⋊#95—21no—
95C22⋊(C11⋊C8)—24no—
96C4⋊(C11⋊C8)—24no—
97#24208—111nomaximal, Sylow
98C24×C11—28no—
99C24×C11—24no—
100C24×C11—44no—
101C24×C11—44no—
102C24×C11—44no—
103C24×C11—44no—
104C24×C11—44no—
105C24×C11—44no—
106C24×C11C2×D411yescharacteristic
107C23×D11—21no—
108C2×D4×C11—28no—
109C2×D4×C11—28no—
110C2×D4×C11—28no—
111C2×D4×C11—28no—
112C2×D4×C11—28no—
113C2×D4×C11—24no—
114C2×D4×C11—24no—
115C2×D4×C11—24no—
116C2×D4×C11—24no—
117C2×D4×C11—24no—
118C2×D4×C11—416no—
119C2×D4×C11—416no—
120C2×D4×C11—432no—
121C2×D4×C11—44no—
122C2×D4×C11—44no—
123C2×D4×C11—44no—
124C2×D4×C11—44no—
125C2×D4×C11—44no—
126C2×D4×C11—432no—
127C2×D4×C11—44no—
128C2×D4×C11—44no—
129C2×D4×C11—44no—
130C2×D4×C11—44no—
131C2×D4×C11—44no—
132C2×D4×C11C2×D418yes—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11D814yescomplemented
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D412yes—
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11#4112yes—
148C22×C4×C11C2411yescharacteristic
149C2×C22⋊D11—24no—
150C2×C22⋊D11—42no—
151C2×C22⋊D11—42no—
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11—21no—
155C2×D44—22no—
156C2×D44—21no—
157C2×D44—22no—
158C2×D44C2×D412yescomplemented
159C2×C4×D11—42no—
160C2×C4×D11—42no—
161C2×C4×D11—42no—
162C42×C11—22no—
163C42×C11—22no—
164C42×C11—22no—
165C42×C11C2×D414yes—
166C22⋊Dic11—42no—
167#4323—416no—
168(C2×D11)⋊C4—24no—
169(C2×D11)⋊C4—42no—
170(C2×D11)⋊C4—42no—
171(C2×D11)⋊C4—42no—
172C4⋊Dic11—22no—
173C4⋊Dic11—21no—
174C4⋊Dic11—22no—
175C4⋊Dic11C2×D412yescomplemented
176Dic11⋊C4—42no—
177C4×Dic11—42no—
178C2×C11⋊C8—24no—
179C2×C11⋊C8—24no—
180C2×C11⋊C8—24no—
181C22×#127D1111yescharacteristic, complemented
182C2×#459—112no—
183C2×#447—112no—
184C4×#121—111no—
185#2041—112no—
186#2011—112no—
187#1982—112no—
188#1797—111no—
189#1786—112no—
190C23×C11—21no—
191C23×C11—21no—
192C23×C11—21no—
193C23×C11—21no—
194C23×C11—28no—
195C23×C11—416no—
196C23×C11—416no—
197C23×C11—416no—
198C23×C11—44no—
199C23×C11—44no—
200C23×C11—44no—
201C23×C11—44no—
202C23×C11—44no—
203C23×C11—44no—
204C23×C11—88no—
205C23×C11—88no—
206C23×C11—88no—
207C23×C11—88no—
208C23×C11#12112yes—
209C23×C11C2×D812yes—
210C23×C11AGL(1,ℤ/8)12yes—
211C23×C11C22×D411yescharacteristic
212C22×D11—22no—
213C22×D11—41no—
214C22×D11—41no—
215C22×D11—41no—
216C22×D11—41no—
217C22×D11—41no—
218C22×D11—41no—
219D4×C11—28no—
220D4×C11—28no—
221D4×C11—416no—
222D4×C11—416no—
223D4×C11—416no—
224D4×C11—416no—
225D4×C11—44no—
226D4×C11—44no—
227D4×C11—416no—
228C2×C4×C11—28no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—24no—
238C2×C4×C11—24no—
239C2×C4×C11—28no—
240C2×C4×C11#12012yes—
241C2×C4×C11#12012yes—
242C2×C4×C11#12112yes—
243C2×C4×C11C2×D812yes—
244C2×C4×C11C2×D812yes—
245C2×C4×C11AGL(1,ℤ/8)12yes—
246C2×C4×C11AGL(1,ℤ/8)12yes—
247C2×C4×C11C22×D411yescharacteristic
248C2×C4×C11C22×D412yes—
249C2×C4×C11C2×#4111yescharacteristic
250C2×C4×C11H(5,𝔽2)12yes—
251C22⋊D11—48no—
252C2×Dic11—22no—
253C2×Dic11—41no—
254C2×Dic11—41no—
255C2×Dic11—41no—
256C2×Dic11—41no—
257C2×Dic11—41no—
258C2×Dic11—41no—
259C2×Dic11—41no—
260C2×Dic11—41no—
261D44—24no—
262D44—42no—
263C4×D11—84no—
264C11⋊C8—44no—
265C23×D4—21no—
266C23×D4—21no—
267C23×D4C2×D1112yes—
268C22×D8—114no—
269C2×#127—28no—
270C2×#127—21no—
271C2×#127—21no—
272C2×#127C2×D1112yes—
273C2×#127C2×D1112yes—
274C2×#121—111no—
275C2×C4×D4—111no—
276C2×C4×D4—221no—
277C22×C42C2×D1111yescharacteristic
278#459—228no—
279#447—228no—
280C2×C4⋊C8—112no—
281C2×#102—114no—
282C2×#102—114no—
283C2×#102—114no—
284C2×C22⋊C8—112no—
285#390—111no—
286#389—111no—
287#388—221no—
288#386—221no—
289#380—111no—
290C4×C4⋊C4—111no—
291C4×C22⋊C4—221no—
292#336—112no—
293C22×C11—22no—
294C22×C11—22no—
295C22×C11—22no—
296C22×C11—22no—
297C22×C11—22no—
298C22×C11—22no—
299C22×C11—48no—
300C22×C11—48no—
301C22×C11—48no—
302C22×C11—832no—
303C22×C11—84no—
304C22×C11—84no—
305C22×C11—84no—
306C22×C11—84no—
307C22×C11#45914yescomplemented
308C22×C11C2×#12011yescharacteristic
309C22×C11C2×#12111yescharacteristic
310C22×C11#53511yescharacteristic
311C22×C11C22×D811yescharacteristic
312C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
313C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
314C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
315C2×D11—42no—
316C2×D11—42no—
317C2×D11—42no—
318C2×D11—81no—
319C2×D11—81no—
320C2×D11—81no—
321C2×D11—81no—
322C4×C11—22no—
323C4×C11—22no—
324C4×C11—22no—
325C4×C11—22no—
326C4×C11#44714yescomplemented
327C4×C11D4212yes—
328C4×C11#54612yes—
329Dic11—42no—
330Dic11—81no—
331Dic11—81no—
332C25—22no—
333C22×D4—28no—
334C22×D4—28no—
335C22×D4—28no—
336C22×D4—24no—
337C22×D4—24no—
338C22×D4—22no—
339C22×D4—22no—
340C22×D4—22no—
341C22×D4—22no—
342C22×D4—22no—
343C22×D4—44no—
344C22×D4—44no—
345C22×D4—44no—
346C22×D4—44no—
347C22×D4—44no—
348C22×D4—111no—
349C22×D4—221no—
350C22×D4C22×D1114yes—
351C23×C4—221no—
352C23×C4C22⋊D1111yescharacteristic
353C23×C4C22⋊D1111yescharacteristic
354C23×C4C22×D1111yescharacteristic
355C2×D8—228no—
356C2×D8—228no—
357C2×D8—444no—
358C22×C8—114no—
359#127—28no—
360#127—28no—
361#127—28no—
362#127—24no—
363#127C22⋊D1118yescomplemented
364#121—114no—
365#121—222no—
366C4×D4—224no—
367C4×D4—444no—
368C2×C4⋊C4—111no—
369C2×C4⋊C4—111no—
370C2×C4⋊C4—111no—
371C2×C4⋊C4—221no—
372C2×C22⋊C4—221no—
373C2×C22⋊C4—221no—
374C2×C22⋊C4—221no—
375C2×C22⋊C4—221no—
376C2×C22⋊C4—221no—
377C2×C42—24no—
378C2×C42—221no—
379C2×C42C22⋊D1111yescharacteristic
380C2×C42C22⋊D1111yescharacteristic
381C2×C42C22×D1111yescharacteristic
382C2×C42C22×D1111yescharacteristic
383C4⋊C8—224no—
384#102—228no—
385#102—228no—
386#102—444no—
387C22⋊C8—224no—
388#95—221no—
389#95—221no—
390#95—221no—
391C2×C11—24no—
392C2×C11—88no—
393C2×C11#240811yescharacteristic
394C2×C11C2×#44711yescharacteristic
395C2×C11#300311yescharacteristic
396C2×C11C2×#45911yescharacteristic
397C2×C11#303811yescharacteristic
398C2×C11#320511yescharacteristic
399C2×C11#321711yescharacteristic
400D11—82no—
401C24—28no—
402C24—24no—
403C24—44no—
404C24—44no—
405C24—44no—
406C24—44no—
407C24—44no—
408C24—44no—
409C24—221no—
410C24C2×C22⋊D1111yescharacteristic
411C2×D4—28no—
412C2×D4—28no—
413C2×D4—28no—
414C2×D4—28no—
415C2×D4—28no—
416C2×D4—24no—
417C2×D4—24no—
418C2×D4—24no—
419C2×D4—24no—
420C2×D4—24no—
421C2×D4—416no—
422C2×D4—416no—
423C2×D4—432no—
424C2×D4—44no—
425C2×D4—44no—
426C2×D4—44no—
427C2×D4—44no—
428C2×D4—44no—
429C2×D4—432no—
430C2×D4—44no—
431C2×D4—44no—
432C2×D4—44no—
433C2×D4—44no—
434C2×D4—44no—
435C2×D4—112no—
436C2×D4—224no—
437C2×D4—221no—
438C2×D4—222no—
439C2×D4—222no—
440C2×D4—442no—
441C2×D4—442no—
442C2×D4C2×C22⋊D1118yes—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—221no—
451C22×C4—221no—
452C22×C4—221no—
453C22×C4—442no—
454C22×C4—442no—
455C22×C4—442no—
456C22×C4#432314yescomplemented
457C22×C4D4×D1112yes—
458C22×C4#434112yes—
459C22×C4C2×C22⋊D1111yescharacteristic
460C22×C4C2×C22⋊D1111yescharacteristic
461C22×C4C2×C22⋊D1111yescharacteristic
462C22×C4C2×C22⋊D1111yescharacteristic
463C22×C4C2×C22⋊D1111yescharacteristic
464C22×C4C23×D1111yescharacteristic
465D8—4416no—
466C2×C8—224no—
467C2×C8—224no—
468C2×C8—224no—
469C4⋊C4—112no—
470C4⋊C4—221no—
471C4⋊C4—222no—
472C4⋊C4—222no—
473C4⋊C4—442no—
474C22⋊C4—224no—
475C22⋊C4—442no—
476C22⋊C4—442no—
477C22⋊C4—442no—
478C22⋊C4—442no—
479C42—22no—
480C42—22no—
481C42—22no—
482C42—442no—
483C42C2×C22⋊D1114yes—
484C11#2420811yescharacteristic, complemented, Sylow
485C23—21no—
486C23—21no—
487C23—21no—
488C23—21no—
489C23—28no—
490C23—416no—
491C23—416no—
492C23—416no—
493C23—44no—
494C23—44no—
495C23—44no—
496C23—44no—
497C23—44no—
498C23—44no—
499C23—88no—
500C23—88no—
501C23—88no—
502C23—88no—
503C23—222no—
504C23—441no—
505C23—441no—
506C23—441no—
507C23—441no—
508C23—441no—
509C23—441no—
510C23C2×#432312yes—
511C23#6698512yes—
512C23#6699112yes—
513C23C22×C22⋊D1111yescharacteristic
514D4—28no—
515D4—28no—
516D4—416no—
517D4—416no—
518D4—416no—
519D4—416no—
520D4—44no—
521D4—44no—
522D4—416no—
523D4—224no—
524D4—448no—
525D4—442no—
526C2×C4—28no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—24no—
536C2×C4—24no—
537C2×C4—28no—
538C2×C4—222no—
539C2×C4—441no—
540C2×C4—441no—
541C2×C4—441no—
542C2×C4—441no—
543C2×C4—441no—
544C2×C4—441no—
545C2×C4—441no—
546C2×C4—441no—
547C2×C4—884no—
548C2×C4C2×#432312yes—
549C2×C4C2×#432312yes—
550C2×C4#6698512yes—
551C2×C4#6698512yes—
552C2×C4#6699112yes—
553C2×C4#6700612yes—
554C2×C4#6700612yes—
555C2×C4C2×D4×D1111yescharacteristic
556C2×C4C2×#434111yescharacteristic
557C2×C4#6703712yes—
558C2×C4C22×C22⋊D1112yes—
559C8—444no—
560C22—22no—
561C22—22no—
562C22—22no—
563C22—22no—
564C22—22no—
565C22—22no—
566C22—48no—
567C22—48no—
568C22—48no—
569C22—832no—
570C22—84no—
571C22—84no—
572C22—84no—
573C22—84no—
574C22—442no—
575C22—442no—
576C22—442no—
577C22—881no—
578C22—881no—
579C22—881no—
580C22—881no—
581C22#1062268514yescomplemented
582C22C22×#432311yescharacteristic
583C22C2×#6698511yescharacteristic
584C22C2×#6698511yescharacteristic
585C22C2×#6698511yescharacteristic
586C22C2×#6699111yescharacteristic
587C22#1062333611yescharacteristic
588C22C2×#6700611yescharacteristic
589C4—22no—
590C4—22no—
591C4—22no—
592C4—22no—
593C4—442no—
594C4—881no—
595C4—881no—
596C4#1062283014yescomplemented
597C4D4×C22⋊D1112yes—
598C4#1062333712yes—
599C2—24no—
600C2—88no—
601C2—882no—
602C2#1307196611yescharacteristic
603C2C2×#1062283011yescharacteristic
604C2#1307784311yescharacteristic
605C2C2×#1062268511yescharacteristic
606C2#1307809211yescharacteristic
607C2#1307953411yescharacteristic
608C2#1307963411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC22×C11×#127C2
socleC23×C11C22×D4
hypercenterC22×#127D11
hypocenterC11#24208
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C22×#127

Complements

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

NH ≅ G/Ntype
1. C2×#10622685C2semidirect
2. C2×#10622830C2semidirect
3. C4×#66983C2semidirect
4. #13069847C2semidirect
5. #13069687C2semidirect
6. #13069544C2semidirect
7. #13068596C2semidirect
8. #13068547C2semidirect
9. C22×C11×#127C2semidirect
19. C22×#4323C22semidirect
22. C2×C4×D44C22semidirect
24. C2×#66896C22semidirect
25. C2×#66896C22semidirect
26. C2×#66896C22semidirect
32. #10622552C22semidirect
34. C4×C4⋊Dic11C22semidirect
35. #10622541C22semidirect
36. C2×C4⋊(C11⋊C8)C22semidirect
37. #10622162C22semidirect
65. C11×#127D4semidirect
76. #66983D4semidirect
140. C22×C4×C11D8semidirect
158. C2×D44C2×D4semidirect
175. C4⋊Dic11C2×D4semidirect
181. C22×#127D11semidirect
307. C22×C11#459semidirect
326. C4×C11#447semidirect
363. #127C22⋊D11semidirect
456. C22×C4#4323semidirect
484. C11#24208semidirect
581. C22#10622685semidirect
596. C4#10622830semidirect

Maximal subgroups

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

subgroupindex
C2×#106226852
C2×#106228302
C4×#669832
#130698472
#130696872
#130695442
#130685962
#130685472
C22×C11×#1272
#2420811