Finite Group Databasebeta

← #14788807

Subgroups — #14788807

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
1C22×#66927C211yesmaximal, characteristic, complemented
2C2×#10622456C212yesmaximal, complemented
3C2×#10622345C212yesmaximal, complemented
4C4×#66983C211yesmaximal, characteristic, complemented
5#13069851C212yesmaximal, complemented
6#13069689C212yesmaximal, complemented
7#13069542C212yesmaximal, complemented
8#13068548C212yesmaximal, complemented
9C11×#1797C211yesmaximal, characteristic, complemented
10C23×D44—21no—
11C23×D44—21no—
12C23×D44C2212yes—
13C22×C42×C11C2211yescharacteristic
14C2×#66983C2211yescharacteristic
15C2×C4×C22⋊D11—21no—
16C22×D88C2214yescomplemented
17C2×#66927—21no—
18C2×#66927—21no—
19C2×#66927—28no—
20C2×#66927C2212yes—
21C2×#66927C2212yes—
22C2×C4×D44C2211yescharacteristic, complemented
23C2×C11×C4⋊C8C2212yescomplemented
24C2×C11×C22⋊C8C2212yes—
25#10622826—21no—
26#10622825C2211yescharacteristic
27C2×#66885C2214yescomplemented
28C2×#66885C2214yescomplemented
29C2×#66885C2214yescomplemented
30#10622553—21no—
31#10622552C2211yescharacteristic, complemented
32C4×(C2×D11)⋊C4—21no—
33C4×C4⋊Dic11C2211yescharacteristic, complemented
34#10622541C2211yescharacteristic, complemented
35#10622456—28no—
36#10622345—28no—
37C11×#336C2212yescomplemented
38C24×D11—22no—
39C23×C4×C11D411yescharacteristic
40C23×C4×C11D411yescharacteristic
41C23×C4×C11C2311yescharacteristic
42C22×C22⋊D11—21no—
43C22×D44—28no—
44C22×D44—28no—
45C22×D44—22no—
46C22×D44—22no—
47C22×D44—22no—
48C22×D44—22no—
49C22×D44—22no—
50C22×D44—28no—
51C22×D44—24no—
52C22×D44—24no—
53C22×D44—44no—
54C22×D44—44no—
55C22×D44—44no—
56C22×D44—44no—
57C22×D44—44no—
58C22×D44C2314yes—
59C22×D44C2311yescharacteristic
60C22×C4×D11—21no—
61C22×C8×C11C2314yes—
62C2×C42×C11—24no—
63C2×C42×C11D411yescharacteristic
64C2×C42×C11D411yescharacteristic
65C2×C42×C11C2311yescharacteristic
66C2×C42×C11C2311yescharacteristic
67C2×C22⋊Dic11—21no—
68#66983—22no—
69#66983D414yescomplemented
70C4×C22⋊D11—44no—
71C2×(C2×D11)⋊C4—21no—
72C2×(C2×D11)⋊C4—21no—
73C2×(C2×D11)⋊C4—21no—
74C2×(C2×D11)⋊C4—21no—
75C2×C4⋊Dic11C2311yescharacteristic
76C2×C4⋊Dic11C2311yescharacteristic
77C2×C4⋊Dic11C2311yescharacteristic
78C2×Dic11⋊C4—21no—
79C2×C4×Dic11—21no—
80C2×D88—28no—
81C2×D88—28no—
82C2×D88—44no—
83#66927—28no—
84#66927—28no—
85#66927—28no—
86#66927—24no—
87#66927D418yescomplemented
88C4×D44—24no—
89C11×C4⋊C8—24no—
90C11×C22⋊C8—24no—
91C11⋊#95—21no—
92C11⋊#95—21no—
93C11⋊#95—21no—
94#66885—28no—
95#66885—28no—
96#66885—44no—
97#24208—111nomaximal, Sylow
98C24×C11C2×D411yescharacteristic
99C23×D11—28no—
100C23×D11—21no—
101C23×D11—24no—
102C23×D11—44no—
103C23×D11—44no—
104C23×D11—44no—
105C23×D11—44no—
106C23×D11—44no—
107C23×D11—44no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11D814yescomplemented
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11C2×D412yes—
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11#4112yes—
123C22×C4×C11C2411yescharacteristic
124C2×C22⋊D11—24no—
125C2×C22⋊D11—42no—
126C2×C22⋊D11—42no—
127C22×Dic11—21no—
128C22×Dic11—21no—
129C22×Dic11—21no—
130C2×D44—28no—
131C2×D44—28no—
132C2×D44—28no—
133C2×D44—28no—
134C2×D44—28no—
135C2×D44—24no—
136C2×D44—24no—
137C2×D44—22no—
138C2×D44—21no—
139C2×D44—24no—
140C2×D44—24no—
141C2×D44—22no—
142C2×D44—24no—
143C2×D44—416no—
144C2×D44—416no—
145C2×D44—432no—
146C2×D44—44no—
147C2×D44—44no—
148C2×D44—44no—
149C2×D44—44no—
150C2×D44—44no—
151C2×D44—432no—
152C2×D44—44no—
153C2×D44—44no—
154C2×D44—44no—
155C2×D44—44no—
156C2×D44—44no—
157C2×D44C2×D418yes—
158C2×D44C2×D412yescomplemented
159C2×C4×D11—42no—
160C2×C4×D11—42no—
161C2×C4×D11—42no—
162C2×C8×C11—24no—
163C2×C8×C11—24no—
164C2×C8×C11—24no—
165C42×C11—22no—
166C42×C11—22no—
167C42×C11—22no—
168C42×C11C2×D414yes—
169C22⋊Dic11—42no—
170(C2×D11)⋊C4—24no—
171(C2×D11)⋊C4—42no—
172(C2×D11)⋊C4—42no—
173(C2×D11)⋊C4—42no—
174C4⋊Dic11—22no—
175C4⋊Dic11—21no—
176C4⋊Dic11—22no—
177C4⋊Dic11C2×D412yescomplemented
178Dic11⋊C4—42no—
179C4×Dic11—42no—
180D88—416no—
181C22×#127—111no—
182C2×#459—112no—
183C2×#447—112no—
184C4×#121—111no—
185#2041—112no—
186#2011—112no—
187#1982—112no—
188#1797D1111yescharacteristic, complemented
189#1786—112no—
190C23×C11—21no—
191C23×C11—21no—
192C23×C11—21no—
193C23×C11—21no—
194C23×C11#12112yes—
195C23×C11C2×D812yes—
196C23×C11AGL(1,ℤ/8)12yes—
197C23×C11C22×D411yescharacteristic
198C22×D11—28no—
199C22×D11—22no—
200C22×D11—416no—
201C22×D11—416no—
202C22×D11—416no—
203C22×D11—41no—
204C22×D11—44no—
205C22×D11—44no—
206C22×D11—41no—
207C22×D11—41no—
208C22×D11—44no—
209C22×D11—41no—
210C22×D11—41no—
211C22×D11—44no—
212C22×D11—44no—
213C22×D11—44no—
214C22×D11—41no—
215C22×D11—88no—
216C22×D11—88no—
217C22×D11—88no—
218C22×D11—88no—
219C2×C4×C11—28no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—24no—
229C2×C4×C11—24no—
230C2×C4×C11—28no—
231C2×C4×C11#12012yes—
232C2×C4×C11#12012yes—
233C2×C4×C11#12112yes—
234C2×C4×C11C2×D812yes—
235C2×C4×C11C2×D812yes—
236C2×C4×C11AGL(1,ℤ/8)12yes—
237C2×C4×C11AGL(1,ℤ/8)12yes—
238C2×C4×C11C22×D411yescharacteristic
239C2×C4×C11C22×D412yes—
240C2×C4×C11C2×#4111yescharacteristic
241C2×C4×C11H(5,𝔽2)12yes—
242C22⋊D11—48no—
243C2×Dic11—22no—
244C2×Dic11—41no—
245C2×Dic11—41no—
246C2×Dic11—41no—
247C2×Dic11—41no—
248C2×Dic11—41no—
249C2×Dic11—41no—
250C2×Dic11—41no—
251C2×Dic11—41no—
252D44—24no—
253D44—28no—
254D44—28no—
255D44—416no—
256D44—416no—
257D44—416no—
258D44—416no—
259D44—44no—
260D44—42no—
261D44—44no—
262D44—416no—
263C4×D11—84no—
264C8×C11—44no—
265C23×D4—112no—
266C23×D4—221no—
267C23×D4—221no—
268C22×D8—114no—
269C2×#127—112no—
270C2×#127—112no—
271C2×#127—228no—
272C2×#127—221no—
273C2×#127—221no—
274C2×#121—111no—
275C2×C4×D4—111no—
276C2×C4×D4—221no—
277C22×C42C2×D1111yescharacteristic
278#459—228no—
279#447—228no—
280C2×C4⋊C8C2×D1112yescomplemented
281C2×#102—114no—
282C2×#102—114no—
283C2×#102—114no—
284C2×C22⋊C8C2×D1112yes—
285#390—111no—
286#389—111no—
287#388—221no—
288#386—221no—
289#380—111no—
290C4×C4⋊C4—111no—
291C4×C22⋊C4—221no—
292#336C2×D1112yescomplemented
293C22×C11—22no—
294C22×C11—22no—
295C22×C11—22no—
296C22×C11—22no—
297C22×C11—22no—
298C22×C11—22no—
299C22×C11#45914yescomplemented
300C22×C11C2×#12011yescharacteristic
301C22×C11C2×#12111yescharacteristic
302C22×C11#53511yescharacteristic
303C22×C11C22×D811yescharacteristic
304C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
305C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
306C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
307C2×D11—48no—
308C2×D11—42no—
309C2×D11—48no—
310C2×D11—48no—
311C2×D11—42no—
312C2×D11—42no—
313C2×D11—832no—
314C2×D11—81no—
315C2×D11—84no—
316C2×D11—81no—
317C2×D11—84no—
318C2×D11—81no—
319C2×D11—81no—
320C2×D11—84no—
321C2×D11—84no—
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—222no—
333C22×D4—111no—
334C22×D4—114no—
335C22×D4—228no—
336C22×D4—228no—
337C22×D4—228no—
338C22×D4—221no—
339C22×D4—222no—
340C22×D4—222no—
341C22×D4—222no—
342C22×D4—222no—
343C22×D4—222no—
344C22×D4—224no—
345C22×D4—224no—
346C22×D4—444no—
347C22×D4—444no—
348C22×D4—444no—
349C22×D4—444no—
350C22×D4—444no—
351C23×C4—221no—
352C23×C4D4411yescharacteristic
353C23×C4D4411yescharacteristic
354C23×C4C22×D1111yescharacteristic
355C2×D8—228no—
356C2×D8—228no—
357C2×D8—444no—
358C22×C8C22×D1114yes—
359#127—118no—
360#127—228no—
361#127—228no—
362#127—228no—
363#127—224no—
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×C42D4411yescharacteristic
380C2×C42D4411yescharacteristic
381C2×C42C22×D1111yescharacteristic
382C2×C42C22×D1111yescharacteristic
383C4⋊C8—24no—
384#102—228no—
385#102—228no—
386#102—444no—
387C22⋊C8—24no—
388#95—221no—
389#95—221no—
390#95—221no—
391C2×C11—24no—
392C2×C11#240811yescharacteristic
393C2×C11C2×#44711yescharacteristic
394C2×C11#300311yescharacteristic
395C2×C11C2×#45911yescharacteristic
396C2×C11#303811yescharacteristic
397C2×C11#320511yescharacteristic
398C2×C11#321711yescharacteristic
399D11—82no—
400D11—88no—
401C24—228no—
402C24—221no—
403C24—224no—
404C24—444no—
405C24—444no—
406C24—444no—
407C24—444no—
408C24—444no—
409C24—444no—
410C24C2×D4411yescharacteristic
411C2×D4—118no—
412C2×D4—112no—
413C2×D4—228no—
414C2×D4—228no—
415C2×D4—228no—
416C2×D4—224no—
417C2×D4—228no—
418C2×D4—228no—
419C2×D4—224no—
420C2×D4—222no—
421C2×D4—224no—
422C2×D4—224no—
423C2×D4—221no—
424C2×D4—224no—
425C2×D4—222no—
426C2×D4—224no—
427C2×D4—4416no—
428C2×D4—4416no—
429C2×D4—4432no—
430C2×D4—444no—
431C2×D4—444no—
432C2×D4—444no—
433C2×D4—444no—
434C2×D4—444no—
435C2×D4—4432no—
436C2×D4—442no—
437C2×D4—442no—
438C2×D4—444no—
439C2×D4—444no—
440C2×D4—444no—
441C2×D4—444no—
442C2×D4—444no—
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×C4D8814yescomplemented
457C22×C4C2×D4411yescharacteristic
458C22×C4C2×D4411yescharacteristic
459C22×C4C2×D4411yescharacteristic
460C22×C4C2×D4411yescharacteristic
461C22×C4C2×D4411yescharacteristic
462C22×C4D4×D1112yes—
463C22×C4#434312yes—
464C22×C4C23×D1111yescharacteristic
465D8—4416no—
466C2×C8—24no—
467C2×C8—24no—
468C2×C8—24no—
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—
483C42D4×D1114yes—
484C11#2420811yescharacteristic, complemented, Sylow
485C23—21no—
486C23—21no—
487C23—21no—
488C23—21no—
489C23—228no—
490C23—222no—
491C23—4416no—
492C23—4416no—
493C23—4416no—
494C23—441no—
495C23—444no—
496C23—441no—
497C23—441no—
498C23—441no—
499C23—444no—
500C23—444no—
501C23—444no—
502C23—441no—
503C23—444no—
504C23—444no—
505C23—441no—
506C23—888no—
507C23—888no—
508C23—888no—
509C23—888no—
510C23#6694812yes—
511C23C2×D8812yes—
512C23#6696112yes—
513C23C22×D4411yescharacteristic
514D4—224no—
515D4—228no—
516D4—228no—
517D4—4416no—
518D4—4416no—
519D4—4416no—
520D4—4416no—
521D4—448no—
522D4—4416no—
523D4—444no—
524D4—444no—
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—28no—
536C2×C4—24no—
537C2×C4—24no—
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×C4#6693512yes—
549C2×C4#6693512yes—
550C2×C4#6694812yes—
551C2×C4C2×D8812yes—
552C2×C4C2×D8812yes—
553C2×C4#6696112yes—
554C2×C4#6696112yes—
555C2×C4C2×D4×D1111yescharacteristic
556C2×C4C2×D4×D1112yes—
557C2×C4C2×#434311yescharacteristic
558C2×C4#6704212yes—
559C8—44no—
560C22—22no—
561C22—22no—
562C22—22no—
563C22—22no—
564C22—22no—
565C22—22no—
566C22—442no—
567C22—448no—
568C22—442no—
569C22—448no—
570C22—448no—
571C22—442no—
572C22—8832no—
573C22—884no—
574C22—881no—
575C22—884no—
576C22—884no—
577C22—881no—
578C22—881no—
579C22—884no—
580C22—881no—
581C22#1062245614yescomplemented
582C22C2×#6693511yescharacteristic
583C22C2×#6694811yescharacteristic
584C22#1062305611yescharacteristic
585C22C22×D8811yescharacteristic
586C22C2×#6696111yescharacteristic
587C22C2×#6696111yescharacteristic
588C22C2×#6696111yescharacteristic
589C4—22no—
590C4—22no—
591C4—22no—
592C4—22no—
593C4—442no—
594C4—881no—
595C4—881no—
596C4#1062234514yescomplemented
597C4#1062314012yes—
598C4#1062316112yes—
599C2—24no—
600C2—888no—
601C2—882no—
602C2#1307197311yescharacteristic
603C2C2×#1062234511yescharacteristic
604C2#1307784611yescharacteristic
605C2C2×#1062245611yescharacteristic
606C2#1307809711yescharacteristic
607C2#1307953611yescharacteristic
608C2#1307963611yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1797C2
socleC23×C11C22×D4
hypercenter#1797D11
hypocenterC11#24208
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1797

Complements

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

NH ≅ G/Ntype
1. C22×#66927C2semidirect
2. C2×#10622456C2semidirect
3. C2×#10622345C2semidirect
4. C4×#66983C2semidirect
5. #13069851C2semidirect
6. #13069689C2semidirect
7. #13069542C2semidirect
8. #13068548C2semidirect
9. C11×#1797C2semidirect
16. C22×D88C22semidirect
22. C2×C4×D44C22semidirect
23. C2×C11×C4⋊C8C22semidirect
27. C2×#66885C22semidirect
28. C2×#66885C22semidirect
29. C2×#66885C22semidirect
31. #10622552C22semidirect
33. C4×C4⋊Dic11C22semidirect
34. #10622541C22semidirect
37. C11×#336C22semidirect
69. #66983D4semidirect
87. #66927D4semidirect
115. C22×C4×C11D8semidirect
158. C2×D44C2×D4semidirect
177. C4⋊Dic11C2×D4semidirect
188. #1797D11semidirect
280. C2×C4⋊C8C2×D11semidirect
292. #336C2×D11semidirect
299. C22×C11#459semidirect
326. C4×C11#447semidirect
456. C22×C4D88semidirect
484. C11#24208semidirect
581. C22#10622456semidirect
596. C4#10622345semidirect

Maximal subgroups

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

subgroupindex
C22×#669272
C2×#106224562
C2×#106223452
C4×#669832
#130698512
#130696892
#130695422
#130685482
C11×#17972
#2420811