Finite Group Databasebeta

← #14769428

Subgroups — #14769428

Order 2816.

1530 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623257C211yesmaximal, characteristic
2C2×#10622451C211yesmaximal, characteristic, complemented
3C2×#10622416C212yesmaximal, complemented
4C4⋊C4×D44C211yesmaximal, characteristic, complemented
5#13069419C211yesmaximal, characteristic, complemented
6#13069046C212yesmaximal, complemented
7#13068920C212yesmaximal, complemented
8#13068617C211yesmaximal, characteristic, complemented
9#13068555C212yesmaximal, complemented
10C4×#66873C211yesmaximal, characteristic, complemented
11C11×#1981C211yesmaximal, characteristic, complemented
12C22×#4343C2212yes—
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×#66999C2212yes—
15C22×#4313C2212yes—
16#10623257—24no—
17#10623257C418yescomplemented
18C2×#66948—21no—
19C2×#66947—22no—
20C2×C4⋊C4×D11—21no—
21C2×C4⋊C4×D11C2212yes—
22C2×C4×D44—21no—
23C2×C4×D44C2211yescharacteristic
24C2×C4×D44C2211yescharacteristic
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C11×#103C2212yes—
27C2×C11×#103C2212yes—
28C4×C11×C4⋊C4C2211yescharacteristic
29C2×#66899C2212yes—
30C2×#66899C2212yes—
31C2×#66885C2212yes—
32C2×(C2×D11)⋊C8C2212yes—
33#10622600C2212yes—
34C2×#66873C2211yescharacteristic
35C2×#66873C2211yescharacteristic
36#10622548C2211yescharacteristic
37#10622541—21no—
38C2×C4×C11⋊C8C2211yescharacteristic
39#10622451—24no—
40#10622416—28no—
41#10622281—22no—
42#10622189C2212yes—
43#10622167C2211yescharacteristic
44#10622167C2211yescharacteristic
45C22×Q8×C11C2312yes—
46C2×#4343—24no—
47C2×#4343—24no—
48C2×#4343—24no—
49C2×#4343—42no—
50C2×#4343—42no—
51C2×#4343C2×C418yescomplemented
52C22×D44—22no—
53C22×D44D411yescharacteristic
54C22×D44C2311yescharacteristic
55C22×C4×D11—21no—
56C22×C4×D11—22no—
57C22×C4×D11—22no—
58C22×C4×D11C2312yes—
59C22×C8×C11C2312yes—
60C11×C4⋊Q8—22no—
61C11×C4⋊Q8C2×C414yescomplemented
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4C2311yescharacteristic
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C42×C11—21no—
67C2×C42×C11C2311yescharacteristic
68#66999—24no—
69#66999C2×C418yescomplemented
70C2×(C2×D11)⋊C4—22no—
71C2×(C2×D11)⋊C4—21no—
72C2×(C2×D11)⋊C4—22no—
73C2×(C2×D11)⋊C4D412yes—
74C2×C4⋊Dic11—21no—
75C2×C4⋊Dic11—21no—
76C2×C4⋊Dic11D411yescharacteristic
77C2×C4⋊Dic11C2312yes—
78C2×C4⋊Dic11C2311yescharacteristic
79C2×Dic11⋊C4—22no—
80C2×Dic11⋊C4—22no—
81C22×C11⋊C8C2311yescharacteristic
82C22×C11⋊C8C2311yescharacteristic
83C2×#4313—24no—
84C2×#4313—24no—
85C2×#4313—42no—
86#66948—28no—
87#66947—216no—
88C4⋊C4×D11—28no—
89C4⋊C4×D11—24no—
90C4⋊C4×D11—42no—
91C4×D44—22no—
92C4×D44—44no—
93C4×D44C2×C414yes—
94C4×D44C2×C414yescomplemented
95C4×D44D414yes—
96C11×C4⋊C8—22no—
97C11×#103—24no—
98C11×#103—42no—
99C11×#95—21no—
100#66899—24no—
101#66899—42no—
102C11⋊#95—22no—
103#66885—24no—
104(C2×D11)⋊C8—24no—
105#66873—22no—
106#66873D414yescomplemented
107C4×C11⋊C8—22no—
108#22431—111nomaximal, Sylow
109C23×D11—21no—
110C23×D11C2×D412yes—
111C2×Q8×C11—22no—
112C2×Q8×C11—22no—
113C2×Q8×C11—22no—
114C2×Q8×C11—22no—
115C2×Q8×C11—22no—
116C2×Q8×C11C22×C414yes—
117C22×C4×C11—21no—
118C22×C4×C11—22no—
119C22×C4×C11—21no—
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2411yescharacteristic
123C22×Dic11—21no—
124C22×Dic11—22no—
125C22×Dic11C2×D412yes—
126#4343—216no—
127#4343—48no—
128#4343—48no—
129#4343—48no—
130C2×D44—28no—
131C2×D44—22no—
132C2×D44—22no—
133C2×D44—21no—
134C2×D44—21no—
135C2×D44—21no—
136C2×D44—44no—
137C2×D44—44no—
138C2×D44C22⋊C414yes—
139C2×D44C22×C412yes—
140C2×D44C2×D412yes—
141C2×D44#4112yes—
142C2×C4×D11—28no—
143C2×C4×D11—24no—
144C2×C4×D11—22no—
145C2×C4×D11—22no—
146C2×C4×D11—22no—
147C2×C4×D11—22no—
148C2×C4×D11—44no—
149C2×C4×D11—44no—
150C2×C4×D11—44no—
151C2×C4×D11—44no—
152C2×C4×D11—42no—
153C2×C4×D11—42no—
154C2×C4×D11—82no—
155C2×C4×D11C22×C414yes—
156C2×C4×D11C2×D414yes—
157C2×C8×C11—22no—
158C2×C8×C11—22no—
159C2×C8×C11—22no—
160C11×C4⋊C4—24no—
161C11×C4⋊C4—24no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4C2×D412yes—
166C42×C11—42no—
167C42×C11C22×C412yes—
168C42×C11C2×D412yes—
169(C2×D11)⋊C4—28no—
170(C2×D11)⋊C4—24no—
171(C2×D11)⋊C4—44no—
172(C2×D11)⋊C4C22⋊C418yes—
173C4⋊Dic11—21no—
174C4⋊Dic11—22no—
175C4⋊Dic11—22no—
176C4⋊Dic11—42no—
177C4⋊Dic11—81no—
178C4⋊Dic11C22⋊C414yes—
179C4⋊Dic11C22×C412yes—
180Dic11⋊C4—28no—
181Dic11⋊C4—44no—
182C2×C11⋊C8—21no—
183C2×C11⋊C8—21no—
184C2×C11⋊C8—21no—
185C2×C11⋊C8—21no—
186C2×C11⋊C8—21no—
187C2×C11⋊C8C2×D412yes—
188#4313—48no—
189C2×#547—111no—
190C2×#436—111no—
191C2×#417—112no—
192D4×C4⋊C4—111no—
193#1981D1111yescharacteristic, complemented
194#1956—111no—
195#1894—112no—
196#1872—112no—
197#1802—111no—
198#1788—112no—
199C4×#102—111no—
200C23×C11C22×D411yescharacteristic
201C22×D11—22no—
202C22×D11—22no—
203C22×D11—22no—
204C22×D11—22no—
205C22×D11—22no—
206C22×D11—22no—
207C22×D11—22no—
208C22×D11—22no—
209C22×D11—22no—
210C22×D11—41no—
211C22×D11—41no—
212C22×D11—41no—
213C22×D11—41no—
214C22×D11C2×C22⋊C414yes—
215Q8×C11—24no—
216Q8×C11—24no—
217Q8×C11—42no—
218Q8×C11—42no—
219C2×C4×C11—21no—
220C2×C4×C11—21no—
221C2×C4×C11—24no—
222C2×C4×C11—22no—
223C2×C4×C11—42no—
224C2×C4×C11—42no—
225C2×C4×C11—41no—
226C2×C4×C11—41no—
227C2×C4×C11—41no—
228C2×C4×C11—41no—
229C2×C4×C11—41no—
230C2×C4×C11C2×C22⋊C412yes—
231C2×C4×C11C2×C22⋊C412yes—
232C2×C4×C11AGL(1,ℤ/8)12yes—
233C2×C4×C11#13712yes—
234C2×C4×C11C23×C411yescharacteristic
235C2×C4×C11C22×D411yescharacteristic
236C2×C4×C11C22×D411yescharacteristic
237C2×C4×C11C2×#4111yescharacteristic
238C2×C4×C11H(5,𝔽2)11yescharacteristic
239C2×C4×C11H(5,𝔽2)11yescharacteristic
240C2×Dic11—22no—
241C2×Dic11—22no—
242C2×Dic11—22no—
243C2×Dic11—41no—
244C2×Dic11—41no—
245C2×Dic11—42no—
246C2×Dic11—42no—
247C2×Dic11—42no—
248C2×Dic11C2×C22⋊C414yes—
249D44—22no—
250D44—22no—
251D44—22no—
252D44—28no—
253D44—416no—
254D44C4×D414yescomplemented
255C4×D11—24no—
256C4×D11—24no—
257C4×D11—24no—
258C4×D11—24no—
259C4×D11—416no—
260C4×D11—48no—
261C4×D11—88no—
262C8×C11—42no—
263C11⋊C8—22no—
264C11⋊C8—41no—
265C22×#41—112no—
266C22×M16—112no—
267#547—118no—
268#547—224no—
269C2×C4⋊Q8C2×D1111yescharacteristic
270C2×#123—222no—
271C2×C22⋊Q8—112no—
272C2×#121—221no—
273C2×C4×D4—111no—
274C2×C4×D4—111no—
275C2×C4×D4—221no—
276C22×C4⋊C4—112no—
277C22×C4⋊C4—221no—
278#436—224no—
279C2×C4⋊C8C2×D1111yescharacteristic
280#417—228no—
281C2×#103—112no—
282C2×#103—112no—
283C2×#103C2×D1112yes—
284C2×#103C2×D1112yes—
285C2×#102—111no—
286C2×#102—112no—
287C2×#102—111no—
288C2×C22⋊C8—112no—
289C2×C4×C8—111no—
290#389—221no—
291#385—222no—
292#384—111no—
293#380—112no—
294C4×C4⋊C4C2×D1111yescharacteristic
295#340—112no—
296#340—111no—
297#340—111no—
298C22×C11C22×C22⋊C411yescharacteristic
299C22×C11D4211yescharacteristic
300C22×C11#54611yescharacteristic
301C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
302C22×C11C2×#13711yescharacteristic
303C22×C11#57711yescharacteristic
304C22×C11#57811yescharacteristic
305C2×D11—24no—
306C2×D11—24no—
307C2×D11—24no—
308C2×D11—24no—
309C2×D11—42no—
310C2×D11—42no—
311C2×D11—42no—
312C2×D11—42no—
313C2×D11—42no—
314C2×D11—42no—
315C2×D11—42no—
316C2×D11—42no—
317C2×D11—42no—
318C2×D11—42no—
319C4×C11—22no—
320C4×C11—44no—
321C4×C11—42no—
322C4×C11—81no—
323C4×C11#41714yescomplemented
324C4×C11C2×C4×D411yescharacteristic
325C4×C11#51811yescharacteristic
326C4×C11D4211yescharacteristic
327C4×C11#54611yescharacteristic
328Dic11—24no—
329Dic11—42no—
330Dic11—82no—
331C2×#41—118no—
332C2×#41—224no—
333C2×#41—224no—
334C2×#41—224no—
335C2×#41—442no—
336C2×#41—442no—
337C22×Q8C22×D1112yes—
338C22×D4—111no—
339C22×D4—111no—
340C22×D4—222no—
341C23×C4—112no—
342C23×C4—222no—
343C23×C4—222no—
344C23×C4—221no—
345C2×M16—224no—
346C2×M16—224no—
347C2×M16—442no—
348C22×C8—111no—
349C22×C8—111no—
350C22×C8C22×D1112yes—
351C4⋊Q8—22no—
352C4⋊Q8C4×D1114yescomplemented
353#123—2216no—
354C22⋊Q8—118no—
355C22⋊Q8—224no—
356#121—228no—
357C4×D4—114no—
358C4×D4—114no—
359C4×D4—114no—
360C4×D4—222no—
361C4×D4—444no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—111no—
365C2×C4⋊C4—111no—
366C2×C4⋊C4—112no—
367C2×C4⋊C4—228no—
368C2×C4⋊C4—222no—
369C2×C4⋊C4—224no—
370C2×C4⋊C4—222no—
371C2×C4⋊C4—221no—
372C2×C4⋊C4—221no—
373C2×C4⋊C4—442no—
374C2×C4⋊C4C22×D1111yescharacteristic
375C2×C4⋊C4C22×D1111yescharacteristic
376C2×C22⋊C4—112no—
377C2×C22⋊C4—222no—
378C2×C22⋊C4—221no—
379C2×C22⋊C4—222no—
380C2×C42—21no—
381C2×C42C22×D1111yescharacteristic
382C4⋊C8—22no—
383#103—24no—
384#103—42no—
385#103—224no—
386#103—442no—
387#102—114no—
388#102—222no—
389#102—224no—
390C22⋊C8—224no—
391C4×C8—222no—
392#95—21no—
393#95—222no—
394C2×C11D4×C22⋊C411yescharacteristic
395C2×C11C2×#41711yescharacteristic
396C2×C11#289811yescharacteristic
397C2×C11#327211yescharacteristic
398C2×C11#327611yescharacteristic
399C2×C11#333011yescharacteristic
400C2×C11#333111yescharacteristic
401D11—44no—
402D11—44no—
403C24—112no—
404C24—221no—
405#41—2216no—
406#41—448no—
407#41—448no—
408#41—448no—
409C2×Q8—22no—
410C2×Q8—22no—
411C2×Q8—22no—
412C2×Q8—22no—
413C2×Q8—22no—
414C2×Q8C2×C4×D1114yes—
415C2×D4—114no—
416C2×D4—112no—
417C2×D4—112no—
418C2×D4—112no—
419C2×D4—228no—
420C2×D4—222no—
421C2×D4—222no—
422C2×D4—221no—
423C2×D4—221no—
424C2×D4—221no—
425C2×D4—444no—
426C2×D4—444no—
427C22×C4—21no—
428C22×C4—22no—
429C22×C4—21no—
430C22×C4—112no—
431C22×C4—114no—
432C22×C4—114no—
433C22×C4—228no—
434C22×C4—222no—
435C22×C4—222no—
436C22×C4—222no—
437C22×C4—222no—
438C22×C4—221no—
439C22×C4—224no—
440C22×C4—222no—
441C22×C4—444no—
442C22×C4—444no—
443C22×C4—444no—
444C22×C4—444no—
445C22×C4—442no—
446C22×C4—442no—
447C22×C4—882no—
448C22×C4D4×D1111yescharacteristic
449C22×C4D4×D1111yescharacteristic
450C22×C4C23×D1111yescharacteristic
451M16—448no—
452C2×C8—22no—
453C2×C8—22no—
454C2×C8—22no—
455C2×C8—112no—
456C2×C8—221no—
457C2×C8—221no—
458C2×C8—221no—
459C2×C8—221no—
460C2×C8—221no—
461C4⋊C4—24no—
462C4⋊C4—24no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—114no—
467C4⋊C4—112no—
468C4⋊C4—228no—
469C4⋊C4—221no—
470C4⋊C4—222no—
471C4⋊C4—222no—
472C4⋊C4—444no—
473C4⋊C4—442no—
474C4⋊C4—881no—
475C4⋊C4D4×D1112yes—
476C22⋊C4—118no—
477C22⋊C4—228no—
478C22⋊C4—224no—
479C22⋊C4—444no—
480C42—42no—
481C42C2×C4×D1112yes—
482C42D4×D1112yes—
483C11#2243111yescharacteristic, complemented, Sylow
484C23—114no—
485C23—222no—
486C23—222no—
487C23—222no—
488C23—222no—
489C23—222no—
490C23—222no—
491C23—222no—
492C23—222no—
493C23—222no—
494C23—441no—
495C23—441no—
496C23—441no—
497C23—441no—
498C23C2×D4×D1111yescharacteristic
499Q8—24no—
500Q8—24no—
501Q8—42no—
502Q8—42no—
503D4—114no—
504D4—222no—
505D4—222no—
506D4—228no—
507D4—222no—
508D4—4416no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—24no—
512C2×C4—22no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—114no—
521C2×C4—222no—
522C2×C4—222no—
523C2×C4—224no—
524C2×C4—224no—
525C2×C4—224no—
526C2×C4—224no—
527C2×C4—222no—
528C2×C4—4416no—
529C2×C4—441no—
530C2×C4—441no—
531C2×C4—448no—
532C2×C4—442no—
533C2×C4—442no—
534C2×C4—442no—
535C2×C4—888no—
536C2×C4C22⋊C4×D1112yes—
537C2×C4C22⋊C4×D1112yes—
538C2×C4#6696712yes—
539C2×C4#6697112yes—
540C2×C4C22×C4×D1111yescharacteristic
541C2×C4C2×D4×D1111yescharacteristic
542C2×C4C2×D4×D1111yescharacteristic
543C2×C4#6703711yescharacteristic
544C2×C4#41×D1111yescharacteristic
545C2×C4#6704211yescharacteristic
546C8—42no—
547C8—222no—
548C8—441no—
549C22—224no—
550C22—224no—
551C22—224no—
552C22—224no—
553C22—442no—
554C22—442no—
555C22—442no—
556C22—442no—
557C22—442no—
558C22—442no—
559C22—442no—
560C22—442no—
561C22—442no—
562C22—442no—
563C22C2×C22⋊C4×D1111yescharacteristic
564C22#1062314011yescharacteristic
565C22#1062314311yescharacteristic
566C22C2×#6696711yescharacteristic
567C22C2×#6697111yescharacteristic
568C22#1062330911yescharacteristic
569C22#1062331011yescharacteristic
570C4—22no—
571C4—44no—
572C4—42no—
573C4—81no—
574C4—224no—
575C4—442no—
576C4—882no—
577C4#1062241614yescomplemented
578C4C4×D4×D1111yescharacteristic
579C4#1062307611yescharacteristic
580C4#1062320711yescharacteristic
581C4#1062324811yescharacteristic
582C2—444no—
583C2—444no—
584C2#1307143711yescharacteristic
585C2C2×#1062241611yescharacteristic
586C2#1307714811yescharacteristic
587C2#1308021911yescharacteristic
588C2#1308025711yescharacteristic
589C2#1308092411yescharacteristic
590C2#1308093511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1981C2
socleC23×C11C22×D4
prime radicalC2×#10623257C2
cosocleC22×C4×C11C24
hypercenter#1981D11
hypocenterC11#22431
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1981

Complements

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

NH ≅ G/Ntype
2. C2×#10622451C2semidirect
3. C2×#10622416C2semidirect
4. C4⋊C4×D44C2semidirect
5. #13069419C2semidirect
6. #13069046C2semidirect
7. #13068920C2semidirect
8. #13068617C2semidirect
9. #13068555C2semidirect
10. C4×#66873C2semidirect
11. C11×#1981C2semidirect
17. #10623257C4semidirect
51. C2×#4343C2×C4semidirect
61. C11×C4⋊Q8C2×C4semidirect
69. #66999C2×C4semidirect
94. C4×D44C2×C4semidirect
106. #66873D4semidirect
193. #1981D11semidirect
254. D44C4×D4semidirect
323. C4×C11#417semidirect
352. C4⋊Q8C4×D11semidirect
483. C11#22431semidirect
577. C4#10622416semidirect

Maximal subgroups

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

subgroupindex
C2×#106232572
C2×#106224512
C2×#106224162
C4⋊C4×D442
#130694192
#130690462
#130689202
#130686172
#130685552
C4×#668732
C11×#19812
#2243111