Finite Group Databasebeta

← #14755192

Subgroups — #14755192

Order 2816.

1926 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66985C211yesmaximal, characteristic
2C2×#10623035C211yesmaximal, characteristic, complemented
3C2×#10622726C211yesmaximal, characteristic, complemented
4#13071198C211yesmaximal, characteristic, complemented
5#13068968C214yesmaximal, complemented
6#13068961C214yesmaximal, complemented
7#13068335C211yesmaximal, characteristic, complemented
8#13068312C211yesmaximal, characteristic, complemented
9C22×C11×#102C211yesmaximal, characteristic, complemented
10C23×D4×C11C2211yescharacteristic
11C22×#4339C2211yescharacteristic
12C23×C8×C11C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×#4324C2212yes—
15C2×#66985—24no—
16C2×#66985—24no—
17C2×#66985C418yescomplemented
18C22×#4323C2212yes—
19C2×C4×C22⋊D11—22no—
20C2×#66979C2211yescharacteristic
21C2×#66979C2211yescharacteristic
22C22×#4318C2211yescharacteristic
23#10623035—24no—
24#10623035—24no—
25C2×#66946C2212yescomplemented
26C2×#66945—21no—
27C2×C4⋊C4×D11—21no—
28C2×#66940C2212yescomplemented
29C2×C11×#102—24no—
30C2×C11×#102C2214yes—
31#10622860—22no—
32#10622834—21no—
33#10622834—21no—
34#10622834C2214yes—
35#10622726—24no—
36C2×#66885C2212yescomplemented
37C2×#66880C2212yescomplemented
38#10622188C2214yescomplemented
39#10622167C2214yescomplemented
40C25×C11—21no—
41C22×D4×C11—22no—
42C22×D4×C11—22no—
43C22×D4×C11—22no—
44C22×D4×C11—21no—
45C22×D4×C11—22no—
46C22×D4×C11—22no—
47C22×D4×C11C2×C414yescomplemented
48C22×D4×C11C2312yes—
49C23×C4×C11—21no—
50C23×C4×C11C2311yescharacteristic
51C22×C22⋊D11—21no—
52C2×#4339—22no—
53C2×#4339—22no—
54C2×#4339—22no—
55C2×#4339C2×C414yes—
56C2×#4339D414yes—
57C2×#4339D414yes—
58C22×D44C2311yescharacteristic
59C22×C4×D11—21no—
60C22×C4×D11—22no—
61C22×Dic22C2311yescharacteristic
62C22×C8×C11—22no—
63C22×C8×C11—22no—
64C22×C8×C11—22no—
65C22×C8×C11C2312yes—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4—22no—
68C2×C11×C4⋊C4D414yes—
69C2×C11×C4⋊C4C2312yes—
70C2×C22⋊Dic11—21no—
71C2×C22⋊Dic11—24no—
72C2×C22⋊Dic11—24no—
73C2×C22⋊Dic11D412yes—
74C2×#4324—24no—
75C2×#4324—24no—
76C2×#4324C2×C418yescomplemented
77#66985—232no—
78C2×#4323—24no—
79C2×#4323—24no—
80C2×#4323C2×C418yescomplemented
81C4×C22⋊D11—216no—
82C2×(C2×D11)⋊C4—22no—
83#66979—22no—
84#66979—22no—
85#66979—22no—
86#66979—22no—
87C2×C4⋊Dic11D411yescharacteristic
88C2×C4⋊Dic11D411yescharacteristic
89C2×C4⋊Dic11C2312yes—
90C2×Dic11⋊C4—22no—
91C2×C4×Dic11—22no—
92C2×C4×Dic11—21no—
93C2×C4×Dic11C2312yes—
94C2×#4318—22no—
95C2×#4318—22no—
96C2×#4318C2×C414yescomplemented
97C22×C11⋊C8C2312yes—
98#66946—24no—
99#66946—24no—
100#66945—28no—
101C4⋊C4×D11—28no—
102#66940—24no—
103#66940—24no—
104C11×#102—28no—
105#66885—24no—
106#66880—24no—
107#20932—111nomaximal, Sylow
108C24×C11—22no—
109C24×C11—24no—
110C24×C11—42no—
111C24×C11—42no—
112C24×C11—82no—
113C24×C11—82no—
114C24×C11C2×D411yescharacteristic
115C23×D11—21no—
116C2×D4×C11—28no—
117C2×D4×C11—28no—
118C2×D4×C11—24no—
119C2×D4×C11—22no—
120C2×D4×C11—22no—
121C2×D4×C11—22no—
122C2×D4×C11—22no—
123C2×D4×C11—22no—
124C2×D4×C11—42no—
125C2×D4×C11—42no—
126C2×D4×C11—44no—
127C2×D4×C11—44no—
128C2×D4×C11C22×C414yes—
129C22×C4×C11—22no—
130C22×C4×C11—24no—
131C22×C4×C11—82no—
132C22×C4×C11C22×C412yes—
133C22×C4×C11C2×D412yes—
134C22×C4×C11C2×D412yes—
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D412yes—
137C22×C4×C11#4112yes—
138C22×C4×C11#4112yes—
139C22×C4×C11C2411yescharacteristic
140C2×C22⋊D11—24no—
141C2×C22⋊D11—24no—
142C2×C22⋊D11—24no—
143C22×Dic11—21no—
144C22×Dic11—22no—
145C22×Dic11C2×D412yes—
146C22×Dic11C2×D412yes—
147#4339—28no—
148#4339—28no—
149#4339—28no—
150#4339C22⋊C4116yescomplemented
151C2×D44—21no—
152C2×D44—21no—
153C2×D44—21no—
154C2×D44C22×C412yes—
155C2×D44C2×D412yes—
156C2×D44C2×D412yes—
157C2×C4×D11—28no—
158C2×C4×D11—24no—
159C2×C4×D11—24no—
160C2×C4×D11—24no—
161C2×C4×D11—84no—
162C2×Dic22—21no—
163C2×Dic22—21no—
164C2×Dic22—21no—
165C2×Dic22C22×C412yes—
166C2×Dic22C2×D412yes—
167C2×Dic22C2×D412yes—
168C2×C8×C11—22no—
169C2×C8×C11—22no—
170C2×C8×C11—22no—
171C2×C8×C11—44no—
172C11×C4⋊C4—24no—
173C11×C4⋊C4—22no—
174C11×C4⋊C4C2×D414yes—
175C22⋊Dic11—24no—
176C22⋊Dic11—42no—
177C22⋊Dic11—84no—
178C22⋊Dic11—84no—
179#4324—216no—
180#4323—216no—
181(C2×D11)⋊C4—28no—
182C4⋊Dic11—22no—
183C4⋊Dic11—22no—
184C4⋊Dic11—22no—
185C4⋊Dic11—22no—
186Dic11⋊C4—28no—
187C4×Dic11—28no—
188C4×Dic11—22no—
189C4×Dic11—22no—
190C4×Dic11—42no—
191#4318—28no—
192C2×C11⋊C8—22no—
193C2×C11⋊C8—22no—
194C2×C11⋊C8C22×C414yes—
195C22×AGL(1,ℤ/8)—111no—
196C2×#520—111no—
197C2×#416—111no—
198C22×#102D1111yescharacteristic, complemented
199#2309—111no—
200#1880—114no—
201#1879—114no—
202#1736—111no—
203#1729—111no—
204C23×C11—22no—
205C23×C11—22no—
206C23×C11—24no—
207C23×C11—42no—
208C23×C11—42no—
209C23×C11—44no—
210C23×C11—44no—
211C23×C11—48no—
212C23×C11—88no—
213C23×C11—84no—
214C23×C11—84no—
215C23×C11—88no—
216C23×C11C4×D412yes—
217C23×C11#12012yes—
218C23×C11#12112yes—
219C23×C11C22×D411yescharacteristic
220C22×D11—22no—
221C22×D11—22no—
222C22×D11—22no—
223C22×D11—42no—
224C22×D11—42no—
225D4×C11—24no—
226D4×C11—24no—
227D4×C11—42no—
228D4×C11—42no—
229D4×C11—48no—
230C2×C4×C11—24no—
231C2×C4×C11—44no—
232C2×C4×C11—84no—
233C2×C4×C11C2×C22⋊C414yes—
234C2×C4×C11C4×D412yes—
235C2×C4×C11C4×D414yes—
236C2×C4×C11#12012yes—
237C2×C4×C11#12112yes—
238C2×C4×C11#12114yes—
239C2×C4×C11#12314yes—
240C2×C4×C11C23×C411yescharacteristic
241C2×C4×C11C22×D411yescharacteristic
242C2×C4×C11C22×D411yescharacteristic
243C2×C4×C11C22×D411yescharacteristic
244C2×C4×C11C2×#4111yescharacteristic
245C2×C4×C11C2×#4111yescharacteristic
246C22⋊D11—216no—
247C2×Dic11—22no—
248C2×Dic11—22no—
249C2×Dic11—22no—
250C2×Dic11—22no—
251C2×Dic11—22no—
252C2×Dic11—24no—
253C2×Dic11—24no—
254C2×Dic11—42no—
255C2×Dic11—42no—
256C2×Dic11—42no—
257D44—22no—
258D44—22no—
259D44—22no—
260D44C2×C22⋊C414yes—
261C4×D11—216no—
262C4×D11—88no—
263Dic22—22no—
264Dic22—22no—
265Dic22—22no—
266Dic22C2×C22⋊C414yes—
267C8×C11—42no—
268C11⋊C8—24no—
269C22×#41—111no—
270C23×D4C2×D1111yescharacteristic
271C2×AGL(1,ℤ/8)—118no—
272C2×AGL(1,ℤ/8)—224no—
273C2×AGL(1,ℤ/8)—224no—
274C22×SD16—112no—
275C22×D8—112no—
276C22×M16—111no—
277C23×C8C2×D1111yescharacteristic
278#520—224no—
279#520—224no—
280C2×C4×Q8—112no—
281C2×C4×D4—112no—
282C2×C4×D4—222no—
283C2×#117—111no—
284C2×#117—111no—
285C2×#117—221no—
286C22×C4⋊C4—221no—
287C22×C4⋊C4C2×D1111yescharacteristic
288#416—224no—
289C2×#103—112no—
290C2×#102—24no—
291C2×#102—112no—
292C2×#102C2×D1114yes—
293#390—114no—
294#390—221no—
295#390—221no—
296#379—222no—
297#340—114no—
298#336—114no—
299C22×C11—24no—
300C22×C11—22no—
301C22×C11—22no—
302C22×C11—24no—
303C22×C11—48no—
304C22×C11—44no—
305C22×C11—816no—
306C22×C11—82no—
307C22×C11—82no—
308C22×C11—84no—
309C22×C11#38614yes—
310C22×C11C2×C4×D411yescharacteristic
311C22×C11C2×#12011yescharacteristic
312C22×C11C2×#12111yescharacteristic
313C22×C11#57612yes—
314C22×C11#57712yes—
315C2×D11—24no—
316C2×D11—44no—
317C2×D11—42no—
318C2×D11—42no—
319C2×D11—44no—
320C4×C11—44no—
321C4×C11#38614yes—
322C4×C11C22×C22⋊C411yescharacteristic
323C4×C11C2×C4×D411yescharacteristic
324C4×C11C2×#12111yescharacteristic
325C4×C11C2×#12311yescharacteristic
326Dic11—24no—
327Dic11—42no—
328Dic11—42no—
329Dic11—82no—
330C25—21no—
331C2×#41—114no—
332C2×#41—114no—
333C2×#41—114no—
334C2×#41—222no—
335C2×#41—222no—
336C2×#41—222no—
337C22×Q8—111no—
338C22×D4—22no—
339C22×D4—22no—
340C22×D4—22no—
341C22×D4—21no—
342C22×D4—22no—
343C22×D4—22no—
344C22×D4—111no—
345C22×D4—221no—
346C22×D4C4×D1114yescomplemented
347C22×D4C22×D1112yes—
348C23×C4—21no—
349C23×C4—222no—
350C23×C4—221no—
351C23×C4C22×D1111yescharacteristic
352AGL(1,ℤ/8)—2232no—
353C2×SD16—118no—
354C2×SD16—224no—
355C2×SD16—224no—
356C2×D8—118no—
357C2×D8—224no—
358C2×D8—224no—
359C2×M16—114no—
360C2×M16—222no—
361C2×M16—222no—
362C22×C8—22no—
363C22×C8—22no—
364C22×C8—22no—
365C22×C8—112no—
366C22×C8C22×D1112yes—
367C4×Q8—224no—
368C4×Q8—224no—
369C4×D4—224no—
370C4×D4—2216no—
371C4×D4—224no—
372#117—228no—
373#117—222no—
374#117—222no—
375#117—222no—
376#117—222no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—111no—
380C2×C4⋊C4—111no—
381C2×C4⋊C4—112no—
382C2×C4⋊C4—228no—
383C2×C4⋊C4—222no—
384C2×C4⋊C4C22⋊D1114yes—
385C2×C4⋊C4C22×D1112yes—
386C2×C22⋊C4—112no—
387C2×C22⋊C4—222no—
388C2×C22⋊C4—221no—
389C2×C22⋊C4—224no—
390C2×C22⋊C4—224no—
391C2×C42—112no—
392C2×C42—222no—
393C2×C42—221no—
394#103—224no—
395#102—28no—
396#102—224no—
397C2×C11—24no—
398C2×C11—84no—
399C2×C11C2×#38611yescharacteristic
400C2×C11#294612yes—
401C2×C11#300811yescharacteristic
402C2×C11#301011yescharacteristic
403C2×C11#304512yes—
404D11—44no—
405C24—22no—
406C24—24no—
407C24—42no—
408C24—42no—
409C24—82no—
410C24—82no—
411C24—221no—
412C24D4×D1111yescharacteristic
413#41—1116no—
414#41—228no—
415#41—228no—
416#41—228no—
417C2×Q8—112no—
418C2×Q8—112no—
419C2×Q8—112no—
420C2×Q8—221no—
421C2×Q8—221no—
422C2×Q8—221no—
423C2×D4—28no—
424C2×D4—24no—
425C2×D4—28no—
426C2×D4—22no—
427C2×D4—22no—
428C2×D4—22no—
429C2×D4—22no—
430C2×D4—22no—
431C2×D4—44no—
432C2×D4—42no—
433C2×D4—42no—
434C2×D4—44no—
435C2×D4—112no—
436C2×D4—112no—
437C2×D4—112no—
438C2×D4—224no—
439C2×D4—224no—
440C2×D4—224no—
441C2×D4—221no—
442C2×D4—221no—
443C2×D4—221no—
444C2×D4C2×C4×D1114yes—
445C22×C4—22no—
446C22×C4—24no—
447C22×C4—82no—
448C22×C4—112no—
449C22×C4—112no—
450C22×C4—228no—
451C22×C4—221no—
452C22×C4—224no—
453C22×C4—224no—
454C22×C4—224no—
455C22×C4—222no—
456C22×C4—884no—
457C22×C4C2×C4×D1112yes—
458C22×C4#433912yes—
459C22×C4D4×D1112yes—
460C22×C4D4×D1112yes—
461C22×C4D4×D1111yescharacteristic
462C22×C4#434112yes—
463C22×C4C2×C22⋊D1112yes—
464C22×C4C23×D1111yescharacteristic
465SD16—2216no—
466D8—2216no—
467M16—228no—
468C2×C8—22no—
469C2×C8—22no—
470C2×C8—22no—
471C2×C8—44no—
472C2×C8—114no—
473C2×C8—222no—
474C2×C8—222no—
475C4⋊C4—24no—
476C4⋊C4—22no—
477C4⋊C4—228no—
478C4⋊C4—222no—
479C4⋊C4—222no—
480C4⋊C4—222no—
481C4⋊C4—222no—
482C4⋊C4C2×C22⋊D1114yes—
483C22⋊C4—228no—
484C22⋊C4—224no—
485C22⋊C4—442no—
486C22⋊C4—884no—
487C22⋊C4—884no—
488C42—228no—
489C42—222no—
490C42—222no—
491C42—442no—
492C11#2093211yescharacteristic, complemented, Sylow
493C23—22no—
494C23—22no—
495C23—24no—
496C23—42no—
497C23—44no—
498C23—44no—
499C23—42no—
500C23—48no—
501C23—88no—
502C23—84no—
503C23—84no—
504C23—88no—
505C23—222no—
506C23—222no—
507C23—222no—
508C23—442no—
509C23—442no—
510C23(C22⋊D11)⋊C412yes—
511C23#6693712yes—
512C23#6699012yes—
513C23C2×D4×D1111yescharacteristic
514Q8—114no—
515Q8—222no—
516Q8—222no—
517Q8—222no—
518D4—24no—
519D4—24no—
520D4—42no—
521D4—42no—
522D4—48no—
523D4—114no—
524D4—2216no—
525D4—222no—
526D4—222no—
527D4—222no—
528C2×C4—24no—
529C2×C4—44no—
530C2×C4—84no—
531C2×C4—222no—
532C2×C4—222no—
533C2×C4—222no—
534C2×C4—2216no—
535C2×C4—224no—
536C2×C4—224no—
537C2×C4—222no—
538C2×C4—222no—
539C2×C4—442no—
540C2×C4—442no—
541C2×C4—442no—
542C2×C4—888no—
543C2×C4C22⋊C4×D1114yes—
544C2×C4(C22⋊D11)⋊C412yes—
545C2×C4#6693614yes—
546C2×C4#6693712yes—
547C2×C4C4×C22⋊D1114yes—
548C2×C4#6699012yes—
549C2×C4#6699114yes—
550C2×C4C22×C4×D1111yescharacteristic
551C2×C4C2×#433911yescharacteristic
552C2×C4C2×D4×D1111yescharacteristic
553C2×C4C2×D4×D1111yescharacteristic
554C2×C4C2×#434111yescharacteristic
555C2×C4C22×C22⋊D1111yescharacteristic
556C8—42no—
557C8—224no—
558C22—22no—
559C22—22no—
560C22—24no—
561C22—24no—
562C22—44no—
563C22—48no—
564C22—816no—
565C22—82no—
566C22—82no—
567C22—84no—
568C22—224no—
569C22—442no—
570C22—442no—
571C22—444no—
572C22—444no—
573C22#1062256914yes—
574C22C2×(C22⋊D11)⋊C411yescharacteristic
575C22C2×#6693711yescharacteristic
576C22#1062328812yes—
577C22#1062329312yes—
578C22C2×#6699011yescharacteristic
579C4—44no—
580C4—224no—
581C4—442no—
582C4—442no—
583C4—882no—
584C4#1062256914yes—
585C4C2×C22⋊C4×D1111yescharacteristic
586C4C2×#6693611yescharacteristic
587C4C2×C4×C22⋊D1111yescharacteristic
588C4C2×#6699111yescharacteristic
589C2—24no—
590C2—84no—
591C2—444no—
592C2C2×#1062256911yescharacteristic
593C2#1307744212yes—
594C2#1307788011yescharacteristic
595C2#1307789811yescharacteristic
596C2#1307816012yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC22×C11×#102C2
socleC23×C11C22×D4
prime radicalC22×#66985C2
cosocleC22×C4×C11C24
hypercenterC22×#102D11
hypocenterC11#20932
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#102

Complements

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

NH ≅ G/Ntype
2. C2×#10623035C2semidirect
3. C2×#10622726C2semidirect
4. #13071198C2semidirect
5. #13068968C2semidirect
6. #13068961C2semidirect
7. #13068335C2semidirect
8. #13068312C2semidirect
9. C22×C11×#102C2semidirect
17. C2×#66985C4semidirect
25. C2×#66946C22semidirect
28. C2×#66940C22semidirect
36. C2×#66885C22semidirect
37. C2×#66880C22semidirect
38. #10622188C22semidirect
39. #10622167C22semidirect
47. C22×D4×C11C2×C4semidirect
76. C2×#4324C2×C4semidirect
80. C2×#4323C2×C4semidirect
96. C2×#4318C2×C4semidirect
150. #4339C22⋊C4semidirect
198. C22×#102D11semidirect
346. C22×D4C4×D11semidirect
492. C11#20932semidirect

Maximal subgroups

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

subgroupindex
C22×#669852
C2×#106230352
C2×#106227262
#130711982
#130689682
#130689612
#130683352
#130683122
C22×C11×#1022
#2093211