Finite Group Databasebeta

← #14755038

Subgroups — #14755038

Order 2816.

1970 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623361C211yesmaximal, characteristic
2C2×#10622614C211yesmaximal, characteristic, complemented
3C22×#66873C211yesmaximal, characteristic, complemented
4C2×#10622847C211yesmaximal, characteristic, complemented
5#13068938C214yesmaximal, complemented
6#13068933C214yesmaximal, complemented
7#13068335C211yesmaximal, characteristic, complemented
8#13068332C211yesmaximal, characteristic, complemented
9C2×C11×#520C211yesmaximal, characteristic, complemented
10C22×C11×#41C2211yescharacteristic
11C23×D44C2211yescharacteristic
12C11×#520—24no—
13C11×#520—24no—
14C2×C4×Q8×C11—21no—
15C2×C4×D4×C11—21no—
16C2×C4×D4×C11—22no—
17C2×C11×#117C2211yescharacteristic
18C2×C11×#117C2212yescomplemented
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C11×C4⋊C4C2212yescomplemented
21#10623361—24no—
22#10623361C418yescomplemented
23C2×#67000—21no—
24C2×#66993—21no—
25C2×#66990—22no—
26C2×#66983C2214yes—
27C2×#66979C2211yescharacteristic
28C22×#4318C2211yescharacteristic
29C23×C11⋊C8C2211yescharacteristic
30#10622847—24no—
31C2×C22⋊(C11⋊C8)C2214yescomplemented
32#10622614—24no—
33C2×#66873—24no—
34C2×#66873C2214yes—
35C2×#66873C2212yes—
36C2×#66873C2212yes—
37#10622167C2212yescomplemented
38#10622167C2212yescomplemented
39#10622167C2214yescomplemented
40C24×D11—21no—
41C2×C11×#41—22no—
42C2×C11×#41—22no—
43C2×C11×#41—22no—
44C2×C11×#41—22no—
45C2×C11×#41C2×C414yes—
46C2×C11×#41D414yes—
47C22×Q8×C11D411yescharacteristic
48C22×D4×C11D412yes—
49C22×D4×C11D411yescharacteristic
50C23×C4×C11—21no—
51C23×C4×C11—22no—
52C23×C4×C11C2312yes—
53C23×C4×C11C2311yescharacteristic
54C22×C22⋊D11—24no—
55C22×D44—22no—
56C22×D44—22no—
57C22×D44—22no—
58C22×D44—22no—
59C22×D44—21no—
60C22×D44—22no—
61C22×D44C2×C414yescomplemented
62C22×D44C2312yes—
63C4×Q8×C11—28no—
64C4×D4×C11—216no—
65C4×D4×C11—28no—
66C11×#117—22no—
67C11×#117—24no—
68C11×#117—24no—
69C11×#117D414yescomplemented
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—22no—
72C2×C11×C4⋊C4—22no—
73C2×C11×C4⋊C4—24no—
74C2×C11×C4⋊C4—24no—
75C2×C11×C4⋊C4D414yescomplemented
76C2×C11×C4⋊C4C2312yes—
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C22⋊C4—21no—
80C2×C11×C22⋊C4—22no—
81C2×C42×C11—21no—
82C2×C42×C11—22no—
83C2×C22⋊Dic11—21no—
84#67000—28no—
85#66993—28no—
86#66990—216no—
87#66983—28no—
88#66983C2×C4116yescomplemented
89C2×(C2×D11)⋊C4—24no—
90#66979—22no—
91#66979C2×C414yescomplemented
92C2×C4⋊Dic11C2312yes—
93C2×C4×Dic11—21no—
94C2×#4318—22no—
95C2×#4318—22no—
96C2×#4318—22no—
97C22×C11⋊C8—22no—
98C22×C11⋊C8—22no—
99C22×C11⋊C8—22no—
100C22×C11⋊C8C2312yes—
101C22×C11⋊C8C2312yes—
102C22⋊(C11⋊C8)—28no—
103#66873—28no—
104#66873—24no—
105#66873—24no—
106#20914—111nomaximal, Sylow
107C24×C11C2×D412yes—
108C24×C11C2×D411yescharacteristic
109C23×D11—22no—
110C23×D11—24no—
111C23×D11—42no—
112C23×D11—42no—
113C23×D11—82no—
114C23×D11—82no—
115C11×#41—28no—
116C11×#41—28no—
117C11×#41—28no—
118C11×#41—28no—
119C2×Q8×C11—22no—
120C2×Q8×C11—22no—
121C2×Q8×C11C22⋊C414yes—
122C2×D4×C11—24no—
123C2×D4×C11—24no—
124C2×D4×C11—22no—
125C2×D4×C11—22no—
126C2×D4×C11C22⋊C418yes—
127C2×D4×C11C22⋊C414yes—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—22no—
135C22×C4×C11—28no—
136C22×C4×C11—24no—
137C22×C4×C11—82no—
138C22×C4×C11—84no—
139C22×C4×C11C22×C414yes—
140C22×C4×C11C22×C412yes—
141C22×C4×C11C2×D412yes—
142C22×C4×C11C2×D414yes—
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D412yes—
145C22×C4×C11C2×D412yes—
146C22×C4×C11C2×D412yes—
147C22×C4×C11#4112yes—
148C22×C4×C11#4112yes—
149C22×C4×C11C2411yescharacteristic
150C2×C22⋊D11—216no—
151C2×C22⋊D11—84no—
152C2×C22⋊D11—84no—
153C22×Dic11—22no—
154C2×D44—24no—
155C2×D44—28no—
156C2×D44—28no—
157C2×D44—22no—
158C2×D44—22no—
159C2×D44—22no—
160C2×D44—22no—
161C2×D44—22no—
162C2×D44—42no—
163C2×D44—44no—
164C2×D44—44no—
165C2×D44—42no—
166C2×D44C22×C414yes—
167C11×C4⋊C4—28no—
168C11×C4⋊C4—24no—
169C11×C4⋊C4—22no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4C2×D412yes—
173C11×C4⋊C4C2×D414yes—
174C11×C4⋊C4C2×D412yes—
175C11×C22⋊C4—28no—
176C11×C22⋊C4—24no—
177C42×C11—28no—
178C42×C11—24no—
179C22⋊Dic11—24no—
180(C2×D11)⋊C4—216no—
181C4⋊Dic11—22no—
182C4⋊Dic11C22×C414yes—
183C4×Dic11—24no—
184#4318—44no—
185C2×C11⋊C8—22no—
186C2×C11⋊C8—22no—
187C2×C11⋊C8—22no—
188C2×C11⋊C8—22no—
189C2×C11⋊C8—22no—
190C2×C11⋊C8—22no—
191C2×C11⋊C8—44no—
192C2×#535—111no—
193C2×#520D1111yescharacteristic, complemented
194C2×#418—111no—
195C22×#102—111no—
196C2×#408—111no—
197#1875—114no—
198#1874—114no—
199#1736—111no—
200#1735—111no—
201C23×C11—22no—
202C23×C11—22no—
203C23×C11—22no—
204C23×C11—22no—
205C23×C11—24no—
206C23×C11—24no—
207C23×C11C2×C22⋊C414yes—
208C23×C11C2×C22⋊C412yes—
209C23×C11#12012yes—
210C23×C11#12312yes—
211C23×C11C22×D411yescharacteristic
212C22×D11—24no—
213C22×D11—42no—
214C22×D11—42no—
215C22×D11—44no—
216C22×D11—44no—
217C22×D11—48no—
218C22×D11—88no—
219C22×D11—88no—
220C22×D11—84no—
221C22×D11—84no—
222Q8×C11—28no—
223D4×C11—216no—
224D4×C11—28no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—24no—
228C2×C4×C11—24no—
229C2×C4×C11—24no—
230C2×C4×C11—24no—
231C2×C4×C11—22no—
232C2×C4×C11—24no—
233C2×C4×C11—22no—
234C2×C4×C11—44no—
235C2×C4×C11—42no—
236C2×C4×C11—42no—
237C2×C4×C11—84no—
238C2×C4×C11—88no—
239C2×C4×C11C2×C22⋊C414yes—
240C2×C4×C11C2×C22⋊C412yes—
241C2×C4×C11C4×D414yes—
242C2×C4×C11C4×D414yes—
243C2×C4×C11#12012yes—
244C2×C4×C11#12114yes—
245C2×C4×C11#12114yes—
246C2×C4×C11#12312yes—
247C2×C4×C11C23×C411yescharacteristic
248C2×C4×C11C22×D411yescharacteristic
249C2×C4×C11C22×D411yescharacteristic
250C2×C4×C11C22×D411yescharacteristic
251C2×C4×C11C2×#4111yescharacteristic
252C2×C4×C11C2×#4111yescharacteristic
253C22⋊D11—816no—
254C2×Dic11—24no—
255C2×Dic11—42no—
256C2×Dic11—42no—
257D44—24no—
258D44—24no—
259D44—42no—
260D44—42no—
261D44—48no—
262C11⋊C8—42no—
263C11⋊C8—42no—
264C22×#41C2×D1111yescharacteristic
265C23×D4—111no—
266C22×M16—111no—
267C23×C8—111no—
268#535—118no—
269#535—224no—
270C2×#127—221no—
271C2×#124—221no—
272C2×#121—114no—
273C2×#120—222no—
274#520—24no—
275#520—24no—
276C2×C4×Q8—21no—
277C2×C4×D4—21no—
278C2×C4×D4—22no—
279C2×#117—111no—
280C2×#117C2×D1111yescharacteristic
281C2×#117C2×D1112yescomplemented
282C22×C4⋊C4C2×D1111yescharacteristic
283C22×C4⋊C4C2×D1112yescomplemented
284#418—224no—
285C2×#102—114no—
286C2×#102—112no—
287C2×#102—112no—
288C2×#102—224no—
289#408—224no—
290C2×C22⋊C8—114no—
291#340—112no—
292#340—114no—
293#340—112no—
294C22×C11—24no—
295C22×C11—24no—
296C22×C11—22no—
297C22×C11—22no—
298C22×C11—28no—
299C22×C11—24no—
300C22×C11—44no—
301C22×C11—42no—
302C22×C11—42no—
303C22×C11#38614yes—
304C22×C11C22×C22⋊C411yescharacteristic
305C22×C11C2×#12011yescharacteristic
306C22×C11C2×#12311yescharacteristic
307C22×C11#57612yes—
308C22×C11#57712yes—
309C2×D11—48no—
310C2×D11—44no—
311C2×D11—816no—
312C2×D11—84no—
313C2×D11—82no—
314C2×D11—82no—
315C4×C11—24no—
316C4×C11—44no—
317C4×C11—42no—
318C4×C11—42no—
319C4×C11#38614yes—
320C4×C11C2×C4×D411yescharacteristic
321C4×C11C2×C4×D411yescharacteristic
322C4×C11C2×#12111yescharacteristic
323C4×C11C2×#12111yescharacteristic
324Dic11—44no—
325C25—221no—
326C2×#41—22no—
327C2×#41—22no—
328C2×#41—22no—
329C2×#41—22no—
330C2×#41C4×D1114yes—
331C2×#41D4414yes—
332C22×Q8C22⋊D1111yescharacteristic
333C22×D4—114no—
334C22×D4—112no—
335C22×D4—224no—
336C22×D4—222no—
337C22×D4—222no—
338C22×D4—222no—
339C22×D4—222no—
340C22×D4—222no—
341C22×D4—221no—
342C22×D4C22⋊D1112yes—
343C22×D4C22⋊D1111yescharacteristic
344C23×C4—21no—
345C23×C4—22no—
346C23×C4C22×D1112yes—
347C23×C4C22×D1111yescharacteristic
348C2×M16—222no—
349C2×M16—222no—
350C2×M16—222no—
351C22×C8—112no—
352C22×C8—112no—
353C22×C8—222no—
354C22×C8—222no—
355C22×C8—222no—
356#127—228no—
357#124—228no—
358#121—1116no—
359#121—228no—
360#120—2216no—
361C4×Q8—28no—
362C4×D4—216no—
363C4×D4—28no—
364#117—22no—
365#117—24no—
366#117—24no—
367#117—114no—
368#117—222no—
369#117C22⋊D1114yescomplemented
370C2×C4⋊C4—21no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—24no—
374C2×C4⋊C4—24no—
375C2×C4⋊C4—112no—
376C2×C4⋊C4C22⋊D1114yescomplemented
377C2×C4⋊C4C22×D1112yes—
378C2×C4⋊C4C22×D1111yescharacteristic
379C2×C4⋊C4C22×D1111yescharacteristic
380C2×C22⋊C4—21no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—221no—
383C2×C22⋊C4—224no—
384C2×C42—21no—
385C2×C42—22no—
386C2×C42—221no—
387#102—228no—
388#102—224no—
389#102—224no—
390C22⋊C8—228no—
391C2×C11—24no—
392C2×C11—44no—
393C2×C11C2×#38611yescharacteristic
394C2×C11#289712yes—
395C2×C11#300811yescharacteristic
396C2×C11#301011yescharacteristic
397C2×C11#309612yes—
398D11—84no—
399C24—222no—
400C24—224no—
401C24—442no—
402C24—442no—
403C24—882no—
404C24—882no—
405C24C2×C22⋊D1112yes—
406C24C2×C22⋊D1111yescharacteristic
407#41—28no—
408#41—28no—
409#41—28no—
410#41—28no—
411C2×Q8—22no—
412C2×Q8—22no—
413C2×Q8(C2×D11)⋊C414yes—
414C2×D4—24no—
415C2×D4—24no—
416C2×D4—22no—
417C2×D4—22no—
418C2×D4—114no—
419C2×D4—2216no—
420C2×D4—224no—
421C2×D4—228no—
422C2×D4—228no—
423C2×D4—222no—
424C2×D4—222no—
425C2×D4—222no—
426C2×D4—222no—
427C2×D4—222no—
428C2×D4—442no—
429C2×D4—444no—
430C2×D4—444no—
431C2×D4—442no—
432C2×D4—884no—
433C2×D4—884no—
434C2×D4(C2×D11)⋊C418yes—
435C2×D4(C2×D11)⋊C414yes—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—22no—
443C22×C4—28no—
444C22×C4—24no—
445C22×C4—82no—
446C22×C4—84no—
447C22×C4—222no—
448C22×C4C2×C4×D1114yes—
449C22×C4C2×C4×D1112yes—
450C22×C4C2×D4414yes—
451C22×C4C2×D4412yes—
452C22×C4#433912yes—
453C22×C4#433912yes—
454C22×C4C2×C22⋊D1112yes—
455C22×C4C2×C22⋊D1111yescharacteristic
456C22×C4C2×C22⋊D1112yes—
457C22×C4C2×C22⋊D1112yes—
458C22×C4C23×D1111yescharacteristic
459M16—444no—
460C2×C8—222no—
461C2×C8—222no—
462C2×C8—222no—
463C2×C8—222no—
464C2×C8—222no—
465C2×C8—222no—
466C2×C8—444no—
467C4⋊C4—28no—
468C4⋊C4—24no—
469C4⋊C4—22no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—114no—
473C4⋊C4—222no—
474C4⋊C4C2×C22⋊D1112yes—
475C4⋊C4C2×C22⋊D1114yes—
476C4⋊C4C2×C22⋊D1112yes—
477C22⋊C4—28no—
478C22⋊C4—24no—
479C22⋊C4—224no—
480C22⋊C4—2216no—
481C42—28no—
482C42—24no—
483C42—224no—
484C11#2091411yescharacteristic, complemented, Sylow
485C23—22no—
486C23—22no—
487C23—22no—
488C23—24no—
489C23—24no—
490C23—22no—
491C23—224no—
492C23—442no—
493C23—448no—
494C23—444no—
495C23—444no—
496C23—442no—
497C23—888no—
498C23—888no—
499C23—884no—
500C23—884no—
501C23C2×(C2×D11)⋊C414yes—
502C23C2×(C2×D11)⋊C412yes—
503C23#6698212yes—
504C23#6700612yes—
505C23C22×C22⋊D1111yescharacteristic
506Q8—28no—
507D4—216no—
508D4—28no—
509D4—224no—
510D4—224no—
511D4—442no—
512D4—442no—
513D4—448no—
514D4—8816no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—24no—
518C2×C4—24no—
519C2×C4—24no—
520C2×C4—24no—
521C2×C4—22no—
522C2×C4—24no—
523C2×C4—22no—
524C2×C4—44no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—84no—
528C2×C4—88no—
529C2×C4—224no—
530C2×C4—442no—
531C2×C4—442no—
532C2×C4C2×(C2×D11)⋊C414yes—
533C2×C4C2×(C2×D11)⋊C412yes—
534C2×C4C4×C22⋊D1114yes—
535C2×C4C4×C22⋊D1114yes—
536C2×C4#6698212yes—
537C2×C4#6698314yes—
538C2×C4#6698314yes—
539C2×C4#6700612yes—
540C2×C4C22×C4×D1111yescharacteristic
541C2×C4C22×D4411yescharacteristic
542C2×C4C2×#433911yescharacteristic
543C2×C4C2×#433911yescharacteristic
544C2×C4C22×C22⋊D1111yescharacteristic
545C2×C4C22×C22⋊D1111yescharacteristic
546C8—442no—
547C8—442no—
548C22—24no—
549C22—22no—
550C22—22no—
551C22—24no—
552C22—28no—
553C22—24no—
554C22—44no—
555C22—42no—
556C22—42no—
557C22—448no—
558C22—444no—
559C22—8816no—
560C22—884no—
561C22—882no—
562C22—882no—
563C22#1062282614yes—
564C22C22×(C2×D11)⋊C411yescharacteristic
565C22C2×#6698211yescharacteristic
566C22#1062336612yes—
567C22#1062336812yes—
568C22C2×#6700611yescharacteristic
569C4—24no—
570C4—44no—
571C4—42no—
572C4—42no—
573C4—444no—
574C4#1062282614yes—
575C4C2×C4×C22⋊D1111yescharacteristic
576C4C2×C4×C22⋊D1111yescharacteristic
577C4C2×#6698311yescharacteristic
578C4C2×#6698311yescharacteristic
579C2—24no—
580C2—44no—
581C2—884no—
582C2C2×#1062282611yescharacteristic
583C2#1307713912yes—
584C2#1307788411yescharacteristic
585C2#1307790211yescharacteristic
586C2#1307857412yes—
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#520C2
socleC23×C11C22×D4
prime radicalC2×#10623361C2
cosocleC22×C4×C11C24
hypercenterC2×#520D11
hypocenterC11#20914
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×#41 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
2. C2×#10622614C2semidirect
3. C22×#66873C2semidirect
4. C2×#10622847C2semidirect
5. #13068938C2semidirect
6. #13068933C2semidirect
7. #13068335C2semidirect
8. #13068332C2semidirect
9. C2×C11×#520C2semidirect
18. C2×C11×#117C22semidirect
20. C22×C11×C4⋊C4C22semidirect
22. #10623361C4semidirect
31. C2×C22⋊(C11⋊C8)C22semidirect
37. #10622167C22semidirect
38. #10622167C22semidirect
39. #10622167C22semidirect
61. C22×D44C2×C4semidirect
69. C11×#117D4semidirect
75. C2×C11×C4⋊C4D4semidirect
88. #66983C2×C4semidirect
91. #66979C2×C4semidirect
193. C2×#520D11semidirect
281. C2×#117C2×D11semidirect
283. C22×C4⋊C4C2×D11semidirect
369. #117C22⋊D11semidirect
376. C2×C4⋊C4C22⋊D11semidirect
484. C11#20914semidirect

Maximal subgroups

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

subgroupindex
C2×#106233612
C2×#106226142
C22×#668732
C2×#106228472
#130689382
#130689332
#130683352
#130683322
C2×C11×#5202
#2091411