Finite Group Databasebeta

← #14780583

Subgroups — #14780583

Order 2816.

2334 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#4323C211yesmaximal, characteristic, complemented
2C2×#10623361C211yesmaximal, characteristic, complemented
3C2×#10622828C211yesmaximal, characteristic, complemented
4C2×#10622614C211yesmaximal, characteristic, complemented
5C2×#10622847C211yesmaximal, characteristic, complemented
6#13069612C218yesmaximal, complemented
7#13068332C211yesmaximal, characteristic, complemented
8C2×C11×#535C211yesmaximal, characteristic, complemented
9C22×C11×#41C2211yescharacteristic
10C23×D4×C11C2211yescharacteristic
11C23×D44C2211yescharacteristic
12C11×#535—24no—
13C11×#535—24no—
14C2×C11×#127—21no—
15C2×C11×#124—21no—
16C2×C11×#121C2214yescomplemented
17C2×C11×#120—22no—
18C2×C11×#117C2211yescharacteristic
19#10623361—24no—
20#10623361—24no—
21C2×#67000—21no—
22C2×#66993—21no—
23C2×#66990—22no—
24C22×#4323—24no—
25C22×#4323—24no—
26C22×#4323—24no—
27C22×#4323C2214yes—
28C2×#66983C2214yescomplemented
29C2×#66979C2211yescharacteristic
30C22×#4318C2211yescharacteristic
31C23×C11⋊C8C2211yescharacteristic
32#10622847—24no—
33#10622828—24no—
34C2×#66896C2214yescomplemented
35C2×C22⋊(C11⋊C8)C2214yescomplemented
36#10622614—24no—
37C2×#66873C2214yescomplemented
38#10622167C2214yescomplemented
39C25×C11—21no—
40C24×D11—21no—
41C2×C11×#41—22no—
42C2×C11×#41—22no—
43C2×C11×#41—22no—
44C2×C11×#41—22no—
45C2×C11×#41—22no—
46C2×C11×#41—22no—
47C22×Q8×C11D411yescharacteristic
48C22×D4×C11—24no—
49C22×D4×C11—22no—
50C22×D4×C11—22no—
51C22×D4×C11—22no—
52C22×D4×C11—21no—
53C22×D4×C11—22no—
54C22×D4×C11—22no—
55C22×D4×C11D412yes—
56C22×D4×C11D411yescharacteristic
57C22×D4×C11D414yescomplemented
58C22×D4×C11C2312yes—
59C23×C4×C11C2312yes—
60C23×C4×C11C2311yescharacteristic
61C22×C22⋊D11—24no—
62C22×D44—22no—
63C22×D44—22no—
64C22×D44—22no—
65C22×D44—22no—
66C22×D44—21no—
67C22×D44—22no—
68C22×D44D414yescomplemented
69C22×D44C2312yes—
70C11×#127—28no—
71C11×#124—28no—
72C11×#121—28no—
73C11×#121—28no—
74C11×#120—216no—
75C11×#117—22no—
76C11×#117D414yescomplemented
77C2×C11×C4⋊C4C2312yes—
78C2×C11×C22⋊C4—21no—
79C2×C11×C22⋊C4—24no—
80C2×C42×C11—21no—
81C2×C22⋊Dic11—21no—
82#67000—28no—
83#66993—28no—
84#66990—216no—
85C2×#4323—232no—
86C2×#4323—28no—
87C2×#4323—28no—
88C2×#4323—28no—
89#66983—28no—
90#66983—28no—
91C2×(C2×D11)⋊C4—24no—
92#66979—22no—
93#66979D414yescomplemented
94C2×C4⋊Dic11C2312yes—
95C2×C4×Dic11—21no—
96C2×#4318—22no—
97C2×#4318—22no—
98C2×#4318—22no—
99C22×C11⋊C8—22no—
100C22×C11⋊C8—22no—
101C22×C11⋊C8D414yescomplemented
102C22×C11⋊C8C2312yes—
103C22×C11⋊C8C2312yes—
104#66896—28no—
105C22⋊(C11⋊C8)—28no—
106#66873—28no—
107#23387—111nomaximal, Sylow
108C24×C11—22no—
109C24×C11—24no—
110C24×C11—42no—
111C24×C11—42no—
112C24×C11—84no—
113C24×C11C2×D412yes—
114C24×C11C2×D411yescharacteristic
115C23×D11—22no—
116C23×D11—24no—
117C23×D11—42no—
118C23×D11—42no—
119C23×D11—84no—
120C11×#41—44no—
121C11×#41—44no—
122C11×#41—44no—
123C11×#41—44no—
124C2×Q8×C11—22no—
125C2×Q8×C11—22no—
126C2×Q8×C11—22no—
127C2×D4×C11—24no—
128C2×D4×C11—24no—
129C2×D4×C11—24no—
130C2×D4×C11—216no—
131C2×D4×C11—28no—
132C2×D4×C11—22no—
133C2×D4×C11—24no—
134C2×D4×C11—22no—
135C2×D4×C11—28no—
136C2×D4×C11—22no—
137C2×D4×C11—22no—
138C2×D4×C11—22no—
139C2×D4×C11—22no—
140C2×D4×C11—22no—
141C2×D4×C11—22no—
142C2×D4×C11—42no—
143C2×D4×C11—44no—
144C2×D4×C11—42no—
145C2×D4×C11—44no—
146C2×D4×C11—88no—
147C2×D4×C11C2×D414yes—
148C22×C4×C11—22no—
149C22×C4×C11—22no—
150C22×C4×C11—22no—
151C22×C4×C11—22no—
152C22×C4×C11—22no—
153C22×C4×C11—22no—
154C22×C4×C11—22no—
155C22×C4×C11C2×D412yes—
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D412yes—
158C22×C4×C11C2×D412yes—
159C22×C4×C11C2×D412yes—
160C22×C4×C11C2×D412yes—
161C22×C4×C11C2×D412yes—
162C22×C4×C11#4112yes—
163C22×C4×C11C2411yescharacteristic
164C2×C22⋊D11—216no—
165C2×C22⋊D11—88no—
166C22×Dic11—22no—
167C2×D44—24no—
168C2×D44—28no—
169C2×D44—28no—
170C2×D44—22no—
171C2×D44—22no—
172C2×D44—22no—
173C2×D44—22no—
174C2×D44—22no—
175C2×D44—42no—
176C2×D44—44no—
177C2×D44—42no—
178C2×D44—44no—
179C2×D44C2×D414yes—
180C11×C4⋊C4—22no—
181C11×C4⋊C4C2×D414yes—
182C11×C22⋊C4—216no—
183C11×C22⋊C4—24no—
184C42×C11—24no—
185C22⋊Dic11—24no—
186#4323—232no—
187(C2×D11)⋊C4—216no—
188C4⋊Dic11—22no—
189C4⋊Dic11C2×D414yes—
190C4×Dic11—24no—
191#4318—44no—
192C2×C11⋊C8—28no—
193C2×C11⋊C8—22no—
194C2×C11⋊C8—22no—
195C2×C11⋊C8—22no—
196C2×C11⋊C8—22no—
197C2×C11⋊C8—22no—
198C2×C11⋊C8C2×D414yes—
199C23×D8—111no—
200C2×#535—111no—
201C2×#535D1111yescharacteristic, complemented
202C2×#418—111no—
203C2×#418—111no—
204C2×#408—111no—
205#1999—118no—
206#1735—111no—
207C23×C11—24no—
208C23×C11—24no—
209C23×C11—22no—
210C23×C11—22no—
211C23×C11—22no—
212C23×C11—28no—
213C23×C11—42no—
214C23×C11—42no—
215C23×C11—48no—
216C23×C11—48no—
217C23×C11—88no—
218C23×C11—88no—
219C23×C11—88no—
220C23×C11#12012yes—
221C23×C11#12012yes—
222C23×C11#12112yes—
223C23×C11C22×D411yescharacteristic
224C22×D11—24no—
225C22×D11—42no—
226C22×D11—42no—
227C22×D11—48no—
228C22×D11—48no—
229C22×D11—88no—
230C22×D11—88no—
231C22×D11—88no—
232Q8×C11—44no—
233D4×C11—24no—
234D4×C11—24no—
235D4×C11—48no—
236D4×C11—42no—
237D4×C11—42no—
238D4×C11—48no—
239D4×C11—44no—
240D4×C11—816no—
241C2×C4×C11—22no—
242C2×C4×C11—24no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—44no—
246C2×C4×C11—42no—
247C2×C4×C11—42no—
248C2×C4×C11—42no—
249C2×C4×C11—42no—
250C2×C4×C11#12014yes—
251C2×C4×C11#12012yes—
252C2×C4×C11#12012yes—
253C2×C4×C11#12114yes—
254C2×C4×C11#12114yes—
255C2×C4×C11#12112yes—
256C2×C4×C11#12714yes—
257C2×C4×C11C22×D411yescharacteristic
258C2×C4×C11C22×D411yescharacteristic
259C2×C4×C11C22×D411yescharacteristic
260C2×C4×C11C22×D411yescharacteristic
261C2×C4×C11C22×D411yescharacteristic
262C2×C4×C11C2×#4111yescharacteristic
263C22⋊D11—816no—
264C2×Dic11—24no—
265C2×Dic11—44no—
266D44—24no—
267D44—24no—
268D44—42no—
269D44—42no—
270D44—48no—
271C11⋊C8—24no—
272C11⋊C8—42no—
273C22×#41C2×D1111yescharacteristic
274C23×D4—111no—
275C23×D4C2×D1111yescharacteristic
276C22×D8—114no—
277C22×D8—224no—
278C22×D8—224no—
279C22×D8—224no—
280C22×M16—111no—
281C23×C8—111no—
282#535—24no—
283#535—24no—
284#535—224no—
285#535—224no—
286C2×#127—21no—
287C2×#127—221no—
288C2×#124—21no—
289C2×#124—221no—
290C2×#121—114no—
291C2×#121C2×D1114yescomplemented
292C2×#120—22no—
293C2×#120—222no—
294C2×#117—111no—
295C2×#117C2×D1111yescharacteristic
296#418—224no—
297#418—224no—
298C2×#102—114no—
299C2×#102—114no—
300#408—224no—
301C2×C22⋊C8—114no—
302#340—114no—
303C22×C11—24no—
304C22×C11—24no—
305C22×C11—24no—
306C22×C11—42no—
307C22×C11—44no—
308C22×C11—44no—
309C22×C11—48no—
310C22×C11—44no—
311C22×C11—44no—
312C22×C11—816no—
313C22×C11—84no—
314C22×C11—84no—
315C22×C11#39214yes—
316C22×C11C2×#12011yescharacteristic
317C22×C11C2×#12011yescharacteristic
318C22×C11C2×#12111yescharacteristic
319C22×C11#57614yes—
320C2×D11—44no—
321C2×D11—48no—
322C2×D11—816no—
323C2×D11—84no—
324C2×D11—84no—
325C4×C11—42no—
326C4×C11—44no—
327C4×C11#39214yes—
328C4×C11C2×#12011yescharacteristic
329C4×C11C2×#12111yescharacteristic
330C4×C11C2×#12111yescharacteristic
331C4×C11C2×#12711yescharacteristic
332Dic11—44no—
333C25—21no—
334C25—221no—
335C2×#41—22no—
336C2×#41—22no—
337C2×#41—22no—
338C2×#41—22no—
339C2×#41—22no—
340C2×#41—22no—
341C22×Q8C22⋊D1111yescharacteristic
342C22×D4—24no—
343C22×D4—22no—
344C22×D4—22no—
345C22×D4—22no—
346C22×D4—22no—
347C22×D4—21no—
348C22×D4—22no—
349C22×D4—114no—
350C22×D4—112no—
351C22×D4—224no—
352C22×D4—222no—
353C22×D4—222no—
354C22×D4—222no—
355C22×D4—222no—
356C22×D4—222no—
357C22×D4—221no—
358C22×D4C22⋊D1112yes—
359C22×D4C22⋊D1111yescharacteristic
360C22×D4C22⋊D1114yescomplemented
361C22×D4C22×D1112yes—
362C23×C4C22×D1112yes—
363C23×C4C22×D1111yescharacteristic
364C2×D8—228no—
365C2×D8—228no—
366C2×D8—2232no—
367C2×D8—228no—
368C2×M16—222no—
369C2×M16—222no—
370C2×M16—222no—
371C22×C8—114no—
372C22×C8—112no—
373C22×C8—112no—
374C22×C8—222no—
375C22×C8—222no—
376#127—28no—
377#127—228no—
378#124—28no—
379#124—228no—
380#121—28no—
381#121—28no—
382#121—228no—
383#121—228no—
384#120—216no—
385#120—2216no—
386#117—22no—
387#117—114no—
388#117—222no—
389#117C22⋊D1114yescomplemented
390C2×C4⋊C4—112no—
391C2×C4⋊C4C22×D1112yes—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—24no—
394C2×C22⋊C4—221no—
395C2×C22⋊C4—224no—
396C2×C42—21no—
397C2×C42—221no—
398#102—228no—
399#102—228no—
400C22⋊C8—228no—
401C2×C11—24no—
402C2×C11—82no—
403C2×C11—84no—
404C2×C11C2×#39211yescharacteristic
405C2×C11#300812yes—
406C2×C11#300812yes—
407C2×C11#305812yes—
408D11—84no—
409C24—22no—
410C24—24no—
411C24—42no—
412C24—42no—
413C24—84no—
414C24—222no—
415C24—224no—
416C24—442no—
417C24—442no—
418C24—884no—
419C24C2×C22⋊D1112yes—
420C24C2×C22⋊D1111yescharacteristic
421#41—44no—
422#41—44no—
423#41—44no—
424#41—44no—
425C2×Q8—22no—
426C2×Q8—22no—
427C2×Q8—22no—
428C2×D4—24no—
429C2×D4—24no—
430C2×D4—24no—
431C2×D4—216no—
432C2×D4—28no—
433C2×D4—22no—
434C2×D4—28no—
435C2×D4—22no—
436C2×D4—24no—
437C2×D4—22no—
438C2×D4—22no—
439C2×D4—22no—
440C2×D4—22no—
441C2×D4—22no—
442C2×D4—22no—
443C2×D4—42no—
444C2×D4—44no—
445C2×D4—42no—
446C2×D4—44no—
447C2×D4—88no—
448C2×D4—114no—
449C2×D4—2216no—
450C2×D4—228no—
451C2×D4—224no—
452C2×D4—228no—
453C2×D4—222no—
454C2×D4—222no—
455C2×D4—222no—
456C2×D4—222no—
457C2×D4—222no—
458C2×D4—444no—
459C2×D4—442no—
460C2×D4—444no—
461C2×D4—442no—
462C2×D4—888no—
463C2×D4C2×C22⋊D1114yes—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—222no—
472C22×C4D4×D1112yes—
473C22×C4D4×D1112yes—
474C22×C4D4×D1112yes—
475C22×C4#434112yes—
476C22×C4C2×C22⋊D1112yes—
477C22×C4C2×C22⋊D1111yescharacteristic
478C22×C4C2×C22⋊D1112yes—
479C22×C4C2×C22⋊D1112yes—
480C22×C4C23×D1111yescharacteristic
481D8—2232no—
482M16—444no—
483C2×C8—114no—
484C2×C8—228no—
485C2×C8—222no—
486C2×C8—222no—
487C2×C8—222no—
488C2×C8—222no—
489C2×C8—222no—
490C4⋊C4—22no—
491C4⋊C4—114no—
492C4⋊C4—222no—
493C4⋊C4C2×C22⋊D1114yes—
494C22⋊C4—216no—
495C22⋊C4—24no—
496C22⋊C4—2216no—
497C22⋊C4—224no—
498C42—24no—
499C42—224no—
500C11#2338711yescharacteristic, complemented, Sylow
501C23—24no—
502C23—22no—
503C23—22no—
504C23—28no—
505C23—24no—
506C23—22no—
507C23—42no—
508C23—42no—
509C23—48no—
510C23—48no—
511C23—88no—
512C23—88no—
513C23—88no—
514C23—224no—
515C23—442no—
516C23—448no—
517C23—448no—
518C23—442no—
519C23—888no—
520C23—888no—
521C23—888no—
522C23#6699012yes—
523C23#6699212yes—
524C23#6700612yes—
525C23C22×C22⋊D1111yescharacteristic
526Q8—44no—
527D4—24no—
528D4—24no—
529D4—48no—
530D4—42no—
531D4—42no—
532D4—48no—
533D4—44no—
534D4—816no—
535D4—224no—
536D4—224no—
537D4—442no—
538D4—442no—
539D4—448no—
540D4—8816no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—24no—
544C2×C4—22no—
545C2×C4—44no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—224no—
551C2×C4—444no—
552C2×C4#6699014yes—
553C2×C4#6699012yes—
554C2×C4#6699114yes—
555C2×C4#6699214yes—
556C2×C4#6699212yes—
557C2×C4#6699314yes—
558C2×C4#6700612yes—
559C2×C4C2×D4×D1111yescharacteristic
560C2×C4C2×D4×D1111yescharacteristic
561C2×C4C2×D4×D1111yescharacteristic
562C2×C4C2×#434111yescharacteristic
563C2×C4C22×C22⋊D1111yescharacteristic
564C2×C4C22×C22⋊D1111yescharacteristic
565C8—224no—
566C8—442no—
567C22—24no—
568C22—24no—
569C22—24no—
570C22—44no—
571C22—44no—
572C22—48no—
573C22—42no—
574C22—44no—
575C22—44no—
576C22—816no—
577C22—84no—
578C22—84no—
579C22—448no—
580C22—444no—
581C22—8816no—
582C22—884no—
583C22—884no—
584C22#1062283614yes—
585C22C2×#6699011yescharacteristic
586C22C2×#6699211yescharacteristic
587C22#1062336614yes—
588C22C2×#6700611yescharacteristic
589C4—44no—
590C4—42no—
591C4—444no—
592C4#1062283614yes—
593C4C2×#6699011yescharacteristic
594C4C2×#6699111yescharacteristic
595C4C2×#6699211yescharacteristic
596C4C2×#6699311yescharacteristic
597C2—24no—
598C2—82no—
599C2—84no—
600C2—884no—
601C2C2×#1062283611yescharacteristic
602C2#1307788212yes—
603C2#1307788412yes—
604C2#1307826112yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#535C2
socleC23×C11C22×D4
hypercenterC2×#535D11
hypocenterC11#23387
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×#41 ◁ C2×#535

Complements

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

NH ≅ G/Ntype
1. C23×#4323C2semidirect
2. C2×#10623361C2semidirect
3. C2×#10622828C2semidirect
4. C2×#10622614C2semidirect
5. C2×#10622847C2semidirect
6. #13069612C2semidirect
7. #13068332C2semidirect
8. C2×C11×#535C2semidirect
16. C2×C11×#121C22semidirect
28. C2×#66983C22semidirect
34. C2×#66896C22semidirect
35. C2×C22⋊(C11⋊C8)C22semidirect
37. C2×#66873C22semidirect
38. #10622167C22semidirect
57. C22×D4×C11D4semidirect
68. C22×D44D4semidirect
76. C11×#117D4semidirect
93. #66979D4semidirect
101. C22×C11⋊C8D4semidirect
201. C2×#535D11semidirect
291. C2×#121C2×D11semidirect
360. C22×D4C22⋊D11semidirect
389. #117C22⋊D11semidirect
500. C11#23387semidirect

Maximal subgroups

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

subgroupindex
C23×#43232
C2×#106233612
C2×#106228282
C2×#106226142
C2×#106228472
#130696122
#130683322
C2×C11×#5352
#2338711