Finite Group Databasebeta

← #14755297

Subgroups — #14755297

Order 2816.

1702 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×#67004C211yesmaximal, characteristic
2C2×#10622849C211yesmaximal, characteristic
3C2×#10622617C211yesmaximal, characteristic, complemented
4#13071200C211yesmaximal, characteristic, complemented
5#13068985C218yesmaximal, complemented
6#13068355C211yesmaximal, characteristic, complemented
7#13068325C211yesmaximal, characteristic, complemented
8C11×#3428C211yesmaximal, characteristic
9C22×C11×#41C2211yescharacteristic
10C23×Dic22C2211yescharacteristic
11C11×#520—22no—
12C11×#520C2214yes—
13C11×#519—21no—
14C11×#518—21no—
15C11×#518—22no—
16C4×C11×#41—22no—
17C4×C11×#41—22no—
18C2×C11×#117—22no—
19C2×C11×#117C2211yescharacteristic
20C2×C11×#117C2211yescharacteristic
21C2×#67004—24no—
22C2×#67004—22no—
23C2×#67004C418yescomplemented
24C2×#67004C2214yes—
25C22×#4326—21no—
26C22×#4324—21no—
27C2×#66979C2211yescharacteristic
28C22×#4318C2211yescharacteristic
29C22×#4318C2211yescharacteristic
30#10622849—24no—
31C2×#66901C2214yes—
32#10622617—22no—
33#10622617C2214yescomplemented
34#10622587C2214yescomplemented
35C2×#66874—22no—
36#10622556—22no—
37#10622542—22no—
38#10622170C2214yescomplemented
39#10622168C2214yescomplemented
40C2×C11×#41—21no—
41C2×C11×#41—21no—
42C2×C11×#41—22no—
43C2×C11×#41—22no—
44C2×C11×#41C2×C414yes—
45C2×C11×#41D414yes—
46C2×C11×#41D412yes—
47C2×C11×#41C2312yes—
48C22×Q8×C11D411yescharacteristic
49C22×D4×C11—21no—
50C22×D4×C11D411yescharacteristic
51C23×C4×C11—21no—
52C23×C4×C11C2311yescharacteristic
53C23×Dic11—21no—
54C22×Dic22—21no—
55C22×Dic22—21no—
56C22×Dic22—22no—
57C22×Dic22—21no—
58C22×Dic22—21no—
59C22×Dic22—22no—
60C22×Dic22—21no—
61C22×Dic22—22no—
62C22×Dic22C2×C414yescomplemented
63C22×Dic22C2312yes—
64C4×Q8×C11—24no—
65C4×Q8×C11—24no—
66C4×D4×C11—28no—
67C4×D4×C11—24no—
68C4×D4×C11—24no—
69C4×D4×C11—28no—
70C11×#117—24no—
71C11×#117—24no—
72C11×#117—21no—
73C11×#117—21no—
74C11×#117—21no—
75C11×#117—21no—
76C11×#117—21no—
77C11×#117—21no—
78C11×#117—24no—
79C11×#117D412yes—
80C11×#117C2312yes—
81C2×C11×C4⋊C4—24no—
82C2×C11×C4⋊C4D412yes—
83C2×C11×C4⋊C4C2312yes—
84C2×C11×C22⋊C4—24no—
85C2×C11×C22⋊C4—21no—
86C2×C11×C22⋊C4D412yes—
87C2×C42×C11—24no—
88C2×C42×C11—21no—
89C2×C42×C11D412yes—
90C2×C22⋊Dic11—21no—
91#67004—216no—
92#67004—28no—
93#67004C2×C4116yescomplemented
94C2×#4326—28no—
95C2×#4326—24no—
96C2×#4324—28no—
97C2×#4324—24no—
98#66979—22no—
99#66979—22no—
100C2×C4⋊Dic11—21no—
101C2×C4×Dic11C2312yes—
102C2×#4318—22no—
103C2×#4318—21no—
104C2×#4318—21no—
105C2×#4318—22no—
106C2×#4318—22no—
107C2×#4318C2×C414yescomplemented
108C2×#4318C2312yes—
109C2×#4318C2312yes—
110C22×C11⋊C8—21no—
111C22×C11⋊C8—21no—
112#66901—28no—
113C11⋊#95—28no—
114#66874—28no—
115#20944—111nomaximal, Sylow
116C24×C11—21no—
117C24×C11C2×D411yescharacteristic
118C11×#41—24no—
119C11×#41—24no—
120C11×#41—24no—
121C11×#41—24no—
122C11×#41—24no—
123C11×#41—22no—
124C11×#41—22no—
125C11×#41C22⋊C418yes—
126C11×#41C22×C414yes—
127C11×#41C2×D414yes—
128C2×Q8×C11—21no—
129C2×Q8×C11—22no—
130C2×Q8×C11C22⋊C414yes—
131C2×Q8×C11C2×D412yes—
132C2×D4×C11—24no—
133C2×D4×C11—22no—
134C2×D4×C11—24no—
135C2×D4×C11—22no—
136C2×D4×C11—21no—
137C2×D4×C11—22no—
138C2×D4×C11C22⋊C414yes—
139C2×D4×C11C2×D412yes—
140C22×C4×C11—21no—
141C22×C4×C11—24no—
142C22×C4×C11—22no—
143C22×C4×C11—24no—
144C22×C4×C11—22no—
145C22×C4×C11—28no—
146C22×C4×C11—22no—
147C22×C4×C11C22×C412yes—
148C22×C4×C11C2×D414yes—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D412yes—
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11#4112yes—
156C22×C4×C11#4112yes—
157C22×C4×C11C2411yescharacteristic
158C22×Dic11—24no—
159C22×Dic11—22no—
160C22×Dic11—22no—
161C22×Dic11—41no—
162C22×Dic11—41no—
163C22×Dic11—42no—
164C2×Dic22—24no—
165C2×Dic22—24no—
166C2×Dic22—24no—
167C2×Dic22—24no—
168C2×Dic22—24no—
169C2×Dic22—22no—
170C2×Dic22—22no—
171C2×Dic22—22no—
172C2×Dic22—22no—
173C2×Dic22—22no—
174C2×Dic22—41no—
175C2×Dic22—41no—
176C2×Dic22—42no—
177C2×Dic22—42no—
178C2×Dic22—42no—
179C2×Dic22—42no—
180C2×Dic22—42no—
181C2×Dic22C22×C414yes—
182C11×C4⋊C4—28no—
183C11×C4⋊C4—22no—
184C11×C4⋊C4—22no—
185C11×C4⋊C4—22no—
186C11×C4⋊C4C2×D414yes—
187C11×C22⋊C4—28no—
188C11×C22⋊C4—22no—
189C11×C22⋊C4—22no—
190C11×C22⋊C4—22no—
191C11×C22⋊C4—22no—
192C42×C11—28no—
193C42×C11—22no—
194C42×C11—22no—
195C42×C11—22no—
196C42×C11—22no—
197C22⋊Dic11—42no—
198#4326—216no—
199#4324—216no—
200C4⋊Dic11—42no—
201C4×Dic11—22no—
202C4×Dic11—22no—
203#4318—24no—
204#4318—22no—
205#4318—22no—
206#4318—22no—
207#4318—42no—
208#4318C22×C414yes—
209C2×C11⋊C8—24no—
210C2×C11⋊C8—22no—
211C2×C11⋊C8—22no—
212C2×C11⋊C8—42no—
213C22×#137—111no—
214#3428D1111yescharacteristic
215C2×#421—111no—
216C2×#419—111no—
217#2310—111no—
218#1882—118no—
219#1742—111no—
220#1733—111no—
221C23×C11—22no—
222C23×C11—24no—
223C23×C11—42no—
224C23×C11—82no—
225C23×C11C4×D412yes—
226C23×C11#12011yescharacteristic
227C23×C11#12011yescharacteristic
228C23×C11#12112yes—
229C23×C11C22×D411yescharacteristic
230Q8×C11—22no—
231Q8×C11—24no—
232Q8×C11C2×C22⋊C414yes—
233D4×C11—24no—
234D4×C11—24no—
235D4×C11—28no—
236D4×C11—22no—
237D4×C11—24no—
238D4×C11C2×C22⋊C414yes—
239C2×C4×C11—22no—
240C2×C4×C11—24no—
241C2×C4×C11—24no—
242C2×C4×C11—24no—
243C2×C4×C11—28no—
244C2×C4×C11—24no—
245C2×C4×C11—24no—
246C2×C4×C11—44no—
247C2×C4×C11—82no—
248C2×C4×C11—88no—
249C2×C4×C11C2×C22⋊C412yes—
250C2×C4×C11C2×C22⋊C412yes—
251C2×C4×C11C4×D412yes—
252C2×C4×C11C4×D412yes—
253C2×C4×C11C4×D412yes—
254C2×C4×C11#12011yescharacteristic
255C2×C4×C11#12011yescharacteristic
256C2×C4×C11#12112yes—
257C2×C4×C11#12112yes—
258C2×C4×C11#12112yes—
259C2×C4×C11#12312yes—
260C2×C4×C11#12312yes—
261C2×C4×C11C23×C411yescharacteristic
262C2×C4×C11C22×D411yescharacteristic
263C2×C4×C11C22×D411yescharacteristic
264C2×C4×C11C22×D411yescharacteristic
265C2×C4×C11C2×#4111yescharacteristic
266C2×C4×C11C2×#4111yescharacteristic
267C2×Dic11—24no—
268C2×Dic11—42no—
269C2×Dic11—42no—
270C2×Dic11—44no—
271C2×Dic11—44no—
272C2×Dic11—44no—
273C2×Dic11—42no—
274Dic22—24no—
275Dic22—24no—
276Dic22—42no—
277Dic22—42no—
278Dic22—44no—
279Dic22—44no—
280C11⋊C8—24no—
281C11⋊C8—42no—
282C22×#41C2×D1111yescharacteristic
283C23×Q8—111no—
284C2×#137—114no—
285C2×#137—118no—
286C2×#137—224no—
287C2×#137—222no—
288C22×Q16—221no—
289C22×SD16—221no—
290C22×M16—111no—
291C22×M16—111no—
292#520—22no—
293#520C2×D1114yes—
294#519—21no—
295#518—21no—
296#518—22no—
297C4×#41—22no—
298C4×#41—22no—
299C2×#117—22no—
300C2×#117—111no—
301C2×#117C2×D1111yescharacteristic
302C2×#117C2×D1111yescharacteristic
303#421—224no—
304C2×#104—114no—
305#419—114no—
306#419—222no—
307C2×#103—222no—
308#391—114no—
309#391—222no—
310#381—222no—
311#343—114no—
312#339—114no—
313C22×C11—22no—
314C22×C11—22no—
315C22×C11—22no—
316C22×C11—24no—
317C22×C11—42no—
318C22×C11—42no—
319C22×C11—44no—
320C22×C11—84no—
321C22×C11#38612yes—
322C22×C11#38612yes—
323C22×C11C2×C4×D411yescharacteristic
324C22×C11C2×#12011yescharacteristic
325C22×C11C2×#12111yescharacteristic
326C4×C11—24no—
327C4×C11—44no—
328C4×C11—44no—
329C4×C11#38612yes—
330C4×C11#38612yes—
331C4×C11C22×C22⋊C411yescharacteristic
332C4×C11C2×C4×D411yescharacteristic
333C4×C11C2×#12111yescharacteristic
334C4×C11C2×#12311yescharacteristic
335Dic11—44no—
336Dic11—82no—
337C2×#41—22no—
338C2×#41—22no—
339C2×#41—21no—
340C2×#41—21no—
341C2×#41C4×D1114yes—
342C2×#41D4414yes—
343C2×#41C22⋊D1112yes—
344C2×#41C22×D1112yes—
345C22×Q8—114no—
346C22×Q8—112no—
347C22×Q8—222no—
348C22×Q8—221no—
349C22×Q8—222no—
350C22×Q8—222no—
351C22×Q8—221no—
352C22×Q8—221no—
353C22×Q8—221no—
354C22×Q8—221no—
355C22×Q8C22⋊D1111yescharacteristic
356C22×D4—21no—
357C22×D4C22⋊D1111yescharacteristic
358C23×C4—21no—
359C23×C4—221no—
360C23×C4C22×D1111yescharacteristic
361#137—1116no—
362#137—2216no—
363#137—228no—
364C2×Q16—228no—
365C2×Q16—224no—
366C2×SD16—228no—
367C2×SD16—224no—
368C2×M16—114no—
369C2×M16—112no—
370C2×M16—112no—
371C2×M16—222no—
372C2×M16—221no—
373C2×M16—221no—
374C2×M16—222no—
375C2×M16—222no—
376C22×C8—221no—
377C22×C8—221no—
378C4×Q8—24no—
379C4×Q8—24no—
380C4×D4—28no—
381C4×D4—24no—
382C4×D4—24no—
383C4×D4—28no—
384#117—24no—
385#117—24no—
386#117—21no—
387#117—21no—
388#117—21no—
389#117—21no—
390#117—21no—
391#117—21no—
392#117—24no—
393#117—222no—
394#117—222no—
395#117C22⋊D1112yes—
396#117C22×D1112yes—
397C2×C4⋊C4—24no—
398C2×C4⋊C4—221no—
399C2×C4⋊C4C22⋊D1112yes—
400C2×C4⋊C4C22×D1112yes—
401C2×C22⋊C4—24no—
402C2×C22⋊C4—21no—
403C2×C22⋊C4—221no—
404C2×C22⋊C4C22⋊D1112yes—
405C2×C42—24no—
406C2×C42—21no—
407C2×C42—112no—
408C2×C42C22⋊D1112yes—
409#104—228no—
410#103—228no—
411#95—228no—
412C2×C11—21no—
413C2×C11—22no—
414C2×C11—21no—
415C2×C11—22no—
416C2×C11—44no—
417C2×C11C2×#38611yescharacteristic
418C2×C11#302212yes—
419C24—21no—
420C24C2×C22⋊D1111yescharacteristic
421#41—24no—
422#41—24no—
423#41—24no—
424#41—24no—
425#41—24no—
426#41—22no—
427#41—22no—
428#41(C2×D11)⋊C418yes—
429#41C2×C4×D1114yes—
430#41C2×D4414yes—
431C2×Q8—22no—
432C2×Q8—21no—
433C2×Q8—114no—
434C2×Q8—224no—
435C2×Q8—222no—
436C2×Q8—224no—
437C2×Q8—224no—
438C2×Q8—224no—
439C2×Q8—224no—
440C2×Q8—222no—
441C2×Q8—222no—
442C2×Q8—222no—
443C2×Q8—222no—
444C2×Q8—442no—
445C2×Q8—442no—
446C2×Q8—442no—
447C2×Q8—442no—
448C2×Q8—442no—
449C2×Q8—441no—
450C2×Q8—441no—
451C2×Q8(C2×D11)⋊C414yes—
452C2×Q8C2×C22⋊D1112yes—
453C2×D4—24no—
454C2×D4—24no—
455C2×D4—22no—
456C2×D4—22no—
457C2×D4—22no—
458C2×D4—21no—
459C2×D4(C2×D11)⋊C414yes—
460C2×D4C2×C22⋊D1112yes—
461C22×C4—21no—
462C22×C4—24no—
463C22×C4—24no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—28no—
467C22×C4—22no—
468C22×C4—224no—
469C22×C4—222no—
470C22×C4—222no—
471C22×C4—442no—
472C22×C4—441no—
473C22×C4—441no—
474C22×C4C2×C4×D1112yes—
475C22×C4C2×D4412yes—
476C22×C4#433912yes—
477C22×C4#433912yes—
478C22×C4C2×C22⋊D1114yes—
479C22×C4C2×C22⋊D1111yescharacteristic
480C22×C4C2×C22⋊D1111yescharacteristic
481C22×C4C2×C22⋊D1111yescharacteristic
482C22×C4C2×C22⋊D1111yescharacteristic
483C22×C4C2×C22⋊D1111yescharacteristic
484C22×C4C23×D1111yescharacteristic
485Q16—2216no—
486SD16—2216no—
487M16—114no—
488M16—224no—
489M16—222no—
490M16—222no—
491M16—222no—
492M16—442no—
493C2×C8—224no—
494C2×C8—222no—
495C2×C8—222no—
496C2×C8—442no—
497C4⋊C4—28no—
498C4⋊C4—22no—
499C4⋊C4—22no—
500C4⋊C4—22no—
501C4⋊C4—442no—
502C4⋊C4C2×C22⋊D1114yes—
503C22⋊C4—28no—
504C22⋊C4—22no—
505C22⋊C4—22no—
506C22⋊C4—22no—
507C22⋊C4—22no—
508C22⋊C4—442no—
509C42—28no—
510C42—22no—
511C42—22no—
512C42—22no—
513C42—22no—
514C42—222no—
515C42—222no—
516C11#2094411yescharacteristic, complemented, Sylow
517C23—22no—
518C23—24no—
519C23—42no—
520C23—82no—
521C23C4×C22⋊D1112yes—
522C23#6698312yes—
523C23#6700611yescharacteristic
524C23#6700611yescharacteristic
525C23C22×C22⋊D1111yescharacteristic
526Q8—22no—
527Q8—24no—
528Q8—224no—
529Q8—224no—
530Q8—442no—
531Q8—442no—
532Q8—444no—
533Q8—444no—
534Q8C2×(C2×D11)⋊C414yes—
535D4—24no—
536D4—24no—
537D4—28no—
538D4—22no—
539D4—24no—
540D4C2×(C2×D11)⋊C414yes—
541C2×C4—24no—
542C2×C4—22no—
543C2×C4—24no—
544C2×C4—24no—
545C2×C4—28no—
546C2×C4—24no—
547C2×C4—24no—
548C2×C4—44no—
549C2×C4—82no—
550C2×C4—88no—
551C2×C4—224no—
552C2×C4—442no—
553C2×C4—444no—
554C2×C4—444no—
555C2×C4—442no—
556C2×C4—444no—
557C2×C4—442no—
558C2×C4C2×(C2×D11)⋊C412yes—
559C2×C4C2×(C2×D11)⋊C412yes—
560C2×C4C4×C22⋊D1112yes—
561C2×C4C4×C22⋊D1112yes—
562C2×C4C4×C22⋊D1112yes—
563C2×C4#6698212yes—
564C2×C4#6698212yes—
565C2×C4#6698312yes—
566C2×C4#6698312yes—
567C2×C4#6698312yes—
568C2×C4#6700611yescharacteristic
569C2×C4#6700611yescharacteristic
570C2×C4C22×C4×D1111yescharacteristic
571C2×C4C22×D4411yescharacteristic
572C2×C4C2×#433911yescharacteristic
573C2×C4C2×#433911yescharacteristic
574C2×C4C22×C22⋊D1111yescharacteristic
575C2×C4C22×C22⋊D1111yescharacteristic
576C8—224no—
577C8—442no—
578C22—22no—
579C22—22no—
580C22—22no—
581C22—24no—
582C22—42no—
583C22—42no—
584C22—44no—
585C22—84no—
586C22#1062282612yes—
587C22#1062282612yes—
588C22C2×C4×C22⋊D1111yescharacteristic
589C22C2×#6698311yescharacteristic
590C22C2×#6700611yescharacteristic
591C4—24no—
592C4—44no—
593C4—44no—
594C4—444no—
595C4—882no—
596C4#1062282612yes—
597C4#1062282612yes—
598C4C22×(C2×D11)⋊C411yescharacteristic
599C4C2×C4×C22⋊D1111yescharacteristic
600C4C2×#6698211yescharacteristic
601C4C2×#6698311yescharacteristic
602C2—21no—
603C2—22no—
604C2—21no—
605C2—22no—
606C2—44no—
607C2C2×#1062282611yescharacteristic
608C2#1307799512yes—
subgroupG/H
centerC22C2×#67006
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#3428C2
socleC22×C11C2×#120
prime radicalC22×C11×#41C22
cosocleC22×C4×C11C24
hypercenter#3428D11
hypocenterC11#20944
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3428

Complements

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

NH ≅ G/Ntype
3. C2×#10622617C2semidirect
4. #13071200C2semidirect
5. #13068985C2semidirect
6. #13068355C2semidirect
7. #13068325C2semidirect
23. C2×#67004C4semidirect
33. #10622617C22semidirect
34. #10622587C22semidirect
38. #10622170C22semidirect
39. #10622168C22semidirect
62. C22×Dic22C2×C4semidirect
93. #67004C2×C4semidirect
107. C2×#4318C2×C4semidirect
516. C11#20944semidirect

Maximal subgroups

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

subgroupindex
C22×#670042
C2×#106228492
C2×#106226172
#130712002
#130689852
#130683552
#130683252
C11×#34282
#2094411