Finite Group Databasebeta

← #14755156

Subgroups — #14755156

Order 2816.

2046 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66985C211yesmaximal, characteristic
2C2×#10623053C211yesmaximal, characteristic, complemented
3C2×#10622746C211yesmaximal, characteristic, complemented
4C2×#10622834C211yesmaximal, characteristic, complemented
5#13068968C214yesmaximal, complemented
6#13068961C214yesmaximal, complemented
7#13068337C211yesmaximal, characteristic, complemented
8#13068309C211yesmaximal, characteristic, complemented
9C2×C11×#418C211yesmaximal, characteristic, complemented
10C23×D4×C11C2211yescharacteristic
11C22×#4339C2211yescharacteristic
12C22×C11×M16C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14C22×C22⋊Dic11—22no—
15C22×#4324C2212yes—
16C2×#66985—24no—
17C2×#66985—24no—
18C2×#66985C418yescomplemented
19C22×#4323C2212yes—
20C22×C4⋊Dic11C2211yescharacteristic
21C22×C4×Dic11C2211yescharacteristic
22C22×#4318C2211yescharacteristic
23#10623053—24no—
24#10623053—24no—
25C2×#66946C2212yescomplemented
26C2×#66940C2212yescomplemented
27C2×(C22⋊D11)⋊C4—22no—
28C2×#66925—21no—
29C2×C42×D11—21no—
30C11×#418—24no—
31C2×C11×#102C2214yes—
32#10622834—21no—
33#10622834—21no—
34#10622834C2214yes—
35#10622746—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×C11C2311yescharacteristic
50C22×C22⋊D11—21no—
51C23×Dic11—21no—
52C23×Dic11D412yes—
53C2×#4339—22no—
54C2×#4339—22no—
55C2×#4339—22no—
56C2×#4339C2×C414yes—
57C2×#4339D414yes—
58C2×#4339D414yes—
59C22×D44C2311yescharacteristic
60C22×C4×D11—21no—
61C22×C4×D11—22no—
62C22×Dic22C2311yescharacteristic
63C2×C11×M16—22no—
64C2×C11×M16—22no—
65C2×C11×M16—22no—
66C22×C8×C11C2312yes—
67C11×#117—22no—
68C11×#117D414yes—
69C2×C11×C4⋊C4C2312yes—
70C2×C11×C22⋊C4—21no—
71C2×C42×C11—21no—
72C2×C22⋊Dic11—24no—
73C2×C22⋊Dic11—24no—
74C2×C22⋊Dic11—48no—
75C2×#4324—24no—
76C2×#4324—24no—
77C2×#4324C2×C418yescomplemented
78#66985—232no—
79C2×#4323—24no—
80C2×#4323—24no—
81C2×#4323C2×C418yescomplemented
82C2×(C2×D11)⋊C4—22no—
83C2×C4⋊Dic11—22no—
84C2×C4⋊Dic11—22no—
85C2×C4⋊Dic11—21no—
86C2×C4⋊Dic11C2312yes—
87C2×Dic11⋊C4—22no—
88C2×C4×Dic11—22no—
89C2×C4×Dic11—22no—
90C2×C4×Dic11—22no—
91C2×C4×Dic11D411yescharacteristic
92C2×C4×Dic11D411yescharacteristic
93C2×C4×Dic11C2312yes—
94C2×#4318—22no—
95C2×#4318—22no—
96C2×#4318C2×C414yescomplemented
97C22×C11⋊C8C2312yes—
98#66946—24no—
99#66946—24no—
100#66940—24no—
101#66940—24no—
102(C22⋊D11)⋊C4—216no—
103#66925—28no—
104C42×D11—28no—
105C11×#102—28no—
106#66885—24no—
107#66880—24no—
108#20928—111nomaximal, Sylow
109C24×C11—24no—
110C24×C11—22no—
111C24×C11—44no—
112C24×C11—44no—
113C24×C11—42no—
114C24×C11—42no—
115C24×C11C2×D411yescharacteristic
116C23×D11—21no—
117C2×D4×C11—28no—
118C2×D4×C11—28no—
119C2×D4×C11—24no—
120C2×D4×C11—22no—
121C2×D4×C11—22no—
122C2×D4×C11—22no—
123C2×D4×C11—22no—
124C2×D4×C11—22no—
125C2×D4×C11—42no—
126C2×D4×C11—42no—
127C2×D4×C11—44no—
128C2×D4×C11—44no—
129C2×D4×C11C22×C414yes—
130C22×C4×C11—22no—
131C22×C4×C11C22×C412yes—
132C22×C4×C11C2×D412yes—
133C22×C4×C11C2×D412yes—
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D412yes—
136C22×C4×C11#4112yes—
137C22×C4×C11#4112yes—
138C22×C4×C11C2411yescharacteristic
139C2×C22⋊D11—24no—
140C2×C22⋊D11—24no—
141C2×C22⋊D11—24no—
142C22×Dic11—24no—
143C22×Dic11—24no—
144C22×Dic11—21no—
145C22×Dic11—22no—
146C22×Dic11—42no—
147C22×Dic11—44no—
148C22×Dic11—42no—
149C22×Dic11C2×D412yes—
150C22×Dic11C2×D412yes—
151#4339—28no—
152#4339—28no—
153#4339—28no—
154#4339C22⋊C4116yescomplemented
155C2×D44—21no—
156C2×D44—21no—
157C2×D44—21no—
158C2×D44C22×C412yes—
159C2×D44C2×D412yes—
160C2×D44C2×D412yes—
161C2×C4×D11—28no—
162C2×C4×D11—24no—
163C2×C4×D11—24no—
164C2×C4×D11—24no—
165C2×C4×D11—44no—
166C2×C4×D11—44no—
167C2×Dic22—21no—
168C2×Dic22—21no—
169C2×Dic22—21no—
170C2×Dic22C22×C412yes—
171C2×Dic22C2×D412yes—
172C2×Dic22C2×D412yes—
173C11×M16—44no—
174C2×C8×C11—22no—
175C2×C8×C11—22no—
176C2×C8×C11—22no—
177C11×C4⋊C4—22no—
178C11×C4⋊C4C2×D414yes—
179C11×C22⋊C4—24no—
180C42×C11—24no—
181C22⋊Dic11—48no—
182C22⋊Dic11—48no—
183#4324—216no—
184#4323—216no—
185(C2×D11)⋊C4—28no—
186C4⋊Dic11—22no—
187C4⋊Dic11—22no—
188C4⋊Dic11—42no—
189Dic11⋊C4—28no—
190C4×Dic11—28no—
191C4×Dic11—22no—
192C4×Dic11—22no—
193C4×Dic11—22no—
194C4×Dic11—22no—
195#4318—28no—
196C2×C11⋊C8—22no—
197C2×C11⋊C8—22no—
198C2×C11⋊C8C22×C414yes—
199C22×AGL(1,ℤ/8)—111no—
200C2×C4×#41—111no—
201C2×#417—111no—
202C2×#418D1111yescharacteristic, complemented
203C2×#390—111no—
204#1880—114no—
205#1879—114no—
206#1736—111no—
207#1728—111no—
208C23×C11—22no—
209C23×C11—22no—
210C23×C11—24no—
211C23×C11—416no—
212C23×C11—42no—
213C23×C11—42no—
214C23×C11—44no—
215C23×C11—44no—
216C23×C11—48no—
217C23×C11—88no—
218C23×C11—84no—
219C23×C11—84no—
220C23×C11C4×D412yes—
221C23×C11#12012yes—
222C23×C11#12112yes—
223C23×C11C22×D411yescharacteristic
224C22×D11—22no—
225C22×D11—22no—
226C22×D11—22no—
227C22×D11—42no—
228C22×D11—42no—
229D4×C11—24no—
230D4×C11—24no—
231D4×C11—42no—
232D4×C11—42no—
233D4×C11—48no—
234C2×C4×C11—24no—
235C2×C4×C11—42no—
236C2×C4×C11—42no—
237C2×C4×C11C2×C22⋊C414yes—
238C2×C4×C11C4×D412yes—
239C2×C4×C11C4×D414yes—
240C2×C4×C11#12012yes—
241C2×C4×C11#12112yes—
242C2×C4×C11#12114yes—
243C2×C4×C11#12314yes—
244C2×C4×C11C23×C411yescharacteristic
245C2×C4×C11C22×D411yescharacteristic
246C2×C4×C11C22×D411yescharacteristic
247C2×C4×C11C22×D411yescharacteristic
248C2×C4×C11C2×#4111yescharacteristic
249C2×C4×C11C2×#4111yescharacteristic
250C22⋊D11—216no—
251C2×Dic11—22no—
252C2×Dic11—22no—
253C2×Dic11—22no—
254C2×Dic11—22no—
255C2×Dic11—22no—
256C2×Dic11—22no—
257C2×Dic11—22no—
258C2×Dic11—22no—
259C2×Dic11—48no—
260C2×Dic11—42no—
261C2×Dic11—44no—
262C2×Dic11—84no—
263C2×Dic11AGL(1,ℤ/8)14yescomplemented
264D44—22no—
265D44—22no—
266D44—22no—
267D44C2×C22⋊C414yescomplemented
268C4×D11—216no—
269C4×D11—416no—
270Dic22—22no—
271Dic22—22no—
272Dic22—22no—
273Dic22C2×C22⋊C414yescomplemented
274C8×C11—42no—
275C11⋊C8—24no—
276C22×#41—111no—
277C23×D4C2×D1111yescharacteristic
278C2×AGL(1,ℤ/8)—118no—
279C2×AGL(1,ℤ/8)—224no—
280C2×AGL(1,ℤ/8)—224no—
281C22×SD16—112no—
282C22×D8—112no—
283C22×M16—111no—
284C22×M16C2×D1111yescharacteristic
285C4×#41—224no—
286C4×#41—224no—
287C2×C4×Q8—112no—
288C2×C4×D4—112no—
289C2×C4×D4—222no—
290C2×#117—221no—
291C2×#117C2×D1111yescharacteristic
292C22×C4⋊C4—111no—
293C22×C22⋊C4—222no—
294C22×C42—111no—
295C22×C42—221no—
296#418—24no—
297#417—224no—
298C2×#103—112no—
299C2×#102—112no—
300C2×#102C2×D1114yes—
301#390—114no—
302#390—221no—
303#390—221no—
304#340—114no—
305#336—114no—
306C22×C11—24no—
307C22×C11—24no—
308C22×C11—22no—
309C22×C11—22no—
310C22×C11—48no—
311C22×C11—44no—
312C22×C11—816no—
313C22×C11—84no—
314C22×C11—82no—
315C22×C11—82no—
316C22×C11#38614yes—
317C22×C11C2×C4×D411yescharacteristic
318C22×C11C2×#12011yescharacteristic
319C22×C11C2×#12111yescharacteristic
320C22×C11C2×AGL(1,ℤ/8)12yes—
321C22×C11#57512yes—
322C2×D11—24no—
323C2×D11—44no—
324C2×D11—44no—
325C2×D11—42no—
326C2×D11—42no—
327C4×C11—44no—
328C4×C11#38614yes—
329C4×C11C22×C22⋊C411yescharacteristic
330C4×C11C2×C4×D411yescharacteristic
331C4×C11C2×#12111yescharacteristic
332C4×C11C2×#12311yescharacteristic
333Dic11—24no—
334Dic11—24no—
335Dic11—42no—
336Dic11—82no—
337C25—21no—
338C2×#41—114no—
339C2×#41—114no—
340C2×#41—114no—
341C2×#41—222no—
342C2×#41—222no—
343C2×#41—222no—
344C22×Q8—111no—
345C22×D4—22no—
346C22×D4—22no—
347C22×D4—22no—
348C22×D4—21no—
349C22×D4—22no—
350C22×D4—22no—
351C22×D4—111no—
352C22×D4—221no—
353C22×D4C4×D1114yescomplemented
354C22×D4C22×D1112yes—
355C23×C4—112no—
356C23×C4—222no—
357C23×C4—221no—
358C23×C4—221no—
359C23×C4C22×D1111yescharacteristic
360AGL(1,ℤ/8)—2232no—
361C2×SD16—118no—
362C2×SD16—224no—
363C2×SD16—224no—
364C2×D8—118no—
365C2×D8—224no—
366C2×D8—224no—
367C2×M16—22no—
368C2×M16—22no—
369C2×M16—22no—
370C2×M16—114no—
371C2×M16—222no—
372C2×M16—222no—
373C22×C8—112no—
374C22×C8C22×D1112yes—
375C4×Q8—224no—
376C4×Q8—224no—
377C4×D4—2216no—
378C4×D4—224no—
379C4×D4—224no—
380#117—22no—
381#117—228no—
382#117C22⋊D1114yes—
383C2×C4⋊C4—112no—
384C2×C4⋊C4—222no—
385C2×C4⋊C4—222no—
386C2×C4⋊C4—222no—
387C2×C4⋊C4—221no—
388C2×C4⋊C4C22×D1112yes—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—222no—
391C2×C22⋊C4—224no—
392C2×C22⋊C4—224no—
393C2×C22⋊C4—448no—
394C2×C42—21no—
395C2×C42—111no—
396C2×C42—111no—
397C2×C42—112no—
398C2×C42—228no—
399C2×C42—222no—
400C2×C42—222no—
401C2×C42—222no—
402#103—224no—
403#102—28no—
404#102—224no—
405C2×C11—24no—
406C2×C11—84no—
407C2×C11C2×#38611yescharacteristic
408C2×C11C4×AGL(1,ℤ/8)12yes—
409C2×C11#300612yes—
410C2×C11#303811yescharacteristic
411C2×C11#304011yescharacteristic
412D11—44no—
413C24—24no—
414C24—22no—
415C24—44no—
416C24—44no—
417C24—42no—
418C24—42no—
419C24—221no—
420C24D4×D1111yescharacteristic
421#41—1116no—
422#41—228no—
423#41—228no—
424#41—228no—
425C2×Q8—112no—
426C2×Q8—112no—
427C2×Q8—112no—
428C2×Q8—221no—
429C2×Q8—221no—
430C2×Q8—221no—
431C2×D4—28no—
432C2×D4—24no—
433C2×D4—28no—
434C2×D4—22no—
435C2×D4—22no—
436C2×D4—22no—
437C2×D4—22no—
438C2×D4—22no—
439C2×D4—44no—
440C2×D4—42no—
441C2×D4—42no—
442C2×D4—44no—
443C2×D4—112no—
444C2×D4—112no—
445C2×D4—112no—
446C2×D4—224no—
447C2×D4—224no—
448C2×D4—224no—
449C2×D4—221no—
450C2×D4—221no—
451C2×D4—221no—
452C2×D4C2×C4×D1114yes—
453C22×C4—22no—
454C22×C4—112no—
455C22×C4—112no—
456C22×C4—228no—
457C22×C4—224no—
458C22×C4—221no—
459C22×C4—224no—
460C22×C4—224no—
461C22×C4—224no—
462C22×C4—224no—
463C22×C4—222no—
464C22×C4—444no—
465C22×C4—444no—
466C22×C4—442no—
467C22×C4—444no—
468C22×C4—442no—
469C22×C4C2×C4×D1112yes—
470C22×C4#433912yes—
471C22×C4D4×D1112yes—
472C22×C4D4×D1112yes—
473C22×C4D4×D1111yescharacteristic
474C22×C4#434112yes—
475C22×C4C2×C22⋊D1112yes—
476C22×C4C23×D1111yescharacteristic
477SD16—2216no—
478D8—2216no—
479M16—44no—
480M16—228no—
481C2×C8—22no—
482C2×C8—22no—
483C2×C8—22no—
484C2×C8—114no—
485C2×C8—222no—
486C2×C8—222no—
487C4⋊C4—22no—
488C4⋊C4—228no—
489C4⋊C4—222no—
490C4⋊C4—222no—
491C4⋊C4—442no—
492C4⋊C4C2×C22⋊D1114yes—
493C22⋊C4—24no—
494C22⋊C4—228no—
495C22⋊C4—448no—
496C22⋊C4—448no—
497C42—24no—
498C42—228no—
499C42—222no—
500C42—222no—
501C42—222no—
502C42—222no—
503C11#2092811yescharacteristic, complemented, Sylow
504C23—22no—
505C23—22no—
506C23—24no—
507C23—416no—
508C23—42no—
509C23—44no—
510C23—44no—
511C23—42no—
512C23—48no—
513C23—84no—
514C23—84no—
515C23—88no—
516C23—222no—
517C23—222no—
518C23—222no—
519C23—442no—
520C23—442no—
521C23(C22⋊D11)⋊C412yes—
522C23#6693712yes—
523C23#6699012yes—
524C23C2×D4×D1111yescharacteristic
525Q8—114no—
526Q8—222no—
527Q8—222no—
528Q8—222no—
529D4—24no—
530D4—24no—
531D4—42no—
532D4—42no—
533D4—48no—
534D4—114no—
535D4—2216no—
536D4—222no—
537D4—222no—
538D4—222no—
539C2×C4—24no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—114no—
543C2×C4—222no—
544C2×C4—222no—
545C2×C4—222no—
546C2×C4—222no—
547C2×C4—222no—
548C2×C4—2216no—
549C2×C4—222no—
550C2×C4—222no—
551C2×C4—222no—
552C2×C4—4416no—
553C2×C4—448no—
554C2×C4—442no—
555C2×C4—444no—
556C2×C4—884no—
557C2×C4C22⋊C4×D1114yes—
558C2×C4(C22⋊D11)⋊C412yes—
559C2×C4#6693614yes—
560C2×C4#6693712yes—
561C2×C4C4×C22⋊D1114yes—
562C2×C4#6699012yes—
563C2×C4#6699114yes—
564C2×C4C22×C4×D1111yescharacteristic
565C2×C4C2×#433911yescharacteristic
566C2×C4C2×D4×D1111yescharacteristic
567C2×C4C2×D4×D1111yescharacteristic
568C2×C4C2×#434111yescharacteristic
569C2×C4C22×C22⋊D1111yescharacteristic
570C8—42no—
571C8—224no—
572C22—22no—
573C22—22no—
574C22—24no—
575C22—24no—
576C22—48no—
577C22—44no—
578C22—816no—
579C22—82no—
580C22—82no—
581C22—84no—
582C22—224no—
583C22—442no—
584C22—442no—
585C22—444no—
586C22—444no—
587C22#1062256914yes—
588C22C2×(C22⋊D11)⋊C411yescharacteristic
589C22C2×#6693711yescharacteristic
590C22D11×AGL(1,ℤ/8)12yes—
591C22#1062330412yes—
592C22C2×#6699011yescharacteristic
593C4—44no—
594C4—224no—
595C4—224no—
596C4—442no—
597C4—882no—
598C4#1062256914yes—
599C4C2×C22⋊C4×D1111yescharacteristic
600C4C2×#6693611yescharacteristic
601C4C2×C4×C22⋊D1111yescharacteristic
602C4C2×#6699111yescharacteristic
603C2—24no—
604C2—84no—
605C2—444no—
606C2C2×#1062256911yescharacteristic
607C2#1307742012yes—
608C2#1307786412yes—
609C2#1307809511yescharacteristic
610C2#1307810911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#418C2
socleC23×C11C22×D4
prime radicalC22×#66985C2
cosocleC22×C4×C11C24
hypercenterC2×#418D11
hypocenterC11#20928
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#418

Complements

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

NH ≅ G/Ntype
2. C2×#10623053C2semidirect
3. C2×#10622746C2semidirect
4. C2×#10622834C2semidirect
5. #13068968C2semidirect
6. #13068961C2semidirect
7. #13068337C2semidirect
8. #13068309C2semidirect
9. C2×C11×#418C2semidirect
18. C2×#66985C4semidirect
25. C2×#66946C22semidirect
26. C2×#66940C22semidirect
36. C2×#66885C22semidirect
37. C2×#66880C22semidirect
38. #10622188C22semidirect
39. #10622167C22semidirect
47. C22×D4×C11C2×C4semidirect
77. C2×#4324C2×C4semidirect
81. C2×#4323C2×C4semidirect
96. C2×#4318C2×C4semidirect
154. #4339C22⋊C4semidirect
202. C2×#418D11semidirect
263. C2×Dic11AGL(1,ℤ/8)semidirect
267. D44C2×C22⋊C4semidirect
273. Dic22C2×C22⋊C4semidirect
353. C22×D4C4×D11semidirect
503. C11#20928semidirect

Maximal subgroups

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

subgroupindex
C22×#669852
C2×#106230532
C2×#106227462
C2×#106228342
#130689682
#130689612
#130683372
#130683092
C2×C11×#4182
#2092811