Finite Group Databasebeta

← #14769477

Subgroups — #14769477

Order 2816.

1818 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#4323C211yesmaximal, characteristic
2C2×#10622398C212yesmaximal, complemented
3D4×C22⋊Dic11C211yesmaximal, characteristic, complemented
4#13071436C211yesmaximal, characteristic, complemented
5#13069489C212yesmaximal, complemented
6#13068962C212yesmaximal, complemented
7#13068961C212yesmaximal, complemented
8#13068639C211yesmaximal, characteristic, complemented
9#13068548C211yesmaximal, characteristic, complemented
10#13068395C211yesmaximal, characteristic, complemented
11C11×#1786C211yesmaximal, characteristic, complemented
12C23×D4×C11C2211yescharacteristic
13C23×D44C2211yescharacteristic
14C22×C22⋊Dic11—21no—
15C2×D4×Dic11C2212yescomplemented
16C22×#4323—28no—
17C22×#4323C418yescomplemented
18C22×#4323C2211yescharacteristic
19C22×#4323C2211yescharacteristic
20C22×#4323C2211yescharacteristic
21C22×#4323C2211yescharacteristic
22C23×C11⋊C8C2211yescharacteristic
23C2×#66946C2212yescomplemented
24C2×C22⋊C4×D11—21no—
25C2×C11×#102C2212yescomplemented
26C2×C11×#102C2212yescomplemented
27C2×C11×C22⋊C8C2211yescharacteristic
28C11×#380C2211yescharacteristic
29#10622860—21no—
30#10622834C2212yescomplemented
31#10622833—22no—
32#10622825C2211yescharacteristic
33C4×C22⋊Dic11C2211yescharacteristic
34C2×#66885C2212yescomplemented
35C2×#66885C2212yescomplemented
36C2×#66879C2212yescomplemented
37#10622601C2212yescomplemented
38C2×#66872C2212yescomplemented
39#10622568—21no—
40#10622398—28no—
41#10622278—22no—
42#10622188C2212yescomplemented
43#10622167C2212yescomplemented
44C25×C11—21no—
45C24×D11—21no—
46C22×D4×C11—24no—
47C22×D4×C11—21no—
48C22×D4×C11—22no—
49C22×D4×C11—42no—
50C22×D4×C11C2×C414yescomplemented
51C22×D4×C11C2311yescharacteristic
52C22×D4×C11C2311yescharacteristic
53C23×C4×C11C2311yescharacteristic
54C23×Dic11—22no—
55C22×D44—24no—
56C22×D44—21no—
57C22×D44—22no—
58C22×D44—42no—
59C22×D44C2×C414yescomplemented
60C22×D44C2311yescharacteristic
61C22×D44C2311yescharacteristic
62C22×C4×D11—22no—
63C22×C8×C11C2312yes—
64C2×C11×C4⋊C4C2312yes—
65C2×C11×C22⋊C4—21no—
66C2×C22⋊Dic11—21no—
67C2×C22⋊Dic11—22no—
68C2×C22⋊Dic11—22no—
69C2×C22⋊Dic11—22no—
70C2×C22⋊Dic11—44no—
71C2×C22⋊Dic11D411yescharacteristic
72C2×C22⋊Dic11D411yescharacteristic
73D4×Dic11—24no—
74D4×Dic11—42no—
75C2×#4323—24no—
76C2×#4323—24no—
77C2×#4323—232no—
78C2×#4323—24no—
79C2×#4323C2×C414yes—
80C2×#4323C2×C414yescomplemented
81C2×#4323C2×C414yescomplemented
82C2×#4323C2×C414yescomplemented
83C2×#4323D418yes—
84C2×(C2×D11)⋊C4—22no—
85C2×(C2×D11)⋊C4—22no—
86C2×(C2×D11)⋊C4—22no—
87C2×C4⋊Dic11C2312yes—
88C2×C4×Dic11C2312yes—
89C22×C11⋊C8—24no—
90C22×C11⋊C8C2×C414yescomplemented
91C22×C11⋊C8C2311yescharacteristic
92C22×C11⋊C8C2311yescharacteristic
93#66946—24no—
94#66946—42no—
95C22⋊C4×D11—44no—
96C11×#102—24no—
97C11×#102—42no—
98C11×C22⋊C8—22no—
99C11×#95—21no—
100C11⋊#95—21no—
101C11⋊#95D412yes—
102#66885—24no—
103#66885—42no—
104#66879—24no—
105#66872—24no—
106#22436—111nomaximal, Sylow
107C24×C11—21no—
108C24×C11—21no—
109C24×C11—24no—
110C24×C11—44no—
111C24×C11—42no—
112C24×C11—42no—
113C24×C11—82no—
114C24×C11C2×D411yescharacteristic
115C23×D11—21no—
116C23×D11—21no—
117C23×D11—24no—
118C23×D11—44no—
119C23×D11—42no—
120C23×D11—42no—
121C23×D11—82no—
122C2×D4×C11—28no—
123C2×D4×C11—24no—
124C2×D4×C11—22no—
125C2×D4×C11—21no—
126C2×D4×C11—21no—
127C2×D4×C11—22no—
128C2×D4×C11—22no—
129C2×D4×C11—44no—
130C2×D4×C11—48no—
131C2×D4×C11—44no—
132C2×D4×C11C22×C412yes—
133C2×D4×C11C22×C412yes—
134C2×D4×C11C2×D414yes—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11C22×C412yes—
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11#4112yes—
141C22×C4×C11C2411yescharacteristic
142C22×Dic11—22no—
143C22×Dic11—44no—
144C22×Dic11—44no—
145C22×Dic11—82no—
146C22×Dic11C2×D412yes—
147C22×Dic11C2×D412yes—
148C2×D44—28no—
149C2×D44—24no—
150C2×D44—22no—
151C2×D44—21no—
152C2×D44—21no—
153C2×D44—22no—
154C2×D44—22no—
155C2×D44—44no—
156C2×D44—44no—
157C2×D44—48no—
158C2×D44C22×C412yes—
159C2×D44C22×C412yes—
160C2×D44C2×D414yes—
161C2×C4×D11—44no—
162C2×C4×D11—44no—
163C2×C4×D11—82no—
164C2×C8×C11—22no—
165C2×C8×C11—22no—
166C2×C8×C11—22no—
167C11×C4⋊C4—22no—
168C11×C4⋊C4—22no—
169C11×C22⋊C4—42no—
170C22⋊Dic11—22no—
171C22⋊Dic11—22no—
172C22⋊Dic11—44no—
173C22⋊Dic11—44no—
174C22⋊Dic11—42no—
175C22⋊Dic11—82no—
176#4323—28no—
177#4323—28no—
178#4323—28no—
179#4323C22⋊C4116yescomplemented
180(C2×D11)⋊C4—44no—
181(C2×D11)⋊C4—44no—
182(C2×D11)⋊C4—82no—
183C4⋊Dic11—22no—
184C4⋊Dic11—22no—
185C4×Dic11—22no—
186C4×Dic11—22no—
187C2×C11⋊C8—28no—
188C2×C11⋊C8—22no—
189C2×C11⋊C8C22×C412yes—
190C2×C11⋊C8C22×C412yes—
191C2×C11⋊C8C2×D414yes—
192C23×D8—111no—
193C2×#442—112no—
194D4×C22⋊C4—111no—
195D4×C22⋊C4—111no—
196#1972—112no—
197#1879—112no—
198#1879—112no—
199#1807—111no—
200#1786—111no—
201#1786D1111yescharacteristic, complemented
202#1752—111no—
203C23×C11—22no—
204C23×C11—22no—
205C23×C11—22no—
206C23×C11—24no—
207C23×C11—22no—
208C23×C11—48no—
209C23×C11—41no—
210C23×C11—41no—
211C23×C11—42no—
212C23×C11—42no—
213C23×C11—41no—
214C23×C11—41no—
215C23×C11—42no—
216C23×C11—48no—
217C23×C11—84no—
218C23×C11—88no—
219C23×C11—88no—
220C23×C11C4×D412yes—
221C23×C11AGL(1,ℤ/8)12yes—
222C23×C11AGL(1,ℤ/8)12yes—
223C23×C11C22×D411yescharacteristic
224C22×D11—22no—
225C22×D11—24no—
226C22×D11—22no—
227C22×D11—48no—
228C22×D11—41no—
229C22×D11—41no—
230C22×D11—42no—
231C22×D11—42no—
232C22×D11—41no—
233C22×D11—41no—
234C22×D11—42no—
235C22×D11—48no—
236C22×D11—84no—
237C22×D11—88no—
238C22×D11—88no—
239D4×C11—22no—
240D4×C11—22no—
241D4×C11—22no—
242D4×C11—24no—
243D4×C11—48no—
244D4×C11—42no—
245D4×C11C2×C22⋊C414yescomplemented
246C2×C4×C11—22no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—24no—
250C2×C4×C11—42no—
251C2×C4×C11—42no—
252C2×C4×C11—42no—
253C2×C4×C11C4×D412yes—
254C2×C4×C11C23×C411yescharacteristic
255C2×C4×C11C22×D412yes—
256C2×C4×C11C2×#4111yescharacteristic
257C2×C4×C11H(5,𝔽2)12yes—
258C2×Dic11—22no—
259C2×Dic11—22no—
260C2×Dic11—22no—
261C2×Dic11—22no—
262C2×Dic11—22no—
263C2×Dic11—22no—
264C2×Dic11—42no—
265C2×Dic11—42no—
266C2×Dic11—42no—
267C2×Dic11—88no—
268D44—22no—
269D44—22no—
270D44—22no—
271D44—24no—
272D44—48no—
273D44—42no—
274D44C2×C22⋊C414yescomplemented
275C4×D11—88no—
276C8×C11—42no—
277C11⋊C8—22no—
278C11⋊C8C2×C22⋊C414yescomplemented
279C23×D4—111no—
280C23×D4C2×D1111yescharacteristic
281C22×D8—111no—
282C22×D8—111no—
283C22×D8—111no—
284C22×D8—111no—
285C22×D8—118no—
286C22×D8—228no—
287C23×C8—111no—
288C2×C4×D4—112no—
289C2×C4×D4—112no—
290C22×C22⋊C4—221no—
291C22×C22⋊C4—221no—
292#442—228no—
293C2×#106—112no—
294C2×#102—112no—
295C2×#102—112no—
296C2×#102C2×D1112yescomplemented
297C2×#102C2×D1112yescomplemented
298C2×C22⋊C8C2×D1111yescharacteristic
299C2×#97—112no—
300#390—112no—
301#390—112no—
302#386—222no—
303#386—222no—
304#380—111no—
305#380C2×D1111yescharacteristic
306#379—221no—
307#379—221no—
308C4×C22⋊C4—111no—
309#340—112no—
310#336—112no—
311C22×C11—22no—
312C22×C11—22no—
313C22×C11—24no—
314C22×C11—24no—
315C22×C11—24no—
316C22×C11—42no—
317C22×C11—42no—
318C22×C11—44no—
319C22×C11—44no—
320C22×C11—42no—
321C22×C11—42no—
322C22×C11—42no—
323C22×C11—816no—
324C22×C11—82no—
325C22×C11—82no—
326C22×C11#44214yescomplemented
327C22×C11C2×C4×D411yescharacteristic
328C22×C11D4212yes—
329C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
330C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
331C22×C11#57612yes—
332C2×D11—24no—
333C2×D11—42no—
334C2×D11—42no—
335C2×D11—44no—
336C2×D11—44no—
337C2×D11—42no—
338C2×D11—42no—
339C2×D11—42no—
340C2×D11—816no—
341C2×D11—82no—
342C2×D11—82no—
343C4×C11—22no—
344C4×C11—82no—
345C4×C11C22×C22⋊C411yescharacteristic
346C4×C11#51811yescharacteristic
347C4×C11#54612yes—
348Dic11—42no—
349Dic11—42no—
350Dic11—82no—
351C25—21no—
352C25—221no—
353C22×D4—24no—
354C22×D4—21no—
355C22×D4—22no—
356C22×D4—42no—
357C22×D4—114no—
358C22×D4—111no—
359C22×D4—111no—
360C22×D4—224no—
361C22×D4—221no—
362C22×D4—222no—
363C22×D4—442no—
364C22×D4C4×D1114yescomplemented
365C22×D4C22×D1111yescharacteristic
366C22×D4C22×D1111yescharacteristic
367C23×C4—222no—
368C23×C4—222no—
369C23×C4C22×D1111yescharacteristic
370C2×D8—114no—
371C2×D8—118no—
372C2×D8—114no—
373C2×D8—114no—
374C2×D8—114no—
375C2×D8—224no—
376C2×D8—2232no—
377C2×D8—224no—
378C2×D8—224no—
379C22×C8—111no—
380C22×C8—114no—
381C22×C8—111no—
382C22×C8—224no—
383C22×C8C22×D1112yes—
384C4×D4—224no—
385C4×D4—224no—
386C4×D4—442no—
387C4×D4—442no—
388C2×C4⋊C4—112no—
389C2×C4⋊C4C22×D1112yes—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—111no—
392C2×C22⋊C4—111no—
393C2×C22⋊C4—222no—
394C2×C22⋊C4—222no—
395C2×C22⋊C4—222no—
396C2×C22⋊C4—222no—
397C2×C22⋊C4—221no—
398C2×C22⋊C4—222no—
399C2×C22⋊C4—222no—
400C2×C22⋊C4—444no—
401C2×C22⋊C4—444no—
402C2×C42—112no—
403#106—224no—
404#102—24no—
405#102—42no—
406#102—224no—
407#102—442no—
408C22⋊C8—22no—
409#97—224no—
410#95—21no—
411#95—112no—
412#95—221no—
413C2×C11—24no—
414C2×C11—44no—
415C2×C11—82no—
416C2×C11D4×C22⋊C411yescharacteristic
417C2×C11C2×#44211yescharacteristic
418C2×C11#294811yescharacteristic
419C2×C11#326412yes—
420C2×C11#326412yes—
421D11—44no—
422D11—82no—
423C24—21no—
424C24—21no—
425C24—24no—
426C24—44no—
427C24—42no—
428C24—42no—
429C24—82no—
430C24—221no—
431C24—221no—
432C24—224no—
433C24—444no—
434C24—442no—
435C24—442no—
436C24—882no—
437C24D4×D1111yescharacteristic
438C2×D4—28no—
439C2×D4—24no—
440C2×D4—22no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—22no—
444C2×D4—22no—
445C2×D4—44no—
446C2×D4—48no—
447C2×D4—44no—
448C2×D4—112no—
449C2×D4—112no—
450C2×D4—114no—
451C2×D4—228no—
452C2×D4—224no—
453C2×D4—222no—
454C2×D4—221no—
455C2×D4—221no—
456C2×D4—222no—
457C2×D4—222no—
458C2×D4—444no—
459C2×D4—448no—
460C2×D4—444no—
461C2×D4C2×C4×D1112yes—
462C2×D4C2×C4×D1112yes—
463C2×D4D4×D1114yes—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—112no—
468C22×C4—112no—
469C22×C4—222no—
470C22×C4—444no—
471C22×C4—444no—
472C22×C4—444no—
473C22×C4—444no—
474C22×C4—882no—
475C22×C4—882no—
476C22×C4C2×C4×D1112yes—
477C22×C4D4×D1111yescharacteristic
478C22×C4#434112yes—
479C22×C4C23×D1111yescharacteristic
480D8—1116no—
481D8—228no—
482D8—228no—
483D8—228no—
484C2×C8—22no—
485C2×C8—22no—
486C2×C8—22no—
487C2×C8—112no—
488C2×C8—114no—
489C2×C8—112no—
490C2×C8—228no—
491C2×C8—222no—
492C4⋊C4—22no—
493C4⋊C4—22no—
494C4⋊C4—222no—
495C4⋊C4—222no—
496C22⋊C4—42no—
497C22⋊C4—222no—
498C22⋊C4—222no—
499C22⋊C4—444no—
500C22⋊C4—444no—
501C22⋊C4—444no—
502C22⋊C4—444no—
503C22⋊C4—442no—
504C22⋊C4—882no—
505C22⋊C4—882no—
506C42—222no—
507C42—222no—
508C11#2243611yescharacteristic, complemented, Sylow
509C23—22no—
510C23—22no—
511C23—22no—
512C23—24no—
513C23—22no—
514C23—48no—
515C23—41no—
516C23—41no—
517C23—42no—
518C23—41no—
519C23—41no—
520C23—42no—
521C23—42no—
522C23—48no—
523C23—84no—
524C23—88no—
525C23—88no—
526C23—222no—
527C23—224no—
528C23—222no—
529C23—448no—
530C23—441no—
531C23—441no—
532C23—442no—
533C23—441no—
534C23—441no—
535C23—442no—
536C23—442no—
537C23—448no—
538C23—884no—
539C23—888no—
540C23—888no—
541C23(C22⋊D11)⋊C412yes—
542C23#6696412yes—
543C23#6696712yes—
544C23C2×D4×D1111yescharacteristic
545D4—22no—
546D4—22no—
547D4—22no—
548D4—24no—
549D4—48no—
550D4—42no—
551D4—114no—
552D4—222no—
553D4—222no—
554D4—222no—
555D4—224no—
556D4—448no—
557D4—442no—
558D4C22⋊C4×D1114yescomplemented
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—24no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—222no—
567C2×C4—222no—
568C2×C4—222no—
569C2×C4—222no—
570C2×C4—222no—
571C2×C4—222no—
572C2×C4—442no—
573C2×C4—442no—
574C2×C4—442no—
575C2×C4—888no—
576C2×C4—888no—
577C2×C4(C22⋊D11)⋊C412yes—
578C2×C4C22×C4×D1111yescharacteristic
579C2×C4C2×D4×D1112yes—
580C2×C4C2×#434111yescharacteristic
581C2×C4#6703712yes—
582C8—42no—
583C8—114no—
584C8—222no—
585C22—24no—
586C22—24no—
587C22—22no—
588C22—22no—
589C22—24no—
590C22—44no—
591C22—44no—
592C22—42no—
593C22—42no—
594C22—42no—
595C22—42no—
596C22—42no—
597C22—816no—
598C22—82no—
599C22—82no—
600C22—224no—
601C22—444no—
602C22—444no—
603C22—442no—
604C22—442no—
605C22—442no—
606C22—442no—
607C22—442no—
608C22—8816no—
609C22—882no—
610C22—882no—
611C22#1062239814yescomplemented
612C22C2×(C22⋊D11)⋊C411yescharacteristic
613C22#1062312112yes—
614C22C2×#6696411yescharacteristic
615C22C2×#6696711yescharacteristic
616C22#1062330512yes—
617C4—22no—
618C4—82no—
619C4—442no—
620C4—442no—
621C4—882no—
622C4C2×C22⋊C4×D1111yescharacteristic
623C4#1062301711yescharacteristic
624C4#1062312212yes—
625C2—24no—
626C2—44no—
627C2—82no—
628C2—444no—
629C2—882no—
630C2#1307143211yescharacteristic
631C2C2×#1062239811yescharacteristic
632C2#1307746411yescharacteristic
633C2#1308008912yes—
634C2#1308010012yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1786C2
socleC23×C11C22×D4
prime radicalC23×#4323C2
cosocleC22×C4×C11C24
hypercenter#1786D11
hypocenterC11#22436
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1786

Complements

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

NH ≅ G/Ntype
2. C2×#10622398C2semidirect
3. D4×C22⋊Dic11C2semidirect
4. #13071436C2semidirect
5. #13069489C2semidirect
6. #13068962C2semidirect
7. #13068961C2semidirect
8. #13068639C2semidirect
9. #13068548C2semidirect
10. #13068395C2semidirect
11. C11×#1786C2semidirect
15. C2×D4×Dic11C22semidirect
17. C22×#4323C4semidirect
23. C2×#66946C22semidirect
25. C2×C11×#102C22semidirect
26. C2×C11×#102C22semidirect
30. #10622834C22semidirect
34. C2×#66885C22semidirect
35. C2×#66885C22semidirect
36. C2×#66879C22semidirect
37. #10622601C22semidirect
38. C2×#66872C22semidirect
42. #10622188C22semidirect
43. #10622167C22semidirect
50. C22×D4×C11C2×C4semidirect
59. C22×D44C2×C4semidirect
80. C2×#4323C2×C4semidirect
81. C2×#4323C2×C4semidirect
82. C2×#4323C2×C4semidirect
90. C22×C11⋊C8C2×C4semidirect
179. #4323C22⋊C4semidirect
201. #1786D11semidirect
245. D4×C11C2×C22⋊C4semidirect
274. D44C2×C22⋊C4semidirect
278. C11⋊C8C2×C22⋊C4semidirect
296. C2×#102C2×D11semidirect
297. C2×#102C2×D11semidirect
326. C22×C11#442semidirect
364. C22×D4C4×D11semidirect
508. C11#22436semidirect
558. D4C22⋊C4×D11semidirect
611. C22#10622398semidirect

Maximal subgroups

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

subgroupindex
C23×#43232
C2×#106223982
D4×C22⋊Dic112
#130714362
#130694892
#130689622
#130689612
#130686392
#130685482
#130683952
C11×#17862
#2243611