Finite Group Databasebeta

← #14810418

Subgroups — #14810418

Order 2816.

1116 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66943C211yesmaximal, characteristic, complemented
2C2×#10622413C212yesmaximal, complemented
3#13076919C211yesmaximal, characteristic
4#13069765C212yesmaximal, complemented
5#13069761C212yesmaximal, complemented
6#13069579C212yesmaximal, complemented
7#13068933C211yesmaximal, characteristic
8#13068931C211yesmaximal, characteristic
9#13068924C211yesmaximal, characteristic, complemented
10C22⋊C8×Dic11C211yesmaximal, characteristic, complemented
11C11×#1872C211yesmaximal, characteristic, complemented
12C2×C11×C22⋊Q8C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C2×#67000C2211yescharacteristic
15C2×#66983C2211yescharacteristic
16C22×C4⋊Dic11—21no—
17C22×C4⋊Dic11C2211yescharacteristic
18C22×Dic11⋊C4—21no—
19C22×C4×Dic11C2211yescharacteristic
20C2×#66943—21no—
21C2×#66943—21no—
22C2×#66943—28no—
23C2×#66943C2212yes—
24C2×#66943C2212yes—
25C2×C11×#103C2212yes—
26C2×C11×C22⋊C8C2211yescharacteristic
27#10622843C2211yescharacteristic
28C2×#66899C2212yes—
29C2×C22⋊(C11⋊C8)C2211yescharacteristic
30C2×#66885C2212yes—
31C2×C8×Dic11C2212yes—
32#10622603—21no—
33#10622603—21no—
34#10622601C2211yescharacteristic
35#10622590C2211yescharacteristic
36C2×#66873C2212yes—
37#10622571—21no—
38#10622571—21no—
39#10622413—28no—
40C11×#340C2212yes—
41#10622189C2212yes—
42#10622188C2212yes—
43#10622167C2212yes—
44#10622167C2212yes—
45C22×Q8×C11C2311yescharacteristic
46C23×C4×C11—21no—
47C23×C4×C11C2311yescharacteristic
48C22×C22⋊D11—21no—
49C23×Dic11—21no—
50C23×Dic11D411yescharacteristic
51C23×Dic11D411yescharacteristic
52C22×D44C2311yescharacteristic
53C22×C8×C11C2312yes—
54C11×C22⋊Q8—22no—
55C11×C22⋊Q8—22no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4—24no—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4C2311yescharacteristic
60C2×C11×C4⋊C4C2312yes—
61C2×C11×C22⋊C4—21no—
62#67000—24no—
63#66983—22no—
64#66983—22no—
65C2×(C2×D11)⋊C4—21no—
66C2×(C2×D11)⋊C4—21no—
67C2×(C2×D11)⋊C4—21no—
68C2×(C2×D11)⋊C4—21no—
69C2×(C2×D11)⋊C4—21no—
70C2×C4⋊Dic11—28no—
71C2×C4⋊Dic11—21no—
72C2×C4⋊Dic11—22no—
73C2×C4⋊Dic11—22no—
74C2×C4⋊Dic11—24no—
75C2×C4⋊Dic11C2311yescharacteristic
76C2×C4⋊Dic11C2312yes—
77C2×Dic11⋊C4—28no—
78C2×Dic11⋊C4—22no—
79C2×Dic11⋊C4—22no—
80C2×C4×Dic11—24no—
81C2×C4×Dic11D411yescharacteristic
82C2×C4×Dic11D411yescharacteristic
83C2×C4×Dic11C2311yescharacteristic
84C2×C4×Dic11C2311yescharacteristic
85C22×C11⋊C8C2312yes—
86#66943—28no—
87#66943—28no—
88#66943—24no—
89#66943—24no—
90#66943—24no—
91#66943D418yescomplemented
92C11×#103—24no—
93C11×C22⋊C8—22no—
94#66899—24no—
95C11⋊#95—21no—
96C11⋊#95—21no—
97C11⋊#95—21no—
98C11⋊#95—21no—
99C22⋊(C11⋊C8)—22no—
100#66885—24no—
101C8×Dic11—24no—
102#66873—24no—
103#25907—111nomaximal, Sylow
104C24×C11C2×D411yescharacteristic
105C23×D11—21no—
106C2×Q8×C11—22no—
107C2×Q8×C11—21no—
108C2×Q8×C11—21no—
109C2×Q8×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—24no—
113C22×C4×C11—22no—
114C22×C4×C11—21no—
115C22×C4×C11—21no—
116C22×C4×C11—42no—
117C22×C4×C11—42no—
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11#4112yes—
120C22×C4×C11#4112yes—
121C22×C4×C11C2411yescharacteristic
122C2×C22⋊D11—42no—
123C2×C22⋊D11—42no—
124C2×C22⋊D11—42no—
125C22×Dic11—24no—
126C22×Dic11—22no—
127C22×Dic11—22no—
128C22×Dic11—22no—
129C22×Dic11—22no—
130C22×Dic11—22no—
131C22×Dic11—21no—
132C22×Dic11—41no—
133C22×Dic11—41no—
134C22×Dic11—42no—
135C22×Dic11—42no—
136C22×Dic11C2×D411yescharacteristic
137C22×Dic11C2×D411yescharacteristic
138C22×Dic11C2×D411yescharacteristic
139C22×Dic11C2×D411yescharacteristic
140C2×D44—22no—
141C2×D44—21no—
142C2×D44—21no—
143C2×D44—22no—
144C2×C8×C11—22no—
145C2×C8×C11—22no—
146C2×C8×C11—22no—
147C11×C4⋊C4—24no—
148C11×C4⋊C4—22no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—42no—
152C11×C4⋊C4C2×D414yes—
153C11×C22⋊C4—42no—
154(C2×D11)⋊C4—42no—
155(C2×D11)⋊C4—42no—
156(C2×D11)⋊C4—42no—
157(C2×D11)⋊C4—42no—
158(C2×D11)⋊C4—42no—
159C4⋊Dic11—24no—
160C4⋊Dic11—28no—
161C4⋊Dic11—28no—
162C4⋊Dic11—22no—
163C4⋊Dic11—21no—
164C4⋊Dic11—21no—
165C4⋊Dic11C2×D414yes—
166Dic11⋊C4—28no—
167Dic11⋊C4—28no—
168C4×Dic11—22no—
169C4×Dic11—22no—
170C4×Dic11—22no—
171C4×Dic11C2×D414yes—
172C2×C11⋊C8—22no—
173C2×C11⋊C8—22no—
174C2×C11⋊C8—22no—
175C22×#125—111no—
176C2×#488—112no—
177#2850—111no—
178#2026—112no—
179#2025—112no—
180#1991—112no—
181#1874—111no—
182#1874—111no—
183#1872—111no—
184#1872D1111yescharacteristic, complemented
185C4×C22⋊C8—111no—
186C23×C11—21no—
187C23×C11—21no—
188C23×C11—21no—
189C23×C11—21no—
190C23×C11#12412yes—
191C23×C11#13512yes—
192C23×C11#13512yes—
193C23×C11C22×D411yescharacteristic
194C22×D11—41no—
195C22×D11—41no—
196C22×D11—41no—
197C22×D11—41no—
198C22×D11—41no—
199C22×D11—41no—
200C22×D11—41no—
201Q8×C11—42no—
202Q8×C11—42no—
203C2×C4×C11—21no—
204C2×C4×C11—21no—
205C2×C4×C11—24no—
206C2×C4×C11—24no—
207C2×C4×C11—24no—
208C2×C4×C11—48no—
209C2×C4×C11—42no—
210C2×C4×C11—42no—
211C2×C4×C11—41no—
212C2×C4×C11—41no—
213C2×C4×C11—41no—
214C2×C4×C11—41no—
215C2×C4×C11—41no—
216C2×C4×C11—41no—
217C2×C4×C11#12412yes—
218C2×C4×C11C22×D412yes—
219C2×C4×C11C2×#4111yescharacteristic
220C2×C4×C11C2×#4111yescharacteristic
221C2×C4×C112−1+412yes—
222C22⋊D11—84no—
223C2×Dic11—21no—
224C2×Dic11—21no—
225C2×Dic11—21no—
226C2×Dic11—21no—
227C2×Dic11—21no—
228C2×Dic11—21no—
229C2×Dic11—24no—
230C2×Dic11—21no—
231C2×Dic11—21no—
232C2×Dic11—21no—
233C2×Dic11—21no—
234C2×Dic11—44no—
235C2×Dic11—44no—
236C2×Dic11—48no—
237C2×Dic11—42no—
238C2×Dic11—42no—
239C2×Dic11—41no—
240C2×Dic11—41no—
241C2×Dic11—41no—
242C2×Dic11#12012yes—
243C2×Dic11#12012yes—
244D44—42no—
245D44—42no—
246C8×C11—42no—
247C11⋊C8—42no—
248C2×#125—112no—
249C2×#125—112no—
250C2×#125—221no—
251C2×#125—221no—
252C2×#125—228no—
253C2×#124—111no—
254C2×C22⋊Q8C2×D1111yescharacteristic
255C2×#121—111no—
256C22×C4⋊C4—111no—
257C22×C4⋊C4—221no—
258C22×C4⋊C4—221no—
259C22×C4⋊C4C2×D1111yescharacteristic
260C22×C42—111no—
261#488—228no—
262C2×#103—112no—
263C2×#103C2×D1112yes—
264C2×#102—112no—
265C2×#102—112no—
266C2×C22⋊C8—111no—
267C2×C22⋊C8C2×D1111yescharacteristic
268C2×C4×C8—112no—
269#391—111no—
270#390—111no—
271#388—221no—
272#388—221no—
273#386—221no—
274#386—221no—
275#382—111no—
276#340—112no—
277#340—112no—
278#340—112no—
279#340C2×D1112yes—
280#336—112no—
281C22×C11—22no—
282C22×C11—22no—
283C22×C11—22no—
284C22×C11—22no—
285C22×C11—22no—
286C22×C11—22no—
287C22×C11#48814yescomplemented
288C22×C11C2×#12011yescharacteristic
289C22×C11C2×#12411yescharacteristic
290C22×C11#53611yescharacteristic
291C22×C11C2×#13511yescharacteristic
292C22×C11C2×#13511yescharacteristic
293C22×C11#57511yescharacteristic
294C22×C11#57511yescharacteristic
295C2×D11—81no—
296C2×D11—81no—
297C2×D11—81no—
298C2×D11—81no—
299C2×D11—81no—
300C2×D11—81no—
301C2×D11—81no—
302C4×C11—22no—
303C4×C11—44no—
304C4×C11—81no—
305C4×C11—81no—
306C4×C11#54812yes—
307C4×C11#54812yes—
308Dic11—22no—
309Dic11—22no—
310Dic11—41no—
311Dic11—41no—
312Dic11—44no—
313Dic11—81no—
314C22×Q8C22×D1111yescharacteristic
315C22×D4—111no—
316C22×D4—221no—
317C23×C4—21no—
318C23×C4—111no—
319C23×C4—111no—
320C23×C4—221no—
321C23×C4C22×D1111yescharacteristic
322C22×C8—112no—
323C22×C8C22×D1112yes—
324#125—118no—
325#125—224no—
326#125—224no—
327#125—228no—
328#125—228no—
329#125—224no—
330#124—224no—
331C22⋊Q8—22no—
332C22⋊Q8—22no—
333#121—222no—
334#121—222no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—112no—
339C2×C4⋊C4—111no—
340C2×C4⋊C4—224no—
341C2×C4⋊C4—222no—
342C2×C4⋊C4—222no—
343C2×C4⋊C4—222no—
344C2×C4⋊C4—222no—
345C2×C4⋊C4—228no—
346C2×C4⋊C4—228no—
347C2×C4⋊C4—221no—
348C2×C4⋊C4C22×D1111yescharacteristic
349C2×C4⋊C4C22×D1112yes—
350C2×C22⋊C4—21no—
351C2×C22⋊C4—221no—
352C2×C22⋊C4—221no—
353C2×C22⋊C4—221no—
354C2×C22⋊C4—221no—
355C2×C22⋊C4—221no—
356C2×C42—111no—
357C2×C42—111no—
358C2×C42—111no—
359C2×C42—111no—
360C2×C42—224no—
361#103—24no—
362#103—224no—
363#102—224no—
364#102—224no—
365C22⋊C8—22no—
366C22⋊C8—222no—
367C4×C8—224no—
368#95—221no—
369#95—221no—
370#95—221no—
371#95—221no—
372C2×C11—24no—
373C2×C11#243611yescharacteristic
374C2×C11#300211yescharacteristic
375C2×C11#300211yescharacteristic
376C2×C11C2×#48811yescharacteristic
377C2×C11#314211yescharacteristic
378C2×C11#323211yescharacteristic
379C2×C11#323211yescharacteristic
380D11—161no—
381C24—221no—
382C24D4×D1111yescharacteristic
383C2×Q8—21no—
384C2×Q8—22no—
385C2×Q8—21no—
386C2×Q8—22no—
387C2×D4—221no—
388C2×D4—222no—
389C2×D4—221no—
390C2×D4—222no—
391C2×D4—442no—
392C2×D4—442no—
393C2×D4—442no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—24no—
397C22×C4—22no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—42no—
401C22×C4—42no—
402C22×C4—111no—
403C22×C4—111no—
404C22×C4—111no—
405C22×C4—111no—
406C22×C4—222no—
407C22×C4—222no—
408C22×C4—224no—
409C22×C4—222no—
410C22×C4—222no—
411C22×C4—222no—
412C22×C4—221no—
413C22×C4—441no—
414C22×C4—441no—
415C22×C4—442no—
416C22×C4—442no—
417C22×C4#433912yes—
418C22×C4D4×D1111yescharacteristic
419C22×C4#434112yes—
420C22×C4C23×D1111yescharacteristic
421C2×C8—22no—
422C2×C8—22no—
423C2×C8—22no—
424C2×C8—222no—
425C2×C8—222no—
426C2×C8—222no—
427C4⋊C4—24no—
428C4⋊C4—22no—
429C4⋊C4—21no—
430C4⋊C4—21no—
431C4⋊C4—42no—
432C4⋊C4—114no—
433C4⋊C4—228no—
434C4⋊C4—228no—
435C4⋊C4—228no—
436C4⋊C4—224no—
437C4⋊C4—228no—
438C4⋊C4—222no—
439C4⋊C4—221no—
440C4⋊C4—221no—
441C4⋊C4D4×D1114yes—
442C22⋊C4—42no—
443C22⋊C4—442no—
444C22⋊C4—442no—
445C22⋊C4—442no—
446C22⋊C4—442no—
447C22⋊C4—442no—
448C42—114no—
449C42—222no—
450C42—222no—
451C42—222no—
452C11#2590711yescharacteristic, complemented, Sylow
453C23—21no—
454C23—21no—
455C23—21no—
456C23—21no—
457C23—441no—
458C23—441no—
459C23—441no—
460C23—441no—
461C23—441no—
462C23—441no—
463C23—441no—
464C23#6693812yes—
465C23#6696912yes—
466C23#6697212yes—
467C23C2×D4×D1111yescharacteristic
468Q8—42no—
469Q8—42no—
470D4—442no—
471D4—442no—
472D4—884no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—24no—
476C2×C4—24no—
477C2×C4—24no—
478C2×C4—48no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—112no—
488C2×C4—112no—
489C2×C4—221no—
490C2×C4—221no—
491C2×C4—221no—
492C2×C4—221no—
493C2×C4—221no—
494C2×C4—221no—
495C2×C4—221no—
496C2×C4—221no—
497C2×C4—221no—
498C2×C4—221no—
499C2×C4—224no—
500C2×C4—444no—
501C2×C4—444no—
502C2×C4—448no—
503C2×C4—442no—
504C2×C4—442no—
505C2×C4—441no—
506C2×C4—441no—
507C2×C4—441no—
508C2×C4#6693812yes—
509C2×C4C2×#433911yescharacteristic
510C2×C4C2×D4×D1112yes—
511C2×C4C2×#434111yescharacteristic
512C2×C4#6704312yes—
513C8—42no—
514C8—442no—
515C22—22no—
516C22—22no—
517C22—22no—
518C22—22no—
519C22—22no—
520C22—22no—
521C22—881no—
522C22—881no—
523C22—881no—
524C22—881no—
525C22—881no—
526C22—881no—
527C22—881no—
528C22#1062241314yescomplemented
529C22C2×#6693811yescharacteristic
530C22D11×#12011yescharacteristic
531C22#1062317911yescharacteristic
532C22C2×#6696911yescharacteristic
533C22C2×#6697211yescharacteristic
534C22#1062330411yescharacteristic
535C22#1062330811yescharacteristic
536C4—22no—
537C4—44no—
538C4—81no—
539C4—81no—
540C4—222no—
541C4—222no—
542C4—441no—
543C4—441no—
544C4—444no—
545C4—881no—
546C4#1062308312yes—
547C4#1062312912yes—
548C2—24no—
549C2—1761no—
550C2#1307227211yescharacteristic
551C2#1307783511yescharacteristic
552C2#1307783911yescharacteristic
553C2C2×#1062241311yescharacteristic
554C2#1307901411yescharacteristic
555C2#1307978711yescharacteristic
556C2#1307978911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1872C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
hypercenter#1872D11
hypocenterC11#25907
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1872

Complements

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

NH ≅ G/Ntype
1. C22×#66943C2semidirect
2. C2×#10622413C2semidirect
4. #13069765C2semidirect
5. #13069761C2semidirect
6. #13069579C2semidirect
9. #13068924C2semidirect
10. C22⋊C8×Dic11C2semidirect
11. C11×#1872C2semidirect
91. #66943D4semidirect
184. #1872D11semidirect
287. C22×C11#488semidirect
452. C11#25907semidirect
528. C22#10622413semidirect

Maximal subgroups

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

subgroupindex
C22×#669432
C2×#106224132
#130769192
#130697652
#130697612
#130695792
#130689332
#130689312
#130689242
C22⋊C8×Dic112
C11×#18722
#2590711