Finite Group Databasebeta

← #14789835

Subgroups — #14789835

Order 2816.

1378 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66941C211yesmaximal, characteristic, complemented
2C2×#10622503C212yesmaximal, complemented
3#13071122C211yesmaximal, characteristic
4#13069942C212yesmaximal, complemented
5#13069751C212yesmaximal, complemented
6#13069566C212yesmaximal, complemented
7#13068933C211yesmaximal, characteristic
8#13068931C211yesmaximal, characteristic
9#13068803C211yesmaximal, characteristic, complemented
10#13068594C211yesmaximal, characteristic, complemented
11C11×#1852C211yesmaximal, characteristic, complemented
12C23×Dic22—21no—
13C22×C11×C4⋊C4C2211yescharacteristic
14C2×#66983C2211yescharacteristic
15C22×C4⋊Dic11C2211yescharacteristic
16C22×Dic11⋊C4—21no—
17C22×C4×Dic11C2211yescharacteristic
18C2×#66946C2211yescharacteristic
19C2×#66941—21no—
20C2×#66941—21no—
21C2×#66941—28no—
22C2×#66941C2212yes—
23C2×#66941C2212yes—
24C2×(C22⋊D11)⋊C4—21no—
25C2×C11×#107C2212yes—
26C2×C11×C22⋊C8C2211yescharacteristic
27C11×#380C2211yescharacteristic
28C2×C22⋊(C11⋊C8)C2211yescharacteristic
29C2×#66885C2212yes—
30C2×Dic11⋊C8C2212yes—
31#10622601C2211yescharacteristic
32C4⋊C4×Dic11C2211yescharacteristic
33#10622586C2211yescharacteristic
34C2×#66873C2212yes—
35C2×#66871C2212yes—
36#10622571—21no—
37#10622503—28no—
38#10622282—21no—
39#10622279—21no—
40C11×#340C2212yes—
41#10622189C2212yes—
42#10622188C2212yes—
43#10622167C2212yes—
44#10622167C2212yes—
45C23×C4×C11—21no—
46C23×C4×C11C2311yescharacteristic
47C22×C22⋊D11—21no—
48C23×Dic11—21no—
49C23×Dic11D411yescharacteristic
50C23×Dic11D411yescharacteristic
51C22×D44C2311yescharacteristic
52C22×C4×D11—21no—
53C22×Dic22—28no—
54C22×Dic22—22no—
55C22×Dic22—22no—
56C22×Dic22—44no—
57C22×Dic22—44no—
58C22×C8×C11C2312yes—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4—24no—
61C2×C11×C4⋊C4C2311yescharacteristic
62C2×C11×C4⋊C4C2311yescharacteristic
63C2×C11×C4⋊C4C2312yes—
64C2×C11×C22⋊C4—21no—
65#66983—22no—
66#66983Q814yescomplemented
67C2×(C2×D11)⋊C4—21no—
68C2×(C2×D11)⋊C4—21no—
69C2×(C2×D11)⋊C4—21no—
70C2×(C2×D11)⋊C4—21no—
71C2×C4⋊Dic11—21no—
72C2×C4⋊Dic11—24no—
73C2×C4⋊Dic11C2312yes—
74C2×C4⋊Dic11C2311yescharacteristic
75C2×Dic11⋊C4—28no—
76C2×Dic11⋊C4—22no—
77C2×Dic11⋊C4—22no—
78C2×Dic11⋊C4—21no—
79C2×C4×Dic11—24no—
80C2×C4×Dic11—21no—
81C2×C4×Dic11D411yescharacteristic
82C2×C4×Dic11D411yescharacteristic
83C2×C4×Dic11C2311yescharacteristic
84C2×C4×Dic11C2311yescharacteristic
85C22×C11⋊C8C2312yes—
86#66946—24no—
87#66941—28no—
88#66941—28no—
89#66941—24no—
90#66941—24no—
91#66941—24no—
92#66941D418yescomplemented
93(C22⋊D11)⋊C4—44no—
94C11×#107—24no—
95C11×C22⋊C8—22no—
96C11×#95—21no—
97C11⋊#95—21no—
98C11⋊#95—21no—
99C22⋊(C11⋊C8)—22no—
100#66885—24no—
101Dic11⋊C8—24no—
102#66873—24no—
103#66871—24no—
104#24298—111nomaximal, Sylow
105C24×C11C2×D411yescharacteristic
106C23×D11—21no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—24no—
110C22×C4×C11—22no—
111C22×C4×C11—21no—
112C22×C4×C11—21no—
113C22×C4×C11—42no—
114C22×C4×C11—42no—
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×Q812yes—
117C22×C4×C11#4112yes—
118C22×C4×C11C2411yescharacteristic
119C2×C22⋊D11—24no—
120C2×C22⋊D11—42no—
121C2×C22⋊D11—42no—
122C22×Dic11—22no—
123C22×Dic11—22no—
124C22×Dic11—22no—
125C22×Dic11—22no—
126C22×Dic11—24no—
127C22×Dic11—22no—
128C22×Dic11—21no—
129C22×Dic11—22no—
130C22×Dic11—42no—
131C22×Dic11—42no—
132C22×Dic11D814yes—
133C22×Dic11C2×D411yescharacteristic
134C22×Dic11C2×D411yescharacteristic
135C22×Dic11C2×D411yescharacteristic
136C22×Dic11C2×D411yescharacteristic
137C2×D44—22no—
138C2×D44—21no—
139C2×D44—22no—
140C2×D44C2×Q812yescomplemented
141C2×C4×D11—42no—
142C2×C4×D11—42no—
143C2×C4×D11—42no—
144C2×Dic22—28no—
145C2×Dic22—28no—
146C2×Dic22—432no—
147C2×Dic22—44no—
148C2×Dic22—44no—
149C2×Dic22—44no—
150C2×Dic22—44no—
151C2×C8×C11—22no—
152C2×C8×C11—22no—
153C2×C8×C11—22no—
154C11×C4⋊C4—24no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—22no—
158C11×C4⋊C4C2×D414yes—
159C11×C22⋊C4—42no—
160(C2×D11)⋊C4—24no—
161(C2×D11)⋊C4—42no—
162(C2×D11)⋊C4—42no—
163(C2×D11)⋊C4—42no—
164C4⋊Dic11—24no—
165C4⋊Dic11—22no—
166C4⋊Dic11—21no—
167C4⋊Dic11C2×D414yes—
168C4⋊Dic11C2×Q812yescomplemented
169Dic11⋊C4—28no—
170Dic11⋊C4—28no—
171Dic11⋊C4—42no—
172C4×Dic11—22no—
173C4×Dic11—22no—
174C4×Dic11—22no—
175C4×Dic11—42no—
176C4×Dic11C2×D414yes—
177C2×C11⋊C8—22no—
178C2×C11⋊C8—22no—
179C2×C11⋊C8—22no—
180C22×C4⋊Q8—111no—
181C2×#474—112no—
182C4×#121—111no—
183#2057—112no—
184#2023—112no—
185#1988—112no—
186#1874—111no—
187#1874—111no—
188#1852—111no—
189#1852D1111yescharacteristic, complemented
190#1797—111no—
191C23×C11—21no—
192C23×C11—21no—
193C23×C11—21no—
194C23×C11—21no—
195C23×C11C22⋊Q812yes—
196C23×C11C2×D812yes—
197C23×C11#13712yes—
198C23×C11C22×D411yescharacteristic
199C22×D11—22no—
200C22×D11—41no—
201C22×D11—41no—
202C22×D11—41no—
203C22×D11—41no—
204C22×D11—41no—
205C22×D11—41no—
206C2×C4×C11—21no—
207C2×C4×C11—21no—
208C2×C4×C11—24no—
209C2×C4×C11—24no—
210C2×C4×C11—24no—
211C2×C4×C11—48no—
212C2×C4×C11—42no—
213C2×C4×C11—42no—
214C2×C4×C11—41no—
215C2×C4×C11—41no—
216C2×C4×C11—41no—
217C2×C4×C11—41no—
218C2×C4×C11—41no—
219C2×C4×C11—41no—
220C2×C4×C11C22⋊Q812yes—
221C2×C4×C11C22×D412yes—
222C2×C4×C11C22×Q811yescharacteristic
223C2×C4×C11C2×#4111yescharacteristic
224C2×C4×C112−1+412yes—
225C22⋊D11—48no—
226C2×Dic11—28no—
227C2×Dic11—21no—
228C2×Dic11—21no—
229C2×Dic11—21no—
230C2×Dic11—21no—
231C2×Dic11—21no—
232C2×Dic11—21no—
233C2×Dic11—28no—
234C2×Dic11—24no—
235C2×Dic11—22no—
236C2×Dic11—48no—
237C2×Dic11—41no—
238C2×Dic11—42no—
239C2×Dic11—42no—
240C2×Dic11—41no—
241C2×Dic11#12012yes—
242C2×Dic11#12012yes—
243C2×Dic11C2×D812yes—
244C2×Dic11C2×D812yes—
245C2×Dic11AGL(1,ℤ/8)12yes—
246C2×Dic11#13712yes—
247D44—24no—
248D44—42no—
249C4×D11—84no—
250Dic22—416no—
251Dic22—416no—
252C8×C11—42no—
253C11⋊C8—42no—
254C23×Q8—221no—
255C2×C4⋊Q8—112no—
256C2×C4⋊Q8—112no—
257C2×C4⋊Q8—221no—
258C2×C4⋊Q8—221no—
259C2×C4⋊Q8—228no—
260C2×#121—111no—
261C2×C4×D4—111no—
262C2×C4×D4—221no—
263C22×C4⋊C4—111no—
264C22×C4⋊C4—221no—
265C22×C4⋊C4C2×D1111yescharacteristic
266C22×C42—111no—
267#474—228no—
268C2×#107—112no—
269C2×#107C2×D1112yes—
270C2×C4⋊C8—112no—
271C2×#102—112no—
272C2×#102—112no—
273C2×C22⋊C8—111no—
274C2×C22⋊C8C2×D1111yescharacteristic
275#390—111no—
276#389—111no—
277#388—221no—
278#386—221no—
279#380C2×D1111yescharacteristic
280C4×C4⋊C4—111no—
281C4×C22⋊C4—221no—
282#340—112no—
283#340—112no—
284#340—112no—
285#340C2×D1112yes—
286#336—112no—
287C22×C11—22no—
288C22×C11—22no—
289C22×C11—22no—
290C22×C11—22no—
291C22×C11—22no—
292C22×C11—22no—
293C22×C11#47414yescomplemented
294C22×C11C2×#12011yescharacteristic
295C22×C11C2×C22⋊Q811yescharacteristic
296C22×C11#53611yescharacteristic
297C22×C11C22×D811yescharacteristic
298C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
299C22×C11C2×#13711yescharacteristic
300C22×C11C2×#13711yescharacteristic
301C2×D11—42no—
302C2×D11—42no—
303C2×D11—42no—
304C2×D11—81no—
305C2×D11—81no—
306C2×D11—81no—
307C2×D11—81no—
308C4×C11—22no—
309C4×C11—44no—
310C4×C11—81no—
311C4×C11—81no—
312C4×C11#54812yes—
313C4×C11D4×Q812yes—
314Dic11—22no—
315Dic11—22no—
316Dic11—22no—
317Dic11—44no—
318Dic11—42no—
319Dic11#44714yes—
320C22×Q8—222no—
321C22×Q8—222no—
322C22×Q8—228no—
323C22×Q8—444no—
324C22×Q8—444no—
325C22×D4—111no—
326C22×D4—221no—
327C23×C4—21no—
328C23×C4—111no—
329C23×C4—111no—
330C23×C4—221no—
331C23×C4—221no—
332C23×C4C22×D1111yescharacteristic
333C22×C8—112no—
334C22×C8C22×D1112yes—
335C4⋊Q8—118no—
336C4⋊Q8—224no—
337C4⋊Q8—224no—
338C4⋊Q8—228no—
339C4⋊Q8—228no—
340C4⋊Q8—224no—
341#121—114no—
342#121—222no—
343C4×D4—224no—
344C4×D4—444no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—24no—
347C2×C4⋊C4—112no—
348C2×C4⋊C4—111no—
349C2×C4⋊C4—224no—
350C2×C4⋊C4—222no—
351C2×C4⋊C4—222no—
352C2×C4⋊C4—228no—
353C2×C4⋊C4—221no—
354C2×C4⋊C4—221no—
355C2×C4⋊C4C22×D1111yescharacteristic
356C2×C4⋊C4C22×D1111yescharacteristic
357C2×C4⋊C4C22×D1112yes—
358C2×C22⋊C4—21no—
359C2×C22⋊C4—221no—
360C2×C22⋊C4—221no—
361C2×C22⋊C4—221no—
362C2×C22⋊C4—221no—
363C2×C42—111no—
364C2×C42—111no—
365C2×C42—111no—
366C2×C42—111no—
367C2×C42—224no—
368C2×C42—221no—
369#107—24no—
370#107—224no—
371C4⋊C8—224no—
372#102—224no—
373#102—224no—
374C22⋊C8—22no—
375C22⋊C8—222no—
376#95—21no—
377#95—221no—
378#95—221no—
379C2×C11—24no—
380C2×C11#240911yescharacteristic
381C2×C11C2×#44711yescharacteristic
382C2×C11#300411yescharacteristic
383C2×C11C2×#47411yescharacteristic
384C2×C11#307911yescharacteristic
385C2×C11#322611yescharacteristic
386C2×C11#323911yescharacteristic
387D11—82no—
388C24—221no—
389C24D4×D1111yescharacteristic
390C2×Q8—228no—
391C2×Q8—228no—
392C2×Q8—444no—
393C2×Q8—444no—
394C2×Q8—444no—
395C2×Q8—4432no—
396C2×Q8—444no—
397C2×D4—112no—
398C2×D4—224no—
399C2×D4—221no—
400C2×D4—222no—
401C2×D4—222no—
402C2×D4—442no—
403C2×D4—442no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—24no—
407C22×C4—22no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—42no—
411C22×C4—42no—
412C22×C4—111no—
413C22×C4—114no—
414C22×C4—111no—
415C22×C4—111no—
416C22×C4—111no—
417C22×C4—222no—
418C22×C4—222no—
419C22×C4—222no—
420C22×C4—222no—
421C22×C4—222no—
422C22×C4—224no—
423C22×C4—221no—
424C22×C4—222no—
425C22×C4—442no—
426C22×C4—442no—
427C22×C4—442no—
428C22×C4—442no—
429C22×C4—442no—
430C22×C4#433912yes—
431C22×C4D4×D1111yescharacteristic
432C22×C4Q8×D1112yes—
433C22×C4C23×D1111yescharacteristic
434C2×C8—22no—
435C2×C8—22no—
436C2×C8—22no—
437C2×C8—222no—
438C2×C8—222no—
439C2×C8—222no—
440C4⋊C4—24no—
441C4⋊C4—22no—
442C4⋊C4—22no—
443C4⋊C4—22no—
444C4⋊C4—114no—
445C4⋊C4—112no—
446C4⋊C4—228no—
447C4⋊C4—228no—
448C4⋊C4—224no—
449C4⋊C4—221no—
450C4⋊C4—222no—
451C4⋊C4—442no—
452C4⋊C4D4×D1114yes—
453C22⋊C4—42no—
454C22⋊C4—224no—
455C22⋊C4—442no—
456C22⋊C4—442no—
457C22⋊C4—442no—
458C42—114no—
459C42—222no—
460C42—222no—
461C42—222no—
462C42—442no—
463C11#2429811yescharacteristic, complemented, Sylow
464C23—21no—
465C23—21no—
466C23—21no—
467C23—21no—
468C23—222no—
469C23—441no—
470C23—441no—
471C23—441no—
472C23—441no—
473C23—441no—
474C23—441no—
475C23#6694912yes—
476C23D8×D1112yes—
477C23#6697112yes—
478C23C2×D4×D1111yescharacteristic
479Q8—4416no—
480Q8—4416no—
481D4—224no—
482D4—448no—
483D4—442no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—24no—
489C2×C4—48no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—112no—
499C2×C4—112no—
500C2×C4—112no—
501C2×C4—112no—
502C2×C4—112no—
503C2×C4—112no—
504C2×C4—228no—
505C2×C4—228no—
506C2×C4—221no—
507C2×C4—221no—
508C2×C4—221no—
509C2×C4—221no—
510C2×C4—221no—
511C2×C4—221no—
512C2×C4—222no—
513C2×C4—224no—
514C2×C4—448no—
515C2×C4—441no—
516C2×C4—442no—
517C2×C4—441no—
518C2×C4—442no—
519C2×C4—884no—
520C2×C4#6694912yes—
521C2×C4C2×#433911yescharacteristic
522C2×C4C2×D4×D1112yes—
523C2×C4C2×Q8×D1111yescharacteristic
524C2×C4#6704312yes—
525C8—42no—
526C8—442no—
527C22—22no—
528C22—22no—
529C22—22no—
530C22—22no—
531C22—22no—
532C22—22no—
533C22—442no—
534C22—442no—
535C22—442no—
536C22—881no—
537C22—881no—
538C22—881no—
539C22—881no—
540C22#1062250314yescomplemented
541C22C2×#6694911yescharacteristic
542C22D11×#12011yescharacteristic
543C22#1062317911yescharacteristic
544C22C2×D8×D1111yescharacteristic
545C22C2×#6697111yescharacteristic
546C22D11×AGL(1,ℤ/8)11yescharacteristic
547C22D11×#13711yescharacteristic
548C4—22no—
549C4—44no—
550C4—81no—
551C4—81no—
552C4—114no—
553C4—222no—
554C4—222no—
555C4—222no—
556C4—444no—
557C4—442no—
558C4#1062308312yes—
559C4#1062316312yes—
560C2—24no—
561C2—882no—
562C2#1307198011yescharacteristic
563C2D11×#44711yescharacteristic
564C2#1307785111yescharacteristic
565C2C2×#1062250311yescharacteristic
566C2#1307842911yescharacteristic
567C2#1307973511yescharacteristic
568C2#1307984911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1852C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
hypercenter#1852D11
hypocenterC11#24298
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1852

Complements

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

NH ≅ G/Ntype
1. C22×#66941C2semidirect
2. C2×#10622503C2semidirect
4. #13069942C2semidirect
5. #13069751C2semidirect
6. #13069566C2semidirect
9. #13068803C2semidirect
10. #13068594C2semidirect
11. C11×#1852C2semidirect
66. #66983Q8semidirect
92. #66941D4semidirect
140. C2×D44C2×Q8semidirect
168. C4⋊Dic11C2×Q8semidirect
189. #1852D11semidirect
293. C22×C11#474semidirect
463. C11#24298semidirect
540. C22#10622503semidirect

Maximal subgroups

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

subgroupindex
C22×#669412
C2×#106225032
#130711222
#130699422
#130697512
#130695662
#130689332
#130689312
#130688032
#130685942
C11×#18522
#2429811