Finite Group Databasebeta

← #14789833

Subgroups — #14789833

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×#10622372C212yesmaximal, complemented
3#121×Dic11C211yesmaximal, characteristic
4#13069943C212yesmaximal, complemented
5#13069750C212yesmaximal, complemented
6#13069566C212yesmaximal, complemented
7#13068934C211yesmaximal, characteristic
8#13068806C211yesmaximal, characteristic, complemented
9#13068804C211yesmaximal, characteristic, complemented
10#13068594C211yesmaximal, characteristic, complemented
11C11×#1874C211yesmaximal, characteristic
12C23×Dic22—21no—
13C2×C11×#121C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C2×D4×Dic11—21no—
16C2×D4×Dic11C2211yescharacteristic
17C22×C4⋊Dic11C2211yescharacteristic
18C22×Dic11⋊C4—21no—
19C22×C4×Dic11C2211yescharacteristic
20C2×#66941—21no—
21C2×#66941—21no—
22C2×#66941—28no—
23C2×#66941C2212yes—
24C2×#66941C2212yes—
25C2×C11×#102C2212yes—
26C2×C11×C22⋊C8C2211yescharacteristic
27#10622834C2211yescharacteristic
28#10622833—21no—
29C2×#66896C2212yes—
30#10622825C2211yescharacteristic
31C2×C22⋊(C11⋊C8)C2211yescharacteristic
32C2×#66882C2212yes—
33C2×Dic11⋊C8C2212yes—
34#10622598C2211yescharacteristic
35C4⋊C4×Dic11C2211yescharacteristic
36C2×#66871C2212yes—
37#10622564—21no—
38C22⋊C4×Dic11—21no—
39#10622372—28no—
40C11×#340C2212yes—
41#10622189C2212yes—
42#10622188C2212yes—
43#10622167C2212yes—
44#10622167C2212yes—
45C22×D4×C11—21no—
46C22×D4×C11C2311yescharacteristic
47C23×C4×C11—21no—
48C23×C4×C11C2311yescharacteristic
49C23×Dic11—21no—
50C23×Dic11—21no—
51C23×Dic11D411yescharacteristic
52C23×Dic11D411yescharacteristic
53C22×Dic22—28no—
54C22×Dic22—22no—
55C22×Dic22—22no—
56C22×Dic22—44no—
57C22×Dic22—44no—
58C22×C8×C11C2312yes—
59C11×#121—22no—
60C11×#121Q814yescomplemented
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4—24no—
63C2×C11×C4⋊C4C2312yes—
64C2×C11×C4⋊C4C2311yescharacteristic
65C2×C11×C22⋊C4—21no—
66C2×C22⋊Dic11—21no—
67C2×C22⋊Dic11—21no—
68C2×C22⋊Dic11—21no—
69C2×C22⋊Dic11—21no—
70D4×Dic11—24no—
71D4×Dic11—44no—
72C2×C4⋊Dic11—21no—
73C2×C4⋊Dic11—24no—
74C2×C4⋊Dic11—21no—
75C2×C4⋊Dic11C2311yescharacteristic
76C2×C4⋊Dic11C2311yescharacteristic
77C2×C4⋊Dic11C2312yes—
78C2×Dic11⋊C4—28no—
79C2×Dic11⋊C4—22no—
80C2×Dic11⋊C4—22no—
81C2×C4×Dic11—24no—
82C2×C4×Dic11—21no—
83C2×C4×Dic11D411yescharacteristic
84C2×C4×Dic11D411yescharacteristic
85C2×C4×Dic11C2311yescharacteristic
86C2×C4×Dic11C2311yescharacteristic
87C22×C11⋊C8C2312yes—
88#66941—28no—
89#66941—28no—
90#66941—24no—
91#66941—24no—
92#66941—24no—
93#66941D418yescomplemented
94C11×#102—24no—
95C11×C22⋊C8—22no—
96#66896—24no—
97C11⋊#95—21no—
98C11⋊#95—21no—
99C11⋊#95—21no—
100C22⋊(C11⋊C8)—22no—
101#66882—24no—
102Dic11⋊C8—24no—
103#66871—24no—
104#24298—111nomaximal, Sylow
105C24×C11—21no—
106C24×C11C2×D411yescharacteristic
107C2×D4×C11—24no—
108C2×D4×C11—22no—
109C2×D4×C11—21no—
110C2×D4×C11—22no—
111C2×D4×C11—42no—
112C2×D4×C11—42no—
113C2×D4×C11C2×Q812yescomplemented
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—24no—
117C22×C4×C11—21no—
118C22×C4×C11—22no—
119C22×C4×C11—42no—
120C22×C4×C11—42no—
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×Q812yes—
123C22×C4×C11#4112yes—
124C22×C4×C11C2411yescharacteristic
125C22×Dic11—22no—
126C22×Dic11—22no—
127C22×Dic11—22no—
128C22×Dic11—22no—
129C22×Dic11—24no—
130C22×Dic11—22no—
131C22×Dic11—22no—
132C22×Dic11—21no—
133C22×Dic11—21no—
134C22×Dic11—42no—
135C22×Dic11—42no—
136C22×Dic11—42no—
137C22×Dic11—42no—
138C22×Dic11—42no—
139C22×Dic11D814yes—
140C22×Dic11C2×D411yescharacteristic
141C22×Dic11C2×D411yescharacteristic
142C22×Dic11C2×D411yescharacteristic
143C22×Dic11C2×D411yescharacteristic
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—21no—
157C11×C4⋊C4C2×D414yes—
158C11×C4⋊C4C2×Q812yescomplemented
159C11×C22⋊C4—24no—
160C22⋊Dic11—42no—
161C22⋊Dic11—42no—
162C22⋊Dic11—42no—
163C22⋊Dic11—42no—
164C4⋊Dic11—24no—
165C4⋊Dic11—22no—
166C4⋊Dic11—22no—
167C4⋊Dic11—22no—
168C4⋊Dic11—42no—
169C4⋊Dic11C2×D414yes—
170Dic11⋊C4—28no—
171Dic11⋊C4—28no—
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#1874D1111yescharacteristic
188#1852—111no—
189#1852—111no—
190#1797—111no—
191C23×C11—21no—
192C23×C11—21no—
193C23×C11—21no—
194C23×C11—21no—
195C23×C11—22no—
196C23×C11—41no—
197C23×C11—41no—
198C23×C11—41no—
199C23×C11—41no—
200C23×C11—41no—
201C23×C11—41no—
202C23×C11C22⋊Q812yes—
203C23×C11C2×D812yes—
204C23×C11#13712yes—
205C23×C11C22×D411yescharacteristic
206D4×C11—24no—
207D4×C11—48no—
208D4×C11—42no—
209C2×C4×C11—21no—
210C2×C4×C11—21no—
211C2×C4×C11—24no—
212C2×C4×C11—24no—
213C2×C4×C11—24no—
214C2×C4×C11—22no—
215C2×C4×C11—48no—
216C2×C4×C11—41no—
217C2×C4×C11—42no—
218C2×C4×C11—42no—
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—
225C2×Dic11—28no—
226C2×Dic11—21no—
227C2×Dic11—21no—
228C2×Dic11—21no—
229C2×Dic11—21no—
230C2×Dic11—21no—
231C2×Dic11—21no—
232C2×Dic11—28no—
233C2×Dic11—24no—
234C2×Dic11—48no—
235C2×Dic11—42no—
236C2×Dic11—42no—
237C2×Dic11—41no—
238C2×Dic11—41no—
239C2×Dic11—41no—
240C2×Dic11—41no—
241C2×Dic11—41no—
242C2×Dic11—41no—
243C2×Dic11—84no—
244C2×Dic11#12012yes—
245C2×Dic11#12012yes—
246C2×Dic11C2×D812yes—
247C2×Dic11C2×D812yes—
248C2×Dic11AGL(1,ℤ/8)12yes—
249C2×Dic11#13712yes—
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×#121C2×D1111yescharacteristic
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×#107—112no—
270C2×C4⋊C8—112no—
271C2×#102—112no—
272C2×#102C2×D1112yes—
273C2×C22⋊C8—111no—
274C2×C22⋊C8C2×D1111yescharacteristic
275#390—111no—
276#389—111no—
277#388—221no—
278#386—221no—
279#380—111no—
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—42no—
294C22×C11—42no—
295C22×C11—42no—
296C22×C11—81no—
297C22×C11—81no—
298C22×C11—81no—
299C22×C11—81no—
300C22×C11#47414yescomplemented
301C22×C11C2×#12011yescharacteristic
302C22×C11C2×C22⋊Q811yescharacteristic
303C22×C11#53611yescharacteristic
304C22×C11C22×D811yescharacteristic
305C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
306C22×C11C2×#13711yescharacteristic
307C22×C11C2×#13711yescharacteristic
308C4×C11—22no—
309C4×C11—44no—
310C4×C11—42no—
311C4×C11#54812yes—
312C4×C11D4×Q812yes—
313Dic11—22no—
314Dic11—22no—
315Dic11—22no—
316Dic11—44no—
317Dic11—81no—
318Dic11—81no—
319Dic11#44714yes—
320C22×Q8—222no—
321C22×Q8—222no—
322C22×Q8—228no—
323C22×Q8—444no—
324C22×Q8—444no—
325C22×D4—21no—
326C22×D4C22×D1111yescharacteristic
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—22no—
342#121Dic2214yescomplemented
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—111no—
350C2×C4⋊C4—224no—
351C2×C4⋊C4—222no—
352C2×C4⋊C4—222no—
353C2×C4⋊C4—228no—
354C2×C4⋊C4—221no—
355C2×C4⋊C4—221no—
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—224no—
370#107—224no—
371C4⋊C8—224no—
372#102—24no—
373#102—224no—
374C22⋊C8—22no—
375C22⋊C8—222no—
376#95—221no—
377#95—221no—
378#95—221no—
379C2×C11—24no—
380C2×C11—82no—
381C2×C11#240911yescharacteristic
382C2×C11C2×#44711yescharacteristic
383C2×C11#300411yescharacteristic
384C2×C11C2×#47411yescharacteristic
385C2×C11#307911yescharacteristic
386C2×C11#322611yescharacteristic
387C2×C11#323911yescharacteristic
388C24—21no—
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—24no—
398C2×D4—22no—
399C2×D4—21no—
400C2×D4—22no—
401C2×D4—42no—
402C2×D4—42no—
403C2×D4C2×Dic2212yescomplemented
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—24no—
407C22×C4—21no—
408C22×C4—22no—
409C22×C4—42no—
410C22×C4—42no—
411C22×C4—111no—
412C22×C4—114no—
413C22×C4—111no—
414C22×C4—111no—
415C22×C4—111no—
416C22×C4—222no—
417C22×C4—222no—
418C22×C4—222no—
419C22×C4—222no—
420C22×C4—222no—
421C22×C4—224no—
422C22×C4—222no—
423C22×C4—221no—
424C22×C4—221no—
425C22×C4—442no—
426C22×C4—442no—
427C22×C4—442no—
428C22×C4—442no—
429C22×C4—442no—
430C22×C4C2×Dic2212yes—
431C22×C4D4×D1111yescharacteristic
432C22×C4#434112yes—
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—21no—
443C4⋊C4—114no—
444C4⋊C4—228no—
445C4⋊C4—228no—
446C4⋊C4—224no—
447C4⋊C4—222no—
448C4⋊C4—222no—
449C4⋊C4—222no—
450C4⋊C4—442no—
451C4⋊C4C2×Dic2212yescomplemented
452C4⋊C4D4×D1114yes—
453C22⋊C4—24no—
454C22⋊C4—442no—
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—22no—
469C23—41no—
470C23—41no—
471C23—41no—
472C23—41no—
473C23—41no—
474C23—41no—
475C23#6693112yes—
476C23D8×D1112yes—
477C23#6696812yes—
478C23C2×D4×D1111yescharacteristic
479Q8—4416no—
480Q8—4416no—
481D4—24no—
482D4—48no—
483D4—42no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—22no—
489C2×C4—24no—
490C2×C4—48no—
491C2×C4—41no—
492C2×C4—42no—
493C2×C4—41no—
494C2×C4—42no—
495C2×C4—112no—
496C2×C4—112no—
497C2×C4—112no—
498C2×C4—112no—
499C2×C4—112no—
500C2×C4—112no—
501C2×C4—228no—
502C2×C4—228no—
503C2×C4—221no—
504C2×C4—221no—
505C2×C4—221no—
506C2×C4—221no—
507C2×C4—221no—
508C2×C4—221no—
509C2×C4—224no—
510C2×C4—448no—
511C2×C4—442no—
512C2×C4—442no—
513C2×C4—441no—
514C2×C4—441no—
515C2×C4—441no—
516C2×C4—441no—
517C2×C4—441no—
518C2×C4—441no—
519C2×C4—884no—
520C2×C4#6693112yes—
521C2×C4C22×Dic2211yescharacteristic
522C2×C4C2×D4×D1112yes—
523C2×C4C2×#434111yescharacteristic
524C2×C4#6704312yes—
525C8—42no—
526C8—442no—
527C22—22no—
528C22—22no—
529C22—22no—
530C22—22no—
531C22—22no—
532C22—22no—
533C22—42no—
534C22—42no—
535C22—42no—
536C22—81no—
537C22—81no—
538C22—81no—
539C22—81no—
540C22#1062237214yescomplemented
541C22C2×#6693111yescharacteristic
542C22D11×#12011yescharacteristic
543C22#1062317911yescharacteristic
544C22C2×D8×D1111yescharacteristic
545C22C2×#6696811yescharacteristic
546C22D11×AGL(1,ℤ/8)11yescharacteristic
547C22D11×#13711yescharacteristic
548C4—22no—
549C4—44no—
550C4—42no—
551C4—114no—
552C4—222no—
553C4—222no—
554C4—222no—
555C4—444no—
556C4—881no—
557C4—881no—
558C4D4×Dic2212yes—
559C4#1062312912yes—
560C2—24no—
561C2—82no—
562C2#1307197811yescharacteristic
563C2D11×#44711yescharacteristic
564C2#1307784711yescharacteristic
565C2C2×#1062237211yescharacteristic
566C2#1307842711yescharacteristic
567C2#1307973511yescharacteristic
568C2#1307984411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1874C2
socleC23×C11C22×D4
prime radicalC2×C11×#121C22
hypercenter#1874D11
hypocenterC11#24298
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1874

Complements

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

NH ≅ G/Ntype
1. C22×#66941C2semidirect
2. C2×#10622372C2semidirect
4. #13069943C2semidirect
5. #13069750C2semidirect
6. #13069566C2semidirect
8. #13068806C2semidirect
9. #13068804C2semidirect
10. #13068594C2semidirect
60. C11×#121Q8semidirect
93. #66941D4semidirect
113. C2×D4×C11C2×Q8semidirect
158. C11×C4⋊C4C2×Q8semidirect
300. C22×C11#474semidirect
342. #121Dic22semidirect
403. C2×D4C2×Dic22semidirect
451. C4⋊C4C2×Dic22semidirect
463. C11#24298semidirect
540. C22#10622372semidirect

Maximal subgroups

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

subgroupindex
C22×#669412
C2×#106223722
#121×Dic112
#130699432
#130697502
#130695662
#130689342
#130688062
#130688042
#130685942
C11×#18742
#2429811