Finite Group Databasebeta

← #14645725

Subgroups — #14645725

Order 2816.

836 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13069544C211yesmaximal, characteristic, complemented
2#13068636C211yesmaximal, characteristic, complemented
3#13067306C211yesmaximal, characteristic, complemented
4#13067284C211yesmaximal, characteristic, complemented
5#13067115C211yesmaximal, characteristic, complemented
6#13067003C211yesmaximal, characteristic, complemented
7C11×#3508C211yesmaximal, characteristic
8C11×#559—21no—
9C11×#559C412yescomplemented
10C11×#550—21no—
11C11×#550C412yescomplemented
12C11×#546—22no—
13C11×#546—22no—
14C11×#540—22no—
15C11×#535—21no—
16C11×#533C2211yescharacteristic
17C11×#532—21no—
18C11×#532—21no—
19C2×C11×#127C2211yescharacteristic
20C11×#518—21no—
21C4×C11×#41C2211yescharacteristic
22C2×#66901—21no—
23C2×#66896—22no—
24C4×C4⋊Dic11C2211yescharacteristic
25#10622538C2211yescharacteristic
26#10622537C2211yescharacteristic
27C2×C4⋊(C11⋊C8)C2211yescharacteristic
28#10622185—21no—
29#10622184—21no—
30#10622182—22no—
31#10622176—22no—
32Q8⋊(C11⋊C8)—21no—
33D4⋊(C11⋊C8)—21no—
34#10622170—21no—
35C2×C11×#41—22no—
36C2×C11×#41—22no—
37C2×C11×#41D411yescharacteristic
38C22×D4×C11—21no—
39C22×D4×C11—21no—
40C22×D4×C11D412yes—
41C11×C4⋊Q8D411yescharacteristic
42C11×C4⋊Q8D411yescharacteristic
43C11×#127—22no—
44C11×#127—21no—
45C11×#127—21no—
46C11×#127C2×C412yes—
47C11×#127D412yes—
48C11×#125—21no—
49C11×#124—22no—
50C11×#124—22no—
51C11×#124—22no—
52C11×#123—24no—
53C11×#123—24no—
54C11×C22⋊Q8—21no—
55C11×C22⋊Q8D412yes—
56C11×#121—22no—
57C11×#121—22no—
58C11×#121—22no—
59C11×#121—24no—
60C11×#121—24no—
61C11×#121—22no—
62C11×#120—24no—
63C4×Q8×C11—21no—
64C4×Q8×C11C2×C411yescharacteristic
65C4×Q8×C11C2×C412yes—
66C4×Q8×C11D411yescharacteristic
67C4×D4×C11—22no—
68C4×D4×C11—22no—
69C4×D4×C11—22no—
70C4×D4×C11—21no—
71C4×D4×C11—21no—
72C4×D4×C11—22no—
73C4×D4×C11—22no—
74C4×D4×C11—22no—
75C4×D4×C11C2×C411yescharacteristic
76C4×D4×C11D411yescharacteristic
77C11×#117—21no—
78C11×#117—21no—
79C11×#117D411yescharacteristic
80C2×C11×C22⋊C4—24no—
81C2×C42×C11—21no—
82C2×C42×C11C2311yescharacteristic
83C2×C4⋊Dic11—21no—
84C2×C4×Dic11—21no—
85C2×#4318—21no—
86C22×C11⋊C8—21no—
87#66901—42no—
88#66896—44no—
89C11⋊#95—21no—
90C22⋊(C11⋊C8)—21no—
91C4⋊(C11⋊C8)—21no—
92C4⋊(C11⋊C8)—21no—
93C4⋊(C11⋊C8)—21no—
94C4⋊(C11⋊C8)—21no—
95C4⋊(C11⋊C8)—21no—
96C4×C11⋊C8—21no—
97#8426—111nomaximal, Sylow
98C24×C11—22no—
99C11×#41—21no—
100C11×#41—21no—
101C11×#41—21no—
102C11×#41—21no—
103C11×#41—84no—
104C11×#41—82no—
105C11×#41—82no—
106C2×Q8×C11—21no—
107C2×Q8×C11C22⋊C411yescharacteristic
108C2×Q8×C11C22⋊C412yes—
109C2×D4×C11—21no—
110C2×D4×C11—24no—
111C2×D4×C11—24no—
112C2×D4×C11—22no—
113C2×D4×C11—22no—
114C2×D4×C11—22no—
115C2×D4×C11—22no—
116C2×D4×C11—22no—
117C2×D4×C11—42no—
118C2×D4×C11—42no—
119C2×D4×C11—41no—
120C2×D4×C11—41no—
121C2×D4×C11—41no—
122C2×D4×C11—41no—
123C2×D4×C11—82no—
124C2×D4×C11C22⋊C411yescharacteristic
125C2×D4×C11C22⋊C414yes—
126C22×C4×C11—24no—
127C22×C4×C11—24no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×Dic11—41no—
135C11×C4⋊C4—21no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—21no—
138C11×C4⋊C4—21no—
139C11×C4⋊C4—21no—
140C11×C4⋊C4—21no—
141C11×C4⋊C4—22no—
142C11×C4⋊C4C22⋊C411yescharacteristic
143C11×C4⋊C4C22⋊C411yescharacteristic
144C11×C4⋊C4C22⋊C412yes—
145C11×C22⋊C4—24no—
146C11×C22⋊C4—24no—
147C11×C22⋊C4—24no—
148C11×C22⋊C4—24no—
149C11×C22⋊C4—21no—
150C11×C22⋊C4—22no—
151C11×C22⋊C4—21no—
152C11×C22⋊C4—21no—
153C42×C11—21no—
154C42×C11—22no—
155C42×C11—21no—
156C42×C11—21no—
157C42×C11C22×C411yescharacteristic
158C42×C11C2×D411yescharacteristic
159C42×C11C2×D411yescharacteristic
160C42×C11C2×D411yescharacteristic
161C4⋊Dic11—22no—
162C4⋊Dic11—41no—
163C4×Dic11—41no—
164C4×Dic11—41no—
165#4318—41no—
166#4318—41no—
167C2×C11⋊C8—42no—
168C2×C11⋊C8—41no—
169C2×C11⋊C8—41no—
170C2×C11⋊C8—41no—
171#3508D1111yescharacteristic
172#1982—111no—
173#1806—111no—
174#1550—111no—
175#1545—111no—
176#1503—111no—
177#1477—111no—
178C23×C11—24no—
179C23×C11—21no—
180C23×C11—42no—
181C23×C11—42no—
182C23×C11—82no—
183C23×C11—82no—
184C23×C11#12011yescharacteristic
185Q8×C11—21no—
186Q8×C11—21no—
187Q8×C11—42no—
188Q8×C11—41no—
189Q8×C11—41no—
190D4×C11—21no—
191D4×C11—21no—
192D4×C11—44no—
193D4×C11—44no—
194D4×C11—41no—
195D4×C11—41no—
196D4×C11—42no—
197D4×C11—42no—
198D4×C11—42no—
199D4×C11—42no—
200D4×C11—42no—
201D4×C11—42no—
202D4×C11—82no—
203D4×C11—84no—
204D4×C11—84no—
205C2×C4×C11—21no—
206C2×C4×C11—21no—
207C2×C4×C11—21no—
208C2×C4×C11—21no—
209C2×C4×C11—21no—
210C2×C4×C11—22no—
211C2×C4×C11—22no—
212C2×C4×C11—41no—
213C2×C4×C11—42no—
214C2×C4×C11—41no—
215C2×C4×C11—41no—
216C2×C4×C11—41no—
217C2×C4×C11—41no—
218C2×C4×C11—84no—
219C2×C4×C11—84no—
220C2×C4×C11C2×C22⋊C411yescharacteristic
221C2×C4×C11C2×C22⋊C411yescharacteristic
222C2×C4×C11C2×C22⋊C411yescharacteristic
223C2×C4×C11#12011yescharacteristic
224C2×C4×C11#12011yescharacteristic
225C2×C4×C11#12011yescharacteristic
226C2×C4×C11#13511yescharacteristic
227C2×C4×C11#13511yescharacteristic
228C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
229C2×C4×C11#13711yescharacteristic
230C2×Dic11—42no—
231C2×Dic11—81no—
232C2×Dic11—81no—
233C11⋊C8—81no—
234C11⋊C8—81no—
235C11⋊C8—81no—
236#559—21no—
237#559Dic1112yescomplemented
238#550—21no—
239#550Dic1112yescomplemented
240#546—22no—
241#546—22no—
242#540—22no—
243#535—21no—
244#533C2×D1111yescharacteristic
245#532—21no—
246#532—21no—
247C2×#127C2×D1111yescharacteristic
248#518—21no—
249C4×#41C2×D1111yescharacteristic
250#431—111no—
251#423—111no—
252C2×C4⋊C8—111no—
253C2×#104—221no—
254C2×#102—222no—
255C4×C4⋊C4—111no—
256#339—221no—
257#333—221no—
258#332—221no—
259#331—222no—
260#328—222no—
261Q8⋊C8—221no—
262D4⋊C8—221no—
263C22×C11—21no—
264C22×C11—21no—
265C22×C11—41no—
266C22×C11—44no—
267C22×C11—41no—
268C22×C11—44no—
269C22×C11—41no—
270C22×C11—44no—
271C22×C11—162no—
272C22×C11—162no—
273C22×C11#37911yescharacteristic
274C22×C11#44911yescharacteristic
275C22×C11#45211yescharacteristic
276C4×C11—21no—
277C4×C11—21no—
278C4×C11—21no—
279C4×C11—41no—
280C4×C11—42no—
281C4×C11—41no—
282C4×C11—42no—
283C4×C11—41no—
284C4×C11#41611yescharacteristic
285C4×C11#41711yescharacteristic
286C4×C11#44911yescharacteristic
287C4×C11#45211yescharacteristic
288C4×C11#45311yescharacteristic
289C4×C11#45511yescharacteristic
290Dic11—82no—
291C2×#41—22no—
292C2×#41—22no—
293C2×#41C22⋊D1111yescharacteristic
294C22×D4—21no—
295C22×D4—21no—
296C22×D4C22⋊D1112yes—
297C2×M16—221no—
298C22×C8—221no—
299C4⋊Q8C22⋊D1111yescharacteristic
300C4⋊Q8C22⋊D1111yescharacteristic
301#127—22no—
302#127—21no—
303#127—21no—
304#127C2×Dic1112yes—
305#127C22⋊D1112yes—
306#125—21no—
307#124—22no—
308#124—22no—
309#124—22no—
310#123—24no—
311#123—24no—
312C22⋊Q8—21no—
313C22⋊Q8C22⋊D1112yes—
314#121—22no—
315#121—22no—
316#121—22no—
317#121—24no—
318#121—24no—
319#121—22no—
320#120—24no—
321C4×Q8—21no—
322C4×Q8C2×Dic1111yescharacteristic
323C4×Q8C2×Dic1112yes—
324C4×Q8C22⋊D1111yescharacteristic
325C4×D4—22no—
326C4×D4—22no—
327C4×D4—22no—
328C4×D4—21no—
329C4×D4—21no—
330C4×D4—22no—
331C4×D4—22no—
332C4×D4—22no—
333C4×D4C2×Dic1111yescharacteristic
334C4×D4C22⋊D1111yescharacteristic
335#117—21no—
336#117—21no—
337#117C22⋊D1111yescharacteristic
338C2×C4⋊C4—221no—
339C2×C22⋊C4—24no—
340C2×C42—21no—
341C2×C42—221no—
342C2×C42C22×D1111yescharacteristic
343C4⋊C8—221no—
344C4⋊C8—221no—
345C4⋊C8—221no—
346C4⋊C8—221no—
347C4⋊C8—221no—
348#104—442no—
349#102—444no—
350C22⋊C8—221no—
351C4×C8—221no—
352#95—221no—
353C2×C11—21no—
354C2×C11—21no—
355C2×C11—81no—
356C2×C11—84no—
357C2×C11#178811yescharacteristic
358C2×C11#179211yescharacteristic
359C2×C11#179511yescharacteristic
360C24—22no—
361#41—21no—
362#41—21no—
363#41—21no—
364#41—21no—
365#41—84no—
366#41—82no—
367#41—82no—
368C2×Q8—21no—
369C2×Q8C22⋊Dic1111yescharacteristic
370C2×Q8C22⋊Dic1112yes—
371C2×D4—21no—
372C2×D4—24no—
373C2×D4—24no—
374C2×D4—22no—
375C2×D4—22no—
376C2×D4—22no—
377C2×D4—22no—
378C2×D4—22no—
379C2×D4—42no—
380C2×D4—42no—
381C2×D4—41no—
382C2×D4—41no—
383C2×D4—41no—
384C2×D4—41no—
385C2×D4—82no—
386C2×D4C22⋊Dic1111yescharacteristic
387C2×D4C22⋊Dic1114yes—
388C22×C4—24no—
389C22×C4—24no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—441no—
394C22×C4C2×C22⋊D1111yescharacteristic
395C22×C4C2×C22⋊D1111yescharacteristic
396C22×C4C2×C22⋊D1111yescharacteristic
397M16—441no—
398M16—441no—
399C2×C8—442no—
400C2×C8—441no—
401C2×C8—441no—
402C2×C8—441no—
403C4⋊C4—21no—
404C4⋊C4—22no—
405C4⋊C4—21no—
406C4⋊C4—21no—
407C4⋊C4—21no—
408C4⋊C4—21no—
409C4⋊C4—22no—
410C4⋊C4—222no—
411C4⋊C4—441no—
412C4⋊C4C22⋊Dic1111yescharacteristic
413C4⋊C4C22⋊Dic1111yescharacteristic
414C4⋊C4C22⋊Dic1112yes—
415C22⋊C4—24no—
416C22⋊C4—24no—
417C22⋊C4—24no—
418C22⋊C4—24no—
419C22⋊C4—21no—
420C22⋊C4—22no—
421C22⋊C4—21no—
422C22⋊C4—21no—
423C42—21no—
424C42—22no—
425C42—21no—
426C42—21no—
427C42—441no—
428C42—441no—
429C42C22×Dic1111yescharacteristic
430C42C2×C22⋊D1111yescharacteristic
431C42C2×C22⋊D1111yescharacteristic
432C42C2×C22⋊D1111yescharacteristic
433C11#842611yescharacteristic, complemented, Sylow
434C23—24no—
435C23—21no—
436C23—42no—
437C23—42no—
438C23—82no—
439C23—82no—
440C23#6700611yescharacteristic
441Q8—21no—
442Q8—21no—
443Q8—42no—
444Q8—41no—
445Q8—41no—
446D4—21no—
447D4—21no—
448D4—44no—
449D4—44no—
450D4—41no—
451D4—41no—
452D4—42no—
453D4—42no—
454D4—42no—
455D4—42no—
456D4—42no—
457D4—42no—
458D4—82no—
459D4—84no—
460D4—84no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—41no—
469C2×C4—42no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—84no—
475C2×C4—84no—
476C2×C4—442no—
477C2×C4—881no—
478C2×C4—881no—
479C2×C4#6700211yescharacteristic
480C2×C4#6700311yescharacteristic
481C2×C4#6700311yescharacteristic
482C2×C4#6700411yescharacteristic
483C2×C4C2×C22⋊Dic1111yescharacteristic
484C2×C4C2×C22⋊Dic1111yescharacteristic
485C2×C4C2×C22⋊Dic1111yescharacteristic
486C2×C4#6700611yescharacteristic
487C2×C4#6700611yescharacteristic
488C2×C4#6700611yescharacteristic
489C8—881no—
490C8—881no—
491C8—881no—
492C22—21no—
493C22—21no—
494C22—41no—
495C22—44no—
496C22—41no—
497C22—44no—
498C22—41no—
499C22—44no—
500C22—162no—
501C22—162no—
502C22#1062285111yescharacteristic
503C22#1062285211yescharacteristic
504C22#1062286011yescharacteristic
505C4—21no—
506C4—21no—
507C4—21no—
508C4—41no—
509C4—41no—
510C4—42no—
511C4—41no—
512C4—42no—
513C4—882no—
514C4#1062284511yescharacteristic
515C4#1062284611yescharacteristic
516C4#1062285111yescharacteristic
517C4#1062285211yescharacteristic
518C4#1062285411yescharacteristic
519C4#1062285511yescharacteristic
520C2—21no—
521C2—21no—
522C2—84no—
523C2—81no—
524C2#1306855611yescharacteristic
525C2#1306857011yescharacteristic
526C2#1306858611yescharacteristic
subgroupG/H
centerC22#10622860
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
Fitting, prime radicalC11×#3508C2
socleC22×C11#379
cosocleC2×C42×C11C23
hypercenter#3508D11
hypocenterC11#8426
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3508

Complements

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

NH ≅ G/Ntype
1. #13069544C2semidirect
2. #13068636C2semidirect
3. #13067306C2semidirect
4. #13067284C2semidirect
5. #13067115C2semidirect
6. #13067003C2semidirect
9. C11×#559C4semidirect
11. C11×#550C4semidirect
237. #559Dic11semidirect
239. #550Dic11semidirect
433. C11#8426semidirect

Maximal subgroups

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

subgroupindex
#130695442
#130686362
#130673062
#130672842
#130671152
#130670032
C11×#35082
#842611