Finite Group Databasebeta

← #14646172

Subgroups — #14646172

Order 2816.

676 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13069590C211yesmaximal, characteristic, complemented
2#13067333C211yesmaximal, characteristic, complemented
3#13067236C211yesmaximal, characteristic, complemented
4#13067236C211yesmaximal, characteristic, complemented
5#13067154C211yesmaximal, characteristic, complemented
6#13067154C211yesmaximal, characteristic, complemented
7C11×#3552C211yesmaximal, characteristic
8C11×#563—22no—
9C11×#557C411yescharacteristic, complemented
10C11×#556C411yescharacteristic, complemented
11C11×#554—21no—
12C11×#553—21no—
13D4×Q8×C11—21no—
14D4×Q8×C11C411yescharacteristic, complemented
15C11×#548—21no—
16C11×#547C411yescharacteristic, complemented
17C11×#544—21no—
18C11×#542—21no—
19C11×#541—21no—
20C11×#539—22no—
21C11×#536—21no—
22C2×C11×C4⋊Q8C2211yescharacteristic
23C11×#529C2211yescharacteristic
24C11×#529C2211yescharacteristic
25#10622549C2211yescharacteristic
26#10622539C2211yescharacteristic
27#10622539C2211yescharacteristic
28C2×#66867C2211yescharacteristic
29#10622185—22no—
30#10622181—21no—
31#10622181—21no—
32#10622178—21no—
33#10622178—21no—
34#10622176—21no—
35#10622176—21no—
36#10622175—21no—
37#10622175—21no—
38#10622167—22no—
39C2×C11×#41—21no—
40C22×Q8×C11—21no—
41C22×Q8×C11—21no—
42C11×C4⋊Q8—22no—
43C11×C4⋊Q8—21no—
44C11×C4⋊Q8—21no—
45C11×C4⋊Q8—21no—
46C11×C4⋊Q8—21no—
47C11×C4⋊Q8C2×C411yescharacteristic
48C11×C4⋊Q8C2×C411yescharacteristic
49C11×C4⋊Q8D412yes—
50C11×#126—22no—
51C11×#126—22no—
52C11×#126—22no—
53C11×#126—21no—
54C11×#126—21no—
55C11×#125—22no—
56C11×#125—22no—
57C11×#125—22no—
58C11×#125—21no—
59C11×#125D411yescharacteristic
60C11×#125D411yescharacteristic
61C11×#124—22no—
62C11×#124—21no—
63C11×#124D411yescharacteristic
64C11×#124D411yescharacteristic
65C11×#123—22no—
66C11×#123—22no—
67C11×#123—21no—
68C11×#123—21no—
69C11×#123—22no—
70C11×C22⋊Q8—22no—
71C11×C22⋊Q8—22no—
72C11×C22⋊Q8—22no—
73C11×C22⋊Q8—22no—
74C11×C22⋊Q8—22no—
75C11×C22⋊Q8—21no—
76C11×C22⋊Q8—22no—
77C11×C22⋊Q8—21no—
78C11×C22⋊Q8—21no—
79C11×C22⋊Q8D411yescharacteristic
80C11×C22⋊Q8D411yescharacteristic
81C11×#121—22no—
82C11×#121—21no—
83C11×#121D411yescharacteristic
84C11×#121D411yescharacteristic
85C4×Q8×C11—21no—
86C4×Q8×C11—21no—
87C4×Q8×C11—21no—
88C4×Q8×C11C2×C411yescharacteristic
89C4×Q8×C11C2×C411yescharacteristic
90C4×D4×C11—22no—
91C4×D4×C11—22no—
92C4×D4×C11—21no—
93C4×D4×C11—21no—
94C4×D4×C11—21no—
95C4×D4×C11C2×C411yescharacteristic
96C4×D4×C11C2×C411yescharacteristic
97C11×#117—21no—
98C11×#117—21no—
99C11×#117—21no—
100C2×C11×C4⋊C4—21no—
101C2×C11×C4⋊C4—21no—
102C2×C11×C4⋊C4D412yes—
103C2×C42×C11C2311yescharacteristic
104C2×C4⋊Dic11—21no—
105C22×C11⋊C8—21no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C22⋊(C11⋊C8)—21no—
109C22⋊(C11⋊C8)—21no—
110C4⋊(C11⋊C8)—21no—
111C4⋊(C11⋊C8)—21no—
112#66867—21no—
113#66867—21no—
114#66867—21no—
115#66867—21no—
116#8499—111nomaximal, Sylow
117C11×#41—82no—
118C2×Q8×C11—22no—
119C2×Q8×C11—21no—
120C2×Q8×C11—21no—
121C2×Q8×C11—22no—
122C2×Q8×C11—82no—
123C2×Q8×C11—82no—
124C2×Q8×C11C22⋊C411yescharacteristic
125C2×Q8×C11C22⋊C411yescharacteristic
126C2×D4×C11—21no—
127C2×D4×C11—21no—
128C2×D4×C11—22no—
129C2×D4×C11C22⋊C411yescharacteristic
130C2×D4×C11C22⋊C411yescharacteristic
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×Dic11—41no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—22no—
142C11×C4⋊C4—22no—
143C11×C4⋊C4—22no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—22no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—22no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4C22⋊C411yescharacteristic
159C11×C4⋊C4C22⋊C412yes—
160C11×C4⋊C4C22⋊C412yes—
161C11×C4⋊C4C22⋊C411yescharacteristic
162C11×C4⋊C4C22⋊C411yescharacteristic
163C11×C4⋊C4C22⋊C411yescharacteristic
164C11×C22⋊C4—22no—
165C11×C22⋊C4—22no—
166C11×C22⋊C4—22no—
167C11×C22⋊C4—22no—
168C11×C22⋊C4—21no—
169C11×C22⋊C4—21no—
170C11×C22⋊C4—21no—
171C11×C22⋊C4—21no—
172C11×C22⋊C4—21no—
173C11×C22⋊C4—21no—
174C11×C22⋊C4—21no—
175C11×C22⋊C4—21no—
176C11×C22⋊C4—21no—
177C11×C22⋊C4—21no—
178C42×C11—22no—
179C42×C11—22no—
180C42×C11—21no—
181C42×C11—21no—
182C42×C11C22×C411yescharacteristic
183C42×C11C2×D411yescharacteristic
184C42×C11C2×D411yescharacteristic
185C42×C11C2×D411yescharacteristic
186C4⋊Dic11—42no—
187C2×C11⋊C8—22no—
188C2×C11⋊C8—41no—
189C2×C11⋊C8—41no—
190C2×C11⋊C8—41no—
191C2×C11⋊C8—41no—
192#3552D1111yescharacteristic
193#1993—111no—
194#1556—111no—
195#1532—111no—
196#1532—111no—
197#1512—111no—
198#1512—111no—
199C23×C11—21no—
200C23×C11—21no—
201C23×C11#12011yescharacteristic
202Q8×C11—41no—
203Q8×C11—41no—
204Q8×C11—42no—
205Q8×C11—42no—
206Q8×C11—82no—
207Q8×C11—82no—
208D4×C11—41no—
209D4×C11—41no—
210D4×C11—41no—
211D4×C11—41no—
212D4×C11—41no—
213D4×C11—41no—
214D4×C11—82no—
215C2×C4×C11—21no—
216C2×C4×C11—21no—
217C2×C4×C11—21no—
218C2×C4×C11—21no—
219C2×C4×C11—21no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—21no—
225C2×C4×C11—41no—
226C2×C4×C11—41no—
227C2×C4×C11—42no—
228C2×C4×C11—42no—
229C2×C4×C11—82no—
230C2×C4×C11—82no—
231C2×C4×C11—82no—
232C2×C4×C11C2×C22⋊C411yescharacteristic
233C2×C4×C11C2×C22⋊C411yescharacteristic
234C2×C4×C11C2×C22⋊C411yescharacteristic
235C2×C4×C11#12011yescharacteristic
236C2×C4×C11#12011yescharacteristic
237C2×C4×C11#12011yescharacteristic
238C2×Dic11—81no—
239C2×Dic11—81no—
240C2×Dic11—81no—
241C11⋊C8—42no—
242C11⋊C8—81no—
243C11⋊C8—81no—
244#563—22no—
245#557Dic1111yescharacteristic, complemented
246#556Dic1111yescharacteristic, complemented
247#554—21no—
248#553—21no—
249D4×Q8—21no—
250D4×Q8Dic1111yescharacteristic, complemented
251#548—21no—
252#547Dic1111yescharacteristic, complemented
253#544—21no—
254#542—21no—
255#541—21no—
256#539—22no—
257#536—21no—
258C2×C4⋊Q8C2×D1111yescharacteristic
259#529C2×D1111yescharacteristic
260#529C2×D1111yescharacteristic
261#432—111no—
262#432—111no—
263C2×#97—111no—
264#382—111no—
265#340—222no—
266#332—222no—
267#330—221no—
268#330—221no—
269#329—221no—
270#329—221no—
271#328—221no—
272#328—221no—
273#327—221no—
274#327—221no—
275C22×C11—21no—
276C22×C11—21no—
277C22×C11—41no—
278C22×C11—41no—
279C22×C11—41no—
280C22×C11—41no—
281C22×C11—41no—
282C22×C11—41no—
283C22×C11#37911yescharacteristic
284C22×C11#45411yescharacteristic
285C22×C11#45611yescharacteristic
286C4×C11—21no—
287C4×C11—21no—
288C4×C11—21no—
289C4×C11—21no—
290C4×C11—21no—
291C4×C11—21no—
292C4×C11—41no—
293C4×C11—41no—
294C4×C11—41no—
295C4×C11—42no—
296C4×C11—42no—
297C4×C11—41no—
298C4×C11—41no—
299C4×C11—41no—
300Dic11—161no—
301C2×#41—21no—
302C22×Q8—21no—
303C22×Q8—21no—
304C22×C8—221no—
305C4⋊Q8—22no—
306C4⋊Q8—21no—
307C4⋊Q8—21no—
308C4⋊Q8—21no—
309C4⋊Q8—21no—
310C4⋊Q8C2×Dic1111yescharacteristic
311C4⋊Q8C2×Dic1111yescharacteristic
312C4⋊Q8C22⋊D1112yes—
313#126—22no—
314#126—22no—
315#126—22no—
316#126—21no—
317#126—21no—
318#125—22no—
319#125—22no—
320#125—22no—
321#125—21no—
322#125C22⋊D1111yescharacteristic
323#125C22⋊D1111yescharacteristic
324#124—22no—
325#124—21no—
326#124C22⋊D1111yescharacteristic
327#124C22⋊D1111yescharacteristic
328#123—22no—
329#123—22no—
330#123—21no—
331#123—21no—
332#123—22no—
333C22⋊Q8—22no—
334C22⋊Q8—22no—
335C22⋊Q8—22no—
336C22⋊Q8—22no—
337C22⋊Q8—22no—
338C22⋊Q8—21no—
339C22⋊Q8—22no—
340C22⋊Q8—21no—
341C22⋊Q8—21no—
342C22⋊Q8C22⋊D1111yescharacteristic
343C22⋊Q8C22⋊D1111yescharacteristic
344#121—22no—
345#121—21no—
346#121C22⋊D1111yescharacteristic
347#121C22⋊D1111yescharacteristic
348C4×Q8—21no—
349C4×Q8—21no—
350C4×Q8—21no—
351C4×Q8C2×Dic1111yescharacteristic
352C4×Q8C2×Dic1111yescharacteristic
353C4×D4—22no—
354C4×D4—22no—
355C4×D4—21no—
356C4×D4—21no—
357C4×D4—21no—
358C4×D4C2×Dic1111yescharacteristic
359C4×D4C2×Dic1111yescharacteristic
360#117—21no—
361#117—21no—
362#117—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—221no—
366C2×C4⋊C4C22⋊D1112yes—
367C2×C42C22×D1111yescharacteristic
368C4⋊C8—221no—
369C4⋊C8—221no—
370C22⋊C8—221no—
371C22⋊C8—221no—
372#97—221no—
373#97—221no—
374#97—221no—
375#97—221no—
376#95—221no—
377#95—221no—
378C2×C11—21no—
379C2×C11—21no—
380C2×C11—81no—
381C2×C11—81no—
382C2×C11#179311yescharacteristic
383C2×C11#179511yescharacteristic
384C2×C11#179611yescharacteristic
385#41—82no—
386C2×Q8—22no—
387C2×Q8—21no—
388C2×Q8—21no—
389C2×Q8—22no—
390C2×Q8—82no—
391C2×Q8—82no—
392C2×Q8C22⋊Dic1111yescharacteristic
393C2×Q8C22⋊Dic1111yescharacteristic
394C2×D4—21no—
395C2×D4—21no—
396C2×D4—22no—
397C2×D4C22⋊Dic1111yescharacteristic
398C2×D4C22⋊Dic1111yescharacteristic
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—441no—
405C22×C4C2×C22⋊D1111yescharacteristic
406C22×C4C2×C22⋊D1111yescharacteristic
407C22×C4C2×C22⋊D1111yescharacteristic
408C2×C8—222no—
409C2×C8—441no—
410C2×C8—441no—
411C2×C8—441no—
412C2×C8—441no—
413C4⋊C4—22no—
414C4⋊C4—22no—
415C4⋊C4—22no—
416C4⋊C4—22no—
417C4⋊C4—22no—
418C4⋊C4—22no—
419C4⋊C4—21no—
420C4⋊C4—21no—
421C4⋊C4—21no—
422C4⋊C4—21no—
423C4⋊C4—22no—
424C4⋊C4—22no—
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—21no—
429C4⋊C4—21no—
430C4⋊C4—21no—
431C4⋊C4—442no—
432C4⋊C4C22⋊Dic1111yescharacteristic
433C4⋊C4C22⋊Dic1112yes—
434C4⋊C4C22⋊Dic1112yes—
435C4⋊C4C22⋊Dic1111yescharacteristic
436C4⋊C4C22⋊Dic1111yescharacteristic
437C4⋊C4C22⋊Dic1111yescharacteristic
438C22⋊C4—22no—
439C22⋊C4—22no—
440C22⋊C4—22no—
441C22⋊C4—22no—
442C22⋊C4—21no—
443C22⋊C4—21no—
444C22⋊C4—21no—
445C22⋊C4—21no—
446C22⋊C4—21no—
447C22⋊C4—21no—
448C22⋊C4—21no—
449C22⋊C4—21no—
450C22⋊C4—21no—
451C22⋊C4—21no—
452C42—22no—
453C42—22no—
454C42—21no—
455C42—21no—
456C42C22×Dic1111yescharacteristic
457C42C2×C22⋊D1111yescharacteristic
458C42C2×C22⋊D1111yescharacteristic
459C42C2×C22⋊D1111yescharacteristic
460C11#849911yescharacteristic, complemented, Sylow
461C23—21no—
462C23—21no—
463C23#6700611yescharacteristic
464Q8—41no—
465Q8—41no—
466Q8—42no—
467Q8—42no—
468Q8—82no—
469Q8—82no—
470D4—41no—
471D4—41no—
472D4—41no—
473D4—41no—
474D4—41no—
475D4—41no—
476D4—82no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—21no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—82no—
492C2×C4—82no—
493C2×C4—82no—
494C2×C4—881no—
495C2×C4—881no—
496C2×C4—881no—
497C2×C4C2×C22⋊Dic1111yescharacteristic
498C2×C4C2×C22⋊Dic1111yescharacteristic
499C2×C4C2×C22⋊Dic1111yescharacteristic
500C2×C4#6700611yescharacteristic
501C2×C4#6700611yescharacteristic
502C2×C4#6700611yescharacteristic
503C8—442no—
504C8—881no—
505C8—881no—
506C22—21no—
507C22—21no—
508C22—41no—
509C22—41no—
510C22—41no—
511C22—41no—
512C22—41no—
513C22—41no—
514C22#1062285811yescharacteristic
515C22#1062285911yescharacteristic
516C22#1062286011yescharacteristic
517C4—21no—
518C4—21no—
519C4—21no—
520C4—21no—
521C4—21no—
522C4—21no—
523C4—41no—
524C4—41no—
525C4—41no—
526C4—42no—
527C4—42no—
528C4—41no—
529C4—41no—
530C4—41no—
531C4—1761no—
532C2—21no—
533C2—21no—
534C2—81no—
535C2—81no—
536C2#1306857511yescharacteristic
537C2#1306858611yescharacteristic
538C2#1306859111yescharacteristic
subgroupG/H
centerC22#10622860
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
Fitting, prime radicalC11×#3552C2
socleC22×C11#379
cosocleC2×C42×C11C23
hypercenter#3552D11
hypocenterC11#8499
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3552

Complements

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

NH ≅ G/Ntype
1. #13069590C2semidirect
2. #13067333C2semidirect
3. #13067236C2semidirect
4. #13067236C2semidirect
5. #13067154C2semidirect
6. #13067154C2semidirect
9. C11×#557C4semidirect
10. C11×#556C4semidirect
14. D4×Q8×C11C4semidirect
16. C11×#547C4semidirect
245. #557Dic11semidirect
246. #556Dic11semidirect
250. D4×Q8Dic11semidirect
252. #547Dic11semidirect
460. C11#8499semidirect

Maximal subgroups

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

subgroupindex
#130695902
#130673332
#130672362
#130671542
C11×#35522
#849911