Finite Group Databasebeta

← #14728077

Subgroups — #14728077

Order 2816.

1156 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079802C212yesmaximal, complemented
2#13074314C211yesmaximal, characteristic, complemented
3#13067653C212yesmaximal, complemented
4#13067636C212yesmaximal, complemented
5#13067619C212yesmaximal, complemented
6#13067602C212yesmaximal, complemented
7#13067124C212yesmaximal, complemented
8#13066950C211yesmaximal, characteristic, complemented
9C11×#3449C211yesmaximal, characteristic
10C22×C11×#41—21no—
11C11×#537—21no—
12C11×#537C2212yes—
13C11×#536—22no—
14C11×#535—22no—
15C11×#534—21no—
16C11×#534C2212yes—
17C11×#532—21no—
18C11×#532C2212yes—
19C11×#525—24no—
20C2×C11×#117C2211yescharacteristic
21C2×#66923C2211yescharacteristic, complemented
22#10622823—21no—
23#10622693—22no—
24#10622684—22no—
25#10622647C2214yescomplemented
26#10622646C2214yescomplemented
27#10622622—24no—
28#10622599C2211yescharacteristic, complemented
29#10622596C2211yescharacteristic, complemented
30#10622585—21no—
31#10622566C2211yescharacteristic
32#10622562C2211yescharacteristic
33#10622558—21no—
34#10622546—21no—
35#10622545C2211yescharacteristic, complemented
36#10622539C2212yescomplemented
37#10622175C2214yescomplemented
38#10622175C2214yescomplemented
39#10622166C2212yescomplemented
40#10622163C2212yes—
41C2×C11×#41—22no—
42C2×C11×#41—22no—
43C2×C11×#41—22no—
44C2×C11×#41—22no—
45C2×C11×#41—44no—
46C2×C11×#41—44no—
47C22×Q8×C11—21no—
48C22×D4×C11—21no—
49C22×D4×C11—22no—
50C23×C4×C11—22no—
51C23×C4×C11D411yescharacteristic
52C11×C4⋊Q8—21no—
53C11×C4⋊Q8D412yes—
54C11×#127—21no—
55C11×#127D412yes—
56C11×#124—22no—
57C11×#124—22no—
58C11×#123—24no—
59C11×#123—24no—
60C11×C22⋊Q8—24no—
61C11×C22⋊Q8—24no—
62C11×#121—24no—
63C11×#121—24no—
64C11×#121—22no—
65C11×#121—22no—
66C11×#121—22no—
67C11×#121C2314yes—
68C11×#120—24no—
69C11×#120—24no—
70C4×D4×C11—22no—
71C4×D4×C11—22no—
72C4×D4×C11—22no—
73C4×D4×C11D414yes—
74C11×#117—22no—
75C11×#117—22no—
76C2×C11×C4⋊C4D411yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C22⋊C4D411yescharacteristic
79C2×C11×C22⋊C4C2311yescharacteristic
80C2×C42×C11D411yescharacteristic
81C2×C42×C11C2311yescharacteristic
82C2×C22⋊Dic11—21no—
83C2×C22⋊Dic11—21no—
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4—21no—
90C2×C4×Dic11—21no—
91#66923—22no—
92#66923—22no—
93#66896—24no—
94#66896—24no—
95C11⋊#95—21no—
96C11⋊#95—21no—
97C11⋊#95—21no—
98C11⋊#95—21no—
99C11⋊#95—21no—
100C11⋊#95C2311yescharacteristic
101C11⋊#95C2311yescharacteristic
102C22⋊(C11⋊C8)C2314yes—
103#66872—24no—
104#66871—24no—
105C4⋊(C11⋊C8)—22no—
106#66867—22no—
107#18339—111nomaximal, Sylow
108C24×C11—22no—
109C24×C11C2×D411yescharacteristic
110C11×#41—48no—
111C11×#41—48no—
112C11×#41—44no—
113C11×#41—44no—
114C11×#41—44no—
115C11×#41—44no—
116C2×Q8×C11—22no—
117C2×Q8×C11—22no—
118C2×Q8×C11—44no—
119C2×D4×C11—24no—
120C2×D4×C11—22no—
121C2×D4×C11—24no—
122C2×D4×C11—22no—
123C2×D4×C11—22no—
124C2×D4×C11—22no—
125C2×D4×C11—22no—
126C2×D4×C11—44no—
127C2×D4×C11—44no—
128C2×D4×C11—44no—
129C2×D4×C11C2×D414yes—
130C22×C4×C11—22no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—22no—
134C22×C4×C11—24no—
135C22×C4×C11—22no—
136C22×C4×C11—24no—
137C22×C4×C11—48no—
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2411yescharacteristic
144C22×Dic11—21no—
145C22×Dic11—21no—
146C22×Dic11—21no—
147C22×Dic11—21no—
148C11×C4⋊C4—22no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—22no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4C2×D414yes—
154C11×C22⋊C4—24no—
155C11×C22⋊C4—24no—
156C11×C22⋊C4—22no—
157C11×C22⋊C4—24no—
158C11×C22⋊C4—22no—
159C11×C22⋊C4—24no—
160C42×C11—21no—
161C42×C11—21no—
162C42×C11C2×D412yes—
163C42×C11C2×D412yes—
164C22⋊Dic11—42no—
165C22⋊Dic11—42no—
166C4⋊Dic11—22no—
167C4⋊Dic11—22no—
168Dic11⋊C4—42no—
169Dic11⋊C4—41no—
170Dic11⋊C4—41no—
171Dic11⋊C4—42no—
172Dic11⋊C4—42no—
173C4×Dic11—42no—
174C2×C11⋊C8—24no—
175#3449D1111yescharacteristic
176#3234—112no—
177#2611—111no—
178#1616—112no—
179#1613—112no—
180#1610—112no—
181#1607—112no—
182#1505—112no—
183#1464—111no—
184C23×C11—21no—
185C23×C11—21no—
186C23×C11—24no—
187C23×C11—41no—
188C23×C11—41no—
189C23×C11—44no—
190C23×C11—82no—
191C23×C11—82no—
192C23×C11AGL(1,ℤ/8)12yes—
193C23×C11C22×D411yescharacteristic
194Q8×C11—44no—
195Q8×C11—44no—
196D4×C11—44no—
197D4×C11—44no—
198D4×C11—44no—
199D4×C11—48no—
200D4×C11—44no—
201D4×C11—44no—
202D4×C11—82no—
203D4×C11—82no—
204D4×C11—82no—
205C2×C4×C11—24no—
206C2×C4×C11—24no—
207C2×C4×C11—21no—
208C2×C4×C11—21no—
209C2×C4×C11—21no—
210C2×C4×C11—21no—
211C2×C4×C11—21no—
212C2×C4×C11—21no—
213C2×C4×C11—24no—
214C2×C4×C11—41no—
215C2×C4×C11—41no—
216C2×C4×C11—48no—
217C2×C4×C11—48no—
218C2×C4×C11—44no—
219C2×C4×C11—41no—
220C2×C4×C11—41no—
221C2×C4×C11#12011yescharacteristic
222C2×C4×C11#12011yescharacteristic
223C2×C4×C11#12012yes—
224C2×C4×C11AGL(1,ℤ/8)12yes—
225C2×C4×C11C22×D412yes—
226C2×Dic11—22no—
227C2×Dic11—41no—
228C2×Dic11—41no—
229C2×Dic11—41no—
230C2×Dic11—41no—
231C2×Dic11—41no—
232C2×Dic11—41no—
233C2×Dic11—41no—
234C2×Dic11—41no—
235C2×Dic11—41no—
236C2×Dic11—41no—
237C2×Dic11—41no—
238C11⋊C8—44no—
239C22×#41—21no—
240#537—21no—
241#537C2×D1112yes—
242#536—22no—
243#535—22no—
244#534—21no—
245#534C2×D1112yes—
246#532—21no—
247#532C2×D1112yes—
248C2×#125—111no—
249#525—24no—
250C2×#117C2×D1111yescharacteristic
251#501—222no—
252#490—222no—
253#481—114no—
254#480—114no—
255#478—224no—
256#432—112no—
257#400—111no—
258#399—111no—
259#398—111no—
260#397—111no—
261#389—221no—
262#388—221no—
263#387—221no—
264#385—221no—
265#376—111no—
266#327—114no—
267#327—114no—
268#324—112no—
269#323—112no—
270C22×C11—21no—
271C22×C11—21no—
272C22×C11—22no—
273C22×C11—42no—
274C22×C11—41no—
275C22×C11—41no—
276C22×C11—44no—
277C22×C11—44no—
278C22×C11—44no—
279C22×C11—81no—
280C22×C11—88no—
281C22×C11C2×#12011yescharacteristic
282C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
283C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
284C4×C11—21no—
285C4×C11—22no—
286C4×C11—21no—
287C4×C11—22no—
288C4×C11—22no—
289C4×C11—44no—
290C4×C11—41no—
291C4×C11—41no—
292Dic11—42no—
293Dic11—81no—
294Dic11—81no—
295Dic11—81no—
296C2×#41—22no—
297C2×#41—22no—
298C2×#41—22no—
299C2×#41—22no—
300C2×#41—44no—
301C2×#41—44no—
302C22×Q8—21no—
303C22×D4—21no—
304C22×D4—22no—
305C23×C4—22no—
306C23×C4C22⋊D1111yescharacteristic
307C4⋊Q8—21no—
308C4⋊Q8C22⋊D1112yes—
309#127—21no—
310#127C22⋊D1112yes—
311#125—222no—
312#125—222no—
313#124—22no—
314#124—22no—
315#123—24no—
316#123—24no—
317C22⋊Q8—24no—
318C22⋊Q8—24no—
319#121—24no—
320#121—24no—
321#121—22no—
322#121—22no—
323#121—22no—
324#121C22×D1114yes—
325#120—24no—
326#120—24no—
327C4×D4—22no—
328C4×D4—22no—
329C4×D4—22no—
330C4×D4C22⋊D1114yes—
331#117—22no—
332#117—22no—
333C2×C4⋊C4—111no—
334C2×C4⋊C4—111no—
335C2×C4⋊C4—221no—
336C2×C4⋊C4—221no—
337C2×C4⋊C4—221no—
338C2×C4⋊C4—221no—
339C2×C4⋊C4C22⋊D1111yescharacteristic
340C2×C4⋊C4C22×D1111yescharacteristic
341C2×C22⋊C4—221no—
342C2×C22⋊C4—221no—
343C2×C22⋊C4C22⋊D1111yescharacteristic
344C2×C22⋊C4C22×D1111yescharacteristic
345C2×C42—221no—
346C2×C42C22⋊D1111yescharacteristic
347C2×C42C22×D1111yescharacteristic
348#107—224no—
349#106—224no—
350C4⋊C8—222no—
351#102—224no—
352#102—224no—
353C22⋊C8—114no—
354#97—222no—
355#95—111no—
356#95—111no—
357#95—221no—
358#95—221no—
359#95—221no—
360#95—221no—
361#95—221no—
362C2×C11—21no—
363C2×C11—21no—
364C2×C11—42no—
365C2×C11—84no—
366C2×C11#300311yescharacteristic
367C2×C11#301811yescharacteristic
368C2×C11#302811yescharacteristic
369C24—22no—
370C24C2×C22⋊D1111yescharacteristic
371#41—48no—
372#41—48no—
373#41—44no—
374#41—44no—
375#41—44no—
376#41—44no—
377C2×Q8—22no—
378C2×Q8—22no—
379C2×Q8—44no—
380C2×D4—24no—
381C2×D4—22no—
382C2×D4—24no—
383C2×D4—22no—
384C2×D4—22no—
385C2×D4—22no—
386C2×D4—22no—
387C2×D4—44no—
388C2×D4—44no—
389C2×D4—44no—
390C2×D4C2×C22⋊D1114yes—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—24no—
396C22×C4—22no—
397C22×C4—24no—
398C22×C4—48no—
399C22×C4—221no—
400C22×C4—221no—
401C22×C4—221no—
402C22×C4—221no—
403C22×C4C2×C22⋊D1111yescharacteristic
404C22×C4C2×C22⋊D1111yescharacteristic
405C22×C4C2×C22⋊D1111yescharacteristic
406C22×C4C2×C22⋊D1111yescharacteristic
407C22×C4C2×C22⋊D1111yescharacteristic
408C22×C4C23×D1111yescharacteristic
409C2×C8—224no—
410C4⋊C4—22no—
411C4⋊C4—22no—
412C4⋊C4—22no—
413C4⋊C4—22no—
414C4⋊C4—22no—
415C4⋊C4—222no—
416C4⋊C4—222no—
417C4⋊C4—442no—
418C4⋊C4—442no—
419C4⋊C4—441no—
420C4⋊C4—441no—
421C4⋊C4—442no—
422C4⋊C4C2×C22⋊D1114yes—
423C22⋊C4—24no—
424C22⋊C4—24no—
425C22⋊C4—22no—
426C22⋊C4—24no—
427C22⋊C4—22no—
428C22⋊C4—24no—
429C22⋊C4—442no—
430C22⋊C4—442no—
431C42—21no—
432C42—21no—
433C42—442no—
434C42C2×C22⋊D1112yes—
435C42C2×C22⋊D1112yes—
436C11#1833911yescharacteristic, complemented, Sylow
437C23—21no—
438C23—21no—
439C23—24no—
440C23—41no—
441C23—41no—
442C23—44no—
443C23—82no—
444C23—82no—
445C23#6698512yes—
446C23C22×C22⋊D1111yescharacteristic
447Q8—44no—
448Q8—44no—
449D4—44no—
450D4—44no—
451D4—44no—
452D4—48no—
453D4—44no—
454D4—44no—
455D4—82no—
456D4—82no—
457D4—82no—
458C2×C4—24no—
459C2×C4—24no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—24no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—48no—
470C2×C4—48no—
471C2×C4—44no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—222no—
475C2×C4—441no—
476C2×C4—441no—
477C2×C4—441no—
478C2×C4—441no—
479C2×C4—441no—
480C2×C4—441no—
481C2×C4—441no—
482C2×C4—441no—
483C2×C4—441no—
484C2×C4—441no—
485C2×C4—441no—
486C2×C4#6698512yes—
487C2×C4#6700611yescharacteristic
488C2×C4#6700611yescharacteristic
489C2×C4#6700612yes—
490C2×C4C22×C22⋊D1112yes—
491C8—444no—
492C22—21no—
493C22—21no—
494C22—22no—
495C22—42no—
496C22—41no—
497C22—41no—
498C22—44no—
499C22—44no—
500C22—44no—
501C22—81no—
502C22—88no—
503C22C2×#6698511yescharacteristic
504C22C2×#6698511yescharacteristic
505C22C2×#6700611yescharacteristic
506C4—22no—
507C4—21no—
508C4—22no—
509C4—21no—
510C4—22no—
511C4—41no—
512C4—44no—
513C4—41no—
514C4—442no—
515C4—881no—
516C4—881no—
517C4—881no—
518C2—21no—
519C2—21no—
520C2—42no—
521C2—84no—
522C2#1307784311yescharacteristic
523C2#1307796511yescharacteristic
524C2#1307802211yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC11×#3449C2
socleC22×C11C2×#120
hypercenter#3449D11
hypocenterC11#18339
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3449

Complements

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

NH ≅ G/Ntype
1. #13079802C2semidirect
2. #13074314C2semidirect
3. #13067653C2semidirect
4. #13067636C2semidirect
5. #13067619C2semidirect
6. #13067602C2semidirect
7. #13067124C2semidirect
8. #13066950C2semidirect
21. C2×#66923C22semidirect
25. #10622647C22semidirect
26. #10622646C22semidirect
28. #10622599C22semidirect
29. #10622596C22semidirect
35. #10622545C22semidirect
36. #10622539C22semidirect
37. #10622175C22semidirect
38. #10622175C22semidirect
39. #10622166C22semidirect
436. C11#18339semidirect

Maximal subgroups

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

subgroupindex
#130798022
#130743142
#130676532
#130676362
#130676192
#130676022
#130671242
#130669502
C11×#34492
#1833911