Finite Group Databasebeta

← #14728076

Subgroups — #14728076

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#13081949C211yesmaximal, characteristic
2#13079806C212yesmaximal, complemented
3#13067652C212yesmaximal, complemented
4#13067635C212yesmaximal, complemented
5#13067618C212yesmaximal, complemented
6#13067601C212yesmaximal, complemented
7#13067123C212yesmaximal, complemented
8#13066950C211yesmaximal, characteristic, complemented
9C11×#2611C211yesmaximal, characteristic, complemented
10C22×#4339—21no—
11C2×C11×#125C2211yescharacteristic, complemented
12C2×C11×#117C2211yescharacteristic
13#10623057—22no—
14#10623056—22no—
15#10623055—24no—
16#10623041—21no—
17#10623041C2212yes—
18#10623024—21no—
19#10623024C2212yes—
20#10623008—21no—
21#10623008C2212yes—
22C11×#400C2211yescharacteristic, complemented
23C11×#399C2211yescharacteristic
24C11×#398C2211yescharacteristic, complemented
25C11×#397C2211yescharacteristic
26C11×#389—21no—
27C11×#388—21no—
28C11×#387—21no—
29C11×#385—21no—
30C11×#376C2211yescharacteristic, complemented
31#10622680—22no—
32#10622679—24no—
33#10622678—22no—
34#10622581C2214yescomplemented
35#10622580C2214yescomplemented
36#10622539C2212yescomplemented
37#10622166C2212yescomplemented
38#10622163C2212yes—
39#10622089C2214yescomplemented
40#10622089C2214yescomplemented
41C23×C4×C11D411yescharacteristic
42C22×C22⋊D11—22no—
43C2×#4339—22no—
44C2×#4339—22no—
45C2×#4339—22no—
46C2×#4339—22no—
47C2×#4339—44no—
48C2×#4339—44no—
49C22×D44—21no—
50C22×C4×D11—22no—
51C22×Dic22—21no—
52C11×#125—22no—
53C11×#125—22no—
54C11×#117—22no—
55C11×#117—22no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4D411yescharacteristic
61C2×C11×C4⋊C4C2311yescharacteristic
62C2×C11×C4⋊C4C2311yescharacteristic
63C2×C11×C4⋊C4C2311yescharacteristic
64C2×C11×C22⋊C4—21no—
65C2×C11×C22⋊C4—21no—
66C2×C11×C22⋊C4D411yescharacteristic
67C2×C11×C22⋊C4C2311yescharacteristic
68C2×C42×C11—21no—
69C2×C42×C11D411yescharacteristic
70C2×C42×C11C2311yescharacteristic
71#66983—22no—
72#66983—22no—
73#66983—22no—
74#66983C2314yes—
75#66950—24no—
76#66950—24no—
77#66948—24no—
78#66948—24no—
79#66939—24no—
80#66939—24no—
81#66935—24no—
82#66935—24no—
83#66928—22no—
84#66928—22no—
85#66927—21no—
86#66927D412yes—
87C4×D44—22no—
88C4×D44—22no—
89C4×D44—22no—
90C4×D44D414yes—
91#66922—21no—
92#66922D412yes—
93C11×#95—21no—
94C11×#95—21no—
95C11×#95—21no—
96C11×#95—21no—
97C11×#95—21no—
98C11×#95C2311yescharacteristic
99C11×#95C2311yescharacteristic
100C22⋊(C11⋊C8)C2314yes—
101#66873—24no—
102#66873—24no—
103#66872—24no—
104#66871—24no—
105C4⋊(C11⋊C8)—22no—
106#66867—22no—
107#18339—111nomaximal, Sylow
108C24×C11C2×D411yescharacteristic
109C23×D11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—21no—
112C22×C4×C11—21no—
113C22×C4×C11—22no—
114C22×C4×C11—21no—
115C22×C4×C11—21no—
116C22×C4×C11—21no—
117C22×C4×C11—21no—
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2411yescharacteristic
124C2×C22⋊D11—24no—
125C2×C22⋊D11—24no—
126C2×C22⋊D11—44no—
127C2×C22⋊D11—44no—
128C22×Dic11—22no—
129#4339—48no—
130#4339—48no—
131#4339—44no—
132#4339—44no—
133#4339—44no—
134#4339—44no—
135C2×D44—22no—
136C2×D44—22no—
137C2×D44—22no—
138C2×D44—22no—
139C2×D44—22no—
140C2×D44—44no—
141C2×D44C2×D414yes—
142C2×C4×D11—24no—
143C2×C4×D11—24no—
144C2×C4×D11—48no—
145C2×Dic22—22no—
146C2×Dic22—22no—
147C2×Dic22—44no—
148C11×C4⋊C4—22no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—22no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—42no—
153C11×C4⋊C4—42no—
154C11×C4⋊C4—41no—
155C11×C4⋊C4—41no—
156C11×C4⋊C4—42no—
157C11×C22⋊C4—22no—
158C11×C22⋊C4—22no—
159C11×C22⋊C4—42no—
160C11×C22⋊C4—42no—
161C42×C11—21no—
162C42×C11—21no—
163C42×C11—42no—
164C42×C11C2×D412yes—
165C42×C11C2×D412yes—
166(C2×D11)⋊C4—24no—
167(C2×D11)⋊C4—24no—
168(C2×D11)⋊C4—24no—
169(C2×D11)⋊C4—24no—
170C4⋊Dic11—22no—
171C4⋊Dic11—22no—
172C4⋊Dic11—22no—
173C4⋊Dic11C2×D414yes—
174C2×C11⋊C8—24no—
175#3449—111no—
176#3234—112no—
177#2611D1111yescharacteristic, complemented
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—41no—
187C23×C11—41no—
188C23×C11AGL(1,ℤ/8)12yes—
189C23×C11C22×D411yescharacteristic
190C22×D11—24no—
191C22×D11—44no—
192C22×D11—82no—
193C22×D11—82no—
194C2×C4×C11—24no—
195C2×C4×C11—24no—
196C2×C4×C11—21no—
197C2×C4×C11—21no—
198C2×C4×C11—21no—
199C2×C4×C11—21no—
200C2×C4×C11—22no—
201C2×C4×C11—21no—
202C2×C4×C11—21no—
203C2×C4×C11—41no—
204C2×C4×C11—41no—
205C2×C4×C11—41no—
206C2×C4×C11—41no—
207C2×C4×C11—41no—
208C2×C4×C11—41no—
209C2×C4×C11—41no—
210C2×C4×C11—41no—
211C2×C4×C11—41no—
212C2×C4×C11—41no—
213C2×C4×C11—41no—
214C2×C4×C11—41no—
215C2×C4×C11—41no—
216C2×C4×C11—41no—
217C2×C4×C11—41no—
218C2×C4×C11#12012yes—
219C2×C4×C11#12011yescharacteristic
220C2×C4×C11#12011yescharacteristic
221C2×C4×C11AGL(1,ℤ/8)12yes—
222C2×C4×C11C22×D412yes—
223C22⋊D11—48no—
224C22⋊D11—44no—
225C22⋊D11—44no—
226C2×Dic11—24no—
227C2×Dic11—44no—
228D44—44no—
229D44—44no—
230D44—44no—
231D44—82no—
232D44—82no—
233D44—82no—
234C4×D11—48no—
235C4×D11—48no—
236Dic22—44no—
237Dic22—44no—
238C11⋊C8—44no—
239C22×#41—221no—
240#537—112no—
241#537—221no—
242#536—222no—
243#535—222no—
244#534—112no—
245#534—221no—
246#532—112no—
247#532—221no—
248C2×#125C2×D1111yescharacteristic, complemented
249#525—224no—
250C2×#117C2×D1111yescharacteristic
251#501—222no—
252#490—222no—
253#481—114no—
254#480—114no—
255#478—224no—
256#432—112no—
257#400C2×D1111yescharacteristic, complemented
258#399C2×D1111yescharacteristic
259#398C2×D1111yescharacteristic, complemented
260#397C2×D1111yescharacteristic
261#389—21no—
262#388—21no—
263#387—21no—
264#385—21no—
265#376C2×D1111yescharacteristic, complemented
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—81no—
277C22×C11C2×#12011yescharacteristic
278C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
279C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
280C2×D11—44no—
281C2×D11—44no—
282C2×D11—44no—
283C2×D11—88no—
284C4×C11—21no—
285C4×C11—21no—
286C4×C11—22no—
287C4×C11—22no—
288C4×C11—22no—
289C4×C11—42no—
290C4×C11—41no—
291C4×C11—41no—
292C4×C11—81no—
293C4×C11—81no—
294C4×C11—81no—
295Dic11—44no—
296C2×#41—222no—
297C2×#41—222no—
298C2×#41—222no—
299C2×#41—222no—
300C2×#41—444no—
301C2×#41—444no—
302C22×Q8—221no—
303C22×D4—221no—
304C22×D4—222no—
305C23×C4—222no—
306C23×C4C22⋊D1111yescharacteristic
307C4⋊Q8—112no—
308C4⋊Q8—221no—
309#127—112no—
310#127—221no—
311#125—22no—
312#125—22no—
313#124—222no—
314#124—222no—
315#123—224no—
316#123—224no—
317C22⋊Q8—224no—
318C22⋊Q8—224no—
319#121—114no—
320#121—224no—
321#121—224no—
322#121—222no—
323#121—222no—
324#121—222no—
325#120—224no—
326#120—224no—
327C4×D4—114no—
328C4×D4—222no—
329C4×D4—222no—
330C4×D4—222no—
331#117—22no—
332#117—22no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4C22⋊D1111yescharacteristic
338C2×C4⋊C4C22×D1111yescharacteristic
339C2×C4⋊C4C22×D1111yescharacteristic
340C2×C4⋊C4C22×D1111yescharacteristic
341C2×C22⋊C4—21no—
342C2×C22⋊C4—21no—
343C2×C22⋊C4C22⋊D1111yescharacteristic
344C2×C22⋊C4C22×D1111yescharacteristic
345C2×C42—21no—
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—21no—
356#95—21no—
357#95—21no—
358#95—21no—
359#95—21no—
360#95C22×D1111yescharacteristic
361#95C22×D1111yescharacteristic
362C2×C11—21no—
363C2×C11—21no—
364C2×C11—42no—
365C2×C11#300311yescharacteristic
366C2×C11#301811yescharacteristic
367C2×C11#302811yescharacteristic
368D11—84no—
369C24—222no—
370C24C2×C22⋊D1111yescharacteristic
371#41—448no—
372#41—448no—
373#41—444no—
374#41—444no—
375#41—444no—
376#41—444no—
377C2×Q8—222no—
378C2×Q8—222no—
379C2×Q8—444no—
380C2×D4—114no—
381C2×D4—222no—
382C2×D4—222no—
383C2×D4—222no—
384C2×D4—224no—
385C2×D4—224no—
386C2×D4—222no—
387C2×D4—222no—
388C2×D4—444no—
389C2×D4—444no—
390C2×D4—444no—
391C22×C4—22no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—22no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—224no—
400C22×C4—222no—
401C22×C4—224no—
402C22×C4—448no—
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—42no—
415C4⋊C4—41no—
416C4⋊C4—41no—
417C4⋊C4—42no—
418C4⋊C4—42no—
419C4⋊C4—114no—
420C4⋊C4—222no—
421C4⋊C4—222no—
422C4⋊C4—222no—
423C22⋊C4—22no—
424C22⋊C4—22no—
425C22⋊C4—42no—
426C22⋊C4—42no—
427C22⋊C4—224no—
428C22⋊C4—224no—
429C22⋊C4—224no—
430C22⋊C4—224no—
431C42—21no—
432C42—21no—
433C42—42no—
434C42D4×D1112yes—
435C42D4×D1112yes—
436C11#1833911yescharacteristic, complemented, Sylow
437C23—21no—
438C23—21no—
439C23—41no—
440C23—41no—
441C23—224no—
442C23—444no—
443C23—882no—
444C23—882no—
445C23#6700212yes—
446C23C22×C22⋊D1111yescharacteristic
447Q8—444no—
448Q8—444no—
449D4—444no—
450D4—444no—
451D4—444no—
452D4—448no—
453D4—444no—
454D4—444no—
455D4—882no—
456D4—882no—
457D4—882no—
458C2×C4—24no—
459C2×C4—24no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—22no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—224no—
483C2×C4—448no—
484C2×C4—448no—
485C2×C4—444no—
486C2×C4#6699011yescharacteristic
487C2×C4#6699011yescharacteristic
488C2×C4#6699012yes—
489C2×C4#6700212yes—
490C2×C4C2×D4×D1112yes—
491C8—444no—
492C22—21no—
493C22—21no—
494C22—22no—
495C22—42no—
496C22—41no—
497C22—41no—
498C22—81no—
499C22—444no—
500C22—444no—
501C22—444no—
502C22—888no—
503C22C2×#6699011yescharacteristic
504C22C2×#6700211yescharacteristic
505C22C2×#6700211yescharacteristic
506C4—22no—
507C4—21no—
508C4—22no—
509C4—21no—
510C4—22no—
511C4—42no—
512C4—41no—
513C4—41no—
514C4—81no—
515C4—81no—
516C4—81no—
517C4—444no—
518C2—21no—
519C2—21no—
520C2—42no—
521C2—884no—
522C2#1307784211yescharacteristic
523C2#1307796411yescharacteristic
524C2#1307802111yescharacteristic
subgroupG/H
centerC22C2×#66990
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2611C2
socleC22×C11C2×#120
prime radical#13081949C2
hypercenter#2611D11
hypocenterC11#18339
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2611

Complements

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

NH ≅ G/Ntype
2. #13079806C2semidirect
3. #13067652C2semidirect
4. #13067635C2semidirect
5. #13067618C2semidirect
6. #13067601C2semidirect
7. #13067123C2semidirect
8. #13066950C2semidirect
9. C11×#2611C2semidirect
11. C2×C11×#125C22semidirect
22. C11×#400C22semidirect
24. C11×#398C22semidirect
30. C11×#376C22semidirect
34. #10622581C22semidirect
35. #10622580C22semidirect
36. #10622539C22semidirect
37. #10622166C22semidirect
39. #10622089C22semidirect
40. #10622089C22semidirect
177. #2611D11semidirect
248. C2×#125C2×D11semidirect
257. #400C2×D11semidirect
259. #398C2×D11semidirect
265. #376C2×D11semidirect
436. C11#18339semidirect

Maximal subgroups

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

subgroupindex
#130819492
#130798062
#130676522
#130676352
#130676182
#130676012
#130671232
#130669502
C11×#26112
#1833911