Finite Group Databasebeta

← #14726494

Subgroups — #14726494

Order 2816.

1242 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082380C211yesmaximal, characteristic
2#13078556C212yesmaximal, complemented
3#13067652C212yesmaximal, complemented
4#13067635C212yesmaximal, complemented
5#13067618C212yesmaximal, complemented
6#13067601C212yesmaximal, complemented
7#13067131C212yesmaximal, complemented
8#13066954C211yesmaximal, characteristic, complemented
9C11×#2395C211yesmaximal, characteristic, complemented
10C2×#67037—21no—
11C2×C4×D4×C11C2211yescharacteristic
12C2×C11×#117C2211yescharacteristic, complemented
13C2×#66983—21no—
14C2×#66983C2212yes—
15#10623086—22no—
16#10623085—24no—
17D4×D44—22no—
18#10623041C2212yes—
19#10623024—21no—
20#10623024C2212yes—
21#10623008—21no—
22C11×#400C2211yescharacteristic, complemented
23C11×#399C2211yescharacteristic, complemented
24C11×#398C2211yescharacteristic, complemented
25C11×#397—21no—
26C11×#397C2211yescharacteristic, complemented
27C11×#394—21no—
28C4×C11×C4⋊C4—21no—
29C4×C11×C22⋊C4—21no—
30C4×C11×C22⋊C4C2211yescharacteristic, complemented
31#10622820C2212yescomplemented
32#10622616—24no—
33#10622614—22no—
34#10622608—22no—
35#10622581C2214yescomplemented
36#10622580C2214yescomplemented
37#10622166C2212yescomplemented
38#10622163C2212yescomplemented
39#10622089C2214yescomplemented
40#10622089C2214yescomplemented
41C22×D4×C11D411yescharacteristic
42C23×C4×C11D411yescharacteristic
43C23×C4×C11C2311yescharacteristic
44C22×C22⋊D11—22no—
45C22×C22⋊D11—22no—
46#67037—44no—
47#67037—44no—
48C2×#4341—24no—
49C2×D4×D11—24no—
50C2×#4339—22no—
51C22×D44—21no—
52C22×D44D412yes—
53C4×D4×C11—22no—
54C4×D4×C11—22no—
55C11×#117—22no—
56C11×#117—22no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4C2311yescharacteristic
60C2×C11×C4⋊C4C2311yescharacteristic
61C2×C11×C4⋊C4C2311yescharacteristic
62C2×C11×C22⋊C4—21no—
63C2×C11×C22⋊C4—21no—
64C2×C11×C22⋊C4—21no—
65C2×C11×C22⋊C4—21no—
66C2×C11×C22⋊C4D411yescharacteristic
67C2×C11×C22⋊C4C2311yescharacteristic
68C2×C42×C11—21no—
69C2×C42×C11—21no—
70C2×C42×C11D411yescharacteristic
71#66983—22no—
72#66983—22no—
73#66983—22no—
74#66983—22no—
75#66983—22no—
76#66983—22no—
77#66983D414yes—
78#66983C2314yes—
79C2×(C2×D11)⋊C4—22no—
80C2×(C2×D11)⋊C4—22no—
81C2×C4⋊Dic11—21no—
82C2×C4⋊Dic11D412yes—
83C2×#4318—22no—
84#66950—24no—
85#66948—24no—
86#66939—24no—
87#66939—24no—
88#66935—24no—
89#66935—24no—
90#66928—22no—
91#66927—21no—
92C4×D44—22no—
93C4×D44—22no—
94#66922—21no—
95C11×#95—21no—
96C11×#95—21no—
97C11×#95—21no—
98C11×#95—21no—
99C11×#95C2311yescharacteristic
100C11×#95C2311yescharacteristic
101C22⋊(C11⋊C8)—22no—
102C22⋊(C11⋊C8)C2314yes—
103#66873—24no—
104#66873—24no—
105#66872—24no—
106#66871—24no—
107#18173—111nomaximal, Sylow
108C24×C11C2×D411yescharacteristic
109C24×C11C2×D411yescharacteristic
110C23×D11—22no—
111C23×D11—22no—
112C2×D4×C11—22no—
113C2×D4×C11—22no—
114C2×D4×C11—22no—
115C22×C4×C11—21no—
116C22×C4×C11—21no—
117C22×C4×C11—21no—
118C22×C4×C11—21no—
119C22×C4×C11—21no—
120C22×C4×C11—21no—
121C22×C4×C11—42no—
122C22×C4×C11—42no—
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D412yes—
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D412yes—
129C22×C4×C11C2411yescharacteristic
130C2×C22⋊D11—24no—
131C2×C22⋊D11—24no—
132C2×C22⋊D11—24no—
133C2×C22⋊D11—44no—
134C2×C22⋊D11—44no—
135C2×C22⋊D11—44no—
136C2×C22⋊D11—44no—
137C22×Dic11—22no—
138C22×Dic11—22no—
139#4341—416no—
140D4×D11—416no—
141#4339—44no—
142#4339—44no—
143C2×D44—22no—
144C2×D44—22no—
145C2×D44—22no—
146C2×D44—22no—
147C2×D44—44no—
148C2×D44—82no—
149C2×D44C2×D414yes—
150C2×C4×D11—24no—
151C2×Dic22—22no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—42no—
156C11×C4⋊C4—42no—
157C11×C22⋊C4—22no—
158C11×C22⋊C4—22no—
159C11×C22⋊C4—42no—
160C11×C22⋊C4—42no—
161C11×C22⋊C4—42no—
162C11×C22⋊C4—42no—
163C42×C11—21no—
164C42×C11—21no—
165C42×C11—42no—
166C42×C11—41no—
167C42×C11—41no—
168(C2×D11)⋊C4—24no—
169(C2×D11)⋊C4—24no—
170(C2×D11)⋊C4—24no—
171(C2×D11)⋊C4—24no—
172C4⋊Dic11—22no—
173C4⋊Dic11—22no—
174C4⋊Dic11—22no—
175C4⋊Dic11C2×D414yes—
176#4318—44no—
177C2×C11⋊C8—24no—
178#3496—111no—
179#3094—112no—
180#2395D1111yescharacteristic, complemented
181#1616—112no—
182#1613—112no—
183#1610—112no—
184#1607—112no—
185#1507—112no—
186#1465—111no—
187C23×C11—21no—
188C23×C11—21no—
189C23×C11—21no—
190C23×C11—21no—
191C23×C11—41no—
192C23×C11—41no—
193C23×C11—41no—
194C23×C11—41no—
195C23×C11#12012yes—
196C23×C11AGL(1,ℤ/8)12yes—
197C23×C11C22×D411yescharacteristic
198C22×D11—24no—
199C22×D11—44no—
200C22×D11—44no—
201C22×D11—82no—
202C22×D11—82no—
203C22×D11—82no—
204C22×D11—82no—
205D4×C11—28no—
206C2×C4×C11—21no—
207C2×C4×C11—21no—
208C2×C4×C11—24no—
209C2×C4×C11—22no—
210C2×C4×C11—22no—
211C2×C4×C11—21no—
212C2×C4×C11—21no—
213C2×C4×C11—42no—
214C2×C4×C11—41no—
215C2×C4×C11—41no—
216C2×C4×C11—41no—
217C2×C4×C11—42no—
218C2×C4×C11—41no—
219C2×C4×C11—41no—
220C2×C4×C11—41no—
221C2×C4×C11—41no—
222C2×C4×C11—41no—
223C2×C4×C11—41no—
224C2×C4×C11—41no—
225C2×C4×C11—41no—
226C2×C4×C11—41no—
227C2×C4×C11—41no—
228C2×C4×C11—41no—
229C2×C4×C11—81no—
230C2×C4×C11#12011yescharacteristic
231C2×C4×C11#12011yescharacteristic
232C2×C4×C11AGL(1,ℤ/8)12yes—
233C2×C4×C11C22×D412yes—
234C22⋊D11—48no—
235C22⋊D11—48no—
236C22⋊D11—44no—
237C22⋊D11—44no—
238C2×Dic11—24no—
239C2×Dic11—44no—
240C2×Dic11—44no—
241D44—44no—
242D44—44no—
243D44—44no—
244D44—82no—
245D44—82no—
246C4×D11—48no—
247Dic22—44no—
248C11⋊C8—44no—
249C2×H(5,𝔽2)—221no—
250#547—222no—
251#546—224no—
252D42—222no—
253#537—112no—
254#534—112no—
255#534—221no—
256#532—221no—
257C2×#121—112no—
258C2×#121—221no—
259C2×C4×D4C2×D1111yescharacteristic
260C2×#117C2×D1111yescharacteristic, complemented
261#482—224no—
262#481—114no—
263#480—114no—
264#428—222no—
265#418—222no—
266#407—112no—
267#400C2×D1111yescharacteristic, complemented
268#399C2×D1111yescharacteristic, complemented
269#398C2×D1111yescharacteristic, complemented
270#397—21no—
271#397C2×D1111yescharacteristic, complemented
272#394—21no—
273C4×C4⋊C4—21no—
274C4×C22⋊C4—21no—
275C4×C22⋊C4C2×D1111yescharacteristic, complemented
276#327—114no—
277#327—114no—
278#324—112no—
279#323—112no—
280C22×C11—21no—
281C22×C11—21no—
282C22×C11—22no—
283C22×C11—22no—
284C22×C11—22no—
285C22×C11—22no—
286C22×C11—42no—
287C22×C11—41no—
288C22×C11—41no—
289C22×C11—81no—
290C22×C11—81no—
291C22×C11—81no—
292C22×C11C2×#12011yescharacteristic
293C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
294C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
295C2×D11—44no—
296C2×D11—44no—
297C2×D11—44no—
298C2×D11—164no—
299C2×D11—164no—
300C4×C11—22no—
301C4×C11—21no—
302C4×C11—22no—
303C4×C11—42no—
304C4×C11—41no—
305C4×C11—41no—
306C4×C11—81no—
307C4×C11—81no—
308C4×C11—81no—
309C4×C11#45812yes—
310Dic11—44no—
311H(5,𝔽2)—444no—
312H(5,𝔽2)—444no—
313C2×#41—224no—
314C2×#41—222no—
315C22×D4—112no—
316C22×D4—221no—
317C22×D4—224no—
318C22×D4—222no—
319C22×D4—222no—
320C22×D4C22⋊D1111yescharacteristic
321C23×C4C22⋊D1111yescharacteristic
322C23×C4C22×D1111yescharacteristic
323C2×M16—222no—
324C4⋊Q8—221no—
325#127—221no—
326#124—222no—
327#123—224no—
328#123—224no—
329C22⋊Q8—224no—
330#121—114no—
331#121—114no—
332#121—224no—
333#121—222no—
334#121—222no—
335#121—222no—
336#121—222no—
337#121—222no—
338#121—222no—
339#120—224no—
340#120—224no—
341C4×D4—22no—
342C4×D4—22no—
343C4×D4—222no—
344C4×D4—222no—
345#117—22no—
346#117—22no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—112no—
350C2×C4⋊C4—221no—
351C2×C4⋊C4C22×D1111yescharacteristic
352C2×C4⋊C4C22×D1111yescharacteristic
353C2×C4⋊C4C22×D1111yescharacteristic
354C2×C22⋊C4—21no—
355C2×C22⋊C4—21no—
356C2×C22⋊C4—21no—
357C2×C22⋊C4—21no—
358C2×C22⋊C4—222no—
359C2×C22⋊C4—222no—
360C2×C22⋊C4C22⋊D1111yescharacteristic
361C2×C22⋊C4C22×D1111yescharacteristic
362C2×C42—21no—
363C2×C42—21no—
364C2×C42C22⋊D1111yescharacteristic
365#107—224no—
366#106—224no—
367#102—224no—
368#102—224no—
369C22⋊C8—114no—
370C22⋊C8—222no—
371#95—21no—
372#95—21no—
373#95—21no—
374#95—21no—
375#95C22×D1111yescharacteristic
376#95C22×D1111yescharacteristic
377C2×C11—21no—
378C2×C11—21no—
379C2×C11—42no—
380C2×C11—42no—
381C2×C11#300311yescharacteristic
382C2×C11#301811yescharacteristic
383C2×C11C2×#45811yescharacteristic
384D11—84no—
385C24—222no—
386C24—222no—
387C24C2×C22⋊D1111yescharacteristic
388C24C2×C22⋊D1111yescharacteristic
389#41—444no—
390#41—4416no—
391#41—444no—
392C2×Q8—222no—
393C2×D4—22no—
394C2×D4—22no—
395C2×D4—22no—
396C2×D4—114no—
397C2×D4—222no—
398C2×D4—222no—
399C2×D4—222no—
400C2×D4—224no—
401C2×D4—224no—
402C2×D4—224no—
403C2×D4—222no—
404C2×D4—444no—
405C2×D4—4416no—
406C2×D4—444no—
407C2×D4—444no—
408C2×D4—444no—
409C2×D4—444no—
410C2×D4—882no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—42no—
418C22×C4—42no—
419C22×C4—224no—
420C22×C4—222no—
421C22×C4—222no—
422C22×C4D4×D1112yes—
423C22×C4D4×D1112yes—
424C22×C4C2×C22⋊D1111yescharacteristic
425C22×C4C2×C22⋊D1111yescharacteristic
426C22×C4C2×C22⋊D1111yescharacteristic
427C22×C4C2×C22⋊D1111yescharacteristic
428C22×C4C23×D1111yescharacteristic
429M16—444no—
430C2×C8—224no—
431C4⋊C4—22no—
432C4⋊C4—22no—
433C4⋊C4—22no—
434C4⋊C4—42no—
435C4⋊C4—42no—
436C4⋊C4—114no—
437C4⋊C4—222no—
438C4⋊C4—222no—
439C4⋊C4—222no—
440C22⋊C4—22no—
441C22⋊C4—22no—
442C22⋊C4—42no—
443C22⋊C4—42no—
444C22⋊C4—42no—
445C22⋊C4—42no—
446C22⋊C4—224no—
447C22⋊C4—224no—
448C22⋊C4—224no—
449C22⋊C4—224no—
450C42—21no—
451C42—21no—
452C42—42no—
453C42—41no—
454C42—41no—
455C11#1817311yescharacteristic, complemented, Sylow
456C23—21no—
457C23—21no—
458C23—21no—
459C23—21no—
460C23—41no—
461C23—41no—
462C23—41no—
463C23—41no—
464C23—224no—
465C23—444no—
466C23—444no—
467C23—882no—
468C23—882no—
469C23—882no—
470C23—882no—
471C23#6699012yes—
472C23#6700212yes—
473C23C22×C22⋊D1111yescharacteristic
474Q8—444no—
475D4—28no—
476D4—444no—
477D4—444no—
478D4—448no—
479D4—448no—
480D4—444no—
481D4—444no—
482D4—444no—
483D4—882no—
484D4—882no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—22no—
488C2×C4—24no—
489C2×C4—22no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—42no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—42no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—81no—
509C2×C4—224no—
510C2×C4—448no—
511C2×C4—444no—
512C2×C4—444no—
513C2×C4#6699011yescharacteristic
514C2×C4#6699011yescharacteristic
515C2×C4#6700212yes—
516C2×C4C2×D4×D1112yes—
517C8—444no—
518C22—21no—
519C22—21no—
520C22—22no—
521C22—22no—
522C22—22no—
523C22—22no—
524C22—42no—
525C22—41no—
526C22—41no—
527C22—81no—
528C22—81no—
529C22—81no—
530C22—444no—
531C22—444no—
532C22—444no—
533C22—1764no—
534C22—1764no—
535C22C2×#6699011yescharacteristic
536C22C2×#6700211yescharacteristic
537C22C2×#6700211yescharacteristic
538C4—22no—
539C4—22no—
540C4—21no—
541C4—42no—
542C4—41no—
543C4—41no—
544C4—81no—
545C4—81no—
546C4—81no—
547C4—444no—
548C4#1062266612yes—
549C2—21no—
550C2—21no—
551C2—42no—
552C2—42no—
553C2—884no—
554C2#1307784211yescharacteristic
555C2#1307796411yescharacteristic
556C2C2×#1062266611yescharacteristic
subgroupG/H
centerC22C2×#66990
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2395C2
socleC22×C11C2×#120
prime radical#13082380C2
hypercenter#2395D11
hypocenterC11#18173
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2395

Complements

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

NH ≅ G/Ntype
2. #13078556C2semidirect
3. #13067652C2semidirect
4. #13067635C2semidirect
5. #13067618C2semidirect
6. #13067601C2semidirect
7. #13067131C2semidirect
8. #13066954C2semidirect
9. C11×#2395C2semidirect
12. C2×C11×#117C22semidirect
22. C11×#400C22semidirect
23. C11×#399C22semidirect
24. C11×#398C22semidirect
26. C11×#397C22semidirect
30. C4×C11×C22⋊C4C22semidirect
31. #10622820C22semidirect
35. #10622581C22semidirect
36. #10622580C22semidirect
37. #10622166C22semidirect
38. #10622163C22semidirect
39. #10622089C22semidirect
40. #10622089C22semidirect
180. #2395D11semidirect
260. C2×#117C2×D11semidirect
267. #400C2×D11semidirect
268. #399C2×D11semidirect
269. #398C2×D11semidirect
271. #397C2×D11semidirect
275. C4×C22⋊C4C2×D11semidirect
455. C11#18173semidirect

Maximal subgroups

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

subgroupindex
#130823802
#130785562
#130676522
#130676352
#130676182
#130676012
#130671312
#130669542
C11×#23952
#1817311