Finite Group Databasebeta

← #14788998

Subgroups — #14788998

Order 2816.

1494 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078076C212yesmaximal, complemented
2C2×#10622854C212yesmaximal, complemented
3#13071338C211yesmaximal, characteristic, complemented
4#13069842C212yesmaximal, complemented
5#13069658C212yesmaximal, complemented
6#13069449C212yesmaximal, complemented
7#13068608C211yesmaximal, characteristic, complemented
8#13068570C212yesmaximal, complemented
9C11×#3496C211yesmaximal, characteristic, complemented
10C2×C11×H(5,𝔽2)C2212yes—
11C11×#547—22no—
12C11×#546—24no—
13D42×C11—22no—
14C11×#537C2212yes—
15C11×#534—22no—
16C11×#532C2212yes—
17C2×C11×#121—22no—
18C2×C4×D4×C11C2211yescharacteristic
19C2×#67002C2214yescomplemented
20C2×#66993C2211yescharacteristic
21C2×C4×D44C2211yescharacteristic, complemented
22#10622854—28no—
23C2×#66901C2214yescomplemented
24C2×#66901C2214yescomplemented
25#10622845C2214yescomplemented
26#10622834C2211yescharacteristic
27C2×#66897C2212yes—
28#10622826—22no—
29#10622696—22no—
30#10622685—22no—
31#10622670—24no—
32#10622601C2211yescharacteristic, complemented
33#10622590C2211yescharacteristic, complemented
34#10622569—22no—
35#10622545C2211yescharacteristic, complemented
36#10622537C2212yescomplemented
37#10622168C2212yescomplemented
38C11×H(5,𝔽2)—24no—
39C11×H(5,𝔽2)—24no—
40C11×H(5,𝔽2)—44no—
41C2×C11×#41—24no—
42C2×C11×#41C2314yes—
43C22×D4×C11—24no—
44C22×D4×C11—22no—
45C22×D4×C11—24no—
46C22×D4×C11C2311yescharacteristic
47C23×C4×C11D412yes—
48C22×C22⋊D11—22no—
49C22×D44C2311yescharacteristic
50C22×C4×D11—21no—
51C11×C4⋊Q8D412yescomplemented
52C11×#127D412yescomplemented
53C11×#124D414yescomplemented
54C11×#123—28no—
55C11×C22⋊Q8—24no—
56C11×#121—24no—
57C11×#121—24no—
58C11×#121—24no—
59C11×#121—22no—
60C11×#121—24no—
61C11×#121—22no—
62C11×#120—28no—
63C4×D4×C11—22no—
64C4×D4×C11—22no—
65C4×D4×C11—22no—
66C4×D4×C11—22no—
67C2×C11×C4⋊C4—22no—
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C22⋊C4—24no—
70C2×C11×C22⋊C4D412yes—
71C2×C42×C11C2311yescharacteristic
72C2×C22⋊Dic11—22no—
73#67002—28no—
74#67002—44no—
75C2×#4325—24no—
76#66993—22no—
77#66993D414yescomplemented
78C2×#4323—24no—
79C2×(C2×D11)⋊C4—21no—
80C2×(C2×D11)⋊C4—22no—
81C2×C4⋊Dic11C2311yescharacteristic
82C2×C4×Dic11C2311yescharacteristic
83C2×C4×Dic11C2311yescharacteristic
84C2×#4318C2314yes—
85C4×D44—22no—
86C4×D44—22no—
87#66901—28no—
88#66901—44no—
89#66899—24no—
90#66897—24no—
91#66896—24no—
92C11⋊#95—21no—
93C11⋊#95—21no—
94C11⋊#95—22no—
95C4⋊(C11⋊C8)—22no—
96C4⋊(C11⋊C8)—22no—
97#24226—111nomaximal, Sylow
98C24×C11—24no—
99C24×C11C2×D412yes—
100C23×D11—21no—
101C11×#41—24no—
102C11×#41—24no—
103C11×#41—24no—
104C11×#41—24no—
105C11×#41—48no—
106C11×#41—48no—
107C2×Q8×C11C2×D414yes—
108C2×D4×C11—28no—
109C2×D4×C11—24no—
110C2×D4×C11—24no—
111C2×D4×C11—22no—
112C2×D4×C11—22no—
113C2×D4×C11—22no—
114C2×D4×C11—22no—
115C2×D4×C11—48no—
116C2×D4×C11—48no—
117C2×D4×C11—48no—
118C2×D4×C11—48no—
119C2×D4×C11—84no—
120C2×D4×C11C2×D414yes—
121C2×D4×C11C2×D412yes—
122C2×D4×C11#4112yes—
123C22×C4×C11—24no—
124C22×C4×C11—22no—
125C22×C4×C11—24no—
126C22×C4×C11—22no—
127C22×C4×C11—82no—
128C22×C4×C11C2×D412yes—
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2411yescharacteristic
132C2×C22⋊D11—28no—
133C2×C22⋊D11—82no—
134C2×C22⋊D11—82no—
135C22×Dic11—21no—
136C22×Dic11—21no—
137C22×Dic11—21no—
138C2×D44—22no—
139C2×D44—21no—
140C2×D44—22no—
141C2×D44C2×D412yescomplemented
142C2×C4×D11—42no—
143C2×C4×D11—82no—
144C11×C4⋊C4—24no—
145C11×C4⋊C4—22no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—22no—
148C11×C22⋊C4—28no—
149C11×C22⋊C4—24no—
150C11×C22⋊C4—24no—
151C11×C22⋊C4—24no—
152C42×C11C2×D412yes—
153C42×C11C2×D412yes—
154C22⋊Dic11—82no—
155#4325—48no—
156#4323—48no—
157(C2×D11)⋊C4—41no—
158(C2×D11)⋊C4—41no—
159(C2×D11)⋊C4—82no—
160C4⋊Dic11—22no—
161C4×Dic11—21no—
162C4×Dic11—22no—
163C4×Dic11C2×D412yescomplemented
164#4318—24no—
165#4318—24no—
166C2×C11⋊C8—24no—
167#3496D1111yescharacteristic, complemented
168#3036—112no—
169C2×#453—112no—
170#2328—111no—
171#2040—112no—
172#2006—112no—
173#1963—112no—
174#1800—111no—
175#1792—112no—
176C23×C11—22no—
177C23×C11—22no—
178C23×C11—24no—
179C23×C11—42no—
180C23×C11—42no—
181C23×C11—48no—
182C23×C11—84no—
183C23×C11—84no—
184C23×C11#12114yes—
185C23×C11C22×D411yescharacteristic
186C22×D11—22no—
187C22×D11—42no—
188C22×D11—42no—
189C22×D11—41no—
190C22×D11—41no—
191Q8×C11—24no—
192Q8×C11—24no—
193D4×C11—24no—
194D4×C11—24no—
195D4×C11—24no—
196D4×C11—24no—
197D4×C11—44no—
198D4×C11—416no—
199D4×C11—44no—
200D4×C11—44no—
201D4×C11—82no—
202D4×C11—84no—
203C2×C4×C11—22no—
204C2×C4×C11—24no—
205C2×C4×C11—41no—
206C2×C4×C11—41no—
207C2×C4×C11—44no—
208C2×C4×C11—48no—
209C2×C4×C11—44no—
210C2×C4×C11—44no—
211C2×C4×C11—42no—
212C2×C4×C11—82no—
213C2×C4×C11#12011yescharacteristic
214C2×C4×C11#12011yescharacteristic
215C2×C4×C11#12012yes—
216C2×C4×C11C22×D411yescharacteristic
217C2×C4×C11C22×D412yes—
218C2×C4×C11C2×#4111yescharacteristic
219C2×C4×C11H(5,𝔽2)12yes—
220C22⋊D11—88no—
221C2×Dic11—22no—
222C2×Dic11—41no—
223C2×Dic11—41no—
224C2×Dic11—41no—
225C2×Dic11—41no—
226C2×Dic11—42no—
227C2×Dic11—41no—
228C2×Dic11—41no—
229D44—24no—
230D44—42no—
231C4×D11—84no—
232C11⋊C8—44no—
233C2×H(5,𝔽2)C2×D1112yes—
234C2×AGL(1,ℤ/8)—114no—
235#547—22no—
236#546—24no—
237D42—22no—
238#537C2×D1112yes—
239#534—22no—
240#532C2×D1112yes—
241C2×#127—111no—
242C2×#121—22no—
243C2×C4×D4—111no—
244C2×C4×D4C2×D1111yescharacteristic
245#463—224no—
246#461—222no—
247#459—222no—
248#453—228no—
249#423—112no—
250C2×#104—114no—
251C2×#104—114no—
252#417—114no—
253C2×#100—112no—
254#390—111no—
255#390—111no—
256#386—222no—
257#386—222no—
258#382—111no—
259#376—111no—
260#343—112no—
261C22×C11—21no—
262C22×C11—21no—
263C22×C11—24no—
264C22×C11—44no—
265C22×C11—42no—
266C22×C11—42no—
267C22×C11—44no—
268C22×C11—44no—
269C22×C11—44no—
270C22×C11—82no—
271C22×C11—168no—
272C22×C11C2×#12011yescharacteristic
273C22×C11C2×#12111yescharacteristic
274C22×C11#53511yescharacteristic
275C2×D11—44no—
276C2×D11—42no—
277C2×D11—82no—
278C2×D11—81no—
279C2×D11—81no—
280C4×C11—21no—
281C4×C11—21no—
282C4×C11—22no—
283C4×C11—44no—
284C4×C11—42no—
285C4×C11D4212yes—
286C4×C11#54612yes—
287Dic11—42no—
288Dic11—81no—
289Dic11—81no—
290H(5,𝔽2)—24no—
291H(5,𝔽2)—24no—
292H(5,𝔽2)—44no—
293C2×#41—24no—
294C2×#41C22×D1114yes—
295C22×D4—24no—
296C22×D4—22no—
297C22×D4—24no—
298C22×D4—111no—
299C22×D4—222no—
300C22×D4C22×D1111yescharacteristic
301C23×C4—221no—
302C23×C4C22⋊D1112yes—
303AGL(1,ℤ/8)—228no—
304AGL(1,ℤ/8)—444no—
305C2×SD16—224no—
306C2×D8—224no—
307C2×M16—114no—
308C4⋊Q8C22⋊D1112yescomplemented
309#127—114no—
310#127—222no—
311#127C22⋊D1112yescomplemented
312#124C22⋊D1114yescomplemented
313#123—28no—
314C22⋊Q8—24no—
315#121—24no—
316#121—24no—
317#121—24no—
318#121—22no—
319#121—24no—
320#121—22no—
321#120—28no—
322C4×D4—22no—
323C4×D4—22no—
324C4×D4—22no—
325C4×D4—22no—
326C4×D4—222no—
327C4×D4—222no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—111no—
330C2×C4⋊C4C22×D1111yescharacteristic
331C2×C22⋊C4—24no—
332C2×C22⋊C4—221no—
333C2×C22⋊C4—222no—
334C2×C22⋊C4—222no—
335C2×C22⋊C4C22⋊D1112yes—
336C2×C42—111no—
337C2×C42—111no—
338C2×C42C22×D1111yescharacteristic
339C4⋊C8—222no—
340C4⋊C8—222no—
341#104—228no—
342#104—444no—
343#103—224no—
344#102—224no—
345#100—224no—
346#95—221no—
347#95—221no—
348#95—222no—
349C2×C11—21no—
350C2×C11—21no—
351C2×C11—44no—
352C2×C11—84no—
353C2×C11#240811yescharacteristic
354C2×C11#301911yescharacteristic
355C2×C11#302111yescharacteristic
356D11—82no—
357C24—24no—
358C24—221no—
359C24C2×C22⋊D1112yes—
360#41—24no—
361#41—24no—
362#41—24no—
363#41—24no—
364#41—48no—
365#41—48no—
366C2×Q8C2×C22⋊D1114yes—
367C2×D4—28no—
368C2×D4—24no—
369C2×D4—24no—
370C2×D4—22no—
371C2×D4—22no—
372C2×D4—22no—
373C2×D4—22no—
374C2×D4—48no—
375C2×D4—48no—
376C2×D4—48no—
377C2×D4—48no—
378C2×D4—84no—
379C2×D4—112no—
380C2×D4—228no—
381C2×D4—221no—
382C2×D4—222no—
383C2×D4—222no—
384C2×D4—882no—
385C2×D4—882no—
386C2×D4D4×D1112yes—
387C2×D4#434112yes—
388C2×D4C2×C22⋊D1114yes—
389C22×C4—24no—
390C22×C4—22no—
391C22×C4—24no—
392C22×C4—22no—
393C22×C4—82no—
394C22×C4—221no—
395C22×C4—221no—
396C22×C4—221no—
397C22×C4—442no—
398C22×C4—882no—
399C22×C4C2×C22⋊D1112yes—
400C22×C4C2×C22⋊D1111yescharacteristic
401C22×C4C2×C22⋊D1111yescharacteristic
402C22×C4C23×D1111yescharacteristic
403SD16—448no—
404D8—448no—
405M16—224no—
406M16—224no—
407C2×C8—224no—
408C4⋊C4—24no—
409C4⋊C4—22no—
410C4⋊C4—22no—
411C4⋊C4—22no—
412C4⋊C4—222no—
413C22⋊C4—28no—
414C22⋊C4—24no—
415C22⋊C4—24no—
416C22⋊C4—24no—
417C22⋊C4—441no—
418C22⋊C4—441no—
419C22⋊C4—882no—
420C22⋊C4—882no—
421C42—112no—
422C42—221no—
423C42—222no—
424C42C2×C22⋊D1112yes—
425C42C2×C22⋊D1112yes—
426C11#2422611yescharacteristic, complemented, Sylow
427C23—22no—
428C23—22no—
429C23—24no—
430C23—42no—
431C23—42no—
432C23—48no—
433C23—84no—
434C23—84no—
435C23—222no—
436C23—442no—
437C23—442no—
438C23—441no—
439C23—441no—
440C23#6699114yes—
441C23C22×C22⋊D1111yescharacteristic
442Q8—24no—
443Q8—24no—
444D4—24no—
445D4—24no—
446D4—24no—
447D4—24no—
448D4—44no—
449D4—416no—
450D4—44no—
451D4—44no—
452D4—82no—
453D4—84no—
454D4—224no—
455D4—442no—
456D4—888no—
457C2×C4—22no—
458C2×C4—24no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—44no—
462C2×C4—48no—
463C2×C4—44no—
464C2×C4—44no—
465C2×C4—42no—
466C2×C4—82no—
467C2×C4—222no—
468C2×C4—441no—
469C2×C4—441no—
470C2×C4—441no—
471C2×C4—441no—
472C2×C4—442no—
473C2×C4—441no—
474C2×C4—441no—
475C2×C4—884no—
476C2×C4#6700611yescharacteristic
477C2×C4#6700612yes—
478C2×C4#6700611yescharacteristic
479C2×C4C2×D4×D1111yescharacteristic
480C2×C4C2×#434111yescharacteristic
481C2×C4#6703712yes—
482C2×C4C22×C22⋊D1112yes—
483C8—444no—
484C22—21no—
485C22—21no—
486C22—24no—
487C22—44no—
488C22—42no—
489C22—42no—
490C22—44no—
491C22—44no—
492C22—44no—
493C22—82no—
494C22—168no—
495C22—444no—
496C22—442no—
497C22—882no—
498C22—881no—
499C22—881no—
500C22C2×#6699111yescharacteristic
501C22#1062333611yescharacteristic
502C22C2×#6700611yescharacteristic
503C4—21no—
504C4—21no—
505C4—22no—
506C4—44no—
507C4—42no—
508C4—442no—
509C4—881no—
510C4—881no—
511C4D4×C22⋊D1112yes—
512C4#1062333712yes—
513C2—21no—
514C2—21no—
515C2—44no—
516C2—84no—
517C2—882no—
518C2#1307196611yescharacteristic
519C2#1307797311yescharacteristic
520C2#1307798811yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#3496C2
socleC22×C11C2×#120
hypercenter#3496D11
hypocenterC11#24226
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3496

Complements

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

NH ≅ G/Ntype
1. #13078076C2semidirect
2. C2×#10622854C2semidirect
3. #13071338C2semidirect
4. #13069842C2semidirect
5. #13069658C2semidirect
6. #13069449C2semidirect
7. #13068608C2semidirect
8. #13068570C2semidirect
9. C11×#3496C2semidirect
19. C2×#67002C22semidirect
21. C2×C4×D44C22semidirect
23. C2×#66901C22semidirect
24. C2×#66901C22semidirect
25. #10622845C22semidirect
32. #10622601C22semidirect
33. #10622590C22semidirect
35. #10622545C22semidirect
36. #10622537C22semidirect
37. #10622168C22semidirect
51. C11×C4⋊Q8D4semidirect
52. C11×#127D4semidirect
53. C11×#124D4semidirect
77. #66993D4semidirect
141. C2×D44C2×D4semidirect
163. C4×Dic11C2×D4semidirect
167. #3496D11semidirect
308. C4⋊Q8C22⋊D11semidirect
311. #127C22⋊D11semidirect
312. #124C22⋊D11semidirect
426. C11#24226semidirect

Maximal subgroups

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

subgroupindex
#130780762
C2×#106228542
#130713382
#130698422
#130696582
#130694492
#130686082
#130685702
C11×#34962
#2422611