Finite Group Databasebeta

← #14788962

Subgroups — #14788962

Order 2816.

1586 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078076C212yesmaximal, complemented
2C2×#10622854C212yesmaximal, complemented
3C4×#66993C211yesmaximal, characteristic, complemented
4#13069837C212yesmaximal, complemented
5#13069658C212yesmaximal, complemented
6#13069445C212yesmaximal, 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×C22⋊D11—22no—
22C2×C4×D44C2211yescharacteristic, complemented
23#10622854—28no—
24C2×#66901C2214yescomplemented
25C2×#66901C2214yescomplemented
26#10622845C2214yescomplemented
27#10622834C2211yescharacteristic
28C2×#66897C2212yes—
29#10622696—22no—
30#10622685—22no—
31#10622670—24no—
32#10622601C2211yescharacteristic, complemented
33#10622589C2211yescharacteristic, complemented
34#10622570—22no—
35C42×Dic11C2211yescharacteristic, 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—
79C4×C22⋊D11—48no—
80C2×(C2×D11)⋊C4—21no—
81C2×(C2×D11)⋊C4—22no—
82C2×C4⋊Dic11C2311yescharacteristic
83C2×Dic11⋊C4—22no—
84C2×C4×Dic11—21no—
85C2×C4×Dic11—21no—
86C2×C4×Dic11C2311yescharacteristic
87C2×C4×Dic11C2311yescharacteristic
88C2×#4318C2314yes—
89C4×D44—22no—
90C4×D44—22no—
91#66901—28no—
92#66901—44no—
93#66899—24no—
94#66897—24no—
95#66896—24no—
96C4⋊(C11⋊C8)—22no—
97C4⋊(C11⋊C8)—22no—
98#24222—111nomaximal, Sylow
99C24×C11—24no—
100C24×C11C2×D412yes—
101C23×D11—21no—
102C11×#41—24no—
103C11×#41—24no—
104C11×#41—24no—
105C11×#41—24no—
106C11×#41—48no—
107C11×#41—48no—
108C2×Q8×C11C2×D414yes—
109C2×D4×C11—28no—
110C2×D4×C11—24no—
111C2×D4×C11—24no—
112C2×D4×C11—22no—
113C2×D4×C11—22no—
114C2×D4×C11—22no—
115C2×D4×C11—22no—
116C2×D4×C11—48no—
117C2×D4×C11—48no—
118C2×D4×C11—48no—
119C2×D4×C11—48no—
120C2×D4×C11—84no—
121C2×D4×C11C2×D414yes—
122C2×D4×C11C2×D412yes—
123C2×D4×C11#4112yes—
124C22×C4×C11—24no—
125C22×C4×C11—22no—
126C22×C4×C11—24no—
127C22×C4×C11—22no—
128C22×C4×C11—44no—
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D412yes—
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2411yescharacteristic
133C2×C22⋊D11—28no—
134C2×C22⋊D11—44no—
135C2×C22⋊D11—44no—
136C22×Dic11—21no—
137C22×Dic11—21no—
138C22×Dic11—21no—
139C2×D44—22no—
140C2×D44—21no—
141C2×D44—22no—
142C2×D44C2×D412yescomplemented
143C2×C4×D11—44no—
144C2×C4×D11—41no—
145C2×C4×D11—41no—
146C11×C4⋊C4—24no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—22no—
149C11×C4⋊C4—22no—
150C11×C22⋊C4—28no—
151C11×C22⋊C4—24no—
152C11×C22⋊C4—24no—
153C11×C22⋊C4—24no—
154C42×C11C2×D412yes—
155C42×C11C2×D412yes—
156C22⋊Dic11—44no—
157#4325—48no—
158#4323—48no—
159(C2×D11)⋊C4—44no—
160(C2×D11)⋊C4—42no—
161C4⋊Dic11—22no—
162Dic11⋊C4—44no—
163C4×Dic11—24no—
164C4×Dic11—21no—
165C4×Dic11—22no—
166C4×Dic11—42no—
167C4×Dic11C2×D412yescomplemented
168#4318—24no—
169#4318—24no—
170C2×C11⋊C8—24no—
171#3496D1111yescharacteristic, complemented
172#3036—112no—
173C2×#453—112no—
174C4×#127—111no—
175#2039—112no—
176#2006—112no—
177#1962—112no—
178#1800—111no—
179#1792—112no—
180C23×C11—22no—
181C23×C11—22no—
182C23×C11—24no—
183C23×C11—42no—
184C23×C11—42no—
185C23×C11—48no—
186C23×C11—84no—
187C23×C11—84no—
188C23×C11#12114yes—
189C23×C11C22×D411yescharacteristic
190C22×D11—22no—
191C22×D11—42no—
192C22×D11—42no—
193C22×D11—41no—
194C22×D11—41no—
195Q8×C11—24no—
196Q8×C11—24no—
197D4×C11—24no—
198D4×C11—24no—
199D4×C11—24no—
200D4×C11—24no—
201D4×C11—416no—
202D4×C11—44no—
203D4×C11—44no—
204D4×C11—44no—
205D4×C11—82no—
206D4×C11—84no—
207C2×C4×C11—22no—
208C2×C4×C11—22no—
209C2×C4×C11—24no—
210C2×C4×C11—41no—
211C2×C4×C11—48no—
212C2×C4×C11—44no—
213C2×C4×C11—44no—
214C2×C4×C11—44no—
215C2×C4×C11—42no—
216C2×C4×C11—82no—
217C2×C4×C11#12012yes—
218C2×C4×C11#12011yescharacteristic
219C2×C4×C11#12011yescharacteristic
220C2×C4×C11C22×D411yescharacteristic
221C2×C4×C11C22×D412yes—
222C2×C4×C11C2×#4111yescharacteristic
223C2×C4×C11H(5,𝔽2)12yes—
224C22⋊D11—416no—
225C2×Dic11—22no—
226C2×Dic11—22no—
227C2×Dic11—22no—
228C2×Dic11—22no—
229C2×Dic11—41no—
230C2×Dic11—41no—
231C2×Dic11—42no—
232C2×Dic11—41no—
233D44—24no—
234D44—42no—
235C4×D11—82no—
236C4×D11—82no—
237C11⋊C8—44no—
238C2×H(5,𝔽2)C2×D1112yes—
239C2×AGL(1,ℤ/8)—114no—
240#547—22no—
241#546—24no—
242D42—22no—
243#537C2×D1112yes—
244#534—22no—
245#532C2×D1112yes—
246C2×#127—111no—
247C2×#121—22no—
248C2×C4×D4—111no—
249C2×C4×D4—222no—
250C2×C4×D4C2×D1111yescharacteristic
251#463—224no—
252#461—222no—
253#459—222no—
254#453—228no—
255#423—112no—
256C2×#104—114no—
257C2×#104—114no—
258#417—114no—
259C2×#100—112no—
260#390—111no—
261#390—111no—
262#390—222no—
263#384—111no—
264C43—111no—
265#343—112no—
266C22×C11—21no—
267C22×C11—21no—
268C22×C11—24no—
269C22×C11—44no—
270C22×C11—42no—
271C22×C11—42no—
272C22×C11—44no—
273C22×C11—44no—
274C22×C11—44no—
275C22×C11—82no—
276C22×C11—168no—
277C22×C11C2×#12011yescharacteristic
278C22×C11C2×#12111yescharacteristic
279C22×C11#53511yescharacteristic
280C2×D11—44no—
281C2×D11—42no—
282C2×D11—82no—
283C2×D11—81no—
284C2×D11—81no—
285C4×C11—21no—
286C4×C11—22no—
287C4×C11—44no—
288C4×C11—42no—
289C4×C11#45312yescomplemented
290C4×C11D4212yes—
291C4×C11#54612yes—
292Dic11—24no—
293Dic11—42no—
294Dic11—81no—
295H(5,𝔽2)—24no—
296H(5,𝔽2)—24no—
297H(5,𝔽2)—44no—
298C2×#41—24no—
299C2×#41C22×D1114yes—
300C22×D4—24no—
301C22×D4—22no—
302C22×D4—24no—
303C22×D4—111no—
304C22×D4—222no—
305C22×D4C22×D1111yescharacteristic
306C23×C4—221no—
307C23×C4C22⋊D1112yes—
308AGL(1,ℤ/8)—228no—
309AGL(1,ℤ/8)—444no—
310C2×SD16—224no—
311C2×D8—224no—
312C2×M16—114no—
313C4⋊Q8C22⋊D1112yescomplemented
314#127—114no—
315#127—222no—
316#127C22⋊D1112yescomplemented
317#124C22⋊D1114yescomplemented
318#123—28no—
319C22⋊Q8—24no—
320#121—24no—
321#121—24no—
322#121—24no—
323#121—22no—
324#121—24no—
325#121—22no—
326#120—28no—
327C4×D4—22no—
328C4×D4—22no—
329C4×D4—22no—
330C4×D4—22no—
331C4×D4—222no—
332C4×D4—222no—
333C4×D4—448no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—111no—
336C2×C4⋊C4—222no—
337C2×C4⋊C4C22×D1111yescharacteristic
338C2×C22⋊C4—24no—
339C2×C22⋊C4—222no—
340C2×C22⋊C4—221no—
341C2×C22⋊C4—222no—
342C2×C22⋊C4C22⋊D1112yes—
343C2×C42—111no—
344C2×C42—111no—
345C2×C42—221no—
346C2×C42—221no—
347C2×C42C22×D1111yescharacteristic
348C4⋊C8—222no—
349C4⋊C8—222no—
350#104—228no—
351#104—444no—
352#103—224no—
353#102—224no—
354#100—224no—
355C2×C11—21no—
356C2×C11—21no—
357C2×C11—44no—
358C2×C11—84no—
359C2×C11#240811yescharacteristic
360C2×C11C2×#45311yescharacteristic
361C2×C11#301811yescharacteristic
362D11—82no—
363C24—24no—
364C24—221no—
365C24C2×C22⋊D1112yes—
366#41—24no—
367#41—24no—
368#41—24no—
369#41—24no—
370#41—48no—
371#41—48no—
372C2×Q8C2×C22⋊D1114yes—
373C2×D4—28no—
374C2×D4—24no—
375C2×D4—24no—
376C2×D4—22no—
377C2×D4—22no—
378C2×D4—22no—
379C2×D4—22no—
380C2×D4—48no—
381C2×D4—48no—
382C2×D4—48no—
383C2×D4—48no—
384C2×D4—84no—
385C2×D4—112no—
386C2×D4—228no—
387C2×D4—221no—
388C2×D4—222no—
389C2×D4—222no—
390C2×D4—444no—
391C2×D4—444no—
392C2×D4D4×D1112yes—
393C2×D4#434112yes—
394C2×D4C2×C22⋊D1114yes—
395C22×C4—24no—
396C22×C4—22no—
397C22×C4—24no—
398C22×C4—22no—
399C22×C4—44no—
400C22×C4—221no—
401C22×C4—221no—
402C22×C4—221no—
403C22×C4—444no—
404C22×C4—441no—
405C22×C4—441no—
406C22×C4C2×C22⋊D1111yescharacteristic
407C22×C4C2×C22⋊D1112yes—
408C22×C4C2×C22⋊D1111yescharacteristic
409C22×C4C23×D1111yescharacteristic
410SD16—448no—
411D8—448no—
412M16—224no—
413M16—224no—
414C2×C8—224no—
415C4⋊C4—24no—
416C4⋊C4—22no—
417C4⋊C4—22no—
418C4⋊C4—22no—
419C4⋊C4—222no—
420C4⋊C4—444no—
421C22⋊C4—28no—
422C22⋊C4—24no—
423C22⋊C4—24no—
424C22⋊C4—24no—
425C22⋊C4—444no—
426C22⋊C4—444no—
427C22⋊C4—442no—
428C42—112no—
429C42—224no—
430C42—221no—
431C42—222no—
432C42—442no—
433C42C2×C22⋊D1112yes—
434C42C2×C22⋊D1112yes—
435C11#2422211yescharacteristic, complemented, Sylow
436C23—22no—
437C23—22no—
438C23—24no—
439C23—42no—
440C23—42no—
441C23—48no—
442C23—84no—
443C23—84no—
444C23—222no—
445C23—442no—
446C23—442no—
447C23—441no—
448C23—441no—
449C23#6699114yes—
450C23C22×C22⋊D1111yescharacteristic
451Q8—24no—
452Q8—24no—
453D4—24no—
454D4—24no—
455D4—24no—
456D4—24no—
457D4—416no—
458D4—44no—
459D4—44no—
460D4—44no—
461D4—82no—
462D4—84no—
463D4—224no—
464D4—4416no—
465D4—442no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—24no—
469C2×C4—41no—
470C2×C4—48no—
471C2×C4—44no—
472C2×C4—44no—
473C2×C4—44no—
474C2×C4—42no—
475C2×C4—82no—
476C2×C4—222no—
477C2×C4—222no—
478C2×C4—222no—
479C2×C4—222no—
480C2×C4—441no—
481C2×C4—441no—
482C2×C4—442no—
483C2×C4—441no—
484C2×C4—882no—
485C2×C4—882no—
486C2×C4#6700612yes—
487C2×C4#6700611yescharacteristic
488C2×C4#6700611yescharacteristic
489C2×C4C2×D4×D1111yescharacteristic
490C2×C4C2×#434111yescharacteristic
491C2×C4#6703712yes—
492C2×C4C22×C22⋊D1112yes—
493C8—444no—
494C22—21no—
495C22—21no—
496C22—24no—
497C22—44no—
498C22—42no—
499C22—42no—
500C22—44no—
501C22—44no—
502C22—44no—
503C22—82no—
504C22—168no—
505C22—444no—
506C22—442no—
507C22—882no—
508C22—881no—
509C22—881no—
510C22C2×#6699111yescharacteristic
511C22#1062333611yescharacteristic
512C22C2×#6700611yescharacteristic
513C4—21no—
514C4—22no—
515C4—44no—
516C4—42no—
517C4—224no—
518C4—442no—
519C4—881no—
520C4#1062285412yescomplemented
521C4D4×C22⋊D1112yes—
522C4#1062333712yes—
523C2—21no—
524C2—21no—
525C2—44no—
526C2—84no—
527C2—882no—
528C2#1307196611yescharacteristic
529C2C2×#1062285411yescharacteristic
530C2#1307796511yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#3496C2
socleC22×C11C2×#120
hypercenter#3496D11
hypocenterC11#24222
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. C4×#66993C2semidirect
4. #13069837C2semidirect
5. #13069658C2semidirect
6. #13069445C2semidirect
7. #13068608C2semidirect
8. #13068570C2semidirect
9. C11×#3496C2semidirect
19. C2×#67002C22semidirect
22. C2×C4×D44C22semidirect
24. C2×#66901C22semidirect
25. C2×#66901C22semidirect
26. #10622845C22semidirect
32. #10622601C22semidirect
33. #10622589C22semidirect
35. C42×Dic11C22semidirect
36. #10622537C22semidirect
37. #10622168C22semidirect
51. C11×C4⋊Q8D4semidirect
52. C11×#127D4semidirect
53. C11×#124D4semidirect
77. #66993D4semidirect
142. C2×D44C2×D4semidirect
167. C4×Dic11C2×D4semidirect
171. #3496D11semidirect
289. C4×C11#453semidirect
313. C4⋊Q8C22⋊D11semidirect
316. #127C22⋊D11semidirect
317. #124C22⋊D11semidirect
435. C11#24222semidirect
520. C4#10622854semidirect

Maximal subgroups

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

subgroupindex
#130780762
C2×#106228542
C4×#669932
#130698372
#130696582
#130694452
#130686082
#130685702
C11×#34962
#2422211