Finite Group Databasebeta

← #14763142

Subgroups — #14763142

Order 2816.

1442 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623205C211yesmaximal, characteristic
2C2×#10622322C211yesmaximal, characteristic, complemented
3#13071224C211yesmaximal, characteristic, complemented
4#13069545C212yesmaximal, complemented
5#13069541C212yesmaximal, complemented
6#13069440C211yesmaximal, characteristic, complemented
7#13069428C211yesmaximal, characteristic, complemented
8#13069421C211yesmaximal, characteristic, complemented
9#13068555C212yesmaximal, complemented
10#13068545C212yesmaximal, complemented
11C11×#1959C211yesmaximal, characteristic, complemented
12C22×#4343C2211yescharacteristic
13C22×D4×D11C2211yescharacteristic
14C2×C11×#124C2211yescharacteristic
15C2×#67000C2211yescharacteristic
16C2×#66993C2211yescharacteristic
17#10623205—24no—
18#10623205C418yescomplemented
19C2×#66937—22no—
20C2×#66935—22no—
21C2×#66927C2211yescharacteristic
22C2×#66925C2211yescharacteristic
23C2×C11×#103C2212yescomplemented
24C2×C11×#102C2212yes—
25C2×C11×#97C2211yescharacteristic, complemented
26C11×#384C2211yescharacteristic, complemented
27C2×#66899C2212yescomplemented
28C2×#66896C2212yes—
29C2×#66885C2212yes—
30C2×#66885C2212yescomplemented
31C2×(C2×D11)⋊C8C2212yes—
32C2×Dic11⋊C8C2212yescomplemented
33#10622603—22no—
34#10622600C2212yes—
35#10622591—22no—
36C4⋊C4×Dic11C2212yescomplemented
37C2×#66873C2212yes—
38C2×#66873C2212yescomplemented
39#10622549C2211yescharacteristic, complemented
40C2×C4×C11⋊C8C2211yescharacteristic, complemented
41#10622322—24no—
42C24×D11—21no—
43C22×Q8×C11C2311yescharacteristic
44C22×D4×C11C2311yescharacteristic
45C22×C22⋊D11—21no—
46C22×C22⋊D11—22no—
47C2×#4343—22no—
48C2×#4343—42no—
49C2×#4343—42no—
50C2×#4343C2×C414yes—
51C2×D4×D11—22no—
52C2×D4×D11—42no—
53C2×D4×D11—42no—
54C2×D4×D11C2×C414yes—
55C22×D44—21no—
56C22×D44—22no—
57C22×D44C2311yescharacteristic
58C22×D44C2311yescharacteristic
59C22×C4×D11—21no—
60C22×C4×D11C2311yescharacteristic
61C22×C8×C11C2312yes—
62C11×#124—22no—
63C11×#124C2×C414yes—
64C2×C11×C4⋊C4—22no—
65C2×C11×C4⋊C4C2312yes—
66C2×C11×C22⋊C4—22no—
67C2×C42×C11C2311yescharacteristic
68#67000—22no—
69#67000C2×C414yes—
70#66993—22no—
71#66993C2×C414yes—
72C2×(C2×D11)⋊C4—22no—
73C2×(C2×D11)⋊C4—22no—
74C2×(C2×D11)⋊C4D412yes—
75C2×C4⋊Dic11C2312yes—
76C2×Dic11⋊C4D412yes—
77C2×C4×Dic11—22no—
78C2×C4×Dic11C2311yescharacteristic
79C22×C11⋊C8C2312yes—
80#66937—216no—
81#66935—216no—
82#66927—22no—
83#66927C2×C414yes—
84#66925C2×C414yes—
85#66925D414yes—
86C11×#103—42no—
87C11×#102—42no—
88C11×#97—22no—
89#66899—42no—
90#66896—42no—
91C11⋊#95—22no—
92C11⋊#95—22no—
93C11⋊#95—22no—
94#66885—42no—
95#66885—42no—
96(C2×D11)⋊C8—24no—
97Dic11⋊C8—24no—
98#66873—42no—
99#66873—42no—
100C4×C11⋊C8—22no—
101#21813—111nomaximal, Sylow
102C24×C11—21no—
103C23×D11—21no—
104C23×D11—21no—
105C23×D11—24no—
106C23×D11—42no—
107C23×D11—42no—
108C23×D11—82no—
109C23×D11—82no—
110C23×D11C2×D411yescharacteristic
111C2×Q8×C11—21no—
112C2×Q8×C11—22no—
113C2×Q8×C11—22no—
114C2×Q8×C11C22×C412yes—
115C2×D4×C11—21no—
116C2×D4×C11—22no—
117C2×D4×C11—22no—
118C2×D4×C11C22×C412yes—
119C22×C4×C11—21no—
120C22×C4×C11—22no—
121C22×C4×C11C2×D412yes—
122C22×C4×C11C2411yescharacteristic
123C2×C22⋊D11—24no—
124C2×C22⋊D11—28no—
125C2×C22⋊D11—42no—
126C2×C22⋊D11—42no—
127C2×C22⋊D11—82no—
128C2×C22⋊D11—82no—
129C22×Dic11—22no—
130C22×Dic11C2×D411yescharacteristic
131C22×Dic11C2×D412yes—
132#4343—48no—
133#4343—48no—
134D4×D11—48no—
135D4×D11—48no—
136C2×D44—24no—
137C2×D44—28no—
138C2×D44—21no—
139C2×D44—21no—
140C2×D44—22no—
141C2×D44—22no—
142C2×D44—22no—
143C2×D44—22no—
144C2×D44—42no—
145C2×D44—42no—
146C2×D44—82no—
147C2×D44—82no—
148C2×D44C22×C412yes—
149C2×D44C22×C412yes—
150C2×C4×D11—24no—
151C2×C4×D11—22no—
152C2×C4×D11—22no—
153C2×C4×D11—42no—
154C2×C4×D11—42no—
155C2×C4×D11C22×C412yes—
156C2×C4×D11C2×D412yes—
157C2×C8×C11—22no—
158C2×C8×C11—22no—
159C2×C8×C11—22no—
160C11×C4⋊C4—22no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—82no—
163C11×C22⋊C4—28no—
164C42×C11C22×C412yes—
165C42×C11C2×D412yes—
166(C2×D11)⋊C4—28no—
167(C2×D11)⋊C4—82no—
168(C2×D11)⋊C4C22⋊C418yes—
169C4⋊Dic11—22no—
170C4⋊Dic11—22no—
171Dic11⋊C4C22⋊C418yes—
172C4×Dic11—82no—
173C4×Dic11C22×C412yes—
174C4×Dic11C2×D412yes—
175C2×C11⋊C8—22no—
176C2×C11⋊C8—22no—
177C2×C11⋊C8—22no—
178C2×#535—111no—
179C2×#433—111no—
180#2314—111no—
181#1983—112no—
182#1982—112no—
183#1961—111no—
184#1959D1111yescharacteristic, complemented
185#1958—111no—
186#1957—111no—
187#1788—112no—
188#1786—112no—
189C23×C11—22no—
190C23×C11—41no—
191C23×C11—41no—
192C23×C11—42no—
193C23×C11—42no—
194C23×C11C22×D411yescharacteristic
195C22×D11—21no—
196C22×D11—21no—
197C22×D11—22no—
198C22×D11—22no—
199C22×D11—22no—
200C22×D11—22no—
201C22×D11—48no—
202C22×D11—41no—
203C22×D11—41no—
204C22×D11—41no—
205C22×D11—41no—
206C22×D11—42no—
207C22×D11—42no—
208C22×D11—42no—
209C22×D11—42no—
210C22×D11—88no—
211C22×D11—84no—
212C22×D11—84no—
213C22×D11—88no—
214C22×D11C2×C22⋊C412yes—
215Q8×C11—24no—
216Q8×C11—42no—
217D4×C11—24no—
218D4×C11—42no—
219C2×C4×C11—22no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—41no—
223C2×C4×C11—41no—
224C2×C4×C11—42no—
225C2×C4×C11—42no—
226C2×C4×C11—42no—
227C2×C4×C11C2×C22⋊C414yes—
228C2×C4×C11C23×C411yescharacteristic
229C2×C4×C11C22×D411yescharacteristic
230C2×C4×C11H(5,𝔽2)12yes—
231C2×C4×C11H(5,𝔽2)12yes—
232C22⋊D11—48no—
233C22⋊D11—88no—
234C2×Dic11—21no—
235C2×Dic11—21no—
236C2×Dic11—22no—
237C2×Dic11—22no—
238C2×Dic11—42no—
239C2×Dic11—42no—
240C2×Dic11—42no—
241C2×Dic11C2×C22⋊C414yes—
242C2×Dic11C2×C22⋊C412yes—
243D44—24no—
244D44—24no—
245D44—48no—
246D44—42no—
247D44—42no—
248D44—88no—
249C4×D11—24no—
250C4×D11—24no—
251C4×D11—48no—
252C8×C11—42no—
253C11⋊C8—42no—
254C22×#41—111no—
255C23×D4—111no—
256#535—118no—
257#535—224no—
258C2×#127—111no—
259C2×#127—111no—
260C2×#124—111no—
261C2×#124C2×D1111yescharacteristic
262C2×#121—222no—
263C2×#120—222no—
264C2×#117—111no—
265#433—224no—
266C2×C4⋊C8—112no—
267C2×#103—112no—
268C2×#103C2×D1112yescomplemented
269C2×#102—112no—
270C2×#102—112no—
271C2×#102—112no—
272C2×#102—112no—
273C2×#102—112no—
274C2×#102C2×D1112yes—
275C2×C22⋊C8—112no—
276C2×#97C2×D1111yescharacteristic, complemented
277C2×C4×C8—111no—
278#388—222no—
279#387—222no—
280#384C2×D1111yescharacteristic, complemented
281#382—111no—
282#380—112no—
283C4×C4⋊C4—112no—
284C22×C11—42no—
285C22×C11—44no—
286C22×C11—81no—
287C22×C11—81no—
288C22×C11—82no—
289C22×C11C22×C22⋊C411yescharacteristic
290C22×C11#53511yescharacteristic
291C22×C11#53511yescharacteristic
292C22×C11#57612yes—
293C22×C11#57712yes—
294C2×D11—22no—
295C2×D11—24no—
296C2×D11—41no—
297C2×D11—41no—
298C2×D11—42no—
299C2×D11—42no—
300C2×D11—42no—
301C2×D11—44no—
302C2×D11—44no—
303C2×D11—816no—
304C2×D11—81no—
305C2×D11—81no—
306C2×D11—81no—
307C2×D11—81no—
308C2×D11—82no—
309C2×D11—82no—
310C4×C11—24no—
311C4×C11—42no—
312C4×C11—82no—
313C4×C11#51812yes—
314C4×C11#53512yes—
315Dic11—22no—
316Dic11—24no—
317Dic11—82no—
318C25—221no—
319C2×#41—114no—
320C2×#41—222no—
321C2×#41—442no—
322C2×#41—442no—
323C22×Q8C22×D1111yescharacteristic
324C22×D4—114no—
325C22×D4—111no—
326C22×D4—111no—
327C22×D4—221no—
328C22×D4—222no—
329C22×D4—221no—
330C22×D4—222no—
331C22×D4—222no—
332C22×D4—442no—
333C22×D4—442no—
334C22×D4C22×D1111yescharacteristic
335C23×C4—111no—
336C23×C4—221no—
337C22×C8—112no—
338C22×C8C22×D1112yes—
339#127—114no—
340#127—114no—
341#127—222no—
342#127—222no—
343#124—22no—
344#124—114no—
345#124—222no—
346#124C4×D1114yes—
347#121—2216no—
348#120—2216no—
349#117—114no—
350#117—114no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—112no—
353C2×C4⋊C4—112no—
354C2×C4⋊C4C22×D1112yes—
355C2×C22⋊C4—22no—
356C2×C22⋊C4—112no—
357C2×C22⋊C4—222no—
358C2×C22⋊C4—222no—
359C2×C42—111no—
360C2×C42—222no—
361C2×C42C22×D1111yescharacteristic
362C4⋊C8—224no—
363#103—42no—
364#103—442no—
365#102—42no—
366#102—442no—
367#102—442no—
368#102—442no—
369#102—442no—
370#102—442no—
371C22⋊C8—224no—
372#97—22no—
373C4×C8—222no—
374#95—222no—
375#95—222no—
376#95—222no—
377C2×C11—82no—
378C2×C11#230911yescharacteristic
379C2×C11#289712yes—
380C2×C11#322011yescharacteristic
381C2×C11#322211yescharacteristic
382C2×C11#322412yes—
383D11—42no—
384D11—82no—
385D11—82no—
386C24—21no—
387C24—111no—
388C24—224no—
389C24—221no—
390C24—221no—
391C24—442no—
392C24—442no—
393C24—882no—
394C24—882no—
395#41—448no—
396#41—448no—
397C2×Q8—21no—
398C2×Q8—22no—
399C2×Q8—22no—
400C2×Q8C2×C4×D1112yes—
401C2×D4—21no—
402C2×D4—22no—
403C2×D4—22no—
404C2×D4—112no—
405C2×D4—112no—
406C2×D4—224no—
407C2×D4—224no—
408C2×D4—228no—
409C2×D4—228no—
410C2×D4—221no—
411C2×D4—221no—
412C2×D4—222no—
413C2×D4—222no—
414C2×D4—222no—
415C2×D4—222no—
416C2×D4—442no—
417C2×D4—442no—
418C2×D4—448no—
419C2×D4—448no—
420C2×D4—442no—
421C2×D4—442no—
422C2×D4—882no—
423C2×D4—882no—
424C2×D4—882no—
425C2×D4—882no—
426C2×D4C2×C4×D1112yes—
427C22×C4—21no—
428C22×C4—22no—
429C22×C4—111no—
430C22×C4—112no—
431C22×C4—112no—
432C22×C4—112no—
433C22×C4—224no—
434C22×C4—222no—
435C22×C4—222no—
436C22×C4—222no—
437C22×C4—442no—
438C22×C4—442no—
439C22×C4D4×D1112yes—
440C22×C4C23×D1111yescharacteristic
441C2×C8—22no—
442C2×C8—22no—
443C2×C8—22no—
444C2×C8—222no—
445C2×C8—222no—
446C2×C8—222no—
447C4⋊C4—22no—
448C4⋊C4—22no—
449C4⋊C4—82no—
450C4⋊C4—118no—
451C4⋊C4—222no—
452C4⋊C4—222no—
453C22⋊C4—28no—
454C22⋊C4—118no—
455C22⋊C4—228no—
456C22⋊C4—882no—
457C42—112no—
458C42—112no—
459C42—882no—
460C42C2×C4×D1112yes—
461C42D4×D1112yes—
462C11#2181311yescharacteristic, complemented, Sylow
463C23—22no—
464C23—41no—
465C23—42no—
466C23—42no—
467C23—41no—
468C23—112no—
469C23—221no—
470C23—222no—
471C23—222no—
472C23—221no—
473C23—222no—
474C23—222no—
475C23—448no—
476C23—441no—
477C23—441no—
478C23—442no—
479C23—442no—
480C23—442no—
481C23—442no—
482C23—441no—
483C23—441no—
484C23—888no—
485C23—884no—
486C23—884no—
487C23—888no—
488C23C2×D4×D1111yescharacteristic
489Q8—24no—
490Q8—42no—
491D4—24no—
492D4—42no—
493D4—224no—
494D4—224no—
495D4—448no—
496D4—448no—
497D4—442no—
498D4—442no—
499D4—888no—
500D4—888no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—114no—
510C2×C4—112no—
511C2×C4—221no—
512C2×C4—222no—
513C2×C4—222no—
514C2×C4—221no—
515C2×C4—224no—
516C2×C4—224no—
517C2×C4—448no—
518C2×C4—442no—
519C2×C4—442no—
520C2×C4—442no—
521C2×C4C22⋊C4×D1114yes—
522C2×C4C22×C4×D1111yescharacteristic
523C2×C4C2×D4×D1111yescharacteristic
524C2×C4#6703712yes—
525C2×C4#6704212yes—
526C8—42no—
527C8—442no—
528C22—42no—
529C22—44no—
530C22—81no—
531C22—81no—
532C22—82no—
533C22—222no—
534C22—224no—
535C22—441no—
536C22—441no—
537C22—442no—
538C22—442no—
539C22—442no—
540C22—444no—
541C22—444no—
542C22—8816no—
543C22—881no—
544C22—881no—
545C22—881no—
546C22—881no—
547C22—882no—
548C22—882no—
549C22C2×C22⋊C4×D1111yescharacteristic
550C22#1062320511yescharacteristic
551C22#1062324611yescharacteristic
552C22#1062330512yes—
553C22#1062330912yes—
554C4—24no—
555C4—42no—
556C4—82no—
557C4—222no—
558C4—224no—
559C4—882no—
560C4#1062307612yes—
561C4#1062313812yes—
562C2—82no—
563C2—442no—
564C2—882no—
565C2—882no—
566C2#1307119511yescharacteristic
567C2#1307714012yes—
568C2#1307966111yescharacteristic
569C2#1307968311yescharacteristic
570C2#1307971112yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1959C2
socleC23×C11C22×D4
prime radicalC2×#10623205C2
cosocleC22×C4×C11C24
hypercenter#1959D11
hypocenterC11#21813
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1959

Complements

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

NH ≅ G/Ntype
2. C2×#10622322C2semidirect
3. #13071224C2semidirect
4. #13069545C2semidirect
5. #13069541C2semidirect
6. #13069440C2semidirect
7. #13069428C2semidirect
8. #13069421C2semidirect
9. #13068555C2semidirect
10. #13068545C2semidirect
11. C11×#1959C2semidirect
18. #10623205C4semidirect
23. C2×C11×#103C22semidirect
25. C2×C11×#97C22semidirect
26. C11×#384C22semidirect
27. C2×#66899C22semidirect
30. C2×#66885C22semidirect
32. C2×Dic11⋊C8C22semidirect
36. C4⋊C4×Dic11C22semidirect
38. C2×#66873C22semidirect
39. #10622549C22semidirect
40. C2×C4×C11⋊C8C22semidirect
184. #1959D11semidirect
268. C2×#103C2×D11semidirect
276. C2×#97C2×D11semidirect
280. #384C2×D11semidirect
462. C11#21813semidirect

Maximal subgroups

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

subgroupindex
C2×#106232052
C2×#106223222
#130712242
#130695452
#130695412
#130694402
#130694282
#130694212
#130685552
#130685452
C11×#19592
#2181311