Finite Group Databasebeta

← #14763149

Subgroups — #14763149

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×#10623056C211yesmaximal, characteristic
2#13071225C211yesmaximal, characteristic, complemented
3#13069546C212yesmaximal, complemented
4#13069542C212yesmaximal, complemented
5#13069440C211yesmaximal, characteristic, complemented
6#13069432C211yesmaximal, characteristic, complemented
7#13069427C211yesmaximal, characteristic, complemented
8#13069422C211yesmaximal, characteristic, complemented
9#13068557C212yesmaximal, complemented
10#13068548C212yesmaximal, complemented
11C2×C11×#433C211yesmaximal, characteristic, complemented
12C22×#4339C2211yescharacteristic
13C23×D44C2211yescharacteristic
14C2×C11×#117C2211yescharacteristic
15#10623056—24no—
16#10623056C418yescomplemented
17C2×#66948—22no—
18C2×#66935—22no—
19C2×#66928C2211yescharacteristic
20C2×#66928C2211yescharacteristic
21C2×#66927C2211yescharacteristic
22C2×#66927C2211yescharacteristic
23C11×#433—24no—
24C2×C11×C4⋊C8C2212yescomplemented
25C2×C11×C22⋊C8C2212yes—
26C2×C11×#97C2211yescharacteristic, complemented
27C2×C4×C8×C11C2211yescharacteristic, complemented
28#10622825C2212yes—
29C2×#66885C2212yes—
30C2×#66885C2212yes—
31C2×#66885C2212yes—
32C2×#66885C2212yes—
33C2×#66885C2212yescomplemented
34C2×#66885C2212yescomplemented
35C2×#66880C2212yescomplemented
36C2×#66880C2212yescomplemented
37#10622594—22no—
38#10622564—22no—
39#10622549C2211yescharacteristic, complemented
40#10622548C2211yescharacteristic, complemented
41C4×C4⋊Dic11C2212yescomplemented
42C24×D11—21no—
43C23×C4×C11C2311yescharacteristic
44C22×C22⋊D11—21no—
45C2×#4339—22no—
46C2×#4339—42no—
47C2×#4339—42no—
48C2×#4339C2×C414yes—
49C22×D44—21no—
50C22×D44—22no—
51C22×D44—22no—
52C22×D44—22no—
53C22×D44—42no—
54C22×D44—42no—
55C22×D44C2×C414yes—
56C22×D44C2311yescharacteristic
57C22×D44C2311yescharacteristic
58C22×D44C2311yescharacteristic
59C22×C4×D11—21no—
60C22×Dic22C2311yescharacteristic
61C22×C8×C11C2312yes—
62C22×C8×C11C2312yes—
63C11×#117C2×C414yes—
64C11×#117D414yes—
65C2×C11×C4⋊C4D412yes—
66C2×C11×C22⋊C4D412yes—
67C2×C42×C11C2311yescharacteristic
68C2×C42×C11C2311yescharacteristic
69C2×C22⋊Dic11—22no—
70C2×(C2×D11)⋊C4—22no—
71C2×(C2×D11)⋊C4—22no—
72C2×C4⋊Dic11—22no—
73C2×C4⋊Dic11C2312yes—
74C2×C4⋊Dic11C2312yes—
75C2×C4×Dic11—22no—
76#66948—216no—
77#66935—216no—
78#66928—22no—
79#66928—22no—
80#66928C2×C414yes—
81#66928C2×C414yes—
82#66927—22no—
83#66927—22no—
84#66927C2×C414yes—
85#66927C2×C414yes—
86C11×C4⋊C8—24no—
87C11×C22⋊C8—24no—
88C11×#97—22no—
89C4×C8×C11—22no—
90C11⋊#95—22no—
91C11⋊#95—22no—
92C11⋊#95—22no—
93#66885—42no—
94#66885—42no—
95#66885—42no—
96#66885—42no—
97#66885—42no—
98#66885—42no—
99#66880—42no—
100#66880—42no—
101#21813—111nomaximal, Sylow
102C24×C11C2×D411yescharacteristic
103C23×D11—21no—
104C23×D11—21no—
105C23×D11—21no—
106C23×D11—24no—
107C23×D11—42no—
108C23×D11—42no—
109C23×D11—82no—
110C23×D11—82no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11C22×C412yes—
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2×D412yes—
116C22×C4×C11C2×D412yes—
117C22×C4×C11C2×D412yes—
118C22×C4×C11C2411yescharacteristic
119C2×C22⋊D11—24no—
120C2×C22⋊D11—42no—
121C2×C22⋊D11—42no—
122C22×Dic11—21no—
123C22×Dic11—22no—
124C22×Dic11—22no—
125#4339—48no—
126#4339—48no—
127C2×D44—24no—
128C2×D44—28no—
129C2×D44—28no—
130C2×D44—21no—
131C2×D44—21no—
132C2×D44—21no—
133C2×D44—22no—
134C2×D44—22no—
135C2×D44—22no—
136C2×D44—22no—
137C2×D44—22no—
138C2×D44—22no—
139C2×D44—48no—
140C2×D44—42no—
141C2×D44—42no—
142C2×D44—48no—
143C2×D44—82no—
144C2×D44—82no—
145C2×D44—82no—
146C2×D44—82no—
147C2×D44C22×C412yes—
148C2×D44C22×C412yes—
149C2×D44C22×C412yes—
150C2×C4×D11—24no—
151C2×C4×D11—42no—
152C2×C4×D11—42no—
153C2×Dic22—21no—
154C2×Dic22—22no—
155C2×Dic22—22no—
156C2×Dic22C22×C412yes—
157C2×C8×C11—22no—
158C2×C8×C11—22no—
159C2×C8×C11—22no—
160C2×C8×C11—22no—
161C2×C8×C11—22no—
162C2×C8×C11—22no—
163C11×C4⋊C4C22⋊C418yes—
164C11×C22⋊C4C22⋊C418yes—
165C42×C11C22×C412yes—
166C42×C11C22×C412yes—
167C42×C11C2×D412yes—
168C42×C11C2×D412yes—
169C22⋊Dic11—82no—
170(C2×D11)⋊C4—28no—
171(C2×D11)⋊C4—28no—
172C4⋊Dic11—22no—
173C4⋊Dic11—22no—
174C4⋊Dic11—22no—
175C4⋊Dic11—22no—
176C4⋊Dic11—82no—
177C4×Dic11—82no—
178C2×#535—111no—
179C2×#433D1111yescharacteristic, complemented
180#2314—111no—
181#1983—112no—
182#1982—112no—
183#1961—111no—
184#1959—111no—
185#1958—111no—
186#1957—111no—
187#1788—112no—
188#1786—112no—
189C23×C11—21no—
190C23×C11—21no—
191C23×C11—22no—
192C23×C11—22no—
193C23×C11C2×C22⋊C412yes—
194C23×C11C22×D411yescharacteristic
195C22×D11—22no—
196C22×D11—22no—
197C22×D11—22no—
198C22×D11—48no—
199C22×D11—41no—
200C22×D11—41no—
201C22×D11—41no—
202C22×D11—41no—
203C22×D11—41no—
204C22×D11—41no—
205C22×D11—42no—
206C22×D11—42no—
207C22×D11—42no—
208C22×D11—42no—
209C22×D11—42no—
210C22×D11—42no—
211C22×D11—88no—
212C22×D11—84no—
213C22×D11—84no—
214C22×D11—88no—
215C2×C4×C11—21no—
216C2×C4×C11—21no—
217C2×C4×C11—22no—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—22no—
221C2×C4×C11—24no—
222C2×C4×C11—24no—
223C2×C4×C11C2×C22⋊C414yes—
224C2×C4×C11C2×C22⋊C414yes—
225C2×C4×C11C2×C22⋊C412yes—
226C2×C4×C11C23×C411yescharacteristic
227C2×C4×C11C22×D411yescharacteristic
228C2×C4×C11H(5,𝔽2)12yes—
229C2×C4×C11H(5,𝔽2)12yes—
230C22⋊D11—48no—
231C2×Dic11—22no—
232C2×Dic11—41no—
233C2×Dic11—41no—
234C2×Dic11—42no—
235C2×Dic11—42no—
236C2×Dic11—42no—
237C2×Dic11—42no—
238C2×Dic11—42no—
239C2×Dic11—42no—
240D44—24no—
241D44—24no—
242D44—24no—
243D44—48no—
244D44—42no—
245D44—42no—
246D44—42no—
247D44—88no—
248D44—88no—
249C4×D11—48no—
250Dic22—24no—
251Dic22—42no—
252C8×C11—42no—
253C8×C11—42no—
254C22×#41—111no—
255C23×D4—111no—
256#535—118no—
257#535—224no—
258C2×#127—111no—
259C2×#127—111no—
260C2×#124—111no—
261C2×#124—111no—
262C2×#121—222no—
263C2×#120—222no—
264C2×#117C2×D1111yescharacteristic
265#433—24no—
266C2×C4⋊C8C2×D1112yescomplemented
267C2×#103—112no—
268C2×#103—112no—
269C2×#102—112no—
270C2×#102—112no—
271C2×#102—112no—
272C2×#102—112no—
273C2×#102—112no—
274C2×#102—112no—
275C2×C22⋊C8C2×D1112yes—
276C2×#97C2×D1111yescharacteristic, complemented
277C2×C4×C8C2×D1111yescharacteristic, complemented
278#388—222no—
279#387—222no—
280#384—111no—
281#382—111no—
282#380—112no—
283C4×C4⋊C4—112no—
284C22×C11—22no—
285C22×C11—24no—
286C22×C11—41no—
287C22×C11—41no—
288C22×C11—42no—
289C22×C11C22×C22⋊C411yescharacteristic
290C22×C11#53511yescharacteristic
291C22×C11#53511yescharacteristic
292C22×C11#57612yes—
293C22×C11#57712yes—
294C2×D11—42no—
295C2×D11—42no—
296C2×D11—42no—
297C2×D11—44no—
298C2×D11—44no—
299C2×D11—44no—
300C2×D11—816no—
301C2×D11—81no—
302C2×D11—81no—
303C2×D11—81no—
304C2×D11—81no—
305C2×D11—81no—
306C2×D11—81no—
307C2×D11—82no—
308C2×D11—82no—
309C2×D11—82no—
310C4×C11—22no—
311C4×C11—24no—
312C4×C11—24no—
313C4×C11#51812yes—
314C4×C11#53512yes—
315Dic11—42no—
316Dic11—82no—
317Dic11—82no—
318C25—221no—
319C2×#41—114no—
320C2×#41—222no—
321C2×#41—442no—
322C2×#41—442no—
323C22×Q8—111no—
324C22×D4—114no—
325C22×D4—111no—
326C22×D4—111no—
327C22×D4—111no—
328C22×D4—221no—
329C22×D4—221no—
330C22×D4—222no—
331C22×D4—222no—
332C22×D4—222no—
333C22×D4—442no—
334C22×D4—442no—
335C23×C4—221no—
336C23×C4C22×D1111yescharacteristic
337C22×C8C22×D1112yes—
338C22×C8C22×D1112yes—
339#127—114no—
340#127—114no—
341#127—222no—
342#127—222no—
343#124—114no—
344#124—114no—
345#124—222no—
346#124—222no—
347#121—2216no—
348#120—2216no—
349#117C4×D1114yes—
350#117C22⋊D1114yes—
351C2×C4⋊C4—112no—
352C2×C4⋊C4—112no—
353C2×C4⋊C4—222no—
354C2×C4⋊C4D4412yes—
355C2×C22⋊C4—222no—
356C2×C22⋊C4—222no—
357C2×C22⋊C4—222no—
358C2×C22⋊C4D4412yes—
359C2×C42—222no—
360C2×C42C22×D1111yescharacteristic
361C2×C42C22×D1111yescharacteristic
362C4⋊C8—24no—
363#103—442no—
364#103—442no—
365#102—442no—
366#102—442no—
367#102—442no—
368#102—442no—
369#102—442no—
370#102—442no—
371C22⋊C8—24no—
372#97—22no—
373C4×C8—22no—
374#95—222no—
375#95—222no—
376#95—222no—
377C2×C11—42no—
378C2×C11#230911yescharacteristic
379C2×C11#289712yes—
380C2×C11#322011yescharacteristic
381C2×C11#322211yescharacteristic
382C2×C11#322412yes—
383D11—82no—
384D11—82no—
385D11—82no—
386C24—221no—
387C24—221no—
388C24—221no—
389C24—224no—
390C24—442no—
391C24—442no—
392C24—882no—
393C24—882no—
394C24C2×D4411yescharacteristic
395#41—448no—
396#41—448no—
397C2×Q8—112no—
398C2×Q8—221no—
399C2×Q8—222no—
400C2×Q8—222no—
401C2×D4—112no—
402C2×D4—112no—
403C2×D4—112no—
404C2×D4—224no—
405C2×D4—224no—
406C2×D4—228no—
407C2×D4—228no—
408C2×D4—222no—
409C2×D4—222no—
410C2×D4—222no—
411C2×D4—222no—
412C2×D4—222no—
413C2×D4—222no—
414C2×D4—221no—
415C2×D4—221no—
416C2×D4—221no—
417C2×D4—448no—
418C2×D4—442no—
419C2×D4—442no—
420C2×D4—448no—
421C2×D4—442no—
422C2×D4—442no—
423C2×D4—882no—
424C2×D4—882no—
425C2×D4—882no—
426C2×D4—882no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—221no—
430C22×C4—224no—
431C22×C4—222no—
432C22×C4—222no—
433C22×C4—442no—
434C22×C4—442no—
435C22×C4C2×C4×D1112yes—
436C22×C4C2×D4411yescharacteristic
437C22×C4C2×D4412yes—
438C22×C4C2×D4412yes—
439C22×C4C2×C22⋊D1112yes—
440C22×C4C23×D1111yescharacteristic
441C2×C8—22no—
442C2×C8—22no—
443C2×C8—22no—
444C2×C8—22no—
445C2×C8—22no—
446C2×C8—22no—
447C4⋊C4—222no—
448C4⋊C4—222no—
449C4⋊C4—222no—
450C4⋊C4—222no—
451C4⋊C4—882no—
452C4⋊C4(C2×D11)⋊C418yes—
453C22⋊C4—228no—
454C22⋊C4—228no—
455C22⋊C4—882no—
456C22⋊C4(C2×D11)⋊C418yes—
457C42—882no—
458C42C2×C4×D1112yes—
459C42C2×C4×D1112yes—
460C42C2×C22⋊D1112yes—
461C42C2×C22⋊D1112yes—
462C11#2181311yescharacteristic, complemented, Sylow
463C23—22no—
464C23—22no—
465C23—21no—
466C23—21no—
467C23—222no—
468C23—222no—
469C23—222no—
470C23—448no—
471C23—442no—
472C23—442no—
473C23—442no—
474C23—442no—
475C23—442no—
476C23—442no—
477C23—441no—
478C23—441no—
479C23—441no—
480C23—441no—
481C23—441no—
482C23—441no—
483C23—888no—
484C23—884no—
485C23—884no—
486C23—888no—
487C23C2×(C2×D11)⋊C412yes—
488C23C22×D4411yescharacteristic
489Q8—224no—
490Q8—442no—
491D4—224no—
492D4—224no—
493D4—224no—
494D4—448no—
495D4—448no—
496D4—442no—
497D4—442no—
498D4—442no—
499D4—888no—
500D4—888no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—24no—
508C2×C4—24no—
509C2×C4—222no—
510C2×C4—448no—
511C2×C4—441no—
512C2×C4—441no—
513C2×C4—442no—
514C2×C4—442no—
515C2×C4—442no—
516C2×C4—442no—
517C2×C4—442no—
518C2×C4—442no—
519C2×C4C2×(C2×D11)⋊C414yes—
520C2×C4C2×(C2×D11)⋊C414yes—
521C2×C4C2×(C2×D11)⋊C412yes—
522C2×C4C22×C4×D1111yescharacteristic
523C2×C4#6704212yes—
524C2×C4#6704212yes—
525C2×C4C22×C22⋊D1111yescharacteristic
526C8—42no—
527C8—42no—
528C22—22no—
529C22—24no—
530C22—41no—
531C22—41no—
532C22—42no—
533C22—442no—
534C22—442no—
535C22—442no—
536C22—444no—
537C22—444no—
538C22—444no—
539C22—8816no—
540C22—881no—
541C22—881no—
542C22—881no—
543C22—881no—
544C22—881no—
545C22—881no—
546C22—882no—
547C22—882no—
548C22—882no—
549C22#1062305611yescharacteristic
550C22#1062305611yescharacteristic
551C22#1062328212yes—
552C22#1062328312yes—
553C22C22×(C2×D11)⋊C411yescharacteristic
554C4—22no—
555C4—24no—
556C4—24no—
557C4—442no—
558C4—882no—
559C4—882no—
560C4#1062305212yes—
561C4#1062336112yes—
562C2—42no—
563C2—882no—
564C2—882no—
565C2—882no—
566C2#1307119611yescharacteristic
567C2#1307714312yes—
568C2#1307966811yescharacteristic
569C2#1307969011yescharacteristic
570C2#1307971212yes—
subgroupG/H
centerC23C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#433C2
socleC23×C11C22×D4
prime radicalC2×#10623056C2
cosocleC22×C4×C11C24
hypercenterC2×#433D11
hypocenterC11#21813
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
2. #13071225C2semidirect
3. #13069546C2semidirect
4. #13069542C2semidirect
5. #13069440C2semidirect
6. #13069432C2semidirect
7. #13069427C2semidirect
8. #13069422C2semidirect
9. #13068557C2semidirect
10. #13068548C2semidirect
11. C2×C11×#433C2semidirect
16. #10623056C4semidirect
24. C2×C11×C4⋊C8C22semidirect
26. C2×C11×#97C22semidirect
27. C2×C4×C8×C11C22semidirect
33. C2×#66885C22semidirect
34. C2×#66885C22semidirect
35. C2×#66880C22semidirect
36. C2×#66880C22semidirect
39. #10622549C22semidirect
40. #10622548C22semidirect
41. C4×C4⋊Dic11C22semidirect
179. C2×#433D11semidirect
266. C2×C4⋊C8C2×D11semidirect
276. C2×#97C2×D11semidirect
277. C2×C4×C8C2×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×#106230562
#130712252
#130695462
#130695422
#130694402
#130694322
#130694272
#130694222
#130685572
#130685482
C2×C11×#4332
#2181311