Finite Group Databasebeta

← #14781726

Subgroups — #14781726

Order 2816.

1682 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D8×D11C211yesmaximal, characteristic
2C2×#10622452C211yesmaximal, characteristic, complemented
3C2×#10622383C212yesmaximal, complemented
4#13071195C212yesmaximal, complemented
5#13069928C211yesmaximal, characteristic, complemented
6#13069927C211yesmaximal, characteristic, complemented
7#13069926C212yesmaximal, complemented
8#13069925C212yesmaximal, complemented
9#13069924C211yesmaximal, characteristic, complemented
10#13068331C211yesmaximal, characteristic, complemented
11C11×#2054C211yesmaximal, characteristic, complemented
12C22×D4×D11C2212yes—
13C22×C11×D8C2211yescharacteristic
14C22×#4323C2212yes—
15C2×D8×D11—28no—
16C2×D8×D11—24no—
17C22×D88C2211yescharacteristic
18C22×#4313C2211yescharacteristic
19C22×C8×D11C2211yescharacteristic
20C2×#66945C2212yes—
21C2×#66925C2211yescharacteristic
22C2×C11×C4⋊C8C2211yescharacteristic, complemented
23C2×C11×#102C2212yescomplemented
24C11×#390C2212yescomplemented
25#10622834C2212yescomplemented
26C2×#66896C2212yescomplemented
27C2×#66885C2212yescomplemented
28C2×Dic11⋊C8C2211yescharacteristic, complemented
29C2×Dic11⋊C8C2211yescharacteristic, complemented
30#10622601C2212yescomplemented
31C2×#66873C2212yescomplemented
32#10622570—22no—
33#10622570—22no—
34#10622568—22no—
35#10622568—22no—
36#10622552C2212yescomplemented
37C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
38#10622452—24no—
39#10622383—28no—
40C11×#340C2211yescharacteristic, complemented
41#10622189C2211yescharacteristic, complemented
42#10622167C2212yescomplemented
43C24×D11—22no—
44C22×D4×C11C2312yes—
45C22×C22⋊D11—22no—
46C2×D4×D11—24no—
47C2×D4×D11—24no—
48C2×D4×D11—24no—
49C2×D4×D11—24no—
50C2×D4×D11—24no—
51C2×D4×D11D418yes—
52C22×D44C2312yes—
53C22×C4×D11C2311yescharacteristic
54C2×C11×D8—24no—
55C2×C11×D8—22no—
56C22×C8×C11C2311yescharacteristic
57C22×C8×C11C2311yescharacteristic
58C2×C11×C4⋊C4C2312yes—
59C2×C11×C22⋊C4—22no—
60C2×C11×C22⋊C4—22no—
61C2×C42×C11C2311yescharacteristic
62C2×C22⋊Dic11—22no—
63C2×C22⋊Dic11—22no—
64C2×#4323—24no—
65C2×#4323—24no—
66C2×#4323—24no—
67C2×(C2×D11)⋊C4—22no—
68C2×(C2×D11)⋊C4—22no—
69C2×(C2×D11)⋊C4—22no—
70C2×(C2×D11)⋊C4—22no—
71C2×(C2×D11)⋊C4—22no—
72C2×(C2×D11)⋊C4D411yescharacteristic
73C2×(C2×D11)⋊C4D411yescharacteristic
74C2×C4⋊Dic11C2312yes—
75C2×Dic11⋊C4D411yescharacteristic
76C2×Dic11⋊C4D411yescharacteristic
77C2×C4×Dic11—22no—
78C2×C4×Dic11C2311yescharacteristic
79C22×C11⋊C8C2311yescharacteristic
80C22×C11⋊C8C2311yescharacteristic
81D8×D11—232no—
82C2×D88—24no—
83C2×D88—22no—
84C2×#4313—24no—
85C2×#4313—22no—
86C2×C8×D11—24no—
87C2×C8×D11D414yes—
88#66945—24no—
89#66945—24no—
90#66925—22no—
91#66925—22no—
92C11×C4⋊C8—22no—
93C11×#102—24no—
94#66896—24no—
95#66885—24no—
96Dic11⋊C8—22no—
97Dic11⋊C8—22no—
98#66873—24no—
99C4⋊(C11⋊C8)—22no—
100#23540—111nomaximal, Sylow
101C24×C11—22no—
102C23×D11—22no—
103C23×D11—28no—
104C23×D11—44no—
105C23×D11—44no—
106C23×D11—82no—
107C23×D11—82no—
108C23×D11—82no—
109C23×D11—82no—
110C23×D11C2×D411yescharacteristic
111C2×D4×C11—22no—
112C2×D4×C11—22no—
113C2×D4×C11—22no—
114C2×D4×C11—22no—
115C2×D4×C11—22no—
116C2×D4×C11C2×D414yes—
117C22×C4×C11—22no—
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2411yescharacteristic
121C2×C22⋊D11—28no—
122C2×C22⋊D11—44no—
123C2×C22⋊D11—44no—
124C22×Dic11—22no—
125C22×Dic11C2×D411yescharacteristic
126C22×Dic11C2×D411yescharacteristic
127C22×Dic11C2×D411yescharacteristic
128D4×D11—216no—
129D4×D11—216no—
130D4×D11—48no—
131D4×D11—48no—
132C2×D44—22no—
133C2×D44—22no—
134C2×D44—22no—
135C2×D44—22no—
136C2×D44—22no—
137C2×D44C2×D414yes—
138C2×C4×D11C2×D414yes—
139C2×C4×D11C2×D412yes—
140C2×C4×D11#4112yes—
141C2×C4×D11#4114yes—
142C11×D8—28no—
143C2×C8×C11—22no—
144C2×C8×C11—21no—
145C2×C8×C11—22no—
146C2×C8×C11C2×D412yes—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—22no—
149C11×C22⋊C4—82no—
150C11×C22⋊C4—82no—
151C42×C11—21no—
152C42×C11—21no—
153C22⋊Dic11—82no—
154C22⋊Dic11—82no—
155#4323—216no—
156(C2×D11)⋊C4—22no—
157(C2×D11)⋊C4—22no—
158(C2×D11)⋊C4—44no—
159(C2×D11)⋊C4—82no—
160(C2×D11)⋊C4—82no—
161(C2×D11)⋊C4—82no—
162(C2×D11)⋊C4—82no—
163C4⋊Dic11—22no—
164C4⋊Dic11—22no—
165Dic11⋊C4—22no—
166Dic11⋊C4—22no—
167C4×Dic11—21no—
168C4×Dic11—21no—
169C4×Dic11—44no—
170C2×C11⋊C8—22no—
171C2×C11⋊C8—21no—
172C2×C11⋊C8—22no—
173C2×C11⋊C8C2×D412yes—
174D88—28no—
175#4313—44no—
176C8×D11—28no—
177C23×D8—111no—
178C2×#424—111no—
179C2×#418—112no—
180#2309—112no—
181#2054—111no—
182#2054—112no—
183#2054—112no—
184#2054—111no—
185#2054—111no—
186#2054D1111yescharacteristic, complemented
187#1735—111no—
188C23×C11—24no—
189C23×C11—42no—
190C23×C11—42no—
191C23×C11—42no—
192C23×C11—42no—
193C23×C11—42no—
194C23×C11—42no—
195C23×C11C22×D411yescharacteristic
196C22×D11—21no—
197C22×D11—21no—
198C22×D11—22no—
199C22×D11—24no—
200C22×D11—42no—
201C22×D11—42no—
202C22×D11—42no—
203C22×D11—42no—
204C22×D11—42no—
205C22×D11—42no—
206C22×D11—416no—
207C22×D11—88no—
208C22×D11—88no—
209C22×D11—88no—
210C22×D11—88no—
211C22×D11—88no—
212C22×D11—88no—
213C22×D11#12112yes—
214C22×D11#12114yes—
215D4×C11—24no—
216D4×C11—24no—
217D4×C11—42no—
218D4×C11—42no—
219C2×C4×C11—21no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—22no—
223C2×C4×C11—21no—
224C2×C4×C11—42no—
225C2×C4×C11—42no—
226C2×C4×C11—42no—
227C2×C4×C11C22×D412yes—
228C2×C4×C11C22×D411yescharacteristic
229C2×C4×C11C2×#4111yescharacteristic
230C2×C4×C11C2×#4112yes—
231C22⋊D11—416no—
232C2×Dic11—21no—
233C2×Dic11—21no—
234C2×Dic11—21no—
235C2×Dic11—22no—
236C2×Dic11—21no—
237C2×Dic11—42no—
238C2×Dic11—42no—
239C2×Dic11—42no—
240C2×Dic11#12114yes—
241C2×Dic11#12112yes—
242D44—24no—
243D44—24no—
244D44—42no—
245D44—42no—
246C4×D11#12014yes—
247C4×D11#12318yes—
248C4×D11#12414yes—
249C8×C11—22no—
250C8×C11—41no—
251C11⋊C8—22no—
252C11⋊C8—41no—
253C23×D4—112no—
254C22×D8—112no—
255C22×D8—111no—
256C22×D8—224no—
257C22×D8—228no—
258C22×D8C2×D1111yescharacteristic
259C22×M16—111no—
260C23×C8—111no—
261C2×#117—111no—
262C2×#117—112no—
263#424—224no—
264C2×C4⋊C8—111no—
265C2×C4⋊C8—111no—
266C2×C4⋊C8—111no—
267C2×C4⋊C8C2×D1111yescharacteristic, complemented
268#418—228no—
269C2×#102—112no—
270C2×#102—112no—
271C2×#102—112no—
272C2×#102C2×D1112yescomplemented
273#390—112no—
274#390—112no—
275#390—112no—
276#390—222no—
277#390—222no—
278#390C2×D1112yescomplemented
279#379—222no—
280#379—222no—
281#340—111no—
282#340—112no—
283#340C2×D1111yescharacteristic, complemented
284C22×C11—44no—
285C22×C11—44no—
286C22×C11—44no—
287C22×C11—82no—
288C22×C11—82no—
289C22×C11—82no—
290C22×C11—82no—
291C22×C11C2×#12112yes—
292C22×C11C2×#12111yescharacteristic
293C22×C11#57611yescharacteristic
294C22×C11#57611yescharacteristic
295C22×C11#57612yes—
296C2×D11—24no—
297C2×D11—24no—
298C2×D11—22no—
299C2×D11—22no—
300C2×D11—44no—
301C2×D11—44no—
302C2×D11—44no—
303C2×D11—832no—
304C2×D11—82no—
305C2×D11—82no—
306C2×D11—82no—
307C2×D11—82no—
308C2×D11#39414yes—
309C4×C11—41no—
310C4×C11—41no—
311C4×C11—82no—
312C4×C11C2×#12011yescharacteristic
313C4×C11C2×#12312yes—
314C4×C11C2×#12411yescharacteristic
315Dic11—41no—
316Dic11—41no—
317Dic11—82no—
318Dic11#39414yes—
319C25—222no—
320C22×D4—118no—
321C22×D4—112no—
322C22×D4—224no—
323C22×D4—224no—
324C22×D4—224no—
325C22×D4—224no—
326C22×D4—224no—
327C22×D4—222no—
328C22×D4C22×D1112yes—
329C23×C4—111no—
330C2×D8—24no—
331C2×D8—22no—
332C2×D8—224no—
333C2×D8—224no—
334C2×D8—2232no—
335C2×D8—224no—
336C2×D8—224no—
337C2×D8—222no—
338C2×M16—224no—
339C2×M16—222no—
340C22×C8—111no—
341C22×C8—114no—
342C22×C8—111no—
343C22×C8—224no—
344C22×C8C22×D1111yescharacteristic
345C22×C8C22×D1111yescharacteristic
346#117—222no—
347#117—222no—
348#117—224no—
349#117—224no—
350C2×C4⋊C4—111no—
351C2×C4⋊C4—111no—
352C2×C4⋊C4—112no—
353C2×C4⋊C4C22×D1112yes—
354C2×C22⋊C4—22no—
355C2×C22⋊C4—22no—
356C2×C22⋊C4—111no—
357C2×C22⋊C4—111no—
358C2×C22⋊C4—222no—
359C2×C22⋊C4—222no—
360C2×C22⋊C4—222no—
361C2×C22⋊C4—222no—
362C2×C22⋊C4—222no—
363C2×C22⋊C4—222no—
364C2×C22⋊C4—222no—
365C2×C42—111no—
366C2×C42—222no—
367C2×C42C22×D1111yescharacteristic
368C4⋊C8—22no—
369C4⋊C8—222no—
370C4⋊C8—222no—
371C4⋊C8—222no—
372#102—24no—
373#102—224no—
374#102—224no—
375#102—224no—
376C2×C11—84no—
377C2×C11C2×#39411yescharacteristic
378C2×C11#304112yes—
379C2×C11#304112yes—
380C2×C11#305811yescharacteristic
381C2×C11#305811yescharacteristic
382D11—24no—
383D11—84no—
384C24—22no—
385C24—111no—
386C24—228no—
387C24—222no—
388C24—444no—
389C24—444no—
390C24—882no—
391C24—882no—
392C24—882no—
393C24—882no—
394C2×D4—22no—
395C2×D4—22no—
396C2×D4—22no—
397C2×D4—22no—
398C2×D4—22no—
399C2×D4—114no—
400C2×D4—2216no—
401C2×D4—2216no—
402C2×D4—228no—
403C2×D4—222no—
404C2×D4—222no—
405C2×D4—222no—
406C2×D4—222no—
407C2×D4—222no—
408C2×D4—448no—
409C2×D4—448no—
410C2×D4—444no—
411C2×D4—444no—
412C2×D4D4×D1114yes—
413C22×C4—22no—
414C22×C4—111no—
415C22×C4—112no—
416C22×C4—114no—
417C22×C4—114no—
418C22×C4—112no—
419C22×C4—111no—
420C22×C4—111no—
421C22×C4—222no—
422C22×C4D4×D1111yescharacteristic
423C22×C4D4×D1111yescharacteristic
424C22×C4C23×D1111yescharacteristic
425D8—28no—
426D8—228no—
427D8—2216no—
428M16—444no—
429C2×C8—22no—
430C2×C8—22no—
431C2×C8—21no—
432C2×C8—112no—
433C2×C8—228no—
434C2×C8—222no—
435C2×C8—222no—
436C2×C8—221no—
437C2×C8D4×D1112yes—
438C4⋊C4—22no—
439C4⋊C4—22no—
440C4⋊C4—222no—
441C4⋊C4—222no—
442C4⋊C4—222no—
443C4⋊C4—222no—
444C22⋊C4—82no—
445C22⋊C4—82no—
446C22⋊C4—222no—
447C22⋊C4—222no—
448C22⋊C4—444no—
449C22⋊C4—882no—
450C22⋊C4—882no—
451C22⋊C4—882no—
452C22⋊C4—882no—
453C22⋊C4—882no—
454C22⋊C4—882no—
455C42—21no—
456C42—21no—
457C42—221no—
458C42—221no—
459C42—444no—
460C11#2354011yescharacteristic, complemented, Sylow
461C23—24no—
462C23—42no—
463C23—42no—
464C23—42no—
465C23—42no—
466C23—42no—
467C23—42no—
468C23—112no—
469C23—114no—
470C23—221no—
471C23—221no—
472C23—222no—
473C23—224no—
474C23—4416no—
475C23—442no—
476C23—442no—
477C23—442no—
478C23—442no—
479C23—442no—
480C23—442no—
481C23—888no—
482C23—888no—
483C23—888no—
484C23—888no—
485C23—888no—
486C23—888no—
487C23C2×D4×D1111yescharacteristic
488D4—24no—
489D4—24no—
490D4—42no—
491D4—42no—
492D4—224no—
493D4—224no—
494D4—4416no—
495D4—442no—
496D4—442no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—22no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—114no—
506C2×C4—112no—
507C2×C4—114no—
508C2×C4—118no—
509C2×C4—114no—
510C2×C4—221no—
511C2×C4—221no—
512C2×C4—222no—
513C2×C4—221no—
514C2×C4—221no—
515C2×C4—442no—
516C2×C4—442no—
517C2×C4—442no—
518C2×C4C2×D4×D1112yes—
519C2×C4C2×D4×D1111yescharacteristic
520C2×C4#41×D1111yescharacteristic
521C2×C4#41×D1112yes—
522C8—22no—
523C8—41no—
524C8—222no—
525C8—441no—
526C22—44no—
527C22—44no—
528C22—44no—
529C22—82no—
530C22—82no—
531C22—82no—
532C22—82no—
533C22—114no—
534C22—224no—
535C22—224no—
536C22—222no—
537C22—222no—
538C22—444no—
539C22—444no—
540C22—444no—
541C22—8832no—
542C22—882no—
543C22—882no—
544C22—882no—
545C22—882no—
546C22D11×#12112yes—
547C22D11×#12111yescharacteristic
548C22#1062328811yescharacteristic
549C22#1062330011yescharacteristic
550C22#1062330512yes—
551C4—41no—
552C4—41no—
553C4—82no—
554C4—114no—
555C4—441no—
556C4—441no—
557C4—882no—
558C4D11×#12011yescharacteristic
559C4D11×#12312yes—
560C4D11×#12411yescharacteristic
561C2—84no—
562C2—224no—
563C2—884no—
564C2D11×#39411yescharacteristic
565C2#1307811412yes—
566C2#1307811712yes—
567C2#1307825911yescharacteristic
568C2#1307826211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2054C2
socleC23×C11C22×D4
prime radicalC22×D8×D11C2
hypercenter#2054D11
hypocenterC11#23540
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2054

Complements

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

NH ≅ G/Ntype
2. C2×#10622452C2semidirect
3. C2×#10622383C2semidirect
4. #13071195C2semidirect
5. #13069928C2semidirect
6. #13069927C2semidirect
7. #13069926C2semidirect
8. #13069925C2semidirect
9. #13069924C2semidirect
10. #13068331C2semidirect
11. C11×#2054C2semidirect
22. C2×C11×C4⋊C8C22semidirect
23. C2×C11×#102C22semidirect
24. C11×#390C22semidirect
25. #10622834C22semidirect
26. C2×#66896C22semidirect
27. C2×#66885C22semidirect
28. C2×Dic11⋊C8C22semidirect
29. C2×Dic11⋊C8C22semidirect
30. #10622601C22semidirect
31. C2×#66873C22semidirect
36. #10622552C22semidirect
37. C2×C4⋊(C11⋊C8)C22semidirect
40. C11×#340C22semidirect
41. #10622189C22semidirect
42. #10622167C22semidirect
186. #2054D11semidirect
267. C2×C4⋊C8C2×D11semidirect
272. C2×#102C2×D11semidirect
278. #390C2×D11semidirect
283. #340C2×D11semidirect
460. C11#23540semidirect

Maximal subgroups

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

subgroupindex
C22×D8×D112
C2×#106224522
C2×#106223832
#130711952
#130699282
#130699272
#130699262
#130699252
#130699242
#130683312
C11×#20542
#2354011