Finite Group Databasebeta

← #14719795

Subgroups — #14719795

Order 2816.

1080 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623091C211yesmaximal, characteristic
2#13077645C211yesmaximal, characteristic, complemented
3#13066983C212yesmaximal, complemented
4#13066975C212yesmaximal, complemented
5#13066967C212yesmaximal, complemented
6#13066962C212yesmaximal, complemented
7#13066932C212yesmaximal, complemented
8C2×#10622106C212yesmaximal, complemented
9C11×#2972C211yesmaximal, characteristic, complemented
10C2×C4×D4×C11C2211yescharacteristic
11C2×#66992C411yescharacteristic
12C2×#66990C411yescharacteristic
13C2×#66983C2211yescharacteristic
14C2×#66982C2211yescharacteristic
15C2×C4×C22⋊D11C2211yescharacteristic
16C22×(C2×D11)⋊C4C2211yescharacteristic
17#10623091—24no—
18#10623091—24no—
19C2×#66951C411yescharacteristic
20C2×#66947C411yescharacteristic
21C2×#66938C411yescharacteristic
22C2×#66937C411yescharacteristic
23C2×#66935C411yescharacteristic
24C2×#66931C411yescharacteristic
25C2×#66929C2211yescharacteristic
26C2×#66928C2211yescharacteristic
27C8×D4×C11—24no—
28C11×#431C2212yescomplemented
29C2×C11×C22⋊C8C2212yes—
30C2×C11×C22⋊C8C2212yescomplemented
31#10622820C2212yescomplemented
32C2×C22⋊(C11⋊C8)C2212yes—
33#10622624—24no—
34#10622539C2212yescomplemented
35#10622107C2214yescomplemented
36#10622106C2214yes—
37#10622106C2214yes—
38#10622106C2214yescomplemented
39C24×D11C2×C411yescharacteristic
40C22×D4×C11C2×C411yescharacteristic
41C23×C4×C11C2311yescharacteristic
42C23×C4×C11C2311yescharacteristic
43C22×C22⋊D11C2×C411yescharacteristic
44C22×C22⋊D11C2×C411yescharacteristic
45C22×C22⋊D11C2×C411yescharacteristic
46C22×C22⋊D11C2×C411yescharacteristic
47C23×Dic11C2×C411yescharacteristic
48C22×D44C2×C411yescharacteristic
49C22×D44C2×C411yescharacteristic
50C22×C4×D11C2×C411yescharacteristic
51C22×Dic22C2×C411yescharacteristic
52C22×C8×C11—22no—
53C22×C8×C11—22no—
54C4×D4×C11D414yes—
55C4×D4×C11D414yes—
56C2×C11×C4⋊C4C2×C411yescharacteristic
57C2×C11×C22⋊C4C2×C411yescharacteristic
58C2×C11×C22⋊C4C2×C411yescharacteristic
59C2×C42×C11C2311yescharacteristic
60C2×C22⋊Dic11C2×C411yescharacteristic
61C2×C22⋊Dic11C2×C411yescharacteristic
62#66992—24no—
63#66990—24no—
64#66983—22no—
65#66983—22no—
66#66982—22no—
67#66982—22no—
68C4×C22⋊D11—22no—
69C4×C22⋊D11—22no—
70C2×(C2×D11)⋊C4—22no—
71C2×(C2×D11)⋊C4—22no—
72C2×(C2×D11)⋊C4C2×C411yescharacteristic
73C2×(C2×D11)⋊C4C2×C411yescharacteristic
74C2×(C2×D11)⋊C4C2×C411yescharacteristic
75C2×(C2×D11)⋊C4C2×C411yescharacteristic
76C2×(C2×D11)⋊C4C2×C411yescharacteristic
77C2×(C2×D11)⋊C4C2×C411yescharacteristic
78C2×(C2×D11)⋊C4C2×C411yescharacteristic
79C2×(C2×D11)⋊C4C2311yescharacteristic
80C2×(C2×D11)⋊C4C2311yescharacteristic
81C2×(C2×D11)⋊C4C2311yescharacteristic
82C2×C4⋊Dic11C2×C411yescharacteristic
83C2×Dic11⋊C4C2×C411yescharacteristic
84C2×Dic11⋊C4C2×C411yescharacteristic
85C2×Dic11⋊C4C2×C411yescharacteristic
86C2×Dic11⋊C4C2311yescharacteristic
87C2×C4×Dic11C2×C411yescharacteristic
88C2×#4318—22no—
89C22×C11⋊C8—22no—
90#66951—24no—
91#66947—24no—
92#66938—24no—
93#66937—24no—
94#66935—24no—
95#66931—24no—
96#66929—22no—
97#66929—22no—
98#66928—22no—
99#66928—22no—
100C11×C4⋊C8—22no—
101C11×C22⋊C8—22no—
102C11×C22⋊C8—22no—
103C11×C22⋊C8C2314yes—
104C4×C8×C11—22no—
105C22⋊(C11⋊C8)—22no—
106C22⋊(C11⋊C8)—22no—
107C22⋊(C11⋊C8)C2314yes—
108C4⋊(C11⋊C8)—22no—
109#66867—22no—
110#17386—111nomaximal, Sylow
111C24×C11C22×C411yescharacteristic
112C24×C11C22×C411yescharacteristic
113C23×D11—22no—
114C23×D11—24no—
115C23×D11—81no—
116C23×D11—81no—
117C23×D11C22×C411yescharacteristic
118C23×D11C22×C411yescharacteristic
119C23×D11C22×C411yescharacteristic
120C2×D4×C11—24no—
121C2×D4×C11C22⋊C414yes—
122C22×C4×C11—81no—
123C22×C4×C11—81no—
124C22×C4×C11C22×C411yescharacteristic
125C22×C4×C11C22×C411yescharacteristic
126C22×C4×C11C22×C411yescharacteristic
127C22×C4×C11C22×C411yescharacteristic
128C22×C4×C11C2×D412yes—
129C22×C4×C11C2×D412yes—
130C22×C4×C11C2×D412yes—
131C22×C4×C11C2×D412yes—
132C22×C4×C11C2411yescharacteristic
133C2×C22⋊D11—22no—
134C2×C22⋊D11—22no—
135C2×C22⋊D11—22no—
136C2×C22⋊D11—22no—
137C2×C22⋊D11—24no—
138C2×C22⋊D11—81no—
139C2×C22⋊D11—81no—
140C2×C22⋊D11—81no—
141C22×Dic11—22no—
142C22×Dic11—81no—
143C22×Dic11C22×C411yescharacteristic
144C22×Dic11C22×C411yescharacteristic
145C22×Dic11C22×C411yescharacteristic
146C22×Dic11C22×C411yescharacteristic
147C22×Dic11C22×C411yescharacteristic
148C2×D44—22no—
149C2×D44—22no—
150C2×D44—81no—
151C2×D44—81no—
152C2×C4×D11—22no—
153C2×C4×D11—81no—
154C2×Dic22—22no—
155C2×Dic22—81no—
156C2×C8×C11—24no—
157C2×C8×C11—82no—
158C2×C8×C11—82no—
159C11×C4⋊C4C22⋊C414yes—
160C11×C22⋊C4C22⋊C414yes—
161C11×C22⋊C4C22⋊C414yes—
162C42×C11C2×D412yes—
163C42×C11C2×D412yes—
164C22⋊Dic11—22no—
165C22⋊Dic11—22no—
166(C2×D11)⋊C4—22no—
167(C2×D11)⋊C4—22no—
168(C2×D11)⋊C4—22no—
169(C2×D11)⋊C4—22no—
170(C2×D11)⋊C4—22no—
171(C2×D11)⋊C4—22no—
172(C2×D11)⋊C4—22no—
173(C2×D11)⋊C4—21no—
174(C2×D11)⋊C4—21no—
175(C2×D11)⋊C4—21no—
176(C2×D11)⋊C4—21no—
177(C2×D11)⋊C4—21no—
178(C2×D11)⋊C4—21no—
179C4⋊Dic11—22no—
180Dic11⋊C4—22no—
181Dic11⋊C4—22no—
182Dic11⋊C4—22no—
183Dic11⋊C4—21no—
184Dic11⋊C4—21no—
185C4×Dic11—22no—
186#4318—82no—
187C2×C11⋊C8—24no—
188C2×C11⋊C8—82no—
189C2×#538—111no—
190#2973—111no—
191#2972D1111yescharacteristic, complemented
192#1473—112no—
193#1471—112no—
194#1469—112no—
195#1468—112no—
196#1459—112no—
197C2×#323—112no—
198C23×C11—22no—
199C23×C11—41no—
200C23×C11—41no—
201C23×C11—41no—
202C23×C11—41no—
203C23×C11C2×C22⋊C412yes—
204C23×C11C2×C22⋊C412yes—
205C23×C11#13114yes—
206C23×C11C23×C411yescharacteristic
207C22×D11—21no—
208C22×D11—21no—
209C22×D11—21no—
210C22×D11—22no—
211C22×D11—22no—
212C22×D11—22no—
213C22×D11—44no—
214C22×D11—41no—
215C22×D11—41no—
216C22×D11—41no—
217C22×D11—41no—
218C22×D11—41no—
219C22×D11—41no—
220C22×D11—82no—
221C22×D11—82no—
222C22×D11—88no—
223D4×C11—28no—
224C2×C4×C11—22no—
225C2×C4×C11—42no—
226C2×C4×C11—42no—
227C2×C4×C11—42no—
228C2×C4×C11—42no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11—41no—
232C2×C4×C11—41no—
233C2×C4×C11C2×C22⋊C412yes—
234C2×C4×C11C2×C22⋊C412yes—
235C2×C4×C11C2×C22⋊C412yes—
236C2×C4×C11C2×C22⋊C412yes—
237C2×C4×C11C22×D411yescharacteristic
238C2×C4×C11C22×D411yescharacteristic
239C22⋊D11—44no—
240C22⋊D11—82no—
241C22⋊D11—82no—
242C22⋊D11—82no—
243C2×Dic11—21no—
244C2×Dic11—21no—
245C2×Dic11—21no—
246C2×Dic11—21no—
247C2×Dic11—21no—
248C2×Dic11—22no—
249C2×Dic11—41no—
250C2×Dic11—41no—
251C2×Dic11—41no—
252C2×Dic11—41no—
253C2×Dic11—82no—
254D44—82no—
255D44—82no—
256C4×D11—82no—
257Dic22—82no—
258C8×C11—44no—
259C11⋊C8—44no—
260#538—224no—
261#538—224no—
262C2×#126—111no—
263C2×#126—111no—
264C2×#124—111no—
265C2×#124—111no—
266C2×#123—111no—
267C2×#123—111no—
268C2×C22⋊Q8—111no—
269C2×#121—111no—
270C2×#121—111no—
271C2×#121—111no—
272C2×#120—111no—
273C2×#120—111no—
274C2×C4×D4—111no—
275C2×C4×D4C2×D1111yescharacteristic
276C22×C22⋊C4—111no—
277#435—224no—
278C8×D4—24no—
279#432—112no—
280#431C2×D1112yescomplemented
281#407—112no—
282C2×C22⋊C8—112no—
283C2×C22⋊C8C2×D1112yes—
284C2×C22⋊C8C2×D1112yescomplemented
285#324—114no—
286#323—114no—
287#323—114no—
288#323—114no—
289C22×C11—21no—
290C22×C11—22no—
291C22×C11—21no—
292C22×C11—22no—
293C22×C11—22no—
294C22×C11—22no—
295C22×C11—22no—
296C22×C11—44no—
297C22×C11—82no—
298C22×C11#40814yes—
299C22×C11C22×C22⋊C411yescharacteristic
300C22×C11C2×#13112yes—
301C2×D11—41no—
302C2×D11—41no—
303C2×D11—41no—
304C2×D11—41no—
305C2×D11—41no—
306C2×D11—41no—
307C2×D11—41no—
308C2×D11—41no—
309C2×D11—41no—
310C2×D11—88no—
311C2×D11—82no—
312C2×D11—82no—
313C2×D11—82no—
314C4×C11—22no—
315C4×C11—21no—
316C4×C11—21no—
317C4×C11—22no—
318C4×C11—22no—
319C4×C11—22no—
320Dic11—41no—
321Dic11—41no—
322Dic11—41no—
323Dic11—41no—
324Dic11—41no—
325C25—111no—
326C22×Q8—111no—
327C22×D4—111no—
328C22×D4—111no—
329C22×D4—111no—
330C22×D4—111no—
331C22×D4—111no—
332C22×D4—111no—
333C22×D4C4×D1111yescharacteristic
334C23×C4—111no—
335C23×C4—111no—
336C23×C4C22×D1111yescharacteristic
337C23×C4C22×D1111yescharacteristic
338C2×M16—222no—
339C22×C8—22no—
340C22×C8—22no—
341C22×C8—222no—
342#126—224no—
343#126—222no—
344#126—222no—
345#124—224no—
346#124—222no—
347#124—222no—
348#123—222no—
349#123—222no—
350#123—224no—
351C22⋊Q8—224no—
352#121—224no—
353#121—222no—
354#121—222no—
355#121—224no—
356#120—224no—
357#120—224no—
358C4×D4—222no—
359C4×D4—222no—
360C4×D4D4414yes—
361C4×D4C22⋊D1114yes—
362C2×C4⋊C4—111no—
363C2×C4⋊C4—111no—
364C2×C4⋊C4—111no—
365C2×C4⋊C4—111no—
366C2×C4⋊C4—111no—
367C2×C4⋊C4C4×D1111yescharacteristic
368C2×C22⋊C4—111no—
369C2×C22⋊C4—111no—
370C2×C22⋊C4—111no—
371C2×C22⋊C4—111no—
372C2×C22⋊C4—111no—
373C2×C22⋊C4—111no—
374C2×C22⋊C4—111no—
375C2×C22⋊C4—111no—
376C2×C22⋊C4—111no—
377C2×C22⋊C4—111no—
378C2×C22⋊C4—111no—
379C2×C22⋊C4—111no—
380C2×C22⋊C4—222no—
381C2×C22⋊C4—222no—
382C2×C22⋊C4C4×D1111yescharacteristic
383C2×C22⋊C4C4×D1111yescharacteristic
384C2×C42—111no—
385C2×C42C22×D1111yescharacteristic
386C4⋊C8—22no—
387C4⋊C8—222no—
388C22⋊C8—22no—
389C22⋊C8—22no—
390C22⋊C8—114no—
391C22⋊C8—222no—
392C22⋊C8—222no—
393C22⋊C8C22×D1114yes—
394#97—222no—
395C4×C8—22no—
396C2×C11—22no—
397C2×C11—24no—
398C2×C11—42no—
399C2×C11C2×#40811yescharacteristic
400C2×C11#288311yescharacteristic
401C2×C11#288811yescharacteristic
402D11—81no—
403D11—81no—
404D11—81no—
405C24—111no—
406C24—111no—
407C24—111no—
408C24—224no—
409C24—222no—
410C24—881no—
411C24—881no—
412C24C2×C4×D1111yescharacteristic
413C24C2×C4×D1111yescharacteristic
414C2×Q8—222no—
415C2×Q8—881no—
416C2×D4—24no—
417C2×D4—224no—
418C2×D4—222no—
419C2×D4—222no—
420C2×D4—222no—
421C2×D4—222no—
422C2×D4—222no—
423C2×D4—222no—
424C2×D4—881no—
425C2×D4—881no—
426C2×D4—881no—
427C2×D4—881no—
428C2×D4—881no—
429C2×D4(C2×D11)⋊C414yes—
430C22×C4—81no—
431C22×C4—81no—
432C22×C4—111no—
433C22×C4—111no—
434C22×C4—111no—
435C22×C4—111no—
436C22×C4—111no—
437C22×C4—222no—
438C22×C4—222no—
439C22×C4—881no—
440C22×C4—881no—
441C22×C4C2×C4×D1111yescharacteristic
442C22×C4C2×C4×D1111yescharacteristic
443C22×C4C2×C4×D1111yescharacteristic
444C22×C4C2×C4×D1111yescharacteristic
445C22×C4C2×D4412yes—
446C22×C4C2×D4412yes—
447C22×C4C2×C22⋊D1112yes—
448C22×C4C2×C22⋊D1112yes—
449C22×C4C23×D1111yescharacteristic
450M16—882no—
451C2×C8—24no—
452C2×C8—82no—
453C2×C8—82no—
454C2×C8—224no—
455C2×C8—882no—
456C4⋊C4—222no—
457C4⋊C4—222no—
458C4⋊C4—222no—
459C4⋊C4—222no—
460C4⋊C4—221no—
461C4⋊C4—221no—
462C4⋊C4(C2×D11)⋊C414yes—
463C22⋊C4—222no—
464C22⋊C4—222no—
465C22⋊C4—222no—
466C22⋊C4—222no—
467C22⋊C4—222no—
468C22⋊C4—222no—
469C22⋊C4—222no—
470C22⋊C4—222no—
471C22⋊C4—222no—
472C22⋊C4—221no—
473C22⋊C4—221no—
474C22⋊C4—221no—
475C22⋊C4—221no—
476C22⋊C4—221no—
477C22⋊C4—221no—
478C22⋊C4(C2×D11)⋊C414yes—
479C22⋊C4(C2×D11)⋊C414yes—
480C42—222no—
481C42C2×D4412yes—
482C42C2×C22⋊D1112yes—
483C11#1738611yescharacteristic, complemented, Sylow
484C23—22no—
485C23—41no—
486C23—41no—
487C23—41no—
488C23—41no—
489C23—221no—
490C23—221no—
491C23—221no—
492C23—222no—
493C23—222no—
494C23—222no—
495C23—441no—
496C23—441no—
497C23—441no—
498C23—441no—
499C23—441no—
500C23—441no—
501C23—444no—
502C23—882no—
503C23—882no—
504C23—888no—
505C23#6695414yes—
506C23C2×(C2×D11)⋊C412yes—
507C23C2×(C2×D11)⋊C412yes—
508C23C22×C4×D1111yescharacteristic
509Q8—882no—
510D4—28no—
511D4—444no—
512D4—882no—
513D4—882no—
514D4—882no—
515D4—882no—
516D4—882no—
517C2×C4—22no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—222no—
527C2×C4—221no—
528C2×C4—221no—
529C2×C4—221no—
530C2×C4—221no—
531C2×C4—221no—
532C2×C4—441no—
533C2×C4—441no—
534C2×C4—441no—
535C2×C4—441no—
536C2×C4—882no—
537C2×C4—882no—
538C2×C4C2×(C2×D11)⋊C412yes—
539C2×C4C2×(C2×D11)⋊C412yes—
540C2×C4C2×(C2×D11)⋊C412yes—
541C2×C4C2×(C2×D11)⋊C412yes—
542C2×C4C22×D4411yescharacteristic
543C2×C4C22×C22⋊D1111yescharacteristic
544C8—44no—
545C8—444no—
546C22—21no—
547C22—22no—
548C22—21no—
549C22—22no—
550C22—22no—
551C22—22no—
552C22—22no—
553C22—44no—
554C22—82no—
555C22—441no—
556C22—441no—
557C22—441no—
558C22—441no—
559C22—441no—
560C22—441no—
561C22—441no—
562C22—441no—
563C22—441no—
564C22—882no—
565C22—882no—
566C22—882no—
567C22—888no—
568C22#1062272314yes—
569C22C2×#6695412yes—
570C22C22×(C2×D11)⋊C411yescharacteristic
571C4—22no—
572C4—21no—
573C4—21no—
574C4—22no—
575C4—22no—
576C4—22no—
577C4—441no—
578C4—441no—
579C4—441no—
580C4—441no—
581C4—441no—
582C2—22no—
583C2—24no—
584C2—42no—
585C2—881no—
586C2—881no—
587C2—881no—
588C2C2×#1062272311yescharacteristic
589C2#1307707611yescharacteristic
590C2#1307709411yescharacteristic
subgroupG/H
centerC22C22×(C2×D11)⋊C4
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2972C2
socleC22×C11C22×C22⋊C4
prime radicalC2×#10623091C2
cosocleC22×C4×C11C24
hypercenter#2972D11
hypocenterC11#17386
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #2972

Complements

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

NH ≅ G/Ntype
2. #13077645C2semidirect
3. #13066983C2semidirect
4. #13066975C2semidirect
5. #13066967C2semidirect
6. #13066962C2semidirect
7. #13066932C2semidirect
8. C2×#10622106C2semidirect
9. C11×#2972C2semidirect
28. C11×#431C22semidirect
30. C2×C11×C22⋊C8C22semidirect
31. #10622820C22semidirect
34. #10622539C22semidirect
35. #10622107C22semidirect
38. #10622106C22semidirect
191. #2972D11semidirect
280. #431C2×D11semidirect
284. C2×C22⋊C8C2×D11semidirect
483. C11#17386semidirect

Maximal subgroups

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

subgroupindex
C2×#106230912
#130776452
#130669832
#130669752
#130669672
#130669622
#130669322
C2×#106221062
C11×#29722
#1738611