Finite Group Databasebeta

← #14720942

Subgroups — #14720942

Order 2816.

1108 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081912C211yesmaximal, characteristic
2C2×#10622539C211yesmaximal, characteristic, complemented
3#13067139C214yesmaximal, complemented
4#13067127C212yesmaximal, complemented
5#13067123C212yesmaximal, complemented
6#13067105C214yesmaximal, complemented
7C4×C11×#117C211yesmaximal, characteristic, complemented
8C2×C11×#117—21no—
9C22×C42×C11C2211yescharacteristic
10#10623322—21no—
11#10623322—21no—
12#10623322C2212yes—
13#10623010—21no—
14#10623010—21no—
15#10623010—21no—
16#10623010—21no—
17#10623010C412yescomplemented
18#10623010C2212yes—
19#10623008C411yescharacteristic, complemented
20#10623008C411yescharacteristic, complemented
21#10623008C2211yescharacteristic
22C4×#4339—21no—
23C4×#4339—21no—
24C4×#4339C412yescomplemented
25#10623001C411yescharacteristic, complemented
26#10623001C411yescharacteristic, complemented
27#10623001C2211yescharacteristic
28C4×C11×C4⋊C4—21no—
29C4×C11×C4⋊C4C2212yes—
30C4×C11×C22⋊C4—21no—
31C4×C11×C22⋊C4C2212yes—
32C11×#376C2212yes—
33C43×C11—21no—
34C2×C22⋊(C11⋊C8)C2212yes—
35#10622539—21no—
36#10622539—21no—
37#10622539C2212yes—
38#10622539C2212yes—
39C2×C4⋊(C11⋊C8)—21no—
40C2×#66867—21no—
41#10622090C2218yes—
42#10622089C2218yes—
43C23×C4×C11D411yescharacteristic
44C23×C4×C11D411yescharacteristic
45C23×C4×C11C2311yescharacteristic
46C2×#4339—21no—
47C2×#4339—21no—
48C2×#4339C2×C412yes—
49C11×#117—28no—
50C2×C11×C4⋊C4—22no—
51C2×C11×C22⋊C4—22no—
52C2×C42×C11—22no—
53C2×C42×C11—22no—
54C2×C42×C11—22no—
55C2×C42×C11C2×C411yescharacteristic
56C2×C42×C11C2×C411yescharacteristic
57C2×C42×C11C2×C411yescharacteristic
58C2×C42×C11C2×C411yescharacteristic
59C2×C42×C11D411yescharacteristic
60C2×C42×C11D411yescharacteristic
61C2×C42×C11D411yescharacteristic
62C2×C42×C11D411yescharacteristic
63C2×C42×C11D411yescharacteristic
64C2×C42×C11D411yescharacteristic
65C2×C42×C11C2311yescharacteristic
66C2×C42×C11C2311yescharacteristic
67#67006—22no—
68#66983—21no—
69#66983—21no—
70#66983—21no—
71#66983—21no—
72#66983C2×C412yes—
73#66983C2312yes—
74#66982—22no—
75#66982—22no—
76#66982—22no—
77C4×C22⋊D11—22no—
78C4×C22⋊D11—22no—
79C4×C22⋊D11—22no—
80C4×C22⋊D11—22no—
81C4×C22⋊D11—22no—
82C4×C22⋊D11—22no—
83#66979—21no—
84#66979—21no—
85#66979C2×C412yes—
86#66977—21no—
87#66977—21no—
88#66977—21no—
89#66977—21no—
90#66977C2×C412yes—
91#66977C2312yes—
92C22×C11⋊C8—22no—
93#66929—22no—
94#66929—22no—
95#66928—21no—
96#66928—21no—
97#66928C2×C412yes—
98#66927C2×C411yescharacteristic
99C4×D44—21no—
100C4×D44—21no—
101C4×D44—21no—
102C4×D44—21no—
103C4×D44C2×C412yes—
104C4×D44C2×C412yes—
105#66925—22no—
106#66925—22no—
107#66925—22no—
108C42×D11—22no—
109#66923—21no—
110#66923—21no—
111#66923C2×C412yes—
112#66922C2×C411yescharacteristic
113#66922C2×C411yescharacteristic
114#66922C2×C411yescharacteristic
115C4×Dic22—21no—
116C4×Dic22—21no—
117C4×Dic22—21no—
118C4×Dic22—21no—
119C4×Dic22C2×C412yes—
120C4×Dic22C2×C412yes—
121C11×#95—22no—
122C11×#95C2314yes—
123C22⋊(C11⋊C8)—22no—
124C22⋊(C11⋊C8)C2314yes—
125C4⋊(C11⋊C8)—22no—
126C4⋊(C11⋊C8)—22no—
127#66867—22no—
128#66867—22no—
129#17543—111nomaximal, Sylow
130C24×C11C2×D411yescharacteristic
131C22×C4×C11—24no—
132C22×C4×C11—24no—
133C22×C4×C11—42no—
134C22×C4×C11—42no—
135C22×C4×C11C22⋊C411yescharacteristic
136C22×C4×C11C22⋊C411yescharacteristic
137C22×C4×C11C22⋊C411yescharacteristic
138C22×C4×C11C22⋊C411yescharacteristic
139C22×C4×C11C22⋊C411yescharacteristic
140C22×C4×C11C22⋊C411yescharacteristic
141C22×C4×C11C22⋊C411yescharacteristic
142C22×C4×C11C22⋊C411yescharacteristic
143C22×C4×C11C22×C411yescharacteristic
144C22×C4×C11C22×C411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2411yescharacteristic
153C2×C22⋊D11—22no—
154C2×C22⋊D11—22no—
155C2×C22⋊D11—22no—
156#4339—44no—
157#4339—44no—
158#4339—44no—
159C2×D44—21no—
160C2×D44—21no—
161C2×D44C22×C412yes—
162C2×C4×D11—22no—
163C2×C4×D11—22no—
164C2×C4×D11—22no—
165C2×Dic22—21no—
166C2×Dic22—21no—
167C2×Dic22C22×C412yes—
168C11×C4⋊C4—28no—
169C11×C22⋊C4—28no—
170C42×C11—28no—
171C42×C11—44no—
172C42×C11—44no—
173C42×C11C22⋊C411yescharacteristic
174C42×C11C22⋊C411yescharacteristic
175C42×C11C22⋊C411yescharacteristic
176C42×C11C22⋊C411yescharacteristic
177C42×C11C22⋊C411yescharacteristic
178C42×C11C22⋊C411yescharacteristic
179C42×C11C22⋊C411yescharacteristic
180C42×C11C22⋊C411yescharacteristic
181C42×C11C22×C411yescharacteristic
182C42×C11C22×C411yescharacteristic
183C42×C11C22×C411yescharacteristic
184C42×C11C22×C411yescharacteristic
185C42×C11C2×D411yescharacteristic
186C42×C11C2×D411yescharacteristic
187C42×C11C2×D411yescharacteristic
188C42×C11C2×D411yescharacteristic
189C22⋊Dic11—22no—
190C22⋊Dic11—22no—
191C22⋊Dic11—22no—
192(C2×D11)⋊C4—22no—
193(C2×D11)⋊C4—22no—
194(C2×D11)⋊C4—22no—
195(C2×D11)⋊C4—22no—
196(C2×D11)⋊C4—22no—
197(C2×D11)⋊C4—22no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11C22×C412yes—
203C4⋊Dic11C22×C412yes—
204Dic11⋊C4—22no—
205Dic11⋊C4—22no—
206Dic11⋊C4—22no—
207Dic11⋊C4—22no—
208Dic11⋊C4—22no—
209Dic11⋊C4—22no—
210C4×Dic11—22no—
211C4×Dic11—22no—
212C4×Dic11—22no—
213C2×C11⋊C8—24no—
214C2×C11⋊C8—44no—
215#3444—111no—
216C2×#432—111no—
217C4×#117D1111yescharacteristic, complemented
218#1509—114no—
219#1506—112no—
220#1505—112no—
221#1501—114no—
222C23×C11—22no—
223C23×C11—22no—
224C23×C11—41no—
225C23×C11C2×C22⋊C411yescharacteristic
226C23×C11C2×C22⋊C411yescharacteristic
227C23×C11C22×D411yescharacteristic
228C22×D11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—28no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—44no—
248C2×C4×C11—44no—
249C2×C4×C11#10414yes—
250C2×C4×C11C2×C22⋊C411yescharacteristic
251C2×C4×C11C2×C22⋊C411yescharacteristic
252C2×C4×C11C2×C22⋊C411yescharacteristic
253C2×C4×C11C2×C22⋊C411yescharacteristic
254C2×C4×C11C2×C22⋊C411yescharacteristic
255C2×C4×C11C2×C22⋊C411yescharacteristic
256C2×C4×C11C2×C22⋊C411yescharacteristic
257C2×C4×C11C2×C22⋊C411yescharacteristic
258C2×C4×C11C2×C22⋊C411yescharacteristic
259C2×C4×C11C2×C22⋊C411yescharacteristic
260C2×C4×C11C23×C411yescharacteristic
261C2×C4×C11C22×D411yescharacteristic
262C22⋊D11—44no—
263C22⋊D11—44no—
264C22⋊D11—44no—
265C2×Dic11—22no—
266C2×Dic11—22no—
267C2×Dic11—22no—
268D44—42no—
269D44—42no—
270D44—42no—
271C4×D11—44no—
272C4×D11—44no—
273C4×D11—44no—
274Dic22—42no—
275Dic22—42no—
276Dic22—42no—
277C11⋊C8—44no—
278#533—111no—
279#533—111no—
280#533—111no—
281#532—111no—
282#532—111no—
283#532—111no—
284#529—112no—
285#529—112no—
286#529—221no—
287#529—221no—
288#529—221no—
289#529—221no—
290#525—112no—
291#525—221no—
292#525—221no—
293C4×#41—112no—
294C4×#41—221no—
295C4×#41—221no—
296C2×#117—21no—
297C22×C42C2×D1111yescharacteristic
298#432—112no—
299#432—112no—
300#432—221no—
301#432—221no—
302C2×C4⋊C8—221no—
303C2×C22⋊C8—112no—
304C2×#97—221no—
305C4×C4⋊C4—21no—
306C4×C4⋊C4C2×D1112yes—
307C4×C22⋊C4—21no—
308C4×C22⋊C4C2×D1112yes—
309#376C2×D1112yes—
310C43—21no—
311#328—118no—
312#327—118no—
313C22×C11—21no—
314C22×C11—21no—
315C22×C11—21no—
316C22×C11—21no—
317C22×C11—21no—
318C22×C11—21no—
319C22×C11—21no—
320C22×C11—44no—
321C22×C11C2×#10412yes—
322C22×C11C22×C22⋊C411yescharacteristic
323C22×C11#57512yes—
324C2×D11—42no—
325C2×D11—42no—
326C2×D11—42no—
327C4×C11—21no—
328C4×C11—21no—
329C4×C11—21no—
330C4×C11—21no—
331C4×C11—21no—
332C4×C11—21no—
333C4×C11—21no—
334C4×C11—21no—
335C4×C11—21no—
336C4×C11—48no—
337C4×C11#41012yes—
338C4×C11C2×#10412yes—
339C4×C11C2×#10412yes—
340Dic11—42no—
341Dic11—42no—
342Dic11—42no—
343C2×#41—112no—
344C2×#41—221no—
345C2×#41—221no—
346C23×C4C22⋊D1111yescharacteristic
347C23×C4C22⋊D1111yescharacteristic
348C23×C4C22×D1111yescharacteristic
349C22×C8—222no—
350C4⋊Q8—111no—
351C4⋊Q8—111no—
352C4⋊Q8—111no—
353#127—111no—
354#126—222no—
355#126—222no—
356#125—112no—
357#125—221no—
358#125—221no—
359#124—112no—
360#124—221no—
361#124—221no—
362#123—222no—
363#123—222no—
364#123—222no—
365C22⋊Q8—112no—
366C22⋊Q8—112no—
367C22⋊Q8—221no—
368C22⋊Q8—221no—
369C22⋊Q8—221no—
370C22⋊Q8—221no—
371#121—112no—
372#121—112no—
373#121—221no—
374#121—221no—
375#121—221no—
376#121—221no—
377#120—222no—
378C4×Q8—112no—
379C4×Q8—112no—
380C4×Q8—221no—
381C4×Q8—221no—
382C4×Q8—221no—
383C4×Q8—221no—
384C4×D4—112no—
385C4×D4—112no—
386C4×D4—222no—
387C4×D4—222no—
388C4×D4—222no—
389C4×D4—222no—
390C4×D4—222no—
391C4×D4—222no—
392C4×D4—221no—
393C4×D4—221no—
394C4×D4—221no—
395C4×D4—221no—
396#117—28no—
397#117—112no—
398#117—221no—
399#117—221no—
400#117—222no—
401#117—222no—
402#117—222no—
403C2×C4⋊C4—22no—
404C2×C22⋊C4—22no—
405C2×C42—22no—
406C2×C42—22no—
407C2×C42—22no—
408C2×C42—222no—
409C2×C42C4×D1111yescharacteristic
410C2×C42C4×D1111yescharacteristic
411C2×C42C4×D1111yescharacteristic
412C2×C42C4×D1111yescharacteristic
413C2×C42D4411yescharacteristic
414C2×C42D4411yescharacteristic
415C2×C42D4411yescharacteristic
416C2×C42D4411yescharacteristic
417C2×C42C22⋊D1111yescharacteristic
418C2×C42C22⋊D1111yescharacteristic
419C2×C42C22×D1111yescharacteristic
420C2×C42C22×D1111yescharacteristic
421C4⋊C8—222no—
422C4⋊C8—222no—
423C22⋊C8—114no—
424C22⋊C8—222no—
425#97—222no—
426#97—222no—
427#95—22no—
428#95C22×D1114yes—
429C2×C11—22no—
430C2×C11—22no—
431C2×C11—41no—
432C2×C11C2×#41011yescharacteristic
433C2×C11#289611yescharacteristic
434C2×C11C22×#10411yescharacteristic
435D11—82no—
436C24C2×C22⋊D1111yescharacteristic
437#41—444no—
438#41—444no—
439#41—444no—
440C2×Q8—112no—
441C2×Q8—221no—
442C2×Q8—221no—
443C2×D4—112no—
444C2×D4—222no—
445C2×D4—222no—
446C2×D4—222no—
447C2×D4—221no—
448C2×D4—221no—
449C22×C4—24no—
450C22×C4—24no—
451C22×C4—42no—
452C22×C4—42no—
453C22×C4—222no—
454C22×C4—222no—
455C22×C4—222no—
456C22×C4(C2×D11)⋊C411yescharacteristic
457C22×C4(C2×D11)⋊C411yescharacteristic
458C22×C4(C2×D11)⋊C411yescharacteristic
459C22×C4(C2×D11)⋊C411yescharacteristic
460C22×C4(C2×D11)⋊C411yescharacteristic
461C22×C4(C2×D11)⋊C411yescharacteristic
462C22×C4(C2×D11)⋊C411yescharacteristic
463C22×C4(C2×D11)⋊C411yescharacteristic
464C22×C4C2×C4×D1111yescharacteristic
465C22×C4C2×C4×D1111yescharacteristic
466C22×C4C2×D4411yescharacteristic
467C22×C4C2×D4411yescharacteristic
468C22×C4C2×C22⋊D1111yescharacteristic
469C22×C4C2×C22⋊D1111yescharacteristic
470C22×C4C2×C22⋊D1111yescharacteristic
471C22×C4C2×C22⋊D1111yescharacteristic
472C22×C4C2×C22⋊D1111yescharacteristic
473C22×C4C23×D1111yescharacteristic
474C2×C8—224no—
475C2×C8—444no—
476C4⋊C4—28no—
477C4⋊C4—112no—
478C4⋊C4—112no—
479C4⋊C4—222no—
480C4⋊C4—222no—
481C4⋊C4—221no—
482C4⋊C4—221no—
483C4⋊C4—221no—
484C4⋊C4—221no—
485C4⋊C4—222no—
486C4⋊C4—222no—
487C4⋊C4—222no—
488C4⋊C4—222no—
489C22⋊C4—28no—
490C22⋊C4—222no—
491C22⋊C4—222no—
492C22⋊C4—222no—
493C22⋊C4—222no—
494C22⋊C4—222no—
495C22⋊C4—222no—
496C22⋊C4—222no—
497C22⋊C4—222no—
498C22⋊C4—222no—
499C42—28no—
500C42—44no—
501C42—44no—
502C42—222no—
503C42—222no—
504C42—222no—
505C42(C2×D11)⋊C411yescharacteristic
506C42(C2×D11)⋊C411yescharacteristic
507C42(C2×D11)⋊C411yescharacteristic
508C42(C2×D11)⋊C411yescharacteristic
509C42(C2×D11)⋊C411yescharacteristic
510C42(C2×D11)⋊C411yescharacteristic
511C42(C2×D11)⋊C411yescharacteristic
512C42(C2×D11)⋊C411yescharacteristic
513C42C2×C4×D1111yescharacteristic
514C42C2×C4×D1111yescharacteristic
515C42C2×C4×D1111yescharacteristic
516C42C2×C4×D1111yescharacteristic
517C42C2×D4411yescharacteristic
518C42C2×D4411yescharacteristic
519C42C2×D4411yescharacteristic
520C42C2×D4411yescharacteristic
521C11#1754311yescharacteristic, complemented, Sylow
522C23—22no—
523C23—22no—
524C23—41no—
525C23—222no—
526C23C2×(C2×D11)⋊C411yescharacteristic
527C23C2×(C2×D11)⋊C411yescharacteristic
528C23C22×C22⋊D1111yescharacteristic
529Q8—442no—
530Q8—442no—
531Q8—442no—
532D4—442no—
533D4—442no—
534D4—444no—
535D4—444no—
536D4—444no—
537D4—442no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—28no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—44no—
557C2×C4—44no—
558C2×C4—222no—
559C2×C4—222no—
560C2×C4—222no—
561C2×C4—444no—
562C2×C4—444no—
563C2×C4—444no—
564C2×C4#6686914yes—
565C2×C4C2×(C2×D11)⋊C411yescharacteristic
566C2×C4C2×(C2×D11)⋊C411yescharacteristic
567C2×C4C2×(C2×D11)⋊C411yescharacteristic
568C2×C4C2×(C2×D11)⋊C411yescharacteristic
569C2×C4C2×(C2×D11)⋊C411yescharacteristic
570C2×C4C2×(C2×D11)⋊C411yescharacteristic
571C2×C4C2×(C2×D11)⋊C411yescharacteristic
572C2×C4C2×(C2×D11)⋊C411yescharacteristic
573C2×C4C2×(C2×D11)⋊C411yescharacteristic
574C2×C4C2×(C2×D11)⋊C411yescharacteristic
575C2×C4C22×C4×D1111yescharacteristic
576C2×C4C22×D4411yescharacteristic
577C8—444no—
578C22—21no—
579C22—21no—
580C22—21no—
581C22—21no—
582C22—21no—
583C22—21no—
584C22—21no—
585C22—44no—
586C22—442no—
587C22—442no—
588C22—442no—
589C22C2×#6686912yes—
590C22C22×(C2×D11)⋊C411yescharacteristic
591C22#1062335312yes—
592C4—21no—
593C4—21no—
594C4—21no—
595C4—21no—
596C4—21no—
597C4—21no—
598C4—21no—
599C4—21no—
600C4—21no—
601C4—48no—
602C4—442no—
603C4—442no—
604C4—442no—
605C4C2×#6686912yes—
606C4C2×#6686912yes—
607C4#1062261912yes—
608C2—22no—
609C2—22no—
610C2—41no—
611C2—882no—
612C2C2×#1062261911yescharacteristic
613C2#1307713311yescharacteristic
614C2C22×#6686911yescharacteristic
subgroupG/H
centerC2×C4C2×(C2×D11)⋊C4
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC4×C11×#117C2
socleC22×C11C22×C22⋊C4
prime radical#13081912C2
cosocleC22×C4×C11C24
hypercenterC4×#117D11
hypocenterC11#17543
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ C4×#117

Complements

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

NH ≅ G/Ntype
2. C2×#10622539C2semidirect
3. #13067139C2semidirect
4. #13067127C2semidirect
5. #13067123C2semidirect
6. #13067105C2semidirect
7. C4×C11×#117C2semidirect
17. #10623010C4semidirect
19. #10623008C4semidirect
20. #10623008C4semidirect
24. C4×#4339C4semidirect
25. #10623001C4semidirect
26. #10623001C4semidirect
217. C4×#117D11semidirect
521. C11#17543semidirect

Maximal subgroups

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

subgroupindex
#130819122
C2×#106225392
#130671392
#130671272
#130671232
#130671052
C4×C11×#1172
#1754311