Finite Group Databasebeta

← #14763587

Subgroups — #14763587

Order 2816.

1158 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623010C211yesmaximal, characteristic
2#13071014C211yesmaximal, characteristic, complemented
3#13069600C212yesmaximal, complemented
4#13069451C212yesmaximal
5#13069074C214yesmaximal, complemented
6#13068601C214yesmaximal, complemented
7C11×#2285C211yesmaximal, characteristic, complemented
8C2×C11×#117C2212yes—
9C22×C42×C11C2211yescharacteristic
10C2×#66983C2211yescharacteristic
11C2×#66982C2212yes—
12C2×C4×C22⋊D11C2212yes—
13C2×#66977C2211yescharacteristic
14#10623010—21no—
15#10623010—21no—
16#10623010—21no—
17#10623010—21no—
18#10623010—21no—
19#10623010—21no—
20#10623010—21no—
21#10623010—21no—
22C2×#66929C412yescomplemented
23C2×#66928C411yescharacteristic, complemented
24C2×C4×D44C411yescharacteristic, complemented
25C2×#66925C412yescomplemented
26C2×#66923C411yescharacteristic, complemented
27C2×C4×Dic22C411yescharacteristic, complemented
28C11×#384—21no—
29C11×#382—21no—
30C11×#380C2212yes—
31C11×#380C2212yes—
32C4×C11×C4⋊C4—21no—
33C4×C11×C4⋊C4—21no—
34#10622825C2212yes—
35#10622824C2212yes—
36C4×C22⋊Dic11C2212yes—
37C2×#66870C2218yes—
38#10622550—21no—
39#10622549—21no—
40C4×C4⋊Dic11—21no—
41#10622545—21no—
42#10622165C2218yes—
43C23×C4×C11C2311yescharacteristic
44C23×C4×C11C2311yescharacteristic
45C23×C4×C11C2311yescharacteristic
46C22×C22⋊D11C2312yes—
47C22×D44C2×C411yescharacteristic
48C22×C4×D11C2×C412yes—
49C22×Dic22C2×C411yescharacteristic
50C11×#117—44no—
51C2×C11×C4⋊C4—22no—
52C2×C11×C4⋊C4—22no—
53C2×C11×C4⋊C4—22no—
54C2×C11×C22⋊C4C2314yes—
55C2×C42×C11—22no—
56C2×C42×C11C2×C411yescharacteristic
57C2×C42×C11C2×C411yescharacteristic
58C2×C42×C11C2×C411yescharacteristic
59C2×C42×C11C2×C411yescharacteristic
60C2×C42×C11D411yescharacteristic
61C2×C42×C11D411yescharacteristic
62C2×C42×C11D411yescharacteristic
63C2×C42×C11D411yescharacteristic
64C2×C42×C11D411yescharacteristic
65C2×C42×C11D411yescharacteristic
66C2×C42×C11D411yescharacteristic
67C2×C42×C11D411yescharacteristic
68C2×C22⋊Dic11C2314yes—
69C2×C22⋊Dic11C2312yes—
70#66983—21no—
71#66983—21no—
72#66983—21no—
73#66983—21no—
74#66982—22no—
75#66982—22no—
76#66982—22no—
77#66982—22no—
78C4×C22⋊D11—22no—
79C4×C22⋊D11—22no—
80C4×C22⋊D11—22no—
81C4×C22⋊D11—22no—
82C2×(C2×D11)⋊C4C2×C412yes—
83C2×(C2×D11)⋊C4C2×C412yes—
84C2×(C2×D11)⋊C4C2×C412yes—
85C2×(C2×D11)⋊C4C2×C412yes—
86C2×C4⋊Dic11—22no—
87C2×C4⋊Dic11C2×C411yescharacteristic
88C2×C4⋊Dic11C2×C411yescharacteristic
89#66977—21no—
90#66977—21no—
91#66977—21no—
92#66977—21no—
93C2×Dic11⋊C4C2×C412yes—
94C2×Dic11⋊C4C2×C412yes—
95C2×Dic11⋊C4C2×C412yes—
96C2×Dic11⋊C4C2×C412yes—
97C2×C4×Dic11—22no—
98C2×C4×Dic11C2×C412yes—
99#66929—22no—
100#66929—22no—
101#66929—22no—
102#66929—22no—
103#66928—21no—
104#66928—21no—
105#66928—21no—
106#66928—21no—
107C4×D44—21no—
108C4×D44—21no—
109C4×D44—21no—
110C4×D44—21no—
111#66925—22no—
112#66925—22no—
113#66925—22no—
114#66925—22no—
115#66923—21no—
116#66923—21no—
117#66923—21no—
118#66923—21no—
119C4×Dic22—21no—
120C4×Dic22—21no—
121C4×Dic22—21no—
122C4×Dic22—21no—
123C11×#95—22no—
124C11×#95—22no—
125C11⋊#95—22no—
126C11⋊#95—22no—
127C11⋊#95—22no—
128C11⋊#95—22no—
129#66870—48no—
130#21875—111nomaximal, Sylow
131C24×C11C2411yescharacteristic
132C23×D11C22×C412yes—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—24no—
136C22×C4×C11—42no—
137C22×C4×C11—42no—
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×C11C2×D411yescharacteristic
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×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C2×C22⋊D11—22no—
157C2×C22⋊D11—22no—
158C2×C22⋊D11—24no—
159C2×C22⋊D11—24no—
160C22×Dic11—24no—
161C22×Dic11C22×C412yes—
162C22×Dic11C22×C412yes—
163C22×Dic11C22×C412yes—
164C2×D44—21no—
165C2×D44—21no—
166C2×D44—42no—
167C2×C4×D11—22no—
168C2×C4×D11—22no—
169C2×C4×D11—44no—
170C2×Dic22—21no—
171C2×Dic22—21no—
172C2×Dic22—42no—
173C11×C4⋊C4—44no—
174C11×C4⋊C4—44no—
175C11×C4⋊C4—44no—
176C11×C22⋊C4—28no—
177C42×C11—44no—
178C42×C11C22⋊C411yescharacteristic
179C42×C11C22⋊C411yescharacteristic
180C42×C11C22⋊C411yescharacteristic
181C42×C11C22⋊C411yescharacteristic
182C42×C11C22⋊C411yescharacteristic
183C42×C11C22⋊C411yescharacteristic
184C42×C11C22⋊C411yescharacteristic
185C42×C11C22⋊C411yescharacteristic
186C42×C11C22⋊C411yescharacteristic
187C42×C11C22⋊C411yescharacteristic
188C42×C11C22⋊C411yescharacteristic
189C42×C11C22⋊C411yescharacteristic
190C42×C11C22⋊C411yescharacteristic
191C42×C11C22⋊C411yescharacteristic
192C42×C11C22⋊C411yescharacteristic
193C42×C11C22⋊C411yescharacteristic
194C22⋊Dic11—22no—
195C22⋊Dic11—22no—
196C22⋊Dic11—24no—
197C22⋊Dic11—24no—
198(C2×D11)⋊C4—22no—
199(C2×D11)⋊C4—22no—
200(C2×D11)⋊C4—22no—
201(C2×D11)⋊C4—22no—
202(C2×D11)⋊C4—22no—
203(C2×D11)⋊C4—22no—
204(C2×D11)⋊C4—22no—
205(C2×D11)⋊C4—22no—
206C4⋊Dic11—21no—
207C4⋊Dic11—21no—
208C4⋊Dic11—21no—
209C4⋊Dic11—21no—
210C4⋊Dic11—44no—
211Dic11⋊C4—22no—
212Dic11⋊C4—22no—
213Dic11⋊C4—22no—
214Dic11⋊C4—22no—
215Dic11⋊C4—22no—
216Dic11⋊C4—22no—
217Dic11⋊C4—22no—
218Dic11⋊C4—22no—
219C4×Dic11—22no—
220C4×Dic11—22no—
221C4×Dic11—44no—
222C2×#529—111no—
223#2285D1111yescharacteristic, complemented
224#2283—111no—
225#1996—112no—
226#1964—112no—
227#1899—114no—
228#1799—114no—
229C23×C11—41no—
230C23×C11—41no—
231C23×C11C23×C411yescharacteristic
232C23×C11C22×D411yescharacteristic
233C23×C11C22×D411yescharacteristic
234C23×C11H(5,𝔽2)12yes—
235C23×C112−1+412yes—
236C22×D11—22no—
237C22×D11—24no—
238C22×D11—42no—
239C22×D11—42no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—22no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—22no—
250C2×C4×C11—22no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—44no—
261C2×C4×C11—44no—
262C2×C4×C11—44no—
263C2×C4×C11C2×C22⋊C411yescharacteristic
264C2×C4×C11C2×C22⋊C411yescharacteristic
265C2×C4×C11C2×C22⋊C411yescharacteristic
266C2×C4×C11C2×C22⋊C411yescharacteristic
267C2×C4×C11C2×C22⋊C411yescharacteristic
268C2×C4×C11C2×C22⋊C411yescharacteristic
269C2×C4×C11C2×C22⋊C411yescharacteristic
270C2×C4×C11C2×C22⋊C411yescharacteristic
271C2×C4×C11C2×C22⋊C411yescharacteristic
272C2×C4×C11C2×C22⋊C411yescharacteristic
273C2×C4×C11C2×C22⋊C411yescharacteristic
274C2×C4×C11C2×C22⋊C411yescharacteristic
275C22⋊D11—42no—
276C22⋊D11—42no—
277C22⋊D11—44no—
278C2×Dic11—22no—
279C2×Dic11—22no—
280C2×Dic11—22no—
281C2×Dic11—24no—
282C2×Dic11—42no—
283C2×Dic11—42no—
284C2×Dic11—44no—
285C2×Dic11—44no—
286C2×Dic11—44no—
287D44—42no—
288D44—42no—
289C4×D11—44no—
290C4×D11—44no—
291Dic22—42no—
292Dic22—42no—
293#529—221no—
294#529—221no—
295#529—221no—
296#529—221no—
297#529—221no—
298#529—221no—
299#529—221no—
300#529—221no—
301C2×#126—112no—
302C2×#125—111no—
303C2×#124—111no—
304C2×#123—112no—
305C2×C22⋊Q8—111no—
306C2×#121—111no—
307C2×C4×Q8—111no—
308C2×C4×D4—112no—
309C2×C4×D4—111no—
310C2×#117—112no—
311C2×#117C2×D1112yes—
312C22×C42C2×D1111yescharacteristic
313C2×#99—118no—
314#384—21no—
315#383—221no—
316#382—21no—
317#382—221no—
318#381—112no—
319#380—112no—
320#380C2×D1112yes—
321#380C2×D1112yes—
322C4×C4⋊C4—21no—
323C4×C4⋊C4—21no—
324C4×C4⋊C4—221no—
325C4×C22⋊C4—112no—
326#376—221no—
327#342—118no—
328C22×C11—21no—
329C22×C11—21no—
330C22×C11—21no—
331C22×C11—21no—
332C22×C11—21no—
333C22×C11—21no—
334C22×C11—42no—
335C22×C11—42no—
336C22×C11C22×C22⋊C411yescharacteristic
337C22×C11#52012yes—
338C22×C11#53511yescharacteristic
339C22×C11#53611yescharacteristic
340C22×C11#53712yes—
341C2×D11—42no—
342C2×D11—42no—
343C2×D11—42no—
344C2×D11—84no—
345C4×C11—21no—
346C4×C11—21no—
347C4×C11—21no—
348C4×C11—21no—
349C4×C11—21no—
350C4×C11—21no—
351C4×C11—21no—
352C4×C11—21no—
353C4×C11—21no—
354C4×C11—21no—
355C4×C11—84no—
356C4×C11#41012yes—
357C4×C11#41012yes—
358Dic11—42no—
359Dic11—42no—
360Dic11—42no—
361Dic11—84no—
362C22×Q8—111no—
363C22×D4—112no—
364C22×D4—111no—
365C23×C4—112no—
366C23×C4C22×D1111yescharacteristic
367C23×C4C22×D1111yescharacteristic
368C23×C4C22×D1111yescharacteristic
369#126—222no—
370#126—222no—
371#126—222no—
372#126—222no—
373#125—221no—
374#125—221no—
375#125—221no—
376#125—221no—
377#124—221no—
378#124—221no—
379#124—221no—
380#124—221no—
381#123—222no—
382#123—222no—
383#123—222no—
384#123—222no—
385C22⋊Q8—221no—
386C22⋊Q8—221no—
387C22⋊Q8—221no—
388C22⋊Q8—221no—
389#121—221no—
390#121—221no—
391#121—221no—
392#121—221no—
393C4×Q8—221no—
394C4×Q8—221no—
395C4×Q8—221no—
396C4×Q8—221no—
397C4×D4—222no—
398C4×D4—222no—
399C4×D4—222no—
400C4×D4—222no—
401C4×D4—221no—
402C4×D4—221no—
403C4×D4—221no—
404C4×D4—221no—
405#117—44no—
406#117—222no—
407#117—222no—
408#117—222no—
409#117—222no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—112no—
414C2×C4⋊C4—112no—
415C2×C4⋊C4—111no—
416C2×C4⋊C4—112no—
417C2×C4⋊C4—111no—
418C2×C4⋊C4—112no—
419C2×C4⋊C4—222no—
420C2×C22⋊C4—112no—
421C2×C22⋊C4—112no—
422C2×C22⋊C4—112no—
423C2×C22⋊C4—112no—
424C2×C22⋊C4—112no—
425C2×C22⋊C4—114no—
426C2×C22⋊C4C22×D1114yes—
427C2×C42—22no—
428C2×C42—112no—
429C2×C42—222no—
430C2×C42C4×D1111yescharacteristic
431C2×C42C4×D1111yescharacteristic
432C2×C42C4×D1111yescharacteristic
433C2×C42C4×D1111yescharacteristic
434C2×C42D4411yescharacteristic
435C2×C42D4411yescharacteristic
436C2×C42D4411yescharacteristic
437C2×C42D4411yescharacteristic
438C2×C42C22⋊D1111yescharacteristic
439C2×C42C22⋊D1111yescharacteristic
440C2×C42C22⋊D1111yescharacteristic
441C2×C42C22⋊D1111yescharacteristic
442#99—448no—
443#95—22no—
444#95—22no—
445#95—222no—
446#95—222no—
447#95—222no—
448#95—222no—
449C2×C11—22no—
450C2×C11—21no—
451C2×C11—22no—
452C2×C11—21no—
453C2×C11#231111yescharacteristic
454C2×C11C2×#41011yescharacteristic
455C2×C11C2×#41011yescharacteristic
456D11—82no—
457C24—112no—
458C24C23×D1111yescharacteristic
459C2×Q8—221no—
460C2×Q8—221no—
461C2×Q8—442no—
462C2×D4—222no—
463C2×D4—224no—
464C2×D4—224no—
465C2×D4—222no—
466C2×D4—221no—
467C2×D4—221no—
468C2×D4—442no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—24no—
472C22×C4—42no—
473C22×C4—42no—
474C22×C4—112no—
475C22×C4—112no—
476C22×C4—112no—
477C22×C4—222no—
478C22×C4—222no—
479C22×C4—224no—
480C22×C4—444no—
481C22×C4C2×C4×D1111yescharacteristic
482C22×C4C2×C4×D1111yescharacteristic
483C22×C4C2×C4×D1111yescharacteristic
484C22×C4C2×C4×D1111yescharacteristic
485C22×C4C2×C4×D1111yescharacteristic
486C22×C4C2×C4×D1111yescharacteristic
487C22×C4C2×D4411yescharacteristic
488C22×C4C2×D4411yescharacteristic
489C22×C4C2×D4411yescharacteristic
490C22×C4C2×D4411yescharacteristic
491C22×C4C2×D4411yescharacteristic
492C22×C4C2×D4411yescharacteristic
493C22×C4C2×C22⋊D1111yescharacteristic
494C22×C4C2×C22⋊D1111yescharacteristic
495C22×C4C2×C22⋊D1111yescharacteristic
496C22×C4C2×C22⋊D1111yescharacteristic
497C22×C4C2×C22⋊D1111yescharacteristic
498C22×C4C2×C22⋊D1111yescharacteristic
499C4⋊C4—44no—
500C4⋊C4—44no—
501C4⋊C4—44no—
502C4⋊C4—222no—
503C4⋊C4—222no—
504C4⋊C4—222no—
505C4⋊C4—222no—
506C4⋊C4—221no—
507C4⋊C4—221no—
508C4⋊C4—222no—
509C4⋊C4—222no—
510C4⋊C4—221no—
511C4⋊C4—221no—
512C4⋊C4—222no—
513C4⋊C4—222no—
514C4⋊C4—444no—
515C22⋊C4—28no—
516C22⋊C4—222no—
517C22⋊C4—222no—
518C22⋊C4—222no—
519C22⋊C4—222no—
520C22⋊C4—222no—
521C22⋊C4—222no—
522C22⋊C4—222no—
523C22⋊C4—222no—
524C22⋊C4—222no—
525C22⋊C4—222no—
526C22⋊C4—224no—
527C22⋊C4—224no—
528C42—44no—
529C42—222no—
530C42—222no—
531C42—444no—
532C42(C2×D11)⋊C411yescharacteristic
533C42(C2×D11)⋊C411yescharacteristic
534C42(C2×D11)⋊C411yescharacteristic
535C42(C2×D11)⋊C411yescharacteristic
536C42(C2×D11)⋊C411yescharacteristic
537C42(C2×D11)⋊C411yescharacteristic
538C42(C2×D11)⋊C411yescharacteristic
539C42(C2×D11)⋊C411yescharacteristic
540C42(C2×D11)⋊C411yescharacteristic
541C42(C2×D11)⋊C411yescharacteristic
542C42(C2×D11)⋊C411yescharacteristic
543C42(C2×D11)⋊C411yescharacteristic
544C42(C2×D11)⋊C411yescharacteristic
545C42(C2×D11)⋊C411yescharacteristic
546C42(C2×D11)⋊C411yescharacteristic
547C42(C2×D11)⋊C411yescharacteristic
548C11#2187511yescharacteristic, complemented, Sylow
549C23—41no—
550C23—41no—
551C23—222no—
552C23—224no—
553C23—442no—
554C23—442no—
555C23C22×C4×D1111yescharacteristic
556C23C22×D4411yescharacteristic
557C23#6703712yes—
558C23#6704012yes—
559C23C22×C22⋊D1111yescharacteristic
560Q8—442no—
561Q8—442no—
562D4—442no—
563D4—444no—
564D4—442no—
565D4—442no—
566D4—442no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—44no—
588C2×C4—44no—
589C2×C4—44no—
590C2×C4—224no—
591C2×C4—222no—
592C2×C4—222no—
593C2×C4—222no—
594C2×C4—444no—
595C2×C4—444no—
596C2×C4—442no—
597C2×C4—442no—
598C2×C4—444no—
599C2×C4—444no—
600C2×C4—444no—
601C2×C4C2×(C2×D11)⋊C411yescharacteristic
602C2×C4C2×(C2×D11)⋊C411yescharacteristic
603C2×C4C2×(C2×D11)⋊C411yescharacteristic
604C2×C4C2×(C2×D11)⋊C411yescharacteristic
605C2×C4C2×(C2×D11)⋊C411yescharacteristic
606C2×C4C2×(C2×D11)⋊C411yescharacteristic
607C2×C4C2×(C2×D11)⋊C411yescharacteristic
608C2×C4C2×(C2×D11)⋊C411yescharacteristic
609C2×C4C2×(C2×D11)⋊C411yescharacteristic
610C2×C4C2×(C2×D11)⋊C411yescharacteristic
611C2×C4C2×(C2×D11)⋊C411yescharacteristic
612C2×C4C2×(C2×D11)⋊C411yescharacteristic
613C22—21no—
614C22—21no—
615C22—21no—
616C22—21no—
617C22—21no—
618C22—21no—
619C22—42no—
620C22—42no—
621C22—442no—
622C22—442no—
623C22—442no—
624C22—884no—
625C22#1062303512yes—
626C22#1062304112yes—
627C22C22×(C2×D11)⋊C411yescharacteristic
628C22#1062333611yescharacteristic
629C22#1062334711yescharacteristic
630C4—21no—
631C4—21no—
632C4—21no—
633C4—21no—
634C4—21no—
635C4—21no—
636C4—21no—
637C4—21no—
638C4—21no—
639C4—21no—
640C4—84no—
641C4—442no—
642C4—442no—
643C4—442no—
644C4—884no—
645C4#1062261912yes—
646C4#1062261912yes—
647C2—21no—
648C2—22no—
649C2—22no—
650C2—21no—
651C2—882no—
652C2#1307120911yescharacteristic
653C2C2×#1062261911yescharacteristic
654C2C2×#1062261911yescharacteristic
subgroupG/H
centerC22C22×(C2×D11)⋊C4
commutatorC23×C11C23×C4
FrattiniC24C23×D11
FittingC11×#2285C2
socleC22×C11C22×C22⋊C4
prime radicalC2×#66983C22
cosocleC24×C11C24
hypercenter#2285D11
hypocenterC11#21875
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C42 ◁ #2285

Complements

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

NH ≅ G/Ntype
2. #13071014C2semidirect
3. #13069600C2semidirect
5. #13069074C2semidirect
6. #13068601C2semidirect
7. C11×#2285C2semidirect
22. C2×#66929C4semidirect
23. C2×#66928C4semidirect
24. C2×C4×D44C4semidirect
25. C2×#66925C4semidirect
26. C2×#66923C4semidirect
27. C2×C4×Dic22C4semidirect
223. #2285D11semidirect
548. C11#21875semidirect

Maximal subgroups

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

subgroupindex
C2×#106230102
#130710142
#130696002
#130694512
#130690742
#130686012
C11×#22852
#2187511