Finite Group Databasebeta

← #14923647

Subgroups — #14923647

Order 2816.

2738 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623322C211yesmaximal, characteristic
2#13073104C211yesmaximal, characteristic, complemented
3#13073097C211yesmaximal, characteristic, complemented
4#13073090C211yesmaximal, characteristic, complemented
5#13073083C211yesmaximal, characteristic, complemented
6#13073074C212yesmaximal, complemented
7#13073065C212yesmaximal, complemented
8#13073054C214yesmaximal, complemented
9#13072012C214yesmaximal, complemented
10#13071873C214yesmaximal, complemented
11C4×#66982C214yesmaximal, complemented
12#13071104C212yesmaximal, complemented
13#13071019C212yesmaximal, complemented
14C2×C4×C22⋊Dic11C211yesmaximal, characteristic, complemented
15C22×C11×#117C211yesmaximal, characteristic, complemented
16C24×C4×C11C2211yescharacteristic
17C22×#4339C2211yescharacteristic
18C2×C11×#117—28no—
19C2×C11×#117C2212yes—
20C2×C11×#117C2212yes—
21C2×C11×#117C2212yes—
22C2×C11×#117C2212yes—
23C22×C11×C4⋊C4C2211yescharacteristic
24C22×C11×C4⋊C4C2211yescharacteristic
25C22×C11×C22⋊C4C2212yes—
26C22×C42×C11C2212yes—
27C2×#67006C2212yes—
28C22×C22⋊Dic11C2212yes—
29#10623322—28no—
30C2×#66983C2211yescharacteristic
31C2×#66983C2211yescharacteristic
32C2×#66982C2212yes—
33C2×#66982C2214yes—
34C2×C4×C22⋊D11C2212yes—
35C2×C4×C22⋊D11C2212yes—
36C2×#66979C2211yescharacteristic
37C2×#66977C2211yescharacteristic
38C2×#66977C2211yescharacteristic
39C22×C4×Dic11C2212yes—
40#10622826C2214yes—
41#10622824C2214yes—
42#10622823C2214yes—
43C4×C22⋊Dic11C2212yes—
44C4×C22⋊Dic11C2212yes—
45C4×C22⋊Dic11C2212yes—
46C4×C22⋊Dic11C2211yescharacteristic
47C4×C22⋊Dic11C2211yescharacteristic
48C2×C11⋊#95C2212yes—
49#10622606C2214yescomplemented
50#10622605C2214yescomplemented
51#10622601C2212yescomplemented
52#10622601C2212yescomplemented
53#10622595C2214yescomplemented
54#10622593C2214yescomplemented
55#10622590C2212yescomplemented
56#10622590C2212yescomplemented
57#10622589C2212yescomplemented
58#10622589C2212yescomplemented
59#10622587C2212yescomplemented
60#10622587C2212yescomplemented
61#10622572C2218yes—
62#10622571C2218yes—
63#10622565C2218yes—
64#10622555C2218yes—
65#10622553C2218yescomplemented
66C4×(C2×D11)⋊C4C2218yescomplemented
67#10622546C2218yescomplemented
68C4×Dic11⋊C4C2218yescomplemented
69C25×C11C2311yescharacteristic
70C23×C4×C11—28no—
71C23×C4×C11D418yes—
72C23×C4×C11C2312yes—
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C23×C4×C11C2312yes—
79C23×C4×C11C2311yescharacteristic
80C22×C22⋊D11C2312yes—
81C22×C22⋊D11C2312yes—
82C22×C22⋊D11C2312yes—
83C23×Dic11C2314yes—
84C2×#4339—24no—
85C2×#4339—28no—
86C22×D44C2311yescharacteristic
87C22×C4×D11C2312yes—
88C22×Dic22C2311yescharacteristic
89C11×#117—28no—
90C11×#117—28no—
91C11×#117—28no—
92C11×#117—28no—
93C2×C11×C4⋊C4—24no—
94C2×C11×C4⋊C4—24no—
95C2×C11×C4⋊C4C2312yes—
96C2×C11×C4⋊C4C2312yes—
97C2×C11×C4⋊C4C2312yes—
98C2×C11×C4⋊C4C2312yes—
99C2×C11×C22⋊C4—28no—
100C2×C11×C22⋊C4C2314yes—
101C2×C11×C22⋊C4C2314yes—
102C2×C42×C11—28no—
103C2×C42×C11C2314yes—
104C2×C42×C11C2314yes—
105#67006—28no—
106C2×C22⋊Dic11—28no—
107C2×C22⋊Dic11C2312yes—
108C2×C22⋊Dic11C2312yes—
109C2×C22⋊Dic11C2312yes—
110C2×C22⋊Dic11C2314yes—
111C2×C22⋊Dic11C2312yes—
112C2×C22⋊Dic11C2312yes—
113#66983—24no—
114#66983—24no—
115#66982—28no—
116#66982—216no—
117C4×C22⋊D11—28no—
118C4×C22⋊D11—28no—
119C2×(C2×D11)⋊C4C2318yes—
120C2×(C2×D11)⋊C4C2312yes—
121C2×(C2×D11)⋊C4C2312yes—
122C2×(C2×D11)⋊C4C2318yes—
123#66979—24no—
124C2×C4⋊Dic11C2311yescharacteristic
125C2×C4⋊Dic11C2311yescharacteristic
126#66977—24no—
127#66977—24no—
128C2×Dic11⋊C4C2318yes—
129C2×Dic11⋊C4C2312yes—
130C2×Dic11⋊C4C2312yes—
131C2×Dic11⋊C4C2318yes—
132C2×C4×Dic11—28no—
133C2×C4×Dic11C2312yes—
134C2×C4×Dic11C2314yes—
135C2×C4×Dic11C2312yes—
136C2×C4×Dic11C2312yes—
137C11⋊#95C2318yes—
138C11⋊#95C2318yes—
139C11⋊#95C2314yes—
140C11⋊#95C2318yes—
141C11⋊#95C2318yes—
142C11⋊#95C2312yes—
143C11⋊#95C2312yes—
144#34810—111nomaximal, Sylow
145C24×C11—24no—
146C24×C11—24no—
147C24×C11—42no—
148C24×C11C2×D414yes—
149C24×C11C2411yescharacteristic
150C24×C11C2411yescharacteristic
151C24×C11C2411yescharacteristic
152C23×D11C2412yes—
153C22×C4×C11—24no—
154C22×C4×C11—232no—
155C22×C4×C11—24no—
156C22×C4×C11—24no—
157C22×C4×C11—24no—
158C22×C4×C11—24no—
159C22×C4×C11—24no—
160C22×C4×C11—24no—
161C22×C4×C11—28no—
162C22×C4×C11—44no—
163C22×C4×C11C2×D414yes—
164C22×C4×C11C2×D414yes—
165C22×C4×C11C2×D414yes—
166C22×C4×C11C2×D414yes—
167C22×C4×C11C2×D414yes—
168C22×C4×C11C2×D414yes—
169C22×C4×C11#4118yes—
170C22×C4×C11C2414yes—
171C22×C4×C11C2414yes—
172C22×C4×C11C2411yescharacteristic
173C22×C4×C11C2411yescharacteristic
174C22×C4×C11C2411yescharacteristic
175C22×C4×C11C2411yescharacteristic
176C2×C22⋊D11—24no—
177C2×C22⋊D11—24no—
178C2×C22⋊D11—24no—
179C2×C22⋊D11—28no—
180C2×C22⋊D11—28no—
181C2×C22⋊D11—44no—
182C22×Dic11—28no—
183C22×Dic11—28no—
184C22×Dic11—44no—
185C22×Dic11C2414yes—
186C22×Dic11C2412yes—
187C22×Dic11C2412yes—
188C22×Dic11C2412yes—
189C22×Dic11C2414yes—
190#4339—416no—
191C2×D44—22no—
192C2×D44—24no—
193C2×C4×D11—24no—
194C2×C4×D11—28no—
195C2×Dic22—22no—
196C2×Dic22—24no—
197C11×C4⋊C4—24no—
198C11×C4⋊C4—24no—
199C11×C4⋊C4—24no—
200C11×C4⋊C4—24no—
201C11×C22⋊C4—28no—
202C11×C22⋊C4—28no—
203C42×C11—28no—
204C42×C11—28no—
205C22⋊Dic11—28no—
206C22⋊Dic11—24no—
207C22⋊Dic11—24no—
208C22⋊Dic11—24no—
209C22⋊Dic11—24no—
210C22⋊Dic11#4118yescomplemented
211(C2×D11)⋊C4—216no—
212(C2×D11)⋊C4—24no—
213(C2×D11)⋊C4—24no—
214(C2×D11)⋊C4—48no—
215C4⋊Dic11—22no—
216C4⋊Dic11—22no—
217Dic11⋊C4—216no—
218Dic11⋊C4—24no—
219Dic11⋊C4—24no—
220Dic11⋊C4—48no—
221C4×Dic11—24no—
222C4×Dic11—24no—
223C4×Dic11—24no—
224C4×Dic11—28no—
225C2×#525—111no—
226C22×#117D1111yescharacteristic, complemented
227#2504—111no—
228#2503—111no—
229#2502—111no—
230#2501—111no—
231#2500—112no—
232#2499—112no—
233#2498—114no—
234#2412—114no—
235#2395—114no—
236C4×#123—114no—
237#2297—112no—
238#2285—112no—
239C2×C4×C22⋊C4—111no—
240C23×C11—22no—
241C23×C11—22no—
242C23×C11—22no—
243C23×C11—22no—
244C23×C11—28no—
245C23×C11—28no—
246C23×C11—22no—
247C23×C11—22no—
248C23×C11—22no—
249C23×C11—44no—
250C23×C11—416no—
251C23×C11C22×D412yes—
252C23×C11C22×D412yes—
253C23×C11C22×D412yes—
254C23×C11C2×#4114yes—
255C23×C11C2×#4114yes—
256C23×C11C2511yescharacteristic
257C22×D11—22no—
258C22×D11—24no—
259C22×D11—24no—
260C22×D11—24no—
261C2×C4×C11—28no—
262C2×C4×C11—22no—
263C2×C4×C11—22no—
264C2×C4×C11—28no—
265C2×C4×C11—28no—
266C2×C4×C11—28no—
267C2×C4×C11—28no—
268C2×C4×C11—24no—
269C2×C4×C11—24no—
270C2×C4×C11—28no—
271C2×C4×C11—28no—
272C2×C4×C11—48no—
273C2×C4×C11—48no—
274C2×C4×C11#123116yescomplemented
275C2×C4×C11C22×D412yes—
276C2×C4×C11C22×D412yes—
277C2×C4×C11C22×D412yes—
278C2×C4×C11C22×D412yes—
279C2×C4×C11C2×#4114yes—
280C2×C4×C11C2×#4114yes—
281C22⋊D11—48no—
282C22⋊D11—48no—
283C22⋊D11—48no—
284C2×Dic11—24no—
285C2×Dic11—24no—
286C2×Dic11—22no—
287C2×Dic11—22no—
288C2×Dic11—22no—
289C2×Dic11—24no—
290C2×Dic11—24no—
291C2×Dic11—24no—
292C2×Dic11—24no—
293C2×Dic11—24no—
294C2×Dic11—24no—
295C2×Dic11—416no—
296C2×Dic11C2×#4118yes—
297D44—44no—
298C4×D11—48no—
299Dic22—44no—
300C22×#41—111no—
301C24×C4C2×D1111yescharacteristic
302#525—228no—
303C2×#123—112no—
304C2×#123—114no—
305C2×C22⋊Q8—111no—
306C2×C22⋊Q8—111no—
307C2×#121—111no—
308C2×#121—111no—
309C2×#120—112no—
310C2×C4×D4—112no—
311C2×C4×D4—112no—
312C2×#117—28no—
313C2×#117—111no—
314C2×#117C2×D1112yes—
315C2×#117C2×D1112yes—
316C2×#117C2×D1112yes—
317C2×#117C2×D1112yes—
318C22×C4⋊C4C2×D1111yescharacteristic
319C22×C4⋊C4C2×D1111yescharacteristic
320C22×C22⋊C4—112no—
321C22×C22⋊C4C2×D1112yes—
322C22×C42—112no—
323C22×C42C2×D1112yes—
324#400—114no—
325#399—114no—
326#398—114no—
327#397—114no—
328#397—118no—
329#394—118no—
330#391—112no—
331#391—112no—
332#390—112no—
333#390—112no—
334#388—118no—
335#387—118no—
336#386—114no—
337#386—118no—
338#385—114no—
339#384—112no—
340#384—112no—
341#382—112no—
342#382—112no—
343#381—114no—
344#380—118no—
345C4×C4⋊C4—118no—
346C4×C22⋊C4—112no—
347C4×C22⋊C4—112no—
348C4×C22⋊C4—111no—
349C4×C22⋊C4—111no—
350C4×C22⋊C4—112no—
351C4×C22⋊C4—118no—
352C2×#95—112no—
353C22×C11—22no—
354C22×C11—22no—
355C22×C11—22no—
356C22×C11—22no—
357C22×C11—28no—
358C22×C11—28no—
359C22×C11—22no—
360C22×C11—22no—
361C22×C11—22no—
362C22×C11—416no—
363C22×C11—44no—
364C22×C11C2×#12314yes—
365C22×C11#53214yes—
366C22×C11C23×D411yescharacteristic
367C22×C11C22×#4112yes—
368C22×C11C22×#4112yes—
369C22×C11#58512yes—
370C2×D11—42no—
371C2×D11—42no—
372C2×D11—42no—
373C2×D11—48no—
374C4×C11—22no—
375C4×C11—22no—
376C4×C11—44no—
377C4×C11—44no—
378C4×C11C2×#12314yes—
379C4×C11C2×#12314yes—
380Dic11—28no—
381Dic11—42no—
382Dic11—42no—
383Dic11—42no—
384Dic11—44no—
385C25C22×D1111yescharacteristic
386C2×#41—228no—
387C2×#41—224no—
388C22×Q8—111no—
389C22×D4—112no—
390C22×D4—112no—
391C22×D4—112no—
392C22×D4—111no—
393C23×C4—28no—
394C23×C4—114no—
395C23×C4—112no—
396C23×C4C22⋊D1118yes—
397C23×C4C22×D1112yes—
398C23×C4C22×D1111yescharacteristic
399C23×C4C22×D1111yescharacteristic
400C23×C4C22×D1111yescharacteristic
401C23×C4C22×D1111yescharacteristic
402C23×C4C22×D1111yescharacteristic
403C23×C4C22×D1112yes—
404C23×C4C22×D1111yescharacteristic
405#123—2216no—
406#123—228no—
407C22⋊Q8—224no—
408C22⋊Q8—224no—
409#121—224no—
410#121—224no—
411#120—228no—
412C4×D4—228no—
413C4×D4—228no—
414#117—28no—
415#117—28no—
416#117—28no—
417#117—28no—
418#117—224no—
419C2×C4⋊C4—24no—
420C2×C4⋊C4—24no—
421C2×C4⋊C4—111no—
422C2×C4⋊C4—111no—
423C2×C4⋊C4—112no—
424C2×C4⋊C4—112no—
425C2×C4⋊C4—118no—
426C2×C4⋊C4—118no—
427C2×C4⋊C4C22×D1112yes—
428C2×C4⋊C4C22×D1112yes—
429C2×C4⋊C4C22×D1112yes—
430C2×C4⋊C4C22×D1112yes—
431C2×C22⋊C4—28no—
432C2×C22⋊C4—112no—
433C2×C22⋊C4—112no—
434C2×C22⋊C4—114no—
435C2×C22⋊C4—112no—
436C2×C22⋊C4—112no—
437C2×C22⋊C4—112no—
438C2×C22⋊C4—112no—
439C2×C22⋊C4—112no—
440C2×C22⋊C4—118no—
441C2×C22⋊C4—118no—
442C2×C22⋊C4—228no—
443C2×C22⋊C4C22×D1114yes—
444C2×C22⋊C4C22×D1114yes—
445C2×C42—28no—
446C2×C42—112no—
447C2×C42—112no—
448C2×C42—112no—
449C2×C42—114no—
450C2×C42—228no—
451C2×C42C22×D1114yes—
452C2×C42C22×D1114yes—
453#95—114no—
454#95—112no—
455#95—112no—
456#95—118no—
457#95—118no—
458#95—118no—
459#95—118no—
460C2×C11—24no—
461C2×C11—24no—
462C2×C11—42no—
463C2×C11C22×#12311yescharacteristic
464C2×C11C2×#53211yescharacteristic
465C2×C11#344911yescharacteristic
466C2×C11#347514yes—
467D11—82no—
468C24—24no—
469C24—24no—
470C24—42no—
471C24—112no—
472C24C2×C22⋊D1114yes—
473C24C23×D1111yescharacteristic
474C24C23×D1111yescharacteristic
475C24C23×D1111yescharacteristic
476#41—4416no—
477C2×Q8—224no—
478C2×Q8—222no—
479C2×D4—228no—
480C2×D4—228no—
481C2×D4—224no—
482C2×D4—224no—
483C2×D4—224no—
484C2×D4—224no—
485C2×D4—222no—
486C2×D4—444no—
487C22×C4—24no—
488C22×C4—232no—
489C22×C4—24no—
490C22×C4—24no—
491C22×C4—24no—
492C22×C4—24no—
493C22×C4—28no—
494C22×C4—24no—
495C22×C4—24no—
496C22×C4—44no—
497C22×C4—114no—
498C22×C4—114no—
499C22×C4—112no—
500C22×C4—112no—
501C22×C4—112no—
502C22×C4—228no—
503C22×C4—228no—
504C22×C4—228no—
505C22×C4—224no—
506C22×C4—444no—
507C22×C4#433918yes—
508C22×C4C2×C22⋊D1114yes—
509C22×C4C2×C22⋊D1114yes—
510C22×C4C2×C22⋊D1114yes—
511C22×C4C2×C22⋊D1114yes—
512C22×C4C2×C22⋊D1114yes—
513C22×C4C2×C22⋊D1114yes—
514C22×C4C23×D1114yes—
515C22×C4C23×D1114yes—
516C22×C4C23×D1111yescharacteristic
517C22×C4C23×D1111yescharacteristic
518C22×C4C23×D1111yescharacteristic
519C22×C4C23×D1111yescharacteristic
520C4⋊C4—24no—
521C4⋊C4—24no—
522C4⋊C4—24no—
523C4⋊C4—24no—
524C4⋊C4—2216no—
525C4⋊C4—222no—
526C4⋊C4—222no—
527C4⋊C4—224no—
528C4⋊C4—224no—
529C4⋊C4—448no—
530C22⋊C4—28no—
531C22⋊C4—28no—
532C22⋊C4—118no—
533C22⋊C4—2216no—
534C22⋊C4—228no—
535C22⋊C4—224no—
536C22⋊C4—224no—
537C22⋊C4—224no—
538C22⋊C4—224no—
539C22⋊C4—224no—
540C22⋊C4—224no—
541C22⋊C4—448no—
542C42—28no—
543C42—28no—
544C42—224no—
545C42—228no—
546C42—224no—
547C42—224no—
548C11#3481011yescharacteristic, complemented, Sylow
549C23—22no—
550C23—22no—
551C23—22no—
552C23—22no—
553C23—28no—
554C23—28no—
555C23—22no—
556C23—22no—
557C23—22no—
558C23—44no—
559C23—416no—
560C23—224no—
561C23—224no—
562C23—224no—
563C23—222no—
564C23C2×#433914yes—
565C23#41×D1114yes—
566C23C22×C22⋊D1112yes—
567C23C22×C22⋊D1112yes—
568C23C22×C22⋊D1112yes—
569C23C24×D1111yescharacteristic
570Q8—444no—
571D4—448no—
572D4—448no—
573D4—448no—
574D4—444no—
575C2×C4—28no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—28no—
579C2×C4—28no—
580C2×C4—28no—
581C2×C4—28no—
582C2×C4—28no—
583C2×C4—28no—
584C2×C4—24no—
585C2×C4—24no—
586C2×C4—48no—
587C2×C4—48no—
588C2×C4—118no—
589C2×C4—224no—
590C2×C4—224no—
591C2×C4—224no—
592C2×C4—224no—
593C2×C4—224no—
594C2×C4—224no—
595C2×C4—224no—
596C2×C4—224no—
597C2×C4—222no—
598C2×C4—222no—
599C2×C4—222no—
600C2×C4—4416no—
601C2×C4—448no—
602C2×C4#66982116yescomplemented
603C2×C4C2×#433914yes—
604C2×C4C2×#433914yes—
605C2×C4C22×C22⋊D1112yes—
606C2×C4C22×C22⋊D1112yes—
607C2×C4C22×C22⋊D1112yes—
608C2×C4C22×C22⋊D1112yes—
609C22—22no—
610C22—28no—
611C22—28no—
612C22—22no—
613C22—22no—
614C22—22no—
615C22—22no—
616C22—22no—
617C22—22no—
618C22—416no—
619C22—44no—
620C22—442no—
621C22—448no—
622C22—442no—
623C22—442no—
624C22C2×#6698214yes—
625C22#1062336314yes—
626C22C22×#433912yes—
627C22C2×#41×D1112yes—
628C22#1062345312yes—
629C22C23×C22⋊D1111yescharacteristic
630C4—22no—
631C4—22no—
632C4—44no—
633C4—44no—
634C4—228no—
635C4—442no—
636C4—444no—
637C4—442no—
638C4—442no—
639C4C2×#6698214yes—
640C4C2×#6698214yes—
641C2—24no—
642C2—24no—
643C2—42no—
644C2—882no—
645C2C22×#6698211yescharacteristic
646C2C2×#1062336311yescharacteristic
647C2#1308194511yescharacteristic
648C2#1308217014yes—
subgroupG/H
centerC22×C4C23×D11
commutator, socle, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC22×C11×#117C2
prime radicalC2×#10623322C2
hypercenterC22×#117D11
hypocenterC11#34810
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C22×#117

Complements

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

NH ≅ G/Ntype
2. #13073104C2semidirect
3. #13073097C2semidirect
4. #13073090C2semidirect
5. #13073083C2semidirect
6. #13073074C2semidirect
7. #13073065C2semidirect
8. #13073054C2semidirect
9. #13072012C2semidirect
10. #13071873C2semidirect
11. C4×#66982C2semidirect
12. #13071104C2semidirect
13. #13071019C2semidirect
14. C2×C4×C22⋊Dic11C2semidirect
15. C22×C11×#117C2semidirect
49. #10622606C22semidirect
50. #10622605C22semidirect
51. #10622601C22semidirect
52. #10622601C22semidirect
53. #10622595C22semidirect
54. #10622593C22semidirect
55. #10622590C22semidirect
56. #10622590C22semidirect
57. #10622589C22semidirect
58. #10622589C22semidirect
59. #10622587C22semidirect
60. #10622587C22semidirect
65. #10622553C22semidirect
66. C4×(C2×D11)⋊C4C22semidirect
67. #10622546C22semidirect
68. C4×Dic11⋊C4C22semidirect
210. C22⋊Dic11#41semidirect
226. C22×#117D11semidirect
274. C2×C4×C11#123semidirect
548. C11#34810semidirect
602. C2×C4#66982semidirect

Maximal subgroups

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

subgroupindex
C2×#106233222
#130731042
#130730972
#130730902
#130730832
#130730742
#130730652
#130730542
#130720122
#130718732
C4×#669822
#130711042
#130710192
C2×C4×C22⋊Dic112
C22×C11×#1172
#3481011