Finite Group Databasebeta

← #14916769

Subgroups — #14916769

Order 2816.

2134 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66951C211yesmaximal, characteristic
2#13071806C214yesmaximal, complemented
3#13071735C214yesmaximal, complemented
4#13071491C212yesmaximal, complemented
5#13071480C212yesmaximal, complemented
6#13071468C212yesmaximal
7#13071458C212yesmaximal
8#13071396C214yesmaximal, complemented
9#13071394C214yesmaximal, complemented
10#13071234C211yesmaximal, characteristic, complemented
11#13071229C211yesmaximal, characteristic
12#13071213C211yesmaximal, characteristic
13#13071018C211yesmaximal, characteristic, complemented
14#13071011C211yesmaximal, characteristic, complemented
15C11×#2313C211yesmaximal, characteristic, complemented
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×(C2×D11)⋊C4C2211yescharacteristic
18C22×(C2×D11)⋊C4C2211yescharacteristic
19C22×(C2×D11)⋊C4C2211yescharacteristic
20C2×#66979C2212yes—
21C22×C4⋊Dic11C2211yescharacteristic
22C22×Dic11⋊C4C2211yescharacteristic
23C22×C4×Dic11C2211yescharacteristic
24C2×#66951C4116yescomplemented
25C2×#66951C2212yes—
26C2×#66951C2212yes—
27C2×#66951C2212yes—
28C2×#66951C2212yes—
29C2×C22⋊C4×D11C2212yes—
30C2×#66930C2212yes—
31C11×#387C2214yescomplemented
32C11×#387C2214yescomplemented
33C11×#381C2212yes—
34C11×#380C2211yescharacteristic
35C11×#380C2211yescharacteristic
36C4×C11×C22⋊C4C2212yes—
37#10622825C2212yes—
38#10622825C2211yescharacteristic
39#10622825C2211yescharacteristic
40#10622603C2214yes—
41#10622602C2214yes—
42#10622598C2214yescomplemented
43#10622598C2214yescomplemented
44#10622590C2212yescomplemented
45#10622589C2212yescomplemented
46C4⋊C4×Dic11C2212yescomplemented
47C4⋊C4×Dic11C2212yescomplemented
48#10622568C2212yes—
49#10622556C2212yes—
50#10622555C2212yes—
51#10622555C2212yes—
52C22⋊C4×Dic11C2212yes—
53C22⋊C4×Dic11C2212yes—
54#10622553C2214yes—
55C4×(C2×D11)⋊C4C2214yes—
56C4×C4⋊Dic11C2214yescomplemented
57#10622541C2214yescomplemented
58#10622283C2214yes—
59#10622283C2214yes—
60#10622283C2214yes—
61#10622282C2214yes—
62#10622281C2214yes—
63#10622281C2214yes—
64#10622281C2214yes—
65#10622279C2214yes—
66#10622268C2214yescomplemented
67#10622267C2214yescomplemented
68#10622267C2214yescomplemented
69#10622265C2214yescomplemented
70#10622264C2212yescomplemented
71#10622263C2212yescomplemented
72#10622262C2212yescomplemented
73#10622262C2214yescomplemented
74#10622261C2212yescomplemented
75#10622260C2214yescomplemented
76C24×D11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C23×Dic11C2311yescharacteristic
81C23×Dic11C2311yescharacteristic
82C23×Dic11C2311yescharacteristic
83C22×C4×D11C2314yes—
84C2×C11×C4⋊C4C2×C418yescomplemented
85C2×C11×C4⋊C4C2312yes—
86C2×C11×C4⋊C4C2312yes—
87C2×C11×C4⋊C4C2312yes—
88C2×C11×C4⋊C4C2312yes—
89C2×C11×C22⋊C4C2312yes—
90C2×C11×C22⋊C4C2312yes—
91C2×C42×C11C2314yes—
92C2×C22⋊Dic11C2312yes—
93C2×C22⋊Dic11C2312yes—
94C2×(C2×D11)⋊C4C2×C418yes—
95C2×(C2×D11)⋊C4C2×C418yes—
96C2×(C2×D11)⋊C4C2×C418yes—
97C2×(C2×D11)⋊C4C2314yes—
98C2×(C2×D11)⋊C4C2314yes—
99C2×(C2×D11)⋊C4C2314yes—
100C2×(C2×D11)⋊C4C2312yes—
101C2×(C2×D11)⋊C4C2312yes—
102C2×(C2×D11)⋊C4C2312yes—
103C2×(C2×D11)⋊C4C2312yes—
104C2×(C2×D11)⋊C4C2312yes—
105C2×(C2×D11)⋊C4C2312yes—
106#66979—44no—
107C2×C4⋊Dic11C2×C418yescomplemented
108C2×C4⋊Dic11C2314yes—
109C2×C4⋊Dic11C2312yes—
110C2×C4⋊Dic11C2314yes—
111C2×C4⋊Dic11C2312yes—
112C2×C4⋊Dic11C2312yes—
113C2×C4⋊Dic11C2312yes—
114C2×Dic11⋊C4C2×C418yescomplemented
115C2×Dic11⋊C4C2314yes—
116C2×Dic11⋊C4C2314yes—
117C2×Dic11⋊C4C2314yes—
118C2×Dic11⋊C4C2312yes—
119C2×Dic11⋊C4C2312yes—
120C2×C4×Dic11C2×C418yescomplemented
121C2×C4×Dic11C2314yes—
122C2×C4×Dic11C2314yes—
123C2×C4×Dic11C2314yes—
124C2×C4×Dic11C2314yes—
125C2×C4×Dic11C2311yescharacteristic
126C2×C4×Dic11C2311yescharacteristic
127C2×C4×Dic11C2311yescharacteristic
128C2×C4×Dic11C2311yescharacteristic
129#66951C2×C4116yescomplemented
130#66951C2×C4116yescomplemented
131#66951C2×C4116yescomplemented
132#66951C2×C4116yescomplemented
133C22⋊C4×D11—44no—
134#66930—44no—
135C11×#95C2314yes—
136C11×#95C2312yes—
137C11×#95C2312yes—
138C11×#95C2314yes—
139C11×#95C2314yes—
140C11⋊#95C2314yes—
141C11⋊#95C2314yes—
142C11⋊#95C2312yes—
143C11⋊#95C2312yes—
144C11⋊#95C2314yes—
145C11⋊#95C2314yes—
146C11⋊#95C2314yes—
147C11⋊#95C2314yes—
148C11⋊#95C2314yes—
149#34381—111nomaximal, Sylow
150C24×C11C2411yescharacteristic
151C23×D11—22no—
152C23×D11—22no—
153C23×D11—42no—
154C23×D11—42no—
155C23×D11C22×C414yes—
156C23×D11C2412yes—
157C22×C4×C11—22no—
158C22×C4×C11—22no—
159C22×C4×C11—42no—
160C22×C4×C11—42no—
161C22×C4×C11C22×C414yes—
162C22×C4×C11C22×C414yes—
163C22×C4×C11C22×C414yes—
164C22×C4×C11C2414yes—
165C22×C4×C11C2414yes—
166C22×C4×C11C2411yescharacteristic
167C22×C4×C11C2411yescharacteristic
168C22×C4×C11C2412yes—
169C22×C4×C11C2412yes—
170C22×Dic11—22no—
171C22×Dic11—22no—
172C22×Dic11—42no—
173C22×Dic11—42no—
174C22×Dic11C22×C414yes—
175C22×Dic11C22×C414yes—
176C22×Dic11C22×C414yes—
177C22×Dic11C2414yes—
178C22×Dic11C2414yes—
179C22×Dic11C2411yescharacteristic
180C22×Dic11C2411yescharacteristic
181C22×Dic11C2411yescharacteristic
182C22×Dic11C2412yes—
183C22×Dic11C2411yescharacteristic
184C2×C4×D11—44no—
185C2×C4×D11—44no—
186C2×C4×D11—44no—
187C11×C4⋊C4—42no—
188C11×C4⋊C4—42no—
189C11×C4⋊C4C22×C418yes—
190C11×C4⋊C4C22×C418yes—
191C11×C22⋊C4—24no—
192C11×C22⋊C4—24no—
193C42×C11—44no—
194C22⋊Dic11—24no—
195C22⋊Dic11—24no—
196(C2×D11)⋊C4—44no—
197(C2×D11)⋊C4—44no—
198(C2×D11)⋊C4—44no—
199(C2×D11)⋊C4C22×C418yes—
200(C2×D11)⋊C4C22×C418yes—
201(C2×D11)⋊C4C22×C418yes—
202(C2×D11)⋊C4C22×C418yes—
203(C2×D11)⋊C4C22×C418yes—
204(C2×D11)⋊C4C22×C418yes—
205C4⋊Dic11—44no—
206C4⋊Dic11—42no—
207C4⋊Dic11—42no—
208C4⋊Dic11—44no—
209C4⋊Dic11C22×C418yes—
210C4⋊Dic11C22×C418yes—
211Dic11⋊C4—44no—
212Dic11⋊C4—44no—
213Dic11⋊C4—44no—
214Dic11⋊C4C22×C418yes—
215Dic11⋊C4C22×C418yes—
216C4×Dic11—44no—
217C4×Dic11—44no—
218C4×Dic11—44no—
219C4×Dic11—44no—
220C4×Dic11C22×C414yes—
221C4×Dic11C22×C414yes—
222C4×Dic11C22×C414yes—
223C4×Dic11C22×C414yes—
224C22×#126—111no—
225#2383—114no—
226#2373—114no—
227#2345—112no—
228#2344—112no—
229#2342—112no—
230#2342—112no—
231#2334—114no—
232#2334—114no—
233#2316—111no—
234#2315—111no—
235#2313D1111yescharacteristic, complemented
236#2312—111no—
237#2285—111no—
238#2283—111no—
239C23×C11—22no—
240C23×C11—22no—
241C23×C11C23×C412yes—
242C23×C11H(5,𝔽2)12yes—
243C23×C112−1+412yes—
244C23×C11C2511yescharacteristic
245C22×D11—22no—
246C22×D11—22no—
247C22×D11—24no—
248C22×D11—24no—
249C22×D11—28no—
250C22×D11—44no—
251C22×D11—44no—
252C22×D11—84no—
253C22×D11—84no—
254C22×D11C23×C414yes—
255C2×C4×C11—28no—
256C2×C4×C11—22no—
257C2×C4×C11—22no—
258C2×C4×C11—24no—
259C2×C4×C11—22no—
260C2×C4×C11—22no—
261C2×C4×C11—24no—
262C2×C4×C11—24no—
263C2×C4×C11—24no—
264C2×C4×C11—24no—
265C2×C4×C11—24no—
266C2×C4×C11—24no—
267C2×C4×C11—44no—
268C2×C4×C11—44no—
269C2×C4×C11C23×C412yes—
270C2×C4×C11C23×C412yes—
271C2×C4×C11C23×C414yes—
272C2×C4×C11C23×C414yes—
273C2×Dic11—28no—
274C2×Dic11—21no—
275C2×Dic11—21no—
276C2×Dic11—21no—
277C2×Dic11—21no—
278C2×Dic11—22no—
279C2×Dic11—24no—
280C2×Dic11—22no—
281C2×Dic11—24no—
282C2×Dic11—24no—
283C2×Dic11—24no—
284C2×Dic11—24no—
285C2×Dic11—24no—
286C2×Dic11—24no—
287C2×Dic11—44no—
288C2×Dic11—44no—
289C2×Dic11C23×C412yes—
290C2×Dic11C23×C412yes—
291C2×Dic11C23×C412yes—
292C2×Dic11C23×C412yes—
293C2×Dic11C23×C414yes—
294C4×D11—88no—
295C2×#126—112no—
296C2×#126—112no—
297C2×#126—112no—
298C2×#126—112no—
299C2×#126—1116no—
300C2×#117—112no—
301C2×#117—112no—
302C22×C4⋊C4—111no—
303C22×C4⋊C4—111no—
304C22×C4⋊C4C2×D1111yescharacteristic
305C22×C22⋊C4—111no—
306C22×C22⋊C4—111no—
307C22×C22⋊C4—111no—
308C22×C22⋊C4—112no—
309C22×C42—111no—
310#389—114no—
311#389—114no—
312#389—114no—
313#389—114no—
314#388—114no—
315#388—114no—
316#388—114no—
317#388—114no—
318#388—114no—
319#388—114no—
320#387—114no—
321#387—114no—
322#387—114no—
323#387—114no—
324#387C2×D1114yescomplemented
325#387C2×D1114yescomplemented
326#385—114no—
327#385—114no—
328#385—114no—
329#385—114no—
330#384—112no—
331#383—112no—
332#382—112no—
333#382—112no—
334#381—112no—
335#381C2×D1112yes—
336#380—111no—
337#380—111no—
338#380—112no—
339#380—112no—
340#380—112no—
341#380C2×D1111yescharacteristic
342#380C2×D1111yescharacteristic
343#379—112no—
344C4×C4⋊C4—112no—
345C4×C4⋊C4—112no—
346C4×C4⋊C4—114no—
347C4×C4⋊C4—112no—
348C4×C4⋊C4—114no—
349C4×C22⋊C4—112no—
350C4×C22⋊C4—112no—
351C4×C22⋊C4—114no—
352C4×C22⋊C4—114no—
353C4×C22⋊C4C2×D1112yes—
354#376—112no—
355C22×C11—22no—
356C22×C11—22no—
357C22×C11—24no—
358C22×C11—24no—
359C22×C11#52014yes—
360C22×C11C24×C411yescharacteristic
361C22×C11C2×H(5,𝔽2)11yescharacteristic
362C22×C11C2×2−1+411yescharacteristic
363C22×C11#58512yes—
364C22×C11#58512yes—
365C2×D11—24no—
366C2×D11—24no—
367C2×D11—24no—
368C2×D11—44no—
369C2×D11—44no—
370C2×D11—88no—
371C4×C11—24no—
372C4×C11—24no—
373C4×C11—22no—
374C4×C11—22no—
375C4×C11—44no—
376C4×C11—44no—
377Dic11—22no—
378Dic11—22no—
379Dic11—22no—
380Dic11—24no—
381Dic11—22no—
382Dic11—44no—
383Dic11—44no—
384C25—111no—
385C23×C4—111no—
386C23×C4—111no—
387C23×C4—111no—
388C23×C4—114no—
389C23×C4C22×D1111yescharacteristic
390C23×C4C22×D1111yescharacteristic
391C23×C4C22×D1111yescharacteristic
392#126—1116no—
393#126—1116no—
394#126—1116no—
395#126—1116no—
396#117—444no—
397#117—444no—
398C2×C4⋊C4—118no—
399C2×C4⋊C4—118no—
400C2×C4⋊C4—112no—
401C2×C4⋊C4—112no—
402C2×C4⋊C4—112no—
403C2×C4⋊C4—112no—
404C2×C4⋊C4—114no—
405C2×C4⋊C4—114no—
406C2×C4⋊C4—112no—
407C2×C4⋊C4—114no—
408C2×C4⋊C4—112no—
409C2×C4⋊C4—114no—
410C2×C4⋊C4—114no—
411C2×C4⋊C4C4×D1118yescomplemented
412C2×C4⋊C4C22×D1112yes—
413C2×C4⋊C4C22×D1112yes—
414C2×C4⋊C4C22×D1112yes—
415C2×C4⋊C4C22×D1112yes—
416C2×C22⋊C4—118no—
417C2×C22⋊C4—118no—
418C2×C22⋊C4—118no—
419C2×C22⋊C4—112no—
420C2×C22⋊C4—112no—
421C2×C22⋊C4—112no—
422C2×C22⋊C4—112no—
423C2×C22⋊C4—112no—
424C2×C22⋊C4—112no—
425C2×C22⋊C4—112no—
426C2×C22⋊C4—112no—
427C2×C22⋊C4—114no—
428C2×C22⋊C4—114no—
429C2×C22⋊C4—114no—
430C2×C22⋊C4—444no—
431C2×C22⋊C4C22×D1112yes—
432C2×C22⋊C4C22×D1112yes—
433C2×C42—118no—
434C2×C42—111no—
435C2×C42—111no—
436C2×C42—111no—
437C2×C42—111no—
438C2×C42—114no—
439C2×C42—114no—
440C2×C42—114no—
441C2×C42—114no—
442C2×C42C22×D1114yes—
443#95—114no—
444#95—112no—
445#95—114no—
446#95—114no—
447#95—114no—
448#95—114no—
449#95—112no—
450#95—114no—
451#95—114no—
452#95C22×D1112yes—
453#95C22×D1114yes—
454#95C22×D1114yes—
455#95C22×D1112yes—
456#95C22×D1114yes—
457C2×C11—24no—
458C2×C11C2×#52011yescharacteristic
459C2×C11#342811yescharacteristic
460C2×C11#342811yescharacteristic
461C2×C11#356012yes—
462C2×C11#356412yes—
463D11—44no—
464C24—112no—
465C24—114no—
466C24—222no—
467C24—222no—
468C24—442no—
469C24—442no—
470C24C23×D1111yescharacteristic
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—42no—
474C22×C4—42no—
475C22×C4—114no—
476C22×C4—111no—
477C22×C4—111no—
478C22×C4—111no—
479C22×C4—111no—
480C22×C4—112no—
481C22×C4—114no—
482C22×C4—114no—
483C22×C4—114no—
484C22×C4—114no—
485C22×C4—222no—
486C22×C4—222no—
487C22×C4—444no—
488C22×C4—444no—
489C22×C4—444no—
490C22×C4—442no—
491C22×C4—442no—
492C22×C4C2×C4×D1114yes—
493C22×C4C2×C4×D1114yes—
494C22×C4C2×C4×D1114yes—
495C22×C4C23×D1114yes—
496C22×C4C23×D1114yes—
497C22×C4C23×D1111yescharacteristic
498C22×C4C23×D1111yescharacteristic
499C22×C4C23×D1112yes—
500C22×C4C23×D1112yes—
501C4⋊C4—42no—
502C4⋊C4—42no—
503C4⋊C4—118no—
504C4⋊C4—118no—
505C4⋊C4—118no—
506C4⋊C4—118no—
507C4⋊C4—444no—
508C4⋊C4—444no—
509C4⋊C4—444no—
510C4⋊C4—444no—
511C4⋊C4—444no—
512C4⋊C4—442no—
513C4⋊C4—442no—
514C4⋊C4C2×C4×D1118yes—
515C4⋊C4C2×C4×D1118yes—
516C22⋊C4—24no—
517C22⋊C4—24no—
518C22⋊C4—118no—
519C22⋊C4—118no—
520C22⋊C4—118no—
521C22⋊C4—118no—
522C22⋊C4—118no—
523C22⋊C4—118no—
524C22⋊C4—224no—
525C22⋊C4—224no—
526C22⋊C4—444no—
527C22⋊C4—444no—
528C22⋊C4—444no—
529C42—44no—
530C42—114no—
531C42—114no—
532C42—114no—
533C42—114no—
534C42—444no—
535C42—444no—
536C42—444no—
537C42—444no—
538C11#3438111yescharacteristic, complemented, Sylow
539C23—22no—
540C23—22no—
541C23—114no—
542C23—222no—
543C23—222no—
544C23—224no—
545C23—224no—
546C23—228no—
547C23—444no—
548C23—444no—
549C23—884no—
550C23—884no—
551C23C22×C4×D1112yes—
552C23#6704212yes—
553C23#6704312yes—
554C23C24×D1111yescharacteristic
555C2×C4—28no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—24no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—24no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—44no—
568C2×C4—44no—
569C2×C4—112no—
570C2×C4—112no—
571C2×C4—112no—
572C2×C4—112no—
573C2×C4—114no—
574C2×C4—228no—
575C2×C4—221no—
576C2×C4—221no—
577C2×C4—221no—
578C2×C4—221no—
579C2×C4—222no—
580C2×C4—224no—
581C2×C4—222no—
582C2×C4—224no—
583C2×C4—224no—
584C2×C4—224no—
585C2×C4—224no—
586C2×C4—224no—
587C2×C4—224no—
588C2×C4—444no—
589C2×C4—444no—
590C2×C4—888no—
591C2×C4C22×C4×D1112yes—
592C2×C4C22×C4×D1112yes—
593C2×C4C22×C4×D1114yes—
594C2×C4C22×C4×D1114yes—
595C22—24no—
596C22—24no—
597C22—22no—
598C22—22no—
599C22—224no—
600C22—224no—
601C22—224no—
602C22—444no—
603C22—444no—
604C22—888no—
605C22#1062305414yes—
606C22C23×C4×D1111yescharacteristic
607C22C2×#6704211yescharacteristic
608C22C2×#6704311yescharacteristic
609C22#1062345512yes—
610C22#1062345712yes—
611C4—24no—
612C4—24no—
613C4—22no—
614C4—22no—
615C4—44no—
616C4—44no—
617C4—222no—
618C4—222no—
619C4—222no—
620C4—222no—
621C4—224no—
622C4—444no—
623C4—444no—
624C2—24no—
625C2—444no—
626C2C2×#1062305411yescharacteristic
627C2#1308181411yescharacteristic
628C2#1308181811yescharacteristic
629C2#1308317312yes—
630C2#1308324512yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2313C2
socle, cosocleC23×C11C25
prime radicalC24×D11C23
hypercenter#2313D11
hypocenterC11#34381
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2313

Complements

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

NH ≅ G/Ntype
2. #13071806C2semidirect
3. #13071735C2semidirect
4. #13071491C2semidirect
5. #13071480C2semidirect
8. #13071396C2semidirect
9. #13071394C2semidirect
10. #13071234C2semidirect
13. #13071018C2semidirect
14. #13071011C2semidirect
15. C11×#2313C2semidirect
24. C2×#66951C4semidirect
31. C11×#387C22semidirect
32. C11×#387C22semidirect
42. #10622598C22semidirect
43. #10622598C22semidirect
44. #10622590C22semidirect
45. #10622589C22semidirect
46. C4⋊C4×Dic11C22semidirect
47. C4⋊C4×Dic11C22semidirect
56. C4×C4⋊Dic11C22semidirect
57. #10622541C22semidirect
66. #10622268C22semidirect
67. #10622267C22semidirect
68. #10622267C22semidirect
69. #10622265C22semidirect
70. #10622264C22semidirect
71. #10622263C22semidirect
72. #10622262C22semidirect
73. #10622262C22semidirect
74. #10622261C22semidirect
75. #10622260C22semidirect
84. C2×C11×C4⋊C4C2×C4semidirect
107. C2×C4⋊Dic11C2×C4semidirect
114. C2×Dic11⋊C4C2×C4semidirect
120. C2×C4×Dic11C2×C4semidirect
129. #66951C2×C4semidirect
130. #66951C2×C4semidirect
131. #66951C2×C4semidirect
132. #66951C2×C4semidirect
235. #2313D11semidirect
324. #387C2×D11semidirect
325. #387C2×D11semidirect
411. C2×C4⋊C4C4×D11semidirect
538. C11#34381semidirect

Maximal subgroups

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

subgroupindex
C22×#669512
#130718062
#130717352
#130714912
#130714802
#130714682
#130714582
#130713962
#130713942
#130712342
#130712292
#130712132
#130710182
#130710112
C11×#23132
#3438111