Finite Group Databasebeta

← #14914158

Subgroups — #14914158

Order 2816.

3054 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×#10623363C211yesmaximal, characteristic
2C2×#10623358C211yesmaximal, characteristic, complemented
3C2×#10623035C211yesmaximal, characteristic, complemented
4#13071664C218yesmaximal, complemented
5#13071547C214yesmaximal, complemented
6#13071538C214yesmaximal, complemented
7#13071340C212yesmaximal, complemented
8#13071334C212yesmaximal, complemented
9#13071204C211yesmaximal, characteristic, complemented
10#13071163C212yesmaximal, complemented
11#13071159C212yesmaximal, complemented
12C2×#10622590C211yesmaximal, characteristic, complemented
13#117×Dic11C211yesmaximal, characteristic, complemented
14C11×#2311C211yesmaximal, characteristic, complemented
15C22×C11×#41C2211yescharacteristic
16C22×#4339C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19#10623363C4116yescomplemented
20#10623358—28no—
21C2×#67000C2211yescharacteristic
22C2×Q8×Dic11C2212yes—
23C2×#66997C2211yescharacteristic
24C2×#66993C2211yescharacteristic
25C2×#66992C2214yes—
26C2×#66989C2211yescharacteristic
27C2×D4×Dic11C2214yes—
28C2×D4×Dic11C2212yes—
29C2×C4×C22⋊D11C2214yes—
30C2×C4×C22⋊D11C2214yes—
31C2×#66979C2212yes—
32C2×#66979C2211yescharacteristic
33C22×C4⋊Dic11C2211yescharacteristic
34C22×C4⋊Dic11C2212yes—
35C22×C4×Dic11C2211yescharacteristic
36#10623035—28no—
37C2×#66946C2212yes—
38C2×#66945C2212yes—
39C2×C4⋊C4×D11C2212yes—
40C2×#66940C2212yes—
41C11×#391C2212yes—
42C11×#390C2212yes—
43C11×#386C2214yes—
44C11×#380C2214yes—
45C2×C11⋊#95C2214yes—
46#10622600C2214yes—
47#10622590C2212yes—
48#10622590C2214yes—
49#10622590C2212yes—
50C4⋊C4×Dic11C2212yes—
51C4⋊C4×Dic11C2212yes—
52#10622571C2214yes—
53#10622571C2218yes—
54#10622569C2218yes—
55#10622557C2218yes—
56C22⋊C4×Dic11C2214yes—
57C22⋊C4×Dic11C2218yes—
58#10622552C2212yes—
59#10622545C2212yes—
60C42×Dic11C2212yes—
61#10622542C2212yes—
62#10622283C2218yes—
63#10622279C2218yes—
64#10622268C2218yes—
65#10622265C2218yes—
66C2×C11×#41—24no—
67C2×C11×#41—24no—
68C2×C11×#41C2×C418yescomplemented
69C22×Q8×C11C2311yescharacteristic
70C22×D4×C11C2311yescharacteristic
71C22×D4×C11C2312yes—
72C23×C4×C11C2312yes—
73C23×C4×C11C2312yes—
74C23×C4×C11C2311yescharacteristic
75C22×C22⋊D11C2312yes—
76C22×C22⋊D11C2314yes—
77C23×Dic11C2314yes—
78C23×Dic11C2312yes—
79C23×Dic11C2312yes—
80C2×#4339—24no—
81C2×#4339—24no—
82C2×#4339C2×C418yescomplemented
83C22×D44C2311yescharacteristic
84C22×C4×D11C2312yes—
85C22×C4×D11C2314yes—
86C22×Dic22C2311yescharacteristic
87C11×#117—24no—
88C2×C11×C4⋊C4—24no—
89C2×C11×C4⋊C4C2312yes—
90C2×C11×C4⋊C4C2312yes—
91C2×C11×C4⋊C4C2312yes—
92C2×C11×C22⋊C4C2312yes—
93C2×C11×C22⋊C4C2318yes—
94C2×C42×C11C2312yes—
95C2×C22⋊Dic11C2314yes—
96C2×C22⋊Dic11C2314yes—
97C2×C22⋊Dic11C2312yes—
98#67000C2×C418yescomplemented
99Q8×Dic11—28no—
100#66997C2×C418yescomplemented
101#66993C2×C418yescomplemented
102#66992C2×C4132yescomplemented
103#66989C2×C418yescomplemented
104D4×Dic11—216no—
105D4×Dic11—28no—
106C4×C22⋊D11—216no—
107C4×C22⋊D11C2×C4132yescomplemented
108C2×(C2×D11)⋊C4C2314yes—
109C2×(C2×D11)⋊C4C2318yes—
110C2×(C2×D11)⋊C4C2314yes—
111#66979—28no—
112#66979D418yescomplemented
113C2×C4⋊Dic11—24no—
114C2×C4⋊Dic11—28no—
115C2×C4⋊Dic11C2314yes—
116C2×C4⋊Dic11C2312yes—
117C2×C4⋊Dic11C2312yes—
118C2×C4⋊Dic11C2311yescharacteristic
119C2×C4⋊Dic11C2311yescharacteristic
120C2×Dic11⋊C4C2314yes—
121C2×Dic11⋊C4C2314yes—
122C2×C4×Dic11C2×C418yescomplemented
123C2×C4×Dic11C2314yes—
124C2×C4×Dic11C2314yes—
125C2×C4×Dic11C2314yes—
126C2×C4×Dic11C2314yes—
127C2×C4×Dic11C2311yescharacteristic
128C2×C4×Dic11C2311yescharacteristic
129C2×C4×Dic11C2312yes—
130C2×C4×Dic11C2312yes—
131#66946—28no—
132#66945—28no—
133C4⋊C4×D11—28no—
134#66940—28no—
135C11×#95C2318yes—
136C11⋊#95C2314yes—
137C11⋊#95C2318yes—
138C11⋊#95C2318yes—
139C11⋊#95C2314yes—
140C11⋊#95C2318yes—
141#34208—111nomaximal, Sylow
142C24×C11C2412yes—
143C24×C11C2411yescharacteristic
144C23×D11C2412yes—
145C11×#41—232no—
146C2×Q8×C11—22no—
147C2×Q8×C11—22no—
148C2×Q8×C11C22×C414yes—
149C2×D4×C11—24no—
150C2×D4×C11—24no—
151C2×D4×C11—22no—
152C2×D4×C11—22no—
153C2×D4×C11C22×C414yes—
154C2×D4×C11C22×C418yes—
155C22×C4×C11—24no—
156C22×C4×C11—24no—
157C22×C4×C11—24no—
158C22×C4×C11—44no—
159C22×C4×C11C22×C418yes—
160C22×C4×C11C22×C414yes—
161C22×C4×C11C2×D414yes—
162C22×C4×C11#4114yes—
163C22×C4×C11C2414yes—
164C22×C4×C11C2414yes—
165C22×C4×C11C2412yes—
166C22×C4×C11C2411yescharacteristic
167C22×C4×C11C2411yescharacteristic
168C2×C22⋊D11—24no—
169C2×C22⋊D11—24no—
170C2×C22⋊D11—44no—
171C2×C22⋊D11—44no—
172C2×C22⋊D11C22×C418yes—
173C2×C22⋊D11C22×C4116yes—
174C22×Dic11—28no—
175C22×Dic11—24no—
176C22×Dic11—42no—
177C22×Dic11—42no—
178C22×Dic11—44no—
179C22×Dic11—48no—
180C22×Dic11C22×C418yes—
181C22×Dic11C2414yes—
182C22×Dic11C2412yes—
183C22×Dic11C2412yes—
184C22×Dic11C2412yes—
185C22×Dic11C2412yes—
186C22×Dic11C2412yes—
187#4339—232no—
188C2×D44—22no—
189C2×D44—22no—
190C2×D44C22×C414yes—
191C2×C4×D11—28no—
192C2×C4×D11—24no—
193C2×C4×D11—24no—
194C2×C4×D11—48no—
195C2×C4×D11C22×C418yes—
196C2×Dic22—22no—
197C2×Dic22—22no—
198C2×Dic22C22×C414yes—
199C11×C4⋊C4—24no—
200C11×C4⋊C4—24no—
201C11×C4⋊C4—24no—
202C11×C22⋊C4—24no—
203C11×C22⋊C4—48no—
204C42×C11—24no—
205C22⋊Dic11—28no—
206C22⋊Dic11C22×C4116yes—
207C22⋊Dic11C2×D418yes—
208(C2×D11)⋊C4—28no—
209(C2×D11)⋊C4—48no—
210(C2×D11)⋊C4C22×C4116yes—
211C4⋊Dic11—28no—
212C4⋊Dic11—24no—
213C4⋊Dic11—24no—
214C4⋊Dic11C2×D414yes—
215C4⋊Dic11C2×D414yes—
216Dic11⋊C4—28no—
217Dic11⋊C4C22×C4116yes—
218C4×Dic11—28no—
219C4×Dic11—28no—
220C4×Dic11—44no—
221C4×Dic11—44no—
222C4×Dic11C22×C418yes—
223C4×Dic11C22×C414yes—
224C4×Dic11C22×C414yes—
225C4×Dic11C2×D418yes—
226C2×#532—111no—
227C2×#520—111no—
228C2×#520—111no—
229#2364—118no—
230#2352—114no—
231#2352—114no—
232#2328—112no—
233#2327—112no—
234#2311—111no—
235#2311D1111yescharacteristic, complemented
236C4×#124—112no—
237C4×#124—112no—
238C2×#382—111no—
239C4×#117—111no—
240C23×C11—22no—
241C23×C11—22no—
242C23×C11—22no—
243C23×C11—22no—
244C23×C11—24no—
245C23×C11—24no—
246C23×C11C23×C414yes—
247C23×C11C23×C412yes—
248C23×C11C22×D412yes—
249C23×C11C2×#4112yes—
250C23×C11C2511yescharacteristic
251C22×D11—22no—
252C22×D11—22no—
253C22×D11—24no—
254C22×D11—24no—
255C22×D11C23×C414yes—
256Q8×C11—28no—
257D4×C11—216no—
258D4×C11—28no—
259C2×C4×C11—22no—
260C2×C4×C11—22no—
261C2×C4×C11—216no—
262C2×C4×C11—24no—
263C2×C4×C11—24no—
264C2×C4×C11—24no—
265C2×C4×C11—24no—
266C2×C4×C11—28no—
267C2×C4×C11—84no—
268C2×C4×C11C4×D4116yes—
269C2×C4×C11C23×C414yes—
270C2×C4×C11C23×C412yes—
271C2×C4×C11C23×C412yes—
272C2×C4×C11C22×D412yes—
273C2×C4×C11C22×D412yes—
274C2×C4×C11C2×#4112yes—
275C2×C4×C11C2×#4112yes—
276C22⋊D11—216no—
277C22⋊D11—416no—
278C2×Dic11—22no—
279C2×Dic11—22no—
280C2×Dic11—22no—
281C2×Dic11—22no—
282C2×Dic11—24no—
283C2×Dic11—24no—
284C2×Dic11—22no—
285C2×Dic11—22no—
286C2×Dic11—24no—
287C2×Dic11—28no—
288C2×Dic11—48no—
289C2×Dic11—88no—
290C2×Dic11—84no—
291C2×Dic11C23×C414yes—
292C2×Dic11C23×C414yes—
293C2×Dic11C23×C414yes—
294C2×Dic11C22×D414yes—
295C2×Dic11C22×D414yes—
296D44—28no—
297C4×D11—216no—
298C4×D11—88no—
299Dic22—28no—
300C22×#41—111no—
301C22×#41C2×D1111yescharacteristic
302#532—1116no—
303C2×C4⋊Q8—111no—
304C2×#127—111no—
305C2×#124—111no—
306C2×#124—111no—
307C2×#121—114no—
308#520—228no—
309#520—228no—
310C2×C4×Q8—112no—
311C2×C4×Q8—112no—
312C2×C4×D4—114no—
313C2×C4×D4—112no—
314C2×C4×D4—114no—
315C2×C4×D4—114no—
316C2×C4×D4—112no—
317C2×#117—111no—
318C2×#117—112no—
319C2×#117—112no—
320C2×#117C2×D1111yescharacteristic
321C22×C4⋊C4—111no—
322C22×C4⋊C4—112no—
323C22×C4⋊C4—112no—
324C22×C4⋊C4C2×D1111yescharacteristic
325C22×C42—111no—
326#391—112no—
327#391C2×D1112yes—
328#390—112no—
329#390C2×D1112yes—
330#388—118no—
331#388—118no—
332#387—118no—
333#387—118no—
334#386—114no—
335#386—118no—
336#386—118no—
337#386C2×D1114yes—
338#382—112no—
339#382—114no—
340#382—112no—
341#380—114no—
342#380C2×D1114yes—
343C4×C4⋊C4—112no—
344C4×C4⋊C4—112no—
345C4×C22⋊C4—118no—
346C4×C22⋊C4—114no—
347C4×C22⋊C4—118no—
348#376—112no—
349C2×#95—114no—
350C43—112no—
351C22×C11—24no—
352C22×C11—22no—
353C22×C11—22no—
354C22×C11—24no—
355C22×C11—24no—
356C22×C11—28no—
357C22×C11—42no—
358C22×C11—42no—
359C22×C11—44no—
360C22×C11C2×C4×D414yes—
361C22×C11C24×C411yescharacteristic
362C22×C11C23×D411yescharacteristic
363C22×C11C22×#4111yescharacteristic
364C22×C11#58512yes—
365C22×C11#58512yes—
366C2×D11—24no—
367C2×D11—28no—
368C2×D11—42no—
369C2×D11—42no—
370C2×D11—44no—
371C4×C11—24no—
372C4×C11—44no—
373C4×C11—44no—
374C4×C11C2×C4×D414yes—
375C4×C11C2×C4×D414yes—
376Dic11—24no—
377Dic11—24no—
378Dic11—24no—
379Dic11—24no—
380Dic11—24no—
381Dic11—44no—
382C2×#41—24no—
383C2×#41—24no—
384C2×#41—118no—
385C2×#41—224no—
386C2×#41—224no—
387C2×#41C4×D1118yescomplemented
388C22×Q8—111no—
389C22×Q8C22×D1111yescharacteristic
390C22×D4—112no—
391C22×D4—114no—
392C22×D4—111no—
393C22×D4C22×D1112yes—
394C22×D4C22×D1111yescharacteristic
395C23×C4—112no—
396C23×C4—112no—
397C23×C4—112no—
398C23×C4—114no—
399C23×C4—114no—
400C23×C4C22×D1112yes—
401C23×C4C22×D1112yes—
402C23×C4C22×D1111yescharacteristic
403C4⋊Q8—118no—
404#127—118no—
405#124—118no—
406#124—118no—
407#121—1132no—
408C4×Q8—228no—
409C4×Q8—228no—
410C4×D4—1132no—
411C4×D4—228no—
412C4×D4—228no—
413C4×D4—2216no—
414C4×D4—2216no—
415#117—24no—
416#117—118no—
417#117—228no—
418#117—228no—
419C2×C4⋊C4—24no—
420C2×C4⋊C4—111no—
421C2×C4⋊C4—111no—
422C2×C4⋊C4—114no—
423C2×C4⋊C4—112no—
424C2×C4⋊C4—112no—
425C2×C4⋊C4—114no—
426C2×C4⋊C4—114no—
427C2×C4⋊C4—228no—
428C2×C4⋊C4—228no—
429C2×C4⋊C4—224no—
430C2×C4⋊C4C22×D1112yes—
431C2×C4⋊C4C22×D1112yes—
432C2×C4⋊C4C22×D1112yes—
433C2×C22⋊C4—112no—
434C2×C22⋊C4—114no—
435C2×C22⋊C4—114no—
436C2×C22⋊C4—114no—
437C2×C22⋊C4—114no—
438C2×C22⋊C4—118no—
439C2×C22⋊C4C22×D1112yes—
440C2×C22⋊C4C22×D1118yes—
441C2×C42—118no—
442C2×C42—112no—
443C2×C42—112no—
444C2×C42—111no—
445C2×C42—111no—
446C2×C42—114no—
447C2×C42—114no—
448C2×C42—114no—
449C2×C42—114no—
450C2×C42C22×D1112yes—
451#95—118no—
452#95—118no—
453#95—114no—
454#95—114no—
455#95—118no—
456#95C22×D1118yes—
457C2×C11—24no—
458C2×C11—44no—
459C2×C11C22×C4×D411yescharacteristic
460C2×C11#342812yes—
461C2×C11#350011yescharacteristic
462C2×C11#350011yescharacteristic
463C2×C11#351212yes—
464D11—44no—
465C24—112no—
466C24C23×D1112yes—
467C24C23×D1111yescharacteristic
468#41—232no—
469#41—2232no—
470C2×Q8—22no—
471C2×Q8—22no—
472C2×Q8—114no—
473C2×Q8—222no—
474C2×Q8—222no—
475C2×Q8C2×C4×D1114yes—
476C2×D4—24no—
477C2×D4—24no—
478C2×D4—22no—
479C2×D4—22no—
480C2×D4—118no—
481C2×D4—1116no—
482C2×D4—114no—
483C2×D4—224no—
484C2×D4—224no—
485C2×D4—222no—
486C2×D4—222no—
487C2×D4—444no—
488C2×D4—444no—
489C2×D4C2×C4×D1118yes—
490C2×D4C2×C4×D1114yes—
491C22×C4—24no—
492C22×C4—24no—
493C22×C4—24no—
494C22×C4—44no—
495C22×C4—112no—
496C22×C4—112no—
497C22×C4—112no—
498C22×C4—112no—
499C22×C4—112no—
500C22×C4—118no—
501C22×C4—118no—
502C22×C4—114no—
503C22×C4—228no—
504C22×C4—228no—
505C22×C4—224no—
506C22×C4—224no—
507C22×C4—224no—
508C22×C4—448no—
509C22×C4—442no—
510C22×C4—442no—
511C22×C4—448no—
512C22×C4—444no—
513C22×C4C2×C4×D1118yes—
514C22×C4C2×C4×D1114yes—
515C22×C4D4×D1114yes—
516C22×C4#434114yes—
517C22×C4C23×D1114yes—
518C22×C4C23×D1114yes—
519C22×C4C23×D1112yes—
520C22×C4C23×D1111yescharacteristic
521C22×C4C23×D1111yescharacteristic
522C4⋊C4—24no—
523C4⋊C4—24no—
524C4⋊C4—24no—
525C4⋊C4—1116no—
526C4⋊C4—114no—
527C4⋊C4—114no—
528C4⋊C4—228no—
529C4⋊C4—228no—
530C4⋊C4—224no—
531C4⋊C4—224no—
532C22⋊C4—24no—
533C22⋊C4—48no—
534C22⋊C4—1116no—
535C22⋊C4—118no—
536C22⋊C4—1116no—
537C22⋊C4—228no—
538C22⋊C4—228no—
539C22⋊C4—448no—
540C42—24no—
541C42—118no—
542C42—114no—
543C42—114no—
544C42—118no—
545C42—228no—
546C42—228no—
547C42—444no—
548C42—444no—
549C11#3420811yescharacteristic, complemented, Sylow
550C23—22no—
551C23—22no—
552C23—22no—
553C23—22no—
554C23—24no—
555C23—24no—
556C23—114no—
557C23—222no—
558C23—222no—
559C23—224no—
560C23—224no—
561C23C22×C4×D1114yes—
562C23C22×C4×D1112yes—
563C23C2×D4×D1112yes—
564C23C2×#434112yes—
565C23C24×D1111yescharacteristic
566Q8—28no—
567Q8—228no—
568D4—216no—
569D4—28no—
570D4—2216no—
571D4—228no—
572D4—4416no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—216no—
576C2×C4—24no—
577C2×C4—24no—
578C2×C4—24no—
579C2×C4—28no—
580C2×C4—24no—
581C2×C4—84no—
582C2×C4—114no—
583C2×C4—114no—
584C2×C4—114no—
585C2×C4—114no—
586C2×C4—114no—
587C2×C4—222no—
588C2×C4—222no—
589C2×C4—222no—
590C2×C4—224no—
591C2×C4—222no—
592C2×C4—222no—
593C2×C4—224no—
594C2×C4—222no—
595C2×C4—2216no—
596C2×C4—224no—
597C2×C4—228no—
598C2×C4—448no—
599C2×C4—888no—
600C2×C4—888no—
601C2×C4—884no—
602C2×C4(C22⋊D11)⋊C4116yes—
603C2×C4C22×C4×D1114yes—
604C2×C4C22×C4×D1112yes—
605C2×C4C22×C4×D1112yes—
606C2×C4C2×D4×D1112yes—
607C2×C4C2×D4×D1112yes—
608C2×C4C2×#434112yes—
609C2×C4C2×#434112yes—
610C22—22no—
611C22—22no—
612C22—24no—
613C22—24no—
614C22—24no—
615C22—28no—
616C22—42no—
617C22—42no—
618C22—44no—
619C22—224no—
620C22—228no—
621C22—442no—
622C22—442no—
623C22—444no—
624C22C2×(C22⋊D11)⋊C414yes—
625C22C23×C4×D1111yescharacteristic
626C22C22×D4×D1111yescharacteristic
627C22C22×#434111yescharacteristic
628C22#1062345512yes—
629C22#1062345712yes—
630C4—24no—
631C4—44no—
632C4—44no—
633C4—224no—
634C4—224no—
635C4—224no—
636C4—224no—
637C4—224no—
638C4—444no—
639C4C2×(C22⋊D11)⋊C414yes—
640C4C2×(C22⋊D11)⋊C414yes—
641C2—24no—
642C2—44no—
643C2—444no—
644C2C22×(C22⋊D11)⋊C411yescharacteristic
645C2#1308181612yes—
646C2#1308240511yescharacteristic
647C2#1308240811yescharacteristic
648C2#1308253712yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2311C2
socle, cosocleC23×C11C25
prime radicalC2×#10623363C2
hypercenter#2311D11
hypocenterC11#34208
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2311

Complements

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

NH ≅ G/Ntype
2. C2×#10623358C2semidirect
3. C2×#10623035C2semidirect
4. #13071664C2semidirect
5. #13071547C2semidirect
6. #13071538C2semidirect
7. #13071340C2semidirect
8. #13071334C2semidirect
9. #13071204C2semidirect
10. #13071163C2semidirect
11. #13071159C2semidirect
12. C2×#10622590C2semidirect
13. #117×Dic11C2semidirect
14. C11×#2311C2semidirect
19. #10623363C4semidirect
68. C2×C11×#41C2×C4semidirect
82. C2×#4339C2×C4semidirect
98. #67000C2×C4semidirect
100. #66997C2×C4semidirect
101. #66993C2×C4semidirect
102. #66992C2×C4semidirect
103. #66989C2×C4semidirect
107. C4×C22⋊D11C2×C4semidirect
112. #66979D4semidirect
122. C2×C4×Dic11C2×C4semidirect
235. #2311D11semidirect
387. C2×#41C4×D11semidirect
549. C11#34208semidirect

Maximal subgroups

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

subgroupindex
C2×#106233632
C2×#106233582
C2×#106230352
#130716642
#130715472
#130715382
#130713402
#130713342
#130712042
#130711632
#130711592
C2×#106225902
#117×Dic112
C11×#23112
#3420811