Finite Group Databasebeta

← #14914149

Subgroups — #14914149

Order 2816.

3254 conjugacy classes of subgroups.

The subgroup lattice has 658 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#13071627C218yesmaximal, complemented
5#13071560C214yesmaximal, complemented
6#13071512C214yesmaximal, complemented
7#13071330C212yesmaximal, complemented
8#13071326C212yesmaximal, complemented
9#13071204C211yesmaximal, characteristic, complemented
10#13071185C212yesmaximal, complemented
11#13071180C212yesmaximal, complemented
12C2×#10622589C211yesmaximal, 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×Dic11⋊C4C2214yes—
36C22×C4×Dic11C2211yescharacteristic
37#10623035—28no—
38C2×#66946C2212yes—
39C2×#66945C2212yes—
40C2×C4⋊C4×D11C2212yes—
41C2×#66940C2212yes—
42C2×(C22⋊D11)⋊C4C2218yes—
43C11×#391C2212yes—
44C11×#390C2212yes—
45C11×#386C2214yes—
46C11×#380C2214yes—
47#10622600C2214yes—
48#10622589C2212yes—
49#10622589C2214yes—
50#10622589C2212yes—
51C4⋊C4×Dic11C2212yes—
52C4⋊C4×Dic11C2212yes—
53#10622571C2214yes—
54#10622570C2218yes—
55#10622559C2218yes—
56#10622558C2218yes—
57C22⋊C4×Dic11C2214yes—
58#10622552C2212yes—
59#10622545C2212yes—
60C42×Dic11C2212yes—
61#10622542C2212yes—
62#10622282C2218yes—
63#10622281C2218yes—
64#10622262C2218yes—
65#10622260C2218yes—
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⋊D11C2314yes—
76C22×C22⋊D11C2312yes—
77C23×Dic11C2312yes—
78C23×Dic11C2314yes—
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⋊C4—48no—
121C2×Dic11⋊C4C2318yes—
122C2×Dic11⋊C4C2314yes—
123C2×Dic11⋊C4C2318yes—
124C2×Dic11⋊C4C2314yes—
125C2×C4×Dic11C2×C418yescomplemented
126C2×C4×Dic11C2314yes—
127C2×C4×Dic11C2314yes—
128C2×C4×Dic11C2314yes—
129C2×C4×Dic11C2314yes—
130C2×C4×Dic11C2311yescharacteristic
131C2×C4×Dic11C2311yescharacteristic
132C2×C4×Dic11C2312yes—
133C2×C4×Dic11C2312yes—
134#66946—28no—
135#66945—28no—
136C4⋊C4×D11—28no—
137#66940—28no—
138(C22⋊D11)⋊C4—416no—
139C11×#95C2318yes—
140C11⋊#95C2318yes—
141C11⋊#95C2314yes—
142C11⋊#95C2314yes—
143#34207—111nomaximal, Sylow
144C24×C11C2412yes—
145C24×C11C2411yescharacteristic
146C23×D11C2412yes—
147C11×#41—232no—
148C2×Q8×C11—22no—
149C2×Q8×C11—22no—
150C2×Q8×C11C22×C414yes—
151C2×D4×C11—24no—
152C2×D4×C11—24no—
153C2×D4×C11—22no—
154C2×D4×C11—22no—
155C2×D4×C11C22×C414yes—
156C2×D4×C11C22×C418yes—
157C22×C4×C11—24no—
158C22×C4×C11—24no—
159C22×C4×C11—24no—
160C22×C4×C11—44no—
161C22×C4×C11C22×C418yes—
162C22×C4×C11C22×C414yes—
163C22×C4×C11C2×D414yes—
164C22×C4×C11#4114yes—
165C22×C4×C11C2414yes—
166C22×C4×C11C2414yes—
167C22×C4×C11C2412yes—
168C22×C4×C11C2411yescharacteristic
169C22×C4×C11C2411yescharacteristic
170C2×C22⋊D11—28no—
171C2×C22⋊D11—28no—
172C2×C22⋊D11—24no—
173C2×C22⋊D11—24no—
174C2×C22⋊D11C22×C4116yes—
175C2×C22⋊D11C22×C418yes—
176C22×Dic11—24no—
177C22×Dic11—24no—
178C22×Dic11—28no—
179C22×Dic11—24no—
180C22×Dic11—48no—
181C22×Dic11—44no—
182C22×Dic11C22×C418yes—
183C22×Dic11C2414yes—
184C22×Dic11C2412yes—
185C22×Dic11C2412yes—
186C22×Dic11C2412yes—
187C22×Dic11C2412yes—
188C22×Dic11C2412yes—
189#4339—232no—
190C2×D44—22no—
191C2×D44—22no—
192C2×D44C22×C414yes—
193C2×C4×D11—28no—
194C2×C4×D11—24no—
195C2×C4×D11—24no—
196C2×C4×D11—48no—
197C2×C4×D11C22×C418yes—
198C2×Dic22—22no—
199C2×Dic22—22no—
200C2×Dic22C22×C414yes—
201C11×C4⋊C4—24no—
202C11×C4⋊C4—24no—
203C11×C4⋊C4—24no—
204C11×C22⋊C4—24no—
205C11×C22⋊C4—48no—
206C42×C11—24no—
207C22⋊Dic11—28no—
208C22⋊Dic11C22×C4116yes—
209C22⋊Dic11C2×D418yes—
210(C2×D11)⋊C4—28no—
211(C2×D11)⋊C4—48no—
212(C2×D11)⋊C4C22×C4116yes—
213C4⋊Dic11—28no—
214C4⋊Dic11—24no—
215C4⋊Dic11—24no—
216C4⋊Dic11C2×D414yes—
217C4⋊Dic11C2×D414yes—
218Dic11⋊C4—28no—
219Dic11⋊C4—216no—
220Dic11⋊C4—48no—
221Dic11⋊C4C22×C4116yes—
222C4×Dic11—28no—
223C4×Dic11—28no—
224C4×Dic11—28no—
225C4×Dic11—28no—
226C4×Dic11C22×C418yes—
227C4×Dic11C22×C414yes—
228C4×Dic11C22×C414yes—
229C4×Dic11C2×D418yes—
230C2×#532—111no—
231C2×#520—111no—
232C2×#520—111no—
233#2361—118no—
234#2354—114no—
235D4×C4⋊C4—114no—
236#2326—112no—
237#2326—112no—
238#2311—111no—
239#2311D1111yescharacteristic, complemented
240C4×C4⋊Q8—112no—
241C4×#127—112no—
242C2×#384—111no—
243C4×#117—111no—
244C23×C11—22no—
245C23×C11—22no—
246C23×C11—22no—
247C23×C11—22no—
248C23×C11—24no—
249C23×C11—24no—
250C23×C11C23×C414yes—
251C23×C11C23×C412yes—
252C23×C11C22×D412yes—
253C23×C11C2×#4112yes—
254C23×C11C2511yescharacteristic
255C22×D11—22no—
256C22×D11—22no—
257C22×D11—24no—
258C22×D11—24no—
259C22×D11C23×C414yes—
260Q8×C11—28no—
261D4×C11—216no—
262D4×C11—28no—
263C2×C4×C11—22no—
264C2×C4×C11—22no—
265C2×C4×C11—216no—
266C2×C4×C11—24no—
267C2×C4×C11—24no—
268C2×C4×C11—24no—
269C2×C4×C11—28no—
270C2×C4×C11—24no—
271C2×C4×C11—84no—
272C2×C4×C11C4×D4116yescomplemented
273C2×C4×C11C23×C414yes—
274C2×C4×C11C23×C412yes—
275C2×C4×C11C23×C412yes—
276C2×C4×C11C22×D412yes—
277C2×C4×C11C22×D412yes—
278C2×C4×C11C2×#4112yes—
279C2×C4×C11C2×#4112yes—
280C22⋊D11—216no—
281C22⋊D11—232no—
282C2×Dic11—22no—
283C2×Dic11—22no—
284C2×Dic11—24no—
285C2×Dic11—22no—
286C2×Dic11—24no—
287C2×Dic11—22no—
288C2×Dic11—216no—
289C2×Dic11—24no—
290C2×Dic11—28no—
291C2×Dic11—88no—
292C2×Dic11—84no—
293C2×Dic11C23×C414yes—
294C2×Dic11C23×C414yes—
295C2×Dic11C23×C414yes—
296C2×Dic11C22×D414yes—
297C2×Dic11C22×D414yes—
298C2×Dic11H(5,𝔽2)14yes—
299C2×Dic112−1+414yes—
300D44—28no—
301C4×D11—216no—
302C4×D11—88no—
303Dic22—28no—
304C22×#41—111no—
305C22×#41C2×D1111yescharacteristic
306#532—1116no—
307C2×C4⋊Q8—111no—
308C2×#127—111no—
309C2×#124—111no—
310C2×#124—111no—
311C2×#121—114no—
312#520—228no—
313#520—228no—
314C2×C4×Q8—112no—
315C2×C4×Q8—112no—
316C2×C4×D4—114no—
317C2×C4×D4—112no—
318C2×C4×D4—114no—
319C2×C4×D4—114no—
320C2×C4×D4—112no—
321C2×C4×D4—118no—
322C2×#117—111no—
323C2×#117—112no—
324C2×#117—112no—
325C2×#117C2×D1111yescharacteristic
326C22×C4⋊C4—111no—
327C22×C4⋊C4—112no—
328C22×C4⋊C4—114no—
329C22×C4⋊C4—112no—
330C22×C4⋊C4C2×D1111yescharacteristic
331C22×C42—111no—
332#391—112no—
333#391C2×D1112yes—
334#390—118no—
335#390—112no—
336#390C2×D1112yes—
337#389—118no—
338#388—118no—
339#388—118no—
340#386—114no—
341#386C2×D1114yes—
342#385—118no—
343#385—118no—
344#384—112no—
345#384—112no—
346#384—114no—
347#380—114no—
348#380C2×D1114yes—
349C4×C4⋊C4—112no—
350C4×C4⋊C4—112no—
351C4×C4⋊C4—118no—
352C4×C22⋊C4—114no—
353#376—112no—
354C43—112no—
355C22×C11—24no—
356C22×C11—22no—
357C22×C11—22no—
358C22×C11—24no—
359C22×C11—24no—
360C22×C11—28no—
361C22×C11—42no—
362C22×C11—42no—
363C22×C11—44no—
364C22×C11C2×C4×D414yes—
365C22×C11C24×C411yescharacteristic
366C22×C11C23×D411yescharacteristic
367C22×C11C22×#4111yescharacteristic
368C22×C11C2×H(5,𝔽2)12yes—
369C22×C11C2×2−1+412yes—
370C2×D11—24no—
371C2×D11—28no—
372C2×D11—42no—
373C2×D11—42no—
374C2×D11—44no—
375C4×C11—24no—
376C4×C11—44no—
377C4×C11—44no—
378C4×C11C2×C4×D414yes—
379C4×C11C2×C4×D414yes—
380Dic11—24no—
381Dic11—24no—
382Dic11—24no—
383Dic11—24no—
384Dic11—44no—
385Dic11#52018yescomplemented
386C2×#41—24no—
387C2×#41—24no—
388C2×#41—118no—
389C2×#41—224no—
390C2×#41—224no—
391C2×#41C4×D1118yescomplemented
392C22×Q8—111no—
393C22×Q8C22×D1111yescharacteristic
394C22×D4—114no—
395C22×D4—112no—
396C22×D4—111no—
397C22×D4C22×D1112yes—
398C22×D4C22×D1111yescharacteristic
399C23×C4—112no—
400C23×C4—112no—
401C23×C4—112no—
402C23×C4—114no—
403C23×C4—114no—
404C23×C4C22×D1112yes—
405C23×C4C22×D1112yes—
406C23×C4C22×D1111yescharacteristic
407C4⋊Q8—118no—
408#127—118no—
409#124—118no—
410#124—118no—
411#121—1132no—
412C4×Q8—228no—
413C4×Q8—228no—
414C4×D4—1132no—
415C4×D4—228no—
416C4×D4—228no—
417C4×D4—2216no—
418C4×D4—2216no—
419C4×D4—4416no—
420#117—24no—
421#117—118no—
422#117—228no—
423#117—228no—
424C2×C4⋊C4—24no—
425C2×C4⋊C4—111no—
426C2×C4⋊C4—111no—
427C2×C4⋊C4—114no—
428C2×C4⋊C4—112no—
429C2×C4⋊C4—112no—
430C2×C4⋊C4—114no—
431C2×C4⋊C4—114no—
432C2×C4⋊C4—118no—
433C2×C4⋊C4—118no—
434C2×C4⋊C4—228no—
435C2×C4⋊C4—228no—
436C2×C4⋊C4—224no—
437C2×C4⋊C4—448no—
438C2×C4⋊C4C22×D1112yes—
439C2×C4⋊C4C22×D1112yes—
440C2×C4⋊C4C22×D1112yes—
441C2×C22⋊C4—112no—
442C2×C22⋊C4—114no—
443C2×C22⋊C4—114no—
444C2×C22⋊C4—114no—
445C2×C22⋊C4—114no—
446C2×C22⋊C4—118no—
447C2×C22⋊C4C22×D1112yes—
448C2×C22⋊C4C22×D1118yes—
449C2×C42—118no—
450C2×C42—112no—
451C2×C42—112no—
452C2×C42—111no—
453C2×C42—111no—
454C2×C42—114no—
455C2×C42—114no—
456C2×C42—114no—
457C2×C42—114no—
458C2×C42C22×D1112yes—
459#95—114no—
460#95—114no—
461#95—118no—
462#95C22×D1118yes—
463C2×C11—24no—
464C2×C11—44no—
465C2×C11C22×C4×D411yescharacteristic
466C2×C11C2×#52012yes—
467C2×C11#349811yescharacteristic
468C2×C11#349911yescharacteristic
469C2×C11#351112yes—
470D11—44no—
471C24—112no—
472C24C23×D1112yes—
473C24C23×D1111yescharacteristic
474#41—232no—
475#41—2232no—
476C2×Q8—22no—
477C2×Q8—22no—
478C2×Q8—114no—
479C2×Q8—222no—
480C2×Q8—222no—
481C2×Q8C2×C4×D1114yes—
482C2×D4—24no—
483C2×D4—24no—
484C2×D4—22no—
485C2×D4—22no—
486C2×D4—1116no—
487C2×D4—118no—
488C2×D4—114no—
489C2×D4—228no—
490C2×D4—228no—
491C2×D4—224no—
492C2×D4—224no—
493C2×D4—222no—
494C2×D4—222no—
495C2×D4C2×C4×D1118yes—
496C2×D4C2×C4×D1114yes—
497C22×C4—24no—
498C22×C4—24no—
499C22×C4—24no—
500C22×C4—44no—
501C22×C4—112no—
502C22×C4—118no—
503C22×C4—112no—
504C22×C4—112no—
505C22×C4—112no—
506C22×C4—112no—
507C22×C4—118no—
508C22×C4—114no—
509C22×C4—228no—
510C22×C4—224no—
511C22×C4—224no—
512C22×C4—228no—
513C22×C4—224no—
514C22×C4—224no—
515C22×C4—224no—
516C22×C4—448no—
517C22×C4—444no—
518C22×C4—448no—
519C22×C4C2×C4×D1118yes—
520C22×C4C2×C4×D1114yes—
521C22×C4D4×D1114yes—
522C22×C4#434114yes—
523C22×C4C23×D1114yes—
524C22×C4C23×D1114yes—
525C22×C4C23×D1112yes—
526C22×C4C23×D1111yescharacteristic
527C22×C4C23×D1111yescharacteristic
528C4⋊C4—24no—
529C4⋊C4—24no—
530C4⋊C4—24no—
531C4⋊C4—1116no—
532C4⋊C4—114no—
533C4⋊C4—114no—
534C4⋊C4—228no—
535C4⋊C4—228no—
536C4⋊C4—2216no—
537C4⋊C4—224no—
538C4⋊C4—224no—
539C4⋊C4—448no—
540C22⋊C4—24no—
541C22⋊C4—48no—
542C22⋊C4—1116no—
543C22⋊C4—118no—
544C22⋊C4—1116no—
545C22⋊C4—228no—
546C22⋊C4—228no—
547C22⋊C4—448no—
548C42—24no—
549C42—118no—
550C42—114no—
551C42—114no—
552C42—118no—
553C42—228no—
554C42—228no—
555C42—228no—
556C42—228no—
557C11#3420711yescharacteristic, complemented, Sylow
558C23—22no—
559C23—22no—
560C23—22no—
561C23—22no—
562C23—24no—
563C23—24no—
564C23—114no—
565C23—222no—
566C23—222no—
567C23—224no—
568C23—224no—
569C23C22×C4×D1114yes—
570C23C22×C4×D1112yes—
571C23C2×D4×D1112yes—
572C23C2×#434112yes—
573C23C24×D1111yescharacteristic
574Q8—28no—
575Q8—228no—
576D4—216no—
577D4—28no—
578D4—2232no—
579D4—2216no—
580D4—228no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—216no—
584C2×C4—24no—
585C2×C4—24no—
586C2×C4—24no—
587C2×C4—28no—
588C2×C4—24no—
589C2×C4—84no—
590C2×C4—114no—
591C2×C4—114no—
592C2×C4—114no—
593C2×C4—114no—
594C2×C4—114no—
595C2×C4—114no—
596C2×C4—114no—
597C2×C4—2216no—
598C2×C4—222no—
599C2×C4—222no—
600C2×C4—224no—
601C2×C4—222no—
602C2×C4—224no—
603C2×C4—222no—
604C2×C4—2216no—
605C2×C4—224no—
606C2×C4—228no—
607C2×C4—888no—
608C2×C4—888no—
609C2×C4—884no—
610C2×C4(C22⋊D11)⋊C4116yescomplemented
611C2×C4C22×C4×D1114yes—
612C2×C4C22×C4×D1112yes—
613C2×C4C22×C4×D1112yes—
614C2×C4C2×D4×D1112yes—
615C2×C4C2×D4×D1112yes—
616C2×C4C2×#434112yes—
617C2×C4C2×#434112yes—
618C22—22no—
619C22—22no—
620C22—24no—
621C22—24no—
622C22—24no—
623C22—28no—
624C22—42no—
625C22—42no—
626C22—44no—
627C22—224no—
628C22—228no—
629C22—442no—
630C22—442no—
631C22—444no—
632C22C2×(C22⋊D11)⋊C414yes—
633C22C23×C4×D1111yescharacteristic
634C22C22×D4×D1111yescharacteristic
635C22C22×#434111yescharacteristic
636C22D11×H(5,𝔽2)12yes—
637C22D11×2−1+412yes—
638C4—24no—
639C4—44no—
640C4—44no—
641C4—118no—
642C4—224no—
643C4—224no—
644C4—224no—
645C4—224no—
646C4—444no—
647C4C2×(C22⋊D11)⋊C414yes—
648C4C2×(C22⋊D11)⋊C414yes—
649C2—24no—
650C2—44no—
651C2—444no—
652C2C22×(C22⋊D11)⋊C411yescharacteristic
653C2D11×#52012yes—
654C2#1308239111yescharacteristic
655C2#1308239811yescharacteristic
656C2#1308252512yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2311C2
socle, cosocleC23×C11C25
prime radicalC2×#10623363C2
hypercenter#2311D11
hypocenterC11#34207
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. #13071627C2semidirect
5. #13071560C2semidirect
6. #13071512C2semidirect
7. #13071330C2semidirect
8. #13071326C2semidirect
9. #13071204C2semidirect
10. #13071185C2semidirect
11. #13071180C2semidirect
12. C2×#10622589C2semidirect
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
125. C2×C4×Dic11C2×C4semidirect
239. #2311D11semidirect
272. C2×C4×C11C4×D4semidirect
385. Dic11#520semidirect
391. C2×#41C4×D11semidirect
557. C11#34207semidirect
610. C2×C4(C22⋊D11)⋊C4semidirect

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
#130716272
#130715602
#130715122
#130713302
#130713262
#130712042
#130711852
#130711802
C2×#106225892
#117×Dic112
C11×#23112
#3420711