Finite Group Databasebeta

← #14914930

Subgroups — #14914930

Order 2816.

3586 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
1C2×#10623056C211yesmaximal, characteristic
2C2×#10623035C211yesmaximal, characteristic, complemented
3C22×#66946C211yesmaximal, characteristic, complemented
4#13071687C214yesmaximal, complemented
5#13071680C214yesmaximal, complemented
6#13071656C214yesmaximal, complemented
7#13071634C214yesmaximal, complemented
8#13071276C214yesmaximal, complemented
9#13071196C211yesmaximal, characteristic, complemented
10C4×#66935C214yesmaximal, complemented
11#13071104C211yesmaximal, characteristic, complemented
12#13071100C211yesmaximal, characteristic, complemented
13C11×#2274C211yesmaximal, characteristic, complemented
14C22×#4339C2211yescharacteristic
15C23×D44C2211yescharacteristic
16C23×C4×D11C2212yes—
17C2×C11×#117C2211yescharacteristic
18C2×C11×#117C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C2×C4×C22⋊D11C2214yes—
21C22×(C2×D11)⋊C4C2212yes—
22C2×#66979C2211yescharacteristic
23C22×C4×Dic11C2211yescharacteristic
24#10623056C4116yescomplemented
25C2×#66948C2214yes—
26#10623035—28no—
27C2×#66946—28no—
28C2×#66946C2214yes—
29C2×#66946C2214yes—
30C2×#66946C2212yescomplemented
31C2×#66945C2212yescomplemented
32C2×C4⋊C4×D11C2212yescomplemented
33C2×#66940C2212yescomplemented
34C2×#66935C2214yes—
35C2×#66928C2212yes—
36C2×#66927C2212yes—
37C2×C4×D44C2218yescomplemented
38C4×C11×C4⋊C4C2214yescomplemented
39C4×C11×C4⋊C4C2214yescomplemented
40C4×C11×C22⋊C4C2214yes—
41#10622601C2214yes—
42#10622601C2212yescomplemented
43#10622598C2212yescomplemented
44#10622598C2212yescomplemented
45#10622587C2212yescomplemented
46#10622571C2212yes—
47#10622571C2212yes—
48#10622568C2214yes—
49#10622563C2212yes—
50#10622563C2212yes—
51#10622553C2218yescomplemented
52#10622552C2212yes—
53#10622552C2212yes—
54#10622552C2218yescomplemented
55C4×(C2×D11)⋊C4C2214yescomplemented
56C4×(C2×D11)⋊C4C2218yescomplemented
57C4×C4⋊Dic11C2214yescomplemented
58#10622283C2218yescomplemented
59#10622281C2218yescomplemented
60#10622278C2218yescomplemented
61#10622278C2218yescomplemented
62C24×D11C2312yes—
63C23×C4×C11C2312yes—
64C23×C4×C11C2311yescharacteristic
65C22×C22⋊D11C2312yes—
66C23×Dic11C2311yescharacteristic
67C23×Dic11C2311yescharacteristic
68C2×#4339—24no—
69C2×#4339—24no—
70C2×#4339C2×C418yescomplemented
71C22×D44—24no—
72C22×D44—24no—
73C22×D44C2×C418yescomplemented
74C22×D44C2312yes—
75C22×D44C2312yes—
76C22×D44C2311yescharacteristic
77C22×D44C2318yes—
78C22×C4×D11—28no—
79C22×C4×D11—48no—
80C22×C4×D11C2318yes—
81C22×C4×D11C2312yes—
82C22×C4×D11C2314yes—
83C22×Dic22C2311yescharacteristic
84C11×#117—24no—
85C11×#117C2×C418yescomplemented
86C2×C11×C4⋊C4D418yescomplemented
87C2×C11×C4⋊C4C2312yes—
88C2×C11×C4⋊C4C2312yes—
89C2×C11×C4⋊C4C2312yes—
90C2×C11×C4⋊C4C2312yes—
91C2×C11×C22⋊C4C2312yes—
92C2×C11×C22⋊C4C2312yes—
93C2×C42×C11C2312yes—
94C2×C42×C11C2318yes—
95C2×C42×C11C2312yes—
96C2×C22⋊Dic11C2312yes—
97C4×C22⋊D11—216no—
98C2×(C2×D11)⋊C4—28no—
99C2×(C2×D11)⋊C4C2314yes—
100C2×(C2×D11)⋊C4C2314yes—
101C2×(C2×D11)⋊C4C2318yes—
102C2×(C2×D11)⋊C4C2318yes—
103C2×(C2×D11)⋊C4C2314yes—
104C2×(C2×D11)⋊C4C2318yes—
105C2×(C2×D11)⋊C4C2318yes—
106#66979—24no—
107C2×C4⋊Dic11C2314yes—
108C2×C4⋊Dic11C2311yescharacteristic
109C2×C4⋊Dic11C2311yescharacteristic
110C2×C4⋊Dic11C2314yes—
111C2×Dic11⋊C4C2314yes—
112C2×C4×Dic11—24no—
113C2×C4×Dic11C2314yes—
114C2×C4×Dic11C2312yes—
115C2×C4×Dic11C2312yes—
116C2×C4×Dic11C2312yes—
117#66948C2×C4132yescomplemented
118#66946—216no—
119#66946—216no—
120#66946—28no—
121#66945—28no—
122C4⋊C4×D11—28no—
123#66940—28no—
124#66935C2×C4132yescomplemented
125#66928C2×C4116yescomplemented
126#66927C2×C4116yescomplemented
127C4×D44—416no—
128C11×#95C2318yes—
129C11⋊#95C2314yes—
130C11⋊#95C2314yes—
131C11⋊#95C2314yes—
132C11⋊#95C2314yes—
133#34265—111nomaximal, Sylow
134C24×C11C2411yescharacteristic
135C23×D11—24no—
136C23×D11—24no—
137C23×D11—44no—
138C23×D11—44no—
139C23×D11C22×C418yes—
140C23×D11C2414yes—
141C23×D11C2412yes—
142C22×C4×C11—44no—
143C22×C4×C11C22×C414yes—
144C22×C4×C11C2×D418yes—
145C22×C4×C11C2×D414yes—
146C22×C4×C11#4114yes—
147C22×C4×C11C2414yes—
148C22×C4×C11C2414yes—
149C22×C4×C11C2414yes—
150C22×C4×C11C2411yescharacteristic
151C22×C4×C11C2411yescharacteristic
152C2×C22⋊D11—24no—
153C2×C22⋊D11—24no—
154C2×C22⋊D11C22×C418yes—
155C22×Dic11—24no—
156C22×Dic11—22no—
157C22×Dic11—22no—
158C22×Dic11—42no—
159C22×Dic11C2412yes—
160C22×Dic11C2412yes—
161C22×Dic11C2412yes—
162C22×Dic11C2412yes—
163C22×Dic11C2412yes—
164#4339—232no—
165C2×D44—232no—
166C2×D44—24no—
167C2×D44—24no—
168C2×D44—22no—
169C2×D44—24no—
170C2×D44—24no—
171C2×D44—22no—
172C2×D44—48no—
173C2×D44—48no—
174C2×D44C22×C418yes—
175C2×D44C22×C418yes—
176C2×D44C22×C414yescomplemented
177C2×D44C22×C4132yescomplemented
178C2×C4×D11—216no—
179C2×C4×D11—24no—
180C2×C4×D11—216no—
181C2×C4×D11—28no—
182C2×C4×D11—24no—
183C2×C4×D11—48no—
184C2×C4×D11—48no—
185C2×C4×D11—432no—
186C2×C4×D11C22×C418yescomplemented
187C2×Dic22—22no—
188C2×Dic22—22no—
189C2×Dic22C22×C414yescomplemented
190C11×C4⋊C4—24no—
191C11×C4⋊C4C22×C418yescomplemented
192C11×C4⋊C4C2×D418yes—
193C11×C4⋊C4C2×D418yes—
194C11×C22⋊C4—24no—
195C11×C22⋊C4C22×C418yes—
196C42×C11—24no—
197C42×C11—48no—
198C42×C11C22×C418yescomplemented
199C22⋊Dic11—24no—
200(C2×D11)⋊C4—28no—
201(C2×D11)⋊C4—28no—
202(C2×D11)⋊C4—216no—
203(C2×D11)⋊C4—48no—
204(C2×D11)⋊C4—44no—
205(C2×D11)⋊C4—48no—
206(C2×D11)⋊C4C22×C4132yescomplemented
207C4⋊Dic11—28no—
208C4⋊Dic11—22no—
209C4⋊Dic11—22no—
210C4⋊Dic11—44no—
211Dic11⋊C4—28no—
212C4×Dic11—28no—
213C4×Dic11—24no—
214C4×Dic11—24no—
215C4×Dic11—24no—
216C2×#535—111no—
217C2×#520—111no—
218C22×C4×D4—111no—
219#2367—114no—
220#2366—114no—
221#2363—114no—
222#2361—114no—
223#2321—114no—
224#2309—111no—
225C4×#120—114no—
226#2297—111no—
227#2296—111no—
228#2274D1111yescharacteristic, complemented
229C23×C11—22no—
230C23×C11—22no—
231C23×C11C23×C412yes—
232C23×C11C22×D412yes—
233C23×C11C2×#4112yes—
234C23×C11C2511yescharacteristic
235C22×D11—216no—
236C22×D11—22no—
237C22×D11—24no—
238C22×D11—22no—
239C22×D11—24no—
240C22×D11—24no—
241C22×D11—28no—
242C22×D11—24no—
243C22×D11—28no—
244C22×D11—416no—
245C22×D11—48no—
246C22×D11—48no—
247C22×D11—416no—
248C22×D11C23×C418yes—
249C22×D11C23×C414yes—
250C2×C4×C11—24no—
251C2×C4×C11—28no—
252C2×C4×C11—24no—
253C2×C4×C11—24no—
254C2×C4×C11—24no—
255C2×C4×C11—24no—
256C2×C4×C11—48no—
257C2×C4×C11C4×D4116yescomplemented
258C2×C4×C11C23×C418yes—
259C2×C4×C11C23×C412yes—
260C2×C4×C11C23×C412yes—
261C2×C4×C11C22×D418yes—
262C2×C4×C11C22×D412yes—
263C2×C4×C11C22×D412yes—
264C2×C4×C11C2×#4112yes—
265C2×C4×C11C2×#4112yes—
266C22⋊D11—216no—
267C2×Dic11—28no—
268C2×Dic11—22no—
269C2×Dic11—22no—
270C2×Dic11—22no—
271C2×Dic11—22no—
272C2×Dic11—22no—
273C2×Dic11—22no—
274C2×Dic11—22no—
275C2×Dic11—24no—
276C2×Dic11—22no—
277C2×Dic11—24no—
278C2×Dic11—22no—
279C2×Dic11—44no—
280C2×Dic11C23×C414yes—
281C2×Dic11H(5,𝔽2)14yes—
282D44—216no—
283D44—216no—
284D44—28no—
285D44—432no—
286C4×D11—216no—
287C4×D11—432no—
288C4×D11—88no—
289Dic22—28no—
290C22×#41—111no—
291C23×D4—111no—
292C24×C4—112no—
293#535—1116no—
294C2×#127—112no—
295C2×#124—112no—
296C2×#121—114no—
297C2×#120—114no—
298#520—228no—
299C2×C4×Q8—112no—
300C2×C4×D4—114no—
301C2×C4×D4—114no—
302C2×C4×D4—114no—
303C2×C4×D4—112no—
304C2×C4×D4—118no—
305C2×C4×D4—228no—
306C2×#117—111no—
307C2×#117—112no—
308C2×#117C2×D1111yescharacteristic
309C2×#117C2×D1111yescharacteristic
310C22×C4⋊C4—112no—
311C22×C4⋊C4C2×D1111yescharacteristic
312C22×C22⋊C4—112no—
313C22×C42—111no—
314#391—112no—
315#390—114no—
316#390—112no—
317#390—112no—
318#390—112no—
319#390—118no—
320#389—112no—
321#389—112no—
322#388—118no—
323#388—118no—
324#386—112no—
325#386—112no—
326#386—118no—
327#386—118no—
328#385—112no—
329#385—112no—
330#385—118no—
331#379—114no—
332C4×C4⋊C4—114no—
333C4×C4⋊C4C2×D1114yescomplemented
334C4×C4⋊C4C2×D1114yescomplemented
335C4×C22⋊C4—114no—
336C4×C22⋊C4—118no—
337C4×C22⋊C4C2×D1114yes—
338C22×C11—24no—
339C22×C11—22no—
340C22×C11—22no—
341C22×C11—24no—
342C22×C11C2×C4×D414yes—
343C22×C11C24×C411yescharacteristic
344C22×C11C23×D411yescharacteristic
345C22×C11C22×#4111yescharacteristic
346C22×C11C2×H(5,𝔽2)12yes—
347C22×C11#58512yes—
348C2×D11—28no—
349C2×D11—24no—
350C2×D11—216no—
351C2×D11—28no—
352C2×D11—432no—
353C2×D11—44no—
354C2×D11—42no—
355C2×D11—42no—
356C2×D11—44no—
357C2×D11—44no—
358C2×D11—48no—
359C4×C11—28no—
360C4×C11—28no—
361C4×C11—44no—
362C4×C11C2×C4×D414yes—
363C4×C11C2×C4×D414yes—
364Dic11—24no—
365Dic11—24no—
366Dic11—42no—
367Dic11—42no—
368Dic11—42no—
369C25—112no—
370C2×#41—118no—
371C2×#41—224no—
372C2×#41—224no—
373C22×Q8—111no—
374C22×D4—112no—
375C22×D4—118no—
376C22×D4—112no—
377C22×D4—112no—
378C22×D4—111no—
379C22×D4—118no—
380C22×D4—224no—
381C22×D4—224no—
382C23×C4—112no—
383C23×C4—111no—
384C23×C4—111no—
385C23×C4—118no—
386C23×C4—114no—
387C23×C4—228no—
388C23×C4—448no—
389C23×C4C22×D1112yes—
390C23×C4C22×D1111yescharacteristic
391#127—1116no—
392#124—1116no—
393#121—1132no—
394#120—1132no—
395C4×Q8—228no—
396C4×D4—2216no—
397C4×D4—2216no—
398C4×D4—2216no—
399C4×D4—228no—
400C4×D4—4416no—
401#117—24no—
402#117—224no—
403#117—228no—
404#117C4×D1118yescomplemented
405C2×C4⋊C4—111no—
406C2×C4⋊C4—114no—
407C2×C4⋊C4—111no—
408C2×C4⋊C4—114no—
409C2×C4⋊C4—114no—
410C2×C4⋊C4—228no—
411C2×C4⋊C4D4418yescomplemented
412C2×C4⋊C4C22×D1112yes—
413C2×C4⋊C4C22×D1112yes—
414C2×C4⋊C4C22×D1112yes—
415C2×C4⋊C4C22×D1112yes—
416C2×C22⋊C4—118no—
417C2×C22⋊C4—112no—
418C2×C22⋊C4—118no—
419C2×C22⋊C4—114no—
420C2×C22⋊C4—114no—
421C2×C22⋊C4—118no—
422C2×C22⋊C4—118no—
423C2×C22⋊C4—114no—
424C2×C22⋊C4—228no—
425C2×C22⋊C4C22×D1112yes—
426C2×C22⋊C4C22×D1112yes—
427C2×C42—114no—
428C2×C42—112no—
429C2×C42—112no—
430C2×C42—112no—
431C2×C42—224no—
432C2×C42C22×D1112yes—
433C2×C42C22×D1118yes—
434C2×C42C22×D1112yes—
435#95—114no—
436#95—114no—
437#95—114no—
438#95—114no—
439#95C22×D1118yes—
440C2×C11—24no—
441C2×C11C22×C4×D411yescharacteristic
442C2×C11C4×H(5,𝔽2)12yes—
443C2×C11#348411yescharacteristic
444C2×C11#348711yescharacteristic
445C2×C11#350612yes—
446D11—44no—
447D11—48no—
448C24—114no—
449C24—112no—
450C24—118no—
451C24—224no—
452C24—224no—
453C24—444no—
454C24—444no—
455C24C23×D1111yescharacteristic
456#41—2232no—
457C2×Q8—114no—
458C2×Q8—222no—
459C2×Q8—222no—
460C2×D4—118no—
461C2×D4—118no—
462C2×D4—118no—
463C2×D4—114no—
464C2×D4—1132no—
465C2×D4—224no—
466C2×D4—224no—
467C2×D4—2232no—
468C2×D4—224no—
469C2×D4—224no—
470C2×D4—222no—
471C2×D4—224no—
472C2×D4—224no—
473C2×D4—222no—
474C2×D4—448no—
475C2×D4—448no—
476C22×C4—44no—
477C22×C4—112no—
478C22×C4—112no—
479C22×C4—118no—
480C22×C4—112no—
481C22×C4—112no—
482C22×C4—112no—
483C22×C4—2216no—
484C22×C4—224no—
485C22×C4—222no—
486C22×C4—224no—
487C22×C4—224no—
488C22×C4—222no—
489C22×C4—2216no—
490C22×C4—228no—
491C22×C4—448no—
492C22×C4—448no—
493C22×C4—4432no—
494C22×C4—442no—
495C22×C4C2×C4×D1114yes—
496C22×C4C2×D4418yes—
497C22×C4C2×D4414yes—
498C22×C4#433914yes—
499C22×C4C23×D1114yes—
500C22×C4C23×D1114yes—
501C22×C4C23×D1114yes—
502C22×C4C23×D1111yescharacteristic
503C22×C4C23×D1111yescharacteristic
504C4⋊C4—24no—
505C4⋊C4—228no—
506C4⋊C4—222no—
507C4⋊C4—228no—
508C4⋊C4—222no—
509C4⋊C4—444no—
510C4⋊C4C2×C4×D1118yescomplemented
511C4⋊C4C2×D4418yes—
512C4⋊C4C2×D4418yes—
513C22⋊C4—24no—
514C22⋊C4—1132no—
515C22⋊C4—228no—
516C22⋊C4—224no—
517C22⋊C4—2216no—
518C22⋊C4—228no—
519C22⋊C4—448no—
520C22⋊C4—448no—
521C22⋊C4—444no—
522C22⋊C4C2×C4×D1118yes—
523C42—24no—
524C42—48no—
525C42—224no—
526C42—224no—
527C42—228no—
528C42—224no—
529C42C2×C4×D1118yescomplemented
530C11#3426511yescharacteristic, complemented, Sylow
531C23—22no—
532C23—22no—
533C23—118no—
534C23—114no—
535C23—2216no—
536C23—222no—
537C23—224no—
538C23—222no—
539C23—224no—
540C23—224no—
541C23—228no—
542C23—224no—
543C23—228no—
544C23—4416no—
545C23—448no—
546C23—4416no—
547C23—448no—
548C23C22×C4×D1112yes—
549C23C22×D4412yes—
550C23C2×#433912yes—
551C23C24×D1111yescharacteristic
552Q8—228no—
553D4—2216no—
554D4—2216no—
555D4—2216no—
556D4—228no—
557D4—4432no—
558C2×C4—24no—
559C2×C4—28no—
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—48no—
565C2×C4—114no—
566C2×C4—114no—
567C2×C4—228no—
568C2×C4—222no—
569C2×C4—222no—
570C2×C4—222no—
571C2×C4—222no—
572C2×C4—2216no—
573C2×C4—222no—
574C2×C4—222no—
575C2×C4—222no—
576C2×C4—224no—
577C2×C4—224no—
578C2×C4—222no—
579C2×C4—222no—
580C2×C4—4432no—
581C2×C4—444no—
582C2×C4—888no—
583C2×C4C4×D44116yescomplemented
584C2×C4C22×C4×D1118yes—
585C2×C4C22×C4×D1112yes—
586C2×C4C22×C4×D1112yes—
587C2×C4C22×D4418yes—
588C2×C4C22×D4412yes—
589C2×C4C22×D4412yes—
590C2×C4C2×#433912yes—
591C2×C4C2×#433912yes—
592C22—24no—
593C22—22no—
594C22—22no—
595C22—24no—
596C22—224no—
597C22—228no—
598C22—228no—
599C22—2216no—
600C22—4432no—
601C22—448no—
602C22—444no—
603C22—444no—
604C22—442no—
605C22—444no—
606C22—442no—
607C22C2×C4×D4414yes—
608C22C23×C4×D1111yescharacteristic
609C22C23×D4411yescharacteristic
610C22C22×#433911yescharacteristic
611C22D11×H(5,𝔽2)12yes—
612C22#1062345712yes—
613C4—28no—
614C4—28no—
615C4—44no—
616C4—224no—
617C4—224no—
618C4—442no—
619C4—442no—
620C4—442no—
621C4C2×C4×D4414yes—
622C4C2×C4×D4414yes—
623C2—24no—
624C2—448no—
625C2—444no—
626C2C22×C4×D4411yescharacteristic
627C2#1308182212yes—
628C2#1308225211yescharacteristic
629C2#1308227511yescharacteristic
630C2#1308246112yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2274C2
socle, cosocleC23×C11C25
prime radicalC2×#10623056C2
hypercenter#2274D11
hypocenterC11#34265
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2274

Complements

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

NH ≅ G/Ntype
2. C2×#10623035C2semidirect
3. C22×#66946C2semidirect
4. #13071687C2semidirect
5. #13071680C2semidirect
6. #13071656C2semidirect
7. #13071634C2semidirect
8. #13071276C2semidirect
9. #13071196C2semidirect
10. C4×#66935C2semidirect
11. #13071104C2semidirect
12. #13071100C2semidirect
13. C11×#2274C2semidirect
24. #10623056C4semidirect
30. C2×#66946C22semidirect
31. C2×#66945C22semidirect
32. C2×C4⋊C4×D11C22semidirect
33. C2×#66940C22semidirect
37. C2×C4×D44C22semidirect
38. C4×C11×C4⋊C4C22semidirect
39. C4×C11×C4⋊C4C22semidirect
42. #10622601C22semidirect
43. #10622598C22semidirect
44. #10622598C22semidirect
45. #10622587C22semidirect
51. #10622553C22semidirect
54. #10622552C22semidirect
55. C4×(C2×D11)⋊C4C22semidirect
56. C4×(C2×D11)⋊C4C22semidirect
57. C4×C4⋊Dic11C22semidirect
58. #10622283C22semidirect
59. #10622281C22semidirect
60. #10622278C22semidirect
61. #10622278C22semidirect
70. C2×#4339C2×C4semidirect
73. C22×D44C2×C4semidirect
85. C11×#117C2×C4semidirect
86. C2×C11×C4⋊C4D4semidirect
117. #66948C2×C4semidirect
124. #66935C2×C4semidirect
125. #66928C2×C4semidirect
126. #66927C2×C4semidirect
176. C2×D44C22×C4semidirect
177. C2×D44C22×C4semidirect
186. C2×C4×D11C22×C4semidirect
189. C2×Dic22C22×C4semidirect
191. C11×C4⋊C4C22×C4semidirect
198. C42×C11C22×C4semidirect
206. (C2×D11)⋊C4C22×C4semidirect
228. #2274D11semidirect
257. C2×C4×C11C4×D4semidirect
333. C4×C4⋊C4C2×D11semidirect
334. C4×C4⋊C4C2×D11semidirect
404. #117C4×D11semidirect
411. C2×C4⋊C4D44semidirect
510. C4⋊C4C2×C4×D11semidirect
529. C42C2×C4×D11semidirect
530. C11#34265semidirect
583. C2×C4C4×D44semidirect

Maximal subgroups

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

subgroupindex
C2×#106230562
C2×#106230352
C22×#669462
#130716872
#130716802
#130716562
#130716342
#130712762
#130711962
C4×#669352
#130711042
#130711002
C11×#22742
#3426511