Finite Group Databasebeta

← #14914072

Subgroups — #14914072

Order 2816.

3118 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623359C211yesmaximal, characteristic
2C2×#10623358C211yesmaximal, characteristic, complemented
3C22×#66945C211yesmaximal, characteristic, complemented
4#13071659C214yesmaximal, complemented
5#13071648C214yesmaximal, complemented
6#13071560C214yesmaximal, complemented
7#13071547C214yesmaximal, complemented
8#13071279C214yesmaximal, complemented
9#13071240C211yesmaximal, characteristic, complemented
10#13071141C214yesmaximal, complemented
11#13070995C211yesmaximal, characteristic, complemented
12#13070972C211yesmaximal, characteristic, complemented
13C11×#2311C211yesmaximal, characteristic, complemented
14C22×C11×#41C2211yescharacteristic
15C23×C4×D11C2211yescharacteristic
16C2×C11×#117C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18#10623359C4116yescomplemented
19#10623358—28no—
20C2×#66999C2212yes—
21C2×Q8×Dic11C2212yescomplemented
22C2×#66991C2212yes—
23C2×#66990C2212yes—
24C2×#66988C2212yes—
25C2×D4×Dic11C2214yes—
26C2×D4×Dic11C2212yescomplemented
27C2×C4×C22⋊D11C2214yes—
28C22×(C2×D11)⋊C4C2212yes—
29C2×#66979C2211yescharacteristic
30C2×#66979C2211yescharacteristic
31C2×#66979C2212yescomplemented
32C22×C4⋊Dic11C2211yescharacteristic
33C22×C4⋊Dic11C2212yescomplemented
34C22×C4×Dic11C2212yes—
35C2×#66945—28no—
36C2×#66945C2214yes—
37C2×#66945C2214yes—
38C11×#391C2212yescomplemented
39C11×#390C2212yescomplemented
40C11×#386C2214yes—
41C11×#380C2214yescomplemented
42#10622823C2214yes—
43#10622600C2212yes—
44#10622600C2212yes—
45#10622590C2212yescomplemented
46#10622589C2212yescomplemented
47C4⋊C4×Dic11C2214yescomplemented
48#10622586C2214yescomplemented
49#10622571C2218yes—
50#10622570C2218yes—
51#10622568C2212yes—
52#10622558C2218yescomplemented
53#10622556C2212yes—
54C22⋊C4×Dic11C2214yes—
55C22⋊C4×Dic11C2218yescomplemented
56C4×(C2×D11)⋊C4C2214yes—
57C4×C4⋊Dic11C2214yescomplemented
58#10622283C2218yes—
59#10622282C2218yes—
60#10622268C2218yescomplemented
61#10622262C2218yescomplemented
62C24×D11C2311yescharacteristic
63C2×C11×#41—24no—
64C2×C11×#41—24no—
65C2×C11×#41C2×C418yes—
66C22×Q8×C11C2311yescharacteristic
67C22×D4×C11C2312yes—
68C22×D4×C11C2311yescharacteristic
69C23×C4×C11C2312yes—
70C23×C4×C11C2312yes—
71C23×C4×C11C2311yescharacteristic
72C22×C22⋊D11C2314yes—
73C23×Dic11C2311yescharacteristic
74C23×Dic11C2314yes—
75C23×Dic11C2312yes—
76C22×C4×D11—24no—
77C22×C4×D11—24no—
78C22×C4×D11C2×C418yescomplemented
79C22×C4×D11C2312yes—
80C22×C4×D11C2312yes—
81C11×#117—24no—
82C2×C11×C4⋊C4—24no—
83C2×C11×C4⋊C4C2312yes—
84C2×C11×C4⋊C4C2312yes—
85C2×C11×C4⋊C4C2312yes—
86C2×C11×C22⋊C4C2312yes—
87C2×C11×C22⋊C4C2318yes—
88C2×C42×C11C2312yes—
89C2×C22⋊Dic11C2312yes—
90C2×C22⋊Dic11C2314yes—
91C2×C22⋊Dic11C2312yes—
92C2×C22⋊Dic11C2314yes—
93#66999C2×C4116yescomplemented
94Q8×Dic11—28no—
95#66991C2×C4116yescomplemented
96#66990C2×C4116yescomplemented
97#66988C2×C4116yescomplemented
98D4×Dic11—216no—
99D4×Dic11—28no—
100C4×C22⋊D11C2×C4132yescomplemented
101C2×(C2×D11)⋊C4—28no—
102C2×(C2×D11)⋊C4C2318yes—
103C2×(C2×D11)⋊C4C2314yes—
104C2×(C2×D11)⋊C4C2314yes—
105C2×(C2×D11)⋊C4C2314yes—
106#66979—24no—
107#66979—28no—
108#66979C2×C418yescomplemented
109C2×C4⋊Dic11—28no—
110C2×C4⋊Dic11D418yescomplemented
111C2×C4⋊Dic11C2314yes—
112C2×C4⋊Dic11C2311yescharacteristic
113C2×C4⋊Dic11C2311yescharacteristic
114C2×C4⋊Dic11C2312yes—
115C2×C4⋊Dic11C2312yes—
116C2×C4⋊Dic11C2312yes—
117C2×Dic11⋊C4C2318yes—
118C2×Dic11⋊C4C2314yes—
119C2×C4×Dic11—28no—
120C2×C4×Dic11C2314yes—
121C2×C4×Dic11C2318yes—
122C2×C4×Dic11C2312yes—
123C2×C4×Dic11C2318yes—
124C2×C4×Dic11C2312yes—
125#66945—216no—
126#66945—216no—
127C11×#95C2318yes—
128C11⋊#95C2314yes—
129C11⋊#95C2314yes—
130C11⋊#95C2318yes—
131C11⋊#95C2318yes—
132#34201—111nomaximal, Sylow
133C24×C11C2412yes—
134C24×C11C2411yescharacteristic
135C23×D11—22no—
136C23×D11—22no—
137C23×D11—42no—
138C23×D11—42no—
139C23×D11C22×C414yes—
140C23×D11C2412yes—
141C11×#41—232no—
142C2×Q8×C11—22no—
143C2×Q8×C11—22no—
144C2×Q8×C11C22×C414yes—
145C2×D4×C11—24no—
146C2×D4×C11—24no—
147C2×D4×C11—22no—
148C2×D4×C11—22no—
149C2×D4×C11C22×C418yes—
150C2×D4×C11C22×C414yes—
151C22×C4×C11—24no—
152C22×C4×C11—24no—
153C22×C4×C11—24no—
154C22×C4×C11—44no—
155C22×C4×C11C22×C418yes—
156C22×C4×C11C22×C414yes—
157C22×C4×C11C2×D414yes—
158C22×C4×C11#4114yes—
159C22×C4×C11C2414yes—
160C22×C4×C11C2414yes—
161C22×C4×C11C2412yes—
162C22×C4×C11C2411yescharacteristic
163C22×C4×C11C2411yescharacteristic
164C2×C22⋊D11—44no—
165C2×C22⋊D11—44no—
166C2×C22⋊D11C22×C4116yes—
167C22×Dic11—28no—
168C22×Dic11—22no—
169C22×Dic11—22no—
170C22×Dic11—44no—
171C22×Dic11—48no—
172C22×Dic11C22×C414yes—
173C22×Dic11C2×D418yes—
174C22×Dic11C2412yes—
175C22×Dic11C2412yes—
176C22×Dic11C2412yes—
177C22×Dic11C2414yes—
178C22×Dic11C2414yes—
179C2×C4×D11—232no—
180C2×C4×D11—24no—
181C2×C4×D11—24no—
182C2×C4×D11—24no—
183C2×C4×D11—24no—
184C2×C4×D11C22×C418yes—
185C2×C4×D11C22×C418yes—
186C11×C4⋊C4—24no—
187C11×C4⋊C4—24no—
188C11×C4⋊C4—24no—
189C11×C22⋊C4—24no—
190C11×C22⋊C4—48no—
191C42×C11—24no—
192C22⋊Dic11—28no—
193C22⋊Dic11—24no—
194C22⋊Dic11C22×C418yes—
195C22⋊Dic11C22×C4116yes—
196(C2×D11)⋊C4—216no—
197(C2×D11)⋊C4—44no—
198(C2×D11)⋊C4—44no—
199(C2×D11)⋊C4C22×C4116yes—
200C4⋊Dic11—28no—
201C4⋊Dic11—22no—
202C4⋊Dic11—22no—
203C4⋊Dic11C22×C418yes—
204C4⋊Dic11C2×D418yes—
205C4⋊Dic11C2×D418yes—
206Dic11⋊C4—48no—
207Dic11⋊C4C22×C4116yes—
208C4×Dic11—216no—
209C4×Dic11—28no—
210C4×Dic11—24no—
211C4×Dic11—48no—
212C4×Dic11C22×C418yes—
213C2×#525—111no—
214C2×#520—111no—
215C22×#117—111no—
216#2363—114no—
217#2362—114no—
218#2354—114no—
219#2352—114no—
220#2321—114no—
221#2317—111no—
222#2311D1111yescharacteristic, complemented
223C4×#123—114no—
224#2280—111no—
225#2274—111no—
226C23×C11—22no—
227C23×C11—22no—
228C23×C11—22no—
229C23×C11—22no—
230C23×C11—24no—
231C23×C11—24no—
232C23×C11C23×C414yes—
233C23×C11C23×C412yes—
234C23×C11C22×D412yes—
235C23×C11C2×#4112yes—
236C23×C11C2511yescharacteristic
237C22×D11—28no—
238C22×D11—22no—
239C22×D11—22no—
240C22×D11—22no—
241C22×D11—22no—
242C22×D11—22no—
243C22×D11—22no—
244C22×D11—48no—
245C22×D11—44no—
246C22×D11—44no—
247C22×D11—48no—
248C22×D11C23×C414yes—
249Q8×C11—28no—
250D4×C11—216no—
251D4×C11—28no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—216no—
255C2×C4×C11—24no—
256C2×C4×C11—24no—
257C2×C4×C11—24no—
258C2×C4×C11—28no—
259C2×C4×C11—24no—
260C2×C4×C11—48no—
261C2×C4×C11C4×D4116yes—
262C2×C4×C11C23×C414yes—
263C2×C4×C11C23×C412yes—
264C2×C4×C11C23×C412yes—
265C2×C4×C11C22×D412yes—
266C2×C4×C11C22×D412yes—
267C2×C4×C11C2×#4112yes—
268C2×C4×C11C2×#4112yes—
269C22⋊D11—416no—
270C2×Dic11—28no—
271C2×Dic11—22no—
272C2×Dic11—22no—
273C2×Dic11—24no—
274C2×Dic11—28no—
275C2×Dic11—24no—
276C2×Dic11—22no—
277C2×Dic11—22no—
278C2×Dic11—24no—
279C2×Dic11—24no—
280C2×Dic11—48no—
281C2×Dic11—88no—
282C2×Dic11C23×C418yes—
283C2×Dic11C23×C414yes—
284C2×Dic11C22×D418yes—
285C4×D11—216no—
286C4×D11—216no—
287C22×#41C2×D1111yescharacteristic
288C24×C4—111no—
289#525—1116no—
290C2×#123—112no—
291C2×C22⋊Q8—112no—
292C2×#121—112no—
293C2×#120—112no—
294#520—228no—
295C2×C4×Q8—112no—
296C2×C4×D4—114no—
297C2×C4×D4—114no—
298C2×C4×D4—112no—
299C2×#117—111no—
300C2×#117—111no—
301C2×#117—112no—
302C2×#117—114no—
303C2×#117—114no—
304C2×#117—228no—
305C2×#117C2×D1111yescharacteristic
306C22×C4⋊C4—111no—
307C22×C4⋊C4—112no—
308C22×C4⋊C4C2×D1111yescharacteristic
309C22×C22⋊C4—112no—
310C22×C42—112no—
311#391C2×D1112yescomplemented
312#390—118no—
313#390C2×D1112yescomplemented
314#389—114no—
315#388—118no—
316#388—118no—
317#388—118no—
318#387—118no—
319#386—118no—
320#386C2×D1114yes—
321#385—114no—
322#384—112no—
323#382—112no—
324#381—112no—
325#380—112no—
326#380—112no—
327#380C2×D1114yescomplemented
328#379—112no—
329C4×C4⋊C4—114no—
330C4×C4⋊C4—114no—
331C4×C4⋊C4—118no—
332C4×C22⋊C4—114no—
333C4×C22⋊C4—118no—
334C4×C22⋊C4—114no—
335C22×C11—24no—
336C22×C11—22no—
337C22×C11—22no—
338C22×C11—24no—
339C22×C11—24no—
340C22×C11—28no—
341C22×C11—42no—
342C22×C11—42no—
343C22×C11—44no—
344C22×C11C2×C4×D414yes—
345C22×C11C24×C411yescharacteristic
346C22×C11C23×D411yescharacteristic
347C22×C11C22×#4111yescharacteristic
348C22×C11#58512yes—
349C22×C11#58512yes—
350C2×D11—24no—
351C2×D11—24no—
352C2×D11—24no—
353C2×D11—416no—
354C2×D11—42no—
355C2×D11—42no—
356C2×D11—42no—
357C2×D11—42no—
358C4×C11—24no—
359C4×C11—44no—
360C4×C11—44no—
361C4×C11C2×C4×D414yes—
362C4×C11C2×C4×D414yes—
363Dic11—24no—
364Dic11—28no—
365Dic11—28no—
366Dic11—42no—
367Dic11—42no—
368C25—111no—
369C2×#41—24no—
370C2×#41—24no—
371C2×#41C4×D1118yes—
372C22×Q8C22×D1111yescharacteristic
373C22×D4—114no—
374C22×D4C22×D1112yes—
375C22×D4C22×D1111yescharacteristic
376C23×C4—111no—
377C23×C4—112no—
378C23×C4—118no—
379C23×C4—112no—
380C23×C4—112no—
381C23×C4—114no—
382C23×C4—224no—
383C23×C4—224no—
384C23×C4C22×D1112yes—
385C23×C4C22×D1112yes—
386C23×C4C22×D1111yescharacteristic
387#123—1116no—
388C22⋊Q8—1116no—
389#121—1116no—
390#120—1116no—
391C4×Q8—228no—
392C4×D4—1132no—
393C4×D4—228no—
394C4×D4—2216no—
395#117—24no—
396#117—118no—
397#117—2216no—
398#117—2216no—
399#117—228no—
400#117—224no—
401C2×C4⋊C4—24no—
402C2×C4⋊C4—118no—
403C2×C4⋊C4—112no—
404C2×C4⋊C4—112no—
405C2×C4⋊C4—112no—
406C2×C4⋊C4—114no—
407C2×C4⋊C4—111no—
408C2×C4⋊C4—114no—
409C2×C4⋊C4—111no—
410C2×C4⋊C4—118no—
411C2×C4⋊C4—228no—
412C2×C4⋊C4C22×D1112yes—
413C2×C4⋊C4C22×D1112yes—
414C2×C4⋊C4C22×D1112yes—
415C2×C22⋊C4—112no—
416C2×C22⋊C4—114no—
417C2×C22⋊C4—114no—
418C2×C22⋊C4—112no—
419C2×C22⋊C4—114no—
420C2×C22⋊C4—118no—
421C2×C22⋊C4—114no—
422C2×C22⋊C4—114no—
423C2×C22⋊C4—228no—
424C2×C22⋊C4C22×D1112yes—
425C2×C22⋊C4C22×D1118yes—
426C2×C42—112no—
427C2×C42—118no—
428C2×C42—112no—
429C2×C42—114no—
430C2×C42—118no—
431C2×C42—228no—
432C2×C42C22×D1112yes—
433#95—114no—
434#95—114no—
435#95—118no—
436#95—118no—
437#95C22×D1118yes—
438C2×C11—24no—
439C2×C11—44no—
440C2×C11C22×C4×D411yescharacteristic
441C2×C11#342812yes—
442C2×C11#348511yescharacteristic
443C2×C11#348711yescharacteristic
444C2×C11#349312yes—
445D11—44no—
446C24—112no—
447C24—114no—
448C24—222no—
449C24—222no—
450C24—442no—
451C24—442no—
452C24C23×D1112yes—
453C24C23×D1111yescharacteristic
454#41—232no—
455C2×Q8—22no—
456C2×Q8—22no—
457C2×Q8C2×C4×D1114yes—
458C2×D4—24no—
459C2×D4—24no—
460C2×D4—22no—
461C2×D4—22no—
462C2×D4—1116no—
463C2×D4—444no—
464C2×D4—444no—
465C2×D4C2×C4×D1118yes—
466C2×D4C2×C4×D1114yes—
467C22×C4—24no—
468C22×C4—24no—
469C22×C4—24no—
470C22×C4—44no—
471C22×C4—114no—
472C22×C4—112no—
473C22×C4—114no—
474C22×C4—114no—
475C22×C4—118no—
476C22×C4—118no—
477C22×C4—118no—
478C22×C4—112no—
479C22×C4—112no—
480C22×C4—228no—
481C22×C4—222no—
482C22×C4—222no—
483C22×C4—2232no—
484C22×C4—224no—
485C22×C4—224no—
486C22×C4—224no—
487C22×C4—224no—
488C22×C4—444no—
489C22×C4—448no—
490C22×C4C2×C4×D1118yes—
491C22×C4C2×C4×D1114yes—
492C22×C4D4×D1114yes—
493C22×C4#434114yes—
494C22×C4C23×D1114yes—
495C22×C4C23×D1114yes—
496C22×C4C23×D1112yes—
497C22×C4C23×D1111yescharacteristic
498C22×C4C23×D1111yescharacteristic
499C4⋊C4—24no—
500C4⋊C4—24no—
501C4⋊C4—24no—
502C4⋊C4—118no—
503C4⋊C4—1116no—
504C4⋊C4—118no—
505C4⋊C4—118no—
506C4⋊C4—228no—
507C4⋊C4—222no—
508C4⋊C4—222no—
509C4⋊C4—448no—
510C22⋊C4—24no—
511C22⋊C4—48no—
512C22⋊C4—118no—
513C22⋊C4—1116no—
514C22⋊C4—1116no—
515C22⋊C4—2216no—
516C22⋊C4—228no—
517C22⋊C4—224no—
518C22⋊C4—444no—
519C22⋊C4—444no—
520C42—24no—
521C42—118no—
522C42—2216no—
523C42—228no—
524C42—224no—
525C42—448no—
526C11#3420111yescharacteristic, complemented, Sylow
527C23—22no—
528C23—22no—
529C23—22no—
530C23—22no—
531C23—24no—
532C23—24no—
533C23—114no—
534C23—228no—
535C23—222no—
536C23—222no—
537C23—222no—
538C23—222no—
539C23—222no—
540C23—222no—
541C23—448no—
542C23—444no—
543C23—444no—
544C23—448no—
545C23C22×C4×D1114yes—
546C23C22×C4×D1112yes—
547C23C2×D4×D1112yes—
548C23C2×#434112yes—
549C23C24×D1111yescharacteristic
550Q8—28no—
551D4—216no—
552D4—28no—
553D4—4416no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—216no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—24no—
560C2×C4—28no—
561C2×C4—24no—
562C2×C4—48no—
563C2×C4—118no—
564C2×C4—114no—
565C2×C4—118no—
566C2×C4—228no—
567C2×C4—222no—
568C2×C4—222no—
569C2×C4—224no—
570C2×C4—224no—
571C2×C4—228no—
572C2×C4—2216no—
573C2×C4—2216no—
574C2×C4—222no—
575C2×C4—222no—
576C2×C4—224no—
577C2×C4—224no—
578C2×C4—448no—
579C2×C4—888no—
580C2×C4(C22⋊D11)⋊C4116yes—
581C2×C4C22×C4×D1114yes—
582C2×C4C22×C4×D1112yes—
583C2×C4C22×C4×D1112yes—
584C2×C4C2×D4×D1112yes—
585C2×C4C2×D4×D1112yes—
586C2×C4C2×#434112yes—
587C2×C4C2×#434112yes—
588C22—22no—
589C22—22no—
590C22—24no—
591C22—24no—
592C22—24no—
593C22—28no—
594C22—42no—
595C22—42no—
596C22—44no—
597C22—224no—
598C22—224no—
599C22—224no—
600C22—4416no—
601C22—442no—
602C22—442no—
603C22—442no—
604C22—442no—
605C22C2×(C22⋊D11)⋊C414yes—
606C22C23×C4×D1111yescharacteristic
607C22C22×D4×D1111yescharacteristic
608C22C22×#434111yescharacteristic
609C22#1062345512yes—
610C22#1062345712yes—
611C4—24no—
612C4—44no—
613C4—44no—
614C4—228no—
615C4—224no—
616C4—228no—
617C4—442no—
618C4—442no—
619C4C2×(C22⋊D11)⋊C414yes—
620C4C2×(C22⋊D11)⋊C414yes—
621C2—24no—
622C2—44no—
623C2—444no—
624C2C22×(C22⋊D11)⋊C411yescharacteristic
625C2#1308181612yes—
626C2#1308225911yescharacteristic
627C2#1308227211yescharacteristic
628C2#1308233512yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2311C2
socle, cosocleC23×C11C25
prime radicalC2×#10623359C2
hypercenter#2311D11
hypocenterC11#34201
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. C22×#66945C2semidirect
4. #13071659C2semidirect
5. #13071648C2semidirect
6. #13071560C2semidirect
7. #13071547C2semidirect
8. #13071279C2semidirect
9. #13071240C2semidirect
10. #13071141C2semidirect
11. #13070995C2semidirect
12. #13070972C2semidirect
13. C11×#2311C2semidirect
18. #10623359C4semidirect
21. C2×Q8×Dic11C22semidirect
26. C2×D4×Dic11C22semidirect
31. C2×#66979C22semidirect
33. C22×C4⋊Dic11C22semidirect
38. C11×#391C22semidirect
39. C11×#390C22semidirect
41. C11×#380C22semidirect
45. #10622590C22semidirect
46. #10622589C22semidirect
47. C4⋊C4×Dic11C22semidirect
48. #10622586C22semidirect
52. #10622558C22semidirect
55. C22⋊C4×Dic11C22semidirect
57. C4×C4⋊Dic11C22semidirect
60. #10622268C22semidirect
61. #10622262C22semidirect
78. C22×C4×D11C2×C4semidirect
93. #66999C2×C4semidirect
95. #66991C2×C4semidirect
96. #66990C2×C4semidirect
97. #66988C2×C4semidirect
100. C4×C22⋊D11C2×C4semidirect
108. #66979C2×C4semidirect
110. C2×C4⋊Dic11D4semidirect
222. #2311D11semidirect
311. #391C2×D11semidirect
313. #390C2×D11semidirect
327. #380C2×D11semidirect
526. C11#34201semidirect

Maximal subgroups

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

subgroupindex
C2×#106233592
C2×#106233582
C22×#669452
#130716592
#130716482
#130715602
#130715472
#130712792
#130712402
#130711412
#130709952
#130709722
C11×#23112
#3420111