Finite Group Databasebeta

← #14914100

Subgroups — #14914100

Order 2816.

3038 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66950C211yesmaximal, characteristic
2C2×#10623047C211yesmaximal, characteristic, complemented
3C2×D11×#117C211yesmaximal, characteristic
4#13071645C214yesmaximal, complemented
5#13071623C214yesmaximal, complemented
6#13071483C214yesmaximal, complemented
7#13071468C214yesmaximal
8#13071299C214yesmaximal, complemented
9#13071234C211yesmaximal, characteristic, complemented
10#13071200C211yesmaximal, characteristic, complemented
11C4×#66950C214yesmaximal, complemented
12#13070995C211yesmaximal, characteristic
13C11×#2274C211yesmaximal, characteristic, complemented
14C23×C4×D11C2211yescharacteristic
15C23×Dic22C2211yescharacteristic
16C2×C11×#117C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×(C2×D11)⋊C4C2212yes—
20C2×#66979C2211yescharacteristic
21C2×#66979C2211yescharacteristic
22C22×C4⋊Dic11C2212yes—
23D11×#117—28no—
24#10623047—28no—
25C2×#66950C4116yescomplemented
26C2×#66950C2212yes—
27C2×#66950C2212yes—
28C2×#66950C2212yes—
29C2×#66950C2212yes—
30C2×#66945C2212yes—
31C2×C4⋊C4×D11C2212yes—
32C2×#66940C2214yescomplemented
33C2×C22⋊C4×D11C2212yes—
34C2×#66930C2214yes—
35C2×#66930C2212yes—
36C2×#66925C2212yes—
37C2×C42×D11C2212yes—
38C2×C4×Dic22C2214yescomplemented
39C4×C11×C4⋊C4C2214yescomplemented
40C4×C11×C4⋊C4C2214yescomplemented
41C4×C11×C22⋊C4C2214yes—
42#10622825C2214yes—
43#10622600C2212yes—
44#10622600C2212yes—
45#10622598C2214yescomplemented
46#10622598C2214yescomplemented
47#10622587C2214yescomplemented
48#10622568C2212yes—
49#10622556C2214yes—
50#10622556C2212yes—
51#10622553C2218yes—
52C4×(C2×D11)⋊C4C2212yes—
53C4×(C2×D11)⋊C4C2218yes—
54C4×(C2×D11)⋊C4C2212yes—
55C4×C4⋊Dic11C2218yescomplemented
56#10622542C2214yescomplemented
57#10622541C2218yescomplemented
58#10622283C2218yes—
59#10622281C2218yes—
60#10622266C2218yescomplemented
61#10622266C2218yescomplemented
62C24×D11C2311yescharacteristic
63C23×C4×C11C2312yes—
64C23×C4×C11C2311yescharacteristic
65C23×Dic11C2311yescharacteristic
66C23×Dic11C2312yes—
67C22×C4×D11—24no—
68C22×C4×D11—24no—
69C22×C4×D11C2×C418yes—
70C22×C4×D11C2314yes—
71C22×C4×D11C2311yescharacteristic
72C22×C4×D11C2311yescharacteristic
73C22×C4×D11C2311yescharacteristic
74C22×C4×D11C2311yescharacteristic
75C22×Dic22—24no—
76C22×Dic22—24no—
77C22×Dic22C2×C418yescomplemented
78C22×Dic22C2312yes—
79C22×Dic22C2312yes—
80C11×#117—24no—
81C11×#117D418yes—
82C2×C11×C4⋊C4C2×C418yescomplemented
83C2×C11×C4⋊C4C2312yes—
84C2×C11×C4⋊C4C2312yes—
85C2×C11×C4⋊C4C2312yes—
86C2×C11×C4⋊C4C2312yes—
87C2×C11×C22⋊C4C2312yes—
88C2×C11×C22⋊C4C2312yes—
89C2×C42×C11C2312yes—
90C2×C42×C11C2318yes—
91C2×C42×C11C2312yes—
92C2×C22⋊Dic11C2312yes—
93C2×C22⋊Dic11C2312yes—
94C2×(C2×D11)⋊C4C2×C4116yes—
95C2×(C2×D11)⋊C4C2314yes—
96C2×(C2×D11)⋊C4C2314yes—
97C2×(C2×D11)⋊C4C2314yes—
98C2×(C2×D11)⋊C4C2314yes—
99C2×(C2×D11)⋊C4C2314yes—
100#66979—24no—
101#66979—24no—
102C2×C4⋊Dic11C2×C4116yescomplemented
103C2×C4⋊Dic11C2312yes—
104C2×C4⋊Dic11C2312yes—
105C2×C4⋊Dic11C2318yes—
106C2×C4⋊Dic11C2314yes—
107C2×C4⋊Dic11C2314yes—
108C2×Dic11⋊C4C2318yes—
109C2×Dic11⋊C4C2314yes—
110C2×C4×Dic11C2318yes—
111C2×C4×Dic11C2312yes—
112C2×C4×Dic11C2314yes—
113C2×C4×Dic11C2312yes—
114#66950C2×C4116yes—
115#66950C2×C4116yes—
116#66950C2×C4116yescomplemented
117#66950C2×C4116yescomplemented
118#66945—28no—
119C4⋊C4×D11—28no—
120#66940—216no—
121C22⋊C4×D11—28no—
122#66930—216no—
123#66930—28no—
124#66925—28no—
125C42×D11—28no—
126C4×Dic22—216no—
127C11×#95C2318yes—
128C11⋊#95C2314yes—
129C11⋊#95C2314yes—
130C11⋊#95C2318yes—
131C11⋊#95C2318yes—
132C11⋊#95C2318yes—
133#34203—111nomaximal, Sylow
134C24×C11C2411yescharacteristic
135C23×D11—22no—
136C23×D11—22no—
137C23×D11—24no—
138C23×D11—42no—
139C23×D11C22×C414yes—
140C23×D11C2411yescharacteristic
141C23×D11C2411yescharacteristic
142C22×C4×C11—44no—
143C22×C4×C11C22×C418yes—
144C22×C4×C11C22×C414yes—
145C22×C4×C11C2×D414yes—
146C22×C4×C11#4114yes—
147C22×C4×C11C2414yes—
148C22×C4×C11C2414yes—
149C22×C4×C11C2414yes—
150C22×C4×C11C2411yescharacteristic
151C22×C4×C11C2411yescharacteristic
152C22×Dic11—24no—
153C22×Dic11—22no—
154C22×Dic11—24no—
155C22×Dic11—22no—
156C22×Dic11C22×C414yes—
157C22×Dic11C22×C418yes—
158C22×Dic11C2414yes—
159C22×Dic11C2414yes—
160C22×Dic11C2411yescharacteristic
161C22×Dic11C2414yes—
162C22×Dic11C2411yescharacteristic
163C2×C4×D11—28no—
164C2×C4×D11—232no—
165C2×C4×D11—22no—
166C2×C4×D11—22no—
167C2×C4×D11—22no—
168C2×C4×D11—22no—
169C2×C4×D11—28no—
170C2×C4×D11—22no—
171C2×C4×D11—22no—
172C2×C4×D11—22no—
173C2×C4×D11—22no—
174C2×C4×D11—44no—
175C2×C4×D11C22×C414yes—
176C2×C4×D11C22×C414yes—
177C2×C4×D11C22×C414yes—
178C2×C4×D11C22×C414yes—
179C2×Dic22—232no—
180C2×Dic22—24no—
181C2×Dic22—24no—
182C2×Dic22—24no—
183C2×Dic22—24no—
184C2×Dic22C22×C418yes—
185C2×Dic22C22×C418yes—
186C11×C4⋊C4—24no—
187C11×C4⋊C4C22×C418yes—
188C11×C4⋊C4C22×C418yes—
189C11×C4⋊C4C2×D418yes—
190C11×C22⋊C4—24no—
191C11×C22⋊C4C2×D418yes—
192C42×C11—24no—
193C42×C11—48no—
194C42×C11C2×D418yes—
195C22⋊Dic11—24no—
196C22⋊Dic11—24no—
197(C2×D11)⋊C4—28no—
198(C2×D11)⋊C4—28no—
199(C2×D11)⋊C4—44no—
200(C2×D11)⋊C4C22×C4116yes—
201(C2×D11)⋊C4C22×C4116yes—
202C4⋊Dic11—24no—
203C4⋊Dic11—24no—
204C4⋊Dic11—48no—
205C4⋊Dic11C22×C4116yes—
206C4⋊Dic11C22×C4116yes—
207Dic11⋊C4—216no—
208Dic11⋊C4—28no—
209C4×Dic11—216no—
210C4×Dic11—24no—
211C4×Dic11—28no—
212C4×Dic11—24no—
213C22×C22⋊Q8—111no—
214C2×#519—111no—
215C22×#117—111no—
216#2362—114no—
217#2360—114no—
218#2344—114no—
219#2342—114no—
220#2323—114no—
221#2316—111no—
222#2310—111no—
223C4×C22⋊Q8—114no—
224#2280—111no—
225#2274D1111yescharacteristic, complemented
226C23×C11—22no—
227C23×C11—22no—
228C23×C11C23×C412yes—
229C23×C11C22×D412yes—
230C23×C11C2×#4112yes—
231C23×C11C2511yescharacteristic
232C22×D11—21no—
233C22×D11—21no—
234C22×D11—22no—
235C22×D11—28no—
236C22×D11—21no—
237C22×D11—21no—
238C22×D11—22no—
239C22×D11—22no—
240C22×D11—28no—
241C22×D11—44no—
242C22×D11—48no—
243C22×D11—48no—
244C22×D11C23×C412yes—
245C22×D11C23×C412yes—
246C22×D112−1+414yes—
247C2×C4×C11—24no—
248C2×C4×C11—28no—
249C2×C4×C11—24no—
250C2×C4×C11—24no—
251C2×C4×C11—24no—
252C2×C4×C11—24no—
253C2×C4×C11—48no—
254C2×C4×C11C4×D4116yes—
255C2×C4×C11C23×C418yes—
256C2×C4×C11C23×C412yes—
257C2×C4×C11C23×C412yes—
258C2×C4×C11C22×D418yes—
259C2×C4×C11C22×D412yes—
260C2×C4×C11C22×D412yes—
261C2×C4×C11C2×#4112yes—
262C2×C4×C11C2×#4112yes—
263C2×Dic11—216no—
264C2×Dic11—28no—
265C2×Dic11—21no—
266C2×Dic11—24no—
267C2×Dic11—21no—
268C2×Dic11—24no—
269C2×Dic11—21no—
270C2×Dic11—21no—
271C2×Dic11—24no—
272C2×Dic11—24no—
273C2×Dic11—24no—
274C2×Dic11—24no—
275C2×Dic11—24no—
276C2×Dic11—24no—
277C2×Dic11C23×C412yes—
278C2×Dic11C23×C412yes—
279C2×Dic11C23×C418yes—
280C4×D11—28no—
281C4×D11—28no—
282C4×D11—28no—
283C4×D11—28no—
284C4×D11—416no—
285Dic22—216no—
286Dic22—216no—
287C23×Q8—111no—
288C24×C4—111no—
289C2×C22⋊Q8—112no—
290C2×C22⋊Q8—112no—
291C2×C22⋊Q8—112no—
292C2×C22⋊Q8—112no—
293C2×C22⋊Q8—1116no—
294#519—228no—
295C2×C4×Q8—114no—
296C2×C4×Q8—114no—
297C2×#117—111no—
298C2×#117—111no—
299C2×#117—112no—
300C2×#117—114no—
301C2×#117—112no—
302C2×#117—112no—
303C2×#117—228no—
304C2×#117C2×D1111yescharacteristic
305C2×#117C2×D1111yescharacteristic
306C22×C4⋊C4—112no—
307C22×C4⋊C4—112no—
308C22×C4⋊C4C2×D1111yescharacteristic
309C22×C22⋊C4—112no—
310C22×C22⋊C4—112no—
311C22×C42—112no—
312#391—114no—
313#391—114no—
314#389—114no—
315#389—114no—
316#389—118no—
317#388—118no—
318#388—118no—
319#387—118no—
320#387—118no—
321#385—118no—
322#381—114no—
323#381—112no—
324#380—114no—
325#380—112no—
326#380—112no—
327#379—112no—
328C4×C4⋊C4—118no—
329C4×C4⋊C4C2×D1114yescomplemented
330C4×C4⋊C4C2×D1114yescomplemented
331C4×C22⋊C4—118no—
332C4×C22⋊C4—112no—
333C4×C22⋊C4—112no—
334C4×C22⋊C4C2×D1114yes—
335C22×C11—22no—
336C22×C11—22no—
337C22×C11—24no—
338C22×C11—24no—
339C22×C11C2×C4×D414yes—
340C22×C11C24×C411yescharacteristic
341C22×C11C23×D411yescharacteristic
342C22×C11C22×#4111yescharacteristic
343C22×C11C2×2−1+412yes—
344C22×C11#58512yes—
345C2×D11—22no—
346C2×D11—22no—
347C2×D11—24no—
348C2×D11—24no—
349C2×D11—22no—
350C2×D11—22no—
351C2×D11—22no—
352C2×D11—416no—
353C2×D11—42no—
354C2×D11—42no—
355C2×D11#51914yescomplemented
356C4×C11—28no—
357C4×C11—28no—
358C4×C11—44no—
359C4×C11C2×C4×D414yes—
360C4×C11C2×C4×D414yes—
361Dic11—28no—
362Dic11—22no—
363Dic11—22no—
364Dic11—44no—
365Dic11—44no—
366C25—111no—
367C22×Q8—118no—
368C22×Q8—112no—
369C22×Q8—112no—
370C22×Q8—224no—
371C22×Q8—224no—
372C23×C4—112no—
373C23×C4—111no—
374C23×C4—118no—
375C23×C4—111no—
376C23×C4—111no—
377C23×C4—111no—
378C23×C4—111no—
379C23×C4—114no—
380C23×C4—224no—
381C23×C4—224no—
382C23×C4C22×D1112yes—
383C23×C4C22×D1111yescharacteristic
384C22⋊Q8—1116no—
385C22⋊Q8—1116no—
386C22⋊Q8—1116no—
387C22⋊Q8—1116no—
388C4×Q8—2216no—
389C4×Q8—2216no—
390#117—24no—
391#117—224no—
392#117—224no—
393#117—228no—
394#117—228no—
395#117—2216no—
396#117—228no—
397#117D4418yes—
398C2×C4⋊C4—1116no—
399C2×C4⋊C4—114no—
400C2×C4⋊C4—114no—
401C2×C4⋊C4—114no—
402C2×C4⋊C4—112no—
403C2×C4⋊C4—112no—
404C2×C4⋊C4—118no—
405C2×C4⋊C4—118no—
406C2×C4⋊C4—228no—
407C2×C4⋊C4C4×D1118yescomplemented
408C2×C4⋊C4C22×D1112yes—
409C2×C4⋊C4C22×D1112yes—
410C2×C4⋊C4C22×D1112yes—
411C2×C4⋊C4C22×D1112yes—
412C2×C22⋊C4—1116no—
413C2×C22⋊C4—114no—
414C2×C22⋊C4—114no—
415C2×C22⋊C4—112no—
416C2×C22⋊C4—112no—
417C2×C22⋊C4—114no—
418C2×C22⋊C4—114no—
419C2×C22⋊C4—114no—
420C2×C22⋊C4—228no—
421C2×C22⋊C4C22×D1112yes—
422C2×C22⋊C4C22×D1112yes—
423C2×C42—114no—
424C2×C42—112no—
425C2×C42—112no—
426C2×C42—118no—
427C2×C42—228no—
428C2×C42C22×D1112yes—
429C2×C42C22×D1118yes—
430C2×C42C22×D1112yes—
431#95—114no—
432#95—114no—
433#95—118no—
434#95—118no—
435#95—118no—
436#95C22×D1118yes—
437C2×C11—24no—
438C2×C11C22×C4×D411yescharacteristic
439C2×C11C2×#51911yescharacteristic
440C2×C11#342811yescharacteristic
441C2×C11#348912yes—
442C2×C11#349512yes—
443D11—24no—
444D11—42no—
445C24—111no—
446C24—111no—
447C24—114no—
448C24—224no—
449C24—222no—
450C24—222no—
451C24—442no—
452C24C23×D1111yescharacteristic
453C2×Q8—118no—
454C2×Q8—118no—
455C2×Q8—2232no—
456C2×Q8—224no—
457C2×Q8—224no—
458C2×Q8—224no—
459C2×Q8—224no—
460C22×C4—44no—
461C22×C4—118no—
462C22×C4—114no—
463C22×C4—111no—
464C22×C4—114no—
465C22×C4—111no—
466C22×C4—114no—
467C22×C4—114no—
468C22×C4—114no—
469C22×C4—114no—
470C22×C4—114no—
471C22×C4—114no—
472C22×C4—228no—
473C22×C4—222no—
474C22×C4—224no—
475C22×C4—222no—
476C22×C4—224no—
477C22×C4—2232no—
478C22×C4—222no—
479C22×C4—222no—
480C22×C4—222no—
481C22×C4—222no—
482C22×C4—222no—
483C22×C4—222no—
484C22×C4—222no—
485C22×C4—222no—
486C22×C4—228no—
487C22×C4—444no—
488C22×C4C2×C4×D1118yes—
489C22×C4C2×C4×D1114yes—
490C22×C4C2×D4414yes—
491C22×C4#433914yes—
492C22×C4C23×D1114yes—
493C22×C4C23×D1114yes—
494C22×C4C23×D1114yes—
495C22×C4C23×D1111yescharacteristic
496C22×C4C23×D1111yescharacteristic
497C4⋊C4—24no—
498C4⋊C4—1116no—
499C4⋊C4—1116no—
500C4⋊C4—228no—
501C4⋊C4—224no—
502C4⋊C4—2216no—
503C4⋊C4—224no—
504C4⋊C4—448no—
505C4⋊C4C2×C4×D1118yes—
506C4⋊C4C2×C4×D1118yes—
507C4⋊C4C2×D4418yes—
508C22⋊C4—24no—
509C22⋊C4—1116no—
510C22⋊C4—1116no—
511C22⋊C4—228no—
512C22⋊C4—224no—
513C22⋊C4—224no—
514C22⋊C4—228no—
515C22⋊C4—444no—
516C22⋊C4C2×D4418yes—
517C42—24no—
518C42—48no—
519C42—228no—
520C42—224no—
521C42—2216no—
522C42—224no—
523C42C2×D4418yes—
524C11#3420311yescharacteristic, complemented, Sylow
525C23—22no—
526C23—22no—
527C23—112no—
528C23—114no—
529C23—112no—
530C23—228no—
531C23—221no—
532C23—221no—
533C23—222no—
534C23—228no—
535C23—221no—
536C23—221no—
537C23—222no—
538C23—222no—
539C23—444no—
540C23—448no—
541C23—448no—
542C23C22×C4×D1112yes—
543C23C22×D4412yes—
544C23C2×#433912yes—
545C23C24×D1111yescharacteristic
546Q8—2216no—
547Q8—2216no—
548C2×C4—24no—
549C2×C4—28no—
550C2×C4—24no—
551C2×C4—24no—
552C2×C4—24no—
553C2×C4—24no—
554C2×C4—48no—
555C2×C4—118no—
556C2×C4—112no—
557C2×C4—112no—
558C2×C4—228no—
559C2×C4—2216no—
560C2×C4—221no—
561C2×C4—224no—
562C2×C4—221no—
563C2×C4—221no—
564C2×C4—221no—
565C2×C4—224no—
566C2×C4—228no—
567C2×C4—228no—
568C2×C4—228no—
569C2×C4—228no—
570C2×C4—224no—
571C2×C4—224no—
572C2×C4—224no—
573C2×C4—224no—
574C2×C4—224no—
575C2×C4—224no—
576C2×C4—4416no—
577C2×C4C4×D44116yes—
578C2×C4C22×C4×D1118yes—
579C2×C4C22×C4×D1112yes—
580C2×C4C22×C4×D1112yes—
581C2×C4C22×D4418yes—
582C2×C4C22×D4412yes—
583C2×C4C22×D4412yes—
584C2×C4C2×#433912yes—
585C2×C4C2×#433912yes—
586C22—24no—
587C22—24no—
588C22—22no—
589C22—22no—
590C22—114no—
591C22—224no—
592C22—224no—
593C22—222no—
594C22—222no—
595C22—222no—
596C22—222no—
597C22—222no—
598C22—4416no—
599C22—442no—
600C22—442no—
601C22C2×C4×D4414yes—
602C22C23×C4×D1111yescharacteristic
603C22C23×D4411yescharacteristic
604C22C22×#433911yescharacteristic
605C22#1062345512yes—
606C22D11×2−1+412yes—
607C4—28no—
608C4—28no—
609C4—44no—
610C4—222no—
611C4—222no—
612C4—228no—
613C4—444no—
614C4—444no—
615C4C2×C4×D4414yes—
616C4C2×C4×D4414yes—
617C2—24no—
618C2—224no—
619C2—442no—
620C2C22×C4×D4411yescharacteristic
621C2D11×#51911yescharacteristic
622C2#1308181411yescharacteristic
623C2#1308229712yes—
624C2#1308236912yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2274C2
socle, cosocleC23×C11C25
prime radicalC24×D11C23
hypercenter#2274D11
hypocenterC11#34203
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2274

Complements

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

NH ≅ G/Ntype
2. C2×#10623047C2semidirect
4. #13071645C2semidirect
5. #13071623C2semidirect
6. #13071483C2semidirect
8. #13071299C2semidirect
9. #13071234C2semidirect
10. #13071200C2semidirect
11. C4×#66950C2semidirect
13. C11×#2274C2semidirect
25. C2×#66950C4semidirect
32. C2×#66940C22semidirect
38. C2×C4×Dic22C22semidirect
39. C4×C11×C4⋊C4C22semidirect
40. C4×C11×C4⋊C4C22semidirect
45. #10622598C22semidirect
46. #10622598C22semidirect
47. #10622587C22semidirect
55. C4×C4⋊Dic11C22semidirect
56. #10622542C22semidirect
57. #10622541C22semidirect
60. #10622266C22semidirect
61. #10622266C22semidirect
77. C22×Dic22C2×C4semidirect
82. C2×C11×C4⋊C4C2×C4semidirect
102. C2×C4⋊Dic11C2×C4semidirect
116. #66950C2×C4semidirect
117. #66950C2×C4semidirect
225. #2274D11semidirect
329. C4×C4⋊C4C2×D11semidirect
330. C4×C4⋊C4C2×D11semidirect
355. C2×D11#519semidirect
407. C2×C4⋊C4C4×D11semidirect
524. C11#34203semidirect

Maximal subgroups

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

subgroupindex
C22×#669502
C2×#106230472
C2×D11×#1172
#130716452
#130716232
#130714832
#130714682
#130712992
#130712342
#130712002
C4×#669502
#130709952
C11×#22742
#3420311