Finite Group Databasebeta

← #14926807

Subgroups — #14926807

Order 2816.

2650 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66999C211yesmaximal, characteristic
2C2×D11×C22⋊Q8C211yesmaximal, characteristic
3#13076965C212yesmaximal, complemented
4#13076963C212yesmaximal, complemented
5#13074729C214yesmaximal, complemented
6#13073995C214yesmaximal, complemented
7#13073992C214yesmaximal, complemented
8#13073095C211yesmaximal, characteristic, complemented
9#13073094C211yesmaximal, characteristic, complemented
10#13073093C212yesmaximal, complemented
11#13072257C212yesmaximal, complemented
12#13072256C211yesmaximal, characteristic, complemented
13#13071227C214yesmaximal
14C4×C22⋊C4×D11C211yesmaximal, characteristic
15C11×#2434C211yesmaximal, characteristic, complemented
16C23×Q8×C11C2211yescharacteristic
17C22×Q8×D11C2211yescharacteristic
18C23×C4×D11C2211yescharacteristic
19C2×C11×C4⋊Q8C2212yescomplemented
20C2×C11×C22⋊Q8C2211yescharacteristic
21C2×#66999—28no—
22C2×#66999C2212yes—
23C2×#66999C2212yes—
24C2×#66999C2212yes—
25C2×#66999C2211yescharacteristic
26C2×#66999C2212yes—
27C2×#66997C2212yescomplemented
28C22×(C2×D11)⋊C4C2212yes—
29C22×C4⋊Dic11C2211yescharacteristic
30C2×#66977C2211yescharacteristic
31C22×Dic11⋊C4C2212yes—
32D11×C22⋊Q8—28no—
33C2×#66950C2211yescharacteristic
34C2×#66949C2212yes—
35C2×C4⋊C4×D11C2212yes—
36C2×C4⋊C4×D11C2211yescharacteristic
37C2×C22⋊C4×D11C2212yes—
38C2×C22⋊C4×D11C2212yes—
39C2×#66931C2212yes—
40C2×C42×D11C2212yes—
41C11×#395C2214yescomplemented
42C11×#391C2212yescomplemented
43C11×#385C2214yes—
44C4×C11×C22⋊C4C2211yescharacteristic
45#10622843C2212yescomplemented
46#10622843C2212yescomplemented
47#10622842C2214yescomplemented
48#10622823C2214yes—
49C4×C22⋊Dic11C2211yescharacteristic
50#10622602C2218yes—
51#10622600C2218yes—
52#10622596C2214yescomplemented
53#10622592C2218yescomplemented
54#10622589C2212yescomplemented
55#10622586C2218yescomplemented
56#10622563C2214yes—
57#10622559C2214yes—
58C22⋊C4×Dic11C2212yes—
59C4×(C2×D11)⋊C4C2212yes—
60#10622548C2212yescomplemented
61#10622542C2212yescomplemented
62#10622281C2218yes—
63#10622280C2218yes—
64#10622279C2212yes—
65D11×#95C2212yes—
66#10622274C2214yescomplemented
67#10622270C2218yescomplemented
68#10622260C2218yescomplemented
69C24×D11C2311yescharacteristic
70C22×Q8×C11—24no—
71C22×Q8×C11—44no—
72C22×Q8×C11C2312yes—
73C22×Q8×C11C2311yescharacteristic
74C22×Q8×C11C2312yes—
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2312yes—
77C23×Dic11C2312yes—
78C23×Dic11C2311yescharacteristic
79C2×Q8×D11—24no—
80C2×Q8×D11—44no—
81C22×C4×D11—44no—
82C22×C4×D11D418yes—
83C22×C4×D11C2311yescharacteristic
84C22×C4×D11C2311yescharacteristic
85C22×C4×D11C2312yes—
86C22×C4×D11C2312yes—
87C22×C4×D11C2311yescharacteristic
88C22×C4×D11C2311yescharacteristic
89C22×C4×D11C2314yes—
90C22×Dic22C2311yescharacteristic
91C22×Dic22C2312yes—
92C11×C4⋊Q8—44no—
93C11×C22⋊Q8—24no—
94C2×C11×C4⋊C4C2312yes—
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C4⋊C4C2318yes—
97C2×C11×C22⋊C4C2312yes—
98C2×C11×C22⋊C4C2312yes—
99C2×C42×C11C2312yes—
100C2×C22⋊Dic11C2312yes—
101C2×C22⋊Dic11C2312yes—
102#66999—28no—
103#66999—28no—
104#66999—28no—
105#66999—28no—
106#66999—24no—
107#66997—44no—
108C2×(C2×D11)⋊C4—28no—
109C2×(C2×D11)⋊C4C2312yes—
110C2×(C2×D11)⋊C4C2312yes—
111C2×(C2×D11)⋊C4C2314yes—
112C2×(C2×D11)⋊C4C2314yes—
113C2×(C2×D11)⋊C4C2314yes—
114C2×C4⋊Dic11—24no—
115C2×C4⋊Dic11C2312yes—
116C2×C4⋊Dic11C2311yescharacteristic
117C2×C4⋊Dic11C2312yes—
118C2×C4⋊Dic11C2312yes—
119C2×C4⋊Dic11C2318yes—
120#66977—24no—
121C2×Dic11⋊C4—28no—
122C2×Dic11⋊C4C2312yes—
123C2×Dic11⋊C4C2312yes—
124C2×Dic11⋊C4C2314yes—
125C2×Dic11⋊C4C2312yes—
126C2×Dic11⋊C4C2314yes—
127C2×Dic11⋊C4C2318yes—
128C2×Dic11⋊C4C2318yes—
129C2×C4×Dic11C2312yes—
130C2×C4×Dic11C2314yes—
131#66950—24no—
132#66949—28no—
133C4⋊C4×D11—24no—
134C4⋊C4×D11—28no—
135C22⋊C4×D11—28no—
136C22⋊C4×D11Q8116yescomplemented
137#66931—28no—
138C42×D11—44no—
139C11×#95C2318yes—
140C11×#95C2312yes—
141C11⋊#95C2318yes—
142C11⋊#95C2314yes—
143C11⋊#95C2318yes—
144C11⋊#95C2312yes—
145C11⋊#95C2318yes—
146#35011—111nomaximal, Sylow
147C24×C11C2411yescharacteristic
148C23×D11—42no—
149C23×D11—42no—
150C23×D11C2×D414yes—
151C23×D11C2×Q818yes—
152C23×D11C2411yescharacteristic
153C23×D11C2411yescharacteristic
154C2×Q8×C11—24no—
155C2×Q8×C11—24no—
156C2×Q8×C11—22no—
157C2×Q8×C11—24no—
158C2×Q8×C11—24no—
159C2×Q8×C11—24no—
160C2×Q8×C11—44no—
161C2×Q8×C11—416no—
162C22×C4×C11—24no—
163C22×C4×C11—24no—
164C22×C4×C11—44no—
165C22×C4×C11C2×D414yes—
166C22×C4×C11C2412yes—
167C22×C4×C11C2414yes—
168C22×C4×C11C2412yes—
169C22×C4×C11C2411yescharacteristic
170C22×C4×C11C2414yes—
171C22×C4×C11C2411yescharacteristic
172C22×Dic11—24no—
173C22×Dic11—42no—
174C22×Dic11—44no—
175C22×Dic11C2×D414yes—
176C22×Dic11C2412yes—
177C22×Dic11C2414yes—
178C22×Dic11C2412yes—
179C22×Dic11C2411yescharacteristic
180C22×Dic11C2411yescharacteristic
181C22×Dic11C2414yes—
182Q8×D11—416no—
183C2×C4×D11—24no—
184C2×C4×D11—24no—
185C2×C4×D11—24no—
186C2×C4×D11—24no—
187C2×C4×D11—44no—
188C2×C4×D11—42no—
189C2×C4×D11—42no—
190C2×C4×D11—44no—
191C2×C4×D11—44no—
192C2×C4×D11—44no—
193C2×C4×D11—416no—
194C2×C4×D11C2×D414yes—
195C2×C4×D11C2×D414yes—
196C2×C4×D11C2×D414yes—
197C2×C4×D11C2×D414yes—
198C2×C4×D11C2×Q8116yescomplemented
199C2×Dic22—24no—
200C2×Dic22—22no—
201C2×Dic22—24no—
202C2×Dic22—44no—
203C11×C4⋊C4—24no—
204C11×C4⋊C4—22no—
205C11×C4⋊C4—48no—
206C11×C22⋊C4—24no—
207C11×C22⋊C4C2×Q818yescomplemented
208C42×C11—24no—
209C22⋊Dic11—24no—
210C22⋊Dic11C2×Q818yescomplemented
211(C2×D11)⋊C4—24no—
212(C2×D11)⋊C4—24no—
213(C2×D11)⋊C4—28no—
214(C2×D11)⋊C4—28no—
215(C2×D11)⋊C4C2×Q8116yescomplemented
216C4⋊Dic11—24no—
217C4⋊Dic11—22no—
218C4⋊Dic11—24no—
219C4⋊Dic11—24no—
220C4⋊Dic11—48no—
221Dic11⋊C4—24no—
222Dic11⋊C4—24no—
223Dic11⋊C4—28no—
224Dic11⋊C4—28no—
225Dic11⋊C4—24no—
226Dic11⋊C4—48no—
227Dic11⋊C4—48no—
228C4×Dic11—24no—
229C4×Dic11—44no—
230C22×C22⋊Q8—111no—
231C22×C22⋊Q8—111no—
232#2857—112no—
233#2857—112no—
234#2659—114no—
235#2583—114no—
236#2583—114no—
237#2502—112no—
238#2502—111no—
239#2502—111no—
240#2434—111no—
241#2434—112no—
242#2434D1111yescharacteristic, complemented
243#2315—114no—
244C2×C4×C22⋊C4—111no—
245C23×C11—22no—
246C23×C11—22no—
247C23×C11C22×D412yes—
248C23×C11C22×Q814yes—
249C23×C11C2511yescharacteristic
250C22×D11—22no—
251C22×D11—22no—
252C22×D11—22no—
253C22×D11—22no—
254C22×D11—44no—
255C22×D11—44no—
256C22×D11—416no—
257C22×D11C4⋊Q8116yescomplemented
258C22×D11C22×D412yes—
259C22×D11C22×D412yes—
260C22×D11C22×Q814yes—
261C22×D11C22×Q814yes—
262Q8×C11—48no—
263Q8×C11—44no—
264Q8×C11—48no—
265C2×C4×C11—24no—
266C2×C4×C11—22no—
267C2×C4×C11—24no—
268C2×C4×C11—28no—
269C2×C4×C11—24no—
270C2×C4×C11—22no—
271C2×C4×C11—22no—
272C2×C4×C11—24no—
273C2×C4×C11—24no—
274C2×C4×C11—24no—
275C2×C4×C11—24no—
276C2×C4×C11—48no—
277C2×C4×C11C22×D412yes—
278C2×C4×C11C22×D412yes—
279C2×C4×C11C22×Q818yes—
280C2×C4×C11H(5,𝔽2)14yes—
281C2×Dic11—24no—
282C2×Dic11—22no—
283C2×Dic11—22no—
284C2×Dic11—24no—
285C2×Dic11—22no—
286C2×Dic11—24no—
287C2×Dic11—22no—
288C2×Dic11—24no—
289C2×Dic11—28no—
290C2×Dic11—24no—
291C2×Dic11—44no—
292C2×Dic11—48no—
293C2×Dic11C22×D412yes—
294C2×Dic11C22×D412yes—
295C2×Dic11C22×Q818yes—
296C4×D11—28no—
297C4×D11—28no—
298C4×D11—44no—
299C4×D11—44no—
300C4×D11—416no—
301C4×D11—48no—
302C4×D11—48no—
303Dic22—48no—
304Dic22—44no—
305C23×Q8—111no—
306C23×Q8C2×D1111yescharacteristic
307C24×C4—111no—
308C2×C4⋊Q8—112no—
309C2×C4⋊Q8C2×D1112yescomplemented
310C2×C22⋊Q8—112no—
311C2×C22⋊Q8—112no—
312C2×C22⋊Q8—111no—
313C2×C22⋊Q8—112no—
314C2×C22⋊Q8—112no—
315C2×C22⋊Q8—111no—
316C2×C22⋊Q8—111no—
317C2×C22⋊Q8—112no—
318C2×C22⋊Q8—112no—
319C2×C22⋊Q8—228no—
320C2×C22⋊Q8—228no—
321C2×C22⋊Q8C2×D1111yescharacteristic
322C22×C4⋊C4—112no—
323C22×C4⋊C4—111no—
324C22×C4⋊C4—112no—
325C22×C4⋊C4—111no—
326C22×C22⋊C4—112no—
327C22×C22⋊C4—112no—
328C22×C22⋊C4—112no—
329C22×C42—112no—
330#398—114no—
331#398—118no—
332#398—114no—
333#395—114no—
334#395—118no—
335#395C2×D1114yescomplemented
336#391—112no—
337#391—112no—
338#391—112no—
339#391C2×D1112yescomplemented
340#389—118no—
341#389—118no—
342#385—114no—
343#385—118no—
344#385—114no—
345#385—114no—
346#385—118no—
347#385C2×D1114yes—
348#384—112no—
349#384—112no—
350#380—118no—
351#380—118no—
352C4×C22⋊C4—111no—
353C4×C22⋊C4—112no—
354C4×C22⋊C4—112no—
355C4×C22⋊C4—112no—
356C4×C22⋊C4C2×D1111yescharacteristic
357C2×#95—112no—
358C22×C11—22no—
359C22×C11—22no—
360C22×C11—28no—
361C22×C11C2×C4⋊Q814yes—
362C22×C11C23×D411yescharacteristic
363C22×C11C23×Q812yes—
364C22×C11C2×H(5,𝔽2)12yes—
365C22×C11#58512yes—
366C2×D11—22no—
367C2×D11—22no—
368C2×D11—22no—
369C2×D11—22no—
370C2×D11—28no—
371C2×D11—28no—
372C2×D11—416no—
373C2×D11C2×C4⋊Q814yes—
374C2×D11C2×C4⋊Q814yes—
375C4×C11—22no—
376C4×C11—28no—
377C4×C11—44no—
378C4×C11—42no—
379C4×C11—42no—
380C4×C11#53414yes—
381Dic11—22no—
382Dic11—22no—
383Dic11—28no—
384Dic11—42no—
385Dic11—42no—
386Dic11—44no—
387C25—111no—
388C22×Q8—24no—
389C22×Q8—44no—
390C22×Q8—111no—
391C22×Q8—112no—
392C22×Q8—224no—
393C22×Q8—444no—
394C22×Q8C22×D1112yes—
395C22×Q8C22×D1111yescharacteristic
396C22×Q8C22×D1112yes—
397C23×C4—111no—
398C23×C4—111no—
399C23×C4—111no—
400C23×C4—118no—
401C23×C4—114no—
402C23×C4—111no—
403C23×C4—111no—
404C23×C4—112no—
405C23×C4—112no—
406C23×C4—112no—
407C23×C4—444no—
408C23×C4C22×D1111yescharacteristic
409C23×C4C22×D1112yes—
410C4⋊Q8—44no—
411C4⋊Q8—444no—
412C22⋊Q8—24no—
413C22⋊Q8—228no—
414C22⋊Q8—228no—
415C22⋊Q8—224no—
416C22⋊Q8—228no—
417C22⋊Q8—224no—
418C22⋊Q8—228no—
419C22⋊Q8—228no—
420C22⋊Q8—228no—
421C22⋊Q8—224no—
422C2×C4⋊C4—112no—
423C2×C4⋊C4—111no—
424C2×C4⋊C4—112no—
425C2×C4⋊C4—114no—
426C2×C4⋊C4—112no—
427C2×C4⋊C4—114no—
428C2×C4⋊C4—112no—
429C2×C4⋊C4—112no—
430C2×C4⋊C4—112no—
431C2×C4⋊C4—118no—
432C2×C4⋊C4—118no—
433C2×C4⋊C4—118no—
434C2×C4⋊C4—224no—
435C2×C4⋊C4—228no—
436C2×C4⋊C4—228no—
437C2×C4⋊C4—224no—
438C2×C4⋊C4C22×D1111yescharacteristic
439C2×C4⋊C4C22×D1112yes—
440C2×C4⋊C4C22×D1118yes—
441C2×C22⋊C4—112no—
442C2×C22⋊C4—114no—
443C2×C22⋊C4—1116no—
444C2×C22⋊C4—112no—
445C2×C22⋊C4—112no—
446C2×C22⋊C4—114no—
447C2×C22⋊C4—112no—
448C2×C22⋊C4—114no—
449C2×C22⋊C4—228no—
450C2×C22⋊C4—228no—
451C2×C22⋊C4C22×D1112yes—
452C2×C22⋊C4C22×D1112yes—
453C2×C42—112no—
454C2×C42—114no—
455C2×C42—444no—
456C2×C42C22×D1112yes—
457#95—112no—
458#95—114no—
459#95—118no—
460#95—118no—
461#95—118no—
462#95C22×D1112yes—
463#95C22×D1118yes—
464C2×C11—24no—
465C2×C11C22×C4⋊Q811yescharacteristic
466C2×C11C2×#53411yescharacteristic
467C2×C11#344911yescharacteristic
468C2×C11#350114yes—
469D11—24no—
470D11—24no—
471C24—111no—
472C24—111no—
473C24—114no—
474C24—118no—
475C24—442no—
476C24—442no—
477C24C23×D1111yescharacteristic
478C2×Q8—22no—
479C2×Q8—24no—
480C2×Q8—24no—
481C2×Q8—24no—
482C2×Q8—24no—
483C2×Q8—24no—
484C2×Q8—44no—
485C2×Q8—416no—
486C2×Q8—224no—
487C2×Q8—222no—
488C2×Q8—224no—
489C2×Q8—444no—
490C2×Q8—4416no—
491C22×C4—24no—
492C22×C4—24no—
493C22×C4—44no—
494C22×C4—114no—
495C22×C4—111no—
496C22×C4—111no—
497C22×C4—114no—
498C22×C4—114no—
499C22×C4—114no—
500C22×C4—114no—
501C22×C4—114no—
502C22×C4—1116no—
503C22×C4—112no—
504C22×C4—114no—
505C22×C4—112no—
506C22×C4—224no—
507C22×C4—224no—
508C22×C4—224no—
509C22×C4—224no—
510C22×C4—224no—
511C22×C4—4416no—
512C22×C4—444no—
513C22×C4—442no—
514C22×C4—442no—
515C22×C4—444no—
516C22×C4—444no—
517C22×C4—444no—
518C22×C4—442no—
519C22×C4—444no—
520C22×C4D4×D1114yes—
521C22×C4C23×D1112yes—
522C22×C4C23×D1114yes—
523C22×C4C23×D1112yes—
524C22×C4C23×D1111yescharacteristic
525C22×C4C23×D1114yes—
526C22×C4C23×D1111yescharacteristic
527C4⋊C4—22no—
528C4⋊C4—24no—
529C4⋊C4—48no—
530C4⋊C4—224no—
531C4⋊C4—224no—
532C4⋊C4—228no—
533C4⋊C4—228no—
534C4⋊C4—224no—
535C4⋊C4—224no—
536C4⋊C4—224no—
537C4⋊C4—222no—
538C4⋊C4—224no—
539C4⋊C4—448no—
540C4⋊C4—448no—
541C4⋊C4—448no—
542C22⋊C4—24no—
543C22⋊C4—118no—
544C22⋊C4—1116no—
545C22⋊C4—224no—
546C22⋊C4—224no—
547C22⋊C4—228no—
548C22⋊C4—228no—
549C22⋊C4—224no—
550C22⋊C4Q8×D1118yescomplemented
551C42—24no—
552C42—224no—
553C42—444no—
554C11#3501111yescharacteristic, complemented, Sylow
555C23—22no—
556C23—22no—
557C23—112no—
558C23—112no—
559C23—114no—
560C23—114no—
561C23—1116no—
562C23—222no—
563C23—222no—
564C23—222no—
565C23—222no—
566C23—444no—
567C23—4416no—
568C23—444no—
569C23C2×D4×D1112yes—
570C23C2×Q8×D1114yes—
571C23C24×D1111yescharacteristic
572Q8—48no—
573Q8—48no—
574Q8—44no—
575Q8—448no—
576Q8—444no—
577C2×C4—24no—
578C2×C4—22no—
579C2×C4—24no—
580C2×C4—28no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—24no—
584C2×C4—24no—
585C2×C4—24no—
586C2×C4—24no—
587C2×C4—24no—
588C2×C4—48no—
589C2×C4—112no—
590C2×C4—112no—
591C2×C4—118no—
592C2×C4—224no—
593C2×C4—222no—
594C2×C4—222no—
595C2×C4—224no—
596C2×C4—228no—
597C2×C4—228no—
598C2×C4—224no—
599C2×C4—222no—
600C2×C4—222no—
601C2×C4—224no—
602C2×C4—228no—
603C2×C4—224no—
604C2×C4—444no—
605C2×C4—444no—
606C2×C4—4416no—
607C2×C4—448no—
608C2×C4—448no—
609C2×C4—444no—
610C2×C4—448no—
611C2×C4C2×D4×D1112yes—
612C2×C4C2×D4×D1112yes—
613C2×C4#6703714yes—
614C2×C4C2×Q8×D1118yes—
615C22—28no—
616C22—22no—
617C22—22no—
618C22—114no—
619C22—114no—
620C22—228no—
621C22—228no—
622C22—222no—
623C22—222no—
624C22—222no—
625C22—222no—
626C22—4416no—
627C22D11×C4⋊Q814yes—
628C22C22×D4×D1111yescharacteristic
629C22C2×#6703712yes—
630C22C22×Q8×D1112yes—
631C22#1062345712yes—
632C4—28no—
633C4—22no—
634C4—44no—
635C4—42no—
636C4—42no—
637C4—228no—
638C4—222no—
639C4—222no—
640C4—442no—
641C4—442no—
642C4—444no—
643C4#1062312014yes—
644C2—24no—
645C2—224no—
646C2—224no—
647C2C2×D11×C4⋊Q811yescharacteristic
648C2C2×#1062312011yescharacteristic
649C2#1308194811yescharacteristic
650C2#1308241114yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2434C2
prime radicalC24×D11C23
hypercenter#2434D11
hypocenterC11#35011
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2434

Complements

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

NH ≅ G/Ntype
3. #13076965C2semidirect
4. #13076963C2semidirect
5. #13074729C2semidirect
6. #13073995C2semidirect
7. #13073992C2semidirect
8. #13073095C2semidirect
9. #13073094C2semidirect
10. #13073093C2semidirect
11. #13072257C2semidirect
12. #13072256C2semidirect
15. C11×#2434C2semidirect
19. C2×C11×C4⋊Q8C22semidirect
27. C2×#66997C22semidirect
41. C11×#395C22semidirect
42. C11×#391C22semidirect
45. #10622843C22semidirect
46. #10622843C22semidirect
47. #10622842C22semidirect
52. #10622596C22semidirect
53. #10622592C22semidirect
54. #10622589C22semidirect
55. #10622586C22semidirect
60. #10622548C22semidirect
61. #10622542C22semidirect
66. #10622274C22semidirect
67. #10622270C22semidirect
68. #10622260C22semidirect
136. C22⋊C4×D11Q8semidirect
198. C2×C4×D11C2×Q8semidirect
207. C11×C22⋊C4C2×Q8semidirect
210. C22⋊Dic11C2×Q8semidirect
215. (C2×D11)⋊C4C2×Q8semidirect
242. #2434D11semidirect
257. C22×D11C4⋊Q8semidirect
309. C2×C4⋊Q8C2×D11semidirect
335. #395C2×D11semidirect
339. #391C2×D11semidirect
550. C22⋊C4Q8×D11semidirect
554. C11#35011semidirect

Maximal subgroups

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

subgroupindex
C22×#669992
C2×D11×C22⋊Q82
#130769652
#130769632
#130747292
#130739952
#130739922
#130730952
#130730942
#130730932
#130722572
#130722562
#130712272
C4×C22⋊C4×D112
C11×#24342
#3501111