Finite Group Databasebeta

← D11×#3195 #15624379

Subgroups — D11×#3195 #15624379

Order 2816.

2322 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×C22⋊Q8C212yesmaximal
2#13079440C211yesmaximal, characteristic, complemented
3#13079439C214yesmaximal, complemented
4#13079438C214yesmaximal, complemented
5#13079437C212yesmaximal, complemented
6#13079436C214yesmaximal, complemented
7D11×#483C214yesmaximal, complemented
8D11×#470C214yesmaximal, complemented
9D11×#451C214yesmaximal, complemented
10D11×#407C211yesmaximal, characteristic
11C11×#3195C211yesmaximal, characteristic, complemented
12C22×Q8×D11C2212yes—
13C23×C4×D11C2211yescharacteristic
14C2×C11×C22⋊Q8C2212yes—
15C2×#66999C2212yes—
16C2×#66977C2212yes—
17C2×Q16×D11C2214yescomplemented
18C2×M16×D11C2212yes—
19D11×C22⋊Q8—22no—
20D11×C22⋊Q8—22no—
21D11×C22⋊Q8—22no—
22D11×C22⋊Q8—22no—
23D11×C22⋊Q8C2214yes—
24D11×C22⋊Q8C2214yes—
25D11×C22⋊Q8C2214yes—
26D11×C22⋊Q8C2214yes—
27C2×#66950C2212yes—
28C2×#66949—22no—
29C2×C4⋊C4×D11—22no—
30C2×C4⋊C4×D11C2212yes—
31C2×C22⋊C4×D11—22no—
32C2×#66931—22no—
33C11×#483C2214yescomplemented
34C11×#470C2214yescomplemented
35C11×#451C2214yescomplemented
36C11×#407C2211yescharacteristic
37#10622841C2214yescomplemented
38#10622820C2211yescharacteristic
39#10622802C2214yescomplemented
40#10622799C2218yescomplemented
41#10622750C2214yescomplemented
42#10622739C2212yes—
43#10622665C2218yescomplemented
44#10622663C2214yescomplemented
45#10622656C2214yescomplemented
46#10622584C2214yescomplemented
47#10622481C2214yescomplemented
48#10622475C2218yescomplemented
49D11×#106C2214yescomplemented
50#10622429C2218yescomplemented
51#10622421C2218yescomplemented
52#10622418C2218yescomplemented
53D11×#103C2218yescomplemented
54#10622352C2214yescomplemented
55#10622339C2214yes—
56D11×C22⋊C8C2214yes—
57#10622334C2214yescomplemented
58C24×D11D411yescharacteristic
59C22×Q8×C11C2312yes—
60C23×C4×C11C2311yescharacteristic
61C23×Dic11D411yescharacteristic
62C2×Q8×D11—22no—
63C2×Q8×D11—22no—
64C2×Q8×D11—48no—
65C2×Q8×D11C2314yes—
66C2×Q8×D11C2314yes—
67C22×C4×D11—22no—
68C22×C4×D11—22no—
69C22×C4×D11—44no—
70C22×C4×D11D412yes—
71C22×C4×D11D412yes—
72C22×C4×D11D411yescharacteristic
73C22×C4×D11D411yescharacteristic
74C22×C4×D11C2311yescharacteristic
75C22×C4×D11C2312yes—
76C22×C4×D11C2311yescharacteristic
77C22×C4×D11C2312yes—
78C22×Dic22—22no—
79C22×Dic22C2312yes—
80C2×C11×Q16C2314yescomplemented
81C2×C11×M16C2312yes—
82C11×C22⋊Q8—22no—
83C11×C22⋊Q8—22no—
84C11×C22⋊Q8C2314yes—
85C11×C22⋊Q8C2314yes—
86C2×C11×C4⋊C4—22no—
87C2×C11×C4⋊C4C2312yes—
88C2×C11×C22⋊C4—22no—
89C2×C22⋊Dic11—22no—
90#66999—22no—
91#66999—22no—
92#66999C2314yes—
93#66999C2314yes—
94C2×#4326C2318yescomplemented
95C2×(C2×D11)⋊C4—22no—
96C2×(C2×D11)⋊C4—22no—
97C2×C4⋊Dic11—22no—
98C2×C4⋊Dic11C2312yes—
99#66977—22no—
100#66977—22no—
101#66977C2314yes—
102#66977C2314yes—
103C2×Dic11⋊C4—22no—
104C2×Dic11⋊C4—22no—
105C2×Dic11⋊C4—22no—
106C2×#4318C2312yes—
107Q16×D11—48no—
108M16×D11—44no—
109C2×Dic44C2314yescomplemented
110C2×#4313C2314yes—
111C2×C8×D11C2314yes—
112#66950—22no—
113#66950—22no—
114#66950C2314yes—
115#66950C2314yes—
116#66949—24no—
117#66949—24no—
118#66949—24no—
119#66949—24no—
120C4⋊C4×D11—24no—
121C4⋊C4×D11—24no—
122C4⋊C4×D11—24no—
123C4⋊C4×D11—24no—
124C4⋊C4×D11—22no—
125C4⋊C4×D11—22no—
126C4⋊C4×D11C2314yes—
127C4⋊C4×D11C2314yes—
128C22⋊C4×D11—24no—
129C22⋊C4×D11—24no—
130C22⋊C4×D11—24no—
131C22⋊C4×D11—24no—
132#66931—24no—
133#66931—24no—
134#66931—24no—
135#66931—24no—
136C11×#106C2314yescomplemented
137C11×#103C2318yescomplemented
138C11×C22⋊C8C2314yes—
139#66899C2318yescomplemented
140C22⋊(C11⋊C8)C2314yes—
141(C2×D11)⋊C8C2318yes—
142#66881C2314yescomplemented
143#66880C2318yescomplemented
144#66874C2318yescomplemented
145#66872C2318yescomplemented
146C2×#3195—111nomaximal, Sylow
147C24×C11C2×D411yescharacteristic
148C23×D11—28no—
149C23×D11—42no—
150C23×D11C2×D411yescharacteristic
151C23×D11C2×D411yescharacteristic
152C23×D11C2×D412yes—
153C23×D11C2×D412yes—
154C2×Q8×C11—22no—
155C2×Q8×C11—44no—
156C2×Q8×C11C2414yes—
157C22×C4×C11—22no—
158C22×C4×C11—22no—
159C22×C4×C11—42no—
160C22×C4×C11C2×D412yes—
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11C2412yes—
163C22×C4×C11C2411yescharacteristic
164C22×Dic11—22no—
165C22×Dic11—22no—
166C22×Dic11—42no—
167C22×Dic11C2×D411yescharacteristic
168C22×Dic11C2×D412yes—
169C22×Dic11C2×D411yescharacteristic
170C22×Dic11C2×D412yes—
171Q8×D11—216no—
172Q8×D11—48no—
173Q8×D11—48no—
174Q8×D11—48no—
175C2×C4×D11—24no—
176C2×C4×D11—28no—
177C2×C4×D11—24no—
178C2×C4×D11—24no—
179C2×C4×D11—24no—
180C2×C4×D11—24no—
181C2×C4×D11—42no—
182C2×C4×D11—44no—
183C2×C4×D11—44no—
184C2×C4×D11—42no—
185C2×C4×D11—48no—
186C2×C4×D11—44no—
187C2×C4×D11—42no—
188C2×C4×D11—48no—
189C2×C4×D11C2×D411yescharacteristic
190C2×C4×D11C2×D412yes—
191C2×C4×D11C2×D412yes—
192C2×C4×D11C2×D411yescharacteristic
193C2×C4×D11C2×D412yes—
194C2×C4×D11C2×D412yes—
195C2×C4×D11C2×D412yes—
196C2×C4×D11C2412yes—
197C2×C4×D11C2411yescharacteristic
198C2×C4×D11C2411yescharacteristic
199C2×Dic22—24no—
200C2×Dic22—24no—
201C2×Dic22—22no—
202C2×Dic22—44no—
203C2×Dic22—48no—
204C2×Dic22C2414yes—
205C11×Q16—44no—
206C11×M16—42no—
207C2×C8×C11C2414yes—
208C11×C4⋊C4—24no—
209C11×C4⋊C4—24no—
210C11×C4⋊C4—22no—
211C11×C4⋊C4C2414yes—
212C11×C22⋊C4—24no—
213C11×C22⋊C4—24no—
214C22⋊Dic11—24no—
215C22⋊Dic11—24no—
216#4326—48no—
217(C2×D11)⋊C4—24no—
218(C2×D11)⋊C4—24no—
219(C2×D11)⋊C4—24no—
220(C2×D11)⋊C4—24no—
221C4⋊Dic11—24no—
222C4⋊Dic11—24no—
223C4⋊Dic11—22no—
224C4⋊Dic11C2414yes—
225Dic11⋊C4—24no—
226Dic11⋊C4—24no—
227Dic11⋊C4—24no—
228Dic11⋊C4—24no—
229Dic11⋊C4—24no—
230Dic11⋊C4—24no—
231#4318—42no—
232C2×C11⋊C8C2414yes—
233Dic44—44no—
234#4313—44no—
235C8×D11—28no—
236C22×C22⋊Q8—112no—
237#3195—114no—
238#3195—114no—
239#3195—114no—
240#3195—111no—
241#3195—112no—
242#3195D1111yescharacteristic, direct product factor
243C2×#483—114no—
244C2×#470—114no—
245C2×#451—114no—
246C2×#407—111no—
247C23×C11—24no—
248C23×C11—41no—
249C23×C11C22×D411yescharacteristic
250C23×C11C22×D412yes—
251C22×D11—24no—
252C22×D11—24no—
253C22×D11—24no—
254C22×D11—22no—
255C22×D11—24no—
256C22×D11—24no—
257C22×D11—24no—
258C22×D11—41no—
259C22×D11—42no—
260C22×D11—416no—
261C22×D11#13718yes—
262C22×D11C22×D411yescharacteristic
263C22×D11C22×D412yes—
264C22×D11C22×D411yescharacteristic
265Q8×C11—28no—
266Q8×C11—44no—
267C2×C4×C11—22no—
268C2×C4×C11—24no—
269C2×C4×C11—24no—
270C2×C4×C11—24no—
271C2×C4×C11—41no—
272C2×C4×C11—42no—
273C2×C4×C11—44no—
274C2×C4×C11—44no—
275C2×C4×C11C22×D411yescharacteristic
276C2×C4×C11C22×D412yes—
277C2×C4×C11C2511yescharacteristic
278C2×Dic11—24no—
279C2×Dic11—22no—
280C2×Dic11—24no—
281C2×Dic11—24no—
282C2×Dic11—41no—
283C2×Dic11—42no—
284C2×Dic11—44no—
285C2×Dic11—44no—
286C2×Dic11C22×D411yescharacteristic
287C2×Dic11C22×D412yes—
288C2×Dic11C22×D411yescharacteristic
289C4×D11—22no—
290C4×D11—24no—
291C4×D11—22no—
292C4×D11—24no—
293C4×D11—22no—
294C4×D11—24no—
295C4×D11—42no—
296C4×D11—42no—
297C4×D11—42no—
298C4×D11—48no—
299C4×D11—48no—
300C4×D11—48no—
301C4×D11—48no—
302C4×D11H(5,𝔽2)14yes—
303Dic22—28no—
304Dic22—48no—
305Dic22—44no—
306Dic22—48no—
307C8×C11—24no—
308C11⋊C8—24no—
309C23×Q8—112no—
310C24×C4—111no—
311C22×Q16—114no—
312C22×M16—112no—
313C2×C22⋊Q8—112no—
314C2×C22⋊Q8—112no—
315C2×C22⋊Q8—114no—
316C2×C22⋊Q8—114no—
317C2×C22⋊Q8—114no—
318C2×C22⋊Q8—114no—
319C2×C22⋊Q8—112no—
320C2×C22⋊Q8—222no—
321C2×C22⋊Q8—222no—
322C2×C22⋊Q8—222no—
323C2×C22⋊Q8—222no—
324C2×C22⋊Q8—222no—
325C2×C22⋊Q8—222no—
326C2×C22⋊Q8C2×D1112yes—
327C22×C4⋊C4—112no—
328C22×C4⋊C4—222no—
329C22×C22⋊C4—222no—
330#483—114no—
331#483—114no—
332#483—118no—
333#483—118no—
334#483—114no—
335#483C2×D1114yescomplemented
336#470—114no—
337#470—114no—
338#470—118no—
339#470—114no—
340#470—118no—
341#470C2×D1114yescomplemented
342#451—114no—
343#451—118no—
344#451—114no—
345#451—118no—
346#451—114no—
347#451C2×D1114yescomplemented
348C2×#106—114no—
349C2×#103—118no—
350#407—111no—
351#407—112no—
352#407—114no—
353#407C2×D1111yescharacteristic
354C2×C22⋊C8—114no—
355C22×C11—22no—
356C22×C11—22no—
357C22×C11—21no—
358C22×C11—22no—
359C22×C11—44no—
360C22×C11C2×#13714yes—
361C22×C11C23×D411yescharacteristic
362C2×D11—22no—
363C2×D11—22no—
364C2×D11—216no—
365C2×D11—21no—
366C2×D11—22no—
367C2×D11—44no—
368C2×D11—48no—
369C2×D11—44no—
370C2×D11#53412yes—
371C2×D11C2×#13714yes—
372C2×D11C2×#13714yes—
373C4×C11—22no—
374C4×C11—21no—
375C4×C11—44no—
376C4×C11—44no—
377C4×C11C2×H(5,𝔽2)12yes—
378Dic11—22no—
379Dic11—21no—
380Dic11—44no—
381Dic11—44no—
382Dic11#53412yes—
383C25—111no—
384C22×Q8—114no—
385C22×Q8—114no—
386C22×Q8—112no—
387C22×Q8—222no—
388C22×Q8—222no—
389C22×Q8—222no—
390C22×Q8—448no—
391C22×Q8C22×D1112yes—
392C23×C4—111no—
393C23×C4—112no—
394C23×C4—111no—
395C23×C4—112no—
396C23×C4—112no—
397C23×C4—111no—
398C23×C4—111no—
399C23×C4—112no—
400C23×C4—111no—
401C23×C4—222no—
402C23×C4—222no—
403C23×C4—444no—
404C23×C4C22×D1111yescharacteristic
405C2×Q16—118no—
406C2×Q16—114no—
407C2×Q16—448no—
408C2×Q16C22×D1114yescomplemented
409C2×M16—112no—
410C2×M16—114no—
411C2×M16—444no—
412C2×M16C22×D1112yes—
413C22×C8—114no—
414C22⋊Q8—22no—
415C22⋊Q8—22no—
416C22⋊Q8—114no—
417C22⋊Q8—114no—
418C22⋊Q8—114no—
419C22⋊Q8—114no—
420C22⋊Q8—114no—
421C22⋊Q8—114no—
422C22⋊Q8—224no—
423C22⋊Q8—224no—
424C22⋊Q8—224no—
425C22⋊Q8—224no—
426C22⋊Q8—224no—
427C22⋊Q8—224no—
428C22⋊Q8—224no—
429C22⋊Q8—224no—
430C22⋊Q8—222no—
431C22⋊Q8—222no—
432C22⋊Q8—222no—
433C22⋊Q8—222no—
434C22⋊Q8—222no—
435C22⋊Q8—222no—
436C22⋊Q8C22×D1114yes—
437C22⋊Q8C22×D1114yes—
438C2×C4⋊C4—22no—
439C2×C4⋊C4—112no—
440C2×C4⋊C4—114no—
441C2×C4⋊C4—114no—
442C2×C4⋊C4—222no—
443C2×C4⋊C4—222no—
444C2×C4⋊C4—224no—
445C2×C4⋊C4—224no—
446C2×C4⋊C4—224no—
447C2×C4⋊C4—224no—
448C2×C4⋊C4—222no—
449C2×C4⋊C4—222no—
450C2×C4⋊C4—222no—
451C2×C4⋊C4—222no—
452C2×C4⋊C4C22×D1112yes—
453C2×C22⋊C4—22no—
454C2×C22⋊C4—224no—
455C2×C22⋊C4—224no—
456C2×C22⋊C4—224no—
457C2×C22⋊C4—224no—
458C2×C22⋊C4—222no—
459C2×C22⋊C4—222no—
460C2×C22⋊C4—222no—
461#106—114no—
462#106—118no—
463#106C22×D1114yescomplemented
464#103—118no—
465#103—118no—
466#103—118no—
467#103C22×D1118yescomplemented
468C22⋊C8—114no—
469C22⋊C8—118no—
470C22⋊C8C22×D1114yes—
471C2×C11—24no—
472C2×C11—41no—
473C2×C11C2×#53411yescharacteristic
474C2×C11C22×#13712yes—
475D11—24no—
476D11—41no—
477D11#319514yesdirect product factor
478C24—112no—
479C24—111no—
480C24—111no—
481C24—112no—
482C24—228no—
483C24—442no—
484C24D4×D1111yescharacteristic
485C2×Q8—22no—
486C2×Q8—44no—
487C2×Q8—114no—
488C2×Q8—224no—
489C2×Q8—224no—
490C2×Q8—2216no—
491C2×Q8—222no—
492C2×Q8—444no—
493C2×Q8—448no—
494C2×Q8—448no—
495C2×Q8—448no—
496C2×Q8—448no—
497C2×Q8C23×D1114yes—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—42no—
501C22×C4—111no—
502C22×C4—112no—
503C22×C4—111no—
504C22×C4—112no—
505C22×C4—111no—
506C22×C4—111no—
507C22×C4—112no—
508C22×C4—112no—
509C22×C4—111no—
510C22×C4—112no—
511C22×C4—111no—
512C22×C4—112no—
513C22×C4—112no—
514C22×C4—112no—
515C22×C4—224no—
516C22×C4—228no—
517C22×C4—224no—
518C22×C4—224no—
519C22×C4—224no—
520C22×C4—224no—
521C22×C4—222no—
522C22×C4—222no—
523C22×C4—442no—
524C22×C4—444no—
525C22×C4—442no—
526C22×C4—444no—
527C22×C4—442no—
528C22×C4—444no—
529C22×C4—448no—
530C22×C4—448no—
531C22×C4—442no—
532C22×C4D4×D1112yes—
533C22×C4D4×D1111yescharacteristic
534C22×C4C23×D1112yes—
535C22×C4C23×D1111yescharacteristic
536Q16—44no—
537Q16—444no—
538Q16—448no—
539M16—42no—
540M16—444no—
541M16—442no—
542C2×C8—114no—
543C2×C8—228no—
544C2×C8C23×D1114yes—
545C4⋊C4—24no—
546C4⋊C4—24no—
547C4⋊C4—22no—
548C4⋊C4—114no—
549C4⋊C4—224no—
550C4⋊C4—224no—
551C4⋊C4—224no—
552C4⋊C4—224no—
553C4⋊C4—224no—
554C4⋊C4—224no—
555C4⋊C4—222no—
556C4⋊C4—224no—
557C4⋊C4—224no—
558C4⋊C4C23×D1114yes—
559C22⋊C4—24no—
560C22⋊C4—24no—
561C22⋊C4—224no—
562C22⋊C4—224no—
563C22⋊C4—224no—
564C22⋊C4—224no—
565C22⋊C4—224no—
566C22⋊C4—224no—
567C11C2×#319511yescharacteristic, complemented, Sylow
568C23—24no—
569C23—41no—
570C23—111no—
571C23—118no—
572C23—112no—
573C23—111no—
574C23—224no—
575C23—224no—
576C23—222no—
577C23—224no—
578C23—224no—
579C23—224no—
580C23—224no—
581C23—442no—
582C23—441no—
583C23—4416no—
584C23C2×D4×D1111yescharacteristic
585C23C2×D4×D1112yes—
586Q8—28no—
587Q8—44no—
588Q8—228no—
589Q8—444no—
590Q8—448no—
591Q8—448no—
592C2×C4—22no—
593C2×C4—24no—
594C2×C4—24no—
595C2×C4—24no—
596C2×C4—41no—
597C2×C4—42no—
598C2×C4—44no—
599C2×C4—44no—
600C2×C4—111no—
601C2×C4—114no—
602C2×C4—111no—
603C2×C4—112no—
604C2×C4—224no—
605C2×C4—222no—
606C2×C4—224no—
607C2×C4—222no—
608C2×C4—224no—
609C2×C4—222no—
610C2×C4—222no—
611C2×C4—224no—
612C2×C4—224no—
613C2×C4—224no—
614C2×C4—442no—
615C2×C4—442no—
616C2×C4—442no—
617C2×C4—448no—
618C2×C4—448no—
619C2×C4—448no—
620C2×C4—448no—
621C2×C4—441no—
622C2×C4—442no—
623C2×C4—444no—
624C2×C4—444no—
625C2×C4C2×D4×D1111yescharacteristic
626C2×C4C2×D4×D1112yes—
627C2×C4C24×D1111yescharacteristic
628C8—24no—
629C8—224no—
630C22—22no—
631C22—22no—
632C22—21no—
633C22—22no—
634C22—44no—
635C22—112no—
636C22—114no—
637C22—114no—
638C22—2216no—
639C22—222no—
640C22—222no—
641C22—221no—
642C22—222no—
643C22—448no—
644C22—444no—
645C22—444no—
646C22D11×#13714yes—
647C22C22×D4×D1111yescharacteristic
648C4—22no—
649C4—21no—
650C4—44no—
651C4—44no—
652C4—112no—
653C4—222no—
654C4—221no—
655C4—444no—
656C4—444no—
657C4D11×H(5,𝔽2)12yes—
658C2—24no—
659C2—41no—
660C2—114no—
661C2—224no—
662C2—441no—
663C2D11×#53411yescharacteristic
664C2C2×D11×#13712yes—
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3195C2
socleC22×C11C23×D4
prime radicalC24×D11D4
hypercenter#3195D11
hypocenterC11C2×#3195
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3195

Complements

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

NH ≅ G/Ntype
2. #13079440C2semidirect
3. #13079439C2semidirect
4. #13079438C2semidirect
5. #13079437C2semidirect
6. #13079436C2semidirect
7. D11×#483C2semidirect
8. D11×#470C2semidirect
9. D11×#451C2semidirect
11. C11×#3195C2semidirect
17. C2×Q16×D11C22semidirect
33. C11×#483C22semidirect
34. C11×#470C22semidirect
35. C11×#451C22semidirect
37. #10622841C22semidirect
39. #10622802C22semidirect
40. #10622799C22semidirect
41. #10622750C22semidirect
43. #10622665C22semidirect
44. #10622663C22semidirect
45. #10622656C22semidirect
46. #10622584C22semidirect
47. #10622481C22semidirect
48. #10622475C22semidirect
49. D11×#106C22semidirect
50. #10622429C22semidirect
51. #10622421C22semidirect
52. #10622418C22semidirect
53. D11×#103C22semidirect
54. #10622352C22semidirect
57. #10622334C22semidirect
80. C2×C11×Q16C23semidirect
94. C2×#4326C23semidirect
109. C2×Dic44C23semidirect
136. C11×#106C23semidirect
137. C11×#103C23semidirect
139. #66899C23semidirect
142. #66881C23semidirect
143. #66880C23semidirect
144. #66874C23semidirect
145. #66872C23semidirect
242. #3195D11direct (N × H)
335. #483C2×D11semidirect
341. #470C2×D11semidirect
347. #451C2×D11semidirect
408. C2×Q16C22×D11semidirect
463. #106C22×D11semidirect
467. #103C22×D11semidirect
477. D11#3195direct (N × H)
567. C11C2×#3195semidirect

Maximal subgroups

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

subgroupindex
C2×D11×C22⋊Q82
#130794402
#130794392
#130794382
#130794372
#130794362
D11×#4832
D11×#4702
D11×#4512
D11×#4072
C11×#31952
C2×#319511