Finite Group Databasebeta

← D11×#2621 #14920983

Subgroups — D11×#2621 #14920983

Order 2816.

3046 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×C4⋊Q8C211yesmaximal, characteristic, complemented
2C2×D11×C22⋊Q8C212yesmaximal
3C2×D11×#117C211yesmaximal, characteristic
4#13074387C212yesmaximal, complemented
5#13074386C212yesmaximal, complemented
6#13074385C211yesmaximal, characteristic, complemented
7#13074384C214yesmaximal, complemented
8#13074383C211yesmaximal, characteristic, complemented
9#13074382C211yesmaximal, characteristic, complemented
10#13074381C214yesmaximal, complemented
11D11×#398C214yesmaximal, complemented
12D11×#397C214yesmaximal
13D11×#391C212yesmaximal, complemented
14D11×#382C211yesmaximal, characteristic, complemented
15C11×#2621C211yesmaximal, characteristic, complemented
16C22×Q8×D11C2212yes—
17C23×C4×D11C2211yescharacteristic
18C2×C11×C4⋊Q8C2211yescharacteristic, complemented
19C2×C11×C22⋊Q8C2212yes—
20C2×C11×#117C2211yescharacteristic
21C2×#66999C2212yes—
22C2×#66997C2212yescomplemented
23C2×#66979C2211yescharacteristic
24C2×#66977C2212yes—
25D11×C4⋊Q8—28no—
26D11×C22⋊Q8—216no—
27D11×#117—28no—
28C2×#66950C2212yes—
29C2×#66949C2214yes—
30C2×#66945C2212yes—
31C2×C4⋊C4×D11C2214yes—
32C2×C4⋊C4×D11C2212yes—
33C2×C4⋊C4×D11C2212yes—
34C2×C4⋊C4×D11C2214yes—
35C2×#66941C2214yescomplemented
36C2×C22⋊C4×D11C2212yes—
37C2×C22⋊C4×D11C2214yes—
38C2×#66931C2214yes—
39C2×#66930C2212yes—
40C2×#66925C2211yescharacteristic
41C2×#66925C2211yescharacteristic
42C2×C42×D11C2211yescharacteristic
43C2×C42×D11C2211yescharacteristic
44C2×#66922C2211yescharacteristic, complemented
45C11×#398C2214yescomplemented
46C11×#397C2214yes—
47C11×#391C2212yescomplemented
48C11×#382C2211yescharacteristic, complemented
49#10622843C2212yescomplemented
50#10622606C2214yes—
51#10622597C2218yescomplemented
52#10622596C2214yescomplemented
53#10622593C2214yescomplemented
54#10622590C2212yescomplemented
55#10622587C2212yescomplemented
56#10622566C2214yes—
57#10622565C2218yes—
58#10622549C2211yescharacteristic, complemented
59#10622542C2212yescomplemented
60#10622288C2218yes—
61#10622287C2214yes—
62D11×#95C2214yes—
63D11×#95C2218yes—
64#10622274C2214yescomplemented
65#10622270C2218yescomplemented
66#10622263C2214yescomplemented
67#10622259C2218yescomplemented
68C24×D11C2311yescharacteristic
69C22×Q8×C11C2312yes—
70C23×C4×C11C2311yescharacteristic
71C23×Dic11C2311yescharacteristic
72C2×Q8×D11—28no—
73C2×Q8×D11—28no—
74C2×Q8×D11—28no—
75C22×C4×D11—24no—
76C22×C4×D11—24no—
77C22×C4×D11D418yes—
78C22×C4×D11C2312yes—
79C22×C4×D11C2314yes—
80C22×C4×D11C2314yes—
81C22×C4×D11C2312yes—
82C22×C4×D11C2311yescharacteristic
83C22×C4×D11C2311yescharacteristic
84C22×C4×D11C2311yescharacteristic
85C22×C4×D11C2311yescharacteristic
86C22×Dic22C2312yes—
87C22×Dic22C2314yes—
88C11×C4⋊Q8—24no—
89C11×C22⋊Q8—28no—
90C11×#117—24no—
91C2×C11×C4⋊C4C2314yes—
92C2×C11×C4⋊C4C2312yes—
93C2×C11×C4⋊C4C2314yes—
94C2×C11×C4⋊C4C2312yes—
95C2×C11×C22⋊C4C2312yes—
96C2×C11×C22⋊C4C2314yes—
97C2×C42×C11C2311yescharacteristic
98C2×C42×C11C2311yescharacteristic
99C2×C22⋊Dic11C2312yes—
100C2×C22⋊Dic11C2314yes—
101#66999—28no—
102#66997—28no—
103C2×(C2×D11)⋊C4C2312yes—
104C2×(C2×D11)⋊C4C2312yes—
105C2×(C2×D11)⋊C4C2314yes—
106C2×(C2×D11)⋊C4C2314yes—
107#66979—24no—
108C2×C4⋊Dic11C2314yes—
109C2×C4⋊Dic11C2314yes—
110C2×C4⋊Dic11C2312yes—
111C2×C4⋊Dic11C2312yes—
112#66977—28no—
113C2×Dic11⋊C4C2312yes—
114C2×Dic11⋊C4C2312yes—
115C2×Dic11⋊C4C2314yes—
116C2×Dic11⋊C4C2314yes—
117C2×Dic11⋊C4C2318yes—
118C2×Dic11⋊C4C2314yes—
119C2×C4×Dic11C2311yescharacteristic
120C2×C4×Dic11C2312yes—
121C2×C4×Dic11C2311yescharacteristic
122C2×C4×Dic11C2312yes—
123#66950—28no—
124#66949—216no—
125#66945—28no—
126C4⋊C4×D11—216no—
127C4⋊C4×D11—28no—
128C4⋊C4×D11—28no—
129C4⋊C4×D11—216no—
130#66941—216no—
131C22⋊C4×D11—216no—
132C22⋊C4×D11—28no—
133#66931—216no—
134#66930—28no—
135#66925—24no—
136#66925—24no—
137C42×D11—24no—
138C42×D11D418yes—
139#66922—24no—
140C11×#95C2318yes—
141C11×#95C2314yes—
142C11⋊#95C2318yes—
143C11⋊#95C2318yes—
144C11⋊#95C2318yes—
145C11⋊#95C2318yes—
146C11⋊#95C2314yes—
147C2×#2621—111nomaximal, Sylow
148C24×C11C2411yescharacteristic
149C23×D11—22no—
150C23×D11—22no—
151C23×D11—28no—
152C23×D11C2×D414yes—
153C23×D11C2411yescharacteristic
154C23×D11C2411yescharacteristic
155C2×Q8×C11—24no—
156C2×Q8×C11—24no—
157C2×Q8×C11—24no—
158C22×C4×C11—22no—
159C22×C4×C11—22no—
160C22×C4×C11C2×D414yes—
161C22×C4×C11C2412yes—
162C22×C4×C11C2414yes—
163C22×C4×C11C2414yes—
164C22×C4×C11C2412yes—
165C22×C4×C11C2411yescharacteristic
166C22×C4×C11C2411yescharacteristic
167C22×Dic11—22no—
168C22×Dic11—22no—
169C22×Dic11C2×D414yes—
170C22×Dic11C2412yes—
171C22×Dic11C2414yes—
172C22×Dic11C2414yes—
173C22×Dic11C2412yes—
174C22×Dic11C2411yescharacteristic
175C22×Dic11C2411yescharacteristic
176Q8×D11—432no—
177C2×C4×D11—22no—
178C2×C4×D11—22no—
179C2×C4×D11—232no—
180C2×C4×D11—22no—
181C2×C4×D11—24no—
182C2×C4×D11—28no—
183C2×C4×D11—28no—
184C2×C4×D11—28no—
185C2×C4×D11—22no—
186C2×C4×D11—28no—
187C2×C4×D11—28no—
188C2×C4×D11—28no—
189C2×C4×D11—216no—
190C2×C4×D11—22no—
191C2×C4×D11—22no—
192C2×C4×D11C2×D418yes—
193C2×C4×D11C2×D414yes—
194C2×C4×D11C2×D414yes—
195C2×C4×D11C2×D414yes—
196C2×C4×D11C2×D414yes—
197C2×C4×D11C2×D414yes—
198C2×C4×D11#4114yes—
199C2×Dic22—28no—
200C2×Dic22—28no—
201C2×Dic22—28no—
202C2×Dic22—24no—
203C2×Dic22—24no—
204C2×Dic22—24no—
205C11×C4⋊C4—28no—
206C11×C4⋊C4—24no—
207C11×C4⋊C4—28no—
208C11×C4⋊C4—24no—
209C11×C22⋊C4—28no—
210C11×C22⋊C4—24no—
211C42×C11—22no—
212C42×C11C2×D414yes—
213C22⋊Dic11—24no—
214C22⋊Dic11—28no—
215(C2×D11)⋊C4—24no—
216(C2×D11)⋊C4—28no—
217(C2×D11)⋊C4—28no—
218(C2×D11)⋊C4—24no—
219C4⋊Dic11—28no—
220C4⋊Dic11—24no—
221C4⋊Dic11—28no—
222C4⋊Dic11—24no—
223Dic11⋊C4—24no—
224Dic11⋊C4—28no—
225Dic11⋊C4—28no—
226Dic11⋊C4—216no—
227Dic11⋊C4—24no—
228Dic11⋊C4—28no—
229C4×Dic11—24no—
230C4×Dic11—22no—
231C4×Dic11C2×D414yes—
232C4×Dic11C2×D418yes—
233C22×C4⋊Q8—111no—
234C22×C22⋊Q8—112no—
235C22×#117—111no—
236#2621—114no—
237#2621—114no—
238#2621—112no—
239#2621—111no—
240#2621—111no—
241#2621—112no—
242#2621—111no—
243#2621D1111yescharacteristic, direct product factor
244C2×#398—114no—
245C2×#397—114no—
246C2×#391—112no—
247C2×#382—111no—
248C23×C11—21no—
249C23×C11—21no—
250C23×C11—24no—
251C23×C11C22×D412yes—
252C23×C11C2511yescharacteristic
253C22×D11—21no—
254C22×D11—21no—
255C22×D11—24no—
256C22×D11—28no—
257C22×D11—216no—
258C22×D11—48no—
259C22×D11—48no—
260C22×D11C22×D412yes—
261C22×D11C22×D412yes—
262C22×D11C22×D412yes—
263C22×D11C2×#4112yes—
264C22×D112−1+418yes—
265Q8×C11—48no—
266C2×C4×C11—21no—
267C2×C4×C11—21no—
268C2×C4×C11—24no—
269C2×C4×C11—28no—
270C2×C4×C11—22no—
271C2×C4×C11—24no—
272C2×C4×C11—24no—
273C2×C4×C11—24no—
274C2×C4×C11—24no—
275C2×C4×C11—24no—
276C2×C4×C11—28no—
277C2×C4×C11C22×D414yes—
278C2×C4×C11C22×D412yes—
279C2×C4×C11C22×D412yes—
280C2×C4×C11C22×D412yes—
281C2×C4×C11C2×#4112yes—
282C2×Dic11—21no—
283C2×Dic11—21no—
284C2×Dic11—24no—
285C2×Dic11—28no—
286C2×Dic11—22no—
287C2×Dic11—24no—
288C2×Dic11—24no—
289C2×Dic11—24no—
290C2×Dic11—24no—
291C2×Dic11—24no—
292C2×Dic11—28no—
293C2×Dic11C22×D414yes—
294C2×Dic11C22×D412yes—
295C2×Dic11C22×D412yes—
296C2×Dic11C22×D412yes—
297C2×Dic11C2×#4112yes—
298C4×D11—28no—
299C4×D11—216no—
300C4×D11—28no—
301C4×D11—28no—
302C4×D11—416no—
303C4×D11—416no—
304C4×D11—48no—
305C4×D11#121116yes—
306Dic22—48no—
307Dic22—416no—
308C23×Q8—112no—
309C24×C4—111no—
310C2×C4⋊Q8—112no—
311C2×C4⋊Q8—114no—
312C2×C4⋊Q8—111no—
313C2×C4⋊Q8—228no—
314C2×C4⋊Q8C2×D1111yescharacteristic, complemented
315C2×C22⋊Q8—112no—
316C2×C22⋊Q8—112no—
317C2×C22⋊Q8—114no—
318C2×C22⋊Q8—112no—
319C2×C22⋊Q8—114no—
320C2×C22⋊Q8—2216no—
321C2×C22⋊Q8C2×D1112yes—
322C2×#117—111no—
323C2×#117—112no—
324C2×#117—112no—
325C2×#117—111no—
326C2×#117—111no—
327C2×#117—228no—
328C2×#117C2×D1111yescharacteristic
329C22×C4⋊C4—114no—
330C22×C4⋊C4—112no—
331C22×C4⋊C4—114no—
332C22×C4⋊C4—112no—
333C22×C22⋊C4—112no—
334C22×C22⋊C4—114no—
335C22×C42—111no—
336C22×C42—111no—
337#398—114no—
338#398—114no—
339#398—118no—
340#398—118no—
341#398—114no—
342#398C2×D1114yescomplemented
343#397—114no—
344#397—118no—
345#397—114no—
346#397—114no—
347#397—118no—
348#397C2×D1114yes—
349#391—112no—
350#391—112no—
351#391—112no—
352#391—118no—
353#391C2×D1112yescomplemented
354#382—112no—
355#382—111no—
356#382—114no—
357#382C2×D1111yescharacteristic, complemented
358C2×#95—114no—
359C2×#95—118no—
360C22×C11—22no—
361C22×C11—24no—
362C22×C11—42no—
363C22×C11—42no—
364C22×C11C23×D411yescharacteristic
365C22×C11C23×D411yescharacteristic
366C22×C11C22×#4111yescharacteristic
367C22×C11C2×2−1+414yes—
368C2×D11—22no—
369C2×D11—24no—
370C2×D11—42no—
371C2×D11—42no—
372C2×D11—416no—
373C2×D11C2×#12114yes—
374C2×D11#53618yes—
375C2×D11#53618yes—
376C2×D11#54118yes—
377C4×C11—22no—
378C4×C11—24no—
379C4×C11—44no—
380C4×C11—42no—
381C4×C11—44no—
382C4×C11C2×#12114yes—
383Dic11—22no—
384Dic11—24no—
385Dic11—44no—
386Dic11—42no—
387Dic11—44no—
388Dic11C2×#12114yes—
389C25—111no—
390C22×Q8—114no—
391C22×Q8—112no—
392C22×Q8—228no—
393C22×Q8—228no—
394C22×Q8—228no—
395C22×Q8C22×D1112yes—
396C23×C4—111no—
397C23×C4—111no—
398C23×C4—118no—
399C23×C4—112no—
400C23×C4—111no—
401C23×C4—111no—
402C23×C4—111no—
403C23×C4—114no—
404C23×C4—114no—
405C23×C4—112no—
406C23×C4—224no—
407C23×C4—224no—
408C23×C4C22×D1111yescharacteristic
409C4⋊Q8—24no—
410C4⋊Q8—2216no—
411C4⋊Q8—228no—
412C4⋊Q8—224no—
413C22⋊Q8—28no—
414C22⋊Q8—2216no—
415C22⋊Q8—2216no—
416C22⋊Q8—228no—
417C22⋊Q8—228no—
418C22⋊Q8—228no—
419#117—24no—
420#117—224no—
421#117—228no—
422#117—228no—
423#117—224no—
424#117—224no—
425C2×C4⋊C4—112no—
426C2×C4⋊C4—112no—
427C2×C4⋊C4—112no—
428C2×C4⋊C4—114no—
429C2×C4⋊C4—112no—
430C2×C4⋊C4—114no—
431C2×C4⋊C4—114no—
432C2×C4⋊C4—114no—
433C2×C4⋊C4—118no—
434C2×C4⋊C4—114no—
435C2×C4⋊C4—228no—
436C2×C4⋊C4—228no—
437C2×C4⋊C4—2216no—
438C2×C4⋊C4—2216no—
439C2×C4⋊C4C22×D1112yes—
440C2×C4⋊C4C22×D1112yes—
441C2×C4⋊C4C22×D1114yes—
442C2×C4⋊C4C22×D1114yes—
443C2×C22⋊C4—112no—
444C2×C22⋊C4—114no—
445C2×C22⋊C4—112no—
446C2×C22⋊C4—112no—
447C2×C22⋊C4—114no—
448C2×C22⋊C4—114no—
449C2×C22⋊C4—228no—
450C2×C22⋊C4—2216no—
451C2×C22⋊C4C22×D1112yes—
452C2×C22⋊C4C22×D1114yes—
453C2×C42—112no—
454C2×C42—111no—
455C2×C42—118no—
456C2×C42—112no—
457C2×C42—111no—
458C2×C42—224no—
459C2×C42C22×D1111yescharacteristic
460C2×C42C22×D1111yescharacteristic
461#95—118no—
462#95—114no—
463#95—118no—
464#95—118no—
465#95—118no—
466#95C22×D1114yes—
467#95C22×D1118yes—
468C2×C11—42no—
469C2×C11C22×#12111yescharacteristic
470C2×C11C2×#53612yes—
471C2×C11C2×#53612yes—
472C2×C11C2×#54112yes—
473D11—42no—
474D11#262118yesdirect product factor
475C24—111no—
476C24—114no—
477C24—111no—
478C24—222no—
479C24—222no—
480C24—228no—
481C24C23×D1111yescharacteristic
482C2×Q8—24no—
483C2×Q8—24no—
484C2×Q8—24no—
485C2×Q8—228no—
486C2×Q8—228no—
487C2×Q8—228no—
488C2×Q8—224no—
489C2×Q8—224no—
490C2×Q8—224no—
491C2×Q8—4432no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—111no—
495C22×C4—114no—
496C22×C4—114no—
497C22×C4—114no—
498C22×C4—114no—
499C22×C4—112no—
500C22×C4—111no—
501C22×C4—118no—
502C22×C4—114no—
503C22×C4—114no—
504C22×C4—114no—
505C22×C4—112no—
506C22×C4—114no—
507C22×C4—114no—
508C22×C4—222no—
509C22×C4—222no—
510C22×C4—2232no—
511C22×C4—222no—
512C22×C4—222no—
513C22×C4—228no—
514C22×C4—224no—
515C22×C4—228no—
516C22×C4—228no—
517C22×C4—228no—
518C22×C4—228no—
519C22×C4—2216no—
520C22×C4—228no—
521C22×C4—222no—
522C22×C4—222no—
523C22×C4—222no—
524C22×C4—222no—
525C22×C4D4×D1114yes—
526C22×C4C23×D1112yes—
527C22×C4C23×D1114yes—
528C22×C4C23×D1114yes—
529C22×C4C23×D1112yes—
530C22×C4C23×D1111yescharacteristic
531C22×C4C23×D1111yescharacteristic
532C4⋊C4—24no—
533C4⋊C4—24no—
534C4⋊C4—28no—
535C4⋊C4—28no—
536C4⋊C4—224no—
537C4⋊C4—224no—
538C4⋊C4—228no—
539C4⋊C4—228no—
540C4⋊C4—228no—
541C4⋊C4—2216no—
542C4⋊C4—224no—
543C4⋊C4—228no—
544C4⋊C4—224no—
545C4⋊C4—228no—
546C22⋊C4—28no—
547C22⋊C4—24no—
548C22⋊C4—224no—
549C22⋊C4—228no—
550C22⋊C4—228no—
551C22⋊C4—224no—
552C22⋊C4—228no—
553C22⋊C4—224no—
554C42—22no—
555C42—118no—
556C42—114no—
557C42—224no—
558C42—222no—
559C42D4×D1114yes—
560C11C2×#262111yescharacteristic, complemented, Sylow
561C23—21no—
562C23—21no—
563C23—24no—
564C23—112no—
565C23—112no—
566C23—112no—
567C23—118no—
568C23—112no—
569C23—228no—
570C23—2216no—
571C23—221no—
572C23—221no—
573C23—224no—
574C23—448no—
575C23—448no—
576C23C2×D4×D1112yes—
577C23C24×D1111yescharacteristic
578Q8—48no—
579Q8—4416no—
580Q8—448no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—24no—
584C2×C4—28no—
585C2×C4—22no—
586C2×C4—24no—
587C2×C4—24no—
588C2×C4—24no—
589C2×C4—24no—
590C2×C4—24no—
591C2×C4—28no—
592C2×C4—112no—
593C2×C4—112no—
594C2×C4—112no—
595C2×C4—1116no—
596C2×C4—114no—
597C2×C4—112no—
598C2×C4—228no—
599C2×C4—228no—
600C2×C4—2216no—
601C2×C4—228no—
602C2×C4—221no—
603C2×C4—221no—
604C2×C4—224no—
605C2×C4—228no—
606C2×C4—222no—
607C2×C4—224no—
608C2×C4—224no—
609C2×C4—224no—
610C2×C4—224no—
611C2×C4—224no—
612C2×C4—228no—
613C2×C4—4416no—
614C2×C4—448no—
615C2×C4—4416no—
616C2×C4C2×D4×D1114yes—
617C2×C4C2×D4×D1112yes—
618C2×C4C2×D4×D1112yes—
619C2×C4C2×D4×D1112yes—
620C2×C4#41×D1112yes—
621C22—24no—
622C22—22no—
623C22—42no—
624C22—42no—
625C22—118no—
626C22—118no—
627C22—118no—
628C22—114no—
629C22—224no—
630C22—222no—
631C22—4416no—
632C22—442no—
633C22—442no—
634C22C22×D4×D1111yescharacteristic
635C22C22×D4×D1111yescharacteristic
636C22C2×#41×D1111yescharacteristic
637C22D11×2−1+414yes—
638C4—24no—
639C4—22no—
640C4—42no—
641C4—44no—
642C4—44no—
643C4—114no—
644C4—224no—
645C4—222no—
646C4—442no—
647C4—444no—
648C4—444no—
649C4D11×#12114yes—
650C2—42no—
651C2—118no—
652C2—442no—
653C2C2×D11×#12111yescharacteristic
654C2D11×#53612yes—
655C2D11×#53612yes—
656C2D11×#54112yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2621C2
prime radicalC24×D11C23
hypercenter#2621D11
hypocenterC11C2×#2621
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2621

Complements

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

NH ≅ G/Ntype
1. C2×D11×C4⋊Q8C2semidirect
4. #13074387C2semidirect
5. #13074386C2semidirect
6. #13074385C2semidirect
7. #13074384C2semidirect
8. #13074383C2semidirect
9. #13074382C2semidirect
10. #13074381C2semidirect
11. D11×#398C2semidirect
13. D11×#391C2semidirect
14. D11×#382C2semidirect
15. C11×#2621C2semidirect
18. C2×C11×C4⋊Q8C22semidirect
22. C2×#66997C22semidirect
35. C2×#66941C22semidirect
44. C2×#66922C22semidirect
45. C11×#398C22semidirect
47. C11×#391C22semidirect
48. C11×#382C22semidirect
49. #10622843C22semidirect
51. #10622597C22semidirect
52. #10622596C22semidirect
53. #10622593C22semidirect
54. #10622590C22semidirect
55. #10622587C22semidirect
58. #10622549C22semidirect
59. #10622542C22semidirect
64. #10622274C22semidirect
65. #10622270C22semidirect
66. #10622263C22semidirect
67. #10622259C22semidirect
243. #2621D11direct (N × H)
314. C2×C4⋊Q8C2×D11semidirect
342. #398C2×D11semidirect
353. #391C2×D11semidirect
357. #382C2×D11semidirect
474. D11#2621direct (N × H)
560. C11C2×#2621semidirect

Maximal subgroups

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

subgroupindex
C2×D11×C4⋊Q82
C2×D11×C22⋊Q82
C2×D11×#1172
#130743872
#130743862
#130743852
#130743842
#130743832
#130743822
#130743812
D11×#3982
D11×#3972
D11×#3912
D11×#3822
C11×#26212
C2×#262111