Finite Group Databasebeta

← D11×#1546 #14722093

Subgroups — D11×#1546 #14722093

Order 2816.

1246 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×C4⋊Q8C211yesmaximal, characteristic
2D11×#431C211yesmaximal, characteristic
3D11×#423C211yesmaximal, characteristic
4#13067289C211yesmaximal, characteristic, complemented
5#13067288C211yesmaximal, characteristic, complemented
6#13067287C211yesmaximal, characteristic, complemented
7#13067286C214yesmaximal, complemented
8D11×#332C214yesmaximal, complemented
9C11×#1546C211yesmaximal, characteristic, complemented
10C22×Q8×D11—21no—
11C2×C11×C4⋊Q8C2211yescharacteristic
12C2×#66997—21no—
13C2×M16×D11—21no—
14D11×C4⋊Q8—21no—
15D11×C4⋊Q8—21no—
16D11×C4⋊Q8—21no—
17D11×C4⋊Q8—21no—
18D11×C4⋊Q8C412yes—
19D11×C4⋊Q8C412yes—
20D11×C4⋊Q8C2212yes—
21D11×C4⋊Q8C2212yes—
22C2×C4⋊C4×D11—21no—
23C2×C4⋊C4×D11C412yes—
24C2×#66941—21no—
25C2×#66941C412yes—
26C2×C42×D11C2211yescharacteristic
27C2×#66922C2211yescharacteristic
28C11×#431C2211yescharacteristic
29C11×#423C2211yescharacteristic
30#10622731—21no—
31#10622538C2211yescharacteristic
32#10622537C2211yescharacteristic
33#10622450—21no—
34#10622450C2212yes—
35#10622446C2212yes—
36D11×C4⋊C8—21no—
37D11×C4⋊C8C2212yes—
38D11×C4⋊C8C2212yes—
39D11×C22⋊C8—21no—
40#10622331—21no—
41#10622298—21no—
42C4×C8×D11—21no—
43C11×#332C2214yescomplemented
44#10622185C2214yescomplemented
45#10622124C2214yescomplemented
46#10622120C2214yescomplemented
47C22×Q8×C11—21no—
48C2×Q8×D11—22no—
49C2×Q8×D11—22no—
50C2×Q8×D11—22no—
51C2×Q8×D11—22no—
52C2×Q8×D11—44no—
53C2×Q8×D11—44no—
54C22×C4×D11—22no—
55C22×C4×D11C2×C411yescharacteristic
56C22×C4×D11D411yescharacteristic
57C22×C4×D11D411yescharacteristic
58C22×Dic22—21no—
59C22×Dic22—22no—
60C2×C11×M16—21no—
61C11×C4⋊Q8—21no—
62C11×C4⋊Q8—21no—
63C11×C4⋊Q8C2×C412yes—
64C11×C4⋊Q8C2312yes—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4C2×C412yes—
67C2×C42×C11C2311yescharacteristic
68#66997—22no—
69#66997—22no—
70#66997—22no—
71#66997—22no—
72C2×C4⋊Dic11—21no—
73C2×C4⋊Dic11C2×C412yes—
74C2×Dic11⋊C4—22no—
75C2×Dic11⋊C4—22no—
76C2×C4×Dic11C2×C411yescharacteristic
77C2×C4×Dic11D411yescharacteristic
78C2×C4×Dic11D411yescharacteristic
79C2×#4318—21no—
80M16×D11—44no—
81C2×#4313—22no—
82C2×C8×D11—22no—
83C2×C8×D11—22no—
84C4⋊C4×D11—22no—
85C4⋊C4×D11—22no—
86C4⋊C4×D11—22no—
87C4⋊C4×D11—22no—
88C4⋊C4×D11—22no—
89C4⋊C4×D11—22no—
90C4⋊C4×D11C2×C414yes—
91C4⋊C4×D11C2×C414yes—
92#66941—22no—
93#66941—22no—
94#66941—22no—
95#66941—22no—
96#66941—22no—
97#66941—22no—
98#66941C2×C414yes—
99#66941C2×C414yes—
100C42×D11C2×C411yescharacteristic
101C42×D11C2×C411yescharacteristic
102C42×D11D411yescharacteristic
103C42×D11D411yescharacteristic
104C42×D11D411yescharacteristic
105C42×D11D411yescharacteristic
106C42×D11C2311yescharacteristic
107C42×D11C2311yescharacteristic
108#66922—21no—
109#66922—21no—
110#66922C2×C412yes—
111#66922C2312yes—
112C11×C4⋊C8—21no—
113C11×C4⋊C8C2312yes—
114C11×C4⋊C8C2312yes—
115C11×C22⋊C8—21no—
116C4×C8×C11—21no—
117C22⋊(C11⋊C8)—21no—
118(C2×D11)⋊C8—22no—
119Dic11⋊C8—22no—
120Dic11⋊C8—22no—
121Dic11⋊C8—22no—
122C8×Dic11—22no—
123C4⋊(C11⋊C8)—21no—
124C4⋊(C11⋊C8)C2312yes—
125C4⋊(C11⋊C8)C2312yes—
126C4×C11⋊C8—21no—
127C2×#1546—111nomaximal, Sylow
128C23×D11C22⋊C411yescharacteristic
129C2×Q8×C11—22no—
130C2×Q8×C11—22no—
131C2×Q8×C11—42no—
132C2×Q8×C11—42no—
133C22×C4×C11—22no—
134C22×C4×C11C22×C411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×Dic11—22no—
138C22×Dic11C22⋊C411yescharacteristic
139C22×Dic11C22⋊C411yescharacteristic
140C22×Dic11C22⋊C411yescharacteristic
141Q8×D11—48no—
142Q8×D11—48no—
143Q8×D11—44no—
144Q8×D11—44no—
145Q8×D11—44no—
146Q8×D11—44no—
147C2×C4×D11—24no—
148C2×C4×D11—24no—
149C2×C4×D11—24no—
150C2×C4×D11—24no—
151C2×C4×D11—48no—
152C2×C4×D11C22⋊C411yescharacteristic
153C2×C4×D11C22⋊C411yescharacteristic
154C2×C4×D11C22⋊C411yescharacteristic
155C2×C4×D11C22⋊C411yescharacteristic
156C2×C4×D11C22⋊C411yescharacteristic
157C2×C4×D11C22⋊C411yescharacteristic
158C2×C4×D11D814yes—
159C2×C4×D11SD1614yes—
160C2×C4×D11C22×C411yescharacteristic
161C2×C4×D11C22×C411yescharacteristic
162C2×C4×D11C2×D411yescharacteristic
163C2×C4×D11C2×D411yescharacteristic
164C2×C4×D11C2×D411yescharacteristic
165C2×C4×D11C2×D411yescharacteristic
166C2×Dic22—24no—
167C2×Dic22—24no—
168C2×Dic22—22no—
169C2×Dic22—22no—
170C2×Dic22—48no—
171C2×Dic22—42no—
172C2×Dic22—42no—
173C11×M16—42no—
174C2×C8×C11—22no—
175C2×C8×C11—22no—
176C11×C4⋊C4—22no—
177C11×C4⋊C4—22no—
178C11×C4⋊C4—22no—
179C11×C4⋊C4C22×C414yes—
180C42×C11C22×C411yescharacteristic
181C42×C11C2×D411yescharacteristic
182C42×C11C2×D411yescharacteristic
183C42×C11C2411yescharacteristic
184C4⋊Dic11—22no—
185C4⋊Dic11—22no—
186C4⋊Dic11—22no—
187C4⋊Dic11C22×C414yes—
188Dic11⋊C4—24no—
189Dic11⋊C4—24no—
190Dic11⋊C4—24no—
191Dic11⋊C4—24no—
192C4×Dic11C22⋊C411yescharacteristic
193C4×Dic11C22⋊C411yescharacteristic
194C4×Dic11C22⋊C411yescharacteristic
195C4×Dic11C22⋊C411yescharacteristic
196C4×Dic11C22⋊C411yescharacteristic
197C4×Dic11C22⋊C411yescharacteristic
198C4×Dic11C22×C411yescharacteristic
199C4×Dic11C22×C411yescharacteristic
200C4×Dic11C2×D411yescharacteristic
201C4×Dic11C2×D411yescharacteristic
202C4×Dic11C2×D411yescharacteristic
203C4×Dic11C2×D411yescharacteristic
204#4318—42no—
205C2×C11⋊C8—22no—
206C2×C11⋊C8—22no—
207#4313—44no—
208C8×D11—44no—
209C8×D11—44no—
210C22×C4⋊Q8—111no—
211C2×#431—111no—
212C2×#423—111no—
213#1546—111no—
214#1546—111no—
215#1546—114no—
216#1546—111no—
217#1546D1111yescharacteristic, direct product factor
218C2×#332—114no—
219C23×C11C2×C22⋊C411yescharacteristic
220C22×D11—22no—
221C22×D11—22no—
222C22×D11#10214yes—
223C22×D11C2×C22⋊C411yescharacteristic
224C22×D11C2×C22⋊C411yescharacteristic
225Q8×C11—42no—
226Q8×C11—42no—
227Q8×C11—44no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—24no—
231C2×C4×C11—44no—
232C2×C4×C11C2×C22⋊C411yescharacteristic
233C2×C4×C11C2×C22⋊C411yescharacteristic
234C2×C4×C11C2×C22⋊C411yescharacteristic
235C2×C4×C11C2×D812yes—
236C2×C4×C11C2×SD1612yes—
237C2×C4×C11C23×C411yescharacteristic
238C2×C4×C11C22×D411yescharacteristic
239C2×C4×C11C22×D411yescharacteristic
240C2×Dic11—22no—
241C2×Dic11—22no—
242C2×Dic11—24no—
243C2×Dic11—44no—
244C2×Dic11#10214yes—
245C2×Dic11C2×C22⋊C411yescharacteristic
246C2×Dic11C2×C22⋊C411yescharacteristic
247C2×Dic11C2×C22⋊C411yescharacteristic
248C2×Dic11C2×C22⋊C411yescharacteristic
249C2×Dic11C2×C22⋊C411yescharacteristic
250C2×Dic11C2×C22⋊C411yescharacteristic
251C4×D11—22no—
252C4×D11—22no—
253C4×D11—22no—
254C4×D11—22no—
255C4×D11—22no—
256C4×D11—22no—
257C4×D11—48no—
258C4×D11—48no—
259C4×D11#10114yes—
260C4×D11#10214yes—
261C4×D11#10214yes—
262C4×D11C2×D812yes—
263C4×D11C2×D812yes—
264C4×D11C2×SD1612yes—
265C4×D11C2×SD1612yes—
266C4×D11#13714yes—
267Dic22—42no—
268Dic22—42no—
269Dic22—44no—
270Dic22—48no—
271Dic22—48no—
272C8×C11—42no—
273C8×C11—42no—
274C11⋊C8—42no—
275C11⋊C8—42no—
276C23×Q8—221no—
277C22×M16—221no—
278C2×C4⋊Q8—112no—
279C2×C4⋊Q8—112no—
280C2×C4⋊Q8—112no—
281C2×C4⋊Q8—112no—
282C2×C4⋊Q8—112no—
283C2×C4⋊Q8—111no—
284C2×C4⋊Q8—221no—
285C2×C4⋊Q8—221no—
286C2×C4⋊Q8—221no—
287C2×C4⋊Q8—221no—
288C2×C4⋊Q8—221no—
289C2×C4⋊Q8—221no—
290C2×C4⋊Q8C2×D1111yescharacteristic
291C22×C4⋊C4—112no—
292C22×C4⋊C4—221no—
293C22×C42—111no—
294#431—111no—
295#431—112no—
296#431—221no—
297#431—221no—
298#431C2×D1111yescharacteristic
299#423—111no—
300#423—112no—
301#423—221no—
302#423—221no—
303#423C2×D1111yescharacteristic
304C2×C4⋊C8—112no—
305C2×C4⋊C8—112no—
306C2×C4⋊C8—221no—
307C2×C22⋊C8—221no—
308C2×C4×C8—221no—
309#332—114no—
310#332—114no—
311#332—114no—
312#332C2×D1114yescomplemented
313C22×C11—21no—
314C22×C11—21no—
315C22×C11C2×#10212yes—
316C22×C11C22×C22⋊C411yescharacteristic
317C2×D11—21no—
318C2×D11—21no—
319C2×D11—28no—
320C2×D11C2×#10112yes—
321C2×D11C2×#10212yes—
322C2×D11C2×#10212yes—
323C2×D11#41912yes—
324C4×C11—21no—
325C4×C11—21no—
326C4×C11—44no—
327C4×C11C2×#10112yes—
328C4×C11C2×#10212yes—
329C4×C11C22×D811yescharacteristic
330C4×C11C22×SD1611yescharacteristic
331C4×C11C2×#13712yes—
332Dic11—21no—
333Dic11—21no—
334Dic11—44no—
335Dic11C2×#10112yes—
336Dic11C2×#10212yes—
337Dic11C2×#10212yes—
338Dic11#41912yes—
339C22×Q8—21no—
340C22×Q8—222no—
341C22×Q8—222no—
342C22×Q8—222no—
343C22×Q8—222no—
344C22×Q8—222no—
345C22×Q8—221no—
346C22×Q8—444no—
347C22×Q8—444no—
348C23×C4—111no—
349C23×C4—111no—
350C23×C4—111no—
351C23×C4—222no—
352C2×M16—21no—
353C2×M16—222no—
354C2×M16—221no—
355C2×M16—444no—
356C22×C8—222no—
357C22×C8—222no—
358C4⋊Q8—21no—
359C4⋊Q8—21no—
360C4⋊Q8—114no—
361C4⋊Q8—114no—
362C4⋊Q8—112no—
363C4⋊Q8—112no—
364C4⋊Q8—222no—
365C4⋊Q8—222no—
366C4⋊Q8—222no—
367C4⋊Q8—222no—
368C4⋊Q8—222no—
369C4⋊Q8—222no—
370C4⋊Q8—222no—
371C4⋊Q8—222no—
372C4⋊Q8—222no—
373C4⋊Q8—222no—
374C4⋊Q8—221no—
375C4⋊Q8—221no—
376C4⋊Q8C4×D1112yes—
377C4⋊Q8C22×D1112yes—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—112no—
380C2×C4⋊C4—114no—
381C2×C4⋊C4—114no—
382C2×C4⋊C4—222no—
383C2×C4⋊C4—222no—
384C2×C4⋊C4—222no—
385C2×C4⋊C4—222no—
386C2×C4⋊C4—222no—
387C2×C4⋊C4—222no—
388C2×C4⋊C4—222no—
389C2×C4⋊C4—222no—
390C2×C4⋊C4—221no—
391C2×C4⋊C4C4×D1112yes—
392C2×C42—111no—
393C2×C42—111no—
394C2×C42—111no—
395C2×C42—111no—
396C2×C42—111no—
397C2×C42—111no—
398C2×C42—111no—
399C2×C42—111no—
400C2×C42—111no—
401C2×C42—111no—
402C2×C42—111no—
403C2×C42C22×D1111yescharacteristic
404C4⋊C8—21no—
405C4⋊C8—112no—
406C4⋊C8—112no—
407C4⋊C8—222no—
408C4⋊C8—222no—
409C4⋊C8—222no—
410C4⋊C8—221no—
411C4⋊C8C22×D1112yes—
412C4⋊C8C22×D1112yes—
413C22⋊C8—21no—
414C22⋊C8—222no—
415C22⋊C8—221no—
416C4×C8—21no—
417C4×C8—222no—
418C4×C8—221no—
419C2×C11—22no—
420C2×C11C22×#10111yescharacteristic
421C2×C11C22×#10211yescharacteristic
422C2×C11C2×#41911yescharacteristic
423D11—22no—
424D11#154614yesdirect product factor
425C24—111no—
426C2×Q8—22no—
427C2×Q8—22no—
428C2×Q8—42no—
429C2×Q8—42no—
430C2×Q8—224no—
431C2×Q8—224no—
432C2×Q8—222no—
433C2×Q8—222no—
434C2×Q8—448no—
435C2×Q8—444no—
436C2×Q8—444no—
437C2×Q8—444no—
438C2×Q8—444no—
439C2×Q8—448no—
440C2×Q8—448no—
441C2×Q8—442no—
442C2×Q8—442no—
443C22×C4—22no—
444C22×C4—111no—
445C22×C4—111no—
446C22×C4—111no—
447C22×C4—111no—
448C22×C4—114no—
449C22×C4—114no—
450C22×C4—111no—
451C22×C4—111no—
452C22×C4—111no—
453C22×C4—111no—
454C22×C4—111no—
455C22×C4—111no—
456C22×C4—111no—
457C22×C4—111no—
458C22×C4—111no—
459C22×C4—111no—
460C22×C4—111no—
461C22×C4—224no—
462C22×C4—224no—
463C22×C4—224no—
464C22×C4—224no—
465C22×C4—222no—
466C22×C4—448no—
467C22×C4C2×C4×D1111yescharacteristic
468C22×C4D4×D1111yescharacteristic
469C22×C4D4×D1111yescharacteristic
470M16—42no—
471M16—444no—
472M16—442no—
473C2×C8—22no—
474C2×C8—22no—
475C2×C8—222no—
476C2×C8—222no—
477C2×C8—444no—
478C2×C8—444no—
479C4⋊C4—22no—
480C4⋊C4—22no—
481C4⋊C4—22no—
482C4⋊C4—114no—
483C4⋊C4—224no—
484C4⋊C4—224no—
485C4⋊C4—224no—
486C4⋊C4—224no—
487C4⋊C4—222no—
488C4⋊C4—222no—
489C4⋊C4—222no—
490C4⋊C4C2×C4×D1114yes—
491C42—111no—
492C42—111no—
493C42—111no—
494C42—111no—
495C42—111no—
496C42—111no—
497C42—111no—
498C42—111no—
499C42—111no—
500C42—111no—
501C42—111no—
502C42—111no—
503C42C2×C4×D1111yescharacteristic
504C42D4×D1111yescharacteristic
505C42D4×D1111yescharacteristic
506C42C23×D1111yescharacteristic
507C11C2×#154611yescharacteristic, complemented, Sylow
508C23—111no—
509C23—111no—
510C23—114no—
511C23—222no—
512C23—222no—
513C23C22⋊C4×D1111yescharacteristic
514Q8—42no—
515Q8—42no—
516Q8—44no—
517Q8—448no—
518Q8—448no—
519Q8—442no—
520Q8—442no—
521Q8—444no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—24no—
525C2×C4—44no—
526C2×C4—111no—
527C2×C4—111no—
528C2×C4—111no—
529C2×C4—111no—
530C2×C4—114no—
531C2×C4—112no—
532C2×C4—112no—
533C2×C4—112no—
534C2×C4—112no—
535C2×C4—114no—
536C2×C4—114no—
537C2×C4—114no—
538C2×C4—114no—
539C2×C4—111no—
540C2×C4—111no—
541C2×C4—222no—
542C2×C4—222no—
543C2×C4—222no—
544C2×C4—222no—
545C2×C4—222no—
546C2×C4—222no—
547C2×C4—222no—
548C2×C4—222no—
549C2×C4—224no—
550C2×C4—448no—
551C2×C4—448no—
552C2×C4—444no—
553C2×C4C22⋊C4×D1111yescharacteristic
554C2×C4C22⋊C4×D1111yescharacteristic
555C2×C4C22⋊C4×D1111yescharacteristic
556C2×C4D8×D1112yes—
557C2×C4SD16×D1112yes—
558C2×C4C22×C4×D1111yescharacteristic
559C2×C4C2×D4×D1111yescharacteristic
560C2×C4C2×D4×D1111yescharacteristic
561C8—42no—
562C8—42no—
563C8—442no—
564C8—442no—
565C22—21no—
566C22—21no—
567C22—112no—
568C22—112no—
569C22—112no—
570C22—112no—
571C22—228no—
572C22—221no—
573C22—221no—
574C22D11×#10212yes—
575C22C2×C22⋊C4×D1111yescharacteristic
576C4—21no—
577C4—21no—
578C4—44no—
579C4—112no—
580C4—112no—
581C4—112no—
582C4—112no—
583C4—221no—
584C4—221no—
585C4—444no—
586C4D11×#10112yes—
587C4D11×#10212yes—
588C4C2×D8×D1111yescharacteristic
589C4C2×SD16×D1111yescharacteristic
590C4D11×#13712yes—
591C2—22no—
592C2—114no—
593C2—222no—
594C2C2×D11×#10111yescharacteristic
595C2C2×D11×#10211yescharacteristic
596C2D11×#41911yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1546C2
socleC22×C11C22×C22⋊C4
prime radicalC23×D11C22⋊C4
cosocleC42×C11C24
hypercenter#1546D11
hypocenterC11C2×#1546
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1546

Complements

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

NH ≅ G/Ntype
4. #13067289C2semidirect
5. #13067288C2semidirect
6. #13067287C2semidirect
7. #13067286C2semidirect
8. D11×#332C2semidirect
9. C11×#1546C2semidirect
43. C11×#332C22semidirect
44. #10622185C22semidirect
45. #10622124C22semidirect
46. #10622120C22semidirect
217. #1546D11direct (N × H)
312. #332C2×D11semidirect
424. D11#1546direct (N × H)
507. C11C2×#1546semidirect

Maximal subgroups

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

subgroupindex
C2×D11×C4⋊Q82
D11×#4312
D11×#4232
#130672892
#130672882
#130672872
#130672862
D11×#3322
C11×#15462
C2×#154611