Finite Group Databasebeta

← C2×D11×#489 #15622979

Subgroups — C2×D11×#489 #15622979

Order 2816.

2486 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×C4⋊Q8C211yesmaximal, characteristic, complemented
2C2×D11×#124C211yesmaximal, characteristic
3C2×#10622702C211yesmaximal, characteristic, complemented
4C2×#10622408C212yesmaximal, complemented
5C2×#10622327C211yesmaximal, characteristic, complemented
6C2×#10622668C211yesmaximal, characteristic, complemented
7C2×#10622378C212yesmaximal, complemented
8D11×#489C2116yesmaximal, direct product factor
9C2×D11×#103C212yesmaximal, complemented
10C2×D11×#102C212yesmaximal
11C2×D11×#97C211yesmaximal, characteristic, complemented
12C2×C11×#489C211yesmaximal, characteristic, complemented
13C22×Q8×D11—21no—
14C22×Q8×D11C2211yescharacteristic
15C22×D4×D11C2211yescharacteristic
16C2×C11×C4⋊Q8C2211yescharacteristic, complemented
17C2×C11×#124C2211yescharacteristic
18C2×#67000C2211yescharacteristic
19C2×#66997—21no—
20C2×#66989C2211yescharacteristic
21C22×C8×D11C2212yes—
22D11×C4⋊Q8—24no—
23D11×C4⋊Q8C2218yescomplemented
24D11×#124—24no—
25D11×#124C2218yes—
26C2×C4⋊C4×D11—21no—
27C2×C4⋊C4×D11C2212yes—
28C2×#66941—21no—
29C2×#66941C2212yescomplemented
30C2×#66938—21no—
31C2×#66938—21no—
32C2×C22⋊C4×D11—21no—
33C2×C22⋊C4×D11—21no—
34C2×#66928C2211yescharacteristic
35C2×C42×D11C2211yescharacteristic
36C2×#66922C2211yescharacteristic, complemented
37C11×#489C2218yescomplemented
38C2×C11×#103C2212yescomplemented
39C2×C11×#102C2212yes—
40C2×C11×#97C2211yescharacteristic, complemented
41C2×#66899C2212yescomplemented
42C2×#66896C2212yes—
43C2×#66885C2212yes—
44C2×#66880C2212yescomplemented
45C2×#66879C2212yescomplemented
46#10622702C2218yescomplemented
47#10622668C2218yescomplemented
48C2×#66874C2212yescomplemented
49C2×#66873C2212yes—
50C2×#66867C2211yescharacteristic, complemented
51D11×#103C22116yescomplemented
52#10622408C22116yescomplemented
53D11×#102C22116yes—
54#10622378C22116yescomplemented
55#10622327C2218yescomplemented
56D11×#97C2218yescomplemented
57C24×D11—21no—
58C22×Q8×C11—21no—
59C22×Q8×C11C2311yescharacteristic
60C22×D4×C11C2311yescharacteristic
61C22×C22⋊D11—21no—
62C2×Q8×D11—28no—
63C2×Q8×D11—22no—
64C2×Q8×D11—28no—
65C2×Q8×D11—48no—
66C2×Q8×D11C2314yes—
67C2×D4×D11—22no—
68C2×D4×D11—28no—
69C2×D4×D11C2314yes—
70C22×D44C2311yescharacteristic
71C22×C4×D11—21no—
72C22×C4×D11—22no—
73C22×C4×D11D411yescharacteristic
74C22×C4×D11D411yescharacteristic
75C22×C4×D11C2311yescharacteristic
76C22×Dic22—21no—
77C22×Dic22—21no—
78C22×Dic22—22no—
79C22×Dic22C2311yescharacteristic
80C22×C8×C11C2312yes—
81C11×C4⋊Q8—22no—
82C11×C4⋊Q8C2314yescomplemented
83C11×#124—22no—
84C11×#124C2314yes—
85C2×C11×C4⋊C4—21no—
86C2×C11×C4⋊C4C2312yes—
87C2×C11×C22⋊C4—21no—
88C2×C11×C22⋊C4—21no—
89C2×C42×C11C2311yescharacteristic
90C2×C22⋊Dic11—21no—
91C2×C22⋊Dic11—21no—
92#67000—22no—
93#67000C2314yes—
94#66997—28no—
95#66989—22no—
96#66989C2314yes—
97C2×(C2×D11)⋊C4—21no—
98C2×(C2×D11)⋊C4—21no—
99C2×(C2×D11)⋊C4—21no—
100C2×(C2×D11)⋊C4—21no—
101C2×C4⋊Dic11—21no—
102C2×C4⋊Dic11C2312yes—
103C2×Dic11⋊C4—22no—
104C2×Dic11⋊C4—22no—
105C2×C4×Dic11D411yescharacteristic
106C2×C4×Dic11D411yescharacteristic
107C2×C4×Dic11C2311yescharacteristic
108C22×C11⋊C8C2312yes—
109C2×C8×D11—28no—
110C2×C8×D11C2318yes—
111C4⋊C4×D11—24no—
112C4⋊C4×D11—28no—
113C4⋊C4×D11C2318yes—
114#66941—24no—
115#66941—28no—
116#66941C2318yescomplemented
117#66938—28no—
118#66938—28no—
119C22⋊C4×D11—28no—
120C22⋊C4×D11—28no—
121#66928—22no—
122#66928C2314yes—
123C42×D11D414yes—
124C42×D11C2314yes—
125#66922—22no—
126#66922C2314yescomplemented
127C11×#103C2318yescomplemented
128C11×#102C2318yes—
129C11×#97C2314yescomplemented
130#66899C2318yescomplemented
131#66896C2318yes—
132#66885C2318yes—
133#66880C2318yescomplemented
134#66879C2318yescomplemented
135#66874C2318yescomplemented
136#66873C2318yes—
137#66867C2314yescomplemented
138C22×#489—111nomaximal, Sylow
139C24×C11—21no—
140C23×D11—21no—
141C23×D11—24no—
142C23×D11—44no—
143C23×D11—44no—
144C23×D11—44no—
145C23×D11C2×D411yescharacteristic
146C2×Q8×C11—24no—
147C2×Q8×C11—21no—
148C2×Q8×C11—24no—
149C2×Q8×C11—44no—
150C2×Q8×C11C2412yes—
151C2×D4×C11—21no—
152C2×D4×C11—24no—
153C2×D4×C11C2412yes—
154C22×C4×C11—22no—
155C22×C4×C11—21no—
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2411yescharacteristic
159C2×C22⋊D11—24no—
160C2×C22⋊D11—44no—
161C22×Dic11—22no—
162C22×Dic11—21no—
163C22×Dic11C2×D411yescharacteristic
164C22×Dic11C2×D411yescharacteristic
165C22×Dic11C2×D411yescharacteristic
166Q8×D11—216no—
167Q8×D11—432no—
168Q8×D11—48no—
169D4×D11—216no—
170D4×D11—48no—
171C2×D44—21no—
172C2×D44—24no—
173C2×D44C2412yes—
174C2×C4×D11—24no—
175C2×C4×D11—24no—
176C2×C4×D11—24no—
177C2×C4×D11—28no—
178C2×C4×D11—44no—
179C2×C4×D11—48no—
180C2×C4×D11C2×D414yes—
181C2×C4×D11C2×D414yes—
182C2×C4×D11C2×D412yes—
183C2×C4×D11#4118yes—
184C2×C4×D11C2412yes—
185C2×Dic22—24no—
186C2×Dic22—28no—
187C2×Dic22—24no—
188C2×Dic22—21no—
189C2×Dic22—24no—
190C2×Dic22—44no—
191C2×Dic22—48no—
192C2×Dic22—44no—
193C2×Dic22C2412yes—
194C2×C8×C11—24no—
195C2×C8×C11C2414yes—
196C11×C4⋊C4—24no—
197C11×C4⋊C4—22no—
198C11×C4⋊C4C2414yes—
199C11×C22⋊C4—24no—
200C11×C22⋊C4—24no—
201C42×C11C2×D412yes—
202C42×C11C2412yes—
203C22⋊Dic11—24no—
204C22⋊Dic11—24no—
205(C2×D11)⋊C4—24no—
206(C2×D11)⋊C4—24no—
207(C2×D11)⋊C4—24no—
208(C2×D11)⋊C4—24no—
209C4⋊Dic11—22no—
210C4⋊Dic11—24no—
211C4⋊Dic11C2414yes—
212Dic11⋊C4—28no—
213Dic11⋊C4—28no—
214C4×Dic11C2×D412yes—
215C4×Dic11C2×D414yes—
216C4×Dic11C2×D414yes—
217C4×Dic11C2412yes—
218C2×C11⋊C8—24no—
219C2×C11⋊C8C2414yes—
220C8×D11—216no—
221C22×C4⋊Q8—111no—
222C22×#124—111no—
223C2×#489—1116no—
224C2×#489—112no—
225C2×#489—112no—
226C2×#489—111no—
227C2×#489—111no—
228C2×#489—111no—
229C2×#489D1111yescharacteristic, direct product factor
230C22×#103—112no—
231C22×#102—112no—
232C22×#97—111no—
233C23×C11—22no—
234C23×C11—42no—
235C23×C11—42no—
236C23×C11—42no—
237C23×C11C22×D411yescharacteristic
238C22×D11—22no—
239C22×D11—42no—
240C22×D11—42no—
241C22×D11—42no—
242C22×D11—48no—
243C22×D11—48no—
244C22×D11—48no—
245C22×D11—816no—
246C22×D11#12414yes—
247C22×D11AGL(1,ℤ/8)14yes—
248C22×D11#13714yes—
249C22×D11C22×D412yes—
250Q8×C11—24no—
251Q8×C11—48no—
252Q8×C11—42no—
253D4×C11—24no—
254D4×C11—42no—
255C2×C4×C11—22no—
256C2×C4×C11—22no—
257C2×C4×C11—24no—
258C2×C4×C11—22no—
259C2×C4×C11—42no—
260C2×C4×C11—44no—
261C2×C4×C11C22×D412yes—
262C2×C4×C11C22×D412yes—
263C2×C4×C11C22×D411yescharacteristic
264C2×C4×C11C2×#4114yes—
265C2×C4×C11C2511yescharacteristic
266C22⋊D11—48no—
267C2×Dic11—22no—
268C2×Dic11—22no—
269C2×Dic11—24no—
270C2×Dic11—22no—
271C2×Dic11—42no—
272C2×Dic11—44no—
273C2×Dic11#12414yes—
274C2×Dic11C22×D412yes—
275C2×Dic11C22×D412yes—
276C2×Dic11C22×D412yes—
277D44—24no—
278D44—42no—
279C4×D11—28no—
280C4×D11—28no—
281C4×D11—48no—
282C4×D11—416no—
283C4×D11#12418yes—
284C4×D11C2×#4118yes—
285Dic22—24no—
286Dic22—416no—
287Dic22—48no—
288Dic22—42no—
289Dic22—48no—
290C8×C11—24no—
291C11⋊C8—24no—
292C23×Q8—111no—
293C23×Q8—221no—
294C23×D4—111no—
295C23×C8—112no—
296C2×C4⋊Q8—118no—
297C2×C4⋊Q8—112no—
298C2×C4⋊Q8—111no—
299C2×C4⋊Q8—221no—
300C2×C4⋊Q8—224no—
301C2×C4⋊Q8—221no—
302C2×C4⋊Q8C2×D1111yescharacteristic, complemented
303C2×#124—111no—
304C2×#124—111no—
305C2×#124—118no—
306C2×#124—111no—
307C2×#124—221no—
308C2×#124—221no—
309C2×#124—224no—
310C2×#124C2×D1111yescharacteristic
311C22×C4⋊C4—112no—
312C22×C4⋊C4—221no—
313C22×C22⋊C4—221no—
314C22×C22⋊C4—221no—
315C22×C42—111no—
316#489—118no—
317#489—118no—
318#489—1116no—
319#489—1116no—
320#489—118no—
321#489C2×D1118yesdirect product factor
322C2×#103—112no—
323C2×#103—112no—
324C2×#103—112no—
325C2×#103—1116no—
326C2×#103C2×D1112yescomplemented
327C2×#102—112no—
328C2×#102—112no—
329C2×#102—112no—
330C2×#102—1116no—
331C2×#102C2×D1112yes—
332C2×#97—112no—
333C2×#97—111no—
334C2×#97—118no—
335C2×#97C2×D1111yescharacteristic, complemented
336C22×C11—42no—
337C22×C11—42no—
338C22×C11—42no—
339C22×C11—84no—
340C22×C11C2×#12412yes—
341C22×C11C2×AGL(1,ℤ/8)12yes—
342C22×C11C2×#13712yes—
343C22×C11C23×D411yescharacteristic
344C2×D11—42no—
345C2×D11—42no—
346C2×D11—42no—
347C2×D11—84no—
348C2×D11—816no—
349C2×D11#489116yesdirect product factor
350C2×D11C2×#12414yes—
351C2×D11C2×AGL(1,ℤ/8)14yes—
352C2×D11C2×#13714yes—
353C4×C11—22no—
354C4×C11—22no—
355C4×C11—42no—
356C4×C11—44no—
357C4×C11C2×#12412yes—
358C4×C11C22×#4112yes—
359Dic11—22no—
360Dic11—22no—
361Dic11—42no—
362Dic11—44no—
363Dic11C2×#12414yes—
364C25—221no—
365C22×Q8—21no—
366C22×Q8—114no—
367C22×Q8—111no—
368C22×Q8—221no—
369C22×Q8—222no—
370C22×Q8—222no—
371C22×Q8—228no—
372C22×Q8—228no—
373C22×Q8—221no—
374C22×Q8—448no—
375C22×Q8C22×D1111yescharacteristic
376C22×D4—114no—
377C22×D4—111no—
378C22×D4—228no—
379C22×D4—222no—
380C22×D4—221no—
381C22×D4C22×D1111yescharacteristic
382C23×C4—111no—
383C23×C4—111no—
384C23×C4—111no—
385C23×C4—221no—
386C23×C4—222no—
387C22×C8—112no—
388C22×C8—118no—
389C22×C8—228no—
390C22×C8C22×D1112yes—
391C4⋊Q8—22no—
392C4⋊Q8—118no—
393C4⋊Q8—114no—
394C4⋊Q8—228no—
395C4⋊Q8—224no—
396C4⋊Q8—228no—
397C4⋊Q8—222no—
398C4⋊Q8C22×D1114yescomplemented
399#124—22no—
400#124—114no—
401#124—114no—
402#124—114no—
403#124—228no—
404#124—228no—
405#124—222no—
406#124—222no—
407#124—222no—
408#124C22×D1114yes—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—112no—
411C2×C4⋊C4—118no—
412C2×C4⋊C4—224no—
413C2×C4⋊C4—228no—
414C2×C4⋊C4—222no—
415C2×C4⋊C4—222no—
416C2×C4⋊C4—221no—
417C2×C4⋊C4C22×D1112yes—
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4—228no—
421C2×C22⋊C4—228no—
422C2×C22⋊C4—221no—
423C2×C22⋊C4—221no—
424C2×C22⋊C4—221no—
425C2×C22⋊C4—221no—
426C2×C22⋊C4—221no—
427C2×C22⋊C4—221no—
428C2×C42—111no—
429C2×C42—111no—
430C2×C42—111no—
431C2×C42—114no—
432C2×C42—114no—
433C2×C42C22×D1111yescharacteristic
434#103—118no—
435#103—118no—
436#103—118no—
437#103C22×D1118yescomplemented
438#102—118no—
439#102—118no—
440#102—118no—
441#102C22×D1118yes—
442#97—118no—
443#97—114no—
444#97C22×D1114yescomplemented
445C2×C11—82no—
446C2×C11C2×#48914yescomplemented
447C2×C11C22×#12411yescharacteristic
448C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
449C2×C11C22×#13711yescharacteristic
450D11—82no—
451D11C2×#48918yesdirect product factor
452C24—21no—
453C24—111no—
454C24—224no—
455C24—221no—
456C24—444no—
457C24—444no—
458C24—444no—
459C2×Q8—21no—
460C2×Q8—24no—
461C2×Q8—24no—
462C2×Q8—44no—
463C2×Q8—112no—
464C2×Q8—224no—
465C2×Q8—228no—
466C2×Q8—2216no—
467C2×Q8—221no—
468C2×Q8—224no—
469C2×Q8—224no—
470C2×Q8—444no—
471C2×Q8—444no—
472C2×Q8—448no—
473C2×Q8—448no—
474C2×Q8—4432no—
475C2×Q8C23×D1112yes—
476C2×D4—21no—
477C2×D4—24no—
478C2×D4—112no—
479C2×D4—2216no—
480C2×D4—224no—
481C2×D4—221no—
482C2×D4—224no—
483C2×D4—448no—
484C2×D4—444no—
485C2×D4C23×D1112yes—
486C22×C4—21no—
487C22×C4—22no—
488C22×C4—111no—
489C22×C4—112no—
490C22×C4—118no—
491C22×C4—112no—
492C22×C4—111no—
493C22×C4—111no—
494C22×C4—114no—
495C22×C4—114no—
496C22×C4—224no—
497C22×C4—224no—
498C22×C4—224no—
499C22×C4—228no—
500C22×C4—221no—
501C22×C4—222no—
502C22×C4—444no—
503C22×C4—448no—
504C22×C4D4×D1111yescharacteristic
505C22×C4D4×D1111yescharacteristic
506C22×C4C23×D1111yescharacteristic
507C2×C8—24no—
508C2×C8—114no—
509C2×C8—2216no—
510C2×C8—224no—
511C2×C8C23×D1114yes—
512C4⋊C4—24no—
513C4⋊C4—22no—
514C4⋊C4—114no—
515C4⋊C4—228no—
516C4⋊C4—228no—
517C4⋊C4—222no—
518C4⋊C4—224no—
519C4⋊C4C23×D1114yes—
520C22⋊C4—24no—
521C22⋊C4—24no—
522C22⋊C4—224no—
523C22⋊C4—224no—
524C22⋊C4—224no—
525C22⋊C4—224no—
526C22⋊C4—224no—
527C22⋊C4—224no—
528C42—114no—
529C42—114no—
530C42—112no—
531C42—112no—
532C42D4×D1112yes—
533C42C23×D1112yes—
534C11C22×#48911yescharacteristic, complemented, Sylow
535C23—22no—
536C23—42no—
537C23—42no—
538C23—42no—
539C23—114no—
540C23—114no—
541C23—112no—
542C23—114no—
543C23—222no—
544C23—448no—
545C23—448no—
546C23—448no—
547C23—442no—
548C23—442no—
549C23—442no—
550C23—8816no—
551C23C2×D4×D1111yescharacteristic
552Q8—24no—
553Q8—48no—
554Q8—42no—
555Q8—224no—
556Q8—448no—
557Q8—448no—
558Q8—4416no—
559Q8—442no—
560D4—24no—
561D4—42no—
562D4—224no—
563D4—448no—
564D4—442no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—24no—
569C2×C4—44no—
570C2×C4—42no—
571C2×C4—112no—
572C2×C4—114no—
573C2×C4—118no—
574C2×C4—118no—
575C2×C4—112no—
576C2×C4—112no—
577C2×C4—228no—
578C2×C4—228no—
579C2×C4—222no—
580C2×C4—222no—
581C2×C4—222no—
582C2×C4—224no—
583C2×C4—448no—
584C2×C4—4416no—
585C2×C4—444no—
586C2×C4—442no—
587C2×C4C2×D4×D1112yes—
588C2×C4C2×D4×D1112yes—
589C2×C4C2×D4×D1111yescharacteristic
590C2×C4#41×D1114yes—
591C2×C4C24×D1111yescharacteristic
592C8—24no—
593C8—224no—
594C22—42no—
595C22—42no—
596C22—42no—
597C22—84no—
598C22—114no—
599C22—1116no—
600C22—114no—
601C22—114no—
602C22—442no—
603C22—442no—
604C22—442no—
605C22—8816no—
606C22—884no—
607C22D11×#12412yes—
608C22D11×AGL(1,ℤ/8)12yes—
609C22D11×#13712yes—
610C22C22×D4×D1111yescharacteristic
611C4—22no—
612C4—22no—
613C4—42no—
614C4—44no—
615C4—114no—
616C4—222no—
617C4—222no—
618C4—442no—
619C4—444no—
620C4D11×#12412yes—
621C4C2×#41×D1112yes—
622C2—82no—
623C2—118no—
624C2—882no—
625C2D11×#48914yesdirect product factor
626C2C2×D11×#12411yescharacteristic
627C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
628C2C2×D11×#13711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#489C2
socleC23×C11C22×D4
prime radicalC22×D4×D11C22
hypercenterC2×#489D11
hypocenterC11C22×#489
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#489

Complements

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

NH ≅ G/Ntype
1. C2×D11×C4⋊Q8C2semidirect
3. C2×#10622702C2semidirect
4. C2×#10622408C2semidirect
5. C2×#10622327C2semidirect
6. C2×#10622668C2semidirect
7. C2×#10622378C2semidirect
8. D11×#489C2direct (N × H)
9. C2×D11×#103C2semidirect
11. C2×D11×#97C2semidirect
12. C2×C11×#489C2semidirect
16. C2×C11×C4⋊Q8C22semidirect
23. D11×C4⋊Q8C22semidirect
29. C2×#66941C22semidirect
36. C2×#66922C22semidirect
37. C11×#489C22semidirect
38. C2×C11×#103C22semidirect
40. C2×C11×#97C22semidirect
41. C2×#66899C22semidirect
44. C2×#66880C22semidirect
45. C2×#66879C22semidirect
46. #10622702C22semidirect
47. #10622668C22semidirect
48. C2×#66874C22semidirect
50. C2×#66867C22semidirect
51. D11×#103C22semidirect
52. #10622408C22semidirect
54. #10622378C22semidirect
55. #10622327C22semidirect
56. D11×#97C22semidirect
82. C11×C4⋊Q8C23semidirect
116. #66941C23semidirect
126. #66922C23semidirect
127. C11×#103C23semidirect
129. C11×#97C23semidirect
130. #66899C23semidirect
133. #66880C23semidirect
134. #66879C23semidirect
135. #66874C23semidirect
137. #66867C23semidirect
229. C2×#489D11direct (N × H)
302. C2×C4⋊Q8C2×D11semidirect
321. #489C2×D11direct (N × H)
326. C2×#103C2×D11semidirect
335. C2×#97C2×D11semidirect
349. C2×D11#489direct (N × H)
398. C4⋊Q8C22×D11semidirect
437. #103C22×D11semidirect
444. #97C22×D11semidirect
446. C2×C11C2×#489semidirect
451. D11C2×#489direct (N × H)
534. C11C22×#489semidirect
625. C2D11×#489direct (N × H)

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×#1242
C2×#106227022
C2×#106224082
C2×#106223272
C2×#106226682
C2×#106223782
D11×#4892
C2×D11×#1032
C2×D11×#1022
C2×D11×#972
C2×C11×#4892
C22×#48911