Finite Group Databasebeta

← C2×D11×#467 #15620867

Subgroups — C2×D11×#467 #15620867

Order 2816.

3006 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Q16×D11C211yesmaximal, characteristic, complemented
2C23×C8×D11C211yesmaximal, characteristic
3C2×D11×C22⋊Q8C212yesmaximal
4C2×#10622500C211yesmaximal, characteristic, complemented
5C2×#10622729C211yesmaximal, characteristic, complemented
6C2×#10622426C212yesmaximal, complemented
7C2×#10622664C212yesmaximal, complemented
8C2×#10622801C211yesmaximal, characteristic, complemented
9D11×#467C2116yesmaximal, direct product factor
10C2×D11×#107C211yesmaximal, characteristic, complemented
11C2×D11×#103C212yesmaximal, complemented
12C2×C11×#467C211yesmaximal, characteristic, complemented
13C22×Q8×D11C2212yes—
14C23×C4×D11C2211yescharacteristic
15C22×C11×Q16C2211yescharacteristic, complemented
16C23×C8×C11C2211yescharacteristic
17C2×C11×C22⋊Q8C2212yes—
18C2×#66999C2212yes—
19C22×#4326C2212yescomplemented
20C2×#66977C2212yes—
21C23×C11⋊C8C2211yescharacteristic
22C2×Q16×D11—28no—
23C2×Q16×D11C2218yescomplemented
24C22×Dic44C2211yescharacteristic, complemented
25C22×C8×D11—28no—
26C22×C8×D11C2211yescharacteristic
27C22×C8×D11C2218yes—
28C22×C8×D11C2211yescharacteristic
29C22×C8×D11C2211yescharacteristic
30C22×C8×D11C2211yescharacteristic
31D11×C22⋊Q8—28no—
32D11×C22⋊Q8C22116yes—
33C2×#66950C2212yes—
34C2×#66949—22no—
35C2×C4⋊C4×D11—22no—
36C2×C4⋊C4×D11C2212yes—
37C2×C22⋊C4×D11—22no—
38C2×#66931—22no—
39C11×#467C2218yescomplemented
40C2×C11×#107C2211yescharacteristic, complemented
41C2×C11×#103C2212yescomplemented
42C2×#66899C2212yescomplemented
43#10622801C2218yescomplemented
44#10622729C2218yescomplemented
45C2×#66882C2211yescharacteristic, complemented
46C2×#66880C2212yescomplemented
47#10622664C22116yescomplemented
48C2×#66874C2212yescomplemented
49C2×#66871C2212yescomplemented
50#10622500C2218yescomplemented
51D11×#107C2218yescomplemented
52#10622426C22116yescomplemented
53D11×#103C22116yescomplemented
54C24×D11D411yescharacteristic
55C22×Q8×C11C2312yes—
56C23×C4×C11C2311yescharacteristic
57C23×Dic11D411yescharacteristic
58C2×Q8×D11—24no—
59C2×Q8×D11—28no—
60C2×Q8×D11—28no—
61C2×Q8×D11C2318yes—
62C22×C4×D11—24no—
63C22×C4×D11—24no—
64C22×C4×D11—22no—
65C22×C4×D11—22no—
66C22×C4×D11D411yescharacteristic
67C22×C4×D11D411yescharacteristic
68C22×C4×D11D414yes—
69C22×C4×D11C2311yescharacteristic
70C22×C4×D11C2314yes—
71C22×C4×D11C2311yescharacteristic
72C22×Dic22—22no—
73C22×Dic22C2312yes—
74C2×C11×Q16—24no—
75C2×C11×Q16C2314yescomplemented
76C22×C8×C11—24no—
77C22×C8×C11C2314yes—
78C22×C8×C11C2311yescharacteristic
79C22×C8×C11C2311yescharacteristic
80C11×C22⋊Q8—24no—
81C11×C22⋊Q8C2318yes—
82C2×C11×C4⋊C4—22no—
83C2×C11×C4⋊C4C2312yes—
84C2×C11×C22⋊C4—22no—
85C2×C22⋊Dic11—22no—
86#66999—24no—
87#66999C2318yes—
88C2×#4326—28no—
89C2×#4326C2318yescomplemented
90C2×(C2×D11)⋊C4—22no—
91C2×(C2×D11)⋊C4—22no—
92C2×C4⋊Dic11—22no—
93C2×C4⋊Dic11C2312yes—
94#66977—24no—
95#66977C2318yes—
96C2×Dic11⋊C4—22no—
97C2×Dic11⋊C4—22no—
98C2×Dic11⋊C4—22no—
99C22×C11⋊C8—24no—
100C22×C11⋊C8C2311yescharacteristic
101C22×C11⋊C8C2314yes—
102C22×C11⋊C8C2311yescharacteristic
103Q16×D11—232no—
104C2×Dic44—24no—
105C2×Dic44C2314yescomplemented
106C2×C8×D11—24no—
107C2×C8×D11—24no—
108C2×C8×D11—24no—
109C2×C8×D11—232no—
110C2×C8×D11D418yes—
111C2×C8×D11C2314yes—
112C2×C8×D11C2314yes—
113C2×C8×D11C2314yes—
114C2×C8×D11C2314yes—
115#66950—24no—
116#66950C2318yes—
117#66949—216no—
118C4⋊C4×D11—216no—
119C4⋊C4×D11—24no—
120C4⋊C4×D11C2318yes—
121C22⋊C4×D11—216no—
122#66931—216no—
123C11×#107C2314yescomplemented
124C11×#103C2318yescomplemented
125#66899C2318yescomplemented
126#66882C2314yescomplemented
127#66880C2318yescomplemented
128#66874C2318yescomplemented
129#66871C2318yescomplemented
130C22×#467—111nomaximal, Sylow
131C24×C11C2×D411yescharacteristic
132C23×D11—24no—
133C23×D11—24no—
134C23×D11Q1618yescomplemented
135C23×D11C2×D414yes—
136C23×D11C2×D411yescharacteristic
137C23×D11C2×D411yescharacteristic
138C2×Q8×C11—22no—
139C2×Q8×C11—24no—
140C2×Q8×C11—24no—
141C2×Q8×C11C2414yes—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—22no—
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D412yes—
148C22×C4×C11C2412yes—
149C22×C4×C11C2411yescharacteristic
150C22×Dic11—24no—
151C22×Dic11—22no—
152C22×Dic11—22no—
153C22×Dic11C2×D414yes—
154C22×Dic11C2×D411yescharacteristic
155C22×Dic11C2×D411yescharacteristic
156Q8×D11—216no—
157Q8×D11—216no—
158Q8×D11—416no—
159C2×C4×D11—24no—
160C2×C4×D11—216no—
161C2×C4×D11—28no—
162C2×C4×D11—28no—
163C2×C4×D11—24no—
164C2×C4×D11—28no—
165C2×C4×D11—28no—
166C2×C4×D11—22no—
167C2×C4×D11—22no—
168C2×C4×D11—48no—
169C2×C4×D11—48no—
170C2×C4×D11C2×D414yes—
171C2×C4×D11C2×D414yes—
172C2×C4×D11C2×D414yes—
173C2×C4×D11C2×D412yes—
174C2×C4×D11C2×D412yes—
175C2×C4×D11#4114yes—
176C2×C4×D11C2412yes—
177C2×C4×D11C2412yes—
178C2×Dic22—28no—
179C2×Dic22—24no—
180C2×Dic22—22no—
181C2×Dic22—24no—
182C2×Dic22—48no—
183C2×Dic22C2414yes—
184C11×Q16—28no—
185C2×C8×C11—28no—
186C2×C8×C11—22no—
187C2×C8×C11C2×D414yes—
188C2×C8×C11C2412yes—
189C2×C8×C11C2412yes—
190C11×C4⋊C4—28no—
191C11×C4⋊C4—22no—
192C11×C4⋊C4C2414yes—
193C11×C22⋊C4—28no—
194C22⋊Dic11—28no—
195#4326—216no—
196(C2×D11)⋊C4—28no—
197(C2×D11)⋊C4—28no—
198C4⋊Dic11—28no—
199C4⋊Dic11—22no—
200C4⋊Dic11C2414yes—
201Dic11⋊C4—28no—
202Dic11⋊C4—28no—
203Dic11⋊C4—28no—
204C2×C11⋊C8—28no—
205C2×C11⋊C8—22no—
206C2×C11⋊C8C2×D414yes—
207C2×C11⋊C8C2412yes—
208C2×C11⋊C8C2412yes—
209Dic44—28no—
210C8×D11—28no—
211C8×D11—28no—
212C8×D11—28no—
213C8×D11C2×D4116yes—
214C23×Q16—111no—
215C24×C8—111no—
216C22×C22⋊Q8—112no—
217C2×#467—1116no—
218C2×#467—111no—
219C2×#467—112no—
220C2×#467—111no—
221C2×#467—111no—
222C2×#467—112no—
223C2×#467D1111yescharacteristic, direct product factor
224C22×#107—111no—
225C22×#103—112no—
226C23×C11—22no—
227C23×C11—22no—
228C23×C11C2×Q1614yescomplemented
229C23×C11C22×D412yes—
230C23×C11C22×D411yescharacteristic
231C22×D11—22no—
232C22×D11—22no—
233C22×D11—28no—
234C22×D11—28no—
235C22×D11—232no—
236C22×D11#12114yes—
237C22×D11C2×Q1614yes—
238C22×D11C2×Q16116yescomplemented
239C22×D11C2×Q1614yescomplemented
240C22×D11#13514yes—
241C22×D11C22×D412yes—
242C22×D11C22×D412yes—
243Q8×C11—24no—
244Q8×C11—24no—
245Q8×C11—44no—
246C2×C4×C11—22no—
247C2×C4×C11—24no—
248C2×C4×C11—22no—
249C2×C4×C11—22no—
250C2×C4×C11—24no—
251C2×C4×C11—24no—
252C2×C4×C11—44no—
253C2×C4×C11—44no—
254C2×C4×C11C22×D412yes—
255C2×C4×C11C22×D411yescharacteristic
256C2×C4×C11C22×D412yes—
257C2×C4×C11C2×#4112yes—
258C2×C4×C11C2511yescharacteristic
259C2×Dic11—22no—
260C2×Dic11—28no—
261C2×Dic11—24no—
262C2×Dic11—24no—
263C2×Dic11—44no—
264C2×Dic11—44no—
265C2×Dic11#12114yes—
266C2×Dic11C22×D412yes—
267C2×Dic11C22×D412yes—
268C4×D11—28no—
269C4×D11—24no—
270C4×D11—22no—
271C4×D11—22no—
272C4×D11—28no—
273C4×D11—416no—
274C4×D11—416no—
275C4×D11#12118yes—
276C4×D11C22×D414yes—
277C4×D11C2×#4114yes—
278Dic22—24no—
279Dic22—24no—
280Dic22—44no—
281Dic22—416no—
282C8×C11—22no—
283C8×C11C22×D414yes—
284C11⋊C8—22no—
285C11⋊C8C22×D414yes—
286C23×Q8—112no—
287C24×C4—111no—
288C22×Q16—112no—
289C22×Q16—118no—
290C22×Q16—111no—
291C22×Q16—228no—
292C22×Q16C2×D1111yescharacteristic, complemented
293C23×C8—111no—
294C23×C8—111no—
295C23×C8—111no—
296C23×C8—111no—
297C23×C8—118no—
298C23×C8—111no—
299C23×C8—228no—
300C23×C8C2×D1111yescharacteristic
301C2×C22⋊Q8—112no—
302C2×C22⋊Q8—112no—
303C2×C22⋊Q8—1116no—
304C2×C22⋊Q8—112no—
305C2×C22⋊Q8—222no—
306C2×C22⋊Q8—222no—
307C2×C22⋊Q8—228no—
308C2×C22⋊Q8C2×D1112yes—
309C22×C4⋊C4—112no—
310C22×C4⋊C4—222no—
311C22×C22⋊C4—222no—
312#467—118no—
313#467—118no—
314#467—1116no—
315#467—118no—
316#467—1116no—
317#467C2×D1118yesdirect product factor
318C2×#107—111no—
319C2×#107—112no—
320C2×#107—118no—
321C2×#107C2×D1111yescharacteristic, complemented
322C2×#103—112no—
323C2×#103—112no—
324C2×#103—112no—
325C2×#103—1116no—
326C2×#103C2×D1112yescomplemented
327C22×C11—22no—
328C22×C11—28no—
329C22×C11—22no—
330C22×C11C2×#12112yes—
331C22×C11C22×Q1612yes—
332C22×C11C22×Q1614yescomplemented
333C22×C11C2×#13512yes—
334C22×C11C23×D411yescharacteristic
335C2×D11—22no—
336C2×D11—28no—
337C2×D11—22no—
338C2×D11—232no—
339C2×D11#467116yesdirect product factor
340C2×D11C2×#12114yes—
341C2×D11C22×Q1614yes—
342C2×D11C22×Q1614yescomplemented
343C2×D11C2×#13514yes—
344C4×C11—22no—
345C4×C11—44no—
346C4×C11—44no—
347C4×C11C2×#12112yes—
348C4×C11C23×D411yescharacteristic
349C4×C11C22×#4111yescharacteristic
350Dic11—22no—
351Dic11—44no—
352Dic11—44no—
353Dic11C2×#12114yes—
354C25—111no—
355C22×Q8—118no—
356C22×Q8—112no—
357C22×Q8—222no—
358C22×Q8—224no—
359C22×Q8—228no—
360C22×Q8—228no—
361C22×Q8C22×D1112yes—
362C23×C4—111no—
363C23×C4—111no—
364C23×C4—111no—
365C23×C4—111no—
366C23×C4—114no—
367C23×C4—114no—
368C23×C4—111no—
369C23×C4—224no—
370C23×C4—224no—
371C23×C4—222no—
372C23×C4—222no—
373C23×C4C22×D1111yescharacteristic
374C2×Q16—24no—
375C2×Q16—118no—
376C2×Q16—114no—
377C2×Q16—2232no—
378C2×Q16—228no—
379C2×Q16—224no—
380C2×Q16C22×D1114yescomplemented
381C22×C8—24no—
382C22×C8—111no—
383C22×C8—118no—
384C22×C8—114no—
385C22×C8—111no—
386C22×C8—114no—
387C22×C8—114no—
388C22×C8—114no—
389C22×C8—114no—
390C22×C8—224no—
391C22×C8—2232no—
392C22×C8—224no—
393C22×C8—224no—
394C22×C8—224no—
395C22×C8C22×D1111yescharacteristic
396C22×C8C22×D1114yes—
397C22×C8C22×D1111yescharacteristic
398C22⋊Q8—24no—
399C22⋊Q8—118no—
400C22⋊Q8—118no—
401C22⋊Q8—118no—
402C22⋊Q8—2216no—
403C22⋊Q8—2216no—
404C22⋊Q8—224no—
405C22⋊Q8—224no—
406C22⋊Q8—224no—
407C22⋊Q8C22×D1118yes—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—112no—
410C2×C4⋊C4—118no—
411C2×C4⋊C4—224no—
412C2×C4⋊C4—2216no—
413C2×C4⋊C4—222no—
414C2×C4⋊C4—222no—
415C2×C4⋊C4—222no—
416C2×C4⋊C4—222no—
417C2×C4⋊C4C22×D1112yes—
418C2×C22⋊C4—22no—
419C2×C22⋊C4—2216no—
420C2×C22⋊C4—222no—
421C2×C22⋊C4—222no—
422C2×C22⋊C4—222no—
423#107—114no—
424#107—118no—
425#107C22×D1114yescomplemented
426#103—118no—
427#103—118no—
428#103—118no—
429#103C22×D1118yescomplemented
430C2×C11—24no—
431C2×C11C2×#46714yescomplemented
432C2×C11C22×#12111yescharacteristic
433C2×C11C23×Q1611yescharacteristic
434C2×C11C22×#13511yescharacteristic
435D11—24no—
436D11C2×#46718yesdirect product factor
437C24—111no—
438C24—118no—
439C24—114no—
440C24—111no—
441C24—224no—
442C24—224no—
443C24D4×D1111yescharacteristic
444C2×Q8—22no—
445C2×Q8—24no—
446C2×Q8—24no—
447C2×Q8—114no—
448C2×Q8—228no—
449C2×Q8—2216no—
450C2×Q8—2216no—
451C2×Q8—222no—
452C2×Q8—224no—
453C2×Q8—224no—
454C2×Q8—448no—
455C2×Q8—4416no—
456C2×Q8C23×D1114yes—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—111no—
462C22×C4—112no—
463C22×C4—114no—
464C22×C4—114no—
465C22×C4—112no—
466C22×C4—114no—
467C22×C4—111no—
468C22×C4—114no—
469C22×C4—114no—
470C22×C4—112no—
471C22×C4—112no—
472C22×C4—228no—
473C22×C4—224no—
474C22×C4—2216no—
475C22×C4—228no—
476C22×C4—224no—
477C22×C4—228no—
478C22×C4—228no—
479C22×C4—224no—
480C22×C4—222no—
481C22×C4—222no—
482C22×C4—222no—
483C22×C4—222no—
484C22×C4—448no—
485C22×C4—448no—
486C22×C4D4×D1112yes—
487C22×C4D4×D1111yescharacteristic
488C22×C4C23×D1112yes—
489C22×C4C23×D1111yescharacteristic
490Q16—28no—
491Q16—2216no—
492Q16—228no—
493C2×C8—22no—
494C2×C8—28no—
495C2×C8—114no—
496C2×C8—112no—
497C2×C8—1116no—
498C2×C8—112no—
499C2×C8—228no—
500C2×C8—228no—
501C2×C8—228no—
502C2×C8—222no—
503C2×C8—228no—
504C2×C8D4×D1114yes—
505C2×C8C23×D1112yes—
506C2×C8C23×D1112yes—
507C4⋊C4—28no—
508C4⋊C4—22no—
509C4⋊C4—114no—
510C4⋊C4—228no—
511C4⋊C4—228no—
512C4⋊C4—228no—
513C4⋊C4—222no—
514C4⋊C4—228no—
515C4⋊C4C23×D1114yes—
516C22⋊C4—28no—
517C22⋊C4—228no—
518C22⋊C4—228no—
519C22⋊C4—228no—
520C11C22×#46711yescharacteristic, complemented, Sylow
521C23—22no—
522C23—22no—
523C23—114no—
524C23—114no—
525C23—114no—
526C23—112no—
527C23—114no—
528C23—1116no—
529C23—112no—
530C23—228no—
531C23—2232no—
532C23—228no—
533C23—222no—
534C23—222no—
535C23Q16×D1114yescomplemented
536C23C2×D4×D1112yes—
537C23C2×D4×D1111yescharacteristic
538Q8—24no—
539Q8—24no—
540Q8—44no—
541Q8—224no—
542Q8—224no—
543Q8—4416no—
544Q8—444no—
545C2×C4—22no—
546C2×C4—24no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—24no—
550C2×C4—24no—
551C2×C4—44no—
552C2×C4—44no—
553C2×C4—114no—
554C2×C4—112no—
555C2×C4—118no—
556C2×C4—114no—
557C2×C4—114no—
558C2×C4—112no—
559C2×C4—228no—
560C2×C4—228no—
561C2×C4—228no—
562C2×C4—222no—
563C2×C4—224no—
564C2×C4—222no—
565C2×C4—222no—
566C2×C4—224no—
567C2×C4—224no—
568C2×C4—4416no—
569C2×C4—4416no—
570C2×C4—444no—
571C2×C4—444no—
572C2×C4C2×D4×D1112yes—
573C2×C4C2×D4×D1111yescharacteristic
574C2×C4C2×D4×D1112yes—
575C2×C4#41×D1112yes—
576C2×C4C24×D1111yescharacteristic
577C8—22no—
578C8—114no—
579C8—222no—
580C8C2×D4×D1114yes—
581C22—28no—
582C22—22no—
583C22—22no—
584C22—1116no—
585C22—114no—
586C22—114no—
587C22—114no—
588C22—114no—
589C22—2232no—
590C22—228no—
591C22—222no—
592C22—222no—
593C22D11×#12112yes—
594C22C2×Q16×D1112yes—
595C22C2×Q16×D1114yescomplemented
596C22D11×#13512yes—
597C22C22×D4×D1111yescharacteristic
598C4—22no—
599C4—44no—
600C4—44no—
601C4—114no—
602C4—222no—
603C4—444no—
604C4—444no—
605C4D11×#12112yes—
606C4C22×D4×D1111yescharacteristic
607C4C2×#41×D1111yescharacteristic
608C2—24no—
609C2—118no—
610C2—224no—
611C2D11×#46714yesdirect product factor
612C2C2×D11×#12111yescharacteristic
613C2C22×Q16×D1111yescharacteristic
614C2C2×D11×#13511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#467C2
socleC23×C11C22×D4
prime radicalC24×D11D4
hypercenterC2×#467D11
hypocenterC11C22×#467
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#467

Complements

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

NH ≅ G/Ntype
1. C22×Q16×D11C2semidirect
4. C2×#10622500C2semidirect
5. C2×#10622729C2semidirect
6. C2×#10622426C2semidirect
7. C2×#10622664C2semidirect
8. C2×#10622801C2semidirect
9. D11×#467C2direct (N × H)
10. C2×D11×#107C2semidirect
11. C2×D11×#103C2semidirect
12. C2×C11×#467C2semidirect
15. C22×C11×Q16C22semidirect
19. C22×#4326C22semidirect
23. C2×Q16×D11C22semidirect
24. C22×Dic44C22semidirect
39. C11×#467C22semidirect
40. C2×C11×#107C22semidirect
41. C2×C11×#103C22semidirect
42. C2×#66899C22semidirect
43. #10622801C22semidirect
44. #10622729C22semidirect
45. C2×#66882C22semidirect
46. C2×#66880C22semidirect
47. #10622664C22semidirect
48. C2×#66874C22semidirect
49. C2×#66871C22semidirect
50. #10622500C22semidirect
51. D11×#107C22semidirect
52. #10622426C22semidirect
53. D11×#103C22semidirect
75. C2×C11×Q16C23semidirect
89. C2×#4326C23semidirect
105. C2×Dic44C23semidirect
123. C11×#107C23semidirect
124. C11×#103C23semidirect
125. #66899C23semidirect
126. #66882C23semidirect
127. #66880C23semidirect
128. #66874C23semidirect
129. #66871C23semidirect
134. C23×D11Q16semidirect
223. C2×#467D11direct (N × H)
228. C23×C11C2×Q16semidirect
238. C22×D11C2×Q16semidirect
239. C22×D11C2×Q16semidirect
292. C22×Q16C2×D11semidirect
317. #467C2×D11direct (N × H)
321. C2×#107C2×D11semidirect
326. C2×#103C2×D11semidirect
332. C22×C11C22×Q16semidirect
339. C2×D11#467direct (N × H)
342. C2×D11C22×Q16semidirect
380. C2×Q16C22×D11semidirect
425. #107C22×D11semidirect
429. #103C22×D11semidirect
431. C2×C11C2×#467semidirect
436. D11C2×#467direct (N × H)
520. C11C22×#467semidirect
535. C23Q16×D11semidirect
595. C22C2×Q16×D11semidirect
611. C2D11×#467direct (N × H)

Maximal subgroups

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

subgroupindex
C22×Q16×D112
C23×C8×D112
C2×D11×C22⋊Q82
C2×#106225002
C2×#106227292
C2×#106224262
C2×#106226642
C2×#106228012
D11×#4672
C2×D11×#1072
C2×D11×#1032
C2×C11×#4672
C22×#46711