Finite Group Databasebeta

← C2×D11×D4⋊C8 #14720113

Subgroups — C2×D11×D4⋊C8 #14720113

Order 2816.

1886 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D4×D11C211yesmaximal, characteristic
2C2×D11×C4⋊C8C211yesmaximal, characteristic, complemented
3C2×C4×C8×D11C211yesmaximal, characteristic, complemented
4C2×#10622097C211yesmaximal, characteristic, complemented
5C2×D4⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
6C2×#10622121C211yesmaximal, characteristic, complemented
7D11×D4⋊C8C218yesmaximal, direct product factor
8C2×C11×D4⋊C8C211yesmaximal, characteristic, complemented
9C22×D4×D11C411yescharacteristic
10C23×C4×D11—21no—
11C2×C4×D4×C11C2211yescharacteristic
12C2×D4×Dic11C411yescharacteristic
13C2×C4×C22⋊D11—21no—
14C22×C8×D11—21no—
15C22×C8×D11—21no—
16C4×D4×D11—22no—
17C4×D4×D11—22no—
18C4×D4×D11C414yes—
19C4×D4×D11C2214yes—
20C2×#66946C411yescharacteristic
21C2×C4⋊C4×D11C411yescharacteristic
22C2×(C22⋊D11)⋊C4—21no—
23C2×C22⋊C4×D11—21no—
24C2×C4×D44C2211yescharacteristic
25C2×C42×D11C2211yescharacteristic
26C2×C11×C4⋊C8C2211yescharacteristic, complemented
27C2×C4×C8×C11C2211yescharacteristic, complemented
28C2×Dic11⋊C8—21no—
29C2×C8×Dic11—21no—
30C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
31C2×C4×C11⋊C8C2211yescharacteristic, complemented
32D11×C4⋊C8—22no—
33D11×C4⋊C8C2214yescomplemented
34C4×C8×D11—22no—
35C4×C8×D11C2214yescomplemented
36C11×D4⋊C8C2214yescomplemented
37D4⋊(C11⋊C8)C2214yescomplemented
38#10622121C2214yescomplemented
39#10622097C2214yescomplemented
40C24×D11—21no—
41C22×D4×C11C2×C411yescharacteristic
42C23×C4×C11—21no—
43C22×C22⋊D11—21no—
44C23×Dic11—21no—
45C2×D4×D11—22no—
46C2×D4×D11—24no—
47C2×D4×D11C818yescomplemented
48C2×D4×D11C2×C414yes—
49C22×D44C2×C411yescharacteristic
50C22×C4×D11—21no—
51C22×C4×D11—21no—
52C22×C4×D11—21no—
53C22×C4×D11—24no—
54C22×C4×D11—24no—
55C22×C4×D11—44no—
56C22×C4×D11—44no—
57C22×C4×D11C2×C411yescharacteristic
58C22×C4×D11D411yescharacteristic
59C22×C4×D11D411yescharacteristic
60C22×C8×C11—21no—
61C22×C8×C11—21no—
62C4×D4×C11—21no—
63C4×D4×C11—21no—
64C4×D4×C11C2×C412yes—
65C4×D4×C11C2312yes—
66C2×C11×C4⋊C4C2×C411yescharacteristic
67C2×C11×C22⋊C4—21no—
68C2×C42×C11C2311yescharacteristic
69C2×C22⋊Dic11—21no—
70D4×Dic11—22no—
71D4×Dic11C2×C414yes—
72C4×C22⋊D11—24no—
73C4×C22⋊D11—24no—
74C2×(C2×D11)⋊C4—21no—
75C2×(C2×D11)⋊C4—21no—
76C2×C4⋊Dic11C2×C411yescharacteristic
77C2×Dic11⋊C4—21no—
78C2×C4×Dic11C2×C411yescharacteristic
79C2×C4×Dic11D411yescharacteristic
80C2×C4×Dic11D411yescharacteristic
81C22×C11⋊C8—21no—
82C22×C11⋊C8—21no—
83C2×C8×D11—28no—
84C2×C8×D11—24no—
85C2×C8×D11—24no—
86C2×C8×D11—44no—
87#66946—22no—
88#66946C2×C414yes—
89C4⋊C4×D11—22no—
90C4⋊C4×D11C2×C414yes—
91(C22⋊D11)⋊C4—24no—
92(C22⋊D11)⋊C4—24no—
93C22⋊C4×D11—24no—
94C22⋊C4×D11—24no—
95C4×D44—21no—
96C4×D44—21no—
97C4×D44C2×C412yes—
98C4×D44C2312yes—
99C42×D11C2×C412yes—
100C42×D11D412yes—
101C42×D11D412yes—
102C42×D11C2312yes—
103C11×C4⋊C8—21no—
104C11×C4⋊C8C2312yescomplemented
105C4×C8×C11—21no—
106C4×C8×C11C2312yescomplemented
107Dic11⋊C8—24no—
108C8×Dic11—24no—
109C4⋊(C11⋊C8)—21no—
110C4⋊(C11⋊C8)C2312yescomplemented
111C4×C11⋊C8—21no—
112C4×C11⋊C8C2312yescomplemented
113C22×D4⋊C8—111nomaximal, Sylow
114C24×C11—21no—
115C23×D11—21no—
116C23×D11—28no—
117C23×D11—24no—
118C23×D11—44no—
119C23×D11—44no—
120C23×D11C22⋊C411yescharacteristic
121C2×D4×C11—21no—
122C2×D4×C11—22no—
123C2×D4×C11C2×C814yescomplemented
124C2×D4×C11C22×C412yes—
125C22×C4×C11—21no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—42no—
129C22×C4×C11—42no—
130C22×C4×C11C22×C411yescharacteristic
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C2×C22⋊D11—28no—
134C2×C22⋊D11—24no—
135C22×Dic11—24no—
136C22×Dic11—21no—
137C22×Dic11—44no—
138C22×Dic11C22⋊C411yescharacteristic
139C22×Dic11C22⋊C411yescharacteristic
140C22×Dic11C22⋊C411yescharacteristic
141D4×D11—216no—
142D4×D11—28no—
143D4×D11C2×C8116yescomplemented
144C2×D44—21no—
145C2×D44—22no—
146C2×D44C2×C814yescomplemented
147C2×D44C22×C412yes—
148C2×C4×D11—24no—
149C2×C4×D11—24no—
150C2×C4×D11—24no—
151C2×C4×D11—22no—
152C2×C4×D11—22no—
153C2×C4×D11—44no—
154C2×C4×D11—416no—
155C2×C4×D11—48no—
156C2×C4×D11—48no—
157C2×C4×D11—44no—
158C2×C4×D11—42no—
159C2×C4×D11—42no—
160C2×C4×D11C22⋊C412yes—
161C2×C4×D11C22⋊C412yes—
162C2×C4×D11C22⋊C412yes—
163C2×C4×D11C2×C814yes—
164C2×C4×D11M1614yes—
165C2×C4×D11D814yes—
166C2×C4×D11SD1614yes—
167C2×C4×D11C22×C412yes—
168C2×C4×D11C2×D412yes—
169C2×C4×D11C2×D412yes—
170C2×C8×C11—24no—
171C2×C8×C11—22no—
172C2×C8×C11—22no—
173C2×C8×C11—42no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4C22×C412yes—
176C11×C22⋊C4—22no—
177C11×C22⋊C4—22no—
178C42×C11C22×C411yescharacteristic
179C42×C11C2×D411yescharacteristic
180C42×C11C2×D411yescharacteristic
181C42×C11C2411yescharacteristic
182C22⋊Dic11—24no—
183(C2×D11)⋊C4—24no—
184(C2×D11)⋊C4—22no—
185(C2×D11)⋊C4—22no—
186C4⋊Dic11—21no—
187C4⋊Dic11C22×C412yes—
188Dic11⋊C4—24no—
189C4×Dic11C22⋊C412yes—
190C4×Dic11C22⋊C412yes—
191C4×Dic11C22⋊C412yes—
192C4×Dic11C22×C412yes—
193C4×Dic11C2×D412yes—
194C4×Dic11C2×D412yes—
195C2×C11⋊C8—24no—
196C2×C11⋊C8—22no—
197C2×C11⋊C8—22no—
198C2×C11⋊C8—42no—
199C8×D11—216no—
200C8×D11—48no—
201C22×C4×D4—111no—
202C22×C4⋊C8—111no—
203C22×C4×C8—111no—
204C2×D4⋊C8—111no—
205C2×D4⋊C8—111no—
206C2×D4⋊C8—118no—
207C2×D4⋊C8—111no—
208C2×D4⋊C8D1111yescharacteristic, direct product factor
209C23×C11—22no—
210C23×C11—24no—
211C23×C11—42no—
212C23×C11—42no—
213C23×C11C2×C22⋊C411yescharacteristic
214C22×D11—22no—
215C22×D11—24no—
216C22×D11—216no—
217C22×D11—42no—
218C22×D11—42no—
219C22×D11—432no—
220C22×D11—48no—
221C22×D11—48no—
222C22×D11C22⋊C814yes—
223C22×D11#10214yes—
224C22×D11#10414yes—
225C22×D11C2×C22⋊C412yes—
226D4×C11—22no—
227D4×C11—24no—
228D4×C11C22×C814yescomplemented
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—42no—
232C2×C4×C11—42no—
233C2×C4×C11—42no—
234C2×C4×C11—44no—
235C2×C4×C11C2×C22⋊C411yescharacteristic
236C2×C4×C11C2×C22⋊C411yescharacteristic
237C2×C4×C11C2×C22⋊C411yescharacteristic
238C2×C4×C11C22×C812yes—
239C2×C4×C11C2×M1612yes—
240C2×C4×C11C2×D812yes—
241C2×C4×C11C2×SD1612yes—
242C2×C4×C11C23×C411yescharacteristic
243C2×C4×C11C22×D411yescharacteristic
244C2×C4×C11C22×D411yescharacteristic
245C22⋊D11—216no—
246C2×Dic11—22no—
247C2×Dic11—22no—
248C2×Dic11—42no—
249C2×Dic11—48no—
250C2×Dic11C22⋊C814yes—
251C2×Dic11#10214yes—
252C2×Dic11C2×C22⋊C412yes—
253C2×Dic11C2×C22⋊C412yes—
254C2×Dic11C2×C22⋊C412yes—
255D44—22no—
256D44—24no—
257D44C22×C814yescomplemented
258C4×D11—24no—
259C4×D11—24no—
260C4×D11—48no—
261C4×D11—42no—
262C4×D11—42no—
263C4×D11—44no—
264C4×D11—48no—
265C4×D11C22⋊C818yes—
266C4×D11#10218yes—
267C4×D11C22×C814yes—
268C4×D11C2×M1614yes—
269C4×D11C2×D814yes—
270C4×D11C2×SD1614yes—
271C8×C11—24no—
272C8×C11—42no—
273C11⋊C8—24no—
274C11⋊C8—42no—
275C23×D4—111no—
276C24×C4—221no—
277C23×C8—221no—
278C23×C8—221no—
279C2×C4×D4—111no—
280C2×C4×D4—114no—
281C2×C4×D4—114no—
282C2×C4×D4—111no—
283C2×C4×D4—111no—
284C2×C4×D4—221no—
285C2×C4×D4—222no—
286C2×C4×D4—222no—
287C2×C4×D4—221no—
288C2×C4×D4C2×D1111yescharacteristic
289C22×C4⋊C4—111no—
290C22×C22⋊C4—221no—
291C22×C42—111no—
292C2×C4⋊C8—111no—
293C2×C4⋊C8—114no—
294C2×C4⋊C8—222no—
295C2×C4⋊C8—221no—
296C2×C4⋊C8C2×D1111yescharacteristic, complemented
297C2×C4×C8—111no—
298C2×C4×C8—114no—
299C2×C4×C8—222no—
300C2×C4×C8—221no—
301C2×C4×C8C2×D1111yescharacteristic, complemented
302D4⋊C8—114no—
303D4⋊C8—114no—
304D4⋊C8—114no—
305D4⋊C8C2×D1114yesdirect product factor
306C22×C11—24no—
307C22×C11—42no—
308C22×C11—42no—
309C22×C11—48no—
310C22×C11C2×C22⋊C812yes—
311C22×C11C2×#10212yes—
312C22×C11C2×#10412yes—
313C22×C11C22×C22⋊C411yescharacteristic
314C2×D11—24no—
315C2×D11—42no—
316C2×D11—42no—
317C2×D11—48no—
318C2×D11—432no—
319C2×D11D4⋊C8116yesdirect product factor
320C2×D11C2×C22⋊C814yes—
321C2×D11C2×#10214yes—
322C2×D11C2×#10414yes—
323C4×C11—21no—
324C4×C11—21no—
325C4×C11—42no—
326C4×C11C2×C22⋊C812yes—
327C4×C11C2×#10212yes—
328C4×C11C23×C811yescharacteristic
329C4×C11C22×M1611yescharacteristic
330C4×C11C22×D811yescharacteristic
331C4×C11C22×SD1611yescharacteristic
332Dic11—22no—
333Dic11—42no—
334Dic11C2×C22⋊C814yes—
335Dic11C2×#10214yes—
336C25—221no—
337C22×D4—118no—
338C22×D4—114no—
339C22×D4—111no—
340C22×D4—222no—
341C22×D4—224no—
342C22×D4—221no—
343C22×D4C4×D1111yescharacteristic
344C23×C4—21no—
345C23×C4—111no—
346C23×C4—111no—
347C23×C4—111no—
348C23×C4—221no—
349C23×C4—224no—
350C23×C4—224no—
351C23×C4—221no—
352C23×C4—221no—
353C23×C4—221no—
354C23×C4—444no—
355C23×C4—444no—
356C22×C8—21no—
357C22×C8—21no—
358C22×C8—224no—
359C22×C8—228no—
360C22×C8—224no—
361C22×C8—221no—
362C22×C8—221no—
363C22×C8—444no—
364C4×D4—21no—
365C4×D4—21no—
366C4×D4—114no—
367C4×D4—114no—
368C4×D4—112no—
369C4×D4—112no—
370C4×D4—224no—
371C4×D4—224no—
372C4×D4—222no—
373C4×D4—224no—
374C4×D4—224no—
375C4×D4—222no—
376C4×D4—221no—
377C4×D4—221no—
378C4×D4C4×D1112yes—
379C4×D4C22×D1112yes—
380C2×C4⋊C4—111no—
381C2×C4⋊C4—114no—
382C2×C4⋊C4—222no—
383C2×C4⋊C4—221no—
384C2×C4⋊C4C4×D1111yescharacteristic
385C2×C22⋊C4—21no—
386C2×C22⋊C4—224no—
387C2×C22⋊C4—224no—
388C2×C22⋊C4—221no—
389C2×C22⋊C4—221no—
390C2×C22⋊C4—221no—
391C2×C42—111no—
392C2×C42—111no—
393C2×C42—111no—
394C2×C42—112no—
395C2×C42—112no—
396C2×C42—112no—
397C2×C42—112no—
398C2×C42C22×D1111yescharacteristic
399C4⋊C8—21no—
400C4⋊C8—112no—
401C4⋊C8—224no—
402C4⋊C8—221no—
403C4⋊C8C22×D1112yescomplemented
404C4×C8—21no—
405C4×C8—112no—
406C4×C8—224no—
407C4×C8—221no—
408C4×C8C22×D1112yescomplemented
409C2×C11—44no—
410C2×C11C2×D4⋊C814yescomplemented
411C2×C11C22×C22⋊C811yescharacteristic
412C2×C11C22×#10211yescharacteristic
413C2×C11C22×#10411yescharacteristic
414D11—44no—
415D11C2×D4⋊C818yesdirect product factor
416C24—21no—
417C24—111no—
418C24—224no—
419C24—228no—
420C24—221no—
421C24—444no—
422C24—444no—
423C2×D4—21no—
424C2×D4—22no—
425C2×D4—1116no—
426C2×D4—114no—
427C2×D4—112no—
428C2×D4—228no—
429C2×D4—2216no—
430C2×D4—224no—
431C2×D4—228no—
432C2×D4—221no—
433C2×D4—222no—
434C2×D4C8×D1114yescomplemented
435C2×D4C2×C4×D1112yes—
436C22×C4—21no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—42no—
440C22×C4—42no—
441C22×C4—111no—
442C22×C4—111no—
443C22×C4—112no—
444C22×C4—112no—
445C22×C4—114no—
446C22×C4—114no—
447C22×C4—114no—
448C22×C4—114no—
449C22×C4—112no—
450C22×C4—112no—
451C22×C4—111no—
452C22×C4—112no—
453C22×C4—112no—
454C22×C4—224no—
455C22×C4—224no—
456C22×C4—224no—
457C22×C4—224no—
458C22×C4—221no—
459C22×C4—222no—
460C22×C4—222no—
461C22×C4—444no—
462C22×C4—448no—
463C22×C4—448no—
464C22×C4—4416no—
465C22×C4—444no—
466C22×C4—444no—
467C22×C4—442no—
468C22×C4—442no—
469C22×C4C2×C4×D1111yescharacteristic
470C22×C4D4×D1111yescharacteristic
471C22×C4D4×D1111yescharacteristic
472C2×C8—24no—
473C2×C8—22no—
474C2×C8—22no—
475C2×C8—42no—
476C2×C8—2216no—
477C2×C8—224no—
478C2×C8—222no—
479C2×C8—222no—
480C2×C8—448no—
481C2×C8—442no—
482C4⋊C4—21no—
483C4⋊C4—112no—
484C4⋊C4—224no—
485C4⋊C4—221no—
486C4⋊C4C2×C4×D1112yes—
487C22⋊C4—22no—
488C22⋊C4—22no—
489C22⋊C4—224no—
490C22⋊C4—224no—
491C22⋊C4—222no—
492C22⋊C4—222no—
493C42—112no—
494C42—112no—
495C42—112no—
496C42—112no—
497C42—112no—
498C42—112no—
499C42C2×C4×D1111yescharacteristic
500C42D4×D1111yescharacteristic
501C42D4×D1111yescharacteristic
502C42C23×D1111yescharacteristic
503C11C22×D4⋊C811yescharacteristic, complemented, Sylow
504C23—22no—
505C23—24no—
506C23—42no—
507C23—42no—
508C23—112no—
509C23—114no—
510C23—114no—
511C23—114no—
512C23—2216no—
513C23—222no—
514C23—224no—
515C23—448no—
516C23—448no—
517C23—4432no—
518C23—442no—
519C23—442no—
520C23C22⋊C4×D1111yescharacteristic
521D4—22no—
522D4—24no—
523D4—114no—
524D4—2216no—
525D4—222no—
526D4—224no—
527D4C2×C8×D1114yescomplemented
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—44no—
534C2×C4—112no—
535C2×C4—112no—
536C2×C4—114no—
537C2×C4—114no—
538C2×C4—114no—
539C2×C4—114no—
540C2×C4—114no—
541C2×C4—114no—
542C2×C4—118no—
543C2×C4—118no—
544C2×C4—112no—
545C2×C4—224no—
546C2×C4—224no—
547C2×C4—222no—
548C2×C4—222no—
549C2×C4—448no—
550C2×C4—448no—
551C2×C4—448no—
552C2×C4—442no—
553C2×C4—442no—
554C2×C4—442no—
555C2×C4—444no—
556C2×C4C22⋊C4×D1111yescharacteristic
557C2×C4C22⋊C4×D1111yescharacteristic
558C2×C4C22⋊C4×D1111yescharacteristic
559C2×C4C2×C8×D1112yes—
560C2×C4M16×D1112yes—
561C2×C4D8×D1112yes—
562C2×C4SD16×D1112yes—
563C2×C4C22×C4×D1111yescharacteristic
564C2×C4C2×D4×D1111yescharacteristic
565C2×C4C2×D4×D1111yescharacteristic
566C8—24no—
567C8—42no—
568C8—224no—
569C8—442no—
570C22—24no—
571C22—42no—
572C22—42no—
573C22—48no—
574C22—114no—
575C22—114no—
576C22—114no—
577C22—1116no—
578C22—224no—
579C22—4432no—
580C22—442no—
581C22—442no—
582C22—448no—
583C22D11×C22⋊C812yes—
584C22D11×#10212yes—
585C22D11×#10412yes—
586C22C2×C22⋊C4×D1111yescharacteristic
587C4—21no—
588C4—21no—
589C4—42no—
590C4—114no—
591C4—114no—
592C4—222no—
593C4—442no—
594C4D11×C22⋊C812yes—
595C4D11×#10212yes—
596C4C22×C8×D1111yescharacteristic
597C4C2×M16×D1111yescharacteristic
598C4C2×D8×D1111yescharacteristic
599C4C2×SD16×D1111yescharacteristic
600C2—44no—
601C2—118no—
602C2—444no—
603C2D11×D4⋊C814yesdirect product factor
604C2C2×D11×C22⋊C811yescharacteristic
605C2C2×D11×#10211yescharacteristic
606C2C2×D11×#10411yescharacteristic
subgroupG/H
centerC22×C4D4×D11
commutatorC4×C11C23×C8
FrattiniC42C23×D11
FittingC2×C11×D4⋊C8C2
socleC23×C11C2×C22⋊C4
prime radicalC22×D4×D11C4
cosocleC42×C11C24
hypercenterC2×D4⋊C8D11
hypocenterC11C22×D4⋊C8
LCSG ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×D4⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×D11×C4⋊C8C2semidirect
3. C2×C4×C8×D11C2semidirect
4. C2×#10622097C2semidirect
5. C2×D4⋊(C11⋊C8)C2semidirect
6. C2×#10622121C2semidirect
7. D11×D4⋊C8C2direct (N × H)
8. C2×C11×D4⋊C8C2semidirect
26. C2×C11×C4⋊C8C22semidirect
27. C2×C4×C8×C11C22semidirect
30. C2×C4⋊(C11⋊C8)C22semidirect
31. C2×C4×C11⋊C8C22semidirect
33. D11×C4⋊C8C22semidirect
35. C4×C8×D11C22semidirect
36. C11×D4⋊C8C22semidirect
37. D4⋊(C11⋊C8)C22semidirect
38. #10622121C22semidirect
39. #10622097C22semidirect
47. C2×D4×D11C8semidirect
104. C11×C4⋊C8C23semidirect
106. C4×C8×C11C23semidirect
110. C4⋊(C11⋊C8)C23semidirect
112. C4×C11⋊C8C23semidirect
123. C2×D4×C11C2×C8semidirect
143. D4×D11C2×C8semidirect
146. C2×D44C2×C8semidirect
208. C2×D4⋊C8D11direct (N × H)
228. D4×C11C22×C8semidirect
257. D44C22×C8semidirect
296. C2×C4⋊C8C2×D11semidirect
301. C2×C4×C8C2×D11semidirect
305. D4⋊C8C2×D11direct (N × H)
319. C2×D11D4⋊C8direct (N × H)
403. C4⋊C8C22×D11semidirect
408. C4×C8C22×D11semidirect
410. C2×C11C2×D4⋊C8semidirect
415. D11C2×D4⋊C8direct (N × H)
434. C2×D4C8×D11semidirect
503. C11C22×D4⋊C8semidirect
527. D4C2×C8×D11semidirect
603. C2D11×D4⋊C8direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×D4×D112
C2×D11×C4⋊C82
C2×C4×C8×D112
C2×#106220972
C2×D4⋊(C11⋊C8)2
C2×#106221212
D11×D4⋊C82
C2×C11×D4⋊C82
C22×D4⋊C811