Finite Group Databasebeta

← D4×C11×#103 #14599608

Subgroups — D4×C11×#103 #14599608

Order 2816.

1530 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×Q8×C11C211yesmaximal, characteristic
2C2×C8×D4×C11C211yesmaximal, characteristic
3C22×C11×#103C212yesmaximal, complemented
4D4×C11×C4⋊C4C211yesmaximal, characteristic
5C11×#1981C211yesmaximal, characteristic, complemented
6C11×#1956C211yesmaximal, characteristic, complemented
7C11×#1892C212yesmaximal, complemented
8C11×#1872C212yesmaximal, complemented
9C11×#1803C211yesmaximal, characteristic, complemented
10C11×#1787C212yesmaximal, complemented
11C4×C11×#103C211yesmaximal, characteristic, complemented
12C23×Q8×C11C2212yes—
13C23×C8×C11C2212yes—
14D4×Q8×C11—24no—
15D4×Q8×C11C418yescomplemented
16C2×C11×C4⋊Q8—21no—
17C2×C11×C4⋊Q8C2211yescharacteristic
18C2×C11×C22⋊Q8—22no—
19C2×C11×C22⋊Q8C2212yes—
20C2×C4×Q8×C11C2211yescharacteristic
21C2×C4×D4×C11—21no—
22C2×C4×D4×C11—21no—
23C2×C4×D4×C11C2211yescharacteristic
24C22×C11×C4⋊C4C2212yes—
25C8×D4×C11—24no—
26C2×C11×C4⋊C8C2211yescharacteristic
27C2×C11×#103—28no—
28C2×C11×#103C2212yes—
29C2×C11×#103C2212yes—
30C2×C11×#103C2212yes—
31C2×C11×#103C2211yescharacteristic
32C2×C11×#103C2212yes—
33C2×C11×#103C2212yes—
34C2×C11×#103C2211yescharacteristic
35C2×C11×C22⋊C8C2212yes—
36C2×C4×C8×C11C2211yescharacteristic
37C11×#389—21no—
38C11×#385—22no—
39C11×#384C2211yescharacteristic
40C11×#380C2212yes—
41C4×C11×C4⋊C4C2211yescharacteristic
42C11×#340C2211yescharacteristic
43C11×#340C2212yes—
44C11×#340C2211yescharacteristic
45C22×Q8×C11—22no—
46C22×Q8×C11—24no—
47C22×Q8×C11—24no—
48C22×Q8×C11—24no—
49C22×Q8×C11—42no—
50C22×Q8×C11—42no—
51C22×Q8×C11C2×C418yescomplemented
52C22×Q8×C11C2312yes—
53C22×Q8×C11C2311yescharacteristic
54C22×D4×C11D411yescharacteristic
55C23×C4×C11—22no—
56C23×C4×C11—22no—
57C23×C4×C11C2312yes—
58C22×C8×C11—24no—
59C22×C8×C11—24no—
60C22×C8×C11—42no—
61C22×C8×C11C2311yescharacteristic
62C22×C8×C11C2312yes—
63C22×C8×C11C2311yescharacteristic
64C11×C4⋊Q8—28no—
65C11×C4⋊Q8—22no—
66C11×C4⋊Q8C2×C414yescomplemented
67C11×C22⋊Q8—24no—
68C11×C22⋊Q8—216no—
69C11×C22⋊Q8C2×C418yescomplemented
70C4×Q8×C11—22no—
71C4×Q8×C11C2×C414yescomplemented
72C4×D4×C11—28no—
73C4×D4×C11—44no—
74C4×D4×C11C2×C414yes—
75C4×D4×C11D414yes—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—22no—
80C2×C11×C4⋊C4—24no—
81C2×C11×C4⋊C4—22no—
82C2×C11×C4⋊C4—21no—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4—42no—
85C2×C11×C4⋊C4D411yescharacteristic
86C2×C11×C4⋊C4C2312yes—
87C2×C11×C4⋊C4C2311yescharacteristic
88C2×C11×C4⋊C4C2311yescharacteristic
89C2×C11×C4⋊C4C2311yescharacteristic
90C2×C11×C22⋊C4—22no—
91C2×C11×C22⋊C4—22no—
92C2×C11×C22⋊C4D412yes—
93C2×C42×C11—21no—
94C2×C42×C11—21no—
95C2×C42×C11C2311yescharacteristic
96C11×C4⋊C8—22no—
97C11×#103—24no—
98C11×#103—22no—
99C11×#103—24no—
100C11×#103—24no—
101C11×#103—42no—
102C11×#103—42no—
103C11×#103D414yesdirect product factor
104C11×C22⋊C8—24no—
105C4×C8×C11—22no—
106C11×#95—21no—
107C11×#95—22no—
108D4×#103C1111yesmaximal, characteristic, direct product factor, Sylow
109C24×C11C2×D412yes—
110C2×Q8×C11—28no—
111C2×Q8×C11—21no—
112C2×Q8×C11—22no—
113C2×Q8×C11—21no—
114C2×Q8×C11—21no—
115C2×Q8×C11—216no—
116C2×Q8×C11—22no—
117C2×Q8×C11—22no—
118C2×Q8×C11—22no—
119C2×Q8×C11—22no—
120C2×Q8×C11—44no—
121C2×Q8×C11—44no—
122C2×Q8×C11—48no—
123C2×Q8×C11—48no—
124C2×Q8×C11—48no—
125C2×Q8×C11C22×C414yes—
126C2×Q8×C11C22×C412yes—
127C2×Q8×C11C2×D412yes—
128C2×Q8×C11#4112yes—
129C2×D4×C11C22⋊C414yes—
130C2×D4×C11SD1614yes—
131C2×D4×C11Q1614yes—
132C22×C4×C11—21no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—28no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—22no—
141C22×C4×C11—21no—
142C22×C4×C11—22no—
143C22×C4×C11—44no—
144C22×C4×C11—44no—
145C22×C4×C11—44no—
146C22×C4×C11—44no—
147C22×C4×C11—82no—
148C22×C4×C11C22×C414yes—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D412yes—
151C22×C4×C11C2×D414yes—
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2411yescharacteristic
154C2×C8×C11—21no—
155C2×C8×C11—21no—
156C2×C8×C11—22no—
157C2×C8×C11—22no—
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11—22no—
162C2×C8×C11—48no—
163C2×C8×C11C2×D412yes—
164C11×C4⋊C4—24no—
165C11×C4⋊C4—24no—
166C11×C4⋊C4—24no—
167C11×C4⋊C4—28no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—22no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—22no—
174C11×C4⋊C4—44no—
175C11×C4⋊C4—42no—
176C11×C4⋊C4—81no—
177C11×C4⋊C4C22⋊C414yes—
178C11×C4⋊C4C22×C412yes—
179C11×C4⋊C4C2×D412yes—
180C11×C22⋊C4—28no—
181C11×C22⋊C4—44no—
182C11×C22⋊C4C22⋊C418yes—
183C42×C11—24no—
184C42×C11—42no—
185C42×C11C22×C412yes—
186C42×C11C2×D412yes—
187C2×D4×Q8C2×C1111yescharacteristic
188C2×C8×D4C2×C1111yescharacteristic
189C22×#103C2×C1112yescomplemented
190D4×C4⋊C4C2×C1111yescharacteristic
191#1981C2×C1111yescharacteristic, complemented
192#1956C2×C1111yescharacteristic, complemented
193#1892C2×C1112yescomplemented
194#1872C2×C1112yescomplemented
195#1803C2×C1111yescharacteristic, complemented
196#1787C2×C1112yescomplemented
197C4×#103C2×C1111yescharacteristic, complemented
198C23×C11—22no—
199C23×C11—22no—
200C23×C11—22no—
201C23×C11—22no—
202C23×C11C2×C22⋊C414yes—
203C23×C11C2×SD1614yes—
204C23×C11C2×Q1614yes—
205C23×C11C22×D411yescharacteristic
206Q8×C11—22no—
207Q8×C11—22no—
208Q8×C11—22no—
209Q8×C11—24no—
210Q8×C11—24no—
211Q8×C11—416no—
212Q8×C11—42no—
213Q8×C11—42no—
214Q8×C11C4×D414yescomplemented
215D4×C11#103116yesdirect product factor
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—22no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—24no—
224C2×C4×C11—24no—
225C2×C4×C11—24no—
226C2×C4×C11—24no—
227C2×C4×C11—22no—
228C2×C4×C11—24no—
229C2×C4×C11—22no—
230C2×C4×C11—416no—
231C2×C4×C11—42no—
232C2×C4×C11—42no—
233C2×C4×C11—41no—
234C2×C4×C11—41no—
235C2×C4×C11—41no—
236C2×C4×C11—41no—
237C2×C4×C11—42no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—42no—
241C2×C4×C11—42no—
242C2×C4×C11—41no—
243C2×C4×C11—88no—
244C2×C4×C11C2×C22⋊C412yes—
245C2×C4×C11C2×C22⋊C414yes—
246C2×C4×C11C2×C22⋊C412yes—
247C2×C4×C11C2×SD1612yes—
248C2×C4×C11C2×Q1612yes—
249C2×C4×C11C23×C411yescharacteristic
250C2×C4×C11C22×D411yescharacteristic
251C2×C4×C11C22×D411yescharacteristic
252C2×C4×C11C2×#4111yescharacteristic
253C2×C4×C11H(5,𝔽2)11yescharacteristic
254C2×C4×C11H(5,𝔽2)11yescharacteristic
255C8×C11—22no—
256C8×C11—42no—
257C8×C11—41no—
258C23×Q8C22×C1112yes—
259C23×C8C22×C1112yes—
260D4×Q8—24no—
261D4×Q8C4×C1118yescomplemented
262C2×C4⋊Q8—21no—
263C2×C4⋊Q8C22×C1111yescharacteristic
264C2×C22⋊Q8—22no—
265C2×C22⋊Q8C22×C1112yes—
266C2×C4×Q8C22×C1111yescharacteristic
267C2×C4×D4—21no—
268C2×C4×D4—21no—
269C2×C4×D4C22×C1111yescharacteristic
270C22×C4⋊C4C22×C1112yes—
271C8×D4—24no—
272C2×C4⋊C8C22×C1111yescharacteristic
273C2×#103—28no—
274C2×#103C22×C1112yes—
275C2×#103C22×C1112yes—
276C2×#103C22×C1112yes—
277C2×#103C22×C1111yescharacteristic
278C2×#103C22×C1112yes—
279C2×#103C22×C1112yes—
280C2×#103C22×C1111yescharacteristic
281C2×C22⋊C8C22×C1112yes—
282C2×C4×C8C22×C1111yescharacteristic
283#389—21no—
284#385—22no—
285#384C22×C1111yescharacteristic
286#380C22×C1112yes—
287C4×C4⋊C4C22×C1111yescharacteristic
288#340C22×C1112yes—
289#340C22×C1111yescharacteristic
290#340C22×C1111yescharacteristic
291C22×C11—24no—
292C22×C11—24no—
293C22×C11—24no—
294C22×C11—24no—
295C22×C11—24no—
296C22×C11—24no—
297C22×C11C2×#10318yescomplemented
298C22×C11C22×C22⋊C411yescharacteristic
299C22×C11D4211yescharacteristic
300C22×C11#54611yescharacteristic
301C22×C11C22×SD1611yescharacteristic
302C22×C11C22×Q1611yescharacteristic
303C22×C11#57711yescharacteristic
304C22×C11#57811yescharacteristic
305C4×C11—24no—
306C4×C11—24no—
307C4×C11—22no—
308C4×C11—44no—
309C4×C11—42no—
310C4×C11—42no—
311C4×C11—82no—
312C4×C11—81no—
313C4×C11C2×#10314yescomplemented
314C4×C11C2×C4×D411yescharacteristic
315C4×C11#51811yescharacteristic
316C4×C11D4211yescharacteristic
317C4×C11#54611yescharacteristic
318C22×Q8—22no—
319C22×Q8—24no—
320C22×Q8—24no—
321C22×Q8—24no—
322C22×Q8—42no—
323C22×Q8—42no—
324C22×Q8C2×C4×C1118yescomplemented
325C22×Q8C23×C1112yes—
326C22×Q8C23×C1111yescharacteristic
327C22×D4D4×C1111yescharacteristic
328C23×C4—22no—
329C23×C4—22no—
330C23×C4C23×C1112yes—
331C22×C8—24no—
332C22×C8—24no—
333C22×C8—42no—
334C22×C8C23×C1112yes—
335C22×C8C23×C1111yescharacteristic
336C22×C8C23×C1111yescharacteristic
337C4⋊Q8—28no—
338C4⋊Q8—22no—
339C4⋊Q8C2×C4×C1114yescomplemented
340C22⋊Q8—24no—
341C22⋊Q8—216no—
342C22⋊Q8C2×C4×C1118yescomplemented
343C4×Q8—22no—
344C4×Q8C2×C4×C1114yescomplemented
345C4×D4—28no—
346C4×D4—44no—
347C4×D4C2×C4×C1114yes—
348C4×D4D4×C1114yes—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—24no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—42no—
358C2×C4⋊C4D4×C1111yescharacteristic
359C2×C4⋊C4C23×C1112yes—
360C2×C4⋊C4C23×C1111yescharacteristic
361C2×C4⋊C4C23×C1111yescharacteristic
362C2×C4⋊C4C23×C1111yescharacteristic
363C2×C22⋊C4—22no—
364C2×C22⋊C4—22no—
365C2×C22⋊C4D4×C1112yes—
366C2×C42—21no—
367C2×C42—21no—
368C2×C42C23×C1111yescharacteristic
369C4⋊C8—22no—
370#103—24no—
371#103—22no—
372#103—24no—
373#103—24no—
374#103—42no—
375#103—42no—
376#103D4×C1114yesdirect product factor
377C22⋊C8—24no—
378C4×C8—22no—
379#95—21no—
380#95—22no—
381C2×C11—28no—
382C2×C11D4×C22⋊C411yescharacteristic
383C2×C11C22×#10311yescharacteristic
384C2×C11#289811yescharacteristic
385C2×C11D4×SD1611yescharacteristic
386C2×C11D4×Q1611yescharacteristic
387C2×C11#329811yescharacteristic
388C2×C11#329911yescharacteristic
389C24C2×D4×C1112yes—
390C2×Q8—28no—
391C2×Q8—21no—
392C2×Q8—22no—
393C2×Q8—21no—
394C2×Q8—21no—
395C2×Q8—216no—
396C2×Q8—22no—
397C2×Q8—22no—
398C2×Q8—22no—
399C2×Q8—22no—
400C2×Q8—44no—
401C2×Q8—44no—
402C2×Q8—48no—
403C2×Q8—48no—
404C2×Q8—48no—
405C2×Q8C22×C4×C1114yes—
406C2×Q8C22×C4×C1112yes—
407C2×Q8C2×D4×C1112yes—
408C2×Q8C11×#4112yes—
409C2×D4C11×C22⋊C414yes—
410C2×D4C11×SD1614yes—
411C2×D4C11×Q1614yes—
412C22×C4—21no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—28no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—22no—
421C22×C4—21no—
422C22×C4—22no—
423C22×C4—44no—
424C22×C4—44no—
425C22×C4—44no—
426C22×C4—44no—
427C22×C4—82no—
428C22×C4C22×C4×C1114yes—
429C22×C4C2×D4×C1111yescharacteristic
430C22×C4C2×D4×C1112yes—
431C22×C4C2×D4×C1114yes—
432C22×C4C2×D4×C1111yescharacteristic
433C22×C4C24×C1111yescharacteristic
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—22no—
438C2×C8—22no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—22no—
442C2×C8—48no—
443C2×C8C2×D4×C1112yes—
444C4⋊C4—24no—
445C4⋊C4—24no—
446C4⋊C4—24no—
447C4⋊C4—28no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—22no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—22no—
454C4⋊C4—44no—
455C4⋊C4—42no—
456C4⋊C4—81no—
457C4⋊C4C11×C22⋊C414yes—
458C4⋊C4C22×C4×C1112yes—
459C4⋊C4C2×D4×C1112yes—
460C22⋊C4—28no—
461C22⋊C4—44no—
462C22⋊C4C11×C22⋊C418yes—
463C42—24no—
464C42—42no—
465C42C22×C4×C1112yes—
466C42C2×D4×C1112yes—
467C11D4×#10311yescharacteristic, direct product factor, Sylow
468C23—22no—
469C23—22no—
470C23—22no—
471C23—22no—
472C23C2×C11×C22⋊C414yes—
473C23C2×C11×SD1614yes—
474C23C2×C11×Q1614yes—
475C23C22×D4×C1111yescharacteristic
476Q8—22no—
477Q8—22no—
478Q8—22no—
479Q8—24no—
480Q8—24no—
481Q8—416no—
482Q8—42no—
483Q8—42no—
484Q8C4×D4×C1114yescomplemented
485D4C11×#103116yesdirect product factor
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—24no—
494C2×C4—24no—
495C2×C4—24no—
496C2×C4—24no—
497C2×C4—22no—
498C2×C4—24no—
499C2×C4—22no—
500C2×C4—416no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—42no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—41no—
513C2×C4—88no—
514C2×C4C2×C11×C22⋊C412yes—
515C2×C4C2×C11×C22⋊C414yes—
516C2×C4C2×C11×C22⋊C412yes—
517C2×C4C2×C11×SD1612yes—
518C2×C4C2×C11×Q1612yes—
519C2×C4C23×C4×C1111yescharacteristic
520C2×C4C22×D4×C1111yescharacteristic
521C2×C4C22×D4×C1111yescharacteristic
522C2×C4C2×C11×#4111yescharacteristic
523C2×C4C11×H(5,𝔽2)11yescharacteristic
524C2×C4C11×H(5,𝔽2)11yescharacteristic
525C8—22no—
526C8—42no—
527C8—41no—
528C22—24no—
529C22—24no—
530C22—24no—
531C22—24no—
532C22—24no—
533C22—24no—
534C22C2×C11×#10318yescomplemented
535C22C22×C11×C22⋊C411yescharacteristic
536C22D42×C1111yescharacteristic
537C22C11×#54611yescharacteristic
538C22C22×C11×SD1611yescharacteristic
539C22C22×C11×Q1611yescharacteristic
540C22C11×#57711yescharacteristic
541C22C11×#57811yescharacteristic
542C4—22no—
543C4—24no—
544C4—24no—
545C4—42no—
546C4—42no—
547C4—44no—
548C4—82no—
549C4—81no—
550C4C2×C11×#10314yescomplemented
551C4C2×C4×D4×C1111yescharacteristic
552C4C11×#51811yescharacteristic
553C4D42×C1111yescharacteristic
554C4C11×#54611yescharacteristic
555C2—28no—
556C2D4×C11×C22⋊C411yescharacteristic
557C2C22×C11×#10311yescharacteristic
558C2C11×#289811yescharacteristic
559C2D4×C11×SD1611yescharacteristic
560C2D4×C11×Q1611yescharacteristic
561C2C11×#329811yescharacteristic
562C2C11×#329911yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C4×D4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
3. C22×C11×#103C2semidirect
5. C11×#1981C2semidirect
6. C11×#1956C2semidirect
7. C11×#1892C2semidirect
8. C11×#1872C2semidirect
9. C11×#1803C2semidirect
10. C11×#1787C2semidirect
11. C4×C11×#103C2semidirect
15. D4×Q8×C11C4semidirect
51. C22×Q8×C11C2×C4semidirect
66. C11×C4⋊Q8C2×C4semidirect
69. C11×C22⋊Q8C2×C4semidirect
71. C4×Q8×C11C2×C4semidirect
103. C11×#103D4direct (N × H)
108. D4×#103C11direct (N × H)
189. C22×#103C2×C11semidirect
191. #1981C2×C11semidirect
192. #1956C2×C11semidirect
193. #1892C2×C11semidirect
194. #1872C2×C11semidirect
195. #1803C2×C11semidirect
196. #1787C2×C11semidirect
197. C4×#103C2×C11semidirect
214. Q8×C11C4×D4semidirect
215. D4×C11#103direct (N × H)
261. D4×Q8C4×C11semidirect
297. C22×C11C2×#103semidirect
313. C4×C11C2×#103semidirect
324. C22×Q8C2×C4×C11semidirect
339. C4⋊Q8C2×C4×C11semidirect
342. C22⋊Q8C2×C4×C11semidirect
344. C4×Q8C2×C4×C11semidirect
376. #103D4×C11direct (N × H)
467. C11D4×#103direct (N × H)
484. Q8C4×D4×C11semidirect
485. D4C11×#103direct (N × H)
534. C22C2×C11×#103semidirect
550. C4C2×C11×#103semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Q8×C112
C2×C8×D4×C112
C22×C11×#1032
D4×C11×C4⋊C42
C11×#19812
C11×#19562
C11×#18922
C11×#18722
C11×#18032
C11×#17872
C4×C11×#1032
D4×#10311