Finite Group Databasebeta

← D4×#66874 #14769199

Subgroups — D4×#66874 #14769199

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×Dic22C211yesmaximal, characteristic
2C2×D4×C11⋊C8C211yesmaximal, characteristic
3C22×#66874C212yesmaximal, complemented
4#13069539C211yesmaximal, characteristic, complemented
5#13069417C211yesmaximal, characteristic, complemented
6#13069037C212yesmaximal, complemented
7#13068923C212yesmaximal, complemented
8#13068618C211yesmaximal, characteristic, complemented
9#13068550C212yesmaximal, complemented
10C4×#66874C211yesmaximal, characteristic, complemented
11D4×C11×C4⋊C4C211yesmaximal, characteristic
12C23×Dic22C2212yes—
13C2×C4×D4×C11—21no—
14C2×C4×D4×C11C2211yescharacteristic
15C22×C11×C4⋊C4C2212yes—
16C2×D4×Dic11—21no—
17C2×#66977C2212yes—
18C23×C11⋊C8C2212yes—
19D4×Dic22—24no—
20D4×Dic22C418yescomplemented
21C2×#66941—21no—
22C2×#66931—22no—
23C2×#66922C2211yescharacteristic
24C2×C4×Dic22C2211yescharacteristic
25C11×#389—21no—
26C11×#385—22no—
27C11×#384C2211yescharacteristic
28C11×#380C2212yes—
29C4×C11×C4⋊C4C2211yescharacteristic
30C2×C22⋊(C11⋊C8)C2212yes—
31D4×C11⋊C8—24no—
32C2×#66874—28no—
33C2×#66874C2211yescharacteristic
34C2×#66874C2212yes—
35C2×#66874C2212yes—
36C2×#66874C2212yes—
37C2×#66874C2212yes—
38C2×#66874C2212yes—
39C2×#66874C2211yescharacteristic
40C2×C4⋊(C11⋊C8)C2211yescharacteristic
41C2×C4×C11⋊C8C2211yescharacteristic
42#10622167C2212yes—
43#10622167C2211yescharacteristic
44#10622167C2211yescharacteristic
45C22×D4×C11D411yescharacteristic
46C23×C4×C11—22no—
47C23×C4×C11C2312yes—
48C23×Dic11—22no—
49C22×Dic22—24no—
50C22×Dic22—24no—
51C22×Dic22—22no—
52C22×Dic22—24no—
53C22×Dic22—42no—
54C22×Dic22—42no—
55C22×Dic22C2×C418yescomplemented
56C22×Dic22C2312yes—
57C22×Dic22C2311yescharacteristic
58C4×D4×C11—44no—
59C4×D4×C11C2×C414yes—
60C4×D4×C11D414yes—
61C2×C11×C4⋊C4—24no—
62C2×C11×C4⋊C4—22no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—42no—
66C2×C11×C4⋊C4D411yescharacteristic
67C2×C11×C4⋊C4C2312yes—
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C22⋊C4—22no—
71C2×C11×C22⋊C4D412yes—
72C2×C42×C11—21no—
73C2×C42×C11C2311yescharacteristic
74C2×C22⋊Dic11—22no—
75D4×Dic11—28no—
76C2×C4⋊Dic11—21no—
77C2×C4⋊Dic11—21no—
78C2×C4⋊Dic11C2311yescharacteristic
79#66977—24no—
80#66977C2×C418yescomplemented
81C2×Dic11⋊C4—21no—
82C2×Dic11⋊C4—22no—
83C2×C4×Dic11—21no—
84C22×C11⋊C8—24no—
85C22×C11⋊C8—24no—
86C22×C11⋊C8—42no—
87C22×C11⋊C8C2311yescharacteristic
88C22×C11⋊C8C2312yes—
89C22×C11⋊C8C2311yescharacteristic
90#66941—28no—
91#66931—216no—
92#66922—22no—
93#66922C2×C414yescomplemented
94C4×Dic22—22no—
95C4×Dic22C2×C414yescomplemented
96C11×#95—21no—
97C11×#95—22no—
98C22⋊(C11⋊C8)—24no—
99#66874—24no—
100#66874—22no—
101#66874—24no—
102#66874—24no—
103#66874—42no—
104#66874—42no—
105#66874D414yesdirect product factor
106C4⋊(C11⋊C8)—22no—
107C4×C11⋊C8—22no—
108D4×#103—111nomaximal, Sylow
109C24×C11C2×D412yes—
110C2×D4×C11C22⋊C414yes—
111C2×D4×C11SD1614yes—
112C2×D4×C11Q1614yes—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—21no—
118C22×C4×C11—21no—
119C22×C4×C11—22no—
120C22×C4×C11—44no—
121C22×C4×C11—44no—
122C22×C4×C11—82no—
123C22×C4×C11C22×C414yes—
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D412yes—
126C22×C4×C11C2×D414yes—
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2411yescharacteristic
129C22×Dic11—28no—
130C22×Dic11—21no—
131C22×Dic11—21no—
132C22×Dic11—22no—
133C22×Dic11—44no—
134C22×Dic11—44no—
135C2×Dic22—216no—
136C2×Dic22—28no—
137C2×Dic22—21no—
138C2×Dic22—22no—
139C2×Dic22—22no—
140C2×Dic22—22no—
141C2×Dic22—21no—
142C2×Dic22—21no—
143C2×Dic22—22no—
144C2×Dic22—22no—
145C2×Dic22—48no—
146C2×Dic22—48no—
147C2×Dic22—48no—
148C2×Dic22—44no—
149C2×Dic22—44no—
150C2×Dic22C22×C414yes—
151C2×Dic22C22×C412yes—
152C2×Dic22C2×D412yes—
153C2×Dic22#4112yes—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—22no—
159C11×C4⋊C4—44no—
160C11×C4⋊C4—42no—
161C11×C4⋊C4—81no—
162C11×C4⋊C4C22⋊C414yes—
163C11×C4⋊C4C2×D412yes—
164C11×C22⋊C4—44no—
165C11×C22⋊C4C22⋊C418yes—
166C42×C11—42no—
167C42×C11C22×C412yes—
168C42×C11C2×D412yes—
169C22⋊Dic11—28no—
170C4⋊Dic11—24no—
171C4⋊Dic11—24no—
172C4⋊Dic11—21no—
173C4⋊Dic11C22×C412yes—
174Dic11⋊C4—24no—
175Dic11⋊C4—28no—
176C4×Dic11—24no—
177C2×C11⋊C8—21no—
178C2×C11⋊C8—21no—
179C2×C11⋊C8—22no—
180C2×C11⋊C8—22no—
181C2×C11⋊C8—21no—
182C2×C11⋊C8—21no—
183C2×C11⋊C8—21no—
184C2×C11⋊C8—22no—
185C2×C11⋊C8—48no—
186C2×C11⋊C8C2×D412yes—
187C2×D4×Q8—111no—
188C2×C8×D4—111no—
189C22×#103—112no—
190D4×C4⋊C4D1111yescharacteristic
191#1981—111no—
192#1956—111no—
193#1892—112no—
194#1872—112no—
195#1803—111no—
196#1787—112no—
197C4×#103—111no—
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
206D4×C11#103116yescomplemented
207C2×C4×C11—22no—
208C2×C4×C11—22no—
209C2×C4×C11—21no—
210C2×C4×C11—21no—
211C2×C4×C11—24no—
212C2×C4×C11—24no—
213C2×C4×C11—24no—
214C2×C4×C11—24no—
215C2×C4×C11—22no—
216C2×C4×C11—41no—
217C2×C4×C11—41no—
218C2×C4×C11—42no—
219C2×C4×C11—41no—
220C2×C4×C11—41no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11—41no—
224C2×C4×C11—88no—
225C2×C4×C11C2×C22⋊C412yes—
226C2×C4×C11C2×C22⋊C414yes—
227C2×C4×C11C2×C22⋊C412yes—
228C2×C4×C11C2×SD1612yes—
229C2×C4×C11C2×Q1612yes—
230C2×C4×C11C23×C411yescharacteristic
231C2×C4×C11C22×D411yescharacteristic
232C2×C4×C11C22×D411yescharacteristic
233C2×C4×C11C2×#4111yescharacteristic
234C2×C4×C11H(5,𝔽2)11yescharacteristic
235C2×C4×C11H(5,𝔽2)11yescharacteristic
236C2×Dic11—22no—
237C2×Dic11—22no—
238C2×Dic11—22no—
239C2×Dic11—22no—
240C2×Dic11—24no—
241C2×Dic11—416no—
242C2×Dic11—42no—
243C2×Dic11—42no—
244C2×Dic11—41no—
245C2×Dic11—41no—
246Dic22—22no—
247Dic22—22no—
248Dic22—22no—
249Dic22—24no—
250Dic22—24no—
251Dic22—416no—
252Dic22—42no—
253Dic22—42no—
254Dic22C4×D414yescomplemented
255C11⋊C8—22no—
256C11⋊C8—42no—
257C11⋊C8—41no—
258C23×Q8—112no—
259C23×C8—112no—
260D4×Q8—118no—
261D4×Q8—224no—
262C2×C4⋊Q8—111no—
263C2×C4⋊Q8—221no—
264C2×C22⋊Q8—112no—
265C2×C22⋊Q8—222no—
266C2×C4×Q8—111no—
267C2×C4×D4—21no—
268C2×C4×D4—221no—
269C2×C4×D4C2×D1111yescharacteristic
270C22×C4⋊C4C2×D1112yes—
271C8×D4—224no—
272C2×C4⋊C8—111no—
273C2×#103—111no—
274C2×#103—112no—
275C2×#103—112no—
276C2×#103—112no—
277C2×#103—111no—
278C2×#103—112no—
279C2×#103—112no—
280C2×#103—228no—
281C2×C22⋊C8—112no—
282C2×C4×C8—111no—
283#389—21no—
284#385—22no—
285#384C2×D1111yescharacteristic
286#380C2×D1112yes—
287C4×C4⋊C4C2×D1111yescharacteristic
288#340—112no—
289#340—111no—
290#340—111no—
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—22no—
307C4×C11—42no—
308C4×C11—82no—
309C4×C11—81no—
310C4×C11C2×#10314yescomplemented
311C4×C11C2×C4×D411yescharacteristic
312C4×C11#51811yescharacteristic
313C4×C11D4211yescharacteristic
314C4×C11#54611yescharacteristic
315Dic11—24no—
316Dic11—44no—
317Dic11—42no—
318C22×Q8—118no—
319C22×Q8—111no—
320C22×Q8—112no—
321C22×Q8—224no—
322C22×Q8—224no—
323C22×Q8—224no—
324C22×Q8—222no—
325C22×Q8—442no—
326C22×Q8—442no—
327C22×D4C22⋊D1111yescharacteristic
328C23×C4—22no—
329C23×C4—222no—
330C23×C4C22×D1112yes—
331C22×C8—111no—
332C22×C8—112no—
333C22×C8—111no—
334C22×C8—224no—
335C22×C8—224no—
336C22×C8—442no—
337C4⋊Q8—114no—
338C4⋊Q8—228no—
339C4⋊Q8—222no—
340C22⋊Q8—118no—
341C22⋊Q8—224no—
342C22⋊Q8—2216no—
343C4×Q8—114no—
344C4×Q8—222no—
345C4×D4—44no—
346C4×D4—228no—
347C4×D4C4×D1114yes—
348C4×D4D4414yes—
349C2×C4⋊C4—24no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—42no—
354C2×C4⋊C4—111no—
355C2×C4⋊C4—221no—
356C2×C4⋊C4—221no—
357C2×C4⋊C4—222no—
358C2×C4⋊C4—221no—
359C2×C4⋊C4C22⋊D1111yescharacteristic
360C2×C4⋊C4C22×D1112yes—
361C2×C4⋊C4C22×D1111yescharacteristic
362C2×C4⋊C4C22×D1111yescharacteristic
363C2×C22⋊C4—22no—
364C2×C22⋊C4—222no—
365C2×C22⋊C4C22⋊D1112yes—
366C2×C42—21no—
367C2×C42—221no—
368C2×C42C22×D1111yescharacteristic
369C4⋊C8—222no—
370#103—114no—
371#103—224no—
372#103—222no—
373#103—224no—
374#103—224no—
375#103—442no—
376#103—442no—
377C22⋊C8—224no—
378C4×C8—222no—
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×C22⋊D1112yes—
390C2×Q8—112no—
391C2×Q8—114no—
392C2×Q8—112no—
393C2×Q8—112no—
394C2×Q8—2216no—
395C2×Q8—228no—
396C2×Q8—221no—
397C2×Q8—222no—
398C2×Q8—221no—
399C2×Q8—221no—
400C2×Q8—222no—
401C2×Q8—222no—
402C2×Q8—222no—
403C2×Q8—222no—
404C2×Q8—444no—
405C2×Q8—444no—
406C2×Q8—448no—
407C2×Q8—448no—
408C2×Q8—448no—
409C2×D4(C2×D11)⋊C414yes—
410C2×D4#432414yes—
411C2×D4#432614yes—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—22no—
419C22×C4—44no—
420C22×C4—44no—
421C22×C4—82no—
422C22×C4—221no—
423C22×C4—228no—
424C22×C4—221no—
425C22×C4—222no—
426C22×C4—444no—
427C22×C4—444no—
428C22×C4C2×C4×D1114yes—
429C22×C4C2×D4414yes—
430C22×C4C2×C22⋊D1111yescharacteristic
431C22×C4C2×C22⋊D1112yes—
432C22×C4C2×C22⋊D1111yescharacteristic
433C22×C4C23×D1111yescharacteristic
434C2×C8—112no—
435C2×C8—221no—
436C2×C8—221no—
437C2×C8—221no—
438C2×C8—222no—
439C2×C8—222no—
440C2×C8—221no—
441C2×C8—221no—
442C2×C8—222no—
443C2×C8—448no—
444C4⋊C4—21no—
445C4⋊C4—22no—
446C4⋊C4—22no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—44no—
450C4⋊C4—42no—
451C4⋊C4—81no—
452C4⋊C4—112no—
453C4⋊C4—224no—
454C4⋊C4—224no—
455C4⋊C4—228no—
456C4⋊C4—224no—
457C4⋊C4—221no—
458C4⋊C4(C2×D11)⋊C414yes—
459C4⋊C4D4×D1112yes—
460C22⋊C4—44no—
461C22⋊C4—228no—
462C22⋊C4(C2×D11)⋊C418yes—
463C42—42no—
464C42—224no—
465C42C2×C4×D1112yes—
466C42C2×D4412yes—
467C11D4×#10311yescharacteristic, complemented, Sylow
468C23—22no—
469C23—22no—
470C23—22no—
471C23—22no—
472C23C2×(C2×D11)⋊C414yes—
473C23C2×#432414yes—
474C23C2×#432614yes—
475C23C22×C22⋊D1111yescharacteristic
476Q8—114no—
477Q8—222no—
478Q8—222no—
479Q8—222no—
480Q8—224no—
481Q8—224no—
482Q8—4416no—
483Q8—442no—
484Q8—442no—
485D4#66874116yesdirect product factor
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—24no—
491C2×C4—24no—
492C2×C4—24no—
493C2×C4—24no—
494C2×C4—22no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—41no—
501C2×C4—42no—
502C2×C4—41no—
503C2×C4—88no—
504C2×C4—222no—
505C2×C4—222no—
506C2×C4—222no—
507C2×C4—222no—
508C2×C4—224no—
509C2×C4—4416no—
510C2×C4—442no—
511C2×C4—442no—
512C2×C4—441no—
513C2×C4—441no—
514C2×C4C2×(C2×D11)⋊C412yes—
515C2×C4C2×(C2×D11)⋊C414yes—
516C2×C4C2×(C2×D11)⋊C412yes—
517C2×C4C2×#432412yes—
518C2×C4C2×#432612yes—
519C2×C4C22×C4×D1111yescharacteristic
520C2×C4C22×D4411yescharacteristic
521C2×C4C2×D4×D1111yescharacteristic
522C2×C4#6703711yescharacteristic
523C2×C4#41×D1111yescharacteristic
524C2×C4#6704211yescharacteristic
525C8—222no—
526C8—442no—
527C8—441no—
528C22—24no—
529C22—24no—
530C22—24no—
531C22—24no—
532C22—24no—
533C22—24no—
534C22C2×#6687418yescomplemented
535C22C22×(C2×D11)⋊C411yescharacteristic
536C22C22×#432411yescharacteristic
537C22D4×C22⋊D1111yescharacteristic
538C22C22×#432611yescharacteristic
539C22#1062336011yescharacteristic
540C22#1062336711yescharacteristic
541C22#1062336911yescharacteristic
542C4—24no—
543C4—22no—
544C4—42no—
545C4—81no—
546C4—82no—
547C4—224no—
548C4—444no—
549C4—442no—
550C4C2×#6687414yescomplemented
551C4C4×D4×D1111yescharacteristic
552C4#1062307611yescharacteristic
553C4D4×D4411yescharacteristic
554C4#1062308511yescharacteristic
555C2—28no—
556C2D4×(C2×D11)⋊C411yescharacteristic
557C2C22×#6687411yescharacteristic
558C2#1307714611yescharacteristic
559C2D4×#432411yescharacteristic
560C2D4×#432611yescharacteristic
561C2#1308047511yescharacteristic
562C2#1308048611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingD4×C11×C4⋊C4C2
socleC23×C11C22×D4
prime radicalC22×D4×C11D4
cosocleC22×C4×C11C24
hypercenterD4×C4⋊C4D11
hypocenterC11D4×#103
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ D4×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C22×#66874C2semidirect
4. #13069539C2semidirect
5. #13069417C2semidirect
6. #13069037C2semidirect
7. #13068923C2semidirect
8. #13068618C2semidirect
9. #13068550C2semidirect
10. C4×#66874C2semidirect
20. D4×Dic22C4semidirect
55. C22×Dic22C2×C4semidirect
80. #66977C2×C4semidirect
93. #66922C2×C4semidirect
95. C4×Dic22C2×C4semidirect
105. #66874D4direct (N × H)
206. D4×C11#103semidirect
254. Dic22C4×D4semidirect
297. C22×C11C2×#103semidirect
310. C4×C11C2×#103semidirect
467. C11D4×#103semidirect
485. D4#66874direct (N × H)
534. C22C2×#66874semidirect
550. C4C2×#66874semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Dic222
C2×D4×C11⋊C82
C22×#668742
#130695392
#130694172
#130690372
#130689232
#130686182
#130685502
C4×#668742
D4×C11×C4⋊C42
D4×#10311