Finite Group Databasebeta

← C2×#13067105 #14720865

Subgroups — C2×#13067105 #14720865

Order 2816.

1606 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623322C211yesmaximal, characteristic
2C22×C22⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
3#13067105C218yesmaximal, direct product factor
4C2×#10622090C212yesmaximal, complemented
5C2×#10622089C212yesmaximal, complemented
6C2×C4×C11×C22⋊C4C211yesmaximal, characteristic, complemented
7C24×C4×C11C2211yescharacteristic
8C22×#4339C411yescharacteristic, complemented
9C22×C11×C22⋊C4—21no—
10C22×C42×C11—21no—
11C2×#67006—21no—
12#10623322—22no—
13#10623322—22no—
14#10623322C414yescomplemented
15#10623322C2214yes—
16C2×#66983C411yescharacteristic, complemented
17C2×#66983C2211yescharacteristic
18C2×#66982—21no—
19C2×C4×C22⋊D11—21no—
20C2×C4×C22⋊D11—21no—
21C2×#66979C411yescharacteristic, complemented
22C2×#66977C411yescharacteristic, complemented
23C2×#66977C2211yescharacteristic
24C23×C11⋊C8—21no—
25C4×C11×C22⋊C4—22no—
26C4×C11×C22⋊C4C2214yescomplemented
27C2×C11×#95C2212yes—
28C2×C22⋊(C11⋊C8)—22no—
29C2×C22⋊(C11⋊C8)—21no—
30C2×C22⋊(C11⋊C8)C2212yes—
31C2×C22⋊(C11⋊C8)C2214yescomplemented
32#10622090C2218yescomplemented
33#10622089C2218yescomplemented
34C25×C11D411yescharacteristic
35C23×C4×C11—22no—
36C23×C4×C11—44no—
37C23×C4×C11C2×C411yescharacteristic
38C23×C4×C11C2×C411yescharacteristic
39C23×C4×C11C2×C412yes—
40C23×C4×C11D411yescharacteristic
41C23×C4×C11D411yescharacteristic
42C23×C4×C11D412yes—
43C23×C4×C11D411yescharacteristic
44C23×C4×C11D412yes—
45C23×C4×C11C2311yescharacteristic
46C23×C4×C11C2312yes—
47C22×C22⋊D11—21no—
48C22×C22⋊D11—21no—
49C22×C22⋊D11—21no—
50C2×#4339—22no—
51C2×#4339—44no—
52C2×#4339C2×C414yescomplemented
53C22×D44C2×C411yescharacteristic
54C22×C4×D11—21no—
55C22×Dic22C2×C411yescharacteristic
56C2×C11×C22⋊C4—28no—
57C2×C11×C22⋊C4—24no—
58C2×C42×C11—24no—
59C2×C42×C11—44no—
60#67006—24no—
61#67006—24no—
62C2×C22⋊Dic11—21no—
63C2×C22⋊Dic11—21no—
64C2×C22⋊Dic11—21no—
65#66983—22no—
66#66983—21no—
67#66983—21no—
68#66983C2×C412yes—
69#66983C2×C414yescomplemented
70#66983C2312yes—
71#66982—24no—
72#66982—24no—
73C4×C22⋊D11—24no—
74C4×C22⋊D11—24no—
75C4×C22⋊D11—24no—
76C4×C22⋊D11—24no—
77C2×(C2×D11)⋊C4—21no—
78C2×(C2×D11)⋊C4—21no—
79#66979—22no—
80#66979C2×C414yescomplemented
81C2×C4⋊Dic11C2×C411yescharacteristic
82C2×C4⋊Dic11C2×C411yescharacteristic
83#66977—22no—
84#66977—21no—
85#66977—21no—
86#66977C2×C412yes—
87#66977C2×C414yescomplemented
88#66977C2312yes—
89C2×Dic11⋊C4—21no—
90C2×Dic11⋊C4—21no—
91C2×C4×Dic11—21no—
92C22×C11⋊C8—22no—
93C22×C11⋊C8—24no—
94C22×C11⋊C8—44no—
95C11×#95—22no—
96C11×#95C2314yes—
97C22⋊(C11⋊C8)—22no—
98C22⋊(C11⋊C8)—24no—
99C22⋊(C11⋊C8)C2314yes—
100C2×#1501—111nomaximal, Sylow
101C24×C11—24no—
102C24×C11—24no—
103C24×C11—42no—
104C24×C11C22⋊C411yescharacteristic
105C24×C11C22⋊C412yes—
106C24×C11C22⋊C411yescharacteristic
107C24×C11C2×D412yes—
108C24×C11C2×D411yescharacteristic
109C23×D11—21no—
110C22×C4×C11—24no—
111C22×C4×C11—24no—
112C22×C4×C11—24no—
113C22×C4×C11—28no—
114C22×C4×C11—24no—
115C22×C4×C11—44no—
116C22×C4×C11—44no—
117C22×C4×C11—44no—
118C22×C4×C11—44no—
119C22×C4×C11—42no—
120C22×C4×C11—42no—
121C22×C4×C11—42no—
122C22×C4×C11—44no—
123C22×C4×C11—44no—
124C22×C4×C11C22⋊C411yescharacteristic
125C22×C4×C11C22⋊C412yes—
126C22×C4×C11C22⋊C412yes—
127C22×C4×C11C22⋊C412yes—
128C22×C4×C11C22⋊C412yes—
129C22×C4×C11C22⋊C412yes—
130C22×C4×C11C22⋊C411yescharacteristic
131C22×C4×C11C22×C411yescharacteristic
132C22×C4×C11C22×C412yes—
133C22×C4×C11C22×C411yescharacteristic
134C22×C4×C11C22×C412yes—
135C22×C4×C11C2×D412yes—
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D412yes—
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D412yes—
141C22×C4×C11C2411yescharacteristic
142C2×C22⋊D11—22no—
143C2×C22⋊D11—24no—
144C2×C22⋊D11—24no—
145C2×C22⋊D11—22no—
146C2×C22⋊D11—44no—
147C2×C22⋊D11—44no—
148C2×C22⋊D11—44no—
149C22×Dic11—21no—
150C22×Dic11—21no—
151C22×Dic11—21no—
152#4339—48no—
153#4339—48no—
154C2×D44—21no—
155C2×D44—42no—
156C2×D44C22×C412yes—
157C2×C4×D11—24no—
158C2×C4×D11—44no—
159C2×Dic22—21no—
160C2×Dic22—42no—
161C2×Dic22C22×C412yes—
162C11×C22⋊C4—216no—
163C42×C11—48no—
164C22⋊Dic11—22no—
165C22⋊Dic11—24no—
166C22⋊Dic11—24no—
167C22⋊Dic11—22no—
168(C2×D11)⋊C4—22no—
169(C2×D11)⋊C4—24no—
170(C2×D11)⋊C4—22no—
171C4⋊Dic11—21no—
172C4⋊Dic11—21no—
173C4⋊Dic11C22×C412yes—
174C4⋊Dic11C22×C412yes—
175Dic11⋊C4—22no—
176Dic11⋊C4—24no—
177Dic11⋊C4—22no—
178C4×Dic11—24no—
179C2×C11⋊C8—24no—
180C2×C11⋊C8—44no—
181C2×C11⋊C8—48no—
182C2×#525—111no—
183C22×C22⋊C8—111no—
184C2×C4×C22⋊C4D1111yescharacteristic, complemented
185#1501—118no—
186C2×#328—112no—
187C2×#327—112no—
188C23×C11—22no—
189C23×C11—22no—
190C23×C11—22no—
191C23×C11—22no—
192C23×C11—24no—
193C23×C11—22no—
194C23×C11—24no—
195C23×C11—22no—
196C23×C11—24no—
197C23×C11—24no—
198C23×C11—22no—
199C23×C11—42no—
200C23×C11—42no—
201C23×C11—416no—
202C23×C11#10414yes—
203C23×C11C2×C22⋊C412yes—
204C23×C11C2×C22⋊C411yescharacteristic
205C23×C11C2×C22⋊C412yes—
206C23×C11C2×C22⋊C411yescharacteristic
207C23×C11#13514yes—
208C23×C11C22×D411yescharacteristic
209C22×D11—22no—
210C22×D11—42no—
211C22×D11—42no—
212C22×D11—42no—
213C2×C4×C11—22no—
214C2×C4×C11—22no—
215C2×C4×C11—22no—
216C2×C4×C11—24no—
217C2×C4×C11—24no—
218C2×C4×C11—24no—
219C2×C4×C11—24no—
220C2×C4×C11—24no—
221C2×C4×C11—24no—
222C2×C4×C11—28no—
223C2×C4×C11—42no—
224C2×C4×C11—42no—
225C2×C4×C11—41no—
226C2×C4×C11—42no—
227C2×C4×C11—42no—
228C2×C4×C11—41no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11—44no—
232C2×C4×C11—416no—
233C2×C4×C11—44no—
234C2×C4×C11#9914yes—
235C2×C4×C11C2×C22⋊C411yescharacteristic
236C2×C4×C11C2×C22⋊C412yes—
237C2×C4×C11C2×C22⋊C411yescharacteristic
238C2×C4×C11C2×C22⋊C412yes—
239C2×C4×C11C23×C411yescharacteristic
240C2×C4×C11C22×D411yescharacteristic
241C22⋊D11—48no—
242C22⋊D11—44no—
243C22⋊D11—44no—
244C22⋊D11—48no—
245C2×Dic11—22no—
246C2×Dic11—22no—
247C2×Dic11—22no—
248C2×Dic11—42no—
249C2×Dic11—42no—
250C2×Dic11—42no—
251D44—42no—
252D44—42no—
253C4×D11—48no—
254Dic22—42no—
255Dic22—42no—
256C11⋊C8—44no—
257C22×#41—111no—
258C24×C4C2×D1111yescharacteristic
259C23×C8—221no—
260#525—114no—
261#525—114no—
262#525—222no—
263#525—222no—
264C2×#123—221no—
265C2×C22⋊Q8—111no—
266C2×C22⋊Q8—111no—
267C2×#121—111no—
268C2×#121—111no—
269C2×#120—221no—
270C2×C4×D4—221no—
271C2×C4×D4—221no—
272C2×#117—111no—
273C22×C22⋊C4—21no—
274C22×C42—21no—
275C2×C22⋊C8—112no—
276C2×C22⋊C8—114no—
277C2×C22⋊C8—221no—
278C2×C22⋊C8—222no—
279C4×C22⋊C4—22no—
280C4×C22⋊C4C2×D1114yescomplemented
281C2×#95C2×D1112yes—
282#328—118no—
283#327—118no—
284C22×C11—21no—
285C22×C11—21no—
286C22×C11—22no—
287C22×C11—22no—
288C22×C11—21no—
289C22×C11—21no—
290C22×C11—28no—
291C22×C11—28no—
292C22×C11—22no—
293C22×C11—22no—
294C22×C11—22no—
295C22×C11—48no—
296C22×C11—48no—
297C22×C11—44no—
298C22×C11C2×#9912yes—
299C22×C11#41612yes—
300C22×C11#41612yes—
301C22×C11C2×#10414yes—
302C22×C11C2×#10412yes—
303C22×C11C22×C22⋊C411yescharacteristic
304C22×C11C2×#13512yes—
305C2×D11—42no—
306C2×D11—42no—
307C2×D11—42no—
308C2×D11—84no—
309C4×C11—21no—
310C4×C11—22no—
311C4×C11—21no—
312C4×C11—21no—
313C4×C11—21no—
314C4×C11—48no—
315C4×C11C2×#9914yes—
316Dic11—42no—
317Dic11—42no—
318Dic11—42no—
319C25C22⋊D1111yescharacteristic
320C2×#41—114no—
321C2×#41—222no—
322C2×#41—444no—
323C22×Q8—111no—
324C22×D4—111no—
325C22×D4—221no—
326C22×D4—221no—
327C22×D4—221no—
328C23×C4—22no—
329C23×C4—44no—
330C23×C4—221no—
331C23×C4C4×D1111yescharacteristic
332C23×C4C4×D1111yescharacteristic
333C23×C4C4×D1112yes—
334C23×C4D4411yescharacteristic
335C23×C4D4411yescharacteristic
336C23×C4D4412yes—
337C23×C4C22⋊D1111yescharacteristic
338C23×C4C22⋊D1112yes—
339C23×C4C22×D1111yescharacteristic
340C23×C4C22×D1112yes—
341C22×C8—222no—
342C22×C8—224no—
343C22×C8—444no—
344#123—224no—
345#123—224no—
346C22⋊Q8—112no—
347C22⋊Q8—114no—
348C22⋊Q8—112no—
349C22⋊Q8—222no—
350C22⋊Q8—221no—
351C22⋊Q8—221no—
352#121—112no—
353#121—114no—
354#121—112no—
355#121—222no—
356#121—221no—
357#121—221no—
358#120—224no—
359#120—224no—
360C4×D4—224no—
361C4×D4—224no—
362C4×D4—224no—
363C4×D4—224no—
364#117—114no—
365#117—222no—
366C2×C4⋊C4—111no—
367C2×C4⋊C4—111no—
368C2×C4⋊C4—221no—
369C2×C4⋊C4—221no—
370C2×C22⋊C4—28no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—221no—
373C2×C22⋊C4—221no—
374C2×C22⋊C4—221no—
375C2×C22⋊C4—221no—
376C2×C22⋊C4—221no—
377C2×C42—24no—
378C2×C42—44no—
379C2×C42—221no—
380C22⋊C8—114no—
381C22⋊C8—222no—
382C22⋊C8—224no—
383#95—22no—
384#95C22×D1114yes—
385C2×C11—22no—
386C2×C11—22no—
387C2×C11—24no—
388C2×C11—42no—
389C2×C11#150114yescomplemented
390C2×C11C22×#9911yescharacteristic
391C2×C11C2×#41611yescharacteristic
392C2×C11C22×#10411yescharacteristic
393D11—82no—
394C24—24no—
395C24—24no—
396C24—42no—
397C24—221no—
398C24(C2×D11)⋊C411yescharacteristic
399C24(C2×D11)⋊C412yes—
400C24(C2×D11)⋊C411yescharacteristic
401C24C2×C22⋊D1112yes—
402C24C2×C22⋊D1111yescharacteristic
403#41—448no—
404#41—448no—
405C2×Q8—112no—
406C2×Q8—221no—
407C2×Q8—442no—
408C2×D4—112no—
409C2×D4—224no—
410C2×D4—222no—
411C2×D4—224no—
412C2×D4—222no—
413C2×D4—221no—
414C2×D4—442no—
415C2×D4—444no—
416C2×D4—444no—
417C2×D4—444no—
418C22×C4—24no—
419C22×C4—24no—
420C22×C4—24no—
421C22×C4—28no—
422C22×C4—24no—
423C22×C4—44no—
424C22×C4—44no—
425C22×C4—44no—
426C22×C4—44no—
427C22×C4—42no—
428C22×C4—42no—
429C22×C4—42no—
430C22×C4—44no—
431C22×C4—44no—
432C22×C4—221no—
433C22×C4—221no—
434C22×C4—221no—
435C22×C4—224no—
436C22×C4—444no—
437C22×C4(C2×D11)⋊C411yescharacteristic
438C22×C4(C2×D11)⋊C412yes—
439C22×C4(C2×D11)⋊C412yes—
440C22×C4(C2×D11)⋊C412yes—
441C22×C4(C2×D11)⋊C412yes—
442C22×C4(C2×D11)⋊C412yes—
443C22×C4(C2×D11)⋊C411yescharacteristic
444C22×C4C2×C4×D1111yescharacteristic
445C22×C4C2×C4×D1112yes—
446C22×C4C2×C4×D1112yes—
447C22×C4C2×C4×D1111yescharacteristic
448C22×C4C2×D4411yescharacteristic
449C22×C4C2×D4412yes—
450C22×C4C2×D4411yescharacteristic
451C22×C4C2×D4412yes—
452C22×C4C2×C22⋊D1112yes—
453C22×C4C2×C22⋊D1111yescharacteristic
454C22×C4C23×D1111yescharacteristic
455C2×C8—224no—
456C2×C8—444no—
457C2×C8—448no—
458C4⋊C4—112no—
459C4⋊C4—112no—
460C4⋊C4—221no—
461C4⋊C4—221no—
462C4⋊C4—224no—
463C4⋊C4—222no—
464C4⋊C4—222no—
465C22⋊C4—216no—
466C22⋊C4—224no—
467C22⋊C4—224no—
468C22⋊C4—222no—
469C22⋊C4—222no—
470C22⋊C4—224no—
471C22⋊C4—222no—
472C22⋊C4—222no—
473C42—48no—
474C42—224no—
475C11C2×#150111yescharacteristic, complemented, Sylow
476C23—22no—
477C23—22no—
478C23—22no—
479C23—22no—
480C23—24no—
481C23—24no—
482C23—22no—
483C23—22no—
484C23—24no—
485C23—24no—
486C23—22no—
487C23—42no—
488C23—42no—
489C23—416no—
490C23—222no—
491C23—442no—
492C23—442no—
493C23—442no—
494C23#6686914yes—
495C23C2×(C2×D11)⋊C412yes—
496C23C2×(C2×D11)⋊C412yes—
497C23C2×(C2×D11)⋊C411yescharacteristic
498C23C2×(C2×D11)⋊C411yescharacteristic
499C23#6700314yes—
500C23C22×C22⋊D1111yescharacteristic
501Q8—442no—
502Q8—442no—
503D4—442no—
504D4—442no—
505D4—448no—
506D4—448no—
507D4—444no—
508D4—444no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—24no—
513C2×C4—24no—
514C2×C4—24no—
515C2×C4—24no—
516C2×C4—24no—
517C2×C4—24no—
518C2×C4—28no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—42no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—44no—
528C2×C4—416no—
529C2×C4—44no—
530C2×C4—222no—
531C2×C4—222no—
532C2×C4—222no—
533C2×C4—442no—
534C2×C4—442no—
535C2×C4—442no—
536C2×C4—448no—
537C2×C4#6687014yes—
538C2×C4C2×(C2×D11)⋊C412yes—
539C2×C4C2×(C2×D11)⋊C411yescharacteristic
540C2×C4C2×(C2×D11)⋊C411yescharacteristic
541C2×C4C2×(C2×D11)⋊C412yes—
542C2×C4C22×C4×D1111yescharacteristic
543C2×C4C22×D4411yescharacteristic
544C8—444no—
545C22—21no—
546C22—22no—
547C22—21no—
548C22—28no—
549C22—28no—
550C22—22no—
551C22—21no—
552C22—21no—
553C22—22no—
554C22—22no—
555C22—22no—
556C22—48no—
557C22—48no—
558C22—44no—
559C22—442no—
560C22—442no—
561C22—442no—
562C22—884no—
563C22C2×#6686914yes—
564C22C2×#6686912yes—
565C22C2×#6687012yes—
566C22#1062261512yes—
567C22#1062261512yes—
568C22C22×(C2×D11)⋊C411yescharacteristic
569C22C2×#6700312yes—
570C4—21no—
571C4—21no—
572C4—21no—
573C4—22no—
574C4—21no—
575C4—48no—
576C4—442no—
577C4—442no—
578C4—442no—
579C4C2×#6687014yes—
580C2—22no—
581C2—24no—
582C2—22no—
583C2—42no—
584C2—882no—
585C2#1306710514yesdirect product factor
586C2C22×#6687011yescharacteristic
587C2C2×#1062261511yescharacteristic
588C2C22×#6686911yescharacteristic
subgroupG/H
centerC22×C4(C2×D11)⋊C4
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C4×C11×C22⋊C4C2
socleC23×C11C2×C22⋊C4
prime radicalC2×#10623322C2
cosocleC22×C4×C11C24
hypercenterC2×C4×C22⋊C4D11
hypocenterC11C2×#1501
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C24×C4 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×C22⋊(C11⋊C8)C2semidirect
3. #13067105C2direct (N × H)
4. C2×#10622090C2semidirect
5. C2×#10622089C2semidirect
6. C2×C4×C11×C22⋊C4C2semidirect
8. C22×#4339C4semidirect
14. #10623322C4semidirect
16. C2×#66983C4semidirect
21. C2×#66979C4semidirect
22. C2×#66977C4semidirect
26. C4×C11×C22⋊C4C22semidirect
31. C2×C22⋊(C11⋊C8)C22semidirect
32. #10622090C22semidirect
33. #10622089C22semidirect
52. C2×#4339C2×C4semidirect
69. #66983C2×C4semidirect
80. #66979C2×C4semidirect
87. #66977C2×C4semidirect
184. C2×C4×C22⋊C4D11semidirect
280. C4×C22⋊C4C2×D11semidirect
389. C2×C11#1501semidirect
475. C11C2×#1501semidirect
585. C2#13067105direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106233222
C22×C22⋊(C11⋊C8)2
#130671052
C2×#106220902
C2×#106220892
C2×C4×C11×C22⋊C42
C2×#150111