Finite Group Databasebeta

← C2×#13067118 #14720911

Subgroups — C2×#13067118 #14720911

Order 2816.

1834 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623322C211yesmaximal, characteristic
2C2×#10622820C211yesmaximal, characteristic, complemented
3#13067118C218yesmaximal, direct product factor
4C2×#10622090C212yesmaximal, complemented
5C2×#10622089C212yesmaximal, complemented
6C22×C11×#95C211yesmaximal, characteristic, complemented
7C24×C4×C11—21no—
8C24×C4×C11C2211yescharacteristic
9C22×#4339C411yescharacteristic, complemented
10C2×#67006—21no—
11#10623322—22no—
12#10623322—22no—
13#10623322C414yescomplemented
14#10623322C2214yes—
15C2×#66983C411yescharacteristic, complemented
16C2×#66983C2211yescharacteristic
17C2×#66982—21no—
18C2×C4×C22⋊D11—21no—
19C2×C4×C22⋊D11—21no—
20C2×#66979C411yescharacteristic, complemented
21C2×#66977C411yescharacteristic, complemented
22C2×#66977C2211yescharacteristic
23C22×#4318—21no—
24C2×C11×#95—22no—
25C2×C11×#95—21no—
26C2×C11×#95C2212yes—
27C2×C11×#95C2214yescomplemented
28#10622820—22no—
29#10622820C2214yescomplemented
30C2×C22⋊(C11⋊C8)—21no—
31C2×C22⋊(C11⋊C8)C2212yes—
32#10622090C2218yescomplemented
33#10622089C2218yescomplemented
34C25×C11D411yescharacteristic
35C23×C4×C11—28no—
36C23×C4×C11—22no—
37C23×C4×C11—24no—
38C23×C4×C11—44no—
39C23×C4×C11—44no—
40C23×C4×C11—44no—
41C23×C4×C11C2×C411yescharacteristic
42C23×C4×C11C2×C411yescharacteristic
43C23×C4×C11C2×C412yes—
44C23×C4×C11D411yescharacteristic
45C23×C4×C11D411yescharacteristic
46C23×C4×C11D412yes—
47C23×C4×C11D411yescharacteristic
48C23×C4×C11D412yes—
49C23×C4×C11C2311yescharacteristic
50C23×C4×C11C2312yes—
51C22×C22⋊D11—21no—
52C22×C22⋊D11—21no—
53C22×C22⋊D11—21no—
54C2×#4339—22no—
55C2×#4339—44no—
56C2×#4339C2×C414yescomplemented
57C22×D44C2×C411yescharacteristic, complemented
58C22×C4×D11—21no—
59C22×Dic22C2×C411yescharacteristic, complemented
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×C414yescomplemented
69#66983C2×C412yescomplemented
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, complemented
82C2×C4⋊Dic11C2×C411yescharacteristic, complemented
83#66977—22no—
84#66977—21no—
85#66977—21no—
86#66977C2×C414yescomplemented
87#66977C2×C412yescomplemented
88#66977C2312yes—
89C2×Dic11⋊C4—21no—
90C2×Dic11⋊C4—21no—
91C2×C4×Dic11—21no—
92C2×#4318—24no—
93C2×#4318—44no—
94C22×C11⋊C8—22no—
95C11×#95—22no—
96C11×#95—24no—
97C11×#95C2314yes—
98C22⋊(C11⋊C8)—24no—
99C22⋊(C11⋊C8)—22no—
100C22⋊(C11⋊C8)C2314yes—
101C2×#1504—111nomaximal, Sylow
102C24×C11—24no—
103C24×C11—24no—
104C24×C11—22no—
105C24×C11—22no—
106C24×C11C22⋊C412yes—
107C24×C11C22⋊C411yescharacteristic
108C24×C11C22⋊C411yescharacteristic
109C24×C11C2×D412yes—
110C24×C11C2×D411yescharacteristic
111C23×D11—21no—
112C22×C4×C11—24no—
113C22×C4×C11—24no—
114C22×C4×C11—28no—
115C22×C4×C11—216no—
116C22×C4×C11—24no—
117C22×C4×C11—42no—
118C22×C4×C11—44no—
119C22×C4×C11—42no—
120C22×C4×C11—44no—
121C22×C4×C11—42no—
122C22×C4×C11—44no—
123C22×C4×C11—42no—
124C22×C4×C11—44no—
125C22×C4×C11—432no—
126C22×C4×C11—44no—
127C22×C4×C11—48no—
128C22×C4×C11—48no—
129C22×C4×C11—44no—
130C22×C4×C11C22⋊C411yescharacteristic
131C22×C4×C11C22⋊C411yescharacteristic
132C22×C4×C11C22⋊C412yes—
133C22×C4×C11C22⋊C412yes—
134C22×C4×C11C22⋊C412yes—
135C22×C4×C11C22⋊C412yes—
136C22×C4×C11C22⋊C412yes—
137C22×C4×C11C22×C411yescharacteristic
138C22×C4×C11C22×C412yes—
139C22×C4×C11C22×C411yescharacteristic
140C22×C4×C11C22×C412yes—
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D412yes—
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D412yes—
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D412yes—
147C22×C4×C11C2411yescharacteristic
148C2×C22⋊D11—22no—
149C2×C22⋊D11—24no—
150C2×C22⋊D11—24no—
151C2×C22⋊D11—22no—
152C2×C22⋊D11—44no—
153C2×C22⋊D11—44no—
154C2×C22⋊D11—42no—
155C2×C22⋊D11—42no—
156C22×Dic11—21no—
157C22×Dic11—21no—
158C22×Dic11—21no—
159#4339—48no—
160#4339—48no—
161C2×D44—21no—
162C2×D44—42no—
163C2×D44C22×C412yescomplemented
164C2×C4×D11—24no—
165C2×C4×D11—44no—
166C2×Dic22—21no—
167C2×Dic22—42no—
168C2×Dic22C22×C412yescomplemented
169C22⋊Dic11—22no—
170C22⋊Dic11—24no—
171C22⋊Dic11—24no—
172C22⋊Dic11—22no—
173(C2×D11)⋊C4—24no—
174(C2×D11)⋊C4—22no—
175(C2×D11)⋊C4—22no—
176C4⋊Dic11—21no—
177C4⋊Dic11—21no—
178C4⋊Dic11C22×C412yescomplemented
179C4⋊Dic11C22×C412yescomplemented
180Dic11⋊C4—24no—
181Dic11⋊C4—22no—
182Dic11⋊C4—22no—
183C4×Dic11—24no—
184#4318—48no—
185C2×C11⋊C8—24no—
186C2×C11⋊C8—44no—
187C2×#525—111no—
188C2×#407—111no—
189C22×#95D1111yescharacteristic, complemented
190#1504—118no—
191C2×#328—112no—
192C2×#327—112no—
193C23×C11—216no—
194C23×C11—216no—
195C23×C11—22no—
196C23×C11—22no—
197C23×C11—24no—
198C23×C11—22no—
199C23×C11—24no—
200C23×C11—22no—
201C23×C11—24no—
202C23×C11—22no—
203C23×C11—22no—
204C23×C11—24no—
205C23×C11—22no—
206C23×C11—24no—
207C23×C11—22no—
208C23×C11#9914yes—
209C23×C11#10414yes—
210C23×C11C2×C22⋊C412yes—
211C23×C11C2×C22⋊C411yescharacteristic
212C23×C11C2×C22⋊C412yes—
213C23×C11C2×C22⋊C411yescharacteristic
214C23×C11AGL(1,ℤ/8)12yes—
215C23×C11#13712yes—
216C23×C11C22×D411yescharacteristic
217C22×D11—22no—
218C22×D11—42no—
219C22×D11—42no—
220C22×D11—42no—
221C2×C4×C11—22no—
222C2×C4×C11—24no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—24no—
226C2×C4×C11—24no—
227C2×C4×C11—24no—
228C2×C4×C11—22no—
229C2×C4×C11—28no—
230C2×C4×C11—42no—
231C2×C4×C11—42no—
232C2×C4×C11—42no—
233C2×C4×C11—41no—
234C2×C4×C11—42no—
235C2×C4×C11—41no—
236C2×C4×C11—42no—
237C2×C4×C11—41no—
238C2×C4×C11—42no—
239C2×C4×C11—41no—
240C2×C4×C11—432no—
241C2×C4×C11—44no—
242C2×C4×C11—416no—
243C2×C4×C11—44no—
244C2×C4×C11C2×C22⋊C412yes—
245C2×C4×C11C2×C22⋊C412yes—
246C2×C4×C11C2×C22⋊C411yescharacteristic
247C2×C4×C11C2×C22⋊C411yescharacteristic
248C2×C4×C11C23×C411yescharacteristic
249C2×C4×C11C22×D411yescharacteristic
250C22⋊D11—42no—
251C22⋊D11—42no—
252C22⋊D11—48no—
253C22⋊D11—44no—
254C22⋊D11—48no—
255C2×Dic11—22no—
256C2×Dic11—22no—
257C2×Dic11—22no—
258C2×Dic11—42no—
259C2×Dic11—42no—
260C2×Dic11—42no—
261D44—42no—
262D44—42no—
263C4×D11—48no—
264Dic22—42no—
265Dic22—42no—
266C11⋊C8—44no—
267C22×#41—111no—
268C24×C4—21no—
269C24×C4C2×D1111yescharacteristic
270C22×M16—221no—
271#525—114no—
272#525—114no—
273#525—222no—
274#525—222no—
275C2×#123—221no—
276C2×C22⋊Q8—111no—
277C2×C22⋊Q8—111no—
278C2×#121—111no—
279C2×#121—111no—
280C2×#120—221no—
281C2×C4×D4—221no—
282C2×C4×D4—221no—
283C2×#117—111no—
284#407—114no—
285#407—222no—
286C2×C22⋊C8—112no—
287C2×C22⋊C8—221no—
288C2×#95—22no—
289C2×#95—21no—
290C2×#95C2×D1112yes—
291C2×#95C2×D1114yescomplemented
292#328—118no—
293#327—118no—
294C22×C11—28no—
295C22×C11—28no—
296C22×C11—216no—
297C22×C11—21no—
298C22×C11—21no—
299C22×C11—22no—
300C22×C11—22no—
301C22×C11—22no—
302C22×C11—21no—
303C22×C11—22no—
304C22×C11—21no—
305C22×C11—24no—
306C22×C11—28no—
307C22×C11—28no—
308C22×C11—24no—
309C22×C11C2×#9914yes—
310C22×C11C2×#9912yes—
311C22×C11#41712yes—
312C22×C11#41712yes—
313C22×C11C2×#10414yes—
314C22×C11C2×#10412yes—
315C22×C11C22×C22⋊C411yescharacteristic
316C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
317C22×C11C2×#13711yescharacteristic
318C2×D11—42no—
319C2×D11—42no—
320C2×D11—42no—
321C2×D11—84no—
322C4×C11—21no—
323C4×C11—22no—
324C4×C11—21no—
325C4×C11—22no—
326C4×C11—21no—
327C4×C11—21no—
328C4×C11—48no—
329Dic11—42no—
330Dic11—42no—
331Dic11—42no—
332C25C22⋊D1111yescharacteristic
333C2×#41—114no—
334C2×#41—222no—
335C2×#41—444no—
336C22×Q8—111no—
337C22×D4—111no—
338C22×D4—221no—
339C22×D4—221no—
340C22×D4—221no—
341C23×C4—28no—
342C23×C4—22no—
343C23×C4—24no—
344C23×C4—44no—
345C23×C4—44no—
346C23×C4—44no—
347C23×C4—221no—
348C23×C4C4×D1111yescharacteristic
349C23×C4C4×D1111yescharacteristic
350C23×C4C4×D1112yes—
351C23×C4D4411yescharacteristic
352C23×C4D4411yescharacteristic
353C23×C4D4412yes—
354C23×C4C22⋊D1111yescharacteristic
355C23×C4C22⋊D1112yes—
356C23×C4C22×D1111yescharacteristic
357C23×C4C22×D1112yes—
358C2×M16—224no—
359C2×M16—444no—
360C22×C8—222no—
361#123—224no—
362#123—224no—
363C22⋊Q8—112no—
364C22⋊Q8—114no—
365C22⋊Q8—112no—
366C22⋊Q8—222no—
367C22⋊Q8—221no—
368C22⋊Q8—221no—
369#121—112no—
370#121—114no—
371#121—112no—
372#121—222no—
373#121—221no—
374#121—221no—
375#120—224no—
376#120—224no—
377C4×D4—224no—
378C4×D4—224no—
379C4×D4—224no—
380C4×D4—224no—
381#117—114no—
382#117—222no—
383C2×C4⋊C4—111no—
384C2×C4⋊C4—111no—
385C2×C4⋊C4—221no—
386C2×C4⋊C4—221no—
387C2×C22⋊C4—221no—
388C2×C22⋊C4—221no—
389C2×C22⋊C4—221no—
390C2×C22⋊C4—221no—
391C2×C22⋊C4—221no—
392C2×C42—221no—
393C22⋊C8—114no—
394C22⋊C8—222no—
395C22⋊C8—224no—
396#95—22no—
397#95—24no—
398#95C22×D1114yes—
399C2×C11—21no—
400C2×C11—21no—
401C2×C11—24no—
402C2×C11—22no—
403C2×C11—24no—
404C2×C11#150414yescomplemented
405C2×C11C22×#9911yescharacteristic
406C2×C11C2×#41711yescharacteristic
407C2×C11C22×#10411yescharacteristic
408D11—82no—
409C24—24no—
410C24—24no—
411C24—22no—
412C24—22no—
413C24—221no—
414C24(C2×D11)⋊C412yes—
415C24(C2×D11)⋊C411yescharacteristic
416C24(C2×D11)⋊C411yescharacteristic
417C24C2×C22⋊D1112yes—
418C24C2×C22⋊D1111yescharacteristic
419#41—448no—
420#41—448no—
421C2×Q8—112no—
422C2×Q8—221no—
423C2×Q8—442no—
424C2×D4—112no—
425C2×D4—224no—
426C2×D4—222no—
427C2×D4—224no—
428C2×D4—222no—
429C2×D4—221no—
430C2×D4—442no—
431C2×D4—444no—
432C2×D4—444no—
433C2×D4—442no—
434C2×D4—442no—
435C22×C4—24no—
436C22×C4—24no—
437C22×C4—28no—
438C22×C4—216no—
439C22×C4—24no—
440C22×C4—42no—
441C22×C4—44no—
442C22×C4—42no—
443C22×C4—44no—
444C22×C4—42no—
445C22×C4—44no—
446C22×C4—42no—
447C22×C4—44no—
448C22×C4—432no—
449C22×C4—44no—
450C22×C4—48no—
451C22×C4—48no—
452C22×C4—44no—
453C22×C4—221no—
454C22×C4—221no—
455C22×C4—221no—
456C22×C4—224no—
457C22×C4—444no—
458C22×C4(C2×D11)⋊C412yes—
459C22×C4(C2×D11)⋊C412yes—
460C22×C4(C2×D11)⋊C411yescharacteristic
461C22×C4(C2×D11)⋊C411yescharacteristic
462C22×C4(C2×D11)⋊C412yes—
463C22×C4(C2×D11)⋊C412yes—
464C22×C4(C2×D11)⋊C412yes—
465C22×C4C2×C4×D1112yes—
466C22×C4C2×C4×D1111yescharacteristic
467C22×C4C2×C4×D1112yes—
468C22×C4C2×C4×D1111yescharacteristic
469C22×C4C2×D4412yes—
470C22×C4C2×D4411yescharacteristic
471C22×C4C2×D4412yes—
472C22×C4C2×D4411yescharacteristic
473C22×C4C2×C22⋊D1112yes—
474C22×C4C2×C22⋊D1111yescharacteristic
475C22×C4C23×D1111yescharacteristic
476M16—448no—
477C2×C8—224no—
478C2×C8—444no—
479C4⋊C4—112no—
480C4⋊C4—112no—
481C4⋊C4—221no—
482C4⋊C4—221no—
483C4⋊C4—224no—
484C4⋊C4—222no—
485C4⋊C4—222no—
486C22⋊C4—224no—
487C22⋊C4—224no—
488C22⋊C4—222no—
489C22⋊C4—222no—
490C22⋊C4—224no—
491C22⋊C4—222no—
492C22⋊C4—222no—
493C42—224no—
494C11C2×#150411yescharacteristic, complemented, Sylow
495C23—216no—
496C23—216no—
497C23—24no—
498C23—22no—
499C23—24no—
500C23—22no—
501C23—22no—
502C23—24no—
503C23—22no—
504C23—24no—
505C23—22no—
506C23—22no—
507C23—24no—
508C23—22no—
509C23—22no—
510C23—222no—
511C23—442no—
512C23—442no—
513C23—442no—
514C23#6686914yes—
515C23#6687014yes—
516C23C2×(C2×D11)⋊C412yes—
517C23C2×(C2×D11)⋊C412yes—
518C23C2×(C2×D11)⋊C411yescharacteristic
519C23C2×(C2×D11)⋊C411yescharacteristic
520C23#6698512yes—
521C23#6699512yes—
522C23C22×C22⋊D1111yescharacteristic
523Q8—442no—
524Q8—442no—
525D4—442no—
526D4—442no—
527D4—448no—
528D4—442no—
529D4—448no—
530D4—442no—
531D4—444no—
532C2×C4—22no—
533C2×C4—24no—
534C2×C4—22no—
535C2×C4—24no—
536C2×C4—22no—
537C2×C4—24no—
538C2×C4—22no—
539C2×C4—24no—
540C2×C4—28no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—41no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—41no—
548C2×C4—42no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—432no—
552C2×C4—44no—
553C2×C4—416no—
554C2×C4—44no—
555C2×C4—222no—
556C2×C4—222no—
557C2×C4—222no—
558C2×C4—448no—
559C2×C4—442no—
560C2×C4—442no—
561C2×C4—442no—
562C2×C4C2×(C2×D11)⋊C412yes—
563C2×C4C2×(C2×D11)⋊C411yescharacteristic
564C2×C4C2×(C2×D11)⋊C412yes—
565C2×C4C2×(C2×D11)⋊C411yescharacteristic
566C2×C4C22×C4×D1111yescharacteristic
567C2×C4C22×D4411yescharacteristic
568C8—444no—
569C22—28no—
570C22—28no—
571C22—216no—
572C22—21no—
573C22—22no—
574C22—21no—
575C22—24no—
576C22—28no—
577C22—28no—
578C22—24no—
579C22—22no—
580C22—22no—
581C22—21no—
582C22—22no—
583C22—21no—
584C22—442no—
585C22—442no—
586C22—442no—
587C22—884no—
588C22C2×#6686914yes—
589C22C2×#6686912yes—
590C22C2×#6687014yes—
591C22C2×#6687012yes—
592C22#1062257912yes—
593C22#1062257912yes—
594C22C22×(C2×D11)⋊C411yescharacteristic
595C22C2×#6698511yescharacteristic
596C22C2×#6699511yescharacteristic
597C4—21no—
598C4—22no—
599C4—21no—
600C4—21no—
601C4—22no—
602C4—21no—
603C4—48no—
604C4—442no—
605C4—442no—
606C4—442no—
607C2—21no—
608C2—24no—
609C2—24no—
610C2—21no—
611C2—22no—
612C2—882no—
613C2#1306711814yesdirect product factor
614C2C22×#6687011yescharacteristic
615C2C2×#1062257911yescharacteristic
616C2C22×#6686911yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC22×C11×#95C2
socleC23×C11C2×C22⋊C4
prime radicalC2×#10623322C2
cosocleC22×C4×C11C24
hypercenterC22×#95D11
hypocenterC11C2×#1504
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C24×C4 ◁ C22×#95

Complements

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

NH ≅ G/Ntype
2. C2×#10622820C2semidirect
3. #13067118C2direct (N × H)
4. C2×#10622090C2semidirect
5. C2×#10622089C2semidirect
6. C22×C11×#95C2semidirect
9. C22×#4339C4semidirect
13. #10623322C4semidirect
15. C2×#66983C4semidirect
20. C2×#66979C4semidirect
21. C2×#66977C4semidirect
27. C2×C11×#95C22semidirect
29. #10622820C22semidirect
32. #10622090C22semidirect
33. #10622089C22semidirect
56. C2×#4339C2×C4semidirect
57. C22×D44C2×C4semidirect
59. C22×Dic22C2×C4semidirect
68. #66983C2×C4semidirect
69. #66983C2×C4semidirect
80. #66979C2×C4semidirect
81. C2×C4⋊Dic11C2×C4semidirect
82. C2×C4⋊Dic11C2×C4semidirect
86. #66977C2×C4semidirect
87. #66977C2×C4semidirect
163. C2×D44C22×C4semidirect
168. C2×Dic22C22×C4semidirect
178. C4⋊Dic11C22×C4semidirect
179. C4⋊Dic11C22×C4semidirect
189. C22×#95D11semidirect
291. C2×#95C2×D11semidirect
404. C2×C11#1504semidirect
494. C11C2×#1504semidirect
613. C2#13067118direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106233222
C2×#106228202
#130671182
C2×#106220902
C2×#106220892
C22×C11×#952
C2×#150411