Finite Group Databasebeta

← C2×#13067107 #14720867

Subgroups — C2×#13067107 #14720867

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
1C22×C22⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
2C2×C4×C22⋊Dic11C211yesmaximal, characteristic, complemented
3#13067107C218yesmaximal, direct product factor
4C2×#10622176C212yesmaximal, complemented
5C2×#10622175C212yesmaximal, complemented
6C2×C11×#525C211yesmaximal, characteristic
7C22×C11×#41C411yescharacteristic, complemented
8C24×C4×C11C2211yescharacteristic
9C11×#525—22no—
10C11×#525—22no—
11C11×#525C414yescomplemented
12C11×#525C2214yes—
13C2×C11×#123—21no—
14C2×C11×C22⋊Q8C411yescharacteristic, complemented
15C2×C11×C22⋊Q8C2211yescharacteristic
16C2×C11×#121C411yescharacteristic, complemented
17C2×C11×#121C2211yescharacteristic
18C2×C11×#120—21no—
19C2×C4×D4×C11—21no—
20C2×C4×D4×C11—21no—
21C2×C11×#117C411yescharacteristic, complemented
22C22×C22⋊Dic11—21no—
23C22×C4×Dic11—21no—
24C23×C11⋊C8—21no—
25C4×C22⋊Dic11—22no—
26C4×C22⋊Dic11C2214yescomplemented
27C2×C11⋊#95C2212yes—
28C2×C22⋊(C11⋊C8)—22no—
29C2×C22⋊(C11⋊C8)—21no—
30C2×C22⋊(C11⋊C8)C2212yes—
31C2×C22⋊(C11⋊C8)C2214yescomplemented
32#10622176C2218yescomplemented
33#10622175C2218yescomplemented
34C25×C11D411yescharacteristic
35C2×C11×#41—22no—
36C2×C11×#41—44no—
37C2×C11×#41C2×C414yescomplemented
38C22×Q8×C11C2×C411yescharacteristic
39C22×D4×C11—21no—
40C22×D4×C11—21no—
41C22×D4×C11—21no—
42C22×D4×C11C2×C411yescharacteristic
43C23×C4×C11—21no—
44C23×C4×C11—44no—
45C23×C4×C11C2×C411yescharacteristic
46C23×C4×C11C2×C411yescharacteristic
47C23×C4×C11C2×C412yes—
48C23×C4×C11D411yescharacteristic
49C23×C4×C11D411yescharacteristic
50C23×C4×C11D412yes—
51C23×C4×C11D411yescharacteristic
52C23×C4×C11D412yes—
53C23×C4×C11C2311yescharacteristic
54C23×C4×C11C2312yes—
55C23×Dic11—22no—
56C11×#123—24no—
57C11×#123—24no—
58C11×C22⋊Q8—22no—
59C11×C22⋊Q8—21no—
60C11×C22⋊Q8—21no—
61C11×C22⋊Q8C2×C412yes—
62C11×C22⋊Q8C2×C414yescomplemented
63C11×C22⋊Q8C2312yes—
64C11×#121—22no—
65C11×#121—21no—
66C11×#121—21no—
67C11×#121C2×C412yes—
68C11×#121C2×C414yescomplemented
69C11×#121C2312yes—
70C11×#120—24no—
71C11×#120—24no—
72C4×D4×C11—24no—
73C4×D4×C11—24no—
74C4×D4×C11—24no—
75C4×D4×C11—24no—
76C11×#117—22no—
77C11×#117C2×C414yescomplemented
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4C2×C411yescharacteristic
81C2×C11×C4⋊C4C2×C411yescharacteristic
82C2×C11×C22⋊C4—21no—
83C2×C11×C22⋊C4—21no—
84C2×C11×C22⋊C4—21no—
85C2×C11×C22⋊C4—21no—
86C2×C11×C22⋊C4—21no—
87C2×C42×C11—21no—
88C2×C22⋊Dic11—28no—
89C2×C22⋊Dic11—24no—
90C2×C4×Dic11—24no—
91C2×C4×Dic11—44no—
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—21no—
104C24×C11—42no—
105C24×C11C22⋊C411yescharacteristic
106C24×C11C22⋊C412yes—
107C24×C11C22⋊C411yescharacteristic
108C24×C11C2×D412yes—
109C24×C11C2×D411yescharacteristic
110C11×#41—48no—
111C11×#41—48no—
112C2×Q8×C11—21no—
113C2×Q8×C11—42no—
114C2×Q8×C11C22×C412yes—
115C2×D4×C11—22no—
116C2×D4×C11—24no—
117C2×D4×C11—24no—
118C2×D4×C11—22no—
119C2×D4×C11—21no—
120C2×D4×C11—42no—
121C2×D4×C11—44no—
122C2×D4×C11—44no—
123C2×D4×C11—44no—
124C2×D4×C11C22×C412yes—
125C22×C4×C11—24no—
126C22×C4×C11—24no—
127C22×C4×C11—24no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—24no—
132C22×C4×C11—44no—
133C22×C4×C11—44no—
134C22×C4×C11—44no—
135C22×C4×C11—44no—
136C22×C4×C11—42no—
137C22×C4×C11—42no—
138C22×C4×C11—42no—
139C22×C4×C11—44no—
140C22×C4×C11C22⋊C411yescharacteristic
141C22×C4×C11C22⋊C412yes—
142C22×C4×C11C22⋊C412yes—
143C22×C4×C11C22⋊C412yes—
144C22×C4×C11C22⋊C412yes—
145C22×C4×C11C22⋊C412yes—
146C22×C4×C11C22⋊C411yescharacteristic
147C22×C4×C11C22×C411yescharacteristic
148C22×C4×C11C22×C412yes—
149C22×C4×C11C22×C411yescharacteristic
150C22×C4×C11C22×C412yes—
151C22×C4×C11C2×D412yes—
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D412yes—
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D412yes—
157C22×C4×C11C2411yescharacteristic
158C22×Dic11—28no—
159C22×Dic11—24no—
160C22×Dic11—44no—
161C22×Dic11—44no—
162C11×C4⋊C4—22no—
163C11×C4⋊C4—24no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—22no—
167C11×C4⋊C4C22×C412yes—
168C11×C4⋊C4C22×C412yes—
169C11×C22⋊C4—24no—
170C11×C22⋊C4—22no—
171C11×C22⋊C4—24no—
172C11×C22⋊C4—22no—
173C11×C22⋊C4—22no—
174C11×C22⋊C4—24no—
175C11×C22⋊C4—22no—
176C42×C11—24no—
177C22⋊Dic11—216no—
178C4×Dic11—48no—
179C2×C11⋊C8—24no—
180C2×C11⋊C8—44no—
181C2×C11⋊C8—48no—
182C2×#525D1111yescharacteristic
183C22×C22⋊C8—111no—
184C2×C4×C22⋊C4—111no—
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—22no—
200C23×C11—42no—
201C23×C11—42no—
202C23×C11—416no—
203C23×C11—42no—
204C23×C11—42no—
205C23×C11—42no—
206C23×C11#10414yes—
207C23×C11C2×C22⋊C412yes—
208C23×C11C2×C22⋊C411yescharacteristic
209C23×C11C2×C22⋊C412yes—
210C23×C11C2×C22⋊C411yescharacteristic
211C23×C11#13514yes—
212C23×C11C22×D411yescharacteristic
213Q8×C11—42no—
214Q8×C11—42no—
215D4×C11—42no—
216D4×C11—42no—
217D4×C11—48no—
218D4×C11—44no—
219D4×C11—44no—
220D4×C11—48no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—24no—
225C2×C4×C11—24no—
226C2×C4×C11—24no—
227C2×C4×C11—24no—
228C2×C4×C11—24no—
229C2×C4×C11—24no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—42no—
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—41no—
241C2×C4×C11—42no—
242C2×C4×C11—42no—
243C2×C4×C11—42no—
244C2×C4×C11—48no—
245C2×C4×C11#9914yes—
246C2×C4×C11C2×C22⋊C411yescharacteristic
247C2×C4×C11C2×C22⋊C412yes—
248C2×C4×C11C2×C22⋊C411yescharacteristic
249C2×C4×C11C2×C22⋊C412yes—
250C2×C4×C11C23×C411yescharacteristic
251C2×C4×C11C22×D411yescharacteristic
252C2×Dic11—28no—
253C2×Dic11—44no—
254C2×Dic11—416no—
255C2×Dic11—44no—
256C11⋊C8—44no—
257C22×#41Dic1111yescharacteristic, complemented
258C24×C4C2×D1111yescharacteristic
259C23×C8—221no—
260#525—22no—
261#525—22no—
262#525Dic1114yescomplemented
263#525C2×D1114yes—
264C2×#123—21no—
265C2×C22⋊Q8Dic1111yescharacteristic, complemented
266C2×C22⋊Q8C2×D1111yescharacteristic
267C2×#121Dic1111yescharacteristic, complemented
268C2×#121C2×D1111yescharacteristic
269C2×#120—21no—
270C2×C4×D4—21no—
271C2×C4×D4—21no—
272C2×#117Dic1111yescharacteristic, complemented
273C22×C22⋊C4—221no—
274C22×C42—221no—
275C2×C22⋊C8—112no—
276C2×C22⋊C8—114no—
277C2×C22⋊C8—221no—
278C2×C22⋊C8—222no—
279C4×C22⋊C4—114no—
280C4×C22⋊C4—222no—
281C2×#95—112no—
282#328—118no—
283#327—118no—
284C22×C11—21no—
285C22×C11—22no—
286C22×C11—21no—
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×C11—42no—
299C22×C11—42no—
300C22×C11—42no—
301C22×C11—84no—
302C22×C11C2×#9912yes—
303C22×C11#41612yes—
304C22×C11#41612yes—
305C22×C11C2×#10414yes—
306C22×C11C2×#10412yes—
307C22×C11C22×C22⋊C411yescharacteristic
308C22×C11C2×#13512yes—
309C4×C11—21no—
310C4×C11—22no—
311C4×C11—21no—
312C4×C11—21no—
313C4×C11—21no—
314C4×C11—42no—
315C4×C11—42no—
316C4×C11—42no—
317C4×C11C2×#9914yes—
318Dic11—48no—
319C25C22⋊D1111yescharacteristic
320C2×#41—22no—
321C2×#41—44no—
322C2×#41C2×Dic1114yescomplemented
323C22×Q8C2×Dic1111yescharacteristic
324C22×D4—21no—
325C22×D4—21no—
326C22×D4—21no—
327C22×D4C2×Dic1111yescharacteristic
328C23×C4—21no—
329C23×C4—44no—
330C23×C4—222no—
331C23×C4C2×Dic1111yescharacteristic
332C23×C4C2×Dic1111yescharacteristic
333C23×C4C2×Dic1112yes—
334C23×C4C22⋊D1111yescharacteristic
335C23×C4C22⋊D1111yescharacteristic
336C23×C4C22⋊D1112yes—
337C23×C4C22⋊D1111yescharacteristic
338C23×C4C22⋊D1112yes—
339C23×C4C22×D1111yescharacteristic
340C23×C4C22×D1112yes—
341C22×C8—222no—
342C22×C8—224no—
343C22×C8—444no—
344#123—24no—
345#123—24no—
346C22⋊Q8—22no—
347C22⋊Q8—21no—
348C22⋊Q8—21no—
349C22⋊Q8C2×Dic1112yes—
350C22⋊Q8C2×Dic1114yescomplemented
351C22⋊Q8C22×D1112yes—
352#121—22no—
353#121—21no—
354#121—21no—
355#121C2×Dic1112yes—
356#121C2×Dic1114yescomplemented
357#121C22×D1112yes—
358#120—24no—
359#120—24no—
360C4×D4—24no—
361C4×D4—24no—
362C4×D4—24no—
363C4×D4—24no—
364#117—22no—
365#117C2×Dic1114yescomplemented
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4C2×Dic1111yescharacteristic
369C2×C4⋊C4C2×Dic1111yescharacteristic
370C2×C22⋊C4—21no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—228no—
376C2×C22⋊C4—224no—
377C2×C42—21no—
378C2×C42—224no—
379C2×C42—444no—
380C22⋊C8—114no—
381C22⋊C8—222no—
382C22⋊C8—224no—
383#95—114no—
384#95—222no—
385C2×C11—22no—
386C2×C11—22no—
387C2×C11—24no—
388C2×C11—42no—
389C2×C11—82no—
390C2×C11#150114yescomplemented
391C2×C11C22×#9911yescharacteristic
392C2×C11C2×#41611yescharacteristic
393C2×C11C22×#10411yescharacteristic
394C24—24no—
395C24—24no—
396C24—21no—
397C24—42no—
398C24C22⋊Dic1111yescharacteristic
399C24C22⋊Dic1112yes—
400C24C22⋊Dic1111yescharacteristic
401C24C2×C22⋊D1112yes—
402C24C2×C22⋊D1111yescharacteristic
403#41—48no—
404#41—48no—
405C2×Q8—21no—
406C2×Q8—42no—
407C2×Q8C22×Dic1112yes—
408C2×D4—22no—
409C2×D4—24no—
410C2×D4—24no—
411C2×D4—22no—
412C2×D4—21no—
413C2×D4—42no—
414C2×D4—44no—
415C2×D4—44no—
416C2×D4—44no—
417C2×D4C22×Dic1112yes—
418C22×C4—24no—
419C22×C4—24no—
420C22×C4—24no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—24no—
425C22×C4—44no—
426C22×C4—44no—
427C22×C4—44no—
428C22×C4—44no—
429C22×C4—42no—
430C22×C4—42no—
431C22×C4—42no—
432C22×C4—44no—
433C22×C4—228no—
434C22×C4—224no—
435C22×C4—444no—
436C22×C4—444no—
437C22×C4C22⋊Dic1111yescharacteristic
438C22×C4C22⋊Dic1112yes—
439C22×C4C22⋊Dic1112yes—
440C22×C4C22⋊Dic1112yes—
441C22×C4C22⋊Dic1112yes—
442C22×C4C22⋊Dic1112yes—
443C22×C4C22⋊Dic1111yescharacteristic
444C22×C4C22×Dic1111yescharacteristic
445C22×C4C22×Dic1112yes—
446C22×C4C22×Dic1111yescharacteristic
447C22×C4C22×Dic1112yes—
448C22×C4C2×C22⋊D1112yes—
449C22×C4C2×C22⋊D1111yescharacteristic
450C22×C4C2×C22⋊D1112yes—
451C22×C4C2×C22⋊D1111yescharacteristic
452C22×C4C2×C22⋊D1111yescharacteristic
453C22×C4C2×C22⋊D1112yes—
454C22×C4C23×D1111yescharacteristic
455C2×C8—224no—
456C2×C8—444no—
457C2×C8—448no—
458C4⋊C4—22no—
459C4⋊C4—24no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—22no—
463C4⋊C4C22×Dic1112yes—
464C4⋊C4C22×Dic1112yes—
465C22⋊C4—24no—
466C22⋊C4—22no—
467C22⋊C4—24no—
468C22⋊C4—22no—
469C22⋊C4—22no—
470C22⋊C4—24no—
471C22⋊C4—22no—
472C22⋊C4—2216no—
473C42—24no—
474C42—448no—
475C11C2×#150111yescharacteristic, complemented, Sylow
476C23—22no—
477C23—22no—
478C23—22no—
479C23—22no—
480C23—22no—
481C23—24no—
482C23—24no—
483C23—22no—
484C23—24no—
485C23—24no—
486C23—22no—
487C23—22no—
488C23—42no—
489C23—42no—
490C23—416no—
491C23—42no—
492C23—42no—
493C23—42no—
494C23#6690114yes—
495C23#6700314yes—
496C23C2×C22⋊Dic1112yes—
497C23C2×C22⋊Dic1111yescharacteristic
498C23C2×C22⋊Dic1112yes—
499C23C2×C22⋊Dic1111yescharacteristic
500C23C22×C22⋊D1111yescharacteristic
501Q8—42no—
502Q8—42no—
503D4—42no—
504D4—42no—
505D4—48no—
506D4—44no—
507D4—44no—
508D4—48no—
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—22no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—42no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—48no—
533C2×C4—228no—
534C2×C4—444no—
535C2×C4—4416no—
536C2×C4—444no—
537C2×C4#6689814yes—
538C2×C4C2×C22⋊Dic1111yescharacteristic
539C2×C4C2×C22⋊Dic1112yes—
540C2×C4C2×C22⋊Dic1111yescharacteristic
541C2×C4C2×C22⋊Dic1112yes—
542C2×C4C23×Dic1111yescharacteristic
543C2×C4C22×C22⋊D1111yescharacteristic
544C8—444no—
545C22—21no—
546C22—21no—
547C22—22no—
548C22—28no—
549C22—28no—
550C22—22no—
551C22—21no—
552C22—21no—
553C22—22no—
554C22—22no—
555C22—22no—
556C22—48no—
557C22—48no—
558C22—44no—
559C22—42no—
560C22—42no—
561C22—42no—
562C22—84no—
563C22C2×#6689812yes—
564C22#1062284612yes—
565C22#1062284612yes—
566C22C2×#6690114yes—
567C22C2×#6690112yes—
568C22C2×#6700312yes—
569C22C22×C22⋊Dic1111yescharacteristic
570C4—21no—
571C4—21no—
572C4—21no—
573C4—22no—
574C4—21no—
575C4—42no—
576C4—42no—
577C4—42no—
578C4—448no—
579C4C2×#6689814yes—
580C2—22no—
581C2—22no—
582C2—24no—
583C2—42no—
584C2—82no—
585C2#1306710714yesdirect product factor
586C2C22×#6689811yescharacteristic
587C2C2×#1062284611yescharacteristic
588C2C22×#6690111yescharacteristic
subgroupG/H
centerC22×C4C22⋊Dic11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×C11×#525C2
socleC23×C11C2×C22⋊C4
cosocleC22×C4×C11C24
hypercenterC2×#525D11
hypocenterC11C2×#1501
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C24×C4 ◁ C2×#525

Complements

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

NH ≅ G/Ntype
1. C22×C22⋊(C11⋊C8)C2semidirect
2. C2×C4×C22⋊Dic11C2semidirect
3. #13067107C2direct (N × H)
4. C2×#10622176C2semidirect
5. C2×#10622175C2semidirect
7. C22×C11×#41C4semidirect
11. C11×#525C4semidirect
14. C2×C11×C22⋊Q8C4semidirect
16. C2×C11×#121C4semidirect
21. C2×C11×#117C4semidirect
26. C4×C22⋊Dic11C22semidirect
31. C2×C22⋊(C11⋊C8)C22semidirect
32. #10622176C22semidirect
33. #10622175C22semidirect
37. C2×C11×#41C2×C4semidirect
62. C11×C22⋊Q8C2×C4semidirect
68. C11×#121C2×C4semidirect
77. C11×#117C2×C4semidirect
257. C22×#41Dic11semidirect
262. #525Dic11semidirect
265. C2×C22⋊Q8Dic11semidirect
267. C2×#121Dic11semidirect
272. C2×#117Dic11semidirect
322. C2×#41C2×Dic11semidirect
350. C22⋊Q8C2×Dic11semidirect
356. #121C2×Dic11semidirect
365. #117C2×Dic11semidirect
390. C2×C11#1501semidirect
475. C11C2×#1501semidirect
585. C2#13067107direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C22⋊(C11⋊C8)2
C2×C4×C22⋊Dic112
#130671072
C2×#106221762
C2×#106221752
C2×C11×#5252
C2×#150111