Finite Group Databasebeta

← C2×#13073085 #14922830

Subgroups — C2×#13073085 #14922830

Order 2816.

4222 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66939C211yesmaximal, characteristic, complemented
2C22×#66982C211yesmaximal, characteristic, complemented
3C22×#66988C211yesmaximal, characteristic, complemented
4C22×#66992C211yesmaximal, characteristic
5C23×Dic11⋊C4C211yesmaximal, characteristic, complemented
6#13073085C2116yesmaximal, direct product factor
7C2×#10622562C212yesmaximal, complemented
8C2×#10622605C212yesmaximal, complemented
9C2×#10622570C212yesmaximal, complemented
10C2×#10622589C212yesmaximal, complemented
11C2×C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
12C22×C11×#123C211yesmaximal, characteristic, complemented
13C23×D4×C11C2211yescharacteristic
14C24×C4×C11C2211yescharacteristic
15C23×C22⋊D11C2211yescharacteristic
16C23×C22⋊D11C2211yescharacteristic
17C24×Dic11C2211yescharacteristic
18C24×Dic11C2211yescharacteristic
19C2×C11×#123—28no—
20C2×C11×#123C2218yescomplemented
21C22×C11×C4⋊C4C2212yes—
22C22×C11×C22⋊C4C2212yes—
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C22⋊Dic11C2212yes—
25C22×C22⋊Dic11C2211yescharacteristic
26C22×C22⋊Dic11C2211yescharacteristic
27C2×#66992—28no—
28C2×#66992C2218yes—
29C2×#66988—28no—
30C2×#66988C2218yescomplemented
31C2×#66982—28no—
32C2×#66982C2218yescomplemented
33C22×(C2×D11)⋊C4C2212yes—
34C22×(C2×D11)⋊C4C2212yes—
35C22×(C2×D11)⋊C4C2211yescharacteristic
36C22×C4⋊Dic11C2212yes—
37C22×Dic11⋊C4—28no—
38C22×Dic11⋊C4C2211yescharacteristic
39C22×Dic11⋊C4C2212yes—
40C22×Dic11⋊C4C2212yes—
41C22×Dic11⋊C4C2212yes—
42C22×Dic11⋊C4C2212yes—
43C22×Dic11⋊C4C2218yescomplemented
44C22×C4×Dic11C2212yes—
45C2×#66939—28no—
46C2×#66939C2218yescomplemented
47C2×C11⋊#95C2212yes—
48#10622605C22116yescomplemented
49#10622589C22116yescomplemented
50#10622570C22116yescomplemented
51#10622562C22116yescomplemented
52C22⋊C4×Dic11C2218yescomplemented
53C25×C11C2311yescharacteristic
54C25×C11C2311yescharacteristic
55C24×D11C2311yescharacteristic
56C22×D4×C11—24no—
57C22×D4×C11—24no—
58C22×D4×C11—24no—
59C22×D4×C11C2314yes—
60C23×C4×C11—24no—
61C23×C4×C11—24no—
62C23×C4×C11—24no—
63C23×C4×C11C2312yes—
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2314yes—
66C23×C4×C11C2312yes—
67C22×C22⋊D11—24no—
68C22×C22⋊D11—24no—
69C22×C22⋊D11—24no—
70C22×C22⋊D11—24no—
71C22×C22⋊D11—28no—
72C22×C22⋊D11C2314yes—
73C22×C22⋊D11C2314yes—
74C23×Dic11—28no—
75C23×Dic11—24no—
76C23×Dic11—24no—
77C23×Dic11—24no—
78C23×Dic11D418yes—
79C23×Dic11C2314yes—
80C23×Dic11C2311yescharacteristic
81C23×Dic11C2312yes—
82C23×Dic11C2312yes—
83C23×Dic11C2311yescharacteristic
84C23×Dic11C2314yes—
85C23×Dic11C2311yescharacteristic
86C11×#123—232no—
87C2×C11×C4⋊C4—28no—
88C2×C11×C4⋊C4C2318yes—
89C2×C11×C22⋊C4—28no—
90C2×C11×C22⋊C4D418yescomplemented
91C2×C11×C22⋊C4C2318yes—
92C2×C11×C22⋊C4C2314yes—
93C2×C22⋊Dic11—28no—
94C2×C22⋊Dic11—24no—
95C2×C22⋊Dic11D418yescomplemented
96C2×C22⋊Dic11C2318yes—
97C2×C22⋊Dic11C2314yes—
98C2×C22⋊Dic11C2314yes—
99#66992—232no—
100#66988—232no—
101#66982—232no—
102C2×(C2×D11)⋊C4—28no—
103C2×(C2×D11)⋊C4—28no—
104C2×(C2×D11)⋊C4—24no—
105C2×(C2×D11)⋊C4C2318yes—
106C2×(C2×D11)⋊C4C2318yes—
107C2×(C2×D11)⋊C4C2314yes—
108C2×C4⋊Dic11—28no—
109C2×C4⋊Dic11C2318yes—
110C2×Dic11⋊C4—28no—
111C2×Dic11⋊C4—28no—
112C2×Dic11⋊C4—232no—
113C2×Dic11⋊C4—28no—
114C2×Dic11⋊C4—28no—
115C2×Dic11⋊C4—24no—
116C2×Dic11⋊C4C2318yes—
117C2×Dic11⋊C4C2318yes—
118C2×Dic11⋊C4C2318yes—
119C2×Dic11⋊C4C2318yes—
120C2×Dic11⋊C4C2314yes—
121C2×C4×Dic11—28no—
122C2×C4×Dic11C2318yes—
123#66939—232no—
124C11⋊#95C2318yes—
125C2×#2501—111nomaximal, Sylow
126C24×C11—24no—
127C24×C11—24no—
128C24×C11—22no—
129C24×C11—22no—
130C24×C11—22no—
131C24×C11—24no—
132C24×C11—24no—
133C24×C11C2×D414yes—
134C24×C11C2×D414yes—
135C24×C11C2×D414yes—
136C24×C11C2412yes—
137C24×C11C2412yes—
138C24×C11C2411yescharacteristic
139C23×D11—22no—
140C23×D11—22no—
141C23×D11—22no—
142C23×D11—24no—
143C23×D11—24no—
144C23×D11C2412yes—
145C2×D4×C11—28no—
146C2×D4×C11—28no—
147C2×D4×C11—28no—
148C2×D4×C11—416no—
149C22×C4×C11—24no—
150C22×C4×C11—24no—
151C22×C4×C11—28no—
152C22×C4×C11—24no—
153C22×C4×C11—22no—
154C22×C4×C11—24no—
155C22×C4×C11—22no—
156C22×C4×C11—28no—
157C22×C4×C11—24no—
158C22×C4×C11—22no—
159C22×C4×C11—28no—
160C22×C4×C11—416no—
161C22×C4×C11C2×D418yes—
162C22×C4×C11C2414yes—
163C22×C4×C11C2412yes—
164C22×C4×C11C2414yes—
165C2×C22⋊D11—28no—
166C2×C22⋊D11—216no—
167C2×C22⋊D11—28no—
168C2×C22⋊D11—28no—
169C2×C22⋊D11—28no—
170C2×C22⋊D11—416no—
171C2×C22⋊D11—416no—
172C22×Dic11—232no—
173C22×Dic11—216no—
174C22×Dic11—28no—
175C22×Dic11—28no—
176C22×Dic11—24no—
177C22×Dic11—22no—
178C22×Dic11—24no—
179C22×Dic11—22no—
180C22×Dic11—22no—
181C22×Dic11—24no—
182C22×Dic11—28no—
183C22×Dic11—24no—
184C22×Dic11—24no—
185C22×Dic11—24no—
186C22×Dic11—416no—
187C22×Dic11C2×D418yes—
188C22×Dic11C2×D414yes—
189C22×Dic11C2×D4116yes—
190C22×Dic11C2×D414yes—
191C22×Dic11#4118yes—
192C22×Dic11C2412yes—
193C22×Dic11C2414yes—
194C22×Dic11C2412yes—
195C22×Dic11C2414yes—
196C22×Dic11C2412yes—
197C11×C4⋊C4—216no—
198C11×C22⋊C4—216no—
199C11×C22⋊C4C2×D4116yescomplemented
200C22⋊Dic11—216no—
201C22⋊Dic11—28no—
202C22⋊Dic11C2×D4116yescomplemented
203(C2×D11)⋊C4—216no—
204(C2×D11)⋊C4—28no—
205(C2×D11)⋊C4—216no—
206C4⋊Dic11—216no—
207Dic11⋊C4—216no—
208Dic11⋊C4—216no—
209Dic11⋊C4—216no—
210Dic11⋊C4—216no—
211Dic11⋊C4—28no—
212C4×Dic11—216no—
213C22×#123—111no—
214C22×#123—111no—
215C22×#123—111no—
216C22×#123D1111yescharacteristic, complemented
217C22×#121—111no—
218C23×C4⋊C4—111no—
219#2501—1116no—
220C2×#399—112no—
221C2×#399—112no—
222C2×#390—112no—
223C2×#384—112no—
224C2×C4×C22⋊C4—111no—
225C23×C11—28no—
226C23×C11—28no—
227C23×C11—216no—
228C23×C11—216no—
229C23×C11—24no—
230C23×C11—24no—
231C23×C11—22no—
232C23×C11—22no—
233C23×C11—22no—
234C23×C11—24no—
235C23×C11—24no—
236C23×C11—44no—
237C23×C11—44no—
238C23×C11—44no—
239C23×C11—48no—
240C23×C11—48no—
241C23×C11#127116yes—
242C23×C11C22×D414yes—
243C23×C11C22×D414yes—
244C23×C11C22×D412yes—
245C23×C11C22×D412yes—
246C23×C11C22×D414yes—
247C23×C11C22×D412yes—
248C23×C11C2×#4114yes—
249C23×C112−1+414yes—
250C23×C11C2511yescharacteristic
251C22×D11—22no—
252C22×D11—22no—
253C22×D11—22no—
254C22×D11—24no—
255C22×D11—24no—
256C22×D11—44no—
257C22×D11—44no—
258C22×D11—44no—
259C22×D11—48no—
260C22×D11—48no—
261D4×C11—416no—
262C2×C4×C11—216no—
263C2×C4×C11—24no—
264C2×C4×C11—24no—
265C2×C4×C11—24no—
266C2×C4×C11—22no—
267C2×C4×C11—24no—
268C2×C4×C11—22no—
269C2×C4×C11—24no—
270C2×C4×C11—22no—
271C2×C4×C11—416no—
272C2×C4×C11—48no—
273C2×C4×C11—44no—
274C2×C4×C11C22×D418yes—
275C22⋊D11—416no—
276C22⋊D11—416no—
277C2×Dic11—28no—
278C2×Dic11—216no—
279C2×Dic11—24no—
280C2×Dic11—24no—
281C2×Dic11—24no—
282C2×Dic11—232no—
283C2×Dic11—24no—
284C2×Dic11—22no—
285C2×Dic11—24no—
286C2×Dic11—22no—
287C2×Dic11—22no—
288C2×Dic11—24no—
289C2×Dic11—416no—
290C2×Dic11—48no—
291C2×Dic11—44no—
292C2×Dic11#123116yescomplemented
293C2×Dic11C22×D418yes—
294C2×Dic11C22×D414yes—
295C2×Dic11C22×D414yes—
296C2×Dic11C2×#4118yes—
297C23×D4—111no—
298C23×D4—111no—
299C23×D4C2×D1111yescharacteristic
300C24×C4—111no—
301C24×C4—111no—
302C24×C4C2×D1111yescharacteristic
303C2×#123—28no—
304C2×#123—118no—
305C2×#123—118no—
306C2×#123—118no—
307C2×#123—228no—
308C2×#123—228no—
309C2×#123—228no—
310C2×#123C2×D1118yescomplemented
311C2×#121—118no—
312C2×#121—228no—
313C22×C4⋊C4—112no—
314C22×C4⋊C4—112no—
315C22×C4⋊C4—112no—
316C22×C4⋊C4—112no—
317C22×C4⋊C4—111no—
318C22×C4⋊C4—118no—
319C22×C4⋊C4—112no—
320C22×C4⋊C4—228no—
321C22×C4⋊C4C2×D1112yes—
322C22×C22⋊C4—111no—
323C22×C22⋊C4—111no—
324C22×C22⋊C4—112no—
325C22×C22⋊C4—111no—
326C22×C22⋊C4—112no—
327C22×C22⋊C4—112no—
328C22×C22⋊C4C2×D1112yes—
329C22×C22⋊C4C2×D1111yescharacteristic
330C22×C42—112no—
331#399—1116no—
332#399—1116no—
333#390—1116no—
334#384—1116no—
335C4×C22⋊C4—118no—
336C2×#95—112no—
337C22×C11—24no—
338C22×C11—24no—
339C22×C11—28no—
340C22×C11—28no—
341C22×C11—232no—
342C22×C11—42no—
343C22×C11—42no—
344C22×C11—42no—
345C22×C11—44no—
346C22×C11—44no—
347C22×C11—88no—
348C22×C11C2×#12314yes—
349C22×C11C2×#12718yes—
350C22×C11C2×#12714yes—
351C22×C11#53614yes—
352C22×C11#54718yes—
353C22×C11#54718yes—
354C22×C11C23×D411yescharacteristic
355C22×C11C23×D411yescharacteristic
356C22×C11C23×D411yescharacteristic
357C22×C11C22×#4112yes—
358C22×C11C2×2−1+412yes—
359C2×D11—42no—
360C2×D11—42no—
361C2×D11—42no—
362C2×D11—44no—
363C2×D11—44no—
364C2×D11—88no—
365C4×C11—28no—
366C4×C11—44no—
367C4×C11—42no—
368Dic11—24no—
369Dic11—28no—
370Dic11—44no—
371Dic11—42no—
372Dic11C2×#12318yescomplemented
373C25—111no—
374C25C22×D1111yescharacteristic
375C25C22×D1111yescharacteristic
376C22×D4—24no—
377C22×D4—24no—
378C22×D4—24no—
379C22×D4—114no—
380C22×D4—114no—
381C22×D4—224no—
382C22×D4—228no—
383C22×D4—224no—
384C22×D4—224no—
385C22×D4—224no—
386C22×D4C22×D1114yes—
387C23×C4—24no—
388C23×C4—24no—
389C23×C4—24no—
390C23×C4—111no—
391C23×C4—118no—
392C23×C4—114no—
393C23×C4—112no—
394C23×C4—111no—
395C23×C4—114no—
396C23×C4—112no—
397C23×C4—111no—
398C23×C4—228no—
399C23×C4—224no—
400C23×C4—224no—
401C23×C4—224no—
402C23×C4C22×D1114yes—
403C23×C4C22×D1112yes—
404C23×C4C22×D1111yescharacteristic
405C23×C4C22×D1112yes—
406#123—232no—
407#123—2232no—
408#123—2232no—
409#123—2232no—
410#121—2232no—
411C2×C4⋊C4—28no—
412C2×C4⋊C4—118no—
413C2×C4⋊C4—118no—
414C2×C4⋊C4—114no—
415C2×C4⋊C4—118no—
416C2×C4⋊C4—118no—
417C2×C4⋊C4—118no—
418C2×C4⋊C4—228no—
419C2×C4⋊C4—228no—
420C2×C4⋊C4—2232no—
421C2×C4⋊C4—224no—
422C2×C4⋊C4—228no—
423C2×C4⋊C4—228no—
424C2×C4⋊C4—228no—
425C2×C4⋊C4C22×D1118yes—
426C2×C22⋊C4—28no—
427C2×C22⋊C4—118no—
428C2×C22⋊C4—114no—
429C2×C22⋊C4—114no—
430C2×C22⋊C4—118no—
431C2×C22⋊C4—114no—
432C2×C22⋊C4—118no—
433C2×C22⋊C4—118no—
434C2×C22⋊C4—224no—
435C2×C22⋊C4—228no—
436C2×C22⋊C4—224no—
437C2×C22⋊C4—228no—
438C2×C22⋊C4—228no—
439C2×C22⋊C4C22⋊D1118yescomplemented
440C2×C22⋊C4C22×D1118yes—
441C2×C22⋊C4C22×D1114yes—
442C2×C42—118no—
443C2×C42—228no—
444#95—118no—
445C2×C11—28no—
446C2×C11—82no—
447C2×C11#250118yescomplemented
448C2×C11C22×#12311yescharacteristic
449C2×C11C22×#12711yescharacteristic
450C2×C11C2×#53611yescharacteristic
451C2×C11C2×#54712yes—
452C2×C11C2×#54712yes—
453D11—82no—
454C24—24no—
455C24—24no—
456C24—22no—
457C24—22no—
458C24—24no—
459C24—24no—
460C24—22no—
461C24—112no—
462C24—222no—
463C24—222no—
464C24—224no—
465C24—224no—
466C24—222no—
467C24D4×D1114yes—
468C24D4×D1114yes—
469C24C2×C22⋊D1114yes—
470C24C23×D1112yes—
471C24C23×D1112yes—
472C24C23×D1111yescharacteristic
473C2×D4—28no—
474C2×D4—28no—
475C2×D4—28no—
476C2×D4—416no—
477C2×D4—228no—
478C2×D4—2216no—
479C2×D4—228no—
480C2×D4—228no—
481C2×D4—228no—
482C2×D4—4416no—
483C2×D4—4416no—
484C22×C4—24no—
485C22×C4—24no—
486C22×C4—24no—
487C22×C4—22no—
488C22×C4—28no—
489C22×C4—24no—
490C22×C4—22no—
491C22×C4—28no—
492C22×C4—24no—
493C22×C4—22no—
494C22×C4—28no—
495C22×C4—416no—
496C22×C4—114no—
497C22×C4—118no—
498C22×C4—112no—
499C22×C4—118no—
500C22×C4—114no—
501C22×C4—1116no—
502C22×C4—112no—
503C22×C4—114no—
504C22×C4—114no—
505C22×C4—112no—
506C22×C4—2232no—
507C22×C4—2216no—
508C22×C4—224no—
509C22×C4—224no—
510C22×C4—224no—
511C22×C4—224no—
512C22×C4—222no—
513C22×C4—228no—
514C22×C4—224no—
515C22×C4—222no—
516C22×C4—228no—
517C22×C4—224no—
518C22×C4—222no—
519C22×C4—228no—
520C22×C4—4416no—
521C22×C4C2×C22⋊D1118yes—
522C22×C4C23×D1114yes—
523C22×C4C23×D1112yes—
524C22×C4C23×D1114yes—
525C4⋊C4—216no—
526C4⋊C4—2216no—
527C4⋊C4—2216no—
528C4⋊C4—228no—
529C4⋊C4—2216no—
530C4⋊C4—2216no—
531C4⋊C4—2216no—
532C22⋊C4—216no—
533C22⋊C4—1116no—
534C22⋊C4—228no—
535C22⋊C4—2216no—
536C22⋊C4—228no—
537C22⋊C4—2216no—
538C22⋊C4—2216no—
539C22⋊C4C2×C22⋊D11116yescomplemented
540C42—2216no—
541C11C2×#250111yescharacteristic, complemented, Sylow
542C23—216no—
543C23—28no—
544C23—28no—
545C23—216no—
546C23—24no—
547C23—24no—
548C23—22no—
549C23—22no—
550C23—24no—
551C23—24no—
552C23—22no—
553C23—44no—
554C23—48no—
555C23—44no—
556C23—44no—
557C23—48no—
558C23—222no—
559C23—222no—
560C23—224no—
561C23—224no—
562C23—222no—
563C23—444no—
564C23—448no—
565C23—444no—
566C23—444no—
567C23—448no—
568C23#66993116yes—
569C23C2×D4×D1114yes—
570C23C2×D4×D1114yes—
571C23C2×D4×D1112yes—
572C23C2×D4×D1112yes—
573C23#41×D1114yes—
574C23#6704314yes—
575C23C22×C22⋊D1114yes—
576C23C22×C22⋊D1112yes—
577C23C24×D1111yescharacteristic
578D4—416no—
579D4—4416no—
580D4—4416no—
581C2×C4—216no—
582C2×C4—24no—
583C2×C4—24no—
584C2×C4—24no—
585C2×C4—22no—
586C2×C4—24no—
587C2×C4—22no—
588C2×C4—24no—
589C2×C4—22no—
590C2×C4—416no—
591C2×C4—48no—
592C2×C4—44no—
593C2×C4—1116no—
594C2×C4—114no—
595C2×C4—118no—
596C2×C4—118no—
597C2×C4—114no—
598C2×C4—2232no—
599C2×C4—228no—
600C2×C4—2216no—
601C2×C4—224no—
602C2×C4—224no—
603C2×C4—224no—
604C2×C4—224no—
605C2×C4—222no—
606C2×C4—224no—
607C2×C4—222no—
608C2×C4—224no—
609C2×C4—222no—
610C2×C4—4416no—
611C2×C4—448no—
612C2×C4—444no—
613C2×C4C22×C22⋊D1118yes—
614C22—24no—
615C22—232no—
616C22—28no—
617C22—28no—
618C22—24no—
619C22—42no—
620C22—42no—
621C22—44no—
622C22—44no—
623C22—42no—
624C22—88no—
625C22—442no—
626C22—442no—
627C22—444no—
628C22—444no—
629C22—442no—
630C22—888no—
631C22#1062317914yes—
632C22D11×#12314yes—
633C22#1062318618yes—
634C22C2×#6699318yes—
635C22C2×#6699314yes—
636C22#1062335518yes—
637C22C22×D4×D1111yescharacteristic
638C22C22×D4×D1111yescharacteristic
639C22C2×#41×D1112yes—
640C22C2×#6704312yes—
641C22C23×C22⋊D1111yescharacteristic
642C4—28no—
643C4—44no—
644C4—42no—
645C4—118no—
646C4—228no—
647C4—224no—
648C4—444no—
649C4—442no—
650C2—28no—
651C2—82no—
652C2—882no—
653C2#1307308518yesdirect product factor
654C2C2×D11×#12311yescharacteristic
655C2C22×#6699311yescharacteristic
656C2C2×#1062317911yescharacteristic
657C2C2×#1062318612yes—
658C2C2×#1062335512yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC22×C11×#123C2
socleC24×C11C24
prime radicalC22×#66992C2
hypercenterC22×#123D11
hypocenterC11C2×#2501
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#123

Complements

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

NH ≅ G/Ntype
1. C22×#66939C2semidirect
2. C22×#66982C2semidirect
3. C22×#66988C2semidirect
5. C23×Dic11⋊C4C2semidirect
6. #13073085C2direct (N × H)
7. C2×#10622562C2semidirect
8. C2×#10622605C2semidirect
9. C2×#10622570C2semidirect
10. C2×#10622589C2semidirect
11. C2×C22⋊C4×Dic11C2semidirect
12. C22×C11×#123C2semidirect
20. C2×C11×#123C22semidirect
30. C2×#66988C22semidirect
32. C2×#66982C22semidirect
43. C22×Dic11⋊C4C22semidirect
46. C2×#66939C22semidirect
48. #10622605C22semidirect
49. #10622589C22semidirect
50. #10622570C22semidirect
51. #10622562C22semidirect
52. C22⋊C4×Dic11C22semidirect
90. C2×C11×C22⋊C4D4semidirect
95. C2×C22⋊Dic11D4semidirect
199. C11×C22⋊C4C2×D4semidirect
202. C22⋊Dic11C2×D4semidirect
216. C22×#123D11semidirect
292. C2×Dic11#123semidirect
310. C2×#123C2×D11semidirect
372. Dic11C2×#123semidirect
439. C2×C22⋊C4C22⋊D11semidirect
447. C2×C11#2501semidirect
539. C22⋊C4C2×C22⋊D11semidirect
541. C11C2×#2501semidirect
653. C2#13073085direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669392
C22×#669822
C22×#669882
C22×#669922
C23×Dic11⋊C42
#130730852
C2×#106225622
C2×#106226052
C2×#106225702
C2×#106225892
C2×C22⋊C4×Dic112
C22×C11×#1232
C2×#250111