Finite Group Databasebeta

← C2×#13067039 #14720165

Subgroups — C2×#13067039 #14720165

Order 2816.

1714 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D4×D11C211yesmaximal, characteristic
2C2×#10622298C211yesmaximal, characteristic, complemented
3C2×#10622450C211yesmaximal, characteristic, complemented
4#13067039C218yesmaximal, direct product factor
5C2×#10622097C211yesmaximal, characteristic, complemented
6C2×D4⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
7C2×#10622121C211yesmaximal, characteristic, complemented
8C2×C11×D4⋊C8C211yesmaximal, characteristic, complemented
9C22×D4×D11C411yescharacteristic
10C23×C4×D11—21no—
11C2×C4×D4×C11C2211yescharacteristic
12C2×D4×Dic11C411yescharacteristic
13C2×C4×C22⋊D11—21no—
14C22×#4313—21no—
15C4×D4×D11—22no—
16C4×D4×D11—22no—
17C4×D4×D11C414yes—
18C4×D4×D11C2214yes—
19C2×#66946C411yescharacteristic
20C2×C4⋊C4×D11C411yescharacteristic
21C2×(C22⋊D11)⋊C4—21no—
22C2×C22⋊C4×D11—21no—
23C2×C4×D44C2211yescharacteristic
24C2×C42×D11C2211yescharacteristic
25C2×C11×C4⋊C8C2211yescharacteristic, complemented
26C2×C4×C8×C11C2211yescharacteristic, complemented
27C2×(C2×D11)⋊C8—21no—
28C2×Dic11⋊C8—21no—
29C2×Dic11⋊C8—21no—
30C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
31C2×C4×C11⋊C8C2211yescharacteristic, complemented
32#10622450—22no—
33#10622450C2214yescomplemented
34#10622298—22no—
35#10622298C2214yescomplemented
36C11×D4⋊C8C2214yescomplemented
37D4⋊(C11⋊C8)C2214yescomplemented
38#10622121C2214yescomplemented
39#10622097C2214yescomplemented
40C24×D11—21no—
41C22×D4×C11C2×C411yescharacteristic
42C23×C4×C11—21no—
43C22×C22⋊D11—21no—
44C23×Dic11—21no—
45C2×D4×D11—24no—
46C2×D4×D11—24no—
47C2×D4×D11—22no—
48C2×D4×D11C2×C414yes—
49C22×D44C2×C411yescharacteristic
50C22×C4×D11—21no—
51C22×C4×D11—21no—
52C22×C4×D11—21no—
53C22×C4×D11—24no—
54C22×C4×D11—24no—
55C22×C4×D11—44no—
56C22×C4×D11—44no—
57C22×C4×D11C2×C411yescharacteristic
58C22×C4×D11D411yescharacteristic
59C22×C4×D11D411yescharacteristic
60C22×C8×C11—21no—
61C22×C8×C11—21no—
62C4×D4×C11—21no—
63C4×D4×C11—21no—
64C4×D4×C11C2×C412yes—
65C4×D4×C11C2312yes—
66C2×C11×C4⋊C4C2×C411yescharacteristic
67C2×C11×C22⋊C4—21no—
68C2×C42×C11C2311yescharacteristic
69C2×C22⋊Dic11—21no—
70D4×Dic11—22no—
71D4×Dic11C2×C414yes—
72C4×C22⋊D11—24no—
73C4×C22⋊D11—24no—
74C2×(C2×D11)⋊C4—21no—
75C2×(C2×D11)⋊C4—21no—
76C2×C4⋊Dic11C2×C411yescharacteristic
77C2×Dic11⋊C4—21no—
78C2×C4×Dic11C2×C411yescharacteristic
79C2×C4×Dic11D411yescharacteristic
80C2×C4×Dic11D411yescharacteristic
81C22×C11⋊C8—21no—
82C22×C11⋊C8—21no—
83C2×#4313—24no—
84C2×#4313—44no—
85#66946—22no—
86#66946C2×C414yes—
87C4⋊C4×D11—22no—
88C4⋊C4×D11C2×C414yes—
89(C22⋊D11)⋊C4—24no—
90(C22⋊D11)⋊C4—24no—
91C22⋊C4×D11—24no—
92C22⋊C4×D11—24no—
93C4×D44—21no—
94C4×D44—21no—
95C4×D44C2×C412yes—
96C4×D44C2312yes—
97C42×D11C2×C412yes—
98C42×D11D412yes—
99C42×D11D412yes—
100C42×D11C2312yes—
101C11×C4⋊C8—21no—
102C11×C4⋊C8C2312yescomplemented
103C4×C8×C11—21no—
104C4×C8×C11C2312yescomplemented
105(C2×D11)⋊C8—24no—
106Dic11⋊C8—24no—
107Dic11⋊C8—24no—
108C4⋊(C11⋊C8)—21no—
109C4⋊(C11⋊C8)C2312yescomplemented
110C4×C11⋊C8—21no—
111C4×C11⋊C8C2312yescomplemented
112C2×#1486—111nomaximal, Sylow
113C24×C11—21no—
114C23×D11—28no—
115C23×D11—21no—
116C23×D11—24no—
117C23×D11—44no—
118C23×D11—44no—
119C23×D11C22⋊C411yescharacteristic
120C2×D4×C11—21no—
121C2×D4×C11—22no—
122C2×D4×C11M1614yescomplemented
123C2×D4×C11C22×C412yes—
124C22×C4×C11—21no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—42no—
128C22×C4×C11—42no—
129C22×C4×C11C22×C411yescharacteristic
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D411yescharacteristic
132C2×C22⋊D11—28no—
133C2×C22⋊D11—24no—
134C22×Dic11—24no—
135C22×Dic11—21no—
136C22×Dic11—44no—
137C22×Dic11C22⋊C411yescharacteristic
138C22×Dic11C22⋊C411yescharacteristic
139C22×Dic11C22⋊C411yescharacteristic
140D4×D11—216no—
141D4×D11—28no—
142D4×D11—28no—
143C2×D44—21no—
144C2×D44—22no—
145C2×D44M1614yescomplemented
146C2×D44C22×C412yes—
147C2×C4×D11—24no—
148C2×C4×D11—24no—
149C2×C4×D11—22no—
150C2×C4×D11—22no—
151C2×C4×D11—22no—
152C2×C4×D11—22no—
153C2×C4×D11—42no—
154C2×C4×D11—44no—
155C2×C4×D11—416no—
156C2×C4×D11—48no—
157C2×C4×D11—48no—
158C2×C4×D11—44no—
159C2×C4×D11—42no—
160C2×C4×D11—42no—
161C2×C4×D11C22⋊C412yes—
162C2×C4×D11C22⋊C412yes—
163C2×C4×D11C22⋊C412yes—
164C2×C4×D11D814yes—
165C2×C4×D11SD1614yes—
166C2×C4×D11C22×C412yes—
167C2×C4×D11C2×D412yes—
168C2×C4×D11C2×D412yes—
169C2×C8×C11—22no—
170C2×C8×C11—22no—
171C2×C8×C11—42no—
172C2×C8×C11—42no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4C22×C412yes—
175C11×C22⋊C4—22no—
176C11×C22⋊C4—22no—
177C42×C11C22×C411yescharacteristic
178C42×C11C2×D411yescharacteristic
179C42×C11C2×D411yescharacteristic
180C42×C11C2411yescharacteristic
181C22⋊Dic11—24no—
182(C2×D11)⋊C4—24no—
183(C2×D11)⋊C4—22no—
184(C2×D11)⋊C4—22no—
185C4⋊Dic11—21no—
186C4⋊Dic11C22×C412yes—
187Dic11⋊C4—24no—
188C4×Dic11C22⋊C412yes—
189C4×Dic11C22⋊C412yes—
190C4×Dic11C22⋊C412yes—
191C4×Dic11C22×C412yes—
192C4×Dic11C2×D412yes—
193C4×Dic11C2×D412yes—
194C2×C11⋊C8—22no—
195C2×C11⋊C8—22no—
196C2×C11⋊C8—42no—
197C2×C11⋊C8—42no—
198#4313—48no—
199C22×C4×D4—111no—
200C2×#431—111no—
201C2×#423—111no—
202#1486—118no—
203C2×D4⋊C8—111no—
204C2×D4⋊C8—111no—
205C2×D4⋊C8—111no—
206C2×D4⋊C8D1111yescharacteristic, complemented
207C23×C11—22no—
208C23×C11—24no—
209C23×C11—42no—
210C23×C11—42no—
211C23×C11C2×C22⋊C411yescharacteristic
212C22×D11—22no—
213C22×D11—22no—
214C22×D11—216no—
215C22×D11—22no—
216C22×D11—24no—
217C22×D11—48no—
218C22×D11—432no—
219C22×D11—42no—
220C22×D11—42no—
221C22×D11—48no—
222C22×D11#10214yes—
223C22×D11C2×C22⋊C412yes—
224D4×C11—22no—
225D4×C11—24no—
226D4×C11C2×M1614yescomplemented
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—42no—
230C2×C4×C11—42no—
231C2×C4×C11—42no—
232C2×C4×C11—44no—
233C2×C4×C11C2×C22⋊C411yescharacteristic
234C2×C4×C11C2×C22⋊C411yescharacteristic
235C2×C4×C11C2×C22⋊C411yescharacteristic
236C2×C4×C11C2×M1612yes—
237C2×C4×C11C2×M1612yes—
238C2×C4×C11C2×D812yes—
239C2×C4×C11C2×SD1612yes—
240C2×C4×C11C23×C411yescharacteristic
241C2×C4×C11C22×D411yescharacteristic
242C2×C4×C11C22×D411yescharacteristic
243C22⋊D11—216no—
244C2×Dic11—22no—
245C2×Dic11—22no—
246C2×Dic11—22no—
247C2×Dic11—42no—
248C2×Dic11—48no—
249C2×Dic11#10214yes—
250C2×Dic11C2×C22⋊C412yes—
251C2×Dic11C2×C22⋊C412yes—
252C2×Dic11C2×C22⋊C412yes—
253D44—22no—
254D44—24no—
255D44C2×M1614yescomplemented
256C4×D11—22no—
257C4×D11—22no—
258C4×D11—24no—
259C4×D11—42no—
260C4×D11—42no—
261C4×D11—48no—
262C4×D11—42no—
263C4×D11—42no—
264C4×D11—44no—
265C4×D11—48no—
266C4×D11#10218yes—
267C4×D11C2×D814yes—
268C4×D11C2×SD1614yes—
269C8×C11—42no—
270C8×C11—42no—
271C11⋊C8—42no—
272C11⋊C8—42no—
273C23×D4—111no—
274C24×C4—221no—
275C22×M16—221no—
276C2×C4×D4—111no—
277C2×C4×D4—114no—
278C2×C4×D4—114no—
279C2×C4×D4—111no—
280C2×C4×D4—111no—
281C2×C4×D4—221no—
282C2×C4×D4—222no—
283C2×C4×D4—222no—
284C2×C4×D4—221no—
285C2×C4×D4C2×D1111yescharacteristic
286C22×C4⋊C4—111no—
287C22×C22⋊C4—221no—
288C22×C42—111no—
289#431—114no—
290#431—222no—
291#423—114no—
292#423—222no—
293C2×C4⋊C8—111no—
294C2×C4⋊C8—221no—
295C2×C4⋊C8—221no—
296C2×C4⋊C8C2×D1111yescharacteristic, complemented
297C2×C22⋊C8—221no—
298C2×C4×C8—111no—
299C2×C4×C8C2×D1111yescharacteristic, complemented
300D4⋊C8—114no—
301D4⋊C8—114no—
302D4⋊C8—114no—
303D4⋊C8C2×D1114yescomplemented
304C22×C11—24no—
305C22×C11—42no—
306C22×C11—42no—
307C22×C11—48no—
308C22×C11#40712yes—
309C22×C11C2×#10212yes—
310C22×C11#42112yes—
311C22×C11C22×C22⋊C411yescharacteristic
312C2×D11—22no—
313C2×D11—22no—
314C2×D11—28no—
315C2×D11—24no—
316C2×D11—432no—
317C2×D11—42no—
318C2×D11—42no—
319C2×D11—48no—
320C2×D11C2×#10214yes—
321C4×C11—21no—
322C4×C11—21no—
323C4×C11—42no—
324C4×C11#40712yes—
325C4×C11C2×#10212yes—
326C4×C11C22×M1611yescharacteristic
327C4×C11C22×M1611yescharacteristic
328C4×C11C22×D811yescharacteristic
329C4×C11C22×SD1611yescharacteristic
330Dic11—22no—
331Dic11—22no—
332Dic11—42no—
333Dic11C2×#10214yes—
334C25—221no—
335C22×D4—114no—
336C22×D4—111no—
337C22×D4—222no—
338C22×D4—221no—
339C22×D4—224no—
340C22×D4—224no—
341C22×D4C4×D1111yescharacteristic
342C23×C4—21no—
343C23×C4—111no—
344C23×C4—111no—
345C23×C4—111no—
346C23×C4—221no—
347C23×C4—224no—
348C23×C4—224no—
349C23×C4—221no—
350C23×C4—221no—
351C23×C4—221no—
352C23×C4—444no—
353C23×C4—444no—
354C2×M16—224no—
355C2×M16—444no—
356C22×C8—21no—
357C22×C8—21no—
358C22×C8—221no—
359C22×C8—221no—
360C4×D4—21no—
361C4×D4—21no—
362C4×D4—114no—
363C4×D4—114no—
364C4×D4—112no—
365C4×D4—112no—
366C4×D4—224no—
367C4×D4—224no—
368C4×D4—222no—
369C4×D4—224no—
370C4×D4—224no—
371C4×D4—222no—
372C4×D4—221no—
373C4×D4—221no—
374C4×D4C4×D1112yes—
375C4×D4C22×D1112yes—
376C2×C4⋊C4—111no—
377C2×C4⋊C4—114no—
378C2×C4⋊C4—222no—
379C2×C4⋊C4—221no—
380C2×C4⋊C4C4×D1111yescharacteristic
381C2×C22⋊C4—21no—
382C2×C22⋊C4—224no—
383C2×C22⋊C4—224no—
384C2×C22⋊C4—221no—
385C2×C22⋊C4—221no—
386C2×C22⋊C4—221no—
387C2×C42—111no—
388C2×C42—111no—
389C2×C42—111no—
390C2×C42—112no—
391C2×C42—112no—
392C2×C42—112no—
393C2×C42—112no—
394C2×C42C22×D1111yescharacteristic
395C4⋊C8—21no—
396C4⋊C8—112no—
397C4⋊C8—224no—
398C4⋊C8—224no—
399C4⋊C8—221no—
400C4⋊C8C22×D1112yescomplemented
401C22⋊C8—224no—
402C4×C8—21no—
403C4×C8—112no—
404C4×C8—221no—
405C4×C8C22×D1112yescomplemented
406C2×C11—44no—
407C2×C11#148614yescomplemented
408C2×C11C2×#40711yescharacteristic
409C2×C11C22×#10211yescharacteristic
410C2×C11C2×#42111yescharacteristic
411D11—24no—
412D11—44no—
413C24—21no—
414C24—111no—
415C24—224no—
416C24—228no—
417C24—221no—
418C24—444no—
419C24—444no—
420C2×D4—21no—
421C2×D4—22no—
422C2×D4—114no—
423C2×D4—112no—
424C2×D4—224no—
425C2×D4—228no—
426C2×D4—2216no—
427C2×D4—228no—
428C2×D4—228no—
429C2×D4—221no—
430C2×D4—222no—
431C2×D4#431314yescomplemented
432C2×D4C2×C4×D1112yes—
433C22×C4—21no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—42no—
437C22×C4—42no—
438C22×C4—111no—
439C22×C4—112no—
440C22×C4—114no—
441C22×C4—114no—
442C22×C4—112no—
443C22×C4—111no—
444C22×C4—111no—
445C22×C4—112no—
446C22×C4—112no—
447C22×C4—112no—
448C22×C4—112no—
449C22×C4—224no—
450C22×C4—224no—
451C22×C4—224no—
452C22×C4—222no—
453C22×C4—222no—
454C22×C4—221no—
455C22×C4—222no—
456C22×C4—222no—
457C22×C4—442no—
458C22×C4—444no—
459C22×C4—448no—
460C22×C4—448no—
461C22×C4—4416no—
462C22×C4—444no—
463C22×C4—444no—
464C22×C4—442no—
465C22×C4—442no—
466C22×C4C2×C4×D1111yescharacteristic
467C22×C4D4×D1111yescharacteristic
468C22×C4D4×D1111yescharacteristic
469M16—448no—
470C2×C8—22no—
471C2×C8—22no—
472C2×C8—42no—
473C2×C8—42no—
474C2×C8—222no—
475C2×C8—222no—
476C2×C8—442no—
477C2×C8—442no—
478C4⋊C4—21no—
479C4⋊C4—112no—
480C4⋊C4—224no—
481C4⋊C4—221no—
482C4⋊C4C2×C4×D1112yes—
483C22⋊C4—22no—
484C22⋊C4—22no—
485C22⋊C4—224no—
486C22⋊C4—224no—
487C22⋊C4—222no—
488C22⋊C4—222no—
489C42—112no—
490C42—112no—
491C42—112no—
492C42—112no—
493C42—112no—
494C42—112no—
495C42C2×C4×D1111yescharacteristic
496C42D4×D1111yescharacteristic
497C42D4×D1111yescharacteristic
498C42C23×D1111yescharacteristic
499C11C2×#148611yescharacteristic, complemented, Sylow
500C23—22no—
501C23—24no—
502C23—42no—
503C23—42no—
504C23—112no—
505C23—114no—
506C23—2216no—
507C23—222no—
508C23—222no—
509C23—222no—
510C23—224no—
511C23—448no—
512C23—4432no—
513C23—448no—
514C23—442no—
515C23—442no—
516C23C22⋊C4×D1111yescharacteristic
517D4—22no—
518D4—24no—
519D4—114no—
520D4—2216no—
521D4—222no—
522D4—224no—
523D4C2×#431314yescomplemented
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—44no—
530C2×C4—112no—
531C2×C4—114no—
532C2×C4—114no—
533C2×C4—114no—
534C2×C4—118no—
535C2×C4—112no—
536C2×C4—112no—
537C2×C4—222no—
538C2×C4—222no—
539C2×C4—222no—
540C2×C4—222no—
541C2×C4—224no—
542C2×C4—222no—
543C2×C4—442no—
544C2×C4—442no—
545C2×C4—448no—
546C2×C4—448no—
547C2×C4—448no—
548C2×C4—442no—
549C2×C4—442no—
550C2×C4—442no—
551C2×C4—444no—
552C2×C4C22⋊C4×D1111yescharacteristic
553C2×C4C22⋊C4×D1111yescharacteristic
554C2×C4C22⋊C4×D1111yescharacteristic
555C2×C4C2×#431312yes—
556C2×C4M16×D1112yes—
557C2×C4D8×D1112yes—
558C2×C4SD16×D1112yes—
559C2×C4C22×C4×D1111yescharacteristic
560C2×C4C2×D4×D1111yescharacteristic
561C2×C4C2×D4×D1111yescharacteristic
562C8—42no—
563C8—42no—
564C8—442no—
565C8—442no—
566C22—24no—
567C22—48no—
568C22—42no—
569C22—42no—
570C22—114no—
571C22—228no—
572C22—222no—
573C22—222no—
574C22—224no—
575C22—4432no—
576C22—448no—
577C22—442no—
578C22—442no—
579C22#1062233912yes—
580C22D11×#10212yes—
581C22#1062243412yes—
582C22C2×C22⋊C4×D1111yescharacteristic
583C4—21no—
584C4—21no—
585C4—42no—
586C4—114no—
587C4—222no—
588C4—222no—
589C4—442no—
590C4#1062233912yes—
591C4D11×#10212yes—
592C4C22×#431311yescharacteristic
593C4C2×M16×D1111yescharacteristic
594C4C2×D8×D1111yescharacteristic
595C4C2×SD16×D1111yescharacteristic
596C2—44no—
597C2—224no—
598C2—444no—
599C2#1306703914yesdirect product factor
600C2C2×#1062233911yescharacteristic
601C2C2×D11×#10211yescharacteristic
602C2C2×#1062243411yescharacteristic
subgroupG/H
centerC22×C4D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC2×C11×D4⋊C8C2
socleC23×C11C2×C22⋊C4
prime radicalC22×D4×D11C4
cosocleC42×C11C24
hypercenterC2×D4⋊C8D11
hypocenterC11C2×#1486
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×D4⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×#10622298C2semidirect
3. C2×#10622450C2semidirect
4. #13067039C2direct (N × H)
5. C2×#10622097C2semidirect
6. C2×D4⋊(C11⋊C8)C2semidirect
7. C2×#10622121C2semidirect
8. C2×C11×D4⋊C8C2semidirect
25. C2×C11×C4⋊C8C22semidirect
26. C2×C4×C8×C11C22semidirect
30. C2×C4⋊(C11⋊C8)C22semidirect
31. C2×C4×C11⋊C8C22semidirect
33. #10622450C22semidirect
35. #10622298C22semidirect
36. C11×D4⋊C8C22semidirect
37. D4⋊(C11⋊C8)C22semidirect
38. #10622121C22semidirect
39. #10622097C22semidirect
102. C11×C4⋊C8C23semidirect
104. C4×C8×C11C23semidirect
109. C4⋊(C11⋊C8)C23semidirect
111. C4×C11⋊C8C23semidirect
122. C2×D4×C11M16semidirect
145. C2×D44M16semidirect
206. C2×D4⋊C8D11semidirect
226. D4×C11C2×M16semidirect
255. D44C2×M16semidirect
296. C2×C4⋊C8C2×D11semidirect
299. C2×C4×C8C2×D11semidirect
303. D4⋊C8C2×D11semidirect
400. C4⋊C8C22×D11semidirect
405. C4×C8C22×D11semidirect
407. C2×C11#1486semidirect
431. C2×D4#4313semidirect
499. C11C2×#1486semidirect
523. D4C2×#4313semidirect
599. C2#13067039direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×D4×D112
C2×#106222982
C2×#106224502
#130670392
C2×#106220972
C2×D4⋊(C11⋊C8)2
C2×#106221212
C2×C11×D4⋊C82
C2×#148611