Finite Group Databasebeta

← C2×#13067106 #14720866

Subgroups — C2×#13067106 #14720866

Order 2816.

1606 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623158C211yesmaximal, characteristic
2C2×D11×C22⋊C8C211yesmaximal, characteristic, complemented
3C2×#10622279C211yesmaximal, characteristic, complemented
4#13067106C218yesmaximal, direct product factor
5C2×#10622176C211yesmaximal, characteristic, complemented
6C2×#10622108C211yesmaximal, characteristic, complemented
7C2×#10622089C211yesmaximal, characteristic, complemented
8C2×C11×#328C211yesmaximal, characteristic, complemented
9C22×#4343C411yescharacteristic, complemented
10C23×C4×D11C2211yescharacteristic
11C2×C11×C22⋊Q8C2211yescharacteristic
12C2×#66999C411yescharacteristic, complemented
13C2×#66983C2211yescharacteristic
14C22×(C2×D11)⋊C4—21no—
15C22×C4×Dic11—21no—
16C22×C8×D11—21no—
17#10623158—22no—
18#10623158—22no—
19#10623158C414yescomplemented
20#10623158C2214yes—
21C2×#66948C411yescharacteristic, complemented
22C2×#66947—21no—
23C2×#66946—21no—
24C2×#66945C411yescharacteristic, complemented
25C2×#66935—21no—
26C2×(C22⋊D11)⋊C4—21no—
27C2×C11×C22⋊C8C2211yescharacteristic
28C2×C11×#95C2211yescharacteristic
29C2×C11⋊#95C2211yescharacteristic
30C2×C22⋊(C11⋊C8)C2211yescharacteristic
31C2×(C2×D11)⋊C8—21no—
32D11×C22⋊C8—22no—
33D11×C22⋊C8C2214yescomplemented
34#10622279—22no—
35#10622279C2214yescomplemented
36C11×#328C2214yescomplemented
37#10622176C2214yescomplemented
38#10622108C2214yescomplemented
39#10622089C2214yescomplemented
40C24×D11D411yescharacteristic
41C22×Q8×C11C2×C411yescharacteristic
42C23×C4×C11—21no—
43C23×C4×C11C2311yescharacteristic
44C22×C22⋊D11—21no—
45C23×Dic11—21no—
46C23×Dic11D411yescharacteristic
47C2×#4343—22no—
48C2×#4343—44no—
49C2×#4343C2×C414yescomplemented
50C22×D44—21no—
51C22×D44—21no—
52C22×D44C2×C411yescharacteristic
53C22×C4×D11—21no—
54C22×C4×D11—44no—
55C22×C4×D11C2×C411yescharacteristic
56C22×C4×D11C2×C411yescharacteristic
57C22×C4×D11C2×C412yes—
58C22×C4×D11D411yescharacteristic
59C22×C4×D11D412yes—
60C22×C4×D11D411yescharacteristic
61C22×C4×D11D412yes—
62C22×C4×D11C2312yes—
63C22×C8×C11—21no—
64C11×C22⋊Q8—21no—
65C11×C22⋊Q8—21no—
66C11×C22⋊Q8C2×C412yes—
67C11×C22⋊Q8C2312yes—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4C2×C411yescharacteristic
70C2×C11×C22⋊C4—21no—
71#66999—22no—
72#66999C2×C414yescomplemented
73#66983—21no—
74#66983—21no—
75#66983C2×C412yes—
76#66983C2312yes—
77C2×(C2×D11)⋊C4—28no—
78C2×(C2×D11)⋊C4—21no—
79C2×(C2×D11)⋊C4—21no—
80C2×(C2×D11)⋊C4—24no—
81C2×(C2×D11)⋊C4—21no—
82C2×(C2×D11)⋊C4—21no—
83C2×C4⋊Dic11C2×C411yescharacteristic
84C2×Dic11⋊C4—21no—
85C2×C4×Dic11—21no—
86C2×C4×Dic11—24no—
87C2×C4×Dic11—44no—
88C22×C11⋊C8—21no—
89C2×C8×D11—24no—
90C2×C8×D11—44no—
91#66948—22no—
92#66948C2×C414yescomplemented
93#66947—24no—
94#66947—24no—
95#66946—24no—
96#66946—24no—
97#66945—22no—
98#66945C2×C414yescomplemented
99#66935—24no—
100#66935—24no—
101(C22⋊D11)⋊C4—24no—
102(C22⋊D11)⋊C4—24no—
103C11×C22⋊C8—21no—
104C11×C22⋊C8C2312yes—
105C11×#95—21no—
106C11×#95C2312yes—
107C11⋊#95—21no—
108C11⋊#95C2312yes—
109C22⋊(C11⋊C8)—21no—
110C22⋊(C11⋊C8)C2312yes—
111(C2×D11)⋊C8—24no—
112C2×#1501—111nomaximal, Sylow
113C24×C11C2×D411yescharacteristic
114C23×D11—22no—
115C23×D11—22no—
116C23×D11—24no—
117C23×D11—21no—
118C23×D11—42no—
119C23×D11C22⋊C411yescharacteristic
120C23×D11C22⋊C412yes—
121C23×D11C22⋊C411yescharacteristic
122C23×D11C2×D412yes—
123C2×Q8×C11—21no—
124C2×Q8×C11—42no—
125C2×Q8×C11C22×C412yes—
126C22×C4×C11—24no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—22no—
130C22×C4×C11—42no—
131C22×C4×C11—42no—
132C22×C4×C11—42no—
133C22×C4×C11C22×C411yescharacteristic
134C22×C4×C11C22×C411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2411yescharacteristic
139C2×C22⋊D11—22no—
140C2×C22⋊D11—22no—
141C2×C22⋊D11—42no—
142C2×C22⋊D11—42no—
143C22×Dic11—24no—
144C22×Dic11—24no—
145C22×Dic11—21no—
146C22×Dic11—22no—
147C22×Dic11—42no—
148C22×Dic11—42no—
149C22×Dic11C22⋊C412yes—
150C22×Dic11C22⋊C411yescharacteristic
151C22×Dic11C22⋊C411yescharacteristic
152C22×Dic11C2×D412yes—
153#4343—48no—
154#4343—48no—
155C2×D44—24no—
156C2×D44—24no—
157C2×D44—21no—
158C2×D44—42no—
159C2×D44—44no—
160C2×D44—44no—
161C2×D44C22×C412yes—
162C2×C4×D11—24no—
163C2×C4×D11—24no—
164C2×C4×D11—24no—
165C2×C4×D11—42no—
166C2×C4×D11—42no—
167C2×C4×D11—44no—
168C2×C4×D11—44no—
169C2×C4×D11—44no—
170C2×C4×D11—44no—
171C2×C4×D11—44no—
172C2×C4×D11C22⋊C412yes—
173C2×C4×D11C22⋊C412yes—
174C2×C4×D11C22⋊C412yes—
175C2×C4×D11C22⋊C412yes—
176C2×C4×D11C22×C412yes—
177C2×C4×D11C22×C412yes—
178C2×C4×D11C2×D412yes—
179C2×C4×D11C2×D412yes—
180C2×C8×C11—22no—
181C2×C8×C11—42no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—22no—
184C11×C4⋊C4—22no—
185C11×C4⋊C4C22×C412yes—
186C11×C22⋊C4—22no—
187C11×C22⋊C4—22no—
188(C2×D11)⋊C4—216no—
189(C2×D11)⋊C4—24no—
190(C2×D11)⋊C4—24no—
191(C2×D11)⋊C4—24no—
192(C2×D11)⋊C4—22no—
193(C2×D11)⋊C4—22no—
194C4⋊Dic11—21no—
195C4⋊Dic11C22×C412yes—
196Dic11⋊C4—24no—
197C4×Dic11—24no—
198C4×Dic11—48no—
199C2×C11⋊C8—22no—
200C2×C11⋊C8—42no—
201C8×D11—48no—
202C2×#525—111no—
203C22×C22⋊C8—111no—
204C2×C4×C22⋊C4—111no—
205#1501—118no—
206C2×#328—111no—
207C2×#328D1111yescharacteristic, complemented
208C2×#327—111no—
209C2×#327—111no—
210C23×C11—22no—
211C23×C11—22no—
212C23×C11C2×C22⋊C411yescharacteristic
213C23×C11C2×C22⋊C411yescharacteristic
214C23×C11#13512yes—
215C23×C11#13512yes—
216C23×C11C22×D411yescharacteristic
217C22×D11—22no—
218C22×D11—22no—
219C22×D11—22no—
220C22×D11—22no—
221C22×D11—22no—
222C22×D11—24no—
223C22×D11—22no—
224C22×D11—22no—
225C22×D11—24no—
226C22×D11—24no—
227C22×D11—22no—
228C22×D11—42no—
229C22×D11—42no—
230C22×D11—48no—
231C22×D11—48no—
232C22×D11—42no—
233C22×D11—42no—
234C22×D11—42no—
235C22×D11#10414yes—
236C22×D11C2×C22⋊C412yes—
237C22×D11C2×C22⋊C412yes—
238Q8×C11—42no—
239Q8×C11—42no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—24no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—42no—
250C2×C4×C11—48no—
251C2×C4×C11—42no—
252C2×C4×C11—42no—
253C2×C4×C11—42no—
254C2×C4×C11C2×C22⋊C411yescharacteristic
255C2×C4×C11C2×C22⋊C411yescharacteristic
256C2×C4×C11C23×C411yescharacteristic
257C2×C4×C11C22×D411yescharacteristic
258C22⋊D11—42no—
259C22⋊D11—42no—
260C22⋊D11—44no—
261C2×Dic11—22no—
262C2×Dic11—24no—
263C2×Dic11—24no—
264C2×Dic11—24no—
265C2×Dic11—22no—
266C2×Dic11—42no—
267C2×Dic11—48no—
268C2×Dic11—42no—
269C2×Dic11—42no—
270C2×Dic11#9914yes—
271C2×Dic11C2×C22⋊C412yes—
272C2×Dic11C2×C22⋊C412yes—
273D44—42no—
274D44—42no—
275D44—48no—
276D44—48no—
277C4×D11—24no—
278C4×D11—24no—
279C4×D11—24no—
280C4×D11—24no—
281C4×D11—42no—
282C4×D11—42no—
283C4×D11—42no—
284C4×D11—42no—
285C4×D11—48no—
286C8×C11—42no—
287C11⋊C8—42no—
288C22×#41—111no—
289C24×C4—111no—
290C23×C8—221no—
291#525—114no—
292#525—114no—
293#525—222no—
294#525—222no—
295C2×#123—221no—
296C2×C22⋊Q8—111no—
297C2×C22⋊Q8C2×D1111yescharacteristic
298C2×#121—111no—
299C2×#121—111no—
300C2×#120—221no—
301C2×C4×D4—221no—
302C2×C4×D4—221no—
303C2×#117—111no—
304C22×C22⋊C4—221no—
305C22×C42—221no—
306C2×C22⋊C8—111no—
307C2×C22⋊C8—114no—
308C2×C22⋊C8—222no—
309C2×C22⋊C8—221no—
310C2×C22⋊C8C2×D1111yescharacteristic
311C4×C22⋊C4—114no—
312C4×C22⋊C4—222no—
313C2×#95—111no—
314C2×#95C2×D1111yescharacteristic
315#328—114no—
316#328C2×D1114yescomplemented
317#327—114no—
318#327—114no—
319C22×C11—21no—
320C22×C11—21no—
321C22×C11—21no—
322C22×C11—21no—
323C22×C11—24no—
324C22×C11—24no—
325C22×C11C2×#9912yes—
326C22×C11#41612yes—
327C22×C11#41612yes—
328C22×C11C2×#10412yes—
329C22×C11C22×C22⋊C411yescharacteristic
330C22×C11C2×#13511yescharacteristic
331C22×C11C2×#13511yescharacteristic
332C2×D11—22no—
333C2×D11—22no—
334C2×D11—28no—
335C2×D11—22no—
336C2×D11—22no—
337C2×D11—22no—
338C2×D11—44no—
339C2×D11—44no—
340C2×D11—48no—
341C2×D11—44no—
342C2×D11—42no—
343C2×D11—42no—
344C2×D11—42no—
345C2×D11—84no—
346C2×D11C2×#10414yes—
347C4×C11—21no—
348C4×C11—21no—
349C4×C11—21no—
350C4×C11—21no—
351C4×C11—44no—
352C4×C11—42no—
353C4×C11—42no—
354Dic11—22no—
355Dic11—44no—
356Dic11—42no—
357Dic11C2×#9914yes—
358C25—111no—
359C2×#41—114no—
360C2×#41—222no—
361C2×#41—444no—
362C22×Q8C4×D1111yescharacteristic
363C22×D4—111no—
364C22×D4—221no—
365C22×D4—221no—
366C22×D4—221no—
367C23×C4—21no—
368C23×C4—111no—
369C23×C4—111no—
370C23×C4—111no—
371C23×C4—111no—
372C23×C4—112no—
373C23×C4—111no—
374C23×C4—112no—
375C23×C4—112no—
376C23×C4—112no—
377C23×C4—221no—
378C23×C4—221no—
379C23×C4—444no—
380C23×C4C22×D1111yescharacteristic
381C22×C8—21no—
382C22×C8—224no—
383C22×C8—221no—
384C22×C8—444no—
385#123—224no—
386#123—224no—
387C22⋊Q8—21no—
388C22⋊Q8—21no—
389C22⋊Q8—114no—
390C22⋊Q8—222no—
391C22⋊Q8C4×D1112yes—
392C22⋊Q8C22×D1112yes—
393#121—112no—
394#121—112no—
395#121—114no—
396#121—222no—
397#121—221no—
398#121—221no—
399#120—224no—
400#120—224no—
401C4×D4—224no—
402C4×D4—224no—
403C4×D4—224no—
404C4×D4—224no—
405#117—114no—
406#117—222no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—111no—
409C2×C4⋊C4—221no—
410C2×C4⋊C4C4×D1111yescharacteristic
411C2×C22⋊C4—21no—
412C2×C22⋊C4—221no—
413C2×C22⋊C4—224no—
414C2×C22⋊C4—221no—
415C2×C22⋊C4—221no—
416C2×C22⋊C4—228no—
417C2×C22⋊C4—221no—
418C2×C42—221no—
419C2×C42—224no—
420C2×C42—444no—
421C22⋊C8—21no—
422C22⋊C8—112no—
423C22⋊C8—224no—
424C22⋊C8—221no—
425C22⋊C8C22×D1112yes—
426#95—21no—
427#95—112no—
428#95—221no—
429#95C22×D1112yes—
430C2×C11—21no—
431C2×C11—21no—
432C2×C11—22no—
433C2×C11#150114yescomplemented
434C2×C11C22×#9911yescharacteristic
435C2×C11C2×#41611yescharacteristic
436C2×C11C22×#10411yescharacteristic
437D11—24no—
438D11—42no—
439D11—82no—
440C24—111no—
441C24—111no—
442C24—112no—
443C24—112no—
444C24—224no—
445C24—222no—
446C24—222no—
447C24—221no—
448C24—442no—
449C24D4×D1111yescharacteristic
450#41—448no—
451#41—448no—
452C2×Q8—21no—
453C2×Q8—42no—
454C2×Q8C2×C4×D1112yes—
455C2×D4—112no—
456C2×D4—224no—
457C2×D4—224no—
458C2×D4—222no—
459C2×D4—222no—
460C2×D4—221no—
461C2×D4—442no—
462C2×D4—444no—
463C2×D4—444no—
464C2×D4—442no—
465C2×D4—442no—
466C22×C4—24no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—22no—
470C22×C4—42no—
471C22×C4—42no—
472C22×C4—42no—
473C22×C4—111no—
474C22×C4—112no—
475C22×C4—111no—
476C22×C4—112no—
477C22×C4—112no—
478C22×C4—112no—
479C22×C4—112no—
480C22×C4—112no—
481C22×C4—112no—
482C22×C4—112no—
483C22×C4—112no—
484C22×C4—112no—
485C22×C4—224no—
486C22×C4—224no—
487C22×C4—224no—
488C22×C4—224no—
489C22×C4—224no—
490C22×C4—221no—
491C22×C4—222no—
492C22×C4—442no—
493C22×C4—442no—
494C22×C4—444no—
495C22×C4—444no—
496C22×C4—444no—
497C22×C4—444no—
498C22×C4—444no—
499C22×C4—442no—
500C22×C4—442no—
501C22×C4C2×C4×D1111yescharacteristic
502C22×C4C2×C4×D1111yescharacteristic
503C22×C4D4×D1111yescharacteristic
504C22×C4D4×D1111yescharacteristic
505C22×C4D4×D1111yescharacteristic
506C22×C4C23×D1111yescharacteristic
507C2×C8—22no—
508C2×C8—42no—
509C2×C8—222no—
510C2×C8—448no—
511C2×C8—442no—
512C4⋊C4—22no—
513C4⋊C4—21no—
514C4⋊C4—22no—
515C4⋊C4—112no—
516C4⋊C4—224no—
517C4⋊C4—221no—
518C4⋊C4C2×C4×D1112yes—
519C22⋊C4—22no—
520C22⋊C4—22no—
521C22⋊C4—224no—
522C22⋊C4—224no—
523C22⋊C4—224no—
524C22⋊C4—2216no—
525C22⋊C4—222no—
526C22⋊C4—222no—
527C42—224no—
528C42—448no—
529C11C2×#150111yescharacteristic, complemented, Sylow
530C23—22no—
531C23—22no—
532C23—112no—
533C23—114no—
534C23—112no—
535C23—224no—
536C23—224no—
537C23—222no—
538C23—222no—
539C23—222no—
540C23—222no—
541C23—222no—
542C23—224no—
543C23—222no—
544C23—222no—
545C23—222no—
546C23—442no—
547C23—442no—
548C23—448no—
549C23—448no—
550C23—442no—
551C23—442no—
552C23—442no—
553C23C22⋊C4×D1111yescharacteristic
554C23C22⋊C4×D1111yescharacteristic
555C23#6696912yes—
556C23#6697212yes—
557C23C2×D4×D1111yescharacteristic
558Q8—42no—
559Q8—42no—
560D4—442no—
561D4—442no—
562D4—448no—
563D4—448no—
564D4—442no—
565D4—442no—
566D4—444no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—24no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—42no—
577C2×C4—48no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—112no—
582C2×C4—114no—
583C2×C4—112no—
584C2×C4—224no—
585C2×C4—224no—
586C2×C4—224no—
587C2×C4—224no—
588C2×C4—224no—
589C2×C4—224no—
590C2×C4—222no—
591C2×C4—224no—
592C2×C4—222no—
593C2×C4—442no—
594C2×C4—442no—
595C2×C4—442no—
596C2×C4—442no—
597C2×C4—448no—
598C2×C4—442no—
599C2×C4—448no—
600C2×C4—442no—
601C2×C4—442no—
602C2×C4C22⋊C4×D1111yescharacteristic
603C2×C4C22⋊C4×D1111yescharacteristic
604C2×C4C22×C4×D1111yescharacteristic
605C2×C4C2×D4×D1111yescharacteristic
606C8—42no—
607C8—442no—
608C22—21no—
609C22—21no—
610C22—24no—
611C22—24no—
612C22—21no—
613C22—21no—
614C22—114no—
615C22—222no—
616C22—228no—
617C22—222no—
618C22—222no—
619C22—222no—
620C22—222no—
621C22—444no—
622C22—444no—
623C22—448no—
624C22—444no—
625C22—442no—
626C22—442no—
627C22—442no—
628C22—884no—
629C22D11×#9912yes—
630C22#1062241712yes—
631C22#1062241712yes—
632C22D11×#10412yes—
633C22C2×C22⋊C4×D1111yescharacteristic
634C22C2×#6696911yescharacteristic
635C22C2×#6697211yescharacteristic
636C4—21no—
637C4—21no—
638C4—21no—
639C4—21no—
640C4—44no—
641C4—42no—
642C4—42no—
643C4—114no—
644C4—222no—
645C4—444no—
646C4—442no—
647C2—21no—
648C2—21no—
649C2—22no—
650C2—224no—
651C2—442no—
652C2—882no—
653C2#1306710614yesdirect product factor
654C2C2×D11×#9911yescharacteristic
655C2C2×#1062241711yescharacteristic
656C2C2×D11×#10411yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#328C2
socleC23×C11C2×C22⋊C4
prime radicalC2×#10623158C2
cosocleC22×C4×C11C24
hypercenterC2×#328D11
hypocenterC11C2×#1501
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#328

Complements

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

NH ≅ G/Ntype
2. C2×D11×C22⋊C8C2semidirect
3. C2×#10622279C2semidirect
4. #13067106C2direct (N × H)
5. C2×#10622176C2semidirect
6. C2×#10622108C2semidirect
7. C2×#10622089C2semidirect
8. C2×C11×#328C2semidirect
9. C22×#4343C4semidirect
12. C2×#66999C4semidirect
19. #10623158C4semidirect
21. C2×#66948C4semidirect
24. C2×#66945C4semidirect
33. D11×C22⋊C8C22semidirect
35. #10622279C22semidirect
36. C11×#328C22semidirect
37. #10622176C22semidirect
38. #10622108C22semidirect
39. #10622089C22semidirect
49. C2×#4343C2×C4semidirect
72. #66999C2×C4semidirect
92. #66948C2×C4semidirect
98. #66945C2×C4semidirect
207. C2×#328D11semidirect
316. #328C2×D11semidirect
433. C2×C11#1501semidirect
529. C11C2×#1501semidirect
653. C2#13067106direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231582
C2×D11×C22⋊C82
C2×#106222792
#130671062
C2×#106221762
C2×#106221082
C2×#106220892
C2×C11×#3282
C2×#150111