Finite Group Databasebeta

← C2×#13067117 #14720910

Subgroups — C2×#13067117 #14720910

Order 2816.

1834 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623137C211yesmaximal, characteristic
2C2×#10622339C211yesmaximal, characteristic, complemented
3C2×D11×#95C211yesmaximal, characteristic, complemented
4#13067117C218yesmaximal, direct product factor
5C2×#10622105C211yesmaximal, characteristic, complemented
6C2×#10622090C211yesmaximal, characteristic, complemented
7C2×#10622175C211yesmaximal, characteristic, complemented
8C2×C11×#327C211yesmaximal, characteristic, complemented
9C22×#4341C411yescharacteristic, complemented
10C23×C4×D11—21no—
11C23×C4×D11C2211yescharacteristic
12C2×C11×#121C2211yescharacteristic
13C2×#66991C411yescharacteristic, complemented
14C2×#66990—21no—
15C2×D4×Dic11—21no—
16C2×#66977C2211yescharacteristic
17C22×#4313—21no—
18#10623137—22no—
19#10623137—22no—
20#10623137C414yescomplemented
21#10623137C2214yes—
22C2×#66950C411yescharacteristic, complemented
23C2×#66945C411yescharacteristic, complemented
24C2×#66936—21no—
25C2×(C22⋊D11)⋊C4—21no—
26C2×C11×C22⋊C8C2211yescharacteristic
27C2×C11×#95C2211yescharacteristic
28C2×C11⋊#95—21no—
29C2×C11⋊#95C2211yescharacteristic
30C2×C22⋊(C11⋊C8)C2211yescharacteristic
31C2×(C2×D11)⋊C8—21no—
32#10622339—22no—
33#10622339C2214yescomplemented
34D11×#95—22no—
35D11×#95C2214yescomplemented
36C11×#327C2214yescomplemented
37#10622175C2214yescomplemented
38#10622105C2214yescomplemented
39#10622090C2214yescomplemented
40C24×D11D411yescharacteristic
41C22×D4×C11—21no—
42C22×D4×C11C2×C411yescharacteristic, complemented
43C23×C4×C11—21no—
44C23×C4×C11C2311yescharacteristic
45C22×C22⋊D11—21no—
46C22×C22⋊D11—21no—
47C23×Dic11—21no—
48C23×Dic11—21no—
49C23×Dic11D411yescharacteristic
50C2×#4341—22no—
51C2×#4341—44no—
52C2×#4341C2×C414yescomplemented
53C22×C4×D11—28no—
54C22×C4×D11—24no—
55C22×C4×D11—44no—
56C22×C4×D11—44no—
57C22×C4×D11—44no—
58C22×C4×D11C2×C411yescharacteristic
59C22×C4×D11C2×C411yescharacteristic
60C22×C4×D11C2×C412yes—
61C22×C4×D11D411yescharacteristic
62C22×C4×D11D412yes—
63C22×C4×D11D411yescharacteristic
64C22×C4×D11D412yes—
65C22×C4×D11C2312yes—
66C22×Dic22C2×C411yescharacteristic, complemented
67C22×C8×C11—21no—
68C11×#121—21no—
69C11×#121—21no—
70C11×#121C2×C412yescomplemented
71C11×#121C2312yes—
72C2×C11×C4⋊C4C2×C411yescharacteristic, complemented
73C2×C11×C22⋊C4—21no—
74C2×C22⋊Dic11—21no—
75C2×C22⋊Dic11—21no—
76#66991—22no—
77#66991C2×C414yescomplemented
78#66990—24no—
79#66990—24no—
80D4×Dic11—24no—
81D4×Dic11—24no—
82C2×(C2×D11)⋊C4—21no—
83C2×(C2×D11)⋊C4—21no—
84C2×C4⋊Dic11—21no—
85C2×C4⋊Dic11C2×C411yescharacteristic, complemented
86#66977—21no—
87#66977—21no—
88#66977C2×C412yescomplemented
89#66977C2312yes—
90C2×Dic11⋊C4—21no—
91C2×C4×Dic11—21no—
92C22×C11⋊C8—21no—
93C2×#4313—24no—
94C2×#4313—44no—
95#66950—22no—
96#66950C2×C414yescomplemented
97#66945—22no—
98#66945C2×C414yescomplemented
99#66936—24no—
100#66936—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⋊#95—24no—
109C11⋊#95C2312yes—
110C22⋊(C11⋊C8)—21no—
111C22⋊(C11⋊C8)C2312yes—
112(C2×D11)⋊C8—24no—
113C2×#1504—111nomaximal, Sylow
114C24×C11—21no—
115C24×C11C2×D411yescharacteristic
116C23×D11—22no—
117C23×D11—22no—
118C23×D11—24no—
119C23×D11—24no—
120C23×D11C22⋊C412yes—
121C23×D11C22⋊C411yescharacteristic
122C23×D11C22⋊C411yescharacteristic
123C23×D11C2×D412yes—
124C2×D4×C11—22no—
125C2×D4×C11—22no—
126C2×D4×C11—21no—
127C2×D4×C11—42no—
128C2×D4×C11—42no—
129C2×D4×C11—42no—
130C2×D4×C11C22×C412yescomplemented
131C22×C4×C11—24no—
132C22×C4×C11—21no—
133C22×C4×C11—22no—
134C22×C4×C11—42no—
135C22×C4×C11—42no—
136C22×C4×C11—42no—
137C22×C4×C11C22×C411yescharacteristic
138C22×C4×C11C22×C411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2411yescharacteristic
143C2×C22⋊D11—24no—
144C2×C22⋊D11—24no—
145C2×C22⋊D11—44no—
146C2×C22⋊D11—44no—
147C22×Dic11—24no—
148C22×Dic11—24no—
149C22×Dic11—21no—
150C22×Dic11—21no—
151C22×Dic11—22no—
152C22×Dic11—42no—
153C22×Dic11—42no—
154C22×Dic11—44no—
155C22×Dic11—42no—
156C22×Dic11C22⋊C411yescharacteristic
157C22×Dic11C22⋊C411yescharacteristic
158C22×Dic11C22⋊C412yes—
159C22×Dic11C2×D412yes—
160#4341—48no—
161#4341—48no—
162C2×C4×D11—216no—
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—432no—
172C2×C4×D11—48no—
173C2×C4×D11—48no—
174C2×C4×D11C22⋊C412yes—
175C2×C4×D11C22⋊C412yes—
176C2×C4×D11C22⋊C412yes—
177C2×C4×D11C22⋊C412yes—
178C2×C4×D11C22×C412yes—
179C2×C4×D11C22×C412yes—
180C2×C4×D11C2×D412yes—
181C2×C4×D11C2×D412yes—
182C2×Dic22—21no—
183C2×Dic22—42no—
184C2×Dic22C22×C412yescomplemented
185C2×C8×C11—22no—
186C2×C8×C11—42no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4C22×C412yescomplemented
189C11×C22⋊C4—22no—
190C11×C22⋊C4—22no—
191C22⋊Dic11—24no—
192C22⋊Dic11—22no—
193C22⋊Dic11—22no—
194(C2×D11)⋊C4—24no—
195(C2×D11)⋊C4—24no—
196C4⋊Dic11—24no—
197C4⋊Dic11—21no—
198C4⋊Dic11C22×C412yescomplemented
199Dic11⋊C4—22no—
200Dic11⋊C4—22no—
201C4×Dic11—24no—
202C2×C11⋊C8—22no—
203C2×C11⋊C8—42no—
204#4313—48no—
205C2×#525—111no—
206C2×#407—111no—
207C22×#95—111no—
208#1504—118no—
209C2×#328—111no—
210C2×#328—111no—
211C2×#327—111no—
212C2×#327D1111yescharacteristic, complemented
213C23×C11—22no—
214C23×C11—22no—
215C23×C11—22no—
216C23×C11—42no—
217C23×C11—42no—
218C23×C11—42no—
219C23×C11C2×C22⋊C411yescharacteristic
220C23×C11C2×C22⋊C411yescharacteristic
221C23×C11AGL(1,ℤ/8)12yes—
222C23×C11#13712yes—
223C23×C11C22×D411yescharacteristic
224C22×D11—216no—
225C22×D11—216no—
226C22×D11—22no—
227C22×D11—22no—
228C22×D11—22no—
229C22×D11—24no—
230C22×D11—22no—
231C22×D11—22no—
232C22×D11—22no—
233C22×D11—24no—
234C22×D11—24no—
235C22×D11—24no—
236C22×D11—24no—
237C22×D11#9914yes—
238C22×D11#10414yes—
239C22×D11C2×C22⋊C412yes—
240C22×D11C2×C22⋊C412yes—
241D4×C11—42no—
242D4×C11—42no—
243D4×C11—42no—
244D4×C11—42no—
245D4×C11—44no—
246C2×C4×C11—22no—
247C2×C4×C11—22no—
248C2×C4×C11—24no—
249C2×C4×C11—22no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—42no—
255C2×C4×C11—48no—
256C2×C4×C11—42no—
257C2×C4×C11—42no—
258C2×C4×C11C2×C22⋊C411yescharacteristic
259C2×C4×C11C2×C22⋊C411yescharacteristic
260C2×C4×C11C23×C411yescharacteristic
261C2×C4×C11C22×D411yescharacteristic
262C22⋊D11—48no—
263C22⋊D11—48no—
264C2×Dic11—22no—
265C2×Dic11—22no—
266C2×Dic11—24no—
267C2×Dic11—22no—
268C2×Dic11—22no—
269C2×Dic11—42no—
270C2×Dic11—42no—
271C2×Dic11—48no—
272C2×Dic11—42no—
273C2×Dic11—48no—
274C2×Dic11—42no—
275C2×Dic11—42no—
276C2×Dic11—42no—
277C2×Dic11C2×C22⋊C412yes—
278C2×Dic11C2×C22⋊C412yes—
279C4×D11—24no—
280C4×D11—24no—
281C4×D11—24no—
282C4×D11—24no—
283C4×D11—42no—
284C4×D11—42no—
285C4×D11—42no—
286C4×D11—42no—
287C4×D11—432no—
288Dic22—42no—
289Dic22—42no—
290C8×C11—42no—
291C11⋊C8—42no—
292C22×#41—111no—
293C24×C4—111no—
294C24×C4—221no—
295C22×M16—221no—
296#525—114no—
297#525—114no—
298#525—222no—
299#525—222no—
300C2×#123—221no—
301C2×C22⋊Q8—111no—
302C2×C22⋊Q8—111no—
303C2×#121—111no—
304C2×#121C2×D1111yescharacteristic
305C2×#120—221no—
306C2×C4×D4—221no—
307C2×C4×D4—221no—
308C2×#117—111no—
309#407—114no—
310#407—222no—
311C2×C22⋊C8—111no—
312C2×C22⋊C8—221no—
313C2×C22⋊C8C2×D1111yescharacteristic
314C2×#95—111no—
315C2×#95—114no—
316C2×#95—222no—
317C2×#95—221no—
318C2×#95C2×D1111yescharacteristic
319#328—114no—
320#328—114no—
321#327—114no—
322#327C2×D1114yescomplemented
323C22×C11—21no—
324C22×C11—21no—
325C22×C11—21no—
326C22×C11—21no—
327C22×C11—24no—
328C22×C11—24no—
329C22×C11—42no—
330C22×C11—42no—
331C22×C11—42no—
332C22×C11—84no—
333C22×C11C2×#9912yes—
334C22×C11#41712yes—
335C22×C11#41712yes—
336C22×C11C2×#10412yes—
337C22×C11C22×C22⋊C411yescharacteristic
338C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
339C22×C11C2×#13711yescharacteristic
340C2×D11—28no—
341C2×D11—216no—
342C2×D11—28no—
343C2×D11—22no—
344C2×D11—22no—
345C2×D11—22no—
346C2×D11—22no—
347C2×D11—28no—
348C2×D11—28no—
349C2×D11C2×#9914yes—
350C2×D11C2×#10414yes—
351C4×C11—21no—
352C4×C11—21no—
353C4×C11—21no—
354C4×C11—21no—
355C4×C11—44no—
356C4×C11—42no—
357Dic11—22no—
358Dic11—22no—
359Dic11—44no—
360Dic11—42no—
361Dic11—42no—
362C25—111no—
363C2×#41—114no—
364C2×#41—222no—
365C2×#41—444no—
366C22×Q8—111no—
367C22×D4—21no—
368C22×D4—221no—
369C22×D4—221no—
370C22×D4C4×D1111yescharacteristic, complemented
371C23×C4—21no—
372C23×C4—111no—
373C23×C4—111no—
374C23×C4—111no—
375C23×C4—111no—
376C23×C4—112no—
377C23×C4—111no—
378C23×C4—112no—
379C23×C4—112no—
380C23×C4—112no—
381C23×C4—224no—
382C23×C4—228no—
383C23×C4—221no—
384C23×C4—221no—
385C23×C4—444no—
386C23×C4—444no—
387C23×C4—444no—
388C23×C4C22×D1111yescharacteristic
389C2×M16—224no—
390C2×M16—444no—
391C22×C8—21no—
392C22×C8—221no—
393#123—224no—
394#123—224no—
395C22⋊Q8—112no—
396C22⋊Q8—112no—
397C22⋊Q8—114no—
398C22⋊Q8—222no—
399C22⋊Q8—221no—
400C22⋊Q8—221no—
401#121—21no—
402#121—21no—
403#121—114no—
404#121—222no—
405#121C4×D1112yescomplemented
406#121C22×D1112yes—
407#120—224no—
408#120—224no—
409C4×D4—224no—
410C4×D4—224no—
411C4×D4—224no—
412C4×D4—224no—
413#117—114no—
414#117—222no—
415C2×C4⋊C4—111no—
416C2×C4⋊C4—221no—
417C2×C4⋊C4—221no—
418C2×C4⋊C4C4×D1111yescharacteristic, complemented
419C2×C22⋊C4—21no—
420C2×C22⋊C4—221no—
421C2×C22⋊C4—221no—
422C2×C22⋊C4—221no—
423C2×C22⋊C4—221no—
424C2×C42—221no—
425C22⋊C8—21no—
426C22⋊C8—112no—
427C22⋊C8—224no—
428C22⋊C8—221no—
429C22⋊C8C22×D1112yes—
430#95—21no—
431#95—112no—
432#95—224no—
433#95—221no—
434#95C22×D1112yes—
435C2×C11—21no—
436C2×C11—21no—
437C2×C11—22no—
438C2×C11—82no—
439C2×C11#150414yescomplemented
440C2×C11C22×#9911yescharacteristic
441C2×C11C2×#41711yescharacteristic
442C2×C11C22×#10411yescharacteristic
443D11—24no—
444D11—24no—
445C24—21no—
446C24—111no—
447C24—111no—
448C24—112no—
449C24—112no—
450C24—224no—
451C24—224no—
452C24—222no—
453C24—222no—
454C24D4×D1111yescharacteristic
455#41—448no—
456#41—448no—
457C2×Q8—112no—
458C2×Q8—221no—
459C2×Q8—442no—
460C2×D4—22no—
461C2×D4—22no—
462C2×D4—21no—
463C2×D4—42no—
464C2×D4—42no—
465C2×D4—42no—
466C2×D4—224no—
467C2×D4—224no—
468C2×D4—444no—
469C2×D4—444no—
470C2×D4C2×C4×D1112yescomplemented
471C22×C4—24no—
472C22×C4—21no—
473C22×C4—22no—
474C22×C4—42no—
475C22×C4—42no—
476C22×C4—42no—
477C22×C4—111no—
478C22×C4—111no—
479C22×C4—112no—
480C22×C4—112no—
481C22×C4—112no—
482C22×C4—112no—
483C22×C4—112no—
484C22×C4—112no—
485C22×C4—112no—
486C22×C4—112no—
487C22×C4—112no—
488C22×C4—112no—
489C22×C4—224no—
490C22×C4—224no—
491C22×C4—2216no—
492C22×C4—224no—
493C22×C4—224no—
494C22×C4—221no—
495C22×C4—221no—
496C22×C4—222no—
497C22×C4—442no—
498C22×C4—442no—
499C22×C4—444no—
500C22×C4—444no—
501C22×C4—444no—
502C22×C4—444no—
503C22×C4—448no—
504C22×C4—4432no—
505C22×C4—448no—
506C22×C4—442no—
507C22×C4—444no—
508C22×C4—442no—
509C22×C4—442no—
510C22×C4C2×C4×D1111yescharacteristic
511C22×C4C2×C4×D1111yescharacteristic
512C22×C4D4×D1111yescharacteristic
513C22×C4D4×D1111yescharacteristic
514C22×C4D4×D1111yescharacteristic
515C22×C4C23×D1111yescharacteristic
516M16—448no—
517C2×C8—22no—
518C2×C8—42no—
519C2×C8—222no—
520C2×C8—442no—
521C4⋊C4—21no—
522C4⋊C4—112no—
523C4⋊C4—224no—
524C4⋊C4—221no—
525C4⋊C4—222no—
526C4⋊C4—222no—
527C4⋊C4C2×C4×D1112yescomplemented
528C22⋊C4—22no—
529C22⋊C4—22no—
530C22⋊C4—224no—
531C22⋊C4—224no—
532C22⋊C4—224no—
533C22⋊C4—222no—
534C22⋊C4—222no—
535C42—224no—
536C11C2×#150411yescharacteristic, complemented, Sylow
537C23—22no—
538C23—22no—
539C23—22no—
540C23—42no—
541C23—42no—
542C23—42no—
543C23—112no—
544C23—112no—
545C23—114no—
546C23—114no—
547C23—224no—
548C23—224no—
549C23—224no—
550C23—224no—
551C23—2216no—
552C23—2216no—
553C23—222no—
554C23—222no—
555C23—222no—
556C23—224no—
557C23—222no—
558C23—222no—
559C23—222no—
560C23C22⋊C4×D1111yescharacteristic
561C23C22⋊C4×D1111yescharacteristic
562C23#6696412yes—
563C23#6696812yes—
564C23C2×D4×D1111yescharacteristic
565Q8—442no—
566Q8—442no—
567D4—42no—
568D4—42no—
569D4—42no—
570D4—42no—
571D4—44no—
572D4—448no—
573D4—448no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—24no—
577C2×C4—22no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—42no—
583C2×C4—48no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—112no—
587C2×C4—112no—
588C2×C4—224no—
589C2×C4—224no—
590C2×C4—224no—
591C2×C4—224no—
592C2×C4—222no—
593C2×C4—222no—
594C2×C4—224no—
595C2×C4—222no—
596C2×C4—222no—
597C2×C4—442no—
598C2×C4—442no—
599C2×C4—442no—
600C2×C4—442no—
601C2×C4—4432no—
602C2×C4—442no—
603C2×C4—442no—
604C2×C4—448no—
605C2×C4—442no—
606C2×C4—448no—
607C2×C4—442no—
608C2×C4—442no—
609C2×C4—442no—
610C2×C4C22⋊C4×D1111yescharacteristic
611C2×C4C22⋊C4×D1111yescharacteristic
612C2×C4C22×C4×D1111yescharacteristic
613C2×C4C2×D4×D1111yescharacteristic
614C8—42no—
615C8—442no—
616C22—21no—
617C22—21no—
618C22—24no—
619C22—24no—
620C22—21no—
621C22—21no—
622C22—42no—
623C22—42no—
624C22—42no—
625C22—84no—
626C22—114no—
627C22—114no—
628C22—228no—
629C22—228no—
630C22—2216no—
631C22—222no—
632C22—228no—
633C22—228no—
634C22—222no—
635C22—222no—
636C22—222no—
637C22D11×#9912yes—
638C22#1062238412yes—
639C22#1062238412yes—
640C22D11×#10412yes—
641C22C2×C22⋊C4×D1111yescharacteristic
642C22C2×#6696411yescharacteristic
643C22C2×#6696811yescharacteristic
644C4—21no—
645C4—21no—
646C4—21no—
647C4—21no—
648C4—44no—
649C4—42no—
650C4—222no—
651C4—222no—
652C4—444no—
653C4—442no—
654C4—442no—
655C2—21no—
656C2—21no—
657C2—22no—
658C2—82no—
659C2—224no—
660C2—224no—
661C2#1306711714yesdirect product factor
662C2C2×D11×#9911yescharacteristic
663C2C2×#1062238411yescharacteristic
664C2C2×D11×#10411yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#327C2
socleC23×C11C2×C22⋊C4
prime radicalC2×#10623137C2
cosocleC22×C4×C11C24
hypercenterC2×#327D11
hypocenterC11C2×#1504
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#327

Complements

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

NH ≅ G/Ntype
2. C2×#10622339C2semidirect
3. C2×D11×#95C2semidirect
4. #13067117C2direct (N × H)
5. C2×#10622105C2semidirect
6. C2×#10622090C2semidirect
7. C2×#10622175C2semidirect
8. C2×C11×#327C2semidirect
9. C22×#4341C4semidirect
13. C2×#66991C4semidirect
20. #10623137C4semidirect
22. C2×#66950C4semidirect
23. C2×#66945C4semidirect
33. #10622339C22semidirect
35. D11×#95C22semidirect
36. C11×#327C22semidirect
37. #10622175C22semidirect
38. #10622105C22semidirect
39. #10622090C22semidirect
42. C22×D4×C11C2×C4semidirect
52. C2×#4341C2×C4semidirect
66. C22×Dic22C2×C4semidirect
70. C11×#121C2×C4semidirect
72. C2×C11×C4⋊C4C2×C4semidirect
77. #66991C2×C4semidirect
85. C2×C4⋊Dic11C2×C4semidirect
88. #66977C2×C4semidirect
96. #66950C2×C4semidirect
98. #66945C2×C4semidirect
130. C2×D4×C11C22×C4semidirect
184. C2×Dic22C22×C4semidirect
188. C11×C4⋊C4C22×C4semidirect
198. C4⋊Dic11C22×C4semidirect
212. C2×#327D11semidirect
322. #327C2×D11semidirect
370. C22×D4C4×D11semidirect
405. #121C4×D11semidirect
418. C2×C4⋊C4C4×D11semidirect
439. C2×C11#1504semidirect
470. C2×D4C2×C4×D11semidirect
527. C4⋊C4C2×C4×D11semidirect
536. C11C2×#1504semidirect
661. C2#13067117direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231372
C2×#106223392
C2×D11×#952
#130671172
C2×#106221052
C2×#106220902
C2×#106221752
C2×C11×#3272
C2×#150411