Finite Group Databasebeta

← C2×#13078751 #15621882

Subgroups — C2×#13078751 #15621882

Order 2816.

2582 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623131C211yesmaximal, characteristic, complemented
2C22×#66946C211yesmaximal, characteristic, complemented
3#13078751C2116yesmaximal, direct product factor
4C2×#10622584C211yesmaximal, characteristic, complemented
5C2×#10622504C212yesmaximal, complemented
6C2×#10622400C212yesmaximal, complemented
7C2×#10622344C211yesmaximal, characteristic, complemented
8C2×#10622649C211yesmaximal, characteristic
9C2×#10622398C212yesmaximal, complemented
10C2×#10622502C212yesmaximal, complemented
11C2×#10622332C211yesmaximal, characteristic, complemented
12C2×C11×#480C211yesmaximal, characteristic, complemented
13C23×D44C2211yescharacteristic
14C23×C4×D11—21no—
15C2×C11×#121C2211yescharacteristic
16C22×C11×C4⋊C4C2211yescharacteristic
17C2×#66989C2211yescharacteristic, complemented
18C2×#66988—21no—
19C2×D4×Dic11—21no—
20C2×D4×Dic11C2211yescharacteristic, complemented
21C22×#4323C2212yes—
22C22×(C2×D11)⋊C4—21no—
23C2×#66977C2211yescharacteristic
24C22×C4×Dic11C2211yescharacteristic
25C22×#4314C2212yes—
26#10623131—24no—
27#10623131C2218yescomplemented
28C2×#66946—24no—
29C2×#66946—21no—
30C2×#66946—21no—
31C2×#66946C2212yes—
32C2×#66946C2212yes—
33C2×#66946C2218yescomplemented
34C2×#66943C2211yescharacteristic, complemented
35C2×#66940C2211yescharacteristic, complemented
36C2×#66932—21no—
37C2×#66930—21no—
38C11×#480C2218yescomplemented
39C2×C11×#107C2212yescomplemented
40C2×C11×#102C2212yescomplemented
41C2×C11×C22⋊C8C2211yescharacteristic
42C2×C22⋊(C11⋊C8)C2211yescharacteristic
43C2×#66885C2212yes—
44C2×#66879C2212yescomplemented
45C2×Dic11⋊C8C2212yescomplemented
46#10622649C2218yes—
47#10622584C2218yescomplemented
48C2×#66874C2212yescomplemented
49C2×#66873C2212yes—
50C2×#66872C2212yescomplemented
51#10622504C22116yescomplemented
52#10622502C22116yescomplemented
53#10622400C22116yescomplemented
54#10622398C22116yescomplemented
55#10622344C2218yescomplemented
56#10622332C2218yescomplemented
57C24×D11—21no—
58C22×D4×C11—21no—
59C22×D4×C11C2311yescharacteristic
60C23×C4×C11—21no—
61C23×C4×C11C2311yescharacteristic
62C23×Dic11—21no—
63C23×Dic11D411yescharacteristic
64C23×Dic11D411yescharacteristic
65C22×D44—21no—
66C22×D44—22no—
67C22×D44—28no—
68C22×D44C2314yes—
69C22×D44C2312yes—
70C22×C4×D11—22no—
71C22×C4×D11—22no—
72C22×C4×D11—28no—
73C22×C4×D11—48no—
74C22×Dic22C2311yescharacteristic
75C22×C8×C11C2312yes—
76C11×#121—22no—
77C11×#121C2314yes—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—22no—
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C4⋊C4C2312yes—
82C2×C11×C4⋊C4C2314yes—
83C2×C11×C22⋊C4—21no—
84C2×C22⋊Dic11—21no—
85C2×C22⋊Dic11—21no—
86C2×C22⋊Dic11—21no—
87C2×C22⋊Dic11—21no—
88#66989—22no—
89#66989C2314yescomplemented
90#66988—28no—
91D4×Dic11—28no—
92D4×Dic11—22no—
93D4×Dic11C2314yescomplemented
94C2×#4323—28no—
95C2×#4323C2318yes—
96C2×(C2×D11)⋊C4—22no—
97C2×(C2×D11)⋊C4—22no—
98C2×(C2×D11)⋊C4—28no—
99C2×C4⋊Dic11—21no—
100C2×C4⋊Dic11C2311yescharacteristic
101#66977—22no—
102#66977C2314yes—
103C2×Dic11⋊C4—21no—
104C2×Dic11⋊C4—21no—
105C2×Dic11⋊C4—21no—
106C2×C4×Dic11—21no—
107C2×C4×Dic11D411yescharacteristic
108C2×C4×Dic11D411yescharacteristic
109C2×C4×Dic11D414yes—
110C2×C4×Dic11C2311yescharacteristic
111C2×C4×Dic11C2311yescharacteristic
112C2×C4×Dic11C2314yes—
113C22×C11⋊C8C2312yes—
114C2×#4314—28no—
115C2×#4314C2318yes—
116#66946—24no—
117#66946—24no—
118#66946—28no—
119#66946—28no—
120#66946C2318yes—
121#66946C2318yes—
122#66943—22no—
123#66943C2314yescomplemented
124#66940—22no—
125#66940C2314yescomplemented
126#66932—28no—
127#66930—28no—
128C11×#107C2318yescomplemented
129C11×#102C2318yescomplemented
130C11×C22⋊C8C2314yes—
131C22⋊(C11⋊C8)C2314yes—
132#66885C2318yes—
133#66879C2318yescomplemented
134Dic11⋊C8C2318yescomplemented
135#66874C2318yescomplemented
136#66873C2318yes—
137#66872C2318yescomplemented
138C2×#3114—111nomaximal, Sylow
139C24×C11—21no—
140C24×C11C2×D411yescharacteristic
141C23×D11—28no—
142C23×D11—24no—
143C23×D11—22no—
144C23×D11—44no—
145C23×D11—44no—
146C2×D4×C11—24no—
147C2×D4×C11—21no—
148C2×D4×C11—24no—
149C2×D4×C11—44no—
150C2×D4×C11C2412yes—
151C22×C4×C11—24no—
152C22×C4×C11—21no—
153C22×C4×C11—24no—
154C22×C4×C11—22no—
155C22×C4×C11—44no—
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D412yes—
158C22×C4×C11C2412yes—
159C22×C4×C11C2411yescharacteristic
160C22×Dic11—24no—
161C22×Dic11—24no—
162C22×Dic11—21no—
163C22×Dic11—21no—
164C22×Dic11—42no—
165C22×Dic11—44no—
166C22×Dic11C2×D411yescharacteristic
167C22×Dic11C2×D411yescharacteristic
168C22×Dic11C2×D411yescharacteristic
169C22×Dic11C2×D411yescharacteristic
170C22×Dic11C2×D414yes—
171C22×Dic11C2×D414yes—
172C2×D44—28no—
173C2×D44—216no—
174C2×D44—216no—
175C2×D44—24no—
176C2×D44—22no—
177C2×D44—24no—
178C2×D44#4118yes—
179C2×D44C2414yes—
180C2×C4×D11—28no—
181C2×C4×D11—28no—
182C2×C4×D11—48no—
183C2×C4×D11—48no—
184C2×C4×D11—432no—
185C2×Dic22—21no—
186C2×Dic22—24no—
187C2×Dic22C2412yes—
188C2×C8×C11—24no—
189C2×C8×C11C2414yes—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—24no—
192C11×C4⋊C4—22no—
193C11×C4⋊C4C2414yes—
194C11×C4⋊C4C2412yes—
195C11×C22⋊C4—24no—
196C22⋊Dic11—24no—
197C22⋊Dic11—24no—
198C22⋊Dic11—24no—
199C22⋊Dic11—24no—
200#4323—216no—
201(C2×D11)⋊C4—28no—
202(C2×D11)⋊C4—28no—
203C4⋊Dic11—24no—
204C4⋊Dic11—21no—
205C4⋊Dic11C2412yes—
206Dic11⋊C4—24no—
207Dic11⋊C4—24no—
208Dic11⋊C4—24no—
209C4×Dic11—24no—
210C4×Dic11C2×D414yes—
211C4×Dic11C2×D414yes—
212C4×Dic11C2×D412yes—
213C4×Dic11C2×D412yes—
214C4×Dic11C2412yes—
215C4×Dic11C2412yes—
216C2×C11⋊C8—24no—
217C2×C11⋊C8C2414yes—
218#4314—216no—
219C2×#529—111no—
220C22×C4×D4—111no—
221#3114—1116no—
222C2×#483—111no—
223C2×#480D1111yescharacteristic, complemented
224C2×#478—112no—
225C2×#463—112no—
226C2×#450—111no—
227C2×#447—111no—
228C2×#442—112no—
229C2×#440—112no—
230C2×#432—111no—
231C23×C11—22no—
232C23×C11—22no—
233C23×C11—22no—
234C23×C11—42no—
235C23×C11—42no—
236C23×C11—42no—
237C23×C11AGL(1,ℤ/8)14yes—
238C23×C11C22×D412yes—
239C23×C11C22×D411yescharacteristic
240C22×D11—216no—
241C22×D11—28no—
242C22×D11—24no—
243C22×D11—432no—
244C22×D11—48no—
245C22×D11—48no—
246C22×D11—44no—
247C22×D11—44no—
248D4×C11—24no—
249D4×C11—48no—
250D4×C11—42no—
251C2×C4×C11—22no—
252C2×C4×C11—24no—
253C2×C4×C11—24no—
254C2×C4×C11—22no—
255C2×C4×C11—24no—
256C2×C4×C11—48no—
257C2×C4×C11—44no—
258C2×C4×C11—42no—
259C2×C4×C11C22×D412yes—
260C2×C4×C11C22×D411yescharacteristic
261C2×C4×C11C2×#4114yes—
262C2×C4×C11C2511yescharacteristic
263C2×Dic11—28no—
264C2×Dic11—22no—
265C2×Dic11—22no—
266C2×Dic11—22no—
267C2×Dic11—22no—
268C2×Dic11—22no—
269C2×Dic11—22no—
270C2×Dic11—44no—
271C2×Dic11—48no—
272C2×Dic11—42no—
273C2×Dic11—42no—
274C2×Dic11C22×D412yes—
275C2×Dic11C22×D412yes—
276C2×Dic11C22×D412yes—
277C2×Dic11C22×D412yes—
278D44—216no—
279D44—28no—
280D44—24no—
281D44C2×#4118yes—
282C4×D11—416no—
283C4×D11—416no—
284Dic22—24no—
285Dic22—42no—
286C8×C11—24no—
287C11⋊C8—24no—
288C23×D4—111no—
289C24×C4—221no—
290C22×SD16—112no—
291C22×D8—112no—
292#529—118no—
293#529—224no—
294C2×#126—221no—
295C2×#125—111no—
296C2×#124—111no—
297C2×#123—221no—
298C2×C22⋊Q8—111no—
299C2×#121C2×D1111yescharacteristic
300C2×C4×Q8—111no—
301C2×C4×D4—111no—
302C2×C4×D4—112no—
303C2×C4×D4—118no—
304C2×C4×D4—112no—
305C2×C4×D4—221no—
306C2×C4×D4—221no—
307C2×C4×D4—224no—
308C2×C4×D4—221no—
309C2×#117—221no—
310C22×C4⋊C4C2×D1111yescharacteristic
311C22×C22⋊C4—221no—
312C22×C42—111no—
313#483—118no—
314#480C2×D1118yescomplemented
315#478—1116no—
316#463—1116no—
317#450—118no—
318#447—118no—
319#442—1116no—
320#440—1116no—
321#432—118no—
322C2×#107C2×D1112yescomplemented
323C2×#106—112no—
324C2×C4⋊C8—112no—
325C2×#103—112no—
326C2×#102—112no—
327C2×#102—112no—
328C2×#102C2×D1112yescomplemented
329C2×C22⋊C8—111no—
330C2×C22⋊C8C2×D1111yescharacteristic
331C2×#97—112no—
332C22×C11—28no—
333C22×C11—22no—
334C22×C11—22no—
335C22×C11—42no—
336C22×C11—42no—
337C22×C11—42no—
338C22×C11—84no—
339C22×C11#52512yes—
340C22×C11C2×AGL(1,ℤ/8)14yes—
341C22×C11C2×AGL(1,ℤ/8)12yes—
342C22×C11#57512yes—
343C22×C11C23×D411yescharacteristic
344C2×D11—28no—
345C2×D11—432no—
346C2×D11—416no—
347C2×D11—44no—
348C2×D11—44no—
349C4×C11—22no—
350C4×C11—44no—
351C4×C11—42no—
352C4×C11#52512yes—
353C4×C11C22×#4112yes—
354Dic11—22no—
355Dic11—22no—
356Dic11—22no—
357Dic11—22no—
358Dic11—42no—
359Dic11—42no—
360C25—221no—
361C22×Q8—111no—
362C22×D4—21no—
363C22×D4—112no—
364C22×D4—114no—
365C22×D4—228no—
366C22×D4—222no—
367C22×D4—221no—
368C22×D4C22×D1111yescharacteristic
369C23×C4—21no—
370C23×C4—111no—
371C23×C4—111no—
372C23×C4—228no—
373C23×C4—222no—
374C23×C4—222no—
375C23×C4—221no—
376C23×C4—448no—
377C23×C4C22×D1111yescharacteristic
378C2×SD16—118no—
379C2×SD16—228no—
380C2×D8—118no—
381C2×D8—228no—
382C22×C8—112no—
383C22×C8C22×D1112yes—
384#126—228no—
385#125—114no—
386#125—222no—
387#124—114no—
388#124—222no—
389#123—228no—
390C22⋊Q8—114no—
391C22⋊Q8—222no—
392#121—22no—
393#121C22×D1114yes—
394C4×Q8—114no—
395C4×Q8—222no—
396C4×D4—114no—
397C4×D4—118no—
398C4×D4—118no—
399C4×D4—228no—
400C4×D4—224no—
401C4×D4—224no—
402C4×D4—228no—
403C4×D4—222no—
404C4×D4—228no—
405#117—228no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—111no—
409C2×C4⋊C4—221no—
410C2×C4⋊C4—221no—
411C2×C4⋊C4—221no—
412C2×C4⋊C4—221no—
413C2×C4⋊C4C22×D1112yes—
414C2×C4⋊C4C22×D1114yes—
415C2×C4⋊C4C22×D1111yescharacteristic
416C2×C22⋊C4—21no—
417C2×C22⋊C4—228no—
418C2×C22⋊C4—222no—
419C2×C22⋊C4—222no—
420C2×C22⋊C4—221no—
421C2×C22⋊C4—221no—
422C2×C22⋊C4—221no—
423C2×C22⋊C4—221no—
424C2×C42—111no—
425C2×C42—111no—
426C2×C42—114no—
427C2×C42—111no—
428C2×C42—111no—
429C2×C42—114no—
430C2×C42—221no—
431#107C22×D1118yescomplemented
432#106—118no—
433C4⋊C8—118no—
434#103—118no—
435#102—118no—
436#102—118no—
437#102C22×D1118yescomplemented
438C22⋊C8—114no—
439C22⋊C8C22×D1114yes—
440#97—118no—
441C2×C11—24no—
442C2×C11—82no—
443C2×C11#311414yescomplemented
444C2×C11C2×#52511yescharacteristic
445C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
446C2×C11C2×#57511yescharacteristic
447D11—48no—
448C24—21no—
449C24—228no—
450C24—224no—
451C24—222no—
452C24—444no—
453C24—444no—
454C24D4×D1111yescharacteristic
455C2×Q8—112no—
456C2×Q8—221no—
457C2×Q8—224no—
458C2×D4—24no—
459C2×D4—21no—
460C2×D4—24no—
461C2×D4—44no—
462C2×D4—118no—
463C2×D4—114no—
464C2×D4—2216no—
465C2×D4—228no—
466C2×D4—2216no—
467C2×D4—224no—
468C2×D4—222no—
469C2×D4—224no—
470C2×D4C23×D1112yes—
471C22×C4—24no—
472C22×C4—24no—
473C22×C4—21no—
474C22×C4—22no—
475C22×C4—44no—
476C22×C4—114no—
477C22×C4—111no—
478C22×C4—111no—
479C22×C4—111no—
480C22×C4—111no—
481C22×C4—114no—
482C22×C4—228no—
483C22×C4—228no—
484C22×C4—224no—
485C22×C4—224no—
486C22×C4—221no—
487C22×C4—221no—
488C22×C4—4432no—
489C22×C4—448no—
490C22×C4—448no—
491C22×C4—442no—
492C22×C4—444no—
493C22×C4D4×D1112yes—
494C22×C4D4×D1111yescharacteristic
495C22×C4C23×D1112yes—
496C22×C4C23×D1111yescharacteristic
497SD16—2216no—
498D8—2216no—
499C2×C8—24no—
500C2×C8—114no—
501C2×C8—224no—
502C2×C8C23×D1114yes—
503C4⋊C4—24no—
504C4⋊C4—22no—
505C4⋊C4—21no—
506C4⋊C4—112no—
507C4⋊C4—224no—
508C4⋊C4—224no—
509C4⋊C4—224no—
510C4⋊C4—221no—
511C4⋊C4—224no—
512C4⋊C4C23×D1112yes—
513C4⋊C4C23×D1114yes—
514C22⋊C4—24no—
515C22⋊C4—228no—
516C22⋊C4—228no—
517C22⋊C4—224no—
518C22⋊C4—224no—
519C22⋊C4—224no—
520C22⋊C4—224no—
521C42—114no—
522C42—112no—
523C42—112no—
524C42—114no—
525C42—112no—
526C42—112no—
527C42—224no—
528C11C2×#311411yescharacteristic, complemented, Sylow
529C23—22no—
530C23—22no—
531C23—22no—
532C23—42no—
533C23—42no—
534C23—42no—
535C23—2216no—
536C23—228no—
537C23—224no—
538C23—4432no—
539C23—448no—
540C23—448no—
541C23—444no—
542C23—444no—
543C23#6696414yes—
544C23C2×D4×D1112yes—
545C23C2×D4×D1111yescharacteristic
546Q8—224no—
547Q8—442no—
548D4—24no—
549D4—48no—
550D4—42no—
551D4—118no—
552D4—2216no—
553D4—228no—
554D4—224no—
555C2×C4—22no—
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—22no—
559C2×C4—24no—
560C2×C4—48no—
561C2×C4—44no—
562C2×C4—42no—
563C2×C4—112no—
564C2×C4—112no—
565C2×C4—112no—
566C2×C4—112no—
567C2×C4—228no—
568C2×C4—222no—
569C2×C4—222no—
570C2×C4—222no—
571C2×C4—222no—
572C2×C4—222no—
573C2×C4—222no—
574C2×C4—4416no—
575C2×C4—4416no—
576C2×C4—444no—
577C2×C4—448no—
578C2×C4—442no—
579C2×C4—442no—
580C2×C4C2×D4×D1112yes—
581C2×C4C2×D4×D1111yescharacteristic
582C2×C4#41×D1114yes—
583C2×C4C24×D1111yescharacteristic
584C8—24no—
585C8—224no—
586C22—28no—
587C22—22no—
588C22—22no—
589C22—42no—
590C22—42no—
591C22—42no—
592C22—84no—
593C22—228no—
594C22—4432no—
595C22—444no—
596C22—4416no—
597C22—444no—
598C22#1062318712yes—
599C22C2×#6696414yes—
600C22C2×#6696412yes—
601C22#1062330812yes—
602C22C22×D4×D1111yescharacteristic
603C4—22no—
604C4—44no—
605C4—42no—
606C4—222no—
607C4—222no—
608C4—222no—
609C4—222no—
610C4—442no—
611C4—442no—
612C4#1062318712yes—
613C4C2×#41×D1112yes—
614C2—24no—
615C2—82no—
616C2—448no—
617C2#1307875114yesdirect product factor
618C2C2×#1062318711yescharacteristic
619C2C22×#6696411yescharacteristic
620C2C2×#1062330811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#480C2
socleC23×C11C22×D4
prime radicalC2×#10622649C2
hypercenterC2×#480D11
hypocenterC11C2×#3114
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#480

Complements

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

NH ≅ G/Ntype
1. C2×#10623131C2semidirect
2. C22×#66946C2semidirect
3. #13078751C2direct (N × H)
4. C2×#10622584C2semidirect
5. C2×#10622504C2semidirect
6. C2×#10622400C2semidirect
7. C2×#10622344C2semidirect
9. C2×#10622398C2semidirect
10. C2×#10622502C2semidirect
11. C2×#10622332C2semidirect
12. C2×C11×#480C2semidirect
17. C2×#66989C22semidirect
20. C2×D4×Dic11C22semidirect
27. #10623131C22semidirect
33. C2×#66946C22semidirect
34. C2×#66943C22semidirect
35. C2×#66940C22semidirect
38. C11×#480C22semidirect
39. C2×C11×#107C22semidirect
40. C2×C11×#102C22semidirect
44. C2×#66879C22semidirect
45. C2×Dic11⋊C8C22semidirect
47. #10622584C22semidirect
48. C2×#66874C22semidirect
50. C2×#66872C22semidirect
51. #10622504C22semidirect
52. #10622502C22semidirect
53. #10622400C22semidirect
54. #10622398C22semidirect
55. #10622344C22semidirect
56. #10622332C22semidirect
89. #66989C23semidirect
93. D4×Dic11C23semidirect
123. #66943C23semidirect
125. #66940C23semidirect
128. C11×#107C23semidirect
129. C11×#102C23semidirect
133. #66879C23semidirect
134. Dic11⋊C8C23semidirect
135. #66874C23semidirect
137. #66872C23semidirect
223. C2×#480D11semidirect
314. #480C2×D11semidirect
322. C2×#107C2×D11semidirect
328. C2×#102C2×D11semidirect
431. #107C22×D11semidirect
437. #102C22×D11semidirect
443. C2×C11#3114semidirect
528. C11C2×#3114semidirect
617. C2#13078751direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231312
C22×#669462
#130787512
C2×#106225842
C2×#106225042
C2×#106224002
C2×#106223442
C2×#106226492
C2×#106223982
C2×#106225022
C2×#106223322
C2×C11×#4802
C2×#311411