Finite Group Databasebeta

← C2×#13078756 #15621887

Subgroups — C2×#13078756 #15621887

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×#10623010C211yesmaximal, characteristic, complemented
2C22×C4×D44C211yesmaximal, characteristic, complemented
3#13078756C2116yesmaximal, direct product factor
4C2×#10622334C211yesmaximal, characteristic, complemented
5C2×#10622349C211yesmaximal, characteristic, complemented
6C2×#10622460C212yesmaximal, complemented
7C2×#10622457C212yesmaximal, complemented
8C2×#10622344C211yesmaximal, characteristic, complemented
9C2×#10622345C211yesmaximal, characteristic
10C2×#10622324C212yesmaximal, complemented
11C2×#10622323C212yesmaximal, complemented
12C2×C11×#432C211yesmaximal, characteristic, complemented
13C23×D44C2211yescharacteristic
14C23×C4×D11—21no—
15C22×C42×C11C2211yescharacteristic
16C2×#66983C2211yescharacteristic
17C2×#66982—21no—
18C2×C4×C22⋊D11—21no—
19C22×(C2×D11)⋊C4—21no—
20C22×C4⋊Dic11C2211yescharacteristic
21C2×#66977C2211yescharacteristic
22C22×D88C2212yes—
23C22×#4314C2212yes—
24#10623010—24no—
25#10623010C2218yescomplemented
26C2×#66929—21no—
27C2×#66928C2211yescharacteristic, complemented
28C2×C4×D44—24no—
29C2×C4×D44—21no—
30C2×C4×D44—21no—
31C2×C4×D44C2212yes—
32C2×C4×D44C2212yes—
33C2×C4×D44C2218yescomplemented
34C2×C4×D44C2211yescharacteristic, complemented
35C2×#66925—21no—
36C2×#66923C2211yescharacteristic, complemented
37C2×C4×Dic22C2211yescharacteristic, complemented
38C11×#432C2218yescomplemented
39C2×C11×C4⋊C8C2212yescomplemented
40C2×C11×C22⋊C8C2211yescharacteristic
41C2×C11×C22⋊C8C2211yescharacteristic
42C2×C11×#97C2212yescomplemented
43C2×#66885C2212yes—
44C2×#66885C2212yes—
45C2×#66885C2212yescomplemented
46C2×#66882C2212yescomplemented
47C2×#66881C2212yescomplemented
48C2×#66880C2212yescomplemented
49#10622460C22116yescomplemented
50#10622457C22116yescomplemented
51#10622349C2218yescomplemented
52#10622345C2218yes—
53#10622344C2218yescomplemented
54#10622334C2218yescomplemented
55#10622324C22116yescomplemented
56#10622323C22116yescomplemented
57C24×D11—21no—
58C23×C4×C11D411yescharacteristic
59C23×C4×C11D411yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C22×C22⋊D11—21no—
62C23×Dic11—21no—
63C22×D44—21no—
64C22×D44—22no—
65C22×D44—28no—
66C22×D44C2311yescharacteristic
67C22×D44C2314yes—
68C22×D44C2312yes—
69C22×C4×D11—21no—
70C22×C4×D11—22no—
71C22×C4×D11—22no—
72C22×C4×D11—28no—
73C22×C4×D11—48no—
74C22×Dic22C2311yescharacteristic
75C22×C8×C11C2312yes—
76C22×C8×C11C2312yes—
77C2×C42×C11D411yescharacteristic
78C2×C42×C11D411yescharacteristic
79C2×C42×C11D414yes—
80C2×C42×C11C2311yescharacteristic
81C2×C42×C11C2311yescharacteristic
82C2×C42×C11C2314yes—
83C2×C22⋊Dic11—21no—
84#66983—22no—
85#66983C2314yes—
86#66982—28no—
87C4×C22⋊D11—28no—
88C2×(C2×D11)⋊C4—21no—
89C2×(C2×D11)⋊C4—21no—
90C2×(C2×D11)⋊C4—22no—
91C2×(C2×D11)⋊C4—22no—
92C2×(C2×D11)⋊C4—28no—
93C2×(C2×D11)⋊C4—21no—
94C2×(C2×D11)⋊C4—21no—
95C2×C4⋊Dic11—21no—
96C2×C4⋊Dic11—22no—
97C2×C4⋊Dic11C2311yescharacteristic
98C2×C4⋊Dic11C2311yescharacteristic
99C2×C4⋊Dic11C2312yes—
100C2×C4⋊Dic11C2314yes—
101#66977—22no—
102#66977C2314yes—
103C2×Dic11⋊C4—21no—
104C2×Dic11⋊C4—21no—
105C2×Dic11⋊C4—21no—
106C2×Dic11⋊C4—21no—
107C2×C4×Dic11—21no—
108C2×D88—28no—
109C2×D88C2318yes—
110C2×#4314—28no—
111C2×#4314C2318yes—
112#66929—28no—
113#66928—22no—
114#66928C2314yescomplemented
115C4×D44—24no—
116C4×D44—24no—
117C4×D44—28no—
118C4×D44—28no—
119C4×D44—22no—
120C4×D44C2318yes—
121C4×D44C2318yes—
122C4×D44C2314yescomplemented
123#66925—28no—
124#66923—22no—
125#66923C2314yescomplemented
126C4×Dic22—22no—
127C4×Dic22C2314yescomplemented
128C11×C4⋊C8C2318yescomplemented
129C11×C22⋊C8C2314yes—
130C11×C22⋊C8C2314yes—
131C11×#97C2318yescomplemented
132#66885C2318yes—
133#66885C2318yes—
134#66885C2318yescomplemented
135#66882C2318yescomplemented
136#66881C2318yescomplemented
137#66880C2318yescomplemented
138C2×#3114—111nomaximal, Sylow
139C24×C11C2×D411yescharacteristic
140C23×D11—28no—
141C23×D11—24no—
142C23×D11—22no—
143C23×D11—21no—
144C23×D11—44no—
145C23×D11—44no—
146C22×C4×C11—24no—
147C22×C4×C11—24no—
148C22×C4×C11—42no—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D412yes—
155C22×C4×C11C2×D414yes—
156C22×C4×C11C2×D414yes—
157C22×C4×C11C2412yes—
158C22×C4×C11C2411yescharacteristic
159C2×C22⋊D11—24no—
160C2×C22⋊D11—44no—
161C22×Dic11—21no—
162C22×Dic11—21no—
163C22×Dic11—21no—
164C22×Dic11—24no—
165C22×Dic11—22no—
166C22×Dic11—44no—
167C2×D44—28no—
168C2×D44—216no—
169C2×D44—216no—
170C2×D44—24no—
171C2×D44—22no—
172C2×D44—21no—
173C2×D44—24no—
174C2×D44—24no—
175C2×D44#4118yes—
176C2×D44C2412yes—
177C2×D44C2414yes—
178C2×C4×D11—24no—
179C2×C4×D11—28no—
180C2×C4×D11—28no—
181C2×C4×D11—44no—
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×C11—24no—
190C2×C8×C11C2414yes—
191C2×C8×C11C2414yes—
192C42×C11C2×D412yes—
193C42×C11C2×D412yes—
194C42×C11C2×D414yes—
195C42×C11C2×D414yes—
196C42×C11C2412yes—
197C42×C11C2412yes—
198C22⋊Dic11—24no—
199(C2×D11)⋊C4—24no—
200(C2×D11)⋊C4—24no—
201(C2×D11)⋊C4—28no—
202(C2×D11)⋊C4—28no—
203(C2×D11)⋊C4—24no—
204(C2×D11)⋊C4—24no—
205C4⋊Dic11—21no—
206C4⋊Dic11—21no—
207C4⋊Dic11—24no—
208C4⋊Dic11—22no—
209C4⋊Dic11C2414yes—
210C4⋊Dic11C2412yes—
211C4⋊Dic11C2412yes—
212Dic11⋊C4—24no—
213Dic11⋊C4—24no—
214Dic11⋊C4—24no—
215Dic11⋊C4—24no—
216C4×Dic11—24no—
217D88—216no—
218#4314—216no—
219C2×#529—111no—
220C22×C4×D4—111no—
221#3114—1116no—
222C2×#483—111no—
223C2×#480—111no—
224C2×#478—112no—
225C2×#463—112no—
226C2×#450—111no—
227C2×#447—111no—
228C2×#442—112no—
229C2×#440—112no—
230C2×#432D1111yescharacteristic, complemented
231C23×C11—22no—
232C23×C11—22no—
233C23×C11AGL(1,ℤ/8)14yes—
234C23×C11C22×D412yes—
235C23×C11C22×D411yescharacteristic
236C22×D11—216no—
237C22×D11—28no—
238C22×D11—24no—
239C22×D11—22no—
240C22×D11—432no—
241C22×D11—48no—
242C22×D11—48no—
243C22×D11—44no—
244C22×D11—44no—
245C22×D11—42no—
246C22×D11—42no—
247C22×D11—42no—
248C2×C4×C11—22no—
249C2×C4×C11—28no—
250C2×C4×C11—22no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—24no—
255C2×C4×C11—24no—
256C2×C4×C11—44no—
257C2×C4×C11C22×D412yes—
258C2×C4×C11C22×D412yes—
259C2×C4×C11C22×D412yes—
260C2×C4×C11C22×D412yes—
261C2×C4×C11C22×D412yes—
262C2×C4×C11C22×D411yescharacteristic
263C2×C4×C11C2×#4114yes—
264C2×C4×C11C2511yescharacteristic
265C22⋊D11—48no—
266C2×Dic11—22no—
267C2×Dic11—22no—
268C2×Dic11—22no—
269C2×Dic11—24no—
270C2×Dic11—42no—
271C2×Dic11—48no—
272C2×Dic11—44no—
273C2×Dic11—42no—
274C2×Dic11—42no—
275D44—216no—
276D44—28no—
277D44—24no—
278D44—24no—
279D44—42no—
280D44C2×#4118yes—
281C4×D11—48no—
282C4×D11—416no—
283C4×D11—416no—
284Dic22—24no—
285Dic22—42no—
286C8×C11—24no—
287C8×C11—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×#121—111no—
300C2×C4×Q8—111no—
301C2×C4×D4—112no—
302C2×C4×D4—112no—
303C2×C4×D4—118no—
304C2×C4×D4—111no—
305C2×C4×D4—221no—
306C2×C4×D4—221no—
307C2×C4×D4—221no—
308C2×C4×D4—224no—
309C2×#117—221no—
310C22×C4⋊C4—111no—
311C22×C22⋊C4—221no—
312C22×C42C2×D1111yescharacteristic
313#483—118no—
314#480—118no—
315#478—1116no—
316#463—1116no—
317#450—118no—
318#447—118no—
319#442—1116no—
320#440—1116no—
321#432C2×D1118yescomplemented
322C2×#107—112no—
323C2×#106—112no—
324C2×C4⋊C8C2×D1112yescomplemented
325C2×#103—112no—
326C2×#102—112no—
327C2×#102—112no—
328C2×#102—112no—
329C2×C22⋊C8C2×D1111yescharacteristic
330C2×C22⋊C8C2×D1111yescharacteristic
331C2×#97C2×D1112yescomplemented
332C22×C11—28no—
333C22×C11—22no—
334C22×C11—22no—
335C22×C11#52512yes—
336C22×C11C2×AGL(1,ℤ/8)14yes—
337C22×C11C2×AGL(1,ℤ/8)12yes—
338C22×C11#57512yes—
339C22×C11C23×D411yescharacteristic
340C2×D11—28no—
341C2×D11—432no—
342C2×D11—416no—
343C2×D11—44no—
344C2×D11—44no—
345C2×D11—42no—
346C2×D11—42no—
347C2×D11—42no—
348C2×D11—84no—
349C4×C11—22no—
350C4×C11—22no—
351C4×C11—22no—
352C4×C11—22no—
353C4×C11—22no—
354C4×C11#52512yes—
355C4×C11C22×#4112yes—
356Dic11—42no—
357Dic11—44no—
358Dic11—42no—
359Dic11—42no—
360C25—221no—
361C22×Q8—111no—
362C22×D4—112no—
363C22×D4—114no—
364C22×D4—111no—
365C22×D4—228no—
366C22×D4—221no—
367C22×D4—222no—
368C22×D4—221no—
369C23×C4—221no—
370C23×C4—221no—
371C23×C4—228no—
372C23×C4—222no—
373C23×C4—222no—
374C23×C4—448no—
375C23×C4D4411yescharacteristic
376C23×C4D4411yescharacteristic
377C23×C4C22×D1111yescharacteristic
378C2×SD16—118no—
379C2×SD16—228no—
380C2×D8—118no—
381C2×D8—228no—
382C22×C8C22×D1112yes—
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—114no—
393#121—222no—
394C4×Q8—114no—
395C4×Q8—222no—
396C4×D4—118no—
397C4×D4—118no—
398C4×D4—114no—
399C4×D4—228no—
400C4×D4—228no—
401C4×D4—224no—
402C4×D4—224no—
403C4×D4—228no—
404C4×D4—222no—
405#117—228no—
406C2×C4⋊C4—112no—
407C2×C4⋊C4—114no—
408C2×C4⋊C4—111no—
409C2×C4⋊C4—111no—
410C2×C4⋊C4—222no—
411C2×C4⋊C4—221no—
412C2×C4⋊C4—221no—
413C2×C4⋊C4—221no—
414C2×C4⋊C4—221no—
415C2×C4⋊C4—221no—
416C2×C22⋊C4—221no—
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—221no—
425C2×C42D4411yescharacteristic
426C2×C42D4411yescharacteristic
427C2×C42D4414yes—
428C2×C42C22×D1111yescharacteristic
429C2×C42C22×D1111yescharacteristic
430C2×C42C22×D1114yes—
431#107—118no—
432#106—118no—
433C4⋊C8C22×D1118yescomplemented
434#103—118no—
435#102—118no—
436#102—118no—
437#102—118no—
438C22⋊C8C22×D1114yes—
439C22⋊C8C22×D1114yes—
440#97C22×D1118yescomplemented
441C2×C11—24no—
442C2×C11#311414yescomplemented
443C2×C11C2×#52511yescharacteristic
444C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
445C2×C11C2×#57511yescharacteristic
446D11—48no—
447D11—82no—
448C24—228no—
449C24—224no—
450C24—222no—
451C24—221no—
452C24—444no—
453C24—444no—
454C24C2×D4411yescharacteristic
455C2×Q8—112no—
456C2×Q8—221no—
457C2×Q8—224no—
458C2×D4—118no—
459C2×D4—114no—
460C2×D4—112no—
461C2×D4—2216no—
462C2×D4—228no—
463C2×D4—2216no—
464C2×D4—224no—
465C2×D4—224no—
466C2×D4—222no—
467C2×D4—221no—
468C2×D4—224no—
469C2×D4—224no—
470C2×D4—444no—
471C22×C4—24no—
472C22×C4—24no—
473C22×C4—42no—
474C22×C4—224no—
475C22×C4—221no—
476C22×C4—221no—
477C22×C4—221no—
478C22×C4—222no—
479C22×C4—224no—
480C22×C4—228no—
481C22×C4—228no—
482C22×C4—4432no—
483C22×C4—448no—
484C22×C4—448no—
485C22×C4—444no—
486C22×C4—444no—
487C22×C4C2×D4414yes—
488C22×C4C2×D4412yes—
489C22×C4C2×D4411yescharacteristic
490C22×C4C2×D4411yescharacteristic
491C22×C4C2×D4411yescharacteristic
492C22×C4C2×D4411yescharacteristic
493C22×C4C2×D4411yescharacteristic
494C22×C4C2×D4414yes—
495C22×C4C23×D1112yes—
496C22×C4C23×D1111yescharacteristic
497SD16—2216no—
498D8—2216no—
499C2×C8—24no—
500C2×C8—24no—
501C2×C8C23×D1114yes—
502C2×C8C23×D1114yes—
503C4⋊C4—112no—
504C4⋊C4—112no—
505C4⋊C4—114no—
506C4⋊C4—224no—
507C4⋊C4—222no—
508C4⋊C4—221no—
509C4⋊C4—221no—
510C4⋊C4—224no—
511C4⋊C4—224no—
512C4⋊C4—224no—
513C4⋊C4—224no—
514C22⋊C4—224no—
515C22⋊C4—228no—
516C22⋊C4—228no—
517C22⋊C4—224no—
518C22⋊C4—224no—
519C22⋊C4—224no—
520C22⋊C4—224no—
521C42—224no—
522C42C2×D4414yes—
523C42C2×D4412yes—
524C42C2×D4412yes—
525C42C2×D4414yes—
526C42C23×D1112yes—
527C42C23×D1112yes—
528C11C2×#311411yescharacteristic, complemented, Sylow
529C23—22no—
530C23—22no—
531C23—2216no—
532C23—228no—
533C23—224no—
534C23—222no—
535C23—448no—
536C23—4432no—
537C23—448no—
538C23—444no—
539C23—444no—
540C23—442no—
541C23—442no—
542C23—442no—
543C23#6696114yes—
544C23C22×D4412yes—
545C23C22×D4411yescharacteristic
546Q8—224no—
547Q8—442no—
548D4—118no—
549D4—2216no—
550D4—228no—
551D4—224no—
552D4—224no—
553D4—448no—
554D4—442no—
555C2×C4—28no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—24no—
562C2×C4—24no—
563C2×C4—44no—
564C2×C4—222no—
565C2×C4—222no—
566C2×C4—222no—
567C2×C4—224no—
568C2×C4—4416no—
569C2×C4—4416no—
570C2×C4—448no—
571C2×C4—448no—
572C2×C4—444no—
573C2×C4—442no—
574C2×C4—442no—
575C2×C4—442no—
576C2×C4C22×D4412yes—
577C2×C4C22×D4412yes—
578C2×C4C22×D4412yes—
579C2×C4C22×D4412yes—
580C2×C4C22×D4412yes—
581C2×C4C22×D4411yescharacteristic
582C2×C4#41×D1114yes—
583C2×C4C24×D1111yescharacteristic
584C8—24no—
585C8—24no—
586C22—22no—
587C22—22no—
588C22—28no—
589C22—228no—
590C22—4432no—
591C22—444no—
592C22—444no—
593C22—4416no—
594C22—442no—
595C22—442no—
596C22—442no—
597C22—884no—
598C22#1062305512yes—
599C22C2×#6696114yes—
600C22C2×#6696112yes—
601C22#1062327912yes—
602C22C23×D4411yescharacteristic
603C4—22no—
604C4—22no—
605C4—22no—
606C4—22no—
607C4—22no—
608C4—442no—
609C4—444no—
610C4—442no—
611C4—442no—
612C4#1062305512yes—
613C4C2×#41×D1112yes—
614C2—24no—
615C2—448no—
616C2—882no—
617C2#1307875614yesdirect product factor
618C2C2×#1062305511yescharacteristic
619C2C22×#6696111yescharacteristic
620C2C2×#1062327911yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#432C2
socleC23×C11C22×D4
prime radicalC2×#10622345C2
hypercenterC2×#432D11
hypocenterC11C2×#3114
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#432

Complements

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

NH ≅ G/Ntype
1. C2×#10623010C2semidirect
2. C22×C4×D44C2semidirect
3. #13078756C2direct (N × H)
4. C2×#10622334C2semidirect
5. C2×#10622349C2semidirect
6. C2×#10622460C2semidirect
7. C2×#10622457C2semidirect
8. C2×#10622344C2semidirect
10. C2×#10622324C2semidirect
11. C2×#10622323C2semidirect
12. C2×C11×#432C2semidirect
25. #10623010C22semidirect
27. C2×#66928C22semidirect
33. C2×C4×D44C22semidirect
34. C2×C4×D44C22semidirect
36. C2×#66923C22semidirect
37. C2×C4×Dic22C22semidirect
38. C11×#432C22semidirect
39. C2×C11×C4⋊C8C22semidirect
42. C2×C11×#97C22semidirect
45. C2×#66885C22semidirect
46. C2×#66882C22semidirect
47. C2×#66881C22semidirect
48. C2×#66880C22semidirect
49. #10622460C22semidirect
50. #10622457C22semidirect
51. #10622349C22semidirect
53. #10622344C22semidirect
54. #10622334C22semidirect
55. #10622324C22semidirect
56. #10622323C22semidirect
114. #66928C23semidirect
122. C4×D44C23semidirect
125. #66923C23semidirect
127. C4×Dic22C23semidirect
128. C11×C4⋊C8C23semidirect
131. C11×#97C23semidirect
134. #66885C23semidirect
135. #66882C23semidirect
136. #66881C23semidirect
137. #66880C23semidirect
230. C2×#432D11semidirect
321. #432C2×D11semidirect
324. C2×C4⋊C8C2×D11semidirect
331. C2×#97C2×D11semidirect
433. C4⋊C8C22×D11semidirect
440. #97C22×D11semidirect
442. C2×C11#3114semidirect
528. C11C2×#3114semidirect
617. C2#13078756direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230102
C22×C4×D442
#130787562
C2×#106223342
C2×#106223492
C2×#106224602
C2×#106224572
C2×#106223442
C2×#106223452
C2×#106223242
C2×#106223232
C2×C11×#4322
C2×#311411