Finite Group Databasebeta

← C2×#13078754 #15621885

Subgroups — C2×#13078754 #15621885

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
2#13078754C2116yesmaximal, direct product factor
3C2×#10622584C211yesmaximal, characteristic, complemented
4C2×#10622580C211yesmaximal, characteristic, complemented
5C2×#10622622C212yesmaximal, complemented
6C2×#10622629C212yesmaximal, complemented
7C2×#10622831C211yesmaximal, characteristic, complemented
8C2×#10622830C211yesmaximal, characteristic
9C2×#10622627C212yesmaximal, complemented
10C2×#10622631C212yesmaximal, complemented
11C2×#10622539C211yesmaximal, characteristic, complemented
12C22×C4×D4×C11C211yesmaximal, characteristic, complemented
13C23×D4×C11C2211yescharacteristic
14C24×C4×C11—21no—
15C2×C4×D4×C11—21no—
16C2×C4×D4×C11—21no—
17C2×C4×D4×C11—24no—
18C2×C4×D4×C11C2212yes—
19C2×C4×D4×C11C2212yes—
20C2×C4×D4×C11C2218yescomplemented
21C22×C11×C4⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4—21no—
23C22×C42×C11C2211yescharacteristic
24C22×#4324C2212yes—
25C22×#4323C2212yes—
26C2×#66983C2211yescharacteristic
27C2×#66982—21no—
28C2×C4×C22⋊D11—21no—
29C2×#66977C2211yescharacteristic
30#10623010—24no—
31#10623010C2218yescomplemented
32C2×#66929—21no—
33C2×#66928C2211yescharacteristic, complemented
34C2×C4×D44C2211yescharacteristic, complemented
35C2×#66925—21no—
36C2×#66923C2211yescharacteristic, complemented
37C2×C4×Dic22C2211yescharacteristic, complemented
38#10622831C2218yescomplemented
39#10622830C2218yes—
40C2×#66896C2212yes—
41C2×#66896C2212yes—
42C2×C22⋊(C11⋊C8)C2211yescharacteristic
43C2×C22⋊(C11⋊C8)C2211yescharacteristic
44#10622631C22116yescomplemented
45#10622629C22116yescomplemented
46#10622627C22116yescomplemented
47#10622622C22116yescomplemented
48#10622584C2218yescomplemented
49C2×#66874C2212yescomplemented
50#10622580C2218yescomplemented
51C2×#66873C2212yescomplemented
52C2×#66872C2212yescomplemented
53C2×#66871C2212yescomplemented
54#10622539C2218yescomplemented
55C2×C4⋊(C11⋊C8)C2212yescomplemented
56C2×#66867C2212yescomplemented
57C25×C11—21no—
58C22×D4×C11—28no—
59C22×D4×C11—21no—
60C22×D4×C11—22no—
61C22×D4×C11C2314yes—
62C22×D4×C11C2312yes—
63C23×C4×C11—21no—
64C23×C4×C11—22no—
65C23×C4×C11—22no—
66C23×C4×C11—28no—
67C23×C4×C11—48no—
68C23×C4×C11D411yescharacteristic
69C23×C4×C11D411yescharacteristic
70C23×C4×C11C2311yescharacteristic
71C22×C22⋊D11—21no—
72C22×D44C2311yescharacteristic
73C22×C4×D11—21no—
74C22×Dic22C2311yescharacteristic
75C4×D4×C11—24no—
76C4×D4×C11—24no—
77C4×D4×C11—28no—
78C4×D4×C11—28no—
79C4×D4×C11C2318yes—
80C4×D4×C11C2318yes—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4—22no—
83C2×C11×C4⋊C4C2312yes—
84C2×C11×C4⋊C4C2314yes—
85C2×C11×C22⋊C4—22no—
86C2×C11×C22⋊C4—22no—
87C2×C11×C22⋊C4—28no—
88C2×C42×C11D411yescharacteristic
89C2×C42×C11D411yescharacteristic
90C2×C42×C11D414yes—
91C2×C42×C11C2311yescharacteristic
92C2×C42×C11C2311yescharacteristic
93C2×C42×C11C2314yes—
94C2×C22⋊Dic11—21no—
95C2×#4324—28no—
96C2×#4324C2318yes—
97C2×#4323—28no—
98C2×#4323C2318yes—
99#66983—22no—
100#66983C2314yes—
101#66982—28no—
102C4×C22⋊D11—28no—
103C2×(C2×D11)⋊C4—21no—
104C2×(C2×D11)⋊C4—21no—
105C2×(C2×D11)⋊C4—21no—
106C2×(C2×D11)⋊C4—21no—
107C2×C4⋊Dic11C2311yescharacteristic
108C2×C4⋊Dic11C2311yescharacteristic
109#66977—22no—
110#66977C2314yes—
111C2×Dic11⋊C4—21no—
112C2×Dic11⋊C4—21no—
113C2×Dic11⋊C4—21no—
114C2×Dic11⋊C4—21no—
115C2×C4×Dic11—21no—
116C22×C11⋊C8C2312yes—
117C22×C11⋊C8C2312yes—
118#66929—28no—
119#66928—22no—
120#66928C2314yescomplemented
121C4×D44—22no—
122C4×D44C2314yescomplemented
123#66925—28no—
124#66923—22no—
125#66923C2314yescomplemented
126C4×Dic22—22no—
127C4×Dic22C2314yescomplemented
128#66896C2318yes—
129#66896C2318yes—
130C22⋊(C11⋊C8)C2314yes—
131C22⋊(C11⋊C8)C2314yes—
132#66874C2318yescomplemented
133#66873C2318yescomplemented
134#66872C2318yescomplemented
135#66871C2318yescomplemented
136C4⋊(C11⋊C8)C2318yescomplemented
137#66867C2318yescomplemented
138C2×#3114—111nomaximal, Sylow
139C24×C11—28no—
140C24×C11—24no—
141C24×C11—22no—
142C24×C11—44no—
143C24×C11—44no—
144C24×C11C2×D411yescharacteristic
145C23×D11—21no—
146C2×D4×C11—28no—
147C2×D4×C11—216no—
148C2×D4×C11—216no—
149C2×D4×C11—24no—
150C2×D4×C11—22no—
151C2×D4×C11—24no—
152C2×D4×C11#4118yes—
153C2×D4×C11C2414yes—
154C22×C4×C11—24no—
155C22×C4×C11—24no—
156C22×C4×C11—24no—
157C22×C4×C11—22no—
158C22×C4×C11—28no—
159C22×C4×C11—28no—
160C22×C4×C11—42no—
161C22×C4×C11—48no—
162C22×C4×C11—48no—
163C22×C4×C11—432no—
164C22×C4×C11—44no—
165C22×C4×C11C2×D411yescharacteristic
166C22×C4×C11C2×D411yescharacteristic
167C22×C4×C11C2×D411yescharacteristic
168C22×C4×C11C2×D411yescharacteristic
169C22×C4×C11C2×D411yescharacteristic
170C22×C4×C11C2×D412yes—
171C22×C4×C11C2×D414yes—
172C22×C4×C11C2×D414yes—
173C22×C4×C11C2412yes—
174C22×C4×C11C2411yescharacteristic
175C2×C22⋊D11—24no—
176C2×C22⋊D11—44no—
177C22×Dic11—21no—
178C22×Dic11—21no—
179C22×Dic11—21no—
180C2×D44—21no—
181C2×D44—24no—
182C2×D44C2412yes—
183C2×C4×D11—24no—
184C2×C4×D11—44no—
185C2×Dic22—21no—
186C2×Dic22—24no—
187C2×Dic22C2412yes—
188C11×C4⋊C4—24no—
189C11×C4⋊C4—22no—
190C11×C4⋊C4C2414yes—
191C11×C22⋊C4—28no—
192C11×C22⋊C4—28no—
193C42×C11C2×D412yes—
194C42×C11C2×D412yes—
195C42×C11C2×D414yes—
196C42×C11C2×D414yes—
197C42×C11C2412yes—
198C42×C11C2412yes—
199C22⋊Dic11—24no—
200#4324—216no—
201#4323—216no—
202(C2×D11)⋊C4—24no—
203(C2×D11)⋊C4—24no—
204(C2×D11)⋊C4—24no—
205(C2×D11)⋊C4—24no—
206C4⋊Dic11—21no—
207C4⋊Dic11—21no—
208C4⋊Dic11C2412yes—
209C4⋊Dic11C2412yes—
210Dic11⋊C4—24no—
211Dic11⋊C4—24no—
212Dic11⋊C4—24no—
213Dic11⋊C4—24no—
214C4×Dic11—24no—
215C2×C11⋊C8—24no—
216C2×C11⋊C8—24no—
217C2×C11⋊C8C2414yes—
218C2×C11⋊C8C2414yes—
219C2×#529—111no—
220C22×C4×D4D1111yescharacteristic, complemented
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×#432—111no—
231C23×C11—22no—
232C23×C11—22no—
233C23×C11—216no—
234C23×C11—28no—
235C23×C11—24no—
236C23×C11—432no—
237C23×C11—48no—
238C23×C11—48no—
239C23×C11—44no—
240C23×C11—44no—
241C23×C11AGL(1,ℤ/8)14yes—
242C23×C11C22×D412yes—
243C23×C11C22×D411yescharacteristic
244C22×D11—22no—
245C22×D11—42no—
246C22×D11—42no—
247C22×D11—42no—
248D4×C11—216no—
249D4×C11—28no—
250D4×C11—24no—
251D4×C11C2×#4118yes—
252C2×C4×C11—22no—
253C2×C4×C11—28no—
254C2×C4×C11—22no—
255C2×C4×C11—22no—
256C2×C4×C11—22no—
257C2×C4×C11—22no—
258C2×C4×C11—24no—
259C2×C4×C11—24no—
260C2×C4×C11—24no—
261C2×C4×C11—44no—
262C2×C4×C11—416no—
263C2×C4×C11—416no—
264C2×C4×C11—48no—
265C2×C4×C11—44no—
266C2×C4×C11C22×D412yes—
267C2×C4×C11C22×D412yes—
268C2×C4×C11C22×D412yes—
269C2×C4×C11C22×D412yes—
270C2×C4×C11C22×D412yes—
271C2×C4×C11C22×D411yescharacteristic
272C2×C4×C11C2×#4114yes—
273C2×C4×C11C2511yescharacteristic
274C22⋊D11—48no—
275C2×Dic11—22no—
276C2×Dic11—22no—
277C2×Dic11—22no—
278C2×Dic11—42no—
279C2×Dic11—42no—
280C2×Dic11—42no—
281D44—24no—
282D44—42no—
283C4×D11—48no—
284Dic22—24no—
285Dic22—42no—
286C11⋊C8—24no—
287C11⋊C8—24no—
288C23×D4C2×D1111yescharacteristic
289C24×C4—21no—
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—21no—
302C2×C4×D4—21no—
303C2×C4×D4—24no—
304C2×C4×D4—111no—
305C2×C4×D4—221no—
306C2×C4×D4C2×D1112yes—
307C2×C4×D4C2×D1112yes—
308C2×C4×D4C2×D1118yescomplemented
309C2×#117—221no—
310C22×C4⋊C4C2×D1111yescharacteristic
311C22×C22⋊C4—21no—
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#432—118no—
322C2×#107—112no—
323C2×#106—112no—
324C2×C4⋊C8—112no—
325C2×#103—112no—
326C2×#102—112no—
327C2×#102—112no—
328C2×#102—112no—
329C2×C22⋊C8—111no—
330C2×C22⋊C8—111no—
331C2×#97—112no—
332C22×C11—28no—
333C22×C11—22no—
334C22×C11—22no—
335C22×C11—28no—
336C22×C11—432no—
337C22×C11—416no—
338C22×C11—44no—
339C22×C11—44no—
340C22×C11#52512yes—
341C22×C11C2×AGL(1,ℤ/8)14yes—
342C22×C11C2×AGL(1,ℤ/8)12yes—
343C22×C11#57512yes—
344C22×C11C23×D411yescharacteristic
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—44no—
355C4×C11#52512yes—
356C4×C11C22×#4112yes—
357Dic11—42no—
358Dic11—42no—
359Dic11—42no—
360C25—21no—
361C22×Q8—111no—
362C22×D4—28no—
363C22×D4—22no—
364C22×D4—21no—
365C22×D4—111no—
366C22×D4—221no—
367C22×D4C22×D1114yes—
368C22×D4C22×D1112yes—
369C23×C4—21no—
370C23×C4—22no—
371C23×C4—22no—
372C23×C4—28no—
373C23×C4—48no—
374C23×C4—221no—
375C23×C4C22⋊D1111yescharacteristic
376C23×C4C22⋊D1111yescharacteristic
377C23×C4C22×D1111yescharacteristic
378C2×SD16—118no—
379C2×SD16—228no—
380C2×D8—118no—
381C2×D8—228no—
382C22×C8—112no—
383C22×C8—112no—
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—24no—
397C4×D4—24no—
398C4×D4—28no—
399C4×D4—28no—
400C4×D4—114no—
401C4×D4—228no—
402C4×D4—222no—
403C4×D4C22×D1118yes—
404C4×D4C22×D1118yes—
405#117—228no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—111no—
409C2×C4⋊C4—111no—
410C2×C4⋊C4—221no—
411C2×C4⋊C4—221no—
412C2×C4⋊C4—221no—
413C2×C4⋊C4—221no—
414C2×C4⋊C4C22×D1112yes—
415C2×C4⋊C4C22×D1114yes—
416C2×C22⋊C4—22no—
417C2×C22⋊C4—22no—
418C2×C22⋊C4—28no—
419C2×C22⋊C4—221no—
420C2×C22⋊C4—221no—
421C2×C22⋊C4—221no—
422C2×C22⋊C4—221no—
423C2×C22⋊C4—221no—
424C2×C42—221no—
425C2×C42C22⋊D1111yescharacteristic
426C2×C42C22⋊D1111yescharacteristic
427C2×C42C22⋊D1114yes—
428C2×C42C22×D1111yescharacteristic
429C2×C42C22×D1111yescharacteristic
430C2×C42C22×D1114yes—
431#107—118no—
432#106—118no—
433C4⋊C8—118no—
434#103—118no—
435#102—118no—
436#102—118no—
437#102—118no—
438C22⋊C8—114no—
439C22⋊C8—114no—
440#97—118no—
441C2×C11—24no—
442C2×C11—48no—
443C2×C11#311414yescomplemented
444C2×C11C2×#52511yescharacteristic
445C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
446C2×C11C2×#57511yescharacteristic
447D11—82no—
448C24—28no—
449C24—24no—
450C24—22no—
451C24—44no—
452C24—44no—
453C24—221no—
454C24C2×C22⋊D1111yescharacteristic
455C2×Q8—112no—
456C2×Q8—221no—
457C2×Q8—224no—
458C2×D4—28no—
459C2×D4—216no—
460C2×D4—216no—
461C2×D4—24no—
462C2×D4—24no—
463C2×D4—22no—
464C2×D4—112no—
465C2×D4—224no—
466C2×D4—224no—
467C2×D4—221no—
468C2×D4—444no—
469C2×D4#433918yes—
470C2×D4C23×D1114yes—
471C22×C4—24no—
472C22×C4—24no—
473C22×C4—24no—
474C22×C4—22no—
475C22×C4—28no—
476C22×C4—28no—
477C22×C4—42no—
478C22×C4—48no—
479C22×C4—48no—
480C22×C4—432no—
481C22×C4—44no—
482C22×C4—221no—
483C22×C4—221no—
484C22×C4—221no—
485C22×C4—224no—
486C22×C4—444no—
487C22×C4C2×C22⋊D1114yes—
488C22×C4C2×C22⋊D1112yes—
489C22×C4C2×C22⋊D1111yescharacteristic
490C22×C4C2×C22⋊D1111yescharacteristic
491C22×C4C2×C22⋊D1111yescharacteristic
492C22×C4C2×C22⋊D1111yescharacteristic
493C22×C4C2×C22⋊D1111yescharacteristic
494C22×C4C2×C22⋊D1114yes—
495C22×C4C23×D1112yes—
496C22×C4C23×D1111yescharacteristic
497SD16—2216no—
498D8—2216no—
499C2×C8—114no—
500C2×C8—114no—
501C2×C8—224no—
502C2×C8—224no—
503C4⋊C4—24no—
504C4⋊C4—22no—
505C4⋊C4—112no—
506C4⋊C4—112no—
507C4⋊C4—221no—
508C4⋊C4—221no—
509C4⋊C4—224no—
510C4⋊C4—224no—
511C4⋊C4—224no—
512C4⋊C4—224no—
513C4⋊C4C23×D1114yes—
514C22⋊C4—28no—
515C22⋊C4—28no—
516C22⋊C4—224no—
517C22⋊C4—224no—
518C22⋊C4—224no—
519C22⋊C4—224no—
520C22⋊C4—224no—
521C42—224no—
522C42C2×C22⋊D1114yes—
523C42C2×C22⋊D1112yes—
524C42C2×C22⋊D1112yes—
525C42C2×C22⋊D1114yes—
526C42C23×D1112yes—
527C42C23×D1112yes—
528C11C2×#311411yescharacteristic, complemented, Sylow
529C23—22no—
530C23—22no—
531C23—216no—
532C23—28no—
533C23—24no—
534C23—48no—
535C23—432no—
536C23—48no—
537C23—44no—
538C23—44no—
539C23—222no—
540C23—442no—
541C23—442no—
542C23—442no—
543C23#6698514yes—
544C23C22×C22⋊D1112yes—
545C23C22×C22⋊D1111yescharacteristic
546Q8—224no—
547Q8—442no—
548D4—216no—
549D4—28no—
550D4—24no—
551D4—224no—
552D4—448no—
553D4—442no—
554D4C2×#433918yes—
555C2×C4—22no—
556C2×C4—28no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—24no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—44no—
565C2×C4—416no—
566C2×C4—416no—
567C2×C4—48no—
568C2×C4—44no—
569C2×C4—222no—
570C2×C4—222no—
571C2×C4—222no—
572C2×C4—448no—
573C2×C4—442no—
574C2×C4—442no—
575C2×C4—442no—
576C2×C4C2×#433914yes—
577C2×C4C22×C22⋊D1112yes—
578C2×C4C22×C22⋊D1112yes—
579C2×C4C22×C22⋊D1112yes—
580C2×C4C22×C22⋊D1112yes—
581C2×C4C22×C22⋊D1112yes—
582C2×C4C22×C22⋊D1111yescharacteristic
583C2×C4C24×D1111yescharacteristic
584C8—224no—
585C8—224no—
586C22—22no—
587C22—22no—
588C22—28no—
589C22—28no—
590C22—432no—
591C22—44no—
592C22—44no—
593C22—416no—
594C22—442no—
595C22—442no—
596C22—442no—
597C22—884no—
598C22#1062332212yes—
599C22C2×#6698514yes—
600C22C2×#6698512yes—
601C22#1062335312yes—
602C22C23×C22⋊D1111yescharacteristic
603C4—22no—
604C4—22no—
605C4—22no—
606C4—22no—
607C4—22no—
608C4—44no—
609C4—442no—
610C4—442no—
611C4—442no—
612C4#1062332212yes—
613C4C22×#433912yes—
614C2—24no—
615C2—48no—
616C2—882no—
617C2#1307875414yesdirect product factor
618C2C2×#1062332211yescharacteristic
619C2C22×#6698511yescharacteristic
620C2C2×#1062335311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC22×C4×D4×C11C2
socleC23×C11C22×D4
prime radicalC2×#10622830C2
hypercenterC22×C4×D4D11
hypocenterC11C2×#3114
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×#10623010C2semidirect
2. #13078754C2direct (N × H)
3. C2×#10622584C2semidirect
4. C2×#10622580C2semidirect
5. C2×#10622622C2semidirect
6. C2×#10622629C2semidirect
7. C2×#10622831C2semidirect
9. C2×#10622627C2semidirect
10. C2×#10622631C2semidirect
11. C2×#10622539C2semidirect
12. C22×C4×D4×C11C2semidirect
20. C2×C4×D4×C11C22semidirect
31. #10623010C22semidirect
33. C2×#66928C22semidirect
34. C2×C4×D44C22semidirect
36. C2×#66923C22semidirect
37. C2×C4×Dic22C22semidirect
38. #10622831C22semidirect
44. #10622631C22semidirect
45. #10622629C22semidirect
46. #10622627C22semidirect
47. #10622622C22semidirect
48. #10622584C22semidirect
49. C2×#66874C22semidirect
50. #10622580C22semidirect
51. C2×#66873C22semidirect
52. C2×#66872C22semidirect
53. C2×#66871C22semidirect
54. #10622539C22semidirect
55. C2×C4⋊(C11⋊C8)C22semidirect
56. C2×#66867C22semidirect
120. #66928C23semidirect
122. C4×D44C23semidirect
125. #66923C23semidirect
127. C4×Dic22C23semidirect
132. #66874C23semidirect
133. #66873C23semidirect
134. #66872C23semidirect
135. #66871C23semidirect
136. C4⋊(C11⋊C8)C23semidirect
137. #66867C23semidirect
220. C22×C4×D4D11semidirect
308. C2×C4×D4C2×D11semidirect
443. C2×C11#3114semidirect
528. C11C2×#3114semidirect
617. C2#13078754direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230102
#130787542
C2×#106225842
C2×#106225802
C2×#106226222
C2×#106226292
C2×#106228312
C2×#106228302
C2×#106226272
C2×#106226312
C2×#106225392
C22×C4×D4×C112
C2×#311411