Finite Group Databasebeta

← C2×#13078750 #15621881

Subgroups — C2×#13078750 #15621881

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
1C22×C4×D44C211yesmaximal, characteristic, complemented
2#13078750C2116yesmaximal, direct product factor
3C2×#10622656C211yesmaximal, characteristic, complemented
4C2×#10622646C211yesmaximal, characteristic, complemented
5C2×#10622679C212yesmaximal, complemented
6C2×#10622670C212yesmaximal, complemented
7C2×#10622659C211yesmaximal, characteristic, complemented
8C2×#10622649C211yesmaximal, characteristic
9C2×#10622627C212yesmaximal, complemented
10C2×#10622639C212yesmaximal, complemented
11C2×#10622539C211yesmaximal, characteristic, complemented
12C2×C11×#529C211yesmaximal, characteristic, complemented
13C23×D44C2211yescharacteristic
14C23×C4×D11—21no—
15C11×#529—24no—
16C11×#529C2218yescomplemented
17C2×C11×#126—21no—
18C2×C11×#125C2211yescharacteristic, complemented
19C2×C11×#124C2211yescharacteristic, complemented
20C2×C11×#123—21no—
21C2×C11×C22⋊Q8C2211yescharacteristic
22C2×C11×#121C2211yescharacteristic
23C2×C4×Q8×C11C2211yescharacteristic, complemented
24C2×C4×D4×C11—21no—
25C2×C4×D4×C11C2211yescharacteristic, complemented
26C2×C11×#117—21no—
27C22×C42×C11C2211yescharacteristic
28C22×#4325C2212yes—
29C22×#4323C2212yes—
30C22×(C2×D11)⋊C4—21no—
31C22×C4⋊Dic11C2211yescharacteristic
32C2×C4×D44—24no—
33C2×C4×D44—21no—
34C2×C4×D44—21no—
35C2×C4×D44C2212yes—
36C2×C4×D44C2212yes—
37C2×C4×D44C2218yescomplemented
38C2×#66899C2212yescomplemented
39C2×#66896C2212yescomplemented
40C2×C22⋊(C11⋊C8)C2211yescharacteristic
41C2×C22⋊(C11⋊C8)C2211yescharacteristic
42#10622679C22116yescomplemented
43#10622670C22116yescomplemented
44#10622659C2218yescomplemented
45#10622656C2218yescomplemented
46#10622649C2218yes—
47#10622646C2218yescomplemented
48#10622639C22116yescomplemented
49#10622627C22116yescomplemented
50C2×#66873C2212yes—
51C2×#66873C2212yes—
52C2×#66872C2212yescomplemented
53C2×#66871C2212yescomplemented
54#10622539C2218yescomplemented
55C2×C4⋊(C11⋊C8)C2212yescomplemented
56C2×#66867C2212yescomplemented
57C24×D11—21no—
58C22×Q8×C11C2311yescharacteristic
59C22×D4×C11—21no—
60C22×D4×C11C2311yescharacteristic
61C23×C4×C11—21no—
62C23×C4×C11D411yescharacteristic
63C23×C4×C11D411yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×Dic11—21no—
66C22×D44—21no—
67C22×D44—22no—
68C22×D44—28no—
69C22×D44C2314yes—
70C22×D44C2312yes—
71C22×C4×D11—22no—
72C22×C4×D11—22no—
73C22×C4×D11—28no—
74C22×C4×D11—48no—
75C11×#126—28no—
76C11×#125—22no—
77C11×#125C2314yescomplemented
78C11×#124—22no—
79C11×#124C2314yescomplemented
80C11×#123—28no—
81C11×C22⋊Q8—22no—
82C11×C22⋊Q8C2314yes—
83C11×#121—22no—
84C11×#121C2314yes—
85C4×Q8×C11—22no—
86C4×Q8×C11C2314yescomplemented
87C4×D4×C11—28no—
88C4×D4×C11—22no—
89C4×D4×C11C2314yescomplemented
90C11×#117—28no—
91C2×C11×C4⋊C4—21no—
92C2×C11×C4⋊C4—21no—
93C2×C11×C4⋊C4—21no—
94C2×C11×C4⋊C4—21no—
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C22⋊C4—21no—
98C2×C11×C22⋊C4—21no—
99C2×C11×C22⋊C4—21no—
100C2×C11×C22⋊C4—21no—
101C2×C11×C22⋊C4—21no—
102C2×C42×C11—21no—
103C2×C42×C11D411yescharacteristic
104C2×C42×C11D411yescharacteristic
105C2×C42×C11D414yes—
106C2×C42×C11C2311yescharacteristic
107C2×C42×C11C2311yescharacteristic
108C2×C42×C11C2314yes—
109C2×#4325—28no—
110C2×#4325C2318yes—
111C2×#4323—28no—
112C2×#4323C2318yes—
113C2×(C2×D11)⋊C4—22no—
114C2×(C2×D11)⋊C4—22no—
115C2×(C2×D11)⋊C4—28no—
116C2×C4⋊Dic11—21no—
117C2×C4⋊Dic11—22no—
118C2×C4⋊Dic11C2312yes—
119C2×C4⋊Dic11C2314yes—
120C22×C11⋊C8C2312yes—
121C22×C11⋊C8C2312yes—
122C4×D44—24no—
123C4×D44—24no—
124C4×D44—28no—
125C4×D44—28no—
126C4×D44C2318yes—
127C4×D44C2318yes—
128#66899C2318yescomplemented
129#66896C2318yescomplemented
130C22⋊(C11⋊C8)C2314yes—
131C22⋊(C11⋊C8)C2314yes—
132#66873C2318yes—
133#66873C2318yes—
134#66872C2318yescomplemented
135#66871C2318yescomplemented
136C4⋊(C11⋊C8)C2318yescomplemented
137#66867C2318yescomplemented
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×Q8×C11—21no—
147C2×Q8×C11—24no—
148C2×Q8×C11C2412yes—
149C2×D4×C11—24no—
150C2×D4×C11—21no—
151C2×D4×C11—24no—
152C2×D4×C11—44no—
153C2×D4×C11C2412yes—
154C22×C4×C11—24no—
155C22×C4×C11—24no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—24no—
160C22×C4×C11—42no—
161C22×C4×C11—44no—
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2×D412yes—
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11C2×D411yescharacteristic
166C22×C4×C11C2×D411yescharacteristic
167C22×C4×C11C2×D411yescharacteristic
168C22×C4×C11C2×D414yes—
169C22×C4×C11C2×D414yes—
170C22×C4×C11C2412yes—
171C22×C4×C11C2411yescharacteristic
172C22×Dic11—24no—
173C22×Dic11—22no—
174C22×Dic11—44no—
175C2×D44—28no—
176C2×D44—216no—
177C2×D44—216no—
178C2×D44—24no—
179C2×D44—22no—
180C2×D44—24no—
181C2×D44#4118yes—
182C2×D44C2414yes—
183C2×C4×D11—28no—
184C2×C4×D11—28no—
185C2×C4×D11—48no—
186C2×C4×D11—48no—
187C2×C4×D11—432no—
188C11×C4⋊C4—24no—
189C11×C4⋊C4—24no—
190C11×C4⋊C4—24no—
191C11×C4⋊C4—24no—
192C11×C4⋊C4—21no—
193C11×C4⋊C4—21no—
194C11×C4⋊C4C2412yes—
195C11×C4⋊C4C2412yes—
196C11×C22⋊C4—24no—
197C11×C22⋊C4—24no—
198C11×C22⋊C4—24no—
199C11×C22⋊C4—24no—
200C11×C22⋊C4—24no—
201C42×C11—24no—
202C42×C11C2×D414yes—
203C42×C11C2×D412yes—
204C42×C11C2×D412yes—
205C42×C11C2×D414yes—
206C42×C11C2412yes—
207C42×C11C2412yes—
208#4325—216no—
209#4323—216no—
210(C2×D11)⋊C4—28no—
211(C2×D11)⋊C4—28no—
212C4⋊Dic11—24no—
213C4⋊Dic11—22no—
214C4⋊Dic11C2414yes—
215C2×C11⋊C8—24no—
216C2×C11⋊C8—24no—
217C2×C11⋊C8C2414yes—
218C2×C11⋊C8C2414yes—
219C2×#529D1111yescharacteristic, complemented
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×#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—
248Q8×C11—24no—
249Q8×C11—42no—
250D4×C11—24no—
251D4×C11—48no—
252D4×C11—42no—
253C2×C4×C11—22no—
254C2×C4×C11—28no—
255C2×C4×C11—22no—
256C2×C4×C11—22no—
257C2×C4×C11—22no—
258C2×C4×C11—22no—
259C2×C4×C11—24no—
260C2×C4×C11—24no—
261C2×C4×C11—22no—
262C2×C4×C11—22no—
263C2×C4×C11—22no—
264C2×C4×C11—44no—
265C2×C4×C11—48no—
266C2×C4×C11—42no—
267C2×C4×C11—42no—
268C2×C4×C11—42no—
269C2×C4×C11C22×D412yes—
270C2×C4×C11C22×D412yes—
271C2×C4×C11C22×D412yes—
272C2×C4×C11C22×D412yes—
273C2×C4×C11C22×D412yes—
274C2×C4×C11C22×D411yescharacteristic
275C2×C4×C11C2×#4114yes—
276C2×C4×C11C2511yescharacteristic
277C2×Dic11—24no—
278C2×Dic11—48no—
279C2×Dic11—44no—
280D44—216no—
281D44—28no—
282D44—24no—
283D44C2×#4118yes—
284C4×D11—416no—
285C4×D11—416no—
286C11⋊C8—24no—
287C11⋊C8—24no—
288C23×D4—111no—
289C24×C4—221no—
290C22×SD16—112no—
291C22×D8—112no—
292#529—24no—
293#529C2×D1118yescomplemented
294C2×#126—21no—
295C2×#125C2×D1111yescharacteristic, complemented
296C2×#124C2×D1111yescharacteristic, complemented
297C2×#123—21no—
298C2×C22⋊Q8C2×D1111yescharacteristic
299C2×#121C2×D1111yescharacteristic
300C2×C4×Q8C2×D1111yescharacteristic, complemented
301C2×C4×D4—21no—
302C2×C4×D4—112no—
303C2×C4×D4—112no—
304C2×C4×D4—118no—
305C2×C4×D4—221no—
306C2×C4×D4—221no—
307C2×C4×D4—224no—
308C2×C4×D4C2×D1111yescharacteristic, complemented
309C2×#117—21no—
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#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—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—22no—
351C4×C11—22no—
352C4×C11—22no—
353C4×C11—22no—
354C4×C11—42no—
355C4×C11—42no—
356C4×C11—42no—
357C4×C11#52512yes—
358C4×C11C22×#4112yes—
359Dic11—44no—
360C25—221no—
361C22×Q8C22×D1111yescharacteristic
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—221no—
371C23×C4—228no—
372C23×C4—222no—
373C23×C4—222no—
374C23×C4—448no—
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—28no—
385#125—22no—
386#125C22×D1114yescomplemented
387#124—22no—
388#124C22×D1114yescomplemented
389#123—28no—
390C22⋊Q8—22no—
391C22⋊Q8C22×D1114yes—
392#121—22no—
393#121C22×D1114yes—
394C4×Q8—22no—
395C4×Q8C22×D1114yescomplemented
396C4×D4—28no—
397C4×D4—22no—
398C4×D4—118no—
399C4×D4—118no—
400C4×D4—228no—
401C4×D4—224no—
402C4×D4—224no—
403C4×D4—228no—
404C4×D4C22×D1114yescomplemented
405#117—28no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—112no—
411C2×C4⋊C4—114no—
412C2×C4⋊C4—222no—
413C2×C4⋊C4—221no—
414C2×C4⋊C4C22×D1111yescharacteristic
415C2×C4⋊C4C22×D1111yescharacteristic
416C2×C22⋊C4—21no—
417C2×C22⋊C4—21no—
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—228no—
422C2×C22⋊C4—222no—
423C2×C22⋊C4—222no—
424C2×C42—21no—
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—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—
454C24C2×C22⋊D1111yescharacteristic
455C2×Q8—21no—
456C2×Q8—24no—
457C2×Q8C23×D1112yes—
458C2×D4—24no—
459C2×D4—24no—
460C2×D4—21no—
461C2×D4—44no—
462C2×D4—118no—
463C2×D4—114no—
464C2×D4—2216no—
465C2×D4—228no—
466C2×D4—2216no—
467C2×D4—224no—
468C2×D4—224no—
469C2×D4—222no—
470C2×D4C23×D1112yes—
471C22×C4—24no—
472C22×C4—24no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—24no—
477C22×C4—42no—
478C22×C4—44no—
479C22×C4—224no—
480C22×C4—222no—
481C22×C4—228no—
482C22×C4—228no—
483C22×C4—4432no—
484C22×C4—448no—
485C22×C4—448no—
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—24no—
505C4⋊C4—24no—
506C4⋊C4—24no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—114no—
510C4⋊C4—224no—
511C4⋊C4—222no—
512C4⋊C4C23×D1112yes—
513C4⋊C4C23×D1112yes—
514C22⋊C4—24no—
515C22⋊C4—24no—
516C22⋊C4—24no—
517C22⋊C4—24no—
518C22⋊C4—24no—
519C22⋊C4—228no—
520C22⋊C4—228no—
521C42—24no—
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—22no—
532C23—42no—
533C23—42no—
534C23—42no—
535C23—2216no—
536C23—228no—
537C23—224no—
538C23—4432no—
539C23—448no—
540C23—448no—
541C23—444no—
542C23—444no—
543C23#6700214yes—
544C23C22×C22⋊D1112yes—
545C23C22×C22⋊D1111yescharacteristic
546Q8—24no—
547Q8—42no—
548D4—24no—
549D4—48no—
550D4—42no—
551D4—118no—
552D4—2216no—
553D4—228no—
554D4—224no—
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—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—44no—
567C2×C4—48no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—224no—
572C2×C4—4416no—
573C2×C4—4416no—
574C2×C4—448no—
575C2×C4—444no—
576C2×C4#41×D1114yes—
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—28no—
587C22—22no—
588C22—22no—
589C22—42no—
590C22—42no—
591C22—42no—
592C22—84no—
593C22—228no—
594C22—4432no—
595C22—444no—
596C22—4416no—
597C22—444no—
598C22C2×#6700214yes—
599C22C2×#6700212yes—
600C22#1062335312yes—
601C22#1062335912yes—
602C22C23×C22⋊D1111yescharacteristic
603C4—22no—
604C4—22no—
605C4—22no—
606C4—22no—
607C4—22no—
608C4—42no—
609C4—42no—
610C4—42no—
611C4—444no—
612C4#1062335912yes—
613C4C2×#41×D1112yes—
614C2—24no—
615C2—82no—
616C2—448no—
617C2#1307875014yesdirect product factor
618C2C2×#1062335911yescharacteristic
619C2C22×#6700211yescharacteristic
620C2C2×#1062335311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#529C2
socleC23×C11C22×D4
prime radicalC2×#10622649C2
hypercenterC2×#529D11
hypocenterC11C2×#3114
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. C22×C4×D44C2semidirect
2. #13078750C2direct (N × H)
3. C2×#10622656C2semidirect
4. C2×#10622646C2semidirect
5. C2×#10622679C2semidirect
6. C2×#10622670C2semidirect
7. C2×#10622659C2semidirect
9. C2×#10622627C2semidirect
10. C2×#10622639C2semidirect
11. C2×#10622539C2semidirect
12. C2×C11×#529C2semidirect
16. C11×#529C22semidirect
18. C2×C11×#125C22semidirect
19. C2×C11×#124C22semidirect
23. C2×C4×Q8×C11C22semidirect
25. C2×C4×D4×C11C22semidirect
37. C2×C4×D44C22semidirect
38. C2×#66899C22semidirect
39. C2×#66896C22semidirect
42. #10622679C22semidirect
43. #10622670C22semidirect
44. #10622659C22semidirect
45. #10622656C22semidirect
47. #10622646C22semidirect
48. #10622639C22semidirect
49. #10622627C22semidirect
52. C2×#66872C22semidirect
53. C2×#66871C22semidirect
54. #10622539C22semidirect
55. C2×C4⋊(C11⋊C8)C22semidirect
56. C2×#66867C22semidirect
77. C11×#125C23semidirect
79. C11×#124C23semidirect
86. C4×Q8×C11C23semidirect
89. C4×D4×C11C23semidirect
128. #66899C23semidirect
129. #66896C23semidirect
134. #66872C23semidirect
135. #66871C23semidirect
136. C4⋊(C11⋊C8)C23semidirect
137. #66867C23semidirect
219. C2×#529D11semidirect
293. #529C2×D11semidirect
295. C2×#125C2×D11semidirect
296. C2×#124C2×D11semidirect
300. C2×C4×Q8C2×D11semidirect
308. C2×C4×D4C2×D11semidirect
386. #125C22×D11semidirect
388. #124C22×D11semidirect
395. C4×Q8C22×D11semidirect
404. C4×D4C22×D11semidirect
443. C2×C11#3114semidirect
528. C11C2×#3114semidirect
617. C2#13078750direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×D442
#130787502
C2×#106226562
C2×#106226462
C2×#106226792
C2×#106226702
C2×#106226592
C2×#106226492
C2×#106226272
C2×#106226392
C2×#106225392
C2×C11×#5292
C2×#311411