Finite Group Databasebeta

← C2×#13078755 #15621886

Subgroups — C2×#13078755 #15621886

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×#10623155C211yesmaximal, characteristic, complemented
2C22×D4×Dic11C211yesmaximal, characteristic, complemented
3#13078755C2116yesmaximal, direct product factor
4C2×#10622656C211yesmaximal, characteristic, complemented
5C2×#10622349C211yesmaximal, characteristic, complemented
6C2×#10622379C212yesmaximal, complemented
7C2×#10622778C212yesmaximal, complemented
8C2×#10622830C211yesmaximal, characteristic
9C2×#10622398C212yesmaximal, complemented
10C2×#10622777C212yesmaximal, complemented
11C2×#10622332C211yesmaximal, characteristic, complemented
12C2×C11×#450C211yesmaximal, characteristic, complemented
13C23×D4×C11C2211yescharacteristic
14C24×Dic11—21no—
15C22×C11×SD16C2212yes—
16C2×C11×C22⋊Q8C2211yescharacteristic
17C22×C22⋊Dic11—21no—
18C2×#67000C2211yescharacteristic, complemented
19C2×Q8×Dic11C2211yescharacteristic, complemented
20C2×D4×Dic11—21no—
21C2×D4×Dic11—21no—
22C2×D4×Dic11—24no—
23C2×D4×Dic11C2212yes—
24C2×D4×Dic11C2212yes—
25C2×D4×Dic11C2218yescomplemented
26C22×#4323C2212yes—
27C2×#66983C2211yescharacteristic
28C22×C4⋊Dic11C2211yescharacteristic
29C22×C4×Dic11C2211yescharacteristic
30#10623155—24no—
31#10623155C2218yescomplemented
32C2×#66951—21no—
33C2×#66946C2211yescharacteristic, complemented
34C2×#66945—21no—
35C2×#66943C2211yescharacteristic, complemented
36C2×#66939—21no—
37C2×(C22⋊D11)⋊C4—21no—
38C11×#450C2218yescomplemented
39C2×C11×#102C2212yes—
40C2×C11×C22⋊C8C2211yescharacteristic
41C2×#66899C2212yescomplemented
42#10622830C2218yes—
43C2×#66896C2212yes—
44C2×C22⋊(C11⋊C8)C2211yescharacteristic
45#10622778C22116yescomplemented
46#10622777C22116yescomplemented
47C2×#66885C2212yescomplemented
48C2×#66882C2212yescomplemented
49C2×#66879C2212yescomplemented
50C2×Dic11⋊C8C2212yescomplemented
51#10622656C2218yescomplemented
52C2×#66872C2212yescomplemented
53#10622398C22116yescomplemented
54#10622379C22116yescomplemented
55#10622349C2218yescomplemented
56#10622332C2218yescomplemented
57C25×C11—21no—
58C22×Q8×C11C2311yescharacteristic
59C22×D4×C11—28no—
60C22×D4×C11—21no—
61C22×D4×C11—22no—
62C22×D4×C11C2314yes—
63C22×D4×C11C2312yes—
64C23×C4×C11C2311yescharacteristic
65C22×C22⋊D11—21no—
66C23×Dic11—21no—
67C23×Dic11—22no—
68C23×Dic11—22no—
69C23×Dic11—28no—
70C23×Dic11—48no—
71C23×Dic11D411yescharacteristic
72C23×Dic11D411yescharacteristic
73C22×D44C2311yescharacteristic
74C22×C4×D11—21no—
75C2×C11×SD16—28no—
76C2×C11×SD16C2318yes—
77C22×C8×C11C2312yes—
78C11×C22⋊Q8—22no—
79C11×C22⋊Q8C2314yes—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C22⋊C4—21no—
83C2×C22⋊Dic11—22no—
84C2×C22⋊Dic11—22no—
85C2×C22⋊Dic11—28no—
86#67000—22no—
87#67000C2314yescomplemented
88Q8×Dic11—22no—
89Q8×Dic11C2314yescomplemented
90D4×Dic11—24no—
91D4×Dic11—24no—
92D4×Dic11—28no—
93D4×Dic11—28no—
94D4×Dic11C2318yes—
95D4×Dic11C2318yes—
96C2×#4323—28no—
97C2×#4323C2318yes—
98#66983—22no—
99#66983C2314yes—
100C2×(C2×D11)⋊C4—21no—
101C2×(C2×D11)⋊C4—21no—
102C2×(C2×D11)⋊C4—21no—
103C2×(C2×D11)⋊C4—21no—
104C2×C4⋊Dic11—21no—
105C2×C4⋊Dic11—22no—
106C2×C4⋊Dic11—21no—
107C2×C4⋊Dic11—21no—
108C2×C4⋊Dic11C2312yes—
109C2×C4⋊Dic11C2311yescharacteristic
110C2×C4⋊Dic11C2314yes—
111C2×Dic11⋊C4—21no—
112C2×C4×Dic11—21no—
113C2×C4×Dic11D411yescharacteristic
114C2×C4×Dic11D411yescharacteristic
115C2×C4×Dic11D414yes—
116C2×C4×Dic11C2311yescharacteristic
117C2×C4×Dic11C2311yescharacteristic
118C2×C4×Dic11C2314yes—
119C22×C11⋊C8C2312yes—
120#66951—28no—
121#66946—22no—
122#66946C2314yescomplemented
123#66945—28no—
124#66943—22no—
125#66943C2314yescomplemented
126#66939—28no—
127(C22⋊D11)⋊C4—28no—
128C11×#102C2318yes—
129C11×C22⋊C8C2314yes—
130#66899C2318yescomplemented
131#66896C2318yes—
132C22⋊(C11⋊C8)C2314yes—
133#66885C2318yescomplemented
134#66882C2318yescomplemented
135#66879C2318yescomplemented
136Dic11⋊C8C2318yescomplemented
137#66872C2318yescomplemented
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×Q8×C11—21no—
147C2×Q8×C11—24no—
148C2×Q8×C11C2412yes—
149C2×D4×C11—28no—
150C2×D4×C11—216no—
151C2×D4×C11—216no—
152C2×D4×C11—24no—
153C2×D4×C11—22no—
154C2×D4×C11—24no—
155C2×D4×C11#4118yes—
156C2×D4×C11C2414yes—
157C22×C4×C11—24no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2×D412yes—
162C22×C4×C11C2412yes—
163C22×C4×C11C2411yescharacteristic
164C2×C22⋊D11—24no—
165C2×C22⋊D11—44no—
166C22×Dic11—28no—
167C22×Dic11—28no—
168C22×Dic11—24no—
169C22×Dic11—21no—
170C22×Dic11—24no—
171C22×Dic11—22no—
172C22×Dic11—42no—
173C22×Dic11—48no—
174C22×Dic11—48no—
175C22×Dic11—432no—
176C22×Dic11—44no—
177C22×Dic11C2×D414yes—
178C22×Dic11C2×D411yescharacteristic
179C22×Dic11C2×D411yescharacteristic
180C22×Dic11C2×D411yescharacteristic
181C22×Dic11C2×D411yescharacteristic
182C22×Dic11C2×D414yes—
183C2×D44—21no—
184C2×D44—24no—
185C2×D44C2412yes—
186C2×C4×D11—24no—
187C2×C4×D11—44no—
188C11×SD16—216no—
189C2×C8×C11—24no—
190C2×C8×C11C2414yes—
191C11×C4⋊C4—21no—
192C11×C4⋊C4—24no—
193C11×C4⋊C4C2412yes—
194C11×C22⋊C4—24no—
195C22⋊Dic11—28no—
196C22⋊Dic11—28no—
197#4323—216no—
198(C2×D11)⋊C4—24no—
199(C2×D11)⋊C4—24no—
200(C2×D11)⋊C4—24no—
201(C2×D11)⋊C4—24no—
202C4⋊Dic11—24no—
203C4⋊Dic11—24no—
204C4⋊Dic11—21no—
205C4⋊Dic11—24no—
206C4⋊Dic11—22no—
207C4⋊Dic11C2414yes—
208C4⋊Dic11C2412yes—
209Dic11⋊C4—24no—
210C4×Dic11—24no—
211C4×Dic11C2×D412yes—
212C4×Dic11C2×D414yes—
213C4×Dic11C2×D412yes—
214C4×Dic11C2×D414yes—
215C4×Dic11C2412yes—
216C4×Dic11C2412yes—
217C2×C11⋊C8—24no—
218C2×C11⋊C8C2414yes—
219C2×#529—111no—
220C22×C4×D4—111no—
221#3114—1116no—
222C2×#483—111no—
223C2×#480—111no—
224C2×#478—112no—
225C2×#463—112no—
226C2×#450D1111yescharacteristic, complemented
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—
248Q8×C11—24no—
249Q8×C11—42no—
250D4×C11—216no—
251D4×C11—28no—
252D4×C11—24no—
253D4×C11C2×#4118yes—
254C2×C4×C11—22no—
255C2×C4×C11—24no—
256C2×C4×C11—24no—
257C2×C4×C11—22no—
258C2×C4×C11—22no—
259C2×C4×C11—42no—
260C2×C4×C11—42no—
261C2×C4×C11C22×D412yes—
262C2×C4×C11C22×D411yescharacteristic
263C2×C4×C11C2×#4114yes—
264C2×C4×C11C2511yescharacteristic
265C22⋊D11—48no—
266C2×Dic11—28no—
267C2×Dic11—22no—
268C2×Dic11—22no—
269C2×Dic11—22no—
270C2×Dic11—22no—
271C2×Dic11—22no—
272C2×Dic11—24no—
273C2×Dic11—44no—
274C2×Dic11—416no—
275C2×Dic11—416no—
276C2×Dic11—48no—
277C2×Dic11—44no—
278C2×Dic11—42no—
279C2×Dic11C22×D412yes—
280C2×Dic11C22×D412yes—
281C2×Dic11C22×D412yes—
282C2×Dic11C22×D412yes—
283D44—24no—
284D44—42no—
285C4×D11—48no—
286C8×C11—24no—
287C11⋊C8—24no—
288C23×D4C2×D1111yescharacteristic
289C24×C4—221no—
290C22×SD16C2×D1112yes—
291C22×D8—112no—
292#529—118no—
293#529—224no—
294C2×#126—221no—
295C2×#125—111no—
296C2×#124—111no—
297C2×#123—221no—
298C2×C22⋊Q8C2×D1111yescharacteristic
299C2×#121—111no—
300C2×C4×Q8—111no—
301C2×C4×D4—112no—
302C2×C4×D4—118no—
303C2×C4×D4—112no—
304C2×C4×D4—111no—
305C2×C4×D4—221no—
306C2×C4×D4—221no—
307C2×C4×D4—224no—
308C2×C4×D4—221no—
309C2×#117—221no—
310C22×C4⋊C4—111no—
311C22×C22⋊C4—221no—
312C22×C42—111no—
313#483—118no—
314#480—118no—
315#478—1116no—
316#463—1116no—
317#450C2×D1118yescomplemented
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×#102C2×D1112yes—
329C2×C22⋊C8—111no—
330C2×C22⋊C8C2×D1111yescharacteristic
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—42no—
351C4×C11—42no—
352C4×C11#52512yes—
353C4×C11C22×#4112yes—
354Dic11—22no—
355Dic11—22no—
356Dic11—22no—
357Dic11—22no—
358Dic11—44no—
359Dic11—42no—
360C25—21no—
361C22×Q8C22×D1111yescharacteristic
362C22×D4—28no—
363C22×D4—22no—
364C22×D4—21no—
365C22×D4—111no—
366C22×D4—221no—
367C22×D4C22×D1114yes—
368C22×D4C22×D1112yes—
369C23×C4—111no—
370C23×C4—111no—
371C23×C4—221no—
372C23×C4—228no—
373C23×C4—222no—
374C23×C4—222no—
375C23×C4—221no—
376C23×C4—448no—
377C23×C4C22×D1111yescharacteristic
378C2×SD16—28no—
379C2×SD16C22×D1118yes—
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—22no—
391C22⋊Q8C22×D1114yes—
392#121—114no—
393#121—222no—
394C4×Q8—114no—
395C4×Q8—222no—
396C4×D4—118no—
397C4×D4—118no—
398C4×D4—114no—
399C4×D4—222no—
400C4×D4—228no—
401C4×D4—224no—
402C4×D4—224no—
403C4×D4—228no—
404C4×D4—228no—
405#117—228no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—112no—
408C2×C4⋊C4—114no—
409C2×C4⋊C4—111no—
410C2×C4⋊C4—221no—
411C2×C4⋊C4—221no—
412C2×C4⋊C4—221no—
413C2×C4⋊C4—222no—
414C2×C4⋊C4—221no—
415C2×C4⋊C4C22×D1111yescharacteristic
416C2×C22⋊C4—21no—
417C2×C22⋊C4—221no—
418C2×C22⋊C4—221no—
419C2×C22⋊C4—221no—
420C2×C22⋊C4—222no—
421C2×C22⋊C4—222no—
422C2×C22⋊C4—228no—
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#107—118no—
432#106—118no—
433C4⋊C8—118no—
434#103—118no—
435#102—118no—
436#102—118no—
437#102C22×D1118yes—
438C22⋊C8—114no—
439C22⋊C8C22×D1114yes—
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—
454C24D4×D1111yescharacteristic
455C2×Q8—21no—
456C2×Q8—24no—
457C2×Q8C23×D1112yes—
458C2×D4—28no—
459C2×D4—216no—
460C2×D4—216no—
461C2×D4—24no—
462C2×D4—22no—
463C2×D4—24no—
464C2×D4—112no—
465C2×D4—224no—
466C2×D4—221no—
467C2×D4—224no—
468C2×D4—444no—
469C2×D4#434118yes—
470C2×D4C23×D1114yes—
471C22×C4—24no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—114no—
475C22×C4—111no—
476C22×C4—111no—
477C22×C4—111no—
478C22×C4—111no—
479C22×C4—114no—
480C22×C4—224no—
481C22×C4—228no—
482C22×C4—228no—
483C22×C4—224no—
484C22×C4—224no—
485C22×C4—221no—
486C22×C4—222no—
487C22×C4—444no—
488C22×C4—442no—
489C22×C4—4432no—
490C22×C4—448no—
491C22×C4—448no—
492C22×C4—444no—
493C22×C4D4×D1112yes—
494C22×C4D4×D1111yescharacteristic
495C22×C4C23×D1112yes—
496C22×C4C23×D1111yescharacteristic
497SD16—216no—
498D8—2216no—
499C2×C8—24no—
500C2×C8—114no—
501C2×C8—224no—
502C2×C8C23×D1114yes—
503C4⋊C4—24no—
504C4⋊C4—21no—
505C4⋊C4—112no—
506C4⋊C4—114no—
507C4⋊C4—224no—
508C4⋊C4—224no—
509C4⋊C4—224no—
510C4⋊C4—224no—
511C4⋊C4—222no—
512C4⋊C4—221no—
513C4⋊C4C23×D1112yes—
514C22⋊C4—24no—
515C22⋊C4—224no—
516C22⋊C4—224no—
517C22⋊C4—224no—
518C22⋊C4—228no—
519C22⋊C4—228no—
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—216no—
532C23—28no—
533C23—24no—
534C23—48no—
535C23—432no—
536C23—48no—
537C23—44no—
538C23—44no—
539C23—222no—
540C23—442no—
541C23—442no—
542C23—442no—
543C23#6696714yes—
544C23C2×D4×D1112yes—
545C23C2×D4×D1111yescharacteristic
546Q8—24no—
547Q8—42no—
548D4—216no—
549D4—28no—
550D4—24no—
551D4—224no—
552D4—448no—
553D4—442no—
554D4C2×#434118yes—
555C2×C4—22no—
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—112no—
563C2×C4—112no—
564C2×C4—112no—
565C2×C4—112no—
566C2×C4—228no—
567C2×C4—222no—
568C2×C4—222no—
569C2×C4—222no—
570C2×C4—222no—
571C2×C4—222no—
572C2×C4—224no—
573C2×C4—448no—
574C2×C4—444no—
575C2×C4—4416no—
576C2×C4—4416no—
577C2×C4—448no—
578C2×C4—444no—
579C2×C4—442no—
580C2×C4C2×D4×D1112yes—
581C2×C4C2×D4×D1111yescharacteristic
582C2×C4C2×#434114yes—
583C2×C4C24×D1111yescharacteristic
584C8—24no—
585C8—224no—
586C22—22no—
587C22—28no—
588C22—22no—
589C22—28no—
590C22—432no—
591C22—44no—
592C22—44no—
593C22—416no—
594C22—442no—
595C22—442no—
596C22—442no—
597C22—884no—
598C22#1062311712yes—
599C22C2×#6696714yes—
600C22C2×#6696712yes—
601C22#1062330412yes—
602C22C22×D4×D1111yescharacteristic
603C4—22no—
604C4—42no—
605C4—42no—
606C4—222no—
607C4—222no—
608C4—222no—
609C4—222no—
610C4—444no—
611C4—442no—
612C4#1062311712yes—
613C4C22×#434112yes—
614C2—24no—
615C2—48no—
616C2—882no—
617C2#1307875514yesdirect product factor
618C2C2×#1062311711yescharacteristic
619C2C22×#6696711yescharacteristic
620C2C2×#1062330411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#450C2
socleC23×C11C22×D4
prime radicalC2×#10622830C2
hypercenterC2×#450D11
hypocenterC11C2×#3114
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#450

Complements

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

NH ≅ G/Ntype
1. C2×#10623155C2semidirect
2. C22×D4×Dic11C2semidirect
3. #13078755C2direct (N × H)
4. C2×#10622656C2semidirect
5. C2×#10622349C2semidirect
6. C2×#10622379C2semidirect
7. C2×#10622778C2semidirect
9. C2×#10622398C2semidirect
10. C2×#10622777C2semidirect
11. C2×#10622332C2semidirect
12. C2×C11×#450C2semidirect
18. C2×#67000C22semidirect
19. C2×Q8×Dic11C22semidirect
25. C2×D4×Dic11C22semidirect
31. #10623155C22semidirect
33. C2×#66946C22semidirect
35. C2×#66943C22semidirect
38. C11×#450C22semidirect
41. C2×#66899C22semidirect
45. #10622778C22semidirect
46. #10622777C22semidirect
47. C2×#66885C22semidirect
48. C2×#66882C22semidirect
49. C2×#66879C22semidirect
50. C2×Dic11⋊C8C22semidirect
51. #10622656C22semidirect
52. C2×#66872C22semidirect
53. #10622398C22semidirect
54. #10622379C22semidirect
55. #10622349C22semidirect
56. #10622332C22semidirect
87. #67000C23semidirect
89. Q8×Dic11C23semidirect
122. #66946C23semidirect
125. #66943C23semidirect
130. #66899C23semidirect
133. #66885C23semidirect
134. #66882C23semidirect
135. #66879C23semidirect
136. Dic11⋊C8C23semidirect
137. #66872C23semidirect
226. C2×#450D11semidirect
317. #450C2×D11semidirect
443. C2×C11#3114semidirect
528. C11C2×#3114semidirect
617. C2#13078755direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231552
C22×D4×Dic112
#130787552
C2×#106226562
C2×#106223492
C2×#106223792
C2×#106227782
C2×#106228302
C2×#106223982
C2×#106227772
C2×#106223322
C2×C11×#4502
C2×#311411