Finite Group Databasebeta

← C2×#13078757 #15621888

Subgroups — C2×#13078757 #15621888

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×#66946C211yesmaximal, characteristic, complemented
3#13078757C2116yesmaximal, direct product factor
4C2×#10622580C211yesmaximal, characteristic, complemented
5C2×#10622484C212yesmaximal, complemented
6C2×#10622432C212yesmaximal, complemented
7C2×#10622659C211yesmaximal, characteristic, complemented
8C2×#10622345C211yesmaximal, characteristic
9C2×#10622482C212yesmaximal, complemented
10C2×#10622430C212yesmaximal, complemented
11C2×#10622332C211yesmaximal, characteristic, complemented
12C2×C11×#483C211yesmaximal, characteristic, complemented
13C23×D44C2211yescharacteristic
14C23×C4×D11—21no—
15C2×C11×C22⋊Q8C2211yescharacteristic
16C22×C11×C4⋊C4C2211yescharacteristic
17C2×#67000C2211yescharacteristic, complemented
18C2×Q8×Dic11C2211yescharacteristic, complemented
19C22×#4325C2212yes—
20C2×#66983C2211yescharacteristic
21C22×(C2×D11)⋊C4—21no—
22C22×C4×Dic11C2211yescharacteristic
23C22×D88C2212yes—
24#10623155—24no—
25#10623155C2218yescomplemented
26C2×#66951—21no—
27C2×#66946—24no—
28C2×#66946—21no—
29C2×#66946—21no—
30C2×#66946C2212yes—
31C2×#66946C2212yes—
32C2×#66946C2218yescomplemented
33C2×#66946C2211yescharacteristic, complemented
34C2×#66945—21no—
35C2×#66943C2211yescharacteristic, complemented
36C2×#66939—21no—
37C2×(C22⋊D11)⋊C4—21no—
38C11×#483C2218yescomplemented
39C2×C11×#106C2212yescomplemented
40C2×C11×#103C2212yescomplemented
41C2×C11×C22⋊C8C2211yescharacteristic
42C2×C22⋊(C11⋊C8)C2211yescharacteristic
43C2×#66885C2212yes—
44C2×#66879C2212yescomplemented
45C2×Dic11⋊C8C2212yescomplemented
46#10622659C2218yescomplemented
47#10622580C2218yescomplemented
48C2×#66873C2212yes—
49C2×#66873C2212yescomplemented
50C2×#66871C2212yescomplemented
51#10622484C22116yescomplemented
52#10622482C22116yescomplemented
53#10622432C22116yescomplemented
54#10622430C22116yescomplemented
55#10622345C2218yes—
56#10622332C2218yescomplemented
57C24×D11—21no—
58C22×Q8×C11C2311yescharacteristic
59C23×C4×C11—21no—
60C23×C4×C11C2311yescharacteristic
61C22×C22⋊D11—21no—
62C23×Dic11D411yescharacteristic
63C23×Dic11D411yescharacteristic
64C22×D44—21no—
65C22×D44—22no—
66C22×D44—28no—
67C22×D44C2311yescharacteristic
68C22×D44C2314yes—
69C22×D44C2312yes—
70C22×C4×D11—21no—
71C22×C4×D11—22no—
72C22×C4×D11—22no—
73C22×C4×D11—28no—
74C22×C4×D11—48no—
75C22×C8×C11C2312yes—
76C11×C22⋊Q8—22no—
77C11×C22⋊Q8C2314yes—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—22no—
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C4⋊C4C2312yes—
83C2×C11×C4⋊C4C2314yes—
84C2×C11×C22⋊C4—21no—
85#67000—22no—
86#67000C2314yescomplemented
87Q8×Dic11—22no—
88Q8×Dic11C2314yescomplemented
89C2×#4325—28no—
90C2×#4325C2318yes—
91#66983—22no—
92#66983C2314yes—
93C2×(C2×D11)⋊C4—21no—
94C2×(C2×D11)⋊C4—21no—
95C2×(C2×D11)⋊C4—21no—
96C2×(C2×D11)⋊C4—21no—
97C2×(C2×D11)⋊C4—22no—
98C2×(C2×D11)⋊C4—22no—
99C2×(C2×D11)⋊C4—28no—
100C2×C4⋊Dic11—21no—
101C2×C4⋊Dic11—21no—
102C2×C4⋊Dic11C2311yescharacteristic
103C2×Dic11⋊C4—21no—
104C2×C4×Dic11—21no—
105C2×C4×Dic11D411yescharacteristic
106C2×C4×Dic11D411yescharacteristic
107C2×C4×Dic11D414yes—
108C2×C4×Dic11C2311yescharacteristic
109C2×C4×Dic11C2311yescharacteristic
110C2×C4×Dic11C2314yes—
111C22×C11⋊C8C2312yes—
112C2×D88—28no—
113C2×D88C2318yes—
114#66951—28no—
115#66946—24no—
116#66946—24no—
117#66946—28no—
118#66946—28no—
119#66946—22no—
120#66946C2318yes—
121#66946C2318yes—
122#66946C2314yescomplemented
123#66945—28no—
124#66943—22no—
125#66943C2314yescomplemented
126#66939—28no—
127(C22⋊D11)⋊C4—28no—
128C11×#106C2318yescomplemented
129C11×#103C2318yescomplemented
130C11×C22⋊C8C2314yes—
131C22⋊(C11⋊C8)C2314yes—
132#66885C2318yes—
133#66879C2318yescomplemented
134Dic11⋊C8C2318yescomplemented
135#66873C2318yes—
136#66873C2318yescomplemented
137#66871C2318yescomplemented
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—
146C2×Q8×C11—21no—
147C2×Q8×C11—24no—
148C2×Q8×C11C2412yes—
149C22×C4×C11—24no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—24no—
153C22×C4×C11—22no—
154C22×C4×C11—44no—
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D412yes—
157C22×C4×C11C2412yes—
158C22×C4×C11C2411yescharacteristic
159C2×C22⋊D11—24no—
160C2×C22⋊D11—44no—
161C22×Dic11—24no—
162C22×Dic11—21no—
163C22×Dic11—42no—
164C22×Dic11C2×D414yes—
165C22×Dic11C2×D411yescharacteristic
166C22×Dic11C2×D411yescharacteristic
167C22×Dic11C2×D411yescharacteristic
168C22×Dic11C2×D411yescharacteristic
169C22×Dic11C2×D414yes—
170C2×D44—28no—
171C2×D44—216no—
172C2×D44—216no—
173C2×D44—24no—
174C2×D44—22no—
175C2×D44—21no—
176C2×D44—24no—
177C2×D44—24no—
178C2×D44#4118yes—
179C2×D44C2412yes—
180C2×D44C2414yes—
181C2×C4×D11—24no—
182C2×C4×D11—28no—
183C2×C4×D11—28no—
184C2×C4×D11—44no—
185C2×C4×D11—48no—
186C2×C4×D11—48no—
187C2×C4×D11—432no—
188C2×C8×C11—24no—
189C2×C8×C11C2414yes—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—24no—
192C11×C4⋊C4—24no—
193C11×C4⋊C4—22no—
194C11×C4⋊C4C2414yes—
195C11×C4⋊C4C2412yes—
196C11×C22⋊C4—24no—
197#4325—216no—
198(C2×D11)⋊C4—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—
204C4⋊Dic11—24no—
205C4⋊Dic11—24no—
206C4⋊Dic11—21no—
207C4⋊Dic11C2412yes—
208Dic11⋊C4—24no—
209C4×Dic11—24no—
210C4×Dic11C2×D412yes—
211C4×Dic11C2×D414yes—
212C4×Dic11C2×D412yes—
213C4×Dic11C2×D414yes—
214C4×Dic11C2412yes—
215C4×Dic11C2412yes—
216C2×C11⋊C8—24no—
217C2×C11⋊C8C2414yes—
218D88—216no—
219C2×#529—111no—
220C22×C4×D4—111no—
221#3114—1116no—
222C2×#483D1111yescharacteristic, complemented
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×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—
248Q8×C11—24no—
249Q8×C11—42no—
250C2×C4×C11—22no—
251C2×C4×C11—24no—
252C2×C4×C11—24no—
253C2×C4×C11—22no—
254C2×C4×C11—22no—
255C2×C4×C11—24no—
256C2×C4×C11—42no—
257C2×C4×C11—48no—
258C2×C4×C11—44no—
259C2×C4×C11—42no—
260C2×C4×C11C22×D412yes—
261C2×C4×C11C22×D411yescharacteristic
262C2×C4×C11C2×#4114yes—
263C2×C4×C11C2511yescharacteristic
264C22⋊D11—48no—
265C2×Dic11—28no—
266C2×Dic11—22no—
267C2×Dic11—22no—
268C2×Dic11—22no—
269C2×Dic11—22no—
270C2×Dic11—22no—
271C2×Dic11—44no—
272C2×Dic11—42no—
273C2×Dic11C22×D412yes—
274C2×Dic11C22×D412yes—
275C2×Dic11C22×D412yes—
276C2×Dic11C22×D412yes—
277D44—216no—
278D44—28no—
279D44—24no—
280D44—24no—
281D44—42no—
282D44C2×#4118yes—
283C4×D11—48no—
284C4×D11—416no—
285C4×D11—416no—
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⋊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⋊C4C2×D1111yescharacteristic
311C22×C22⋊C4—221no—
312C22×C42—111no—
313#483C2×D1118yescomplemented
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×#106C2×D1112yescomplemented
324C2×C4⋊C8—112no—
325C2×#103C2×D1112yescomplemented
326C2×#102—112no—
327C2×#102—112no—
328C2×#102—112no—
329C2×C22⋊C8—111no—
330C2×C22⋊C8C2×D1111yescharacteristic
331C2×#97—112no—
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—42no—
351C4×C11—44no—
352C4×C11—42no—
353C4×C11#52512yes—
354C4×C11C22×#4112yes—
355Dic11—22no—
356Dic11—22no—
357Dic11—22no—
358Dic11—22no—
359Dic11—42no—
360C25—221no—
361C22×Q8C22×D1111yescharacteristic
362C22×D4—112no—
363C22×D4—114no—
364C22×D4—111no—
365C22×D4—228no—
366C22×D4—221no—
367C22×D4—222no—
368C22×D4—221no—
369C23×C4—21no—
370C23×C4—111no—
371C23×C4—111no—
372C23×C4—221no—
373C23×C4—228no—
374C23×C4—222no—
375C23×C4—222no—
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—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—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—21no—
409C2×C4⋊C4—111no—
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#107—118no—
432#106C22×D1118yescomplemented
433C4⋊C8—118no—
434#103C22×D1118yescomplemented
435#102—118no—
436#102—118no—
437#102—118no—
438C22⋊C8—114no—
439C22⋊C8C22×D1114yes—
440#97—118no—
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—
454C24D4×D1111yescharacteristic
455C2×Q8—21no—
456C2×Q8—24no—
457C2×Q8C23×D1112yes—
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—21no—
474C22×C4—21no—
475C22×C4—22no—
476C22×C4—44no—
477C22×C4—114no—
478C22×C4—111no—
479C22×C4—111no—
480C22×C4—111no—
481C22×C4—111no—
482C22×C4—114no—
483C22×C4—224no—
484C22×C4—228no—
485C22×C4—228no—
486C22×C4—224no—
487C22×C4—221no—
488C22×C4—4432no—
489C22×C4—448no—
490C22×C4—448no—
491C22×C4—444no—
492C22×C4—442no—
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—24no—
506C4⋊C4—21no—
507C4⋊C4—112no—
508C4⋊C4—224no—
509C4⋊C4—224no—
510C4⋊C4—224no—
511C4⋊C4—221no—
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—2216no—
532C23—228no—
533C23—224no—
534C23—222no—
535C23—448no—
536C23—4432no—
537C23—448no—
538C23—444no—
539C23—444no—
540C23—442no—
541C23—442no—
542C23—442no—
543C23#6696714yes—
544C23C2×D4×D1112yes—
545C23C2×D4×D1111yescharacteristic
546Q8—24no—
547Q8—42no—
548D4—118no—
549D4—2216no—
550D4—228no—
551D4—224no—
552D4—224no—
553D4—448no—
554D4—442no—
555C2×C4—22no—
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—24no—
561C2×C4—48no—
562C2×C4—44no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—112no—
566C2×C4—112no—
567C2×C4—112no—
568C2×C4—112no—
569C2×C4—228no—
570C2×C4—222no—
571C2×C4—222no—
572C2×C4—222no—
573C2×C4—222no—
574C2×C4—222no—
575C2×C4—4416no—
576C2×C4—4416no—
577C2×C4—448no—
578C2×C4—444no—
579C2×C4—442no—
580C2×C4C2×D4×D1112yes—
581C2×C4C2×D4×D1111yescharacteristic
582C2×C4#41×D1114yes—
583C2×C4C24×D1111yescharacteristic
584C8—24no—
585C8—224no—
586C22—22no—
587C22—28no—
588C22—22no—
589C22—228no—
590C22—4432no—
591C22—444no—
592C22—444no—
593C22—4416no—
594C22—442no—
595C22—442no—
596C22—442no—
597C22—884no—
598C22#1062318712yes—
599C22C2×#6696714yes—
600C22C2×#6696712yes—
601C22#1062330812yes—
602C22C22×D4×D1111yescharacteristic
603C4—22no—
604C4—44no—
605C4—42no—
606C4—42no—
607C4—222no—
608C4—222no—
609C4—222no—
610C4—222no—
611C4—442no—
612C4#1062318712yes—
613C4C2×#41×D1112yes—
614C2—24no—
615C2—448no—
616C2—882no—
617C2#1307875714yesdirect product factor
618C2C2×#1062318711yescharacteristic
619C2C22×#6696711yescharacteristic
620C2C2×#1062330811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#483C2
socleC23×C11C22×D4
prime radicalC2×#10622345C2
hypercenterC2×#483D11
hypocenterC11C2×#3114
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#483

Complements

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

NH ≅ G/Ntype
1. C2×#10623155C2semidirect
2. C22×#66946C2semidirect
3. #13078757C2direct (N × H)
4. C2×#10622580C2semidirect
5. C2×#10622484C2semidirect
6. C2×#10622432C2semidirect
7. C2×#10622659C2semidirect
9. C2×#10622482C2semidirect
10. C2×#10622430C2semidirect
11. C2×#10622332C2semidirect
12. C2×C11×#483C2semidirect
17. C2×#67000C22semidirect
18. C2×Q8×Dic11C22semidirect
25. #10623155C22semidirect
32. C2×#66946C22semidirect
33. C2×#66946C22semidirect
35. C2×#66943C22semidirect
38. C11×#483C22semidirect
39. C2×C11×#106C22semidirect
40. C2×C11×#103C22semidirect
44. C2×#66879C22semidirect
45. C2×Dic11⋊C8C22semidirect
46. #10622659C22semidirect
47. #10622580C22semidirect
49. C2×#66873C22semidirect
50. C2×#66871C22semidirect
51. #10622484C22semidirect
52. #10622482C22semidirect
53. #10622432C22semidirect
54. #10622430C22semidirect
56. #10622332C22semidirect
86. #67000C23semidirect
88. Q8×Dic11C23semidirect
122. #66946C23semidirect
125. #66943C23semidirect
128. C11×#106C23semidirect
129. C11×#103C23semidirect
133. #66879C23semidirect
134. Dic11⋊C8C23semidirect
136. #66873C23semidirect
137. #66871C23semidirect
222. C2×#483D11semidirect
313. #483C2×D11semidirect
323. C2×#106C2×D11semidirect
325. C2×#103C2×D11semidirect
432. #106C22×D11semidirect
434. #103C22×D11semidirect
442. C2×C11#3114semidirect
528. C11C2×#3114semidirect
617. C2#13078757direct (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×#669462
#130787572
C2×#106225802
C2×#106224842
C2×#106224322
C2×#106226592
C2×#106223452
C2×#106224822
C2×#106224302
C2×#106223322
C2×C11×#4832
C2×#311411