Finite Group Databasebeta

← C2×#13079743 #15625813

Subgroups — C2×#13079743 #15625813

Order 2816.

2286 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×#10623079C211yesmaximal, characteristic
2C2×D11×C4⋊Q8C211yesmaximal, characteristic, complemented
3#13079743C2116yesmaximal, direct product factor
4C2×#10622468C212yesmaximal, complemented
5C2×#10622373C212yesmaximal, complemented
6C2×#10622476C212yesmaximal, complemented
7C2×#10622390C212yesmaximal, complemented
8C2×#10622455C211yesmaximal, characteristic, complemented
9C2×#10622621C211yesmaximal, characteristic, complemented
10C2×#10622697C211yesmaximal, characteristic, complemented
11C2×#10622446C211yesmaximal, characteristic, complemented
12C2×C11×#476C211yesmaximal, characteristic, complemented
13C22×Q8×D11—21no—
14C22×#4339—21no—
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C4×D4×C11C2211yescharacteristic
17C2×#66997—21no—
18C2×#66993C2211yescharacteristic
19C2×#66991C2211yescharacteristic
20C2×C4×C22⋊D11—21no—
21D11×C4⋊Q8—24no—
22D11×C4⋊Q8C2218yescomplemented
23#10623079—24no—
24#10623079C2218yes—
25C2×#66948C2211yescharacteristic
26C2×C4⋊C4×D11—21no—
27C2×C4⋊C4×D11C2212yes—
28C2×#66941—21no—
29C2×#66941C2212yes—
30C2×#66941C2211yescharacteristic
31C2×#66938—21no—
32C2×#66937—21no—
33C2×C4×D44C2211yescharacteristic
34C2×C42×D11C2211yescharacteristic
35C2×#66922C2211yescharacteristic
36C11×#476C2218yescomplemented
37C2×C11×#106C2212yes—
38C2×C11×C4⋊C8C2211yescharacteristic
39C2×C11×#102C2212yes—
40C2×#66896C2212yes—
41C2×#66885C2212yes—
42C2×(C2×D11)⋊C8C2212yes—
43C2×#66881C2212yes—
44C2×C8×Dic11C2212yes—
45#10622697C2218yescomplemented
46#10622621C2218yescomplemented
47C2×#66873C2212yes—
48C2×#66872C2212yes—
49C2×#66872C2212yes—
50C2×C4⋊(C11⋊C8)C2211yescharacteristic
51#10622476C22116yescomplemented
52#10622468C22116yescomplemented
53#10622455C2218yescomplemented
54#10622446C2218yescomplemented
55#10622390C22116yescomplemented
56#10622373C22116yescomplemented
57C22×Q8×C11—21no—
58C22×D4×C11C2311yescharacteristic
59C23×C4×C11—21no—
60C22×C22⋊D11—21no—
61C22×C22⋊D11—21no—
62C22×C22⋊D11—21no—
63C2×Q8×D11—28no—
64C2×Q8×D11—48no—
65C2×#4339—28no—
66C2×#4339—48no—
67C22×D44—21no—
68C22×D44C2311yescharacteristic
69C22×C4×D11—22no—
70C22×C4×D11—21no—
71C22×C4×D11D411yescharacteristic
72C22×C4×D11D411yescharacteristic
73C22×C4×D11C2311yescharacteristic
74C22×Dic22—21no—
75C22×Dic22—21no—
76C22×Dic22—22no—
77C22×C8×C11C2312yes—
78C11×C4⋊Q8—22no—
79C11×C4⋊Q8C2314yes—
80C4×D4×C11—22no—
81C4×D4×C11C2314yes—
82C2×C11×C4⋊C4—21no—
83C2×C11×C4⋊C4C2312yes—
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C22⋊C4—21no—
86C2×C42×C11C2311yescharacteristic
87C2×C22⋊Dic11—21no—
88#66997—28no—
89#66993—22no—
90#66993C2314yes—
91#66991—22no—
92#66991C2314yes—
93C4×C22⋊D11—28no—
94C2×(C2×D11)⋊C4—21no—
95C2×(C2×D11)⋊C4—21no—
96C2×C4⋊Dic11—21no—
97C2×C4⋊Dic11C2312yes—
98C2×C4⋊Dic11C2311yescharacteristic
99C2×Dic11⋊C4—21no—
100C2×Dic11⋊C4—22no—
101C2×Dic11⋊C4—22no—
102C2×C4×Dic11D411yescharacteristic
103C2×C4×Dic11D411yescharacteristic
104C2×C4×Dic11C2311yescharacteristic
105C22×C11⋊C8C2312yes—
106#66948—22no—
107#66948C2314yes—
108C4⋊C4×D11—24no—
109C4⋊C4×D11—28no—
110C4⋊C4×D11C2318yes—
111#66941—24no—
112#66941—28no—
113#66941—22no—
114#66941C2314yes—
115#66941C2318yes—
116#66938—28no—
117#66937—28no—
118C4×D44—22no—
119C4×D44C2314yes—
120C42×D11D414yes—
121C42×D11C2314yes—
122#66922—22no—
123#66922C2314yes—
124C11×#106C2318yes—
125C11×C4⋊C8C2314yes—
126C11×#102C2318yes—
127#66896C2318yes—
128#66885C2318yes—
129(C2×D11)⋊C8C2318yes—
130#66881C2318yes—
131C8×Dic11C2318yes—
132#66873C2318yes—
133#66872C2318yes—
134#66872C2318yes—
135C4⋊(C11⋊C8)C2314yes—
136C2×#3227—111nomaximal, Sylow
137C24×C11—21no—
138C23×D11—21no—
139C23×D11C2×D411yescharacteristic
140C2×Q8×C11—24no—
141C2×Q8×C11—44no—
142C2×D4×C11—21no—
143C2×D4×C11—22no—
144C2×D4×C11—22no—
145C2×D4×C11C2412yes—
146C22×C4×C11—22no—
147C22×C4×C11—21no—
148C22×C4×C11—24no—
149C22×C4×C11—44no—
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2411yescharacteristic
153C2×C22⋊D11—24no—
154C2×C22⋊D11—24no—
155C2×C22⋊D11—24no—
156C2×C22⋊D11—44no—
157C2×C22⋊D11—44no—
158C2×C22⋊D11—44no—
159C22×Dic11—22no—
160C22×Dic11—21no—
161C22×Dic11C2×D411yescharacteristic
162C22×Dic11C2×D411yescharacteristic
163C22×Dic11C2×D411yescharacteristic
164Q8×D11—432no—
165#4339—432no—
166C2×D44—24no—
167C2×D44—21no—
168C2×D44—22no—
169C2×D44—22no—
170C2×D44—44no—
171C2×D44C2412yes—
172C2×C4×D11—24no—
173C2×C4×D11—28no—
174C2×C4×D11—24no—
175C2×C4×D11—22no—
176C2×C4×D11—22no—
177C2×C4×D11—48no—
178C2×C4×D11—44no—
179C2×C4×D11SD1618yes—
180C2×C4×D11C2×D412yes—
181C2×C4×D11C2×D414yes—
182C2×C4×D11C2×D414yes—
183C2×C4×D11C2412yes—
184C2×Dic22—24no—
185C2×Dic22—28no—
186C2×Dic22—24no—
187C2×Dic22—44no—
188C2×Dic22—44no—
189C2×Dic22—48no—
190C2×C8×C11—24no—
191C2×C8×C11C2414yes—
192C11×C4⋊C4—24no—
193C11×C4⋊C4—22no—
194C11×C4⋊C4—21no—
195C11×C4⋊C4C2412yes—
196C11×C4⋊C4C2414yes—
197C11×C22⋊C4—24no—
198C42×C11C2×D412yes—
199C42×C11C2412yes—
200C22⋊Dic11—24no—
201(C2×D11)⋊C4—24no—
202(C2×D11)⋊C4—24no—
203C4⋊Dic11—22no—
204C4⋊Dic11—24no—
205C4⋊Dic11—21no—
206C4⋊Dic11C2412yes—
207C4⋊Dic11C2414yes—
208Dic11⋊C4—24no—
209Dic11⋊C4—28no—
210Dic11⋊C4—28no—
211C4×Dic11C2×D412yes—
212C4×Dic11C2×D414yes—
213C4×Dic11C2×D414yes—
214C4×Dic11C2412yes—
215C2×C11⋊C8—24no—
216C2×C11⋊C8C2414yes—
217C2×#532—111no—
218C22×C4⋊Q8—111no—
219#3227—1116no—
220C2×#498—112no—
221C2×#486—112no—
222C2×#481—112no—
223C2×#481—112no—
224C2×#476—111no—
225C2×#476—111no—
226C2×#476—111no—
227C2×#476D1111yescharacteristic, complemented
228C2×#431—111no—
229C23×C11—22no—
230C23×C11—42no—
231C23×C11—42no—
232C23×C11—42no—
233C23×C11C22×D411yescharacteristic
234C22×D11—22no—
235C22×D11—22no—
236C22×D11—22no—
237C22×D11—42no—
238C22×D11—42no—
239C22×D11—42no—
240C22×D11C2×SD1614yes—
241C22×D11C22×D412yes—
242Q8×C11—48no—
243D4×C11—22no—
244D4×C11—22no—
245D4×C11—42no—
246C2×C4×C11—22no—
247C2×C4×C11—24no—
248C2×C4×C11—22no—
249C2×C4×C11—42no—
250C2×C4×C11—44no—
251C2×C4×C11—48no—
252C2×C4×C11C2×SD1614yes—
253C2×C4×C11C22×D412yes—
254C2×C4×C11C22×D411yescharacteristic
255C2×C4×C11C22×D412yes—
256C2×C4×C112−1+412yes—
257C2×C4×C112−1+412yes—
258C2×C4×C11C2511yescharacteristic
259C22⋊D11—48no—
260C22⋊D11—48no—
261C22⋊D11—48no—
262C2×Dic11—22no—
263C2×Dic11—24no—
264C2×Dic11—22no—
265C2×Dic11—42no—
266C2×Dic11—44no—
267C2×Dic11C2×SD1614yes—
268C2×Dic11AGL(1,ℤ/8)14yes—
269C2×Dic11C22×D412yes—
270C2×Dic11C22×D412yes—
271C2×Dic11C22×D412yes—
272D44—22no—
273D44—22no—
274D44—48no—
275D44—42no—
276C4×D11—24no—
277C4×D11—22no—
278C4×D11—22no—
279C4×D11—28no—
280C4×D11—416no—
281C4×D11—48no—
282C4×D11C2×SD16116yes—
283Dic22—48no—
284Dic22—48no—
285Dic22—416no—
286C8×C11—24no—
287C11⋊C8—24no—
288C22×#41—221no—
289C23×Q8—221no—
290#532—118no—
291#532—224no—
292C2×C4⋊Q8—118no—
293C2×C4⋊Q8—112no—
294C2×C4⋊Q8—111no—
295C2×C4⋊Q8—111no—
296C2×C4⋊Q8—221no—
297C2×C4⋊Q8—224no—
298C2×C4⋊Q8—221no—
299C2×C4⋊Q8C2×D1111yescharacteristic
300C2×#127—111no—
301C2×#124—221no—
302C2×#121—111no—
303C2×#121—111no—
304C2×#121—221no—
305C2×C4×D4—111no—
306C2×C4×D4—221no—
307C2×C4×D4C2×D1111yescharacteristic
308C22×C4⋊C4—112no—
309C22×C4⋊C4—221no—
310C22×C42—111no—
311#498—1116no—
312#486—1116no—
313#481—1116no—
314#481—1116no—
315#476—118no—
316#476—118no—
317#476—118no—
318#476C2×D1118yescomplemented
319#431—118no—
320C2×#106—112no—
321C2×#106—112no—
322C2×#106—112no—
323C2×#106C2×D1112yes—
324C2×C4⋊C8—111no—
325C2×C4⋊C8C2×D1111yescharacteristic
326C2×#102—112no—
327C2×#102—112no—
328C2×#102—112no—
329C2×#102C2×D1112yes—
330C2×C22⋊C8—112no—
331C2×C4×C8—112no—
332C22×C11—42no—
333C22×C11—42no—
334C22×C11—42no—
335C22×C11—84no—
336C22×C11#53612yes—
337C22×C11C22×SD1612yes—
338C22×C11C2×AGL(1,ℤ/8)12yes—
339C22×C11C23×D411yescharacteristic
340C2×D11—22no—
341C2×D11—28no—
342C2×D11—22no—
343C2×D11—42no—
344C2×D11—42no—
345C2×D11—42no—
346C2×D11—84no—
347C2×D11C22×SD1614yes—
348C4×C11—22no—
349C4×C11—42no—
350C4×C11—44no—
351C4×C11#53612yes—
352C4×C11C22×SD1614yes—
353C4×C11C2×2−1+411yescharacteristic
354C4×C11C2×2−1+411yescharacteristic
355Dic11—22no—
356Dic11—42no—
357Dic11—44no—
358Dic11C22×SD1614yes—
359Dic11C2×AGL(1,ℤ/8)14yes—
360C2×#41—228no—
361C2×#41—448no—
362C22×Q8—21no—
363C22×Q8—221no—
364C22×Q8—222no—
365C22×Q8—228no—
366C22×Q8—221no—
367C22×Q8—448no—
368C22×D4—111no—
369C22×D4—221no—
370C22×D4—221no—
371C22×D4—221no—
372C22×D4—221no—
373C22×D4C22×D1111yescharacteristic
374C23×C4—21no—
375C23×C4—111no—
376C23×C4—111no—
377C23×C4—111no—
378C23×C4—222no—
379C23×C4—221no—
380C22×C8—112no—
381C22×C8C22×D1112yes—
382C4⋊Q8—22no—
383C4⋊Q8—118no—
384C4⋊Q8—114no—
385C4⋊Q8—114no—
386C4⋊Q8—228no—
387C4⋊Q8—224no—
388C4⋊Q8—222no—
389C4⋊Q8—228no—
390C4⋊Q8—222no—
391C4⋊Q8C22×D1114yes—
392#127—114no—
393#127—222no—
394#124—228no—
395#121—114no—
396#121—114no—
397#121—228no—
398#121—222no—
399#121—222no—
400C4×D4—22no—
401C4×D4—114no—
402C4×D4—228no—
403C4×D4—222no—
404C4×D4C22×D1114yes—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—112no—
407C2×C4⋊C4—111no—
408C2×C4⋊C4—118no—
409C2×C4⋊C4—224no—
410C2×C4⋊C4—228no—
411C2×C4⋊C4—222no—
412C2×C4⋊C4—222no—
413C2×C4⋊C4—221no—
414C2×C4⋊C4—221no—
415C2×C4⋊C4C22×D1112yes—
416C2×C4⋊C4C22×D1111yescharacteristic
417C2×C22⋊C4—21no—
418C2×C22⋊C4—221no—
419C2×C22⋊C4—221no—
420C2×C22⋊C4—221no—
421C2×C42—111no—
422C2×C42—111no—
423C2×C42—111no—
424C2×C42—114no—
425C2×C42—114no—
426C2×C42C22×D1111yescharacteristic
427#106—118no—
428#106—118no—
429#106—118no—
430#106C22×D1118yes—
431C4⋊C8—114no—
432C4⋊C8C22×D1114yes—
433#102—118no—
434#102—118no—
435#102—118no—
436#102C22×D1118yes—
437C22⋊C8—118no—
438C4×C8—118no—
439C2×C11—82no—
440C2×C11#322714yescomplemented
441C2×C11C2×#53611yescharacteristic
442C2×C11C23×SD1611yescharacteristic
443C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
444D11—24no—
445D11—82no—
446C24—21no—
447C24—111no—
448C24—221no—
449#41—4432no—
450C2×Q8—24no—
451C2×Q8—44no—
452C2×Q8—224no—
453C2×Q8—228no—
454C2×Q8—224no—
455C2×Q8—444no—
456C2×Q8—448no—
457C2×Q8—444no—
458C2×Q8—4432no—
459C2×D4—21no—
460C2×D4—22no—
461C2×D4—22no—
462C2×D4—112no—
463C2×D4—224no—
464C2×D4—224no—
465C2×D4—224no—
466C2×D4—224no—
467C2×D4—221no—
468C2×D4—222no—
469C2×D4—222no—
470C2×D4—444no—
471C2×D4—444no—
472C2×D4—444no—
473C2×D4—444no—
474C2×D4C23×D1112yes—
475C22×C4—21no—
476C22×C4—22no—
477C22×C4—24no—
478C22×C4—44no—
479C22×C4—111no—
480C22×C4—111no—
481C22×C4—118no—
482C22×C4—114no—
483C22×C4—111no—
484C22×C4—112no—
485C22×C4—114no—
486C22×C4—112no—
487C22×C4—224no—
488C22×C4—228no—
489C22×C4—222no—
490C22×C4—222no—
491C22×C4—221no—
492C22×C4—222no—
493C22×C4—224no—
494C22×C4—448no—
495C22×C4—444no—
496C22×C4D4×D1111yescharacteristic
497C22×C4D4×D1111yescharacteristic
498C22×C4C23×D1111yescharacteristic
499C2×C8—24no—
500C2×C8—114no—
501C2×C8—224no—
502C2×C8C23×D1114yes—
503C4⋊C4—24no—
504C4⋊C4—22no—
505C4⋊C4—21no—
506C4⋊C4—114no—
507C4⋊C4—112no—
508C4⋊C4—228no—
509C4⋊C4—228no—
510C4⋊C4—224no—
511C4⋊C4—222no—
512C4⋊C4—221no—
513C4⋊C4—224no—
514C4⋊C4C23×D1114yes—
515C4⋊C4C23×D1112yes—
516C22⋊C4—24no—
517C22⋊C4—224no—
518C22⋊C4—224no—
519C22⋊C4—224no—
520C42—114no—
521C42—114no—
522C42—112no—
523C42—112no—
524C42D4×D1112yes—
525C42C23×D1112yes—
526C11C2×#322711yescharacteristic, complemented, Sylow
527C23—22no—
528C23—42no—
529C23—42no—
530C23—42no—
531C23—114no—
532C23—112no—
533C23—222no—
534C23—222no—
535C23—222no—
536C23—442no—
537C23—442no—
538C23—442no—
539C23C2×D4×D1111yescharacteristic
540Q8—48no—
541Q8—448no—
542Q8—4416no—
543Q8—448no—
544D4—22no—
545D4—22no—
546D4—42no—
547D4—222no—
548D4—222no—
549D4—448no—
550D4—448no—
551D4—448no—
552D4—448no—
553D4—442no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—24no—
557C2×C4—42no—
558C2×C4—44no—
559C2×C4—48no—
560C2×C4—114no—
561C2×C4—114no—
562C2×C4—112no—
563C2×C4—112no—
564C2×C4—1116no—
565C2×C4—112no—
566C2×C4—228no—
567C2×C4—222no—
568C2×C4—224no—
569C2×C4—222no—
570C2×C4—222no—
571C2×C4—222no—
572C2×C4—224no—
573C2×C4—4416no—
574C2×C4—442no—
575C2×C4—444no—
576C2×C4—448no—
577C2×C4SD16×D1114yes—
578C2×C4C2×D4×D1112yes—
579C2×C4C2×D4×D1112yes—
580C2×C4C2×D4×D1111yescharacteristic
581C2×C4#6704012yes—
582C2×C4#6704312yes—
583C2×C4C24×D1111yescharacteristic
584C8—24no—
585C8—224no—
586C22—42no—
587C22—42no—
588C22—42no—
589C22—84no—
590C22—114no—
591C22—222no—
592C22—228no—
593C22—222no—
594C22—442no—
595C22—442no—
596C22—442no—
597C22—884no—
598C22#1062315912yes—
599C22C2×SD16×D1112yes—
600C22D11×AGL(1,ℤ/8)12yes—
601C22C22×D4×D1111yescharacteristic
602C4—22no—
603C4—42no—
604C4—44no—
605C4—114no—
606C4—114no—
607C4—222no—
608C4—442no—
609C4—444no—
610C4#1062315912yes—
611C4C2×SD16×D1114yes—
612C4C2×#6704011yescharacteristic
613C4C2×#6704311yescharacteristic
614C2—82no—
615C2—224no—
616C2—882no—
617C2#1307974314yesdirect product factor
618C2C2×#1062315911yescharacteristic
619C2C22×SD16×D1111yescharacteristic
620C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#476C2
socleC23×C11C22×D4
prime radicalC2×#10623079C2
hypercenterC2×#476D11
hypocenterC11C2×#3227
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#476

Complements

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

NH ≅ G/Ntype
2. C2×D11×C4⋊Q8C2semidirect
3. #13079743C2direct (N × H)
4. C2×#10622468C2semidirect
5. C2×#10622373C2semidirect
6. C2×#10622476C2semidirect
7. C2×#10622390C2semidirect
8. C2×#10622455C2semidirect
9. C2×#10622621C2semidirect
10. C2×#10622697C2semidirect
11. C2×#10622446C2semidirect
12. C2×C11×#476C2semidirect
22. D11×C4⋊Q8C22semidirect
36. C11×#476C22semidirect
45. #10622697C22semidirect
46. #10622621C22semidirect
51. #10622476C22semidirect
52. #10622468C22semidirect
53. #10622455C22semidirect
54. #10622446C22semidirect
55. #10622390C22semidirect
56. #10622373C22semidirect
227. C2×#476D11semidirect
318. #476C2×D11semidirect
440. C2×C11#3227semidirect
526. C11C2×#3227semidirect
617. C2#13079743direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230792
C2×D11×C4⋊Q82
#130797432
C2×#106224682
C2×#106223732
C2×#106224762
C2×#106223902
C2×#106224552
C2×#106226212
C2×#106226972
C2×#106224462
C2×C11×#4762
C2×#322711