Finite Group Databasebeta

← C2×#13079604 #15625021

Subgroups — C2×#13079604 #15625021

Order 2816.

2522 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623256C211yesmaximal, characteristic, complemented
2C2×D11×#124C211yesmaximal, characteristic, complemented
3#13079604C2116yesmaximal, direct product factor
4C2×#10622671C211yesmaximal, characteristic, complemented
5C2×#10622325C211yesmaximal, characteristic, complemented
6C2×#10622702C211yesmaximal, characteristic, complemented
7C2×#10622432C212yesmaximal, complemented
8C2×#10622400C212yesmaximal, complemented
9C2×#10622419C212yesmaximal, complemented
10C2×#10622386C212yesmaximal, complemented
11C2×#10622318C211yesmaximal, characteristic, complemented
12C2×C11×#489C211yesmaximal, characteristic, complemented
13C22×#4343—21no—
14C22×Q8×D11C2211yescharacteristic
15C22×D4×D11C2211yescharacteristic
16C2×C11×C4⋊Q8C2211yescharacteristic, complemented
17C2×C11×#124C2211yescharacteristic
18C2×#67000—21no—
19C2×#67000C2211yescharacteristic
20C22×#4325C2212yescomplemented
21C2×#66989C2211yescharacteristic
22C22×#4323C2212yes—
23C22×D88C2212yes—
24C22×#4314C2212yescomplemented
25#10623256—24no—
26#10623256C2218yescomplemented
27D11×#124—24no—
28D11×#124C2218yescomplemented
29C2×#66948—21no—
30C2×#66948C2212yes—
31C2×#66946—21no—
32C2×#66946C2212yescomplemented
33C2×#66938—21no—
34C2×#66938—21no—
35C2×C22⋊C4×D11—21no—
36C2×C22⋊C4×D11—21no—
37C2×#66928C2211yescharacteristic
38C2×#66927C2211yescharacteristic, complemented
39C2×C42×D11C2211yescharacteristic
40C11×#489C2218yescomplemented
41C2×C11×#103C2212yescomplemented
42C2×C11×#102C2212yes—
43C2×C11×#97C2211yescharacteristic, complemented
44C2×(C2×D11)⋊C8C2212yes—
45C2×Dic11⋊C8C2212yescomplemented
46#10622702C2218yescomplemented
47#10622671C2218yescomplemented
48C2×#66874C2212yescomplemented
49C2×#66873C2212yes—
50C2×#66867C2211yescharacteristic, complemented
51#10622432C22116yescomplemented
52#10622419C22116yescomplemented
53#10622400C22116yescomplemented
54#10622386C22116yescomplemented
55#10622325C2218yescomplemented
56#10622318C2218yescomplemented
57C24×D11—21no—
58C22×Q8×C11—21no—
59C22×Q8×C11C2311yescharacteristic
60C22×D4×C11C2311yescharacteristic
61C22×C22⋊D11—21no—
62C2×#4343—28no—
63C2×#4343—48no—
64C2×Q8×D11—22no—
65C2×Q8×D11—44no—
66C2×Q8×D11C2314yes—
67C2×D4×D11—22no—
68C2×D4×D11—44no—
69C2×D4×D11C2314yes—
70C22×D44—22no—
71C22×D44—21no—
72C22×D44—21no—
73C22×D44C2312yes—
74C22×D44C2311yescharacteristic
75C22×C4×D11—21no—
76C22×C4×D11—22no—
77C22×C4×D11D411yescharacteristic
78C22×C4×D11D411yescharacteristic
79C22×C4×D11C2311yescharacteristic
80C22×Dic22—21no—
81C22×Dic22C2311yescharacteristic
82C22×C8×C11C2312yes—
83C11×C4⋊Q8—22no—
84C11×C4⋊Q8C2314yescomplemented
85C11×#124—22no—
86C11×#124C2314yes—
87C2×C11×C4⋊C4—21no—
88C2×C11×C4⋊C4C2312yes—
89C2×C11×C22⋊C4—21no—
90C2×C11×C22⋊C4—21no—
91C2×C42×C11C2311yescharacteristic
92C2×C22⋊Dic11—21no—
93C2×C22⋊Dic11—21no—
94#67000—28no—
95#67000—22no—
96#67000C2314yes—
97C2×#4325—44no—
98C2×#4325C2318yescomplemented
99#66989—22no—
100#66989C2314yes—
101C2×#4323—44no—
102C2×#4323C2318yes—
103C2×(C2×D11)⋊C4—21no—
104C2×(C2×D11)⋊C4—21no—
105C2×(C2×D11)⋊C4—21no—
106C2×(C2×D11)⋊C4—21no—
107C2×(C2×D11)⋊C4—22no—
108C2×(C2×D11)⋊C4—22no—
109C2×C4×Dic11D411yescharacteristic
110C2×C4×Dic11D411yescharacteristic
111C2×C4×Dic11C2311yescharacteristic
112C22×C11⋊C8C2312yes—
113C2×D88—44no—
114C2×D88C2318yes—
115C2×#4314—44no—
116C2×#4314C2318yescomplemented
117#66948—24no—
118#66948—28no—
119#66948C2318yes—
120#66946—24no—
121#66946—28no—
122#66946C2318yescomplemented
123#66938—28no—
124#66938—28no—
125C22⋊C4×D11—28no—
126C22⋊C4×D11—28no—
127#66928—22no—
128#66928C2314yes—
129#66927—22no—
130#66927C2314yescomplemented
131C42×D11D414yes—
132C42×D11C2314yes—
133C11×#103C2318yescomplemented
134C11×#102C2318yes—
135C11×#97C2314yescomplemented
136(C2×D11)⋊C8C2318yes—
137Dic11⋊C8C2318yescomplemented
138#66874C2318yescomplemented
139#66873C2318yes—
140#66867C2314yescomplemented
141C2×#3213—111nomaximal, Sylow
142C24×C11—21no—
143C23×D11—21no—
144C23×D11—22no—
145C23×D11—24no—
146C23×D11—44no—
147C23×D11—44no—
148C23×D11—44no—
149C23×D11C2×D411yescharacteristic
150C2×Q8×C11—21no—
151C2×Q8×C11—24no—
152C2×Q8×C11—24no—
153C2×Q8×C11—44no—
154C2×Q8×C11C2412yes—
155C2×D4×C11—21no—
156C2×D4×C11—24no—
157C2×D4×C11C2412yes—
158C22×C4×C11—21no—
159C22×C4×C11—22no—
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11C2411yescharacteristic
163C2×C22⋊D11—24no—
164C2×C22⋊D11—44no—
165C22×Dic11—21no—
166C22×Dic11C2×D411yescharacteristic
167C22×Dic11C2×D411yescharacteristic
168C22×Dic11C2×D411yescharacteristic
169#4343—432no—
170Q8×D11—48no—
171Q8×D11—48no—
172D4×D11—48no—
173D4×D11—48no—
174C2×D44—28no—
175C2×D44—22no—
176C2×D44—24no—
177C2×D44—24no—
178C2×D44—21no—
179C2×D44—24no—
180C2×D44—24no—
181C2×D44—24no—
182C2×D44—44no—
183C2×D44—44no—
184C2×D44—48no—
185C2×D44C2412yes—
186C2×D44C2414yes—
187C2×C4×D11—28no—
188C2×C4×D11—24no—
189C2×C4×D11—24no—
190C2×C4×D11—24no—
191C2×C4×D11—42no—
192C2×C4×D11—44no—
193C2×C4×D11—48no—
194C2×C4×D11C2×D412yes—
195C2×C4×D11C2×D414yes—
196C2×C4×D11C2×D414yes—
197C2×C4×D11C2412yes—
198C2×Dic22—24no—
199C2×Dic22—21no—
200C2×Dic22—24no—
201C2×Dic22—44no—
202C2×Dic22C2412yes—
203C2×C8×C11—24no—
204C2×C8×C11C2414yes—
205C11×C4⋊C4—24no—
206C11×C4⋊C4—22no—
207C11×C4⋊C4C2414yes—
208C11×C22⋊C4—24no—
209C11×C22⋊C4—24no—
210C42×C11C2×D412yes—
211C42×C11C2412yes—
212C22⋊Dic11—24no—
213C22⋊Dic11—24no—
214#4325—48no—
215#4323—48no—
216(C2×D11)⋊C4—24no—
217(C2×D11)⋊C4—24no—
218(C2×D11)⋊C4—28no—
219(C2×D11)⋊C4—28no—
220(C2×D11)⋊C4—24no—
221(C2×D11)⋊C4—24no—
222C4×Dic11C2×D412yes—
223C4×Dic11C2×D414yes—
224C4×Dic11C2×D414yes—
225C4×Dic11C2412yes—
226C2×C11⋊C8—24no—
227C2×C11⋊C8C2414yes—
228D88—48no—
229#4314—48no—
230C2×#532—111no—
231C22×#124—111no—
232#3213—1116no—
233C2×#496—111no—
234C2×#496—111no—
235C2×#489—111no—
236C2×#489D1111yescharacteristic, complemented
237C2×#463—112no—
238C2×#463—112no—
239C2×#448—112no—
240C2×#447—112no—
241C2×#432—111no—
242C23×C11—22no—
243C23×C11—42no—
244C23×C11—42no—
245C23×C11—42no—
246C23×C11C22×D411yescharacteristic
247C22×D11—22no—
248C22×D11—22no—
249C22×D11—22no—
250C22×D11—24no—
251C22×D11—48no—
252C22×D11—48no—
253C22×D11—42no—
254C22×D11—44no—
255C22×D11—44no—
256C22×D11—42no—
257C22×D11—44no—
258C22×D11—42no—
259C22×D11—48no—
260C22×D11—816no—
261C22×D11AGL(1,ℤ/8)14yes—
262C22×D11C22×D412yes—
263Q8×C11—24no—
264Q8×C11—48no—
265Q8×C11—42no—
266D4×C11—24no—
267D4×C11—42no—
268C2×C4×C11—22no—
269C2×C4×C11—22no—
270C2×C4×C11—22no—
271C2×C4×C11—24no—
272C2×C4×C11—42no—
273C2×C4×C11—44no—
274C2×C4×C11C22×D412yes—
275C2×C4×C11C22×D412yes—
276C2×C4×C11C22×D411yescharacteristic
277C2×C4×C11H(5,𝔽2)14yes—
278C2×C4×C11C2511yescharacteristic
279C22⋊D11—48no—
280C2×Dic11—22no—
281C2×Dic11—22no—
282C2×Dic11—22no—
283C2×Dic11—22no—
284C2×Dic11—42no—
285C2×Dic11C22×D412yes—
286C2×Dic11C22×D412yes—
287C2×Dic11C22×D412yes—
288D44—24no—
289D44—24no—
290D44—24no—
291D44—48no—
292D44—48no—
293D44—416no—
294D44—44no—
295D44—42no—
296C4×D11—28no—
297C4×D11—24no—
298C4×D11—24no—
299C4×D11—44no—
300C4×D11—416no—
301C4×D11—48no—
302Dic22—24no—
303Dic22—48no—
304Dic22—42no—
305C8×C11—24no—
306C11⋊C8—24no—
307C22×#41—221no—
308C23×Q8—111no—
309C23×D4—111no—
310C22×SD16—112no—
311C22×SD16—112no—
312C22×D8—112no—
313C22×D8—112no—
314#532—118no—
315#532—224no—
316C2×C4⋊Q8C2×D1111yescharacteristic, complemented
317C2×#127—111no—
318C2×#124—111no—
319C2×#124—111no—
320C2×#124—118no—
321C2×#124—111no—
322C2×#124—221no—
323C2×#124—221no—
324C2×#124—224no—
325C2×#124—221no—
326C2×#124C2×D1111yescharacteristic
327C2×#121—112no—
328C2×#121—221no—
329C2×C4×D4—112no—
330C2×C4×D4—221no—
331C22×C22⋊C4—221no—
332C22×C22⋊C4—221no—
333C22×C42—111no—
334#496—118no—
335#496—118no—
336#489—118no—
337#489C2×D1118yescomplemented
338#463—1116no—
339#463—1116no—
340#448—1116no—
341#447—1116no—
342#432—118no—
343C2×C4⋊C8—112no—
344C2×#103—112no—
345C2×#103C2×D1112yescomplemented
346C2×#102—112no—
347C2×#102C2×D1112yes—
348C2×C22⋊C8—112no—
349C2×#97—111no—
350C2×#97C2×D1111yescharacteristic, complemented
351C22×C11—42no—
352C22×C11—42no—
353C22×C11—42no—
354C22×C11—84no—
355C22×C11#53512yes—
356C22×C11C2×AGL(1,ℤ/8)12yes—
357C22×C11#57512yes—
358C22×C11C23×D411yescharacteristic
359C2×D11—22no—
360C2×D11—28no—
361C2×D11—22no—
362C2×D11—42no—
363C2×D11—44no—
364C2×D11—42no—
365C2×D11—44no—
366C2×D11—42no—
367C2×D11—44no—
368C2×D11—816no—
369C2×D11—88no—
370C2×D11—84no—
371C2×D11C2×AGL(1,ℤ/8)14yes—
372C4×C11—22no—
373C4×C11—22no—
374C4×C11—42no—
375C4×C11—44no—
376C4×C11#53512yes—
377C4×C11C2×H(5,𝔽2)12yes—
378Dic11—22no—
379Dic11—22no—
380Dic11—22no—
381Dic11—42no—
382C25—221no—
383C2×#41—228no—
384C2×#41—448no—
385C22×Q8—21no—
386C22×Q8—114no—
387C22×Q8—111no—
388C22×Q8—221no—
389C22×Q8—222no—
390C22×Q8—444no—
391C22×Q8C22×D1111yescharacteristic
392C22×D4—114no—
393C22×D4—112no—
394C22×D4—111no—
395C22×D4—222no—
396C22×D4—222no—
397C22×D4—221no—
398C22×D4—221no—
399C22×D4—221no—
400C22×D4—444no—
401C22×D4C22×D1111yescharacteristic
402C23×C4—111no—
403C23×C4—111no—
404C23×C4—111no—
405C23×C4—222no—
406C23×C4—221no—
407C2×SD16—118no—
408C2×SD16—118no—
409C2×SD16—444no—
410C2×SD16—444no—
411C2×D8—118no—
412C2×D8—118no—
413C2×D8—444no—
414C2×D8—444no—
415C22×C8—112no—
416C22×C8C22×D1112yes—
417C4⋊Q8—22no—
418C4⋊Q8C22×D1114yescomplemented
419#127—114no—
420#127—222no—
421#124—22no—
422#124—114no—
423#124—114no—
424#124—114no—
425#124—228no—
426#124—228no—
427#124—222no—
428#124—222no—
429#124—228no—
430#124—222no—
431#124C22×D1114yes—
432#121—118no—
433#121—224no—
434#121—228no—
435C4×D4—118no—
436C4×D4—224no—
437C4×D4—228no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4C22×D1112yes—
440C2×C22⋊C4—21no—
441C2×C22⋊C4—21no—
442C2×C22⋊C4—228no—
443C2×C22⋊C4—228no—
444C2×C22⋊C4—221no—
445C2×C22⋊C4—221no—
446C2×C22⋊C4—222no—
447C2×C22⋊C4—222no—
448C2×C22⋊C4—221no—
449C2×C22⋊C4—221no—
450C2×C22⋊C4—221no—
451C2×C22⋊C4—221no—
452C2×C42—111no—
453C2×C42—111no—
454C2×C42—111no—
455C2×C42—114no—
456C2×C42—114no—
457C2×C42C22×D1111yescharacteristic
458C4⋊C8—118no—
459#103—118no—
460#103C22×D1118yescomplemented
461#102—118no—
462#102C22×D1118yes—
463C22⋊C8—118no—
464#97—114no—
465#97C22×D1114yescomplemented
466C2×C11—82no—
467C2×C11#321314yescomplemented
468C2×C11C2×#53511yescharacteristic
469C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
470C2×C11C2×#57511yescharacteristic
471D11—24no—
472D11—84no—
473D11—82no—
474C24—21no—
475C24—111no—
476C24—224no—
477C24—221no—
478C24—222no—
479C24—444no—
480C24—444no—
481C24—444no—
482#41—4432no—
483C2×Q8—21no—
484C2×Q8—24no—
485C2×Q8—24no—
486C2×Q8—44no—
487C2×Q8—112no—
488C2×Q8—224no—
489C2×Q8—221no—
490C2×Q8—224no—
491C2×Q8—444no—
492C2×Q8—448no—
493C2×Q8—448no—
494C2×Q8C23×D1112yes—
495C2×D4—21no—
496C2×D4—24no—
497C2×D4—112no—
498C2×D4—114no—
499C2×D4—228no—
500C2×D4—224no—
501C2×D4—224no—
502C2×D4—222no—
503C2×D4—221no—
504C2×D4—224no—
505C2×D4—224no—
506C2×D4—224no—
507C2×D4—224no—
508C2×D4—444no—
509C2×D4—444no—
510C2×D4—448no—
511C2×D4—448no—
512C2×D4—448no—
513C2×D4—444no—
514C2×D4C23×D1112yes—
515C22×C4—21no—
516C22×C4—22no—
517C22×C4—111no—
518C22×C4—111no—
519C22×C4—111no—
520C22×C4—114no—
521C22×C4—112no—
522C22×C4—112no—
523C22×C4—114no—
524C22×C4—228no—
525C22×C4—224no—
526C22×C4—224no—
527C22×C4—224no—
528C22×C4—221no—
529C22×C4—442no—
530C22×C4—448no—
531C22×C4—444no—
532C22×C4D4×D1111yescharacteristic
533C22×C4D4×D1111yescharacteristic
534C22×C4C23×D1111yescharacteristic
535SD16—448no—
536SD16—448no—
537D8—448no—
538D8—448no—
539C2×C8—24no—
540C2×C8—114no—
541C2×C8—224no—
542C2×C8C23×D1114yes—
543C4⋊C4—24no—
544C4⋊C4—22no—
545C4⋊C4C23×D1114yes—
546C22⋊C4—24no—
547C22⋊C4—24no—
548C22⋊C4—224no—
549C22⋊C4—224no—
550C22⋊C4—228no—
551C22⋊C4—228no—
552C22⋊C4—224no—
553C22⋊C4—224no—
554C22⋊C4—224no—
555C22⋊C4—224no—
556C42—112no—
557C42—114no—
558C42—114no—
559C42—112no—
560C42D4×D1112yes—
561C42C23×D1112yes—
562C11C2×#321311yescharacteristic, complemented, Sylow
563C23—22no—
564C23—42no—
565C23—42no—
566C23—42no—
567C23—114no—
568C23—112no—
569C23—222no—
570C23—222no—
571C23—222no—
572C23—224no—
573C23—448no—
574C23—448no—
575C23—448no—
576C23—444no—
577C23—442no—
578C23—444no—
579C23—442no—
580C23—442no—
581C23—444no—
582C23—8816no—
583C23C2×D4×D1111yescharacteristic
584Q8—24no—
585Q8—48no—
586Q8—42no—
587Q8—224no—
588Q8—448no—
589Q8—442no—
590D4—24no—
591D4—42no—
592D4—224no—
593D4—224no—
594D4—224no—
595D4—448no—
596D4—448no—
597D4—4416no—
598D4—448no—
599D4—442no—
600D4—444no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—24no—
605C2×C4—44no—
606C2×C4—42no—
607C2×C4—112no—
608C2×C4—112no—
609C2×C4—112no—
610C2×C4—228no—
611C2×C4—222no—
612C2×C4—222no—
613C2×C4—222no—
614C2×C4—224no—
615C2×C4—224no—
616C2×C4—222no—
617C2×C4—444no—
618C2×C4—4416no—
619C2×C4—448no—
620C2×C4—442no—
621C2×C4C2×D4×D1112yes—
622C2×C4C2×D4×D1112yes—
623C2×C4C2×D4×D1111yescharacteristic
624C2×C4#6704214yes—
625C2×C4C24×D1111yescharacteristic
626C8—24no—
627C8—224no—
628C22—42no—
629C22—42no—
630C22—42no—
631C22—84no—
632C22—114no—
633C22—228no—
634C22—222no—
635C22—222no—
636C22—442no—
637C22—444no—
638C22—444no—
639C22—442no—
640C22—444no—
641C22—442no—
642C22—8816no—
643C22—884no—
644C22—888no—
645C22#1062320512yes—
646C22D11×AGL(1,ℤ/8)12yes—
647C22#1062330812yes—
648C22C22×D4×D1111yescharacteristic
649C4—22no—
650C4—22no—
651C4—42no—
652C4—44no—
653C4—222no—
654C4—222no—
655C4—222no—
656C4—442no—
657C4#1062320512yes—
658C4C2×#6704212yes—
659C2—82no—
660C2—224no—
661C2—882no—
662C2—884no—
663C2#1307960414yesdirect product factor
664C2C2×#1062320511yescharacteristic
665C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
666C2C2×#1062330811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#489C2
socleC23×C11C22×D4
hypercenterC2×#489D11
hypocenterC11C2×#3213
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#489

Complements

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

NH ≅ G/Ntype
1. C2×#10623256C2semidirect
2. C2×D11×#124C2semidirect
3. #13079604C2direct (N × H)
4. C2×#10622671C2semidirect
5. C2×#10622325C2semidirect
6. C2×#10622702C2semidirect
7. C2×#10622432C2semidirect
8. C2×#10622400C2semidirect
9. C2×#10622419C2semidirect
10. C2×#10622386C2semidirect
11. C2×#10622318C2semidirect
12. C2×C11×#489C2semidirect
16. C2×C11×C4⋊Q8C22semidirect
20. C22×#4325C22semidirect
24. C22×#4314C22semidirect
26. #10623256C22semidirect
28. D11×#124C22semidirect
32. C2×#66946C22semidirect
38. C2×#66927C22semidirect
40. C11×#489C22semidirect
41. C2×C11×#103C22semidirect
43. C2×C11×#97C22semidirect
45. C2×Dic11⋊C8C22semidirect
46. #10622702C22semidirect
47. #10622671C22semidirect
48. C2×#66874C22semidirect
50. C2×#66867C22semidirect
51. #10622432C22semidirect
52. #10622419C22semidirect
53. #10622400C22semidirect
54. #10622386C22semidirect
55. #10622325C22semidirect
56. #10622318C22semidirect
84. C11×C4⋊Q8C23semidirect
98. C2×#4325C23semidirect
116. C2×#4314C23semidirect
122. #66946C23semidirect
130. #66927C23semidirect
133. C11×#103C23semidirect
135. C11×#97C23semidirect
137. Dic11⋊C8C23semidirect
138. #66874C23semidirect
140. #66867C23semidirect
236. C2×#489D11semidirect
316. C2×C4⋊Q8C2×D11semidirect
337. #489C2×D11semidirect
345. C2×#103C2×D11semidirect
350. C2×#97C2×D11semidirect
418. C4⋊Q8C22×D11semidirect
460. #103C22×D11semidirect
465. #97C22×D11semidirect
467. C2×C11#3213semidirect
562. C11C2×#3213semidirect
663. C2#13079604direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232562
C2×D11×#1242
#130796042
C2×#106226712
C2×#106223252
C2×#106227022
C2×#106224322
C2×#106224002
C2×#106224192
C2×#106223862
C2×#106223182
C2×C11×#4892
C2×#321311