Finite Group Databasebeta

← C2×#13078290 #15621002

Subgroups — C2×#13078290 #15621002

Order 2816.

2934 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66960C211yesmaximal, characteristic, complemented
2C2×#10623364C211yesmaximal, characteristic, complemented
3C2×#10623336C211yesmaximal, characteristic, complemented
4#13078290C2116yesmaximal, direct product factor
5C2×#10622772C212yesmaximal, complemented
6C2×#10622787C212yesmaximal, complemented
7C2×#10622770C212yesmaximal, complemented
8C2×#10622784C212yesmaximal, complemented
9C2×#10622734C211yesmaximal, characteristic, complemented
10C2×#10622846C211yesmaximal, characteristic, complemented
11C22×#66896C211yesmaximal, characteristic, complemented
12C22×C11×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
13C22×C11×#41C2211yescharacteristic
14C23×D4×C11C2211yescharacteristic
15C22×#4339C2211yescharacteristic
16C2×C11×AGL(1,ℤ/8)—28no—
17C2×C11×AGL(1,ℤ/8)C2218yescomplemented
18C22×C11×SD16C2212yes—
19C22×C11×D8C2212yes—
20C22×C11×M16C2211yescharacteristic
21C2×#67006—22no—
22#10623364—24no—
23#10623364C2218yescomplemented
24C2×#66999C2212yescomplemented
25#10623336—24no—
26#10623336C2218yescomplemented
27C2×#66993—21no—
28C2×#66992—22no—
29C2×#66991C2212yes—
30C2×#66991C2212yes—
31C2×#66991C2212yescomplemented
32C2×#66989—21no—
33C2×#66983—21no—
34C2×#66979C2211yescharacteristic
35C22×C4⋊Dic11C2211yescharacteristic
36C2×#66977—21no—
37C23×C11⋊C8C2211yescharacteristic
38C2×#66960—28no—
39C2×#66960C2218yescomplemented
40C22×#4313C2212yescomplemented
41C22×C8×D11C2212yescomplemented
42#10622846C2218yescomplemented
43C2×#66899C2211yescharacteristic, complemented
44C2×#66899C2211yescharacteristic, complemented
45C2×#66896C2212yes—
46C2×#66896C2212yes—
47C2×#66896C2218yescomplemented
48C2×#66896C2211yescharacteristic, complemented
49C2×#66896C2211yescharacteristic, complemented
50#10622787C22116yescomplemented
51#10622784C22116yescomplemented
52#10622772C22116yescomplemented
53#10622770C22116yescomplemented
54#10622734C2218yescomplemented
55C2×#66882C2212yescomplemented
56C2×#66881C2212yescomplemented
57C25×C11—21no—
58C2×C11×#41—22no—
59C2×C11×#41—24no—
60C2×C11×#41—24no—
61C2×C11×#41C2314yes—
62C22×Q8×C11C2311yescharacteristic
63C22×D4×C11—21no—
64C22×D4×C11—24no—
65C22×D4×C11—21no—
66C22×D4×C11—22no—
67C22×D4×C11—24no—
68C22×D4×C11C2312yes—
69C22×D4×C11C2311yescharacteristic
70C22×D4×C11C2314yes—
71C23×C4×C11—21no—
72C23×C4×C11C2311yescharacteristic
73C22×C22⋊D11—22no—
74C22×C22⋊D11—22no—
75C22×C22⋊D11—22no—
76C22×C22⋊D11D412yes—
77C23×Dic11—21no—
78C2×#4339—24no—
79C2×#4339—24no—
80C2×#4339D414yes—
81C2×#4339C2314yes—
82C22×D44D411yescharacteristic
83C22×C4×D11C2312yes—
84C22×Dic22D411yescharacteristic
85C11×AGL(1,ℤ/8)—232no—
86C2×C11×SD16—28no—
87C2×C11×SD16C2318yes—
88C2×C11×D8—28no—
89C2×C11×D8C2318yes—
90C2×C11×M16D418yescomplemented
91C2×C11×M16C2314yes—
92C22×C8×C11C2312yes—
93#67006—216no—
94C2×C22⋊Dic11—21no—
95C2×C22⋊Dic11—22no—
96C2×C22⋊Dic11—22no—
97C2×C22⋊Dic11—22no—
98#66999—24no—
99#66999C2318yescomplemented
100#66993—28no—
101#66992—216no—
102#66991—24no—
103#66991—24no—
104#66991—24no—
105#66991C2318yes—
106#66991C2318yes—
107#66991C2318yescomplemented
108#66989—28no—
109#66983—28no—
110C2×(C2×D11)⋊C4—22no—
111#66979—22no—
112#66979C2314yes—
113C2×C4⋊Dic11—21no—
114C2×C4⋊Dic11—22no—
115C2×C4⋊Dic11C2314yes—
116C2×C4⋊Dic11C2312yes—
117C2×C4⋊Dic11C2311yescharacteristic
118C2×C4⋊Dic11C2311yescharacteristic
119#66977—28no—
120C2×Dic11⋊C4—22no—
121C2×C4×Dic11—21no—
122C22×C11⋊C8—24no—
123C22×C11⋊C8C2311yescharacteristic
124C22×C11⋊C8C2311yescharacteristic
125C22×C11⋊C8C2314yes—
126#66960—232no—
127C2×#4313—28no—
128C2×#4313C2318yescomplemented
129C2×C8×D11—28no—
130C2×C8×D11C2318yescomplemented
131#66899C2314yescomplemented
132#66899C2314yescomplemented
133#66896C2318yes—
134#66896C2318yes—
135#66896C2314yescomplemented
136#66896C2314yescomplemented
137#66882C2318yescomplemented
138#66881C2318yescomplemented
139C2×#3062—111nomaximal, Sylow
140C24×C11—21no—
141C24×C11—22no—
142C24×C11—24no—
143C24×C11—44no—
144C24×C11—82no—
145C24×C11—82no—
146C24×C11C2×D411yescharacteristic
147C23×D11C2×D412yes—
148C11×#41—28no—
149C11×#41—28no—
150C11×#41—48no—
151C2×Q8×C11—21no—
152C2×Q8×C11—22no—
153C2×Q8×C11—22no—
154C2×Q8×C11C2412yes—
155C2×D4×C11—24no—
156C2×D4×C11—22no—
157C2×D4×C11—24no—
158C2×D4×C11—28no—
159C2×D4×C11—24no—
160C2×D4×C11—22no—
161C2×D4×C11—21no—
162C2×D4×C11—24no—
163C2×D4×C11—28no—
164C2×D4×C11—22no—
165C2×D4×C11—44no—
166C2×D4×C11—44no—
167C2×D4×C11—48no—
168C2×D4×C11C2414yes—
169C2×D4×C11C2412yes—
170C22×C4×C11—21no—
171C22×C4×C11—24no—
172C22×C4×C11—44no—
173C22×C4×C11C2×D411yescharacteristic
174C22×C4×C11C2×D412yes—
175C22×C4×C11C2×D414yes—
176C22×C4×C11#4114yes—
177C22×C4×C11C2411yescharacteristic
178C22×C4×C11C2412yes—
179C2×C22⋊D11—28no—
180C2×C22⋊D11—28no—
181C2×C22⋊D11—28no—
182C2×C22⋊D11—28no—
183C2×C22⋊D11—84no—
184C2×C22⋊D11—84no—
185C2×C22⋊D11—84no—
186C2×C22⋊D11C2×D418yes—
187C22×Dic11—21no—
188C22×Dic11—21no—
189C22×Dic11—22no—
190C22×Dic11—24no—
191C22×Dic11—82no—
192C22×Dic11C2×D412yes—
193#4339—216no—
194#4339—28no—
195#4339—28no—
196C2×D44—24no—
197C2×D44C2×D414yes—
198C2×C4×D11—24no—
199C2×C4×D11—24no—
200C2×C4×D11C2×D414yes—
201C2×C4×D11C2414yes—
202C2×Dic22—24no—
203C2×Dic22C2×D414yes—
204C11×SD16—216no—
205C11×D8—216no—
206C11×M16C2×D4116yescomplemented
207C2×C8×C11C2×D418yes—
208C2×C8×C11C2414yes—
209C22⋊Dic11—28no—
210C22⋊Dic11—28no—
211C22⋊Dic11—28no—
212C22⋊Dic11—24no—
213(C2×D11)⋊C4—28no—
214C4⋊Dic11—24no—
215C4⋊Dic11—22no—
216C4⋊Dic11—21no—
217C4⋊Dic11—21no—
218C4⋊Dic11C2412yes—
219C4⋊Dic11C2414yes—
220C4⋊Dic11C2412yes—
221Dic11⋊C4—28no—
222C4×Dic11—24no—
223C2×C11⋊C8—22no—
224C2×C11⋊C8—22no—
225C2×C11⋊C8—28no—
226C2×C11⋊C8C2412yes—
227C2×C11⋊C8C2412yes—
228#4313—216no—
229C8×D11—216no—
230C22×AGL(1,ℤ/8)D1111yescharacteristic, complemented
231C22×#131—111no—
232C2×#537—111no—
233C2×#535—111no—
234#3062—1116no—
235C2×#469—112no—
236C2×#468—112no—
237C2×#466—112no—
238C2×#465—112no—
239C2×#428—111no—
240C2×#416—111no—
241C22×#102—111no—
242C23×C11—22no—
243C23×C11—22no—
244C23×C11—22no—
245C23×C11—24no—
246C23×C11—42no—
247C23×C11—48no—
248C23×C11—44no—
249C23×C11—42no—
250C23×C11—44no—
251C23×C11—44no—
252C23×C11—42no—
253C23×C11—84no—
254C23×C11—84no—
255C23×C11—816no—
256C23×C11#12114yes—
257C23×C11C22×D412yes—
258C23×C11C22×D411yescharacteristic
259C22×D11—24no—
260C22×D11—24no—
261C22×D11—24no—
262C22×D11C22×D414yes—
263Q8×C11—22no—
264Q8×C11—22no—
265Q8×C11—42no—
266D4×C11—22no—
267D4×C11—24no—
268D4×C11—24no—
269D4×C11—22no—
270D4×C11—48no—
271D4×C11—48no—
272D4×C11—44no—
273D4×C11—42no—
274C2×C4×C11—22no—
275C2×C4×C11—42no—
276C2×C4×C11—48no—
277C2×C4×C11#12114yes—
278C2×C4×C11#12118yes—
279C2×C4×C11C22×D412yes—
280C2×C4×C11C22×D411yescharacteristic
281C2×C4×C11C22×D412yes—
282C2×C4×C11C22×D414yes—
283C2×C4×C11C2×#4112yes—
284C2×C4×C11C2×#4114yes—
285C2×C4×C11C2511yescharacteristic
286C22⋊D11—216no—
287C22⋊D11—88no—
288C22⋊D11—88no—
289C22⋊D11—88no—
290C2×Dic11—24no—
291C2×Dic11—22no—
292C2×Dic11—22no—
293C2×Dic11—24no—
294C2×Dic11—44no—
295C2×Dic11—42no—
296C2×Dic11—42no—
297C2×Dic11—84no—
298C2×Dic11C22×D414yes—
299D44—28no—
300C4×D11—28no—
301C4×D11—24no—
302C4×D11—24no—
303Dic22—28no—
304C8×C11C22×D418yes—
305C11⋊C8—22no—
306C11⋊C8—22no—
307C22×#41—111no—
308C22×#41C2×D1111yescharacteristic
309C23×D4C2×D1111yescharacteristic
310C2×AGL(1,ℤ/8)—28no—
311C2×AGL(1,ℤ/8)C2×D1118yescomplemented
312C22×SD16C2×D1112yes—
313C22×D8C2×D1112yes—
314C2×#131—118no—
315C2×#131—228no—
316C22×M16—112no—
317C22×M16C2×D1111yescharacteristic
318C23×C8—111no—
319C23×C8—112no—
320#537—118no—
321#537—224no—
322#535—118no—
323#535—224no—
324C2×#127—221no—
325C2×#124—221no—
326C2×C22⋊Q8—112no—
327C2×C22⋊Q8—221no—
328C2×#121—112no—
329C2×#121—112no—
330C2×#121—112no—
331C2×#121—221no—
332C2×#121—222no—
333C2×#120—222no—
334C2×#117—111no—
335C22×C4⋊C4—111no—
336#469—1116no—
337#468—1116no—
338#466—1116no—
339#465—1116no—
340#428—118no—
341C2×#107—112no—
342C2×#106—112no—
343#416—118no—
344C2×#103—111no—
345C2×#103—111no—
346C2×#102—112no—
347C2×#102—112no—
348C2×#102—118no—
349C2×#102—111no—
350C2×#102—111no—
351C22×C11—28no—
352C22×C11—22no—
353C22×C11—22no—
354C22×C11—42no—
355C22×C11—44no—
356C22×C11—44no—
357C22×C11—42no—
358C22×C11—42no—
359C22×C11—44no—
360C22×C11—816no—
361C22×C11—84no—
362C22×C11—88no—
363C22×C11C2×#12114yes—
364C22×C11C2×#12112yes—
365C22×C11#57612yes—
366C22×C11#57712yes—
367C22×C11C23×D411yescharacteristic
368C2×D11—24no—
369C2×D11—24no—
370C2×D11—24no—
371C2×D11—48no—
372C4×C11—42no—
373C4×C11C2×#12114yes—
374C4×C11C2×#12112yes—
375C4×C11C23×D411yescharacteristic
376C4×C11C22×#4111yescharacteristic
377Dic11—24no—
378Dic11—44no—
379Dic11—42no—
380Dic11—42no—
381C25—21no—
382C2×#41—22no—
383C2×#41—24no—
384C2×#41—24no—
385C2×#41—114no—
386C2×#41—114no—
387C2×#41—224no—
388C2×#41—224no—
389C2×#41C22×D1114yes—
390C22×Q8—111no—
391C22×Q8C22×D1111yescharacteristic
392C22×D4—21no—
393C22×D4—21no—
394C22×D4—22no—
395C22×D4—24no—
396C22×D4—24no—
397C22×D4—112no—
398C22×D4—111no—
399C22×D4—222no—
400C22×D4—222no—
401C22×D4—222no—
402C22×D4C22×D1111yescharacteristic
403C22×D4C22×D1112yes—
404C22×D4C22×D1114yes—
405C23×C4—21no—
406C23×C4—112no—
407C23×C4—221no—
408C23×C4C22×D1111yescharacteristic
409AGL(1,ℤ/8)—232no—
410C2×SD16—28no—
411C2×SD16C22×D1118yes—
412C2×D8—28no—
413C2×D8C22×D1118yes—
414#131—2232no—
415C2×M16—118no—
416C2×M16—228no—
417C2×M16C22⋊D1118yescomplemented
418C2×M16C22×D1114yes—
419C22×C8—111no—
420C22×C8—111no—
421C22×C8—114no—
422C22×C8—118no—
423C22×C8—224no—
424C22×C8—228no—
425C22×C8C22×D1112yes—
426#127—228no—
427#124—228no—
428C22⋊Q8—118no—
429C22⋊Q8—228no—
430C22⋊Q8—224no—
431#121—118no—
432#121—118no—
433#121—118no—
434#121—228no—
435#121—224no—
436#121—224no—
437#121—224no—
438#121—2216no—
439#120—2216no—
440#117—114no—
441#117—222no—
442C2×C4⋊C4—112no—
443C2×C4⋊C4—114no—
444C2×C4⋊C4—111no—
445C2×C4⋊C4—111no—
446C2×C4⋊C4—222no—
447C2×C4⋊C4—221no—
448C2×C4⋊C4—222no—
449C2×C22⋊C4—222no—
450C2×C22⋊C4—222no—
451C2×C22⋊C4—222no—
452C2×C22⋊C4—222no—
453C2×C22⋊C4—221no—
454C2×C42—221no—
455#107—118no—
456#106—118no—
457#103—114no—
458#103—114no—
459#102—118no—
460#102—118no—
461#102—114no—
462#102—114no—
463C2×C11—24no—
464C2×C11—82no—
465C2×C11—84no—
466C2×C11#306214yescomplemented
467C2×C11C22×#12111yescharacteristic
468C2×C11C2×#57611yescharacteristic
469C2×C11C2×#57711yescharacteristic
470D11—44no—
471C24—21no—
472C24—22no—
473C24—24no—
474C24—44no—
475C24—82no—
476C24—82no—
477C24—112no—
478C24D4×D1111yescharacteristic
479#41—28no—
480#41—28no—
481#41—48no—
482#41—2216no—
483#41—228no—
484#41—228no—
485C2×Q8—21no—
486C2×Q8—22no—
487C2×Q8—22no—
488C2×Q8—114no—
489C2×Q8—224no—
490C2×Q8C23×D1112yes—
491C2×D4—24no—
492C2×D4—22no—
493C2×D4—21no—
494C2×D4—24no—
495C2×D4—24no—
496C2×D4—28no—
497C2×D4—22no—
498C2×D4—22no—
499C2×D4—24no—
500C2×D4—28no—
501C2×D4—44no—
502C2×D4—44no—
503C2×D4—48no—
504C2×D4—118no—
505C2×D4—114no—
506C2×D4—228no—
507C2×D4—228no—
508C2×D4—228no—
509C2×D4—228no—
510C2×D4—224no—
511C2×D4—884no—
512C2×D4—884no—
513C2×D4—884no—
514C2×D4C23×D1112yes—
515C2×D4C23×D1114yes—
516C22×C4—21no—
517C22×C4—24no—
518C22×C4—44no—
519C22×C4—112no—
520C22×C4—114no—
521C22×C4—114no—
522C22×C4—224no—
523C22×C4—224no—
524C22×C4—221no—
525C22×C4—221no—
526C22×C4—222no—
527C22×C4—224no—
528C22×C4—882no—
529C22×C4D4×D1112yes—
530C22×C4D4×D1111yescharacteristic
531C22×C4#434114yes—
532C22×C4C2×C22⋊D1114yes—
533C22×C4C23×D1112yes—
534C22×C4C23×D1111yescharacteristic
535SD16—216no—
536D8—216no—
537M16—2216no—
538M16C2×C22⋊D11116yescomplemented
539C2×C8—112no—
540C2×C8—112no—
541C2×C8—222no—
542C2×C8—222no—
543C2×C8—228no—
544C2×C8—2216no—
545C2×C8C2×C22⋊D1118yes—
546C2×C8C23×D1114yes—
547C4⋊C4—114no—
548C4⋊C4—112no—
549C4⋊C4—112no—
550C4⋊C4—228no—
551C4⋊C4—224no—
552C4⋊C4—222no—
553C4⋊C4—221no—
554C4⋊C4—221no—
555C22⋊C4—228no—
556C22⋊C4—228no—
557C22⋊C4—228no—
558C22⋊C4—228no—
559C22⋊C4—224no—
560C42—224no—
561C11C2×#306211yescharacteristic, complemented, Sylow
562C23—22no—
563C23—22no—
564C23—22no—
565C23—24no—
566C23—42no—
567C23—44no—
568C23—44no—
569C23—42no—
570C23—42no—
571C23—48no—
572C23—44no—
573C23—84no—
574C23—84no—
575C23—816no—
576C23—114no—
577C23—224no—
578C23—224no—
579C23—224no—
580C23#6699114yes—
581C23C2×D4×D1112yes—
582C23C2×D4×D1111yescharacteristic
583Q8—22no—
584Q8—22no—
585Q8—42no—
586Q8—228no—
587D4—24no—
588D4—22no—
589D4—22no—
590D4—24no—
591D4—48no—
592D4—48no—
593D4—44no—
594D4—42no—
595D4—2216no—
596D4—228no—
597D4—888no—
598D4—888no—
599D4—888no—
600C2×C4—22no—
601C2×C4—42no—
602C2×C4—48no—
603C2×C4—114no—
604C2×C4—224no—
605C2×C4—228no—
606C2×C4—224no—
607C2×C4—224no—
608C2×C4—222no—
609C2×C4—222no—
610C2×C4—224no—
611C2×C4—444no—
612C2×C4—442no—
613C2×C4—442no—
614C2×C4—884no—
615C2×C4#6699114yes—
616C2×C4#6699118yes—
617C2×C4C2×D4×D1112yes—
618C2×C4C2×D4×D1111yescharacteristic
619C2×C4C2×#434112yes—
620C2×C4C2×#434114yes—
621C2×C4C22×C22⋊D1112yes—
622C2×C4C22×C22⋊D1114yes—
623C2×C4C24×D1111yescharacteristic
624C8—222no—
625C8—222no—
626C8C22×C22⋊D1118yes—
627C22—28no—
628C22—22no—
629C22—22no—
630C22—42no—
631C22—44no—
632C22—42no—
633C22—44no—
634C22—44no—
635C22—42no—
636C22—816no—
637C22—88no—
638C22—84no—
639C22—224no—
640C22—224no—
641C22—224no—
642C22—448no—
643C22#1062330512yes—
644C22#1062330612yes—
645C22C2×#6699114yes—
646C22C2×#6699112yes—
647C22C22×D4×D1111yescharacteristic
648C4—42no—
649C4—224no—
650C4—444no—
651C4—442no—
652C4—442no—
653C4C2×#6699114yes—
654C4C2×#6699112yes—
655C4C22×#434111yescharacteristic
656C4C23×C22⋊D1111yescharacteristic
657C2—24no—
658C2—84no—
659C2—82no—
660C2—444no—
661C2#1307829014yesdirect product factor
662C2C22×#6699111yescharacteristic
663C2C2×#1062330511yescharacteristic
664C2C2×#1062330611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC22×C11×AGL(1,ℤ/8)C2
socleC23×C11C22×D4
hypercenterC22×AGL(1,ℤ/8)D11
hypocenterC11C2×#3062
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C22×#66960C2semidirect
2. C2×#10623364C2semidirect
3. C2×#10623336C2semidirect
4. #13078290C2direct (N × H)
5. C2×#10622772C2semidirect
6. C2×#10622787C2semidirect
7. C2×#10622770C2semidirect
8. C2×#10622784C2semidirect
9. C2×#10622734C2semidirect
10. C2×#10622846C2semidirect
11. C22×#66896C2semidirect
12. C22×C11×AGL(1,ℤ/8)C2semidirect
17. C2×C11×AGL(1,ℤ/8)C22semidirect
23. #10623364C22semidirect
24. C2×#66999C22semidirect
26. #10623336C22semidirect
31. C2×#66991C22semidirect
39. C2×#66960C22semidirect
40. C22×#4313C22semidirect
41. C22×C8×D11C22semidirect
42. #10622846C22semidirect
43. C2×#66899C22semidirect
44. C2×#66899C22semidirect
47. C2×#66896C22semidirect
48. C2×#66896C22semidirect
49. C2×#66896C22semidirect
50. #10622787C22semidirect
51. #10622784C22semidirect
52. #10622772C22semidirect
53. #10622770C22semidirect
54. #10622734C22semidirect
55. C2×#66882C22semidirect
56. C2×#66881C22semidirect
90. C2×C11×M16D4semidirect
99. #66999C23semidirect
107. #66991C23semidirect
128. C2×#4313C23semidirect
130. C2×C8×D11C23semidirect
131. #66899C23semidirect
132. #66899C23semidirect
135. #66896C23semidirect
136. #66896C23semidirect
137. #66882C23semidirect
138. #66881C23semidirect
206. C11×M16C2×D4semidirect
230. C22×AGL(1,ℤ/8)D11semidirect
311. C2×AGL(1,ℤ/8)C2×D11semidirect
417. C2×M16C22⋊D11semidirect
466. C2×C11#3062semidirect
538. M16C2×C22⋊D11semidirect
561. C11C2×#3062semidirect
661. C2#13078290direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669602
C2×#106233642
C2×#106233362
#130782902
C2×#106227722
C2×#106227872
C2×#106227702
C2×#106227842
C2×#106227342
C2×#106228462
C22×#668962
C22×C11×AGL(1,ℤ/8)2
C2×#306211