Finite Group Databasebeta

← C2×#13068988 #14755266

Subgroups — C2×#13068988 #14755266

Order 2816.

1802 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66995C211yesmaximal, characteristic
2C2×#10623035C211yesmaximal, characteristic
3C22×#66869C211yesmaximal, characteristic
4C2×#10622838C211yesmaximal, characteristic, complemented
5#13068988C218yesmaximal, direct product factor
6C2×#10622168C211yesmaximal, characteristic, complemented
7C2×#10622161C211yesmaximal, characteristic, complemented
8C2×C11×#391C211yesmaximal, characteristic, complemented
9C23×Q8×C11C2211yescharacteristic
10C22×#4339C2211yescharacteristic
11C22×C11×C4⋊C4C2211yescharacteristic
12C22×C42×C11C2211yescharacteristic
13C22×#4326—21no—
14C2×#66995—24no—
15C2×#66995—22no—
16C2×#66995C418yescomplemented
17C2×#66995C2214yes—
18C22×#4325—21no—
19C2×C4×C22⋊D11—22no—
20C2×#66979C2211yescharacteristic
21C22×#4318C2211yescharacteristic
22C22×#4318C2211yescharacteristic
23#10623035—22no—
24#10623035—22no—
25#10623035—22no—
26#10623035C2214yes—
27C2×#66946—21no—
28C2×#66945—21no—
29C2×C4⋊C4×D11—21no—
30C2×#66940—21no—
31C11×#391—22no—
32C11×#391C2214yescomplemented
33C2×C11×#95—22no—
34#10622838—22no—
35#10622838C2214yescomplemented
36C2×#66899—21no—
37C2×#66899—21no—
38C2×#66869—24no—
39C2×#66869C2214yes—
40#10622168C2214yescomplemented
41#10622161C2214yescomplemented
42C22×Q8×C11—21no—
43C22×Q8×C11—22no—
44C22×Q8×C11—21no—
45C22×Q8×C11—21no—
46C22×Q8×C11—22no—
47C22×Q8×C11—21no—
48C22×Q8×C11—21no—
49C22×Q8×C11—22no—
50C22×Q8×C11C2×C414yescomplemented
51C22×Q8×C11C2312yes—
52C23×C4×C11—21no—
53C23×C4×C11—21no—
54C23×C4×C11D412yes—
55C23×C4×C11C2311yescharacteristic
56C22×C22⋊D11—21no—
57C2×#4339—21no—
58C2×#4339—21no—
59C2×#4339—22no—
60C2×#4339—22no—
61C2×#4339C2×C414yes—
62C2×#4339D414yes—
63C2×#4339D412yes—
64C2×#4339C2312yes—
65C22×D44D411yescharacteristic
66C22×C4×D11—21no—
67C22×C4×D11—22no—
68C22×Dic22D411yescharacteristic
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4D412yes—
74C2×C11×C4⋊C4C2312yes—
75C2×C42×C11—22no—
76C2×C42×C11—22no—
77C2×C42×C11—21no—
78C2×C42×C11C2312yes—
79C2×C22⋊Dic11—21no—
80C2×#4326—28no—
81C2×#4326—24no—
82#66995—216no—
83#66995—28no—
84#66995C2×C4116yescomplemented
85C2×#4325—28no—
86C2×#4325—24no—
87C4×C22⋊D11—28no—
88C4×C22⋊D11—28no—
89C2×(C2×D11)⋊C4—22no—
90#66979—21no—
91#66979—21no—
92#66979D412yes—
93#66979C2312yes—
94C2×C4⋊Dic11D411yescharacteristic
95C2×C4⋊Dic11D411yescharacteristic
96C2×Dic11⋊C4—22no—
97C2×C4×Dic11—22no—
98C2×C4×Dic11—21no—
99C2×#4318—22no—
100C2×#4318—21no—
101C2×#4318—21no—
102C2×#4318—22no—
103C2×#4318—22no—
104C2×#4318C2×C414yescomplemented
105C2×#4318C2312yes—
106C2×#4318C2312yes—
107C22×C11⋊C8—21no—
108C22×C11⋊C8—21no—
109#66946—24no—
110#66946—24no—
111#66945—24no—
112#66945—24no—
113C4⋊C4×D11—24no—
114C4⋊C4×D11—24no—
115#66940—24no—
116#66940—24no—
117C11×#95—28no—
118#66899—24no—
119#66899—24no—
120#66869—28no—
121C2×#1882—111nomaximal, Sylow
122C24×C11C2×D411yescharacteristic
123C23×D11—21no—
124C2×Q8×C11—24no—
125C2×Q8×C11—22no—
126C2×Q8×C11—24no—
127C2×Q8×C11—24no—
128C2×Q8×C11—24no—
129C2×Q8×C11—24no—
130C2×Q8×C11—22no—
131C2×Q8×C11—22no—
132C2×Q8×C11—22no—
133C2×Q8×C11—22no—
134C2×Q8×C11—41no—
135C2×Q8×C11—41no—
136C2×Q8×C11—42no—
137C2×Q8×C11—42no—
138C2×Q8×C11—42no—
139C2×Q8×C11—42no—
140C2×Q8×C11—42no—
141C2×Q8×C11C22×C414yescomplemented
142C22×C4×C11—24no—
143C22×C4×C11—24no—
144C22×C4×C11—22no—
145C22×C4×C11—22no—
146C22×C4×C11—22no—
147C22×C4×C11—22no—
148C22×C4×C11—42no—
149C22×C4×C11—41no—
150C22×C4×C11—41no—
151C22×C4×C11—42no—
152C22×C4×C11—42no—
153C22×C4×C11—44no—
154C22×C4×C11C22×C412yes—
155C22×C4×C11C2×D414yes—
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D412yes—
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11#4112yes—
163C22×C4×C11#4112yes—
164C22×C4×C11C2411yescharacteristic
165C2×C22⋊D11—24no—
166C2×C22⋊D11—22no—
167C2×C22⋊D11—24no—
168C2×C22⋊D11—22no—
169C22×Dic11—21no—
170C22×Dic11—21no—
171C22×Dic11—21no—
172#4339—24no—
173#4339—24no—
174#4339—24no—
175#4339—24no—
176#4339—24no—
177#4339—22no—
178#4339—22no—
179#4339C22⋊C418yes—
180#4339C22×C414yes—
181#4339C2×D414yes—
182C2×D44—21no—
183C2×D44—22no—
184C2×D44C22⋊C414yes—
185C2×D44C2×D412yes—
186C2×C4×D11—28no—
187C2×C4×D11—24no—
188C2×C4×D11—22no—
189C2×C4×D11—24no—
190C2×C4×D11—22no—
191C2×C4×D11—84no—
192C2×Dic22—21no—
193C2×Dic22—22no—
194C2×Dic22C22⋊C414yes—
195C2×Dic22C2×D412yes—
196C11×C4⋊C4—22no—
197C11×C4⋊C4—22no—
198C11×C4⋊C4—22no—
199C11×C4⋊C4—22no—
200C42×C11—22no—
201C42×C11—22no—
202C42×C11—42no—
203C22⋊Dic11—22no—
204C22⋊Dic11—22no—
205#4326—216no—
206#4325—216no—
207(C2×D11)⋊C4—28no—
208C4⋊Dic11—21no—
209C4⋊Dic11—21no—
210C4⋊Dic11C2×D412yes—
211C4⋊Dic11C2×D412yes—
212Dic11⋊C4—28no—
213C4×Dic11—28no—
214C4×Dic11—22no—
215C4×Dic11—22no—
216#4318—24no—
217#4318—22no—
218#4318—22no—
219#4318—22no—
220#4318—42no—
221#4318C22×C414yescomplemented
222C2×C11⋊C8—24no—
223C2×C11⋊C8—22no—
224C2×C11⋊C8—22no—
225C2×C11⋊C8—42no—
226C22×#137—111no—
227C2×#520—111no—
228C22×#104—111no—
229C2×#419—111no—
230C2×#391D1111yescharacteristic, complemented
231#1882—118no—
232C2×#343—111no—
233C2×#339—111no—
234C23×C11—22no—
235C23×C11—22no—
236C23×C11C4×D412yes—
237C23×C11#12011yescharacteristic
238C23×C11#12011yescharacteristic
239C23×C11#12112yes—
240C23×C11C22×D411yescharacteristic
241C22×D11—22no—
242C22×D11—24no—
243C22×D11—42no—
244C22×D11—42no—
245Q8×C11—24no—
246Q8×C11—24no—
247Q8×C11—42no—
248Q8×C11—42no—
249Q8×C11—44no—
250Q8×C11—44no—
251C2×C4×C11—24no—
252C2×C4×C11—24no—
253C2×C4×C11—24no—
254C2×C4×C11—48no—
255C2×C4×C11—42no—
256C2×C4×C11—42no—
257C2×C4×C11—42no—
258C2×C4×C11—42no—
259C2×C4×C11—44no—
260C2×C4×C11—44no—
261C2×C4×C11—44no—
262C2×C4×C11—44no—
263C2×C4×C11—82no—
264C2×C4×C11C2×C22⋊C412yes—
265C2×C4×C11C2×C22⋊C412yes—
266C2×C4×C11C4×D412yes—
267C2×C4×C11C4×D412yes—
268C2×C4×C11C4×D412yes—
269C2×C4×C11#12011yescharacteristic
270C2×C4×C11#12011yescharacteristic
271C2×C4×C11#12112yes—
272C2×C4×C11#12112yes—
273C2×C4×C11#12112yes—
274C2×C4×C11#12312yes—
275C2×C4×C11#12312yes—
276C2×C4×C11C23×C411yescharacteristic
277C2×C4×C11C22×D411yescharacteristic
278C2×C4×C11C22×D411yescharacteristic
279C2×C4×C11C22×D411yescharacteristic
280C2×C4×C11C2×#4111yescharacteristic
281C2×C4×C11C2×#4111yescharacteristic
282C22⋊D11—24no—
283C22⋊D11—24no—
284C22⋊D11—28no—
285C2×Dic11—22no—
286C2×Dic11—24no—
287C2×Dic11—22no—
288C2×Dic11—22no—
289C2×Dic11—42no—
290C2×Dic11—42no—
291D44—22no—
292D44—24no—
293D44C2×C22⋊C414yes—
294C4×D11—24no—
295C4×D11—24no—
296C4×D11—28no—
297C4×D11—88no—
298Dic22—22no—
299Dic22—24no—
300Dic22C2×C22⋊C414yes—
301C11⋊C8—24no—
302C11⋊C8—42no—
303C22×#41—111no—
304C23×Q8C2×D1111yescharacteristic
305C2×#137—114no—
306C2×#137—118no—
307C2×#137—222no—
308C2×#137—224no—
309C22×Q16—221no—
310C22×SD16—221no—
311C22×M16—111no—
312C22×M16—111no—
313#520—114no—
314#520—222no—
315#520—222no—
316#520—222no—
317C2×C4×Q8—221no—
318C2×C4×D4—221no—
319C2×C4×D4—222no—
320C2×#117—111no—
321C2×#117—221no—
322C22×C4⋊C4—221no—
323C22×C4⋊C4C2×D1111yescharacteristic
324C22×C42C2×D1111yescharacteristic
325C2×#104—114no—
326C2×#104—224no—
327#419—114no—
328#419—222no—
329C2×#103—221no—
330C2×#103—221no—
331#391—22no—
332#391C2×D1114yescomplemented
333C2×#95—22no—
334#343—114no—
335#339—114no—
336C22×C11—24no—
337C22×C11—24no—
338C22×C11—21no—
339C22×C11—21no—
340C22×C11—21no—
341C22×C11—21no—
342C22×C11#38612yes—
343C22×C11#38612yes—
344C22×C11#45512yes—
345C22×C11#45612yes—
346C22×C11C2×C4×D411yescharacteristic
347C22×C11C2×#12011yescharacteristic
348C22×C11C2×#12111yescharacteristic
349C2×D11—24no—
350C2×D11—48no—
351C2×D11—42no—
352C2×D11—42no—
353C4×C11—44no—
354C4×C11—44no—
355C4×C11—44no—
356C4×C11#38612yes—
357C4×C11#38612yes—
358C4×C11C22×C22⋊C411yescharacteristic
359C4×C11C2×C4×D411yescharacteristic
360C4×C11C2×#12111yescharacteristic
361C4×C11C2×#12311yescharacteristic
362Dic11—24no—
363Dic11—42no—
364Dic11—42no—
365C2×#41—114no—
366C2×#41—112no—
367C2×#41—114no—
368C2×#41—112no—
369C2×#41—222no—
370C2×#41—221no—
371C2×#41—222no—
372C2×#41—221no—
373C22×Q8—22no—
374C22×Q8—21no—
375C22×Q8—21no—
376C22×Q8—21no—
377C22×Q8—22no—
378C22×Q8—21no—
379C22×Q8—21no—
380C22×Q8—22no—
381C22×Q8—111no—
382C22×Q8C4×D1114yescomplemented
383C22×Q8C22×D1112yes—
384C22×D4—111no—
385C22×D4—221no—
386C23×C4—21no—
387C23×C4—21no—
388C23×C4—222no—
389C23×C4—221no—
390C23×C4C22⋊D1112yes—
391C23×C4C22×D1111yescharacteristic
392#137—1116no—
393#137—2216no—
394#137—228no—
395C2×Q16—228no—
396C2×Q16—224no—
397C2×SD16—228no—
398C2×SD16—224no—
399C2×M16—114no—
400C2×M16—112no—
401C2×M16—112no—
402C2×M16—222no—
403C2×M16—221no—
404C2×M16—221no—
405C2×M16—222no—
406C2×M16—222no—
407C22×C8—221no—
408C22×C8—221no—
409C4×Q8—224no—
410C4×Q8—224no—
411C4×D4—224no—
412C4×D4—224no—
413C4×D4—228no—
414C4×D4—228no—
415#117—112no—
416#117—112no—
417#117—224no—
418#117—224no—
419#117—221no—
420#117—221no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—111no—
426C2×C4⋊C4—111no—
427C2×C4⋊C4—224no—
428C2×C4⋊C4—224no—
429C2×C4⋊C4—222no—
430C2×C4⋊C4C22⋊D1112yes—
431C2×C4⋊C4C22×D1112yes—
432C2×C22⋊C4—222no—
433C2×C22⋊C4—221no—
434C2×C42—22no—
435C2×C42—22no—
436C2×C42—21no—
437C2×C42—222no—
438C2×C42—221no—
439C2×C42C22×D1112yes—
440#104—228no—
441#103—224no—
442#103—224no—
443#95—28no—
444C2×C11—21no—
445C2×C11—21no—
446C2×C11—22no—
447C2×C11#188214yescomplemented
448C2×C11C2×#38611yescharacteristic
449C2×C11C2×#45511yescharacteristic
450C2×C11C2×#45611yescharacteristic
451D11—44no—
452C24—221no—
453C24C2×C22⋊D1111yescharacteristic
454#41—118no—
455#41—114no—
456#41—114no—
457#41—224no—
458#41—224no—
459#41—224no—
460#41—224no—
461#41—224no—
462#41—222no—
463#41—222no—
464C2×Q8—24no—
465C2×Q8—22no—
466C2×Q8—24no—
467C2×Q8—24no—
468C2×Q8—24no—
469C2×Q8—24no—
470C2×Q8—22no—
471C2×Q8—22no—
472C2×Q8—22no—
473C2×Q8—22no—
474C2×Q8—42no—
475C2×Q8—42no—
476C2×Q8—42no—
477C2×Q8—42no—
478C2×Q8—41no—
479C2×Q8—41no—
480C2×Q8—42no—
481C2×Q8—114no—
482C2×Q8—112no—
483C2×Q8—222no—
484C2×Q8—221no—
485C2×Q8C2×C4×D1114yescomplemented
486C2×D4—114no—
487C2×D4—112no—
488C2×D4—224no—
489C2×D4—222no—
490C2×D4—224no—
491C2×D4—222no—
492C2×D4—222no—
493C2×D4—221no—
494C22×C4—24no—
495C22×C4—24no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—42no—
501C22×C4—41no—
502C22×C4—41no—
503C22×C4—42no—
504C22×C4—42no—
505C22×C4—44no—
506C22×C4—228no—
507C22×C4—221no—
508C22×C4—224no—
509C22×C4—224no—
510C22×C4—222no—
511C22×C4—222no—
512C22×C4—221no—
513C22×C4—221no—
514C22×C4—884no—
515C22×C4C2×C4×D1112yes—
516C22×C4#433912yes—
517C22×C4D4×D1111yescharacteristic
518C22×C4D4×D1111yescharacteristic
519C22×C4D4×D1112yes—
520C22×C4D4×D1111yescharacteristic
521C22×C4D4×D1111yescharacteristic
522C22×C4#434112yes—
523C22×C4C2×C22⋊D1114yes—
524C22×C4C2×C22⋊D1111yescharacteristic
525C22×C4C23×D1111yescharacteristic
526Q16—2216no—
527SD16—2216no—
528M16—114no—
529M16—224no—
530M16—222no—
531M16—222no—
532M16—222no—
533M16—442no—
534C2×C8—224no—
535C2×C8—222no—
536C2×C8—222no—
537C2×C8—442no—
538C4⋊C4—22no—
539C4⋊C4—22no—
540C4⋊C4—22no—
541C4⋊C4—22no—
542C4⋊C4—112no—
543C4⋊C4—112no—
544C4⋊C4—228no—
545C4⋊C4—221no—
546C4⋊C4—221no—
547C22⋊C4—228no—
548C22⋊C4—222no—
549C22⋊C4—222no—
550C42—22no—
551C42—22no—
552C42—42no—
553C42—228no—
554C42—222no—
555C42—222no—
556C11C2×#188211yescharacteristic, complemented, Sylow
557C23—22no—
558C23—22no—
559C23—222no—
560C23—224no—
561C23—442no—
562C23—442no—
563C23C4×C22⋊D1112yes—
564C23#6699011yescharacteristic
565C23#6699011yescharacteristic
566C23#6699112yes—
567C23C22×C22⋊D1111yescharacteristic
568Q8—24no—
569Q8—24no—
570Q8—42no—
571Q8—42no—
572Q8—44no—
573Q8—44no—
574Q8—114no—
575Q8—222no—
576Q8—224no—
577D4—114no—
578D4—224no—
579D4—224no—
580D4—228no—
581D4—222no—
582D4—224no—
583C2×C4—24no—
584C2×C4—24no—
585C2×C4—24no—
586C2×C4—42no—
587C2×C4—48no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—44no—
592C2×C4—44no—
593C2×C4—44no—
594C2×C4—44no—
595C2×C4—82no—
596C2×C4—222no—
597C2×C4—224no—
598C2×C4—224no—
599C2×C4—224no—
600C2×C4—228no—
601C2×C4—222no—
602C2×C4—222no—
603C2×C4—442no—
604C2×C4—442no—
605C2×C4—888no—
606C2×C4C22⋊C4×D1112yes—
607C2×C4C22⋊C4×D1112yes—
608C2×C4(C22⋊D11)⋊C412yes—
609C2×C4(C22⋊D11)⋊C412yes—
610C2×C4#6693612yes—
611C2×C4#6693612yes—
612C2×C4#6693712yes—
613C2×C4#6693712yes—
614C2×C4C4×C22⋊D1112yes—
615C2×C4#6699011yescharacteristic
616C2×C4#6699011yescharacteristic
617C2×C4#6699112yes—
618C2×C4C22×C4×D1111yescharacteristic
619C2×C4C2×#433911yescharacteristic
620C2×C4C2×D4×D1111yescharacteristic
621C2×C4C2×D4×D1111yescharacteristic
622C2×C4C2×D4×D1111yescharacteristic
623C2×C4C2×#434111yescharacteristic
624C8—224no—
625C8—442no—
626C22—21no—
627C22—21no—
628C22—24no—
629C22—24no—
630C22—21no—
631C22—21no—
632C22—224no—
633C22—442no—
634C22—448no—
635C22—442no—
636C22#1062256912yes—
637C22#1062256912yes—
638C22#1062267412yes—
639C22#1062270812yes—
640C22C2×C4×C22⋊D1111yescharacteristic
641C22C2×#6699011yescharacteristic
642C22C2×#6699111yescharacteristic
643C4—44no—
644C4—44no—
645C4—44no—
646C4—224no—
647C4—442no—
648C4—442no—
649C4#1062256912yes—
650C4#1062256912yes—
651C4C2×C22⋊C4×D1111yescharacteristic
652C4C2×(C22⋊D11)⋊C411yescharacteristic
653C4C2×#6693611yescharacteristic
654C4C2×#6693711yescharacteristic
655C2—21no—
656C2—21no—
657C2—22no—
658C2—444no—
659C2#1306898814yesdirect product factor
660C2C2×#1062256911yescharacteristic
661C2C2×#1062267411yescharacteristic
662C2C2×#1062270811yescharacteristic
subgroupG/H
centerC23#66990
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#391C2
socleC23×C11#120
prime radicalC22×#4339C22
cosocleC22×C4×C11C24
hypercenterC2×#391D11
hypocenterC11C2×#1882
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
4. C2×#10622838C2semidirect
5. #13068988C2direct (N × H)
6. C2×#10622168C2semidirect
7. C2×#10622161C2semidirect
8. C2×C11×#391C2semidirect
16. C2×#66995C4semidirect
32. C11×#391C22semidirect
35. #10622838C22semidirect
40. #10622168C22semidirect
41. #10622161C22semidirect
50. C22×Q8×C11C2×C4semidirect
84. #66995C2×C4semidirect
104. C2×#4318C2×C4semidirect
141. C2×Q8×C11C22×C4semidirect
221. #4318C22×C4semidirect
230. C2×#391D11semidirect
332. #391C2×D11semidirect
382. C22×Q8C4×D11semidirect
447. C2×C11#1882semidirect
485. C2×Q8C2×C4×D11semidirect
556. C11C2×#1882semidirect
659. C2#13068988direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669952
C2×#106230352
C22×#668692
C2×#106228382
#130689882
C2×#106221682
C2×#106221612
C2×C11×#3912
C2×#188211