Finite Group Databasebeta

← C2×#13069788 #14781197

Subgroups — C2×#13069788 #14781197

Order 2816.

1234 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623001C211yesmaximal, characteristic, complemented
2C2×#10622849C211yesmaximal, characteristic
3C2×#10622853C211yesmaximal, characteristic
4#13069788C218yesmaximal, direct product factor
5C2×#10622197C211yesmaximal, characteristic, complemented
6C2×#10622161C211yesmaximal, characteristic, complemented
7C2×#10622195C211yesmaximal, characteristic, complemented
8C22×C11×#104C211yesmaximal, characteristic
9C22×C11×#41C2211yescharacteristic
10C22×C11×M16C2211yescharacteristic
11C22×C42×C11C2211yescharacteristic
12C2×#66979C2211yescharacteristic
13C2×#66979C2211yescharacteristic
14C2×#66979C2211yescharacteristic
15C2×#66977—22no—
16C22×#4318C2211yescharacteristic
17#10623001—22no—
18#10623001—22no—
19#10623001—22no—
20#10623001C2214yescomplemented
21C2×#66923—21no—
22C2×#66922—21no—
23C2×C4×Dic22—22no—
24C2×C11×#104—21no—
25C2×C11×#104—21no—
26C2×C11×#104—22no—
27C2×C11×#104C2214yes—
28#10622853—22no—
29#10622853C2214yes—
30#10622849—22no—
31#10622849C2214yes—
32C2×#66901—22no—
33C2×#66898—22no—
34#10622197C2214yescomplemented
35#10622195C2214yescomplemented
36#10622161C2214yescomplemented
37C2×C11×#41—21no—
38C2×C11×#41—21no—
39C2×C11×#41—21no—
40C2×C11×#41—21no—
41C2×C11×#41—21no—
42C2×C11×#41—21no—
43C2×C11×#41—21no—
44C2×C11×#41—21no—
45C2×C11×#41—21no—
46C2×C11×#41—21no—
47C2×C11×#41Q812yescomplemented
48C2×C11×#41C2312yes—
49C22×Q8×C11Q811yescharacteristic, complemented
50C22×D4×C11—21no—
51C22×D4×C11Q811yescharacteristic, complemented
52C23×C4×C11—21no—
53C23×C4×C11—21no—
54C23×C4×C11C2311yescharacteristic
55C22×Dic22—22no—
56C2×C11×M16—21no—
57C2×C11×M16—21no—
58C2×C11×M16—21no—
59C2×C11×M16—21no—
60C2×C11×M16—21no—
61C2×C11×M16C2312yes—
62C22×C8×C11—21no—
63C2×C42×C11—21no—
64C2×C42×C11—21no—
65C2×C42×C11—21no—
66C2×C42×C11D411yescharacteristic
67C2×C42×C11D411yescharacteristic
68C2×C42×C11D412yes—
69C2×C42×C11C2312yes—
70C2×C22⋊Dic11—21no—
71C2×C22⋊Dic11—21no—
72C2×C22⋊Dic11D412yes—
73#66979—21no—
74#66979—21no—
75#66979—21no—
76#66979—21no—
77#66979—21no—
78#66979—21no—
79#66979—21no—
80#66979D412yes—
81#66979D412yes—
82#66979C2312yes—
83#66979C2312yes—
84#66979C2312yes—
85C2×C4⋊Dic11—22no—
86C2×C4⋊Dic11—21no—
87C2×C4⋊Dic11—21no—
88C2×C4⋊Dic11—21no—
89#66977—28no—
90#66977—28no—
91C2×Dic11⋊C4—24no—
92C2×C4×Dic11—21no—
93C2×C4×Dic11—21no—
94C2×C4×Dic11D412yes—
95C2×#4318—21no—
96C2×#4318—21no—
97C2×#4318—21no—
98C2×#4318—21no—
99C2×#4318—21no—
100C2×#4318C2312yes—
101C22×C11⋊C8—21no—
102#66923—24no—
103#66923—24no—
104#66922—24no—
105#66922—24no—
106C4×Dic22—28no—
107C4×Dic22—28no—
108C11×#104—24no—
109C11×#104—24no—
110#66901—28no—
111#66898—28no—
112C2×#2031—111nomaximal, Sylow
113C24×C11—21no—
114C24×C11C2×D411yescharacteristic
115C11×#41—22no—
116C11×#41—22no—
117C11×#41—22no—
118C11×#41—22no—
119C11×#41—22no—
120C11×#41—22no—
121C11×#41—22no—
122C11×#41—22no—
123C11×#41—41no—
124C11×#41—41no—
125C11×#41—41no—
126C11×#41—41no—
127C11×#41—41no—
128C11×#41—41no—
129C11×#41—41no—
130C11×#41—41no—
131C2×Q8×C11—21no—
132C2×Q8×C11—21no—
133C2×Q8×C11—21no—
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11C2×Q812yescomplemented
137C2×D4×C11—22no—
138C2×D4×C11—22no—
139C2×D4×C11—21no—
140C2×D4×C11—21no—
141C2×D4×C11—21no—
142C2×D4×C11—21no—
143C2×D4×C11—21no—
144C2×D4×C11—41no—
145C2×D4×C11—41no—
146C2×D4×C11—41no—
147C2×D4×C11—41no—
148C2×D4×C11C2×Q812yescomplemented
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—22no—
152C22×C4×C11—21no—
153C22×C4×C11—22no—
154C22×C4×C11—22no—
155C22×C4×C11—22no—
156C22×C4×C11—44no—
157C22×C4×C11—41no—
158C22×C4×C11—41no—
159C22×C4×C11—41no—
160C22×C4×C11—41no—
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11C2×D411yescharacteristic
166C22×C4×C11C2×Q811yescharacteristic
167C22×C4×C11C2×Q811yescharacteristic
168C22×C4×C11#4111yescharacteristic
169C22×C4×C11#4111yescharacteristic
170C22×C4×C11#4111yescharacteristic
171C22×C4×C11#4111yescharacteristic
172C22×C4×C11#4111yescharacteristic
173C22×C4×C11#4111yescharacteristic
174C22×C4×C11C2411yescharacteristic
175C22×Dic11—22no—
176C22×Dic11—22no—
177C22×Dic11—41no—
178C2×Dic22—28no—
179C2×Dic22—48no—
180C11×M16—22no—
181C11×M16—22no—
182C11×M16—41no—
183C11×M16—41no—
184C2×C8×C11—22no—
185C2×C8×C11—41no—
186C2×C8×C11—41no—
187C42×C11—22no—
188C42×C11—21no—
189C42×C11—21no—
190C42×C11—22no—
191C42×C11C2×D412yes—
192C42×C11C2×D412yes—
193C22⋊Dic11—22no—
194C22⋊Dic11—22no—
195C22⋊Dic11—22no—
196C22⋊Dic11—22no—
197C22⋊Dic11—41no—
198C22⋊Dic11C2×D414yes—
199C4⋊Dic11—28no—
200C4⋊Dic11—22no—
201C4⋊Dic11—22no—
202C4⋊Dic11—22no—
203C4⋊Dic11—22no—
204C4⋊Dic11—22no—
205C4⋊Dic11—41no—
206Dic11⋊C4—216no—
207C4×Dic11—22no—
208C4×Dic11—22no—
209C4×Dic11—22no—
210C4×Dic11—22no—
211C4×Dic11—41no—
212C4×Dic11C2×D414yes—
213#4318—22no—
214#4318—22no—
215#4318—41no—
216#4318—41no—
217C2×C11⋊C8—22no—
218C2×C11⋊C8—41no—
219C2×C11⋊C8—41no—
220C2×#533—111no—
221C2×#421—111no—
222C22×#104D1111yescharacteristic
223C2×#410—111no—
224#2031—118no—
225C2×#344—111no—
226C2×#339—111no—
227C2×H(3,ℤ/4)—111no—
228C23×C11—22no—
229C23×C11—42no—
230C23×C11—41no—
231C23×C11—41no—
232C23×C11—82no—
233C23×C11#12011yescharacteristic
234C23×C11#12011yescharacteristic
235C23×C11C22⋊Q811yescharacteristic
236C23×C11C22⋊Q811yescharacteristic
237C23×C11#12411yescharacteristic
238C23×C11#12411yescharacteristic
239C23×C11C22×D411yescharacteristic
240Q8×C11—22no—
241Q8×C11—22no—
242Q8×C11—41no—
243Q8×C11—41no—
244D4×C11—22no—
245D4×C11—22no—
246D4×C11—42no—
247D4×C11—42no—
248D4×C11—42no—
249D4×C11—42no—
250D4×C11—41no—
251D4×C11—41no—
252C2×C4×C11—24no—
253C2×C4×C11—22no—
254C2×C4×C11—22no—
255C2×C4×C11—22no—
256C2×C4×C11—44no—
257C2×C4×C11—44no—
258C2×C4×C11—42no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—42no—
262C2×C4×C11—42no—
263C2×C4×C11—42no—
264C2×C4×C11—42no—
265C2×C4×C11#12011yescharacteristic
266C2×C4×C11#12011yescharacteristic
267C2×C4×C11C22⋊Q811yescharacteristic
268C2×C4×C11C22⋊Q811yescharacteristic
269C2×C4×C11C22⋊Q811yescharacteristic
270C2×C4×C11C22⋊Q811yescharacteristic
271C2×C4×C11C22⋊Q811yescharacteristic
272C2×C4×C11C22⋊Q811yescharacteristic
273C2×C4×C11C22⋊Q811yescharacteristic
274C2×C4×C11C22⋊Q811yescharacteristic
275C2×C4×C11C22⋊Q811yescharacteristic
276C2×C4×C11C22⋊Q811yescharacteristic
277C2×C4×C11#12411yescharacteristic
278C2×C4×C11#12411yescharacteristic
279C2×C4×C11#12411yescharacteristic
280C2×C4×C11#12411yescharacteristic
281C2×C4×C11#12411yescharacteristic
282C2×C4×C11#12411yescharacteristic
283C2×C4×C11#12411yescharacteristic
284C2×C4×C11#12411yescharacteristic
285C2×C4×C11#12411yescharacteristic
286C2×C4×C11#12411yescharacteristic
287C2×C4×C11C22×D411yescharacteristic
288C2×C4×C11C22×D411yescharacteristic
289C2×C4×C11C22×Q811yescharacteristic
290C2×C4×C11C2×#4111yescharacteristic
291C2×C4×C11C2×#4111yescharacteristic
292C2×C4×C11C2×#4111yescharacteristic
293C2×Dic11—24no—
294C2×Dic11—24no—
295C2×Dic11—44no—
296C2×Dic11—44no—
297C2×Dic11—42no—
298C2×Dic11—82no—
299Dic22—416no—
300C8×C11—42no—
301C11⋊C8—42no—
302C22×#41C2×D1111yescharacteristic
303C22×M16—111no—
304C22×M16C2×D1111yescharacteristic
305#533—114no—
306#533—222no—
307#533—222no—
308#533—222no—
309C2×C4⋊Q8—221no—
310C2×#125—221no—
311C2×C22⋊Q8—222no—
312C2×C4×Q8—222no—
313C2×#117—111no—
314C2×#117—111no—
315C2×#117—111no—
316C22×C42C2×D1111yescharacteristic
317#421—114no—
318#421—222no—
319C2×#104—21no—
320C2×#104—21no—
321C2×#104—22no—
322C2×#104—222no—
323C2×#104C2×D1114yes—
324#410—114no—
325#410—222no—
326C2×#99—222no—
327#344—114no—
328#339—114no—
329H(3,ℤ/4)—114no—
330C22×C11—22no—
331C22×C11—22no—
332C22×C11—22no—
333C22×C11—41no—
334C22×C11—41no—
335C22×C11—41no—
336C22×C11—41no—
337C22×C11—42no—
338C22×C11—82no—
339C22×C11—82no—
340C22×C11—82no—
341C22×C11#39311yescharacteristic
342C22×C11#39311yescharacteristic
343C22×C11#39311yescharacteristic
344C22×C11#39311yescharacteristic
345C22×C11C2×#12011yescharacteristic
346C22×C11C2×C22⋊Q811yescharacteristic
347C22×C11C2×#12411yescharacteristic
348C4×C11—24no—
349C4×C11—42no—
350C4×C11—42no—
351C4×C11#39311yescharacteristic
352C4×C11#39311yescharacteristic
353C4×C11#39311yescharacteristic
354C4×C11#39311yescharacteristic
355C4×C11C2×C22⋊Q811yescharacteristic
356C4×C11C2×C22⋊Q811yescharacteristic
357C4×C11C2×#12411yescharacteristic
358C4×C11C2×#12411yescharacteristic
359Dic11—44no—
360Dic11—44no—
361Dic11—82no—
362C2×#41—21no—
363C2×#41—21no—
364C2×#41—21no—
365C2×#41—21no—
366C2×#41—21no—
367C2×#41—21no—
368C2×#41—21no—
369C2×#41—21no—
370C2×#41—21no—
371C2×#41—21no—
372C2×#41Dic2212yescomplemented
373C2×#41C22×D1112yes—
374C22×Q8—222no—
375C22×Q8Dic2211yescharacteristic, complemented
376C22×D4—21no—
377C22×D4Dic2211yescharacteristic, complemented
378C23×C4—21no—
379C23×C4—21no—
380C23×C4C22×D1111yescharacteristic
381C2×M16—21no—
382C2×M16—21no—
383C2×M16—21no—
384C2×M16—21no—
385C2×M16—21no—
386C2×M16—112no—
387C2×M16—221no—
388C2×M16—221no—
389C2×M16—221no—
390C2×M16—221no—
391C2×M16—221no—
392C2×M16C22×D1112yes—
393C22×C8—21no—
394C22×C8—221no—
395C4⋊Q8—224no—
396C4⋊Q8—224no—
397#125—224no—
398#125—224no—
399C22⋊Q8—228no—
400C22⋊Q8—228no—
401C4×Q8—228no—
402C4×Q8—228no—
403#117—112no—
404#117—112no—
405#117—112no—
406#117—112no—
407#117—112no—
408#117—221no—
409#117—221no—
410#117—221no—
411#117—221no—
412#117—221no—
413#117—221no—
414#117—221no—
415C2×C4⋊C4—224no—
416C2×C4⋊C4—222no—
417C2×C4⋊C4—221no—
418C2×C4⋊C4—221no—
419C2×C4⋊C4—221no—
420C2×C22⋊C4—112no—
421C2×C22⋊C4—221no—
422C2×C22⋊C4—221no—
423C2×C42—21no—
424C2×C42—21no—
425C2×C42—21no—
426C2×C42—112no—
427C2×C42—221no—
428C2×C42—221no—
429C2×C42C22⋊D1111yescharacteristic
430C2×C42C22⋊D1111yescharacteristic
431C2×C42C22⋊D1112yes—
432C2×C42C22×D1112yes—
433#104—24no—
434#104—24no—
435#104—228no—
436#99—228no—
437C2×C11—21no—
438C2×C11—21no—
439C2×C11—21no—
440C2×C11—21no—
441C2×C11—21no—
442C2×C11—21no—
443C2×C11—82no—
444C2×C11#203112yescomplemented
445C2×C11C2×#39311yescharacteristic
446C24—21no—
447C24D4×D1111yescharacteristic
448#41—22no—
449#41—22no—
450#41—22no—
451#41—22no—
452#41—22no—
453#41—22no—
454#41—22no—
455#41—22no—
456#41—41no—
457#41—41no—
458#41—41no—
459#41—41no—
460#41—41no—
461#41—41no—
462#41—41no—
463#41—41no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8—21no—
469C2×Q8—228no—
470C2×Q8—448no—
471C2×Q8C2×Dic2212yescomplemented
472C2×D4—22no—
473C2×D4—22no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—41no—
480C2×D4—41no—
481C2×D4—41no—
482C2×D4—41no—
483C2×D4C2×Dic2212yescomplemented
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—44no—
492C22×C4—41no—
493C22×C4—41no—
494C22×C4—41no—
495C22×C4—41no—
496C22×C4—222no—
497C22×C4—222no—
498C22×C4—441no—
499C22×C4C2×Dic2211yescharacteristic
500C22×C4C2×Dic2211yescharacteristic
501C22×C4#433911yescharacteristic
502C22×C4#433911yescharacteristic
503C22×C4D4×D1111yescharacteristic
504C22×C4D4×D1111yescharacteristic
505C22×C4D4×D1111yescharacteristic
506C22×C4#434111yescharacteristic
507C22×C4#434111yescharacteristic
508C22×C4#434111yescharacteristic
509C22×C4#434111yescharacteristic
510C22×C4C2×C22⋊D1111yescharacteristic
511C22×C4C2×C22⋊D1111yescharacteristic
512C22×C4C23×D1111yescharacteristic
513M16—22no—
514M16—22no—
515M16—41no—
516M16—41no—
517M16—222no—
518M16—222no—
519M16—441no—
520M16—441no—
521C2×C8—22no—
522C2×C8—41no—
523C2×C8—41no—
524C2×C8—222no—
525C2×C8—441no—
526C2×C8—441no—
527C4⋊C4—2216no—
528C4⋊C4—228no—
529C4⋊C4—222no—
530C4⋊C4—222no—
531C4⋊C4—222no—
532C4⋊C4—222no—
533C4⋊C4—222no—
534C4⋊C4—441no—
535C22⋊C4—114no—
536C22⋊C4—222no—
537C22⋊C4—222no—
538C22⋊C4—222no—
539C22⋊C4—222no—
540C22⋊C4—441no—
541C42—22no—
542C42—21no—
543C42—21no—
544C42—22no—
545C42—114no—
546C42—222no—
547C42—222no—
548C42—222no—
549C42—222no—
550C42—441no—
551C42C2×C22⋊D1112yes—
552C42C2×C22⋊D1112yes—
553C11C2×#203111yescharacteristic, complemented, Sylow
554C23—22no—
555C23—42no—
556C23—41no—
557C23—41no—
558C23—82no—
559C23#6693111yescharacteristic
560C23#6693111yescharacteristic
561C23#6693811yescharacteristic
562C23#6693811yescharacteristic
563C23#6699011yescharacteristic
564C23#6699011yescharacteristic
565C23C2×D4×D1111yescharacteristic
566Q8—22no—
567Q8—22no—
568Q8—41no—
569Q8—41no—
570Q8—4416no—
571D4—22no—
572D4—22no—
573D4—42no—
574D4—42no—
575D4—42no—
576D4—42no—
577D4—41no—
578D4—41no—
579C2×C4—24no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—44no—
584C2×C4—44no—
585C2×C4—42no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—224no—
593C2×C4—224no—
594C2×C4—444no—
595C2×C4—444no—
596C2×C4—442no—
597C2×C4—882no—
598C2×C4#6693111yescharacteristic
599C2×C4#6693111yescharacteristic
600C2×C4#6693111yescharacteristic
601C2×C4#6693111yescharacteristic
602C2×C4#6693111yescharacteristic
603C2×C4#6693111yescharacteristic
604C2×C4#6693811yescharacteristic
605C2×C4#6693811yescharacteristic
606C2×C4#6693811yescharacteristic
607C2×C4#6693811yescharacteristic
608C2×C4#6693811yescharacteristic
609C2×C4#6693811yescharacteristic
610C2×C4#6697711yescharacteristic
611C2×C4#6697711yescharacteristic
612C2×C4#6697711yescharacteristic
613C2×C4#6697711yescharacteristic
614C2×C4#6698911yescharacteristic
615C2×C4#6698911yescharacteristic
616C2×C4#6698911yescharacteristic
617C2×C4#6698911yescharacteristic
618C2×C4#6699011yescharacteristic
619C2×C4#6699011yescharacteristic
620C2×C4C22×Dic2211yescharacteristic
621C2×C4C2×#433911yescharacteristic
622C2×C4C2×D4×D1111yescharacteristic
623C2×C4C2×#434111yescharacteristic
624C2×C4C2×#434111yescharacteristic
625C2×C4C22×C22⋊D1111yescharacteristic
626C8—42no—
627C8—442no—
628C22—22no—
629C22—22no—
630C22—22no—
631C22—41no—
632C22—41no—
633C22—41no—
634C22—41no—
635C22—42no—
636C22—82no—
637C22—82no—
638C22—82no—
639C22#1062256011yescharacteristic
640C22#1062256011yescharacteristic
641C22#1062256011yescharacteristic
642C22#1062256011yescharacteristic
643C22C2×#6693111yescharacteristic
644C22C2×#6693811yescharacteristic
645C22C2×#6699011yescharacteristic
646C4—24no—
647C4—42no—
648C4—42no—
649C4—444no—
650C4—444no—
651C4—882no—
652C4#1062256011yescharacteristic
653C4#1062256011yescharacteristic
654C4#1062256011yescharacteristic
655C4#1062256011yescharacteristic
656C4C2×#6693111yescharacteristic
657C4C2×#6693811yescharacteristic
658C4C2×#6697711yescharacteristic
659C4C2×#6698911yescharacteristic
660C2—21no—
661C2—21no—
662C2—21no—
663C2—21no—
664C2—21no—
665C2—21no—
666C2—82no—
667C2#1306978812yesdirect product factor
668C2C2×#1062256011yescharacteristic
subgroupG/H
centerC2×C4#66938
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC22×C11×#104C2
socleC22×C11#393
prime radicalC22×C11×#41C22
hypercenterC22×#104D11
hypocenterC11C2×#2031
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×#104

Complements

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

NH ≅ G/Ntype
1. C2×#10623001C2semidirect
4. #13069788C2direct (N × H)
5. C2×#10622197C2semidirect
6. C2×#10622161C2semidirect
7. C2×#10622195C2semidirect
20. #10623001C22semidirect
34. #10622197C22semidirect
35. #10622195C22semidirect
36. #10622161C22semidirect
47. C2×C11×#41Q8semidirect
49. C22×Q8×C11Q8semidirect
51. C22×D4×C11Q8semidirect
136. C2×Q8×C11C2×Q8semidirect
148. C2×D4×C11C2×Q8semidirect
372. C2×#41Dic22semidirect
375. C22×Q8Dic22semidirect
377. C22×D4Dic22semidirect
444. C2×C11#2031semidirect
471. C2×Q8C2×Dic22semidirect
483. C2×D4C2×Dic22semidirect
553. C11C2×#2031semidirect
667. C2#13069788direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230012
C2×#106228492
C2×#106228532
#130697882
C2×#106221972
C2×#106221612
C2×#106221952
C22×C11×#1042
C2×#203111