Finite Group Databasebeta

← C2×#13069790 #14781199

Subgroups — C2×#13069790 #14781199

Order 2816.

1234 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623048C211yesmaximal, characteristic, complemented
2C2×#10622849C211yesmaximal, characteristic
3C22×#66901C211yesmaximal, characteristic
4#13069790C218yesmaximal, direct product factor
5C2×#10622171C211yesmaximal, characteristic, complemented
6C2×#10622170C211yesmaximal, characteristic, complemented
7C2×#10622169C211yesmaximal, characteristic, complemented
8C2×C11×#410C211yesmaximal, characteristic
9C22×C11×#41C2211yescharacteristic
10C2×C11×#117C2211yescharacteristic
11C2×C11×#117C2211yescharacteristic
12C2×#66979C2211yescharacteristic
13C22×C4×Dic11C2211yescharacteristic
14C22×#4318C2211yescharacteristic
15C22×#4318C2211yescharacteristic
16#10623048—22no—
17#10623048—22no—
18#10623048—22no—
19#10623048C2214yescomplemented
20C2×#66943—21no—
21C2×#66941—21no—
22C2×#66931—22no—
23C2×C4×Dic22—22no—
24C11×#410—22no—
25C11×#410C2214yes—
26C2×C11×#99—22no—
27#10622849—22no—
28#10622849C2214yes—
29C2×#66901—21no—
30C2×#66901—21no—
31C2×#66901—22no—
32C2×#66901—22no—
33C2×#66901C2214yes—
34#10622171C2214yescomplemented
35#10622170C2214yescomplemented
36#10622169C2214yescomplemented
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×C11C2311yescharacteristic
54C23×Dic11—21no—
55C22×Dic22—22no—
56C11×#117—21no—
57C11×#117—21no—
58C11×#117—21no—
59C11×#117—21no—
60C11×#117—21no—
61C11×#117D412yes—
62C11×#117C2312yes—
63C11×#117C2312yes—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C22⋊C4—21no—
67C2×C11×C22⋊C4D412yes—
68C2×C42×C11—21no—
69C2×C42×C11—21no—
70C2×C22⋊Dic11—21no—
71#66979—21no—
72#66979—21no—
73#66979D412yes—
74#66979C2312yes—
75C2×C4⋊Dic11—22no—
76C2×C4⋊Dic11—21no—
77C2×Dic11⋊C4—22no—
78C2×Dic11⋊C4—22no—
79C2×C4×Dic11—21no—
80C2×C4×Dic11—21no—
81C2×C4×Dic11—21no—
82C2×C4×Dic11D412yes—
83C2×C4×Dic11D411yescharacteristic
84C2×C4×Dic11D411yescharacteristic
85C2×C4×Dic11D412yes—
86C2×C4×Dic11C2312yes—
87C2×#4318—21no—
88C2×#4318—21no—
89C2×#4318—21no—
90C2×#4318—21no—
91C2×#4318—21no—
92C2×#4318—21no—
93C2×#4318—21no—
94C2×#4318—21no—
95C2×#4318—21no—
96C2×#4318—21no—
97C2×#4318C2312yes—
98C2×#4318C2312yes—
99C22×C11⋊C8—21no—
100C22×C11⋊C8—21no—
101#66943—24no—
102#66943—24no—
103#66941—24no—
104#66941—24no—
105#66931—28no—
106#66931—28no—
107C4×Dic22—28no—
108C4×Dic22—28no—
109C11×#99—28no—
110#66901—24no—
111#66901—24no—
112#66901—28no—
113C2×#2031—111nomaximal, Sylow
114C24×C11—21no—
115C24×C11C2×D411yescharacteristic
116C11×#41—22no—
117C11×#41—22no—
118C11×#41—22no—
119C11×#41—22no—
120C11×#41—22no—
121C11×#41—22no—
122C11×#41—22no—
123C11×#41—22no—
124C11×#41—41no—
125C11×#41—41no—
126C11×#41—41no—
127C11×#41—41no—
128C11×#41—41no—
129C11×#41—41no—
130C11×#41—41no—
131C11×#41—41no—
132C2×Q8×C11—21no—
133C2×Q8×C11—21no—
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11C2×Q812yescomplemented
138C2×D4×C11—22no—
139C2×D4×C11—22no—
140C2×D4×C11—21no—
141C2×D4×C11—21no—
142C2×D4×C11—21no—
143C2×D4×C11—21no—
144C2×D4×C11—21no—
145C2×D4×C11—41no—
146C2×D4×C11—41no—
147C2×D4×C11—41no—
148C2×D4×C11—41no—
149C2×D4×C11C2×Q812yescomplemented
150C22×C4×C11—22no—
151C22×C4×C11—21no—
152C22×C4×C11—22no—
153C22×C4×C11—22no—
154C22×C4×C11—41no—
155C22×C4×C11—41no—
156C22×C4×C11—41no—
157C22×C4×C11—41no—
158C22×C4×C11—41no—
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11C2×Q811yescharacteristic
165C22×C4×C11C2×Q811yescharacteristic
166C22×C4×C11#4111yescharacteristic
167C22×C4×C11#4111yescharacteristic
168C22×C4×C11#4111yescharacteristic
169C22×C4×C11#4111yescharacteristic
170C22×C4×C11#4111yescharacteristic
171C22×C4×C11#4111yescharacteristic
172C22×C4×C11C2411yescharacteristic
173C22×Dic11—21no—
174C22×Dic11—22no—
175C22×Dic11—21no—
176C22×Dic11—22no—
177C22×Dic11—22no—
178C22×Dic11—44no—
179C2×Dic22—28no—
180C2×Dic22—48no—
181C11×C4⋊C4—22no—
182C11×C4⋊C4—22no—
183C11×C4⋊C4—22no—
184C11×C4⋊C4—41no—
185C11×C22⋊C4—22no—
186C11×C22⋊C4—22no—
187C11×C22⋊C4—41no—
188C11×C22⋊C4C2×D414yes—
189C42×C11—22no—
190C42×C11—22no—
191C42×C11—22no—
192C42×C11—41no—
193C22⋊Dic11—22no—
194C22⋊Dic11—22no—
195C4⋊Dic11—28no—
196C4⋊Dic11—22no—
197C4⋊Dic11—22no—
198Dic11⋊C4—28no—
199Dic11⋊C4—28no—
200C4×Dic11—22no—
201C4×Dic11—22no—
202C4×Dic11—21no—
203C4×Dic11—21no—
204C4×Dic11—22no—
205C4×Dic11C2×D414yes—
206C4×Dic11C2×D412yes—
207C4×Dic11C2×D412yes—
208#4318—22no—
209#4318—22no—
210#4318—22no—
211#4318—22no—
212#4318—41no—
213#4318—41no—
214#4318—41no—
215#4318—41no—
216C2×C11⋊C8—22no—
217C2×C11⋊C8—22no—
218C2×C11⋊C8—41no—
219C2×C11⋊C8—41no—
220C2×C11⋊C8—41no—
221C2×C11⋊C8—41no—
222C2×#533—111no—
223C2×#421—111no—
224C22×#104—111no—
225C2×#410D1111yescharacteristic
226#2031—118no—
227C2×#344—111no—
228C2×#339—111no—
229C2×H(3,ℤ/4)—111no—
230C23×C11—22no—
231C23×C11—42no—
232C23×C11—41no—
233C23×C11—41no—
234C23×C11—82no—
235C23×C11#12011yescharacteristic
236C23×C11#12011yescharacteristic
237C23×C11C22⋊Q811yescharacteristic
238C23×C11C22⋊Q811yescharacteristic
239C23×C11#12411yescharacteristic
240C23×C11#12411yescharacteristic
241C23×C11C22×D411yescharacteristic
242Q8×C11—22no—
243Q8×C11—22no—
244Q8×C11—41no—
245Q8×C11—41no—
246D4×C11—22no—
247D4×C11—22no—
248D4×C11—42no—
249D4×C11—42no—
250D4×C11—42no—
251D4×C11—42no—
252D4×C11—41no—
253D4×C11—41no—
254C2×C4×C11—24no—
255C2×C4×C11—22no—
256C2×C4×C11—44no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—42no—
260C2×C4×C11—42no—
261C2×C4×C11—42no—
262C2×C4×C11—42no—
263C2×C4×C11—42no—
264C2×C4×C11—82no—
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—22no—
295C2×Dic11—22no—
296C2×Dic11—24no—
297C2×Dic11—44no—
298C2×Dic11—44no—
299C2×Dic11—44no—
300C2×Dic11—42no—
301Dic22—416no—
302C11⋊C8—42no—
303C11⋊C8—42no—
304C22×#41C2×D1111yescharacteristic
305C22×M16—111no—
306C22×M16—111no—
307#533—114no—
308#533—222no—
309#533—222no—
310#533—222no—
311C2×C4⋊Q8—221no—
312C2×#125—221no—
313C2×C22⋊Q8—222no—
314C2×C4×Q8—222no—
315C2×#117—111no—
316C2×#117C2×D1111yescharacteristic
317C2×#117C2×D1111yescharacteristic
318C22×C42—111no—
319#421—114no—
320#421—222no—
321C2×#104—114no—
322C2×#104—221no—
323C2×#104—221no—
324C2×#104—222no—
325C2×#104—222no—
326#410—22no—
327#410C2×D1114yes—
328C2×#99—22no—
329#344—114no—
330#339—114no—
331H(3,ℤ/4)—114no—
332C22×C11—22no—
333C22×C11—22no—
334C22×C11—22no—
335C22×C11—41no—
336C22×C11—41no—
337C22×C11—41no—
338C22×C11—41no—
339C22×C11—42no—
340C22×C11—82no—
341C22×C11—82no—
342C22×C11—82no—
343C22×C11#39311yescharacteristic
344C22×C11#39311yescharacteristic
345C22×C11#39311yescharacteristic
346C22×C11#39311yescharacteristic
347C22×C11C2×#12011yescharacteristic
348C22×C11C2×C22⋊Q811yescharacteristic
349C22×C11C2×#12411yescharacteristic
350C4×C11—44no—
351C4×C11—42no—
352C4×C11—82no—
353C4×C11#39311yescharacteristic
354C4×C11#39311yescharacteristic
355C4×C11#39311yescharacteristic
356C4×C11#39311yescharacteristic
357C4×C11C2×C22⋊Q811yescharacteristic
358C4×C11C2×C22⋊Q811yescharacteristic
359C4×C11C2×#12411yescharacteristic
360C4×C11C2×#12411yescharacteristic
361Dic11—24no—
362Dic11—44no—
363Dic11—42no—
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×#41—21no—
373C2×#41—21no—
374C2×#41Dic2212yescomplemented
375C2×#41C22×D1112yes—
376C22×Q8—222no—
377C22×Q8Dic2211yescharacteristic, complemented
378C22×D4—21no—
379C22×D4Dic2211yescharacteristic, complemented
380C23×C4—21no—
381C23×C4—221no—
382C23×C4C22×D1111yescharacteristic
383C2×M16—112no—
384C2×M16—112no—
385C2×M16—221no—
386C2×M16—221no—
387C2×M16—221no—
388C2×M16—221no—
389C2×M16—221no—
390C2×M16—221no—
391C2×M16—221no—
392C2×M16—221no—
393C2×M16—221no—
394C2×M16—221no—
395C22×C8—221no—
396C22×C8—221no—
397C4⋊Q8—224no—
398C4⋊Q8—224no—
399#125—224no—
400#125—224no—
401C22⋊Q8—228no—
402C22⋊Q8—228no—
403C4×Q8—228no—
404C4×Q8—228no—
405#117—21no—
406#117—21no—
407#117—21no—
408#117—21no—
409#117—21no—
410#117—112no—
411#117—112no—
412#117—221no—
413#117—221no—
414#117C22⋊D1112yes—
415#117C22×D1112yes—
416#117C22×D1112yes—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—222no—
420C2×C4⋊C4—222no—
421C2×C4⋊C4—222no—
422C2×C4⋊C4—221no—
423C2×C22⋊C4—21no—
424C2×C22⋊C4—221no—
425C2×C22⋊C4C22⋊D1112yes—
426C2×C42—21no—
427C2×C42—21no—
428C2×C42—112no—
429C2×C42—111no—
430C2×C42—111no—
431C2×C42—112no—
432C2×C42—112no—
433C2×C42—221no—
434C2×C42—221no—
435C2×C42—221no—
436#104—224no—
437#104—224no—
438#104—228no—
439#99—28no—
440C2×C11—21no—
441C2×C11—21no—
442C2×C11—21no—
443C2×C11—21no—
444C2×C11—21no—
445C2×C11—21no—
446C2×C11—82no—
447C2×C11#203112yescomplemented
448C2×C11C2×#39311yescharacteristic
449C24—21no—
450C24C2×C22⋊D1111yescharacteristic
451#41—22no—
452#41—22no—
453#41—22no—
454#41—22no—
455#41—22no—
456#41—22no—
457#41—22no—
458#41—22no—
459#41—41no—
460#41—41no—
461#41—41no—
462#41—41no—
463#41—41no—
464#41—41no—
465#41—41no—
466#41—41no—
467C2×Q8—21no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8—21no—
472C2×Q8—228no—
473C2×Q8—448no—
474C2×Q8C2×Dic2212yescomplemented
475C2×D4—22no—
476C2×D4—22no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—21no—
481C2×D4—21no—
482C2×D4—41no—
483C2×D4—41no—
484C2×D4—41no—
485C2×D4—41no—
486C2×D4C2×Dic2212yescomplemented
487C22×C4—21no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—41no—
492C22×C4—41no—
493C22×C4—41no—
494C22×C4—41no—
495C22×C4—41no—
496C22×C4—221no—
497C22×C4—221no—
498C22×C4—222no—
499C22×C4—222no—
500C22×C4—222no—
501C22×C4—444no—
502C22×C4C2×Dic2211yescharacteristic
503C22×C4C2×Dic2211yescharacteristic
504C22×C4#433911yescharacteristic
505C22×C4#433911yescharacteristic
506C22×C4D4×D1111yescharacteristic
507C22×C4D4×D1111yescharacteristic
508C22×C4D4×D1111yescharacteristic
509C22×C4D4×D1111yescharacteristic
510C22×C4#434111yescharacteristic
511C22×C4#434111yescharacteristic
512C22×C4#434111yescharacteristic
513C22×C4#434111yescharacteristic
514C22×C4C2×C22⋊D1111yescharacteristic
515C22×C4C23×D1111yescharacteristic
516M16—222no—
517M16—222no—
518M16—222no—
519M16—222no—
520M16—441no—
521M16—441no—
522M16—441no—
523M16—441no—
524C2×C8—222no—
525C2×C8—222no—
526C2×C8—441no—
527C2×C8—441no—
528C2×C8—441no—
529C2×C8—441no—
530C4⋊C4—22no—
531C4⋊C4—22no—
532C4⋊C4—22no—
533C4⋊C4—41no—
534C4⋊C4—228no—
535C4⋊C4—228no—
536C4⋊C4—228no—
537C4⋊C4—222no—
538C4⋊C4—222no—
539C22⋊C4—22no—
540C22⋊C4—22no—
541C22⋊C4—41no—
542C22⋊C4—222no—
543C22⋊C4—222no—
544C22⋊C4C2×C22⋊D1114yes—
545C42—22no—
546C42—22no—
547C42—22no—
548C42—41no—
549C42—112no—
550C42—112no—
551C42—114no—
552C42—222no—
553C42—221no—
554C42—221no—
555C42—222no—
556C42—222no—
557C11C2×#203111yescharacteristic, complemented, Sylow
558C23—22no—
559C23—42no—
560C23—41no—
561C23—41no—
562C23—82no—
563C23#6697711yescharacteristic
564C23#6697711yescharacteristic
565C23#6698911yescharacteristic
566C23#6698911yescharacteristic
567C23#6699011yescharacteristic
568C23#6699011yescharacteristic
569C23C22×C22⋊D1111yescharacteristic
570Q8—22no—
571Q8—22no—
572Q8—41no—
573Q8—41no—
574Q8—4416no—
575D4—22no—
576D4—22no—
577D4—42no—
578D4—42no—
579D4—42no—
580D4—42no—
581D4—41no—
582D4—41no—
583C2×C4—22no—
584C2×C4—24no—
585C2×C4—44no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—82no—
594C2×C4—224no—
595C2×C4—222no—
596C2×C4—222no—
597C2×C4—224no—
598C2×C4—444no—
599C2×C4—444no—
600C2×C4—442no—
601C2×C4—444no—
602C2×C4#6693111yescharacteristic
603C2×C4#6693111yescharacteristic
604C2×C4#6693111yescharacteristic
605C2×C4#6693111yescharacteristic
606C2×C4#6693111yescharacteristic
607C2×C4#6693111yescharacteristic
608C2×C4#6693111yescharacteristic
609C2×C4#6693111yescharacteristic
610C2×C4#6693811yescharacteristic
611C2×C4#6693811yescharacteristic
612C2×C4#6693811yescharacteristic
613C2×C4#6693811yescharacteristic
614C2×C4#6693811yescharacteristic
615C2×C4#6693811yescharacteristic
616C2×C4#6693811yescharacteristic
617C2×C4#6693811yescharacteristic
618C2×C4#6697711yescharacteristic
619C2×C4#6697711yescharacteristic
620C2×C4#6698911yescharacteristic
621C2×C4#6698911yescharacteristic
622C2×C4#6699011yescharacteristic
623C2×C4#6699011yescharacteristic
624C2×C4C22×Dic2211yescharacteristic
625C2×C4C2×#433911yescharacteristic
626C2×C4C2×D4×D1111yescharacteristic
627C2×C4C2×D4×D1111yescharacteristic
628C2×C4C2×#434111yescharacteristic
629C2×C4C2×#434111yescharacteristic
630C8—442no—
631C8—442no—
632C22—22no—
633C22—22no—
634C22—22no—
635C22—41no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22—42no—
640C22—82no—
641C22—82no—
642C22—82no—
643C22#1062256011yescharacteristic
644C22#1062256011yescharacteristic
645C22#1062256011yescharacteristic
646C22#1062256011yescharacteristic
647C22C2×#6697711yescharacteristic
648C22C2×#6698911yescharacteristic
649C22C2×#6699011yescharacteristic
650C4—44no—
651C4—42no—
652C4—82no—
653C4—224no—
654C4—442no—
655C4—444no—
656C4#1062256011yescharacteristic
657C4#1062256011yescharacteristic
658C4#1062256011yescharacteristic
659C4#1062256011yescharacteristic
660C4C2×#6693111yescharacteristic
661C4C2×#6693111yescharacteristic
662C4C2×#6693811yescharacteristic
663C4C2×#6693811yescharacteristic
664C2—21no—
665C2—21no—
666C2—21no—
667C2—21no—
668C2—21no—
669C2—21no—
670C2—82no—
671C2#1306979012yesdirect product factor
672C2C2×#1062256011yescharacteristic
subgroupG/H
centerC2×C4#66938
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#410C2
socleC22×C11#393
prime radicalC22×C11×#41C22
hypercenterC2×#410D11
hypocenterC11C2×#2031
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#410

Complements

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

NH ≅ G/Ntype
1. C2×#10623048C2semidirect
4. #13069790C2direct (N × H)
5. C2×#10622171C2semidirect
6. C2×#10622170C2semidirect
7. C2×#10622169C2semidirect
19. #10623048C22semidirect
34. #10622171C22semidirect
35. #10622170C22semidirect
36. #10622169C22semidirect
47. C2×C11×#41Q8semidirect
49. C22×Q8×C11Q8semidirect
51. C22×D4×C11Q8semidirect
137. C2×Q8×C11C2×Q8semidirect
149. C2×D4×C11C2×Q8semidirect
374. C2×#41Dic22semidirect
377. C22×Q8Dic22semidirect
379. C22×D4Dic22semidirect
447. C2×C11#2031semidirect
474. C2×Q8C2×Dic22semidirect
486. C2×D4C2×Dic22semidirect
557. C11C2×#2031semidirect
671. C2#13069790direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230482
C2×#106228492
C22×#669012
#130697902
C2×#106221712
C2×#106221702
C2×#106221692
C2×C11×#4102
C2×#203111