Finite Group Databasebeta

← C2×#13069839 #14781407

Subgroups — C2×#13069839 #14781407

Order 2816.

1586 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623364C211yesmaximal, characteristic
2C22×#66869C211yesmaximal, characteristic, complemented
3C2×#10622746C211yesmaximal, characteristic, complemented
4C2×#10622845C211yesmaximal, characteristic, complemented
5C2×#10622548C211yesmaximal, characteristic, complemented
6#13069839C218yesmaximal, direct product factor
7C2×#10622192C211yesmaximal, characteristic, complemented
8C22×C11×#104C211yesmaximal, characteristic, complemented
9C22×C11×#41C2211yescharacteristic
10C22×#4339C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
12C22×C42×C11C2211yescharacteristic
13#10623364—22no—
14#10623364—22no—
15#10623364—22no—
16#10623364C2214yes—
17C2×#66999—21no—
18C2×#66992—22no—
19C2×#66991—21no—
20C2×#66983—21no—
21C22×C4⋊Dic11—22no—
22C22×C4⋊Dic11C2211yescharacteristic
23C22×C4⋊Dic11C2211yescharacteristic
24C2×#66977—21no—
25C22×#4318C2211yescharacteristic
26C2×C11×#104—24no—
27C2×C11×#104C2214yescomplemented
28#10622845—22no—
29#10622845C2214yescomplemented
30C2×#66899—21no—
31C2×#66896—21no—
32#10622746—22no—
33#10622746C2214yescomplemented
34C2×#66885—21no—
35C2×#66880—21no—
36#10622548—22no—
37#10622548C2214yescomplemented
38C2×#66869—24no—
39C2×#66869C2214yescomplemented
40#10622192C2214yescomplemented
41C2×C11×#41—21no—
42C2×C11×#41—21no—
43C2×C11×#41—22no—
44C2×C11×#41—22no—
45C2×C11×#41—22no—
46C2×C11×#41—22no—
47C2×C11×#41D412yes—
48C2×C11×#41C2312yes—
49C22×Q8×C11D411yescharacteristic
50C22×D4×C11—21no—
51C22×D4×C11D411yescharacteristic
52C23×C4×C11—21no—
53C23×C4×C11—21no—
54C23×C4×C11C2311yescharacteristic
55C22×C22⋊D11—21no—
56C22×C22⋊D11—22no—
57C23×Dic11—21no—
58C23×Dic11D412yes—
59C2×#4339—21no—
60C2×#4339—21no—
61C2×#4339—22no—
62C2×#4339—22no—
63C2×#4339—22no—
64C2×#4339—22no—
65C2×#4339D412yes—
66C2×#4339C2312yes—
67C22×D44D411yescharacteristic
68C22×C4×D11—21no—
69C22×Dic22D411yescharacteristic
70C2×C11×M16—21no—
71C2×C11×M16—22no—
72C2×C11×M16—22no—
73C2×C11×M16C2312yes—
74C22×C8×C11—21no—
75C2×C42×C11—21no—
76C2×C42×C11—22no—
77C2×C42×C11D414yescomplemented
78C2×C42×C11C2312yes—
79C2×C22⋊Dic11—22no—
80#66999—24no—
81#66999—24no—
82#66992—28no—
83#66992—28no—
84#66991—24no—
85#66991—24no—
86#66983—24no—
87#66983—24no—
88C2×(C2×D11)⋊C4—22no—
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11—21no—
92C2×C4⋊Dic11—21no—
93C2×C4⋊Dic11—21no—
94C2×C4⋊Dic11—21no—
95C2×C4⋊Dic11—21no—
96C2×C4⋊Dic11—21no—
97C2×C4⋊Dic11—21no—
98C2×C4⋊Dic11—28no—
99C2×C4⋊Dic11—48no—
100C2×C4⋊Dic11D412yes—
101C2×C4⋊Dic11C2312yes—
102C2×C4⋊Dic11C2312yes—
103#66977—24no—
104#66977—24no—
105C2×Dic11⋊C4—22no—
106C2×#4318—21no—
107C2×#4318—22no—
108C2×#4318—22no—
109C2×#4318C2312yes—
110C22×C11⋊C8—21no—
111C11×#104—28no—
112#66899—24no—
113#66896—24no—
114#66885—24no—
115#66880—24no—
116#66869—28no—
117C2×#2039—111nomaximal, Sylow
118C24×C11—21no—
119C24×C11C2×D411yescharacteristic
120C23×D11—21no—
121C11×#41—24no—
122C11×#41—24no—
123C11×#41—22no—
124C11×#41—22no—
125C11×#41—22no—
126C11×#41—22no—
127C11×#41—42no—
128C11×#41—42no—
129C11×#41—42no—
130C11×#41—42no—
131C2×Q8×C11—21no—
132C2×Q8×C11—22no—
133C2×Q8×C11—22no—
134C2×Q8×C11C2×D412yes—
135C2×D4×C11—22no—
136C2×D4×C11—22no—
137C2×D4×C11—21no—
138C2×D4×C11—22no—
139C2×D4×C11—22no—
140C2×D4×C11—42no—
141C2×D4×C11—42no—
142C2×D4×C11C2×D412yes—
143C22×C4×C11—24no—
144C22×C4×C11—24no—
145C22×C4×C11—24no—
146C22×C4×C11—22no—
147C22×C4×C11—21no—
148C22×C4×C11—22no—
149C22×C4×C11—22no—
150C22×C4×C11—42no—
151C22×C4×C11—42no—
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D412yes—
158C22×C4×C11#4112yes—
159C22×C4×C11#4112yes—
160C22×C4×C11#4112yes—
161C22×C4×C11C2411yescharacteristic
162C2×C22⋊D11—28no—
163C2×C22⋊D11—22no—
164C2×C22⋊D11—22no—
165C2×C22⋊D11—42no—
166C2×C22⋊D11—42no—
167C2×C22⋊D11—84no—
168C22×Dic11—21no—
169C22×Dic11—22no—
170C22×Dic11—22no—
171C22×Dic11—22no—
172C22×Dic11—44no—
173C22×Dic11—44no—
174C22×Dic11—41no—
175C22×Dic11—41no—
176C22×Dic11C2×D414yes—
177#4339—24no—
178#4339—24no—
179#4339—22no—
180#4339—22no—
181#4339—22no—
182#4339—22no—
183#4339—42no—
184#4339—42no—
185#4339—42no—
186#4339—42no—
187C2×D44—21no—
188C2×D44—22no—
189C2×D44—22no—
190C2×D44C2×D412yes—
191C2×C4×D11—22no—
192C2×C4×D11—22no—
193C2×C4×D11—42no—
194C2×C4×D11—42no—
195C2×Dic22—21no—
196C2×Dic22—22no—
197C2×Dic22—22no—
198C2×Dic22C2×D412yes—
199C11×M16—22no—
200C11×M16—22no—
201C11×M16—42no—
202C2×C8×C11—22no—
203C2×C8×C11—42no—
204C42×C11—24no—
205C42×C11—22no—
206C42×C11C2×D414yescomplemented
207C22⋊Dic11—28no—
208(C2×D11)⋊C4—28no—
209C4⋊Dic11—22no—
210C4⋊Dic11—22no—
211C4⋊Dic11—22no—
212C4⋊Dic11—22no—
213C4⋊Dic11—22no—
214C4⋊Dic11—22no—
215C4⋊Dic11—416no—
216C4⋊Dic11—41no—
217C4⋊Dic11—41no—
218Dic11⋊C4—28no—
219#4318—22no—
220#4318—22no—
221#4318—42no—
222C2×C11⋊C8—22no—
223C2×C11⋊C8—42no—
224C2×#537—111no—
225C22×#104—111no—
226C22×#104D1111yescharacteristic, complemented
227C2×#417—111no—
228C2×#417—111no—
229C2×#384—111no—
230#2039—118no—
231C2×#343—111no—
232C23×C11—22no—
233C23×C11—22no—
234C23×C11—22no—
235C23×C11—42no—
236C23×C11—42no—
237C23×C11—42no—
238C23×C11#12011yescharacteristic
239C23×C11#12011yescharacteristic
240C23×C11#12112yes—
241C23×C11#12412yes—
242C23×C11C22×D411yescharacteristic
243C22×D11—22no—
244C22×D11—42no—
245C22×D11—42no—
246C22×D11—42no—
247Q8×C11—22no—
248Q8×C11—22no—
249Q8×C11—42no—
250D4×C11—22no—
251D4×C11—22no—
252D4×C11—42no—
253D4×C11—42no—
254D4×C11—44no—
255D4×C11—42no—
256C2×C4×C11—24no—
257C2×C4×C11—24no—
258C2×C4×C11—216no—
259C2×C4×C11—24no—
260C2×C4×C11—22no—
261C2×C4×C11—42no—
262C2×C4×C11—42no—
263C2×C4×C11—42no—
264C2×C4×C11—44no—
265C2×C4×C11#12011yescharacteristic
266C2×C4×C11#12011yescharacteristic
267C2×C4×C11#12112yes—
268C2×C4×C11#12112yes—
269C2×C4×C11#12112yes—
270C2×C4×C11#12112yes—
271C2×C4×C11#12112yes—
272C2×C4×C11#12312yes—
273C2×C4×C11#12312yes—
274C2×C4×C11#12312yes—
275C2×C4×C11#12312yes—
276C2×C4×C11#12412yes—
277C2×C4×C11C22×D411yescharacteristic
278C2×C4×C11C22×D411yescharacteristic
279C2×C4×C11C22×D411yescharacteristic
280C2×C4×C11C2×#4111yescharacteristic
281C2×C4×C11C2×#4111yescharacteristic
282C2×C4×C11C2×#4111yescharacteristic
283C22⋊D11—42no—
284C22⋊D11—42no—
285C22⋊D11—44no—
286C22⋊D11—88no—
287C2×Dic11—22no—
288C2×Dic11—24no—
289C2×Dic11—42no—
290C2×Dic11—44no—
291C2×Dic11—44no—
292C2×Dic11—44no—
293C2×Dic11—42no—
294C2×Dic11—82no—
295C2×Dic11—82no—
296C2×Dic11—82no—
297D44—22no—
298D44—22no—
299D44—42no—
300C4×D11—42no—
301C4×D11—42no—
302C4×D11—44no—
303Dic22—22no—
304Dic22—22no—
305Dic22—42no—
306C8×C11—42no—
307C11⋊C8—42no—
308C22×#41—111no—
309C22×#41C2×D1111yescharacteristic
310C22×M16—111no—
311C22×M16C2×D1111yescharacteristic
312#537—114no—
313#537—222no—
314#537—222no—
315#537—222no—
316C2×C22⋊Q8—221no—
317C2×C22⋊Q8—221no—
318C2×#121—221no—
319C2×#121—222no—
320C2×#121—221no—
321C22×C4⋊C4—111no—
322C22×C4⋊C4—111no—
323C22×C4⋊C4—222no—
324C22×C42C2×D1111yescharacteristic
325C2×#104—24no—
326C2×#104—114no—
327C2×#104—224no—
328C2×#104C2×D1114yescomplemented
329#417—114no—
330#417—114no—
331#417—222no—
332#417—222no—
333C2×#103—221no—
334C2×#103—221no—
335C2×#102—221no—
336C2×#102—221no—
337#384—114no—
338#384—222no—
339#343—114no—
340C22×C11—21no—
341C22×C11—21no—
342C22×C11—21no—
343C22×C11—21no—
344C22×C11—24no—
345C22×C11—24no—
346C22×C11—42no—
347C22×C11—42no—
348C22×C11—42no—
349C22×C11—84no—
350C22×C11#39412yes—
351C22×C11#39412yes—
352C22×C11#45312yes—
353C22×C11#45612yes—
354C22×C11C2×#12011yescharacteristic
355C22×C11C2×#12111yescharacteristic
356C22×C11C2×#12411yescharacteristic
357C2×D11—42no—
358C2×D11—42no—
359C2×D11—42no—
360C2×D11—84no—
361C4×C11—28no—
362C4×C11—42no—
363C4×C11#39412yes—
364C4×C11#39412yes—
365C4×C11C2×#12111yescharacteristic
366C4×C11C2×#12111yescharacteristic
367C4×C11C2×#12311yescharacteristic
368C4×C11C2×#12311yescharacteristic
369Dic11—42no—
370Dic11—44no—
371Dic11—82no—
372C2×#41—21no—
373C2×#41—21no—
374C2×#41—22no—
375C2×#41—22no—
376C2×#41—22no—
377C2×#41—22no—
378C2×#41—112no—
379C2×#41—112no—
380C2×#41—221no—
381C2×#41—221no—
382C2×#41—222no—
383C2×#41—222no—
384C2×#41—222no—
385C2×#41—222no—
386C2×#41D4412yes—
387C2×#41C22×D1112yes—
388C22×Q8—111no—
389C22×Q8D4411yescharacteristic
390C22×D4—21no—
391C22×D4—111no—
392C22×D4—221no—
393C22×D4—222no—
394C22×D4D4411yescharacteristic
395C23×C4—21no—
396C23×C4—21no—
397C23×C4—112no—
398C23×C4—221no—
399C23×C4—221no—
400C23×C4C22×D1111yescharacteristic
401C2×M16—21no—
402C2×M16—22no—
403C2×M16—22no—
404C2×M16—112no—
405C2×M16—221no—
406C2×M16—222no—
407C2×M16—222no—
408C2×M16C22×D1112yes—
409C22×C8—21no—
410C22×C8—221no—
411C22⋊Q8—224no—
412C22⋊Q8—224no—
413C22⋊Q8—224no—
414C22⋊Q8—224no—
415#121—224no—
416#121—224no—
417#121—228no—
418#121—224no—
419#121—228no—
420#121—224no—
421C2×C4⋊C4—112no—
422C2×C4⋊C4—112no—
423C2×C4⋊C4—112no—
424C2×C4⋊C4—222no—
425C2×C4⋊C4—221no—
426C2×C4⋊C4—221no—
427C2×C4⋊C4—221no—
428C2×C4⋊C4—221no—
429C2×C4⋊C4—221no—
430C2×C4⋊C4—221no—
431C2×C4⋊C4—221no—
432C2×C4⋊C4—221no—
433C2×C4⋊C4—228no—
434C2×C4⋊C4—221no—
435C2×C4⋊C4—448no—
436C2×C22⋊C4—222no—
437C2×C22⋊C4—222no—
438C2×C42—21no—
439C2×C42—22no—
440C2×C42C22⋊D1114yescomplemented
441C2×C42C22×D1112yes—
442#104—28no—
443#104—228no—
444#103—224no—
445#103—224no—
446#102—224no—
447#102—224no—
448C2×C11—21no—
449C2×C11—21no—
450C2×C11—22no—
451C2×C11—82no—
452C2×C11#203914yescomplemented
453C2×C11C2×#39411yescharacteristic
454C2×C11C2×#45311yescharacteristic
455C2×C11C2×#45611yescharacteristic
456D11—82no—
457C24—21no—
458C24—221no—
459C24D4×D1111yescharacteristic
460#41—24no—
461#41—24no—
462#41—22no—
463#41—22no—
464#41—22no—
465#41—22no—
466#41—42no—
467#41—42no—
468#41—42no—
469#41—42no—
470#41—224no—
471#41—224no—
472#41—222no—
473#41—222no—
474#41—222no—
475#41—222no—
476#41—442no—
477#41—442no—
478#41—442no—
479#41—442no—
480C2×Q8—21no—
481C2×Q8—22no—
482C2×Q8—22no—
483C2×Q8—112no—
484C2×Q8—221no—
485C2×Q8—222no—
486C2×Q8—222no—
487C2×Q8C2×D4412yes—
488C2×D4—22no—
489C2×D4—22no—
490C2×D4—21no—
491C2×D4—22no—
492C2×D4—22no—
493C2×D4—42no—
494C2×D4—42no—
495C2×D4—112no—
496C2×D4—222no—
497C2×D4—222no—
498C2×D4—228no—
499C2×D4—221no—
500C2×D4—222no—
501C2×D4—222no—
502C2×D4—442no—
503C2×D4—442no—
504C2×D4—884no—
505C2×D4C2×D4412yes—
506C22×C4—24no—
507C22×C4—24no—
508C22×C4—24no—
509C22×C4—22no—
510C22×C4—21no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—42no—
514C22×C4—42no—
515C22×C4—114no—
516C22×C4—222no—
517C22×C4—221no—
518C22×C4—222no—
519C22×C4—222no—
520C22×C4—222no—
521C22×C4—222no—
522C22×C4—442no—
523C22×C4—442no—
524C22×C4—444no—
525C22×C4—444no—
526C22×C4—441no—
527C22×C4—441no—
528C22×C4C2×D4411yescharacteristic
529C22×C4C2×D4411yescharacteristic
530C22×C4#433912yes—
531C22×C4D4×D1111yescharacteristic
532C22×C4D4×D1111yescharacteristic
533C22×C4D4×D1111yescharacteristic
534C22×C4#434112yes—
535C22×C4#434112yes—
536C22×C4C2×C22⋊D1112yes—
537C22×C4C23×D1111yescharacteristic
538M16—22no—
539M16—22no—
540M16—42no—
541M16—222no—
542M16—222no—
543M16—442no—
544C2×C8—22no—
545C2×C8—42no—
546C2×C8—222no—
547C2×C8—442no—
548C4⋊C4—228no—
549C4⋊C4—222no—
550C4⋊C4—222no—
551C4⋊C4—222no—
552C4⋊C4—222no—
553C4⋊C4—222no—
554C4⋊C4—222no—
555C4⋊C4—4416no—
556C4⋊C4—441no—
557C4⋊C4—441no—
558C22⋊C4—228no—
559C22⋊C4—228no—
560C42—24no—
561C42—22no—
562C42C2×C22⋊D1114yescomplemented
563C11C2×#203911yescharacteristic, complemented, Sylow
564C23—22no—
565C23—22no—
566C23—22no—
567C23—42no—
568C23—42no—
569C23—42no—
570C23—222no—
571C23—442no—
572C23—442no—
573C23—442no—
574C23#6693511yescharacteristic
575C23#6693511yescharacteristic
576C23#6693812yes—
577C23#6699212yes—
578C23C2×D4×D1111yescharacteristic
579Q8—22no—
580Q8—22no—
581Q8—42no—
582Q8—222no—
583Q8—222no—
584Q8—442no—
585D4—22no—
586D4—22no—
587D4—42no—
588D4—42no—
589D4—44no—
590D4—42no—
591D4—222no—
592D4—222no—
593D4—442no—
594D4—442no—
595D4—444no—
596D4—442no—
597D4—888no—
598C2×C4—24no—
599C2×C4—216no—
600C2×C4—24no—
601C2×C4—24no—
602C2×C4—22no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4—44no—
607C2×C4—224no—
608C2×C4—222no—
609C2×C4—442no—
610C2×C4—444no—
611C2×C4—442no—
612C2×C4—442no—
613C2×C4—444no—
614C2×C4—444no—
615C2×C4—444no—
616C2×C4—442no—
617C2×C4—882no—
618C2×C4—882no—
619C2×C4—882no—
620C2×C4#6693511yescharacteristic
621C2×C4#6693511yescharacteristic
622C2×C4#6693612yes—
623C2×C4#6693612yes—
624C2×C4#6693812yes—
625C2×C4#6693912yes—
626C2×C4#6693912yes—
627C2×C4#6698312yes—
628C2×C4#6698312yes—
629C2×C4#6699112yes—
630C2×C4#6699112yes—
631C2×C4#6699212yes—
632C2×C4C22×D4411yescharacteristic
633C2×C4C2×#433911yescharacteristic
634C2×C4C2×D4×D1111yescharacteristic
635C2×C4C2×#434111yescharacteristic
636C2×C4C2×#434111yescharacteristic
637C2×C4C22×C22⋊D1111yescharacteristic
638C8—42no—
639C8—442no—
640C22—24no—
641C22—24no—
642C22—21no—
643C22—21no—
644C22—21no—
645C22—21no—
646C22—42no—
647C22—42no—
648C22—42no—
649C22—84no—
650C22—442no—
651C22—442no—
652C22—442no—
653C22—884no—
654C22#1062243512yes—
655C22#1062243912yes—
656C22#1062257412yes—
657C22#1062257412yes—
658C22C2×#6693511yescharacteristic
659C22C2×#6693811yescharacteristic
660C22C2×#6699211yescharacteristic
661C4—28no—
662C4—42no—
663C4—444no—
664C4—442no—
665C4—882no—
666C4#1062257412yes—
667C4#1062257412yes—
668C4C2×#6693611yescharacteristic
669C4C2×#6693911yescharacteristic
670C4C2×#6698311yescharacteristic
671C4C2×#6699111yescharacteristic
672C2—21no—
673C2—21no—
674C2—22no—
675C2—82no—
676C2—882no—
677C2#1306983914yesdirect product factor
678C2C2×#1062257411yescharacteristic
679C2C2×#1062243511yescharacteristic
680C2C2×#1062243911yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC22×C11×#104C2
socleC23×C11#120
prime radicalC2×#10623364C2
hypercenterC22×#104D11
hypocenterC11C2×#2039
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#104

Complements

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

NH ≅ G/Ntype
2. C22×#66869C2semidirect
3. C2×#10622746C2semidirect
4. C2×#10622845C2semidirect
5. C2×#10622548C2semidirect
6. #13069839C2direct (N × H)
7. C2×#10622192C2semidirect
8. C22×C11×#104C2semidirect
27. C2×C11×#104C22semidirect
29. #10622845C22semidirect
33. #10622746C22semidirect
37. #10622548C22semidirect
39. C2×#66869C22semidirect
40. #10622192C22semidirect
77. C2×C42×C11D4semidirect
206. C42×C11C2×D4semidirect
226. C22×#104D11semidirect
328. C2×#104C2×D11semidirect
440. C2×C42C22⋊D11semidirect
452. C2×C11#2039semidirect
562. C42C2×C22⋊D11semidirect
563. C11C2×#2039semidirect
677. C2#13069839direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106233642
C22×#668692
C2×#106227462
C2×#106228452
C2×#106225482
#130698392
C2×#106221922
C22×C11×#1042
C2×#203911