Finite Group Databasebeta

← C2×#13070268 #14906508

Subgroups — C2×#13070268 #14906508

Order 2816.

1214 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623179C211yesmaximal, characteristic
2C2×#10622358C211yesmaximal, characteristic
3C2×#10622353C211yesmaximal, characteristic
4#13070268C218yesmaximal, direct product factor
5C2×#10622114C211yesmaximal, characteristic, complemented
6C2×#10622177C211yesmaximal, characteristic, complemented
7C2×#10622110C211yesmaximal, characteristic, complemented
8C2×C11×#352C211yesmaximal, characteristic, complemented
9C22×#4341C2211yescharacteristic
10C23×Dic22C411yescharacteristic, complemented
11C2×C11×#123C2211yescharacteristic
12C2×#66988C2211yescharacteristic
13C2×#66982C411yescharacteristic, complemented
14C2×M16×D11—21no—
15#10623179—22no—
16#10623179—22no—
17#10623179C414yescomplemented
18#10623179C2214yes—
19C2×#66949—21no—
20C2×#66941—21no—
21C2×#66939C411yescharacteristic, complemented
22C2×#66938—21no—
23C2×#66931—21no—
24C2×#66930—21no—
25C2×#66930C411yescharacteristic, complemented
26C2×C11×#100C2211yescharacteristic
27C2×C11×#99C2211yescharacteristic
28C2×#66898C2211yescharacteristic
29C2×#66897C2211yescharacteristic
30C2×#66888—21no—
31C2×#66870—21no—
32#10622358—22no—
33#10622358C2214yes—
34#10622353—22no—
35#10622353C2214yes—
36C11×#352C2214yescomplemented
37#10622177C2214yescomplemented
38#10622114C2214yescomplemented
39#10622110C2214yescomplemented
40C22×D4×C11C2311yescharacteristic
41C23×C4×C11C2×C411yescharacteristic
42C22×C22⋊D11C2×C411yescharacteristic
43C22×C22⋊D11D411yescharacteristic
44C23×Dic11C2×C411yescharacteristic
45C23×Dic11C2×C411yescharacteristic
46C23×Dic11D411yescharacteristic
47C2×#4341—41no—
48C2×#4341—41no—
49C2×#4341—42no—
50C2×#4341C2×C412yes—
51C2×#4341D412yes—
52C2×#4341D412yes—
53C2×#4341C2312yes—
54C22×C4×D11D411yescharacteristic
55C22×Dic22—21no—
56C22×Dic22—21no—
57C22×Dic22—22no—
58C22×Dic22—42no—
59C22×Dic22—41no—
60C22×Dic22—41no—
61C22×Dic22C2×C414yescomplemented
62C22×Dic22D411yescharacteristic
63C2×C11×M16—21no—
64C11×#123—21no—
65C11×#123—21no—
66C11×#123C2×C412yes—
67C11×#123C2312yes—
68C2×C11×C4⋊C4—21no—
69C2×C11×C22⋊C4—21no—
70C2×C11×C22⋊C4—21no—
71C2×C11×C22⋊C4C2×C411yescharacteristic
72C2×C22⋊Dic11—21no—
73C2×C22⋊Dic11—21no—
74C2×C22⋊Dic11C2×C411yescharacteristic
75#66988—21no—
76#66988—21no—
77#66988C2×C412yes—
78#66988C2312yes—
79#66982—22no—
80#66982C2×C414yescomplemented
81C2×(C2×D11)⋊C4—21no—
82C2×(C2×D11)⋊C4—21no—
83C2×C4⋊Dic11—21no—
84C2×Dic11⋊C4—21no—
85C2×Dic11⋊C4—21no—
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4—41no—
88C2×C4×Dic11—21no—
89C2×C4×Dic11—41no—
90C2×#4318—21no—
91M16×D11—24no—
92M16×D11—42no—
93C2×#4313—41no—
94C2×C8×D11—41no—
95#66949—24no—
96#66949—24no—
97#66941—24no—
98#66941—24no—
99#66939—22no—
100#66939C2×C414yescomplemented
101#66938—24no—
102#66938—24no—
103#66931—24no—
104#66931—24no—
105#66930—22no—
106#66930—24no—
107#66930—42no—
108#66930C2×C414yescomplemented
109C11×#100—21no—
110C11×#100C2312yes—
111C11×#99—21no—
112C11×#99C2312yes—
113#66898—21no—
114#66898C2312yes—
115#66897—21no—
116#66897C2312yes—
117#66888—24no—
118#66870—24no—
119C2×#2123—111nomaximal, Sylow
120C24×C11C22×C411yescharacteristic
121C24×C11C2×D411yescharacteristic
122C23×D11C22⋊C411yescharacteristic
123C2×D4×C11—41no—
124C2×D4×C11—41no—
125C2×D4×C11C22×C411yescharacteristic
126C2×D4×C11C2×D411yescharacteristic
127C2×D4×C11C2×D411yescharacteristic
128C2×D4×C11C2411yescharacteristic
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—41no—
133C22×C4×C11—41no—
134C22×C4×C11—41no—
135C22×C4×C11C22×C412yes—
136C22×C4×C11C2×D411yescharacteristic
137C2×C22⋊D11—41no—
138C2×C22⋊D11—41no—
139C2×C22⋊D11—41no—
140C2×C22⋊D11—41no—
141C2×C22⋊D11C22⋊C412yes—
142C2×C22⋊D11C22⋊C412yes—
143C2×C22⋊D11C22×C412yes—
144C2×C22⋊D11C2×D412yes—
145C22×Dic11—22no—
146C22×Dic11—21no—
147C22×Dic11—21no—
148C22×Dic11—22no—
149C22×Dic11—21no—
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11—41no—
155C22×Dic11—41no—
156C22×Dic11—41no—
157C22×Dic11C22⋊C412yes—
158C22×Dic11C22⋊C412yes—
159C22×Dic11C22⋊C411yescharacteristic
160C22×Dic11C22⋊C411yescharacteristic
161C22×Dic11C22⋊C411yescharacteristic
162C22×Dic11C22×C412yes—
163C22×Dic11C22×C412yes—
164C22×Dic11C2×D412yes—
165#4341—42no—
166#4341—42no—
167#4341—42no—
168#4341—42no—
169#4341—42no—
170#4341—42no—
171#4341—42no—
172#4341—42no—
173C2×C4×D11—21no—
174C2×C4×D11—21no—
175C2×C4×D11—22no—
176C2×C4×D11C22⋊C412yes—
177C2×C4×D11C2×D412yes—
178C2×Dic22—24no—
179C2×Dic22—24no—
180C2×Dic22—41no—
181C2×Dic22—41no—
182C2×Dic22—44no—
183C2×Dic22—44no—
184C2×Dic22—42no—
185C2×Dic22—42no—
186C2×Dic22—42no—
187C2×Dic22—41no—
188C2×Dic22—41no—
189C2×Dic22—44no—
190C2×Dic22—44no—
191C2×Dic22C22⋊C412yes—
192C2×Dic22C2×D412yes—
193C11×M16—22no—
194C11×M16—41no—
195C2×C8×C11—41no—
196C11×C4⋊C4—22no—
197C11×C4⋊C4—22no—
198C11×C22⋊C4—21no—
199C11×C22⋊C4—22no—
200C11×C22⋊C4—22no—
201C11×C22⋊C4—22no—
202C11×C22⋊C4—41no—
203C11×C22⋊C4C22×C412yes—
204C22⋊Dic11—21no—
205C22⋊Dic11—22no—
206C22⋊Dic11—22no—
207C22⋊Dic11—22no—
208C22⋊Dic11—41no—
209C22⋊Dic11C22×C412yes—
210(C2×D11)⋊C4—24no—
211(C2×D11)⋊C4—24no—
212C4⋊Dic11—24no—
213Dic11⋊C4—24no—
214Dic11⋊C4—24no—
215Dic11⋊C4—22no—
216Dic11⋊C4—22no—
217Dic11⋊C4—44no—
218C4×Dic11—24no—
219C4×Dic11—44no—
220#4318—22no—
221#4318—41no—
222C2×C11⋊C8—41no—
223#4313—44no—
224C8×D11—44no—
225C2×#536—111no—
226C2×#413—111no—
227C2×#410—111no—
228#2123—118no—
229C2×#352—111no—
230C2×#352—111no—
231C2×#352—111no—
232C2×#352D1111yescharacteristic, complemented
233C23×C11—21no—
234C23×C11—21no—
235C23×C11—21no—
236C23×C11—21no—
237C23×C11—42no—
238C23×C11—42no—
239C23×C11C2×C22⋊C411yescharacteristic
240C23×C11C2×C22⋊C411yescharacteristic
241C23×C11C2×C22⋊C411yescharacteristic
242C23×C11C23×C411yescharacteristic
243C23×C11C22×D411yescharacteristic
244C22×D11—21no—
245C22×D11—21no—
246C22×D11—42no—
247C22×D11C2×C22⋊C412yes—
248D4×C11—41no—
249D4×C11—41no—
250D4×C11—41no—
251D4×C11—41no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—22no—
255C2×C4×C11—22no—
256C2×C4×C11—42no—
257C2×C4×C11—42no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—42no—
261C2×C4×C11—42no—
262C2×C4×C11—82no—
263C2×C4×C11C2×C22⋊C411yescharacteristic
264C2×C4×C11C22×D411yescharacteristic
265C22⋊D11—42no—
266C22⋊D11—42no—
267C22⋊D11—42no—
268C22⋊D11—42no—
269C2×Dic11—21no—
270C2×Dic11—21no—
271C2×Dic11—21no—
272C2×Dic11—21no—
273C2×Dic11—22no—
274C2×Dic11—22no—
275C2×Dic11—22no—
276C2×Dic11—22no—
277C2×Dic11—22no—
278C2×Dic11—22no—
279C2×Dic11—22no—
280C2×Dic11—22no—
281C2×Dic11—22no—
282C2×Dic11—22no—
283C2×Dic11—42no—
284C2×Dic11—42no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—42no—
288C2×Dic11—42no—
289C2×Dic11—82no—
290C2×Dic11#9912yes—
291C2×Dic11#9911yescharacteristic
292C2×Dic11#9911yescharacteristic
293C2×Dic11C2×C22⋊C412yes—
294C2×Dic11C2×C22⋊C412yes—
295C2×Dic11C2×C22⋊C412yes—
296C4×D11—22no—
297C4×D11—22no—
298C4×D11—22no—
299C4×D11—22no—
300Dic22—42no—
301Dic22—42no—
302Dic22—48no—
303Dic22—44no—
304Dic22—44no—
305C8×C11—42no—
306C11⋊C8—42no—
307C22×#41—111no—
308C23×Q8—111no—
309C22×M16—221no—
310#536—114no—
311#536—114no—
312#536—222no—
313#536—222no—
314C2×C4⋊Q8—221no—
315C2×#124—221no—
316C2×#123—111no—
317C2×#123—111no—
318C2×#123—111no—
319C2×#123C2×D1111yescharacteristic
320C2×C22⋊Q8—221no—
321C2×C22⋊Q8—221no—
322C2×#117—111no—
323C2×#117—221no—
324#413—114no—
325#413—222no—
326C2×#101—221no—
327C2×#100—111no—
328C2×#100C2×D1111yescharacteristic
329#410—114no—
330#410—222no—
331C2×#99—111no—
332C2×#99—221no—
333C2×#99C2×D1111yescharacteristic
334#352—114no—
335#352—114no—
336#352—114no—
337#352C2×D1114yescomplemented
338C22×C11—22no—
339C22×C11—21no—
340C22×C11—21no—
341C22×C11—21no—
342C22×C11—21no—
343C22×C11—41no—
344C22×C11—41no—
345C22×C11—41no—
346C22×C11—41no—
347C22×C11—42no—
348C22×C11—42no—
349C22×C11—42no—
350C22×C11—81no—
351C22×C11C2×#9911yescharacteristic
352C22×C11C2×#9911yescharacteristic
353C22×C11C22×C22⋊C411yescharacteristic
354C2×D11—22no—
355C2×D11—42no—
356C2×D11—42no—
357C2×D11—81no—
358C4×C11—21no—
359C4×C11—21no—
360C4×C11—42no—
361C4×C11—42no—
362C4×C11—82no—
363Dic11—22no—
364Dic11—22no—
365Dic11—42no—
366Dic11—42no—
367Dic11—82no—
368Dic11C2×#9912yes—
369Dic11C2×#9912yes—
370C2×#41—112no—
371C2×#41—112no—
372C2×#41—112no—
373C2×#41—112no—
374C2×#41—441no—
375C2×#41—441no—
376C2×#41—442no—
377C22×Q8—114no—
378C22×Q8—111no—
379C22×Q8—221no—
380C22×Q8—221no—
381C22×Q8—222no—
382C22×Q8—442no—
383C22×Q8—441no—
384C22×Q8—441no—
385C22×D4—111no—
386C22×D4—111no—
387C22×D4C22×D1111yescharacteristic
388C23×C4—111no—
389C23×C4—111no—
390C23×C4—111no—
391C23×C4—111no—
392C23×C4C4×D1111yescharacteristic
393C2×M16—21no—
394C2×M16—224no—
395C2×M16—221no—
396C2×M16—441no—
397C2×M16—442no—
398C22×C8—441no—
399C4⋊Q8—224no—
400C4⋊Q8—224no—
401#124—224no—
402#124—224no—
403#123—21no—
404#123—21no—
405#123—112no—
406#123—112no—
407#123—114no—
408#123—114no—
409#123—222no—
410#123—222no—
411#123—221no—
412#123—221no—
413#123C4×D1112yes—
414#123C22×D1112yes—
415C22⋊Q8—224no—
416C22⋊Q8—224no—
417C22⋊Q8—224no—
418C22⋊Q8—224no—
419#117—114no—
420#117—222no—
421#117—224no—
422#117—442no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—221no—
425C2×C4⋊C4—221no—
426C2×C4⋊C4—221no—
427C2×C4⋊C4—221no—
428C2×C4⋊C4—441no—
429C2×C22⋊C4—21no—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—111no—
432C2×C22⋊C4—221no—
433C2×C22⋊C4—221no—
434C2×C22⋊C4—221no—
435C2×C22⋊C4—221no—
436C2×C22⋊C4C4×D1111yescharacteristic
437C2×C42—221no—
438C2×C42—441no—
439#101—224no—
440#100—21no—
441#100—112no—
442#100—221no—
443#100C22×D1112yes—
444#99—21no—
445#99—112no—
446#99—224no—
447#99—221no—
448#99C22×D1112yes—
449C2×C11—21no—
450C2×C11—21no—
451C2×C11—41no—
452C2×C11—41no—
453C2×C11—41no—
454C2×C11—41no—
455C2×C11#212312yescomplemented
456C2×C11C22×#9911yescharacteristic
457D11—42no—
458C24—111no—
459C24C2×C4×D1111yescharacteristic
460C24D4×D1111yescharacteristic
461#41—442no—
462#41—442no—
463#41—442no—
464#41—442no—
465#41—442no—
466#41—442no—
467#41—442no—
468#41—442no—
469C2×Q8—112no—
470C2×Q8—112no—
471C2×Q8—224no—
472C2×Q8—224no—
473C2×Q8—441no—
474C2×Q8—441no—
475C2×Q8—442no—
476C2×Q8—441no—
477C2×Q8—441no—
478C2×Q8—444no—
479C2×Q8—444no—
480C2×Q8—444no—
481C2×Q8—444no—
482C2×Q8—442no—
483C2×Q8—442no—
484C2×D4—41no—
485C2×D4—41no—
486C2×D4—112no—
487C2×D4—112no—
488C2×D4—112no—
489C2×D4—112no—
490C2×D4—441no—
491C2×D4—441no—
492C2×D4—441no—
493C2×D4—441no—
494C2×D4C2×C4×D1111yescharacteristic
495C2×D4D4×D1111yescharacteristic
496C2×D4D4×D1111yescharacteristic
497C2×D4C23×D1111yescharacteristic
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—41no—
502C22×C4—41no—
503C22×C4—41no—
504C22×C4—111no—
505C22×C4—112no—
506C22×C4—112no—
507C22×C4—111no—
508C22×C4—111no—
509C22×C4—112no—
510C22×C4—112no—
511C22×C4—112no—
512C22×C4—112no—
513C22×C4—112no—
514C22×C4—221no—
515C22×C4—222no—
516C22×C4—221no—
517C22×C4—221no—
518C22×C4—221no—
519C22×C4—222no—
520C22×C4—222no—
521C22×C4—221no—
522C22×C4—221no—
523C22×C4—221no—
524C22×C4—221no—
525C22×C4—221no—
526C22×C4—441no—
527C22×C4—441no—
528C22×C4—441no—
529C22×C4C2×C4×D1112yes—
530C22×C4D4×D1111yescharacteristic
531M16—22no—
532M16—41no—
533M16—222no—
534M16—444no—
535M16—441no—
536C2×C8—41no—
537C2×C8—444no—
538C2×C8—441no—
539C4⋊C4—22no—
540C4⋊C4—22no—
541C4⋊C4—224no—
542C4⋊C4—224no—
543C4⋊C4—224no—
544C4⋊C4—222no—
545C4⋊C4—222no—
546C4⋊C4—444no—
547C22⋊C4—22no—
548C22⋊C4—21no—
549C22⋊C4—22no—
550C22⋊C4—22no—
551C22⋊C4—41no—
552C22⋊C4—112no—
553C22⋊C4—224no—
554C22⋊C4—224no—
555C22⋊C4—221no—
556C22⋊C4—222no—
557C22⋊C4—222no—
558C22⋊C4—222no—
559C22⋊C4—441no—
560C22⋊C4C2×C4×D1112yes—
561C42—224no—
562C42—444no—
563C11C2×#212311yescharacteristic, complemented, Sylow
564C23—21no—
565C23—21no—
566C23—21no—
567C23—21no—
568C23—42no—
569C23—42no—
570C23—112no—
571C23—221no—
572C23—221no—
573C23—442no—
574C23C22⋊C4×D1111yescharacteristic
575C23C22⋊C4×D1111yescharacteristic
576C23C22⋊C4×D1111yescharacteristic
577C23C22×C4×D1111yescharacteristic
578C23C2×D4×D1111yescharacteristic
579Q8—442no—
580Q8—442no—
581Q8—444no—
582Q8—444no—
583Q8—448no—
584D4—41no—
585D4—41no—
586D4—41no—
587D4—41no—
588D4—442no—
589D4—442no—
590D4—442no—
591D4—442no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—82no—
603C2×C4—112no—
604C2×C4—112no—
605C2×C4—111no—
606C2×C4—111no—
607C2×C4—112no—
608C2×C4—112no—
609C2×C4—222no—
610C2×C4—222no—
611C2×C4—222no—
612C2×C4—222no—
613C2×C4—222no—
614C2×C4—222no—
615C2×C4—222no—
616C2×C4—222no—
617C2×C4—222no—
618C2×C4—222no—
619C2×C4—222no—
620C2×C4—222no—
621C2×C4—221no—
622C2×C4—221no—
623C2×C4—221no—
624C2×C4—221no—
625C2×C4—222no—
626C2×C4—222no—
627C2×C4—442no—
628C2×C4—442no—
629C2×C4—441no—
630C2×C4—441no—
631C2×C4—442no—
632C2×C4—442no—
633C2×C4—882no—
634C2×C4C22⋊C4×D1111yescharacteristic
635C2×C4C2×D4×D1111yescharacteristic
636C8—42no—
637C8—442no—
638C22—22no—
639C22—21no—
640C22—21no—
641C22—21no—
642C22—21no—
643C22—41no—
644C22—41no—
645C22—41no—
646C22—41no—
647C22—42no—
648C22—42no—
649C22—42no—
650C22—81no—
651C22—222no—
652C22—442no—
653C22—442no—
654C22—881no—
655C22D11×#9911yescharacteristic
656C22D11×#9911yescharacteristic
657C22C2×C22⋊C4×D1111yescharacteristic
658C4—21no—
659C4—21no—
660C4—42no—
661C4—42no—
662C4—82no—
663C4—112no—
664C4—112no—
665C4—222no—
666C4—222no—
667C4—442no—
668C4—442no—
669C4—882no—
670C2—21no—
671C2—21no—
672C2—41no—
673C2—41no—
674C2—41no—
675C2—41no—
676C2—442no—
677C2#1307026812yesdirect product factor
678C2C2×D11×#9911yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC23×C11C23×C4
FrattiniC2×D4C23×D11
FittingC2×C11×#352C2
socleC22×C11C2×#99
prime radicalC22×#4341C22
cosocleC2×D4×C11C24
hypercenterC2×#352D11
hypocenterC11C2×#2123
LCSG ▷ C23×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ C2×#352

Complements

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

NH ≅ G/Ntype
4. #13070268C2direct (N × H)
5. C2×#10622114C2semidirect
6. C2×#10622177C2semidirect
7. C2×#10622110C2semidirect
8. C2×C11×#352C2semidirect
10. C23×Dic22C4semidirect
13. C2×#66982C4semidirect
17. #10623179C4semidirect
21. C2×#66939C4semidirect
25. C2×#66930C4semidirect
36. C11×#352C22semidirect
37. #10622177C22semidirect
38. #10622114C22semidirect
39. #10622110C22semidirect
61. C22×Dic22C2×C4semidirect
80. #66982C2×C4semidirect
100. #66939C2×C4semidirect
108. #66930C2×C4semidirect
232. C2×#352D11semidirect
337. #352C2×D11semidirect
455. C2×C11#2123semidirect
563. C11C2×#2123semidirect
677. C2#13070268direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231792
C2×#106223582
C2×#106223532
#130702682
C2×#106221142
C2×#106221772
C2×#106221102
C2×C11×#3522
C2×#212311