Finite Group Databasebeta

← C2×#13067562 #14725964

Subgroups — C2×#13067562 #14725964

Order 2816.

1716 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622659C211yesmaximal, characteristic, complemented
2C2×#10622649C211yesmaximal, characteristic, complemented
3C2×#10622573C211yesmaximal, characteristic, complemented
4#13067562C218yesmaximal, direct product factor
5C2×#10622176C211yesmaximal, characteristic, complemented
6C2×#10622175C211yesmaximal, characteristic, complemented
7C2×#10622163C211yesmaximal, characteristic, complemented
8C2×C11×#538C211yesmaximal, characteristic, complemented
9C23×C22⋊D11—21no—
10C23×D44C2211yescharacteristic
11C11×#538—22no—
12C11×#538—22no—
13C11×#538—22no—
14C11×#538C2214yescomplemented
15C2×C11×#126—21no—
16C2×C11×#124—21no—
17C2×C11×#123—21no—
18C2×C11×C22⋊Q8C2211yescharacteristic
19C2×C11×#121—21no—
20C2×C11×#121C2211yescharacteristic
21C2×C11×#120—21no—
22C2×C4×D4×C11—21no—
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×#4325—21no—
25C22×#4323—21no—
26C22×(C2×D11)⋊C4—21no—
27C2×C11⋊#95C2211yescharacteristic
28C2×C22⋊(C11⋊C8)C2211yescharacteristic
29C2×C22⋊(C11⋊C8)C2211yescharacteristic
30#10622659—22no—
31#10622659C2214yescomplemented
32#10622649—22no—
33#10622649C2214yescomplemented
34C2×#66873—21no—
35C2×#66873—21no—
36#10622573—22no—
37#10622573C2214yescomplemented
38#10622176C2214yescomplemented
39#10622175C2214yescomplemented
40#10622163C2214yescomplemented
41C25×C11D411yescharacteristic
42C24×D11—21no—
43C22×Q8×C11D411yescharacteristic, complemented
44C22×D4×C11—21no—
45C22×D4×C11—21no—
46C22×D4×C11—21no—
47C22×D4×C11D411yescharacteristic, complemented
48C23×C4×C11—21no—
49C23×C4×C11D411yescharacteristic
50C23×C4×C11C2311yescharacteristic
51C22×C22⋊D11—24no—
52C22×C22⋊D11—44no—
53C22×C22⋊D11—44no—
54C22×C22⋊D11—44no—
55C23×Dic11—21no—
56C22×D44—21no—
57C22×D44—21no—
58C22×D44—21no—
59C22×D44—21no—
60C22×D44—21no—
61C22×D44—44no—
62C22×D44C2312yes—
63C11×#126—24no—
64C11×#126—24no—
65C11×#124—24no—
66C11×#124—24no—
67C11×#123—24no—
68C11×#123—24no—
69C11×C22⋊Q8—21no—
70C11×C22⋊Q8—21no—
71C11×C22⋊Q8D412yescomplemented
72C11×C22⋊Q8C2312yes—
73C11×#121—24no—
74C11×#121—24no—
75C11×#121—21no—
76C11×#121—21no—
77C11×#121D412yescomplemented
78C11×#121C2312yes—
79C11×#120—24no—
80C11×#120—24no—
81C4×D4×C11—24no—
82C4×D4×C11—24no—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4—21no—
85C2×C11×C4⋊C4D411yescharacteristic, complemented
86C2×C11×C4⋊C4D411yescharacteristic, complemented
87C2×C11×C22⋊C4—21no—
88C2×C11×C22⋊C4—21no—
89C2×C11×C22⋊C4—21no—
90C2×C11×C22⋊C4—21no—
91C2×C11×C22⋊C4—21no—
92C2×C11×C22⋊C4—21no—
93C2×C11×C22⋊C4—21no—
94C2×C11×C22⋊C4—21no—
95C2×C11×C22⋊C4—21no—
96C2×C11×C22⋊C4D412yes—
97C2×C11×C22⋊C4C2312yes—
98C2×C42×C11—21no—
99C2×#4325—24no—
100C2×#4325—44no—
101C2×#4323—24no—
102C2×#4323—44no—
103C2×(C2×D11)⋊C4—24no—
104C2×(C2×D11)⋊C4—44no—
105C22×C11⋊C8—21no—
106C22×C11⋊C8—21no—
107C11⋊#95—21no—
108C11⋊#95C2312yes—
109C22⋊(C11⋊C8)—21no—
110C22⋊(C11⋊C8)—21no—
111C22⋊(C11⋊C8)C2312yes—
112C22⋊(C11⋊C8)C2312yes—
113#66873—24no—
114#66873—24no—
115C2×#1600—111nomaximal, Sylow
116C24×C11—21no—
117C24×C11—21no—
118C24×C11—22no—
119C24×C11—21no—
120C24×C11—22no—
121C24×C11—42no—
122C24×C11—42no—
123C24×C11C2×D411yescharacteristic
124C24×C11C2×D412yes—
125C23×D11—24no—
126C23×D11—22no—
127C23×D11—42no—
128C23×D11—42no—
129C23×D11—42no—
130C23×D11—41no—
131C23×D11—41no—
132C23×D11—42no—
133C23×D11—42no—
134C2×Q8×C11—21no—
135C2×Q8×C11—42no—
136C2×Q8×C11C2×D412yescomplemented
137C2×D4×C11—22no—
138C2×D4×C11—22no—
139C2×D4×C11—24no—
140C2×D4×C11—24no—
141C2×D4×C11—21no—
142C2×D4×C11—42no—
143C2×D4×C11—42no—
144C2×D4×C11—42no—
145C2×D4×C11—82no—
146C2×D4×C11—82no—
147C2×D4×C11C2×D412yescomplemented
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—24no—
153C22×C4×C11—21no—
154C22×C4×C11—42no—
155C22×C4×C11—42no—
156C22×C4×C11—82no—
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2×D412yes—
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2411yescharacteristic
164C2×C22⋊D11—48no—
165C2×C22⋊D11—48no—
166C2×C22⋊D11—48no—
167C2×C22⋊D11—432no—
168C22×Dic11—24no—
169C22×Dic11—22no—
170C22×Dic11—42no—
171C22×Dic11—42no—
172C2×D44—24no—
173C2×D44—24no—
174C2×D44—22no—
175C2×D44—22no—
176C2×D44—42no—
177C2×D44—42no—
178C2×D44—44no—
179C2×D44—44no—
180C2×D44—44no—
181C2×D44—44no—
182C2×D44—41no—
183C2×D44—41no—
184C11×C4⋊C4—24no—
185C11×C4⋊C4—22no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—22no—
189C11×C4⋊C4C2×D412yescomplemented
190C11×C4⋊C4C2×D412yescomplemented
191C11×C22⋊C4—24no—
192C11×C22⋊C4—24no—
193C11×C22⋊C4—24no—
194C11×C22⋊C4—22no—
195C11×C22⋊C4—22no—
196C11×C22⋊C4—22no—
197C11×C22⋊C4—22no—
198C11×C22⋊C4—22no—
199C11×C22⋊C4—22no—
200C11×C22⋊C4—22no—
201C11×C22⋊C4—22no—
202C42×C11—24no—
203#4325—48no—
204#4323—48no—
205(C2×D11)⋊C4—48no—
206C2×C11⋊C8—22no—
207C2×C11⋊C8—22no—
208C2×C11⋊C8—42no—
209C2×C11⋊C8—42no—
210C2×#538D1111yescharacteristic, complemented
211C2×#450—111no—
212C2×#447—111no—
213C2×#392—111no—
214#1600—118no—
215C2×#328—111no—
216C2×#327—111no—
217C2×#323—111no—
218C23×C11—22no—
219C23×C11—22no—
220C23×C11—22no—
221C23×C11—22no—
222C23×C11—22no—
223C23×C11—22no—
224C23×C11—42no—
225C23×C11—42no—
226C23×C11—48no—
227C23×C11—42no—
228C23×C11—42no—
229C23×C11—42no—
230C23×C11—42no—
231C23×C11—42no—
232C23×C11—42no—
233C23×C11—42no—
234C23×C11—81no—
235C23×C11—81no—
236C23×C11—84no—
237C23×C11#12011yescharacteristic
238C23×C11#12011yescharacteristic
239C23×C11#13512yes—
240C23×C11AGL(1,ℤ/8)12yes—
241C23×C11C22×D411yescharacteristic
242C22×D11—24no—
243C22×D11—42no—
244C22×D11—42no—
245C22×D11—44no—
246C22×D11—48no—
247C22×D11—42no—
248C22×D11—48no—
249C22×D11—42no—
250C22×D11—42no—
251C22×D11—42no—
252C22×D11—44no—
253C22×D11—84no—
254C22×D11—84no—
255C22×D11—82no—
256C22×D11—82no—
257C22×D11—82no—
258C22×D11—82no—
259Q8×C11—42no—
260Q8×C11—81no—
261D4×C11—42no—
262D4×C11—42no—
263D4×C11—42no—
264D4×C11—44no—
265D4×C11—81no—
266D4×C11—84no—
267D4×C11—84no—
268C2×C4×C11—22no—
269C2×C4×C11—22no—
270C2×C4×C11—22no—
271C2×C4×C11—22no—
272C2×C4×C11—22no—
273C2×C4×C11—22no—
274C2×C4×C11—41no—
275C2×C4×C11—41no—
276C2×C4×C11—41no—
277C2×C4×C11—41no—
278C2×C4×C11—42no—
279C2×C4×C11—42no—
280C2×C4×C11—42no—
281C2×C4×C11—42no—
282C2×C4×C11—42no—
283C2×C4×C11—81no—
284C2×C4×C11—84no—
285C2×C4×C11#12011yescharacteristic
286C2×C4×C11#12011yescharacteristic
287C2×C4×C11C22×D411yescharacteristic
288C2×C4×C11C22×D411yescharacteristic
289C22⋊D11—432no—
290C2×Dic11—24no—
291C2×Dic11—48no—
292C2×Dic11—42no—
293C2×Dic11—42no—
294D44—24no—
295D44—24no—
296D44—44no—
297D44—44no—
298D44—42no—
299D44—42no—
300C11⋊C8—42no—
301C11⋊C8—42no—
302C23×D4—111no—
303C23×D4—221no—
304C22×SD16—221no—
305C22×D8—221no—
306#538—22no—
307#538—22no—
308#538—22no—
309#538C2×D1114yescomplemented
310C2×#126—21no—
311C2×#124—21no—
312C2×#123—21no—
313C2×C22⋊Q8C2×D1111yescharacteristic
314C2×#121—21no—
315C2×#121C2×D1111yescharacteristic
316C2×#120—21no—
317C2×C4×D4—21no—
318C22×C22⋊C4—221no—
319C22×C22⋊C4C2×D1111yescharacteristic
320#450—114no—
321#450—222no—
322#447—114no—
323#447—222no—
324C2×#102—221no—
325C2×#102—221no—
326C2×C22⋊C8—111no—
327C2×C22⋊C8—111no—
328#392—114no—
329#392—222no—
330C2×#95—111no—
331#328—114no—
332#327—114no—
333#323—114no—
334C22×C11—24no—
335C22×C11—24no—
336C22×C11—21no—
337C22×C11—21no—
338C22×C11—21no—
339C22×C11—21no—
340C22×C11—44no—
341C22×C11—42no—
342C22×C11—42no—
343C22×C11—42no—
344C22×C11—42no—
345C22×C11—42no—
346C22×C11—42no—
347C22×C11—82no—
348C22×C11—84no—
349C22×C11—84no—
350C22×C11—84no—
351C22×C11#44912yes—
352C22×C11#44912yes—
353C22×C11#45312yes—
354C22×C11B(4,𝔽2)12yes—
355C22×C11C2×#12011yescharacteristic
356C22×C11C2×#13511yescharacteristic
357C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
358C2×D11—44no—
359C2×D11—44no—
360C2×D11—44no—
361C2×D11—82no—
362C2×D11—82no—
363C2×D11—88no—
364C2×D11—88no—
365C2×D11—82no—
366C2×D11—82no—
367C4×C11—21no—
368C4×C11—21no—
369C4×C11—21no—
370C4×C11—21no—
371C4×C11—42no—
372C4×C11—42no—
373C4×C11—42no—
374C4×C11—42no—
375Dic11—44no—
376C25—221no—
377C25C22⋊D1111yescharacteristic
378C22×Q8C22⋊D1111yescharacteristic, complemented
379C22×D4—21no—
380C22×D4—21no—
381C22×D4—21no—
382C22×D4—112no—
383C22×D4—224no—
384C22×D4—221no—
385C22×D4—221no—
386C22×D4—221no—
387C22×D4—221no—
388C22×D4—221no—
389C22×D4—444no—
390C22×D4—444no—
391C22×D4—444no—
392C22×D4—444no—
393C22×D4C22⋊D1111yescharacteristic, complemented
394C23×C4—21no—
395C23×C4—221no—
396C23×C4C22⋊D1111yescharacteristic
397C23×C4C22×D1111yescharacteristic
398C2×SD16—224no—
399C2×SD16—444no—
400C2×D8—224no—
401C2×D8—444no—
402C22×C8—221no—
403C22×C8—221no—
404#126—24no—
405#126—24no—
406#124—24no—
407#124—24no—
408#123—24no—
409#123—24no—
410C22⋊Q8—21no—
411C22⋊Q8—21no—
412C22⋊Q8C22⋊D1112yescomplemented
413C22⋊Q8C22×D1112yes—
414#121—24no—
415#121—24no—
416#121—21no—
417#121—21no—
418#121C22⋊D1112yescomplemented
419#121C22×D1112yes—
420#120—24no—
421#120—24no—
422C4×D4—24no—
423C4×D4—24no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4C22⋊D1111yescharacteristic, complemented
427C2×C4⋊C4C22⋊D1111yescharacteristic, complemented
428C2×C22⋊C4—21no—
429C2×C22⋊C4—21no—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—21no—
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—224no—
438C2×C22⋊C4—444no—
439C2×C22⋊C4C22⋊D1112yes—
440C2×C22⋊C4C22×D1112yes—
441C2×C42—21no—
442#102—224no—
443#102—224no—
444C22⋊C8—112no—
445C22⋊C8—112no—
446C22⋊C8—221no—
447C22⋊C8—221no—
448#95—112no—
449#95—221no—
450C2×C11—21no—
451C2×C11—21no—
452C2×C11—22no—
453C2×C11—82no—
454C2×C11—82no—
455C2×C11#160014yescomplemented
456C2×C11C2×#44911yescharacteristic
457C2×C11C2×#45311yescharacteristic
458C2×C11C2×B(4,𝔽2)11yescharacteristic
459D11—84no—
460C24—22no—
461C24—21no—
462C24—21no—
463C24—22no—
464C24—21no—
465C24—42no—
466C24—42no—
467C24—224no—
468C24—222no—
469C24—442no—
470C24—442no—
471C24—442no—
472C24—442no—
473C24—442no—
474C24—441no—
475C24—441no—
476C24C2×C22⋊D1111yescharacteristic
477C24C2×C22⋊D1112yes—
478C2×Q8—21no—
479C2×Q8—42no—
480C2×Q8C2×C22⋊D1112yescomplemented
481C2×D4—22no—
482C2×D4—22no—
483C2×D4—24no—
484C2×D4—24no—
485C2×D4—21no—
486C2×D4—42no—
487C2×D4—42no—
488C2×D4—42no—
489C2×D4—82no—
490C2×D4—82no—
491C2×D4—224no—
492C2×D4—224no—
493C2×D4—222no—
494C2×D4—222no—
495C2×D4—442no—
496C2×D4—442no—
497C2×D4—444no—
498C2×D4—444no—
499C2×D4—444no—
500C2×D4—444no—
501C2×D4—448no—
502C2×D4—448no—
503C2×D4—448no—
504C2×D4—4432no—
505C2×D4—441no—
506C2×D4—441no—
507C2×D4C2×C22⋊D1112yescomplemented
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—24no—
513C22×C4—21no—
514C22×C4—42no—
515C22×C4—42no—
516C22×C4—82no—
517C22×C4—224no—
518C22×C4—222no—
519C22×C4—442no—
520C22×C4—442no—
521C22×C4C2×C22⋊D1111yescharacteristic
522C22×C4C2×C22⋊D1111yescharacteristic
523C22×C4C2×C22⋊D1112yes—
524C22×C4C2×C22⋊D1111yescharacteristic
525C22×C4C2×C22⋊D1111yescharacteristic
526C22×C4C2×C22⋊D1111yescharacteristic
527C22×C4C23×D1111yescharacteristic
528SD16—448no—
529D8—448no—
530C2×C8—222no—
531C2×C8—222no—
532C2×C8—442no—
533C2×C8—442no—
534C4⋊C4—24no—
535C4⋊C4—22no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—22no—
539C4⋊C4C2×C22⋊D1112yescomplemented
540C4⋊C4C2×C22⋊D1112yescomplemented
541C22⋊C4—24no—
542C22⋊C4—24no—
543C22⋊C4—24no—
544C22⋊C4—22no—
545C22⋊C4—22no—
546C22⋊C4—22no—
547C22⋊C4—22no—
548C22⋊C4—22no—
549C22⋊C4—22no—
550C22⋊C4—22no—
551C22⋊C4—22no—
552C22⋊C4—448no—
553C42—24no—
554C11C2×#160011yescharacteristic, complemented, Sylow
555C23—22no—
556C23—22no—
557C23—22no—
558C23—22no—
559C23—22no—
560C23—22no—
561C23—42no—
562C23—42no—
563C23—48no—
564C23—42no—
565C23—42no—
566C23—42no—
567C23—42no—
568C23—42no—
569C23—42no—
570C23—42no—
571C23—81no—
572C23—81no—
573C23—84no—
574C23—224no—
575C23—442no—
576C23—448no—
577C23—442no—
578C23—442no—
579C23—444no—
580C23—448no—
581C23—442no—
582C23—442no—
583C23—444no—
584C23—442no—
585C23—884no—
586C23—884no—
587C23—882no—
588C23—882no—
589C23—882no—
590C23—882no—
591C23#6700212yes—
592C23#6700312yes—
593C23#6700611yescharacteristic
594C23#6700611yescharacteristic
595C23C22×C22⋊D1111yescharacteristic
596Q8—42no—
597Q8—81no—
598D4—42no—
599D4—42no—
600D4—42no—
601D4—44no—
602D4—81no—
603D4—84no—
604D4—84no—
605D4—224no—
606D4—224no—
607D4—442no—
608D4—442no—
609D4—444no—
610D4—444no—
611D4—4432no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—42no—
623C2×C4—42no—
624C2×C4—42no—
625C2×C4—42no—
626C2×C4—42no—
627C2×C4—81no—
628C2×C4—84no—
629C2×C4—224no—
630C2×C4—448no—
631C2×C4—442no—
632C2×C4—442no—
633C2×C4#6700611yescharacteristic
634C2×C4#6700611yescharacteristic
635C2×C4C22×C22⋊D1111yescharacteristic
636C2×C4C22×C22⋊D1111yescharacteristic
637C8—442no—
638C8—442no—
639C22—24no—
640C22—24no—
641C22—21no—
642C22—21no—
643C22—21no—
644C22—21no—
645C22—44no—
646C22—42no—
647C22—42no—
648C22—42no—
649C22—42no—
650C22—42no—
651C22—42no—
652C22—82no—
653C22—84no—
654C22—84no—
655C22—84no—
656C22—444no—
657C22—444no—
658C22—444no—
659C22—882no—
660C22—882no—
661C22—888no—
662C22—888no—
663C22—882no—
664C22—882no—
665C22#1062285112yes—
666C22#1062285112yes—
667C22#1062285412yes—
668C22#1062285712yes—
669C22C2×#6700211yescharacteristic
670C22C2×#6700311yescharacteristic
671C22C2×#6700611yescharacteristic
672C4—21no—
673C4—21no—
674C4—21no—
675C4—21no—
676C4—42no—
677C4—42no—
678C4—42no—
679C4—42no—
680C4—444no—
681C2—21no—
682C2—21no—
683C2—22no—
684C2—82no—
685C2—82no—
686C2—884no—
687C2#1306756214yesdirect product factor
688C2C2×#1062285111yescharacteristic
689C2C2×#1062285411yescharacteristic
690C2C2×#1062285711yescharacteristic
subgroupG/H
centerC23#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#538C2
socleC23×C11#120
hypercenterC2×#538D11
hypocenterC11C2×#1600
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#538

Complements

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

NH ≅ G/Ntype
1. C2×#10622659C2semidirect
2. C2×#10622649C2semidirect
3. C2×#10622573C2semidirect
4. #13067562C2direct (N × H)
5. C2×#10622176C2semidirect
6. C2×#10622175C2semidirect
7. C2×#10622163C2semidirect
8. C2×C11×#538C2semidirect
14. C11×#538C22semidirect
31. #10622659C22semidirect
33. #10622649C22semidirect
37. #10622573C22semidirect
38. #10622176C22semidirect
39. #10622175C22semidirect
40. #10622163C22semidirect
43. C22×Q8×C11D4semidirect
47. C22×D4×C11D4semidirect
71. C11×C22⋊Q8D4semidirect
77. C11×#121D4semidirect
85. C2×C11×C4⋊C4D4semidirect
86. C2×C11×C4⋊C4D4semidirect
136. C2×Q8×C11C2×D4semidirect
147. C2×D4×C11C2×D4semidirect
189. C11×C4⋊C4C2×D4semidirect
190. C11×C4⋊C4C2×D4semidirect
210. C2×#538D11semidirect
309. #538C2×D11semidirect
378. C22×Q8C22⋊D11semidirect
393. C22×D4C22⋊D11semidirect
412. C22⋊Q8C22⋊D11semidirect
418. #121C22⋊D11semidirect
426. C2×C4⋊C4C22⋊D11semidirect
427. C2×C4⋊C4C22⋊D11semidirect
455. C2×C11#1600semidirect
480. C2×Q8C2×C22⋊D11semidirect
507. C2×D4C2×C22⋊D11semidirect
539. C4⋊C4C2×C22⋊D11semidirect
540. C4⋊C4C2×C22⋊D11semidirect
554. C11C2×#1600semidirect
687. C2#13067562direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106226592
C2×#106226492
C2×#106225732
#130675622
C2×#106221762
C2×#106221752
C2×#106221632
C2×C11×#5382
C2×#160011