Finite Group Databasebeta

← C2×#13074474 #14920486

Subgroups — C2×#13074474 #14920486

Order 2816.

3670 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#67000C211yesmaximal, characteristic, complemented
2C22×(C22⋊D11)⋊C4C211yesmaximal, characteristic, complemented
3#13074474C2116yesmaximal, direct product factor
4C2×#10622288C212yesmaximal, complemented
5C2×#10622844C211yesmaximal, characteristic, complemented
6C2×#10622284C211yesmaximal, characteristic, complemented
7C2×#10622573C212yesmaximal, complemented
8C2×#10622573C211yesmaximal, characteristic, complemented
9C2×#10622278C212yesmaximal, complemented
10C2×#10622571C212yesmaximal, complemented
11C2×#10622264C211yesmaximal, characteristic, complemented
12C2×C11×#393C211yesmaximal, characteristic, complemented
13C23×Q8×C11C2211yescharacteristic
14C23×C22⋊D11C2211yescharacteristic
15C23×C22⋊D11C2212yes—
16C24×Dic11C2211yescharacteristic
17C23×D44C2211yescharacteristic
18C23×D44C2212yes—
19C23×C4×D11C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2212yes—
22C2×#67000—28no—
23C2×#67000C2218yescomplemented
24C22×(C2×D11)⋊C4C2212yes—
25C22×(C2×D11)⋊C4C2212yes—
26C22×(C2×D11)⋊C4C2211yescharacteristic
27C22×(C2×D11)⋊C4C2212yes—
28C22×(C2×D11)⋊C4C2212yes—
29C22×(C2×D11)⋊C4C2212yes—
30C22×Dic11⋊C4C2211yescharacteristic
31C22×C4×Dic11C2211yescharacteristic
32C2×(C22⋊D11)⋊C4—28no—
33C2×(C22⋊D11)⋊C4C2218yescomplemented
34C11×#393C2218yescomplemented
35C2×C11×#95C2211yescharacteristic
36C2×C11×#95C2212yes—
37#10622844C2218yescomplemented
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2211yescharacteristic
40C2×C11⋊#95C2212yes—
41C2×C11⋊#95C2212yes—
42#10622573C22116yescomplemented
43#10622573C2218yescomplemented
44#10622571C22116yescomplemented
45#10622288C22116yescomplemented
46#10622284C2218yescomplemented
47#10622278C22116yescomplemented
48#10622264C2218yescomplemented
49C25×C11C2311yescharacteristic
50C24×D11C2312yes—
51C24×D11C2311yescharacteristic
52C22×Q8×C11—24no—
53C22×Q8×C11—44no—
54C22×Q8×C11C2314yes—
55C23×C4×C11C2311yescharacteristic
56C23×C4×C11C2312yes—
57C23×C4×C11C2312yes—
58C23×C4×C11C2311yescharacteristic
59C22×C22⋊D11—24no—
60C22×C22⋊D11—24no—
61C22×C22⋊D11—28no—
62C22×C22⋊D11—24no—
63C22×C22⋊D11—44no—
64C22×C22⋊D11—44no—
65C22×C22⋊D11C2314yes—
66C22×C22⋊D11C2318yes—
67C23×Dic11—24no—
68C23×Dic11—44no—
69C23×Dic11C2311yescharacteristic
70C23×Dic11C2312yes—
71C23×Dic11C2311yescharacteristic
72C23×Dic11C2311yescharacteristic
73C23×Dic11C2314yes—
74C22×D44—28no—
75C22×D44—24no—
76C22×D44—44no—
77C22×D44—44no—
78C22×D44—44no—
79C22×D44C2318yes—
80C22×D44C2314yes—
81C22×C4×D11—24no—
82C22×C4×D11—44no—
83C22×C4×D11C2314yes—
84C2×C11×C22⋊C4—24no—
85C2×C11×C22⋊C4—44no—
86C2×C11×C22⋊C4C2314yes—
87C2×C11×C22⋊C4C2318yes—
88#67000—232no—
89C2×(C2×D11)⋊C4—24no—
90C2×(C2×D11)⋊C4—28no—
91C2×(C2×D11)⋊C4—28no—
92C2×(C2×D11)⋊C4—44no—
93C2×(C2×D11)⋊C4—44no—
94C2×(C2×D11)⋊C4—44no—
95C2×(C2×D11)⋊C4C2314yes—
96C2×(C2×D11)⋊C4C2318yes—
97C2×(C2×D11)⋊C4C2318yes—
98C2×(C2×D11)⋊C4C2318yes—
99C2×(C2×D11)⋊C4C2318yes—
100C2×(C2×D11)⋊C4C2318yes—
101C2×Dic11⋊C4—24no—
102C2×Dic11⋊C4C2314yes—
103C2×C4×Dic11D418yescomplemented
104C2×C4×Dic11C2314yes—
105(C22⋊D11)⋊C4—232no—
106C11×#95C2314yes—
107C11×#95C2318yes—
108C11⋊#95C2318yes—
109C11⋊#95C2318yes—
110C11⋊#95C2314yes—
111C11⋊#95C2318yes—
112C2×#2631—111nomaximal, Sylow
113C24×C11—22no—
114C24×C11—22no—
115C24×C11—24no—
116C24×C11—24no—
117C24×C11#4114yes—
118C24×C11C2412yes—
119C24×C11C2411yescharacteristic
120C23×D11—22no—
121C23×D11—22no—
122C23×D11—24no—
123C23×D11—24no—
124C23×D11—24no—
125C23×D11—24no—
126C23×D11—24no—
127C23×D11—24no—
128C23×D11—24no—
129C23×D11—24no—
130C23×D11—24no—
131C23×D11#4114yes—
132C23×D11C2414yes—
133C23×D11C2412yes—
134C2×Q8×C11—28no—
135C2×Q8×C11—48no—
136C2×Q8×C11—416no—
137C22×C4×C11—24no—
138C22×C4×C11—22no—
139C22×C4×C11—24no—
140C22×C4×C11—24no—
141C22×C4×C11—24no—
142C22×C4×C11—24no—
143C22×C4×C11—24no—
144C22×C4×C11—24no—
145C22×C4×C11—24no—
146C22×C4×C11C2×D414yes—
147C22×C4×C11C2414yes—
148C22×C4×C11C2414yes—
149C22×C4×C11C2412yes—
150C22×C4×C11C2412yes—
151C2×C22⋊D11—232no—
152C2×C22⋊D11—28no—
153C2×C22⋊D11—28no—
154C2×C22⋊D11—216no—
155C2×C22⋊D11—28no—
156C2×C22⋊D11—48no—
157C2×C22⋊D11—48no—
158C2×C22⋊D11—432no—
159C22×Dic11—28no—
160C22×Dic11—22no—
161C22×Dic11—22no—
162C22×Dic11—22no—
163C22×Dic11—24no—
164C22×Dic11—24no—
165C22×Dic11—24no—
166C22×Dic11—24no—
167C22×Dic11—24no—
168C22×Dic11—48no—
169C22×Dic11—416no—
170C22×Dic11C2×D414yes—
171C22×Dic11C2×D414yes—
172C22×Dic11C2414yes—
173C22×Dic11C2412yes—
174C22×Dic11C2412yes—
175C22×Dic11C2412yes—
176C2×D44—216no—
177C2×D44—28no—
178C2×D44—48no—
179C2×D44—48no—
180C2×D44—48no—
181C2×D44—416no—
182C2×D44—432no—
183C2×C4×D11—28no—
184C2×C4×D11—48no—
185C2×C4×D11—416no—
186C11×C22⋊C4—28no—
187C11×C22⋊C4—48no—
188(C2×D11)⋊C4—216no—
189(C2×D11)⋊C4—216no—
190(C2×D11)⋊C4—28no—
191(C2×D11)⋊C4—48no—
192(C2×D11)⋊C4—48no—
193(C2×D11)⋊C4—48no—
194Dic11⋊C4—28no—
195C4×Dic11C2×D4116yescomplemented
196C22×#124—111no—
197C22×C4×D4—111no—
198#2631—1116no—
199C2×#397—112no—
200C2×#393—111no—
201C2×#393D1111yescharacteristic, complemented
202C2×#392—111no—
203C2×#392—112no—
204C2×#392—111no—
205C2×#386—112no—
206C2×#386—112no—
207C2×#383—111no—
208C23×C11—28no—
209C23×C11—216no—
210C23×C11—22no—
211C23×C11—22no—
212C23×C11—24no—
213C23×C11—24no—
214C23×C11—44no—
215C23×C11—44no—
216C23×C11—48no—
217C23×C11C22×D412yes—
218C23×C11C2×#4114yes—
219C23×C11C2×#4112yes—
220C23×C11C2×#4112yes—
221C23×C11H(5,𝔽2)14yes—
222C23×C11H(5,𝔽2)14yes—
223C23×C11C2511yescharacteristic
224C22×D11—28no—
225C22×D11—216no—
226C22×D11—22no—
227C22×D11—22no—
228C22×D11—24no—
229C22×D11—24no—
230C22×D11—24no—
231C22×D11—24no—
232C22×D11—24no—
233C22×D11—24no—
234C22×D11—24no—
235C22×D11—24no—
236C22×D11—24no—
237C22×D11—44no—
238C22×D11—44no—
239C22×D11—48no—
240C22×D11—48no—
241C22×D11—48no—
242C22×D11—48no—
243C22×D11—48no—
244C22×D11—48no—
245C22×D11—48no—
246C22×D11—48no—
247C22×D11C2×#4114yes—
248Q8×C11—416no—
249C2×C4×C11—28no—
250C2×C4×C11—24no—
251C2×C4×C11—22no—
252C2×C4×C11—24no—
253C2×C4×C11—24no—
254C2×C4×C11—24no—
255C2×C4×C11—24no—
256C2×C4×C11—24no—
257C2×C4×C11—24no—
258C2×C4×C11—24no—
259C2×C4×C11—44no—
260C2×C4×C11—48no—
261C2×C4×C11—48no—
262C2×C4×C11C22×D414yes—
263C22⋊D11—232no—
264C22⋊D11—432no—
265C2×Dic11—28no—
266C2×Dic11—28no—
267C2×Dic11—22no—
268C2×Dic11—22no—
269C2×Dic11—24no—
270C2×Dic11—22no—
271C2×Dic11—24no—
272C2×Dic11—24no—
273C2×Dic11—24no—
274C2×Dic11—24no—
275C2×Dic11—416no—
276C2×Dic11—44no—
277C2×Dic11—48no—
278C2×Dic11C22×D414yes—
279C2×Dic11C22×D414yes—
280D44—416no—
281D44—432no—
282C4×D11—416no—
283C23×Q8C2×D1111yescharacteristic
284C23×D4—111no—
285C23×D4—112no—
286C23×D4—111no—
287C23×D4—112no—
288C24×C4—111no—
289C24×C4—111no—
290C2×#124—118no—
291C2×#124—228no—
292C2×C4×D4—118no—
293C2×C4×D4—228no—
294C22×C4⋊C4—111no—
295C22×C22⋊C4—111no—
296C22×C22⋊C4—112no—
297C22×C22⋊C4—112no—
298C22×C22⋊C4—112no—
299C22×C22⋊C4—112no—
300C22×C22⋊C4—112no—
301C22×C22⋊C4C2×D1111yescharacteristic
302C22×C22⋊C4C2×D1112yes—
303C22×C42—111no—
304#397—1116no—
305#393—118no—
306#393C2×D1118yescomplemented
307#392—118no—
308#392—1116no—
309#392—118no—
310#386—1116no—
311#386—1116no—
312#383—118no—
313C2×#95—111no—
314C2×#95—112no—
315C2×#95—112no—
316C2×#95—112no—
317C2×#95C2×D1111yescharacteristic
318C2×#95C2×D1112yes—
319C22×C11—24no—
320C22×C11—28no—
321C22×C11—416no—
322C22×C11—42no—
323C22×C11—42no—
324C22×C11—44no—
325C22×C11#52514yes—
326C22×C11#53514yes—
327C22×C11#53514yes—
328C22×C11#53818yes—
329C22×C11#53818yes—
330C22×C11C23×D411yescharacteristic
331C22×C11C22×#4111yescharacteristic
332C22×C11C22×#4111yescharacteristic
333C22×C11C2×H(5,𝔽2)12yes—
334C22×C11C2×H(5,𝔽2)12yes—
335C2×D11—24no—
336C2×D11—28no—
337C2×D11—416no—
338C2×D11—42no—
339C2×D11—42no—
340C2×D11—44no—
341C2×D11—44no—
342C2×D11—44no—
343C2×D11—44no—
344C2×D11—44no—
345C2×D11—44no—
346C2×D11—44no—
347C2×D11—44no—
348C2×D11—816no—
349C4×C11—24no—
350C4×C11—44no—
351C4×C11—42no—
352C4×C11—44no—
353Dic11—24no—
354Dic11—24no—
355Dic11—42no—
356Dic11—44no—
357C25—111no—
358C25—112no—
359C25C22×D1111yescharacteristic
360C22×Q8—24no—
361C22×Q8—44no—
362C22×Q8C22×D1114yes—
363C22×D4—114no—
364C22×D4—118no—
365C22×D4—114no—
366C22×D4—118no—
367C22×D4—228no—
368C22×D4—224no—
369C22×D4—224no—
370C22×D4—224no—
371C22×D4—228no—
372C22×D4—224no—
373C22×D4—444no—
374C22×D4—444no—
375C22×D4—444no—
376C22×D4—444no—
377C22×D4—444no—
378C23×C4—111no—
379C23×C4—111no—
380C23×C4—111no—
381C23×C4—112no—
382C23×C4—114no—
383C23×C4—114no—
384C23×C4—224no—
385C23×C4—224no—
386C23×C4—444no—
387C23×C4—444no—
388C23×C4C22×D1112yes—
389C23×C4C22×D1111yescharacteristic
390C23×C4C22×D1112yes—
391C23×C4C22×D1111yescharacteristic
392#124—2232no—
393C4×D4—2232no—
394C2×C4⋊C4—114no—
395C2×C4⋊C4—224no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4—44no—
398C2×C22⋊C4—114no—
399C2×C22⋊C4—118no—
400C2×C22⋊C4—118no—
401C2×C22⋊C4—118no—
402C2×C22⋊C4—118no—
403C2×C22⋊C4—118no—
404C2×C22⋊C4—228no—
405C2×C22⋊C4—228no—
406C2×C22⋊C4—224no—
407C2×C22⋊C4—444no—
408C2×C22⋊C4—444no—
409C2×C22⋊C4—444no—
410C2×C22⋊C4C22×D1114yes—
411C2×C22⋊C4C22×D1118yes—
412C2×C42—118no—
413C2×C42—114no—
414#95—118no—
415#95—114no—
416#95—118no—
417#95—118no—
418#95C22×D1114yes—
419#95C22×D1118yes—
420C2×C11—44no—
421C2×C11#263118yescomplemented
422C2×C11C2×#52511yescharacteristic
423C2×C11C2×#53511yescharacteristic
424C2×C11C2×#53511yescharacteristic
425C2×C11C2×#53812yes—
426C2×C11C2×#53812yes—
427D11—44no—
428D11—84no—
429C24—22no—
430C24—24no—
431C24—22no—
432C24—24no—
433C24—114no—
434C24—112no—
435C24—114no—
436C24—222no—
437C24—224no—
438C24—222no—
439C24—224no—
440C24—224no—
441C24—224no—
442C24—224no—
443C24—224no—
444C24—224no—
445C24—224no—
446C24—224no—
447C24#434314yes—
448C24C23×D1112yes—
449C24C23×D1111yescharacteristic
450C2×Q8—28no—
451C2×Q8—48no—
452C2×Q8—416no—
453C2×D4—2216no—
454C2×D4—228no—
455C2×D4—228no—
456C2×D4—2232no—
457C2×D4—228no—
458C2×D4—2216no—
459C2×D4—228no—
460C2×D4—448no—
461C2×D4—448no—
462C2×D4—448no—
463C2×D4—4416no—
464C2×D4—4432no—
465C2×D4—448no—
466C2×D4—448no—
467C2×D4—4432no—
468C22×C4—24no—
469C22×C4—22no—
470C22×C4—24no—
471C22×C4—24no—
472C22×C4—24no—
473C22×C4—24no—
474C22×C4—24no—
475C22×C4—24no—
476C22×C4—24no—
477C22×C4—114no—
478C22×C4—114no—
479C22×C4—112no—
480C22×C4—112no—
481C22×C4—114no—
482C22×C4—112no—
483C22×C4—228no—
484C22×C4—228no—
485C22×C4—222no—
486C22×C4—222no—
487C22×C4—224no—
488C22×C4—222no—
489C22×C4—224no—
490C22×C4—224no—
491C22×C4—224no—
492C22×C4—224no—
493C22×C4—448no—
494C22×C4—4416no—
495C22×C4—448no—
496C22×C4—4416no—
497C22×C4D4×D1114yes—
498C22×C4C23×D1114yes—
499C22×C4C23×D1114yes—
500C22×C4C23×D1112yes—
501C22×C4C23×D1112yes—
502C4⋊C4—228no—
503C22⋊C4—28no—
504C22⋊C4—48no—
505C22⋊C4—2216no—
506C22⋊C4—2216no—
507C22⋊C4—228no—
508C22⋊C4—448no—
509C22⋊C4—448no—
510C22⋊C4—448no—
511C42—1116no—
512C11C2×#263111yescharacteristic, complemented, Sylow
513C23—28no—
514C23—216no—
515C23—22no—
516C23—24no—
517C23—22no—
518C23—24no—
519C23—44no—
520C23—44no—
521C23—48no—
522C23—114no—
523C23—228no—
524C23—222no—
525C23—224no—
526C23—222no—
527C23—224no—
528C23—2216no—
529C23—224no—
530C23—224no—
531C23—224no—
532C23—224no—
533C23—224no—
534C23—224no—
535C23—224no—
536C23—444no—
537C23—448no—
538C23—444no—
539C23—448no—
540C23—448no—
541C23—448no—
542C23—448no—
543C23—448no—
544C23—448no—
545C23—448no—
546C23C2×D4×D1112yes—
547C23#6703714yes—
548C23C2×#434314yes—
549C23C2×#434312yes—
550C23#41×D1112yes—
551C23#6704214yes—
552C23C24×D1111yescharacteristic
553Q8—416no—
554D4—2232no—
555D4—4416no—
556D4—4432no—
557D4—4432no—
558C2×C4—28no—
559C2×C4—24no—
560C2×C4—22no—
561C2×C4—24no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—48no—
569C2×C4—44no—
570C2×C4—48no—
571C2×C4—114no—
572C2×C4—114no—
573C2×C4—228no—
574C2×C4—222no—
575C2×C4—222no—
576C2×C4—224no—
577C2×C4—228no—
578C2×C4—222no—
579C2×C4—224no—
580C2×C4—224no—
581C2×C4—224no—
582C2×C4—224no—
583C2×C4—4416no—
584C2×C4—4416no—
585C2×C4—448no—
586C2×C4—444no—
587C2×C4C2×D4×D1114yes—
588C22—24no—
589C22—28no—
590C22—416no—
591C22—42no—
592C22—42no—
593C22—44no—
594C22—224no—
595C22—228no—
596C22—4416no—
597C22—442no—
598C22—442no—
599C22—444no—
600C22—444no—
601C22—444no—
602C22—444no—
603C22—444no—
604C22—444no—
605C22—444no—
606C22—444no—
607C22—8816no—
608C22#1062312314yes—
609C22#1062315814yes—
610C22#1062317518yes—
611C22#1062320514yes—
612C22#1062320918yes—
613C22C22×D4×D1111yescharacteristic
614C22C2×#6703712yes—
615C22C22×#434311yescharacteristic
616C22C2×#41×D1111yescharacteristic
617C22C2×#6704212yes—
618C4—24no—
619C4—44no—
620C4—42no—
621C4—44no—
622C4—224no—
623C4—224no—
624C4—442no—
625C4—444no—
626C2—44no—
627C2—444no—
628C2—884no—
629C2#1307447418yesdirect product factor
630C2C2×#1062315811yescharacteristic
631C2C2×#1062312311yescharacteristic
632C2C2×#1062320511yescharacteristic
633C2C2×#1062320912yes—
634C2C2×#1062317512yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#393C2
socleC24×C11C24
hypercenterC2×#393D11
hypocenterC11C2×#2631
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#393

Complements

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

NH ≅ G/Ntype
1. C22×#67000C2semidirect
2. C22×(C22⋊D11)⋊C4C2semidirect
3. #13074474C2direct (N × H)
4. C2×#10622288C2semidirect
5. C2×#10622844C2semidirect
6. C2×#10622284C2semidirect
7. C2×#10622573C2semidirect
8. C2×#10622573C2semidirect
9. C2×#10622278C2semidirect
10. C2×#10622571C2semidirect
11. C2×#10622264C2semidirect
12. C2×C11×#393C2semidirect
23. C2×#67000C22semidirect
33. C2×(C22⋊D11)⋊C4C22semidirect
34. C11×#393C22semidirect
37. #10622844C22semidirect
42. #10622573C22semidirect
43. #10622573C22semidirect
44. #10622571C22semidirect
45. #10622288C22semidirect
46. #10622284C22semidirect
47. #10622278C22semidirect
48. #10622264C22semidirect
103. C2×C4×Dic11D4semidirect
195. C4×Dic11C2×D4semidirect
201. C2×#393D11semidirect
306. #393C2×D11semidirect
421. C2×C11#2631semidirect
512. C11C2×#2631semidirect
629. C2#13074474direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#670002
C22×(C22⋊D11)⋊C42
#130744742
C2×#106222882
C2×#106228442
C2×#106222842
C2×#106225732
C2×#106222782
C2×#106225712
C2×#106222642
C2×C11×#3932
C2×#263111