Finite Group Databasebeta

← C2×#13074470 #14920484

Subgroups — C2×#13074470 #14920484

Order 2816.

3670 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66938C211yesmaximal, characteristic, complemented
2C22×#66946C211yesmaximal, characteristic, complemented
3#13074470C2116yesmaximal, direct product factor
4C2×#10622606C211yesmaximal, characteristic, complemented
5C2×#10622286C212yesmaximal, complemented
6C2×#10622284C211yesmaximal, characteristic, complemented
7C2×#10622573C212yesmaximal, complemented
8C2×#10622573C211yesmaximal, characteristic, complemented
9C2×#10622278C212yesmaximal, complemented
10C2×#10622569C212yesmaximal, complemented
11C2×#10622264C211yesmaximal, characteristic, complemented
12C2×C11×#397C211yesmaximal, characteristic, complemented
13C23×C22⋊D11C2211yescharacteristic
14C23×C22⋊D11C2212yes—
15C23×D44C2211yescharacteristic
16C23×D44C2212yes—
17C23×C4×D11C2212yes—
18C23×Dic22C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2212yes—
22C22×C22⋊Dic11C2211yescharacteristic
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×(C2×D11)⋊C4C2211yescharacteristic
25C22×(C2×D11)⋊C4C2212yes—
26C22×(C2×D11)⋊C4C2212yes—
27C22×(C2×D11)⋊C4C2212yes—
28C22×(C2×D11)⋊C4C2212yes—
29C22×C4×Dic11C2211yescharacteristic
30C2×#66946—28no—
31C2×#66946C2218yescomplemented
32C2×#66938—28no—
33C2×#66938C2218yescomplemented
34C11×#397C2218yescomplemented
35C2×C11×#95C2211yescharacteristic
36C2×C11×#95C2212yes—
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2211yescharacteristic
40C2×C11⋊#95C2212yes—
41#10622606C2218yescomplemented
42#10622573C22116yescomplemented
43#10622573C2218yescomplemented
44#10622569C22116yescomplemented
45#10622286C22116yescomplemented
46#10622284C2218yescomplemented
47#10622278C22116yescomplemented
48#10622264C2218yescomplemented
49C25×C11C2311yescharacteristic
50C24×D11C2311yescharacteristic
51C24×D11C2312yes—
52C23×C4×C11C2311yescharacteristic
53C23×C4×C11C2312yes—
54C23×C4×C11C2312yes—
55C23×C4×C11C2311yescharacteristic
56C22×C22⋊D11—28no—
57C22×C22⋊D11—24no—
58C22×C22⋊D11—44no—
59C22×C22⋊D11—44no—
60C22×C22⋊D11—44no—
61C22×C22⋊D11C2314yes—
62C22×C22⋊D11C2318yes—
63C23×Dic11C2311yescharacteristic
64C23×Dic11C2312yes—
65C23×Dic11C2311yescharacteristic
66C23×Dic11C2311yescharacteristic
67C22×D44—28no—
68C22×D44—24no—
69C22×D44—28no—
70C22×D44—44no—
71C22×D44—44no—
72C22×D44C2314yes—
73C22×D44C2318yes—
74C22×C4×D11—28no—
75C22×C4×D11—44no—
76C22×C4×D11—44no—
77C22×C4×D11C2318yes—
78C22×Dic22—24no—
79C22×Dic22—44no—
80C22×Dic22C2314yes—
81C2×C11×C4⋊C4—24no—
82C2×C11×C4⋊C4C2314yes—
83C2×C11×C22⋊C4—24no—
84C2×C11×C22⋊C4—44no—
85C2×C11×C22⋊C4C2314yes—
86C2×C11×C22⋊C4C2318yes—
87C2×C22⋊Dic11—24no—
88C2×C22⋊Dic11C2314yes—
89C2×(C2×D11)⋊C4—24no—
90C2×(C2×D11)⋊C4—24no—
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)⋊C4C2314yes—
97C2×(C2×D11)⋊C4C2318yes—
98C2×(C2×D11)⋊C4C2318yes—
99C2×(C2×D11)⋊C4C2318yes—
100C2×(C2×D11)⋊C4C2318yes—
101C2×C4×Dic11D418yescomplemented
102C2×C4×Dic11C2314yes—
103#66946—232no—
104#66938—232no—
105C11×#95C2314yes—
106C11×#95C2318yes—
107C11⋊#95C2318yes—
108C11⋊#95C2318yes—
109C11⋊#95C2314yes—
110C11⋊#95C2318yes—
111C2×#2631—111nomaximal, Sylow
112C24×C11—22no—
113C24×C11—24no—
114C24×C11—22no—
115C24×C11—24no—
116C24×C11—22no—
117C24×C11C2412yes—
118C24×C11C2411yescharacteristic
119C23×D11—24no—
120C23×D11—24no—
121C23×D11—24no—
122C23×D11—24no—
123C23×D11—24no—
124C23×D11—24no—
125C23×D11—22no—
126C23×D11—24no—
127C23×D11—22no—
128C23×D11—22no—
129C23×D11—24no—
130C23×D11#4118yes—
131C23×D11C2412yes—
132C23×D11C2414yes—
133C22×C4×C11—24no—
134C22×C4×C11—22no—
135C22×C4×C11—24no—
136C22×C4×C11—24no—
137C22×C4×C11—24no—
138C22×C4×C11—24no—
139C22×C4×C11—24no—
140C22×C4×C11—24no—
141C22×C4×C11—24no—
142C22×C4×C11C2×D414yes—
143C22×C4×C11C2414yes—
144C22×C4×C11C2414yes—
145C22×C4×C11C2412yes—
146C22×C4×C11C2412yes—
147C2×C22⋊D11—28no—
148C2×C22⋊D11—216no—
149C2×C22⋊D11—48no—
150C2×C22⋊D11—48no—
151C2×C22⋊D11—48no—
152C2×C22⋊D11—432no—
153C2×C22⋊D11—416no—
154C22×Dic11—22no—
155C22×Dic11—24no—
156C22×Dic11—24no—
157C22×Dic11—22no—
158C22×Dic11—22no—
159C22×Dic11—24no—
160C22×Dic11—24no—
161C22×Dic11—24no—
162C22×Dic11C2×D414yes—
163C22×Dic11C2×D414yes—
164C22×Dic11C2414yes—
165C22×Dic11C2412yes—
166C22×Dic11C2412yes—
167C22×Dic11C2412yes—
168C2×D44—232no—
169C2×D44—216no—
170C2×D44—216no—
171C2×D44—28no—
172C2×D44—48no—
173C2×D44—48no—
174C2×D44—432no—
175C2×C4×D11—216no—
176C2×C4×D11—48no—
177C2×C4×D11—48no—
178C2×C4×D11—432no—
179C2×Dic22—28no—
180C2×Dic22—48no—
181C2×Dic22—416no—
182C11×C4⋊C4—28no—
183C11×C22⋊C4—28no—
184C11×C22⋊C4—48no—
185C22⋊Dic11—28no—
186(C2×D11)⋊C4—28no—
187(C2×D11)⋊C4—216no—
188(C2×D11)⋊C4—28no—
189(C2×D11)⋊C4—48no—
190(C2×D11)⋊C4—48no—
191(C2×D11)⋊C4—48no—
192C4×Dic11C2×D4116yescomplemented
193C22×#124—111no—
194C22×C4×D4—111no—
195#2631—1116no—
196C2×#397—111no—
197C2×#397D1111yescharacteristic, complemented
198C2×#393—112no—
199C2×#392—111no—
200C2×#392—112no—
201C2×#392—111no—
202C2×#386—112no—
203C2×#386—112no—
204C2×#383—111no—
205C23×C11—22no—
206C23×C11—24no—
207C23×C11—22no—
208C23×C11—22no—
209C23×C11—24no—
210C23×C11—44no—
211C23×C11—44no—
212C23×C11—44no—
213C23×C11—48no—
214C23×C11—48no—
215C23×C11C22×D412yes—
216C23×C11C2×#4114yes—
217C23×C11H(5,𝔽2)12yes—
218C23×C11H(5,𝔽2)12yes—
219C23×C11H(5,𝔽2)14yes—
220C23×C11C2511yescharacteristic
221C22×D11—216no—
222C22×D11—216no—
223C22×D11—216no—
224C22×D11—24no—
225C22×D11—24no—
226C22×D11—24no—
227C22×D11—24no—
228C22×D11—24no—
229C22×D11—24no—
230C22×D11—22no—
231C22×D11—24no—
232C22×D11—22no—
233C22×D11—22no—
234C22×D11—24no—
235C22×D11—48no—
236C22×D11—48no—
237C22×D11—48no—
238C22×D11—48no—
239C22×D11—44no—
240C22×D11—44no—
241C22×D11—44no—
242C22×D11—48no—
243C22×D11—48no—
244C22×D11C2×#4118yes—
245C2×C4×C11—28no—
246C2×C4×C11—24no—
247C2×C4×C11—22no—
248C2×C4×C11—24no—
249C2×C4×C11—24no—
250C2×C4×C11—24no—
251C2×C4×C11—24no—
252C2×C4×C11—24no—
253C2×C4×C11—24no—
254C2×C4×C11—24no—
255C2×C4×C11—44no—
256C2×C4×C11—48no—
257C2×C4×C11—48no—
258C2×C4×C11C22×D414yes—
259C22⋊D11—416no—
260C22⋊D11—432no—
261C2×Dic11—28no—
262C2×Dic11—28no—
263C2×Dic11—24no—
264C2×Dic11—22no—
265C2×Dic11—22no—
266C2×Dic11—22no—
267C2×Dic11—24no—
268C2×Dic11—24no—
269C2×Dic11—24no—
270C2×Dic11—24no—
271C2×Dic11—44no—
272C2×Dic11—48no—
273C2×Dic11C22×D414yes—
274C2×Dic11C22×D414yes—
275D44—232no—
276D44—432no—
277C4×D11—432no—
278Dic22—416no—
279C23×Q8—111no—
280C23×D4—111no—
281C23×D4—112no—
282C23×D4—111no—
283C23×D4—112no—
284C24×C4—112no—
285C2×#124—118no—
286C2×#124—228no—
287C2×C4×D4—118no—
288C2×C4×D4—228no—
289C22×C4⋊C4C2×D1111yescharacteristic
290C22×C22⋊C4—111no—
291C22×C22⋊C4—112no—
292C22×C22⋊C4—111no—
293C22×C22⋊C4—111no—
294C22×C22⋊C4—112no—
295C22×C22⋊C4—112no—
296C22×C22⋊C4—112no—
297C22×C22⋊C4C2×D1111yescharacteristic
298C22×C22⋊C4C2×D1112yes—
299C22×C42—111no—
300#397—118no—
301#397C2×D1118yescomplemented
302#393—1116no—
303#392—1116no—
304#392—118no—
305#392—118no—
306#386—1116no—
307#386—1116no—
308#383—118no—
309C2×#95—112no—
310C2×#95—111no—
311C2×#95—112no—
312C2×#95—112no—
313C2×#95C2×D1111yescharacteristic
314C2×#95C2×D1112yes—
315C22×C11—42no—
316C22×C11—42no—
317C22×C11—42no—
318C22×C11—44no—
319C22×C11—44no—
320C22×C11—88no—
321C22×C11#52514yes—
322C22×C11#53514yes—
323C22×C11#53514yes—
324C22×C11#53818yes—
325C22×C11#53818yes—
326C22×C11C23×D411yescharacteristic
327C22×C11C22×#4112yes—
328C22×C11C2×H(5,𝔽2)11yescharacteristic
329C22×C11C2×H(5,𝔽2)11yescharacteristic
330C22×C11C2×H(5,𝔽2)12yes—
331C2×D11—28no—
332C2×D11—28no—
333C2×D11—28no—
334C2×D11—432no—
335C2×D11—44no—
336C2×D11—44no—
337C2×D11—44no—
338C2×D11—44no—
339C2×D11—42no—
340C2×D11—42no—
341C2×D11—42no—
342C2×D11—44no—
343C2×D11—44no—
344C2×D11—88no—
345C4×C11—24no—
346C4×C11—42no—
347C4×C11—44no—
348C4×C11—44no—
349Dic11—24no—
350Dic11—24no—
351Dic11—42no—
352Dic11—44no—
353C25—112no—
354C25—111no—
355C25C22×D1111yescharacteristic
356C22×Q8—114no—
357C22×Q8—224no—
358C22×Q8—444no—
359C22×D4—114no—
360C22×D4—118no—
361C22×D4—114no—
362C22×D4—118no—
363C22×D4—228no—
364C22×D4—228no—
365C22×D4—224no—
366C22×D4—228no—
367C22×D4—224no—
368C22×D4—444no—
369C22×D4—444no—
370C22×D4—444no—
371C22×D4—444no—
372C22×D4—444no—
373C23×C4—111no—
374C23×C4—111no—
375C23×C4—111no—
376C23×C4—112no—
377C23×C4—118no—
378C23×C4—228no—
379C23×C4—444no—
380C23×C4—444no—
381C23×C4C22×D1111yescharacteristic
382C23×C4C22×D1112yes—
383C23×C4C22×D1112yes—
384C23×C4C22×D1111yescharacteristic
385#124—2232no—
386C4×D4—2232no—
387C2×C4⋊C4—24no—
388C2×C4⋊C4C22×D1114yes—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—44no—
391C2×C22⋊C4—114no—
392C2×C22⋊C4—118no—
393C2×C22⋊C4—114no—
394C2×C22⋊C4—114no—
395C2×C22⋊C4—118no—
396C2×C22⋊C4—118no—
397C2×C22⋊C4—118no—
398C2×C22⋊C4—228no—
399C2×C22⋊C4—224no—
400C2×C22⋊C4—224no—
401C2×C22⋊C4—224no—
402C2×C22⋊C4—444no—
403C2×C22⋊C4—444no—
404C2×C22⋊C4—444no—
405C2×C22⋊C4C22×D1114yes—
406C2×C22⋊C4C22×D1118yes—
407C2×C42—118no—
408C2×C42—114no—
409#95—118no—
410#95—118no—
411#95—114no—
412#95—118no—
413#95C22×D1114yes—
414#95C22×D1118yes—
415C2×C11—82no—
416C2×C11#263118yescomplemented
417C2×C11C2×#52511yescharacteristic
418C2×C11C2×#53511yescharacteristic
419C2×C11C2×#53511yescharacteristic
420C2×C11C2×#53812yes—
421C2×C11C2×#53812yes—
422D11—48no—
423D11—82no—
424C24—22no—
425C24—22no—
426C24—24no—
427C24—22no—
428C24—24no—
429C24—118no—
430C24—114no—
431C24—112no—
432C24—224no—
433C24—224no—
434C24—224no—
435C24—224no—
436C24—224no—
437C24—224no—
438C24—222no—
439C24—222no—
440C24—224no—
441C24—222no—
442C24—224no—
443C24C23×D1112yes—
444C24C23×D1111yescharacteristic
445C2×Q8—228no—
446C2×Q8—448no—
447C2×Q8—4416no—
448C2×D4—2216no—
449C2×D4—2232no—
450C2×D4—2216no—
451C2×D4—228no—
452C2×D4—2216no—
453C2×D4—228no—
454C2×D4—448no—
455C2×D4—448no—
456C2×D4—4432no—
457C2×D4—448no—
458C2×D4—448no—
459C2×D4—448no—
460C2×D4—4416no—
461C2×D4—4432no—
462C22×C4—24no—
463C22×C4—22no—
464C22×C4—24no—
465C22×C4—24no—
466C22×C4—24no—
467C22×C4—24no—
468C22×C4—24no—
469C22×C4—24no—
470C22×C4—24no—
471C22×C4—114no—
472C22×C4—114no—
473C22×C4—112no—
474C22×C4—112no—
475C22×C4—114no—
476C22×C4—112no—
477C22×C4—2216no—
478C22×C4—222no—
479C22×C4—222no—
480C22×C4—224no—
481C22×C4—222no—
482C22×C4—224no—
483C22×C4—224no—
484C22×C4—224no—
485C22×C4—224no—
486C22×C4—448no—
487C22×C4—448no—
488C22×C4—4432no—
489C22×C4D4×D1114yes—
490C22×C4C23×D1114yes—
491C22×C4C23×D1114yes—
492C22×C4C23×D1112yes—
493C22×C4C23×D1112yes—
494C4⋊C4—28no—
495C22⋊C4—28no—
496C22⋊C4—48no—
497C22⋊C4—2216no—
498C22⋊C4—228no—
499C22⋊C4—228no—
500C22⋊C4—228no—
501C22⋊C4—448no—
502C22⋊C4—448no—
503C22⋊C4—448no—
504C42—1116no—
505C11C2×#263111yescharacteristic, complemented, Sylow
506C23—22no—
507C23—22no—
508C23—24no—
509C23—22no—
510C23—24no—
511C23—48no—
512C23—44no—
513C23—44no—
514C23—48no—
515C23—44no—
516C23—118no—
517C23—2216no—
518C23—2216no—
519C23—2216no—
520C23—224no—
521C23—224no—
522C23—224no—
523C23—224no—
524C23—224no—
525C23—224no—
526C23—222no—
527C23—222no—
528C23—224no—
529C23—222no—
530C23—224no—
531C23—448no—
532C23—448no—
533C23—448no—
534C23—448no—
535C23—448no—
536C23—444no—
537C23—444no—
538C23—448no—
539C23—444no—
540C23C2×D4×D1112yes—
541C23#6703712yes—
542C23#41×D1114yes—
543C23#6704212yes—
544C23#6704214yes—
545C23C24×D1111yescharacteristic
546Q8—4416no—
547D4—2232no—
548D4—4432no—
549D4—4416no—
550D4—4432no—
551C2×C4—28no—
552C2×C4—24no—
553C2×C4—22no—
554C2×C4—24no—
555C2×C4—24no—
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—24no—
560C2×C4—24no—
561C2×C4—48no—
562C2×C4—48no—
563C2×C4—44no—
564C2×C4—114no—
565C2×C4—114no—
566C2×C4—228no—
567C2×C4—222no—
568C2×C4—222no—
569C2×C4—224no—
570C2×C4—228no—
571C2×C4—222no—
572C2×C4—224no—
573C2×C4—224no—
574C2×C4—224no—
575C2×C4—224no—
576C2×C4—4432no—
577C2×C4—448no—
578C2×C4—444no—
579C2×C4C2×D4×D1114yes—
580C22—42no—
581C22—42no—
582C22—44no—
583C22—44no—
584C22—42no—
585C22—88no—
586C22—228no—
587C22—228no—
588C22—228no—
589C22—4432no—
590C22—444no—
591C22—444no—
592C22—444no—
593C22—444no—
594C22—442no—
595C22—442no—
596C22—444no—
597C22—444no—
598C22—442no—
599C22—888no—
600C22#1062313814yes—
601C22#1062318714yes—
602C22#1062318818yes—
603C22#1062320514yes—
604C22#1062323518yes—
605C22C22×D4×D1111yescharacteristic
606C22C2×#6703711yescharacteristic
607C22C2×#41×D1112yes—
608C22C2×#6704211yescharacteristic
609C22C2×#6704212yes—
610C4—24no—
611C4—44no—
612C4—42no—
613C4—44no—
614C4—224no—
615C4—224no—
616C4—442no—
617C4—444no—
618C2—82no—
619C2—448no—
620C2—882no—
621C2#1307447018yesdirect product factor
622C2C2×#1062318711yescharacteristic
623C2C2×#1062313811yescharacteristic
624C2C2×#1062320511yescharacteristic
625C2C2×#1062318812yes—
626C2C2×#1062323512yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#397C2
socleC24×C11C24
hypercenterC2×#397D11
hypocenterC11C2×#2631
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#397

Complements

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

NH ≅ G/Ntype
1. C22×#66938C2semidirect
2. C22×#66946C2semidirect
3. #13074470C2direct (N × H)
4. C2×#10622606C2semidirect
5. C2×#10622286C2semidirect
6. C2×#10622284C2semidirect
7. C2×#10622573C2semidirect
8. C2×#10622573C2semidirect
9. C2×#10622278C2semidirect
10. C2×#10622569C2semidirect
11. C2×#10622264C2semidirect
12. C2×C11×#397C2semidirect
31. C2×#66946C22semidirect
33. C2×#66938C22semidirect
34. C11×#397C22semidirect
41. #10622606C22semidirect
42. #10622573C22semidirect
43. #10622573C22semidirect
44. #10622569C22semidirect
45. #10622286C22semidirect
46. #10622284C22semidirect
47. #10622278C22semidirect
48. #10622264C22semidirect
101. C2×C4×Dic11D4semidirect
192. C4×Dic11C2×D4semidirect
197. C2×#397D11semidirect
301. #397C2×D11semidirect
416. C2×C11#2631semidirect
505. C11C2×#2631semidirect
621. C2#13074470direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669382
C22×#669462
#130744702
C2×#106226062
C2×#106222862
C2×#106222842
C2×#106225732
C2×#106222782
C2×#106225692
C2×#106222642
C2×C11×#3972
C2×#263111