Finite Group Databasebeta

← C2×#13076663 #14960289

Subgroups — C2×#13076663 #14960289

Order 2816.

3342 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×#66989C211yesmaximal, characteristic, complemented
2C22×#66938C211yesmaximal, characteristic, complemented
3#13076663C2116yesmaximal, direct product factor
4C2×#10622572C212yesmaximal, complemented
5C2×#10622835C212yesmaximal, complemented
6C2×#10622286C211yesmaximal, characteristic, complemented
7C2×#10622560C211yesmaximal, characteristic, complemented
8C2×#10622560C212yesmaximal, complemented
9C2×#10622836C211yesmaximal, characteristic, complemented
10C2×#10622836C212yesmaximal, complemented
11C2×#10622263C211yesmaximal, characteristic, complemented
12C2×C11×#392C211yesmaximal, characteristic, complemented
13C23×D4×C11C2211yescharacteristic
14C23×D4×C11C2212yes—
15C23×C22⋊D11C2211yescharacteristic
16C23×C22⋊D11C2212yes—
17C23×Dic22C2211yescharacteristic
18C23×Dic22C2211yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2212yes—
21C22×C22⋊Dic11C2211yescharacteristic
22C22×C22⋊Dic11C2212yes—
23C22×C22⋊Dic11C2212yes—
24C22×C22⋊Dic11C2212yes—
25C22×C22⋊Dic11C2212yes—
26C2×#66989—28no—
27C2×#66989C2218yescomplemented
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C22×(C2×D11)⋊C4C2212yes—
31C22×Dic11⋊C4C2212yes—
32C22×C4×Dic11C2211yescharacteristic
33C2×#66938—28no—
34C2×#66938C2218yescomplemented
35C11×#392C2218yescomplemented
36C2×C11×#95C2211yescharacteristic
37#10622836C2218yescomplemented
38#10622836C22116yescomplemented
39#10622835C22116yescomplemented
40C2×C11⋊#95C2211yescharacteristic
41C2×C11⋊#95C2212yes—
42C2×C11⋊#95C2212yes—
43C2×C11⋊#95C2212yes—
44#10622572C22116yescomplemented
45#10622560C22116yescomplemented
46#10622560C2218yescomplemented
47#10622286C2218yescomplemented
48#10622263C2218yescomplemented
49C25×C11C2312yes—
50C25×C11C2311yescharacteristic
51C24×D11C2311yescharacteristic
52C22×D4×C11—24no—
53C22×D4×C11—44no—
54C22×D4×C11—44no—
55C22×D4×C11—44no—
56C22×D4×C11—44no—
57C22×D4×C11C2314yes—
58C22×D4×C11C2318yes—
59C23×C4×C11C2312yes—
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C22×C22⋊D11—24no—
63C22×C22⋊D11—44no—
64C22×C22⋊D11—44no—
65C22×C22⋊D11—44no—
66C22×C22⋊D11—44no—
67C22×C22⋊D11C2314yes—
68C22×C22⋊D11C2318yes—
69C23×Dic11C2312yes—
70C23×Dic11C2311yescharacteristic
71C23×Dic11C2312yes—
72C23×Dic11C2311yescharacteristic
73C23×Dic11C2311yescharacteristic
74C22×Dic22—24no—
75C22×Dic22—24no—
76C22×Dic22—44no—
77C22×Dic22—44no—
78C22×Dic22C2314yes—
79C22×Dic22C2314yes—
80C2×C11×C22⋊C4—24no—
81C2×C11×C22⋊C4—44no—
82C2×C11×C22⋊C4C2314yes—
83C2×C11×C22⋊C4C2318yes—
84C2×C22⋊Dic11—24no—
85C2×C22⋊Dic11—28no—
86C2×C22⋊Dic11—28no—
87C2×C22⋊Dic11—44no—
88C2×C22⋊Dic11—44no—
89C2×C22⋊Dic11C2314yes—
90C2×C22⋊Dic11C2318yes—
91C2×C22⋊Dic11C2318yes—
92C2×C22⋊Dic11C2318yes—
93C2×C22⋊Dic11C2318yes—
94#66989—232no—
95C2×(C2×D11)⋊C4—24no—
96C2×(C2×D11)⋊C4—24no—
97C2×(C2×D11)⋊C4—44no—
98C2×(C2×D11)⋊C4C2314yes—
99C2×(C2×D11)⋊C4C2314yes—
100C2×(C2×D11)⋊C4C2318yes—
101C2×Dic11⋊C4—44no—
102C2×Dic11⋊C4C2318yes—
103C2×C4×Dic11D418yescomplemented
104C2×C4×Dic11C2314yes—
105#66938—232no—
106C11×#95C2314yes—
107C11⋊#95C2314yes—
108C11⋊#95C2318yes—
109C11⋊#95C2318yes—
110C11⋊#95C2318yes—
111C2×#2819—111nomaximal, Sylow
112C24×C11—24no—
113C24×C11—22no—
114C24×C11—24no—
115C24×C11—24no—
116C24×C11—24no—
117C24×C11—24no—
118C24×C11—24no—
119C24×C11—24no—
120C24×C11—24no—
121C24×C11—22no—
122C24×C11—24no—
123C24×C11—22no—
124C24×C11C2414yes—
125C24×C11C2412yes—
126C24×C11C2411yescharacteristic
127C23×D11—22no—
128C23×D11—24no—
129C23×D11—24no—
130C23×D11—22no—
131C23×D11—22no—
132C23×D11C2412yes—
133C2×D4×C11—28no—
134C2×D4×C11—48no—
135C2×D4×C11—48no—
136C2×D4×C11—48no—
137C2×D4×C11—48no—
138C2×D4×C11—416no—
139C2×D4×C11—432no—
140C22×C4×C11—24no—
141C22×C4×C11—22no—
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×C11C2412yes—
149C22×C4×C11C2412yes—
150C2×C22⋊D11—28no—
151C2×C22⋊D11—48no—
152C2×C22⋊D11—48no—
153C2×C22⋊D11—48no—
154C2×C22⋊D11—48no—
155C2×C22⋊D11—416no—
156C2×C22⋊D11—432no—
157C22×Dic11—22no—
158C22×Dic11—24no—
159C22×Dic11—22no—
160C22×Dic11—24no—
161C22×Dic11—24no—
162C22×Dic11—24no—
163C22×Dic11—24no—
164C22×Dic11—24no—
165C22×Dic11—24no—
166C22×Dic11—24no—
167C22×Dic11—22no—
168C22×Dic11C2×D414yes—
169C22×Dic11C2×D414yes—
170C22×Dic11C2414yes—
171C22×Dic11C2412yes—
172C22×Dic11C2414yes—
173C22×Dic11C2412yes—
174C22×Dic11C2412yes—
175C2×Dic22—28no—
176C2×Dic22—28no—
177C2×Dic22—48no—
178C2×Dic22—48no—
179C2×Dic22—416no—
180C2×Dic22—416no—
181C11×C22⋊C4—28no—
182C11×C22⋊C4—48no—
183C22⋊Dic11—28no—
184C22⋊Dic11—216no—
185C22⋊Dic11—216no—
186C22⋊Dic11—48no—
187C22⋊Dic11—48no—
188(C2×D11)⋊C4—28no—
189(C2×D11)⋊C4—28no—
190(C2×D11)⋊C4—48no—
191Dic11⋊C4—48no—
192C4×Dic11C2×D4116yescomplemented
193C22×#124—111no—
194C22×#124—111no—
195#2819—1116no—
196C2×#394—112no—
197C2×#394—112no—
198C2×#393—111no—
199C2×#393—112no—
200C2×#393—111no—
201C2×#392—112no—
202C2×#392—111no—
203C2×#392D1111yescharacteristic, complemented
204C2×#382—111no—
205C23×C11—24no—
206C23×C11—22no—
207C23×C11—24no—
208C23×C11—24no—
209C23×C11—24no—
210C23×C11—24no—
211C23×C11—24no—
212C23×C11—24no—
213C23×C11—24no—
214C23×C11—22no—
215C23×C11—24no—
216C23×C11—22no—
217C23×C11—44no—
218C23×C11—48no—
219C23×C11—48no—
220C23×C11—44no—
221C23×C11—48no—
222C23×C11—44no—
223C23×C11—48no—
224C23×C11—48no—
225C23×C11—48no—
226C23×C11—48no—
227C23×C11—48no—
228C23×C11—48no—
229C23×C11C22×D412yes—
230C23×C11H(5,𝔽2)14yes—
231C23×C11H(5,𝔽2)14yes—
232C23×C11H(5,𝔽2)12yes—
233C23×C112−1+412yes—
234C23×C11C2511yescharacteristic
235C22×D11—22no—
236C22×D11—24no—
237C22×D11—24no—
238C22×D11—22no—
239C22×D11—22no—
240C22×D11—44no—
241C22×D11—44no—
242C22×D11—44no—
243C22×D11—48no—
244C22×D11—48no—
245D4×C11—416no—
246D4×C11—432no—
247C2×C4×C11—28no—
248C2×C4×C11—24no—
249C2×C4×C11—22no—
250C2×C4×C11—24no—
251C2×C4×C11—24no—
252C2×C4×C11—24no—
253C2×C4×C11—24no—
254C2×C4×C11—44no—
255C2×C4×C11—48no—
256C2×C4×C11C22×D414yes—
257C22⋊D11—416no—
258C22⋊D11—432no—
259C2×Dic11—28no—
260C2×Dic11—28no—
261C2×Dic11—22no—
262C2×Dic11—24no—
263C2×Dic11—22no—
264C2×Dic11—22no—
265C2×Dic11—24no—
266C2×Dic11—24no—
267C2×Dic11—24no—
268C2×Dic11—24no—
269C2×Dic11—24no—
270C2×Dic11—24no—
271C2×Dic11—24no—
272C2×Dic11—44no—
273C2×Dic11—48no—
274C2×Dic11—48no—
275C2×Dic11C22×D414yes—
276C2×Dic11C22×D414yes—
277Dic22—416no—
278Dic22—416no—
279C23×Q8—111no—
280C23×Q8—111no—
281C23×D4—111no—
282C23×D4—112no—
283C23×D4C2×D1111yescharacteristic
284C23×D4C2×D1112yes—
285C2×#124—118no—
286C2×#124—118no—
287C2×#124—228no—
288C2×#124—228no—
289C22×C4⋊C4—112no—
290C22×C22⋊C4—112no—
291C22×C22⋊C4—111no—
292C22×C22⋊C4—112no—
293C22×C22⋊C4—111no—
294C22×C22⋊C4—111no—
295C22×C22⋊C4—112no—
296C22×C22⋊C4—112no—
297C22×C22⋊C4—112no—
298C22×C22⋊C4C2×D1111yescharacteristic
299C22×C22⋊C4C2×D1112yes—
300C22×C42—111no—
301#394—1116no—
302#394—1116no—
303#393—1116no—
304#393—118no—
305#393—118no—
306#392—1116no—
307#392—118no—
308#392C2×D1118yescomplemented
309#382—118no—
310C2×#95—112no—
311C2×#95—111no—
312C2×#95—112no—
313C2×#95—112no—
314C2×#95C2×D1111yescharacteristic
315C22×C11—44no—
316C22×C11—44no—
317C22×C11—42no—
318C22×C11—42no—
319C22×C11—44no—
320C22×C11—42no—
321C22×C11—44no—
322C22×C11—44no—
323C22×C11—44no—
324C22×C11—44no—
325C22×C11—44no—
326C22×C11—44no—
327C22×C11—88no—
328C22×C11—816no—
329C22×C11#53514yes—
330C22×C11#53514yes—
331C22×C11#53714yes—
332C22×C11H(3,𝔽4)18yes—
333C22×C11#56218yes—
334C22×C11C23×D411yescharacteristic
335C22×C11C2×H(5,𝔽2)12yes—
336C22×C11C2×H(5,𝔽2)12yes—
337C22×C11C2×H(5,𝔽2)11yescharacteristic
338C22×C11C2×2−1+411yescharacteristic
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—
348Dic11—24no—
349Dic11—24no—
350Dic11—42no—
351Dic11—44no—
352Dic11—44no—
353C25—111no—
354C25C22×D1111yescharacteristic
355C25C22×D1112yes—
356C22×Q8—114no—
357C22×Q8—114no—
358C22×Q8—224no—
359C22×Q8—224no—
360C22×Q8—444no—
361C22×Q8—444no—
362C22×D4—24no—
363C22×D4—44no—
364C22×D4—44no—
365C22×D4—44no—
366C22×D4—44no—
367C22×D4—114no—
368C22×D4—118no—
369C22×D4—224no—
370C22×D4—444no—
371C22×D4—444no—
372C22×D4—444no—
373C22×D4—444no—
374C22×D4C22×D1114yes—
375C22×D4C22×D1118yes—
376C23×C4—111no—
377C23×C4—111no—
378C23×C4—112no—
379C23×C4—111no—
380C23×C4—112no—
381C23×C4C22×D1111yescharacteristic
382C23×C4C22×D1112yes—
383C23×C4C22×D1111yescharacteristic
384#124—2232no—
385#124—2232no—
386C2×C4⋊C4—118no—
387C2×C4⋊C4—444no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—44no—
390C2×C22⋊C4—118no—
391C2×C22⋊C4—118no—
392C2×C22⋊C4—114no—
393C2×C22⋊C4—114no—
394C2×C22⋊C4—114no—
395C2×C22⋊C4—118no—
396C2×C22⋊C4—118no—
397C2×C22⋊C4—118no—
398C2×C22⋊C4—224no—
399C2×C22⋊C4—224no—
400C2×C22⋊C4—228no—
401C2×C22⋊C4—228no—
402C2×C22⋊C4—224no—
403C2×C22⋊C4—444no—
404C2×C22⋊C4—444no—
405C2×C22⋊C4—444no—
406C2×C22⋊C4C22×D1114yes—
407C2×C22⋊C4C22×D1118yes—
408C2×C42—118no—
409C2×C42—114no—
410#95—118no—
411#95—114no—
412#95—118no—
413#95—118no—
414#95C22×D1114yes—
415C2×C11—84no—
416C2×C11—82no—
417C2×C11#281918yescomplemented
418C2×C11C2×#53511yescharacteristic
419C2×C11C2×#53511yescharacteristic
420C2×C11C2×#53711yescharacteristic
421C2×C11C2×H(3,𝔽4)12yes—
422C2×C11C2×#56212yes—
423D11—82no—
424C24—22no—
425C24—24no—
426C24—24no—
427C24—24no—
428C24—24no—
429C24—24no—
430C24—22no—
431C24—24no—
432C24—24no—
433C24—24no—
434C24—22no—
435C24—24no—
436C24—112no—
437C24—222no—
438C24—224no—
439C24—224no—
440C24—222no—
441C24—222no—
442C24C23×D1112yes—
443C24C23×D1114yes—
444C24C23×D1111yescharacteristic
445C2×Q8—228no—
446C2×Q8—228no—
447C2×Q8—448no—
448C2×Q8—448no—
449C2×Q8—4416no—
450C2×Q8—4416no—
451C2×D4—28no—
452C2×D4—48no—
453C2×D4—48no—
454C2×D4—48no—
455C2×D4—48no—
456C2×D4—416no—
457C2×D4—432no—
458C2×D4—228no—
459C2×D4—448no—
460C2×D4—448no—
461C2×D4—448no—
462C2×D4—448no—
463C2×D4—4416no—
464C2×D4—4432no—
465C22×C4—24no—
466C22×C4—22no—
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—114no—
477C22×C4—112no—
478C22×C4—222no—
479C22×C4—224no—
480C22×C4—222no—
481C22×C4—222no—
482C22×C4—224no—
483C22×C4—224no—
484C22×C4—224no—
485C22×C4—224no—
486C22×C4—224no—
487C22×C4—224no—
488C22×C4—224no—
489C22×C4D4×D1114yes—
490C22×C4C23×D1114yes—
491C22×C4C23×D1112yes—
492C22×C4C23×D1112yes—
493C4⋊C4—448no—
494C22⋊C4—28no—
495C22⋊C4—48no—
496C22⋊C4—228no—
497C22⋊C4—228no—
498C22⋊C4—2216no—
499C22⋊C4—2216no—
500C22⋊C4—228no—
501C22⋊C4—448no—
502C22⋊C4—448no—
503C22⋊C4—448no—
504C42—1116no—
505C11C2×#281911yescharacteristic, complemented, Sylow
506C23—22no—
507C23—24no—
508C23—24no—
509C23—24no—
510C23—24no—
511C23—24no—
512C23—22no—
513C23—24no—
514C23—24no—
515C23—24no—
516C23—22no—
517C23—24no—
518C23—44no—
519C23—48no—
520C23—48no—
521C23—44no—
522C23—48no—
523C23—48no—
524C23—48no—
525C23—44no—
526C23—48no—
527C23—48no—
528C23—48no—
529C23—48no—
530C23—222no—
531C23—224no—
532C23—224no—
533C23—222no—
534C23—222no—
535C23—444no—
536C23—444no—
537C23—448no—
538C23—444no—
539C23—448no—
540C23C2×D4×D1112yes—
541C23#6703714yes—
542C23#6703714yes—
543C23#6703712yes—
544C23#6704312yes—
545C23C24×D1111yescharacteristic
546Q8—4416no—
547Q8—4416no—
548D4—416no—
549D4—432no—
550D4—4416no—
551D4—4432no—
552C2×C4—28no—
553C2×C4—24no—
554C2×C4—22no—
555C2×C4—24no—
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—44no—
560C2×C4—48no—
561C2×C4—114no—
562C2×C4—114no—
563C2×C4—228no—
564C2×C4—228no—
565C2×C4—222no—
566C2×C4—224no—
567C2×C4—222no—
568C2×C4—222no—
569C2×C4—224no—
570C2×C4—224no—
571C2×C4—224no—
572C2×C4—224no—
573C2×C4—224no—
574C2×C4—224no—
575C2×C4—224no—
576C2×C4—444no—
577C2×C4—448no—
578C2×C4—448no—
579C2×C4C2×D4×D1114yes—
580C22—42no—
581C22—44no—
582C22—44no—
583C22—42no—
584C22—42no—
585C22—44no—
586C22—44no—
587C22—44no—
588C22—44no—
589C22—44no—
590C22—44no—
591C22—44no—
592C22—88no—
593C22—816no—
594C22—442no—
595C22—442no—
596C22—442no—
597C22—444no—
598C22—444no—
599C22—888no—
600C22#1062312314yes—
601C22#1062312518yes—
602C22#1062313914yes—
603C22#1062315218yes—
604C22#1062324614yes—
605C22C22×D4×D1111yescharacteristic
606C22C2×#6703712yes—
607C22C2×#6703712yes—
608C22C2×#6703711yescharacteristic
609C22C2×#6704311yescharacteristic
610C4—24no—
611C4—42no—
612C4—44no—
613C4—224no—
614C4—224no—
615C4—442no—
616C4—444no—
617C4—444no—
618C2—82no—
619C2—84no—
620C2—882no—
621C2#1307666318yesdirect product factor
622C2C2×#1062324611yescharacteristic
623C2C2×#1062312311yescharacteristic
624C2C2×#1062313911yescharacteristic
625C2C2×#1062312512yes—
626C2C2×#1062315212yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#392C2
socleC24×C11C24
hypercenterC2×#392D11
hypocenterC11C2×#2819
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#392

Complements

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

NH ≅ G/Ntype
1. C22×#66989C2semidirect
2. C22×#66938C2semidirect
3. #13076663C2direct (N × H)
4. C2×#10622572C2semidirect
5. C2×#10622835C2semidirect
6. C2×#10622286C2semidirect
7. C2×#10622560C2semidirect
8. C2×#10622560C2semidirect
9. C2×#10622836C2semidirect
10. C2×#10622836C2semidirect
11. C2×#10622263C2semidirect
12. C2×C11×#392C2semidirect
27. C2×#66989C22semidirect
34. C2×#66938C22semidirect
35. C11×#392C22semidirect
37. #10622836C22semidirect
38. #10622836C22semidirect
39. #10622835C22semidirect
44. #10622572C22semidirect
45. #10622560C22semidirect
46. #10622560C22semidirect
47. #10622286C22semidirect
48. #10622263C22semidirect
103. C2×C4×Dic11D4semidirect
192. C4×Dic11C2×D4semidirect
203. C2×#392D11semidirect
308. #392C2×D11semidirect
417. C2×C11#2819semidirect
505. C11C2×#2819semidirect
621. C2#13076663direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669892
C22×#669382
#130766632
C2×#106225722
C2×#106228352
C2×#106222862
C2×#106225602
C2×#106228362
C2×#106222632
C2×C11×#3922
C2×#281911