Finite Group Databasebeta

← C2×#13076664 #14960291

Subgroups — C2×#13076664 #14960291

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×#67000C211yesmaximal, characteristic, complemented
2C22×#66938C211yesmaximal, characteristic, complemented
3#13076664C2116yesmaximal, direct product factor
4C2×#10622285C212yesmaximal, complemented
5C2×#10622572C212yesmaximal, complemented
6C2×#10622286C212yesmaximal, complemented
7C2×#10622844C211yesmaximal, characteristic, complemented
8C2×#10622284C211yesmaximal, characteristic, complemented
9C2×#10622573C212yesmaximal, complemented
10C2×#10622573C211yesmaximal, characteristic, complemented
11C2×#10622263C211yesmaximal, characteristic, complemented
12C2×C11×#393C211yesmaximal, characteristic, complemented
13C23×Q8×C11C2211yescharacteristic
14C23×C22⋊D11C2211yescharacteristic
15C23×C22⋊D11C2212yes—
16C23×D44C2211yescharacteristic
17C23×D44C2212yes—
18C23×Dic22C2211yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2212yes—
21C22×C22⋊Dic11C2211yescharacteristic
22C2×#67000—28no—
23C2×#67000C2218yescomplemented
24C22×(C2×D11)⋊C4C2211yescharacteristic
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C22×(C2×D11)⋊C4C2212yes—
27C22×(C2×D11)⋊C4C2212yes—
28C22×(C2×D11)⋊C4C2212yes—
29C22×(C2×D11)⋊C4C2212yes—
30C22×(C2×D11)⋊C4C2212yes—
31C22×Dic11⋊C4C2212yes—
32C22×C4×Dic11C2211yescharacteristic
33C2×#66938—28no—
34C2×#66938C2218yescomplemented
35C11×#393C2218yescomplemented
36C2×C11×#95C2211yescharacteristic
37C2×C11×#95C2212yes—
38#10622844C2218yescomplemented
39C2×C11⋊#95C2211yescharacteristic
40C2×C11⋊#95C2212yes—
41C2×C11⋊#95C2212yes—
42#10622573C22116yescomplemented
43#10622573C2218yescomplemented
44#10622572C22116yescomplemented
45#10622286C22116yescomplemented
46#10622285C22116yescomplemented
47#10622284C2218yescomplemented
48#10622263C2218yescomplemented
49C25×C11C2311yescharacteristic
50C24×D11C2312yes—
51C24×D11C2311yescharacteristic
52C22×Q8×C11—24no—
53C22×Q8×C11—44no—
54C22×Q8×C11C2314yes—
55C23×C4×C11C2312yes—
56C23×C4×C11C2312yes—
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C22×C22⋊D11—24no—
60C22×C22⋊D11—44no—
61C22×C22⋊D11—44no—
62C22×C22⋊D11—44no—
63C22×C22⋊D11—44no—
64C22×C22⋊D11C2314yes—
65C22×C22⋊D11C2318yes—
66C23×Dic11C2312yes—
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2311yescharacteristic
69C23×Dic11C2311yescharacteristic
70C22×D44—24no—
71C22×D44—44no—
72C22×D44—44no—
73C22×D44—44no—
74C22×D44—44no—
75C22×D44C2314yes—
76C22×D44C2318yes—
77C22×Dic22—24no—
78C22×Dic22—44no—
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⋊Dic11C2314yes—
86#67000—232no—
87C2×(C2×D11)⋊C4—24no—
88C2×(C2×D11)⋊C4—24no—
89C2×(C2×D11)⋊C4—28no—
90C2×(C2×D11)⋊C4—28no—
91C2×(C2×D11)⋊C4—44no—
92C2×(C2×D11)⋊C4—44no—
93C2×(C2×D11)⋊C4—44no—
94C2×(C2×D11)⋊C4C2314yes—
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—44no—
102C2×Dic11⋊C4C2318yes—
103C2×C4×Dic11D418yescomplemented
104C2×C4×Dic11C2314yes—
105#66938—232no—
106C11×#95C2314yes—
107C11×#95C2318yes—
108C11⋊#95C2318yes—
109C11⋊#95C2314yes—
110C11⋊#95C2318yes—
111C2×#2819—111nomaximal, Sylow
112C24×C11—22no—
113C24×C11—24no—
114C24×C11—24no—
115C24×C11—22no—
116C24×C11—22no—
117C24×C11C2412yes—
118C24×C11C2411yescharacteristic
119C23×D11—24no—
120C23×D11—22no—
121C23×D11—24no—
122C23×D11—24no—
123C23×D11—24no—
124C23×D11—24no—
125C23×D11—22no—
126C23×D11—24no—
127C23×D11—24no—
128C23×D11—24no—
129C23×D11—24no—
130C23×D11—22no—
131C23×D11C2414yes—
132C23×D11C2412yes—
133C2×Q8×C11—28no—
134C2×Q8×C11—48no—
135C2×Q8×C11—416no—
136C22×C4×C11—24no—
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×C11C2×D414yes—
146C22×C4×C11C2414yes—
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—22no—
159C22×Dic11—24no—
160C22×Dic11—24no—
161C22×Dic11—24no—
162C22×Dic11—24no—
163C22×Dic11—24no—
164C22×Dic11—22no—
165C22×Dic11C2×D414yes—
166C22×Dic11C2×D414yes—
167C22×Dic11C2414yes—
168C22×Dic11C2412yes—
169C22×Dic11C2412yes—
170C22×Dic11C2412yes—
171C2×D44—28no—
172C2×D44—48no—
173C2×D44—48no—
174C2×D44—48no—
175C2×D44—48no—
176C2×D44—416no—
177C2×D44—432no—
178C2×Dic22—28no—
179C2×Dic22—48no—
180C2×Dic22—416no—
181C11×C22⋊C4—28no—
182C11×C22⋊C4—48no—
183C22⋊Dic11—28no—
184(C2×D11)⋊C4—28no—
185(C2×D11)⋊C4—216no—
186(C2×D11)⋊C4—216no—
187(C2×D11)⋊C4—28no—
188(C2×D11)⋊C4—48no—
189(C2×D11)⋊C4—48no—
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—112no—
199C2×#393—111no—
200C2×#393D1111yescharacteristic, complemented
201C2×#392—111no—
202C2×#392—112no—
203C2×#392—111no—
204C2×#382—111no—
205C23×C11—22no—
206C23×C11—24no—
207C23×C11—24no—
208C23×C11—22no—
209C23×C11—22no—
210C23×C11—44no—
211C23×C11—44no—
212C23×C11—44no—
213C23×C11—48no—
214C23×C11—48no—
215C23×C11C22×D412yes—
216C23×C11H(5,𝔽2)14yes—
217C23×C11H(5,𝔽2)14yes—
218C23×C11H(5,𝔽2)12yes—
219C23×C112−1+412yes—
220C23×C11C2511yescharacteristic
221C22×D11—24no—
222C22×D11—22no—
223C22×D11—24no—
224C22×D11—24no—
225C22×D11—24no—
226C22×D11—24no—
227C22×D11—22no—
228C22×D11—24no—
229C22×D11—24no—
230C22×D11—24no—
231C22×D11—24no—
232C22×D11—22no—
233C22×D11—48no—
234C22×D11—44no—
235C22×D11—44no—
236C22×D11—48no—
237C22×D11—48no—
238C22×D11—44no—
239C22×D11—48no—
240C22×D11—48no—
241C22×D11—48no—
242C22×D11—48no—
243C22×D11—48no—
244C22×D11—48no—
245Q8×C11—416no—
246C2×C4×C11—28no—
247C2×C4×C11—24no—
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—24no—
255C2×C4×C11—24no—
256C2×C4×C11—44no—
257C2×C4×C11—48no—
258C2×C4×C11—48no—
259C2×C4×C11C22×D414yes—
260C22⋊D11—416no—
261C22⋊D11—432no—
262C2×Dic11—28no—
263C2×Dic11—28no—
264C2×Dic11—22no—
265C2×Dic11—24no—
266C2×Dic11—22no—
267C2×Dic11—22no—
268C2×Dic11—24no—
269C2×Dic11—24no—
270C2×Dic11—24no—
271C2×Dic11—24no—
272C2×Dic11—44no—
273C2×Dic11—48no—
274C2×Dic11C22×D414yes—
275C2×Dic11C22×D414yes—
276D44—416no—
277D44—432no—
278Dic22—416no—
279C23×Q8—111no—
280C23×Q8C2×D1111yescharacteristic
281C23×D4—111no—
282C23×D4—112no—
283C23×D4—111no—
284C23×D4—112no—
285C2×#124—118no—
286C2×#124—118no—
287C2×#124—228no—
288C2×#124—228no—
289C22×C4⋊C4—112no—
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⋊C4—112no—
298C22×C22⋊C4C2×D1111yescharacteristic
299C22×C22⋊C4C2×D1112yes—
300C22×C42—111no—
301#394—1116no—
302#394—1116no—
303#393—118no—
304#393—1116no—
305#393C2×D1118yescomplemented
306#392—1116no—
307#392—118no—
308#392—118no—
309#382—118no—
310C2×#95—112no—
311C2×#95—111no—
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#53514yes—
322C22×C11#53514yes—
323C22×C11#53714yes—
324C22×C11H(3,𝔽4)18yes—
325C22×C11#56218yes—
326C22×C11C23×D411yescharacteristic
327C22×C11C2×H(5,𝔽2)12yes—
328C22×C11C2×H(5,𝔽2)12yes—
329C22×C11C2×H(5,𝔽2)11yescharacteristic
330C22×C11C2×2−1+411yescharacteristic
331C2×D11—42no—
332C2×D11—44no—
333C2×D11—44no—
334C2×D11—42no—
335C2×D11—44no—
336C2×D11—42no—
337C2×D11—44no—
338C2×D11—44no—
339C2×D11—44no—
340C2×D11—44no—
341C2×D11—44no—
342C2×D11—44no—
343C2×D11—816no—
344C2×D11—88no—
345C4×C11—24no—
346C4×C11—44no—
347C4×C11—42no—
348C4×C11—44no—
349Dic11—24no—
350Dic11—24no—
351Dic11—42no—
352Dic11—44no—
353C25—111no—
354C25—112no—
355C25C22×D1111yescharacteristic
356C22×Q8—24no—
357C22×Q8—44no—
358C22×Q8—114no—
359C22×Q8—224no—
360C22×Q8—444no—
361C22×Q8C22×D1114yes—
362C22×D4—114no—
363C22×D4—118no—
364C22×D4—114no—
365C22×D4—118no—
366C22×D4—224no—
367C22×D4—224no—
368C22×D4—444no—
369C22×D4—444no—
370C22×D4—444no—
371C22×D4—444no—
372C22×D4—444no—
373C22×D4—444no—
374C22×D4—444no—
375C22×D4—444no—
376C23×C4—111no—
377C23×C4—111no—
378C23×C4—111no—
379C23×C4—112no—
380C23×C4C22×D1111yescharacteristic
381C23×C4C22×D1112yes—
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—114no—
391C2×C22⋊C4—118no—
392C2×C22⋊C4—114no—
393C2×C22⋊C4—118no—
394C2×C22⋊C4—114no—
395C2×C22⋊C4—118no—
396C2×C22⋊C4—118no—
397C2×C22⋊C4—118no—
398C2×C22⋊C4—224no—
399C2×C22⋊C4—228no—
400C2×C22⋊C4—228no—
401C2×C22⋊C4—224no—
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#95C22×D1114yes—
414#95C22×D1118yes—
415C2×C11—82no—
416C2×C11#281918yescomplemented
417C2×C11C2×#53511yescharacteristic
418C2×C11C2×#53511yescharacteristic
419C2×C11C2×#53711yescharacteristic
420C2×C11C2×H(3,𝔽4)12yes—
421C2×C11C2×#56212yes—
422D11—84no—
423D11—82no—
424C24—22no—
425C24—24no—
426C24—22no—
427C24—22no—
428C24—24no—
429C24—112no—
430C24—114no—
431C24—224no—
432C24—222no—
433C24—224no—
434C24—224no—
435C24—224no—
436C24—222no—
437C24—224no—
438C24—224no—
439C24—224no—
440C24—222no—
441C24—224no—
442C24—224no—
443C24C23×D1112yes—
444C24C23×D1111yescharacteristic
445C2×Q8—28no—
446C2×Q8—48no—
447C2×Q8—416no—
448C2×Q8—228no—
449C2×Q8—448no—
450C2×Q8—4416no—
451C2×D4—228no—
452C2×D4—228no—
453C2×D4—448no—
454C2×D4—448no—
455C2×D4—448no—
456C2×D4—448no—
457C2×D4—4416no—
458C2×D4—4432no—
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—24no—
472C22×C4—24no—
473C22×C4—24no—
474C22×C4—114no—
475C22×C4—114no—
476C22×C4—112no—
477C22×C4—112no—
478C22×C4—114no—
479C22×C4—112no—
480C22×C4—222no—
481C22×C4—222no—
482C22×C4—224no—
483C22×C4—222no—
484C22×C4—224no—
485C22×C4—224no—
486C22×C4—224no—
487C22×C4—224no—
488C22×C4D4×D1114yes—
489C22×C4C23×D1114yes—
490C22×C4C23×D1114yes—
491C22×C4C23×D1112yes—
492C22×C4C23×D1112yes—
493C4⋊C4—448no—
494C22⋊C4—28no—
495C22⋊C4—48no—
496C22⋊C4—228no—
497C22⋊C4—2216no—
498C22⋊C4—2216no—
499C22⋊C4—228no—
500C22⋊C4—228no—
501C22⋊C4—448no—
502C22⋊C4—448no—
503C22⋊C4—448no—
504C42—1116no—
505C11C2×#281911yescharacteristic, complemented, Sylow
506C23—22no—
507C23—24no—
508C23—22no—
509C23—24no—
510C23—22no—
511C23—44no—
512C23—44no—
513C23—48no—
514C23—44no—
515C23—48no—
516C23—224no—
517C23—222no—
518C23—224no—
519C23—224no—
520C23—224no—
521C23—222no—
522C23—224no—
523C23—224no—
524C23—224no—
525C23—224no—
526C23—222no—
527C23—224no—
528C23—448no—
529C23—444no—
530C23—448no—
531C23—444no—
532C23—448no—
533C23—448no—
534C23—448no—
535C23—444no—
536C23—448no—
537C23—448no—
538C23—448no—
539C23—448no—
540C23C2×D4×D1112yes—
541C23#6703714yes—
542C23#6704012yes—
543C23#6704212yes—
544C23#6704214yes—
545C23C24×D1111yescharacteristic
546Q8—416no—
547Q8—4416no—
548D4—4416no—
549D4—4432no—
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—24no—
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—48no—
563C2×C4—44no—
564C2×C4—48no—
565C2×C4—114no—
566C2×C4—114no—
567C2×C4—228no—
568C2×C4—222no—
569C2×C4—222no—
570C2×C4—224no—
571C2×C4—228no—
572C2×C4—222no—
573C2×C4—224no—
574C2×C4—224no—
575C2×C4—224no—
576C2×C4—224no—
577C2×C4—444no—
578C2×C4—448no—
579C2×C4C2×D4×D1114yes—
580C22—42no—
581C22—42no—
582C22—42no—
583C22—44no—
584C22—44no—
585C22—88no—
586C22—444no—
587C22—442no—
588C22—442no—
589C22—444no—
590C22—444no—
591C22—442no—
592C22—444no—
593C22—444no—
594C22—444no—
595C22—444no—
596C22—444no—
597C22—444no—
598C22—8816no—
599C22—888no—
600C22#1062312314yes—
601C22#1062316014yes—
602C22#1062317818yes—
603C22#1062320514yes—
604C22#1062321418yes—
605C22C22×D4×D1111yescharacteristic
606C22C2×#6703712yes—
607C22C2×#6704011yescharacteristic
608C22C2×#6704212yes—
609C22C2×#6704211yescharacteristic
610C4—24no—
611C4—44no—
612C4—42no—
613C4—44no—
614C4—224no—
615C4—224no—
616C4—442no—
617C4—444no—
618C2—82no—
619C2—884no—
620C2—882no—
621C2#1307666418yesdirect product factor
622C2C2×#1062312311yescharacteristic
623C2C2×#1062320511yescharacteristic
624C2C2×#1062316011yescharacteristic
625C2C2×#1062321412yes—
626C2C2×#1062317812yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#393C2
socleC24×C11C24
hypercenterC2×#393D11
hypocenterC11C2×#2819
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×#66938C2semidirect
3. #13076664C2direct (N × H)
4. C2×#10622285C2semidirect
5. C2×#10622572C2semidirect
6. C2×#10622286C2semidirect
7. C2×#10622844C2semidirect
8. C2×#10622284C2semidirect
9. C2×#10622573C2semidirect
10. C2×#10622573C2semidirect
11. C2×#10622263C2semidirect
12. C2×C11×#393C2semidirect
23. C2×#67000C22semidirect
34. C2×#66938C22semidirect
35. C11×#393C22semidirect
38. #10622844C22semidirect
42. #10622573C22semidirect
43. #10622573C22semidirect
44. #10622572C22semidirect
45. #10622286C22semidirect
46. #10622285C22semidirect
47. #10622284C22semidirect
48. #10622263C22semidirect
103. C2×C4×Dic11D4semidirect
192. C4×Dic11C2×D4semidirect
200. C2×#393D11semidirect
305. #393C2×D11semidirect
416. C2×C11#2819semidirect
505. C11C2×#2819semidirect
621. C2#13076664direct (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×#669382
#130766642
C2×#106222852
C2×#106225722
C2×#106222862
C2×#106228442
C2×#106222842
C2×#106225732
C2×#106222632
C2×C11×#3932
C2×#281911