Finite Group Databasebeta

← C2×#13076615 #14959918

Subgroups — C2×#13076615 #14959918

Order 2816.

3322 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66936C211yesmaximal, characteristic, complemented
2C22×#66991C211yesmaximal, characteristic, complemented
3#13076615C2116yesmaximal, direct product factor
4C2×#10622272C211yesmaximal, characteristic, complemented
5C2×#10622562C211yesmaximal, characteristic, complemented
6C2×#10622561C212yesmaximal, complemented
7C2×#10622572C212yesmaximal, complemented
8C2×#10622835C211yesmaximal, characteristic, complemented
9C2×#10622835C212yesmaximal, complemented
10C2×#10622836C212yesmaximal, complemented
11C2×#10622280C211yesmaximal, characteristic, complemented
12C2×C11×#392C211yesmaximal, characteristic, complemented
13C23×D4×C11C2211yescharacteristic
14C23×D4×C11C2212yes—
15C23×C22⋊D11C2211yescharacteristic
16C23×C22⋊D11C2212yes—
17C23×C4×D11C2211yescharacteristic
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2212yes—
20C22×C22⋊Dic11C2211yescharacteristic
21C22×C22⋊Dic11C2212yes—
22C22×C22⋊Dic11C2212yes—
23C22×C22⋊Dic11C2212yes—
24C22×C22⋊Dic11C2212yes—
25C2×#66991—28no—
26C2×#66991C2218yescomplemented
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×(C2×D11)⋊C4C2212yes—
29C22×C4⋊Dic11C2211yescharacteristic
30C22×C4⋊Dic11C2211yescharacteristic
31C22×Dic11⋊C4C2211yescharacteristic
32C22×Dic11⋊C4C2212yes—
33C22×Dic11⋊C4C2212yes—
34C2×#66936—28no—
35C2×#66936C2218yescomplemented
36C11×#392C2218yescomplemented
37C2×C11×#95C2211yescharacteristic
38#10622836C22116yescomplemented
39#10622835C22116yescomplemented
40#10622835C2218yescomplemented
41C2×C11⋊#95C2211yescharacteristic
42C2×C11⋊#95C2212yes—
43C2×C11⋊#95C2212yes—
44#10622572C22116yescomplemented
45#10622562C2218yescomplemented
46#10622561C22116yescomplemented
47#10622280C2218yescomplemented
48#10622272C2218yescomplemented
49C25×C11C2311yescharacteristic
50C25×C11C2312yes—
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×C11C2311yescharacteristic
60C23×C4×C11C2312yes—
61C23×C4×C11C2311yescharacteristic
62C22×C22⋊D11—24no—
63C22×C22⋊D11—28no—
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×C4×D11—44no—
75C22×C4×D11D418yescomplemented
76C22×C4×D11C2314yes—
77C2×C11×C22⋊C4—24no—
78C2×C11×C22⋊C4—44no—
79C2×C11×C22⋊C4C2314yes—
80C2×C11×C22⋊C4C2318yes—
81C2×C22⋊Dic11—24no—
82C2×C22⋊Dic11—28no—
83C2×C22⋊Dic11—44no—
84C2×C22⋊Dic11—44no—
85C2×C22⋊Dic11—44no—
86C2×C22⋊Dic11C2314yes—
87C2×C22⋊Dic11C2318yes—
88C2×C22⋊Dic11C2318yes—
89C2×C22⋊Dic11C2318yes—
90C2×C22⋊Dic11C2318yes—
91#66991—232no—
92C2×(C2×D11)⋊C4—24no—
93C2×(C2×D11)⋊C4—44no—
94C2×(C2×D11)⋊C4C2314yes—
95C2×(C2×D11)⋊C4C2318yes—
96C2×C4⋊Dic11—24no—
97C2×C4⋊Dic11—24no—
98C2×C4⋊Dic11C2314yes—
99C2×C4⋊Dic11C2314yes—
100C2×Dic11⋊C4—24no—
101C2×Dic11⋊C4—44no—
102C2×Dic11⋊C4—44no—
103C2×Dic11⋊C4C2314yes—
104C2×Dic11⋊C4C2318yes—
105C2×Dic11⋊C4C2318yes—
106#66936—232no—
107C11×#95C2314yes—
108C11⋊#95C2318yes—
109C11⋊#95C2318yes—
110C11⋊#95C2314yes—
111C2×#2813—111nomaximal, Sylow
112C24×C11—22no—
113C24×C11—24no—
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—22no—
123C24×C11—24no—
124C24×C11C2412yes—
125C24×C11C2414yes—
126C24×C11C2411yescharacteristic
127C23×D11—22no—
128C23×D11—24no—
129C23×D11—24no—
130C23×D11—22no—
131C23×D11C2×D414yes—
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—216no—
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—24no—
165C22×Dic11—22no—
166C22×Dic11—24no—
167C22×Dic11—24no—
168C22×Dic11—22no—
169C22×Dic11C2×D414yes—
170C22×Dic11C2412yes—
171C22×Dic11C2414yes—
172C22×Dic11C2412yes—
173C22×Dic11C2414yes—
174C22×Dic11C2412yes—
175C2×C4×D11—416no—
176C2×C4×D11—48no—
177C2×C4×D11C2×D4116yescomplemented
178C11×C22⋊C4—28no—
179C11×C22⋊C4—48no—
180C22⋊Dic11—28no—
181C22⋊Dic11—216no—
182C22⋊Dic11—48no—
183C22⋊Dic11—48no—
184C22⋊Dic11—48no—
185(C2×D11)⋊C4—28no—
186(C2×D11)⋊C4—48no—
187C4⋊Dic11—28no—
188C4⋊Dic11—28no—
189Dic11⋊C4—28no—
190Dic11⋊C4—48no—
191Dic11⋊C4—48no—
192C22×#123—111no—
193C22×#121—111no—
194#2813—1116no—
195C2×#400—111no—
196C2×#399—111no—
197C2×#396—112no—
198C2×#394—112no—
199C2×#394—111no—
200C2×#394—112no—
201C2×#392—112no—
202C2×#392D1111yescharacteristic, complemented
203C2×#380—111no—
204C23×C11—22no—
205C23×C11—24no—
206C23×C11—24no—
207C23×C11—24no—
208C23×C11—24no—
209C23×C11—24no—
210C23×C11—24no—
211C23×C11—24no—
212C23×C11—24no—
213C23×C11—22no—
214C23×C11—22no—
215C23×C11—24no—
216C23×C11—44no—
217C23×C11—48no—
218C23×C11—48no—
219C23×C11—44no—
220C23×C11—44no—
221C23×C11—48no—
222C23×C11—48no—
223C23×C11—48no—
224C23×C11—48no—
225C23×C11—48no—
226C23×C11—48no—
227C23×C11—48no—
228C23×C11C22×D412yes—
229C23×C11H(5,𝔽2)14yes—
230C23×C11H(5,𝔽2)14yes—
231C23×C11H(5,𝔽2)12yes—
232C23×C112−1+412yes—
233C23×C11C2511yescharacteristic
234C22×D11—28no—
235C22×D11—28no—
236C22×D11—28no—
237C22×D11—22no—
238C22×D11—24no—
239C22×D11—24no—
240C22×D11—22no—
241C22×D11—48no—
242C22×D11—48no—
243C22×D11C22×D414yes—
244D4×C11—416no—
245D4×C11—432no—
246C2×C4×C11—28no—
247C2×C4×C11—24no—
248C2×C4×C11—22no—
249C2×C4×C11—24no—
250C2×C4×C11—24no—
251C2×C4×C11—24no—
252C2×C4×C11—24no—
253C2×C4×C11—44no—
254C2×C4×C11—48no—
255C2×C4×C11C22×D414yes—
256C22⋊D11—416no—
257C22⋊D11—432no—
258C2×Dic11—28no—
259C2×Dic11—24no—
260C2×Dic11—22no—
261C2×Dic11—22no—
262C2×Dic11—24no—
263C2×Dic11—24no—
264C2×Dic11—24no—
265C2×Dic11—24no—
266C2×Dic11—24no—
267C2×Dic11—22no—
268C2×Dic11—24no—
269C2×Dic11—24no—
270C2×Dic11—22no—
271C2×Dic11—44no—
272C2×Dic11—48no—
273C2×Dic11—44no—
274C2×Dic11—48no—
275C2×Dic11C22×D414yes—
276C4×D11—416no—
277C23×D4—111no—
278C23×D4—112no—
279C23×D4C2×D1111yescharacteristic
280C23×D4C2×D1112yes—
281C24×C4—111no—
282C2×#123—118no—
283C2×#123—228no—
284C2×#121—118no—
285C2×#121—228no—
286C22×C4⋊C4—111no—
287C22×C4⋊C4—111no—
288C22×C4⋊C4—111no—
289C22×C4⋊C4—112no—
290C22×C4⋊C4—112no—
291C22×C22⋊C4—111no—
292C22×C22⋊C4—112no—
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—
300#400—118no—
301#399—118no—
302#396—1116no—
303#394—118no—
304#394—1116no—
305#394—1116no—
306#392—1116no—
307#392C2×D1118yescomplemented
308#380—118no—
309C2×#95—112no—
310C2×#95—112no—
311C2×#95—111no—
312C2×#95C2×D1111yescharacteristic
313C22×C11—44no—
314C22×C11—42no—
315C22×C11—42no—
316C22×C11—44no—
317C22×C11—42no—
318C22×C11—44no—
319C22×C11—44no—
320C22×C11—44no—
321C22×C11—44no—
322C22×C11—44no—
323C22×C11—44no—
324C22×C11—44no—
325C22×C11—88no—
326C22×C11—816no—
327C22×C11#53414yes—
328C22×C11#53514yes—
329C22×C11#53714yes—
330C22×C11#56018yes—
331C22×C11#56218yes—
332C22×C11C23×D411yescharacteristic
333C22×C11C2×H(5,𝔽2)12yes—
334C22×C11C2×H(5,𝔽2)12yes—
335C22×C11C2×H(5,𝔽2)11yescharacteristic
336C22×C11C2×2−1+411yescharacteristic
337C2×D11—24no—
338C2×D11—24no—
339C2×D11—24no—
340C2×D11—44no—
341C2×D11—44no—
342C2×D11—416no—
343C4×C11—24no—
344C4×C11—42no—
345C4×C11—44no—
346Dic11—24no—
347Dic11—42no—
348Dic11—44no—
349Dic11—42no—
350Dic11—44no—
351C25—111no—
352C25C22×D1111yescharacteristic
353C25C22×D1112yes—
354C22×D4—24no—
355C22×D4—44no—
356C22×D4—44no—
357C22×D4—44no—
358C22×D4—44no—
359C22×D4—118no—
360C22×D4—114no—
361C22×D4—228no—
362C22×D4—224no—
363C22×D4—444no—
364C22×D4—444no—
365C22×D4—444no—
366C22×D4C22×D1114yes—
367C22×D4C22×D1118yes—
368C23×C4—111no—
369C23×C4—118no—
370C23×C4—114no—
371C23×C4—112no—
372C23×C4—111no—
373C23×C4—112no—
374C23×C4—111no—
375C23×C4—444no—
376C23×C4C22×D1111yescharacteristic
377C23×C4C22×D1112yes—
378C23×C4C22×D1111yescharacteristic
379#123—2232no—
380#121—2232no—
381C2×C4⋊C4—114no—
382C2×C4⋊C4—114no—
383C2×C4⋊C4—114no—
384C2×C4⋊C4—118no—
385C2×C4⋊C4—118no—
386C2×C4⋊C4—224no—
387C2×C4⋊C4—224no—
388C2×C4⋊C4—224no—
389C2×C4⋊C4—444no—
390C2×C4⋊C4—444no—
391C2×C22⋊C4—24no—
392C2×C22⋊C4—44no—
393C2×C22⋊C4—118no—
394C2×C22⋊C4—114no—
395C2×C22⋊C4—114no—
396C2×C22⋊C4—118no—
397C2×C22⋊C4—118no—
398C2×C22⋊C4—118no—
399C2×C22⋊C4—118no—
400C2×C22⋊C4—224no—
401C2×C22⋊C4—228no—
402C2×C22⋊C4—224no—
403C2×C22⋊C4—444no—
404C2×C22⋊C4—444no—
405C2×C22⋊C4—444no—
406C2×C22⋊C4—444no—
407C2×C22⋊C4C22×D1114yes—
408C2×C22⋊C4C22×D1118yes—
409#95—114no—
410#95—118no—
411#95—118no—
412#95C22×D1114yes—
413C2×C11—84no—
414C2×C11—82no—
415C2×C11#281318yescomplemented
416C2×C11C2×#53411yescharacteristic
417C2×C11C2×#53511yescharacteristic
418C2×C11C2×#53711yescharacteristic
419C2×C11C2×#56012yes—
420C2×C11C2×#56212yes—
421D11—44no—
422C24—22no—
423C24—24no—
424C24—24no—
425C24—24no—
426C24—24no—
427C24—24no—
428C24—24no—
429C24—22no—
430C24—24no—
431C24—24no—
432C24—22no—
433C24—24no—
434C24—114no—
435C24—112no—
436C24—222no—
437C24—224no—
438C24—224no—
439C24—222no—
440C24C23×D1112yes—
441C24C23×D1114yes—
442C24C23×D1111yescharacteristic
443C2×D4—28no—
444C2×D4—48no—
445C2×D4—48no—
446C2×D4—48no—
447C2×D4—48no—
448C2×D4—416no—
449C2×D4—432no—
450C2×D4—2216no—
451C2×D4—228no—
452C2×D4—448no—
453C2×D4—448no—
454C2×D4—448no—
455C2×D4—4432no—
456C2×D4—4416no—
457C22×C4—24no—
458C22×C4—22no—
459C22×C4—24no—
460C22×C4—24no—
461C22×C4—24no—
462C22×C4—24no—
463C22×C4—114no—
464C22×C4—112no—
465C22×C4—1116no—
466C22×C4—112no—
467C22×C4—114no—
468C22×C4—112no—
469C22×C4—114no—
470C22×C4—224no—
471C22×C4—222no—
472C22×C4—224no—
473C22×C4—222no—
474C22×C4—224no—
475C22×C4—222no—
476C22×C4—224no—
477C22×C4—224no—
478C22×C4—224no—
479C22×C4—224no—
480C22×C4—224no—
481C22×C4—222no—
482C22×C4—4416no—
483C22×C4—448no—
484C22×C4D4×D1114yes—
485C22×C4C23×D1114yes—
486C22×C4C23×D1112yes—
487C22×C4C23×D1112yes—
488C4⋊C4—228no—
489C4⋊C4—228no—
490C4⋊C4—228no—
491C4⋊C4—448no—
492C4⋊C4—448no—
493C22⋊C4—28no—
494C22⋊C4—48no—
495C22⋊C4—228no—
496C22⋊C4—2216no—
497C22⋊C4—228no—
498C22⋊C4—448no—
499C22⋊C4—448no—
500C22⋊C4—448no—
501C22⋊C4—448no—
502C11C2×#281311yescharacteristic, complemented, Sylow
503C23—22no—
504C23—24no—
505C23—24no—
506C23—24no—
507C23—24no—
508C23—24no—
509C23—24no—
510C23—22no—
511C23—24no—
512C23—24no—
513C23—22no—
514C23—24no—
515C23—48no—
516C23—44no—
517C23—48no—
518C23—44no—
519C23—48no—
520C23—48no—
521C23—48no—
522C23—44no—
523C23—48no—
524C23—48no—
525C23—48no—
526C23—48no—
527C23—114no—
528C23—228no—
529C23—228no—
530C23—228no—
531C23—222no—
532C23—224no—
533C23—224no—
534C23—222no—
535C23—448no—
536C23—448no—
537C23C2×D4×D1112yes—
538C23#6703714yes—
539C23#6703714yes—
540C23#6703712yes—
541C23#6704312yes—
542C23C24×D1111yescharacteristic
543D4—416no—
544D4—432no—
545D4—4416no—
546D4—4432no—
547C2×C4—28no—
548C2×C4—24no—
549C2×C4—22no—
550C2×C4—24no—
551C2×C4—24no—
552C2×C4—24no—
553C2×C4—24no—
554C2×C4—44no—
555C2×C4—48no—
556C2×C4—114no—
557C2×C4—228no—
558C2×C4—224no—
559C2×C4—222no—
560C2×C4—224no—
561C2×C4—222no—
562C2×C4—222no—
563C2×C4—224no—
564C2×C4—224no—
565C2×C4—224no—
566C2×C4—224no—
567C2×C4—224no—
568C2×C4—224no—
569C2×C4—222no—
570C2×C4—4416no—
571C2×C4—448no—
572C2×C4—444no—
573C2×C4—448no—
574C2×C4—444no—
575C2×C4C2×D4×D1114yes—
576C22—44no—
577C22—42no—
578C22—44no—
579C22—42no—
580C22—42no—
581C22—44no—
582C22—44no—
583C22—44no—
584C22—44no—
585C22—44no—
586C22—44no—
587C22—44no—
588C22—816no—
589C22—88no—
590C22—224no—
591C22—224no—
592C22—224no—
593C22—444no—
594C22—444no—
595C22—4416no—
596C22#1062312014yes—
597C22#1062312618yes—
598C22#1062313914yes—
599C22#1062315218yes—
600C22#1062324614yes—
601C22C22×D4×D1111yescharacteristic
602C22C2×#6703712yes—
603C22C2×#6703712yes—
604C22C2×#6703711yescharacteristic
605C22C2×#6704311yescharacteristic
606C4—24no—
607C4—42no—
608C4—44no—
609C4—224no—
610C4—442no—
611C4—444no—
612C4—442no—
613C4—444no—
614C2—84no—
615C2—82no—
616C2—444no—
617C2#1307661518yesdirect product factor
618C2C2×#1062312011yescharacteristic
619C2C2×#1062324611yescharacteristic
620C2C2×#1062313911yescharacteristic
621C2C2×#1062312612yes—
622C2C2×#1062315212yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#392C2
socleC24×C11C24
hypercenterC2×#392D11
hypocenterC11C2×#2813
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#392

Complements

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

NH ≅ G/Ntype
1. C22×#66936C2semidirect
2. C22×#66991C2semidirect
3. #13076615C2direct (N × H)
4. C2×#10622272C2semidirect
5. C2×#10622562C2semidirect
6. C2×#10622561C2semidirect
7. C2×#10622572C2semidirect
8. C2×#10622835C2semidirect
9. C2×#10622835C2semidirect
10. C2×#10622836C2semidirect
11. C2×#10622280C2semidirect
12. C2×C11×#392C2semidirect
26. C2×#66991C22semidirect
35. C2×#66936C22semidirect
36. C11×#392C22semidirect
38. #10622836C22semidirect
39. #10622835C22semidirect
40. #10622835C22semidirect
44. #10622572C22semidirect
45. #10622562C22semidirect
46. #10622561C22semidirect
47. #10622280C22semidirect
48. #10622272C22semidirect
75. C22×C4×D11D4semidirect
177. C2×C4×D11C2×D4semidirect
202. C2×#392D11semidirect
307. #392C2×D11semidirect
415. C2×C11#2813semidirect
502. C11C2×#2813semidirect
617. C2#13076615direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669362
C22×#669912
#130766152
C2×#106222722
C2×#106225622
C2×#106225612
C2×#106225722
C2×#106228352
C2×#106228362
C2×#106222802
C2×C11×#3922
C2×#281311