Finite Group Databasebeta

← C2×#13074747 #14920326

Subgroups — C2×#13074747 #14920326

Order 2816.

3434 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#13074747C2116yesmaximal, direct product factor
4C2×#10622274C211yesmaximal, characteristic, complemented
5C2×#10622566C211yesmaximal, characteristic, complemented
6C2×#10622574C212yesmaximal, complemented
7C2×#10622835C211yesmaximal, characteristic, complemented
8C2×#10622836C212yesmaximal, complemented
9C2×#10622834C212yesmaximal, complemented
10C2×#10622564C212yesmaximal, complemented
11C2×#10622279C211yesmaximal, characteristic, complemented
12C2×C11×#392C211yesmaximal, characteristic, complemented
13C23×D4×C11C2212yes—
14C23×D4×C11C2211yescharacteristic
15C23×C22⋊D11C2211yescharacteristic
16C23×C22⋊D11C2212yes—
17C23×C4×D11C2211yescharacteristic
18C22×C11×C22⋊C4C2212yes—
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C22⋊Dic11C2212yes—
21C22×C22⋊Dic11C2211yescharacteristic
22C22×C22⋊Dic11C2212yes—
23C22×C22⋊Dic11C2212yes—
24C22×C22⋊Dic11C2212yes—
25C2×#66991—28no—
26C2×#66991C2218yescomplemented
27C22×(C2×D11)⋊C4C2212yes—
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C22×C4⋊Dic11C2211yescharacteristic
30C22×C4⋊Dic11C2211yescharacteristic
31C22×C4⋊Dic11C2212yes—
32C22×Dic11⋊C4C2211yescharacteristic
33C22×C4×Dic11C2212yes—
34C2×#66936—28no—
35C2×#66936C2218yescomplemented
36C11×#392C2218yescomplemented
37C2×C11×#95C2211yescharacteristic
38#10622836C22116yescomplemented
39#10622835C2218yescomplemented
40#10622834C22116yescomplemented
41C2×C11⋊#95C2211yescharacteristic
42C2×C11⋊#95C2212yes—
43C2×C11⋊#95C2212yes—
44#10622574C22116yescomplemented
45#10622566C2218yescomplemented
46#10622564C22116yescomplemented
47#10622279C2218yescomplemented
48#10622274C2218yescomplemented
49C25×C11C2311yescharacteristic
50C25×C11C2312yes—
51C24×D11C2311yescharacteristic
52C22×D4×C11—24no—
53C22×D4×C11—28no—
54C22×D4×C11—44no—
55C22×D4×C11—44no—
56C22×D4×C11—44no—
57C22×D4×C11C2314yes—
58C22×D4×C11C2318yes—
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2312yes—
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×Dic11C2311yescharacteristic
72C23×Dic11C2312yes—
73C23×Dic11C2311yescharacteristic
74C22×C4×D11—44no—
75C22×C4×D11D418yescomplemented
76C22×C4×D11C2314yes—
77C2×C11×C22⋊C4—24no—
78C2×C11×C22⋊C4—28no—
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—28no—
94C2×(C2×D11)⋊C4C2314yes—
95C2×(C2×D11)⋊C4C2318yes—
96C2×C4⋊Dic11—24no—
97C2×C4⋊Dic11—24no—
98C2×C4⋊Dic11—44no—
99C2×C4⋊Dic11C2314yes—
100C2×C4⋊Dic11C2314yes—
101C2×C4⋊Dic11C2318yes—
102C2×Dic11⋊C4—24no—
103C2×Dic11⋊C4C2314yes—
104C2×C4×Dic11—44no—
105C2×C4×Dic11C2318yes—
106#66936—232no—
107C11×#95C2314yes—
108C11⋊#95C2318yes—
109C11⋊#95C2314yes—
110C11⋊#95C2318yes—
111C2×#2661—111nomaximal, Sylow
112C24×C11—22no—
113C24×C11—24no—
114C24×C11—24no—
115C24×C11—24no—
116C24×C11—24no—
117C24×C11—22no—
118C24×C11—24no—
119C24×C11—24no—
120C24×C11—24no—
121C24×C11—24no—
122C24×C11—24no—
123C24×C11—22no—
124C24×C11C2412yes—
125C24×C11C2414yes—
126C24×C11C2411yescharacteristic
127C23×D11—24no—
128C23×D11—24no—
129C23×D11—22no—
130C23×D11—22no—
131C23×D11C2×D414yes—
132C23×D11C2412yes—
133C2×D4×C11—28no—
134C2×D4×C11—216no—
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—24no—
142C22×C4×C11—24no—
143C22×C4×C11—22no—
144C22×C4×C11—24no—
145C22×C4×C11C2×D414yes—
146C22×C4×C11#4118yes—
147C22×C4×C11C2412yes—
148C22×C4×C11C2412yes—
149C22×C4×C11C2414yes—
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—22no—
164C22×Dic11—24no—
165C22×Dic11—22no—
166C22×Dic11—24no—
167C22×Dic11—24no—
168C22×Dic11—24no—
169C22×Dic11C2×D414yes—
170C22×Dic11C2414yes—
171C22×Dic11C2412yes—
172C22×Dic11C2414yes—
173C22×Dic11C2412yes—
174C22×Dic11C2412yes—
175C2×C4×D11—416no—
176C2×C4×D11—48no—
177C2×C4×D11C2×D4116yescomplemented
178C11×C22⋊C4—28no—
179C11×C22⋊C4—216no—
180C22⋊Dic11—28no—
181C22⋊Dic11—216no—
182C22⋊Dic11—48no—
183C22⋊Dic11—48no—
184C22⋊Dic11—48no—
185(C2×D11)⋊C4—28no—
186(C2×D11)⋊C4—216no—
187C4⋊Dic11—28no—
188C4⋊Dic11—28no—
189C4⋊Dic11—48no—
190Dic11⋊C4—28no—
191C4×Dic11—48no—
192C22×#123—111no—
193C22×#121—111no—
194#2661—1116no—
195C2×#398—111no—
196C2×#397—111no—
197C2×#394—111no—
198C2×#394—112no—
199C2×#392—112no—
200C2×#392D1111yescharacteristic, complemented
201C2×#390—112no—
202C2×#388—112no—
203C2×C4×C22⋊C4—111no—
204C23×C11—22no—
205C23×C11—24no—
206C23×C11—24no—
207C23×C11—24no—
208C23×C11—24no—
209C23×C11—22no—
210C23×C11—24no—
211C23×C11—24no—
212C23×C11—24no—
213C23×C11—24no—
214C23×C11—24no—
215C23×C11—22no—
216C23×C11—44no—
217C23×C11—48no—
218C23×C11—44no—
219C23×C11—48no—
220C23×C11—48no—
221C23×C11—44no—
222C23×C11—48no—
223C23×C11—48no—
224C23×C11—48no—
225C23×C11—48no—
226C23×C11—48no—
227C23×C11—48no—
228C23×C11C22×D412yes—
229C23×C11C2×#4114yes—
230C23×C11H(5,𝔽2)14yes—
231C23×C11H(5,𝔽2)12yes—
232C23×C11H(5,𝔽2)12yes—
233C23×C11C2511yescharacteristic
234C22×D11—28no—
235C22×D11—28no—
236C22×D11—28no—
237C22×D11—24no—
238C22×D11—24no—
239C22×D11—22no—
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—216no—
248C2×C4×C11—24no—
249C2×C4×C11—24no—
250C2×C4×C11—24no—
251C2×C4×C11—22no—
252C2×C4×C11—24no—
253C2×C4×C11—44no—
254C2×C4×C11C22×D414yes—
255C2×C4×C11C2×#4118yes—
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—22no—
266C2×Dic11—24no—
267C2×Dic11—22no—
268C2×Dic11—24no—
269C2×Dic11—24no—
270C2×Dic11—24no—
271C2×Dic11—44no—
272C2×Dic11—44no—
273C2×Dic11—48no—
274C2×Dic11—48no—
275C2×Dic11C22×D414yes—
276C4×D11—416no—
277C23×D4—111no—
278C23×D4—112no—
279C23×D4C2×D1112yes—
280C23×D4C2×D1111yescharacteristic
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×C22⋊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⋊C4C2×D1112yes—
298C22×C22⋊C4C2×D1111yescharacteristic
299C22×C42—112no—
300#398—118no—
301#397—118no—
302#394—118no—
303#394—1116no—
304#392—1116no—
305#392C2×D1118yescomplemented
306#390—1116no—
307#388—1116no—
308C4×C22⋊C4—118no—
309C2×#95—112no—
310C2×#95—111no—
311C2×#95—112no—
312C2×#95C2×D1111yescharacteristic
313C22×C11—42no—
314C22×C11—44no—
315C22×C11—44no—
316C22×C11—42no—
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#53214yes—
328C22×C11#53414yes—
329C22×C11#53514yes—
330C22×C11#53818yes—
331C22×C11#54018yes—
332C22×C11C23×D411yescharacteristic
333C22×C11C22×#4112yes—
334C22×C11C2×H(5,𝔽2)12yes—
335C22×C11C2×H(5,𝔽2)11yescharacteristic
336C22×C11C2×H(5,𝔽2)11yescharacteristic
337C2×D11—24no—
338C2×D11—24no—
339C2×D11—24no—
340C2×D11—416no—
341C2×D11—44no—
342C2×D11—44no—
343C4×C11—24no—
344C4×C11—28no—
345C4×C11—42no—
346Dic11—24no—
347Dic11—42no—
348Dic11—42no—
349Dic11—44no—
350Dic11—44no—
351C25—111no—
352C25C22×D1111yescharacteristic
353C25C22×D1112yes—
354C22×D4—24no—
355C22×D4—28no—
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—111no—
372C23×C4—112no—
373C23×C4—112no—
374C23×C4—111no—
375C23×C4—444no—
376C23×C4C22×D1111yescharacteristic
377C23×C4C22×D1111yescharacteristic
378C23×C4C22×D1112yes—
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—224no—
386C2×C4⋊C4—224no—
387C2×C4⋊C4—224no—
388C2×C4⋊C4—444no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—28no—
391C2×C22⋊C4—118no—
392C2×C22⋊C4—114no—
393C2×C22⋊C4—114no—
394C2×C22⋊C4—118no—
395C2×C22⋊C4—118no—
396C2×C22⋊C4—118no—
397C2×C22⋊C4—118no—
398C2×C22⋊C4—224no—
399C2×C22⋊C4—228no—
400C2×C22⋊C4—224no—
401C2×C22⋊C4—228no—
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—444no—
409#95—114no—
410#95—118no—
411#95—118no—
412#95C22×D1114yes—
413C2×C11—84no—
414C2×C11—82no—
415C2×C11#266118yescomplemented
416C2×C11C2×#53211yescharacteristic
417C2×C11C2×#53411yescharacteristic
418C2×C11C2×#53511yescharacteristic
419C2×C11C2×#53812yes—
420C2×C11C2×#54012yes—
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—224no—
437C24—224no—
438C24—222no—
439C24—222no—
440C24C23×D1112yes—
441C24C23×D1114yes—
442C24C23×D1111yescharacteristic
443C2×D4—28no—
444C2×D4—216no—
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—4416no—
456C2×D4—4432no—
457C22×C4—24no—
458C22×C4—24no—
459C22×C4—24no—
460C22×C4—22no—
461C22×C4—24no—
462C22×C4—114no—
463C22×C4—112no—
464C22×C4—1116no—
465C22×C4—114no—
466C22×C4—114no—
467C22×C4—112no—
468C22×C4—112no—
469C22×C4—224no—
470C22×C4—222no—
471C22×C4—224no—
472C22×C4—222no—
473C22×C4—224no—
474C22×C4—224no—
475C22×C4—224no—
476C22×C4—222no—
477C22×C4—224no—
478C22×C4—222no—
479C22×C4—224no—
480C22×C4—224no—
481C22×C4—4416no—
482C22×C4—448no—
483C22×C4D4×D1114yes—
484C22×C4#434118yes—
485C22×C4C23×D1112yes—
486C22×C4C23×D1112yes—
487C22×C4C23×D1114yes—
488C4⋊C4—228no—
489C4⋊C4—228no—
490C4⋊C4—228no—
491C4⋊C4—448no—
492C22⋊C4—28no—
493C22⋊C4—216no—
494C22⋊C4—228no—
495C22⋊C4—2216no—
496C22⋊C4—228no—
497C22⋊C4—2216no—
498C22⋊C4—448no—
499C22⋊C4—448no—
500C22⋊C4—448no—
501C42—448no—
502C11C2×#266111yescharacteristic, 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—44no—
516C23—48no—
517C23—48no—
518C23—44no—
519C23—48no—
520C23—48no—
521C23—48no—
522C23—48no—
523C23—44no—
524C23—48no—
525C23—48no—
526C23—48no—
527C23—114no—
528C23—228no—
529C23—228no—
530C23—228no—
531C23—224no—
532C23—224no—
533C23—222no—
534C23—222no—
535C23—448no—
536C23—448no—
537C23C2×D4×D1112yes—
538C23C2×#434114yes—
539C23#6703714yes—
540C23#6703712yes—
541C23#6704212yes—
542C23C24×D1111yescharacteristic
543D4—416no—
544D4—432no—
545D4—4416no—
546D4—4432no—
547C2×C4—28no—
548C2×C4—216no—
549C2×C4—24no—
550C2×C4—24no—
551C2×C4—24no—
552C2×C4—22no—
553C2×C4—24no—
554C2×C4—44no—
555C2×C4—114no—
556C2×C4—228no—
557C2×C4—224no—
558C2×C4—222no—
559C2×C4—224no—
560C2×C4—222no—
561C2×C4—224no—
562C2×C4—224no—
563C2×C4—224no—
564C2×C4—222no—
565C2×C4—224no—
566C2×C4—222no—
567C2×C4—224no—
568C2×C4—224no—
569C2×C4—4416no—
570C2×C4—444no—
571C2×C4—448no—
572C2×C4—444no—
573C2×C4—448no—
574C2×C4C2×D4×D1114yes—
575C2×C4C2×#434118yes—
576C22—42no—
577C22—44no—
578C22—44no—
579C22—42no—
580C22—44no—
581C22—42no—
582C22—44no—
583C22—44no—
584C22—44no—
585C22—44no—
586C22—44no—
587C22—44no—
588C22—816no—
589C22—88no—
590C22—224no—
591C22—224no—
592C22—224no—
593C22—4416no—
594C22—444no—
595C22—444no—
596C22#1062312014yes—
597C22#1062312418yes—
598C22#1062313814yes—
599C22#1062315018yes—
600C22#1062324714yes—
601C22C22×D4×D1111yescharacteristic
602C22C22×#434112yes—
603C22C2×#6703712yes—
604C22C2×#6703711yescharacteristic
605C22C2×#6704211yescharacteristic
606C4—24no—
607C4—28no—
608C4—42no—
609C4—224no—
610C4—442no—
611C4—444no—
612C4—442no—
613C4—444no—
614C2—84no—
615C2—82no—
616C2—444no—
617C2#1307474718yesdirect product factor
618C2C2×#1062324711yescharacteristic
619C2C2×#1062312011yescharacteristic
620C2C2×#1062313811yescharacteristic
621C2C2×#1062312412yes—
622C2C2×#1062315012yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#392C2
socleC24×C11C24
hypercenterC2×#392D11
hypocenterC11C2×#2661
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. #13074747C2direct (N × H)
4. C2×#10622274C2semidirect
5. C2×#10622566C2semidirect
6. C2×#10622574C2semidirect
7. C2×#10622835C2semidirect
8. C2×#10622836C2semidirect
9. C2×#10622834C2semidirect
10. C2×#10622564C2semidirect
11. C2×#10622279C2semidirect
12. C2×C11×#392C2semidirect
26. C2×#66991C22semidirect
35. C2×#66936C22semidirect
36. C11×#392C22semidirect
38. #10622836C22semidirect
39. #10622835C22semidirect
40. #10622834C22semidirect
44. #10622574C22semidirect
45. #10622566C22semidirect
46. #10622564C22semidirect
47. #10622279C22semidirect
48. #10622274C22semidirect
75. C22×C4×D11D4semidirect
177. C2×C4×D11C2×D4semidirect
200. C2×#392D11semidirect
305. #392C2×D11semidirect
415. C2×C11#2661semidirect
502. C11C2×#2661semidirect
617. C2#13074747direct (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
#130747472
C2×#106222742
C2×#106225662
C2×#106225742
C2×#106228352
C2×#106228362
C2×#106228342
C2×#106225642
C2×#106222792
C2×C11×#3922
C2×#266111