Finite Group Databasebeta

← C2×#13074750 #14920327

Subgroups — C2×#13074750 #14920327

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×#66948C211yesmaximal, characteristic, complemented
3#13074750C2116yesmaximal, direct product factor
4C2×#10622593C211yesmaximal, characteristic, complemented
5C2×#10622285C211yesmaximal, characteristic, complemented
6C2×#10622285C212yesmaximal, complemented
7C2×#10622573C212yesmaximal, complemented
8C2×#10622573C211yesmaximal, characteristic, complemented
9C2×#10622570C212yesmaximal, complemented
10C2×#10622283C212yesmaximal, complemented
11C2×#10622279C211yesmaximal, characteristic, complemented
12C2×C11×#397C211yesmaximal, characteristic, complemented
13C23×C22⋊D11C2212yes—
14C23×C22⋊D11C2211yescharacteristic
15C23×D44C2212yes—
16C23×D44C2211yescharacteristic
17C23×C4×D11C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2212yes—
21C22×C22⋊Dic11C2211yescharacteristic
22C22×(C2×D11)⋊C4C2212yes—
23C22×(C2×D11)⋊C4C2212yes—
24C22×(C2×D11)⋊C4C2212yes—
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C22×(C2×D11)⋊C4C2212yes—
27C22×(C2×D11)⋊C4C2212yes—
28C22×C4⋊Dic11C2211yescharacteristic
29C22×Dic11⋊C4C2211yescharacteristic
30C22×Dic11⋊C4C2212yes—
31C22×C4×Dic11C2212yes—
32C2×#66948—28no—
33C2×#66948C2218yescomplemented
34C2×#66936—28no—
35C2×#66936C2218yescomplemented
36C11×#397C2218yescomplemented
37C2×C11×#95C2211yescharacteristic
38C2×C11×#95C2212yes—
39C2×C11⋊#95C2211yescharacteristic
40C2×C11⋊#95C2212yes—
41#10622593C2218yescomplemented
42#10622573C2218yescomplemented
43#10622573C22116yescomplemented
44#10622570C22116yescomplemented
45#10622285C2218yescomplemented
46#10622285C22116yescomplemented
47#10622283C22116yescomplemented
48#10622279C2218yescomplemented
49C25×C11C2311yescharacteristic
50C24×D11C2312yes—
51C24×D11C2311yescharacteristic
52C23×C4×C11C2312yes—
53C23×C4×C11C2312yes—
54C23×C4×C11C2311yescharacteristic
55C23×C4×C11C2311yescharacteristic
56C22×C22⋊D11—24no—
57C22×C22⋊D11—28no—
58C22×C22⋊D11—44no—
59C22×C22⋊D11—44no—
60C22×C22⋊D11—44no—
61C22×C22⋊D11C2314yes—
62C22×C22⋊D11C2318yes—
63C23×Dic11C2311yescharacteristic
64C23×Dic11C2311yescharacteristic
65C23×Dic11C2311yescharacteristic
66C23×Dic11C2312yes—
67C22×D44—28no—
68C22×D44—24no—
69C22×D44—44no—
70C22×D44—44no—
71C22×D44—44no—
72C22×D44C2318yes—
73C22×D44C2314yes—
74C22×C4×D11—44no—
75C22×C4×D11D418yescomplemented
76C22×C4×D11C2314yes—
77C2×C11×C4⋊C4—24no—
78C2×C11×C4⋊C4C2314yes—
79C2×C11×C22⋊C4—24no—
80C2×C11×C22⋊C4—44no—
81C2×C11×C22⋊C4C2314yes—
82C2×C11×C22⋊C4C2318yes—
83C2×C22⋊Dic11—24no—
84C2×C22⋊Dic11C2314yes—
85C2×(C2×D11)⋊C4—24no—
86C2×(C2×D11)⋊C4—28no—
87C2×(C2×D11)⋊C4—28no—
88C2×(C2×D11)⋊C4—28no—
89C2×(C2×D11)⋊C4—44no—
90C2×(C2×D11)⋊C4—44no—
91C2×(C2×D11)⋊C4C2314yes—
92C2×(C2×D11)⋊C4C2318yes—
93C2×(C2×D11)⋊C4C2318yes—
94C2×(C2×D11)⋊C4C2318yes—
95C2×(C2×D11)⋊C4C2318yes—
96C2×(C2×D11)⋊C4C2318yes—
97C2×C4⋊Dic11—24no—
98C2×C4⋊Dic11C2314yes—
99C2×Dic11⋊C4—24no—
100C2×Dic11⋊C4—44no—
101C2×Dic11⋊C4C2314yes—
102C2×Dic11⋊C4C2318yes—
103C2×C4×Dic11—44no—
104C2×C4×Dic11C2318yes—
105#66948—232no—
106#66936—232no—
107C11×#95C2314yes—
108C11×#95C2318yes—
109C11⋊#95C2314yes—
110C11⋊#95C2318yes—
111C2×#2661—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—22no—
122C23×D11—22no—
123C23×D11—24no—
124C23×D11—24no—
125C23×D11—24no—
126C23×D11—24no—
127C23×D11—24no—
128C23×D11—24no—
129C23×D11—24no—
130C23×D11C2×D414yes—
131C23×D11C2414yes—
132C23×D11C2412yes—
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—216no—
148C2×C22⋊D11—28no—
149C2×C22⋊D11—48no—
150C2×C22⋊D11—48no—
151C2×C22⋊D11—48no—
152C2×C22⋊D11—416no—
153C2×C22⋊D11—432no—
154C22×Dic11—22no—
155C22×Dic11—22no—
156C22×Dic11—24no—
157C22×Dic11—24no—
158C22×Dic11—24no—
159C22×Dic11—22no—
160C22×Dic11—22no—
161C22×Dic11—24no—
162C22×Dic11C2×D414yes—
163C22×Dic11#4118yes—
164C22×Dic11C2412yes—
165C22×Dic11C2412yes—
166C22×Dic11C2412yes—
167C22×Dic11C2414yes—
168C2×D44—216no—
169C2×D44—28no—
170C2×D44—48no—
171C2×D44—48no—
172C2×D44—48no—
173C2×D44—416no—
174C2×D44—432no—
175C2×C4×D11—416no—
176C2×C4×D11—48no—
177C2×C4×D11C2×D4116yescomplemented
178C11×C4⋊C4—28no—
179C11×C22⋊C4—28no—
180C11×C22⋊C4—48no—
181C22⋊Dic11—28no—
182(C2×D11)⋊C4—216no—
183(C2×D11)⋊C4—216no—
184(C2×D11)⋊C4—216no—
185(C2×D11)⋊C4—28no—
186(C2×D11)⋊C4—48no—
187(C2×D11)⋊C4—48no—
188C4⋊Dic11—28no—
189Dic11⋊C4—28no—
190Dic11⋊C4—48no—
191C4×Dic11—48no—
192C22×#123—111no—
193C22×#121—111no—
194#2661—1116no—
195C2×#398—111no—
196C2×#397D1111yescharacteristic, complemented
197C2×#394—112no—
198C2×#394—111no—
199C2×#392—112no—
200C2×#392—111no—
201C2×#390—112no—
202C2×#388—112no—
203C2×C4×C22⋊C4—111no—
204C23×C11—22no—
205C23×C11—24no—
206C23×C11—22no—
207C23×C11—24no—
208C23×C11—22no—
209C23×C11—44no—
210C23×C11—44no—
211C23×C11—44no—
212C23×C11—48no—
213C23×C11—48no—
214C23×C11C22×D412yes—
215C23×C11C2×#4114yes—
216C23×C11H(5,𝔽2)12yes—
217C23×C11H(5,𝔽2)14yes—
218C23×C11H(5,𝔽2)12yes—
219C23×C11C2511yescharacteristic
220C22×D11—28no—
221C22×D11—28no—
222C22×D11—28no—
223C22×D11—24no—
224C22×D11—24no—
225C22×D11—22no—
226C22×D11—22no—
227C22×D11—24no—
228C22×D11—24no—
229C22×D11—24no—
230C22×D11—24no—
231C22×D11—24no—
232C22×D11—24no—
233C22×D11—24no—
234C22×D11—48no—
235C22×D11—48no—
236C22×D11—48no—
237C22×D11—48no—
238C22×D11—48no—
239C22×D11—48no—
240C22×D11—48no—
241C22×D11—48no—
242C22×D11—48no—
243C22×D11C22×D414yes—
244C2×C4×C11—28no—
245C2×C4×C11—24no—
246C2×C4×C11—22no—
247C2×C4×C11—24no—
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—44no—
255C2×C4×C11—48no—
256C2×C4×C11—48no—
257C2×C4×C11C22×D414yes—
258C22⋊D11—432no—
259C22⋊D11—416no—
260C2×Dic11—28no—
261C2×Dic11—216no—
262C2×Dic11—24no—
263C2×Dic11—24no—
264C2×Dic11—24no—
265C2×Dic11—22no—
266C2×Dic11—22no—
267C2×Dic11—22no—
268C2×Dic11—22no—
269C2×Dic11—24no—
270C2×Dic11—44no—
271C2×Dic11—44no—
272C2×Dic11C22×D414yes—
273C2×Dic11C2×#4118yes—
274D44—416no—
275D44—432no—
276C4×D11—416no—
277C23×D4—111no—
278C23×D4—112no—
279C23×D4—112no—
280C23×D4—111no—
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—112no—
289C22×C4⋊C4C2×D1111yescharacteristic
290C22×C22⋊C4—111no—
291C22×C22⋊C4—112no—
292C22×C22⋊C4—112no—
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—112no—
300#398—118no—
301#397C2×D1118yescomplemented
302#394—118no—
303#394—1116no—
304#392—118no—
305#392—1116no—
306#390—1116no—
307#388—1116no—
308C4×C22⋊C4—118no—
309C2×#95—111no—
310C2×#95—112no—
311C2×#95C2×D1111yescharacteristic
312C2×#95C2×D1112yes—
313C22×C11—42no—
314C22×C11—42no—
315C22×C11—42no—
316C22×C11—44no—
317C22×C11—44no—
318C22×C11—88no—
319C22×C11#53214yes—
320C22×C11#53414yes—
321C22×C11#53514yes—
322C22×C11#53818yes—
323C22×C11#54018yes—
324C22×C11C23×D411yescharacteristic
325C22×C11C22×#4112yes—
326C22×C11C2×H(5,𝔽2)11yescharacteristic
327C22×C11C2×H(5,𝔽2)12yes—
328C22×C11C2×H(5,𝔽2)11yescharacteristic
329C2×D11—24no—
330C2×D11—24no—
331C2×D11—24no—
332C2×D11—416no—
333C2×D11—44no—
334C2×D11—44no—
335C2×D11—44no—
336C2×D11—44no—
337C2×D11—44no—
338C2×D11—44no—
339C2×D11—44no—
340C2×D11—44no—
341C2×D11—44no—
342C2×D11—816no—
343C4×C11—24no—
344C4×C11—42no—
345C4×C11—44no—
346C4×C11—44no—
347Dic11—24no—
348Dic11—28no—
349Dic11—42no—
350Dic11—42no—
351C25—111no—
352C25—112no—
353C25C22×D1111yescharacteristic
354C22×D4—114no—
355C22×D4—118no—
356C22×D4—118no—
357C22×D4—114no—
358C22×D4—228no—
359C22×D4—228no—
360C22×D4—224no—
361C22×D4—224no—
362C22×D4—444no—
363C22×D4—444no—
364C22×D4—444no—
365C22×D4—444no—
366C22×D4—444no—
367C22×D4—444no—
368C23×C4—111no—
369C23×C4—112no—
370C23×C4—118no—
371C23×C4—114no—
372C23×C4—111no—
373C23×C4—111no—
374C23×C4—444no—
375C23×C4C22×D1111yescharacteristic
376C23×C4C22×D1112yes—
377C23×C4C22×D1112yes—
378C23×C4C22×D1111yescharacteristic
379#123—2232no—
380#121—2232no—
381C2×C4⋊C4—24no—
382C2×C4⋊C4—114no—
383C2×C4⋊C4—114no—
384C2×C4⋊C4—118no—
385C2×C4⋊C4—224no—
386C2×C4⋊C4—224no—
387C2×C4⋊C4—444no—
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—118no—
395C2×C22⋊C4—118no—
396C2×C22⋊C4—118no—
397C2×C22⋊C4—118no—
398C2×C22⋊C4—228no—
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⋊C4C22×D1114yes—
406C2×C22⋊C4C22×D1118yes—
407C2×C42—118no—
408C2×C42—444no—
409#95—114no—
410#95—118no—
411#95C22×D1114yes—
412#95C22×D1118yes—
413C2×C11—82no—
414C2×C11#266118yescomplemented
415C2×C11C2×#53211yescharacteristic
416C2×C11C2×#53411yescharacteristic
417C2×C11C2×#53511yescharacteristic
418C2×C11C2×#53812yes—
419C2×C11C2×#54012yes—
420D11—44no—
421D11—84no—
422C24—22no—
423C24—22no—
424C24—24no—
425C24—22no—
426C24—24no—
427C24—114no—
428C24—112no—
429C24—114no—
430C24—222no—
431C24—224no—
432C24—224no—
433C24—222no—
434C24—224no—
435C24—224no—
436C24—224no—
437C24—224no—
438C24—224no—
439C24—224no—
440C24—224no—
441C24C23×D1112yes—
442C24C23×D1111yescharacteristic
443C2×D4—2216no—
444C2×D4—2216no—
445C2×D4—228no—
446C2×D4—228no—
447C2×D4—448no—
448C2×D4—448no—
449C2×D4—448no—
450C2×D4—4416no—
451C2×D4—4432no—
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—24no—
464C22×C4—24no—
465C22×C4—24no—
466C22×C4—114no—
467C22×C4—118no—
468C22×C4—114no—
469C22×C4—112no—
470C22×C4—1116no—
471C22×C4—112no—
472C22×C4—112no—
473C22×C4—224no—
474C22×C4—224no—
475C22×C4—224no—
476C22×C4—222no—
477C22×C4—222no—
478C22×C4—222no—
479C22×C4—224no—
480C22×C4—222no—
481C22×C4—4416no—
482C22×C4—448no—
483C22×C4D4×D1114yes—
484C22×C4C23×D1114yes—
485C22×C4C23×D1114yes—
486C22×C4C23×D1112yes—
487C22×C4C23×D1112yes—
488C4⋊C4—28no—
489C4⋊C4—228no—
490C4⋊C4—228no—
491C4⋊C4—448no—
492C22⋊C4—28no—
493C22⋊C4—48no—
494C22⋊C4—2216no—
495C22⋊C4—2216no—
496C22⋊C4—2216no—
497C22⋊C4—228no—
498C22⋊C4—228no—
499C22⋊C4—448no—
500C22⋊C4—448no—
501C42—448no—
502C11C2×#266111yescharacteristic, complemented, Sylow
503C23—22no—
504C23—22no—
505C23—24no—
506C23—24no—
507C23—22no—
508C23—48no—
509C23—44no—
510C23—44no—
511C23—48no—
512C23—44no—
513C23—114no—
514C23—228no—
515C23—228no—
516C23—222no—
517C23—224no—
518C23—224no—
519C23—222no—
520C23—228no—
521C23—224no—
522C23—224no—
523C23—224no—
524C23—224no—
525C23—224no—
526C23—224no—
527C23—224no—
528C23—448no—
529C23—448no—
530C23—448no—
531C23—448no—
532C23—448no—
533C23—448no—
534C23—448no—
535C23—448no—
536C23—448no—
537C23C2×D4×D1112yes—
538C23#6703712yes—
539C23#41×D1114yes—
540C23#6704212yes—
541C23#6704214yes—
542C23C24×D1111yescharacteristic
543D4—4416no—
544D4—4432no—
545D4—4432no—
546D4—4416no—
547C2×C4—28no—
548C2×C4—24no—
549C2×C4—22no—
550C2×C4—24no—
551C2×C4—24no—
552C2×C4—24no—
553C2×C4—24no—
554C2×C4—24no—
555C2×C4—24no—
556C2×C4—24no—
557C2×C4—48no—
558C2×C4—48no—
559C2×C4—44no—
560C2×C4—114no—
561C2×C4—118no—
562C2×C4—2216no—
563C2×C4—228no—
564C2×C4—224no—
565C2×C4—224no—
566C2×C4—224no—
567C2×C4—222no—
568C2×C4—222no—
569C2×C4—222no—
570C2×C4—224no—
571C2×C4—222no—
572C2×C4—4416no—
573C2×C4—444no—
574C2×C4—444no—
575C2×C4C2×D4×D1114yes—
576C22—42no—
577C22—42no—
578C22—42no—
579C22—44no—
580C22—44no—
581C22—88no—
582C22—224no—
583C22—224no—
584C22—224no—
585C22—4416no—
586C22—444no—
587C22—444no—
588C22—444no—
589C22—444no—
590C22—444no—
591C22—444no—
592C22—444no—
593C22—444no—
594C22—444no—
595C22—8816no—
596C22#1062313814yes—
597C22#1062318414yes—
598C22#1062319418yes—
599C22#1062319914yes—
600C22#1062323518yes—
601C22C22×D4×D1111yescharacteristic
602C22C2×#6703711yescharacteristic
603C22C2×#41×D1112yes—
604C22C2×#6704212yes—
605C22C2×#6704211yescharacteristic
606C4—24no—
607C4—42no—
608C4—44no—
609C4—44no—
610C4—224no—
611C4—228no—
612C4—442no—
613C4—442no—
614C2—82no—
615C2—444no—
616C2—884no—
617C2#1307475018yesdirect product factor
618C2C2×#1062319911yescharacteristic
619C2C2×#1062318411yescharacteristic
620C2C2×#1062313811yescharacteristic
621C2C2×#1062323512yes—
622C2C2×#1062319412yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#397C2
socleC24×C11C24
hypercenterC2×#397D11
hypocenterC11C2×#2661
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#397

Complements

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

NH ≅ G/Ntype
1. C22×#66936C2semidirect
2. C22×#66948C2semidirect
3. #13074750C2direct (N × H)
4. C2×#10622593C2semidirect
5. C2×#10622285C2semidirect
6. C2×#10622285C2semidirect
7. C2×#10622573C2semidirect
8. C2×#10622573C2semidirect
9. C2×#10622570C2semidirect
10. C2×#10622283C2semidirect
11. C2×#10622279C2semidirect
12. C2×C11×#397C2semidirect
33. C2×#66948C22semidirect
35. C2×#66936C22semidirect
36. C11×#397C22semidirect
41. #10622593C22semidirect
42. #10622573C22semidirect
43. #10622573C22semidirect
44. #10622570C22semidirect
45. #10622285C22semidirect
46. #10622285C22semidirect
47. #10622283C22semidirect
48. #10622279C22semidirect
75. C22×C4×D11D4semidirect
177. C2×C4×D11C2×D4semidirect
196. C2×#397D11semidirect
301. #397C2×D11semidirect
414. C2×C11#2661semidirect
502. C11C2×#2661semidirect
617. C2#13074750direct (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×#669482
#130747502
C2×#106225932
C2×#106222852
C2×#106225732
C2×#106225702
C2×#106222832
C2×#106222792
C2×C11×#3972
C2×#266111